[{"data":1,"prerenderedAt":100114},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-imek-detail-predmetu":1626,"course-stats-imek":1954,"course-topics-imek":1958,"backlinks-imek-detail-predmetu":100110,"related-imek-detail-predmetu":100113},{"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":1953},{"id":1628,"title":1629,"body":1630,"course":1128,"courses":659,"created":1129,"description":1943,"extension":661,"meta":1944,"navigation":664,"path":1945,"seo":1946,"sources":1947,"stem":1948,"tags":1949,"type":1951,"updated":677,"__hash__":1952},"summaries\u002Fsummaries\u002Fimek-detail-predmetu.md","Matematická ekonomie — Detail předmětu",{"type":9,"value":1631,"toc":1931},[1632,1635,1645,1649,1736,1740,1743,1763,1767,1778,1782,1796,1799,1803,1814,1818,1880,1883,1886,1888,1920,1922,1924,1928],[12,1633,1629],{"id":1634},"matematická-ekonomie-detail-předmětu",[724,1636,1637,1638,1644],{},"Viz ",[207,1639,1643],{"className":1640,"dataFsResolvedFilePath":1641,"href":1642},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","přehled kurzu",".",[115,1646,1648],{"id":1647},"administrativa","Administrativa",[16,1650,1651,1661],{},[19,1652,1653],{},[22,1654,1655,1658],{},[25,1656,1657],{},"Atribut",[25,1659,1660],{},"Hodnota",[30,1662,1663,1670,1677,1685,1692,1700,1708,1715,1721,1728],{},[22,1664,1665,1667],{},[35,1666,40],{},[35,1668,1669],{},"ImeK",[22,1671,1672,1674],{},[35,1673,50],{},[35,1675,1676],{},"FP VUT",[22,1678,1679,1682],{},[35,1680,1681],{},"Akademický rok",[35,1683,1684],{},"2025\u002F2026",[22,1686,1687,1689],{},[35,1688,80],{},[35,1690,1691],{},"doc. RNDr. Bedřich Půža, CSc.",[22,1693,1694,1697],{},[35,1695,1696],{},"Garantující ústav",[35,1698,1699],{},"Ústav informatiky FP",[22,1701,1702,1705],{},[35,1703,1704],{},"Vyučující (KS)",[35,1706,1707],{},"Mgr. Martina Bobalová, Ph.D.",[22,1709,1710,1713],{},[35,1711,1712],{},"Jazyk výuky",[35,1714,1220],{},[22,1716,1717,1719],{},[35,1718,70],{},[35,1720,73],{},[22,1722,1723,1725],{},[35,1724,60],{},[35,1726,1727],{},"letní",[22,1729,1730,1733],{},[35,1731,1732],{},"Konzultace v KS",[35,1734,1735],{},"20 hod. nepovinná",[115,1737,1739],{"id":1738},"cíl-a-anotace","Cíl a anotace",[724,1741,1742],{},"Cílem je hlouběji proniknout do kauzální podstaty ekonomických vztahů, rozvíjet schopnost vyjadřovat ekonomické vztahy exaktními prostředky a provádět jejich analýzy. Předmět navazuje na mikro- a makroekonomii — syntetizuje je prostředky matematiky s potenciálem pro komputerizaci. Těžištěm je matematické modelování základních ekonomických zákonitostí:",[120,1744,1745,1748,1751,1754,1757,1760],{},[123,1746,1747],{},"analýza poptávky a nabídky",[123,1749,1750],{},"příjem, náklady, zisk",[123,1752,1753],{},"elasticita",[123,1755,1756],{},"produkce",[123,1758,1759],{},"užitečnost",[123,1761,1762],{},"národní důchod",[115,1764,1766],{"id":1765},"průběh-zkoušky","Průběh zkoušky",[724,1768,1769,1770,1773,1774,1777],{},"Zkouška = ",[38,1771,1772],{},"písemná"," (60 min, těžiště hodnocení) + ",[38,1775,1776],{},"ústní"," (~10 min, upřesnění klasifikace).",[198,1779,1781],{"id":1780},"zadání-písemné-části","Zadání písemné části",[152,1783,1784,1787,1790,1793],{},[123,1785,1786],{},"Rozhodovací úloha o ekonomické funkci — 10 b.",[123,1788,1789],{},"Definice, formulace vlastnosti, interpretace ekonomické veličiny — 20 b.",[123,1791,1792],{},"Výpočetní úloha — 30 b.",[123,1794,1795],{},"Výpočetní úloha — 40 b.",[724,1797,1798],{},"Celkem 100 b. Doporučeno mít kalkulátor (přípustný je i dobrý odhad).",[198,1800,1802],{"id":1801},"dílčí-podmínky-pro-ae","Dílčí podmínky pro A–E",[120,1804,1805,1808,1811],{},[123,1806,1807],{},"≥ 11 bodů v součtu úloh 1 + 2",[123,1809,1810],{},"≥ 10 bodů v úloze 3",[123,1812,1813],{},"≥ 10 bodů v úloze 4",[198,1815,1817],{"id":1816},"stupnice","Stupnice",[16,1819,1820,1830],{},[19,1821,1822],{},[22,1823,1824,1827],{},[25,1825,1826],{},"Známka",[25,1828,1829],{},"Body",[30,1831,1832,1840,1848,1856,1864,1872],{},[22,1833,1834,1837],{},[35,1835,1836],{},"A",[35,1838,1839],{},"90–100",[22,1841,1842,1845],{},[35,1843,1844],{},"B",[35,1846,1847],{},"80–89",[22,1849,1850,1853],{},[35,1851,1852],{},"C",[35,1854,1855],{},"70–79",[22,1857,1858,1861],{},[35,1859,1860],{},"D",[35,1862,1863],{},"60–69",[22,1865,1866,1869],{},[35,1867,1868],{},"E",[35,1870,1871],{},"50–59",[22,1873,1874,1877],{},[35,1875,1876],{},"F",[35,1878,1879],{},"0–49 nebo nesplnění podmínek",[724,1881,1882],{},"Student může odmítnout klasifikaci B–E před uzavřením; pak je F a může jít na další termín.",[724,1884,1885],{},"Účast na přednáškách není kontrolována.",[115,1887,1023],{"id":1022},[120,1889,1890,1896,1902,1908,1914],{},[123,1891,1892,1893,1895],{},"Mezník, I. ",[614,1894,1031],{}," — FP VUT \u002F CERM, Brno 2017 (CZ, doporučeno)",[123,1897,1898,1899,1901],{},"Chiang, A. C. ",[614,1900,1038],{}," — McGraw-Hill, 1984",[123,1903,1904,1905,1907],{},"Jacques, J. ",[614,1906,1059],{}," — Addison-Wesley, 1995",[123,1909,1910,1911,1913],{},"Koch, J. U. & Ostrosky, L. A. ",[614,1912,1045],{}," — McGraw-Hill, 1994",[123,1915,1916,1917,1919],{},"McKenna, C. J. & Rees, R. ",[614,1918,1052],{}," — Oxford UP, 1992",[115,1921,1064],{"id":1063},[724,1923,1067],{},[115,1925,1927],{"id":1926},"elearning","eLearning",[724,1929,1930],{},"Moodle VUT — aktuální otevřený kurz.",{"title":641,"searchDepth":642,"depth":642,"links":1932},[1933,1934,1935,1940,1941,1942],{"id":1647,"depth":642,"text":1648},{"id":1738,"depth":642,"text":1739},{"id":1765,"depth":642,"text":1766,"children":1936},[1937,1938,1939],{"id":1780,"depth":649,"text":1781},{"id":1801,"depth":649,"text":1802},{"id":1816,"depth":649,"text":1817},{"id":1022,"depth":642,"text":1023},{"id":1063,"depth":642,"text":1064},{"id":1926,"depth":642,"text":1927},"Viz přehled kurzu.",{},"\u002Fsummaries\u002Fimek-detail-predmetu",{"title":1629,"description":1943},[1134],"summaries\u002Fimek-detail-predmetu",[1128,1950],"zkouska","summary","HbE7Shpid43OlvVaEKLZsPSS1RryulK33e-e-2LTZvI","summaries",{"zapisku":1625,"topics":1955,"summaries":1956,"outputs":1957},15,5,1,[1959,3867,9574,11129,12001,16285,17892,27770,36764,50831,55123,74467,86579,95537,95825],{"id":1960,"title":1961,"body":1962,"course":1128,"courses":659,"created":1129,"description":3855,"extension":661,"meta":3856,"navigation":664,"path":3857,"seo":3858,"sources":3859,"stem":3860,"tags":3861,"type":3865,"updated":677,"__hash__":3866},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":1963,"toc":3838},[1964,1967,1985,1989,2073,2076,2207,2364,2367,2450,2454,2515,2565,2574,2578,2714,2765,2769,2812,2881,2952,2960,2964,3003,3075,3079,3160,3209,3253,3257,3261,3331,3335,3385,3464,3471,3474,3527,3797,3801],[12,1965,1961],{"id":1966},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,1968,1969,1970,1973,1974,1977,1978,1981,1982,1644],{},"Matematický aparát kurzu ",[207,1971,1669],{"className":1972,"dataFsResolvedFilePath":1641,"href":1642},[210],". Bez derivace se neobejdou ",[38,1975,1976],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,1979,1980],{},"maximalizace zisku"," ani ",[38,1983,1984],{},"minimalizace nákladů",[115,1986,1988],{"id":1987},"funkce-a-polynomy","Funkce a polynomy",[724,1990,1991,1992,2024,2025,2038,2039,2052,2053,1644],{},"Funkce jedné proměnné ",[883,1993,1995],{"className":1994},[886],[888,1996,1997],{"xmlns":890},[892,1998,1999,2021],{},[895,2000,2001,2004,2008,2011,2015,2018],{},[898,2002,2003],{},"y",[2005,2006,2007],"mo",{},"=",[898,2009,2010],{},"f",[2005,2012,2014],{"stretchy":2013},"false","(",[898,2016,2017],{},"x",[2005,2019,2020],{"stretchy":2013},")",[902,2022,2023],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,2026,2028],{"className":2027},[886],[888,2029,2030],{"xmlns":890},[892,2031,2032,2036],{},[895,2033,2034],{},[898,2035,2017],{},[902,2037,2017],{"encoding":904}," (nezávislá) → ",[883,2040,2042],{"className":2041},[886],[888,2043,2044],{"xmlns":890},[892,2045,2046,2050],{},[895,2047,2048],{},[898,2049,2003],{},[902,2051,2003],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,2054,2056],{"className":2055},[886],[888,2057,2058],{"xmlns":890},[892,2059,2060,2070],{},[895,2061,2062,2064,2066,2068],{},[898,2063,2010],{},[2005,2065,2014],{"stretchy":2013},[898,2067,207],{},[2005,2069,2020],{"stretchy":2013},[902,2071,2072],{"encoding":904},"f(a)",[724,2074,2075],{},"Polynomy:",[120,2077,2078,2111,2155],{},[123,2079,2080],{},[152,2081,2082],{},[123,2083,2084,2085],{},"stupně: ",[883,2086,2088],{"className":2087},[886],[888,2089,2090],{"xmlns":890},[892,2091,2092,2108],{},[895,2093,2094,2096,2098,2100,2102,2105],{},[898,2095,2003],{},[2005,2097,2007],{},[898,2099,207],{},[898,2101,2017],{},[2005,2103,2104],{},"+",[898,2106,2107],{},"b",[902,2109,2110],{"encoding":904},"y = ax + b",[123,2112,2113],{},[152,2114,2115],{"start":642},[123,2116,2084,2117],{},[883,2118,2120],{"className":2119},[886],[888,2121,2122],{"xmlns":890},[892,2123,2124,2152],{},[895,2125,2126,2128,2130,2132,2141,2143,2145,2147,2149],{},[898,2127,2003],{},[2005,2129,2007],{},[898,2131,207],{},[2133,2134,2135,2137],"msup",{},[898,2136,2017],{},[2138,2139,2140],"mn",{},"2",[2005,2142,2104],{},[898,2144,2107],{},[898,2146,2017],{},[2005,2148,2104],{},[898,2150,2151],{},"c",[902,2153,2154],{"encoding":904},"y = ax^2 + bx + c",[123,2156,2157],{},[152,2158,2159],{"start":649},[123,2160,2084,2161],{},[883,2162,2164],{"className":2163},[886],[888,2165,2166],{"xmlns":890},[892,2167,2168,2204],{},[895,2169,2170,2172,2174,2176,2183,2185,2187,2193,2195,2197,2199,2201],{},[898,2171,2003],{},[2005,2173,2007],{},[898,2175,207],{},[2133,2177,2178,2180],{},[898,2179,2017],{},[2138,2181,2182],{},"3",[2005,2184,2104],{},[898,2186,2107],{},[2133,2188,2189,2191],{},[898,2190,2017],{},[2138,2192,2140],{},[2005,2194,2104],{},[898,2196,2151],{},[898,2198,2017],{},[2005,2200,2104],{},[898,2202,2203],{},"d",[902,2205,2206],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,2208,2209,2212,2213,2270,2271,2313,2314,1644],{},[38,2210,2211],{},"Příklad rozkladu:"," ",[883,2214,2216],{"className":2215},[886],[888,2217,2218],{"xmlns":890},[892,2219,2220,2267],{},[895,2221,2222,2224,2226,2232,2235,2238,2240,2242,2245,2247,2249,2251,2253,2255,2257,2259,2261,2263,2265],{},[898,2223,2003],{},[2005,2225,2007],{},[2133,2227,2228,2230],{},[898,2229,2017],{},[2138,2231,2140],{},[2005,2233,2234],{},"−",[2138,2236,2237],{},"5",[898,2239,2017],{},[2005,2241,2104],{},[2138,2243,2244],{},"6",[2005,2246,2007],{},[2005,2248,2014],{"stretchy":2013},[898,2250,2017],{},[2005,2252,2234],{},[2138,2254,2140],{},[2005,2256,2020],{"stretchy":2013},[2005,2258,2014],{"stretchy":2013},[898,2260,2017],{},[2005,2262,2234],{},[2138,2264,2182],{},[2005,2266,2020],{"stretchy":2013},[902,2268,2269],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,2272,2274],{"className":2273},[886],[888,2275,2276],{"xmlns":890},[892,2277,2278,2310],{},[895,2279,2280,2288,2290,2292,2296,2300,2306,2308],{},[2281,2282,2283,2285],"msub",{},[898,2284,2017],{},[2138,2286,2287],{},"1",[2005,2289,2007],{},[2138,2291,2140],{},[2005,2293,2295],{"separator":2294},"true",",",[2297,2298,2299],"mtext",{}," ",[2281,2301,2302,2304],{},[898,2303,2017],{},[2138,2305,2140],{},[2005,2307,2007],{},[2138,2309,2182],{},[902,2311,2312],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,2315,2317],{"className":2316},[886],[888,2318,2319],{"xmlns":890},[892,2320,2321,2361],{},[895,2322,2323,2325,2327,2329,2331,2333,2344,2350,2352],{},[898,2324,2003],{},[2005,2326,2007],{},[2005,2328,2014],{"stretchy":2013},[898,2330,2017],{},[2005,2332,2234],{},[2334,2335,2337],"mstyle",{"scriptlevel":2336,"displaystyle":2013},"0",[2338,2339,2340,2342],"mfrac",{},[2138,2341,2237],{},[2138,2343,2140],{},[2133,2345,2346,2348],{},[2005,2347,2020],{"stretchy":2013},[2138,2349,2140],{},[2005,2351,2234],{},[2334,2353,2354],{"scriptlevel":2336,"displaystyle":2013},[2338,2355,2356,2358],{},[2138,2357,2287],{},[2138,2359,2360],{},"4",[902,2362,2363],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,2365,2366],{"id":1145},"Derivace",[724,2368,2369,2370,1348,2397,2425,2426,1644],{},"Označení ",[883,2371,2373],{"className":2372},[886],[888,2374,2375],{"xmlns":890},[892,2376,2377,2394],{},[895,2378,2379,2388,2390,2392],{},[2133,2380,2381,2383],{},[898,2382,2010],{},[2005,2384,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},"normal","0em","′",[2005,2389,2014],{"stretchy":2013},[898,2391,2017],{},[2005,2393,2020],{"stretchy":2013},[902,2395,2396],{"encoding":904},"f'(x)",[883,2398,2400],{"className":2399},[886],[888,2401,2402],{"xmlns":890},[892,2403,2404,2422],{},[895,2405,2406],{},[2334,2407,2408],{"scriptlevel":2336,"displaystyle":2294},[2338,2409,2410,2416],{},[895,2411,2412,2414],{},[898,2413,2203],{},[898,2415,2003],{},[895,2417,2418,2420],{},[898,2419,2203],{},[898,2421,2017],{},[902,2423,2424],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,2427,2429],{"className":2428},[886],[888,2430,2431],{"xmlns":890},[892,2432,2433,2447],{},[895,2434,2435,2441,2443,2445],{},[2133,2436,2437,2439],{},[898,2438,2010],{},[2005,2440,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,2442,2014],{"stretchy":2013},[898,2444,207],{},[2005,2446,2020],{"stretchy":2013},[902,2448,2449],{"encoding":904},"f'(a)",[198,2451,2453],{"id":2452},"geometrická-interpretace","Geometrická interpretace",[724,2455,2456,2479,2480,2483,2484,2514],{},[883,2457,2459],{"className":2458},[886],[888,2460,2461],{"xmlns":890},[892,2462,2463,2477],{},[895,2464,2465,2471,2473,2475],{},[2133,2466,2467,2469],{},[898,2468,2010],{},[2005,2470,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,2472,2014],{"stretchy":2013},[898,2474,207],{},[2005,2476,2020],{"stretchy":2013},[902,2478,2449],{"encoding":904}," = ",[38,2481,2482],{},"sklon tečny"," ke grafu funkce v bodě ",[883,2485,2487],{"className":2486},[886],[888,2488,2489],{"xmlns":890},[892,2490,2491,2511],{},[895,2492,2493,2496,2498,2500,2502,2504,2506,2508],{},[2005,2494,2495],{"stretchy":2013},"[",[898,2497,207],{},[2005,2499,2295],{"separator":2294},[898,2501,2010],{},[2005,2503,2014],{"stretchy":2013},[898,2505,207],{},[2005,2507,2020],{"stretchy":2013},[2005,2509,2510],{"stretchy":2013},"]",[902,2512,2513],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,2516,2517],{},[883,2518,2520],{"className":2519},[886],[888,2521,2522],{"xmlns":890},[892,2523,2524,2562],{},[895,2525,2526,2528,2530,2532,2534,2536,2538,2540,2546,2548,2550,2552,2554,2556,2558,2560],{},[898,2527,2003],{},[2005,2529,2234],{},[898,2531,2010],{},[2005,2533,2014],{"stretchy":2013},[898,2535,207],{},[2005,2537,2020],{"stretchy":2013},[2005,2539,2007],{},[2133,2541,2542,2544],{},[898,2543,2010],{},[2005,2545,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,2547,2014],{"stretchy":2013},[898,2549,207],{},[2005,2551,2020],{"stretchy":2013},[2005,2553,2014],{"stretchy":2013},[898,2555,2017],{},[2005,2557,2234],{},[898,2559,207],{},[2005,2561,2020],{"stretchy":2013},[902,2563,2564],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,2566,2567],{},[2568,2569],"img",{"alt":2570,"className":2571,"src":2573},"imek-derivace-tecna",[210,2572],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,2575,2577],{"id":2576},"inženýrská-interpretace","Inženýrská interpretace",[724,2579,2580,2479,2603,2212,2606,2619,2620,2633,2634,2652,2653,2666,2667,2680,2681,2694,2695,2713],{},[883,2581,2583],{"className":2582},[886],[888,2584,2585],{"xmlns":890},[892,2586,2587,2601],{},[895,2588,2589,2595,2597,2599],{},[2133,2590,2591,2593],{},[898,2592,2010],{},[2005,2594,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,2596,2014],{"stretchy":2013},[898,2598,207],{},[2005,2600,2020],{"stretchy":2013},[902,2602,2449],{"encoding":904},[38,2604,2605],{},"rychlost změny",[883,2607,2609],{"className":2608},[886],[888,2610,2611],{"xmlns":890},[892,2612,2613,2617],{},[895,2614,2615],{},[898,2616,2003],{},[902,2618,2003],{"encoding":904}," vzhledem k ",[883,2621,2623],{"className":2622},[886],[888,2624,2625],{"xmlns":890},[892,2626,2627,2631],{},[895,2628,2629],{},[898,2630,2017],{},[902,2632,2017],{"encoding":904}," v bodě ",[883,2635,2637],{"className":2636},[886],[888,2638,2639],{"xmlns":890},[892,2640,2641,2649],{},[895,2642,2643,2645,2647],{},[898,2644,2017],{},[2005,2646,2007],{},[898,2648,207],{},[902,2650,2651],{"encoding":904},"x = a","; přibližná změna ",[883,2654,2656],{"className":2655},[886],[888,2657,2658],{"xmlns":890},[892,2659,2660,2664],{},[895,2661,2662],{},[898,2663,2003],{},[902,2665,2003],{"encoding":904}," při změně ",[883,2668,2670],{"className":2669},[886],[888,2671,2672],{"xmlns":890},[892,2673,2674,2678],{},[895,2675,2676],{},[898,2677,2017],{},[902,2679,2017],{"encoding":904}," z ",[883,2682,2684],{"className":2683},[886],[888,2685,2686],{"xmlns":890},[892,2687,2688,2692],{},[895,2689,2690],{},[898,2691,207],{},[902,2693,207],{"encoding":904}," na ",[883,2696,2698],{"className":2697},[886],[888,2699,2700],{"xmlns":890},[892,2701,2702,2710],{},[895,2703,2704,2706,2708],{},[898,2705,207],{},[2005,2707,2104],{},[2138,2709,2287],{},[902,2711,2712],{"encoding":904},"a+1",":",[724,2715,2716],{},[883,2717,2719],{"className":2718},[886],[888,2720,2721],{"xmlns":890},[892,2722,2723,2762],{},[895,2724,2725,2727,2729,2731,2733,2735,2737,2740,2742,2744,2746,2748,2750,2756,2758,2760],{},[898,2726,2010],{},[2005,2728,2014],{"stretchy":2013},[898,2730,207],{},[2005,2732,2104],{},[2138,2734,2287],{},[2005,2736,2020],{"stretchy":2013},[2005,2738,2739],{},"≈",[898,2741,2010],{},[2005,2743,2014],{"stretchy":2013},[898,2745,207],{},[2005,2747,2020],{"stretchy":2013},[2005,2749,2104],{},[2133,2751,2752,2754],{},[898,2753,2010],{},[2005,2755,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,2757,2014],{"stretchy":2013},[898,2759,207],{},[2005,2761,2020],{"stretchy":2013},[902,2763,2764],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,2766,2768],{"id":2767},"příklad-mezní-náklady","Příklad — mezní náklady",[724,2770,2771,2772,1644],{},"Celkové náklady ",[883,2773,2775],{"className":2774},[886],[888,2776,2777],{"xmlns":890},[892,2778,2779,2809],{},[895,2780,2781,2784,2786,2788,2791,2793,2795,2798,2800,2803],{},[898,2782,2783],{},"T",[898,2785,1852],{},[2005,2787,2007],{},[2138,2789,2790],{},"1000",[2005,2792,2104],{},[2138,2794,2140],{},[898,2796,2797],{},"Q",[2005,2799,2104],{},[2138,2801,2802],{},"0,1",[2133,2804,2805,2807],{},[898,2806,2797],{},[2138,2808,2140],{},[902,2810,2811],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,2813,2814,2815,2853,2854,1644],{},"Mezní náklady: ",[883,2816,2818],{"className":2817},[886],[888,2819,2820],{"xmlns":890},[892,2821,2822,2850],{},[895,2823,2824,2827,2829,2831,2833,2839,2841,2843,2845,2848],{},[898,2825,2826],{},"M",[898,2828,1852],{},[2005,2830,2007],{},[898,2832,2783],{},[2133,2834,2835,2837],{},[898,2836,1852],{},[2005,2838,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,2840,2007],{},[2138,2842,2140],{},[2005,2844,2104],{},[2138,2846,2847],{},"0,2",[898,2849,2797],{},[902,2851,2852],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,2855,2857],{"className":2856},[886],[888,2858,2859],{"xmlns":890},[892,2860,2861,2878],{},[895,2862,2863,2865,2867,2869,2872,2874,2876],{},[898,2864,2826],{},[898,2866,1852],{},[2005,2868,2014],{"stretchy":2013},[2138,2870,2871],{},"10",[2005,2873,2020],{"stretchy":2013},[2005,2875,2007],{},[2138,2877,2360],{},[902,2879,2880],{"encoding":904},"MC(10) = 4",[724,2882,2883,2212,2886,2935,2936,2212,2939,1644],{},[38,2884,2885],{},"Skutečný přírůstek:",[883,2887,2889],{"className":2888},[886],[888,2890,2891],{"xmlns":890},[892,2892,2893,2932],{},[895,2894,2895,2898,2900,2902,2904,2906,2908,2910,2913,2915,2917,2919,2921,2923,2925,2927,2929],{},[898,2896,2897],{"mathvariant":2385},"Δ",[898,2899,2783],{},[898,2901,1852],{},[2005,2903,2007],{},[898,2905,2783],{},[898,2907,1852],{},[2005,2909,2014],{"stretchy":2013},[2138,2911,2912],{},"11",[2005,2914,2020],{"stretchy":2013},[2005,2916,2234],{},[898,2918,2783],{},[898,2920,1852],{},[2005,2922,2014],{"stretchy":2013},[2138,2924,2871],{},[2005,2926,2020],{"stretchy":2013},[2005,2928,2007],{},[2138,2930,2931],{},"4,2",[902,2933,2934],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,2937,2938],{},"Přibližný (lineární):",[883,2940,2942],{"className":2941},[886],[888,2943,2944],{"xmlns":890},[892,2945,2946,2950],{},[895,2947,2948],{},[2138,2949,2360],{},[902,2951,2360],{"encoding":904},[724,2953,2954,2955,2959],{},"(Viz aplikace v ",[207,2956,2958],{"className":2957,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,2961,2963],{"id":2962},"diferenciál","Diferenciál",[724,2965,2966],{},[883,2967,2969],{"className":2968},[886],[888,2970,2971],{"xmlns":890},[892,2972,2973,3000],{},[895,2974,2975,2977,2979,2981,2987,2989,2991,2993,2996,2998],{},[898,2976,2203],{},[898,2978,2010],{},[2005,2980,2007],{},[2133,2982,2983,2985],{},[898,2984,2010],{},[2005,2986,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,2988,2014],{"stretchy":2013},[898,2990,2017],{},[2005,2992,2020],{"stretchy":2013},[2297,2994,2995],{}," ",[898,2997,2203],{},[898,2999,2017],{},[902,3001,3002],{"encoding":904},"df = f'(x)\\, dx",[724,3004,3005,3006,3022,3023,3071,3072,1644],{},"Pro malá ",[883,3007,3009],{"className":3008},[886],[888,3010,3011],{"xmlns":890},[892,3012,3013,3019],{},[895,3014,3015,3017],{},[898,3016,2203],{},[898,3018,2017],{},[902,3020,3021],{"encoding":904},"dx"," platí: ",[883,3024,3026],{"className":3025},[886],[888,3027,3028],{"xmlns":890},[892,3029,3030,3068],{},[895,3031,3032,3034,3036,3038,3040,3042,3044,3046,3048,3050,3052,3054,3056,3058,3060,3062,3064,3066],{},[898,3033,2897],{"mathvariant":2385},[898,3035,2010],{},[2005,3037,2007],{},[898,3039,2010],{},[2005,3041,2014],{"stretchy":2013},[898,3043,2017],{},[2005,3045,2104],{},[898,3047,2203],{},[898,3049,2017],{},[2005,3051,2020],{"stretchy":2013},[2005,3053,2234],{},[898,3055,2010],{},[2005,3057,2014],{"stretchy":2013},[898,3059,2017],{},[2005,3061,2020],{"stretchy":2013},[2005,3063,2739],{},[898,3065,2203],{},[898,3067,2010],{},[902,3069,3070],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,3073,3074],{},"lineární odhad přírůstku",[198,3076,3078],{"id":3077},"příklad","Příklad",[724,3080,3081,3112,3113,3138,3139,3159],{},[883,3082,3084],{"className":3083},[886],[888,3085,3086],{"xmlns":890},[892,3087,3088,3109],{},[895,3089,3090,3092,3094,3096,3099,3101,3103],{},[898,3091,2783],{},[898,3093,1852],{},[2005,3095,2007],{},[2138,3097,3098],{},"100",[2005,3100,2104],{},[2138,3102,2802],{},[2133,3104,3105,3107],{},[898,3106,2797],{},[2138,3108,2140],{},[902,3110,3111],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,3114,3116],{"className":3115},[886],[888,3117,3118],{"xmlns":890},[892,3119,3120,3135],{},[895,3121,3122,3124,3126,3129,3132],{},[898,3123,2797],{},[2005,3125,2713],{},[2138,3127,3128],{},"50",[2005,3130,3131],{},"→",[2138,3133,3134],{},"60",[902,3136,3137],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,3140,3142],{"className":3141},[886],[888,3143,3144],{"xmlns":890},[892,3145,3146,3156],{},[895,3147,3148,3150,3152,3154],{},[898,3149,2203],{},[898,3151,2797],{},[2005,3153,2007],{},[2138,3155,2871],{},[902,3157,3158],{"encoding":904},"dQ = 10","):",[724,3161,3162],{},[883,3163,3165],{"className":3164},[886],[888,3166,3167],{"xmlns":890},[892,3168,3169,3206],{},[895,3170,3171,3173,3175,3177,3179,3181,3183,3186,3188,3190,3192,3194,3196,3198,3200,3202,3204],{},[898,3172,2203],{},[898,3174,2783],{},[898,3176,1852],{},[2005,3178,2007],{},[2138,3180,2847],{},[898,3182,2797],{},[2005,3184,3185],{},"⋅",[898,3187,2203],{},[898,3189,2797],{},[2005,3191,2007],{},[2138,3193,2847],{},[2005,3195,3185],{},[2138,3197,3128],{},[2005,3199,3185],{},[2138,3201,2871],{},[2005,3203,2007],{},[2138,3205,3098],{},[902,3207,3208],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,3210,3211,3212,3235,3236,3252],{},"Přesná změna: ",[883,3213,3215],{"className":3214},[886],[888,3216,3217],{"xmlns":890},[892,3218,3219,3232],{},[895,3220,3221,3223,3225,3227,3229],{},[898,3222,2897],{"mathvariant":2385},[898,3224,2783],{},[898,3226,1852],{},[2005,3228,2007],{},[2138,3230,3231],{},"110",[902,3233,3234],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,3237,3239],{"className":3238},[886],[888,3240,3241],{"xmlns":890},[892,3242,3243,3249],{},[895,3244,3245,3247],{},[898,3246,2783],{},[898,3248,1852],{},[902,3250,3251],{"encoding":904},"TC"," je konvexní.",[115,3254,3256],{"id":3255},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,3258,3260],{"id":3259},"nutná-podmínka","Nutná podmínka",[724,3262,3263,3264,2633,3284,3297,3298,3326,3327,3330],{},"Má-li ",[883,3265,3267],{"className":3266},[886],[888,3268,3269],{"xmlns":890},[892,3270,3271,3281],{},[895,3272,3273,3275,3277,3279],{},[898,3274,2010],{},[2005,3276,2014],{"stretchy":2013},[898,3278,2017],{},[2005,3280,2020],{"stretchy":2013},[902,3282,3283],{"encoding":904},"f(x)",[883,3285,3287],{"className":3286},[886],[888,3288,3289],{"xmlns":890},[892,3290,3291,3295],{},[895,3292,3293],{},[898,3294,207],{},[902,3296,207],{"encoding":904}," extrém, pak ",[883,3299,3301],{"className":3300},[886],[888,3302,3303],{"xmlns":890},[892,3304,3305,3323],{},[895,3306,3307,3313,3315,3317,3319,3321],{},[2133,3308,3309,3311],{},[898,3310,2010],{},[2005,3312,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,3314,2014],{"stretchy":2013},[898,3316,207],{},[2005,3318,2020],{"stretchy":2013},[2005,3320,2007],{},[2138,3322,2336],{},[902,3324,3325],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,3328,3329],{},"stacionární"," (podezřelé) body.",[198,3332,3334],{"id":3333},"postačující-podmínka","Postačující podmínka",[724,3336,3337,3338,3351,3352,2713],{},"Pro stacionární bod ",[883,3339,3341],{"className":3340},[886],[888,3342,3343],{"xmlns":890},[892,3344,3345,3349],{},[895,3346,3347],{},[898,3348,207],{},[902,3350,207],{"encoding":904},", je-li ",[883,3353,3355],{"className":3354},[886],[888,3356,3357],{"xmlns":890},[892,3358,3359,3382],{},[895,3360,3361,3371,3373,3375,3377,3380],{},[2133,3362,3363,3365],{},[898,3364,2010],{},[895,3366,3367,3369],{},[2005,3368,2387],{"mathvariant":2385},[2005,3370,2387],{"mathvariant":2385},[2005,3372,2014],{"stretchy":2013},[898,3374,207],{},[2005,3376,2020],{"stretchy":2013},[2005,3378,3379],{"mathvariant":2385},"≠",[2138,3381,2336],{},[902,3383,3384],{"encoding":904},"f''(a) \\neq 0",[120,3386,3387,3426],{},[123,3388,3389,3422,3423],{},[883,3390,3392],{"className":3391},[886],[888,3393,3394],{"xmlns":890},[892,3395,3396,3419],{},[895,3397,3398,3408,3410,3412,3414,3417],{},[2133,3399,3400,3402],{},[898,3401,2010],{},[895,3403,3404,3406],{},[2005,3405,2387],{"mathvariant":2385},[2005,3407,2387],{"mathvariant":2385},[2005,3409,2014],{"stretchy":2013},[898,3411,207],{},[2005,3413,2020],{"stretchy":2013},[2005,3415,3416],{},">",[2138,3418,2336],{},[902,3420,3421],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,3424,3425],{},"lokální minimum",[123,3427,3428,3422,3461],{},[883,3429,3431],{"className":3430},[886],[888,3432,3433],{"xmlns":890},[892,3434,3435,3458],{},[895,3436,3437,3447,3449,3451,3453,3456],{},[2133,3438,3439,3441],{},[898,3440,2010],{},[895,3442,3443,3445],{},[2005,3444,2387],{"mathvariant":2385},[2005,3446,2387],{"mathvariant":2385},[2005,3448,2014],{"stretchy":2013},[898,3450,207],{},[2005,3452,2020],{"stretchy":2013},[2005,3454,3455],{},"\u003C",[2138,3457,2336],{},[902,3459,3460],{"encoding":904},"f''(a) \u003C 0",[38,3462,3463],{},"lokální maximum",[724,3465,3466],{},[2568,3467],{"alt":3468,"className":3469,"src":3470},"imek-extremy-1d",[210,2572],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,3472,3078],{"id":3473},"příklad-1",[724,3475,3476],{},[883,3477,3479],{"className":3478},[886],[888,3480,3481],{"xmlns":890},[892,3482,3483,3524],{},[895,3484,3485,3487,3489,3491,3493,3495,3497,3503,3505,3507,3513,3515,3518,3520,3522],{},[898,3486,2010],{},[2005,3488,2014],{"stretchy":2013},[898,3490,2017],{},[2005,3492,2020],{"stretchy":2013},[2005,3494,2007],{},[2138,3496,2140],{},[2133,3498,3499,3501],{},[898,3500,2017],{},[2138,3502,2182],{},[2005,3504,2234],{},[2138,3506,2182],{},[2133,3508,3509,3511],{},[898,3510,2017],{},[2138,3512,2140],{},[2005,3514,2234],{},[2138,3516,3517],{},"12",[898,3519,2017],{},[2005,3521,2104],{},[2138,3523,2182],{},[902,3525,3526],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,3528,3529,3640,3680,3743],{},[123,3530,3531,3603,3604],{},[883,3532,3534],{"className":3533},[886],[888,3535,3536],{"xmlns":890},[892,3537,3538,3600],{},[895,3539,3540,3546,3548,3550,3552,3554,3556,3562,3564,3566,3568,3570,3572,3574,3576,3578,3580,3582,3584,3586,3588,3590,3592,3594,3596,3598],{},[2133,3541,3542,3544],{},[898,3543,2010],{},[2005,3545,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,3547,2014],{"stretchy":2013},[898,3549,2017],{},[2005,3551,2020],{"stretchy":2013},[2005,3553,2007],{},[2138,3555,2244],{},[2133,3557,3558,3560],{},[898,3559,2017],{},[2138,3561,2140],{},[2005,3563,2234],{},[2138,3565,2244],{},[898,3567,2017],{},[2005,3569,2234],{},[2138,3571,3517],{},[2005,3573,2007],{},[2138,3575,2244],{},[2005,3577,2014],{"stretchy":2013},[898,3579,2017],{},[2005,3581,2104],{},[2138,3583,2287],{},[2005,3585,2020],{"stretchy":2013},[2005,3587,2014],{"stretchy":2013},[898,3589,2017],{},[2005,3591,2234],{},[2138,3593,2140],{},[2005,3595,2020],{"stretchy":2013},[2005,3597,2007],{},[2138,3599,2336],{},[902,3601,3602],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,3605,3607],{"className":3606},[886],[888,3608,3609],{"xmlns":890},[892,3610,3611,3637],{},[895,3612,3613,3619,3621,3623,3625,3627,3633,3635],{},[2281,3614,3615,3617],{},[898,3616,2017],{},[2138,3618,2287],{},[2005,3620,2007],{},[2005,3622,2234],{},[2138,3624,2287],{},[2005,3626,2295],{"separator":2294},[2281,3628,3629,3631],{},[898,3630,2017],{},[2138,3632,2140],{},[2005,3634,2007],{},[2138,3636,2140],{},[902,3638,3639],{"encoding":904},"x_1 = -1, x_2 = 2",[123,3641,3642],{},[883,3643,3645],{"className":3644},[886],[888,3646,3647],{"xmlns":890},[892,3648,3649,3677],{},[895,3650,3651,3661,3663,3665,3667,3669,3671,3673,3675],{},[2133,3652,3653,3655],{},[898,3654,2010],{},[895,3656,3657,3659],{},[2005,3658,2387],{"mathvariant":2385},[2005,3660,2387],{"mathvariant":2385},[2005,3662,2014],{"stretchy":2013},[898,3664,2017],{},[2005,3666,2020],{"stretchy":2013},[2005,3668,2007],{},[2138,3670,3517],{},[898,3672,2017],{},[2005,3674,2234],{},[2138,3676,2244],{},[902,3678,3679],{"encoding":904},"f''(x) = 12x - 6",[123,3681,3682,3422,3723,3726,3727],{},[883,3683,3685],{"className":3684},[886],[888,3686,3687],{"xmlns":890},[892,3688,3689,3720],{},[895,3690,3691,3701,3703,3705,3707,3709,3711,3713,3716,3718],{},[2133,3692,3693,3695],{},[898,3694,2010],{},[895,3696,3697,3699],{},[2005,3698,2387],{"mathvariant":2385},[2005,3700,2387],{"mathvariant":2385},[2005,3702,2014],{"stretchy":2013},[2005,3704,2234],{},[2138,3706,2287],{},[2005,3708,2020],{"stretchy":2013},[2005,3710,2007],{},[2005,3712,2234],{},[2138,3714,3715],{},"18",[2005,3717,3455],{},[2138,3719,2336],{},[902,3721,3722],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,3724,3725],{},"maximum"," v ",[883,3728,3730],{"className":3729},[886],[888,3731,3732],{"xmlns":890},[892,3733,3734,3740],{},[895,3735,3736,3738],{},[2005,3737,2234],{},[2138,3739,2287],{},[902,3741,3742],{"encoding":904},"-1",[123,3744,3745,3422,3781,3726,3784],{},[883,3746,3748],{"className":3747},[886],[888,3749,3750],{"xmlns":890},[892,3751,3752,3778],{},[895,3753,3754,3764,3766,3768,3770,3772,3774,3776],{},[2133,3755,3756,3758],{},[898,3757,2010],{},[895,3759,3760,3762],{},[2005,3761,2387],{"mathvariant":2385},[2005,3763,2387],{"mathvariant":2385},[2005,3765,2014],{"stretchy":2013},[2138,3767,2140],{},[2005,3769,2020],{"stretchy":2013},[2005,3771,2007],{},[2138,3773,3715],{},[2005,3775,3416],{},[2138,3777,2336],{},[902,3779,3780],{"encoding":904},"f''(2) = 18 > 0",[38,3782,3783],{},"minimum",[883,3785,3787],{"className":3786},[886],[888,3788,3789],{"xmlns":890},[892,3790,3791,3795],{},[895,3792,3793],{},[2138,3794,2140],{},[902,3796,2140],{"encoding":904},[115,3798,3800],{"id":3799},"navigace","Navigace",[120,3802,3803,3811,3819],{},[123,3804,3805,2212,3808],{},[38,3806,3807],{},"Předchozí:",[207,3809,757],{"className":3810,"dataFsResolvedFilePath":755,"href":756},[210],[123,3812,3813,2212,3816],{},[38,3814,3815],{},"Navazující:",[207,3817,775],{"className":3818,"dataFsResolvedFilePath":773,"href":774},[210],[123,3820,3821,2212,3824,3827,3828,3832,3833,3837],{},[38,3822,3823],{},"Souvislosti:",[207,3825,784],{"className":3826,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,3829,3831],{"className":3830,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,3834,3836],{"className":3835,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":3839},[3840,3841,3846,3849,3854],{"id":1987,"depth":642,"text":1988},{"id":1145,"depth":642,"text":2366,"children":3842},[3843,3844,3845],{"id":2452,"depth":649,"text":2453},{"id":2576,"depth":649,"text":2577},{"id":2767,"depth":649,"text":2768},{"id":2962,"depth":642,"text":2963,"children":3847},[3848],{"id":3077,"depth":649,"text":3078},{"id":3255,"depth":642,"text":3256,"children":3850},[3851,3852,3853],{"id":3259,"depth":649,"text":3260},{"id":3333,"depth":649,"text":3334},{"id":3473,"depth":649,"text":3078},{"id":3799,"depth":642,"text":3800},"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":1961,"description":3855},[1135],"topics\u002Fderivace",[1128,1145,3862,3863,3864],"diferencial","extremy","mezni-naklady","topic","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":3868,"title":3869,"body":3870,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":9563,"navigation":664,"path":9564,"seo":9565,"sources":9566,"stem":9567,"tags":9568,"type":3865,"updated":677,"__hash__":9573},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":3871,"toc":9535},[3872,3875,3898,3902,3928,3932,3974,4065,4109,4113,4137,4144,4148,4158,4170,4174,4202,4211,4266,4272,4275,4281,4308,4314,4412,4572,4863,4867,4947,4953,4957,5055,5121,5289,5293,5371,5402,5429,5435,5467,5545,5632,5636,5699,5705,5708,5714,5828,5913,5957,5961,6007,6014,6331,6336,6360,6389,6456,6553,6557,6564,6571,6642,6762,6846,6849,6855,7182,7186,7349,7357,7493,7501,7739,7747,7750,7755,8011,8015,8189,8323,8360,8404,8407,8537,8627,8645,8649,8656,8662,8723,8726,8750,8753,8759,8762,8768,8771,8775,8813,8871,9060,9064,9137,9143,9150,9154,9160,9302,9306,9312,9348,9353,9530],[12,3873,3869],{"id":3874},"elasticita-poptávky-a-nabídky",[3876,3877,3878],"blockquote",{},[724,3879,3880,3883,3884,3886,3887,3890,3891,3894,3895,1644],{},[883,3881,3882],{},"!abstract"," TL;DR\n",[38,3885,3836],{}," 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: ",[38,3888,3889],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,3892,3893],{},"křížově-cenovou elasticitu"," a ",[38,3896,3897],{},"důchodovou elasticitu",[115,3899,3901],{"id":3900},"úvod-motivace","Úvod — motivace",[724,3903,3904,3905,3907,3908,3911,3912,3915,3916,3919,3920,3923,3924,3927],{},"Termín ",[614,3906,1753],{}," (alternativně ",[614,3909,3910],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,3913,3914],{},"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 ",[614,3917,3918],{},"cenové elasticity poptávky"," (resp. ",[614,3921,3922],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,3925,2366],{"className":3926,"dataFsResolvedFilePath":764,"href":765},[210],").",[198,3929,3931],{"id":3930},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,3933,3934,3935,3954,3955,3973],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,3936,3938],{"className":3937},[886],[888,3939,3940],{"xmlns":890},[892,3941,3942,3951],{},[895,3943,3944,3947,3949],{},[898,3945,3946],{},"P",[2005,3948,2007],{},[2138,3950,2871],{},[902,3952,3953],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,3956,3958],{"className":3957},[886],[888,3959,3960],{"xmlns":890},[892,3961,3962,3970],{},[895,3963,3964,3966,3968],{},[898,3965,2797],{},[2005,3967,2007],{},[2138,3969,3098],{},[902,3971,3972],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,3975,3976,4022],{},[123,3977,3978,3981,3982,4021],{},[38,3979,3980],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,3983,3985],{"className":3984},[886],[888,3986,3987],{"xmlns":890},[892,3988,3989,4018],{},[895,3990,3991,3994,3997,3999,4001,4004,4006,4009,4011,4013,4015],{},[2297,3992,3993],{},"  ",[2005,3995,3996],{},"⇒",[2297,3998,3993],{},[898,4000,2783],{},[898,4002,4003],{},"R",[2005,4005,2007],{},[2138,4007,4008],{},"9",[2005,4010,3185],{},[2138,4012,3231],{},[2005,4014,2007],{},[2138,4016,4017],{},"990",[902,4019,4020],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,4023,4024,4027,4028,4064],{},[38,4025,4026],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,4029,4031],{"className":4030},[886],[888,4032,4033],{"xmlns":890},[892,4034,4035,4061],{},[895,4036,4037,4039,4041,4043,4045,4047,4049,4051,4053,4056,4058],{},[2297,4038,3993],{},[2005,4040,3996],{},[2297,4042,3993],{},[898,4044,2783],{},[898,4046,4003],{},[2005,4048,2007],{},[2138,4050,4008],{},[2005,4052,3185],{},[2138,4054,4055],{},"120",[2005,4057,2007],{},[2138,4059,4060],{},"1080",[902,4062,4063],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,4066,4067,4068,4071,4072,4075,4076,4079,4080,4083,4084,4087,4088,4104,4105,4108],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,4069,4070],{},"nerozumné",", na Trhu 2 ",[38,4073,4074],{},"rozumné",". Trh 2 je ",[38,4077,4078],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,4081,4082],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,4085,4086],{},"neelastická"," a vyššího ",[883,4089,4091],{"className":4090},[886],[888,4092,4093],{"xmlns":890},[892,4094,4095,4101],{},[895,4096,4097,4099],{},[898,4098,2783],{},[898,4100,4003],{},[902,4102,4103],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,4106,4107],{},"zvýšením"," ceny.",[198,4110,4112],{"id":4111},"hypotéza-41","Hypotéza 4.1",[3876,4114,4115],{},[724,4116,4117,4118],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,4119,4121],{"className":4120},[886],[888,4122,4123],{"xmlns":890},[892,4124,4125,4134],{},[895,4126,4127,4129,4132],{},[2005,4128,2014],{"stretchy":2013},[2138,4130,4131],{},"4.1",[2005,4133,2020],{"stretchy":2013},[902,4135,4136],{"encoding":904},"(4.1)",[724,4138,4139,4140,4143],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,4141,4142],{},"procentní změny"," obou faktorů.",[115,4145,4147],{"id":4146},"pojem-elasticity","Pojem elasticity",[724,4149,4150,4151,4153,4154,4157],{},"Obecně ",[38,4152,1753],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,4155,4156],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[3876,4159,4160],{},[724,4161,4162,4165,4166,4169],{},[883,4163,4164],{},"!info"," Intuice\nElasticitu lze číst jako ",[38,4167,4168],{},"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.",[115,4171,4173],{"id":4172},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,4175,4176,4177,4201],{},"Nechť ",[883,4178,4180],{"className":4179},[886],[888,4181,4182],{"xmlns":890},[892,4183,4184,4198],{},[895,4185,4186,4188,4190,4192,4194,4196],{},[898,4187,2797],{},[2005,4189,2007],{},[898,4191,1860],{},[2005,4193,2014],{"stretchy":2013},[898,4195,3946],{},[2005,4197,2020],{"stretchy":2013},[902,4199,4200],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,4203,4204],{},[883,4205,4210],{"className":4206,"title":4208,"style":4209},[4207],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,4212,4213,4214,3894,4230,4246,4247,4265],{},"Znaménko minus je korekce: změny ",[883,4215,4217],{"className":4216},[886],[888,4218,4219],{"xmlns":890},[892,4220,4221,4227],{},[895,4222,4223,4225],{},[898,4224,2897],{"mathvariant":2385},[898,4226,2797],{},[902,4228,4229],{"encoding":904},"\\Delta Q",[883,4231,4233],{"className":4232},[886],[888,4234,4235],{"xmlns":890},[892,4236,4237,4243],{},[895,4238,4239,4241],{},[898,4240,2897],{"mathvariant":2385},[898,4242,3946],{},[902,4244,4245],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,4248,4250],{"className":4249},[886],[888,4251,4252],{"xmlns":890},[892,4253,4254,4262],{},[895,4255,4256],{},[2133,4257,4258,4260],{},[898,4259,1868],{},[898,4261,1836],{},[902,4263,4264],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,4267,4268],{},[883,4269,4271],{"className":4270,"title":4208,"style":4209},[4207],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,4273,4274],{},"Po dosazení:",[724,4276,4277],{},[883,4278,4280],{"className":4279,"title":4208,"style":4209},[4207],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,4282,4283,4284,4304,4305,4307],{},"Limitním přechodem ",[883,4285,4287],{"className":4286},[886],[888,4288,4289],{"xmlns":890},[892,4290,4291,4301],{},[895,4292,4293,4295,4297,4299],{},[898,4294,2897],{"mathvariant":2385},[898,4296,3946],{},[2005,4298,3131],{},[2138,4300,2336],{},[902,4302,4303],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,4306,3918],{}," (price elasticity of demand):",[724,4309,4310],{},[883,4311,4313],{"className":4312,"title":4208,"style":4209},[4207],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,4315,4316,4317,4340,4341,4364,4365,4389,4390,4411],{},"kde ",[883,4318,4320],{"className":4319},[886],[888,4321,4322],{"xmlns":890},[892,4323,4324,4338],{},[895,4325,4326,4328,4330,4332,4334,4336],{},[898,4327,2797],{},[2005,4329,2007],{},[898,4331,1860],{},[2005,4333,2014],{"stretchy":2013},[898,4335,3946],{},[2005,4337,2020],{"stretchy":2013},[902,4339,4200],{"encoding":904},". Pro pevnou cenu ",[883,4342,4344],{"className":4343},[886],[888,4345,4346],{"xmlns":890},[892,4347,4348,4361],{},[895,4349,4350,4352,4354],{},[898,4351,3946],{},[2005,4353,2007],{},[2133,4355,4356,4358],{},[898,4357,3946],{},[2005,4359,4360],{},"∗",[902,4362,4363],{"encoding":904},"P = P^*"," se ",[883,4366,4368],{"className":4367},[886],[888,4369,4370],{"xmlns":890},[892,4371,4372,4386],{},[895,4373,4374,4376,4378,4384],{},[898,4375,1868],{},[2005,4377,2014],{"stretchy":2013},[2133,4379,4380,4382],{},[898,4381,3946],{},[2005,4383,4360],{},[2005,4385,2020],{"stretchy":2013},[902,4387,4388],{"encoding":904},"E(P^*)"," nazývá ",[614,4391,4392,4393],{},"elasticita poptávky při ceně ",[883,4394,4396],{"className":4395},[886],[888,4397,4398],{"xmlns":890},[892,4399,4400,4408],{},[895,4401,4402],{},[2133,4403,4404,4406],{},[898,4405,3946],{},[2005,4407,4360],{},[902,4409,4410],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[3876,4413,4414],{},[724,4415,4416,4419,4420,4438,4439,4467,4468,4497,4498,1343,4516,1343,4534,4552,4553,4568,4569,1644],{},[883,4417,4418],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[38,4421,4422,4423],{},"explicitní ",[883,4424,4426],{"className":4425},[886],[888,4427,4428],{"xmlns":890},[892,4429,4430,4436],{},[895,4431,4432,4434],{},[2005,4433,2234],{},[2138,4435,2287],{},[902,4437,3742],{"encoding":904}," právě proto, že ",[883,4440,4442],{"className":4441},[886],[888,4443,4444],{"xmlns":890},[892,4445,4446,4464],{},[895,4447,4448,4454,4456,4458,4460,4462],{},[2133,4449,4450,4452],{},[898,4451,2797],{},[2005,4453,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,4455,2014],{"stretchy":2013},[898,4457,3946],{},[2005,4459,2020],{"stretchy":2013},[2005,4461,3455],{},[2138,4463,2336],{},[902,4465,4466],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,4469,4471],{"className":4470},[886],[888,4472,4473],{"xmlns":890},[892,4474,4475,4494],{},[895,4476,4477,4479,4481,4487,4489,4492],{},[898,4478,1868],{},[2005,4480,2014],{"stretchy":2013},[2133,4482,4483,4485],{},[898,4484,3946],{},[2005,4486,4360],{},[2005,4488,2020],{"stretchy":2013},[2005,4490,4491],{},"≥",[2138,4493,2336],{},[902,4495,4496],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,4499,4501],{"className":4500},[886],[888,4502,4503],{"xmlns":890},[892,4504,4505,4513],{},[895,4506,4507,4509,4511],{},[898,4508,1868],{},[2005,4510,3416],{},[2138,4512,2287],{},[902,4514,4515],{"encoding":904},"E > 1",[883,4517,4519],{"className":4518},[886],[888,4520,4521],{"xmlns":890},[892,4522,4523,4531],{},[895,4524,4525,4527,4529],{},[898,4526,1868],{},[2005,4528,3455],{},[2138,4530,2287],{},[902,4532,4533],{"encoding":904},"E \u003C 1",[883,4535,4537],{"className":4536},[886],[888,4538,4539],{"xmlns":890},[892,4540,4541,4549],{},[895,4542,4543,4545,4547],{},[898,4544,1868],{},[2005,4546,2007],{},[2138,4548,2287],{},[902,4550,4551],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,4554,4556],{"className":4555},[886],[888,4557,4558],{"xmlns":890},[892,4559,4560,4566],{},[895,4561,4562,4564],{},[2005,4563,2234],{},[2138,4565,2287],{},[902,4567,3742],{"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 ",[38,4570,4571],{},"absolutní hodnotou",[3876,4573,4574,4594],{},[724,4575,4576,4579,4580,4593],{},[883,4577,4578],{},"!tip"," Postup: jak spočítat ",[883,4581,4583],{"className":4582},[886],[888,4584,4585],{"xmlns":890},[892,4586,4587,4591],{},[895,4588,4589],{},[898,4590,1868],{},[902,4592,1868],{"encoding":904}," v bodě",[152,4595,4596,4648,4688,4741,4806],{},[123,4597,4598,4599,4622,4623,4647],{},"Zapište ",[883,4600,4602],{"className":4601},[886],[888,4603,4604],{"xmlns":890},[892,4605,4606,4620],{},[895,4607,4608,4610,4612,4614,4616,4618],{},[898,4609,2797],{},[2005,4611,2007],{},[898,4613,1860],{},[2005,4615,2014],{"stretchy":2013},[898,4617,3946],{},[2005,4619,2020],{"stretchy":2013},[902,4621,4200],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,4624,4626],{"className":4625},[886],[888,4627,4628],{"xmlns":890},[892,4629,4630,4644],{},[895,4631,4632,4634,4636,4638,4640,4642],{},[898,4633,3946],{},[2005,4635,2007],{},[898,4637,1860],{},[2005,4639,2014],{"stretchy":2013},[898,4641,2797],{},[2005,4643,2020],{"stretchy":2013},[902,4645,4646],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,4649,4650,4651,1644],{},"Spočítejte derivaci ",[883,4652,4654],{"className":4653},[886],[888,4655,4656],{"xmlns":890},[892,4657,4658,4685],{},[895,4659,4660,4666,4668,4670,4672,4674,4676,4678,4681,4683],{},[2133,4661,4662,4664],{},[898,4663,2797],{},[2005,4665,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,4667,2014],{"stretchy":2013},[898,4669,3946],{},[2005,4671,2020],{"stretchy":2013},[2005,4673,2007],{},[898,4675,2203],{"mathvariant":2385},[898,4677,2797],{},[898,4679,4680],{"mathvariant":2385},"\u002F",[898,4682,2203],{"mathvariant":2385},[898,4684,3946],{},[902,4686,4687],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,4689,4690,4691,4708,4709,1644],{},"Dosaďte zadanou cenu ",[883,4692,4694],{"className":4693},[886],[888,4695,4696],{"xmlns":890},[892,4697,4698,4706],{},[895,4699,4700],{},[2133,4701,4702,4704],{},[898,4703,3946],{},[2005,4705,4360],{},[902,4707,4410],{"encoding":904}," a dopočítejte odpovídající ",[883,4710,4712],{"className":4711},[886],[888,4713,4714],{"xmlns":890},[892,4715,4716,4738],{},[895,4717,4718,4724,4726,4728,4730,4736],{},[2133,4719,4720,4722],{},[898,4721,2797],{},[2005,4723,4360],{},[2005,4725,2007],{},[898,4727,1860],{},[2005,4729,2014],{"stretchy":2013},[2133,4731,4732,4734],{},[898,4733,3946],{},[2005,4735,4360],{},[2005,4737,2020],{"stretchy":2013},[902,4739,4740],{"encoding":904},"Q^* = D(P^*)",[123,4742,4743,4744,1644],{},"Dosaďte do (4.5): ",[883,4745,4747],{"className":4746},[886],[888,4748,4749],{"xmlns":890},[892,4750,4751,4803],{},[895,4752,4753,4755,4757,4763,4765,4767,4769,4785,4787,4793,4795,4801],{},[898,4754,1868],{},[2005,4756,2014],{"stretchy":2013},[2133,4758,4759,4761],{},[898,4760,3946],{},[2005,4762,4360],{},[2005,4764,2020],{"stretchy":2013},[2005,4766,2007],{},[2005,4768,2234],{},[2334,4770,4771],{"scriptlevel":2336,"displaystyle":2294},[2338,4772,4773,4779],{},[2133,4774,4775,4777],{},[898,4776,3946],{},[2005,4778,4360],{},[2133,4780,4781,4783],{},[898,4782,2797],{},[2005,4784,4360],{},[2297,4786,2995],{},[2133,4788,4789,4791],{},[898,4790,2797],{},[2005,4792,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,4794,2014],{"stretchy":2013},[2133,4796,4797,4799],{},[898,4798,3946],{},[2005,4800,4360],{},[2005,4802,2020],{"stretchy":2013},[902,4804,4805],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,4807,4808,4809,4826,4827,4844,4845,4862],{},"Klasifikujte: ",[883,4810,4812],{"className":4811},[886],[888,4813,4814],{"xmlns":890},[892,4815,4816,4824],{},[895,4817,4818,4820,4822],{},[898,4819,1868],{},[2005,4821,3416],{},[2138,4823,2287],{},[902,4825,4515],{"encoding":904}," elastická, ",[883,4828,4830],{"className":4829},[886],[888,4831,4832],{"xmlns":890},[892,4833,4834,4842],{},[895,4835,4836,4838,4840],{},[898,4837,1868],{},[2005,4839,2007],{},[2138,4841,2287],{},[902,4843,4551],{"encoding":904}," jednotková, ",[883,4846,4848],{"className":4847},[886],[888,4849,4850],{"xmlns":890},[892,4851,4852,4860],{},[895,4853,4854,4856,4858],{},[898,4855,1868],{},[2005,4857,3455],{},[2138,4859,2287],{},[902,4861,4533],{"encoding":904}," neelastická.",[198,4864,4866],{"id":4865},"interpretace-46","Interpretace (4.6)",[3876,4868,4869],{},[724,4870,4871,4872,4895,4896,4909,4910,4927,4928],{},"Číslo ",[883,4873,4875],{"className":4874},[886],[888,4876,4877],{"xmlns":890},[892,4878,4879,4893],{},[895,4880,4881,4883,4885,4891],{},[898,4882,1868],{},[2005,4884,2014],{"stretchy":2013},[2133,4886,4887,4889],{},[898,4888,3946],{},[2005,4890,4360],{},[2005,4892,2020],{"stretchy":2013},[902,4894,4388],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,4897,4899],{"className":4898},[886],[888,4900,4901],{"xmlns":890},[892,4902,4903,4907],{},[895,4904,4905],{},[898,4906,2797],{},[902,4908,2797],{"encoding":904},", jestliže se cena ",[883,4911,4913],{"className":4912},[886],[888,4914,4915],{"xmlns":890},[892,4916,4917,4925],{},[895,4918,4919],{},[2133,4920,4921,4923],{},[898,4922,3946],{},[2005,4924,4360],{},[902,4926,4410],{"encoding":904}," změní o 1 %. ",[883,4929,4931],{"className":4930},[886],[888,4932,4933],{"xmlns":890},[892,4934,4935,4944],{},[895,4936,4937,4939,4942],{},[2005,4938,2014],{"stretchy":2013},[2138,4940,4941],{},"4.6",[2005,4943,2020],{"stretchy":2013},[902,4945,4946],{"encoding":904},"(4.6)",[724,4948,4949,4952],{},[38,4950,4951],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,4954,4956],{"id":4955},"příklad-41","Příklad 4.1",[724,4958,4959,4960,4994,4995,1343,5021,2713],{},"Poptávka ",[883,4961,4963],{"className":4962},[886],[888,4964,4965],{"xmlns":890},[892,4966,4967,4991],{},[895,4968,4969,4971,4973,4975,4977,4979,4981,4983,4985,4987,4989],{},[898,4970,3946],{},[2005,4972,2007],{},[898,4974,1860],{},[2005,4976,2014],{"stretchy":2013},[898,4978,2797],{},[2005,4980,2020],{"stretchy":2013},[2005,4982,2007],{},[2138,4984,3128],{},[2005,4986,2234],{},[2138,4988,2140],{},[898,4990,2797],{},[902,4992,4993],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,4996,4998],{"className":4997},[886],[888,4999,5000],{"xmlns":890},[892,5001,5002,5018],{},[895,5003,5004,5006,5008,5011,5013,5016],{},[898,5005,2797],{},[2005,5007,2007],{},[2138,5009,5010],{},"25",[2005,5012,2234],{},[2138,5014,5015],{},"0,5",[898,5017,3946],{},[902,5019,5020],{"encoding":904},"Q = 25 - 0{,}5P",[883,5022,5024],{"className":5023},[886],[888,5025,5026],{"xmlns":890},[892,5027,5028,5052],{},[895,5029,5030,5046,5048,5050],{},[2334,5031,5032],{"scriptlevel":2336,"displaystyle":2294},[2338,5033,5034,5040],{},[895,5035,5036,5038],{},[898,5037,2203],{"mathvariant":2385},[898,5039,2797],{},[895,5041,5042,5044],{},[898,5043,2203],{"mathvariant":2385},[898,5045,3946],{},[2005,5047,2007],{},[2005,5049,2234],{},[2138,5051,5015],{},[902,5053,5054],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,5056,5057],{},[883,5058,5060],{"className":5059},[886],[888,5061,5062],{"xmlns":890},[892,5063,5064,5118],{},[895,5065,5066,5068,5070,5072,5086,5088,5090,5092,5094,5096,5098,5116],{},[898,5067,1868],{},[2005,5069,2007],{},[2005,5071,2234],{},[2338,5073,5074,5076],{},[898,5075,3946],{},[895,5077,5078,5080,5082,5084],{},[2138,5079,5010],{},[2005,5081,2234],{},[2138,5083,5015],{},[898,5085,3946],{},[2005,5087,3185],{},[2005,5089,2014],{"stretchy":2013},[2005,5091,2234],{},[2138,5093,5015],{},[2005,5095,2020],{"stretchy":2013},[2005,5097,2007],{},[2338,5099,5100,5106],{},[895,5101,5102,5104],{},[2138,5103,5015],{},[898,5105,3946],{},[895,5107,5108,5110,5112,5114],{},[2138,5109,5010],{},[2005,5111,2234],{},[2138,5113,5015],{},[898,5115,3946],{},[898,5117,1644],{"mathvariant":2385},[902,5119,5120],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,5122,5123,5124,1343,5148,1343,5178,1343,5202,5227,5228,5251,5252,2694,5270,3927],{},"Potom ",[883,5125,5127],{"className":5126},[886],[888,5128,5129],{"xmlns":890},[892,5130,5131,5145],{},[895,5132,5133,5135,5137,5139,5141,5143],{},[898,5134,1868],{},[2005,5136,2014],{"stretchy":2013},[2138,5138,2336],{},[2005,5140,2020],{"stretchy":2013},[2005,5142,2007],{},[2138,5144,2336],{},[902,5146,5147],{"encoding":904},"E(0)=0",[883,5149,5151],{"className":5150},[886],[888,5152,5153],{"xmlns":890},[892,5154,5155,5175],{},[895,5156,5157,5159,5161,5163,5165,5167],{},[898,5158,1868],{},[2005,5160,2014],{"stretchy":2013},[2138,5162,2871],{},[2005,5164,2020],{"stretchy":2013},[2005,5166,2007],{},[2334,5168,5169],{"scriptlevel":2336,"displaystyle":2013},[2338,5170,5171,5173],{},[2138,5172,2287],{},[2138,5174,2360],{},[902,5176,5177],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,5179,5181],{"className":5180},[886],[888,5182,5183],{"xmlns":890},[892,5184,5185,5199],{},[895,5186,5187,5189,5191,5193,5195,5197],{},[898,5188,1868],{},[2005,5190,2014],{"stretchy":2013},[2138,5192,5010],{},[2005,5194,2020],{"stretchy":2013},[2005,5196,2007],{},[2138,5198,2287],{},[902,5200,5201],{"encoding":904},"E(25)=1",[883,5203,5205],{"className":5204},[886],[888,5206,5207],{"xmlns":890},[892,5208,5209,5224],{},[895,5210,5211,5213,5215,5218,5220,5222],{},[898,5212,1868],{},[2005,5214,2014],{"stretchy":2013},[2138,5216,5217],{},"40",[2005,5219,2020],{"stretchy":2013},[2005,5221,2007],{},[2138,5223,2360],{},[902,5225,5226],{"encoding":904},"E(40)=4",". Např. ",[883,5229,5231],{"className":5230},[886],[888,5232,5233],{"xmlns":890},[892,5234,5235,5249],{},[895,5236,5237,5239,5241,5243,5245,5247],{},[898,5238,1868],{},[2005,5240,2014],{"stretchy":2013},[2138,5242,5217],{},[2005,5244,2020],{"stretchy":2013},[2005,5246,2007],{},[2138,5248,2360],{},[902,5250,5226],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,5253,5255],{"className":5254},[886],[888,5256,5257],{"xmlns":890},[892,5258,5259,5267],{},[895,5260,5261,5263,5265],{},[898,5262,2797],{},[2005,5264,2007],{},[2138,5266,2237],{},[902,5268,5269],{"encoding":904},"Q=5",[883,5271,5273],{"className":5272},[886],[888,5274,5275],{"xmlns":890},[892,5276,5277,5286],{},[895,5278,5279,5281,5283],{},[898,5280,2797],{},[2005,5282,2007],{},[2138,5284,5285],{},"4,8",[902,5287,5288],{"encoding":904},"Q=4{,}8",[198,5290,5292],{"id":5291},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,5294,5295,5351],{},[123,5296,5297,5300,5301,5318,5319,1644],{},[38,5298,5299],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,5302,5304],{"className":5303},[886],[888,5305,5306],{"xmlns":890},[892,5307,5308,5316],{},[895,5309,5310],{},[2133,5311,5312,5314],{},[898,5313,1868],{},[898,5315,1836],{},[902,5317,4264],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,5320,5322],{"className":5321},[886],[888,5323,5324],{"xmlns":890},[892,5325,5326,5348],{},[895,5327,5328,5331,5333,5335,5337,5339,5341,5343,5345],{},[2005,5329,5330],{"stretchy":2013},"⟨",[898,5332,3946],{},[2005,5334,2295],{"separator":2294},[2297,5336,2995],{},[898,5338,3946],{},[2005,5340,2104],{},[898,5342,2897],{"mathvariant":2385},[898,5344,3946],{},[2005,5346,5347],{"stretchy":2013},"⟩",[902,5349,5350],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,5352,5353,5356,5357,5370],{},[38,5354,5355],{},"Bodová"," (okamžitá) elasticita: ",[883,5358,5360],{"className":5359},[886],[888,5361,5362],{"xmlns":890},[892,5363,5364,5368],{},[895,5365,5366],{},[898,5367,1868],{},[902,5369,1868],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,5372,5374,5375,5388,5389],{"id":5373},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,5376,5378],{"className":5377},[886],[888,5379,5380],{"xmlns":890},[892,5381,5382,5386],{},[895,5383,5384],{},[898,5385,3946],{},[902,5387,3946],{"encoding":904}," jako funkce ",[883,5390,5392],{"className":5391},[886],[888,5393,5394],{"xmlns":890},[892,5395,5396,5400],{},[895,5397,5398],{},[898,5399,2797],{},[902,5401,2797],{"encoding":904},[724,5403,5404,5405,5428],{},"Pokud je poptávka zadaná ve tvaru ",[883,5406,5408],{"className":5407},[886],[888,5409,5410],{"xmlns":890},[892,5411,5412,5426],{},[895,5413,5414,5416,5418,5420,5422,5424],{},[898,5415,3946],{},[2005,5417,2007],{},[898,5419,1860],{},[2005,5421,2014],{"stretchy":2013},[898,5423,2797],{},[2005,5425,2020],{"stretchy":2013},[902,5427,4646],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,5430,5431],{},[883,5432,5434],{"className":5433,"title":4208,"style":4209},[4207],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,5436,5437,2212,5440,5466],{},[38,5438,5439],{},"Příklad 4.3.",[883,5441,5443],{"className":5442},[886],[888,5444,5445],{"xmlns":890},[892,5446,5447,5463],{},[895,5448,5449,5451,5453,5455,5457],{},[898,5450,3946],{},[2005,5452,2007],{},[2138,5454,3098],{},[2005,5456,2234],{},[2133,5458,5459,5461],{},[898,5460,2797],{},[2138,5462,2140],{},[902,5464,5465],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,5468,5469],{},[883,5470,5472],{"className":5471},[886],[888,5473,5474],{"xmlns":890},[892,5475,5476,5542],{},[895,5477,5478,5480,5482,5484,5500,5502,5514,5516,5540],{},[898,5479,1868],{},[2005,5481,2007],{},[2005,5483,2234],{},[2338,5485,5486,5498],{},[895,5487,5488,5490,5492],{},[2138,5489,3098],{},[2005,5491,2234],{},[2133,5493,5494,5496],{},[898,5495,2797],{},[2138,5497,2140],{},[898,5499,2797],{},[2005,5501,3185],{},[2338,5503,5504,5506],{},[2138,5505,2287],{},[895,5507,5508,5510,5512],{},[2005,5509,2234],{},[2138,5511,2140],{},[898,5513,2797],{},[2005,5515,2007],{},[2338,5517,5518,5530],{},[895,5519,5520,5522,5524],{},[2138,5521,3098],{},[2005,5523,2234],{},[2133,5525,5526,5528],{},[898,5527,2797],{},[2138,5529,2140],{},[895,5531,5532,5534],{},[2138,5533,2140],{},[2133,5535,5536,5538],{},[898,5537,2797],{},[2138,5539,2140],{},[898,5541,1644],{"mathvariant":2385},[902,5543,5544],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,5546,5547,5548,5575,5576,5595,5596,1644],{},"Z rovnice ",[883,5549,5551],{"className":5550},[886],[888,5552,5553],{"xmlns":890},[892,5554,5555,5572],{},[895,5556,5557,5559,5561,5567,5569],{},[2138,5558,3098],{},[2005,5560,2234],{},[2133,5562,5563,5565],{},[898,5564,2797],{},[2138,5566,2140],{},[2005,5568,2007],{},[2138,5570,5571],{},"36",[902,5573,5574],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,5577,5579],{"className":5578},[886],[888,5580,5581],{"xmlns":890},[892,5582,5583,5592],{},[895,5584,5585,5587,5589],{},[898,5586,2797],{},[2005,5588,2007],{},[2138,5590,5591],{},"8",[902,5593,5594],{"encoding":904},"Q = 8",", tedy ",[883,5597,5599],{"className":5598},[886],[888,5600,5601],{"xmlns":890},[892,5602,5603,5629],{},[895,5604,5605,5607,5609,5611,5613,5615,5624,5626],{},[898,5606,1868],{},[2005,5608,2014],{"stretchy":2013},[2138,5610,5591],{},[2005,5612,2020],{"stretchy":2013},[2005,5614,2007],{},[2334,5616,5617],{"scriptlevel":2336,"displaystyle":2013},[2338,5618,5619,5621],{},[2138,5620,5571],{},[2138,5622,5623],{},"128",[2005,5625,2007],{},[2138,5627,5628],{},"0,281",[902,5630,5631],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,5633,5635],{"id":5634},"přibližné-změny","Přibližné změny",[724,5637,5638,5639,5675,5676,5698],{},"Diferenciál ",[883,5640,5642],{"className":5641},[886],[888,5643,5644],{"xmlns":890},[892,5645,5646,5672],{},[895,5647,5648,5650,5652,5654,5660,5662,5664,5666,5668,5670],{},[898,5649,2203],{"mathvariant":2385},[898,5651,2797],{},[2005,5653,2007],{},[2133,5655,5656,5658],{},[898,5657,2797],{},[2005,5659,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,5661,2014],{"stretchy":2013},[898,5663,3946],{},[2005,5665,2020],{"stretchy":2013},[2297,5667,2995],{},[898,5669,2203],{"mathvariant":2385},[898,5671,3946],{},[902,5673,5674],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,5677,5679],{"className":5678},[886],[888,5680,5681],{"xmlns":890},[892,5682,5683,5695],{},[895,5684,5685,5687,5689,5691,5693],{},[898,5686,2203],{"mathvariant":2385},[898,5688,3946],{},[2005,5690,2007],{},[898,5692,2897],{"mathvariant":2385},[898,5694,3946],{},[902,5696,5697],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,5700,5701],{},[883,5702,5704],{"className":5703,"title":4208,"style":4209},[4207],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,5706,5707],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,5709,5710],{},[883,5711,5713],{"className":5712,"title":4208,"style":4209},[4207],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,5715,5716,2212,5719,5754,5755,5774,5775,5809,5810,5827],{},[38,5717,5718],{},"Příklad 4.5.",[883,5720,5722],{"className":5721},[886],[888,5723,5724],{"xmlns":890},[892,5725,5726,5751],{},[895,5727,5728,5730,5732,5734,5740,5742,5744,5746,5748],{},[898,5729,3946],{},[2005,5731,2007],{},[2005,5733,2234],{},[2133,5735,5736,5738],{},[898,5737,2797],{},[2138,5739,2140],{},[2005,5741,2234],{},[2138,5743,2360],{},[898,5745,2797],{},[2005,5747,2104],{},[2138,5749,5750],{},"96",[902,5752,5753],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,5756,5758],{"className":5757},[886],[888,5759,5760],{"xmlns":890},[892,5761,5762,5771],{},[895,5763,5764,5766,5768],{},[898,5765,3946],{},[2005,5767,2007],{},[2138,5769,5770],{},"51",[902,5772,5773],{"encoding":904},"P=51",". Z rovnice ",[883,5776,5778],{"className":5777},[886],[888,5779,5780],{"xmlns":890},[892,5781,5782,5806],{},[895,5783,5784,5786,5788,5790,5796,5798,5800,5802,5804],{},[2138,5785,5770],{},[2005,5787,2007],{},[2005,5789,2234],{},[2133,5791,5792,5794],{},[898,5793,2797],{},[2138,5795,2140],{},[2005,5797,2234],{},[2138,5799,2360],{},[898,5801,2797],{},[2005,5803,2104],{},[2138,5805,5750],{},[902,5807,5808],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,5811,5813],{"className":5812},[886],[888,5814,5815],{"xmlns":890},[892,5816,5817,5825],{},[895,5818,5819,5821,5823],{},[898,5820,2797],{},[2005,5822,2007],{},[2138,5824,2237],{},[902,5826,5269],{"encoding":904},". Elasticita:",[724,5829,5830],{},[883,5831,5833],{"className":5832},[886],[888,5834,5835],{"xmlns":890},[892,5836,5837,5910],{},[895,5838,5839,5841,5843,5881,5883,5887,5889,5891,5893,5895,5897,5904,5907],{},[898,5840,1868],{},[2005,5842,2007],{},[2338,5844,5845,5865],{},[895,5846,5847,5849,5855,5857,5859,5861,5863],{},[2005,5848,2234],{},[2133,5850,5851,5853],{},[898,5852,2797],{},[2138,5854,2140],{},[2005,5856,2234],{},[2138,5858,2360],{},[898,5860,2797],{},[2005,5862,2104],{},[2138,5864,5750],{},[895,5866,5867,5869,5871,5873,5875,5877,5879],{},[898,5868,2797],{},[2005,5870,2014],{"stretchy":2013},[2138,5872,2140],{},[898,5874,2797],{},[2005,5876,2104],{},[2138,5878,2360],{},[2005,5880,2020],{"stretchy":2013},[2005,5882,2295],{"separator":2294},[5884,5885],"mspace",{"width":5886},"2em",[898,5888,1868],{},[2005,5890,2014],{"stretchy":2013},[2138,5892,2237],{},[2005,5894,2020],{"stretchy":2013},[2005,5896,2007],{},[2338,5898,5899,5901],{},[2138,5900,5770],{},[2138,5902,5903],{},"70",[2005,5905,5906],{},"≐",[2138,5908,5909],{},"0,728.",[902,5911,5912],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,5914,5915,5916,1644],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,5917,5919],{"className":5918},[886],[888,5920,5921],{"xmlns":890},[892,5922,5923,5954],{},[895,5924,5925,5927,5929,5932,5934,5936,5939,5941,5943,5945,5947,5950,5952],{},[898,5926,2897],{"mathvariant":2385},[898,5928,2797],{},[898,5930,5931],{"mathvariant":2385},"%",[2005,5933,2739],{},[2005,5935,2234],{},[2138,5937,5938],{},"0,728",[2005,5940,3185],{},[2138,5942,2140],{},[2005,5944,2007],{},[2005,5946,2234],{},[2138,5948,5949],{},"1,456",[2297,5951,2995],{},[898,5953,5931],{"mathvariant":2385},[902,5955,5956],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,5958,5960],{"id":5959},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,5962,5963,5964,5987,5988,2713],{},"V závislosti na hodnotě ",[883,5965,5967],{"className":5966},[886],[888,5968,5969],{"xmlns":890},[892,5970,5971,5985],{},[895,5972,5973,5975,5977,5983],{},[898,5974,1868],{},[2005,5976,2014],{"stretchy":2013},[2133,5978,5979,5981],{},[898,5980,3946],{},[2005,5982,4360],{},[2005,5984,2020],{"stretchy":2013},[902,5986,4388],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,5989,5991],{"className":5990},[886],[888,5992,5993],{"xmlns":890},[892,5994,5995,6004],{},[895,5996,5997,5999,6002],{},[2005,5998,2014],{"stretchy":2013},[2138,6000,6001],{},"4.7",[2005,6003,2020],{"stretchy":2013},[902,6005,6006],{"encoding":904},"(4.7)",[724,6008,6009],{},[2568,6010],{"alt":6011,"className":6012,"src":6013},"imek-typy-elasticity-5panelu",[210,2572],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,6015,6016,6055],{},[19,6017,6018],{},[22,6019,6020,6046,6049,6052],{},[25,6021,6022,6023],{},"Hodnota ",[883,6024,6026],{"className":6025},[886],[888,6027,6028],{"xmlns":890},[892,6029,6030,6044],{},[895,6031,6032,6034,6036,6042],{},[898,6033,1868],{},[2005,6035,2014],{"stretchy":2013},[2133,6037,6038,6040],{},[898,6039,3946],{},[2005,6041,4360],{},[2005,6043,2020],{"stretchy":2013},[902,6045,4388],{"encoding":904},[25,6047,6048],{},"Typ poptávky",[25,6050,6051],{},"Termín",[25,6053,6054],{},"Význam",[30,6056,6057,6090,6152,6227,6284],{},[22,6058,6059,6079,6084,6087],{},[35,6060,6061],{},[883,6062,6064],{"className":6063},[886],[888,6065,6066],{"xmlns":890},[892,6067,6068,6076],{},[895,6069,6070,6072,6074],{},[898,6071,1868],{},[2005,6073,2007],{},[2138,6075,2336],{},[902,6077,6078],{"encoding":904},"E = 0",[35,6080,6081],{},[38,6082,6083],{},"dokonale neelastická",[35,6085,6086],{},"perfectly inelastic",[35,6088,6089],{},"množství se nemění bez ohledu na cenu",[22,6091,6092,6116,6120,6123],{},[35,6093,6094],{},[883,6095,6097],{"className":6096},[886],[888,6098,6099],{"xmlns":890},[892,6100,6101,6113],{},[895,6102,6103,6105,6107,6109,6111],{},[2138,6104,2336],{},[2005,6106,3455],{},[898,6108,1868],{},[2005,6110,3455],{},[2138,6112,2287],{},[902,6114,6115],{"encoding":904},"0 \u003C E \u003C 1",[35,6117,6118],{},[38,6119,4086],{},[35,6121,6122],{},"inelastic",[35,6124,6125,6138,6139],{},[883,6126,6128],{"className":6127},[886],[888,6129,6130],{"xmlns":890},[892,6131,6132,6136],{},[895,6133,6134],{},[898,6135,2797],{},[902,6137,2797],{"encoding":904}," se mění pomaleji než ",[883,6140,6142],{"className":6141},[886],[888,6143,6144],{"xmlns":890},[892,6145,6146,6150],{},[895,6147,6148],{},[898,6149,3946],{},[902,6151,3946],{"encoding":904},[22,6153,6154,6173,6178,6181],{},[35,6155,6156],{},[883,6157,6159],{"className":6158},[886],[888,6160,6161],{"xmlns":890},[892,6162,6163,6171],{},[895,6164,6165,6167,6169],{},[898,6166,1868],{},[2005,6168,2007],{},[2138,6170,2287],{},[902,6172,4551],{"encoding":904},[35,6174,6175],{},[38,6176,6177],{},"jednotkově elastická",[35,6179,6180],{},"unit elastic",[35,6182,6183,6196,6197,6210,6211,6226],{},[883,6184,6186],{"className":6185},[886],[888,6187,6188],{"xmlns":890},[892,6189,6190,6194],{},[895,6191,6192],{},[898,6193,2797],{},[902,6195,2797],{"encoding":904}," i ",[883,6198,6200],{"className":6199},[886],[888,6201,6202],{"xmlns":890},[892,6203,6204,6208],{},[895,6205,6206],{},[898,6207,3946],{},[902,6209,3946],{"encoding":904}," se mění stejně rychle; ",[883,6212,6214],{"className":6213},[886],[888,6215,6216],{"xmlns":890},[892,6217,6218,6224],{},[895,6219,6220,6222],{},[898,6221,2783],{},[898,6223,4003],{},[902,6225,4103],{"encoding":904}," má maximum",[22,6228,6229,6248,6252,6255],{},[35,6230,6231],{},[883,6232,6234],{"className":6233},[886],[888,6235,6236],{"xmlns":890},[892,6237,6238,6246],{},[895,6239,6240,6242,6244],{},[898,6241,1868],{},[2005,6243,3416],{},[2138,6245,2287],{},[902,6247,4515],{"encoding":904},[35,6249,6250],{},[38,6251,4082],{},[35,6253,6254],{},"elastic",[35,6256,6257,6270,6271],{},[883,6258,6260],{"className":6259},[886],[888,6261,6262],{"xmlns":890},[892,6263,6264,6268],{},[895,6265,6266],{},[898,6267,2797],{},[902,6269,2797],{"encoding":904}," se mění rychleji než ",[883,6272,6274],{"className":6273},[886],[888,6275,6276],{"xmlns":890},[892,6277,6278,6282],{},[895,6279,6280],{},[898,6281,3946],{},[902,6283,3946],{"encoding":904},[22,6285,6286,6307,6312,6315],{},[35,6287,6288],{},[883,6289,6291],{"className":6290},[886],[888,6292,6293],{"xmlns":890},[892,6294,6295,6304],{},[895,6296,6297,6299,6301],{},[898,6298,1868],{},[2005,6300,3131],{},[898,6302,6303],{"mathvariant":2385},"∞",[902,6305,6306],{"encoding":904},"E \\to \\infty",[35,6308,6309],{},[38,6310,6311],{},"dokonale elastická",[35,6313,6314],{},"perfectly elastic",[35,6316,6317,6318],{},"sebemenší změna ceny úplně mění ",[883,6319,6321],{"className":6320},[886],[888,6322,6323],{"xmlns":890},[892,6324,6325,6329],{},[895,6326,6327],{},[898,6328,2797],{},[902,6330,2797],{"encoding":904},[724,6332,6333],{},[38,6334,6335],{},"Pravidlo růstu elasticity s cenou:",[3876,6337,6338],{},[724,6339,6340,6341],{},"S rostoucí cenou elasticita poptávky roste. ",[883,6342,6344],{"className":6343},[886],[888,6345,6346],{"xmlns":890},[892,6347,6348,6357],{},[895,6349,6350,6352,6355],{},[2005,6351,2014],{"stretchy":2013},[2138,6353,6354],{},"4.8",[2005,6356,2020],{"stretchy":2013},[902,6358,6359],{"encoding":904},"(4.8)",[724,6361,6362,6363,6366,6367,6370,6371,6388],{},"Z toho plyne, že při ",[614,6364,6365],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,6368,6369],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,6372,6374],{"className":6373},[886],[888,6375,6376],{"xmlns":890},[892,6377,6378,6386],{},[895,6379,6380],{},[2133,6381,6382,6384],{},[898,6383,3946],{},[2005,6385,4360],{},[902,6387,4410],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[3876,6390,6391,6396],{},[724,6392,6393,6395],{},[883,6394,4578],{}," Postup: jak klasifikovat poptávku",[152,6397,6398,6425,6428],{},[123,6399,6400,6401,6424],{},"Spočítejte ",[883,6402,6404],{"className":6403},[886],[888,6405,6406],{"xmlns":890},[892,6407,6408,6422],{},[895,6409,6410,6412,6414,6420],{},[898,6411,1868],{},[2005,6413,2014],{"stretchy":2013},[2133,6415,6416,6418],{},[898,6417,3946],{},[2005,6419,4360],{},[2005,6421,2020],{"stretchy":2013},[902,6423,4388],{"encoding":904}," dle (4.5).",[123,6426,6427],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,6429,6430,6431,6455],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,6432,6434],{"className":6433},[886],[888,6435,6436],{"xmlns":890},[892,6437,6438,6452],{},[895,6439,6440,6442,6444,6446,6448,6450],{},[898,6441,1868],{},[2005,6443,2014],{"stretchy":2013},[898,6445,3946],{},[2005,6447,2020],{"stretchy":2013},[2005,6449,2007],{},[2138,6451,2287],{},[902,6453,6454],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,6457,6458,6461,6462,6479,6480,6498,6499,6526,6527,1644],{},[38,6459,6460],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,6463,6465],{"className":6464},[886],[888,6466,6467],{"xmlns":890},[892,6468,6469,6477],{},[895,6470,6471,6473,6475],{},[898,6472,1868],{},[2005,6474,2007],{},[2138,6476,2287],{},[902,6478,4551],{"encoding":904}," pro ",[883,6481,6483],{"className":6482},[886],[888,6484,6485],{"xmlns":890},[892,6486,6487,6495],{},[895,6488,6489,6491,6493],{},[898,6490,3946],{},[2005,6492,2007],{},[2138,6494,5010],{},[902,6496,6497],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,6500,6502],{"className":6501},[886],[888,6503,6504],{"xmlns":890},[892,6505,6506,6523],{},[895,6507,6508,6510,6513,6515,6517,6519,6521],{},[898,6509,3946],{},[2005,6511,6512],{},"∈",[2005,6514,5330],{"stretchy":2013},[2138,6516,2336],{},[2005,6518,2295],{"separator":2294},[2138,6520,5010],{},[2005,6522,2020],{"stretchy":2013},[902,6524,6525],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,6528,6530],{"className":6529},[886],[888,6531,6532],{"xmlns":890},[892,6533,6534,6550],{},[895,6535,6536,6538,6540,6542,6544,6546,6548],{},[898,6537,3946],{},[2005,6539,6512],{},[2005,6541,2014],{"stretchy":2013},[2138,6543,5010],{},[2005,6545,2295],{"separator":2294},[2138,6547,3128],{},[2005,6549,5347],{"stretchy":2013},[902,6551,6552],{"encoding":904},"P \\in (25, 50\\rangle",[115,6554,6556],{"id":6555},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,6558,6559],{},[2568,6560],{"alt":6561,"className":6562,"src":6563},"imek-elasticita-tr",[210,2572],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,6565,6566],{},[2568,6567],{"alt":6568,"className":6569,"src":6570},"imek-elasticita-podel-linearni-poptavky",[210,2572],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,6572,6573,6574,6624,6625,6641],{},"Pro celkový příjem platí ",[883,6575,6577],{"className":6576},[886],[888,6578,6579],{"xmlns":890},[892,6580,6581,6621],{},[895,6582,6583,6585,6587,6589,6591,6593,6595,6597,6599,6601,6603,6605,6607,6609,6611,6613,6615,6617,6619],{},[898,6584,2783],{},[898,6586,4003],{},[2005,6588,2007],{},[898,6590,2783],{},[898,6592,4003],{},[2005,6594,2014],{"stretchy":2013},[898,6596,2797],{},[2005,6598,2020],{"stretchy":2013},[2005,6600,2007],{},[898,6602,3946],{},[2005,6604,3185],{},[898,6606,2797],{},[2005,6608,2007],{},[898,6610,2797],{},[2005,6612,3185],{},[898,6614,1860],{},[2005,6616,2014],{"stretchy":2013},[898,6618,2797],{},[2005,6620,2020],{"stretchy":2013},[902,6622,6623],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,6626,6628],{"className":6627},[886],[888,6629,6630],{"xmlns":890},[892,6631,6632,6638],{},[895,6633,6634,6636],{},[898,6635,2826],{},[898,6637,4003],{},[902,6639,6640],{"encoding":904},"MR"," odvodíme:",[724,6643,6644],{},[883,6645,6647],{"className":6646},[886],[888,6648,6649],{"xmlns":890},[892,6650,6651,6759],{},[895,6652,6653,6655,6657,6659,6661,6667,6669,6671,6673,6675,6677,6679,6681,6683,6685,6687,6689,6695,6697,6699,6701,6703,6705,6707,6709,6723,6725,6727],{},[898,6654,2826],{},[898,6656,4003],{},[2005,6658,2007],{},[898,6660,2783],{},[2133,6662,6663,6665],{},[898,6664,4003],{},[2005,6666,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,6668,2014],{"stretchy":2013},[898,6670,2797],{},[2005,6672,2020],{"stretchy":2013},[2005,6674,2007],{},[898,6676,1860],{},[2005,6678,2014],{"stretchy":2013},[898,6680,2797],{},[2005,6682,2020],{"stretchy":2013},[2005,6684,2104],{},[898,6686,2797],{},[2297,6688,2995],{},[2133,6690,6691,6693],{},[898,6692,1860],{},[2005,6694,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,6696,2014],{"stretchy":2013},[898,6698,2797],{},[2005,6700,2020],{"stretchy":2013},[2005,6702,2007],{},[898,6704,3946],{},[2005,6706,2104],{},[898,6708,2797],{},[2338,6710,6711,6717],{},[895,6712,6713,6715],{},[898,6714,2203],{"mathvariant":2385},[898,6716,3946],{},[895,6718,6719,6721],{},[898,6720,2203],{"mathvariant":2385},[898,6722,2797],{},[2005,6724,2007],{},[898,6726,3946],{},[895,6728,6729,6731,6733,6735,6741,6743,6757],{},[2005,6730,2014],{"fence":2294},[2138,6732,2287],{},[2005,6734,2104],{},[2338,6736,6737,6739],{},[898,6738,2797],{},[898,6740,3946],{},[2005,6742,3185],{},[2338,6744,6745,6751],{},[895,6746,6747,6749],{},[898,6748,2203],{"mathvariant":2385},[898,6750,3946],{},[895,6752,6753,6755],{},[898,6754,2203],{"mathvariant":2385},[898,6756,2797],{},[2005,6758,2020],{"fence":2294},[902,6760,6761],{"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)",[724,6763,6764],{},[883,6765,6767],{"className":6766},[886],[888,6768,6769],{"xmlns":890},[892,6770,6771,6843],{},[895,6772,6773,6775,6777,6819,6821,6823],{},[2005,6774,2007],{},[898,6776,3946],{},[895,6778,6779,6781,6783,6785,6817],{},[2005,6780,2014],{"fence":2294},[2138,6782,2287],{},[2005,6784,2104],{},[2338,6786,6787,6789],{},[2138,6788,2287],{},[895,6790,6791,6799,6801],{},[2334,6792,6793],{"scriptlevel":2336,"displaystyle":2013},[2338,6794,6795,6797],{},[898,6796,3946],{},[898,6798,2797],{},[2005,6800,3185],{},[2334,6802,6803],{"scriptlevel":2336,"displaystyle":2013},[2338,6804,6805,6811],{},[895,6806,6807,6809],{},[898,6808,2203],{"mathvariant":2385},[898,6810,2797],{},[895,6812,6813,6815],{},[898,6814,2203],{"mathvariant":2385},[898,6816,3946],{},[2005,6818,2020],{"fence":2294},[2005,6820,2007],{},[898,6822,3946],{},[895,6824,6825,6827,6829,6831,6841],{},[2005,6826,2014],{"fence":2294},[2138,6828,2287],{},[2005,6830,2104],{},[2338,6832,6833,6835],{},[2138,6834,2287],{},[895,6836,6837,6839],{},[2005,6838,2234],{},[898,6840,1868],{},[2005,6842,2020],{"fence":2294},[902,6844,6845],{"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)",[724,6847,6848],{},"a tedy",[724,6850,6851],{},[883,6852,6854],{"className":6853,"title":4208,"style":4209},[4207],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[3876,6856,6857,6926,7176],{},[724,6858,6859,6861,6862,6896,6897,6912,6913,2713],{},[883,6860,4164],{}," Intuice: vztah ",[883,6863,6865],{"className":6864},[886],[888,6866,6867],{"xmlns":890},[892,6868,6869,6893],{},[895,6870,6871,6873,6875,6877,6879,6881,6883,6885,6887,6889,6891],{},[898,6872,2826],{},[898,6874,4003],{},[2005,6876,2007],{},[898,6878,3946],{},[2005,6880,2014],{"stretchy":2013},[2138,6882,2287],{},[2005,6884,2234],{},[2138,6886,2287],{},[898,6888,4680],{"mathvariant":2385},[898,6890,1868],{},[2005,6892,2020],{"stretchy":2013},[902,6894,6895],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,6898,6900],{"className":6899},[886],[888,6901,6902],{"xmlns":890},[892,6903,6904,6910],{},[895,6905,6906,6908],{},[898,6907,2826],{},[898,6909,4003],{},[902,6911,6640],{"encoding":904}," jednoznačně určuje hodnota ",[883,6914,6916],{"className":6915},[886],[888,6917,6918],{"xmlns":890},[892,6919,6920,6924],{},[895,6921,6922],{},[898,6923,1868],{},[902,6925,1868],{"encoding":904},[120,6927,6928,7038,7107],{},[123,6929,6930,6947,6948,2212,6962,2212,6988,2212,7001,7021,7022,7037],{},[883,6931,6933],{"className":6932},[886],[888,6934,6935],{"xmlns":890},[892,6936,6937,6945],{},[895,6938,6939,6941,6943],{},[898,6940,1868],{},[2005,6942,3416],{},[2138,6944,2287],{},[902,6946,4515],{"encoding":904}," (elastická) ",[883,6949,6951],{"className":6950},[886],[888,6952,6953],{"xmlns":890},[892,6954,6955,6959],{},[895,6956,6957],{},[2005,6958,3996],{},[902,6960,6961],{"encoding":904},"\\Rightarrow",[883,6963,6965],{"className":6964},[886],[888,6966,6967],{"xmlns":890},[892,6968,6969,6985],{},[895,6970,6971,6973,6975,6977,6979,6981,6983],{},[2138,6972,2287],{},[2005,6974,2234],{},[2138,6976,2287],{},[898,6978,4680],{"mathvariant":2385},[898,6980,1868],{},[2005,6982,3416],{},[2138,6984,2336],{},[902,6986,6987],{"encoding":904},"1 - 1\u002FE > 0",[883,6989,6991],{"className":6990},[886],[888,6992,6993],{"xmlns":890},[892,6994,6995,6999],{},[895,6996,6997],{},[2005,6998,3996],{},[902,7000,6961],{"encoding":904},[883,7002,7004],{"className":7003},[886],[888,7005,7006],{"xmlns":890},[892,7007,7008,7018],{},[895,7009,7010,7012,7014,7016],{},[898,7011,2826],{},[898,7013,4003],{},[2005,7015,3416],{},[2138,7017,2336],{},[902,7019,7020],{"encoding":904},"MR > 0"," — ",[883,7023,7025],{"className":7024},[886],[888,7026,7027],{"xmlns":890},[892,7028,7029,7035],{},[895,7030,7031,7033],{},[898,7032,2783],{},[898,7034,4003],{},[902,7036,4103],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,7039,7040,7057,7058,2212,7071,7021,7091,7106],{},[883,7041,7043],{"className":7042},[886],[888,7044,7045],{"xmlns":890},[892,7046,7047,7055],{},[895,7048,7049,7051,7053],{},[898,7050,1868],{},[2005,7052,2007],{},[2138,7054,2287],{},[902,7056,4551],{"encoding":904}," (jednotková) ",[883,7059,7061],{"className":7060},[886],[888,7062,7063],{"xmlns":890},[892,7064,7065,7069],{},[895,7066,7067],{},[2005,7068,3996],{},[902,7070,6961],{"encoding":904},[883,7072,7074],{"className":7073},[886],[888,7075,7076],{"xmlns":890},[892,7077,7078,7088],{},[895,7079,7080,7082,7084,7086],{},[898,7081,2826],{},[898,7083,4003],{},[2005,7085,2007],{},[2138,7087,2336],{},[902,7089,7090],{"encoding":904},"MR = 0",[883,7092,7094],{"className":7093},[886],[888,7095,7096],{"xmlns":890},[892,7097,7098,7104],{},[895,7099,7100,7102],{},[898,7101,2783],{},[898,7103,4003],{},[902,7105,4103],{"encoding":904}," je extrém (maximum).",[123,7108,7109,7126,7127,2212,7140,7021,7160,7175],{},[883,7110,7112],{"className":7111},[886],[888,7113,7114],{"xmlns":890},[892,7115,7116,7124],{},[895,7117,7118,7120,7122],{},[898,7119,1868],{},[2005,7121,3455],{},[2138,7123,2287],{},[902,7125,4533],{"encoding":904}," (neelastická) ",[883,7128,7130],{"className":7129},[886],[888,7131,7132],{"xmlns":890},[892,7133,7134,7138],{},[895,7135,7136],{},[2005,7137,3996],{},[902,7139,6961],{"encoding":904},[883,7141,7143],{"className":7142},[886],[888,7144,7145],{"xmlns":890},[892,7146,7147,7157],{},[895,7148,7149,7151,7153,7155],{},[898,7150,2826],{},[898,7152,4003],{},[2005,7154,3455],{},[2138,7156,2336],{},[902,7158,7159],{"encoding":904},"MR \u003C 0",[883,7161,7163],{"className":7162},[886],[888,7164,7165],{"xmlns":890},[892,7166,7167,7173],{},[895,7168,7169,7171],{},[898,7170,2783],{},[898,7172,4003],{},[902,7174,4103],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,7177,7178,7179,1644],{},"Viz také ",[207,7180,3831],{"className":7181,"dataFsResolvedFilePath":827,"href":828},[210],[198,7183,7185],{"id":7184},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,7187,7188,7208,7209,7235,7236,7251,7252,7265,7266,7279,7280,7293,7294,7310,7311,2212,7326,7329,7330,7310,7346,1644],{},[38,7189,7190,7191,3927],{},"(a) Poptávka elastická (",[883,7192,7194],{"className":7193},[886],[888,7195,7196],{"xmlns":890},[892,7197,7198,7206],{},[895,7199,7200,7202,7204],{},[898,7201,1868],{},[2005,7203,3416],{},[2138,7205,2287],{},[902,7207,4515],{"encoding":904}," Z (4.12) plyne ",[883,7210,7212],{"className":7211},[886],[888,7213,7214],{"xmlns":890},[892,7215,7216,7232],{},[895,7217,7218,7220,7222,7224,7226,7228,7230],{},[898,7219,2826],{},[898,7221,4003],{},[2005,7223,2014],{"stretchy":2013},[898,7225,2797],{},[2005,7227,2020],{"stretchy":2013},[2005,7229,3416],{},[2138,7231,2336],{},[902,7233,7234],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,7237,7239],{"className":7238},[886],[888,7240,7241],{"xmlns":890},[892,7242,7243,7249],{},[895,7244,7245,7247],{},[898,7246,2783],{},[898,7248,4003],{},[902,7250,4103],{"encoding":904}," je rostoucí funkcí ",[883,7253,7255],{"className":7254},[886],[888,7256,7257],{"xmlns":890},[892,7258,7259,7263],{},[895,7260,7261],{},[898,7262,2797],{},[902,7264,2797],{"encoding":904},". Avšak růst ",[883,7267,7269],{"className":7268},[886],[888,7270,7271],{"xmlns":890},[892,7272,7273,7277],{},[895,7274,7275],{},[898,7276,2797],{},[902,7278,2797],{"encoding":904}," je odezvou na pokles ceny ",[883,7281,7283],{"className":7282},[886],[888,7284,7285],{"xmlns":890},[892,7286,7287,7291],{},[895,7288,7289],{},[898,7290,3946],{},[902,7292,3946],{"encoding":904},". Tudíž s ",[614,7295,7296,7297],{},"poklesem ceny ",[883,7298,7300],{"className":7299},[886],[888,7301,7302],{"xmlns":890},[892,7303,7304,7308],{},[895,7305,7306],{},[898,7307,3946],{},[902,7309,3946],{"encoding":904}," celkový příjem ",[883,7312,7314],{"className":7313},[886],[888,7315,7316],{"xmlns":890},[892,7317,7318,7324],{},[895,7319,7320,7322],{},[898,7321,2783],{},[898,7323,4003],{},[902,7325,4103],{"encoding":904},[614,7327,7328],{},"roste"," a s ",[614,7331,7332,7333],{},"růstem ceny ",[883,7334,7336],{"className":7335},[886],[888,7337,7338],{"xmlns":890},[892,7339,7340,7344],{},[895,7341,7342],{},[898,7343,3946],{},[902,7345,3946],{"encoding":904},[614,7347,7348],{},"klesá",[3876,7350,7351],{},[724,7352,7353,7356],{},[38,7354,7355],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,7358,7359,7208,7379,1343,7405,7420,7421,7434,7435,7448,7449,7462,7463,7310,7476,2212,7491,1644],{},[38,7360,7361,7362,3927],{},"(b) Poptávka neelastická (",[883,7363,7365],{"className":7364},[886],[888,7366,7367],{"xmlns":890},[892,7368,7369,7377],{},[895,7370,7371,7373,7375],{},[898,7372,1868],{},[2005,7374,3455],{},[2138,7376,2287],{},[902,7378,4533],{"encoding":904},[883,7380,7382],{"className":7381},[886],[888,7383,7384],{"xmlns":890},[892,7385,7386,7402],{},[895,7387,7388,7390,7392,7394,7396,7398,7400],{},[898,7389,2826],{},[898,7391,4003],{},[2005,7393,2014],{"stretchy":2013},[898,7395,2797],{},[2005,7397,2020],{"stretchy":2013},[2005,7399,3455],{},[2138,7401,2336],{},[902,7403,7404],{"encoding":904},"MR(Q) \u003C 0",[883,7406,7408],{"className":7407},[886],[888,7409,7410],{"xmlns":890},[892,7411,7412,7418],{},[895,7413,7414,7416],{},[898,7415,2783],{},[898,7417,4003],{},[902,7419,4103],{"encoding":904}," je klesající funkce ",[883,7422,7424],{"className":7423},[886],[888,7425,7426],{"xmlns":890},[892,7427,7428,7432],{},[895,7429,7430],{},[898,7431,2797],{},[902,7433,2797],{"encoding":904},", tj. s růstem ",[883,7436,7438],{"className":7437},[886],[888,7439,7440],{"xmlns":890},[892,7441,7442,7446],{},[895,7443,7444],{},[898,7445,2797],{},[902,7447,2797],{"encoding":904}," (s poklesem ceny ",[883,7450,7452],{"className":7451},[886],[888,7453,7454],{"xmlns":890},[892,7455,7456,7460],{},[895,7457,7458],{},[898,7459,3946],{},[902,7461,3946],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,7464,7466],{"className":7465},[886],[888,7467,7468],{"xmlns":890},[892,7469,7470,7474],{},[895,7471,7472],{},[898,7473,3946],{},[902,7475,3946],{"encoding":904},[883,7477,7479],{"className":7478},[886],[888,7480,7481],{"xmlns":890},[892,7482,7483,7489],{},[895,7484,7485,7487],{},[898,7486,2783],{},[898,7488,4003],{},[902,7490,4103],{"encoding":904},[614,7492,7328],{},[3876,7494,7495],{},[724,7496,7497,7500],{},[38,7498,7499],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,7502,7503,7208,7523,7542,7543,7558,7559,7629,7630,3894,7658,7691,7692,5595,7720,7735,7736,1644],{},[38,7504,7505,7506,3927],{},"(c) Jednotková elasticita (",[883,7507,7509],{"className":7508},[886],[888,7510,7511],{"xmlns":890},[892,7512,7513,7521],{},[895,7514,7515,7517,7519],{},[898,7516,1868],{},[2005,7518,2007],{},[2138,7520,2287],{},[902,7522,4551],{"encoding":904},[883,7524,7526],{"className":7525},[886],[888,7527,7528],{"xmlns":890},[892,7529,7530,7540],{},[895,7531,7532,7534,7536,7538],{},[898,7533,2826],{},[898,7535,4003],{},[2005,7537,2007],{},[2138,7539,2336],{},[902,7541,7090],{"encoding":904}," — nutná podmínka extrému ",[883,7544,7546],{"className":7545},[886],[888,7547,7548],{"xmlns":890},[892,7549,7550,7556],{},[895,7551,7552,7554],{},[898,7553,2783],{},[898,7555,4003],{},[902,7557,4103],{"encoding":904},". Dále ",[883,7560,7562],{"className":7561},[886],[888,7563,7564],{"xmlns":890},[892,7565,7566,7626],{},[895,7567,7568,7570,7580,7582,7584,7590,7592,7598,7600,7602,7604,7606,7608,7610,7620,7622,7624],{},[898,7569,2783],{},[2133,7571,7572,7574],{},[898,7573,4003],{},[895,7575,7576,7578],{},[2005,7577,2387],{"mathvariant":2385},[2005,7579,2387],{"mathvariant":2385},[2005,7581,2007],{},[898,7583,2826],{},[2133,7585,7586,7588],{},[898,7587,4003],{},[2005,7589,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,7591,2007],{},[2133,7593,7594,7596],{},[898,7595,1860],{},[2005,7597,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,7599,2014],{"stretchy":2013},[898,7601,2797],{},[2005,7603,2020],{"stretchy":2013},[2005,7605,2104],{},[898,7607,2797],{},[2297,7609,2995],{},[2133,7611,7612,7614],{},[898,7613,1860],{},[895,7615,7616,7618],{},[2005,7617,2387],{"mathvariant":2385},[2005,7619,2387],{"mathvariant":2385},[2005,7621,2014],{"stretchy":2013},[898,7623,2797],{},[2005,7625,2020],{"stretchy":2013},[902,7627,7628],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,7631,7633],{"className":7632},[886],[888,7634,7635],{"xmlns":890},[892,7636,7637,7655],{},[895,7638,7639,7645,7647,7649,7651,7653],{},[2133,7640,7641,7643],{},[898,7642,1860],{},[2005,7644,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,7646,2014],{"stretchy":2013},[898,7648,2797],{},[2005,7650,2020],{"stretchy":2013},[2005,7652,3455],{},[2138,7654,2336],{},[902,7656,7657],{"encoding":904},"D'(Q) \u003C 0",[883,7659,7661],{"className":7660},[886],[888,7662,7663],{"xmlns":890},[892,7664,7665,7688],{},[895,7666,7667,7677,7679,7681,7683,7686],{},[2133,7668,7669,7671],{},[898,7670,1860],{},[895,7672,7673,7675],{},[2005,7674,2387],{"mathvariant":2385},[2005,7676,2387],{"mathvariant":2385},[2005,7678,2014],{"stretchy":2013},[898,7680,2797],{},[2005,7682,2020],{"stretchy":2013},[2005,7684,7685],{},"≤",[2138,7687,2336],{},[902,7689,7690],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,7693,7695],{"className":7694},[886],[888,7696,7697],{"xmlns":890},[892,7698,7699,7717],{},[895,7700,7701,7703,7713,7715],{},[898,7702,2783],{},[2133,7704,7705,7707],{},[898,7706,4003],{},[895,7708,7709,7711],{},[2005,7710,2387],{"mathvariant":2385},[2005,7712,2387],{"mathvariant":2385},[2005,7714,3455],{},[2138,7716,2336],{},[902,7718,7719],{"encoding":904},"TR'' \u003C 0",[883,7721,7723],{"className":7722},[886],[888,7724,7725],{"xmlns":890},[892,7726,7727,7733],{},[895,7728,7729,7731],{},[898,7730,2783],{},[898,7732,4003],{},[902,7734,4103],{"encoding":904}," nabývá ",[38,7737,7738],{},"maxima",[3876,7740,7741],{},[724,7742,7743,7746],{},[38,7744,7745],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,7748,7749],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,7751,7752],{},[38,7753,7754],{},"Souhrnná tabulka Pravidel 1–3:",[16,7756,7757,7861],{},[19,7758,7759],{},[22,7760,7761,7764,7779,7796,7827,7858],{},[25,7762,7763],{},"Charakter poptávky",[25,7765,7766],{},[883,7767,7769],{"className":7768},[886],[888,7770,7771],{"xmlns":890},[892,7772,7773,7777],{},[895,7774,7775],{},[898,7776,1868],{},[902,7778,1868],{"encoding":904},[25,7780,7781],{},[883,7782,7784],{"className":7783},[886],[888,7785,7786],{"xmlns":890},[892,7787,7788,7794],{},[895,7789,7790,7792],{},[898,7791,2826],{},[898,7793,4003],{},[902,7795,6640],{"encoding":904},[25,7797,7798,7799,2212,7812],{},"Pokles ceny ",[883,7800,7802],{"className":7801},[886],[888,7803,7804],{"xmlns":890},[892,7805,7806,7810],{},[895,7807,7808],{},[2005,7809,3996],{},[902,7811,6961],{"encoding":904},[883,7813,7815],{"className":7814},[886],[888,7816,7817],{"xmlns":890},[892,7818,7819,7825],{},[895,7820,7821,7823],{},[898,7822,2783],{},[898,7824,4003],{},[902,7826,4103],{"encoding":904},[25,7828,7829,7830,2212,7843],{},"Růst ceny ",[883,7831,7833],{"className":7832},[886],[888,7834,7835],{"xmlns":890},[892,7836,7837,7841],{},[895,7838,7839],{},[2005,7840,3996],{},[902,7842,6961],{"encoding":904},[883,7844,7846],{"className":7845},[886],[888,7847,7848],{"xmlns":890},[892,7849,7850,7856],{},[895,7851,7852,7854],{},[898,7853,2783],{},[898,7855,4003],{},[902,7857,4103],{"encoding":904},[25,7859,7860],{},"Doporučení",[30,7862,7863,7912,7962],{},[22,7864,7865,7867,7885,7903,7905,7907],{},[35,7866,4082],{},[35,7868,7869],{},[883,7870,7872],{"className":7871},[886],[888,7873,7874],{"xmlns":890},[892,7875,7876,7882],{},[895,7877,7878,7880],{},[2005,7879,3416],{},[2138,7881,2287],{},[902,7883,7884],{"encoding":904},"> 1",[35,7886,7887],{},[883,7888,7890],{"className":7889},[886],[888,7891,7892],{"xmlns":890},[892,7893,7894,7900],{},[895,7895,7896,7898],{},[2005,7897,3416],{},[2138,7899,2336],{},[902,7901,7902],{"encoding":904},"> 0",[35,7904,7328],{},[35,7906,7348],{},[35,7908,7909],{},[38,7910,7911],{},"snížit cenu",[22,7913,7914,7917,7935,7953,7955,7957],{},[35,7915,7916],{},"jednotková",[35,7918,7919],{},[883,7920,7922],{"className":7921},[886],[888,7923,7924],{"xmlns":890},[892,7925,7926,7932],{},[895,7927,7928,7930],{},[2005,7929,2007],{},[2138,7931,2287],{},[902,7933,7934],{"encoding":904},"= 1",[35,7936,7937],{},[883,7938,7940],{"className":7939},[886],[888,7941,7942],{"xmlns":890},[892,7943,7944,7950],{},[895,7945,7946,7948],{},[2005,7947,2007],{},[2138,7949,2336],{},[902,7951,7952],{"encoding":904},"= 0",[35,7954,3725],{},[35,7956,3725],{},[35,7958,7959],{},[38,7960,7961],{},"držet cenu",[22,7963,7964,7966,7984,8002,8004,8006],{},[35,7965,4086],{},[35,7967,7968],{},[883,7969,7971],{"className":7970},[886],[888,7972,7973],{"xmlns":890},[892,7974,7975,7981],{},[895,7976,7977,7979],{},[2005,7978,3455],{},[2138,7980,2287],{},[902,7982,7983],{"encoding":904},"\u003C 1",[35,7985,7986],{},[883,7987,7989],{"className":7988},[886],[888,7990,7991],{"xmlns":890},[892,7992,7993,7999],{},[895,7994,7995,7997],{},[2005,7996,3455],{},[2138,7998,2336],{},[902,8000,8001],{"encoding":904},"\u003C 0",[35,8003,7348],{},[35,8005,7328],{},[35,8007,8008],{},[38,8009,8010],{},"zvýšit cenu",[198,8012,8014],{"id":8013},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,8016,8017,8018,8043,8044,8066,8067,8080,8081,8094,8095,8108,8109,5595,8136,8188],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,8019,8021],{"className":8020},[886],[888,8022,8023],{"xmlns":890},[892,8024,8025,8041],{},[895,8026,8027,8029,8031,8033,8035],{},[898,8028,3946],{},[2005,8030,2007],{},[2138,8032,3098],{},[2005,8034,2234],{},[2133,8036,8037,8039],{},[898,8038,2797],{},[2138,8040,2140],{},[902,8042,5465],{"encoding":904},". Reálné cenové rozpětí je ",[883,8045,8047],{"className":8046},[886],[888,8048,8049],{"xmlns":890},[892,8050,8051,8063],{},[895,8052,8053,8055,8057,8059,8061],{},[2005,8054,5330],{"stretchy":2013},[2138,8056,2287],{},[2005,8058,2295],{"separator":2294},[2138,8060,3098],{},[2005,8062,5347],{"stretchy":2013},[902,8064,8065],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,8068,8070],{"className":8069},[886],[888,8071,8072],{"xmlns":890},[892,8073,8074,8078],{},[895,8075,8076],{},[898,8077,2797],{},[902,8079,2797],{"encoding":904}," jako funkci ",[883,8082,8084],{"className":8083},[886],[888,8085,8086],{"xmlns":890},[892,8087,8088,8092],{},[895,8089,8090],{},[898,8091,3946],{},[902,8093,3946],{"encoding":904},"; pro nezáporné ",[883,8096,8098],{"className":8097},[886],[888,8099,8100],{"xmlns":890},[892,8101,8102,8106],{},[895,8103,8104],{},[898,8105,2797],{},[902,8107,2797],{"encoding":904}," je ",[883,8110,8112],{"className":8111},[886],[888,8113,8114],{"xmlns":890},[892,8115,8116,8133],{},[895,8117,8118,8120,8122],{},[898,8119,2797],{},[2005,8121,2007],{},[8123,8124,8125],"msqrt",{},[895,8126,8127,8129,8131],{},[2138,8128,3098],{},[2005,8130,2234],{},[898,8132,3946],{},[902,8134,8135],{"encoding":904},"Q = \\sqrt{100 - P}",[883,8137,8139],{"className":8138},[886],[888,8140,8141],{"xmlns":890},[892,8142,8143,8185],{},[895,8144,8145,8161,8163,8165],{},[2334,8146,8147],{"scriptlevel":2336,"displaystyle":2294},[2338,8148,8149,8155],{},[895,8150,8151,8153],{},[898,8152,2203],{"mathvariant":2385},[898,8154,2797],{},[895,8156,8157,8159],{},[898,8158,2203],{"mathvariant":2385},[898,8160,3946],{},[2005,8162,2007],{},[2005,8164,2234],{},[2334,8166,8167],{"scriptlevel":2336,"displaystyle":2294},[2338,8168,8169,8171],{},[2138,8170,2287],{},[895,8172,8173,8175],{},[2138,8174,2140],{},[8123,8176,8177],{},[895,8178,8179,8181,8183],{},[2138,8180,3098],{},[2005,8182,2234],{},[898,8184,3946],{},[902,8186,8187],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,8190,8191],{},[883,8192,8194],{"className":8193},[886],[888,8195,8196],{"xmlns":890},[892,8197,8198,8320],{},[895,8199,8200,8202,8204,8206,8208,8210,8212,8218,8220,8234,8236,8238,8252,8254,8280,8282,8300,8302,8318],{},[898,8201,1868],{},[2005,8203,2014],{"stretchy":2013},[898,8205,3946],{},[2005,8207,2020],{"stretchy":2013},[2005,8209,2007],{},[2005,8211,2234],{},[2338,8213,8214,8216],{},[898,8215,3946],{},[898,8217,2797],{},[2005,8219,3185],{},[2338,8221,8222,8228],{},[895,8223,8224,8226],{},[898,8225,2203],{"mathvariant":2385},[898,8227,2797],{},[895,8229,8230,8232],{},[898,8231,2203],{"mathvariant":2385},[898,8233,3946],{},[2005,8235,2007],{},[2005,8237,2234],{},[2338,8239,8240,8242],{},[898,8241,3946],{},[8123,8243,8244],{},[895,8245,8246,8248,8250],{},[2138,8247,3098],{},[2005,8249,2234],{},[898,8251,3946],{},[2005,8253,3185],{},[895,8255,8256,8258,8260,8278],{},[2005,8257,2014],{"fence":2294},[2005,8259,2234],{},[2338,8261,8262,8264],{},[2138,8263,2287],{},[895,8265,8266,8268],{},[2138,8267,2140],{},[8123,8269,8270],{},[895,8271,8272,8274,8276],{},[2138,8273,3098],{},[2005,8275,2234],{},[898,8277,3946],{},[2005,8279,2020],{"fence":2294},[2005,8281,2007],{},[2338,8283,8284,8286],{},[898,8285,3946],{},[895,8287,8288,8290,8292,8294,8296,8298],{},[2138,8289,2140],{},[2005,8291,2014],{"stretchy":2013},[2138,8293,3098],{},[2005,8295,2234],{},[898,8297,3946],{},[2005,8299,2020],{"stretchy":2013},[2005,8301,2007],{},[2338,8303,8304,8310],{},[895,8305,8306,8308],{},[2138,8307,5015],{},[898,8309,3946],{},[895,8311,8312,8314,8316],{},[2138,8313,3098],{},[2005,8315,2234],{},[898,8317,3946],{},[898,8319,1644],{"mathvariant":2385},[902,8321,8322],{"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}.",[724,8324,8325,8326,2713],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,8327,8329],{"className":8328},[886],[888,8330,8331],{"xmlns":890},[892,8332,8333,8357],{},[895,8334,8335,8353,8355],{},[2334,8336,8337],{"scriptlevel":2336,"displaystyle":2294},[2338,8338,8339,8345],{},[895,8340,8341,8343],{},[2138,8342,5015],{},[898,8344,3946],{},[895,8346,8347,8349,8351],{},[2138,8348,3098],{},[2005,8350,2234],{},[898,8352,3946],{},[2005,8354,2007],{},[2138,8356,2287],{},[902,8358,8359],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,8361,8362],{},[883,8363,8365],{"className":8364},[886],[888,8366,8367],{"xmlns":890},[892,8368,8369,8401],{},[895,8370,8371,8377,8379,8386,8388,8391,8399],{},[2133,8372,8373,8375],{},[898,8374,3946],{},[2005,8376,4360],{},[2005,8378,2007],{},[2338,8380,8381,8384],{},[2138,8382,8383],{},"200",[2138,8385,2182],{},[2005,8387,5906],{},[2138,8389,8390],{},"66,",[8392,8393,8394,8396],"mover",{"accent":2294},[2138,8395,2244],{},[2005,8397,8398],{"stretchy":2294},"‾",[898,8400,1644],{"mathvariant":2385},[902,8402,8403],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,8405,8406],{},"S využitím vlastnosti (4.8):",[120,8408,8409,8455,8497],{},[123,8410,8411,8412,8447,8448,8450,8451,8454],{},"Při cenách ",[883,8413,8415],{"className":8414},[886],[888,8416,8417],{"xmlns":890},[892,8418,8419,8444],{},[895,8420,8421,8423,8425,8427,8429,8432,8434,8436,8442],{},[898,8422,3946],{},[2005,8424,6512],{},[2005,8426,5330],{"stretchy":2013},[2138,8428,2287],{},[2005,8430,8431],{"separator":2294},";",[2297,8433,2995],{},[2138,8435,8390],{},[8392,8437,8438,8440],{"accent":2294},[2138,8439,2244],{},[2005,8441,8398],{"stretchy":2294},[2005,8443,2020],{"stretchy":2013},[902,8445,8446],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,8449,4086],{}," — dle ",[614,8452,8453],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,8456,8411,8457,8447,8491,8450,8493,8496],{},[883,8458,8460],{"className":8459},[886],[888,8461,8462],{"xmlns":890},[892,8463,8464,8488],{},[895,8465,8466,8468,8470,8472,8474,8480,8482,8484,8486],{},[898,8467,3946],{},[2005,8469,6512],{},[2005,8471,2014],{"stretchy":2013},[2138,8473,8390],{},[8392,8475,8476,8478],{"accent":2294},[2138,8477,2244],{},[2005,8479,8398],{"stretchy":2294},[2005,8481,8431],{"separator":2294},[2297,8483,2995],{},[2138,8485,3098],{},[2005,8487,5347],{"stretchy":2013},[902,8489,8490],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,8492,4082],{},[614,8494,8495],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,8498,8499,8500,8503,8504,8532,8533,8536],{},"Dle ",[614,8501,8502],{},"Pravidla 3"," je při ceně ",[883,8505,8507],{"className":8506},[886],[888,8508,8509],{"xmlns":890},[892,8510,8511,8529],{},[895,8512,8513,8519,8521,8523],{},[2133,8514,8515,8517],{},[898,8516,3946],{},[2005,8518,4360],{},[2005,8520,2007],{},[2138,8522,8390],{},[8392,8524,8525,8527],{"accent":2294},[2138,8526,2244],{},[2005,8528,8398],{"stretchy":2294},[902,8530,8531],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,8534,8535],{},"maxima celkového příjmu"," ve výši",[724,8538,8539],{},[883,8540,8542],{"className":8541},[886],[888,8543,8544],{"xmlns":890},[892,8545,8546,8624],{},[895,8547,8548,8550,8552,8554,8560,8562,8564,8570,8572,8586,8588,8594,8596,8604,8606,8619,8621],{},[898,8549,2783],{},[898,8551,4003],{},[2005,8553,2014],{"stretchy":2013},[2133,8555,8556,8558],{},[898,8557,3946],{},[2005,8559,4360],{},[2005,8561,2020],{"stretchy":2013},[2005,8563,2007],{},[2133,8565,8566,8568],{},[898,8567,3946],{},[2005,8569,4360],{},[2005,8571,3185],{},[8123,8573,8574],{},[895,8575,8576,8578,8580],{},[2138,8577,3098],{},[2005,8579,2234],{},[2133,8581,8582,8584],{},[898,8583,3946],{},[2005,8585,4360],{},[2005,8587,2007],{},[2338,8589,8590,8592],{},[2138,8591,8383],{},[2138,8593,2182],{},[2005,8595,3185],{},[8123,8597,8598],{},[2338,8599,8600,8602],{},[2138,8601,3098],{},[2138,8603,2182],{},[2005,8605,2007],{},[2338,8607,8608,8611],{},[2138,8609,8610],{},"2000",[895,8612,8613,8615],{},[2138,8614,2182],{},[8123,8616,8617],{},[2138,8618,2182],{},[2005,8620,5906],{},[2138,8622,8623],{},"384,9.",[902,8625,8626],{"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.",[724,8628,8629,8630,1644],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,8631,8633],{"className":8632},[886],[888,8634,8635],{"xmlns":890},[892,8636,8637,8643],{},[895,8638,8639,8641],{},[898,8640,2783],{},[898,8642,4003],{},[902,8644,4103],{"encoding":904},[115,8646,8648],{"id":8647},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,8650,8651,8652,8655],{},"Analogicky se definuje ",[38,8653,8654],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,8657,8658],{},[883,8659,8661],{"className":8660,"title":4208,"style":4209},[4207],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,8663,4316,8664,8689,8690,8722],{},[883,8665,8667],{"className":8666},[886],[888,8668,8669],{"xmlns":890},[892,8670,8671,8686],{},[895,8672,8673,8675,8677,8680,8682,8684],{},[898,8674,2797],{},[2005,8676,2007],{},[898,8678,8679],{},"S",[2005,8681,2014],{"stretchy":2013},[898,8683,3946],{},[2005,8685,2020],{"stretchy":2013},[902,8687,8688],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,8691,8693],{"className":8692},[886],[888,8694,8695],{"xmlns":890},[892,8696,8697,8719],{},[895,8698,8699,8715,8717],{},[2334,8700,8701],{"scriptlevel":2336,"displaystyle":2294},[2338,8702,8703,8709],{},[895,8704,8705,8707],{},[898,8706,2203],{"mathvariant":2385},[898,8708,2797],{},[895,8710,8711,8713],{},[898,8712,2203],{"mathvariant":2385},[898,8714,3946],{},[2005,8716,3416],{},[2138,8718,2336],{},[902,8720,8721],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,8724,8725],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[3876,8727,8728],{},[724,8729,8730,8731],{},"S rostoucí cenou elasticita nabídky roste. ",[883,8732,8734],{"className":8733},[886],[888,8735,8736],{"xmlns":890},[892,8737,8738,8747],{},[895,8739,8740,8742,8745],{},[2005,8741,2014],{"stretchy":2013},[2138,8743,8744],{},"4.14",[2005,8746,2020],{"stretchy":2013},[902,8748,8749],{"encoding":904},"(4.14)",[724,8751,8752],{},"Pro nominální změny platí",[724,8754,8755],{},[883,8756,8758],{"className":8757,"title":4208,"style":4209},[4207],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,8760,8761],{},"a pro procentní změny",[724,8763,8764],{},[883,8765,8767],{"className":8766,"title":4208,"style":4209},[4207],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,8769,8770],{},"(bez znaménka minus).",[198,8772,8774],{"id":8773},"příklad-47","Příklad 4.7",[724,8776,8777,8778,2713],{},"Nabídka ",[883,8779,8781],{"className":8780},[886],[888,8782,8783],{"xmlns":890},[892,8784,8785,8810],{},[895,8786,8787,8789,8791,8793,8799,8801,8803,8805,8807],{},[898,8788,2797],{},[2005,8790,2007],{},[2138,8792,2802],{},[2133,8794,8795,8797],{},[898,8796,3946],{},[2138,8798,2140],{},[2005,8800,2104],{},[2138,8802,2237],{},[898,8804,3946],{},[2005,8806,2104],{},[2138,8808,8809],{},"150",[902,8811,8812],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,8814,8815],{},[883,8816,8818],{"className":8817},[886],[888,8819,8820],{"xmlns":890},[892,8821,8822,8868],{},[895,8823,8824,8826,8828,8852,8854,8856,8858,8860,8862,8864,8866],{},[898,8825,1868],{},[2005,8827,2007],{},[2338,8829,8830,8832],{},[898,8831,3946],{},[895,8833,8834,8836,8842,8844,8846,8848,8850],{},[2138,8835,2802],{},[2133,8837,8838,8840],{},[898,8839,3946],{},[2138,8841,2140],{},[2005,8843,2104],{},[2138,8845,2237],{},[898,8847,3946],{},[2005,8849,2104],{},[2138,8851,8809],{},[2297,8853,2995],{},[2005,8855,2014],{"stretchy":2013},[2138,8857,2847],{},[898,8859,3946],{},[2005,8861,2104],{},[2138,8863,2237],{},[2005,8865,2020],{"stretchy":2013},[898,8867,1644],{"mathvariant":2385},[902,8869,8870],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,8872,5123,8873,1343,8903,1343,8930,8966,8967,8992,8993,9011,9012,1644],{},[883,8874,8876],{"className":8875},[886],[888,8877,8878],{"xmlns":890},[892,8879,8880,8900],{},[895,8881,8882,8884,8886,8888,8890,8892],{},[898,8883,1868],{},[2005,8885,2014],{"stretchy":2013},[2138,8887,2871],{},[2005,8889,2020],{"stretchy":2013},[2005,8891,2007],{},[2334,8893,8894],{"scriptlevel":2336,"displaystyle":2013},[2338,8895,8896,8898],{},[2138,8897,2287],{},[2138,8899,2182],{},[902,8901,8902],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,8904,8906],{"className":8905},[886],[888,8907,8908],{"xmlns":890},[892,8909,8910,8927],{},[895,8911,8912,8914,8916,8921,8923,8925],{},[898,8913,1868],{},[2005,8915,2014],{"stretchy":2013},[8123,8917,8918],{},[2138,8919,8920],{},"1500",[2005,8922,2020],{"stretchy":2013},[2005,8924,2007],{},[2138,8926,2287],{},[902,8928,8929],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,8931,8933],{"className":8932},[886],[888,8934,8935],{"xmlns":890},[892,8936,8937,8963],{},[895,8938,8939,8941,8943,8945,8947,8949,8958,8960],{},[898,8940,1868],{},[2005,8942,2014],{"stretchy":2013},[2138,8944,3098],{},[2005,8946,2020],{"stretchy":2013},[2005,8948,2007],{},[2334,8950,8951],{"scriptlevel":2336,"displaystyle":2013},[2338,8952,8953,8955],{},[2138,8954,3128],{},[2138,8956,8957],{},"33",[2005,8959,5906],{},[2138,8961,8962],{},"1,515",[902,8964,8965],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,8968,8970],{"className":8969},[886],[888,8971,8972],{"xmlns":890},[892,8973,8974,8989],{},[895,8975,8976,8978,8980,8984,8986],{},[898,8977,3946],{},[2005,8979,3416],{},[8123,8981,8982],{},[2138,8983,8920],{},[2005,8985,2739],{},[2138,8987,8988],{},"38,7",[902,8990,8991],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,8994,8996],{"className":8995},[886],[888,8997,8998],{"xmlns":890},[892,8999,9000,9008],{},[895,9001,9002,9004,9006],{},[898,9003,3946],{},[2005,9005,3455],{},[2138,9007,8988],{},[902,9009,9010],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,9013,9015],{"className":9014},[886],[888,9016,9017],{"xmlns":890},[892,9018,9019,9057],{},[895,9020,9021,9023,9025,9027,9029,9037,9039,9042,9044,9047,9053,9055],{},[898,9022,2897],{"mathvariant":2385},[898,9024,2797],{},[898,9026,5931],{"mathvariant":2385},[2005,9028,2739],{},[2334,9030,9031],{"scriptlevel":2336,"displaystyle":2013},[2338,9032,9033,9035],{},[2138,9034,2287],{},[2138,9036,2182],{},[2005,9038,3185],{},[2138,9040,9041],{},"20",[2005,9043,2007],{},[2138,9045,9046],{},"6,",[8392,9048,9049,9051],{"accent":2294},[2138,9050,2244],{},[2005,9052,8398],{"stretchy":2294},[2297,9054,2995],{},[898,9056,5931],{"mathvariant":2385},[902,9058,9059],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,9061,9063],{"id":9062},"vícefaktorový-model","Vícefaktorový model",[724,9065,9066,9067,9080,9081,2212,9084,9097,9098,2212,9101,9119,9120,2212,9123,2713],{},"Předpokládejme, že poptávané množství ",[883,9068,9070],{"className":9069},[886],[888,9071,9072],{"xmlns":890},[892,9073,9074,9078],{},[895,9075,9076],{},[898,9077,2797],{},[902,9079,2797],{"encoding":904}," závisí na ",[38,9082,9083],{},"ceně základního zboží",[883,9085,9087],{"className":9086},[886],[888,9088,9089],{"xmlns":890},[892,9090,9091,9095],{},[895,9092,9093],{},[898,9094,3946],{},[902,9096,3946],{"encoding":904},", na ",[38,9099,9100],{},"ceně alternativního zboží",[883,9102,9104],{"className":9103},[886],[888,9105,9106],{"xmlns":890},[892,9107,9108,9116],{},[895,9109,9110],{},[2281,9111,9112,9114],{},[898,9113,3946],{},[898,9115,1836],{},[902,9117,9118],{"encoding":904},"P_A"," a na ",[38,9121,9122],{},"důchodu",[883,9124,9126],{"className":9125},[886],[888,9127,9128],{"xmlns":890},[892,9129,9130,9135],{},[895,9131,9132],{},[898,9133,9134],{},"Y",[902,9136,9134],{"encoding":904},[724,9138,9139],{},[883,9140,9142],{"className":9141,"title":4208,"style":4209},[4207],"Q = D(P, P_A, Y). \\tag{4.17}",[724,9144,9145,9146,9149],{},"V analogii jednofaktorového modelu pracujeme s ",[38,9147,9148],{},"parciálními derivacemi"," funkce poptávky.",[198,9151,9153],{"id":9152},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,9155,9156],{},[883,9157,9159],{"className":9158,"title":4208,"style":4209},[4207],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,9161,4316,9162,9183,9184,9197,9198,2935,9220,2212,9223,9269,9270,9283,9284,9301],{},[883,9163,9165],{"className":9164},[886],[888,9166,9167],{"xmlns":890},[892,9168,9169,9180],{},[895,9170,9171],{},[9172,9173,9174,9176,9178],"msubsup",{},[898,9175,2797],{},[898,9177,3946],{},[2005,9179,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,9181,9182],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,9185,9187],{"className":9186},[886],[888,9188,9189],{"xmlns":890},[892,9190,9191,9195],{},[895,9192,9193],{},[898,9194,3946],{},[902,9196,3946],{"encoding":904},". Vždy ",[883,9199,9201],{"className":9200},[886],[888,9202,9203],{"xmlns":890},[892,9204,9205,9217],{},[895,9206,9207,9213,9215],{},[2281,9208,9209,9211],{},[898,9210,1868],{},[898,9212,3946],{},[2005,9214,4491],{},[2138,9216,2336],{},[902,9218,9219],{"encoding":904},"E_P \\ge 0",[614,9221,9222],{},"Interpretace:",[883,9224,9226],{"className":9225},[886],[888,9227,9228],{"xmlns":890},[892,9229,9230,9266],{},[895,9231,9232,9238,9240,9246,9248,9256,9258,9264],{},[2281,9233,9234,9236],{},[898,9235,1868],{},[898,9237,3946],{},[2005,9239,2014],{"stretchy":2013},[2133,9241,9242,9244],{},[898,9243,3946],{},[2005,9245,4360],{},[2005,9247,2295],{"separator":2294},[9172,9249,9250,9252,9254],{},[898,9251,3946],{},[898,9253,1836],{},[2005,9255,4360],{},[2005,9257,2295],{"separator":2294},[2133,9259,9260,9262],{},[898,9261,9134],{},[2005,9263,4360],{},[2005,9265,2020],{"stretchy":2013},[902,9267,9268],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,9271,9273],{"className":9272},[886],[888,9274,9275],{"xmlns":890},[892,9276,9277,9281],{},[895,9278,9279],{},[898,9280,2797],{},[902,9282,2797],{"encoding":904}," při 1% změně ",[883,9285,9287],{"className":9286},[886],[888,9288,9289],{"xmlns":890},[892,9290,9291,9299],{},[895,9292,9293],{},[2133,9294,9295,9297],{},[898,9296,3946],{},[2005,9298,4360],{},[902,9300,4410],{"encoding":904},", ceteris paribus.",[198,9303,9305],{"id":9304},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,9307,9308],{},[883,9309,9311],{"className":9310,"title":4208,"style":4209},[4207],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,9313,9314,9269,9316,9329,9330,9347],{},[614,9315,9222],{},[883,9317,9319],{"className":9318},[886],[888,9320,9321],{"xmlns":890},[892,9322,9323,9327],{},[895,9324,9325],{},[898,9326,2797],{},[902,9328,2797],{"encoding":904}," základního zboží při 1% změně ceny ",[883,9331,9333],{"className":9332},[886],[888,9334,9335],{"xmlns":890},[892,9336,9337,9345],{},[895,9338,9339],{},[2281,9340,9341,9343],{},[898,9342,3946],{},[898,9344,1836],{},[902,9346,9118],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,9349,9350],{},[38,9351,9352],{},"Znaménko závisí na povaze alternativního zboží:",[120,9354,9355,9443],{},[123,9356,9357,9358,9361,9362,9379,9380,2212,9393,1644],{},"Je-li alternativní zboží ",[38,9359,9360],{},"komplement",", růst ",[883,9363,9365],{"className":9364},[886],[888,9366,9367],{"xmlns":890},[892,9368,9369,9377],{},[895,9370,9371],{},[2281,9372,9373,9375],{},[898,9374,3946],{},[898,9376,1836],{},[902,9378,9118],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,9381,9383],{"className":9382},[886],[888,9384,9385],{"xmlns":890},[892,9386,9387,9391],{},[895,9388,9389],{},[898,9390,2797],{},[902,9392,2797],{"encoding":904},[883,9394,9396],{"className":9395},[886],[888,9397,9398],{"xmlns":890},[892,9399,9400,9440],{},[895,9401,9402,9404,9406,9418,9420,9422,9424,9426,9436,9438],{},[2005,9403,3996],{},[2297,9405,3993],{},[9172,9407,9408,9410,9416],{},[898,9409,2797],{},[2281,9411,9412,9414],{},[898,9413,3946],{},[898,9415,1836],{},[2005,9417,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,9419,3455],{},[2138,9421,2336],{},[2005,9423,2295],{"separator":2294},[2297,9425,3993],{},[2281,9427,9428,9430],{},[898,9429,1868],{},[2281,9431,9432,9434],{},[898,9433,3946],{},[898,9435,1836],{},[2005,9437,3455],{},[2138,9439,2336],{},[902,9441,9442],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,9444,9357,9445,9361,9448,9465,9466,9479,9480,1644],{},[38,9446,9447],{},"substitut",[883,9449,9451],{"className":9450},[886],[888,9452,9453],{"xmlns":890},[892,9454,9455,9463],{},[895,9456,9457],{},[2281,9458,9459,9461],{},[898,9460,3946],{},[898,9462,1836],{},[902,9464,9118],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,9467,9469],{"className":9468},[886],[888,9470,9471],{"xmlns":890},[892,9472,9473,9477],{},[895,9474,9475],{},[898,9476,2797],{},[902,9478,2797],{"encoding":904}," roste ",[883,9481,9483],{"className":9482},[886],[888,9484,9485],{"xmlns":890},[892,9486,9487,9527],{},[895,9488,9489,9491,9493,9505,9507,9509,9511,9513,9523,9525],{},[2005,9490,3996],{},[2297,9492,3993],{},[9172,9494,9495,9497,9503],{},[898,9496,2797],{},[2281,9498,9499,9501],{},[898,9500,3946],{},[898,9502,1836],{},[2005,9504,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,9506,3416],{},[2138,9508,2336],{},[2005,9510,2295],{"separator":2294},[2297,9512,3993],{},[2281,9514,9515,9517],{},[898,9516,1868],{},[2281,9518,9519,9521],{},[898,9520,3946],{},[898,9522,1836],{},[2005,9524,3416],{},[2138,9526,2336],{},[902,9528,9529],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,9531,9534],{"className":9532,"title":9533,"style":4209},[4207],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":9536},[9537,9541,9542,9550,9551,9555,9558],{"id":3900,"depth":642,"text":3901,"children":9538},[9539,9540],{"id":3930,"depth":649,"text":3931},{"id":4111,"depth":649,"text":4112},{"id":4146,"depth":642,"text":4147},{"id":4172,"depth":642,"text":4173,"children":9543},[9544,9545,9546,9547,9549],{"id":4865,"depth":649,"text":4866},{"id":4955,"depth":649,"text":4956},{"id":5291,"depth":649,"text":5292},{"id":5373,"depth":649,"text":9548},"Výpočet, je-li dáno PP jako funkce QQ",{"id":5634,"depth":649,"text":5635},{"id":5959,"depth":642,"text":5960},{"id":6555,"depth":642,"text":6556,"children":9552},[9553,9554],{"id":7184,"depth":649,"text":7185},{"id":8013,"depth":649,"text":8014},{"id":8647,"depth":642,"text":8648,"children":9556},[9557],{"id":8773,"depth":649,"text":8774},{"id":9062,"depth":642,"text":9063,"children":9559},[9560,9561],{"id":9152,"depth":649,"text":9153},{"id":9304,"depth":649,"text":9305},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":3869,"description":641},[1138,1136],"topics\u002Felasticita",[1128,1753,9569,9570,9571,9572],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":9575,"title":9576,"body":9577,"course":1128,"courses":659,"created":1129,"description":11117,"extension":661,"meta":11118,"navigation":664,"path":11119,"seo":11120,"sources":11121,"stem":11122,"tags":11123,"type":3865,"updated":677,"__hash__":11128},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":9578,"toc":11102},[9579,9582,9656,9663,9667,9731,9819,9823,9850,9917,9972,9976,10003,10096,10098,10130,10301,10305,10375,10423,10427,10487,10593,10608,10612,10614,10642,10707,10709,10716,10804,10829,11027,11031,11067,11069],[12,9580,9576],{"id":9581},"kalkul-funkcí-více-proměnných",[724,9583,9584,9585,9588,9589,1343,9618,1644],{},"Většina ekonomických veličin závisí na ",[38,9586,9587],{},"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 ",[883,9590,9592],{"className":9591},[886],[888,9593,9594],{"xmlns":890},[892,9595,9596,9615],{},[895,9597,9598,9601,9603,9605,9607,9609,9611,9613],{},[898,9599,9600],{},"z",[2005,9602,2007],{},[898,9604,2010],{},[2005,9606,2014],{"stretchy":2013},[898,9608,2017],{},[2005,9610,2295],{"separator":2294},[898,9612,2003],{},[2005,9614,2020],{"stretchy":2013},[902,9616,9617],{"encoding":904},"z = f(x, y)",[883,9619,9621],{"className":9620},[886],[888,9622,9623],{"xmlns":890},[892,9624,9625,9653],{},[895,9626,9627,9630,9632,9634,9636,9638,9640,9642,9644,9646,9648,9650],{},[898,9628,9629],{},"w",[2005,9631,2007],{},[898,9633,2010],{},[2005,9635,2014],{"stretchy":2013},[898,9637,2017],{},[2005,9639,2295],{"separator":2294},[898,9641,2003],{},[2005,9643,2295],{"separator":2294},[898,9645,9600],{},[2005,9647,2020],{"stretchy":2013},[2005,9649,2295],{"separator":2294},[2005,9651,9652],{},"…",[902,9654,9655],{"encoding":904},"w = f(x, y, z), \\ldots",[724,9657,9658],{},[2568,9659],{"alt":9660,"className":9661,"src":9662},"imek-funkce-2d-vrstevnice",[210,2572],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,9664,9666],{"id":9665},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,9668,9669,9670,9697,9698,9726,9727,9730],{},"Pro ",[883,9671,9673],{"className":9672},[886],[888,9674,9675],{"xmlns":890},[892,9676,9677,9695],{},[895,9678,9679,9681,9683,9685,9687,9689,9691,9693],{},[898,9680,9600],{},[2005,9682,2007],{},[898,9684,2010],{},[2005,9686,2014],{"stretchy":2013},[898,9688,2017],{},[2005,9690,2295],{"separator":2294},[898,9692,2003],{},[2005,9694,2020],{"stretchy":2013},[902,9696,9617],{"encoding":904}," se křivkou s předpisem ",[883,9699,9701],{"className":9700},[886],[888,9702,9703],{"xmlns":890},[892,9704,9705,9723],{},[895,9706,9707,9709,9711,9713,9715,9717,9719,9721],{},[898,9708,2010],{},[2005,9710,2014],{"stretchy":2013},[898,9712,2017],{},[2005,9714,2295],{"separator":2294},[898,9716,2003],{},[2005,9718,2020],{"stretchy":2013},[2005,9720,2007],{},[898,9722,2151],{},[902,9724,9725],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,9728,9729],{},"vrstevnice"," funkce. V ekonomii:",[120,9732,9733,9780],{},[123,9734,9735,9738,9739,9775,9776,1644],{},[38,9736,9737],{},"Indiferenční křivky"," užitečnosti ",[883,9740,9742],{"className":9741},[886],[888,9743,9744],{"xmlns":890},[892,9745,9746,9772],{},[895,9747,9748,9750,9752,9758,9760,9766,9768,9770],{},[898,9749,900],{},[2005,9751,2014],{"stretchy":2013},[2281,9753,9754,9756],{},[898,9755,2797],{},[2138,9757,2287],{},[2005,9759,2295],{"separator":2294},[2281,9761,9762,9764],{},[898,9763,2797],{},[2138,9765,2140],{},[2005,9767,2020],{"stretchy":2013},[2005,9769,2007],{},[898,9771,2151],{},[902,9773,9774],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,9777,9779],{"className":9778,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,9781,9782,9785,9786,9775,9816,1644],{},[38,9783,9784],{},"Izokvanty"," produkce ",[883,9787,9789],{"className":9788},[886],[888,9790,9791],{"xmlns":890},[892,9792,9793,9813],{},[895,9794,9795,9797,9799,9802,9804,9807,9809,9811],{},[898,9796,2797],{},[2005,9798,2014],{"stretchy":2013},[898,9800,9801],{},"L",[2005,9803,2295],{"separator":2294},[898,9805,9806],{},"K",[2005,9808,2020],{"stretchy":2013},[2005,9810,2007],{},[898,9812,2151],{},[902,9814,9815],{"encoding":904},"Q(L, K) = c",[207,9817,1756],{"className":9818,"dataFsResolvedFilePath":857,"href":858},[210],[115,9820,9822],{"id":9821},"parciální-derivace","Parciální derivace",[724,9824,9669,9825,9849],{},[883,9826,9828],{"className":9827},[886],[888,9829,9830],{"xmlns":890},[892,9831,9832,9846],{},[895,9833,9834,9836,9838,9840,9842,9844],{},[898,9835,2010],{},[2005,9837,2014],{"stretchy":2013},[898,9839,2017],{},[2005,9841,2295],{"separator":2294},[898,9843,2003],{},[2005,9845,2020],{"stretchy":2013},[902,9847,9848],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,9851,9852],{},[883,9853,9855],{"className":9854},[886],[888,9856,9857],{"xmlns":890},[892,9858,9859,9914],{},[895,9860,9861,9869,9871,9886,9888,9890,9898,9900],{},[9172,9862,9863,9865,9867],{},[898,9864,2010],{},[898,9866,2017],{},[2005,9868,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,9870,2007],{},[2338,9872,9873,9880],{},[895,9874,9875,9878],{},[898,9876,9877],{"mathvariant":2385},"∂",[898,9879,2010],{},[895,9881,9882,9884],{},[898,9883,9877],{"mathvariant":2385},[898,9885,2017],{},[2005,9887,2295],{"separator":2294},[5884,9889],{"width":5886},[9172,9891,9892,9894,9896],{},[898,9893,2010],{},[898,9895,2003],{},[2005,9897,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,9899,2007],{},[2338,9901,9902,9908],{},[895,9903,9904,9906],{},[898,9905,9877],{"mathvariant":2385},[898,9907,2010],{},[895,9909,9910,9912],{},[898,9911,9877],{"mathvariant":2385},[898,9913,2003],{},[902,9915,9916],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,9918,9919,9920,1644],{},"Hodnoty v bodě: ",[883,9921,9923],{"className":9922},[886],[888,9924,9925],{"xmlns":890},[892,9926,9927,9969],{},[895,9928,9929,9937,9939,9941,9943,9945,9947,9949,9951,9959,9961,9963,9965,9967],{},[9172,9930,9931,9933,9935],{},[898,9932,2010],{},[898,9934,2017],{},[2005,9936,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,9938,2014],{"stretchy":2013},[898,9940,207],{},[2005,9942,2295],{"separator":2294},[898,9944,2107],{},[2005,9946,2020],{"stretchy":2013},[2005,9948,2295],{"separator":2294},[2297,9950,2299],{},[9172,9952,9953,9955,9957],{},[898,9954,2010],{},[898,9956,2003],{},[2005,9958,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,9960,2014],{"stretchy":2013},[898,9962,207],{},[2005,9964,2295],{"separator":2294},[898,9966,2107],{},[2005,9968,2020],{"stretchy":2013},[902,9970,9971],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,9973,9975],{"id":9974},"ekonomické-značení","Ekonomické značení",[724,9977,9978,9979,2713],{},"Pro produkční funkci ",[883,9980,9982],{"className":9981},[886],[888,9983,9984],{"xmlns":890},[892,9985,9986,10000],{},[895,9987,9988,9990,9992,9994,9996,9998],{},[898,9989,2797],{},[2005,9991,2014],{"stretchy":2013},[898,9993,9801],{},[2005,9995,2295],{"separator":2294},[898,9997,9806],{},[2005,9999,2020],{"stretchy":2013},[902,10001,10002],{"encoding":904},"Q(L, K)",[120,10004,10005,10051],{},[123,10006,10007,2479,10027,10030,10031,2020],{},[883,10008,10010],{"className":10009},[886],[888,10011,10012],{"xmlns":890},[892,10013,10014,10024],{},[895,10015,10016],{},[9172,10017,10018,10020,10022],{},[898,10019,2797],{},[898,10021,9801],{},[2005,10023,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,10025,10026],{"encoding":904},"Q'_L",[38,10028,10029],{},"mezní produkt práce"," (",[883,10032,10034],{"className":10033},[886],[888,10035,10036],{"xmlns":890},[892,10037,10038,10048],{},[895,10039,10040,10042],{},[898,10041,2826],{},[2281,10043,10044,10046],{},[898,10045,3946],{},[898,10047,9801],{},[902,10049,10050],{"encoding":904},"MP_L",[123,10052,10053,2479,10073,10030,10076,2020],{},[883,10054,10056],{"className":10055},[886],[888,10057,10058],{"xmlns":890},[892,10059,10060,10070],{},[895,10061,10062],{},[9172,10063,10064,10066,10068],{},[898,10065,2797],{},[898,10067,9806],{},[2005,10069,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,10071,10072],{"encoding":904},"Q'_K",[38,10074,10075],{},"mezní produkt kapitálu",[883,10077,10079],{"className":10078},[886],[888,10080,10081],{"xmlns":890},[892,10082,10083,10093],{},[895,10084,10085,10087],{},[898,10086,2826],{},[2281,10088,10089,10091],{},[898,10090,3946],{},[898,10092,9806],{},[902,10094,10095],{"encoding":904},"MP_K",[198,10097,2577],{"id":2576},[724,10099,10100,2713],{},[883,10101,10103],{"className":10102},[886],[888,10104,10105],{"xmlns":890},[892,10106,10107,10127],{},[895,10108,10109,10117,10119,10121,10123,10125],{},[9172,10110,10111,10113,10115],{},[898,10112,2010],{},[898,10114,2017],{},[2005,10116,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10118,2014],{"stretchy":2013},[898,10120,207],{},[2005,10122,2295],{"separator":2294},[898,10124,2107],{},[2005,10126,2020],{"stretchy":2013},[902,10128,10129],{"encoding":904},"f'_x(a, b)",[120,10131,10132,10190],{},[123,10133,10134,10135,10148,10149,10162,10163,10189],{},"rychlost změny ",[883,10136,10138],{"className":10137},[886],[888,10139,10140],{"xmlns":890},[892,10141,10142,10146],{},[895,10143,10144],{},[898,10145,2010],{},[902,10147,2010],{"encoding":904}," vůči ",[883,10150,10152],{"className":10151},[886],[888,10153,10154],{"xmlns":890},[892,10155,10156,10160],{},[895,10157,10158],{},[898,10159,2017],{},[902,10161,2017],{"encoding":904}," při ",[883,10164,10166],{"className":10165},[886],[888,10167,10168],{"xmlns":890},[892,10169,10170,10186],{},[895,10171,10172,10174,10176,10178,10180,10182,10184],{},[898,10173,2017],{},[2005,10175,2007],{},[898,10177,207],{},[2005,10179,2295],{"separator":2294},[898,10181,2003],{},[2005,10183,2007],{},[898,10185,2107],{},[902,10187,10188],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,10191,10192,10193,2666,10206,10219,10220,10238,10239,1644],{},"přibližná změna ",[883,10194,10196],{"className":10195},[886],[888,10197,10198],{"xmlns":890},[892,10199,10200,10204],{},[895,10201,10202],{},[898,10203,2010],{},[902,10205,2010],{"encoding":904},[883,10207,10209],{"className":10208},[886],[888,10210,10211],{"xmlns":890},[892,10212,10213,10217],{},[895,10214,10215],{},[898,10216,2017],{},[902,10218,2017],{"encoding":904}," o 1 (a pevném ",[883,10221,10223],{"className":10222},[886],[888,10224,10225],{"xmlns":890},[892,10226,10227,10235],{},[895,10228,10229,10231,10233],{},[898,10230,2003],{},[2005,10232,2007],{},[898,10234,2107],{},[902,10236,10237],{"encoding":904},"y = b","): ",[883,10240,10242],{"className":10241},[886],[888,10243,10244],{"xmlns":890},[892,10245,10246,10298],{},[895,10247,10248,10250,10252,10254,10256,10258,10260,10262,10264,10266,10268,10270,10272,10274,10276,10278,10280,10288,10290,10292,10294,10296],{},[898,10249,2010],{},[2005,10251,2014],{"stretchy":2013},[898,10253,207],{},[2005,10255,2104],{},[2138,10257,2287],{},[2005,10259,2295],{"separator":2294},[898,10261,2107],{},[2005,10263,2020],{"stretchy":2013},[2005,10265,2739],{},[898,10267,2010],{},[2005,10269,2014],{"stretchy":2013},[898,10271,207],{},[2005,10273,2295],{"separator":2294},[898,10275,2107],{},[2005,10277,2020],{"stretchy":2013},[2005,10279,2104],{},[9172,10281,10282,10284,10286],{},[898,10283,2010],{},[898,10285,2017],{},[2005,10287,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10289,2014],{"stretchy":2013},[898,10291,207],{},[2005,10293,2295],{"separator":2294},[898,10295,2107],{},[2005,10297,2020],{"stretchy":2013},[902,10299,10300],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,10302,10304],{"id":10303},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,10306,10307],{},[883,10308,10310],{"className":10309},[886],[888,10311,10312],{"xmlns":890},[892,10313,10314,10372],{},[895,10315,10316,10318,10320,10322,10330,10332,10334,10336,10338,10340,10342,10344,10346,10348,10356,10358,10360,10362,10364,10366,10368,10370],{},[898,10317,2203],{},[898,10319,2010],{},[2005,10321,2007],{},[9172,10323,10324,10326,10328],{},[898,10325,2010],{},[898,10327,2017],{},[2005,10329,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10331,2014],{"stretchy":2013},[898,10333,2017],{},[2005,10335,2295],{"separator":2294},[898,10337,2003],{},[2005,10339,2020],{"stretchy":2013},[2297,10341,2995],{},[898,10343,2203],{},[898,10345,2017],{},[2005,10347,2104],{},[9172,10349,10350,10352,10354],{},[898,10351,2010],{},[898,10353,2003],{},[2005,10355,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10357,2014],{"stretchy":2013},[898,10359,2017],{},[2005,10361,2295],{"separator":2294},[898,10363,2003],{},[2005,10365,2020],{"stretchy":2013},[2297,10367,2995],{},[898,10369,2203],{},[898,10371,2003],{},[902,10373,10374],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,10376,3005,10377,10399,10400,10422],{},[883,10378,10380],{"className":10379},[886],[888,10381,10382],{"xmlns":890},[892,10383,10384,10396],{},[895,10385,10386,10388,10390,10392,10394],{},[898,10387,2203],{},[898,10389,2017],{},[2005,10391,2295],{"separator":2294},[898,10393,2203],{},[898,10395,2003],{},[902,10397,10398],{"encoding":904},"dx, dy"," platí ",[883,10401,10403],{"className":10402},[886],[888,10404,10405],{"xmlns":890},[892,10406,10407,10419],{},[895,10408,10409,10411,10413,10415,10417],{},[898,10410,2897],{"mathvariant":2385},[898,10412,2010],{},[2005,10414,2739],{},[898,10416,2203],{},[898,10418,2010],{},[902,10420,10421],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,10424,10426],{"id":10425},"implicitní-funkce","Implicitní funkce",[724,10428,10429,10430,10458,10459,10472,10473,10486],{},"Je-li vztah dán rovnicí ",[883,10431,10433],{"className":10432},[886],[888,10434,10435],{"xmlns":890},[892,10436,10437,10455],{},[895,10438,10439,10441,10443,10445,10447,10449,10451,10453],{},[898,10440,1876],{},[2005,10442,2014],{"stretchy":2013},[898,10444,2017],{},[2005,10446,2295],{"separator":2294},[898,10448,2003],{},[2005,10450,2020],{"stretchy":2013},[2005,10452,2007],{},[2138,10454,2336],{},[902,10456,10457],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,10460,10462],{"className":10461},[886],[888,10463,10464],{"xmlns":890},[892,10465,10466,10470],{},[895,10467,10468],{},[898,10469,2003],{},[902,10471,2003],{"encoding":904}," podle ",[883,10474,10476],{"className":10475},[886],[888,10477,10478],{"xmlns":890},[892,10479,10480,10484],{},[895,10481,10482],{},[898,10483,2017],{},[902,10485,2017],{"encoding":904}," (nebo naopak):",[724,10488,10489],{},[883,10490,10492],{"className":10491},[886],[888,10493,10494],{"xmlns":890},[892,10495,10496,10590],{},[895,10497,10498,10504,10506,10520,10522,10524,10542,10544,10546,10552,10554,10568,10570,10572],{},[2133,10499,10500,10502],{},[898,10501,2003],{},[2005,10503,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10505,2007],{},[2338,10507,10508,10514],{},[895,10509,10510,10512],{},[898,10511,2203],{},[898,10513,2003],{},[895,10515,10516,10518],{},[898,10517,2203],{},[898,10519,2017],{},[2005,10521,2007],{},[2005,10523,2234],{},[2338,10525,10526,10534],{},[9172,10527,10528,10530,10532],{},[898,10529,1876],{},[898,10531,2017],{},[2005,10533,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,10535,10536,10538,10540],{},[898,10537,1876],{},[898,10539,2003],{},[2005,10541,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10543,2295],{"separator":2294},[5884,10545],{"width":5886},[2133,10547,10548,10550],{},[898,10549,2017],{},[2005,10551,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10553,2007],{},[2338,10555,10556,10562],{},[895,10557,10558,10560],{},[898,10559,2203],{},[898,10561,2017],{},[895,10563,10564,10566],{},[898,10565,2203],{},[898,10567,2003],{},[2005,10569,2007],{},[2005,10571,2234],{},[2338,10573,10574,10582],{},[9172,10575,10576,10578,10580],{},[898,10577,1876],{},[898,10579,2003],{},[2005,10581,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,10583,10584,10586,10588],{},[898,10585,1876],{},[898,10587,2017],{},[2005,10589,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,10591,10592],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,10594,10595,10596,10599,10600,3894,10604,1644],{},"Tato vzorec dává ",[38,10597,10598],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,10601,10603],{"className":10602,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,10605,10607],{"className":10606,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,10609,10611],{"id":10610},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,10613,3260],{"id":3259},[724,10615,10616,10617,10641],{},"V bodě extrému ",[883,10618,10620],{"className":10619},[886],[888,10621,10622],{"xmlns":890},[892,10623,10624,10638],{},[895,10625,10626,10628,10630,10632,10634,10636],{},[898,10627,1836],{},[2005,10629,2495],{"stretchy":2013},[898,10631,207],{},[2005,10633,2295],{"separator":2294},[898,10635,2107],{},[2005,10637,2510],{"stretchy":2013},[902,10639,10640],{"encoding":904},"A[a, b]"," musí platit současně:",[724,10643,10644],{},[883,10645,10647],{"className":10646},[886],[888,10648,10649],{"xmlns":890},[892,10650,10651,10704],{},[895,10652,10653,10661,10663,10665,10667,10669,10671,10673,10675,10677,10680,10682,10690,10692,10694,10696,10698,10700,10702],{},[9172,10654,10655,10657,10659],{},[898,10656,2010],{},[898,10658,2017],{},[2005,10660,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10662,2014],{"stretchy":2013},[898,10664,207],{},[2005,10666,2295],{"separator":2294},[898,10668,2107],{},[2005,10670,2020],{"stretchy":2013},[2005,10672,2007],{},[2138,10674,2336],{},[2297,10676,3993],{},[2005,10678,10679],{},"∧",[2297,10681,3993],{},[9172,10683,10684,10686,10688],{},[898,10685,2010],{},[898,10687,2003],{},[2005,10689,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,10691,2014],{"stretchy":2013},[898,10693,207],{},[2005,10695,2295],{"separator":2294},[898,10697,2107],{},[2005,10699,2020],{"stretchy":2013},[2005,10701,2007],{},[2138,10703,2336],{},[902,10705,10706],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,10708,3334],{"id":3333},[724,10710,10711,10712,10715],{},"Definujeme ",[38,10713,10714],{},"diskriminant"," (Hessián zjednodušeně):",[724,10717,10718],{},[883,10719,10721],{"className":10720},[886],[888,10722,10723],{"xmlns":890},[892,10724,10725,10801],{},[895,10726,10727,10729,10731,10733,10735,10737,10739,10741,10757,10759,10775,10777,10779,10795],{},[898,10728,1860],{},[2005,10730,2014],{"stretchy":2013},[898,10732,2017],{},[2005,10734,2295],{"separator":2294},[898,10736,2003],{},[2005,10738,2020],{"stretchy":2013},[2005,10740,2007],{},[9172,10742,10743,10745,10751],{},[898,10744,2010],{},[895,10746,10747,10749],{},[898,10748,2017],{},[898,10750,2017],{},[895,10752,10753,10755],{},[2005,10754,2387],{"mathvariant":2385},[2005,10756,2387],{"mathvariant":2385},[2005,10758,3185],{},[9172,10760,10761,10763,10769],{},[898,10762,2010],{},[895,10764,10765,10767],{},[898,10766,2003],{},[898,10768,2003],{},[895,10770,10771,10773],{},[2005,10772,2387],{"mathvariant":2385},[2005,10774,2387],{"mathvariant":2385},[2005,10776,2234],{},[2005,10778,2014],{"stretchy":2013},[9172,10780,10781,10783,10789],{},[898,10782,2010],{},[895,10784,10785,10787],{},[898,10786,2017],{},[898,10788,2003],{},[895,10790,10791,10793],{},[2005,10792,2387],{"mathvariant":2385},[2005,10794,2387],{"mathvariant":2385},[2133,10796,10797,10799],{},[2005,10798,2020],{"stretchy":2013},[2138,10800,2140],{},[902,10802,10803],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,10805,10806,10807,2713],{},"V podezřelém bodě ",[883,10808,10810],{"className":10809},[886],[888,10811,10812],{"xmlns":890},[892,10813,10814,10826],{},[895,10815,10816,10818,10820,10822,10824],{},[2005,10817,2495],{"stretchy":2013},[898,10819,207],{},[2005,10821,2295],{"separator":2294},[898,10823,2107],{},[2005,10825,2510],{"stretchy":2013},[902,10827,10828],{"encoding":904},"[a, b]",[152,10830,10831,10958,10994],{},[123,10832,10833,10863,10864],{},[38,10834,10835,2713],{},[883,10836,10838],{"className":10837},[886],[888,10839,10840],{"xmlns":890},[892,10841,10842,10860],{},[895,10843,10844,10846,10848,10850,10852,10854,10856,10858],{},[898,10845,1860],{},[2005,10847,2014],{"stretchy":2013},[898,10849,207],{},[2005,10851,2295],{"separator":2294},[898,10853,2107],{},[2005,10855,2020],{"stretchy":2013},[2005,10857,3416],{},[2138,10859,2336],{},[902,10861,10862],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,10865,10866,10912],{},[123,10867,10868,3422,10910],{},[883,10869,10871],{"className":10870},[886],[888,10872,10873],{"xmlns":890},[892,10874,10875,10907],{},[895,10876,10877,10893,10895,10897,10899,10901,10903,10905],{},[9172,10878,10879,10881,10887],{},[898,10880,2010],{},[895,10882,10883,10885],{},[898,10884,2017],{},[898,10886,2017],{},[895,10888,10889,10891],{},[2005,10890,2387],{"mathvariant":2385},[2005,10892,2387],{"mathvariant":2385},[2005,10894,2014],{"stretchy":2013},[898,10896,207],{},[2005,10898,2295],{"separator":2294},[898,10900,2107],{},[2005,10902,2020],{"stretchy":2013},[2005,10904,3416],{},[2138,10906,2336],{},[902,10908,10909],{"encoding":904},"f''_{xx}(a, b) > 0",[38,10911,3783],{},[123,10913,10914,3422,10956],{},[883,10915,10917],{"className":10916},[886],[888,10918,10919],{"xmlns":890},[892,10920,10921,10953],{},[895,10922,10923,10939,10941,10943,10945,10947,10949,10951],{},[9172,10924,10925,10927,10933],{},[898,10926,2010],{},[895,10928,10929,10931],{},[898,10930,2017],{},[898,10932,2017],{},[895,10934,10935,10937],{},[2005,10936,2387],{"mathvariant":2385},[2005,10938,2387],{"mathvariant":2385},[2005,10940,2014],{"stretchy":2013},[898,10942,207],{},[2005,10944,2295],{"separator":2294},[898,10946,2107],{},[2005,10948,2020],{"stretchy":2013},[2005,10950,3455],{},[2138,10952,2336],{},[902,10954,10955],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,10957,3725],{},[123,10959,10960,2212,10990,10993],{},[38,10961,10962,2713],{},[883,10963,10965],{"className":10964},[886],[888,10966,10967],{"xmlns":890},[892,10968,10969,10987],{},[895,10970,10971,10973,10975,10977,10979,10981,10983,10985],{},[898,10972,1860],{},[2005,10974,2014],{"stretchy":2013},[898,10976,207],{},[2005,10978,2295],{"separator":2294},[898,10980,2107],{},[2005,10982,2020],{"stretchy":2013},[2005,10984,3455],{},[2138,10986,2336],{},[902,10988,10989],{"encoding":904},"D(a, b) \u003C 0",[38,10991,10992],{},"sedlo"," (v daném bodě extrém není).",[123,10995,10996,11026],{},[38,10997,10998,2713],{},[883,10999,11001],{"className":11000},[886],[888,11002,11003],{"xmlns":890},[892,11004,11005,11023],{},[895,11006,11007,11009,11011,11013,11015,11017,11019,11021],{},[898,11008,1860],{},[2005,11010,2014],{"stretchy":2013},[898,11012,207],{},[2005,11014,2295],{"separator":2294},[898,11016,2107],{},[2005,11018,2020],{"stretchy":2013},[2005,11020,2007],{},[2138,11022,2336],{},[902,11024,11025],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,11028,11030],{"id":11029},"vázané-extrémy","Vázané extrémy",[724,11032,11033,11034,11063,11064,1644],{},"Pro extrémy s omezující podmínkou ",[883,11035,11037],{"className":11036},[886],[888,11038,11039],{"xmlns":890},[892,11040,11041,11060],{},[895,11042,11043,11046,11048,11050,11052,11054,11056,11058],{},[898,11044,11045],{},"g",[2005,11047,2014],{"stretchy":2013},[898,11049,2017],{},[2005,11051,2295],{"separator":2294},[898,11053,2003],{},[2005,11055,2020],{"stretchy":2013},[2005,11057,2007],{},[2138,11059,2336],{},[902,11061,11062],{"encoding":904},"g(x, y) = 0"," se používá ",[207,11065,793],{"className":11066,"dataFsResolvedFilePath":791,"href":792},[210],[115,11068,3800],{"id":3799},[120,11070,11071,11078,11085],{},[123,11072,11073,2212,11075],{},[38,11074,3807],{},[207,11076,775],{"className":11077,"dataFsResolvedFilePath":773,"href":774},[210],[123,11079,11080,2212,11082],{},[38,11081,3815],{},[207,11083,793],{"className":11084,"dataFsResolvedFilePath":791,"href":792},[210],[123,11086,11087,2212,11089,11093,11094,11097,11098,11101],{},[38,11088,3823],{},[207,11090,11092],{"className":11091,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,11095,880],{"className":11096,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,11099,3836],{"className":11100,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":11103},[11104,11105,11109,11110,11111,11115,11116],{"id":9665,"depth":642,"text":9666},{"id":9821,"depth":642,"text":9822,"children":11106},[11107,11108],{"id":9974,"depth":649,"text":9975},{"id":2576,"depth":649,"text":2577},{"id":10303,"depth":642,"text":10304},{"id":10425,"depth":642,"text":10426},{"id":10610,"depth":642,"text":10611,"children":11112},[11113,11114],{"id":3259,"depth":649,"text":3260},{"id":3333,"depth":649,"text":3334},{"id":11029,"depth":642,"text":11030},{"id":3799,"depth":642,"text":3800},"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":9576,"description":11117},[1135],"topics\u002Ffunkce-vice-promennych",[1128,11124,3862,11125,11126,11127],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":11130,"title":775,"body":11131,"course":1128,"courses":659,"created":1129,"description":11987,"extension":661,"meta":11988,"navigation":664,"path":11989,"seo":11990,"sources":11991,"stem":11992,"tags":11993,"type":3865,"updated":677,"__hash__":12000},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":11132,"toc":11977},[11133,11136,11147,11151,11196,11276,11280,11356,11398,11405,11409,11413,11442,11500,11547,11585,11589,11639,11691,11743,11787,11790,11793,11865,11868,11940,11947,11949],[12,11134,775],{"id":11135},"integrál",[724,11137,11138,11139,11142,11143,11146],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,11140,11141],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,11144,11145],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,11148,11150],{"id":11149},"neurčitý-integrál","Neurčitý integrál",[724,11152,11153],{},[883,11154,11156],{"className":11155},[886],[888,11157,11158],{"xmlns":890},[892,11159,11160,11193],{},[895,11161,11162,11164,11166,11168,11170,11172,11175,11177,11179,11181,11183,11185,11187,11189,11191],{},[898,11163,1876],{},[2005,11165,2014],{"stretchy":2013},[898,11167,2017],{},[2005,11169,2020],{"stretchy":2013},[2005,11171,2007],{},[2005,11173,11174],{},"∫",[898,11176,2010],{},[2005,11178,2014],{"stretchy":2013},[898,11180,2017],{},[2005,11182,2020],{"stretchy":2013},[2297,11184,2995],{},[898,11186,2203],{},[898,11188,2017],{},[2005,11190,2104],{},[898,11192,1852],{},[902,11194,11195],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,11197,4316,11198,2935,11232,8108,11245,11248,11249,1343,11262,11275],{},[883,11199,11201],{"className":11200},[886],[888,11202,11203],{"xmlns":890},[892,11204,11205,11229],{},[895,11206,11207,11213,11215,11217,11219,11221,11223,11225,11227],{},[2133,11208,11209,11211],{},[898,11210,1876],{},[2005,11212,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,11214,2014],{"stretchy":2013},[898,11216,2017],{},[2005,11218,2020],{"stretchy":2013},[2005,11220,2007],{},[898,11222,2010],{},[2005,11224,2014],{"stretchy":2013},[898,11226,2017],{},[2005,11228,2020],{"stretchy":2013},[902,11230,11231],{"encoding":904},"F'(x) = f(x)",[883,11233,11235],{"className":11234},[886],[888,11236,11237],{"xmlns":890},[892,11238,11239,11243],{},[895,11240,11241],{},[898,11242,1876],{},[902,11244,1876],{"encoding":904},[38,11246,11247],{},"primitivní funkce"," k ",[883,11250,11252],{"className":11251},[886],[888,11253,11254],{"xmlns":890},[892,11255,11256,11260],{},[895,11257,11258],{},[898,11259,2010],{},[902,11261,2010],{"encoding":904},[883,11263,11265],{"className":11264},[886],[888,11266,11267],{"xmlns":890},[892,11268,11269,11273],{},[895,11270,11271],{},[898,11272,1852],{},[902,11274,1852],{"encoding":904}," konstanta.",[115,11277,11279],{"id":11278},"určitý-integrál","Určitý integrál",[724,11281,11282],{},[883,11283,11285],{"className":11284},[886],[888,11286,11287],{"xmlns":890},[892,11288,11289,11353],{},[895,11290,11291,11299,11301,11303,11305,11307,11309,11311,11313,11315,11317,11319,11321,11323,11325,11333,11335,11337,11339,11341,11343,11345,11347,11349,11351],{},[9172,11292,11293,11295,11297],{},[2005,11294,11174],{},[898,11296,207],{},[898,11298,2107],{},[898,11300,2010],{},[2005,11302,2014],{"stretchy":2013},[898,11304,2017],{},[2005,11306,2020],{"stretchy":2013},[2297,11308,2995],{},[898,11310,2203],{},[898,11312,2017],{},[2005,11314,2007],{},[2005,11316,2495],{"stretchy":2013},[898,11318,1876],{},[2005,11320,2014],{"stretchy":2013},[898,11322,2017],{},[2005,11324,2020],{"stretchy":2013},[9172,11326,11327,11329,11331],{},[2005,11328,2510],{"stretchy":2013},[898,11330,207],{},[898,11332,2107],{},[2005,11334,2007],{},[898,11336,1876],{},[2005,11338,2014],{"stretchy":2013},[898,11340,2107],{},[2005,11342,2020],{"stretchy":2013},[2005,11344,2234],{},[898,11346,1876],{},[2005,11348,2014],{"stretchy":2013},[898,11350,207],{},[2005,11352,2020],{"stretchy":2013},[902,11354,11355],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,11357,11358,11359,2212,11362,11375,11376,11397],{},"Geometricky ",[38,11360,11361],{},"plocha pod grafem",[883,11363,11365],{"className":11364},[886],[888,11366,11367],{"xmlns":890},[892,11368,11369,11373],{},[895,11370,11371],{},[898,11372,2010],{},[902,11374,2010],{"encoding":904}," na intervalu ",[883,11377,11379],{"className":11378},[886],[888,11380,11381],{"xmlns":890},[892,11382,11383,11395],{},[895,11384,11385,11387,11389,11391,11393],{},[2005,11386,2495],{"stretchy":2013},[898,11388,207],{},[2005,11390,2295],{"separator":2294},[898,11392,2107],{},[2005,11394,2510],{"stretchy":2013},[902,11396,10828],{"encoding":904}," (orientovaná).",[724,11399,11400],{},[2568,11401],{"alt":11402,"className":11403,"src":11404},"imek-integral-plocha",[210,2572],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,11406,11408],{"id":11407},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,11410,11412],{"id":11411},"příklad-tr-z-mr","Příklad — TR z MR",[724,11414,11415,11416,1644],{},"Mezní příjem ",[883,11417,11419],{"className":11418},[886],[888,11420,11421],{"xmlns":890},[892,11422,11423,11439],{},[895,11424,11425,11427,11429,11431,11433,11435,11437],{},[898,11426,2826],{},[898,11428,4003],{},[2005,11430,2007],{},[2138,11432,3098],{},[2005,11434,2234],{},[2138,11436,2140],{},[898,11438,2797],{},[902,11440,11441],{"encoding":904},"MR = 100 - 2Q",[724,11443,11444],{},[883,11445,11447],{"className":11446},[886],[888,11448,11449],{"xmlns":890},[892,11450,11451,11497],{},[895,11452,11453,11455,11457,11459,11461,11463,11465,11467,11469,11471,11473,11475,11477,11479,11481,11483,11485,11487,11493,11495],{},[898,11454,2783],{},[898,11456,4003],{},[2005,11458,2007],{},[2005,11460,11174],{},[2005,11462,2014],{"stretchy":2013},[2138,11464,3098],{},[2005,11466,2234],{},[2138,11468,2140],{},[898,11470,2797],{},[2005,11472,2020],{"stretchy":2013},[2297,11474,2995],{},[898,11476,2203],{},[898,11478,2797],{},[2005,11480,2007],{},[2138,11482,3098],{},[898,11484,2797],{},[2005,11486,2234],{},[2133,11488,11489,11491],{},[898,11490,2797],{},[2138,11492,2140],{},[2005,11494,2104],{},[898,11496,2151],{},[902,11498,11499],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,11501,11502,11503,3422,11529,2713],{},"Okrajová podmínka ",[883,11504,11506],{"className":11505},[886],[888,11507,11508],{"xmlns":890},[892,11509,11510,11526],{},[895,11511,11512,11514,11516,11518,11520,11522,11524],{},[898,11513,2783],{},[898,11515,4003],{},[2005,11517,2014],{"stretchy":2013},[2138,11519,2336],{},[2005,11521,2020],{"stretchy":2013},[2005,11523,2007],{},[2138,11525,2336],{},[902,11527,11528],{"encoding":904},"TR(0) = 0",[883,11530,11532],{"className":11531},[886],[888,11533,11534],{"xmlns":890},[892,11535,11536,11544],{},[895,11537,11538,11540,11542],{},[898,11539,2151],{},[2005,11541,2007],{},[2138,11543,2336],{},[902,11545,11546],{"encoding":904},"c = 0",[724,11548,11549],{},[883,11550,11552],{"className":11551},[886],[888,11553,11554],{"xmlns":890},[892,11555,11556,11582],{},[895,11557,11558,11560,11562,11564,11566,11568,11570,11572,11574,11576],{},[898,11559,2783],{},[898,11561,4003],{},[2005,11563,2014],{"stretchy":2013},[898,11565,2797],{},[2005,11567,2020],{"stretchy":2013},[2005,11569,2007],{},[2138,11571,3098],{},[898,11573,2797],{},[2005,11575,2234],{},[2133,11577,11578,11580],{},[898,11579,2797],{},[2138,11581,2140],{},[902,11583,11584],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,11586,11588],{"id":11587},"příklad-tc-z-mc","Příklad — TC z MC",[724,11590,11591,11592,11618,11619,1644],{},"Mezní náklady ",[883,11593,11595],{"className":11594},[886],[888,11596,11597],{"xmlns":890},[892,11598,11599,11615],{},[895,11600,11601,11603,11605,11607,11609,11611,11613],{},[898,11602,2826],{},[898,11604,1852],{},[2005,11606,2007],{},[2138,11608,2140],{},[2005,11610,2104],{},[2138,11612,2847],{},[898,11614,2797],{},[902,11616,11617],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,11620,11622],{"className":11621},[886],[888,11623,11624],{"xmlns":890},[892,11625,11626,11636],{},[895,11627,11628,11630,11632,11634],{},[898,11629,1876],{},[898,11631,1852],{},[2005,11633,2007],{},[2138,11635,3098],{},[902,11637,11638],{"encoding":904},"FC = 100",[724,11640,11641],{},[883,11642,11644],{"className":11643},[886],[888,11645,11646],{"xmlns":890},[892,11647,11648,11688],{},[895,11649,11650,11652,11654,11656,11658,11660,11662,11664,11666,11668,11670,11672,11674,11676,11678,11684,11686],{},[898,11651,2783],{},[898,11653,1852],{},[2005,11655,2007],{},[2005,11657,11174],{},[898,11659,2826],{},[898,11661,1852],{},[2297,11663,2995],{},[898,11665,2203],{},[898,11667,2797],{},[2005,11669,2007],{},[2138,11671,2140],{},[898,11673,2797],{},[2005,11675,2104],{},[2138,11677,2802],{},[2133,11679,11680,11682],{},[898,11681,2797],{},[2138,11683,2140],{},[2005,11685,2104],{},[898,11687,2151],{},[902,11689,11690],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,11692,11502,11693,3422,11725,2713],{},[883,11694,11696],{"className":11695},[886],[888,11697,11698],{"xmlns":890},[892,11699,11700,11722],{},[895,11701,11702,11704,11706,11708,11710,11712,11714,11716,11718,11720],{},[898,11703,2783],{},[898,11705,1852],{},[2005,11707,2014],{"stretchy":2013},[2138,11709,2336],{},[2005,11711,2020],{"stretchy":2013},[2005,11713,2007],{},[898,11715,1876],{},[898,11717,1852],{},[2005,11719,2007],{},[2138,11721,3098],{},[902,11723,11724],{"encoding":904},"TC(0) = FC = 100",[883,11726,11728],{"className":11727},[886],[888,11729,11730],{"xmlns":890},[892,11731,11732,11740],{},[895,11733,11734,11736,11738],{},[898,11735,2151],{},[2005,11737,2007],{},[2138,11739,3098],{},[902,11741,11742],{"encoding":904},"c = 100",[724,11744,11745],{},[883,11746,11748],{"className":11747},[886],[888,11749,11750],{"xmlns":890},[892,11751,11752,11784],{},[895,11753,11754,11756,11758,11760,11762,11764,11766,11768,11770,11772,11774,11776,11778],{},[898,11755,2783],{},[898,11757,1852],{},[2005,11759,2014],{"stretchy":2013},[898,11761,2797],{},[2005,11763,2020],{"stretchy":2013},[2005,11765,2007],{},[2138,11767,3098],{},[2005,11769,2104],{},[2138,11771,2140],{},[898,11773,2797],{},[2005,11775,2104],{},[2138,11777,2802],{},[2133,11779,11780,11782],{},[898,11781,2797],{},[2138,11783,2140],{},[902,11785,11786],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,11788,820],{"id":11789},"přebytek-spotřebitele-a-výrobce",[724,11791,11792],{},"Přebytek spotřebitele:",[724,11794,11795],{},[883,11796,11798],{"className":11797},[886],[888,11799,11800],{"xmlns":890},[892,11801,11802,11862],{},[895,11803,11804,11806,11808,11810,11816,11818,11820,11832,11834,11836,11838,11840,11842,11844,11846,11848,11854,11856],{},[898,11805,1852],{},[898,11807,8679],{},[2005,11809,2014],{"stretchy":2013},[2281,11811,11812,11814],{},[898,11813,2797],{},[2138,11815,2336],{},[2005,11817,2020],{"stretchy":2013},[2005,11819,2007],{},[9172,11821,11822,11824,11826],{},[2005,11823,11174],{},[2138,11825,2336],{},[2281,11827,11828,11830],{},[898,11829,2797],{},[2138,11831,2336],{},[898,11833,1860],{},[2005,11835,2014],{"stretchy":2013},[898,11837,2797],{},[2005,11839,2020],{"stretchy":2013},[2297,11841,2995],{},[898,11843,2203],{},[898,11845,2797],{},[2005,11847,2234],{},[2281,11849,11850,11852],{},[898,11851,3946],{},[2138,11853,2336],{},[2297,11855,2995],{},[2281,11857,11858,11860],{},[898,11859,2797],{},[2138,11861,2336],{},[902,11863,11864],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,11866,11867],{},"Přebytek výrobce:",[724,11869,11870],{},[883,11871,11873],{"className":11872},[886],[888,11874,11875],{"xmlns":890},[892,11876,11877,11937],{},[895,11878,11879,11881,11883,11885,11891,11893,11895,11901,11903,11909,11911,11923,11925,11927,11929,11931,11933,11935],{},[898,11880,3946],{},[898,11882,8679],{},[2005,11884,2014],{"stretchy":2013},[2281,11886,11887,11889],{},[898,11888,2797],{},[2138,11890,2336],{},[2005,11892,2020],{"stretchy":2013},[2005,11894,2007],{},[2281,11896,11897,11899],{},[898,11898,3946],{},[2138,11900,2336],{},[2297,11902,2995],{},[2281,11904,11905,11907],{},[898,11906,2797],{},[2138,11908,2336],{},[2005,11910,2234],{},[9172,11912,11913,11915,11917],{},[2005,11914,11174],{},[2138,11916,2336],{},[2281,11918,11919,11921],{},[898,11920,2797],{},[2138,11922,2336],{},[898,11924,8679],{},[2005,11926,2014],{"stretchy":2013},[898,11928,2797],{},[2005,11930,2020],{"stretchy":2013},[2297,11932,2995],{},[898,11934,2203],{},[898,11936,2797],{},[902,11938,11939],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,11941,11942,11943,1644],{},"Detailně viz ",[207,11944,11946],{"className":11945,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,11948,3800],{"id":3799},[120,11950,11951,11958,11965],{},[123,11952,11953,2212,11955],{},[38,11954,3807],{},[207,11956,766],{"className":11957,"dataFsResolvedFilePath":764,"href":765},[210],[123,11959,11960,2212,11962],{},[38,11961,3815],{},[207,11963,784],{"className":11964,"dataFsResolvedFilePath":782,"href":783},[210],[123,11966,11967,2212,11969,11972,11973,11976],{},[38,11968,3823],{},[207,11970,3831],{"className":11971,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,11974,11946],{"className":11975,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":11978},[11979,11980,11981,11986],{"id":11149,"depth":642,"text":11150},{"id":11278,"depth":642,"text":11279},{"id":11407,"depth":642,"text":11408,"children":11982},[11983,11984,11985],{"id":11411,"depth":649,"text":11412},{"id":11587,"depth":649,"text":11588},{"id":11789,"depth":649,"text":820},{"id":3799,"depth":642,"text":3800},"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":11987},[1135],"topics\u002Fintegral",[1128,11994,11995,11996,11997,11998,11999],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":12002,"title":12003,"body":12004,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":16273,"navigation":664,"path":16274,"seo":16275,"sources":16276,"stem":16277,"tags":16278,"type":3865,"updated":677,"__hash__":16284},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":12005,"toc":16261},[12006,12009,12013,12157,12164,12168,12238,12276,12379,12383,12413,12479,12526,12529,12598,12601,12636,12672,12676,12724,12731,12777,12823,12826,12905,13002,13085,13089,13133,13163,13169,13198,13220,13270,13323,13389,13392,13458,13487,13546,13562,13649,13747,13878,13882,14039,14188,14568,14572,14575,14634,14637,14723,14751,14789,14792,14829,14869,14903,14905,14942,14974,15072,15077,15201,15253,15335,15474,15478,15598,15605,15716,15723,15727,16202,16204],[12,12007,12003],{"id":12008},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,12010,12012],{"id":12011},"tldr","TL;DR",[724,12014,12015,12018,12019,10030,12022,12035,12036,12050,12051,12054,12055,1343,12058,12061,12062,1343,12065,12068,12069,2212,12072,12102,12103,12106,12107,1343,12121,12134,12135,12138,12139,3927],{},[38,12016,12017],{},"IS-LM"," je makroekonomický model se ",[38,12020,12021],{},"dvěma neznámými",[883,12023,12025],{"className":12024},[886],[888,12026,12027],{"xmlns":890},[892,12028,12029,12033],{},[895,12030,12031],{},[898,12032,9134],{},[902,12034,9134],{"encoding":904}," — národní důchod a ",[883,12037,12039],{"className":12038},[886],[888,12040,12041],{"xmlns":890},[892,12042,12043,12048],{},[895,12044,12045],{},[898,12046,12047],{},"r",[902,12049,12047],{"encoding":904}," — úroková míra) a ",[38,12052,12053],{},"dvěma trhy",": trhem zboží (křivka ",[38,12056,12057],{},"IS",[614,12059,12060],{},"Investment = Savings",") a trhem peněz (křivka ",[38,12063,12064],{},"LM",[614,12066,12067],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,12070,12071],{},"simultánní rovnováhu",[883,12073,12075],{"className":12074},[886],[888,12076,12077],{"xmlns":890},[892,12078,12079,12099],{},[895,12080,12081,12083,12089,12091,12097],{},[2005,12082,2014],{"stretchy":2013},[2133,12084,12085,12087],{},[898,12086,9134],{},[898,12088,1868],{},[2005,12090,2295],{"separator":2294},[2133,12092,12093,12095],{},[898,12094,12047],{},[898,12096,1868],{},[2005,12098,2020],{"stretchy":2013},[902,12100,12101],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,12104,12105],{},"fiskální politiky"," (posun IS změnou ",[883,12108,12110],{"className":12109},[886],[888,12111,12112],{"xmlns":890},[892,12113,12114,12119],{},[895,12115,12116],{},[898,12117,12118],{},"G",[902,12120,12118],{"encoding":904},[883,12122,12124],{"className":12123},[886],[888,12125,12126],{"xmlns":890},[892,12127,12128,12132],{},[895,12129,12130],{},[898,12131,2783],{},[902,12133,2783],{"encoding":904},") a ",[38,12136,12137],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,12140,12142],{"className":12141},[886],[888,12143,12144],{"xmlns":890},[892,12145,12146,12154],{},[895,12147,12148],{},[2133,12149,12150,12152],{},[898,12151,2826],{},[2005,12153,4360],{},[902,12155,12156],{"encoding":904},"M^*",[724,12158,12159],{},[2568,12160],{"alt":12161,"className":12162,"src":12163},"imek-is-lm-model",[210,2572],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,12165,12167],{"id":12166},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,12169,12170,12171,12175,12176,10030,12179,12202,12203,12206,12207,12223,12224,12237],{},"V modelech ",[207,12172,12174],{"className":12173,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,12177,12178],{},"investice pokládány za konstantní",[883,12180,12182],{"className":12181},[886],[888,12183,12184],{"xmlns":890},[892,12185,12186,12199],{},[895,12187,12188,12191,12193],{},[898,12189,12190],{},"I",[2005,12192,2007],{},[2133,12194,12195,12197],{},[898,12196,12190],{},[2005,12198,4360],{},[902,12200,12201],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,12204,12205],{},"ceně peněz",", tedy na ",[38,12208,12209,12210],{},"úrokové míře ",[883,12211,12213],{"className":12212},[886],[888,12214,12215],{"xmlns":890},[892,12216,12217,12221],{},[895,12218,12219],{},[898,12220,12047],{},[902,12222,12047],{"encoding":904},": čím vyšší ",[883,12225,12227],{"className":12226},[886],[888,12228,12229],{"xmlns":890},[892,12230,12231,12235],{},[895,12232,12233],{},[898,12234,12047],{},[902,12236,12047],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,12239,12240,12270],{},[123,12241,12242,2212,12245,12269],{},[38,12243,12244],{},"funkci investic",[883,12246,12248],{"className":12247},[886],[888,12249,12250],{"xmlns":890},[892,12251,12252,12266],{},[895,12253,12254,12256,12258,12260,12262,12264],{},[898,12255,12190],{},[2005,12257,2007],{},[898,12259,12190],{},[2005,12261,2014],{"stretchy":2013},[898,12263,12047],{},[2005,12265,2020],{"stretchy":2013},[902,12267,12268],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,12271,12272,12275],{},[38,12273,12274],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[3876,12277,12278],{},[724,12279,12280,12282,12283,12302,12303,12330,12331,12344,12345,12374,12375,12378],{},[883,12281,4418],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,12284,12286],{"className":12285},[886],[888,12287,12288],{"xmlns":890},[892,12289,12290,12299],{},[895,12291,12292,12294,12297],{},[898,12293,1852],{},[2297,12295,12296],{},"-",[898,12298,12190],{},[902,12300,12301],{"encoding":904},"C\\text{-}I"," až ",[883,12304,12306],{"className":12305},[886],[888,12307,12308],{"xmlns":890},[892,12309,12310,12327],{},[895,12311,12312,12314,12316,12318,12320,12322,12324],{},[898,12313,1852],{},[2297,12315,12296],{},[898,12317,12190],{},[2297,12319,12296],{},[898,12321,12118],{},[2297,12323,12296],{},[898,12325,12326],{},"X",[902,12328,12329],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,12332,12334],{"className":12333},[886],[888,12335,12336],{"xmlns":890},[892,12337,12338,12342],{},[895,12339,12340],{},[898,12341,9134],{},[902,12343,9134],{"encoding":904},". V IS-LM jsou ",[38,12346,12347,12348,3894,12361],{},"dvě neznámé ",[883,12349,12351],{"className":12350},[886],[888,12352,12353],{"xmlns":890},[892,12354,12355,12359],{},[895,12356,12357],{},[898,12358,9134],{},[902,12360,9134],{"encoding":904},[883,12362,12364],{"className":12363},[886],[888,12365,12366],{"xmlns":890},[892,12367,12368,12372],{},[895,12369,12370],{},[898,12371,12047],{},[902,12373,12047],{"encoding":904},", a proto potřebujeme ",[38,12376,12377],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,12380,12382],{"id":12381},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,12384,12385,12386,12399,12400,2713],{},"Lineární závislost investic ",[883,12387,12389],{"className":12388},[886],[888,12390,12391],{"xmlns":890},[892,12392,12393,12397],{},[895,12394,12395],{},[898,12396,12190],{},[902,12398,12190],{"encoding":904}," na úrokové míře ",[883,12401,12403],{"className":12402},[886],[888,12404,12405],{"xmlns":890},[892,12406,12407,12411],{},[895,12408,12409],{},[898,12410,12047],{},[902,12412,12047],{"encoding":904},[724,12414,12415],{},[883,12416,12418],{"className":12417},[886],[888,12419,12420],{"xmlns":890},[892,12421,12422,12476],{},[895,12423,12424,12426,12428,12430,12432,12434,12436,12438,12440,12442,12444,12446,12448,12450,12452,12454,12456,12458,12460,12462,12464,12467,12469,12471,12474],{},[898,12425,12190],{},[2005,12427,2007],{},[898,12429,12190],{},[2005,12431,2014],{"stretchy":2013},[898,12433,12047],{},[2005,12435,2020],{"stretchy":2013},[2005,12437,2007],{},[898,12439,2151],{},[898,12441,12047],{},[2005,12443,2104],{},[898,12445,2203],{},[2005,12447,2295],{"separator":2294},[5884,12449],{"width":5886},[898,12451,2151],{},[2005,12453,3455],{},[2138,12455,2336],{},[2005,12457,2295],{"separator":2294},[2297,12459,2299],{},[898,12461,2203],{},[2005,12463,3416],{},[2138,12465,12466],{},"0.",[5884,12468],{"width":5886},[2005,12470,2014],{"stretchy":2013},[2138,12472,12473],{},"7.11",[2005,12475,2020],{"stretchy":2013},[902,12477,12478],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,12480,12481,12502],{},[123,12482,12483,12501],{},[883,12484,12486],{"className":12485},[886],[888,12487,12488],{"xmlns":890},[892,12489,12490,12498],{},[895,12491,12492,12494,12496],{},[898,12493,2203],{},[2005,12495,3416],{},[2138,12497,2336],{},[902,12499,12500],{"encoding":904},"d > 0"," zřejmé,",[123,12503,12504,12522,12523,1644],{},[883,12505,12507],{"className":12506},[886],[888,12508,12509],{"xmlns":890},[892,12510,12511,12519],{},[895,12512,12513,12515,12517],{},[898,12514,2151],{},[2005,12516,3455],{},[2138,12518,2336],{},[902,12520,12521],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,12524,12525],{},"klesající",[724,12527,12528],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,12530,12531],{},[883,12532,12534],{"className":12533},[886],[888,12535,12536],{"xmlns":890},[892,12537,12538,12595],{},[895,12539,12540,12542,12544,12546,12548,12550,12552,12554,12556,12558,12560,12562,12564,12566,12568,12570,12572,12574,12576,12578,12580,12582,12584,12586,12588,12590,12593],{},[898,12541,1852],{},[2005,12543,2007],{},[898,12545,1852],{},[2005,12547,2014],{"stretchy":2013},[898,12549,9134],{},[2005,12551,2020],{"stretchy":2013},[2005,12553,2007],{},[898,12555,207],{},[898,12557,9134],{},[2005,12559,2104],{},[898,12561,2107],{},[2005,12563,2295],{"separator":2294},[5884,12565],{"width":5886},[2138,12567,2336],{},[2005,12569,3455],{},[898,12571,207],{},[2005,12573,3455],{},[2138,12575,2287],{},[2005,12577,2295],{"separator":2294},[2297,12579,2299],{},[898,12581,2107],{},[2005,12583,3416],{},[2138,12585,12466],{},[5884,12587],{"width":5886},[2005,12589,2014],{"stretchy":2013},[2138,12591,12592],{},"7.12",[2005,12594,2020],{"stretchy":2013},[902,12596,12597],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,12599,12600],{},"Podmínka rovnováhy na trhu zboží:",[724,12602,12603],{},[883,12604,12606],{"className":12605},[886],[888,12607,12608],{"xmlns":890},[892,12609,12610,12633],{},[895,12611,12612,12614,12616,12618,12620,12622,12624,12626,12628,12631],{},[898,12613,9134],{},[2005,12615,2007],{},[898,12617,1852],{},[2005,12619,2104],{},[898,12621,12190],{},[898,12623,1644],{"mathvariant":2385},[5884,12625],{"width":5886},[2005,12627,2014],{"stretchy":2013},[2138,12629,12630],{},"7.13",[2005,12632,2020],{"stretchy":2013},[902,12634,12635],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,12637,12638,12639,2212,12642,12668,12669,1644],{},"To dává ",[38,12640,12641],{},"tři rovnice o čtyřech neznámých",[883,12643,12645],{"className":12644},[886],[888,12646,12647],{"xmlns":890},[892,12648,12649,12665],{},[895,12650,12651,12653,12655,12657,12659,12661,12663],{},[898,12652,9134],{},[2005,12654,2295],{"separator":2294},[898,12656,1852],{},[2005,12658,2295],{"separator":2294},[898,12660,12190],{},[2005,12662,2295],{"separator":2294},[898,12664,12047],{},[902,12666,12667],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,12670,12671],{},"rovnováhy na trhu peněz",[115,12673,12675],{"id":12674},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,12677,12678,12679,5575,12701,12719,12720,12723],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,12680,12682],{"className":12681},[886],[888,12683,12684],{"xmlns":890},[892,12685,12686,12698],{},[895,12687,12688,12690,12692,12694,12696],{},[898,12689,9134],{},[2005,12691,2007],{},[898,12693,1852],{},[2005,12695,2104],{},[898,12697,8679],{},[902,12699,12700],{"encoding":904},"Y = C + S",[883,12702,12704],{"className":12703},[886],[888,12705,12706],{"xmlns":890},[892,12707,12708,12716],{},[895,12709,12710,12712,12714],{},[898,12711,12190],{},[2005,12713,2007],{},[898,12715,8679],{},[902,12717,12718],{"encoding":904},"I = S"," (plánované ",[38,12721,12722],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,12725,12726],{},[2568,12727],{"alt":12728,"className":12729,"src":12730},"imek-odvozeni-is-4panelu",[210,2572],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,12732,12733],{},[883,12734,12736],{"className":12735},[886],[888,12737,12738],{"xmlns":890},[892,12739,12740,12774],{},[895,12741,12742,12744,12746,12748,12750,12752,12754,12756,12758,12760,12762,12764,12766,12768,12770,12772],{},[898,12743,9134],{},[2005,12745,2007],{},[2005,12747,2014],{"stretchy":2013},[898,12749,207],{},[898,12751,9134],{},[2005,12753,2104],{},[898,12755,2107],{},[2005,12757,2020],{"stretchy":2013},[2005,12759,2104],{},[2005,12761,2014],{"stretchy":2013},[898,12763,2151],{},[898,12765,12047],{},[2005,12767,2104],{},[898,12769,2203],{},[2005,12771,2020],{"stretchy":2013},[2005,12773,2295],{"separator":2294},[902,12775,12776],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,12778,12779],{},[883,12780,12782],{"className":12781},[886],[888,12783,12784],{"xmlns":890},[892,12785,12786,12820],{},[895,12787,12788,12790,12792,12794,12796,12798,12800,12802,12804,12806,12808,12810,12812,12814,12816,12818],{},[2005,12789,2014],{"stretchy":2013},[2138,12791,2287],{},[2005,12793,2234],{},[898,12795,207],{},[2005,12797,2020],{"stretchy":2013},[898,12799,9134],{},[2005,12801,2234],{},[898,12803,2151],{},[898,12805,12047],{},[2005,12807,2234],{},[898,12809,2107],{},[2005,12811,2234],{},[898,12813,2203],{},[2005,12815,2007],{},[2138,12817,2336],{},[2005,12819,2295],{"separator":2294},[902,12821,12822],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,12824,12825],{},"odkud",[724,12827,12828],{},[883,12829,12831],{"className":12830},[886],[888,12832,12833],{"xmlns":890},[892,12834,12835,12902],{},[895,12836,12837,12893,12895,12897,12900],{},[12838,12839,12841],"menclose",{"notation":12840},"box",[2334,12842,12843],{"scriptlevel":2336,"displaystyle":2013},[2334,12844,12845],{"scriptlevel":2336,"displaystyle":2013},[2334,12846,12847],{"scriptlevel":2336,"displaystyle":2294},[895,12848,12849,12851,12853,12855,12867,12869,12871,12873,12891],{},[2297,12850,2995],{},[898,12852,9134],{},[2005,12854,2007],{},[2338,12856,12857,12859],{},[898,12858,2151],{},[895,12860,12861,12863,12865],{},[2138,12862,2287],{},[2005,12864,2234],{},[898,12866,207],{},[2297,12868,2995],{},[898,12870,12047],{},[2005,12872,2104],{},[2338,12874,12875,12883],{},[895,12876,12877,12879,12881],{},[898,12878,2107],{},[2005,12880,2104],{},[898,12882,2203],{},[895,12884,12885,12887,12889],{},[2138,12886,2287],{},[2005,12888,2234],{},[898,12890,207],{},[2297,12892,2995],{},[5884,12894],{"width":5886},[2005,12896,2014],{"stretchy":2013},[2138,12898,12899],{},"7.14",[2005,12901,2020],{"stretchy":2013},[902,12903,12904],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,12906,12907,12908,10030,12911,12914,12915,12918,12919,12921,12922,12944,12945,12973,12974,12995,12996,12998,12999,13001],{},"Tento vztah se nazývá ",[38,12909,12910],{},"funkce IS",[614,12912,12913],{},"IS schedule",") a její graf ",[38,12916,12917],{},"křivka IS",". Křivka je ",[38,12920,12525],{}," přímka v rovině ",[883,12923,12925],{"className":12924},[886],[888,12926,12927],{"xmlns":890},[892,12928,12929,12941],{},[895,12930,12931,12933,12935,12937,12939],{},[2005,12932,2014],{"stretchy":2013},[898,12934,12047],{},[2005,12936,2295],{"separator":2294},[898,12938,9134],{},[2005,12940,2020],{"stretchy":2013},[902,12942,12943],{"encoding":904},"(r, Y)",", neboť ",[883,12946,12948],{"className":12947},[886],[888,12949,12950],{"xmlns":890},[892,12951,12952,12970],{},[895,12953,12954,12966,12968],{},[2338,12955,12956,12958],{},[898,12957,2151],{},[895,12959,12960,12962,12964],{},[2138,12961,2287],{},[2005,12963,2234],{},[898,12965,207],{},[2005,12967,3455],{},[2138,12969,2336],{},[902,12971,12972],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,12975,12977],{"className":12976},[886],[888,12978,12979],{"xmlns":890},[892,12980,12981,12993],{},[895,12982,12983,12985,12987,12989,12991],{},[2005,12984,2014],{"stretchy":2013},[898,12986,12047],{},[2005,12988,2295],{"separator":2294},[898,12990,9134],{},[2005,12992,2020],{"stretchy":2013},[902,12994,12943],{"encoding":904},", pro které plánované ",[38,12997,12190],{},"nvestment = ",[38,13000,8679],{},"avings.",[3876,13003,13004],{},[724,13005,13006,13008,13009,13022,13023,2212,13026,13039,13040,13053,13054,3894,13067,13080,13081,13084],{},[883,13007,4164],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,13010,13012],{"className":13011},[886],[888,13013,13014],{"xmlns":890},[892,13015,13016,13020],{},[895,13017,13018],{},[898,13019,12047],{},[902,13021,12047],{"encoding":904}," → levnější úvěr → ",[38,13024,13025],{},"více investic",[883,13027,13029],{"className":13028},[886],[888,13030,13031],{"xmlns":890},[892,13032,13033,13037],{},[895,13034,13035],{},[898,13036,12190],{},[902,13038,12190],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,13041,13043],{"className":13042},[886],[888,13044,13045],{"xmlns":890},[892,13046,13047,13051],{},[895,13048,13049],{},[898,13050,9134],{},[902,13052,9134],{"encoding":904},". Vztah mezi ",[883,13055,13057],{"className":13056},[886],[888,13058,13059],{"xmlns":890},[892,13060,13061,13065],{},[895,13062,13063],{},[898,13064,12047],{},[902,13066,12047],{"encoding":904},[883,13068,13070],{"className":13069},[886],[888,13071,13072],{"xmlns":890},[892,13073,13074,13078],{},[895,13075,13076],{},[898,13077,9134],{},[902,13079,9134],{"encoding":904}," na trhu zboží je proto ",[38,13082,13083],{},"nepřímý"," (klesající křivka).",[115,13086,13088],{"id":13087},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,13090,13091,13092,13110,13111,2935,13129,13132],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,13093,13095],{"className":13094},[886],[888,13096,13097],{"xmlns":890},[892,13098,13099,13107],{},[895,13100,13101],{},[2133,13102,13103,13105],{},[898,13104,2826],{},[898,13106,1860],{},[902,13108,13109],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,13112,13114],{"className":13113},[886],[888,13115,13116],{"xmlns":890},[892,13117,13118,13126],{},[895,13119,13120],{},[2133,13121,13122,13124],{},[898,13123,2826],{},[898,13125,8679],{},[902,13127,13128],{"encoding":904},"M^S",[38,13130,13131],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,13134,13135],{},[883,13136,13138],{"className":13137},[886],[888,13139,13140],{"xmlns":890},[892,13141,13142,13160],{},[895,13143,13144,13150,13152,13158],{},[2133,13145,13146,13148],{},[898,13147,2826],{},[898,13149,8679],{},[2005,13151,2007],{},[2133,13153,13154,13156],{},[898,13155,2826],{},[2005,13157,4360],{},[898,13159,1644],{"mathvariant":2385},[902,13161,13162],{"encoding":904},"M^S = M^*.",[724,13164,13165,13168],{},[38,13166,13167],{},"Poptávka"," po penězích má tři zdroje:",[120,13170,13171,13180,13189],{},[123,13172,13173,10030,13176,13179],{},[38,13174,13175],{},"transakční poptávka",[614,13177,13178],{},"transactions demand",") — peníze pro nákup zboží,",[123,13181,13182,10030,13185,13188],{},[38,13183,13184],{},"opatrnostní poptávka",[614,13186,13187],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,13190,13191,10030,13194,13197],{},[38,13192,13193],{},"spekulační poptávka",[614,13195,13196],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,13199,13200,13201,13219],{},"Součet transakční a opatrnostní poptávky ",[883,13202,13204],{"className":13203},[886],[888,13205,13206],{"xmlns":890},[892,13207,13208,13216],{},[895,13209,13210],{},[2281,13211,13212,13214],{},[898,13213,9801],{},[2138,13215,2287],{},[902,13217,13218],{"encoding":904},"L_1"," je úměrný důchodu:",[724,13221,13222],{},[883,13223,13225],{"className":13224},[886],[888,13226,13227],{"xmlns":890},[892,13228,13229,13267],{},[895,13230,13231,13237,13239,13246,13248,13250,13252,13254,13256,13262,13264],{},[2281,13232,13233,13235],{},[898,13234,9801],{},[2138,13236,2287],{},[2005,13238,2007],{},[2281,13240,13241,13244],{},[898,13242,13243],{},"k",[2138,13245,2287],{},[898,13247,9134],{},[2005,13249,2295],{"separator":2294},[5884,13251],{"width":5886},[2138,13253,2336],{},[2005,13255,3455],{},[2281,13257,13258,13260],{},[898,13259,13243],{},[2138,13261,2287],{},[2005,13263,3455],{},[2138,13265,13266],{},"1.",[902,13268,13269],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,13271,13272,13273,13291,13292,1343,13305,13322],{},"Spekulační poptávka ",[883,13274,13276],{"className":13275},[886],[888,13277,13278],{"xmlns":890},[892,13279,13280,13288],{},[895,13281,13282],{},[2281,13283,13284,13286],{},[898,13285,9801],{},[2138,13287,2140],{},[902,13289,13290],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,13293,13295],{"className":13294},[886],[888,13296,13297],{"xmlns":890},[892,13298,13299,13303],{},[895,13300,13301],{},[898,13302,12047],{},[902,13304,12047],{"encoding":904},[883,13306,13308],{"className":13307},[886],[888,13309,13310],{"xmlns":890},[892,13311,13312,13320],{},[895,13313,13314],{},[2281,13315,13316,13318],{},[898,13317,9801],{},[2138,13319,2140],{},[902,13321,13290],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,13324,13325],{},[883,13326,13328],{"className":13327},[886],[888,13329,13330],{"xmlns":890},[892,13331,13332,13386],{},[895,13333,13334,13340,13342,13348,13350,13352,13358,13360,13362,13368,13370,13372,13374,13376,13382,13384],{},[2281,13335,13336,13338],{},[898,13337,9801],{},[2138,13339,2140],{},[2005,13341,2007],{},[2281,13343,13344,13346],{},[898,13345,13243],{},[2138,13347,2140],{},[898,13349,12047],{},[2005,13351,2104],{},[2281,13353,13354,13356],{},[898,13355,13243],{},[2138,13357,2182],{},[2005,13359,2295],{"separator":2294},[5884,13361],{"width":5886},[2281,13363,13364,13366],{},[898,13365,13243],{},[2138,13367,2140],{},[2005,13369,3455],{},[2138,13371,2336],{},[2005,13373,2295],{"separator":2294},[2297,13375,2299],{},[2281,13377,13378,13380],{},[898,13379,13243],{},[2138,13381,2182],{},[2005,13383,3416],{},[2138,13385,12466],{},[902,13387,13388],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,13390,13391],{},"Celková poptávka po penězích:",[724,13393,13394],{},[883,13395,13397],{"className":13396},[886],[888,13398,13399],{"xmlns":890},[892,13400,13401,13455],{},[895,13402,13403,13409,13411,13417,13419,13425,13427,13433,13435,13437,13443,13445,13447,13453],{},[2133,13404,13405,13407],{},[898,13406,2826],{},[898,13408,1860],{},[2005,13410,2007],{},[2281,13412,13413,13415],{},[898,13414,9801],{},[2138,13416,2287],{},[2005,13418,2104],{},[2281,13420,13421,13423],{},[898,13422,9801],{},[2138,13424,2140],{},[2005,13426,2007],{},[2281,13428,13429,13431],{},[898,13430,13243],{},[2138,13432,2287],{},[898,13434,9134],{},[2005,13436,2104],{},[2281,13438,13439,13441],{},[898,13440,13243],{},[2138,13442,2140],{},[898,13444,12047],{},[2005,13446,2104],{},[2281,13448,13449,13451],{},[898,13450,13243],{},[2138,13452,2182],{},[898,13454,1644],{"mathvariant":2385},[902,13456,13457],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,13459,13460,13461,2713],{},"Podmínka rovnováhy na trhu peněz ",[883,13462,13464],{"className":13463},[886],[888,13465,13466],{"xmlns":890},[892,13467,13468,13484],{},[895,13469,13470,13476,13478],{},[2133,13471,13472,13474],{},[898,13473,2826],{},[898,13475,1860],{},[2005,13477,2007],{},[2133,13479,13480,13482],{},[898,13481,2826],{},[2005,13483,4360],{},[902,13485,13486],{"encoding":904},"M^D = M^*",[724,13488,13489],{},[883,13490,13492],{"className":13491},[886],[888,13493,13494],{"xmlns":890},[892,13495,13496,13543],{},[895,13497,13498,13504,13506,13512,13514,13516,13522,13524,13526,13532,13534,13536,13538,13541],{},[2133,13499,13500,13502],{},[898,13501,2826],{},[2005,13503,4360],{},[2005,13505,2007],{},[2281,13507,13508,13510],{},[898,13509,13243],{},[2138,13511,2287],{},[898,13513,9134],{},[2005,13515,2104],{},[2281,13517,13518,13520],{},[898,13519,13243],{},[2138,13521,2140],{},[898,13523,12047],{},[2005,13525,2104],{},[2281,13527,13528,13530],{},[898,13529,13243],{},[2138,13531,2182],{},[2005,13533,2295],{"separator":2294},[5884,13535],{"width":5886},[2005,13537,2014],{"stretchy":2013},[2138,13539,13540],{},"7.15",[2005,13542,2020],{"stretchy":2013},[902,13544,13545],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,13547,13548,13549,3159],{},"po úpravě (vyjádření ",[883,13550,13552],{"className":13551},[886],[888,13553,13554],{"xmlns":890},[892,13555,13556,13560],{},[895,13557,13558],{},[898,13559,9134],{},[902,13561,9134],{"encoding":904},[724,13563,13564],{},[883,13565,13567],{"className":13566},[886],[888,13568,13569],{"xmlns":890},[892,13570,13571,13646],{},[895,13572,13573,13637,13639,13641,13644],{},[12838,13574,13575],{"notation":12840},[2334,13576,13577],{"scriptlevel":2336,"displaystyle":2013},[2334,13578,13579],{"scriptlevel":2336,"displaystyle":2013},[2334,13580,13581],{"scriptlevel":2336,"displaystyle":2294},[895,13582,13583,13585,13587,13589,13591,13605,13607,13609,13611,13635],{},[2297,13584,2995],{},[898,13586,9134],{},[2005,13588,2007],{},[2005,13590,2234],{},[2338,13592,13593,13599],{},[2281,13594,13595,13597],{},[898,13596,13243],{},[2138,13598,2140],{},[2281,13600,13601,13603],{},[898,13602,13243],{},[2138,13604,2287],{},[2297,13606,2995],{},[898,13608,12047],{},[2005,13610,2104],{},[2338,13612,13613,13629],{},[895,13614,13615,13621,13623],{},[2133,13616,13617,13619],{},[898,13618,2826],{},[2005,13620,4360],{},[2005,13622,2234],{},[2281,13624,13625,13627],{},[898,13626,13243],{},[2138,13628,2182],{},[2281,13630,13631,13633],{},[898,13632,13243],{},[2138,13634,2287],{},[2297,13636,2995],{},[5884,13638],{"width":5886},[2005,13640,2014],{"stretchy":2013},[2138,13642,13643],{},"7.16",[2005,13645,2020],{"stretchy":2013},[902,13647,13648],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,13650,12907,13651,10030,13654,13657,13658,12918,13661,12921,13664,12944,13685,13717,13718,13740,13741,13743,13744,13746],{},[38,13652,13653],{},"funkce LM",[614,13655,13656],{},"LM schedule","), její graf ",[38,13659,13660],{},"křivka LM",[38,13662,13663],{},"rostoucí",[883,13665,13667],{"className":13666},[886],[888,13668,13669],{"xmlns":890},[892,13670,13671,13683],{},[895,13672,13673,13675,13677,13679,13681],{},[2005,13674,2014],{"stretchy":2013},[898,13676,12047],{},[2005,13678,2295],{"separator":2294},[898,13680,9134],{},[2005,13682,2020],{"stretchy":2013},[902,13684,12943],{"encoding":904},[883,13686,13688],{"className":13687},[886],[888,13689,13690],{"xmlns":890},[892,13691,13692,13714],{},[895,13693,13694,13696,13710,13712],{},[2005,13695,2234],{},[2338,13697,13698,13704],{},[2281,13699,13700,13702],{},[898,13701,13243],{},[2138,13703,2140],{},[2281,13705,13706,13708],{},[898,13707,13243],{},[2138,13709,2287],{},[2005,13711,3416],{},[2138,13713,2336],{},[902,13715,13716],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,13719,13721],{"className":13720},[886],[888,13722,13723],{"xmlns":890},[892,13724,13725,13737],{},[895,13726,13727,13733,13735],{},[2281,13728,13729,13731],{},[898,13730,13243],{},[2138,13732,2140],{},[2005,13734,3455],{},[2138,13736,2336],{},[902,13738,13739],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,13742,9801],{},"iquidity of ",[38,13745,2826],{},"oney.",[3876,13748,13749],{},[724,13750,13751,13753,13754,13767,13768,13796,13797,13814,13815,13828,13829,13846,13847,3894,13860,13873,13874,13877],{},[883,13752,4164],{}," Intuice — proč LM roste\nVyšší důchod ",[883,13755,13757],{"className":13756},[886],[888,13758,13759],{"xmlns":890},[892,13760,13761,13765],{},[895,13762,13763],{},[898,13764,9134],{},[902,13766,9134],{"encoding":904}," → větší transakční poptávka po penězích ",[883,13769,13771],{"className":13770},[886],[888,13772,13773],{"xmlns":890},[892,13774,13775,13793],{},[895,13776,13777,13783,13785,13791],{},[2281,13778,13779,13781],{},[898,13780,9801],{},[2138,13782,2287],{},[2005,13784,2007],{},[2281,13786,13787,13789],{},[898,13788,13243],{},[2138,13790,2287],{},[898,13792,9134],{},[902,13794,13795],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,13798,13800],{"className":13799},[886],[888,13801,13802],{"xmlns":890},[892,13803,13804,13812],{},[895,13805,13806],{},[2133,13807,13808,13810],{},[898,13809,2826],{},[2005,13811,4360],{},[902,13813,12156],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,13816,13818],{"className":13817},[886],[888,13819,13820],{"xmlns":890},[892,13821,13822,13826],{},[895,13823,13824],{},[898,13825,12047],{},[902,13827,12047],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,13830,13832],{"className":13831},[886],[888,13833,13834],{"xmlns":890},[892,13835,13836,13844],{},[895,13837,13838],{},[2281,13839,13840,13842],{},[898,13841,9801],{},[2138,13843,2140],{},[902,13845,13290],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,13848,13850],{"className":13849},[886],[888,13851,13852],{"xmlns":890},[892,13853,13854,13858],{},[895,13855,13856],{},[898,13857,9134],{},[902,13859,9134],{"encoding":904},[883,13861,13863],{"className":13862},[886],[888,13864,13865],{"xmlns":890},[892,13866,13867,13871],{},[895,13868,13869],{},[898,13870,12047],{},[902,13872,12047],{"encoding":904}," na trhu peněz je proto ",[38,13875,13876],{},"přímý"," (rostoucí křivka).",[115,13879,13881],{"id":13880},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,13883,13884,13885,13888,13889,2212,13892,3894,13910,2212,13913,13931,13932,13950,13951,13969,13970,13986,13987,3894,14002,14017,14018,1644],{},"Řešením ",[38,13886,13887],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,13890,13891],{},"rovnovážný důchod",[883,13893,13895],{"className":13894},[886],[888,13896,13897],{"xmlns":890},[892,13898,13899,13907],{},[895,13900,13901],{},[2133,13902,13903,13905],{},[898,13904,9134],{},[898,13906,1868],{},[902,13908,13909],{"encoding":904},"Y^E",[38,13911,13912],{},"rovnovážnou úrokovou míru",[883,13914,13916],{"className":13915},[886],[888,13917,13918],{"xmlns":890},[892,13919,13920,13928],{},[895,13921,13922],{},[2133,13923,13924,13926],{},[898,13925,12047],{},[898,13927,1868],{},[902,13929,13930],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,13933,13935],{"className":13934},[886],[888,13936,13937],{"xmlns":890},[892,13938,13939,13947],{},[895,13940,13941],{},[2133,13942,13943,13945],{},[898,13944,12190],{},[898,13946,1868],{},[902,13948,13949],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,13952,13954],{"className":13953},[886],[888,13955,13956],{"xmlns":890},[892,13957,13958,13966],{},[895,13959,13960],{},[2133,13961,13962,13964],{},[898,13963,1852],{},[898,13965,1868],{},[902,13967,13968],{"encoding":904},"C^E",". Graficky jde o ",[38,13971,13972,13973],{},"průsečík ",[883,13974,13976],{"className":13975},[886],[888,13977,13978],{"xmlns":890},[892,13979,13980,13984],{},[895,13981,13982],{},[898,13983,1868],{},[902,13985,1868],{"encoding":904}," křivek ",[883,13988,13990],{"className":13989},[886],[888,13991,13992],{"xmlns":890},[892,13993,13994,14000],{},[895,13995,13996,13998],{},[898,13997,12190],{},[898,13999,8679],{},[902,14001,12057],{"encoding":904},[883,14003,14005],{"className":14004},[886],[888,14006,14007],{"xmlns":890},[892,14008,14009,14015],{},[895,14010,14011,14013],{},[898,14012,9801],{},[898,14014,2826],{},[902,14016,12064],{"encoding":904}," v rovině ",[883,14019,14021],{"className":14020},[886],[888,14022,14023],{"xmlns":890},[892,14024,14025,14037],{},[895,14026,14027,14029,14031,14033,14035],{},[2005,14028,2014],{"stretchy":2013},[898,14030,12047],{},[2005,14032,2295],{"separator":2294},[898,14034,9134],{},[2005,14036,2020],{"stretchy":2013},[902,14038,12943],{"encoding":904},[724,14040,14041],{},[614,14042,14043,14044,14065,14066,14081,14082,14097,14098,14111,14112,14129,14130,12134,14143,14129,14160,14173,14174,14187],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,14045,14047],{"className":14046},[886],[888,14048,14049],{"xmlns":890},[892,14050,14051,14063],{},[895,14052,14053,14055,14057,14059,14061],{},[2005,14054,2014],{"stretchy":2013},[898,14056,12047],{},[2005,14058,2295],{"separator":2294},[898,14060,9134],{},[2005,14062,2020],{"stretchy":2013},[902,14064,12943],{"encoding":904},". Rostoucí přímka ",[883,14067,14069],{"className":14068},[886],[888,14070,14071],{"xmlns":890},[892,14072,14073,14079],{},[895,14074,14075,14077],{},[898,14076,9801],{},[898,14078,2826],{},[902,14080,12064],{"encoding":904}," a klesající přímka ",[883,14083,14085],{"className":14084},[886],[888,14086,14087],{"xmlns":890},[892,14088,14089,14095],{},[895,14090,14091,14093],{},[898,14092,12190],{},[898,14094,8679],{},[902,14096,12057],{"encoding":904}," se protínají v bodě ",[883,14099,14101],{"className":14100},[886],[888,14102,14103],{"xmlns":890},[892,14104,14105,14109],{},[895,14106,14107],{},[898,14108,1868],{},[902,14110,1868],{"encoding":904}," se souřadnicemi ",[883,14113,14115],{"className":14114},[886],[888,14116,14117],{"xmlns":890},[892,14118,14119,14127],{},[895,14120,14121],{},[2133,14122,14123,14125],{},[898,14124,12047],{},[898,14126,1868],{},[902,14128,13930],{"encoding":904}," (na ose ",[883,14131,14133],{"className":14132},[886],[888,14134,14135],{"xmlns":890},[892,14136,14137,14141],{},[895,14138,14139],{},[898,14140,12047],{},[902,14142,12047],{"encoding":904},[883,14144,14146],{"className":14145},[886],[888,14147,14148],{"xmlns":890},[892,14149,14150,14158],{},[895,14151,14152],{},[2133,14153,14154,14156],{},[898,14155,9134],{},[898,14157,1868],{},[902,14159,13909],{"encoding":904},[883,14161,14163],{"className":14162},[886],[888,14164,14165],{"xmlns":890},[892,14166,14167,14171],{},[895,14168,14169],{},[898,14170,9134],{},[902,14172,9134],{"encoding":904},"); tečkované čáry z ",[883,14175,14177],{"className":14176},[886],[888,14178,14179],{"xmlns":890},[892,14180,14181,14185],{},[895,14182,14183],{},[898,14184,1868],{},[902,14186,1868],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[3876,14189,14190,14195],{},[724,14191,14192,14194],{},[883,14193,4578],{}," Postup — jak najít IS-LM rovnováhu",[152,14196,14197,14273,14341,14399,14472],{},[123,14198,14199,14202,14203,3894,14223,14243,14244,3894,14257,14270,14271,1644],{},[38,14200,14201],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,14204,14206],{"className":14205},[886],[888,14207,14208],{"xmlns":890},[892,14209,14210,14220],{},[895,14211,14212,14214,14216,14218],{},[898,14213,1852],{},[2005,14215,2014],{"stretchy":2013},[898,14217,9134],{},[2005,14219,2020],{"stretchy":2013},[902,14221,14222],{"encoding":904},"C(Y)",[883,14224,14226],{"className":14225},[886],[888,14227,14228],{"xmlns":890},[892,14229,14230,14240],{},[895,14231,14232,14234,14236,14238],{},[898,14233,12190],{},[2005,14235,2014],{"stretchy":2013},[898,14237,12047],{},[2005,14239,2020],{"stretchy":2013},[902,14241,14242],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,14245,14247],{"className":14246},[886],[888,14248,14249],{"xmlns":890},[892,14250,14251,14255],{},[895,14252,14253],{},[898,14254,9134],{},[902,14256,9134],{"encoding":904},[883,14258,14260],{"className":14259},[886],[888,14261,14262],{"xmlns":890},[892,14263,14264,14268],{},[895,14265,14266],{},[898,14267,12047],{},[902,14269,12047],{"encoding":904}," — dostaneš rovnici ",[38,14272,12057],{},[123,14274,14275,14278,14279,3894,14296,14313,14314,14270,14339,1644],{},[38,14276,14277],{},"Z trhu peněz (7.15)"," dosaď ",[883,14280,14282],{"className":14281},[886],[888,14283,14284],{"xmlns":890},[892,14285,14286,14294],{},[895,14287,14288],{},[2281,14289,14290,14292],{},[898,14291,9801],{},[2138,14293,2287],{},[902,14295,13218],{"encoding":904},[883,14297,14299],{"className":14298},[886],[888,14300,14301],{"xmlns":890},[892,14302,14303,14311],{},[895,14304,14305],{},[2281,14306,14307,14309],{},[898,14308,9801],{},[2138,14310,2140],{},[902,14312,13290],{"encoding":904}," a vztah ",[883,14315,14317],{"className":14316},[886],[888,14318,14319],{"xmlns":890},[892,14320,14321,14337],{},[895,14322,14323,14329,14331],{},[2133,14324,14325,14327],{},[898,14326,2826],{},[898,14328,1860],{},[2005,14330,2007],{},[2133,14332,14333,14335],{},[898,14334,2826],{},[2005,14336,4360],{},[902,14338,13486],{"encoding":904},[38,14340,12064],{},[123,14342,14343,14346,14347,3894,14360,14373,14374,14398],{},[38,14344,14345],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,14348,14350],{"className":14349},[886],[888,14351,14352],{"xmlns":890},[892,14353,14354,14358],{},[895,14355,14356],{},[898,14357,9134],{},[902,14359,9134],{"encoding":904},[883,14361,14363],{"className":14362},[886],[888,14364,14365],{"xmlns":890},[892,14366,14367,14371],{},[895,14368,14369],{},[898,14370,12047],{},[902,14372,12047],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,14375,14377],{"className":14376},[886],[888,14378,14379],{"xmlns":890},[892,14380,14381,14395],{},[895,14382,14383,14385,14387,14389,14391,14393],{},[898,14384,9134],{},[2005,14386,2007],{},[898,14388,2010],{},[2005,14390,2014],{"stretchy":2013},[898,14392,12047],{},[2005,14394,2020],{"stretchy":2013},[902,14396,14397],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,14400,14401,2212,14404,3894,14438,1644],{},[38,14402,14403],{},"Zpětně dopočítej",[883,14405,14407],{"className":14406},[886],[888,14408,14409],{"xmlns":890},[892,14410,14411,14435],{},[895,14412,14413,14419,14421,14423,14425,14431,14433],{},[2133,14414,14415,14417],{},[898,14416,1852],{},[898,14418,1868],{},[2005,14420,2007],{},[898,14422,207],{},[2297,14424,2995],{},[2133,14426,14427,14429],{},[898,14428,9134],{},[898,14430,1868],{},[2005,14432,2104],{},[898,14434,2107],{},[902,14436,14437],{"encoding":904},"C^E = a\\,Y^E + b",[883,14439,14441],{"className":14440},[886],[888,14442,14443],{"xmlns":890},[892,14444,14445,14469],{},[895,14446,14447,14453,14455,14457,14459,14465,14467],{},[2133,14448,14449,14451],{},[898,14450,12190],{},[898,14452,1868],{},[2005,14454,2007],{},[898,14456,2151],{},[2297,14458,2995],{},[2133,14460,14461,14463],{},[898,14462,12047],{},[898,14464,1868],{},[2005,14466,2104],{},[898,14468,2203],{},[902,14470,14471],{"encoding":904},"I^E = c\\,r^E + d",[123,14473,14474,14477,14478,14512,14513,14567],{},[38,14475,14476],{},"Ověř:"," musí platit ",[883,14479,14481],{"className":14480},[886],[888,14482,14483],{"xmlns":890},[892,14484,14485,14509],{},[895,14486,14487,14493,14495,14501,14503],{},[2133,14488,14489,14491],{},[898,14490,9134],{},[898,14492,1868],{},[2005,14494,2007],{},[2133,14496,14497,14499],{},[898,14498,1852],{},[898,14500,1868],{},[2005,14502,2104],{},[2133,14504,14505,14507],{},[898,14506,12190],{},[898,14508,1868],{},[902,14510,14511],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,14514,14516],{"className":14515},[886],[888,14517,14518],{"xmlns":890},[892,14519,14520,14564],{},[895,14521,14522,14528,14530,14536,14542,14544,14550,14556,14558],{},[2133,14523,14524,14526],{},[898,14525,2826],{},[2005,14527,4360],{},[2005,14529,2007],{},[2281,14531,14532,14534],{},[898,14533,13243],{},[2138,14535,2287],{},[2133,14537,14538,14540],{},[898,14539,9134],{},[898,14541,1868],{},[2005,14543,2104],{},[2281,14545,14546,14548],{},[898,14547,13243],{},[2138,14549,2140],{},[2133,14551,14552,14554],{},[898,14553,12047],{},[898,14555,1868],{},[2005,14557,2104],{},[2281,14559,14560,14562],{},[898,14561,13243],{},[2138,14563,2182],{},[902,14565,14566],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,14569,14571],{"id":14570},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,14573,14574],{},"Pro trh zboží jsou dány:",[120,14576,14577,14605],{},[123,14578,14579,14580,2295],{},"spotřeba ",[883,14581,14583],{"className":14582},[886],[888,14584,14585],{"xmlns":890},[892,14586,14587,14602],{},[895,14588,14589,14591,14593,14596,14598,14600],{},[898,14590,1852],{},[2005,14592,2007],{},[2138,14594,14595],{},"0,8",[898,14597,9134],{},[2005,14599,2104],{},[2138,14601,3098],{},[902,14603,14604],{"encoding":904},"C = 0{,}8Y + 100",[123,14606,14607,14608,1644],{},"investice ",[883,14609,14611],{"className":14610},[886],[888,14612,14613],{"xmlns":890},[892,14614,14615,14631],{},[895,14616,14617,14619,14621,14623,14625,14627,14629],{},[898,14618,12190],{},[2005,14620,2007],{},[2005,14622,2234],{},[2138,14624,9041],{},[898,14626,12047],{},[2005,14628,2104],{},[2138,14630,2790],{},[902,14632,14633],{"encoding":904},"I = -20r + 1000",[724,14635,14636],{},"Pro trh peněz:",[120,14638,14639,14665,14697],{},[123,14640,14641,2295],{},[883,14642,14644],{"className":14643},[886],[888,14645,14646],{"xmlns":890},[892,14647,14648,14662],{},[895,14649,14650,14656,14658,14660],{},[2281,14651,14652,14654],{},[898,14653,9801],{},[2138,14655,2287],{},[2005,14657,2007],{},[2138,14659,2802],{},[898,14661,9134],{},[902,14663,14664],{"encoding":904},"L_1 = 0{,}1Y",[123,14666,14667,2295],{},[883,14668,14670],{"className":14669},[886],[888,14671,14672],{"xmlns":890},[892,14673,14674,14694],{},[895,14675,14676,14682,14684,14686,14688,14690,14692],{},[2281,14677,14678,14680],{},[898,14679,9801],{},[2138,14681,2140],{},[2005,14683,2007],{},[2005,14685,2234],{},[2138,14687,5010],{},[898,14689,12047],{},[2005,14691,2104],{},[2138,14693,8610],{},[902,14695,14696],{"encoding":904},"L_2 = -25r + 2000",[123,14698,14699,14700,1644],{},"nabídka peněz ",[883,14701,14703],{"className":14702},[886],[888,14704,14705],{"xmlns":890},[892,14706,14707,14720],{},[895,14708,14709,14715,14717],{},[2133,14710,14711,14713],{},[898,14712,2826],{},[2005,14714,4360],{},[2005,14716,2007],{},[2138,14718,14719],{},"2375",[902,14721,14722],{"encoding":904},"M^* = 2375",[724,14724,14725,14728,14729,2713],{},[38,14726,14727],{},"Funkce IS"," — dosazením do (7.13) ",[883,14730,14732],{"className":14731},[886],[888,14733,14734],{"xmlns":890},[892,14735,14736,14748],{},[895,14737,14738,14740,14742,14744,14746],{},[898,14739,9134],{},[2005,14741,2007],{},[898,14743,1852],{},[2005,14745,2104],{},[898,14747,12190],{},[902,14749,14750],{"encoding":904},"Y = C + I",[724,14752,14753],{},[883,14754,14756],{"className":14755},[886],[888,14757,14758],{"xmlns":890},[892,14759,14760,14786],{},[895,14761,14762,14764,14766,14768,14770,14772,14774,14776,14778,14780,14782,14784],{},[898,14763,9134],{},[2005,14765,2007],{},[2138,14767,14595],{},[898,14769,9134],{},[2005,14771,2104],{},[2138,14773,3098],{},[2005,14775,2234],{},[2138,14777,9041],{},[898,14779,12047],{},[2005,14781,2104],{},[2138,14783,2790],{},[2005,14785,2295],{"separator":2294},[902,14787,14788],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,14790,14791],{},"tj.",[724,14793,14794],{},[883,14795,14797],{"className":14796},[886],[888,14798,14799],{"xmlns":890},[892,14800,14801,14826],{},[895,14802,14803,14805,14807,14809,14811,14813,14815,14818,14820,14822,14824],{},[2138,14804,2847],{},[898,14806,9134],{},[2005,14808,2104],{},[2138,14810,9041],{},[898,14812,12047],{},[2005,14814,2007],{},[2138,14816,14817],{},"1100.",[5884,14819],{"width":5886},[2005,14821,2014],{"stretchy":2013},[2297,14823,12057],{},[2005,14825,2020],{"stretchy":2013},[902,14827,14828],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,14830,14831,14834,14835,2713],{},[38,14832,14833],{},"Funkce LM"," — dosazením do (7.15) ",[883,14836,14838],{"className":14837},[886],[888,14839,14840],{"xmlns":890},[892,14841,14842,14866],{},[895,14843,14844,14850,14852,14858,14860],{},[2133,14845,14846,14848],{},[898,14847,2826],{},[2005,14849,4360],{},[2005,14851,2007],{},[2281,14853,14854,14856],{},[898,14855,9801],{},[2138,14857,2287],{},[2005,14859,2104],{},[2281,14861,14862,14864],{},[898,14863,9801],{},[2138,14865,2140],{},[902,14867,14868],{"encoding":904},"M^* = L_1 + L_2",[724,14870,14871],{},[883,14872,14874],{"className":14873},[886],[888,14875,14876],{"xmlns":890},[892,14877,14878,14900],{},[895,14879,14880,14882,14884,14886,14888,14890,14892,14894,14896,14898],{},[2138,14881,14719],{},[2005,14883,2007],{},[2138,14885,2802],{},[898,14887,9134],{},[2005,14889,2234],{},[2138,14891,5010],{},[898,14893,12047],{},[2005,14895,2104],{},[2138,14897,8610],{},[2005,14899,2295],{"separator":2294},[902,14901,14902],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,14904,14791],{},[724,14906,14907],{},[883,14908,14910],{"className":14909},[886],[888,14911,14912],{"xmlns":890},[892,14913,14914,14939],{},[895,14915,14916,14918,14920,14922,14924,14926,14928,14931,14933,14935,14937],{},[2138,14917,2802],{},[898,14919,9134],{},[2005,14921,2234],{},[2138,14923,5010],{},[898,14925,12047],{},[2005,14927,2007],{},[2138,14929,14930],{},"375.",[5884,14932],{"width":5886},[2005,14934,2014],{"stretchy":2013},[2297,14936,12064],{},[2005,14938,2020],{"stretchy":2013},[902,14940,14941],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,14943,14944,14947,14948,14973],{},[38,14945,14946],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,14949,14951],{"className":14950},[886],[888,14952,14953],{"xmlns":890},[892,14954,14955,14970],{},[895,14956,14957,14959,14961,14964,14966,14968],{},[898,14958,9134],{},[2005,14960,2007],{},[2138,14962,14963],{},"5500",[2005,14965,2234],{},[2138,14967,3098],{},[898,14969,12047],{},[902,14971,14972],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,14975,14976],{},[883,14977,14979],{"className":14978},[886],[888,14980,14981],{"xmlns":890},[892,14982,14983,15069],{},[895,14984,14985,14987,14989,14991,14993,14995,14997,14999,15001,15003,15005,15007,15010,15012,15015,15017,15020,15022,15024,15026,15028,15030,15032,15034,15036,15038,15040,15042,15045,15047,15049,15052,15054,15056,15058,15064,15066],{},[2138,14986,2802],{},[2005,14988,2014],{"stretchy":2013},[2138,14990,14963],{},[2005,14992,2234],{},[2138,14994,3098],{},[898,14996,12047],{},[2005,14998,2020],{"stretchy":2013},[2005,15000,2234],{},[2138,15002,5010],{},[898,15004,12047],{},[2005,15006,2007],{},[2138,15008,15009],{},"375",[2297,15011,3993],{},[2005,15013,15014],{},"⟹",[2297,15016,3993],{},[2138,15018,15019],{},"550",[2005,15021,2234],{},[2138,15023,2871],{},[898,15025,12047],{},[2005,15027,2234],{},[2138,15029,5010],{},[898,15031,12047],{},[2005,15033,2007],{},[2138,15035,15009],{},[2297,15037,3993],{},[2005,15039,15014],{},[2297,15041,3993],{},[2138,15043,15044],{},"35",[898,15046,12047],{},[2005,15048,2007],{},[2138,15050,15051],{},"175",[2297,15053,3993],{},[2005,15055,15014],{},[2297,15057,3993],{},[2133,15059,15060,15062],{},[898,15061,12047],{},[898,15063,1868],{},[2005,15065,2007],{},[2138,15067,15068],{},"5.",[902,15070,15071],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,15073,15074],{},[38,15075,15076],{},"Zpětné dosazení:",[120,15078,15079,15125,15162],{},[123,15080,15081,2295],{},[883,15082,15084],{"className":15083},[886],[888,15085,15086],{"xmlns":890},[892,15087,15088,15122],{},[895,15089,15090,15096,15098,15100,15102,15104,15106,15108,15110,15112,15114,15117,15119],{},[2133,15091,15092,15094],{},[898,15093,9134],{},[898,15095,1868],{},[2005,15097,2007],{},[2138,15099,14963],{},[2005,15101,2234],{},[2138,15103,3098],{},[2005,15105,3185],{},[2138,15107,2237],{},[2005,15109,2007],{},[2138,15111,14963],{},[2005,15113,2234],{},[2138,15115,15116],{},"500",[2005,15118,2007],{},[2138,15120,15121],{},"5000",[902,15123,15124],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,15126,15127,2295],{},[883,15128,15130],{"className":15129},[886],[888,15131,15132],{"xmlns":890},[892,15133,15134,15159],{},[895,15135,15136,15142,15144,15146,15148,15150,15152,15154,15156],{},[2133,15137,15138,15140],{},[898,15139,1852],{},[898,15141,1868],{},[2005,15143,2007],{},[2138,15145,14595],{},[2005,15147,3185],{},[2138,15149,15121],{},[2005,15151,2104],{},[2138,15153,3098],{},[2005,15155,2007],{},[2138,15157,15158],{},"4100",[902,15160,15161],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,15163,15164,1644],{},[883,15165,15167],{"className":15166},[886],[888,15168,15169],{"xmlns":890},[892,15170,15171,15198],{},[895,15172,15173,15179,15181,15183,15185,15187,15189,15191,15193,15195],{},[2133,15174,15175,15177],{},[898,15176,12190],{},[898,15178,1868],{},[2005,15180,2007],{},[2005,15182,2234],{},[2138,15184,9041],{},[2005,15186,3185],{},[2138,15188,2237],{},[2005,15190,2104],{},[2138,15192,2790],{},[2005,15194,2007],{},[2138,15196,15197],{},"900",[902,15199,15200],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,15202,15203,2212,15206,15252],{},[38,15204,15205],{},"Ověření:",[883,15207,15209],{"className":15208},[886],[888,15210,15211],{"xmlns":890},[892,15212,15213,15249],{},[895,15214,15215,15221,15223,15229,15231,15233,15235,15237,15239,15241,15243],{},[2133,15216,15217,15219],{},[898,15218,1852],{},[898,15220,1868],{},[2005,15222,2104],{},[2133,15224,15225,15227],{},[898,15226,12190],{},[898,15228,1868],{},[2005,15230,2007],{},[2138,15232,15158],{},[2005,15234,2104],{},[2138,15236,15197],{},[2005,15238,2007],{},[2138,15240,15121],{},[2005,15242,2007],{},[2133,15244,15245,15247],{},[898,15246,9134],{},[898,15248,1868],{},[902,15250,15251],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,15254,15255],{},[883,15256,15258],{"className":15257},[886],[888,15259,15260],{"xmlns":890},[892,15261,15262,15332],{},[895,15263,15264],{},[12838,15265,15266],{"notation":12840},[2334,15267,15268],{"scriptlevel":2336,"displaystyle":2013},[2334,15269,15270],{"scriptlevel":2336,"displaystyle":2013},[2334,15271,15272],{"scriptlevel":2336,"displaystyle":2294},[895,15273,15274,15276,15282,15284,15286,15288,15291,15297,15299,15301,15303,15305,15311,15313,15315,15317,15319,15325,15327,15330],{},[2297,15275,2995],{},[2133,15277,15278,15280],{},[898,15279,9134],{},[898,15281,1868],{},[2005,15283,2007],{},[2138,15285,15121],{},[2005,15287,2295],{"separator":2294},[5884,15289],{"width":15290},"1em",[2133,15292,15293,15295],{},[898,15294,12047],{},[898,15296,1868],{},[2005,15298,2007],{},[2138,15300,2237],{},[2005,15302,2295],{"separator":2294},[5884,15304],{"width":15290},[2133,15306,15307,15309],{},[898,15308,1852],{},[898,15310,1868],{},[2005,15312,2007],{},[2138,15314,15158],{},[2005,15316,2295],{"separator":2294},[5884,15318],{"width":15290},[2133,15320,15321,15323],{},[898,15322,12190],{},[898,15324,1868],{},[2005,15326,2007],{},[2138,15328,15329],{},"900.",[2297,15331,2995],{},[902,15333,15334],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,15336,15337],{},[614,15338,15339,15340,15353,15354,15367,15368,15383,15384,15397,15398,15413,15414,15427,15428,15441,15442,1644],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,15341,15343],{"className":15342},[886],[888,15344,15345],{"xmlns":890},[892,15346,15347,15351],{},[895,15348,15349],{},[898,15350,9134],{},[902,15352,9134],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,15355,15357],{"className":15356},[886],[888,15358,15359],{"xmlns":890},[892,15360,15361,15365],{},[895,15362,15363],{},[898,15364,12047],{},[902,15366,12047],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,15369,15371],{"className":15370},[886],[888,15372,15373],{"xmlns":890},[892,15374,15375,15381],{},[895,15376,15377,15379],{},[898,15378,9801],{},[898,15380,2826],{},[902,15382,12064],{"encoding":904}," stoupá z oblasti nízkých ",[883,15385,15387],{"className":15386},[886],[888,15388,15389],{"xmlns":890},[892,15390,15391,15395],{},[895,15392,15393],{},[898,15394,12047],{},[902,15396,12047],{"encoding":904},", přímka ",[883,15399,15401],{"className":15400},[886],[888,15402,15403],{"xmlns":890},[892,15404,15405,15411],{},[895,15406,15407,15409],{},[898,15408,12190],{},[898,15410,8679],{},[902,15412,12057],{"encoding":904}," klesá a protíná osu ",[883,15415,15417],{"className":15416},[886],[888,15418,15419],{"xmlns":890},[892,15420,15421,15425],{},[895,15422,15423],{},[898,15424,12047],{},[902,15426,12047],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,15429,15431],{"className":15430},[886],[888,15432,15433],{"xmlns":890},[892,15434,15435,15439],{},[895,15436,15437],{},[898,15438,1868],{},[902,15440,1868],{"encoding":904}," leží v bodě ",[883,15443,15445],{"className":15444},[886],[888,15446,15447],{"xmlns":890},[892,15448,15449,15471],{},[895,15450,15451,15453,15455,15457,15459,15461,15463,15465,15467,15469],{},[2005,15452,2495],{"stretchy":2013},[898,15454,12047],{},[2005,15456,2007],{},[2138,15458,2237],{},[2005,15460,2295],{"separator":2294},[2297,15462,2299],{},[898,15464,9134],{},[2005,15466,2007],{},[2138,15468,15121],{},[2005,15470,2510],{"stretchy":2013},[902,15472,15473],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,15475,15477],{"id":15476},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,15479,15480,15483,15484,15497,15498,7021,15511,15514,15515,15533,15534,15551,15552,15569,15570,15583,15584,15597],{},[38,15481,15482],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,15485,15487],{"className":15486},[886],[888,15488,15489],{"xmlns":890},[892,15490,15491,15495],{},[895,15492,15493],{},[898,15494,12118],{},[902,15496,12118],{"encoding":904}," nebo snížení daní ",[883,15499,15501],{"className":15500},[886],[888,15502,15503],{"xmlns":890},[892,15504,15505,15509],{},[895,15506,15507],{},[898,15508,2783],{},[902,15510,2783],{"encoding":904},[38,15512,15513],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,15516,15518],{"className":15517},[886],[888,15519,15520],{"xmlns":890},[892,15521,15522,15530],{},[895,15523,15524],{},[2133,15525,15526,15528],{},[898,15527,1868],{},[2005,15529,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,15531,15532],{"encoding":904},"E'"," má vyšší ",[883,15535,15537],{"className":15536},[886],[888,15538,15539],{"xmlns":890},[892,15540,15541,15549],{},[895,15542,15543],{},[2133,15544,15545,15547],{},[898,15546,9134],{},[898,15548,1868],{},[902,15550,13909],{"encoding":904}," i vyšší ",[883,15553,15555],{"className":15554},[886],[888,15556,15557],{"xmlns":890},[892,15558,15559,15567],{},[895,15560,15561],{},[2133,15562,15563,15565],{},[898,15564,12047],{},[898,15566,1868],{},[902,15568,13930],{"encoding":904}," (vyšší ",[883,15571,15573],{"className":15572},[886],[888,15574,15575],{"xmlns":890},[892,15576,15577,15581],{},[895,15578,15579],{},[898,15580,9134],{},[902,15582,9134],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,15585,15587],{"className":15586},[886],[888,15588,15589],{"xmlns":890},[892,15590,15591,15595],{},[895,15592,15593],{},[898,15594,12047],{},[902,15596,12047],{"encoding":904}," nahoru).",[724,15599,15600],{},[2568,15601],{"alt":15602,"className":15603,"src":15604},"imek-posun-is-lm-politiky",[210,2572],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,15606,15607,15610,15611,15628,15629,15632,15633,15650,15651,15668,15669,15682,15683,15702,15703,3927],{},[38,15608,15609],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,15612,15614],{"className":15613},[886],[888,15615,15616],{"xmlns":890},[892,15617,15618,15626],{},[895,15619,15620],{},[2133,15621,15622,15624],{},[898,15623,2826],{},[2005,15625,4360],{},[902,15627,12156],{"encoding":904}," národní bankou — ",[38,15630,15631],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,15634,15636],{"className":15635},[886],[888,15637,15638],{"xmlns":890},[892,15639,15640,15648],{},[895,15641,15642],{},[2133,15643,15644,15646],{},[898,15645,12047],{},[898,15647,1868],{},[902,15649,13930],{"encoding":904}," a vyšší ",[883,15652,15654],{"className":15653},[886],[888,15655,15656],{"xmlns":890},[892,15657,15658,15666],{},[895,15659,15660],{},[2133,15661,15662,15664],{},[898,15663,9134],{},[898,15665,1868],{},[902,15667,13909],{"encoding":904}," (nižší ",[883,15670,15672],{"className":15671},[886],[888,15673,15674],{"xmlns":890},[892,15675,15676,15680],{},[895,15677,15678],{},[898,15679,12047],{},[902,15681,12047],{"encoding":904}," povzbuzuje investice ",[883,15684,15686],{"className":15685},[886],[888,15687,15688],{"xmlns":890},[892,15689,15690,15700],{},[895,15691,15692,15694,15696,15698],{},[898,15693,12190],{},[2005,15695,2014],{"stretchy":2013},[898,15697,12047],{},[2005,15699,2020],{"stretchy":2013},[902,15701,14242],{"encoding":904},", ty zvedají ",[883,15704,15706],{"className":15705},[886],[888,15707,15708],{"xmlns":890},[892,15709,15710,15714],{},[895,15711,15712],{},[898,15713,9134],{},[902,15715,9134],{"encoding":904},[724,15717,15718,15719,15722],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,15720,15721],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,15724,15726],{"id":15725},"klíčové-pojmy","Klíčové pojmy",[120,15728,15729,15802,15848,15930,15980,16047,16104,16145,16178],{},[123,15730,15731,7021,15764,1343,15781,15798,15799,15801],{},[38,15732,15733,15734],{},"Funkce investic ",[883,15735,15737],{"className":15736},[886],[888,15738,15739],{"xmlns":890},[892,15740,15741,15761],{},[895,15742,15743,15745,15747,15749,15751,15753,15755,15757,15759],{},[898,15744,12190],{},[2005,15746,2014],{"stretchy":2013},[898,15748,12047],{},[2005,15750,2020],{"stretchy":2013},[2005,15752,2007],{},[898,15754,2151],{},[898,15756,12047],{},[2005,15758,2104],{},[898,15760,2203],{},[902,15762,15763],{"encoding":904},"I(r) = cr + d",[883,15765,15767],{"className":15766},[886],[888,15768,15769],{"xmlns":890},[892,15770,15771,15779],{},[895,15772,15773,15775,15777],{},[898,15774,2151],{},[2005,15776,3455],{},[2138,15778,2336],{},[902,15780,12521],{"encoding":904},[883,15782,15784],{"className":15783},[886],[888,15785,15786],{"xmlns":890},[892,15787,15788,15796],{},[895,15789,15790,15792,15794],{},[898,15791,2203],{},[2005,15793,3416],{},[2138,15795,2336],{},[902,15797,12500],{"encoding":904},"; ",[38,15800,12525],{}," funkce úrokové míry.",[123,15803,15804,15807,15808,15829,15830,15847],{},[38,15805,15806],{},"Trh zboží"," — rovnováha ",[883,15809,15811],{"className":15810},[886],[888,15812,15813],{"xmlns":890},[892,15814,15815,15827],{},[895,15816,15817,15819,15821,15823,15825],{},[898,15818,9134],{},[2005,15820,2007],{},[898,15822,1852],{},[2005,15824,2104],{},[898,15826,12190],{},[902,15828,14750],{"encoding":904},", ekvivalentně ",[883,15831,15833],{"className":15832},[886],[888,15834,15835],{"xmlns":890},[892,15836,15837,15845],{},[895,15838,15839,15841,15843],{},[898,15840,12190],{},[2005,15842,2007],{},[898,15844,8679],{},[902,15846,12718],{"encoding":904}," (investice = úspory).",[123,15849,15850,10030,15853,15855,15856,15906,15907,12921,15909,1644],{},[38,15851,15852],{},"Křivka IS",[614,15854,12060],{},") — ",[883,15857,15859],{"className":15858},[886],[888,15860,15861],{"xmlns":890},[892,15862,15863,15903],{},[895,15864,15865,15867,15869,15881,15883,15885],{},[898,15866,9134],{},[2005,15868,2007],{},[2338,15870,15871,15873],{},[898,15872,2151],{},[895,15874,15875,15877,15879],{},[2138,15876,2287],{},[2005,15878,2234],{},[898,15880,207],{},[898,15882,12047],{},[2005,15884,2104],{},[2338,15886,15887,15895],{},[895,15888,15889,15891,15893],{},[898,15890,2107],{},[2005,15892,2104],{},[898,15894,2203],{},[895,15896,15897,15899,15901],{},[2138,15898,2287],{},[2005,15900,2234],{},[898,15902,207],{},[902,15904,15905],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,15908,12525],{},[883,15910,15912],{"className":15911},[886],[888,15913,15914],{"xmlns":890},[892,15915,15916,15928],{},[895,15917,15918,15920,15922,15924,15926],{},[2005,15919,2014],{"stretchy":2013},[898,15921,12047],{},[2005,15923,2295],{"separator":2294},[898,15925,9134],{},[2005,15927,2020],{"stretchy":2013},[902,15929,12943],{"encoding":904},[123,15931,15932,15807,15935,15961,15962,1644],{},[38,15933,15934],{},"Trh peněz",[883,15936,15938],{"className":15937},[886],[888,15939,15940],{"xmlns":890},[892,15941,15942,15958],{},[895,15943,15944,15950,15952],{},[2133,15945,15946,15948],{},[898,15947,2826],{},[898,15949,1860],{},[2005,15951,2007],{},[2133,15953,15954,15956],{},[898,15955,2826],{},[898,15957,8679],{},[902,15959,15960],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,15963,15965],{"className":15964},[886],[888,15966,15967],{"xmlns":890},[892,15968,15969,15977],{},[895,15970,15971],{},[2133,15972,15973,15975],{},[898,15974,2826],{},[2005,15976,4360],{},[902,15978,15979],{"encoding":904},"M^* ",[123,15981,15982,7021,15985,1644],{},[38,15983,15984],{},"Transakční, opatrnostní, spekulační poptávka",[883,15986,15988],{"className":15987},[886],[888,15989,15990],{"xmlns":890},[892,15991,15992,16044],{},[895,15993,15994,16000,16002,16008,16010,16016,16018,16024,16026,16028,16034,16036,16038],{},[2133,15995,15996,15998],{},[898,15997,2826],{},[898,15999,1860],{},[2005,16001,2007],{},[2281,16003,16004,16006],{},[898,16005,9801],{},[2138,16007,2287],{},[2005,16009,2104],{},[2281,16011,16012,16014],{},[898,16013,9801],{},[2138,16015,2140],{},[2005,16017,2007],{},[2281,16019,16020,16022],{},[898,16021,13243],{},[2138,16023,2287],{},[898,16025,9134],{},[2005,16027,2104],{},[2281,16029,16030,16032],{},[898,16031,13243],{},[2138,16033,2140],{},[898,16035,12047],{},[2005,16037,2104],{},[2281,16039,16040,16042],{},[898,16041,13243],{},[2138,16043,2182],{},[902,16045,16046],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,16048,16049,10030,16052,15855,16054,16100,16101,16103],{},[38,16050,16051],{},"Křivka LM",[614,16053,12067],{},[883,16055,16057],{"className":16056},[886],[888,16058,16059],{"xmlns":890},[892,16060,16061,16097],{},[895,16062,16063,16069,16071,16077,16079,16081,16087,16089,16091],{},[2133,16064,16065,16067],{},[898,16066,2826],{},[2005,16068,4360],{},[2005,16070,2007],{},[2281,16072,16073,16075],{},[898,16074,13243],{},[2138,16076,2287],{},[898,16078,9134],{},[2005,16080,2104],{},[2281,16082,16083,16085],{},[898,16084,13243],{},[2138,16086,2140],{},[898,16088,12047],{},[2005,16090,2104],{},[2281,16092,16093,16095],{},[898,16094,13243],{},[2138,16096,2182],{},[902,16098,16099],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,16102,13663],{}," přímka.",[123,16105,16106,16109,16110,16144],{},[38,16107,16108],{},"Simultánní rovnováha"," — průsečík ",[883,16111,16113],{"className":16112},[886],[888,16114,16115],{"xmlns":890},[892,16116,16117,16141],{},[895,16118,16119,16121,16123,16125,16131,16133,16139],{},[898,16120,1868],{},[2005,16122,2007],{},[2005,16124,2014],{"stretchy":2013},[2133,16126,16127,16129],{},[898,16128,12047],{},[898,16130,1868],{},[2005,16132,2295],{"separator":2294},[2133,16134,16135,16137],{},[898,16136,9134],{},[898,16138,1868],{},[2005,16140,2020],{"stretchy":2013},[902,16142,16143],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,16146,16147,16150,16151,1343,16164,16177],{},[38,16148,16149],{},"Fiskální politika"," — nástroje ",[883,16152,16154],{"className":16153},[886],[888,16155,16156],{"xmlns":890},[892,16157,16158,16162],{},[895,16159,16160],{},[898,16161,12118],{},[902,16163,12118],{"encoding":904},[883,16165,16167],{"className":16166},[886],[888,16168,16169],{"xmlns":890},[892,16170,16171,16175],{},[895,16172,16173],{},[898,16174,2783],{},[902,16176,2783],{"encoding":904}," posouvající křivku IS.",[123,16179,16180,16183,16184,16201],{},[38,16181,16182],{},"Monetární politika"," — nástroj ",[883,16185,16187],{"className":16186},[886],[888,16188,16189],{"xmlns":890},[892,16190,16191,16199],{},[895,16192,16193],{},[2133,16194,16195,16197],{},[898,16196,2826],{},[2005,16198,4360],{},[902,16200,12156],{"encoding":904}," posouvající křivku LM.",[115,16203,3800],{"id":3799},[120,16205,16206,16215,16224,16234],{},[123,16207,16208,2212,16211],{},[38,16209,16210],{},"Kurz:",[207,16212,16214],{"className":16213,"dataFsResolvedFilePath":1641,"href":1642},[210],"Matematická ekonomie",[123,16216,16217,2212,16220],{},[38,16218,16219],{},"Přednáška:",[207,16221,16223],{"className":16222,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,16225,16226,2212,16229,16233],{},[38,16227,16228],{},"Nadřazené téma:",[207,16230,16232],{"className":16231,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,16235,16236,16239],{},[38,16237,16238],{},"Související:",[120,16240,16241,16248,16254],{},[123,16242,16243,16247],{},[207,16244,16246],{"className":16245,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,16249,16250,16253],{},[207,16251,1145],{"className":16252,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,16255,16256,16260],{},[207,16257,16259],{"className":16258,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":16262},[16263,16264,16265,16266,16267,16268,16269,16270,16271,16272],{"id":12011,"depth":642,"text":12012},{"id":12166,"depth":642,"text":12167},{"id":12381,"depth":642,"text":12382},{"id":12674,"depth":642,"text":12675},{"id":13087,"depth":642,"text":13088},{"id":13880,"depth":642,"text":13881},{"id":14570,"depth":642,"text":14571},{"id":15476,"depth":642,"text":15477},{"id":15725,"depth":642,"text":15726},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Fis-lm",{"title":12003,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,16279,1143,16280,16281,16282,16283,16232],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":16286,"title":16287,"body":16288,"course":659,"courses":17881,"created":1129,"description":17882,"extension":661,"meta":17883,"navigation":664,"path":17884,"seo":17885,"sources":17886,"stem":17887,"tags":17888,"type":3865,"updated":677,"__hash__":17891},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":16289,"toc":17869},[16290,16293,16389,16396,16416,16420,16425,16488,16507,16509,16512,16648,16650,16860,16894,17031,17035,17099,17115,17143,17147,17245,17249,17253,17306,17412,17626,17630,17673,17779,17831,17833],[12,16291,16287],{"id":16292},"lagrangeova-metoda-vázané-extrémy",[724,16294,16295,16296,3919,16319,16351,16352,16355,16356,16383,16384,16388],{},"Hledáme extrém funkce ",[883,16297,16299],{"className":16298},[886],[888,16300,16301],{"xmlns":890},[892,16302,16303,16317],{},[895,16304,16305,16307,16309,16311,16313,16315],{},[898,16306,2010],{},[2005,16308,2014],{"stretchy":2013},[898,16310,2017],{},[2005,16312,2295],{"separator":2294},[898,16314,2003],{},[2005,16316,2020],{"stretchy":2013},[902,16318,9848],{"encoding":904},[883,16320,16322],{"className":16321},[886],[888,16323,16324],{"xmlns":890},[892,16325,16326,16348],{},[895,16327,16328,16330,16332,16338,16340,16346],{},[898,16329,900],{},[2005,16331,2014],{"stretchy":2013},[2281,16333,16334,16336],{},[898,16335,2797],{},[2138,16337,2287],{},[2005,16339,2295],{"separator":2294},[2281,16341,16342,16344],{},[898,16343,2797],{},[2138,16345,2140],{},[2005,16347,2020],{"stretchy":2013},[902,16349,16350],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,16353,16354],{},"podmíněný"," rovnicí ",[883,16357,16359],{"className":16358},[886],[888,16360,16361],{"xmlns":890},[892,16362,16363,16381],{},[895,16364,16365,16367,16369,16371,16373,16375,16377,16379],{},[898,16366,11045],{},[2005,16368,2014],{"stretchy":2013},[898,16370,2017],{},[2005,16372,2295],{"separator":2294},[898,16374,2003],{},[2005,16376,2020],{"stretchy":2013},[2005,16378,2007],{},[2138,16380,2336],{},[902,16382,11062],{"encoding":904},". V ",[207,16385,16387],{"className":16386,"dataFsResolvedFilePath":1641,"href":1642},[210],"matematické ekonomii"," se používá pro:",[724,16390,16391],{},[2568,16392],{"alt":16393,"className":16394,"src":16395},"imek-lagrange-tecnost",[210,2572],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,16397,16398,16407,16413],{},[123,16399,16400,16403,16404,2020],{},[38,16401,16402],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,16405,9779],{"className":16406,"dataFsResolvedFilePath":878,"href":879},[210],[123,16408,16409,16412],{},[38,16410,16411],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,16414,16415],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,16417,16419],{"id":16418},"princip","Princip",[724,16421,10711,16422,2713],{},[38,16423,16424],{},"Lagrangeovu funkci",[724,16426,16427],{},[883,16428,16430],{"className":16429},[886],[888,16431,16432],{"xmlns":890},[892,16433,16434,16485],{},[895,16435,16436,16438,16440,16442,16444,16446,16448,16451,16453,16455,16457,16459,16461,16463,16465,16467,16469,16471,16473,16475,16477,16479,16481,16483],{},[898,16437,9801],{},[2005,16439,2014],{"stretchy":2013},[898,16441,2017],{},[2005,16443,2295],{"separator":2294},[898,16445,2003],{},[2005,16447,2295],{"separator":2294},[898,16449,16450],{},"λ",[2005,16452,2020],{"stretchy":2013},[2005,16454,2007],{},[898,16456,2010],{},[2005,16458,2014],{"stretchy":2013},[898,16460,2017],{},[2005,16462,2295],{"separator":2294},[898,16464,2003],{},[2005,16466,2020],{"stretchy":2013},[2005,16468,2104],{},[898,16470,16450],{},[2297,16472,2995],{},[898,16474,11045],{},[2005,16476,2014],{"stretchy":2013},[898,16478,2017],{},[2005,16480,2295],{"separator":2294},[898,16482,2003],{},[2005,16484,2020],{"stretchy":2013},[902,16486,16487],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,16489,4316,16490,8108,16504,1644],{},[883,16491,16493],{"className":16492},[886],[888,16494,16495],{"xmlns":890},[892,16496,16497,16501],{},[895,16498,16499],{},[898,16500,16450],{},[902,16502,16503],{"encoding":904},"\\lambda",[38,16505,16506],{},"Lagrangeův multiplikátor",[115,16508,3260],{"id":3259},[724,16510,16511],{},"Řešíme soustavu:",[724,16513,16514,16562,16610],{},[883,16515,16517],{"className":16516},[886],[888,16518,16519],{"xmlns":890},[892,16520,16521,16559],{},[895,16522,16523,16531,16533,16541,16543,16545,16547,16555,16557],{},[9172,16524,16525,16527,16529],{},[898,16526,9801],{},[898,16528,2017],{},[2005,16530,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,16532,2007],{},[9172,16534,16535,16537,16539],{},[898,16536,2010],{},[898,16538,2017],{},[2005,16540,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,16542,2104],{},[898,16544,16450],{},[2297,16546,2995],{},[9172,16548,16549,16551,16553],{},[898,16550,11045],{},[898,16552,2017],{},[2005,16554,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,16556,2007],{},[2138,16558,2336],{},[902,16560,16561],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,16563,16565],{"className":16564},[886],[888,16566,16567],{"xmlns":890},[892,16568,16569,16607],{},[895,16570,16571,16579,16581,16589,16591,16593,16595,16603,16605],{},[9172,16572,16573,16575,16577],{},[898,16574,9801],{},[898,16576,2003],{},[2005,16578,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,16580,2007],{},[9172,16582,16583,16585,16587],{},[898,16584,2010],{},[898,16586,2003],{},[2005,16588,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,16590,2104],{},[898,16592,16450],{},[2297,16594,2995],{},[9172,16596,16597,16599,16601],{},[898,16598,11045],{},[898,16600,2003],{},[2005,16602,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,16604,2007],{},[2138,16606,2336],{},[902,16608,16609],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,16611,16613],{"className":16612},[886],[888,16614,16615],{"xmlns":890},[892,16616,16617,16645],{},[895,16618,16619,16627,16629,16631,16633,16635,16637,16639,16641,16643],{},[9172,16620,16621,16623,16625],{},[898,16622,9801],{},[898,16624,16450],{},[2005,16626,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,16628,2007],{},[898,16630,11045],{},[2005,16632,2014],{"stretchy":2013},[898,16634,2017],{},[2005,16636,2295],{"separator":2294},[898,16638,2003],{},[2005,16640,2020],{"stretchy":2013},[2005,16642,2007],{},[2138,16644,2336],{},[902,16646,16647],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,16649,3334],{"id":3333},[724,16651,16652],{},[883,16653,16655],{"className":16654},[886],[888,16656,16657],{"xmlns":890},[892,16658,16659,16857],{},[895,16660,16661,16663,16665,16667,16669,16671,16673,16675,16677,16679,16681,16697,16699,16701,16717,16719,16721,16729,16735,16737,16739,16755,16757,16759,16775,16777,16779,16787,16793,16795,16797,16799,16815,16817,16819,16835,16837,16839,16847,16849],{},[898,16662,1860],{},[2005,16664,2014],{"stretchy":2013},[898,16666,2017],{},[2005,16668,2295],{"separator":2294},[898,16670,2003],{},[2005,16672,2295],{"separator":2294},[898,16674,16450],{},[2005,16676,2020],{"stretchy":2013},[2005,16678,2007],{},[2005,16680,2014],{"stretchy":2013},[9172,16682,16683,16685,16691],{},[898,16684,2010],{},[895,16686,16687,16689],{},[898,16688,2017],{},[898,16690,2017],{},[895,16692,16693,16695],{},[2005,16694,2387],{"mathvariant":2385},[2005,16696,2387],{"mathvariant":2385},[2005,16698,2104],{},[898,16700,16450],{},[9172,16702,16703,16705,16711],{},[898,16704,11045],{},[895,16706,16707,16709],{},[898,16708,2017],{},[898,16710,2017],{},[895,16712,16713,16715],{},[2005,16714,2387],{"mathvariant":2385},[2005,16716,2387],{"mathvariant":2385},[2005,16718,2020],{"stretchy":2013},[2005,16720,2014],{"stretchy":2013},[9172,16722,16723,16725,16727],{},[898,16724,11045],{},[898,16726,2003],{},[2005,16728,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2133,16730,16731,16733],{},[2005,16732,2020],{"stretchy":2013},[2138,16734,2140],{},[2005,16736,2104],{},[2005,16738,2014],{"stretchy":2013},[9172,16740,16741,16743,16749],{},[898,16742,2010],{},[895,16744,16745,16747],{},[898,16746,2003],{},[898,16748,2003],{},[895,16750,16751,16753],{},[2005,16752,2387],{"mathvariant":2385},[2005,16754,2387],{"mathvariant":2385},[2005,16756,2104],{},[898,16758,16450],{},[9172,16760,16761,16763,16769],{},[898,16762,11045],{},[895,16764,16765,16767],{},[898,16766,2003],{},[898,16768,2003],{},[895,16770,16771,16773],{},[2005,16772,2387],{"mathvariant":2385},[2005,16774,2387],{"mathvariant":2385},[2005,16776,2020],{"stretchy":2013},[2005,16778,2014],{"stretchy":2013},[9172,16780,16781,16783,16785],{},[898,16782,11045],{},[898,16784,2017],{},[2005,16786,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2133,16788,16789,16791],{},[2005,16790,2020],{"stretchy":2013},[2138,16792,2140],{},[2005,16794,2234],{},[2138,16796,2140],{},[2005,16798,2014],{"stretchy":2013},[9172,16800,16801,16803,16809],{},[898,16802,2010],{},[895,16804,16805,16807],{},[898,16806,2017],{},[898,16808,2003],{},[895,16810,16811,16813],{},[2005,16812,2387],{"mathvariant":2385},[2005,16814,2387],{"mathvariant":2385},[2005,16816,2104],{},[898,16818,16450],{},[9172,16820,16821,16823,16829],{},[898,16822,11045],{},[895,16824,16825,16827],{},[898,16826,2017],{},[898,16828,2003],{},[895,16830,16831,16833],{},[2005,16832,2387],{"mathvariant":2385},[2005,16834,2387],{"mathvariant":2385},[2005,16836,2020],{"stretchy":2013},[2297,16838,2995],{},[9172,16840,16841,16843,16845],{},[898,16842,11045],{},[898,16844,2017],{},[2005,16846,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,16848,2995],{},[9172,16850,16851,16853,16855],{},[898,16852,11045],{},[898,16854,2003],{},[2005,16856,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,16858,16859],{"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",[724,16861,16862,16863,16893],{},"Je-li ",[883,16864,16866],{"className":16865},[886],[888,16867,16868],{"xmlns":890},[892,16869,16870,16890],{},[895,16871,16872,16874,16876,16878,16880,16882,16888],{},[2005,16873,2495],{"stretchy":2013},[898,16875,207],{},[2005,16877,2295],{"separator":2294},[898,16879,2107],{},[2005,16881,2295],{"separator":2294},[2281,16883,16884,16886],{},[898,16885,16450],{},[2138,16887,2336],{},[2005,16889,2510],{"stretchy":2013},[902,16891,16892],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,16895,16896,16964],{},[123,16897,16898,3422,16934,16936,16937],{},[883,16899,16901],{"className":16900},[886],[888,16902,16903],{"xmlns":890},[892,16904,16905,16931],{},[895,16906,16907,16909,16911,16913,16915,16917,16919,16925,16927,16929],{},[898,16908,1860],{},[2005,16910,2014],{"stretchy":2013},[898,16912,207],{},[2005,16914,2295],{"separator":2294},[898,16916,2107],{},[2005,16918,2295],{"separator":2294},[2281,16920,16921,16923],{},[898,16922,16450],{},[2138,16924,2336],{},[2005,16926,2020],{"stretchy":2013},[2005,16928,3455],{},[2138,16930,2336],{},[902,16932,16933],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,16935,3725],{}," vázané podmínkou ",[883,16938,16940],{"className":16939},[886],[888,16941,16942],{"xmlns":890},[892,16943,16944,16962],{},[895,16945,16946,16948,16950,16952,16954,16956,16958,16960],{},[898,16947,11045],{},[2005,16949,2014],{"stretchy":2013},[898,16951,2017],{},[2005,16953,2295],{"separator":2294},[898,16955,2003],{},[2005,16957,2020],{"stretchy":2013},[2005,16959,2007],{},[2138,16961,2336],{},[902,16963,11062],{"encoding":904},[123,16965,16966,3422,17002,16936,17004],{},[883,16967,16969],{"className":16968},[886],[888,16970,16971],{"xmlns":890},[892,16972,16973,16999],{},[895,16974,16975,16977,16979,16981,16983,16985,16987,16993,16995,16997],{},[898,16976,1860],{},[2005,16978,2014],{"stretchy":2013},[898,16980,207],{},[2005,16982,2295],{"separator":2294},[898,16984,2107],{},[2005,16986,2295],{"separator":2294},[2281,16988,16989,16991],{},[898,16990,16450],{},[2138,16992,2336],{},[2005,16994,2020],{"stretchy":2013},[2005,16996,3416],{},[2138,16998,2336],{},[902,17000,17001],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,17003,3783],{},[883,17005,17007],{"className":17006},[886],[888,17008,17009],{"xmlns":890},[892,17010,17011,17029],{},[895,17012,17013,17015,17017,17019,17021,17023,17025,17027],{},[898,17014,11045],{},[2005,17016,2014],{"stretchy":2013},[898,17018,2017],{},[2005,17020,2295],{"separator":2294},[898,17022,2003],{},[2005,17024,2020],{"stretchy":2013},[2005,17026,2007],{},[2138,17028,2336],{},[902,17030,11062],{"encoding":904},[115,17032,17034],{"id":17033},"význam-multiplikátoru","Význam multiplikátoru",[724,17036,17037],{},[883,17038,17040],{"className":17039},[886],[888,17041,17042],{"xmlns":890},[892,17043,17044,17096],{},[895,17045,17046,17048,17050,17072,17074],{},[898,17047,16450],{},[2005,17049,2007],{},[2338,17051,17052,17060],{},[9172,17053,17054,17056,17058],{},[898,17055,2010],{},[898,17057,2017],{},[2005,17059,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[895,17061,17062,17064],{},[2005,17063,2234],{},[9172,17065,17066,17068,17070],{},[898,17067,11045],{},[898,17069,2017],{},[2005,17071,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,17073,2007],{},[2338,17075,17076,17084],{},[9172,17077,17078,17080,17082],{},[898,17079,2010],{},[898,17081,2003],{},[2005,17083,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[895,17085,17086,17088],{},[2005,17087,2234],{},[9172,17089,17090,17092,17094],{},[898,17091,11045],{},[898,17093,2003],{},[2005,17095,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,17097,17098],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,17100,17101,17114],{},[883,17102,17104],{"className":17103},[886],[888,17105,17106],{"xmlns":890},[892,17107,17108,17112],{},[895,17109,17110],{},[898,17111,16450],{},[902,17113,16503],{"encoding":904}," udává:",[120,17116,17117,17123],{},[123,17118,17119,17120],{},"konstantní ",[38,17121,17122],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,17124,17125,17128,17129,17142],{},[38,17126,17127],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,17130,17132],{"className":17131},[886],[888,17133,17134],{"xmlns":890},[892,17135,17136,17140],{},[895,17137,17138],{},[898,17139,2010],{},[902,17141,2010],{"encoding":904},", uvolní-li se omezení o jednotku",[115,17144,17146],{"id":17145},"alternativní-postup","Alternativní postup",[724,17148,17149,17150,17177,17178,17202,17203,17227,17228,17241,17242,1644],{},"Lze-li z ",[883,17151,17153],{"className":17152},[886],[888,17154,17155],{"xmlns":890},[892,17156,17157,17175],{},[895,17158,17159,17161,17163,17165,17167,17169,17171,17173],{},[898,17160,11045],{},[2005,17162,2014],{"stretchy":2013},[898,17164,2017],{},[2005,17166,2295],{"separator":2294},[898,17168,2003],{},[2005,17170,2020],{"stretchy":2013},[2005,17172,2007],{},[2138,17174,2336],{},[902,17176,11062],{"encoding":904}," vyjádřit ",[883,17179,17181],{"className":17180},[886],[888,17182,17183],{"xmlns":890},[892,17184,17185,17199],{},[895,17186,17187,17189,17191,17193,17195,17197],{},[898,17188,2003],{},[2005,17190,2007],{},[898,17192,2003],{},[2005,17194,2014],{"stretchy":2013},[898,17196,2017],{},[2005,17198,2020],{"stretchy":2013},[902,17200,17201],{"encoding":904},"y = y(x)"," (nebo ",[883,17204,17206],{"className":17205},[886],[888,17207,17208],{"xmlns":890},[892,17209,17210,17224],{},[895,17211,17212,17214,17216,17218,17220,17222],{},[898,17213,2017],{},[2005,17215,2007],{},[898,17217,2017],{},[2005,17219,2014],{"stretchy":2013},[898,17221,2003],{},[2005,17223,2020],{"stretchy":2013},[902,17225,17226],{"encoding":904},"x = x(y)","), dosadíme do ",[883,17229,17231],{"className":17230},[886],[888,17232,17233],{"xmlns":890},[892,17234,17235,17239],{},[895,17236,17237],{},[898,17238,2010],{},[902,17240,2010],{"encoding":904}," a převedeme na ",[38,17243,17244],{},"extrém funkce jedné proměnné",[115,17246,17248],{"id":17247},"použití-v-imek","Použití v ImeK",[198,17250,17252],{"id":17251},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,17254,17255,17256,1644],{},"Rozpočtové omezení: ",[883,17257,17259],{"className":17258},[886],[888,17260,17261],{"xmlns":890},[892,17262,17263,17303],{},[895,17264,17265,17271,17273,17281,17287,17289,17297],{},[2133,17266,17267,17269],{},[898,17268,9134],{},[2005,17270,4360],{},[2005,17272,2007],{},[9172,17274,17275,17277,17279],{},[898,17276,3946],{},[2138,17278,2287],{},[2005,17280,4360],{},[2281,17282,17283,17285],{},[898,17284,2797],{},[2138,17286,2287],{},[2005,17288,2104],{},[9172,17290,17291,17293,17295],{},[898,17292,3946],{},[2138,17294,2140],{},[2005,17296,4360],{},[2281,17298,17299,17301],{},[898,17300,2797],{},[2138,17302,2140],{},[902,17304,17305],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,17307,17308],{},[883,17309,17311],{"className":17310},[886],[888,17312,17313],{"xmlns":890},[892,17314,17315,17409],{},[895,17316,17317,17319,17321,17327,17329,17335,17337,17339,17341,17343,17345,17347,17353,17355,17361,17363,17365,17367,17369,17375,17377,17385,17391,17393,17401,17407],{},[898,17318,9801],{},[2005,17320,2014],{"stretchy":2013},[2281,17322,17323,17325],{},[898,17324,2797],{},[2138,17326,2287],{},[2005,17328,2295],{"separator":2294},[2281,17330,17331,17333],{},[898,17332,2797],{},[2138,17334,2140],{},[2005,17336,2295],{"separator":2294},[898,17338,16450],{},[2005,17340,2020],{"stretchy":2013},[2005,17342,2007],{},[898,17344,900],{},[2005,17346,2014],{"stretchy":2013},[2281,17348,17349,17351],{},[898,17350,2797],{},[2138,17352,2287],{},[2005,17354,2295],{"separator":2294},[2281,17356,17357,17359],{},[898,17358,2797],{},[2138,17360,2140],{},[2005,17362,2020],{"stretchy":2013},[2005,17364,2104],{},[898,17366,16450],{},[2005,17368,2014],{"stretchy":2013},[2133,17370,17371,17373],{},[898,17372,9134],{},[2005,17374,4360],{},[2005,17376,2234],{},[9172,17378,17379,17381,17383],{},[898,17380,3946],{},[2138,17382,2287],{},[2005,17384,4360],{},[2281,17386,17387,17389],{},[898,17388,2797],{},[2138,17390,2287],{},[2005,17392,2234],{},[9172,17394,17395,17397,17399],{},[898,17396,3946],{},[2138,17398,2140],{},[2005,17400,4360],{},[2281,17402,17403,17405],{},[898,17404,2797],{},[2138,17406,2140],{},[2005,17408,2020],{"stretchy":2013},[902,17410,17411],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,17413,17414,17415,1343,17447,1343,17479,17528,17529,17583,17584,1644],{},"Soustava: ",[883,17416,17418],{"className":17417},[886],[888,17419,17420],{"xmlns":890},[892,17421,17422,17444],{},[895,17423,17424,17432,17434,17436],{},[9172,17425,17426,17428,17430],{},[898,17427,900],{},[2138,17429,2287],{},[2005,17431,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,17433,2007],{},[898,17435,16450],{},[9172,17437,17438,17440,17442],{},[898,17439,3946],{},[2138,17441,2287],{},[2005,17443,4360],{},[902,17445,17446],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,17448,17450],{"className":17449},[886],[888,17451,17452],{"xmlns":890},[892,17453,17454,17476],{},[895,17455,17456,17464,17466,17468],{},[9172,17457,17458,17460,17462],{},[898,17459,900],{},[2138,17461,2140],{},[2005,17463,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,17465,2007],{},[898,17467,16450],{},[9172,17469,17470,17472,17474],{},[898,17471,3946],{},[2138,17473,2140],{},[2005,17475,4360],{},[902,17477,17478],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,17480,17482],{"className":17481},[886],[888,17483,17484],{"xmlns":890},[892,17485,17486,17526],{},[895,17487,17488,17494,17496,17504,17510,17512,17520],{},[2133,17489,17490,17492],{},[898,17491,9134],{},[2005,17493,4360],{},[2005,17495,2007],{},[9172,17497,17498,17500,17502],{},[898,17499,3946],{},[2138,17501,2287],{},[2005,17503,4360],{},[2281,17505,17506,17508],{},[898,17507,2797],{},[2138,17509,2287],{},[2005,17511,2104],{},[9172,17513,17514,17516,17518],{},[898,17515,3946],{},[2138,17517,2140],{},[2005,17519,4360],{},[2281,17521,17522,17524],{},[898,17523,2797],{},[2138,17525,2140],{},[902,17527,17305],{"encoding":904},". Z prvních dvou: ",[883,17530,17532],{"className":17531},[886],[888,17533,17534],{"xmlns":890},[892,17535,17536,17580],{},[895,17537,17538,17558,17560],{},[2334,17539,17540],{"scriptlevel":2336,"displaystyle":2013},[2338,17541,17542,17550],{},[9172,17543,17544,17546,17548],{},[898,17545,900],{},[2138,17547,2287],{},[2005,17549,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,17551,17552,17554,17556],{},[898,17553,900],{},[2138,17555,2140],{},[2005,17557,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,17559,2007],{},[2334,17561,17562],{"scriptlevel":2336,"displaystyle":2013},[2338,17563,17564,17572],{},[9172,17565,17566,17568,17570],{},[898,17567,3946],{},[2138,17569,2287],{},[2005,17571,4360],{},[9172,17573,17574,17576,17578],{},[898,17575,3946],{},[2138,17577,2140],{},[2005,17579,4360],{},[902,17581,17582],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,17585,17587],{"className":17586},[886],[888,17588,17589],{"xmlns":890},[892,17590,17591,17623],{},[895,17592,17593,17595,17597,17599,17601,17603],{},[898,17594,2826],{},[898,17596,4003],{},[898,17598,1852],{},[898,17600,8679],{},[2005,17602,2007],{},[2334,17604,17605],{"scriptlevel":2336,"displaystyle":2013},[2338,17606,17607,17615],{},[9172,17608,17609,17611,17613],{},[898,17610,3946],{},[2138,17612,2287],{},[2005,17614,4360],{},[9172,17616,17617,17619,17621],{},[898,17618,3946],{},[2138,17620,2140],{},[2005,17622,4360],{},[902,17624,17625],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,17627,17629],{"id":17628},"minimalizace-výdajů","Minimalizace výdajů",[724,17631,17632,17633,1644],{},"Podmínka dané užitečnosti ",[883,17634,17636],{"className":17635},[886],[888,17637,17638],{"xmlns":890},[892,17639,17640,17670],{},[895,17641,17642,17648,17650,17652,17654,17660,17662,17668],{},[2133,17643,17644,17646],{},[898,17645,900],{},[2005,17647,4360],{},[2005,17649,2007],{},[898,17651,900],{},[2005,17653,2014],{"stretchy":2013},[2281,17655,17656,17658],{},[898,17657,2797],{},[2138,17659,2287],{},[2005,17661,2295],{"separator":2294},[2281,17663,17664,17666],{},[898,17665,2797],{},[2138,17667,2140],{},[2005,17669,2020],{"stretchy":2013},[902,17671,17672],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,17674,17675],{},[883,17676,17678],{"className":17677},[886],[888,17679,17680],{"xmlns":890},[892,17681,17682,17776],{},[895,17683,17684,17686,17688,17694,17696,17702,17704,17706,17708,17710,17718,17724,17726,17734,17740,17742,17744,17746,17752,17754,17756,17758,17764,17766,17772,17774],{},[898,17685,9801],{},[2005,17687,2014],{"stretchy":2013},[2281,17689,17690,17692],{},[898,17691,2797],{},[2138,17693,2287],{},[2005,17695,2295],{"separator":2294},[2281,17697,17698,17700],{},[898,17699,2797],{},[2138,17701,2140],{},[2005,17703,2295],{"separator":2294},[898,17705,16450],{},[2005,17707,2020],{"stretchy":2013},[2005,17709,2007],{},[9172,17711,17712,17714,17716],{},[898,17713,3946],{},[2138,17715,2287],{},[2005,17717,4360],{},[2281,17719,17720,17722],{},[898,17721,2797],{},[2138,17723,2287],{},[2005,17725,2104],{},[9172,17727,17728,17730,17732],{},[898,17729,3946],{},[2138,17731,2140],{},[2005,17733,4360],{},[2281,17735,17736,17738],{},[898,17737,2797],{},[2138,17739,2140],{},[2005,17741,2104],{},[898,17743,16450],{},[2005,17745,2014],{"stretchy":2013},[2133,17747,17748,17750],{},[898,17749,900],{},[2005,17751,4360],{},[2005,17753,2234],{},[898,17755,900],{},[2005,17757,2014],{"stretchy":2013},[2281,17759,17760,17762],{},[898,17761,2797],{},[2138,17763,2287],{},[2005,17765,2295],{"separator":2294},[2281,17767,17768,17770],{},[898,17769,2797],{},[2138,17771,2140],{},[2005,17773,2020],{"stretchy":2013},[2005,17775,2020],{"stretchy":2013},[902,17777,17778],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,17780,17781,17782,1644],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,17783,17785],{"className":17784},[886],[888,17786,17787],{"xmlns":890},[892,17788,17789,17828],{},[895,17790,17791,17798,17800,17806,17808,17814,17816,17822,17824,17826],{},[2281,17792,17793,17795],{},[898,17794,2797],{},[898,17796,17797],{},"i",[2005,17799,2007],{},[2281,17801,17802,17804],{},[898,17803,1860],{},[898,17805,17797],{},[2005,17807,2014],{"stretchy":2013},[2281,17809,17810,17812],{},[898,17811,3946],{},[2138,17813,2287],{},[2005,17815,2295],{"separator":2294},[2281,17817,17818,17820],{},[898,17819,3946],{},[2138,17821,2140],{},[2005,17823,2295],{"separator":2294},[898,17825,900],{},[2005,17827,2020],{"stretchy":2013},[902,17829,17830],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,17832,3800],{"id":3799},[120,17834,17835,17842,17849,17858],{},[123,17836,17837,2212,17839],{},[38,17838,3807],{},[207,17840,784],{"className":17841,"dataFsResolvedFilePath":782,"href":783},[210],[123,17843,17844,2212,17846],{},[38,17845,3815],{},[207,17847,11946],{"className":17848,"dataFsResolvedFilePath":800,"href":801},[210],[123,17850,17851,2212,17854,17857],{},[38,17852,17853],{},"Aplikace v kurzu:",[207,17855,880],{"className":17856,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,17859,17860,2212,17862,1343,17865,17868],{},[38,17861,3823],{},[207,17863,936],{"className":17864,"dataFsResolvedFilePath":934,"href":935},[210],[207,17866,1400],{"className":17867,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":17870},[17871,17872,17873,17874,17875,17876,17880],{"id":16418,"depth":642,"text":16419},{"id":3259,"depth":642,"text":3260},{"id":3333,"depth":642,"text":3334},{"id":17033,"depth":642,"text":17034},{"id":17145,"depth":642,"text":17146},{"id":17247,"depth":642,"text":17248,"children":17877},[17878,17879],{"id":17251,"depth":649,"text":17252},{"id":17628,"depth":649,"text":17629},{"id":3799,"depth":642,"text":3800},[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":16287,"description":17882},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,17889,17890],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":17893,"title":936,"body":17894,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":27760,"navigation":664,"path":27761,"seo":27762,"sources":27763,"stem":27764,"tags":27765,"type":3865,"updated":677,"__hash__":27769},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":17895,"toc":27722},[17896,17899,17901,18024,18159,18163,18166,18279,18283,18311,18358,18361,18427,18471,18474,18500,18531,18535,18539,18583,18627,18689,18744,18747,18751,18754,18801,18898,19004,19010,19087,19116,19255,19259,19288,19338,19485,19575,19579,19605,19643,19670,19708,19770,19845,19923,19981,20047,20091,20095,20153,20202,20247,20460,20580,20586,20590,20613,20617,20624,20628,20659,20694,20698,20748,20836,20878,20899,20961,21021,21025,21096,21164,21236,21351,21399,21403,21406,21447,21486,21509,21623,21787,21795,21822,21852,21855,21932,22085,22169,22508,22512,22636,22772,22908,22961,22964,23214,23294,23298,23301,23359,23391,23394,23443,23446,23517,23713,23717,23868,24098,24136,24189,24235,24238,24294,24343,24547,24637,24641,24657,24664,24833,24837,24908,24989,25070,25149,25295,25383,25387,25570,25701,25746,25843,25847,26586,26588,27639,27641],[12,17897,936],{"id":17898},"národní-důchod",[115,17900,12012],{"id":12011},[724,17902,17903,17904,2212,17908,17911,17912,2212,17915,17928,17929,17932,17933,17936,17937,17940,17941,17943,17944,2212,17946,17963,17964,17981,17982,17985,17986,3927],{},"Kapitola 7 ",[207,17905,17907],{"className":17906,"dataFsResolvedFilePath":1641,"href":1642},[210],"Matematické ekonomie",[38,17909,17910],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,17913,17914],{},"národním důchodem",[883,17916,17918],{"className":17917},[886],[888,17919,17920],{"xmlns":890},[892,17921,17922,17926],{},[895,17923,17924],{},[898,17925,9134],{},[902,17927,9134],{"encoding":904},". Budují se postupně bohatší modely — ",[38,17930,17931],{},"C-I"," (jen spotřeba a investice) → ",[38,17934,17935],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,17938,17939],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,17942,12017],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,17945,13891],{},[883,17947,17949],{"className":17948},[886],[888,17950,17951],{"xmlns":890},[892,17952,17953,17961],{},[895,17954,17955],{},[2133,17956,17957,17959],{},[898,17958,9134],{},[898,17960,1868],{},[902,17962,13909],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,17965,17967],{"className":17966},[886],[888,17968,17969],{"xmlns":890},[892,17970,17971,17979],{},[895,17972,17973],{},[2133,17974,17975,17977],{},[898,17976,9134],{},[898,17978,1868],{},[902,17980,13909],{"encoding":904}," na exogenní veličiny popisují ",[38,17983,17984],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,17987,17989],{"className":17988},[886],[888,17990,17991],{"xmlns":890},[892,17992,17993,18021],{},[895,17994,17995,17997,17999,18001,18003,18005,18007,18009,18011,18013,18015,18017,18019],{},[2138,17996,2287],{},[898,17998,4680],{"mathvariant":2385},[2005,18000,2014],{"stretchy":2013},[2138,18002,2287],{},[2005,18004,2234],{},[898,18006,207],{},[2005,18008,2020],{"stretchy":2013},[2005,18010,2007],{},[2138,18012,2287],{},[898,18014,4680],{"mathvariant":2385},[898,18016,2826],{},[898,18018,3946],{},[898,18020,8679],{},[902,18022,18023],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[3876,18025,18026],{},[724,18027,18028,18030,18031,18034,18035,18053,18054,18084,18085,18132,18133,18135,18136,18158],{},[883,18029,4164],{}," Intuice\n",[38,18032,18033],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,18036,18038],{"className":18037},[886],[888,18039,18040],{"xmlns":890},[892,18041,18042,18050],{},[895,18043,18044,18046,18048],{},[898,18045,2826],{},[898,18047,3946],{},[898,18049,1852],{},[902,18051,18052],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,18055,18057],{"className":18056},[886],[888,18058,18059],{"xmlns":890},[892,18060,18061,18081],{},[895,18062,18063,18065,18067,18069,18071,18073,18075,18077,18079],{},[898,18064,2826],{},[898,18066,3946],{},[898,18068,8679],{},[2005,18070,2007],{},[2138,18072,2287],{},[2005,18074,2234],{},[898,18076,2826],{},[898,18078,3946],{},[898,18080,1852],{},[902,18082,18083],{"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 ",[883,18086,18088],{"className":18087},[886],[888,18089,18090],{"xmlns":890},[892,18091,18092,18129],{},[895,18093,18094,18096,18098,18100,18102,18108,18110,18113,18115,18117,18119,18121,18123,18125,18127],{},[2138,18095,2287],{},[2005,18097,2104],{},[898,18099,207],{},[2005,18101,2104],{},[2133,18103,18104,18106],{},[898,18105,207],{},[2138,18107,2140],{},[2005,18109,2104],{},[2005,18111,18112],{},"⋯",[2005,18114,2007],{},[2138,18116,2287],{},[898,18118,4680],{"mathvariant":2385},[2005,18120,2014],{"stretchy":2013},[2138,18122,2287],{},[2005,18124,2234],{},[898,18126,207],{},[2005,18128,2020],{"stretchy":2013},[902,18130,18131],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,18134,12017],{}," 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 ",[883,18137,18139],{"className":18138},[886],[888,18140,18141],{"xmlns":890},[892,18142,18143,18155],{},[895,18144,18145,18147,18149,18151,18153],{},[2005,18146,2014],{"stretchy":2013},[898,18148,9134],{},[2005,18150,2295],{"separator":2294},[898,18152,12047],{},[2005,18154,2020],{"stretchy":2013},[902,18156,18157],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,18160,18162],{"id":18161},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,18164,18165],{},"Po prostudování kapitoly by čtenář měl umět:",[120,18167,18168,18171,18174,18177,18180,18183,18186,18276],{},[123,18169,18170],{},"popsat zjednodušený model národní ekonomiky,",[123,18172,18173],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,18175,18176],{},"popsat lineární model spotřeby a úspor,",[123,18178,18179],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,18181,18182],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,18184,18185],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,18187,18188,18189,1343,18206,1343,18228,3894,18253,18275],{},"popsat modely ",[883,18190,18192],{"className":18191},[886],[888,18193,18194],{"xmlns":890},[892,18195,18196,18204],{},[895,18197,18198,18200,18202],{},[898,18199,1852],{},[2297,18201,12296],{},[898,18203,12190],{},[902,18205,12301],{"encoding":904},[883,18207,18209],{"className":18208},[886],[888,18210,18211],{"xmlns":890},[892,18212,18213,18225],{},[895,18214,18215,18217,18219,18221,18223],{},[898,18216,1852],{},[2297,18218,12296],{},[898,18220,12190],{},[2297,18222,12296],{},[898,18224,12118],{},[902,18226,18227],{"encoding":904},"C\\text{-}I\\text{-}G",[883,18229,18231],{"className":18230},[886],[888,18232,18233],{"xmlns":890},[892,18234,18235,18251],{},[895,18236,18237,18239,18241,18243,18245,18247,18249],{},[898,18238,1852],{},[2297,18240,12296],{},[898,18242,12190],{},[2297,18244,12296],{},[898,18246,12118],{},[2297,18248,12296],{},[898,18250,12326],{},[902,18252,12329],{"encoding":904},[883,18254,18256],{"className":18255},[886],[888,18257,18258],{"xmlns":890},[892,18259,18260,18272],{},[895,18261,18262,18264,18266,18268,18270],{},[898,18263,12190],{},[898,18265,8679],{},[2297,18267,12296],{},[898,18269,9801],{},[898,18271,2826],{},[902,18273,18274],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,18277,18278],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,18280,18282],{"id":18281},"gnp-a-národní-důchod","GNP a národní důchod",[724,18284,18285,2212,18288,10030,18307,18310],{},[38,18286,18287],{},"Hrubý národní produkt",[883,18289,18291],{"className":18290},[886],[888,18292,18293],{"xmlns":890},[892,18294,18295,18304],{},[895,18296,18297,18299,18302],{},[898,18298,12118],{},[898,18300,18301],{},"N",[898,18303,3946],{},[902,18305,18306],{"encoding":904},"GNP",[614,18308,18309],{},"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:",[724,18312,18313],{},[883,18314,18316],{"className":18315},[886],[888,18317,18318],{"xmlns":890},[892,18319,18320,18355],{},[895,18321,18322,18324,18326,18328,18330,18332,18334,18336,18338,18340,18342,18344,18346,18348,18350,18353],{},[898,18323,12118],{},[898,18325,18301],{},[898,18327,3946],{},[2005,18329,2007],{},[898,18331,1852],{},[2005,18333,2104],{},[898,18335,12190],{},[2005,18337,2104],{},[898,18339,12118],{},[2005,18341,2104],{},[898,18343,12326],{},[2005,18345,2295],{"separator":2294},[5884,18347],{"width":5886},[2005,18349,2014],{"stretchy":2013},[2138,18351,18352],{},"7.1",[2005,18354,2020],{"stretchy":2013},[902,18356,18357],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,18359,18360],{},"kde",[120,18362,18363,18379,18395,18411],{},[123,18364,18365,18378],{},[883,18366,18368],{"className":18367},[886],[888,18369,18370],{"xmlns":890},[892,18371,18372,18376],{},[895,18373,18374],{},[898,18375,1852],{},[902,18377,1852],{"encoding":904}," — výdaje domácností na spotřebu,",[123,18380,18381,18394],{},[883,18382,18384],{"className":18383},[886],[888,18385,18386],{"xmlns":890},[892,18387,18388,18392],{},[895,18389,18390],{},[898,18391,12190],{},[902,18393,12190],{"encoding":904}," — hrubé domácí investice,",[123,18396,18397,18410],{},[883,18398,18400],{"className":18399},[886],[888,18401,18402],{"xmlns":890},[892,18403,18404,18408],{},[895,18405,18406],{},[898,18407,12118],{},[902,18409,12118],{"encoding":904}," — vládní výdaje,",[123,18412,18413,18426],{},[883,18414,18416],{"className":18415},[886],[888,18417,18418],{"xmlns":890},[892,18419,18420,18424],{},[895,18421,18422],{},[898,18423,12326],{},[902,18425,12326],{"encoding":904}," — čistý export.",[724,18428,18429,18430,18447,18448,18451,18452,2212,18454,10030,18467,18470],{},"K měření ",[883,18431,18433],{"className":18432},[886],[888,18434,18435],{"xmlns":890},[892,18436,18437,18445],{},[895,18438,18439,18441,18443],{},[898,18440,12118],{},[898,18442,18301],{},[898,18444,3946],{},[902,18446,18306],{"encoding":904}," se užívá ",[38,18449,18450],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,18453,1762],{},[883,18455,18457],{"className":18456},[886],[888,18458,18459],{"xmlns":890},[892,18460,18461,18465],{},[895,18462,18463],{},[898,18464,9134],{},[902,18466,9134],{"encoding":904},[614,18468,18469],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,18472,18473],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,18475,18476],{},[883,18477,18479],{"className":18478},[886],[888,18480,18481],{"xmlns":890},[892,18482,18483,18497],{},[895,18484,18485,18487,18489,18491,18493,18495],{},[898,18486,12118],{},[898,18488,18301],{},[898,18490,3946],{},[2005,18492,2739],{},[898,18494,9134],{},[2005,18496,2295],{"separator":2294},[902,18498,18499],{"encoding":904},"GNP \\approx Y,",[724,18501,18502,18503,10030,18506,18509,18510,18523,18524,18527,18528,1644],{},"a užívá se společného názvu ",[38,18504,18505],{},"důchod",[614,18507,18508],{},"income",") s označením ",[883,18511,18513],{"className":18512},[886],[888,18514,18515],{"xmlns":890},[892,18516,18517,18521],{},[895,18518,18519],{},[898,18520,9134],{},[902,18522,9134],{"encoding":904},". Domácnosti důchod použijí ke ",[38,18525,18526],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,18529,18530],{},"úspor",[115,18532,18534],{"id":18533},"spotřeba-a-úspory","Spotřeba a úspory",[198,18536,18538],{"id":18537},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,18540,18541,18542,18555,18556,18569,18570,2713],{},"Jak spotřeba ",[883,18543,18545],{"className":18544},[886],[888,18546,18547],{"xmlns":890},[892,18548,18549,18553],{},[895,18550,18551],{},[898,18552,1852],{},[902,18554,1852],{"encoding":904},", tak úspory ",[883,18557,18559],{"className":18558},[886],[888,18560,18561],{"xmlns":890},[892,18562,18563,18567],{},[895,18564,18565],{},[898,18566,8679],{},[902,18568,8679],{"encoding":904}," závisejí na důchodu ",[883,18571,18573],{"className":18572},[886],[888,18574,18575],{"xmlns":890},[892,18576,18577,18581],{},[895,18578,18579],{},[898,18580,9134],{},[902,18582,9134],{"encoding":904},[724,18584,18585],{},[883,18586,18588],{"className":18587},[886],[888,18589,18590],{"xmlns":890},[892,18591,18592,18624],{},[895,18593,18594,18596,18598,18600,18602,18604,18606,18608,18610,18612,18614,18616,18618,18620,18622],{},[898,18595,1852],{},[2005,18597,2007],{},[898,18599,1852],{},[2005,18601,2014],{"stretchy":2013},[898,18603,9134],{},[2005,18605,2020],{"stretchy":2013},[2005,18607,2295],{"separator":2294},[5884,18609],{"width":5886},[898,18611,8679],{},[2005,18613,2007],{},[898,18615,8679],{},[2005,18617,2014],{"stretchy":2013},[898,18619,9134],{},[2005,18621,2020],{"stretchy":2013},[898,18623,1644],{"mathvariant":2385},[902,18625,18626],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,18628,18629,8108,18648,10030,18651,18654,18655,8108,18675,10030,18678,18681,18682,3894,18685,18688],{},[883,18630,18632],{"className":18631},[886],[888,18633,18634],{"xmlns":890},[892,18635,18636,18646],{},[895,18637,18638,18640,18642,18644],{},[898,18639,1852],{},[2005,18641,2014],{"stretchy":2013},[898,18643,9134],{},[2005,18645,2020],{"stretchy":2013},[902,18647,14222],{"encoding":904},[38,18649,18650],{},"funkce spotřeby",[614,18652,18653],{},"consumption function","), ",[883,18656,18658],{"className":18657},[886],[888,18659,18660],{"xmlns":890},[892,18661,18662,18672],{},[895,18663,18664,18666,18668,18670],{},[898,18665,8679],{},[2005,18667,2014],{"stretchy":2013},[898,18669,9134],{},[2005,18671,2020],{"stretchy":2013},[902,18673,18674],{"encoding":904},"S(Y)",[38,18676,18677],{},"funkce úspor",[614,18679,18680],{},"savings function","); jejich grafy se nazývají ",[38,18683,18684],{},"křivka spotřeby",[38,18686,18687],{},"křivka úspor",". Platí základní identita",[724,18690,18691],{},[883,18692,18694],{"className":18693},[886],[888,18695,18696],{"xmlns":890},[892,18697,18698,18741],{},[895,18699,18700,18702,18704,18706,18708,18710,18712,18714,18716,18718,18720,18722,18724,18726,18728,18730,18732,18734,18736,18739],{},[898,18701,9134],{},[2005,18703,2007],{},[898,18705,1852],{},[2005,18707,2104],{},[898,18709,8679],{},[2005,18711,2007],{},[898,18713,1852],{},[2005,18715,2014],{"stretchy":2013},[898,18717,9134],{},[2005,18719,2020],{"stretchy":2013},[2005,18721,2104],{},[898,18723,8679],{},[2005,18725,2014],{"stretchy":2013},[898,18727,9134],{},[2005,18729,2020],{"stretchy":2013},[898,18731,1644],{"mathvariant":2385},[5884,18733],{"width":5886},[2005,18735,2014],{"stretchy":2013},[2138,18737,18738],{},"7.2",[2005,18740,2020],{"stretchy":2013},[902,18742,18743],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,18745,18746],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,18748,18750],{"id":18749},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,18752,18753],{},"Nejjednodušší model předpokládá lineární tvar",[724,18755,18756],{},[883,18757,18759],{"className":18758},[886],[888,18760,18761],{"xmlns":890},[892,18762,18763,18798],{},[895,18764,18765,18767,18769,18771,18773,18775,18777,18779,18781,18783,18785,18787,18789,18791,18793,18796],{},[898,18766,1852],{},[2005,18768,2007],{},[898,18770,1852],{},[2005,18772,2014],{"stretchy":2013},[898,18774,9134],{},[2005,18776,2020],{"stretchy":2013},[2005,18778,2007],{},[898,18780,207],{},[898,18782,9134],{},[2005,18784,2104],{},[898,18786,2107],{},[2005,18788,2295],{"separator":2294},[5884,18790],{"width":5886},[2005,18792,2014],{"stretchy":2013},[2138,18794,18795],{},"7.3",[2005,18797,2020],{"stretchy":2013},[902,18799,18800],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,18802,4316,18803,3894,18821,18843,18844,18884,18885,1644],{},[883,18804,18806],{"className":18805},[886],[888,18807,18808],{"xmlns":890},[892,18809,18810,18818],{},[895,18811,18812,18814,18816],{},[898,18813,2107],{},[2005,18815,3416],{},[2138,18817,2336],{},[902,18819,18820],{"encoding":904},"b > 0",[883,18822,18824],{"className":18823},[886],[888,18825,18826],{"xmlns":890},[892,18827,18828,18840],{},[895,18829,18830,18832,18834,18836,18838],{},[2138,18831,2336],{},[2005,18833,3455],{},[898,18835,207],{},[2005,18837,3455],{},[2138,18839,2287],{},[902,18841,18842],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,18845,18847],{"className":18846},[886],[888,18848,18849],{"xmlns":890},[892,18850,18851,18881],{},[895,18852,18853,18855,18857,18864,18866,18869,18871,18873,18875,18877,18879],{},[898,18854,207],{},[2005,18856,2007],{},[895,18858,18859,18862],{},[898,18860,18861],{"mathvariant":2385},"t",[898,18863,11045],{"mathvariant":2385},[2297,18865,2995],{},[898,18867,18868],{},"α",[2005,18870,2007],{},[898,18872,2897],{"mathvariant":2385},[898,18874,1852],{},[898,18876,4680],{"mathvariant":2385},[898,18878,2897],{"mathvariant":2385},[898,18880,9134],{},[902,18882,18883],{"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 ",[883,18886,18888],{"className":18887},[886],[888,18889,18890],{"xmlns":890},[892,18891,18892,18896],{},[895,18893,18894],{},[898,18895,9134],{},[902,18897,9134],{"encoding":904},[724,18899,18900],{},[614,18901,18902,18903,18927,18928,18966,18967,18983,18984,1644],{},"Obrázek 7.1 — Přímka spotřeby ",[883,18904,18906],{"className":18905},[886],[888,18907,18908],{"xmlns":890},[892,18909,18910,18924],{},[895,18911,18912,18914,18916,18918,18920,18922],{},[898,18913,1852],{},[2005,18915,2007],{},[898,18917,207],{},[898,18919,9134],{},[2005,18921,2104],{},[898,18923,2107],{},[902,18925,18926],{"encoding":904},"C = aY + b"," se směrnicí ",[883,18929,18931],{"className":18930},[886],[888,18932,18933],{"xmlns":890},[892,18934,18935,18963],{},[895,18936,18937,18939,18941,18947,18949,18951,18953,18955,18957,18959,18961],{},[898,18938,207],{},[2005,18940,2007],{},[895,18942,18943,18945],{},[898,18944,18861],{"mathvariant":2385},[898,18946,11045],{"mathvariant":2385},[2297,18948,2995],{},[898,18950,18868],{},[2005,18952,2007],{},[898,18954,2897],{"mathvariant":2385},[898,18956,1852],{},[898,18958,4680],{"mathvariant":2385},[898,18960,2897],{"mathvariant":2385},[898,18962,9134],{},[902,18964,18965],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,18968,18970],{"className":18969},[886],[888,18971,18972],{"xmlns":890},[892,18973,18974,18980],{},[895,18975,18976,18978],{},[898,18977,2897],{"mathvariant":2385},[898,18979,1852],{},[902,18981,18982],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,18985,18987],{"className":18986},[886],[888,18988,18989],{"xmlns":890},[892,18990,18991,19001],{},[895,18992,18993,18995,18997,18999],{},[898,18994,2897],{"mathvariant":2385},[898,18996,9134],{},[2005,18998,2007],{},[2138,19000,2287],{},[902,19002,19003],{"encoding":904},"\\Delta Y = 1",[724,19005,19006,19007,2713],{},"Dosazením do (7.2) plyne ",[38,19008,19009],{},"lineární model úspor",[724,19011,19012],{},[883,19013,19015],{"className":19014},[886],[888,19016,19017],{"xmlns":890},[892,19018,19019,19084],{},[895,19020,19021,19023,19025,19027,19029,19031,19033,19035,19037,19039,19041,19043,19045,19047,19049,19051,19053,19055,19057,19059,19061,19063,19065,19067,19069,19071,19073,19075,19077,19079,19082],{},[898,19022,8679],{},[2005,19024,2007],{},[898,19026,9134],{},[2005,19028,2234],{},[898,19030,1852],{},[2005,19032,2014],{"stretchy":2013},[898,19034,9134],{},[2005,19036,2020],{"stretchy":2013},[2005,19038,2007],{},[898,19040,9134],{},[2005,19042,2234],{},[2005,19044,2014],{"stretchy":2013},[898,19046,207],{},[898,19048,9134],{},[2005,19050,2104],{},[898,19052,2107],{},[2005,19054,2020],{"stretchy":2013},[2005,19056,2007],{},[2005,19058,2014],{"stretchy":2013},[2138,19060,2287],{},[2005,19062,2234],{},[898,19064,207],{},[2005,19066,2020],{"stretchy":2013},[898,19068,9134],{},[2005,19070,2234],{},[898,19072,2107],{},[898,19074,1644],{"mathvariant":2385},[5884,19076],{"width":5886},[2005,19078,2014],{"stretchy":2013},[2138,19080,19081],{},"7.4",[2005,19083,2020],{"stretchy":2013},[902,19085,19086],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,19088,19089,19090,3927],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,19091,19093],{"className":19092},[886],[888,19094,19095],{"xmlns":890},[892,19096,19097,19113],{},[895,19098,19099,19101,19103,19105,19107,19109,19111],{},[2138,19100,2336],{},[2005,19102,3455],{},[2138,19104,2287],{},[2005,19106,2234],{},[898,19108,207],{},[2005,19110,3455],{},[2138,19112,2287],{},[902,19114,19115],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,19117,19118],{},[614,19119,19120,19121,3894,19144,19176,19177,2633,19190,19220,19221,2633,19239,1644],{},"Obrázek 7.2 — Přímky ",[883,19122,19124],{"className":19123},[886],[888,19125,19126],{"xmlns":890},[892,19127,19128,19142],{},[895,19129,19130,19132,19134,19136,19138,19140],{},[898,19131,1852],{},[2005,19133,2007],{},[898,19135,207],{},[898,19137,9134],{},[2005,19139,2104],{},[898,19141,2107],{},[902,19143,18926],{"encoding":904},[883,19145,19147],{"className":19146},[886],[888,19148,19149],{"xmlns":890},[892,19150,19151,19173],{},[895,19152,19153,19155,19157,19159,19161,19163,19165,19167,19169,19171],{},[898,19154,8679],{},[2005,19156,2007],{},[2005,19158,2014],{"stretchy":2013},[2138,19160,2287],{},[2005,19162,2234],{},[898,19164,207],{},[2005,19166,2020],{"stretchy":2013},[898,19168,9134],{},[2005,19170,2234],{},[898,19172,2107],{},[902,19174,19175],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,19178,19180],{"className":19179},[886],[888,19181,19182],{"xmlns":890},[892,19183,19184,19188],{},[895,19185,19186],{},[898,19187,9134],{},[902,19189,9134],{"encoding":904},[883,19191,19193],{"className":19192},[886],[888,19194,19195],{"xmlns":890},[892,19196,19197,19217],{},[895,19198,19199,19201,19203,19205,19207,19209,19211,19213,19215],{},[898,19200,9134],{},[2005,19202,2007],{},[898,19204,2107],{},[898,19206,4680],{"mathvariant":2385},[2005,19208,2014],{"stretchy":2013},[2138,19210,2287],{},[2005,19212,2234],{},[898,19214,207],{},[2005,19216,2020],{"stretchy":2013},[902,19218,19219],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,19222,19224],{"className":19223},[886],[888,19225,19226],{"xmlns":890},[892,19227,19228,19236],{},[895,19229,19230,19232,19234],{},[898,19231,1852],{},[2005,19233,2295],{"separator":2294},[898,19235,8679],{},[902,19237,19238],{"encoding":904},"C, S",[883,19240,19242],{"className":19241},[886],[888,19243,19244],{"xmlns":890},[892,19245,19246,19252],{},[895,19247,19248,19250],{},[2005,19249,2234],{},[898,19251,2107],{},[902,19253,19254],{"encoding":904},"-b",[198,19256,19258],{"id":19257},"příklad-71","Příklad 7.1",[724,19260,19261,19262,19287],{},"Pro spotřebu ",[883,19263,19265],{"className":19264},[886],[888,19266,19267],{"xmlns":890},[892,19268,19269,19284],{},[895,19270,19271,19273,19275,19278,19280,19282],{},[898,19272,1852],{},[2005,19274,2007],{},[2138,19276,19277],{},"0,4",[898,19279,9134],{},[2005,19281,2104],{},[2138,19283,2871],{},[902,19285,19286],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,19289,19290],{},[883,19291,19293],{"className":19292},[886],[888,19294,19295],{"xmlns":890},[892,19296,19297,19335],{},[895,19298,19299,19301,19303,19305,19307,19309,19311,19313,19315,19317,19319,19321,19323,19325,19328,19330,19332],{},[898,19300,8679],{},[2005,19302,2007],{},[898,19304,9134],{},[2005,19306,2234],{},[898,19308,1852],{},[2005,19310,2007],{},[898,19312,9134],{},[2005,19314,2234],{},[2138,19316,19277],{},[898,19318,9134],{},[2005,19320,2234],{},[2138,19322,2871],{},[2005,19324,2007],{},[2138,19326,19327],{},"0,6",[898,19329,9134],{},[2005,19331,2234],{},[2138,19333,19334],{},"10.",[902,19336,19337],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,19339,19340],{},[614,19341,19342,19343,3894,19366,19390,19391,8108,19404,19428,19429,8108,19446,19462,19463,1644],{},"Obrázek 7.3 — Přímky ",[883,19344,19346],{"className":19345},[886],[888,19347,19348],{"xmlns":890},[892,19349,19350,19364],{},[895,19351,19352,19354,19356,19358,19360,19362],{},[898,19353,1852],{},[2005,19355,2007],{},[2138,19357,19277],{},[898,19359,9134],{},[2005,19361,2104],{},[2138,19363,2871],{},[902,19365,19286],{"encoding":904},[883,19367,19369],{"className":19368},[886],[888,19370,19371],{"xmlns":890},[892,19372,19373,19387],{},[895,19374,19375,19377,19379,19381,19383,19385],{},[898,19376,8679],{},[2005,19378,2007],{},[2138,19380,19327],{},[898,19382,9134],{},[2005,19384,2234],{},[2138,19386,2871],{},[902,19388,19389],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,19392,19394],{"className":19393},[886],[888,19395,19396],{"xmlns":890},[892,19397,19398,19402],{},[895,19399,19400],{},[898,19401,9134],{},[902,19403,9134],{"encoding":904},[883,19405,19407],{"className":19406},[886],[888,19408,19409],{"xmlns":890},[892,19410,19411,19425],{},[895,19412,19413,19415,19418],{},[2005,19414,2739],{},[2138,19416,19417],{},"16,",[8392,19419,19420,19422],{"accent":2294},[2138,19421,2244],{},[2005,19423,19424],{},"ˉ",[902,19426,19427],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,19430,19432],{"className":19431},[886],[888,19433,19434],{"xmlns":890},[892,19435,19436,19444],{},[895,19437,19438,19440,19442],{},[898,19439,1852],{},[2005,19441,2295],{"separator":2294},[898,19443,8679],{},[902,19445,19238],{"encoding":904},[883,19447,19449],{"className":19448},[886],[888,19450,19451],{"xmlns":890},[892,19452,19453,19459],{},[895,19454,19455,19457],{},[2005,19456,2234],{},[2138,19458,2871],{},[902,19460,19461],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,19464,19466],{"className":19465},[886],[888,19467,19468],{"xmlns":890},[892,19469,19470,19482],{},[895,19471,19472,19474,19476,19478,19480],{},[2005,19473,2014],{"stretchy":2013},[2138,19475,2336],{},[2005,19477,2295],{"separator":2294},[2138,19479,2871],{},[2005,19481,2020],{"stretchy":2013},[902,19483,19484],{"encoding":904},"(0, 10)",[724,19486,19487,19488,8108,19506,19536,19537,10030,19540,19543,19544,8108,19568,10030,19571,19574],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,19489,19491],{"className":19490},[886],[888,19492,19493],{"xmlns":890},[892,19494,19495,19503],{},[895,19496,19497,19499,19501],{},[898,19498,9134],{},[2005,19500,2007],{},[2138,19502,2336],{},[902,19504,19505],{"encoding":904},"Y = 0",[883,19507,19509],{"className":19508},[886],[888,19510,19511],{"xmlns":890},[892,19512,19513,19533],{},[895,19514,19515,19517,19519,19521,19523,19525,19527,19529,19531],{},[898,19516,8679],{},[2005,19518,2014],{"stretchy":2013},[2138,19520,2336],{},[2005,19522,2020],{"stretchy":2013},[2005,19524,2007],{},[2005,19526,2234],{},[898,19528,2107],{},[2005,19530,3455],{},[2138,19532,2336],{},[902,19534,19535],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,19538,19539],{},"autonomních úsporách",[614,19541,19542],{},"autonomous savings","). Analogicky ",[883,19545,19547],{"className":19546},[886],[888,19548,19549],{"xmlns":890},[892,19550,19551,19565],{},[895,19552,19553,19555,19557,19559,19561,19563],{},[898,19554,1852],{},[2005,19556,2014],{"stretchy":2013},[2138,19558,2336],{},[2005,19560,2020],{"stretchy":2013},[2005,19562,2007],{},[898,19564,2107],{},[902,19566,19567],{"encoding":904},"C(0) = b",[38,19569,19570],{},"autonomní spotřeba",[614,19572,19573],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,19576,19578],{"id":19577},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,19580,19581,2212,19584,10030,19601,19604],{},[38,19582,19583],{},"Mezní sklon ke spotřebě",[883,19585,19587],{"className":19586},[886],[888,19588,19589],{"xmlns":890},[892,19590,19591,19599],{},[895,19592,19593,19595,19597],{},[898,19594,2826],{},[898,19596,3946],{},[898,19598,1852],{},[902,19600,18052],{"encoding":904},[614,19602,19603],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,19606,19607],{},[883,19608,19610],{"className":19609},[886],[888,19611,19612],{"xmlns":890},[892,19613,19614,19640],{},[895,19615,19616,19618,19620,19622,19624,19638],{},[898,19617,2826],{},[898,19619,3946],{},[898,19621,1852],{},[2005,19623,2007],{},[2338,19625,19626,19632],{},[895,19627,19628,19630],{},[898,19629,2203],{"mathvariant":2385},[898,19631,1852],{},[895,19633,19634,19636],{},[898,19635,2203],{"mathvariant":2385},[898,19637,9134],{},[898,19639,1644],{"mathvariant":2385},[902,19641,19642],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,19644,19645,2212,19648,10030,19666,19669],{},[38,19646,19647],{},"Mezní sklon k úsporám",[883,19649,19651],{"className":19650},[886],[888,19652,19653],{"xmlns":890},[892,19654,19655,19663],{},[895,19656,19657,19659,19661],{},[898,19658,2826],{},[898,19660,3946],{},[898,19662,8679],{},[902,19664,19665],{"encoding":904},"MPS",[614,19667,19668],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,19671,19672],{},[883,19673,19675],{"className":19674},[886],[888,19676,19677],{"xmlns":890},[892,19678,19679,19705],{},[895,19680,19681,19683,19685,19687,19689,19703],{},[898,19682,2826],{},[898,19684,3946],{},[898,19686,8679],{},[2005,19688,2007],{},[2338,19690,19691,19697],{},[895,19692,19693,19695],{},[898,19694,2203],{"mathvariant":2385},[898,19696,8679],{},[895,19698,19699,19701],{},[898,19700,2203],{"mathvariant":2385},[898,19702,9134],{},[898,19704,1644],{"mathvariant":2385},[902,19706,19707],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,19709,19710,19711,19769],{},"Z (7.2) plyne ",[883,19712,19714],{"className":19713},[886],[888,19715,19716],{"xmlns":890},[892,19717,19718,19766],{},[895,19719,19720,19734,19736,19750,19752],{},[2338,19721,19722,19728],{},[895,19723,19724,19726],{},[898,19725,2203],{"mathvariant":2385},[898,19727,9134],{},[895,19729,19730,19732],{},[898,19731,2203],{"mathvariant":2385},[898,19733,9134],{},[2005,19735,2007],{},[2338,19737,19738,19744],{},[895,19739,19740,19742],{},[898,19741,2203],{"mathvariant":2385},[898,19743,1852],{},[895,19745,19746,19748],{},[898,19747,2203],{"mathvariant":2385},[898,19749,9134],{},[2005,19751,2104],{},[2338,19753,19754,19760],{},[895,19755,19756,19758],{},[898,19757,2203],{"mathvariant":2385},[898,19759,8679],{},[895,19761,19762,19764],{},[898,19763,2203],{"mathvariant":2385},[898,19765,9134],{},[902,19767,19768],{"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",[724,19771,19772],{},[883,19773,19775],{"className":19774},[886],[888,19776,19777],{"xmlns":890},[892,19778,19779,19842],{},[895,19780,19781,19833,19835,19837,19840],{},[12838,19782,19783],{"notation":12840},[2334,19784,19785],{"scriptlevel":2336,"displaystyle":2013},[2334,19786,19787],{"scriptlevel":2336,"displaystyle":2013},[2334,19788,19789],{"scriptlevel":2336,"displaystyle":2294},[895,19790,19791,19793,19795,19797,19799,19801,19803,19805,19807,19809,19811,19813,19815,19817,19819,19821,19823,19825,19827,19829,19831],{},[898,19792,2826],{},[898,19794,3946],{},[898,19796,1852],{},[2005,19798,2104],{},[898,19800,2826],{},[898,19802,3946],{},[898,19804,8679],{},[2005,19806,2007],{},[2138,19808,2287],{},[2005,19810,2295],{"separator":2294},[5884,19812],{"width":5886},[898,19814,2826],{},[898,19816,3946],{},[898,19818,8679],{},[2005,19820,2007],{},[2138,19822,2287],{},[2005,19824,2234],{},[898,19826,2826],{},[898,19828,3946],{},[898,19830,1852],{},[898,19832,1644],{"mathvariant":2385},[5884,19834],{"width":5886},[2005,19836,2014],{"stretchy":2013},[2138,19838,19839],{},"7.5",[2005,19841,2020],{"stretchy":2013},[902,19843,19844],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,19846,19847,2212,19850,19873,19874,3894,19896,19922],{},[38,19848,19849],{},"Pro lineární model",[883,19851,19853],{"className":19852},[886],[888,19854,19855],{"xmlns":890},[892,19856,19857,19871],{},[895,19858,19859,19861,19863,19865,19867,19869],{},[898,19860,1852],{},[2005,19862,2007],{},[898,19864,207],{},[898,19866,9134],{},[2005,19868,2104],{},[898,19870,2107],{},[902,19872,18926],{"encoding":904}," vychází ",[883,19875,19877],{"className":19876},[886],[888,19878,19879],{"xmlns":890},[892,19880,19881,19893],{},[895,19882,19883,19885,19887,19889,19891],{},[898,19884,2826],{},[898,19886,3946],{},[898,19888,1852],{},[2005,19890,2007],{},[898,19892,207],{},[902,19894,19895],{"encoding":904},"MPC = a",[883,19897,19899],{"className":19898},[886],[888,19900,19901],{"xmlns":890},[892,19902,19903,19919],{},[895,19904,19905,19907,19909,19911,19913,19915,19917],{},[898,19906,2826],{},[898,19908,3946],{},[898,19910,8679],{},[2005,19912,2007],{},[2138,19914,2287],{},[2005,19916,2234],{},[898,19918,207],{},[902,19920,19921],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,19924,19925,19928,19929,19951,19952,19980],{},[38,19926,19927],{},"Interpretace diferenciálem."," Pro pevné ",[883,19930,19932],{"className":19931},[886],[888,19933,19934],{"xmlns":890},[892,19935,19936,19948],{},[895,19937,19938,19940,19942],{},[898,19939,9134],{},[2005,19941,2007],{},[2133,19943,19944,19946],{},[898,19945,9134],{},[2005,19947,4360],{},[902,19949,19950],{"encoding":904},"Y = Y^*"," udává ",[883,19953,19955],{"className":19954},[886],[888,19956,19957],{"xmlns":890},[892,19958,19959,19977],{},[895,19960,19961,19963,19965,19967,19969,19975],{},[898,19962,2826],{},[898,19964,3946],{},[898,19966,1852],{},[2005,19968,2014],{"stretchy":2013},[2133,19970,19971,19973],{},[898,19972,9134],{},[2005,19974,4360],{},[2005,19976,2020],{"stretchy":2013},[902,19978,19979],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,19982,19983],{},[883,19984,19986],{"className":19985},[886],[888,19987,19988],{"xmlns":890},[892,19989,19990,20044],{},[895,19991,19992,19994,19996,19998,20000,20002,20004,20010,20012,20014,20016,20018,20020,20022,20024,20026,20028,20030,20032,20034,20036,20038,20040,20042],{},[898,19993,2897],{"mathvariant":2385},[898,19995,1852],{},[2005,19997,2739],{},[898,19999,2203],{"mathvariant":2385},[898,20001,1852],{},[2005,20003,2007],{},[2133,20005,20006,20008],{},[898,20007,1852],{},[2005,20009,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,20011,2014],{"stretchy":2013},[898,20013,9134],{},[2005,20015,2020],{"stretchy":2013},[2297,20017,2995],{},[898,20019,2203],{"mathvariant":2385},[898,20021,9134],{},[2005,20023,2007],{},[898,20025,2826],{},[898,20027,3946],{},[898,20029,1852],{},[2005,20031,2014],{"stretchy":2013},[898,20033,9134],{},[2005,20035,2020],{"stretchy":2013},[2297,20037,2995],{},[898,20039,2203],{"mathvariant":2385},[898,20041,9134],{},[898,20043,1644],{"mathvariant":2385},[902,20045,20046],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,20048,20049,20050,20086,20087,20090],{},"Analogicky ",[883,20051,20053],{"className":20052},[886],[888,20054,20055],{"xmlns":890},[892,20056,20057,20083],{},[895,20058,20059,20061,20063,20065,20067,20069,20071,20073,20075,20077,20079,20081],{},[898,20060,2897],{"mathvariant":2385},[898,20062,8679],{},[2005,20064,2739],{},[898,20066,2826],{},[898,20068,3946],{},[898,20070,8679],{},[2005,20072,2014],{"stretchy":2013},[898,20074,9134],{},[2005,20076,2020],{"stretchy":2013},[2297,20078,2995],{},[898,20080,2203],{"mathvariant":2385},[898,20082,9134],{},[902,20084,20085],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,20088,1145],{"className":20089,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,20092,20094],{"id":20093},"příklad-72","Příklad 7.2",[724,20096,19261,20097,20132,20133,20152],{},[883,20098,20100],{"className":20099},[886],[888,20101,20102],{"xmlns":890},[892,20103,20104,20129],{},[895,20105,20106,20108,20110,20113,20119,20121,20123,20125,20127],{},[898,20107,1852],{},[2005,20109,2007],{},[2138,20111,20112],{},"0,001",[2133,20114,20115,20117],{},[898,20116,9134],{},[2138,20118,2140],{},[2005,20120,2104],{},[2138,20122,2847],{},[898,20124,9134],{},[2005,20126,2104],{},[2138,20128,3128],{},[902,20130,20131],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,20134,20136],{"className":20135},[886],[888,20137,20138],{"xmlns":890},[892,20139,20140,20149],{},[895,20141,20142,20144,20146],{},[898,20143,9134],{},[2005,20145,3455],{},[2138,20147,20148],{},"400",[902,20150,20151],{"encoding":904},"Y \u003C 400",") platí",[724,20154,20155],{},[883,20156,20158],{"className":20157},[886],[888,20159,20160],{"xmlns":890},[892,20161,20162,20199],{},[895,20163,20164,20166,20168,20170,20172,20186,20188,20191,20193,20195,20197],{},[898,20165,2826],{},[898,20167,3946],{},[898,20169,1852],{},[2005,20171,2007],{},[2338,20173,20174,20180],{},[895,20175,20176,20178],{},[898,20177,2203],{"mathvariant":2385},[898,20179,1852],{},[895,20181,20182,20184],{},[898,20183,2203],{"mathvariant":2385},[898,20185,9134],{},[2005,20187,2007],{},[2138,20189,20190],{},"0,002",[898,20192,9134],{},[2005,20194,2104],{},[2138,20196,2847],{},[2005,20198,2295],{"separator":2294},[902,20200,20201],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,20203,20204],{},[883,20205,20207],{"className":20206},[886],[888,20208,20209],{"xmlns":890},[892,20210,20211,20244],{},[895,20212,20213,20215,20217,20219,20221,20223,20225,20227,20229,20231,20233,20235,20237,20239,20241],{},[898,20214,2826],{},[898,20216,3946],{},[898,20218,8679],{},[2005,20220,2007],{},[2138,20222,2287],{},[2005,20224,2234],{},[898,20226,2826],{},[898,20228,3946],{},[898,20230,1852],{},[2005,20232,2007],{},[2005,20234,2234],{},[2138,20236,20190],{},[898,20238,9134],{},[2005,20240,2104],{},[2138,20242,20243],{},"0,8.",[902,20245,20246],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,20248,20249,20329,20408],{},[123,20250,20251,1343,20279,20307,20308,8108,20326,1644],{},[883,20252,20254],{"className":20253},[886],[888,20255,20256],{"xmlns":890},[892,20257,20258,20276],{},[895,20259,20260,20262,20264,20266,20268,20270,20272,20274],{},[898,20261,2826],{},[898,20263,3946],{},[898,20265,1852],{},[2005,20267,2014],{"stretchy":2013},[2138,20269,3098],{},[2005,20271,2020],{"stretchy":2013},[2005,20273,2007],{},[2138,20275,19277],{},[902,20277,20278],{"encoding":904},"MPC(100) = 0{,}4",[883,20280,20282],{"className":20281},[886],[888,20283,20284],{"xmlns":890},[892,20285,20286,20304],{},[895,20287,20288,20290,20292,20294,20296,20298,20300,20302],{},[898,20289,2826],{},[898,20291,3946],{},[898,20293,8679],{},[2005,20295,2014],{"stretchy":2013},[2138,20297,3098],{},[2005,20299,2020],{"stretchy":2013},[2005,20301,2007],{},[2138,20303,19327],{},[902,20305,20306],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,20309,20311],{"className":20310},[886],[888,20312,20313],{"xmlns":890},[892,20314,20315,20323],{},[895,20316,20317,20319,20321],{},[898,20318,9134],{},[2005,20320,2007],{},[2138,20322,3098],{},[902,20324,20325],{"encoding":904},"Y = 100",[38,20327,20328],{},"větší sklon k úsporám",[123,20330,20331,1343,20359,20307,20387,8108,20405,1644],{},[883,20332,20334],{"className":20333},[886],[888,20335,20336],{"xmlns":890},[892,20337,20338,20356],{},[895,20339,20340,20342,20344,20346,20348,20350,20352,20354],{},[898,20341,2826],{},[898,20343,3946],{},[898,20345,1852],{},[2005,20347,2014],{"stretchy":2013},[2138,20349,8383],{},[2005,20351,2020],{"stretchy":2013},[2005,20353,2007],{},[2138,20355,19327],{},[902,20357,20358],{"encoding":904},"MPC(200) = 0{,}6",[883,20360,20362],{"className":20361},[886],[888,20363,20364],{"xmlns":890},[892,20365,20366,20384],{},[895,20367,20368,20370,20372,20374,20376,20378,20380,20382],{},[898,20369,2826],{},[898,20371,3946],{},[898,20373,8679],{},[2005,20375,2014],{"stretchy":2013},[2138,20377,8383],{},[2005,20379,2020],{"stretchy":2013},[2005,20381,2007],{},[2138,20383,19277],{},[902,20385,20386],{"encoding":904},"MPS(200) = 0{,}4",[883,20388,20390],{"className":20389},[886],[888,20391,20392],{"xmlns":890},[892,20393,20394,20402],{},[895,20395,20396,20398,20400],{},[898,20397,9134],{},[2005,20399,2007],{},[2138,20401,8383],{},[902,20403,20404],{"encoding":904},"Y = 200",[38,20406,20407],{},"větší sklon ke spotřebě",[123,20409,20410,20411,20429,20430,3927],{},"Přesně při ",[883,20412,20414],{"className":20413},[886],[888,20415,20416],{"xmlns":890},[892,20417,20418,20426],{},[895,20419,20420,20422,20424],{},[898,20421,9134],{},[2005,20423,2007],{},[2138,20425,8809],{},[902,20427,20428],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,20431,20433],{"className":20432},[886],[888,20434,20435],{"xmlns":890},[892,20436,20437,20457],{},[895,20438,20439,20441,20443,20445,20447,20449,20451,20453,20455],{},[898,20440,2826],{},[898,20442,3946],{},[898,20444,1852],{},[2005,20446,2007],{},[898,20448,2826],{},[898,20450,3946],{},[898,20452,8679],{},[2005,20454,2007],{},[2138,20456,5015],{},[902,20458,20459],{"encoding":904},"MPC = MPS = 0{,}5",[724,20461,20462,20463,20480,20481,20495,20496,2694,20509,20523,20524,20537,20538,20579],{},"Interpretace: při ",[883,20464,20466],{"className":20465},[886],[888,20467,20468],{"xmlns":890},[892,20469,20470,20478],{},[895,20471,20472,20474,20476],{},[898,20473,9134],{},[2005,20475,2007],{},[2138,20477,3098],{},[902,20479,20325],{"encoding":904}," se spotřeba mění ",[883,20482,20484],{"className":20483},[886],[888,20485,20486],{"xmlns":890},[892,20487,20488,20492],{},[895,20489,20490],{},[2138,20491,19277],{},[902,20493,20494],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,20497,20499],{"className":20498},[886],[888,20500,20501],{"xmlns":890},[892,20502,20503,20507],{},[895,20504,20505],{},[2138,20506,3098],{},[902,20508,3098],{"encoding":904},[883,20510,20512],{"className":20511},[886],[888,20513,20514],{"xmlns":890},[892,20515,20516,20521],{},[895,20517,20518],{},[2138,20519,20520],{},"101",[902,20522,20520],{"encoding":904},", změní se spotřeba přibližně o ",[883,20525,20527],{"className":20526},[886],[888,20528,20529],{"xmlns":890},[892,20530,20531,20535],{},[895,20532,20533],{},[2138,20534,19277],{},[902,20536,20494],{"encoding":904},". Skutečná změna ",[883,20539,20541],{"className":20540},[886],[888,20542,20543],{"xmlns":890},[892,20544,20545,20576],{},[895,20546,20547,20549,20551,20553,20555,20557,20559,20561,20563,20565,20567,20569,20571,20573],{},[898,20548,2897],{"mathvariant":2385},[898,20550,1852],{},[2005,20552,2007],{},[898,20554,1852],{},[2005,20556,2014],{"stretchy":2013},[2138,20558,20520],{},[2005,20560,2020],{"stretchy":2013},[2005,20562,2234],{},[898,20564,1852],{},[2005,20566,2014],{"stretchy":2013},[2138,20568,3098],{},[2005,20570,2020],{"stretchy":2013},[2005,20572,2007],{},[2138,20574,20575],{},"0,401",[902,20577,20578],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,20581,20582,20583],{},"Obecný trend: ",[38,20584,20585],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,20587,20589],{"id":20588},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,20591,20592,20593,10030,20596,20599,20600,10030,20603,12134,20606,10030,20609,20612],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,20594,20595],{},"makroekonomická rovnováha",[614,20597,20598],{},"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 ",[38,20601,20602],{},"agregátní poptávky",[614,20604,20605],{},"aggregate demand",[38,20607,20608],{},"agregátní nabídky",[614,20610,20611],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,20614,20616],{"id":20615},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,20618,20619],{},[2568,20620],{"alt":20621,"className":20622,"src":20623},"imek-keynesian-kriz",[210,2572],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,20625,20627],{"id":20626},"zadání-modelu","Zadání modelu",[724,20629,20630,20631,20644,20645,20658],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,20632,20634],{"className":20633},[886],[888,20635,20636],{"xmlns":890},[892,20637,20638,20642],{},[895,20639,20640],{},[898,20641,1852],{},[902,20643,1852],{"encoding":904}," a investice ",[883,20646,20648],{"className":20647},[886],[888,20649,20650],{"xmlns":890},[892,20651,20652,20656],{},[895,20653,20654],{},[898,20655,12190],{},[902,20657,12190],{"encoding":904},". Podmínka rovnováhy:",[724,20660,20661],{},[883,20662,20664],{"className":20663},[886],[888,20665,20666],{"xmlns":890},[892,20667,20668,20691],{},[895,20669,20670,20672,20674,20676,20678,20680,20682,20684,20686,20689],{},[898,20671,9134],{},[2005,20673,2007],{},[898,20675,1852],{},[2005,20677,2104],{},[898,20679,12190],{},[898,20681,1644],{"mathvariant":2385},[5884,20683],{"width":5886},[2005,20685,2014],{"stretchy":2013},[2138,20687,20688],{},"7.6",[2005,20690,2020],{"stretchy":2013},[902,20692,20693],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,20695,20697],{"id":20696},"soustava-rovnic","Soustava rovnic",[724,20699,20700,20701,20722,20723,20747],{},"Pro pevně zadané (plánované) investice ",[883,20702,20704],{"className":20703},[886],[888,20705,20706],{"xmlns":890},[892,20707,20708,20720],{},[895,20709,20710,20712,20714],{},[898,20711,12190],{},[2005,20713,2007],{},[2133,20715,20716,20718],{},[898,20717,12190],{},[2005,20719,4360],{},[902,20721,12201],{"encoding":904}," a funkci spotřeby ",[883,20724,20726],{"className":20725},[886],[888,20727,20728],{"xmlns":890},[892,20729,20730,20744],{},[895,20731,20732,20734,20736,20738,20740,20742],{},[898,20733,1852],{},[2005,20735,2007],{},[898,20737,1852],{},[2005,20739,2014],{"stretchy":2013},[898,20741,9134],{},[2005,20743,2020],{"stretchy":2013},[902,20745,20746],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,20749,20750],{},[883,20751,20753],{"className":20752},[886],[888,20754,20755],{"xmlns":890},[892,20756,20757,20833],{},[895,20758,20759,20824,20826,20828,20831],{},[20760,20761,20764,20796],"mtable",{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},"0.25em","right left",[20765,20766,20767,20774],"mtr",{},[20768,20769,20770],"mtd",{},[2334,20771,20772],{"scriptlevel":2336,"displaystyle":2294},[898,20773,9134],{},[20768,20775,20776],{},[2334,20777,20778],{"scriptlevel":2336,"displaystyle":2294},[895,20779,20780,20782,20784,20786,20788,20794],{},[895,20781],{},[2005,20783,2007],{},[898,20785,1852],{},[2005,20787,2104],{},[2133,20789,20790,20792],{},[898,20791,12190],{},[2005,20793,4360],{},[2005,20795,2295],{"separator":2294},[20765,20797,20798,20804],{},[20768,20799,20800],{},[2334,20801,20802],{"scriptlevel":2336,"displaystyle":2294},[898,20803,1852],{},[20768,20805,20806],{},[2334,20807,20808],{"scriptlevel":2336,"displaystyle":2294},[895,20809,20810,20812,20814,20816,20818,20820,20822],{},[895,20811],{},[2005,20813,2007],{},[898,20815,1852],{},[2005,20817,2014],{"stretchy":2013},[898,20819,9134],{},[2005,20821,2020],{"stretchy":2013},[2005,20823,2295],{"separator":2294},[5884,20825],{"width":5886},[2005,20827,2014],{"stretchy":2013},[2138,20829,20830],{},"7.7",[2005,20832,2020],{"stretchy":2013},[902,20834,20835],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,20837,20838,20839,2212,20841,3894,20858,2212,20861,1644],{},"jejímž řešením jsou ",[38,20840,13891],{},[883,20842,20844],{"className":20843},[886],[888,20845,20846],{"xmlns":890},[892,20847,20848,20856],{},[895,20849,20850],{},[2133,20851,20852,20854],{},[898,20853,9134],{},[898,20855,1868],{},[902,20857,13909],{"encoding":904},[38,20859,20860],{},"rovnovážná spotřeba",[883,20862,20864],{"className":20863},[886],[888,20865,20866],{"xmlns":890},[892,20867,20868,20876],{},[895,20869,20870],{},[2133,20871,20872,20874],{},[898,20873,1852],{},[898,20875,1868],{},[902,20877,13968],{"encoding":904},[198,20879,20881,20882],{"id":20880},"výpočet-yeye","Výpočet ",[883,20883,20885],{"className":20884},[886],[888,20886,20887],{"xmlns":890},[892,20888,20889,20897],{},[895,20890,20891],{},[2133,20892,20893,20895],{},[898,20894,9134],{},[898,20896,1868],{},[902,20898,13909],{"encoding":904},[724,20900,20901,20902,20925,20926,7691,20958],{},"Pro lineární spotřebu ",[883,20903,20905],{"className":20904},[886],[888,20906,20907],{"xmlns":890},[892,20908,20909,20923],{},[895,20910,20911,20913,20915,20917,20919,20921],{},[898,20912,1852],{},[2005,20914,2007],{},[898,20916,207],{},[898,20918,9134],{},[2005,20920,2104],{},[898,20922,2107],{},[902,20924,18926],{"encoding":904}," plyne z (7.7) rovnice ",[883,20927,20929],{"className":20928},[886],[888,20930,20931],{"xmlns":890},[892,20932,20933,20955],{},[895,20934,20935,20937,20939,20941,20943,20945,20947,20949],{},[898,20936,9134],{},[2005,20938,2007],{},[898,20940,207],{},[898,20942,9134],{},[2005,20944,2104],{},[898,20946,2107],{},[2005,20948,2104],{},[2133,20950,20951,20953],{},[898,20952,12190],{},[2005,20954,4360],{},[902,20956,20957],{"encoding":904},"Y = aY + b + I^*",[38,20959,20960],{},"redukovaný tvar",[724,20962,20963],{},[883,20964,20966],{"className":20965},[886],[888,20967,20968],{"xmlns":890},[892,20969,20970,21018],{},[895,20971,20972],{},[12838,20973,20974],{"notation":12840},[2334,20975,20976],{"scriptlevel":2336,"displaystyle":2013},[2334,20977,20978],{"scriptlevel":2336,"displaystyle":2013},[2334,20979,20980],{"scriptlevel":2336,"displaystyle":2294},[895,20981,20982,20984,20990,20992,21014,21016],{},[2297,20983,2995],{},[2133,20985,20986,20988],{},[898,20987,9134],{},[898,20989,1868],{},[2005,20991,2007],{},[2338,20993,20994,21006],{},[895,20995,20996,20998,21000],{},[898,20997,2107],{},[2005,20999,2104],{},[2133,21001,21002,21004],{},[898,21003,12190],{},[2005,21005,4360],{},[895,21007,21008,21010,21012],{},[2138,21009,2287],{},[2005,21011,2234],{},[898,21013,207],{},[898,21015,1644],{"mathvariant":2385},[2297,21017,2995],{},[902,21019,21020],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,21022,21024],{"id":21023},"příklad-73","Příklad 7.3",[724,21026,21027,21028,8108,21045,3894,21069,21095],{},"V modelu ",[883,21029,21031],{"className":21030},[886],[888,21032,21033],{"xmlns":890},[892,21034,21035,21043],{},[895,21036,21037,21039,21041],{},[898,21038,1852],{},[2297,21040,12296],{},[898,21042,12190],{},[902,21044,12301],{"encoding":904},[883,21046,21048],{"className":21047},[886],[888,21049,21050],{"xmlns":890},[892,21051,21052,21066],{},[895,21053,21054,21056,21058,21060,21062,21064],{},[898,21055,1852],{},[2005,21057,2007],{},[2138,21059,19327],{},[898,21061,9134],{},[2005,21063,2104],{},[2138,21065,2871],{},[902,21067,21068],{"encoding":904},"C = 0{,}6Y + 10",[883,21070,21072],{"className":21071},[886],[888,21073,21074],{"xmlns":890},[892,21075,21076,21092],{},[895,21077,21078,21080,21082,21084,21086],{},[898,21079,12190],{},[2005,21081,2007],{},[2138,21083,3517],{},[2005,21085,2007],{},[2133,21087,21088,21090],{},[898,21089,12190],{},[2005,21091,4360],{},[902,21093,21094],{"encoding":904},"I = 12 = I^*",". Soustava",[724,21097,21098],{},[883,21099,21101],{"className":21100},[886],[888,21102,21103],{"xmlns":890},[892,21104,21105,21161],{},[20760,21106,21107,21133],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,21108,21109,21115],{},[20768,21110,21111],{},[2334,21112,21113],{"scriptlevel":2336,"displaystyle":2294},[898,21114,9134],{},[20768,21116,21117],{},[2334,21118,21119],{"scriptlevel":2336,"displaystyle":2294},[895,21120,21121,21123,21125,21127,21129,21131],{},[895,21122],{},[2005,21124,2007],{},[898,21126,1852],{},[2005,21128,2104],{},[2138,21130,3517],{},[2005,21132,2295],{"separator":2294},[20765,21134,21135,21141],{},[20768,21136,21137],{},[2334,21138,21139],{"scriptlevel":2336,"displaystyle":2294},[898,21140,1852],{},[20768,21142,21143],{},[2334,21144,21145],{"scriptlevel":2336,"displaystyle":2294},[895,21146,21147,21149,21151,21153,21155,21157,21159],{},[895,21148],{},[2005,21150,2007],{},[2138,21152,19327],{},[898,21154,9134],{},[2005,21156,2104],{},[2138,21158,2871],{},[2005,21160,2295],{"separator":2294},[902,21162,21163],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,21165,21166,21167,1343,21190,21213,21214,3927],{},"má řešení ",[883,21168,21170],{"className":21169},[886],[888,21171,21172],{"xmlns":890},[892,21173,21174,21187],{},[895,21175,21176,21182,21184],{},[2133,21177,21178,21180],{},[898,21179,9134],{},[898,21181,1868],{},[2005,21183,2007],{},[2138,21185,21186],{},"55",[902,21188,21189],{"encoding":904},"Y^E = 55",[883,21191,21193],{"className":21192},[886],[888,21194,21195],{"xmlns":890},[892,21196,21197,21210],{},[895,21198,21199,21205,21207],{},[2133,21200,21201,21203],{},[898,21202,1852],{},[898,21204,1868],{},[2005,21206,2007],{},[2138,21208,21209],{},"43",[902,21211,21212],{"encoding":904},"C^E = 43"," (a ",[883,21215,21217],{"className":21216},[886],[888,21218,21219],{"xmlns":890},[892,21220,21221,21233],{},[895,21222,21223,21229,21231],{},[2133,21224,21225,21227],{},[898,21226,8679],{},[898,21228,1868],{},[2005,21230,2007],{},[2138,21232,3517],{},[902,21234,21235],{"encoding":904},"S^E = 12",[724,21237,21238],{},[614,21239,21240,21241,21263,21264,12134,21285,21308,21309,1644],{},"Obrázek 7.5 — Přímky ",[883,21242,21244],{"className":21243},[886],[888,21245,21246],{"xmlns":890},[892,21247,21248,21260],{},[895,21249,21250,21252,21254,21256,21258],{},[898,21251,1852],{},[2005,21253,2007],{},[898,21255,9134],{},[2005,21257,2234],{},[2138,21259,3517],{},[902,21261,21262],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,21265,21267],{"className":21266},[886],[888,21268,21269],{"xmlns":890},[892,21270,21271,21283],{},[895,21272,21273,21275,21277,21279,21281],{},[898,21274,9134],{},[2005,21276,2007],{},[898,21278,1852],{},[2005,21280,2104],{},[898,21282,12190],{},[902,21284,14750],{"encoding":904},[883,21286,21288],{"className":21287},[886],[888,21289,21290],{"xmlns":890},[892,21291,21292,21306],{},[895,21293,21294,21296,21298,21300,21302,21304],{},[898,21295,1852],{},[2005,21297,2007],{},[2138,21299,19327],{},[898,21301,9134],{},[2005,21303,2104],{},[2138,21305,2871],{},[902,21307,21068],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,21310,21312],{"className":21311},[886],[888,21313,21314],{"xmlns":890},[892,21315,21316,21348],{},[895,21317,21318,21320,21326,21328,21334,21336,21338,21340,21342,21344,21346],{},[2005,21319,2495],{"stretchy":2013},[2133,21321,21322,21324],{},[898,21323,9134],{},[898,21325,1868],{},[2005,21327,2295],{"separator":2294},[2133,21329,21330,21332],{},[898,21331,1852],{},[898,21333,1868],{},[2005,21335,2510],{"stretchy":2013},[2005,21337,2007],{},[2005,21339,2495],{"stretchy":2013},[2138,21341,21186],{},[2005,21343,2295],{"separator":2294},[2138,21345,21209],{},[2005,21347,2510],{"stretchy":2013},[902,21349,21350],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,21352,21353,21356,21357,21374,21375,1644],{},[38,21354,21355],{},"Komentář k přechodu."," Model ",[883,21358,21360],{"className":21359},[886],[888,21361,21362],{"xmlns":890},[892,21363,21364,21372],{},[895,21365,21366,21368,21370],{},[898,21367,1852],{},[2297,21369,12296],{},[898,21371,12190],{},[902,21373,12301],{"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 ",[38,21376,21377,21378],{},"model ",[883,21379,21381],{"className":21380},[886],[888,21382,21383],{"xmlns":890},[892,21384,21385,21397],{},[895,21386,21387,21389,21391,21393,21395],{},[898,21388,1852],{},[2297,21390,12296],{},[898,21392,12190],{},[2297,21394,12296],{},[898,21396,12118],{},[902,21398,18227],{"encoding":904},[115,21400,21402],{"id":21401},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,21404,20627],{"id":21405},"zadání-modelu-1",[724,21407,21408,21409,21426,21427,2212,21430,10030,21443,21446],{},"Rozšíření modelu ",[883,21410,21412],{"className":21411},[886],[888,21413,21414],{"xmlns":890},[892,21415,21416,21424],{},[895,21417,21418,21420,21422],{},[898,21419,1852],{},[2297,21421,12296],{},[898,21423,12190],{},[902,21425,12301],{"encoding":904}," o ",[38,21428,21429],{},"vládní výdaje",[883,21431,21433],{"className":21432},[886],[888,21434,21435],{"xmlns":890},[892,21436,21437,21441],{},[895,21438,21439],{},[898,21440,12118],{},[902,21442,12118],{"encoding":904},[614,21444,21445],{},"government expenditure","). Podmínka rovnováhy:",[724,21448,21449],{},[883,21450,21452],{"className":21451},[886],[888,21453,21454],{"xmlns":890},[892,21455,21456,21483],{},[895,21457,21458,21460,21462,21464,21466,21468,21470,21472,21474,21476,21478,21481],{},[898,21459,9134],{},[2005,21461,2007],{},[898,21463,1852],{},[2005,21465,2104],{},[898,21467,12190],{},[2005,21469,2104],{},[898,21471,12118],{},[898,21473,1644],{"mathvariant":2385},[5884,21475],{"width":5886},[2005,21477,2014],{"stretchy":2013},[2138,21479,21480],{},"7.8",[2005,21482,2020],{"stretchy":2013},[902,21484,21485],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,21487,21488,21489,2212,21492,10030,21505,21508],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,21490,21491],{},"zdaněním domácností",[883,21493,21495],{"className":21494},[886],[888,21496,21497],{"xmlns":890},[892,21498,21499,21503],{},[895,21500,21501],{},[898,21502,2783],{},[902,21504,2783],{"encoding":904},[614,21506,21507],{},"taxation","). Zdanění bývá:",[120,21510,21511,21544,21569],{},[123,21512,21513,21514,2295],{},"úměrné důchodu: ",[883,21515,21517],{"className":21516},[886],[888,21518,21519],{"xmlns":890},[892,21520,21521,21541],{},[895,21522,21523,21525,21527,21529,21531,21533,21535,21537,21539],{},[898,21524,2783],{},[2005,21526,2007],{},[898,21528,2783],{},[2005,21530,2014],{"stretchy":2013},[898,21532,9134],{},[2005,21534,2020],{"stretchy":2013},[2005,21536,2007],{},[898,21538,18861],{},[898,21540,9134],{},[902,21542,21543],{"encoding":904},"T = T(Y) = tY",[123,21545,21546,21547,2295],{},"fixní: ",[883,21548,21550],{"className":21549},[886],[888,21551,21552],{"xmlns":890},[892,21553,21554,21566],{},[895,21555,21556,21558,21560],{},[898,21557,2783],{},[2005,21559,2007],{},[2133,21561,21562,21564],{},[898,21563,2783],{},[2005,21565,4360],{},[902,21567,21568],{"encoding":904},"T = T^*",[123,21570,21571,21572,21600,21601,1644],{},"kombinované: ",[883,21573,21575],{"className":21574},[886],[888,21576,21577],{"xmlns":890},[892,21578,21579,21597],{},[895,21580,21581,21583,21585,21591,21593,21595],{},[898,21582,2783],{},[2005,21584,2007],{},[2133,21586,21587,21589],{},[898,21588,2783],{},[2005,21590,4360],{},[2005,21592,2104],{},[898,21594,18861],{},[898,21596,9134],{},[902,21598,21599],{"encoding":904},"T = T^* + tY",", kde ",[883,21602,21604],{"className":21603},[886],[888,21605,21606],{"xmlns":890},[892,21607,21608,21620],{},[895,21609,21610,21612,21614,21616,21618],{},[2138,21611,2336],{},[2005,21613,7685],{},[898,21615,18861],{},[2005,21617,3455],{},[2138,21619,2287],{},[902,21621,21622],{"encoding":904},"0 \\le t \u003C 1",[3876,21624,21625],{},[724,21626,21627,21629,21630,21651,21652,21655,21656,21669,21670,12134,21696,2212,21699,21725,21726,21754,21755,3894,21768,21786],{},[883,21628,4418],{}," Pozor na disponibilní důchod\nV modelu ",[883,21631,21633],{"className":21632},[886],[888,21634,21635],{"xmlns":890},[892,21636,21637,21649],{},[895,21638,21639,21641,21643,21645,21647],{},[898,21640,1852],{},[2297,21642,12296],{},[898,21644,12190],{},[2297,21646,12296],{},[898,21648,12118],{},[902,21650,18227],{"encoding":904}," je nutné ",[38,21653,21654],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,21657,21659],{"className":21658},[886],[888,21660,21661],{"xmlns":890},[892,21662,21663,21667],{},[895,21664,21665],{},[898,21666,9134],{},[902,21668,9134],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,21671,21673],{"className":21672},[886],[888,21674,21675],{"xmlns":890},[892,21676,21677,21693],{},[895,21678,21679,21681,21683,21685,21687,21689,21691],{},[898,21680,9134],{},[2005,21682,2007],{},[898,21684,1852],{},[2005,21686,2104],{},[898,21688,12190],{},[2005,21690,2104],{},[898,21692,12118],{},[902,21694,21695],{"encoding":904},"Y = C + I + G",[38,21697,21698],{},"disponibilní důchod",[883,21700,21702],{"className":21701},[886],[888,21703,21704],{"xmlns":890},[892,21705,21706,21722],{},[895,21707,21708,21714,21716,21718,21720],{},[2281,21709,21710,21712],{},[898,21711,9134],{},[898,21713,1860],{},[2005,21715,2007],{},[898,21717,9134],{},[2005,21719,2234],{},[898,21721,2783],{},[902,21723,21724],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,21727,21729],{"className":21728},[886],[888,21730,21731],{"xmlns":890},[892,21732,21733,21751],{},[895,21734,21735,21737,21739,21741,21743,21749],{},[898,21736,1852],{},[2005,21738,2007],{},[898,21740,1852],{},[2005,21742,2014],{"stretchy":2013},[2281,21744,21745,21747],{},[898,21746,9134],{},[898,21748,1860],{},[2005,21750,2020],{"stretchy":2013},[902,21752,21753],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,21756,21758],{"className":21757},[886],[888,21759,21760],{"xmlns":890},[892,21761,21762,21766],{},[895,21763,21764],{},[898,21765,9134],{},[902,21767,9134],{"encoding":904},[883,21769,21771],{"className":21770},[886],[888,21772,21773],{"xmlns":890},[892,21774,21775,21783],{},[895,21776,21777],{},[2281,21778,21779,21781],{},[898,21780,9134],{},[898,21782,1860],{},[902,21784,21785],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,21788,21789,10030,21792,2020],{},[38,21790,21791],{},"Disponibilní důchod",[614,21793,21794],{},"disposable income",[724,21796,21797],{},[883,21798,21800],{"className":21799},[886],[888,21801,21802],{"xmlns":890},[892,21803,21804,21820],{},[895,21805,21806,21812,21814,21816,21818],{},[2281,21807,21808,21810],{},[898,21809,9134],{},[898,21811,1860],{},[2005,21813,2007],{},[898,21815,9134],{},[2005,21817,2234],{},[898,21819,2783],{},[902,21821,21724],{"encoding":904},[724,21823,21824,21825,1644],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,21826,21828],{"className":21827},[886],[888,21829,21830],{"xmlns":890},[892,21831,21832,21850],{},[895,21833,21834,21836,21838,21840,21842,21848],{},[898,21835,1852],{},[2005,21837,2007],{},[898,21839,1852],{},[2005,21841,2014],{"stretchy":2013},[2281,21843,21844,21846],{},[898,21845,9134],{},[898,21847,1860],{},[2005,21849,2020],{"stretchy":2013},[902,21851,21753],{"encoding":904},[198,21853,20697],{"id":21854},"soustava-rovnic-1",[724,21856,21857,21858,1343,21879,21901,21902,2713],{},"Pro pevně zadané ",[883,21859,21861],{"className":21860},[886],[888,21862,21863],{"xmlns":890},[892,21864,21865,21877],{},[895,21866,21867,21869,21871],{},[898,21868,12190],{},[2005,21870,2007],{},[2133,21872,21873,21875],{},[898,21874,12190],{},[2005,21876,4360],{},[902,21878,12201],{"encoding":904},[883,21880,21882],{"className":21881},[886],[888,21883,21884],{"xmlns":890},[892,21885,21886,21898],{},[895,21887,21888,21890,21892],{},[898,21889,12118],{},[2005,21891,2007],{},[2133,21893,21894,21896],{},[898,21895,12118],{},[2005,21897,4360],{},[902,21899,21900],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,21903,21905],{"className":21904},[886],[888,21906,21907],{"xmlns":890},[892,21908,21909,21929],{},[895,21910,21911,21913,21915,21917,21919,21925,21927],{},[898,21912,9134],{},[2005,21914,2295],{"separator":2294},[898,21916,1852],{},[2005,21918,2295],{"separator":2294},[2281,21920,21921,21923],{},[898,21922,9134],{},[898,21924,1860],{},[2005,21926,2295],{"separator":2294},[898,21928,2783],{},[902,21930,21931],{"encoding":904},"Y, C, Y_D, T",[724,21933,21934],{},[883,21935,21937],{"className":21936},[886],[888,21938,21939],{"xmlns":890},[892,21940,21941,22082],{},[895,21942,21943,22073,22075,22077,22080],{},[20760,21944,21945,21983,22011,22043],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,21946,21947,21953],{},[20768,21948,21949],{},[2334,21950,21951],{"scriptlevel":2336,"displaystyle":2294},[898,21952,9134],{},[20768,21954,21955],{},[2334,21956,21957],{"scriptlevel":2336,"displaystyle":2294},[895,21958,21959,21961,21963,21965,21967,21973,21975,21981],{},[895,21960],{},[2005,21962,2007],{},[898,21964,1852],{},[2005,21966,2104],{},[2133,21968,21969,21971],{},[898,21970,12190],{},[2005,21972,4360],{},[2005,21974,2104],{},[2133,21976,21977,21979],{},[898,21978,12118],{},[2005,21980,4360],{},[2005,21982,2295],{"separator":2294},[20765,21984,21985,21991],{},[20768,21986,21987],{},[2334,21988,21989],{"scriptlevel":2336,"displaystyle":2294},[898,21990,2783],{},[20768,21992,21993],{},[2334,21994,21995],{"scriptlevel":2336,"displaystyle":2294},[895,21996,21997,21999,22001,22003,22005,22007,22009],{},[895,21998],{},[2005,22000,2007],{},[898,22002,2783],{},[2005,22004,2014],{"stretchy":2013},[898,22006,9134],{},[2005,22008,2020],{"stretchy":2013},[2005,22010,2295],{"separator":2294},[20765,22012,22013,22019],{},[20768,22014,22015],{},[2334,22016,22017],{"scriptlevel":2336,"displaystyle":2294},[898,22018,1852],{},[20768,22020,22021],{},[2334,22022,22023],{"scriptlevel":2336,"displaystyle":2294},[895,22024,22025,22027,22029,22031,22033,22039,22041],{},[895,22026],{},[2005,22028,2007],{},[898,22030,1852],{},[2005,22032,2014],{"stretchy":2013},[2281,22034,22035,22037],{},[898,22036,9134],{},[898,22038,1860],{},[2005,22040,2020],{"stretchy":2013},[2005,22042,2295],{"separator":2294},[20765,22044,22045,22055],{},[20768,22046,22047],{},[2334,22048,22049],{"scriptlevel":2336,"displaystyle":2294},[2281,22050,22051,22053],{},[898,22052,9134],{},[898,22054,1860],{},[20768,22056,22057],{},[2334,22058,22059],{"scriptlevel":2336,"displaystyle":2294},[895,22060,22061,22063,22065,22067,22069,22071],{},[895,22062],{},[2005,22064,2007],{},[898,22066,9134],{},[2005,22068,2234],{},[898,22070,2783],{},[2005,22072,2295],{"separator":2294},[5884,22074],{"width":5886},[2005,22076,2014],{"stretchy":2013},[2138,22078,22079],{},"7.9",[2005,22081,2020],{"stretchy":2013},[902,22083,22084],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,22086,22087,22088,22132,22133,1644],{},"s řešeními ",[883,22089,22091],{"className":22090},[886],[888,22092,22093],{"xmlns":890},[892,22094,22095,22129],{},[895,22096,22097,22103,22105,22111,22113,22119,22121],{},[2133,22098,22099,22101],{},[898,22100,9134],{},[898,22102,1868],{},[2005,22104,2295],{"separator":2294},[2133,22106,22107,22109],{},[898,22108,1852],{},[898,22110,1868],{},[2005,22112,2295],{"separator":2294},[2133,22114,22115,22117],{},[898,22116,2783],{},[898,22118,1868],{},[2005,22120,2295],{"separator":2294},[9172,22122,22123,22125,22127],{},[898,22124,9134],{},[898,22126,1860],{},[898,22128,1868],{},[902,22130,22131],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,22134,22136],{"className":22135},[886],[888,22137,22138],{"xmlns":890},[892,22139,22140,22166],{},[895,22141,22142,22148,22150,22158,22160],{},[2133,22143,22144,22146],{},[898,22145,8679],{},[898,22147,1868],{},[2005,22149,2007],{},[9172,22151,22152,22154,22156],{},[898,22153,9134],{},[898,22155,1860],{},[898,22157,1868],{},[2005,22159,2234],{},[2133,22161,22162,22164],{},[898,22163,1852],{},[898,22165,1868],{},[902,22167,22168],{"encoding":904},"S^E = Y_D^E - C^E",[3876,22170,22171,22176],{},[724,22172,22173,22175],{},[883,22174,4578],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,22177,22178,22201,22284,22339,22429],{},[123,22179,22180,22183,22184,1644],{},[38,22181,22182],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,22185,22187],{"className":22186},[886],[888,22188,22189],{"xmlns":890},[892,22190,22191,22199],{},[895,22192,22193],{},[2281,22194,22195,22197],{},[898,22196,9134],{},[898,22198,1860],{},[902,22200,21785],{"encoding":904},[123,22202,22203,22252,22253,22270,22271,1644],{},[38,22204,22205,22206,22226,22227],{},"Dosaď ",[883,22207,22209],{"className":22208},[886],[888,22210,22211],{"xmlns":890},[892,22212,22213,22223],{},[895,22214,22215,22217,22219,22221],{},[898,22216,2783],{},[2005,22218,2014],{"stretchy":2013},[898,22220,9134],{},[2005,22222,2020],{"stretchy":2013},[902,22224,22225],{"encoding":904},"T(Y)"," do ",[883,22228,22230],{"className":22229},[886],[888,22231,22232],{"xmlns":890},[892,22233,22234,22250],{},[895,22235,22236,22242,22244,22246,22248],{},[2281,22237,22238,22240],{},[898,22239,9134],{},[898,22241,1860],{},[2005,22243,2007],{},[898,22245,9134],{},[2005,22247,2234],{},[898,22249,2783],{},[902,22251,21724],{"encoding":904}," — dostaneš ",[883,22254,22256],{"className":22255},[886],[888,22257,22258],{"xmlns":890},[892,22259,22260,22268],{},[895,22261,22262],{},[2281,22263,22264,22266],{},[898,22265,9134],{},[898,22267,1860],{},[902,22269,21785],{"encoding":904}," jako lineární funkci ",[883,22272,22274],{"className":22273},[886],[888,22275,22276],{"xmlns":890},[892,22277,22278,22282],{},[895,22279,22280],{},[898,22281,9134],{},[902,22283,9134],{"encoding":904},[123,22285,22286,22252,22313,22270,22326,1644],{},[38,22287,22205,22288,22312],{},[883,22289,22291],{"className":22290},[886],[888,22292,22293],{"xmlns":890},[892,22294,22295,22309],{},[895,22296,22297,22303,22305,22307],{},[2281,22298,22299,22301],{},[898,22300,9134],{},[898,22302,1860],{},[2005,22304,2014],{"stretchy":2013},[898,22306,9134],{},[2005,22308,2020],{"stretchy":2013},[902,22310,22311],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,22314,22316],{"className":22315},[886],[888,22317,22318],{"xmlns":890},[892,22319,22320,22324],{},[895,22321,22322],{},[898,22323,1852],{},[902,22325,1852],{"encoding":904},[883,22327,22329],{"className":22328},[886],[888,22330,22331],{"xmlns":890},[892,22332,22333,22337],{},[895,22334,22335],{},[898,22336,9134],{},[902,22338,9134],{"encoding":904},[123,22340,22341,2212,22363,22397,22398,22411,22412,1644],{},[38,22342,22205,22343,22362],{},[883,22344,22346],{"className":22345},[886],[888,22347,22348],{"xmlns":890},[892,22349,22350,22360],{},[895,22351,22352,22354,22356,22358],{},[898,22353,1852],{},[2005,22355,2014],{"stretchy":2013},[898,22357,9134],{},[2005,22359,2020],{"stretchy":2013},[902,22361,14222],{"encoding":904}," do podmínky rovnováhy",[883,22364,22366],{"className":22365},[886],[888,22367,22368],{"xmlns":890},[892,22369,22370,22394],{},[895,22371,22372,22374,22376,22378,22380,22386,22388],{},[898,22373,9134],{},[2005,22375,2007],{},[898,22377,1852],{},[2005,22379,2104],{},[2133,22381,22382,22384],{},[898,22383,12190],{},[2005,22385,4360],{},[2005,22387,2104],{},[2133,22389,22390,22392],{},[898,22391,12118],{},[2005,22393,4360],{},[902,22395,22396],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,22399,22401],{"className":22400},[886],[888,22402,22403],{"xmlns":890},[892,22404,22405,22409],{},[895,22406,22407],{},[898,22408,9134],{},[902,22410,9134],{"encoding":904},", odtud ",[883,22413,22415],{"className":22414},[886],[888,22416,22417],{"xmlns":890},[892,22418,22419,22427],{},[895,22420,22421],{},[2133,22422,22423,22425],{},[898,22424,9134],{},[898,22426,1868],{},[902,22428,13909],{"encoding":904},[123,22430,22431,22434,22435,1343,22453,1343,22473,1343,22490,1644],{},[38,22432,22433],{},"Zpětným dosazením"," dopočítej ",[883,22436,22438],{"className":22437},[886],[888,22439,22440],{"xmlns":890},[892,22441,22442,22450],{},[895,22443,22444],{},[2133,22445,22446,22448],{},[898,22447,2783],{},[898,22449,1868],{},[902,22451,22452],{"encoding":904},"T^E",[883,22454,22456],{"className":22455},[886],[888,22457,22458],{"xmlns":890},[892,22459,22460,22470],{},[895,22461,22462],{},[9172,22463,22464,22466,22468],{},[898,22465,9134],{},[898,22467,1860],{},[898,22469,1868],{},[902,22471,22472],{"encoding":904},"Y_D^E",[883,22474,22476],{"className":22475},[886],[888,22477,22478],{"xmlns":890},[892,22479,22480,22488],{},[895,22481,22482],{},[2133,22483,22484,22486],{},[898,22485,1852],{},[898,22487,1868],{},[902,22489,13968],{"encoding":904},[883,22491,22493],{"className":22492},[886],[888,22494,22495],{"xmlns":890},[892,22496,22497,22505],{},[895,22498,22499],{},[2133,22500,22501,22503],{},[898,22502,8679],{},[898,22504,1868],{},[902,22506,22507],{"encoding":904},"S^E",[198,22509,22511],{"id":22510},"příklad-74","Příklad 7.4",[724,22513,21027,22514,22535,22536,1343,22567,1343,22591,1343,22613,22635],{},[883,22515,22517],{"className":22516},[886],[888,22518,22519],{"xmlns":890},[892,22520,22521,22533],{},[895,22522,22523,22525,22527,22529,22531],{},[898,22524,1852],{},[2297,22526,12296],{},[898,22528,12190],{},[2297,22530,12296],{},[898,22532,12118],{},[902,22534,18227],{"encoding":904}," jsou dány ",[883,22537,22539],{"className":22538},[886],[888,22540,22541],{"xmlns":890},[892,22542,22543,22564],{},[895,22544,22545,22547,22549,22552,22554,22560,22562],{},[898,22546,1852],{},[2005,22548,2007],{},[2138,22550,22551],{},"0,9",[2297,22553,2995],{},[2281,22555,22556,22558],{},[898,22557,9134],{},[898,22559,1860],{},[2005,22561,2104],{},[2138,22563,5903],{},[902,22565,22566],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,22568,22570],{"className":22569},[886],[888,22571,22572],{"xmlns":890},[892,22573,22574,22588],{},[895,22575,22576,22578,22580,22582,22584,22586],{},[898,22577,2783],{},[2005,22579,2007],{},[2138,22581,2847],{},[898,22583,9134],{},[2005,22585,2104],{},[2138,22587,5010],{},[902,22589,22590],{"encoding":904},"T = 0{,}2Y + 25",[883,22592,22594],{"className":22593},[886],[888,22595,22596],{"xmlns":890},[892,22597,22598,22610],{},[895,22599,22600,22606,22608],{},[2133,22601,22602,22604],{},[898,22603,12190],{},[2005,22605,4360],{},[2005,22607,2007],{},[2138,22609,15044],{},[902,22611,22612],{"encoding":904},"I^* = 35",[883,22614,22616],{"className":22615},[886],[888,22617,22618],{"xmlns":890},[892,22619,22620,22632],{},[895,22621,22622,22628,22630],{},[2133,22623,22624,22626],{},[898,22625,12118],{},[2005,22627,4360],{},[2005,22629,2007],{},[2138,22631,9041],{},[902,22633,22634],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,22637,22638],{},[883,22639,22641],{"className":22640},[886],[888,22642,22643],{"xmlns":890},[892,22644,22645,22769],{},[20760,22646,22647,22677,22705,22739],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,22648,22649,22655],{},[20768,22650,22651],{},[2334,22652,22653],{"scriptlevel":2336,"displaystyle":2294},[898,22654,9134],{},[20768,22656,22657],{},[2334,22658,22659],{"scriptlevel":2336,"displaystyle":2294},[895,22660,22661,22663,22665,22667,22669,22671,22673,22675],{},[895,22662],{},[2005,22664,2007],{},[898,22666,1852],{},[2005,22668,2104],{},[2138,22670,15044],{},[2005,22672,2104],{},[2138,22674,9041],{},[2005,22676,2295],{"separator":2294},[20765,22678,22679,22685],{},[20768,22680,22681],{},[2334,22682,22683],{"scriptlevel":2336,"displaystyle":2294},[898,22684,2783],{},[20768,22686,22687],{},[2334,22688,22689],{"scriptlevel":2336,"displaystyle":2294},[895,22690,22691,22693,22695,22697,22699,22701,22703],{},[895,22692],{},[2005,22694,2007],{},[2138,22696,2847],{},[898,22698,9134],{},[2005,22700,2104],{},[2138,22702,5010],{},[2005,22704,2295],{"separator":2294},[20765,22706,22707,22713],{},[20768,22708,22709],{},[2334,22710,22711],{"scriptlevel":2336,"displaystyle":2294},[898,22712,1852],{},[20768,22714,22715],{},[2334,22716,22717],{"scriptlevel":2336,"displaystyle":2294},[895,22718,22719,22721,22723,22725,22727,22733,22735,22737],{},[895,22720],{},[2005,22722,2007],{},[2138,22724,22551],{},[2297,22726,2995],{},[2281,22728,22729,22731],{},[898,22730,9134],{},[898,22732,1860],{},[2005,22734,2104],{},[2138,22736,5903],{},[2005,22738,2295],{"separator":2294},[20765,22740,22741,22751],{},[20768,22742,22743],{},[2334,22744,22745],{"scriptlevel":2336,"displaystyle":2294},[2281,22746,22747,22749],{},[898,22748,9134],{},[898,22750,1860],{},[20768,22752,22753],{},[2334,22754,22755],{"scriptlevel":2336,"displaystyle":2294},[895,22756,22757,22759,22761,22763,22765,22767],{},[895,22758],{},[2005,22760,2007],{},[898,22762,9134],{},[2005,22764,2234],{},[898,22766,2783],{},[898,22768,1644],{"mathvariant":2385},[902,22770,22771],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,22773,22774,22777,22778,22832,22833,22879,22880,2713],{},[38,22775,22776],{},"Řešení."," Z definice ",[883,22779,22781],{"className":22780},[886],[888,22782,22783],{"xmlns":890},[892,22784,22785,22829],{},[895,22786,22787,22793,22795,22797,22799,22801,22803,22805,22807,22809,22811,22813,22815,22817,22819,22821,22823,22825,22827],{},[2281,22788,22789,22791],{},[898,22790,9134],{},[898,22792,1860],{},[2005,22794,2007],{},[898,22796,9134],{},[2005,22798,2234],{},[898,22800,2783],{},[2005,22802,2007],{},[898,22804,9134],{},[2005,22806,2234],{},[2005,22808,2014],{"stretchy":2013},[2138,22810,2847],{},[898,22812,9134],{},[2005,22814,2104],{},[2138,22816,5010],{},[2005,22818,2020],{"stretchy":2013},[2005,22820,2007],{},[2138,22822,14595],{},[898,22824,9134],{},[2005,22826,2234],{},[2138,22828,5010],{},[902,22830,22831],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,22834,22836],{"className":22835},[886],[888,22837,22838],{"xmlns":890},[892,22839,22840,22876],{},[895,22841,22842,22844,22846,22848,22850,22852,22854,22856,22858,22860,22862,22864,22866,22869,22871,22873],{},[898,22843,1852],{},[2005,22845,2007],{},[2138,22847,22551],{},[2005,22849,2014],{"stretchy":2013},[2138,22851,14595],{},[898,22853,9134],{},[2005,22855,2234],{},[2138,22857,5010],{},[2005,22859,2020],{"stretchy":2013},[2005,22861,2104],{},[2138,22863,5903],{},[2005,22865,2007],{},[2138,22867,22868],{},"0,72",[898,22870,9134],{},[2005,22872,2104],{},[2138,22874,22875],{},"47,5",[902,22877,22878],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,22881,22883],{"className":22882},[886],[888,22884,22885],{"xmlns":890},[892,22886,22887,22905],{},[895,22888,22889,22891,22893,22895,22897,22899,22901,22903],{},[898,22890,9134],{},[2005,22892,2007],{},[2138,22894,22868],{},[898,22896,9134],{},[2005,22898,2104],{},[2138,22900,22875],{},[2005,22902,2104],{},[2138,22904,21186],{},[902,22906,22907],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,22909,22910],{},[883,22911,22913],{"className":22912},[886],[888,22914,22915],{"xmlns":890},[892,22916,22917,22958],{},[895,22918,22919,22922,22924,22926,22929,22931,22933,22935,22941,22943,22953,22955],{},[2138,22920,22921],{},"0,28",[898,22923,9134],{},[2005,22925,2007],{},[2138,22927,22928],{},"102,5",[2297,22930,3993],{},[2005,22932,15014],{},[2297,22934,3993],{},[2133,22936,22937,22939],{},[898,22938,9134],{},[898,22940,1868],{},[2005,22942,2007],{},[2334,22944,22945],{"scriptlevel":2336,"displaystyle":2013},[2338,22946,22947,22950],{},[2138,22948,22949],{},"5125",[2138,22951,22952],{},"14",[2005,22954,5906],{},[2138,22956,22957],{},"366,071.",[902,22959,22960],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,22962,22963],{},"Rovnovážné veličiny:",[120,22965,22966,23001,23053,23107,23155],{},[123,22967,22968,2295],{},[883,22969,22971],{"className":22970},[886],[888,22972,22973],{"xmlns":890},[892,22974,22975,22998],{},[895,22976,22977,22983,22985,22993,22995],{},[2133,22978,22979,22981],{},[898,22980,9134],{},[898,22982,1868],{},[2005,22984,2007],{},[2334,22986,22987],{"scriptlevel":2336,"displaystyle":2013},[2338,22988,22989,22991],{},[2138,22990,22949],{},[2138,22992,22952],{},[2005,22994,5906],{},[2138,22996,22997],{},"366,071",[902,22999,23000],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,23002,23003,2295],{},[883,23004,23006],{"className":23005},[886],[888,23007,23008],{"xmlns":890},[892,23009,23010,23050],{},[895,23011,23012,23018,23020,23022,23024,23030,23032,23034,23036,23045,23047],{},[2133,23013,23014,23016],{},[898,23015,2783],{},[898,23017,1868],{},[2005,23019,2007],{},[2138,23021,2847],{},[2297,23023,2995],{},[2133,23025,23026,23028],{},[898,23027,9134],{},[898,23029,1868],{},[2005,23031,2104],{},[2138,23033,5010],{},[2005,23035,2007],{},[2334,23037,23038],{"scriptlevel":2336,"displaystyle":2013},[2338,23039,23040,23043],{},[2138,23041,23042],{},"1375",[2138,23044,22952],{},[2005,23046,5906],{},[2138,23048,23049],{},"98,214",[902,23051,23052],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,23054,23055,2295],{},[883,23056,23058],{"className":23057},[886],[888,23059,23060],{"xmlns":890},[892,23061,23062,23104],{},[895,23063,23064,23072,23074,23080,23082,23088,23090,23099,23101],{},[9172,23065,23066,23068,23070],{},[898,23067,9134],{},[898,23069,1860],{},[898,23071,1868],{},[2005,23073,2007],{},[2133,23075,23076,23078],{},[898,23077,9134],{},[898,23079,1868],{},[2005,23081,2234],{},[2133,23083,23084,23086],{},[898,23085,2783],{},[898,23087,1868],{},[2005,23089,2007],{},[2334,23091,23092],{"scriptlevel":2336,"displaystyle":2013},[2338,23093,23094,23097],{},[2138,23095,23096],{},"3750",[2138,23098,22952],{},[2005,23100,5906],{},[2138,23102,23103],{},"267,857",[902,23105,23106],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,23108,23109,2295],{},[883,23110,23112],{"className":23111},[886],[888,23113,23114],{"xmlns":890},[892,23115,23116,23152],{},[895,23117,23118,23124,23126,23132,23134,23136,23138,23147,23149],{},[2133,23119,23120,23122],{},[898,23121,1852],{},[898,23123,1868],{},[2005,23125,2007],{},[2133,23127,23128,23130],{},[898,23129,9134],{},[898,23131,1868],{},[2005,23133,2234],{},[2138,23135,21186],{},[2005,23137,2007],{},[2334,23139,23140],{"scriptlevel":2336,"displaystyle":2013},[2338,23141,23142,23145],{},[2138,23143,23144],{},"4355",[2138,23146,22952],{},[2005,23148,5906],{},[2138,23150,23151],{},"311,071",[902,23153,23154],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,23156,23157,23213],{},[883,23158,23160],{"className":23159},[886],[888,23161,23162],{"xmlns":890},[892,23163,23164,23210],{},[895,23165,23166,23172,23174,23182,23184,23190,23192,23194,23203,23205,23207],{},[2133,23167,23168,23170],{},[898,23169,8679],{},[898,23171,1868],{},[2005,23173,2007],{},[9172,23175,23176,23178,23180],{},[898,23177,9134],{},[898,23179,1860],{},[898,23181,1868],{},[2005,23183,2234],{},[2133,23185,23186,23188],{},[898,23187,1852],{},[898,23189,1868],{},[2005,23191,2007],{},[2005,23193,2234],{},[2334,23195,23196],{"scriptlevel":2336,"displaystyle":2013},[2338,23197,23198,23201],{},[2138,23199,23200],{},"605",[2138,23202,22952],{},[2005,23204,5906],{},[2005,23206,2234],{},[2138,23208,23209],{},"43,214",[902,23211,23212],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,23215,23216,21356,23218,23239,23240,23243,23244,23266,23267,1644],{},[38,23217,21355],{},[883,23219,23221],{"className":23220},[886],[888,23222,23223],{"xmlns":890},[892,23224,23225,23237],{},[895,23226,23227,23229,23231,23233,23235],{},[898,23228,1852],{},[2297,23230,12296],{},[898,23232,12190],{},[2297,23234,12296],{},[898,23236,12118],{},[902,23238,18227],{"encoding":904}," stále uvažuje ",[38,23241,23242],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,23245,23247],{"className":23246},[886],[888,23248,23249],{"xmlns":890},[892,23250,23251,23263],{},[895,23252,23253,23255,23257,23259,23261],{},[898,23254,12326],{},[2005,23256,2007],{},[898,23258,1844],{},[2005,23260,2234],{},[898,23262,2826],{},[902,23264,23265],{"encoding":904},"X = B - M"," dává ",[38,23268,21377,23269],{},[883,23270,23272],{"className":23271},[886],[888,23273,23274],{"xmlns":890},[892,23275,23276,23292],{},[895,23277,23278,23280,23282,23284,23286,23288,23290],{},[898,23279,1852],{},[2297,23281,12296],{},[898,23283,12190],{},[2297,23285,12296],{},[898,23287,12118],{},[2297,23289,12296],{},[898,23291,12326],{},[902,23293,12329],{"encoding":904},[115,23295,23297],{"id":23296},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,23299,20627],{"id":23300},"zadání-modelu-2",[724,23302,23303,23304,2212,23307,21600,23328,23341,23342,12134,23345,23358],{},"Rozšíření o ",[38,23305,23306],{},"čistý export",[883,23308,23310],{"className":23309},[886],[888,23311,23312],{"xmlns":890},[892,23313,23314,23326],{},[895,23315,23316,23318,23320,23322,23324],{},[898,23317,12326],{},[2005,23319,2007],{},[898,23321,1844],{},[2005,23323,2234],{},[898,23325,2826],{},[902,23327,23265],{"encoding":904},[883,23329,23331],{"className":23330},[886],[888,23332,23333],{"xmlns":890},[892,23334,23335,23339],{},[895,23336,23337],{},[898,23338,1844],{},[902,23340,1844],{"encoding":904}," je hrubý export (",[614,23343,23344],{},"brutto export",[883,23346,23348],{"className":23347},[886],[888,23349,23350],{"xmlns":890},[892,23351,23352,23356],{},[895,23353,23354],{},[898,23355,2826],{},[902,23357,2826],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,23360,23361],{},[883,23362,23364],{"className":23363},[886],[888,23365,23366],{"xmlns":890},[892,23367,23368,23388],{},[895,23369,23370,23372,23374,23376,23378,23384,23386],{},[898,23371,2826],{},[2005,23373,2007],{},[898,23375,2826],{},[2005,23377,2014],{"stretchy":2013},[2281,23379,23380,23382],{},[898,23381,9134],{},[898,23383,1860],{},[2005,23385,2020],{"stretchy":2013},[898,23387,1644],{"mathvariant":2385},[902,23389,23390],{"encoding":904},"M = M(Y_D).",[724,23392,23393],{},"Podmínka rovnováhy:",[724,23395,23396],{},[883,23397,23399],{"className":23398},[886],[888,23400,23401],{"xmlns":890},[892,23402,23403,23440],{},[895,23404,23405,23407,23409,23411,23413,23415,23417,23419,23421,23423,23425,23427,23429,23431,23433,23436,23438],{},[898,23406,9134],{},[2005,23408,2007],{},[898,23410,1852],{},[2005,23412,2104],{},[898,23414,12190],{},[2005,23416,2104],{},[898,23418,12118],{},[2005,23420,2104],{},[898,23422,1844],{},[2005,23424,2234],{},[898,23426,2826],{},[898,23428,1644],{"mathvariant":2385},[5884,23430],{"width":5886},[2005,23432,2014],{"stretchy":2013},[2138,23434,23435],{},"7.10",[2297,23437,207],{},[2005,23439,2020],{"stretchy":2013},[902,23441,23442],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,23444,20697],{"id":23445},"soustava-rovnic-2",[724,23447,21857,23448,23482,23483,2713],{},[883,23449,23451],{"className":23450},[886],[888,23452,23453],{"xmlns":890},[892,23454,23455,23479],{},[895,23456,23457,23463,23465,23471,23473],{},[2133,23458,23459,23461],{},[898,23460,12190],{},[2005,23462,4360],{},[2005,23464,2295],{"separator":2294},[2133,23466,23467,23469],{},[898,23468,12118],{},[2005,23470,4360],{},[2005,23472,2295],{"separator":2294},[2133,23474,23475,23477],{},[898,23476,1844],{},[2005,23478,4360],{},[902,23480,23481],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,23484,23486],{"className":23485},[886],[888,23487,23488],{"xmlns":890},[892,23489,23490,23514],{},[895,23491,23492,23494,23496,23498,23500,23502,23504,23510,23512],{},[898,23493,9134],{},[2005,23495,2295],{"separator":2294},[898,23497,1852],{},[2005,23499,2295],{"separator":2294},[898,23501,2783],{},[2005,23503,2295],{"separator":2294},[2281,23505,23506,23508],{},[898,23507,9134],{},[898,23509,1860],{},[2005,23511,2295],{"separator":2294},[898,23513,2826],{},[902,23515,23516],{"encoding":904},"Y, C, T, Y_D, M",[724,23518,23519],{},[883,23520,23522],{"className":23521},[886],[888,23523,23524],{"xmlns":890},[892,23525,23526,23710],{},[895,23527,23528,23702,23704,23706,23708],{},[20760,23529,23530,23562,23592,23620,23652],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,23531,23532,23538],{},[20768,23533,23534],{},[2334,23535,23536],{"scriptlevel":2336,"displaystyle":2294},[898,23537,1852],{},[20768,23539,23540],{},[2334,23541,23542],{"scriptlevel":2336,"displaystyle":2294},[895,23543,23544,23546,23548,23550,23552,23558,23560],{},[895,23545],{},[2005,23547,2007],{},[898,23549,1852],{},[2005,23551,2014],{"stretchy":2013},[2281,23553,23554,23556],{},[898,23555,9134],{},[898,23557,1860],{},[2005,23559,2020],{"stretchy":2013},[2005,23561,2295],{"separator":2294},[20765,23563,23564,23574],{},[20768,23565,23566],{},[2334,23567,23568],{"scriptlevel":2336,"displaystyle":2294},[2281,23569,23570,23572],{},[898,23571,9134],{},[898,23573,1860],{},[20768,23575,23576],{},[2334,23577,23578],{"scriptlevel":2336,"displaystyle":2294},[895,23579,23580,23582,23584,23586,23588,23590],{},[895,23581],{},[2005,23583,2007],{},[898,23585,9134],{},[2005,23587,2234],{},[898,23589,2783],{},[2005,23591,2295],{"separator":2294},[20765,23593,23594,23600],{},[20768,23595,23596],{},[2334,23597,23598],{"scriptlevel":2336,"displaystyle":2294},[898,23599,2783],{},[20768,23601,23602],{},[2334,23603,23604],{"scriptlevel":2336,"displaystyle":2294},[895,23605,23606,23608,23610,23612,23614,23616,23618],{},[895,23607],{},[2005,23609,2007],{},[898,23611,2783],{},[2005,23613,2014],{"stretchy":2013},[898,23615,9134],{},[2005,23617,2020],{"stretchy":2013},[2005,23619,2295],{"separator":2294},[20765,23621,23622,23628],{},[20768,23623,23624],{},[2334,23625,23626],{"scriptlevel":2336,"displaystyle":2294},[898,23627,2826],{},[20768,23629,23630],{},[2334,23631,23632],{"scriptlevel":2336,"displaystyle":2294},[895,23633,23634,23636,23638,23640,23642,23648,23650],{},[895,23635],{},[2005,23637,2007],{},[898,23639,2826],{},[2005,23641,2014],{"stretchy":2013},[2281,23643,23644,23646],{},[898,23645,9134],{},[898,23647,1860],{},[2005,23649,2020],{"stretchy":2013},[2005,23651,2295],{"separator":2294},[20765,23653,23654,23660],{},[20768,23655,23656],{},[2334,23657,23658],{"scriptlevel":2336,"displaystyle":2294},[898,23659,9134],{},[20768,23661,23662],{},[2334,23663,23664],{"scriptlevel":2336,"displaystyle":2294},[895,23665,23666,23668,23670,23672,23674,23680,23682,23688,23690,23696,23698,23700],{},[895,23667],{},[2005,23669,2007],{},[898,23671,1852],{},[2005,23673,2104],{},[2133,23675,23676,23678],{},[898,23677,12190],{},[2005,23679,4360],{},[2005,23681,2104],{},[2133,23683,23684,23686],{},[898,23685,12118],{},[2005,23687,4360],{},[2005,23689,2104],{},[2133,23691,23692,23694],{},[898,23693,1844],{},[2005,23695,4360],{},[2005,23697,2234],{},[898,23699,2826],{},[898,23701,1644],{"mathvariant":2385},[5884,23703],{"width":5886},[2005,23705,2014],{"stretchy":2013},[2138,23707,23435],{},[2005,23709,2020],{"stretchy":2013},[902,23711,23712],{"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)",[198,23714,23716],{"id":23715},"příklad-75","Příklad 7.5",[724,23718,23719,23720,1343,23752,1343,23779,1343,23800,1343,23822,1343,23844,23867],{},"Dáno: ",[883,23721,23723],{"className":23722},[886],[888,23724,23725],{"xmlns":890},[892,23726,23727,23749],{},[895,23728,23729,23731,23733,23736,23738,23744,23746],{},[898,23730,1852],{},[2005,23732,2007],{},[2138,23734,23735],{},"0,75",[2297,23737,2995],{},[2281,23739,23740,23742],{},[898,23741,9134],{},[898,23743,1860],{},[2005,23745,2104],{},[2138,23747,23748],{},"750",[902,23750,23751],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,23753,23755],{"className":23754},[886],[888,23756,23757],{"xmlns":890},[892,23758,23759,23776],{},[895,23760,23761,23763,23765,23768,23770],{},[898,23762,2826],{},[2005,23764,2007],{},[2138,23766,23767],{},"0,15",[2297,23769,2995],{},[2281,23771,23772,23774],{},[898,23773,9134],{},[898,23775,1860],{},[902,23777,23778],{"encoding":904},"M = 0{,}15\\,Y_D",[883,23780,23782],{"className":23781},[886],[888,23783,23784],{"xmlns":890},[892,23785,23786,23797],{},[895,23787,23788,23790,23792,23795],{},[898,23789,2783],{},[2005,23791,2007],{},[2138,23793,23794],{},"0,25",[898,23796,9134],{},[902,23798,23799],{"encoding":904},"T = 0{,}25Y",[883,23801,23803],{"className":23802},[886],[888,23804,23805],{"xmlns":890},[892,23806,23807,23819],{},[895,23808,23809,23815,23817],{},[2133,23810,23811,23813],{},[898,23812,12190],{},[2005,23814,4360],{},[2005,23816,2007],{},[2138,23818,15116],{},[902,23820,23821],{"encoding":904},"I^* = 500",[883,23823,23825],{"className":23824},[886],[888,23826,23827],{"xmlns":890},[892,23828,23829,23841],{},[895,23830,23831,23837,23839],{},[2133,23832,23833,23835],{},[898,23834,12118],{},[2005,23836,4360],{},[2005,23838,2007],{},[2138,23840,8809],{},[902,23842,23843],{"encoding":904},"G^* = 150",[883,23845,23847],{"className":23846},[886],[888,23848,23849],{"xmlns":890},[892,23850,23851,23864],{},[895,23852,23853,23859,23861],{},[2133,23854,23855,23857],{},[898,23856,1844],{},[2005,23858,4360],{},[2005,23860,2007],{},[2138,23862,23863],{},"800",[902,23865,23866],{"encoding":904},"B^* = 800",". Soustava:",[724,23869,23870],{},[883,23871,23873],{"className":23872},[886],[888,23874,23875],{"xmlns":890},[892,23876,23877,24095],{},[20760,23878,23879,23925,23967,24003,24045],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,23880,23881,23897],{},[20768,23882,23883],{},[2334,23884,23885],{"scriptlevel":2336,"displaystyle":2294},[895,23886,23887,23889,23891,23893,23895],{},[2005,23888,2014],{"stretchy":2013},[898,23890,12047],{},[2138,23892,2287],{},[2005,23894,2020],{"stretchy":2013},[2297,23896,2299],{},[20768,23898,23899],{},[2334,23900,23901],{"scriptlevel":2336,"displaystyle":2294},[895,23902,23903,23905,23907,23909,23911,23913,23919,23921,23923],{},[895,23904],{},[898,23906,1852],{},[2005,23908,2007],{},[2138,23910,23735],{},[2297,23912,2995],{},[2281,23914,23915,23917],{},[898,23916,9134],{},[898,23918,1860],{},[2005,23920,2104],{},[2138,23922,23748],{},[2005,23924,2295],{"separator":2294},[20765,23926,23927,23943],{},[20768,23928,23929],{},[2334,23930,23931],{"scriptlevel":2336,"displaystyle":2294},[895,23932,23933,23935,23937,23939,23941],{},[2005,23934,2014],{"stretchy":2013},[898,23936,12047],{},[2138,23938,2140],{},[2005,23940,2020],{"stretchy":2013},[2297,23942,2299],{},[20768,23944,23945],{},[2334,23946,23947],{"scriptlevel":2336,"displaystyle":2294},[895,23948,23949,23951,23957,23959,23961,23963,23965],{},[895,23950],{},[2281,23952,23953,23955],{},[898,23954,9134],{},[898,23956,1860],{},[2005,23958,2007],{},[898,23960,9134],{},[2005,23962,2234],{},[898,23964,2783],{},[2005,23966,2295],{"separator":2294},[20765,23968,23969,23985],{},[20768,23970,23971],{},[2334,23972,23973],{"scriptlevel":2336,"displaystyle":2294},[895,23974,23975,23977,23979,23981,23983],{},[2005,23976,2014],{"stretchy":2013},[898,23978,12047],{},[2138,23980,2182],{},[2005,23982,2020],{"stretchy":2013},[2297,23984,2299],{},[20768,23986,23987],{},[2334,23988,23989],{"scriptlevel":2336,"displaystyle":2294},[895,23990,23991,23993,23995,23997,23999,24001],{},[895,23992],{},[898,23994,2783],{},[2005,23996,2007],{},[2138,23998,23794],{},[898,24000,9134],{},[2005,24002,2295],{"separator":2294},[20765,24004,24005,24021],{},[20768,24006,24007],{},[2334,24008,24009],{"scriptlevel":2336,"displaystyle":2294},[895,24010,24011,24013,24015,24017,24019],{},[2005,24012,2014],{"stretchy":2013},[898,24014,12047],{},[2138,24016,2360],{},[2005,24018,2020],{"stretchy":2013},[2297,24020,2299],{},[20768,24022,24023],{},[2334,24024,24025],{"scriptlevel":2336,"displaystyle":2294},[895,24026,24027,24029,24031,24033,24035,24037,24043],{},[895,24028],{},[898,24030,2826],{},[2005,24032,2007],{},[2138,24034,23767],{},[2297,24036,2995],{},[2281,24038,24039,24041],{},[898,24040,9134],{},[898,24042,1860],{},[2005,24044,2295],{"separator":2294},[20765,24046,24047,24063],{},[20768,24048,24049],{},[2334,24050,24051],{"scriptlevel":2336,"displaystyle":2294},[895,24052,24053,24055,24057,24059,24061],{},[2005,24054,2014],{"stretchy":2013},[898,24056,12047],{},[2138,24058,2237],{},[2005,24060,2020],{"stretchy":2013},[2297,24062,2299],{},[20768,24064,24065],{},[2334,24066,24067],{"scriptlevel":2336,"displaystyle":2294},[895,24068,24069,24071,24073,24075,24077,24079,24081,24083,24085,24087,24089,24091,24093],{},[895,24070],{},[898,24072,9134],{},[2005,24074,2007],{},[898,24076,1852],{},[2005,24078,2104],{},[2138,24080,15116],{},[2005,24082,2104],{},[2138,24084,8809],{},[2005,24086,2104],{},[2138,24088,23863],{},[2005,24090,2234],{},[898,24092,2826],{},[898,24094,1644],{"mathvariant":2385},[902,24096,24097],{"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}",[724,24099,24100,24101,24135],{},"Postupná substituce — z (r3) do (r2): ",[883,24102,24104],{"className":24103},[886],[888,24105,24106],{"xmlns":890},[892,24107,24108,24132],{},[895,24109,24110,24116,24118,24120,24122,24124,24126,24128,24130],{},[2281,24111,24112,24114],{},[898,24113,9134],{},[898,24115,1860],{},[2005,24117,2007],{},[898,24119,9134],{},[2005,24121,2234],{},[2138,24123,23794],{},[898,24125,9134],{},[2005,24127,2007],{},[2138,24129,23735],{},[898,24131,9134],{},[902,24133,24134],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,24137,24138],{},[883,24139,24141],{"className":24140},[886],[888,24142,24143],{"xmlns":890},[892,24144,24145,24186],{},[895,24146,24147,24149,24151,24153,24155,24157,24159,24161,24163,24165,24167,24169,24171,24173,24175,24178,24180,24182,24184],{},[2005,24148,2014],{"stretchy":2013},[898,24150,12047],{},[2138,24152,2244],{},[2005,24154,2020],{"stretchy":2013},[2297,24156,2299],{},[898,24158,1852],{},[2005,24160,2007],{},[2138,24162,23735],{},[2005,24164,3185],{},[2138,24166,23735],{},[898,24168,9134],{},[2005,24170,2104],{},[2138,24172,23748],{},[2005,24174,2007],{},[2138,24176,24177],{},"0,5625",[898,24179,9134],{},[2005,24181,2104],{},[2138,24183,23748],{},[2005,24185,2295],{"separator":2294},[902,24187,24188],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,24190,24191],{},[883,24192,24194],{"className":24193},[886],[888,24195,24196],{"xmlns":890},[892,24197,24198,24232],{},[895,24199,24200,24202,24204,24207,24209,24211,24213,24215,24217,24219,24221,24223,24225,24228,24230],{},[2005,24201,2014],{"stretchy":2013},[898,24203,12047],{},[2138,24205,24206],{},"7",[2005,24208,2020],{"stretchy":2013},[2297,24210,2299],{},[898,24212,2826],{},[2005,24214,2007],{},[2138,24216,23767],{},[2005,24218,3185],{},[2138,24220,23735],{},[898,24222,9134],{},[2005,24224,2007],{},[2138,24226,24227],{},"0,1125",[898,24229,9134],{},[898,24231,1644],{"mathvariant":2385},[902,24233,24234],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,24236,24237],{},"Dosazením do (r5):",[724,24239,24240],{},[883,24241,24243],{"className":24242},[886],[888,24244,24245],{"xmlns":890},[892,24246,24247,24291],{},[895,24248,24249,24251,24253,24255,24257,24259,24261,24263,24265,24267,24269,24271,24273,24275,24277,24279,24281,24284,24286,24288],{},[898,24250,9134],{},[2005,24252,2007],{},[2138,24254,24177],{},[898,24256,9134],{},[2005,24258,2104],{},[2138,24260,23748],{},[2005,24262,2104],{},[2138,24264,15116],{},[2005,24266,2104],{},[2138,24268,8809],{},[2005,24270,2104],{},[2138,24272,23863],{},[2005,24274,2234],{},[2138,24276,24227],{},[898,24278,9134],{},[2005,24280,2007],{},[2138,24282,24283],{},"0,45",[898,24285,9134],{},[2005,24287,2104],{},[2138,24289,24290],{},"2200.",[902,24292,24293],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,24295,24296,24297,5595,24319,24342],{},"Odtud ",[883,24298,24300],{"className":24299},[886],[888,24301,24302],{"xmlns":890},[892,24303,24304,24316],{},[895,24305,24306,24309,24311,24313],{},[2138,24307,24308],{},"0,55",[898,24310,9134],{},[2005,24312,2007],{},[2138,24314,24315],{},"2200",[902,24317,24318],{"encoding":904},"0{,}55Y = 2200",[883,24320,24322],{"className":24321},[886],[888,24323,24324],{"xmlns":890},[892,24325,24326,24339],{},[895,24327,24328,24334,24336],{},[2133,24329,24330,24332],{},[898,24331,9134],{},[898,24333,1868],{},[2005,24335,2007],{},[2138,24337,24338],{},"4000",[902,24340,24341],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,24344,24345,24368,24400,24435,24468,24504],{},[123,24346,24347,2295],{},[883,24348,24350],{"className":24349},[886],[888,24351,24352],{"xmlns":890},[892,24353,24354,24366],{},[895,24355,24356,24362,24364],{},[2133,24357,24358,24360],{},[898,24359,9134],{},[898,24361,1868],{},[2005,24363,2007],{},[2138,24365,24338],{},[902,24367,24341],{"encoding":904},[123,24369,24370,2295],{},[883,24371,24373],{"className":24372},[886],[888,24374,24375],{"xmlns":890},[892,24376,24377,24397],{},[895,24378,24379,24385,24387,24389,24391,24393,24395],{},[2133,24380,24381,24383],{},[898,24382,2783],{},[898,24384,1868],{},[2005,24386,2007],{},[2138,24388,23794],{},[2005,24390,3185],{},[2138,24392,24338],{},[2005,24394,2007],{},[2138,24396,2790],{},[902,24398,24399],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,24401,24402,2295],{},[883,24403,24405],{"className":24404},[886],[888,24406,24407],{"xmlns":890},[892,24408,24409,24432],{},[895,24410,24411,24419,24421,24423,24425,24427,24429],{},[9172,24412,24413,24415,24417],{},[898,24414,9134],{},[898,24416,1860],{},[898,24418,1868],{},[2005,24420,2007],{},[2138,24422,23735],{},[2005,24424,3185],{},[2138,24426,24338],{},[2005,24428,2007],{},[2138,24430,24431],{},"3000",[902,24433,24434],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,24436,24437,2295],{},[883,24438,24440],{"className":24439},[886],[888,24441,24442],{"xmlns":890},[892,24443,24444,24465],{},[895,24445,24446,24452,24454,24456,24458,24460,24462],{},[2133,24447,24448,24450],{},[898,24449,2826],{},[898,24451,1868],{},[2005,24453,2007],{},[2138,24455,23767],{},[2005,24457,3185],{},[2138,24459,24431],{},[2005,24461,2007],{},[2138,24463,24464],{},"450",[902,24466,24467],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,24469,24470,2295],{},[883,24471,24473],{"className":24472},[886],[888,24474,24475],{"xmlns":890},[892,24476,24477,24501],{},[895,24478,24479,24485,24487,24489,24491,24493,24495,24497,24499],{},[2133,24480,24481,24483],{},[898,24482,1852],{},[898,24484,1868],{},[2005,24486,2007],{},[2138,24488,23735],{},[2005,24490,3185],{},[2138,24492,24431],{},[2005,24494,2104],{},[2138,24496,23748],{},[2005,24498,2007],{},[2138,24500,24431],{},[902,24502,24503],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,24505,24506,24546],{},[883,24507,24509],{"className":24508},[886],[888,24510,24511],{"xmlns":890},[892,24512,24513,24543],{},[895,24514,24515,24521,24523,24531,24533,24539,24541],{},[2133,24516,24517,24519],{},[898,24518,8679],{},[898,24520,1868],{},[2005,24522,2007],{},[9172,24524,24525,24527,24529],{},[898,24526,9134],{},[898,24528,1860],{},[898,24530,1868],{},[2005,24532,2234],{},[2133,24534,24535,24537],{},[898,24536,1852],{},[898,24538,1868],{},[2005,24540,2007],{},[2138,24542,2336],{},[902,24544,24545],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,24548,24549,24551,24552,1343,24569,3894,24590,24615,24616,24619,24620,24633,24634,1644],{},[38,24550,21355],{}," Modely ",[883,24553,24555],{"className":24554},[886],[888,24556,24557],{"xmlns":890},[892,24558,24559,24567],{},[895,24560,24561,24563,24565],{},[898,24562,1852],{},[2297,24564,12296],{},[898,24566,12190],{},[902,24568,12301],{"encoding":904},[883,24570,24572],{"className":24571},[886],[888,24573,24574],{"xmlns":890},[892,24575,24576,24588],{},[895,24577,24578,24580,24582,24584,24586],{},[898,24579,1852],{},[2297,24581,12296],{},[898,24583,12190],{},[2297,24585,12296],{},[898,24587,12118],{},[902,24589,18227],{"encoding":904},[883,24591,24593],{"className":24592},[886],[888,24594,24595],{"xmlns":890},[892,24596,24597,24613],{},[895,24598,24599,24601,24603,24605,24607,24609,24611],{},[898,24600,1852],{},[2297,24602,12296],{},[898,24604,12190],{},[2297,24606,12296],{},[898,24608,12118],{},[2297,24610,12296],{},[898,24612,12326],{},[902,24614,12329],{"encoding":904}," pokládají investice za ",[38,24617,24618],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,24621,24623],{"className":24622},[886],[888,24624,24625],{"xmlns":890},[892,24626,24627,24631],{},[895,24628,24629],{},[898,24630,12047],{},[902,24632,12047],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,24635,24636],{},"model IS-LM",[115,24638,24640],{"id":24639},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,24642,24643,24644,24648,24649,24652,24653,24656],{},"V článku ",[207,24645,24647],{"className":24646,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,24650,24651],{},"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 ",[38,24654,24655],{},"výraznější"," než v mikroekonomických modelech.",[724,24658,24659],{},[2568,24660],{"alt":24661,"className":24662,"src":24663},"imek-multiplikatorovy-efekt-chain",[210,2572],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,24665,12170,24666,1343,24683,1343,24704,24729,24730,24733,24734,24752,24753,24771,24772,24790,24791,24794,24795,1343,24812,24829,24830,24832],{},[883,24667,24669],{"className":24668},[886],[888,24670,24671],{"xmlns":890},[892,24672,24673,24681],{},[895,24674,24675,24677,24679],{},[898,24676,1852],{},[2297,24678,12296],{},[898,24680,12190],{},[902,24682,12301],{"encoding":904},[883,24684,24686],{"className":24685},[886],[888,24687,24688],{"xmlns":890},[892,24689,24690,24702],{},[895,24691,24692,24694,24696,24698,24700],{},[898,24693,1852],{},[2297,24695,12296],{},[898,24697,12190],{},[2297,24699,12296],{},[898,24701,12118],{},[902,24703,18227],{"encoding":904},[883,24705,24707],{"className":24706},[886],[888,24708,24709],{"xmlns":890},[892,24710,24711,24727],{},[895,24712,24713,24715,24717,24719,24721,24723,24725],{},[898,24714,1852],{},[2297,24716,12296],{},[898,24718,12190],{},[2297,24720,12296],{},[898,24722,12118],{},[2297,24724,12296],{},[898,24726,12326],{},[902,24728,12329],{"encoding":904}," se vyšetřuje vliv změn ",[38,24731,24732],{},"exogenních"," veličin (plánovaných investic ",[883,24735,24737],{"className":24736},[886],[888,24738,24739],{"xmlns":890},[892,24740,24741,24749],{},[895,24742,24743],{},[2133,24744,24745,24747],{},[898,24746,12190],{},[2005,24748,4360],{},[902,24750,24751],{"encoding":904},"I^*",", vládních výdajů ",[883,24754,24756],{"className":24755},[886],[888,24757,24758],{"xmlns":890},[892,24759,24760,24768],{},[895,24761,24762],{},[2133,24763,24764,24766],{},[898,24765,12118],{},[2005,24767,4360],{},[902,24769,24770],{"encoding":904},"G^*",", exportu ",[883,24773,24775],{"className":24774},[886],[888,24776,24777],{"xmlns":890},[892,24778,24779,24787],{},[895,24780,24781],{},[2133,24782,24783,24785],{},[898,24784,1844],{},[2005,24786,4360],{},[902,24788,24789],{"encoding":904},"B^*",") na změny ",[38,24792,24793],{},"endogenních"," rovnovážných veličin (",[883,24796,24798],{"className":24797},[886],[888,24799,24800],{"xmlns":890},[892,24801,24802,24810],{},[895,24803,24804],{},[2133,24805,24806,24808],{},[898,24807,9134],{},[898,24809,1868],{},[902,24811,13909],{"encoding":904},[883,24813,24815],{"className":24814},[886],[888,24816,24817],{"xmlns":890},[892,24818,24819,24827],{},[895,24820,24821],{},[2133,24822,24823,24825],{},[898,24824,1852],{},[898,24826,1868],{},[902,24828,13968],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,24831,17984],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,24834,24836],{"id":24835},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,24838,20901,24839,24862,24863,24907],{},[883,24840,24842],{"className":24841},[886],[888,24843,24844],{"xmlns":890},[892,24845,24846,24860],{},[895,24847,24848,24850,24852,24854,24856,24858],{},[898,24849,1852],{},[2005,24851,2007],{},[898,24853,207],{},[898,24855,9134],{},[2005,24857,2104],{},[898,24859,2107],{},[902,24861,18926],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,24864,24866],{"className":24865},[886],[888,24867,24868],{"xmlns":890},[892,24869,24870,24904],{},[895,24871,24872,24878,24880],{},[2133,24873,24874,24876],{},[898,24875,9134],{},[898,24877,1868],{},[2005,24879,2007],{},[2334,24881,24882],{"scriptlevel":2336,"displaystyle":2294},[2338,24883,24884,24896],{},[895,24885,24886,24888,24890],{},[898,24887,2107],{},[2005,24889,2104],{},[2133,24891,24892,24894],{},[898,24893,12190],{},[2005,24895,4360],{},[895,24897,24898,24900,24902],{},[2138,24899,2287],{},[2005,24901,2234],{},[898,24903,207],{},[902,24905,24906],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,24909,24910],{},[883,24911,24913],{"className":24912},[886],[888,24914,24915],{"xmlns":890},[892,24916,24917,24986],{},[895,24918,24919,24937,24939,24969,24971],{},[2338,24920,24921,24931],{},[895,24922,24923,24925],{},[898,24924,9877],{"mathvariant":2385},[2133,24926,24927,24929],{},[898,24928,9134],{},[898,24930,1868],{},[895,24932,24933,24935],{},[898,24934,9877],{"mathvariant":2385},[898,24936,207],{},[2005,24938,2007],{},[2338,24940,24941,24953],{},[895,24942,24943,24945,24947],{},[898,24944,2107],{},[2005,24946,2104],{},[2133,24948,24949,24951],{},[898,24950,12190],{},[2005,24952,4360],{},[895,24954,24955,24957,24959,24961,24963],{},[2005,24956,2014],{"stretchy":2013},[2138,24958,2287],{},[2005,24960,2234],{},[898,24962,207],{},[2133,24964,24965,24967],{},[2005,24966,2020],{"stretchy":2013},[2138,24968,2140],{},[5884,24970],{"width":5886},[895,24972,24973,24976,24983],{},[2297,24974,24975],{},"(multiplik",[8392,24977,24978,24980],{"accent":2294},[2297,24979,207],{},[2005,24981,24982],{},"ˊ",[2297,24984,24985],{},"tor MPC)",[902,24987,24988],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,24990,24991],{},[883,24992,24994],{"className":24993},[886],[888,24995,24996],{"xmlns":890},[892,24997,24998,25067],{},[895,24999,25000,25018,25020,25032,25034],{},[2338,25001,25002,25012],{},[895,25003,25004,25006],{},[898,25005,9877],{"mathvariant":2385},[2133,25007,25008,25010],{},[898,25009,9134],{},[898,25011,1868],{},[895,25013,25014,25016],{},[898,25015,9877],{"mathvariant":2385},[898,25017,2107],{},[2005,25019,2007],{},[2338,25021,25022,25024],{},[2138,25023,2287],{},[895,25025,25026,25028,25030],{},[2138,25027,2287],{},[2005,25029,2234],{},[898,25031,207],{},[5884,25033],{"width":5886},[895,25035,25036,25038,25044,25047,25054,25057,25064],{},[2297,25037,24975],{},[8392,25039,25040,25042],{"accent":2294},[2297,25041,207],{},[2005,25043,24982],{},[2297,25045,25046],{},"tor autonomn",[8392,25048,25049,25052],{"accent":2294},[2297,25050,25051],{},"ı",[2005,25053,24982],{},[2297,25055,25056],{}," spot",[8392,25058,25059,25061],{"accent":2294},[2297,25060,12047],{},[2005,25062,25063],{},"ˇ",[2297,25065,25066],{},"eby)",[902,25068,25069],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,25071,25072],{},[883,25073,25075],{"className":25074},[886],[888,25076,25077],{"xmlns":890},[892,25078,25079,25146],{},[895,25080,25081,25103,25105,25117,25119,25131,25133],{},[2338,25082,25083,25093],{},[895,25084,25085,25087],{},[898,25086,9877],{"mathvariant":2385},[2133,25088,25089,25091],{},[898,25090,9134],{},[898,25092,1868],{},[895,25094,25095,25097],{},[898,25096,9877],{"mathvariant":2385},[2133,25098,25099,25101],{},[898,25100,12190],{},[2005,25102,4360],{},[2005,25104,2007],{},[2338,25106,25107,25109],{},[2138,25108,2287],{},[895,25110,25111,25113,25115],{},[2138,25112,2287],{},[2005,25114,2234],{},[898,25116,207],{},[2005,25118,2007],{},[2338,25120,25121,25123],{},[2138,25122,2287],{},[895,25124,25125,25127,25129],{},[898,25126,2826],{},[898,25128,3946],{},[898,25130,8679],{},[5884,25132],{"width":5886},[895,25134,25135,25137,25143],{},[2297,25136,24975],{},[8392,25138,25139,25141],{"accent":2294},[2297,25140,207],{},[2005,25142,24982],{},[2297,25144,25145],{},"tor investic)",[902,25147,25148],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[3876,25150,25151],{},[724,25152,25153,25155,25156,25159,25160,25173,25174,25191,25192,25210,25211,25255,25256,21426,25273,25276,25277,25294],{},[883,25154,4164],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,25157,25158],{},"důchodem","; z něj se utratí ",[883,25161,25163],{"className":25162},[886],[888,25164,25165],{"xmlns":890},[892,25166,25167,25171],{},[895,25168,25169],{},[898,25170,207],{},[902,25172,207],{"encoding":904}," Kč (= ",[883,25175,25177],{"className":25176},[886],[888,25178,25179],{"xmlns":890},[892,25180,25181,25189],{},[895,25182,25183,25185,25187],{},[898,25184,2826],{},[898,25186,3946],{},[898,25188,1852],{},[902,25190,18052],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,25193,25195],{"className":25194},[886],[888,25196,25197],{"xmlns":890},[892,25198,25199,25207],{},[895,25200,25201],{},[2133,25202,25203,25205],{},[898,25204,207],{},[2138,25206,2140],{},[902,25208,25209],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,25212,25214],{"className":25213},[886],[888,25215,25216],{"xmlns":890},[892,25217,25218,25252],{},[895,25219,25220,25222,25224,25226,25228,25234,25236,25238,25240],{},[2138,25221,2287],{},[2005,25223,2104],{},[898,25225,207],{},[2005,25227,2104],{},[2133,25229,25230,25232],{},[898,25231,207],{},[2138,25233,2140],{},[2005,25235,2104],{},[2005,25237,18112],{},[2005,25239,2007],{},[2338,25241,25242,25244],{},[2138,25243,2287],{},[895,25245,25246,25248,25250],{},[2138,25247,2287],{},[2005,25249,2234],{},[898,25251,207],{},[902,25253,25254],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,25257,25259],{"className":25258},[886],[888,25260,25261],{"xmlns":890},[892,25262,25263,25271],{},[895,25264,25265],{},[2133,25266,25267,25269],{},[898,25268,9134],{},[898,25270,1868],{},[902,25272,13909],{"encoding":904},[38,25274,25275],{},"více"," než korunu — čím vyšší ",[883,25278,25280],{"className":25279},[886],[888,25281,25282],{"xmlns":890},[892,25283,25284,25292],{},[895,25285,25286,25288,25290],{},[898,25287,2826],{},[898,25289,3946],{},[898,25291,1852],{},[902,25293,18052],{"encoding":904},", tím silnější multiplikační efekt.",[724,25296,25297,25300,25301,25327,25328,25331,25332,3894,25353,25378,25379,1644],{},[38,25298,25299],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,25302,25304],{"className":25303},[886],[888,25305,25306],{"xmlns":890},[892,25307,25308,25324],{},[895,25309,25310],{},[2334,25311,25312],{"scriptlevel":2336,"displaystyle":2013},[2338,25313,25314,25316],{},[2138,25315,2287],{},[895,25317,25318,25320,25322],{},[2138,25319,2287],{},[2005,25321,2234],{},[898,25323,207],{},[902,25325,25326],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,25329,25330],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,25333,25335],{"className":25334},[886],[888,25336,25337],{"xmlns":890},[892,25338,25339,25351],{},[895,25340,25341,25343,25345,25347,25349],{},[898,25342,1852],{},[2297,25344,12296],{},[898,25346,12190],{},[2297,25348,12296],{},[898,25350,12118],{},[902,25352,18227],{"encoding":904},[883,25354,25356],{"className":25355},[886],[888,25357,25358],{"xmlns":890},[892,25359,25360,25376],{},[895,25361,25362,25364,25366,25368,25370,25372,25374],{},[898,25363,1852],{},[2297,25365,12296],{},[898,25367,12190],{},[2297,25369,12296],{},[898,25371,12118],{},[2297,25373,12296],{},[898,25375,12326],{},[902,25377,12329],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,25380,25382],{"className":25381,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,25384,25386],{"id":25385},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,25388,12170,25389,1343,25406,3894,25427,12175,25452,10030,25455,25476,25477,2212,25480,25493,25494,5675,25523,25540,25541,25544,25545,25547,25548,25569],{},[883,25390,25392],{"className":25391},[886],[888,25393,25394],{"xmlns":890},[892,25395,25396,25404],{},[895,25397,25398,25400,25402],{},[898,25399,1852],{},[2297,25401,12296],{},[898,25403,12190],{},[902,25405,12301],{"encoding":904},[883,25407,25409],{"className":25408},[886],[888,25410,25411],{"xmlns":890},[892,25412,25413,25425],{},[895,25414,25415,25417,25419,25421,25423],{},[898,25416,1852],{},[2297,25418,12296],{},[898,25420,12190],{},[2297,25422,12296],{},[898,25424,12118],{},[902,25426,18227],{"encoding":904},[883,25428,25430],{"className":25429},[886],[888,25431,25432],{"xmlns":890},[892,25433,25434,25450],{},[895,25435,25436,25438,25440,25442,25444,25446,25448],{},[898,25437,1852],{},[2297,25439,12296],{},[898,25441,12190],{},[2297,25443,12296],{},[898,25445,12118],{},[2297,25447,12296],{},[898,25449,12326],{},[902,25451,12329],{"encoding":904},[38,25453,25454],{},"investice konstantní",[883,25456,25458],{"className":25457},[886],[888,25459,25460],{"xmlns":890},[892,25461,25462,25474],{},[895,25463,25464,25466,25468],{},[898,25465,12190],{},[2005,25467,2007],{},[2133,25469,25470,25472],{},[898,25471,12190],{},[2005,25473,4360],{},[902,25475,12201],{"encoding":904},"). Reálnější je předpoklad, že ",[38,25478,25479],{},"investice závisejí na úrokové míře",[883,25481,25483],{"className":25482},[886],[888,25484,25485],{"xmlns":890},[892,25486,25487,25491],{},[895,25488,25489],{},[898,25490,12047],{},[902,25492,12047],{"encoding":904}," — klesající funkce ",[883,25495,25497],{"className":25496},[886],[888,25498,25499],{"xmlns":890},[892,25500,25501,25521],{},[895,25502,25503,25505,25507,25509,25511,25513,25515,25517,25519],{},[898,25504,12190],{},[2005,25506,2014],{"stretchy":2013},[898,25508,12047],{},[2005,25510,2020],{"stretchy":2013},[2005,25512,2007],{},[898,25514,2151],{},[898,25516,12047],{},[2005,25518,2104],{},[898,25520,2203],{},[902,25522,15763],{"encoding":904},[883,25524,25526],{"className":25525},[886],[888,25527,25528],{"xmlns":890},[892,25529,25530,25538],{},[895,25531,25532,25534,25536],{},[898,25533,2151],{},[2005,25535,3455],{},[2138,25537,2336],{},[902,25539,12521],{"encoding":904},". Přidáním ",[38,25542,25543],{},"trhu peněz"," k trhu zboží vzniká model ",[38,25546,12017],{}," se dvěma neznámými ",[883,25549,25551],{"className":25550},[886],[888,25552,25553],{"xmlns":890},[892,25554,25555,25567],{},[895,25556,25557,25559,25561,25563,25565],{},[2005,25558,2014],{"stretchy":2013},[898,25560,9134],{},[2005,25562,2295],{"separator":2294},[898,25564,12047],{},[2005,25566,2020],{"stretchy":2013},[902,25568,18157],{"encoding":904}," a dvěma rovnicemi:",[120,25571,25572,25622],{},[123,25573,25574,10030,25576,25578,25579,25600,25601,1644],{},[38,25575,15852],{},[614,25577,12060],{},") — klesající přímka v rovině ",[883,25580,25582],{"className":25581},[886],[888,25583,25584],{"xmlns":890},[892,25585,25586,25598],{},[895,25587,25588,25590,25592,25594,25596],{},[2005,25589,2014],{"stretchy":2013},[898,25591,12047],{},[2005,25593,2295],{"separator":2294},[898,25595,9134],{},[2005,25597,2020],{"stretchy":2013},[902,25599,12943],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,25602,25604],{"className":25603},[886],[888,25605,25606],{"xmlns":890},[892,25607,25608,25620],{},[895,25609,25610,25612,25614,25616,25618],{},[898,25611,9134],{},[2005,25613,2007],{},[898,25615,1852],{},[2005,25617,2104],{},[898,25619,12190],{},[902,25621,14750],{"encoding":904},[123,25623,25624,10030,25626,25628,25629,21600,25654,25700],{},[38,25625,16051],{},[614,25627,12067],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,25630,25632],{"className":25631},[886],[888,25633,25634],{"xmlns":890},[892,25635,25636,25652],{},[895,25637,25638,25644,25646],{},[2133,25639,25640,25642],{},[898,25641,2826],{},[898,25643,1860],{},[2005,25645,2007],{},[2133,25647,25648,25650],{},[898,25649,2826],{},[2005,25651,4360],{},[902,25653,13486],{"encoding":904},[883,25655,25657],{"className":25656},[886],[888,25658,25659],{"xmlns":890},[892,25660,25661,25697],{},[895,25662,25663,25669,25671,25677,25679,25681,25687,25689,25691],{},[2133,25664,25665,25667],{},[898,25666,2826],{},[898,25668,1860],{},[2005,25670,2007],{},[2281,25672,25673,25675],{},[898,25674,13243],{},[2138,25676,2287],{},[898,25678,9134],{},[2005,25680,2104],{},[2281,25682,25683,25685],{},[898,25684,13243],{},[2138,25686,2140],{},[898,25688,12047],{},[2005,25690,2104],{},[2281,25692,25693,25695],{},[898,25694,13243],{},[2138,25696,2182],{},[902,25698,25699],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,25702,25703,2212,25706,25739,25740,25742,25743,25745],{},[38,25704,25705],{},"Simultánní rovnovážný bod",[883,25707,25709],{"className":25708},[886],[888,25710,25711],{"xmlns":890},[892,25712,25713,25737],{},[895,25714,25715,25717,25719,25721,25727,25729,25735],{},[898,25716,1868],{},[2005,25718,2007],{},[2005,25720,2014],{"stretchy":2013},[2133,25722,25723,25725],{},[898,25724,12047],{},[898,25726,1868],{},[2005,25728,2295],{"separator":2294},[2133,25730,25731,25733],{},[898,25732,9134],{},[898,25734,1868],{},[2005,25736,2020],{"stretchy":2013},[902,25738,16143],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,25741,12105],{}," (posun IS) a ",[38,25744,12137],{}," (posun LM).",[724,25747,25748],{},[38,25749,25750,25751,1343,25773,1343,25795,1343,25817,25839,25840,1644],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,25752,25754],{"className":25753},[886],[888,25755,25756],{"xmlns":890},[892,25757,25758,25770],{},[895,25759,25760,25766,25768],{},[2133,25761,25762,25764],{},[898,25763,9134],{},[898,25765,1868],{},[2005,25767,2007],{},[2138,25769,15121],{},[902,25771,25772],{"encoding":904},"Y^E = 5000",[883,25774,25776],{"className":25775},[886],[888,25777,25778],{"xmlns":890},[892,25779,25780,25792],{},[895,25781,25782,25788,25790],{},[2133,25783,25784,25786],{},[898,25785,12047],{},[898,25787,1868],{},[2005,25789,2007],{},[2138,25791,2237],{},[902,25793,25794],{"encoding":904},"r^E = 5",[883,25796,25798],{"className":25797},[886],[888,25799,25800],{"xmlns":890},[892,25801,25802,25814],{},[895,25803,25804,25810,25812],{},[2133,25805,25806,25808],{},[898,25807,1852],{},[898,25809,1868],{},[2005,25811,2007],{},[2138,25813,15158],{},[902,25815,25816],{"encoding":904},"C^E = 4100",[883,25818,25820],{"className":25819},[886],[888,25821,25822],{"xmlns":890},[892,25823,25824,25836],{},[895,25825,25826,25832,25834],{},[2133,25827,25828,25830],{},[898,25829,12190],{},[898,25831,1868],{},[2005,25833,2007],{},[2138,25835,15197],{},[902,25837,25838],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,25841,945],{"className":25842,"dataFsResolvedFilePath":943,"href":944},[210],[115,25844,25846],{"id":25845},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,25848,25849,25913,26024,26167,26409,26477],{},[123,25850,25851,25854,25855,25877,25878,25912],{},[38,25852,25853],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,25856,25858],{"className":25857},[886],[888,25859,25860],{"xmlns":890},[892,25861,25862,25874],{},[895,25863,25864,25866,25868,25870,25872],{},[898,25865,12118],{},[898,25867,18301],{},[898,25869,3946],{},[2005,25871,2739],{},[898,25873,9134],{},[902,25875,25876],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,25879,25881],{"className":25880},[886],[888,25882,25883],{"xmlns":890},[892,25884,25885,25909],{},[895,25886,25887,25889,25891,25893,25895,25897,25899,25901,25903,25905,25907],{},[898,25888,12118],{},[898,25890,18301],{},[898,25892,3946],{},[2005,25894,2007],{},[898,25896,1852],{},[2005,25898,2104],{},[898,25900,12190],{},[2005,25902,2104],{},[898,25904,12118],{},[2005,25906,2104],{},[898,25908,12326],{},[902,25910,25911],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,25914,25915,25917,25918,25939,25940,1343,25963,25994,25995,26008,26009,1644],{},[38,25916,18534],{}," splňují ",[883,25919,25921],{"className":25920},[886],[888,25922,25923],{"xmlns":890},[892,25924,25925,25937],{},[895,25926,25927,25929,25931,25933,25935],{},[898,25928,9134],{},[2005,25930,2007],{},[898,25932,1852],{},[2005,25934,2104],{},[898,25936,8679],{},[902,25938,12700],{"encoding":904}," (7.2); lineární model ",[883,25941,25943],{"className":25942},[886],[888,25944,25945],{"xmlns":890},[892,25946,25947,25961],{},[895,25948,25949,25951,25953,25955,25957,25959],{},[898,25950,1852],{},[2005,25952,2007],{},[898,25954,207],{},[898,25956,9134],{},[2005,25958,2104],{},[898,25960,2107],{},[902,25962,18926],{"encoding":904},[883,25964,25966],{"className":25965},[886],[888,25967,25968],{"xmlns":890},[892,25969,25970,25992],{},[895,25971,25972,25974,25976,25978,25980,25982,25984,25986,25988,25990],{},[898,25973,8679],{},[2005,25975,2007],{},[2005,25977,2014],{"stretchy":2013},[2138,25979,2287],{},[2005,25981,2234],{},[898,25983,207],{},[2005,25985,2020],{"stretchy":2013},[898,25987,9134],{},[2005,25989,2234],{},[898,25991,2107],{},[902,25993,19175],{"encoding":904}," s autonomní spotřebou ",[883,25996,25998],{"className":25997},[886],[888,25999,26000],{"xmlns":890},[892,26001,26002,26006],{},[895,26003,26004],{},[898,26005,2107],{},[902,26007,2107],{"encoding":904}," a autonomními úsporami ",[883,26010,26012],{"className":26011},[886],[888,26013,26014],{"xmlns":890},[892,26015,26016,26022],{},[895,26017,26018,26020],{},[2005,26019,2234],{},[898,26021,2107],{},[902,26023,19254],{"encoding":904},[123,26025,26026,2212,26029,1343,26059,26089,26090,26120,26121,1343,26142,1644],{},[38,26027,26028],{},"Mezní sklony",[883,26030,26032],{"className":26031},[886],[888,26033,26034],{"xmlns":890},[892,26035,26036,26056],{},[895,26037,26038,26040,26042,26044,26046,26048,26050,26052,26054],{},[898,26039,2826],{},[898,26041,3946],{},[898,26043,1852],{},[2005,26045,2007],{},[898,26047,2203],{"mathvariant":2385},[898,26049,1852],{},[898,26051,4680],{"mathvariant":2385},[898,26053,2203],{"mathvariant":2385},[898,26055,9134],{},[902,26057,26058],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,26060,26062],{"className":26061},[886],[888,26063,26064],{"xmlns":890},[892,26065,26066,26086],{},[895,26067,26068,26070,26072,26074,26076,26078,26080,26082,26084],{},[898,26069,2826],{},[898,26071,3946],{},[898,26073,8679],{},[2005,26075,2007],{},[898,26077,2203],{"mathvariant":2385},[898,26079,8679],{},[898,26081,4680],{"mathvariant":2385},[898,26083,2203],{"mathvariant":2385},[898,26085,9134],{},[902,26087,26088],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,26091,26093],{"className":26092},[886],[888,26094,26095],{"xmlns":890},[892,26096,26097,26117],{},[895,26098,26099,26101,26103,26105,26107,26109,26111,26113,26115],{},[898,26100,2826],{},[898,26102,3946],{},[898,26104,1852],{},[2005,26106,2104],{},[898,26108,2826],{},[898,26110,3946],{},[898,26112,8679],{},[2005,26114,2007],{},[2138,26116,2287],{},[902,26118,26119],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,26122,26124],{"className":26123},[886],[888,26125,26126],{"xmlns":890},[892,26127,26128,26140],{},[895,26129,26130,26132,26134,26136,26138],{},[898,26131,2826],{},[898,26133,3946],{},[898,26135,1852],{},[2005,26137,2007],{},[898,26139,207],{},[902,26141,19895],{"encoding":904},[883,26143,26145],{"className":26144},[886],[888,26146,26147],{"xmlns":890},[892,26148,26149,26165],{},[895,26150,26151,26153,26155,26157,26159,26161,26163],{},[898,26152,2826],{},[898,26154,3946],{},[898,26156,8679],{},[2005,26158,2007],{},[2138,26160,2287],{},[2005,26162,2234],{},[898,26164,207],{},[902,26166,19921],{"encoding":904},[123,26168,26169,26172,26173],{},[38,26170,26171],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,26174,26175,26263,26332],{},[123,26176,26177,26194,26195,26216,26217,2295],{},[883,26178,26180],{"className":26179},[886],[888,26181,26182],{"xmlns":890},[892,26183,26184,26192],{},[895,26185,26186,26188,26190],{},[898,26187,1852],{},[2297,26189,12296],{},[898,26191,12190],{},[902,26193,12301],{"encoding":904},": ",[883,26196,26198],{"className":26197},[886],[888,26199,26200],{"xmlns":890},[892,26201,26202,26214],{},[895,26203,26204,26206,26208,26210,26212],{},[898,26205,9134],{},[2005,26207,2007],{},[898,26209,1852],{},[2005,26211,2104],{},[898,26213,12190],{},[902,26215,14750],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,26218,26220],{"className":26219},[886],[888,26221,26222],{"xmlns":890},[892,26223,26224,26260],{},[895,26225,26226,26232,26234,26236,26238,26240,26246,26248,26250,26252,26254,26256,26258],{},[2133,26227,26228,26230],{},[898,26229,9134],{},[898,26231,1868],{},[2005,26233,2007],{},[2005,26235,2014],{"stretchy":2013},[898,26237,2107],{},[2005,26239,2104],{},[2133,26241,26242,26244],{},[898,26243,12190],{},[2005,26245,4360],{},[2005,26247,2020],{"stretchy":2013},[898,26249,4680],{"mathvariant":2385},[2005,26251,2014],{"stretchy":2013},[2138,26253,2287],{},[2005,26255,2234],{},[898,26257,207],{},[2005,26259,2020],{"stretchy":2013},[902,26261,26262],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,26264,26265,26286,26287,26306,26307,2295],{},[883,26266,26268],{"className":26267},[886],[888,26269,26270],{"xmlns":890},[892,26271,26272,26284],{},[895,26273,26274,26276,26278,26280,26282],{},[898,26275,1852],{},[2297,26277,12296],{},[898,26279,12190],{},[2297,26281,12296],{},[898,26283,12118],{},[902,26285,18227],{"encoding":904},": přidává vládu, zdanění ",[883,26288,26290],{"className":26289},[886],[888,26291,26292],{"xmlns":890},[892,26293,26294,26304],{},[895,26295,26296,26298,26300,26302],{},[898,26297,2783],{},[2005,26299,2014],{"stretchy":2013},[898,26301,9134],{},[2005,26303,2020],{"stretchy":2013},[902,26305,22225],{"encoding":904}," a disponibilní důchod ",[883,26308,26310],{"className":26309},[886],[888,26311,26312],{"xmlns":890},[892,26313,26314,26330],{},[895,26315,26316,26322,26324,26326,26328],{},[2281,26317,26318,26320],{},[898,26319,9134],{},[898,26321,1860],{},[2005,26323,2007],{},[898,26325,9134],{},[2005,26327,2234],{},[898,26329,2783],{},[902,26331,21724],{"encoding":904},[123,26333,26334,26359,26360,21600,26381,1644],{},[883,26335,26337],{"className":26336},[886],[888,26338,26339],{"xmlns":890},[892,26340,26341,26357],{},[895,26342,26343,26345,26347,26349,26351,26353,26355],{},[898,26344,1852],{},[2297,26346,12296],{},[898,26348,12190],{},[2297,26350,12296],{},[898,26352,12118],{},[2297,26354,12296],{},[898,26356,12326],{},[902,26358,12329],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,26361,26363],{"className":26362},[886],[888,26364,26365],{"xmlns":890},[892,26366,26367,26379],{},[895,26368,26369,26371,26373,26375,26377],{},[898,26370,12326],{},[2005,26372,2007],{},[898,26374,1844],{},[2005,26376,2234],{},[898,26378,2826],{},[902,26380,23265],{"encoding":904},[883,26382,26384],{"className":26383},[886],[888,26385,26386],{"xmlns":890},[892,26387,26388,26406],{},[895,26389,26390,26392,26394,26396,26398,26404],{},[898,26391,2826],{},[2005,26393,2007],{},[898,26395,2826],{},[2005,26397,2014],{"stretchy":2013},[2281,26399,26400,26402],{},[898,26401,9134],{},[898,26403,1860],{},[2005,26405,2020],{"stretchy":2013},[902,26407,26408],{"encoding":904},"M = M(Y_D)",[123,26410,26411,26414,26415,2212,26418,26476],{},[38,26412,26413],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,26416,26417],{},"multiplikátor investic",[883,26419,26421],{"className":26420},[886],[888,26422,26423],{"xmlns":890},[892,26424,26425,26473],{},[895,26426,26427,26429,26435,26437,26439,26445,26447,26449,26451,26453,26455,26457,26459,26461,26463,26465,26467,26469,26471],{},[898,26428,9877],{"mathvariant":2385},[2133,26430,26431,26433],{},[898,26432,9134],{},[898,26434,1868],{},[898,26436,4680],{"mathvariant":2385},[898,26438,9877],{"mathvariant":2385},[2133,26440,26441,26443],{},[898,26442,12190],{},[2005,26444,4360],{},[2005,26446,2007],{},[2138,26448,2287],{},[898,26450,4680],{"mathvariant":2385},[2005,26452,2014],{"stretchy":2013},[2138,26454,2287],{},[2005,26456,2234],{},[898,26458,207],{},[2005,26460,2020],{"stretchy":2013},[2005,26462,2007],{},[2138,26464,2287],{},[898,26466,4680],{"mathvariant":2385},[898,26468,2826],{},[898,26470,3946],{},[898,26472,8679],{},[902,26474,26475],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,26478,26479,26481,26482,26497,26498,18654,26515,26530,26531,26556,26557,1644],{},[38,26480,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,26483,26485],{"className":26484},[886],[888,26486,26487],{"xmlns":890},[892,26488,26489,26495],{},[895,26490,26491,26493],{},[898,26492,12190],{},[898,26494,8679],{},[902,26496,12057],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,26499,26501],{"className":26500},[886],[888,26502,26503],{"xmlns":890},[892,26504,26505,26513],{},[895,26506,26507,26509,26511],{},[898,26508,12190],{},[2005,26510,2007],{},[898,26512,8679],{},[902,26514,12718],{"encoding":904},[883,26516,26518],{"className":26517},[886],[888,26519,26520],{"xmlns":890},[892,26521,26522,26528],{},[895,26523,26524,26526],{},[898,26525,9801],{},[898,26527,2826],{},[902,26529,12064],{"encoding":904}," rovnováhu trhu peněz (",[883,26532,26534],{"className":26533},[886],[888,26535,26536],{"xmlns":890},[892,26537,26538,26554],{},[895,26539,26540,26546,26548],{},[2133,26541,26542,26544],{},[898,26543,2826],{},[898,26545,1860],{},[2005,26547,2007],{},[2133,26549,26550,26552],{},[898,26551,2826],{},[2005,26553,4360],{},[902,26555,13486],{"encoding":904},"); průsečík dává ",[883,26558,26560],{"className":26559},[886],[888,26561,26562],{"xmlns":890},[892,26563,26564,26584],{},[895,26565,26566,26568,26574,26576,26582],{},[2005,26567,2014],{"stretchy":2013},[2133,26569,26570,26572],{},[898,26571,9134],{},[898,26573,1868],{},[2005,26575,2295],{"separator":2294},[2133,26577,26578,26580],{},[898,26579,12047],{},[898,26581,1868],{},[2005,26583,2020],{"stretchy":2013},[902,26585,12101],{"encoding":904},[115,26587,15726],{"id":15725},[120,26589,26590,26628,26668,26758,26840,26894,26950,27009,27044,27049,27121,27196,27282,27344,27412,27470,27523,27562],{},[123,26591,26592,7021,26595,25912],{},[38,26593,26594],{},"Hrubý národní produkt (GNP)",[883,26596,26598],{"className":26597},[886],[888,26599,26600],{"xmlns":890},[892,26601,26602,26626],{},[895,26603,26604,26606,26608,26610,26612,26614,26616,26618,26620,26622,26624],{},[898,26605,12118],{},[898,26607,18301],{},[898,26609,3946],{},[2005,26611,2007],{},[898,26613,1852],{},[2005,26615,2104],{},[898,26617,12190],{},[2005,26619,2104],{},[898,26621,12118],{},[2005,26623,2104],{},[898,26625,12326],{},[902,26627,25911],{"encoding":904},[123,26629,26630,26646,26647,1644],{},[38,26631,26632,26633],{},"Národní důchod ",[883,26634,26636],{"className":26635},[886],[888,26637,26638],{"xmlns":890},[892,26639,26640,26644],{},[895,26641,26642],{},[898,26643,9134],{},[902,26645,9134],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,26648,26650],{"className":26649},[886],[888,26651,26652],{"xmlns":890},[892,26653,26654,26666],{},[895,26655,26656,26658,26660,26662,26664],{},[898,26657,12118],{},[898,26659,18301],{},[898,26661,3946],{},[2005,26663,2739],{},[898,26665,9134],{},[902,26667,25876],{"encoding":904},[123,26669,26670,26696,26697,1343,26720,1343,26741,1644],{},[38,26671,26672,26673],{},"Funkce spotřeby ",[883,26674,26676],{"className":26675},[886],[888,26677,26678],{"xmlns":890},[892,26679,26680,26694],{},[895,26681,26682,26684,26686,26688,26690,26692],{},[898,26683,1852],{},[2005,26685,2007],{},[898,26687,1852],{},[2005,26689,2014],{"stretchy":2013},[898,26691,9134],{},[2005,26693,2020],{"stretchy":2013},[902,26695,20746],{"encoding":904}," — lineární model ",[883,26698,26700],{"className":26699},[886],[888,26701,26702],{"xmlns":890},[892,26703,26704,26718],{},[895,26705,26706,26708,26710,26712,26714,26716],{},[898,26707,1852],{},[2005,26709,2007],{},[898,26711,207],{},[898,26713,9134],{},[2005,26715,2104],{},[898,26717,2107],{},[902,26719,18926],{"encoding":904},[883,26721,26723],{"className":26722},[886],[888,26724,26725],{"xmlns":890},[892,26726,26727,26739],{},[895,26728,26729,26731,26733,26735,26737],{},[2138,26730,2336],{},[2005,26732,3455],{},[898,26734,207],{},[2005,26736,3455],{},[2138,26738,2287],{},[902,26740,18842],{"encoding":904},[883,26742,26744],{"className":26743},[886],[888,26745,26746],{"xmlns":890},[892,26747,26748,26756],{},[895,26749,26750,26752,26754],{},[898,26751,2107],{},[2005,26753,3416],{},[2138,26755,2336],{},[902,26757,18820],{"encoding":904},[123,26759,26760,7021,26787,26808,26809,1644],{},[38,26761,26762,26763],{},"Funkce úspor ",[883,26764,26766],{"className":26765},[886],[888,26767,26768],{"xmlns":890},[892,26769,26770,26784],{},[895,26771,26772,26774,26776,26778,26780,26782],{},[898,26773,8679],{},[2005,26775,2007],{},[898,26777,8679],{},[2005,26779,2014],{"stretchy":2013},[898,26781,9134],{},[2005,26783,2020],{"stretchy":2013},[902,26785,26786],{"encoding":904},"S = S(Y)",[883,26788,26790],{"className":26789},[886],[888,26791,26792],{"xmlns":890},[892,26793,26794,26806],{},[895,26795,26796,26798,26800,26802,26804],{},[898,26797,9134],{},[2005,26799,2007],{},[898,26801,1852],{},[2005,26803,2104],{},[898,26805,8679],{},[902,26807,12700],{"encoding":904},"; lineární ",[883,26810,26812],{"className":26811},[886],[888,26813,26814],{"xmlns":890},[892,26815,26816,26838],{},[895,26817,26818,26820,26822,26824,26826,26828,26830,26832,26834,26836],{},[898,26819,8679],{},[2005,26821,2007],{},[2005,26823,2014],{"stretchy":2013},[2138,26825,2287],{},[2005,26827,2234],{},[898,26829,207],{},[2005,26831,2020],{"stretchy":2013},[898,26833,9134],{},[2005,26835,2234],{},[898,26837,2107],{},[902,26839,19175],{"encoding":904},[123,26841,26842,7021,26845,1343,26868,1644],{},[38,26843,26844],{},"Autonomní spotřeba\u002Fúspory",[883,26846,26848],{"className":26847},[886],[888,26849,26850],{"xmlns":890},[892,26851,26852,26866],{},[895,26853,26854,26856,26858,26860,26862,26864],{},[898,26855,1852],{},[2005,26857,2014],{"stretchy":2013},[2138,26859,2336],{},[2005,26861,2020],{"stretchy":2013},[2005,26863,2007],{},[898,26865,2107],{},[902,26867,19567],{"encoding":904},[883,26869,26871],{"className":26870},[886],[888,26872,26873],{"xmlns":890},[892,26874,26875,26891],{},[895,26876,26877,26879,26881,26883,26885,26887,26889],{},[898,26878,8679],{},[2005,26880,2014],{"stretchy":2013},[2138,26882,2336],{},[2005,26884,2020],{"stretchy":2013},[2005,26886,2007],{},[2005,26888,2234],{},[898,26890,2107],{},[902,26892,26893],{"encoding":904},"S(0) = -b",[123,26895,26896,26928,26929,3927],{},[38,26897,26898,26899],{},"Mezní sklon ke spotřebě ",[883,26900,26902],{"className":26901},[886],[888,26903,26904],{"xmlns":890},[892,26905,26906,26926],{},[895,26907,26908,26910,26912,26914,26916,26918,26920,26922,26924],{},[898,26909,2826],{},[898,26911,3946],{},[898,26913,1852],{},[2005,26915,2007],{},[898,26917,2203],{"mathvariant":2385},[898,26919,1852],{},[898,26921,4680],{"mathvariant":2385},[898,26923,2203],{"mathvariant":2385},[898,26925,9134],{},[902,26927,26058],{"encoding":904}," (v lineárním modelu ",[883,26930,26932],{"className":26931},[886],[888,26933,26934],{"xmlns":890},[892,26935,26936,26948],{},[895,26937,26938,26940,26942,26944,26946],{},[898,26939,2826],{},[898,26941,3946],{},[898,26943,1852],{},[2005,26945,2007],{},[898,26947,207],{},[902,26949,19895],{"encoding":904},[123,26951,26952,26928,26984,3927],{},[38,26953,26954,26955],{},"Mezní sklon k úsporám ",[883,26956,26958],{"className":26957},[886],[888,26959,26960],{"xmlns":890},[892,26961,26962,26982],{},[895,26963,26964,26966,26968,26970,26972,26974,26976,26978,26980],{},[898,26965,2826],{},[898,26967,3946],{},[898,26969,8679],{},[2005,26971,2007],{},[898,26973,2203],{"mathvariant":2385},[898,26975,8679],{},[898,26977,4680],{"mathvariant":2385},[898,26979,2203],{"mathvariant":2385},[898,26981,9134],{},[902,26983,26088],{"encoding":904},[883,26985,26987],{"className":26986},[886],[888,26988,26989],{"xmlns":890},[892,26990,26991,27007],{},[895,26992,26993,26995,26997,26999,27001,27003,27005],{},[898,26994,2826],{},[898,26996,3946],{},[898,26998,8679],{},[2005,27000,2007],{},[2138,27002,2287],{},[2005,27004,2234],{},[898,27006,207],{},[902,27008,19921],{"encoding":904},[123,27010,27011,2212,27014,27043],{},[38,27012,27013],{},"Vztah",[883,27015,27017],{"className":27016},[886],[888,27018,27019],{"xmlns":890},[892,27020,27021,27041],{},[895,27022,27023,27025,27027,27029,27031,27033,27035,27037,27039],{},[898,27024,2826],{},[898,27026,3946],{},[898,27028,1852],{},[2005,27030,2104],{},[898,27032,2826],{},[898,27034,3946],{},[898,27036,8679],{},[2005,27038,2007],{},[2138,27040,2287],{},[902,27042,26119],{"encoding":904}," (7.5).",[123,27045,27046,27048],{},[38,27047,20589],{}," — rovnováha agregátní poptávky a nabídky.",[123,27050,27051,27054,27055,15798,27076,1644],{},[38,27052,27053],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,27056,27058],{"className":27057},[886],[888,27059,27060],{"xmlns":890},[892,27061,27062,27074],{},[895,27063,27064,27066,27068,27070,27072],{},[898,27065,9134],{},[2005,27067,2007],{},[898,27069,1852],{},[2005,27071,2104],{},[898,27073,12190],{},[902,27075,14750],{"encoding":904},[883,27077,27079],{"className":27078},[886],[888,27080,27081],{"xmlns":890},[892,27082,27083,27119],{},[895,27084,27085,27091,27093,27095,27097,27099,27105,27107,27109,27111,27113,27115,27117],{},[2133,27086,27087,27089],{},[898,27088,9134],{},[898,27090,1868],{},[2005,27092,2007],{},[2005,27094,2014],{"stretchy":2013},[898,27096,2107],{},[2005,27098,2104],{},[2133,27100,27101,27103],{},[898,27102,12190],{},[2005,27104,4360],{},[2005,27106,2020],{"stretchy":2013},[898,27108,4680],{"mathvariant":2385},[2005,27110,2014],{"stretchy":2013},[2138,27112,2287],{},[2005,27114,2234],{},[898,27116,207],{},[2005,27118,2020],{"stretchy":2013},[902,27120,26262],{"encoding":904},[123,27122,27123,27126,27127,1343,27146,15798,27171,1644],{},[38,27124,27125],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,27128,27130],{"className":27129},[886],[888,27131,27132],{"xmlns":890},[892,27133,27134,27144],{},[895,27135,27136,27138,27140,27142],{},[898,27137,2783],{},[2005,27139,2014],{"stretchy":2013},[898,27141,9134],{},[2005,27143,2020],{"stretchy":2013},[902,27145,22225],{"encoding":904},[883,27147,27149],{"className":27148},[886],[888,27150,27151],{"xmlns":890},[892,27152,27153,27169],{},[895,27154,27155,27161,27163,27165,27167],{},[2281,27156,27157,27159],{},[898,27158,9134],{},[898,27160,1860],{},[2005,27162,2007],{},[898,27164,9134],{},[2005,27166,2234],{},[898,27168,2783],{},[902,27170,21724],{"encoding":904},[883,27172,27174],{"className":27173},[886],[888,27175,27176],{"xmlns":890},[892,27177,27178,27194],{},[895,27179,27180,27182,27184,27186,27188,27190,27192],{},[898,27181,9134],{},[2005,27183,2007],{},[898,27185,1852],{},[2005,27187,2104],{},[898,27189,12190],{},[2005,27191,2104],{},[898,27193,12118],{},[902,27195,21695],{"encoding":904},[123,27197,27198,27201,27202,27223,27224,15798,27248,1644],{},[38,27199,27200],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,27203,27205],{"className":27204},[886],[888,27206,27207],{"xmlns":890},[892,27208,27209,27221],{},[895,27210,27211,27213,27215,27217,27219],{},[898,27212,12326],{},[2005,27214,2007],{},[898,27216,1844],{},[2005,27218,2234],{},[898,27220,2826],{},[902,27222,23265],{"encoding":904},", importem ",[883,27225,27227],{"className":27226},[886],[888,27228,27229],{"xmlns":890},[892,27230,27231,27245],{},[895,27232,27233,27235,27237,27243],{},[898,27234,2826],{},[2005,27236,2014],{"stretchy":2013},[2281,27238,27239,27241],{},[898,27240,9134],{},[898,27242,1860],{},[2005,27244,2020],{"stretchy":2013},[902,27246,27247],{"encoding":904},"M(Y_D)",[883,27249,27251],{"className":27250},[886],[888,27252,27253],{"xmlns":890},[892,27254,27255,27279],{},[895,27256,27257,27259,27261,27263,27265,27267,27269,27271,27273,27275,27277],{},[898,27258,9134],{},[2005,27260,2007],{},[898,27262,1852],{},[2005,27264,2104],{},[898,27266,12190],{},[2005,27268,2104],{},[898,27270,12118],{},[2005,27272,2104],{},[898,27274,1844],{},[2005,27276,2234],{},[898,27278,2826],{},[902,27280,27281],{"encoding":904},"Y = C + I + G + B - M",[123,27283,27284,7021,27287,26476],{},[38,27285,27286],{},"Multiplikátor investic",[883,27288,27290],{"className":27289},[886],[888,27291,27292],{"xmlns":890},[892,27293,27294,27342],{},[895,27295,27296,27298,27304,27306,27308,27314,27316,27318,27320,27322,27324,27326,27328,27330,27332,27334,27336,27338,27340],{},[898,27297,9877],{"mathvariant":2385},[2133,27299,27300,27302],{},[898,27301,9134],{},[898,27303,1868],{},[898,27305,4680],{"mathvariant":2385},[898,27307,9877],{"mathvariant":2385},[2133,27309,27310,27312],{},[898,27311,12190],{},[2005,27313,4360],{},[2005,27315,2007],{},[2138,27317,2287],{},[898,27319,4680],{"mathvariant":2385},[2005,27321,2014],{"stretchy":2013},[2138,27323,2287],{},[2005,27325,2234],{},[898,27327,207],{},[2005,27329,2020],{"stretchy":2013},[2005,27331,2007],{},[2138,27333,2287],{},[898,27335,4680],{"mathvariant":2385},[898,27337,2826],{},[898,27339,3946],{},[898,27341,8679],{},[902,27343,26475],{"encoding":904},[123,27345,27346,7021,27377,1343,27394,27411],{},[38,27347,15733,27348],{},[883,27349,27351],{"className":27350},[886],[888,27352,27353],{"xmlns":890},[892,27354,27355,27375],{},[895,27356,27357,27359,27361,27363,27365,27367,27369,27371,27373],{},[898,27358,12190],{},[2005,27360,2014],{"stretchy":2013},[898,27362,12047],{},[2005,27364,2020],{"stretchy":2013},[2005,27366,2007],{},[898,27368,2151],{},[898,27370,12047],{},[2005,27372,2104],{},[898,27374,2203],{},[902,27376,15763],{"encoding":904},[883,27378,27380],{"className":27379},[886],[888,27381,27382],{"xmlns":890},[892,27383,27384,27392],{},[895,27385,27386,27388,27390],{},[898,27387,2151],{},[2005,27389,3455],{},[2138,27391,2336],{},[902,27393,12521],{"encoding":904},[883,27395,27397],{"className":27396},[886],[888,27398,27399],{"xmlns":890},[892,27400,27401,27409],{},[895,27402,27403,27405,27407],{},[898,27404,2203],{},[2005,27406,3416],{},[2138,27408,2336],{},[902,27410,12500],{"encoding":904},"; klesající.",[123,27413,27414,27416,27417,27419,27420,27469],{},[38,27415,15852],{}," — rovnováha na trhu zboží (",[614,27418,12060],{},"); ",[883,27421,27423],{"className":27422},[886],[888,27424,27425],{"xmlns":890},[892,27426,27427,27467],{},[895,27428,27429,27431,27433,27445,27447,27449],{},[898,27430,9134],{},[2005,27432,2007],{},[2338,27434,27435,27437],{},[898,27436,2151],{},[895,27438,27439,27441,27443],{},[2138,27440,2287],{},[2005,27442,2234],{},[898,27444,207],{},[898,27446,12047],{},[2005,27448,2104],{},[2338,27450,27451,27459],{},[895,27452,27453,27455,27457],{},[898,27454,2107],{},[2005,27456,2104],{},[898,27458,2203],{},[895,27460,27461,27463,27465],{},[2138,27462,2287],{},[2005,27464,2234],{},[898,27466,207],{},[902,27468,15905],{"encoding":904}," (7.14); klesající.",[123,27471,27472,27474,27475,27419,27477,27522],{},[38,27473,16051],{}," — rovnováha na trhu peněz (",[614,27476,12067],{},[883,27478,27480],{"className":27479},[886],[888,27481,27482],{"xmlns":890},[892,27483,27484,27520],{},[895,27485,27486,27492,27494,27500,27502,27504,27510,27512,27514],{},[2133,27487,27488,27490],{},[898,27489,2826],{},[2005,27491,4360],{},[2005,27493,2007],{},[2281,27495,27496,27498],{},[898,27497,13243],{},[2138,27499,2287],{},[898,27501,9134],{},[2005,27503,2104],{},[2281,27505,27506,27508],{},[898,27507,13243],{},[2138,27509,2140],{},[898,27511,12047],{},[2005,27513,2104],{},[2281,27515,27516,27518],{},[898,27517,13243],{},[2138,27519,2182],{},[902,27521,16099],{"encoding":904}," (7.15); rostoucí.",[123,27524,27525,7021,27528,1644],{},[38,27526,27527],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,27529,27531],{"className":27530},[886],[888,27532,27533],{"xmlns":890},[892,27534,27535,27559],{},[895,27536,27537,27543,27545,27551,27553],{},[2133,27538,27539,27541],{},[898,27540,2826],{},[898,27542,1860],{},[2005,27544,2007],{},[2281,27546,27547,27549],{},[898,27548,9801],{},[2138,27550,2287],{},[2005,27552,2104],{},[2281,27554,27555,27557],{},[898,27556,9801],{},[2138,27558,2140],{},[902,27560,27561],{"encoding":904},"M^D = L_1 + L_2",[123,27563,27564,16109,27566,13986,27579,3894,27594,27609,27610,1644],{},[38,27565,945],{},[883,27567,27569],{"className":27568},[886],[888,27570,27571],{"xmlns":890},[892,27572,27573,27577],{},[895,27574,27575],{},[898,27576,1868],{},[902,27578,1868],{"encoding":904},[883,27580,27582],{"className":27581},[886],[888,27583,27584],{"xmlns":890},[892,27585,27586,27592],{},[895,27587,27588,27590],{},[898,27589,12190],{},[898,27591,8679],{},[902,27593,12057],{"encoding":904},[883,27595,27597],{"className":27596},[886],[888,27598,27599],{"xmlns":890},[892,27600,27601,27607],{},[895,27602,27603,27605],{},[898,27604,9801],{},[898,27606,2826],{},[902,27608,12064],{"encoding":904}," určuje ",[883,27611,27613],{"className":27612},[886],[888,27614,27615],{"xmlns":890},[892,27616,27617,27637],{},[895,27618,27619,27621,27627,27629,27635],{},[2005,27620,2014],{"stretchy":2013},[2133,27622,27623,27625],{},[898,27624,9134],{},[898,27626,1868],{},[2005,27628,2295],{"separator":2294},[2133,27630,27631,27633],{},[898,27632,12047],{},[898,27634,1868],{},[2005,27636,2020],{"stretchy":2013},[902,27638,12101],{"encoding":904},[115,27640,3800],{"id":3799},[120,27642,27643,27650,27657],{},[123,27644,27645,2212,27647],{},[38,27646,16210],{},[207,27648,16214],{"className":27649,"dataFsResolvedFilePath":1641,"href":1642},[210],[123,27651,27652,2212,27654],{},[38,27653,16219],{},[207,27655,16223],{"className":27656,"dataFsResolvedFilePath":868,"href":869},[210],[123,27658,27659,27661],{},[38,27660,16238],{},[120,27662,27663,27669,27675,27681],{},[123,27664,27665,27668],{},[207,27666,16279],{"className":27667,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,27670,27671,27674],{},[207,27672,16246],{"className":27673,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,27676,27677,27680],{},[207,27678,2958],{"className":27679,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,27682,27683,27686,27687,1343,27704,27721],{},[207,27684,1145],{"className":27685,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,27688,27690],{"className":27689},[886],[888,27691,27692],{"xmlns":890},[892,27693,27694,27702],{},[895,27695,27696,27698,27700],{},[898,27697,2826],{},[898,27699,3946],{},[898,27701,1852],{},[902,27703,18052],{"encoding":904},[883,27705,27707],{"className":27706},[886],[888,27708,27709],{"xmlns":890},[892,27710,27711,27719],{},[895,27712,27713,27715,27717],{},[898,27714,2826],{},[898,27716,3946],{},[898,27718,8679],{},[902,27720,19665],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":27723},[27724,27725,27726,27727,27732,27735,27736,27743,27748,27753,27756,27757,27758,27759],{"id":12011,"depth":642,"text":12012},{"id":18161,"depth":642,"text":18162},{"id":18281,"depth":642,"text":18282},{"id":18533,"depth":642,"text":18534,"children":27728},[27729,27730,27731],{"id":18537,"depth":649,"text":18538},{"id":18749,"depth":649,"text":18750},{"id":19257,"depth":649,"text":19258},{"id":19577,"depth":642,"text":19578,"children":27733},[27734],{"id":20093,"depth":649,"text":20094},{"id":20588,"depth":642,"text":20589},{"id":20615,"depth":642,"text":20616,"children":27737},[27738,27739,27740,27742],{"id":20626,"depth":649,"text":20627},{"id":20696,"depth":649,"text":20697},{"id":20880,"depth":649,"text":27741},"Výpočet YEY^E",{"id":21023,"depth":649,"text":21024},{"id":21401,"depth":642,"text":21402,"children":27744},[27745,27746,27747],{"id":21405,"depth":649,"text":20627},{"id":21854,"depth":649,"text":20697},{"id":22510,"depth":649,"text":22511},{"id":23296,"depth":642,"text":23297,"children":27749},[27750,27751,27752],{"id":23300,"depth":649,"text":20627},{"id":23445,"depth":649,"text":20697},{"id":23715,"depth":649,"text":23716},{"id":24639,"depth":642,"text":24640,"children":27754},[27755],{"id":24835,"depth":649,"text":24836},{"id":25385,"depth":642,"text":25386},{"id":25845,"depth":642,"text":25846},{"id":15725,"depth":642,"text":15726},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,16232,1143,27766,27767,27768,16279,17890],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":27771,"title":27772,"body":27773,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":36753,"navigation":664,"path":36754,"seo":36755,"sources":36756,"stem":36757,"tags":36758,"type":3865,"updated":677,"__hash__":36763},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":27774,"toc":36722},[27775,27778,27780,28009,28013,28066,28136,28248,28407,28411,28527,28531,28534,28656,28659,28852,28876,28944,29108,29126,29192,29570,29574,29581,29825,29881,29885,29950,30068,30200,30232,30352,30434,30437,30559,30752,30973,30977,31017,31122,31179,31279,31456,31586,31639,31642,31729,31733,31909,31913,31916,32001,32004,32061,32166,32170,32291,32294,32477,32480,32588,32797,33117,33165,33238,33312,33314,33538,33773,34041,34045,34048,34153,34210,34244,34291,34324,34408,34410,34642,34775,34852,34974,35129,35133,35274,35281,35505,35516,35520,35524,35629,35771,35881,35980,35984,36143,36253,36255,36648,36650],[12,27776,27772],{"id":27777},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,27779,12012],{"id":12011},[724,27781,27782,27784,27785,27819,27820,27823,27824,27855,27856,27902,27903,27906,27907,27949,27950,27968,27969,27973,27974,28004,28005,28008],{},[38,27783,913],{}," řeší, jaký svazek zboží ",[883,27786,27788],{"className":27787},[886],[888,27789,27790],{"xmlns":890},[892,27791,27792,27816],{},[895,27793,27794,27796,27804,27806,27814],{},[2005,27795,2495],{"stretchy":2013},[9172,27797,27798,27800,27802],{},[898,27799,2797],{},[2138,27801,2287],{},[2005,27803,4360],{},[2005,27805,2295],{"separator":2294},[9172,27807,27808,27810,27812],{},[898,27809,2797],{},[2138,27811,2140],{},[2005,27813,4360],{},[2005,27815,2510],{"stretchy":2013},[902,27817,27818],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,27821,27822],{},"primární úloha"," — maximalizace užitečnosti ",[883,27825,27827],{"className":27826},[886],[888,27828,27829],{"xmlns":890},[892,27830,27831,27853],{},[895,27832,27833,27835,27837,27843,27845,27851],{},[898,27834,900],{},[2005,27836,2014],{"stretchy":2013},[2281,27838,27839,27841],{},[898,27840,2797],{},[2138,27842,2287],{},[2005,27844,2295],{"separator":2294},[2281,27846,27847,27849],{},[898,27848,2797],{},[2138,27850,2140],{},[2005,27852,2020],{"stretchy":2013},[902,27854,16350],{"encoding":904}," při rozpočtovém omezení ",[883,27857,27859],{"className":27858},[886],[888,27860,27861],{"xmlns":890},[892,27862,27863,27899],{},[895,27864,27865,27871,27873,27879,27885,27887,27893],{},[2133,27866,27867,27869],{},[898,27868,9134],{},[2005,27870,4360],{},[2005,27872,2007],{},[2281,27874,27875,27877],{},[898,27876,3946],{},[2138,27878,2287],{},[2281,27880,27881,27883],{},[898,27882,2797],{},[2138,27884,2287],{},[2005,27886,2104],{},[2281,27888,27889,27891],{},[898,27890,3946],{},[2138,27892,2140],{},[2281,27894,27895,27897],{},[898,27896,2797],{},[2138,27898,2140],{},[902,27900,27901],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,27904,27905],{},"duální úloha"," — minimalizace výdajů ",[883,27908,27910],{"className":27909},[886],[888,27911,27912],{"xmlns":890},[892,27913,27914,27946],{},[895,27915,27916,27918,27920,27926,27932,27934,27940],{},[898,27917,1868],{},[2005,27919,2007],{},[2281,27921,27922,27924],{},[898,27923,3946],{},[2138,27925,2287],{},[2281,27927,27928,27930],{},[898,27929,2797],{},[2138,27931,2287],{},[2005,27933,2104],{},[2281,27935,27936,27938],{},[898,27937,3946],{},[2138,27939,2140],{},[2281,27941,27942,27944],{},[898,27943,2797],{},[2138,27945,2140],{},[902,27947,27948],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,27951,27953],{"className":27952},[886],[888,27954,27955],{"xmlns":890},[892,27956,27957,27965],{},[895,27958,27959],{},[2133,27960,27961,27963],{},[898,27962,900],{},[2005,27964,4360],{},[902,27966,27967],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,27970,27972],{"className":27971,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,27975,27977],{"className":27976},[886],[888,27978,27979],{"xmlns":890},[892,27980,27981,28001],{},[895,27982,27983,27985,27987,27993,27995],{},[2297,27984,10607],{},[2005,27986,2007],{},[2281,27988,27989,27991],{},[898,27990,3946],{},[2138,27992,2287],{},[898,27994,4680],{"mathvariant":2385},[2281,27996,27997,27999],{},[898,27998,3946],{},[2138,28000,2140],{},[902,28002,28003],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,28006,28007],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,28010,28012],{"id":28011},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,28014,28015,28016,28034,28035,28065],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,28017,28019],{"className":28018},[886],[888,28020,28021],{"xmlns":890},[892,28022,28023,28031],{},[895,28024,28025],{},[2133,28026,28027,28029],{},[898,28028,9134],{},[2005,28030,4360],{},[902,28032,28033],{"encoding":904},"Y^*"," a ceny ",[883,28036,28038],{"className":28037},[886],[888,28039,28040],{"xmlns":890},[892,28041,28042,28062],{},[895,28043,28044,28052,28054],{},[9172,28045,28046,28048,28050],{},[898,28047,3946],{},[2138,28049,2287],{},[2005,28051,4360],{},[2005,28053,2295],{"separator":2294},[9172,28055,28056,28058,28060],{},[898,28057,3946],{},[2138,28059,2140],{},[2005,28061,4360],{},[902,28063,28064],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,28067,28069],{"className":28068},[886],[888,28070,28072],{"xmlns":890,"display":28071},"block",[892,28073,28074,28133],{},[20760,28075,28077],{"width":28076},"100%",[20765,28078,28079,28082,28126,28128],{},[20768,28080],{"width":28081},"50%",[20768,28083,28084],{},[895,28085,28086,28092,28094,28102,28108,28110,28118,28124],{},[2133,28087,28088,28090],{},[898,28089,9134],{},[2005,28091,4360],{},[2005,28093,2007],{},[9172,28095,28096,28098,28100],{},[898,28097,3946],{},[2138,28099,2287],{},[2005,28101,4360],{},[2281,28103,28104,28106],{},[898,28105,2797],{},[2138,28107,2287],{},[2005,28109,2104],{},[9172,28111,28112,28114,28116],{},[898,28113,3946],{},[2138,28115,2140],{},[2005,28117,4360],{},[2281,28119,28120,28122],{},[898,28121,2797],{},[2138,28123,2140],{},[2005,28125,2295],{"separator":2294},[20768,28127],{"width":28081},[20768,28129,28130],{},[2297,28131,28132],{},"(6.12)",[902,28134,28135],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,28137,28138,28139,28142,28143,3894,28179,28215,28216,28229,28230,28244,28245,1644],{},"geometricky ",[38,28140,28141],{},"rozpočtová přímka (budget line)"," procházející body ",[883,28144,28146],{"className":28145},[886],[888,28147,28148],{"xmlns":890},[892,28149,28150,28176],{},[895,28151,28152,28154,28160,28162,28170,28172,28174],{},[2005,28153,2495],{"stretchy":2013},[2133,28155,28156,28158],{},[898,28157,9134],{},[2005,28159,4360],{},[898,28161,4680],{"mathvariant":2385},[9172,28163,28164,28166,28168],{},[898,28165,3946],{},[2138,28167,2287],{},[2005,28169,4360],{},[2005,28171,2295],{"separator":2294},[2138,28173,2336],{},[2005,28175,2510],{"stretchy":2013},[902,28177,28178],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,28180,28182],{"className":28181},[886],[888,28183,28184],{"xmlns":890},[892,28185,28186,28212],{},[895,28187,28188,28190,28192,28194,28200,28202,28210],{},[2005,28189,2495],{"stretchy":2013},[2138,28191,2336],{},[2005,28193,2295],{"separator":2294},[2133,28195,28196,28198],{},[898,28197,9134],{},[2005,28199,4360],{},[898,28201,4680],{"mathvariant":2385},[9172,28203,28204,28206,28208],{},[898,28205,3946],{},[2138,28207,2140],{},[2005,28209,4360],{},[2005,28211,2510],{"stretchy":2013},[902,28213,28214],{"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 ",[883,28217,28219],{"className":28218},[886],[888,28220,28221],{"xmlns":890},[892,28222,28223,28227],{},[895,28224,28225],{},[898,28226,900],{},[902,28228,900],{"encoding":904},", indiferenční křivky a ",[883,28231,28233],{"className":28232},[886],[888,28234,28235],{"xmlns":890},[892,28236,28237,28241],{},[895,28238,28239],{},[2297,28240,10607],{},[902,28242,28243],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,28246,880],{"className":28247,"dataFsResolvedFilePath":878,"href":879},[210],[3876,28249,28250],{},[724,28251,28252,28254,28255,28258,28259,28272,28273,28275,28276,28289,28290,2212,28293,28333,28334,28351,28352,28369,28370,28387,28388,28406],{},[883,28253,4418],{}," Pozor — dvě úlohy, totéž řešení\n",[38,28256,28257],{},"Primární úloha"," (max ",[883,28260,28262],{"className":28261},[886],[888,28263,28264],{"xmlns":890},[892,28265,28266,28270],{},[895,28267,28268],{},[898,28269,900],{},[902,28271,900],{"encoding":904}," při pevném rozpočtu) a ",[38,28274,27905],{}," (min ",[883,28277,28279],{"className":28278},[886],[888,28280,28281],{"xmlns":890},[892,28282,28283,28287],{},[895,28284,28285],{},[898,28286,1868],{},[902,28288,1868],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,28291,28292],{},"tentýž bod",[883,28294,28296],{"className":28295},[886],[888,28297,28298],{"xmlns":890},[892,28299,28300,28330],{},[895,28301,28302,28308,28310,28318,28320,28328],{},[2133,28303,28304,28306],{},[898,28305,2797],{},[2005,28307,4360],{},[2005,28309,2495],{"stretchy":2013},[9172,28311,28312,28314,28316],{},[898,28313,2797],{},[2138,28315,2287],{},[2005,28317,4360],{},[2005,28319,2295],{"separator":2294},[9172,28321,28322,28324,28326],{},[898,28323,2797],{},[2138,28325,2140],{},[2005,28327,4360],{},[2005,28329,2510],{"stretchy":2013},[902,28331,28332],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,28335,28337],{"className":28336},[886],[888,28338,28339],{"xmlns":890},[892,28340,28341,28349],{},[895,28342,28343],{},[2133,28344,28345,28347],{},[898,28346,9134],{},[2005,28348,4360],{},[902,28350,28033],{"encoding":904}," a hledáme maximální ",[883,28353,28355],{"className":28354},[886],[888,28356,28357],{"xmlns":890},[892,28358,28359,28367],{},[895,28360,28361],{},[2133,28362,28363,28365],{},[898,28364,900],{},[2005,28366,4360],{},[902,28368,27967],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,28371,28373],{"className":28372},[886],[888,28374,28375],{"xmlns":890},[892,28376,28377,28385],{},[895,28378,28379],{},[2133,28380,28381,28383],{},[898,28382,900],{},[2005,28384,4360],{},[902,28386,27967],{"encoding":904}," a hledáme minimální ",[883,28389,28391],{"className":28390},[886],[888,28392,28393],{"xmlns":890},[892,28394,28395,28403],{},[895,28396,28397],{},[2133,28398,28399,28401],{},[898,28400,1868],{},[2005,28402,4360],{},[902,28404,28405],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,28408,28410],{"id":28409},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,28412,28413,28414,28445,28446,28522,28523,1644],{},"Úlohou je najít maximum ",[883,28415,28417],{"className":28416},[886],[888,28418,28419],{"xmlns":890},[892,28420,28421,28443],{},[895,28422,28423,28425,28427,28433,28435,28441],{},[898,28424,900],{},[2005,28426,2014],{"stretchy":2013},[2281,28428,28429,28431],{},[898,28430,2797],{},[2138,28432,2287],{},[2005,28434,2295],{"separator":2294},[2281,28436,28437,28439],{},[898,28438,2797],{},[2138,28440,2140],{},[2005,28442,2020],{"stretchy":2013},[902,28444,16350],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,28447,28449],{"className":28448},[886],[888,28450,28451],{"xmlns":890},[892,28452,28453,28519],{},[895,28454,28455,28457,28459,28465,28467,28473,28475,28477,28483,28485,28493,28499,28501,28509,28515,28517],{},[898,28456,11045],{},[2005,28458,2014],{"stretchy":2013},[2281,28460,28461,28463],{},[898,28462,2797],{},[2138,28464,2287],{},[2005,28466,2295],{"separator":2294},[2281,28468,28469,28471],{},[898,28470,2797],{},[2138,28472,2140],{},[2005,28474,2020],{"stretchy":2013},[2005,28476,2007],{},[2133,28478,28479,28481],{},[898,28480,9134],{},[2005,28482,4360],{},[2005,28484,2234],{},[9172,28486,28487,28489,28491],{},[898,28488,3946],{},[2138,28490,2287],{},[2005,28492,4360],{},[2281,28494,28495,28497],{},[898,28496,2797],{},[2138,28498,2287],{},[2005,28500,2234],{},[9172,28502,28503,28505,28507],{},[898,28504,3946],{},[2138,28506,2140],{},[2005,28508,4360],{},[2281,28510,28511,28513],{},[898,28512,2797],{},[2138,28514,2140],{},[2005,28516,2007],{},[2138,28518,2336],{},[902,28520,28521],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,28524,28526],{"className":28525,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,28528,28530],{"id":28529},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,28532,28533],{},"Sestavíme",[883,28535,28537],{"className":28536},[886],[888,28538,28539],{"xmlns":890,"display":28071},[892,28540,28541,28653],{},[20760,28542,28543],{"width":28076},[20765,28544,28545,28547,28646,28648],{},[20768,28546],{"width":28081},[20768,28548,28549],{},[895,28550,28551,28554,28556,28562,28564,28570,28572,28574,28576,28578,28580,28582,28588,28590,28596,28598,28600,28602,28604,28610,28612,28620,28626,28628,28636,28642,28644],{},[898,28552,9801],{"mathvariant":28553},"script",[2005,28555,2014],{"stretchy":2013},[2281,28557,28558,28560],{},[898,28559,2797],{},[2138,28561,2287],{},[2005,28563,2295],{"separator":2294},[2281,28565,28566,28568],{},[898,28567,2797],{},[2138,28569,2140],{},[2005,28571,2295],{"separator":2294},[898,28573,16450],{},[2005,28575,2020],{"stretchy":2013},[2005,28577,2007],{},[898,28579,900],{},[2005,28581,2014],{"stretchy":2013},[2281,28583,28584,28586],{},[898,28585,2797],{},[2138,28587,2287],{},[2005,28589,2295],{"separator":2294},[2281,28591,28592,28594],{},[898,28593,2797],{},[2138,28595,2140],{},[2005,28597,2020],{"stretchy":2013},[2005,28599,2104],{},[898,28601,16450],{},[2005,28603,2014],{"stretchy":2013},[2133,28605,28606,28608],{},[898,28607,9134],{},[2005,28609,4360],{},[2005,28611,2234],{},[9172,28613,28614,28616,28618],{},[898,28615,3946],{},[2138,28617,2287],{},[2005,28619,4360],{},[2281,28621,28622,28624],{},[898,28623,2797],{},[2138,28625,2287],{},[2005,28627,2234],{},[9172,28629,28630,28632,28634],{},[898,28631,3946],{},[2138,28633,2140],{},[2005,28635,4360],{},[2281,28637,28638,28640],{},[898,28639,2797],{},[2138,28641,2140],{},[2005,28643,2020],{"stretchy":2013},[898,28645,1644],{"mathvariant":2385},[20768,28647],{"width":28081},[20768,28649,28650],{},[2297,28651,28652],{},"(6.13)",[902,28654,28655],{"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}",[724,28657,28658],{},"Soustava prvního řádu:",[883,28660,28662],{"className":28661},[886],[888,28663,28664],{"xmlns":890,"display":28071},[892,28665,28666,28849],{},[20760,28667,28668],{"width":28076},[20765,28669,28670,28672,28842,28844],{},[20768,28671],{"width":28081},[20768,28673,28674],{},[20760,28675,28676,28726,28776],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,28677,28678,28690],{},[20768,28679,28680],{},[2334,28681,28682],{"scriptlevel":2336,"displaystyle":2294},[9172,28683,28684,28686,28688],{},[898,28685,9801],{"mathvariant":28553},[2138,28687,2287],{},[2005,28689,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,28691,28692],{},[2334,28693,28694],{"scriptlevel":2336,"displaystyle":2294},[895,28695,28696,28698,28700,28708,28710,28712,28720,28722,28724],{},[895,28697],{},[2005,28699,2007],{},[9172,28701,28702,28704,28706],{},[898,28703,900],{},[2138,28705,2287],{},[2005,28707,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,28709,2234],{},[898,28711,16450],{},[9172,28713,28714,28716,28718],{},[898,28715,3946],{},[2138,28717,2287],{},[2005,28719,4360],{},[2005,28721,2007],{},[2138,28723,2336],{},[2005,28725,2295],{"separator":2294},[20765,28727,28728,28740],{},[20768,28729,28730],{},[2334,28731,28732],{"scriptlevel":2336,"displaystyle":2294},[9172,28733,28734,28736,28738],{},[898,28735,9801],{"mathvariant":28553},[2138,28737,2140],{},[2005,28739,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,28741,28742],{},[2334,28743,28744],{"scriptlevel":2336,"displaystyle":2294},[895,28745,28746,28748,28750,28758,28760,28762,28770,28772,28774],{},[895,28747],{},[2005,28749,2007],{},[9172,28751,28752,28754,28756],{},[898,28753,900],{},[2138,28755,2140],{},[2005,28757,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,28759,2234],{},[898,28761,16450],{},[9172,28763,28764,28766,28768],{},[898,28765,3946],{},[2138,28767,2140],{},[2005,28769,4360],{},[2005,28771,2007],{},[2138,28773,2336],{},[2005,28775,2295],{"separator":2294},[20765,28777,28778,28790],{},[20768,28779,28780],{},[2334,28781,28782],{"scriptlevel":2336,"displaystyle":2294},[9172,28783,28784,28786,28788],{},[898,28785,9801],{"mathvariant":28553},[898,28787,16450],{},[2005,28789,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,28791,28792],{},[2334,28793,28794],{"scriptlevel":2336,"displaystyle":2294},[895,28795,28796,28798,28800,28806,28808,28816,28822,28824,28832,28838,28840],{},[895,28797],{},[2005,28799,2007],{},[2133,28801,28802,28804],{},[898,28803,9134],{},[2005,28805,4360],{},[2005,28807,2234],{},[9172,28809,28810,28812,28814],{},[898,28811,3946],{},[2138,28813,2287],{},[2005,28815,4360],{},[2281,28817,28818,28820],{},[898,28819,2797],{},[2138,28821,2287],{},[2005,28823,2234],{},[9172,28825,28826,28828,28830],{},[898,28827,3946],{},[2138,28829,2140],{},[2005,28831,4360],{},[2281,28833,28834,28836],{},[898,28835,2797],{},[2138,28837,2140],{},[2005,28839,2007],{},[2138,28841,12466],{},[20768,28843],{"width":28081},[20768,28845,28846],{},[2297,28847,28848],{},"(6.14)",[902,28850,28851],{"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}",[724,28853,28854,28855,28858,28859,28872,28873,2713],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,28856,28857],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,28860,28862],{"className":28861},[886],[888,28863,28864],{"xmlns":890},[892,28865,28866,28870],{},[895,28867,28868],{},[898,28869,16450],{},[902,28871,16503],{"encoding":904}," dostáváme ",[38,28874,28875],{},"podmínku optimality",[883,28877,28879],{"className":28878},[886],[888,28880,28881],{"xmlns":890,"display":28071},[892,28882,28883,28941],{},[895,28884,28885],{},[12838,28886,28887],{"notation":12840},[2334,28888,28889],{"scriptlevel":2336,"displaystyle":2013},[2334,28890,28891],{"scriptlevel":2336,"displaystyle":2013},[2334,28892,28893],{"scriptlevel":2336,"displaystyle":2294},[895,28894,28895,28897,28899,28901,28919,28921,28939],{},[2297,28896,3993],{},[2297,28898,10607],{},[2005,28900,2007],{},[2338,28902,28903,28911],{},[9172,28904,28905,28907,28909],{},[898,28906,900],{},[2138,28908,2287],{},[2005,28910,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,28912,28913,28915,28917],{},[898,28914,900],{},[2138,28916,2140],{},[2005,28918,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,28920,2007],{},[2338,28922,28923,28931],{},[9172,28924,28925,28927,28929],{},[898,28926,3946],{},[2138,28928,2287],{},[2005,28930,4360],{},[9172,28932,28933,28935,28937],{},[898,28934,3946],{},[2138,28936,2140],{},[2005,28938,4360],{},[2297,28940,3993],{},[902,28942,28943],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[3876,28945,28946],{},[724,28947,28948,28950,28951,28985,28986,28989,28990,29008,29009,29027,29028,29058,29059,29076,29077,29107],{},[883,28949,4164],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,28952,28954],{"className":28953},[886],[888,28955,28956],{"xmlns":890},[892,28957,28958,28982],{},[895,28959,28960,28962,28964,28972,28974],{},[2297,28961,10607],{},[2005,28963,2007],{},[9172,28965,28966,28968,28970],{},[898,28967,3946],{},[2138,28969,2287],{},[2005,28971,4360],{},[898,28973,4680],{"mathvariant":2385},[9172,28975,28976,28978,28980],{},[898,28977,3946],{},[2138,28979,2140],{},[2005,28981,4360],{},[902,28983,28984],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,28987,28988],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,28991,28993],{"className":28992},[886],[888,28994,28995],{"xmlns":890},[892,28996,28997,29005],{},[895,28998,28999],{},[2281,29000,29001,29003],{},[898,29002,2797],{},[2138,29004,2287],{},[902,29006,29007],{"encoding":904},"Q_1"," za ",[883,29010,29012],{"className":29011},[886],[888,29013,29014],{"xmlns":890},[892,29015,29016,29024],{},[895,29017,29018],{},[2281,29019,29020,29022],{},[898,29021,2797],{},[2138,29023,2140],{},[902,29025,29026],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,29029,29031],{"className":29030},[886],[888,29032,29033],{"xmlns":890},[892,29034,29035,29055],{},[895,29036,29037,29039,29041,29047,29049],{},[2297,29038,10607],{},[2005,29040,3416],{},[2281,29042,29043,29045],{},[898,29044,3946],{},[2138,29046,2287],{},[898,29048,4680],{"mathvariant":2385},[2281,29050,29051,29053],{},[898,29052,3946],{},[2138,29054,2140],{},[902,29056,29057],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,29060,29062],{"className":29061},[886],[888,29063,29064],{"xmlns":890},[892,29065,29066,29074],{},[895,29067,29068],{},[2281,29069,29070,29072],{},[898,29071,2797],{},[2138,29073,2287],{},[902,29075,29007],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,29078,29080],{"className":29079},[886],[888,29081,29082],{"xmlns":890},[892,29083,29084,29104],{},[895,29085,29086,29088,29090,29096,29098],{},[2297,29087,10607],{},[2005,29089,3455],{},[2281,29091,29092,29094],{},[898,29093,3946],{},[2138,29095,2287],{},[898,29097,4680],{"mathvariant":2385},[2281,29099,29100,29102],{},[898,29101,3946],{},[2138,29103,2140],{},[902,29105,29106],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,29109,29111,29112,29125],{"id":29110},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,29113,29115],{"className":29114},[886],[888,29116,29117],{"xmlns":890},[892,29118,29119,29123],{},[895,29120,29121],{},[898,29122,16450],{},[902,29124,16503],{"encoding":904}," — mezní užitečnost důchodu",[724,29127,29128,29129,29147,29148,29151,29152,29169,29170,29187,29188,29191],{},"Lagrangeův multiplikátor ",[883,29130,29132],{"className":29131},[886],[888,29133,29134],{"xmlns":890},[892,29135,29136,29144],{},[895,29137,29138],{},[2133,29139,29140,29142],{},[898,29141,16450],{},[2005,29143,4360],{},[902,29145,29146],{"encoding":904},"\\lambda^*"," představuje ",[38,29149,29150],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,29153,29155],{"className":29154},[886],[888,29156,29157],{"xmlns":890},[892,29158,29159,29167],{},[895,29160,29161],{},[2133,29162,29163,29165],{},[898,29164,900],{},[2005,29166,4360],{},[902,29168,27967],{"encoding":904}," při jednotkové změně důchodu ",[883,29171,29173],{"className":29172},[886],[888,29174,29175],{"xmlns":890},[892,29176,29177,29185],{},[895,29178,29179],{},[2133,29180,29181,29183],{},[898,29182,9134],{},[2005,29184,4360],{},[902,29186,28033],{"encoding":904},". Je to ",[38,29189,29190],{},"stínová cena"," rozpočtového omezení.",[3876,29193,29194,29199],{},[724,29195,29196,29198],{},[883,29197,4578],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,29200,29201,29261,29348,29384,29471],{},[123,29202,29203,29206,29207,1644],{},[38,29204,29205],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,29208,29210],{"className":29209},[886],[888,29211,29212],{"xmlns":890},[892,29213,29214,29258],{},[895,29215,29216,29222,29224,29232,29238,29240,29248,29254,29256],{},[2133,29217,29218,29220],{},[898,29219,9134],{},[2005,29221,4360],{},[2005,29223,2234],{},[9172,29225,29226,29228,29230],{},[898,29227,3946],{},[2138,29229,2287],{},[2005,29231,4360],{},[2281,29233,29234,29236],{},[898,29235,2797],{},[2138,29237,2287],{},[2005,29239,2234],{},[9172,29241,29242,29244,29246],{},[898,29243,3946],{},[2138,29245,2140],{},[2005,29247,4360],{},[2281,29249,29250,29252],{},[898,29251,2797],{},[2138,29253,2140],{},[2005,29255,2007],{},[2138,29257,2336],{},[902,29259,29260],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,29262,29263,2212,29266,1644],{},[38,29264,29265],{},"Sestav Lagrangeovu funkci",[883,29267,29269],{"className":29268},[886],[888,29270,29271],{"xmlns":890},[892,29272,29273,29345],{},[895,29274,29275,29277,29279,29281,29283,29289,29291,29297,29299,29301,29303,29305,29311,29313,29321,29327,29329,29337,29343],{},[898,29276,9801],{"mathvariant":28553},[2005,29278,2007],{},[898,29280,900],{},[2005,29282,2014],{"stretchy":2013},[2281,29284,29285,29287],{},[898,29286,2797],{},[2138,29288,2287],{},[2005,29290,2295],{"separator":2294},[2281,29292,29293,29295],{},[898,29294,2797],{},[2138,29296,2140],{},[2005,29298,2020],{"stretchy":2013},[2005,29300,2104],{},[898,29302,16450],{},[2005,29304,2014],{"stretchy":2013},[2133,29306,29307,29309],{},[898,29308,9134],{},[2005,29310,4360],{},[2005,29312,2234],{},[9172,29314,29315,29317,29319],{},[898,29316,3946],{},[2138,29318,2287],{},[2005,29320,4360],{},[2281,29322,29323,29325],{},[898,29324,2797],{},[2138,29326,2287],{},[2005,29328,2234],{},[9172,29330,29331,29333,29335],{},[898,29332,3946],{},[2138,29334,2140],{},[2005,29336,4360],{},[2281,29338,29339,29341],{},[898,29340,2797],{},[2138,29342,2140],{},[2005,29344,2020],{"stretchy":2013},[902,29346,29347],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,29349,29350,10472,29353,29383],{},[38,29351,29352],{},"Spočítej parciální derivace",[883,29354,29356],{"className":29355},[886],[888,29357,29358],{"xmlns":890},[892,29359,29360,29380],{},[895,29361,29362,29368,29370,29376,29378],{},[2281,29363,29364,29366],{},[898,29365,2797],{},[2138,29367,2287],{},[2005,29369,2295],{"separator":2294},[2281,29371,29372,29374],{},[898,29373,2797],{},[2138,29375,2140],{},[2005,29377,2295],{"separator":2294},[898,29379,16450],{},[902,29381,29382],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,29385,29386,29402,29403,29436,29437,3894,29454,1644],{},[38,29387,29388,29389],{},"Vyluč ",[883,29390,29392],{"className":29391},[886],[888,29393,29394],{"xmlns":890},[892,29395,29396,29400],{},[895,29397,29398],{},[898,29399,16450],{},[902,29401,16503],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,29404,29406],{"className":29405},[886],[888,29407,29408],{"xmlns":890},[892,29409,29410,29434],{},[895,29411,29412,29414,29416,29424,29426],{},[2297,29413,10607],{},[2005,29415,2007],{},[9172,29417,29418,29420,29422],{},[898,29419,3946],{},[2138,29421,2287],{},[2005,29423,4360],{},[898,29425,4680],{"mathvariant":2385},[9172,29427,29428,29430,29432],{},[898,29429,3946],{},[2138,29431,2140],{},[2005,29433,4360],{},[902,29435,28984],{"encoding":904},", která dá vztah mezi ",[883,29438,29440],{"className":29439},[886],[888,29441,29442],{"xmlns":890},[892,29443,29444,29452],{},[895,29445,29446],{},[2281,29447,29448,29450],{},[898,29449,2797],{},[2138,29451,2287],{},[902,29453,29007],{"encoding":904},[883,29455,29457],{"className":29456},[886],[888,29458,29459],{"xmlns":890},[892,29460,29461,29469],{},[895,29462,29463],{},[2281,29464,29465,29467],{},[898,29466,2797],{},[2138,29468,2140],{},[902,29470,29026],{"encoding":904},[123,29472,29473,29476,29477,29507,29508,29525,29526,1644],{},[38,29474,29475],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,29478,29480],{"className":29479},[886],[888,29481,29482],{"xmlns":890},[892,29483,29484,29504],{},[895,29485,29486,29494,29496],{},[9172,29487,29488,29490,29492],{},[898,29489,2797],{},[2138,29491,2287],{},[2005,29493,4360],{},[2005,29495,2295],{"separator":2294},[9172,29497,29498,29500,29502],{},[898,29499,2797],{},[2138,29501,2140],{},[2005,29503,4360],{},[902,29505,29506],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,29509,29511],{"className":29510},[886],[888,29512,29513],{"xmlns":890},[892,29514,29515,29523],{},[895,29516,29517],{},[2133,29518,29519,29521],{},[898,29520,16450],{},[2005,29522,4360],{},[902,29524,29146],{"encoding":904}," a maximální užitečnost ",[883,29527,29529],{"className":29528},[886],[888,29530,29531],{"xmlns":890},[892,29532,29533,29567],{},[895,29534,29535,29541,29543,29545,29547,29555,29557,29565],{},[2133,29536,29537,29539],{},[898,29538,900],{},[2005,29540,4360],{},[2005,29542,2007],{},[898,29544,900],{},[2005,29546,2014],{"stretchy":2013},[9172,29548,29549,29551,29553],{},[898,29550,2797],{},[2138,29552,2287],{},[2005,29554,4360],{},[2005,29556,2295],{"separator":2294},[9172,29558,29559,29561,29563],{},[898,29560,2797],{},[2138,29562,2140],{},[2005,29564,4360],{},[2005,29566,2020],{"stretchy":2013},[902,29568,29569],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,29571,29573],{"id":29572},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,29575,29576],{},[2568,29577],{"alt":29578,"className":29579,"src":29580},"imek-uzitecnost-optimum",[210,2572],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,29582,29583],{},[614,29584,29585,29586,29635,29636,3894,29664,29692,29693,29727,29728,29767,29768,29786,29787,29805,29806,29824],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,29587,29589],{"className":29588},[886],[888,29590,29591],{"xmlns":890},[892,29592,29593,29633],{},[895,29594,29595,29601,29603,29611,29617,29619,29627],{},[2133,29596,29597,29599],{},[898,29598,9134],{},[2005,29600,4360],{},[2005,29602,2007],{},[9172,29604,29605,29607,29609],{},[898,29606,3946],{},[2138,29608,2287],{},[2005,29610,4360],{},[2281,29612,29613,29615],{},[898,29614,2797],{},[2138,29616,2287],{},[2005,29618,2104],{},[9172,29620,29621,29623,29625],{},[898,29622,3946],{},[2138,29624,2140],{},[2005,29626,4360],{},[2281,29628,29629,29631],{},[898,29630,2797],{},[2138,29632,2140],{},[902,29634,17305],{"encoding":904}," protíná osy v ",[883,29637,29639],{"className":29638},[886],[888,29640,29641],{"xmlns":890},[892,29642,29643,29661],{},[895,29644,29645,29651,29653],{},[2133,29646,29647,29649],{},[898,29648,9134],{},[2005,29650,4360],{},[898,29652,4680],{"mathvariant":2385},[9172,29654,29655,29657,29659],{},[898,29656,3946],{},[2138,29658,2287],{},[2005,29660,4360],{},[902,29662,29663],{"encoding":904},"Y^*\u002FP_1^*",[883,29665,29667],{"className":29666},[886],[888,29668,29669],{"xmlns":890},[892,29670,29671,29689],{},[895,29672,29673,29679,29681],{},[2133,29674,29675,29677],{},[898,29676,9134],{},[2005,29678,4360],{},[898,29680,4680],{"mathvariant":2385},[9172,29682,29683,29685,29687],{},[898,29684,3946],{},[2138,29686,2140],{},[2005,29688,4360],{},[902,29690,29691],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,29694,29696],{"className":29695},[886],[888,29697,29698],{"xmlns":890},[892,29699,29700,29724],{},[895,29701,29702,29708,29710,29716,29718],{},[2281,29703,29704,29706],{},[898,29705,2151],{},[2138,29707,2287],{},[2005,29709,3455],{},[2133,29711,29712,29714],{},[898,29713,2151],{},[2005,29715,4360],{},[2005,29717,3455],{},[2281,29719,29720,29722],{},[898,29721,2151],{},[2138,29723,2140],{},[902,29725,29726],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,29729,29731],{"className":29730},[886],[888,29732,29733],{"xmlns":890},[892,29734,29735,29765],{},[895,29736,29737,29743,29745,29753,29755,29763],{},[2133,29738,29739,29741],{},[898,29740,2797],{},[2005,29742,4360],{},[2005,29744,2495],{"stretchy":2013},[9172,29746,29747,29749,29751],{},[898,29748,2797],{},[2138,29750,2287],{},[2005,29752,4360],{},[2005,29754,2295],{"separator":2294},[9172,29756,29757,29759,29761],{},[898,29758,2797],{},[2138,29760,2140],{},[2005,29762,4360],{},[2005,29764,2510],{"stretchy":2013},[902,29766,28332],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,29769,29771],{"className":29770},[886],[888,29772,29773],{"xmlns":890},[892,29774,29775,29783],{},[895,29776,29777],{},[2133,29778,29779,29781],{},[898,29780,2151],{},[2005,29782,4360],{},[902,29784,29785],{"encoding":904},"c^*",". Křivka ",[883,29788,29790],{"className":29789},[886],[888,29791,29792],{"xmlns":890},[892,29793,29794,29802],{},[895,29795,29796],{},[2281,29797,29798,29800],{},[898,29799,2151],{},[2138,29801,2287],{},[902,29803,29804],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,29807,29809],{"className":29808},[886],[888,29810,29811],{"xmlns":890},[892,29812,29813,29821],{},[895,29814,29815],{},[2281,29816,29817,29819],{},[898,29818,2151],{},[2138,29820,2140],{},[902,29822,29823],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,29826,29827,29828,29831,29832,29850,29851,29880],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,29829,29830],{},"dotýkají",", tj. mají v bodě ",[883,29833,29835],{"className":29834},[886],[888,29836,29837],{"xmlns":890},[892,29838,29839,29847],{},[895,29840,29841],{},[2133,29842,29843,29845],{},[898,29844,2797],{},[2005,29846,4360],{},[902,29848,29849],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,29852,29854],{"className":29853},[886],[888,29855,29856],{"xmlns":890},[892,29857,29858,29878],{},[895,29859,29860,29862,29864,29870,29872],{},[2297,29861,10607],{},[2005,29863,2007],{},[2281,29865,29866,29868],{},[898,29867,3946],{},[2138,29869,2287],{},[898,29871,4680],{"mathvariant":2385},[2281,29873,29874,29876],{},[898,29875,3946],{},[2138,29877,2140],{},[902,29879,28003],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,29882,29884],{"id":29883},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,29886,9669,29887,29949],{},[883,29888,29890],{"className":29889},[886],[888,29891,29892],{"xmlns":890},[892,29893,29894,29946],{},[895,29895,29896,29898,29900,29906,29908,29914,29916,29918,29932],{},[898,29897,900],{},[2005,29899,2014],{"stretchy":2013},[2281,29901,29902,29904],{},[898,29903,2797],{},[2138,29905,2287],{},[2005,29907,2295],{"separator":2294},[2281,29909,29910,29912],{},[898,29911,2797],{},[2138,29913,2140],{},[2005,29915,2020],{"stretchy":2013},[2005,29917,2007],{},[9172,29919,29920,29922,29924],{},[898,29921,2797],{},[2138,29923,2287],{},[895,29925,29926,29928,29930],{},[2138,29927,2287],{},[898,29929,4680],{"mathvariant":2385},[2138,29931,2140],{},[9172,29933,29934,29936,29938],{},[898,29935,2797],{},[2138,29937,2140],{},[895,29939,29940,29942,29944],{},[2138,29941,2287],{},[898,29943,4680],{"mathvariant":2385},[2138,29945,2140],{},[902,29947,29948],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,29951,29952],{},[883,29953,29955],{"className":29954},[886],[888,29956,29957],{"xmlns":890},[892,29958,29959,30065],{},[895,29960,29961,29963,29965,30047,30049,30063],{},[2297,29962,10607],{},[2005,29964,2007],{},[2338,29966,29967,30007],{},[895,29968,29969,29977,29993],{},[2334,29970,29971],{"scriptlevel":2336,"displaystyle":2013},[2338,29972,29973,29975],{},[2138,29974,2287],{},[2138,29976,2140],{},[9172,29978,29979,29981,29983],{},[898,29980,2797],{},[2138,29982,2287],{},[895,29984,29985,29987,29989,29991],{},[2005,29986,2234],{},[2138,29988,2287],{},[898,29990,4680],{"mathvariant":2385},[2138,29992,2140],{},[9172,29994,29995,29997,29999],{},[898,29996,2797],{},[2138,29998,2140],{},[895,30000,30001,30003,30005],{},[2138,30002,2287],{},[898,30004,4680],{"mathvariant":2385},[2138,30006,2140],{},[895,30008,30009,30017,30031],{},[2334,30010,30011],{"scriptlevel":2336,"displaystyle":2013},[2338,30012,30013,30015],{},[2138,30014,2287],{},[2138,30016,2140],{},[9172,30018,30019,30021,30023],{},[898,30020,2797],{},[2138,30022,2287],{},[895,30024,30025,30027,30029],{},[2138,30026,2287],{},[898,30028,4680],{"mathvariant":2385},[2138,30030,2140],{},[9172,30032,30033,30035,30037],{},[898,30034,2797],{},[2138,30036,2140],{},[895,30038,30039,30041,30043,30045],{},[2005,30040,2234],{},[2138,30042,2287],{},[898,30044,4680],{"mathvariant":2385},[2138,30046,2140],{},[2005,30048,2007],{},[2338,30050,30051,30057],{},[2281,30052,30053,30055],{},[898,30054,2797],{},[2138,30056,2140],{},[2281,30058,30059,30061],{},[898,30060,2797],{},[2138,30062,2287],{},[898,30064,1644],{"mathvariant":2385},[902,30066,30067],{"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}.",[724,30069,30070,30071,2935,30116,30118,30119,30139,30140,30170,30171,1644],{},"Tedy ",[883,30072,30074],{"className":30073},[886],[888,30075,30076],{"xmlns":890},[892,30077,30078,30113],{},[895,30079,30080,30082,30084,30087,30089,30091,30093,30095,30103,30105],{},[2297,30081,10607],{},[2005,30083,2014],{"stretchy":2013},[2138,30085,30086],{},"300",[2005,30088,2295],{"separator":2294},[2138,30090,15116],{},[2005,30092,2020],{"stretchy":2013},[2005,30094,2007],{},[2334,30096,30097],{"scriptlevel":2336,"displaystyle":2013},[2338,30098,30099,30101],{},[2138,30100,15116],{},[2138,30102,30086],{},[2005,30104,2007],{},[2334,30106,30107],{"scriptlevel":2336,"displaystyle":2013},[2338,30108,30109,30111],{},[2138,30110,2237],{},[2138,30112,2182],{},[902,30114,30115],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,30117,9222],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,30120,30122],{"className":30121},[886],[888,30123,30124],{"xmlns":890},[892,30125,30126,30136],{},[895,30127,30128],{},[2334,30129,30130],{"scriptlevel":2336,"displaystyle":2013},[2338,30131,30132,30134],{},[2138,30133,2237],{},[2138,30135,2182],{},[902,30137,30138],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,30141,30143],{"className":30142},[886],[888,30144,30145],{"xmlns":890},[892,30146,30147,30167],{},[895,30148,30149,30151,30153,30159,30161],{},[2297,30150,10607],{},[2005,30152,2007],{},[2281,30154,30155,30157],{},[898,30156,2797],{},[2138,30158,2140],{},[898,30160,4680],{"mathvariant":2385},[2281,30162,30163,30165],{},[898,30164,2797],{},[2138,30166,2287],{},[902,30168,30169],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,30172,30174],{"className":30173},[886],[888,30175,30176],{"xmlns":890},[892,30177,30178,30198],{},[895,30179,30180,30182,30184,30190,30192],{},[2297,30181,10607],{},[2005,30183,2007],{},[2281,30185,30186,30188],{},[898,30187,3946],{},[2138,30189,2287],{},[898,30191,4680],{"mathvariant":2385},[2281,30193,30194,30196],{},[898,30195,3946],{},[2138,30197,2140],{},[902,30199,28003],{"encoding":904},[115,30201,30203,30204],{"id":30202},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,30205,30207],{"className":30206},[886],[888,30208,30209],{"xmlns":890},[892,30210,30211,30229],{},[895,30212,30213,30215,30217,30223],{},[898,30214,900],{},[2005,30216,2007],{},[2281,30218,30219,30221],{},[898,30220,2797],{},[2138,30222,2287],{},[2281,30224,30225,30227],{},[898,30226,2797],{},[2138,30228,2140],{},[902,30230,30231],{"encoding":904},"U = Q_1 Q_2",[724,30233,30234,30235,1343,30281,1343,30305,1343,30329,30351],{},"Je dána ",[883,30236,30238],{"className":30237},[886],[888,30239,30240],{"xmlns":890},[892,30241,30242,30278],{},[895,30243,30244,30246,30248,30254,30256,30262,30264,30266,30272],{},[898,30245,900],{},[2005,30247,2014],{"stretchy":2013},[2281,30249,30250,30252],{},[898,30251,2797],{},[2138,30253,2287],{},[2005,30255,2295],{"separator":2294},[2281,30257,30258,30260],{},[898,30259,2797],{},[2138,30261,2140],{},[2005,30263,2020],{"stretchy":2013},[2005,30265,2007],{},[2281,30267,30268,30270],{},[898,30269,2797],{},[2138,30271,2287],{},[2281,30273,30274,30276],{},[898,30275,2797],{},[2138,30277,2140],{},[902,30279,30280],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,30282,30284],{"className":30283},[886],[888,30285,30286],{"xmlns":890},[892,30287,30288,30302],{},[895,30289,30290,30298,30300],{},[9172,30291,30292,30294,30296],{},[898,30293,3946],{},[2138,30295,2287],{},[2005,30297,4360],{},[2005,30299,2007],{},[2138,30301,2140],{},[902,30303,30304],{"encoding":904},"P_1^* = 2",[883,30306,30308],{"className":30307},[886],[888,30309,30310],{"xmlns":890},[892,30311,30312,30326],{},[895,30313,30314,30322,30324],{},[9172,30315,30316,30318,30320],{},[898,30317,3946],{},[2138,30319,2140],{},[2005,30321,4360],{},[2005,30323,2007],{},[2138,30325,2237],{},[902,30327,30328],{"encoding":904},"P_2^* = 5",[883,30330,30332],{"className":30331},[886],[888,30333,30334],{"xmlns":890},[892,30335,30336,30348],{},[895,30337,30338,30344,30346],{},[2133,30339,30340,30342],{},[898,30341,9134],{},[2005,30343,4360],{},[2005,30345,2007],{},[2138,30347,3098],{},[902,30349,30350],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,30353,30355],{"className":30354},[886],[888,30356,30357],{"xmlns":890,"display":28071},[892,30358,30359,30431],{},[895,30360,30361,30363,30365,30371,30373,30379,30381,30383,30385,30387,30393,30399,30401,30403,30405,30407,30409,30411,30417,30419,30421,30427,30429],{},[898,30362,9801],{"mathvariant":28553},[2005,30364,2014],{"stretchy":2013},[2281,30366,30367,30369],{},[898,30368,2797],{},[2138,30370,2287],{},[2005,30372,2295],{"separator":2294},[2281,30374,30375,30377],{},[898,30376,2797],{},[2138,30378,2140],{},[2005,30380,2295],{"separator":2294},[898,30382,16450],{},[2005,30384,2020],{"stretchy":2013},[2005,30386,2007],{},[2281,30388,30389,30391],{},[898,30390,2797],{},[2138,30392,2287],{},[2281,30394,30395,30397],{},[898,30396,2797],{},[2138,30398,2140],{},[2005,30400,2104],{},[898,30402,16450],{},[2005,30404,2014],{"stretchy":2013},[2138,30406,3098],{},[2005,30408,2234],{},[2138,30410,2140],{},[2281,30412,30413,30415],{},[898,30414,2797],{},[2138,30416,2287],{},[2005,30418,2234],{},[2138,30420,2237],{},[2281,30422,30423,30425],{},[898,30424,2797],{},[2138,30426,2140],{},[2005,30428,2020],{"stretchy":2013},[898,30430,1644],{"mathvariant":2385},[902,30432,30433],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,30435,30436],{},"Soustava:",[883,30438,30440],{"className":30439},[886],[888,30441,30442],{"xmlns":890,"display":28071},[892,30443,30444,30556],{},[20760,30445,30446,30480,30514],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,30447,30448,30466],{},[20768,30449,30450],{},[2334,30451,30452],{"scriptlevel":2336,"displaystyle":2294},[895,30453,30454,30460,30462,30464],{},[2281,30455,30456,30458],{},[898,30457,2797],{},[2138,30459,2140],{},[2005,30461,2234],{},[2138,30463,2140],{},[898,30465,16450],{},[20768,30467,30468],{},[2334,30469,30470],{"scriptlevel":2336,"displaystyle":2294},[895,30471,30472,30474,30476,30478],{},[895,30473],{},[2005,30475,2007],{},[2138,30477,2336],{},[2005,30479,2295],{"separator":2294},[20765,30481,30482,30500],{},[20768,30483,30484],{},[2334,30485,30486],{"scriptlevel":2336,"displaystyle":2294},[895,30487,30488,30494,30496,30498],{},[2281,30489,30490,30492],{},[898,30491,2797],{},[2138,30493,2287],{},[2005,30495,2234],{},[2138,30497,2237],{},[898,30499,16450],{},[20768,30501,30502],{},[2334,30503,30504],{"scriptlevel":2336,"displaystyle":2294},[895,30505,30506,30508,30510,30512],{},[895,30507],{},[2005,30509,2007],{},[2138,30511,2336],{},[2005,30513,2295],{"separator":2294},[20765,30515,30516,30544],{},[20768,30517,30518],{},[2334,30519,30520],{"scriptlevel":2336,"displaystyle":2294},[895,30521,30522,30524,30526,30528,30534,30536,30538],{},[2138,30523,3098],{},[2005,30525,2234],{},[2138,30527,2140],{},[2281,30529,30530,30532],{},[898,30531,2797],{},[2138,30533,2287],{},[2005,30535,2234],{},[2138,30537,2237],{},[2281,30539,30540,30542],{},[898,30541,2797],{},[2138,30543,2140],{},[20768,30545,30546],{},[2334,30547,30548],{"scriptlevel":2336,"displaystyle":2294},[895,30549,30550,30552,30554],{},[895,30551],{},[2005,30553,2007],{},[2138,30555,12466],{},[902,30557,30558],{"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}",[724,30560,30561,30562,1343,30586,30610,30611,5595,30651,30669,30670,30720,30721,1644],{},"Z prvních dvou rovnic ",[883,30563,30565],{"className":30564},[886],[888,30566,30567],{"xmlns":890},[892,30568,30569,30583],{},[895,30570,30571,30577,30579,30581],{},[2281,30572,30573,30575],{},[898,30574,2797],{},[2138,30576,2140],{},[2005,30578,2007],{},[2138,30580,2140],{},[898,30582,16450],{},[902,30584,30585],{"encoding":904},"Q_2 = 2\\lambda",[883,30587,30589],{"className":30588},[886],[888,30590,30591],{"xmlns":890},[892,30592,30593,30607],{},[895,30594,30595,30601,30603,30605],{},[2281,30596,30597,30599],{},[898,30598,2797],{},[2138,30600,2287],{},[2005,30602,2007],{},[2138,30604,2237],{},[898,30606,16450],{},[902,30608,30609],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,30612,30614],{"className":30613},[886],[888,30615,30616],{"xmlns":890},[892,30617,30618,30648],{},[895,30619,30620,30622,30624,30626,30628,30630,30632,30634,30636,30638,30640,30642,30644,30646],{},[2138,30621,3098],{},[2005,30623,2007],{},[2138,30625,2140],{},[2005,30627,3185],{},[2138,30629,2237],{},[898,30631,16450],{},[2005,30633,2104],{},[2138,30635,2237],{},[2005,30637,3185],{},[2138,30639,2140],{},[898,30641,16450],{},[2005,30643,2007],{},[2138,30645,9041],{},[898,30647,16450],{},[902,30649,30650],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,30652,30654],{"className":30653},[886],[888,30655,30656],{"xmlns":890},[892,30657,30658,30666],{},[895,30659,30660,30662,30664],{},[898,30661,16450],{},[2005,30663,2007],{},[2138,30665,2237],{},[902,30667,30668],{"encoding":904},"\\lambda = 5",". Odtud ",[38,30671,30672,1343,30696],{},[883,30673,30675],{"className":30674},[886],[888,30676,30677],{"xmlns":890},[892,30678,30679,30693],{},[895,30680,30681,30689,30691],{},[9172,30682,30683,30685,30687],{},[898,30684,2797],{},[2138,30686,2287],{},[2005,30688,4360],{},[2005,30690,2007],{},[2138,30692,5010],{},[902,30694,30695],{"encoding":904},"Q_1^* = 25",[883,30697,30699],{"className":30698},[886],[888,30700,30701],{"xmlns":890},[892,30702,30703,30717],{},[895,30704,30705,30713,30715],{},[9172,30706,30707,30709,30711],{},[898,30708,2797],{},[2138,30710,2140],{},[2005,30712,4360],{},[2005,30714,2007],{},[2138,30716,2871],{},[902,30718,30719],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,30722,30724],{"className":30723},[886],[888,30725,30726],{"xmlns":890},[892,30727,30728,30749],{},[895,30729,30730,30736,30738,30740,30742,30744,30746],{},[2133,30731,30732,30734],{},[898,30733,900],{},[2005,30735,4360],{},[2005,30737,2007],{},[2138,30739,5010],{},[2005,30741,3185],{},[2138,30743,2871],{},[2005,30745,2007],{},[2138,30747,30748],{},"250",[902,30750,30751],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,30753,30754],{},[614,30755,30756,30757,28142,30795,3894,30819,30843,30844,30874,30875,30899,30900,30922,30923,1644],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,30758,30760],{"className":30759},[886],[888,30761,30762],{"xmlns":890},[892,30763,30764,30792],{},[895,30765,30766,30768,30770,30772,30778,30780,30782,30788,30790],{},[2138,30767,3098],{},[2005,30769,2234],{},[2138,30771,2140],{},[2281,30773,30774,30776],{},[898,30775,2797],{},[2138,30777,2287],{},[2005,30779,2234],{},[2138,30781,2237],{},[2281,30783,30784,30786],{},[898,30785,2797],{},[2138,30787,2140],{},[2005,30789,2007],{},[2138,30791,2336],{},[902,30793,30794],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,30796,30798],{"className":30797},[886],[888,30799,30800],{"xmlns":890},[892,30801,30802,30816],{},[895,30803,30804,30806,30808,30810,30812,30814],{},[898,30805,1836],{},[2005,30807,2495],{"stretchy":2013},[2138,30809,2336],{},[2005,30811,2295],{"separator":2294},[2138,30813,9041],{},[2005,30815,2510],{"stretchy":2013},[902,30817,30818],{"encoding":904},"A[0, 20]",[883,30820,30822],{"className":30821},[886],[888,30823,30824],{"xmlns":890},[892,30825,30826,30840],{},[895,30827,30828,30830,30832,30834,30836,30838],{},[898,30829,1844],{},[2005,30831,2495],{"stretchy":2013},[2138,30833,3128],{},[2005,30835,2295],{"separator":2294},[2138,30837,2336],{},[2005,30839,2510],{"stretchy":2013},[902,30841,30842],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,30845,30847],{"className":30846},[886],[888,30848,30849],{"xmlns":890},[892,30850,30851,30871],{},[895,30852,30853,30859,30861,30863,30865],{},[2281,30854,30855,30857],{},[898,30856,2797],{},[2138,30858,2140],{},[2005,30860,2007],{},[2138,30862,30748],{},[898,30864,4680],{"mathvariant":2385},[2281,30866,30867,30869],{},[898,30868,2797],{},[2138,30870,2287],{},[902,30872,30873],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,30876,30878],{"className":30877},[886],[888,30879,30880],{"xmlns":890},[892,30881,30882,30896],{},[895,30883,30884,30886,30888,30890,30892,30894],{},[898,30885,1868],{},[2005,30887,2495],{"stretchy":2013},[2138,30889,5010],{},[2005,30891,2295],{"separator":2294},[2138,30893,2871],{},[2005,30895,2510],{"stretchy":2013},[902,30897,30898],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,30901,30903],{"className":30902},[886],[888,30904,30905],{"xmlns":890},[892,30906,30907,30919],{},[895,30908,30909,30911],{},[2005,30910,2234],{},[2334,30912,30913],{"scriptlevel":2336,"displaystyle":2013},[2338,30914,30915,30917],{},[2138,30916,2140],{},[2138,30918,2237],{},[902,30920,30921],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,30924,30926],{"className":30925},[886],[888,30927,30928],{"xmlns":890},[892,30929,30930,30970],{},[895,30931,30932,30934,30936,30938,30940,30942,30944,30946,30948,30950,30958,30960,30962],{},[2005,30933,2234],{},[2297,30935,10607],{},[2005,30937,2014],{"stretchy":2013},[2138,30939,5010],{},[2005,30941,2295],{"separator":2294},[2138,30943,2871],{},[2005,30945,2020],{"stretchy":2013},[2005,30947,2007],{},[2005,30949,2234],{},[2334,30951,30952],{"scriptlevel":2336,"displaystyle":2013},[2338,30953,30954,30956],{},[2138,30955,2871],{},[2138,30957,5010],{},[2005,30959,2007],{},[2005,30961,2234],{},[2334,30963,30964],{"scriptlevel":2336,"displaystyle":2013},[2338,30965,30966,30968],{},[2138,30967,2140],{},[2138,30969,2237],{},[902,30971,30972],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,30974,30976],{"id":30975},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,30978,30979,30980,29008,31010,31013,31014,2713],{},"Považujeme-li v úloze ",[883,30981,30983],{"className":30982},[886],[888,30984,30985],{"xmlns":890},[892,30986,30987,31007],{},[895,30988,30989,30995,30997,31003,31005],{},[2281,30990,30991,30993],{},[898,30992,3946],{},[2138,30994,2287],{},[2005,30996,2295],{"separator":2294},[2281,30998,30999,31001],{},[898,31000,3946],{},[2138,31002,2140],{},[2005,31004,2295],{"separator":2294},[898,31006,9134],{},[902,31008,31009],{"encoding":904},"P_1, P_2, Y",[38,31011,31012],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,31015,31016],{},"Marshallovy poptávkové funkce",[883,31018,31020],{"className":31019},[886],[888,31021,31022],{"xmlns":890,"display":28071},[892,31023,31024,31119],{},[20760,31025,31026],{"width":28076},[20765,31027,31028,31030,31112,31114],{},[20768,31029],{"width":28081},[20768,31031,31032],{},[895,31033,31034,31040,31042,31048,31050,31056,31058,31064,31066,31068,31070,31072,31074,31080,31082,31088,31090,31096,31098,31104,31106,31108,31110],{},[2281,31035,31036,31038],{},[898,31037,2797],{},[2138,31039,2287],{},[2005,31041,2007],{},[2281,31043,31044,31046],{},[898,31045,1860],{},[2138,31047,2287],{},[2005,31049,2014],{"stretchy":2013},[2281,31051,31052,31054],{},[898,31053,3946],{},[2138,31055,2287],{},[2005,31057,2295],{"separator":2294},[2281,31059,31060,31062],{},[898,31061,3946],{},[2138,31063,2140],{},[2005,31065,2295],{"separator":2294},[898,31067,9134],{},[2005,31069,2020],{"stretchy":2013},[2005,31071,2295],{"separator":2294},[5884,31073],{"width":15290},[2281,31075,31076,31078],{},[898,31077,2797],{},[2138,31079,2140],{},[2005,31081,2007],{},[2281,31083,31084,31086],{},[898,31085,1860],{},[2138,31087,2140],{},[2005,31089,2014],{"stretchy":2013},[2281,31091,31092,31094],{},[898,31093,3946],{},[2138,31095,2287],{},[2005,31097,2295],{"separator":2294},[2281,31099,31100,31102],{},[898,31101,3946],{},[2138,31103,2140],{},[2005,31105,2295],{"separator":2294},[898,31107,9134],{},[2005,31109,2020],{"stretchy":2013},[2005,31111,2295],{"separator":2294},[20768,31113],{"width":28081},[20768,31115,31116],{},[2297,31117,31118],{},"(6.15)",[902,31120,31121],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,31123,31125],{"className":31124},[886],[888,31126,31127],{"xmlns":890,"display":28071},[892,31128,31129,31176],{},[20760,31130,31131],{"width":28076},[20765,31132,31133,31135,31169,31171],{},[20768,31134],{"width":28081},[20768,31136,31137],{},[895,31138,31139,31141,31143,31145,31147,31153,31155,31161,31163,31165,31167],{},[898,31140,16450],{},[2005,31142,2007],{},[898,31144,16450],{},[2005,31146,2014],{"stretchy":2013},[2281,31148,31149,31151],{},[898,31150,3946],{},[2138,31152,2287],{},[2005,31154,2295],{"separator":2294},[2281,31156,31157,31159],{},[898,31158,3946],{},[2138,31160,2140],{},[2005,31162,2295],{"separator":2294},[898,31164,9134],{},[2005,31166,2020],{"stretchy":2013},[898,31168,1644],{"mathvariant":2385},[20768,31170],{"width":28081},[20768,31172,31173],{},[2297,31174,31175],{},"(6.16)",[902,31177,31178],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,31180,31181,31211,31212,31278],{},[38,31182,31183,31184,1644],{},"Odvození pro ",[883,31185,31187],{"className":31186},[886],[888,31188,31189],{"xmlns":890},[892,31190,31191,31209],{},[895,31192,31193,31195,31197,31203],{},[898,31194,900],{},[2005,31196,2007],{},[2281,31198,31199,31201],{},[898,31200,2797],{},[2138,31202,2287],{},[2281,31204,31205,31207],{},[898,31206,2797],{},[2138,31208,2140],{},[902,31210,30231],{"encoding":904}," Lagrangeova funkce ",[883,31213,31215],{"className":31214},[886],[888,31216,31217],{"xmlns":890},[892,31218,31219,31275],{},[895,31220,31221,31223,31225,31231,31237,31239,31241,31243,31245,31247,31253,31259,31261,31267,31273],{},[898,31222,9801],{"mathvariant":28553},[2005,31224,2007],{},[2281,31226,31227,31229],{},[898,31228,2797],{},[2138,31230,2287],{},[2281,31232,31233,31235],{},[898,31234,2797],{},[2138,31236,2140],{},[2005,31238,2104],{},[898,31240,16450],{},[2005,31242,2014],{"stretchy":2013},[898,31244,9134],{},[2005,31246,2234],{},[2281,31248,31249,31251],{},[898,31250,3946],{},[2138,31252,2287],{},[2281,31254,31255,31257],{},[898,31256,2797],{},[2138,31258,2287],{},[2005,31260,2234],{},[2281,31262,31263,31265],{},[898,31264,3946],{},[2138,31266,2140],{},[2281,31268,31269,31271],{},[898,31270,2797],{},[2138,31272,2140],{},[2005,31274,2020],{"stretchy":2013},[902,31276,31277],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,31280,31282],{"className":31281},[886],[888,31283,31284],{"xmlns":890,"display":28071},[892,31285,31286,31453],{},[20760,31287,31288],{"width":28076},[20765,31289,31290,31292,31446,31448],{},[20768,31291],{"width":28081},[20768,31293,31294],{},[20760,31295,31296,31342,31388],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,31297,31298,31310],{},[20768,31299,31300],{},[2334,31301,31302],{"scriptlevel":2336,"displaystyle":2294},[9172,31303,31304,31306,31308],{},[898,31305,9801],{"mathvariant":28553},[2138,31307,2287],{},[2005,31309,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,31311,31312],{},[2334,31313,31314],{"scriptlevel":2336,"displaystyle":2294},[895,31315,31316,31318,31320,31326,31328,31330,31336,31338,31340],{},[895,31317],{},[2005,31319,2007],{},[2281,31321,31322,31324],{},[898,31323,2797],{},[2138,31325,2140],{},[2005,31327,2234],{},[898,31329,16450],{},[2281,31331,31332,31334],{},[898,31333,3946],{},[2138,31335,2287],{},[2005,31337,2007],{},[2138,31339,2336],{},[2005,31341,2295],{"separator":2294},[20765,31343,31344,31356],{},[20768,31345,31346],{},[2334,31347,31348],{"scriptlevel":2336,"displaystyle":2294},[9172,31349,31350,31352,31354],{},[898,31351,9801],{"mathvariant":28553},[2138,31353,2140],{},[2005,31355,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,31357,31358],{},[2334,31359,31360],{"scriptlevel":2336,"displaystyle":2294},[895,31361,31362,31364,31366,31372,31374,31376,31382,31384,31386],{},[895,31363],{},[2005,31365,2007],{},[2281,31367,31368,31370],{},[898,31369,2797],{},[2138,31371,2287],{},[2005,31373,2234],{},[898,31375,16450],{},[2281,31377,31378,31380],{},[898,31379,3946],{},[2138,31381,2140],{},[2005,31383,2007],{},[2138,31385,2336],{},[2005,31387,2295],{"separator":2294},[20765,31389,31390,31402],{},[20768,31391,31392],{},[2334,31393,31394],{"scriptlevel":2336,"displaystyle":2294},[9172,31395,31396,31398,31400],{},[898,31397,9801],{"mathvariant":28553},[898,31399,16450],{},[2005,31401,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,31403,31404],{},[2334,31405,31406],{"scriptlevel":2336,"displaystyle":2294},[895,31407,31408,31410,31412,31414,31416,31422,31428,31430,31436,31442,31444],{},[895,31409],{},[2005,31411,2007],{},[898,31413,9134],{},[2005,31415,2234],{},[2281,31417,31418,31420],{},[898,31419,3946],{},[2138,31421,2287],{},[2281,31423,31424,31426],{},[898,31425,2797],{},[2138,31427,2287],{},[2005,31429,2234],{},[2281,31431,31432,31434],{},[898,31433,3946],{},[2138,31435,2140],{},[2281,31437,31438,31440],{},[898,31439,2797],{},[2138,31441,2140],{},[2005,31443,2007],{},[2138,31445,12466],{},[20768,31447],{"width":28081},[20768,31449,31450],{},[2297,31451,31452],{},"(6.17)",[902,31454,31455],{"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}",[724,31457,31458,31459,31487,31488,31516,31517,31585],{},"Z prvních dvou: ",[883,31460,31462],{"className":31461},[886],[888,31463,31464],{"xmlns":890},[892,31465,31466,31484],{},[895,31467,31468,31474,31476,31482],{},[2281,31469,31470,31472],{},[898,31471,2797],{},[2138,31473,2140],{},[2005,31475,2007],{},[2281,31477,31478,31480],{},[898,31479,3946],{},[2138,31481,2287],{},[898,31483,16450],{},[902,31485,31486],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,31489,31491],{"className":31490},[886],[888,31492,31493],{"xmlns":890},[892,31494,31495,31513],{},[895,31496,31497,31503,31505,31511],{},[2281,31498,31499,31501],{},[898,31500,2797],{},[2138,31502,2287],{},[2005,31504,2007],{},[2281,31506,31507,31509],{},[898,31508,3946],{},[2138,31510,2140],{},[898,31512,16450],{},[902,31514,31515],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,31518,31520],{"className":31519},[886],[888,31521,31522],{"xmlns":890},[892,31523,31524,31582],{},[895,31525,31526,31528,31530,31536,31538,31544,31546,31548,31554,31556,31562,31564,31566,31568,31574,31580],{},[898,31527,9134],{},[2005,31529,2007],{},[2281,31531,31532,31534],{},[898,31533,3946],{},[2138,31535,2287],{},[2005,31537,3185],{},[2281,31539,31540,31542],{},[898,31541,3946],{},[2138,31543,2140],{},[898,31545,16450],{},[2005,31547,2104],{},[2281,31549,31550,31552],{},[898,31551,3946],{},[2138,31553,2140],{},[2005,31555,3185],{},[2281,31557,31558,31560],{},[898,31559,3946],{},[2138,31561,2287],{},[898,31563,16450],{},[2005,31565,2007],{},[2138,31567,2140],{},[2281,31569,31570,31572],{},[898,31571,3946],{},[2138,31573,2287],{},[2281,31575,31576,31578],{},[898,31577,3946],{},[2138,31579,2140],{},[898,31581,16450],{},[902,31583,31584],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,31587,31589],{"className":31588},[886],[888,31590,31591],{"xmlns":890,"display":28071},[892,31592,31593,31636],{},[20760,31594,31595],{"width":28076},[20765,31596,31597,31599,31629,31631],{},[20768,31598],{"width":28081},[20768,31600,31601],{},[895,31602,31603,31605,31607,31627],{},[898,31604,16450],{},[2005,31606,2007],{},[2338,31608,31609,31611],{},[898,31610,9134],{},[895,31612,31613,31615,31621],{},[2138,31614,2140],{},[2281,31616,31617,31619],{},[898,31618,3946],{},[2138,31620,2287],{},[2281,31622,31623,31625],{},[898,31624,3946],{},[2138,31626,2140],{},[898,31628,1644],{"mathvariant":2385},[20768,31630],{"width":28081},[20768,31632,31633],{},[2297,31634,31635],{},"(6.20)",[902,31637,31638],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,31640,31641],{},"Zpětně:",[883,31643,31645],{"className":31644},[886],[888,31646,31647],{"xmlns":890,"display":28071},[892,31648,31649,31726],{},[20760,31650,31651],{"width":28076},[20765,31652,31653,31655,31719,31721],{},[20768,31654],{"width":28081},[20768,31656,31657],{},[12838,31658,31659],{"notation":12840},[2334,31660,31661],{"scriptlevel":2336,"displaystyle":2013},[2334,31662,31663],{"scriptlevel":2336,"displaystyle":2013},[2334,31664,31665],{"scriptlevel":2336,"displaystyle":2294},[895,31666,31667,31669,31675,31677,31691,31693,31695,31701,31703,31717],{},[2297,31668,3993],{},[2281,31670,31671,31673],{},[898,31672,2797],{},[2138,31674,2287],{},[2005,31676,2007],{},[2338,31678,31679,31681],{},[898,31680,9134],{},[895,31682,31683,31685],{},[2138,31684,2140],{},[2281,31686,31687,31689],{},[898,31688,3946],{},[2138,31690,2287],{},[2005,31692,2295],{"separator":2294},[5884,31694],{"width":15290},[2281,31696,31697,31699],{},[898,31698,2797],{},[2138,31700,2140],{},[2005,31702,2007],{},[2338,31704,31705,31707],{},[898,31706,9134],{},[895,31708,31709,31711],{},[2138,31710,2140],{},[2281,31712,31713,31715],{},[898,31714,3946],{},[2138,31716,2140],{},[2297,31718,3993],{},[20768,31720],{"width":28081},[20768,31722,31723],{},[2297,31724,31725],{},"(6.21)",[902,31727,31728],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,31730,31732],{"id":31731},"engelova-funkce","Engelova funkce",[724,31734,9669,31735,31738,31739,31742,31743,19873,31760,1343,31790,31820,31821,31855,31856,1343,31882,31908],{},[38,31736,31737],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,31740,31741],{},"Engelovou funkcí",": pro ",[883,31744,31746],{"className":31745},[886],[888,31747,31748],{"xmlns":890},[892,31749,31750,31758],{},[895,31751,31752,31754,31756],{},[898,31753,9134],{},[2005,31755,2007],{},[2138,31757,3098],{},[902,31759,20325],{"encoding":904},[883,31761,31763],{"className":31762},[886],[888,31764,31765],{"xmlns":890},[892,31766,31767,31787],{},[895,31768,31769,31775,31777,31779,31781],{},[2281,31770,31771,31773],{},[898,31772,2797],{},[2138,31774,2287],{},[2005,31776,2007],{},[2138,31778,3128],{},[898,31780,4680],{"mathvariant":2385},[2281,31782,31783,31785],{},[898,31784,3946],{},[2138,31786,2287],{},[902,31788,31789],{"encoding":904},"Q_1 = 50\u002FP_1",[883,31791,31793],{"className":31792},[886],[888,31794,31795],{"xmlns":890},[892,31796,31797,31817],{},[895,31798,31799,31805,31807,31809,31811],{},[2281,31800,31801,31803],{},[898,31802,2797],{},[2138,31804,2140],{},[2005,31806,2007],{},[2138,31808,3128],{},[898,31810,4680],{"mathvariant":2385},[2281,31812,31813,31815],{},[898,31814,3946],{},[2138,31816,2140],{},[902,31818,31819],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,31822,31824],{"className":31823},[886],[888,31825,31826],{"xmlns":890},[892,31827,31828,31852],{},[895,31829,31830,31836,31838,31840,31842,31848,31850],{},[2281,31831,31832,31834],{},[898,31833,3946],{},[2138,31835,2287],{},[2005,31837,2007],{},[2138,31839,2871],{},[2005,31841,2295],{"separator":2294},[2281,31843,31844,31846],{},[898,31845,3946],{},[2138,31847,2140],{},[2005,31849,2007],{},[2138,31851,9041],{},[902,31853,31854],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,31857,31859],{"className":31858},[886],[888,31860,31861],{"xmlns":890},[892,31862,31863,31879],{},[895,31864,31865,31871,31873,31875,31877],{},[2281,31866,31867,31869],{},[898,31868,2797],{},[2138,31870,2287],{},[2005,31872,2007],{},[898,31874,9134],{},[898,31876,4680],{"mathvariant":2385},[2138,31878,9041],{},[902,31880,31881],{"encoding":904},"Q_1 = Y\u002F20",[883,31883,31885],{"className":31884},[886],[888,31886,31887],{"xmlns":890},[892,31888,31889,31905],{},[895,31890,31891,31897,31899,31901,31903],{},[2281,31892,31893,31895],{},[898,31894,2797],{},[2138,31896,2140],{},[2005,31898,2007],{},[898,31900,9134],{},[898,31902,4680],{"mathvariant":2385},[2138,31904,5217],{},[902,31906,31907],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,31910,31912],{"id":31911},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,31914,31915],{},"Výdaje spotřebitele jsou",[883,31917,31919],{"className":31918},[886],[888,31920,31921],{"xmlns":890,"display":28071},[892,31922,31923,31998],{},[20760,31924,31925],{"width":28076},[20765,31926,31927,31929,31991,31993],{},[20768,31928],{"width":28081},[20768,31930,31931],{},[895,31932,31933,31935,31937,31939,31941,31947,31949,31955,31957,31959,31967,31973,31975,31983,31989],{},[898,31934,1868],{},[2005,31936,2007],{},[898,31938,1868],{},[2005,31940,2014],{"stretchy":2013},[2281,31942,31943,31945],{},[898,31944,2797],{},[2138,31946,2287],{},[2005,31948,2295],{"separator":2294},[2281,31950,31951,31953],{},[898,31952,2797],{},[2138,31954,2140],{},[2005,31956,2020],{"stretchy":2013},[2005,31958,2007],{},[9172,31960,31961,31963,31965],{},[898,31962,3946],{},[2138,31964,2287],{},[2005,31966,4360],{},[2281,31968,31969,31971],{},[898,31970,2797],{},[2138,31972,2287],{},[2005,31974,2104],{},[9172,31976,31977,31979,31981],{},[898,31978,3946],{},[2138,31980,2140],{},[2005,31982,4360],{},[2281,31984,31985,31987],{},[898,31986,2797],{},[2138,31988,2140],{},[2005,31990,2295],{"separator":2294},[20768,31992],{"width":28081},[20768,31994,31995],{},[2297,31996,31997],{},"(6.22)",[902,31999,32000],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,32002,32003],{},"a je pevně zadána hladina užitečnosti",[883,32005,32007],{"className":32006},[886],[888,32008,32009],{"xmlns":890,"display":28071},[892,32010,32011,32058],{},[20760,32012,32013],{"width":28076},[20765,32014,32015,32017,32051,32053],{},[20768,32016],{"width":28081},[20768,32018,32019],{},[895,32020,32021,32027,32029,32031,32033,32039,32041,32047,32049],{},[2133,32022,32023,32025],{},[898,32024,900],{},[2005,32026,4360],{},[2005,32028,2007],{},[898,32030,900],{},[2005,32032,2014],{"stretchy":2013},[2281,32034,32035,32037],{},[898,32036,2797],{},[2138,32038,2287],{},[2005,32040,2295],{"separator":2294},[2281,32042,32043,32045],{},[898,32044,2797],{},[2138,32046,2140],{},[2005,32048,2020],{"stretchy":2013},[898,32050,1644],{"mathvariant":2385},[20768,32052],{"width":28081},[20768,32054,32055],{},[2297,32056,32057],{},"(6.23)",[902,32059,32060],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,32062,32063,32066,32067,32099,32100,1644],{},[38,32064,32065],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,32068,32070],{"className":32069},[886],[888,32071,32072],{"xmlns":890},[892,32073,32074,32096],{},[895,32075,32076,32078,32080,32086,32088,32094],{},[898,32077,1868],{},[2005,32079,2014],{"stretchy":2013},[2281,32081,32082,32084],{},[898,32083,2797],{},[2138,32085,2287],{},[2005,32087,2295],{"separator":2294},[2281,32089,32090,32092],{},[898,32091,2797],{},[2138,32093,2140],{},[2005,32095,2020],{"stretchy":2013},[902,32097,32098],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,32101,32103],{"className":32102},[886],[888,32104,32105],{"xmlns":890},[892,32106,32107,32163],{},[895,32108,32109,32111,32113,32119,32121,32127,32129,32131,32137,32139,32141,32143,32149,32151,32157,32159,32161],{},[898,32110,11045],{},[2005,32112,2014],{"stretchy":2013},[2281,32114,32115,32117],{},[898,32116,2797],{},[2138,32118,2287],{},[2005,32120,2295],{"separator":2294},[2281,32122,32123,32125],{},[898,32124,2797],{},[2138,32126,2140],{},[2005,32128,2020],{"stretchy":2013},[2005,32130,2007],{},[2133,32132,32133,32135],{},[898,32134,900],{},[2005,32136,4360],{},[2005,32138,2234],{},[898,32140,900],{},[2005,32142,2014],{"stretchy":2013},[2281,32144,32145,32147],{},[898,32146,2797],{},[2138,32148,2287],{},[2005,32150,2295],{"separator":2294},[2281,32152,32153,32155],{},[898,32154,2797],{},[2138,32156,2140],{},[2005,32158,2020],{"stretchy":2013},[2005,32160,2007],{},[2138,32162,2336],{},[902,32164,32165],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,32167,32169],{"id":32168},"lagrangeova-funkce","Lagrangeova funkce",[883,32171,32173],{"className":32172},[886],[888,32174,32175],{"xmlns":890,"display":28071},[892,32176,32177,32288],{},[20760,32178,32179],{"width":28076},[20765,32180,32181,32183,32281,32283],{},[20768,32182],{"width":28081},[20768,32184,32185],{},[895,32186,32187,32189,32191,32197,32199,32205,32207,32209,32211,32213,32221,32227,32229,32237,32243,32245,32247,32249,32255,32257,32259,32261,32267,32269,32275,32277,32279],{},[898,32188,9801],{"mathvariant":28553},[2005,32190,2014],{"stretchy":2013},[2281,32192,32193,32195],{},[898,32194,2797],{},[2138,32196,2287],{},[2005,32198,2295],{"separator":2294},[2281,32200,32201,32203],{},[898,32202,2797],{},[2138,32204,2140],{},[2005,32206,2295],{"separator":2294},[898,32208,16450],{},[2005,32210,2020],{"stretchy":2013},[2005,32212,2007],{},[9172,32214,32215,32217,32219],{},[898,32216,3946],{},[2138,32218,2287],{},[2005,32220,4360],{},[2281,32222,32223,32225],{},[898,32224,2797],{},[2138,32226,2287],{},[2005,32228,2104],{},[9172,32230,32231,32233,32235],{},[898,32232,3946],{},[2138,32234,2140],{},[2005,32236,4360],{},[2281,32238,32239,32241],{},[898,32240,2797],{},[2138,32242,2140],{},[2005,32244,2104],{},[898,32246,16450],{},[2005,32248,2014],{"stretchy":2013},[2133,32250,32251,32253],{},[898,32252,900],{},[2005,32254,4360],{},[2005,32256,2234],{},[898,32258,900],{},[2005,32260,2014],{"stretchy":2013},[2281,32262,32263,32265],{},[898,32264,2797],{},[2138,32266,2287],{},[2005,32268,2295],{"separator":2294},[2281,32270,32271,32273],{},[898,32272,2797],{},[2138,32274,2140],{},[2005,32276,2020],{"stretchy":2013},[2005,32278,2020],{"stretchy":2013},[898,32280,1644],{"mathvariant":2385},[20768,32282],{"width":28081},[20768,32284,32285],{},[2297,32286,32287],{},"(6.24)",[902,32289,32290],{"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}",[724,32292,32293],{},"Soustava podmínek prvního řádu:",[883,32295,32297],{"className":32296},[886],[888,32298,32299],{"xmlns":890,"display":28071},[892,32300,32301,32474],{},[20760,32302,32303],{"width":28076},[20765,32304,32305,32307,32467,32469],{},[20768,32306],{"width":28081},[20768,32308,32309],{},[20760,32310,32311,32361,32411],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,32312,32313,32325],{},[20768,32314,32315],{},[2334,32316,32317],{"scriptlevel":2336,"displaystyle":2294},[9172,32318,32319,32321,32323],{},[898,32320,9801],{"mathvariant":28553},[2138,32322,2287],{},[2005,32324,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,32326,32327],{},[2334,32328,32329],{"scriptlevel":2336,"displaystyle":2294},[895,32330,32331,32333,32335,32343,32345,32347,32355,32357,32359],{},[895,32332],{},[2005,32334,2007],{},[9172,32336,32337,32339,32341],{},[898,32338,3946],{},[2138,32340,2287],{},[2005,32342,4360],{},[2005,32344,2234],{},[898,32346,16450],{},[9172,32348,32349,32351,32353],{},[898,32350,900],{},[2138,32352,2287],{},[2005,32354,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,32356,2007],{},[2138,32358,2336],{},[2005,32360,2295],{"separator":2294},[20765,32362,32363,32375],{},[20768,32364,32365],{},[2334,32366,32367],{"scriptlevel":2336,"displaystyle":2294},[9172,32368,32369,32371,32373],{},[898,32370,9801],{"mathvariant":28553},[2138,32372,2140],{},[2005,32374,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,32376,32377],{},[2334,32378,32379],{"scriptlevel":2336,"displaystyle":2294},[895,32380,32381,32383,32385,32393,32395,32397,32405,32407,32409],{},[895,32382],{},[2005,32384,2007],{},[9172,32386,32387,32389,32391],{},[898,32388,3946],{},[2138,32390,2140],{},[2005,32392,4360],{},[2005,32394,2234],{},[898,32396,16450],{},[9172,32398,32399,32401,32403],{},[898,32400,900],{},[2138,32402,2140],{},[2005,32404,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,32406,2007],{},[2138,32408,2336],{},[2005,32410,2295],{"separator":2294},[20765,32412,32413,32425],{},[20768,32414,32415],{},[2334,32416,32417],{"scriptlevel":2336,"displaystyle":2294},[9172,32418,32419,32421,32423],{},[898,32420,9801],{"mathvariant":28553},[898,32422,16450],{},[2005,32424,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,32426,32427],{},[2334,32428,32429],{"scriptlevel":2336,"displaystyle":2294},[895,32430,32431,32433,32435,32441,32443,32445,32447,32453,32455,32461,32463,32465],{},[895,32432],{},[2005,32434,2007],{},[2133,32436,32437,32439],{},[898,32438,900],{},[2005,32440,4360],{},[2005,32442,2234],{},[898,32444,900],{},[2005,32446,2014],{"stretchy":2013},[2281,32448,32449,32451],{},[898,32450,2797],{},[2138,32452,2287],{},[2005,32454,2295],{"separator":2294},[2281,32456,32457,32459],{},[898,32458,2797],{},[2138,32460,2140],{},[2005,32462,2020],{"stretchy":2013},[2005,32464,2007],{},[2138,32466,12466],{},[20768,32468],{"width":28081},[20768,32470,32471],{},[2297,32472,32473],{},"(6.25)",[902,32475,32476],{"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}",[724,32478,32479],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,32481,32483],{"className":32482},[886],[888,32484,32485],{"xmlns":890,"display":28071},[892,32486,32487,32585],{},[20760,32488,32489],{"width":28076},[20765,32490,32491,32493,32578,32580],{},[20768,32492],{"width":28081},[20768,32494,32495],{},[895,32496,32497,32499,32501,32507,32509,32515,32517,32519,32521,32523,32525,32527,32576],{},[898,32498,1860],{},[2005,32500,2014],{"stretchy":2013},[2281,32502,32503,32505],{},[898,32504,2797],{},[2138,32506,2287],{},[2005,32508,2295],{"separator":2294},[2281,32510,32511,32513],{},[898,32512,2797],{},[2138,32514,2140],{},[2005,32516,2295],{"separator":2294},[898,32518,16450],{},[2005,32520,2020],{"stretchy":2013},[2005,32522,2007],{},[2005,32524,2234],{},[898,32526,16450],{},[895,32528,32529,32531,32543,32545,32558,32560,32562,32574],{},[2005,32530,2014],{"fence":2294},[9172,32532,32533,32535,32537],{},[898,32534,900],{},[2138,32536,2912],{},[895,32538,32539,32541],{},[2005,32540,2387],{"mathvariant":2385},[2005,32542,2387],{"mathvariant":2385},[2005,32544,2104],{},[9172,32546,32547,32549,32552],{},[898,32548,900],{},[2138,32550,32551],{},"22",[895,32553,32554,32556],{},[2005,32555,2387],{"mathvariant":2385},[2005,32557,2387],{"mathvariant":2385},[2005,32559,2104],{},[2138,32561,2140],{},[9172,32563,32564,32566,32568],{},[898,32565,900],{},[2138,32567,3517],{},[895,32569,32570,32572],{},[2005,32571,2387],{"mathvariant":2385},[2005,32573,2387],{"mathvariant":2385},[2005,32575,2020],{"fence":2294},[898,32577,1644],{"mathvariant":2385},[20768,32579],{"width":28081},[20768,32581,32582],{},[2297,32583,32584],{},"(6.26)",[902,32586,32587],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,32589,32590,32593,32594,32633,32634,32673,32674,32724,32725,32751,32752,32769,32770,32796],{},[38,32591,32592],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,32595,32597],{"className":32596},[886],[888,32598,32599],{"xmlns":890},[892,32600,32601,32631],{},[895,32602,32603,32609,32611,32619,32621,32629],{},[2133,32604,32605,32607],{},[898,32606,2797],{},[2005,32608,4360],{},[2005,32610,2495],{"stretchy":2013},[9172,32612,32613,32615,32617],{},[898,32614,2797],{},[2138,32616,2287],{},[2005,32618,4360],{},[2005,32620,2295],{"separator":2294},[9172,32622,32623,32625,32627],{},[898,32624,2797],{},[2138,32626,2140],{},[2005,32628,4360],{},[2005,32630,2510],{"stretchy":2013},[902,32632,28332],{"encoding":904}," dotyku křivky užitečnosti ",[883,32635,32637],{"className":32636},[886],[888,32638,32639],{"xmlns":890},[892,32640,32641,32671],{},[895,32642,32643,32649,32651,32653,32655,32661,32663,32669],{},[2133,32644,32645,32647],{},[898,32646,900],{},[2005,32648,4360],{},[2005,32650,2007],{},[898,32652,900],{},[2005,32654,2014],{"stretchy":2013},[2281,32656,32657,32659],{},[898,32658,2797],{},[2138,32660,2287],{},[2005,32662,2295],{"separator":2294},[2281,32664,32665,32667],{},[898,32666,2797],{},[2138,32668,2140],{},[2005,32670,2020],{"stretchy":2013},[902,32672,17672],{"encoding":904}," s přímkou výdajů ",[883,32675,32677],{"className":32676},[886],[888,32678,32679],{"xmlns":890},[892,32680,32681,32721],{},[895,32682,32683,32689,32691,32699,32705,32707,32715],{},[2133,32684,32685,32687],{},[898,32686,1868],{},[2005,32688,4360],{},[2005,32690,2007],{},[9172,32692,32693,32695,32697],{},[898,32694,3946],{},[2138,32696,2287],{},[2005,32698,4360],{},[2281,32700,32701,32703],{},[898,32702,2797],{},[2138,32704,2287],{},[2005,32706,2104],{},[9172,32708,32709,32711,32713],{},[898,32710,3946],{},[2138,32712,2140],{},[2005,32714,4360],{},[2281,32716,32717,32719],{},[898,32718,2797],{},[2138,32720,2140],{},[902,32722,32723],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,32726,32728],{"className":32727},[886],[888,32729,32730],{"xmlns":890},[892,32731,32732,32748],{},[895,32733,32734,32740,32742],{},[2281,32735,32736,32738],{},[898,32737,1868],{},[2138,32739,2336],{},[2005,32741,3455],{},[2133,32743,32744,32746],{},[898,32745,1868],{},[2005,32747,4360],{},[902,32749,32750],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,32753,32755],{"className":32754},[886],[888,32756,32757],{"xmlns":890},[892,32758,32759,32767],{},[895,32760,32761],{},[2133,32762,32763,32765],{},[898,32764,900],{},[2005,32766,4360],{},[902,32768,27967],{"encoding":904},", hladina ",[883,32771,32773],{"className":32772},[886],[888,32774,32775],{"xmlns":890},[892,32776,32777,32793],{},[895,32778,32779,32785,32787],{},[2281,32780,32781,32783],{},[898,32782,1868],{},[2138,32784,2287],{},[2005,32786,3416],{},[2133,32788,32789,32791],{},[898,32790,1868],{},[2005,32792,4360],{},[902,32794,32795],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[3876,32798,32799,32804],{},[724,32800,32801,32803],{},[883,32802,4578],{}," Postup — duální úloha (minimalizace výdajů)",[152,32805,32806,32856,32942,32982,33057],{},[123,32807,32808,2212,32811,32855],{},[38,32809,32810],{},"Zapiš vazbu",[883,32812,32814],{"className":32813},[886],[888,32815,32816],{"xmlns":890},[892,32817,32818,32852],{},[895,32819,32820,32826,32828,32830,32832,32838,32840,32846,32848,32850],{},[2133,32821,32822,32824],{},[898,32823,900],{},[2005,32825,4360],{},[2005,32827,2234],{},[898,32829,900],{},[2005,32831,2014],{"stretchy":2013},[2281,32833,32834,32836],{},[898,32835,2797],{},[2138,32837,2287],{},[2005,32839,2295],{"separator":2294},[2281,32841,32842,32844],{},[898,32843,2797],{},[2138,32845,2140],{},[2005,32847,2020],{"stretchy":2013},[2005,32849,2007],{},[2138,32851,2336],{},[902,32853,32854],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,32857,32858,2212,32860,1644],{},[38,32859,29265],{},[883,32861,32863],{"className":32862},[886],[888,32864,32865],{"xmlns":890},[892,32866,32867,32939],{},[895,32868,32869,32871,32873,32881,32887,32889,32897,32903,32905,32907,32909,32915,32917,32919,32921,32927,32929,32935,32937],{},[898,32870,9801],{"mathvariant":28553},[2005,32872,2007],{},[9172,32874,32875,32877,32879],{},[898,32876,3946],{},[2138,32878,2287],{},[2005,32880,4360],{},[2281,32882,32883,32885],{},[898,32884,2797],{},[2138,32886,2287],{},[2005,32888,2104],{},[9172,32890,32891,32893,32895],{},[898,32892,3946],{},[2138,32894,2140],{},[2005,32896,4360],{},[2281,32898,32899,32901],{},[898,32900,2797],{},[2138,32902,2140],{},[2005,32904,2104],{},[898,32906,16450],{},[2005,32908,2014],{"stretchy":2013},[2133,32910,32911,32913],{},[898,32912,900],{},[2005,32914,4360],{},[2005,32916,2234],{},[898,32918,900],{},[2005,32920,2014],{"stretchy":2013},[2281,32922,32923,32925],{},[898,32924,2797],{},[2138,32926,2287],{},[2005,32928,2295],{"separator":2294},[2281,32930,32931,32933],{},[898,32932,2797],{},[2138,32934,2140],{},[2005,32936,2020],{"stretchy":2013},[2005,32938,2020],{"stretchy":2013},[902,32940,32941],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,32943,32944,32947,32948,32981],{},[38,32945,32946],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,32949,32951],{"className":32950},[886],[888,32952,32953],{"xmlns":890},[892,32954,32955,32979],{},[895,32956,32957,32959,32961,32969,32971],{},[2297,32958,10607],{},[2005,32960,2007],{},[9172,32962,32963,32965,32967],{},[898,32964,3946],{},[2138,32966,2287],{},[2005,32968,4360],{},[898,32970,4680],{"mathvariant":2385},[9172,32972,32973,32975,32977],{},[898,32974,3946],{},[2138,32976,2140],{},[2005,32978,4360],{},[902,32980,28984],{"encoding":904}," (stejná jako u maximalizace!).",[123,32983,32984,2212,32987,33027,33028,1644],{},[38,32985,32986],{},"Dosaď do vazby",[883,32988,32990],{"className":32989},[886],[888,32991,32992],{"xmlns":890},[892,32993,32994,33024],{},[895,32995,32996,32998,33000,33006,33008,33014,33016,33018],{},[898,32997,900],{},[2005,32999,2014],{"stretchy":2013},[2281,33001,33002,33004],{},[898,33003,2797],{},[2138,33005,2287],{},[2005,33007,2295],{"separator":2294},[2281,33009,33010,33012],{},[898,33011,2797],{},[2138,33013,2140],{},[2005,33015,2020],{"stretchy":2013},[2005,33017,2007],{},[2133,33019,33020,33022],{},[898,33021,900],{},[2005,33023,4360],{},[902,33025,33026],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,33029,33031],{"className":33030},[886],[888,33032,33033],{"xmlns":890},[892,33034,33035,33055],{},[895,33036,33037,33045,33047],{},[9172,33038,33039,33041,33043],{},[898,33040,2797],{},[2138,33042,2287],{},[2005,33044,4360],{},[2005,33046,2295],{"separator":2294},[9172,33048,33049,33051,33053],{},[898,33050,2797],{},[2138,33052,2140],{},[2005,33054,4360],{},[902,33056,29506],{"encoding":904},[123,33058,33059,2212,33062,33116],{},[38,33060,33061],{},"Vypočítej minimální výdaje",[883,33063,33065],{"className":33064},[886],[888,33066,33067],{"xmlns":890},[892,33068,33069,33113],{},[895,33070,33071,33077,33079,33087,33095,33097,33105],{},[2133,33072,33073,33075],{},[898,33074,1868],{},[2005,33076,4360],{},[2005,33078,2007],{},[9172,33080,33081,33083,33085],{},[898,33082,3946],{},[2138,33084,2287],{},[2005,33086,4360],{},[9172,33088,33089,33091,33093],{},[898,33090,2797],{},[2138,33092,2287],{},[2005,33094,4360],{},[2005,33096,2104],{},[9172,33098,33099,33101,33103],{},[898,33100,3946],{},[2138,33102,2140],{},[2005,33104,4360],{},[9172,33106,33107,33109,33111],{},[898,33108,2797],{},[2138,33110,2140],{},[2005,33112,4360],{},[902,33114,33115],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,33118,33120,33121],{"id":33119},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,33122,33124],{"className":33123},[886],[888,33125,33126],{"xmlns":890},[892,33127,33128,33162],{},[895,33129,33130,33132,33134,33148],{},[898,33131,900],{},[2005,33133,2007],{},[9172,33135,33136,33138,33140],{},[898,33137,2797],{},[2138,33139,2287],{},[895,33141,33142,33144,33146],{},[2138,33143,2287],{},[898,33145,4680],{"mathvariant":2385},[2138,33147,2140],{},[9172,33149,33150,33152,33154],{},[898,33151,2797],{},[2138,33153,2140],{},[895,33155,33156,33158,33160],{},[2138,33157,2287],{},[898,33159,4680],{"mathvariant":2385},[2138,33161,2140],{},[902,33163,33164],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,33166,33167,33168,1343,33190,1343,33214,30351],{},"Dáno ",[883,33169,33171],{"className":33170},[886],[888,33172,33173],{"xmlns":890},[892,33174,33175,33187],{},[895,33176,33177,33183,33185],{},[2133,33178,33179,33181],{},[898,33180,900],{},[2005,33182,4360],{},[2005,33184,2007],{},[2138,33186,2140],{},[902,33188,33189],{"encoding":904},"U^* = 2",[883,33191,33193],{"className":33192},[886],[888,33194,33195],{"xmlns":890},[892,33196,33197,33211],{},[895,33198,33199,33207,33209],{},[9172,33200,33201,33203,33205],{},[898,33202,3946],{},[2138,33204,2287],{},[2005,33206,4360],{},[2005,33208,2007],{},[2138,33210,23794],{},[902,33212,33213],{"encoding":904},"P_1^* = 0{,}25",[883,33215,33217],{"className":33216},[886],[888,33218,33219],{"xmlns":890},[892,33220,33221,33235],{},[895,33222,33223,33231,33233],{},[9172,33224,33225,33227,33229],{},[898,33226,3946],{},[2138,33228,2140],{},[2005,33230,4360],{},[2005,33232,2007],{},[2138,33234,2287],{},[902,33236,33237],{"encoding":904},"P_2^* = 1",[883,33239,33241],{"className":33240},[886],[888,33242,33243],{"xmlns":890,"display":28071},[892,33244,33245,33309],{},[895,33246,33247,33249,33251,33253,33259,33261,33267,33269,33271,33273,33275,33277,33291,33305,33307],{},[898,33248,9801],{"mathvariant":28553},[2005,33250,2007],{},[2138,33252,23794],{},[2281,33254,33255,33257],{},[898,33256,2797],{},[2138,33258,2287],{},[2005,33260,2104],{},[2281,33262,33263,33265],{},[898,33264,2797],{},[2138,33266,2140],{},[2005,33268,2104],{},[898,33270,16450],{},[2005,33272,2014],{"stretchy":2013},[2138,33274,2140],{},[2005,33276,2234],{},[9172,33278,33279,33281,33283],{},[898,33280,2797],{},[2138,33282,2287],{},[895,33284,33285,33287,33289],{},[2138,33286,2287],{},[898,33288,4680],{"mathvariant":2385},[2138,33290,2140],{},[9172,33292,33293,33295,33297],{},[898,33294,2797],{},[2138,33296,2140],{},[895,33298,33299,33301,33303],{},[2138,33300,2287],{},[898,33302,4680],{"mathvariant":2385},[2138,33304,2140],{},[2005,33306,2020],{"stretchy":2013},[898,33308,1644],{"mathvariant":2385},[902,33310,33311],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,33313,30436],{},[883,33315,33317],{"className":33316},[886],[888,33318,33319],{"xmlns":890,"display":28071},[892,33320,33321,33535],{},[20760,33322,33323,33399,33475],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,33324,33325,33337],{},[20768,33326,33327],{},[2334,33328,33329],{"scriptlevel":2336,"displaystyle":2294},[9172,33330,33331,33333,33335],{},[898,33332,9801],{"mathvariant":28553},[2138,33334,2287],{},[2005,33336,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,33338,33339],{},[2334,33340,33341],{"scriptlevel":2336,"displaystyle":2294},[895,33342,33343,33345,33347,33349,33351,33353,33355,33363,33379,33393,33395,33397],{},[895,33344],{},[2005,33346,2007],{},[2138,33348,23794],{},[2005,33350,2234],{},[898,33352,16450],{},[2005,33354,3185],{},[2334,33356,33357],{"scriptlevel":2336,"displaystyle":2013},[2338,33358,33359,33361],{},[2138,33360,2287],{},[2138,33362,2140],{},[9172,33364,33365,33367,33369],{},[898,33366,2797],{},[2138,33368,2287],{},[895,33370,33371,33373,33375,33377],{},[2005,33372,2234],{},[2138,33374,2287],{},[898,33376,4680],{"mathvariant":2385},[2138,33378,2140],{},[9172,33380,33381,33383,33385],{},[898,33382,2797],{},[2138,33384,2140],{},[895,33386,33387,33389,33391],{},[2138,33388,2287],{},[898,33390,4680],{"mathvariant":2385},[2138,33392,2140],{},[2005,33394,2007],{},[2138,33396,2336],{},[2005,33398,2295],{"separator":2294},[20765,33400,33401,33413],{},[20768,33402,33403],{},[2334,33404,33405],{"scriptlevel":2336,"displaystyle":2294},[9172,33406,33407,33409,33411],{},[898,33408,9801],{"mathvariant":28553},[2138,33410,2140],{},[2005,33412,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,33414,33415],{},[2334,33416,33417],{"scriptlevel":2336,"displaystyle":2294},[895,33418,33419,33421,33423,33425,33427,33429,33431,33439,33453,33469,33471,33473],{},[895,33420],{},[2005,33422,2007],{},[2138,33424,2287],{},[2005,33426,2234],{},[898,33428,16450],{},[2005,33430,3185],{},[2334,33432,33433],{"scriptlevel":2336,"displaystyle":2013},[2338,33434,33435,33437],{},[2138,33436,2287],{},[2138,33438,2140],{},[9172,33440,33441,33443,33445],{},[898,33442,2797],{},[2138,33444,2287],{},[895,33446,33447,33449,33451],{},[2138,33448,2287],{},[898,33450,4680],{"mathvariant":2385},[2138,33452,2140],{},[9172,33454,33455,33457,33459],{},[898,33456,2797],{},[2138,33458,2140],{},[895,33460,33461,33463,33465,33467],{},[2005,33462,2234],{},[2138,33464,2287],{},[898,33466,4680],{"mathvariant":2385},[2138,33468,2140],{},[2005,33470,2007],{},[2138,33472,2336],{},[2005,33474,2295],{"separator":2294},[20765,33476,33477,33489],{},[20768,33478,33479],{},[2334,33480,33481],{"scriptlevel":2336,"displaystyle":2294},[9172,33482,33483,33485,33487],{},[898,33484,9801],{"mathvariant":28553},[898,33486,16450],{},[2005,33488,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,33490,33491],{},[2334,33492,33493],{"scriptlevel":2336,"displaystyle":2294},[895,33494,33495,33497,33499,33501,33503,33517,33531,33533],{},[895,33496],{},[2005,33498,2007],{},[2138,33500,2140],{},[2005,33502,2234],{},[9172,33504,33505,33507,33509],{},[898,33506,2797],{},[2138,33508,2287],{},[895,33510,33511,33513,33515],{},[2138,33512,2287],{},[898,33514,4680],{"mathvariant":2385},[2138,33516,2140],{},[9172,33518,33519,33521,33523],{},[898,33520,2797],{},[2138,33522,2140],{},[895,33524,33525,33527,33529],{},[2138,33526,2287],{},[898,33528,4680],{"mathvariant":2385},[2138,33530,2140],{},[2005,33532,2007],{},[2138,33534,12466],{},[902,33536,33537],{"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}",[724,33539,33540,33541,17583,33571,33599,33600,5595,33662,1343,33712,33734,33735,1644],{},"Podílem prvních dvou rovnic: ",[883,33542,33544],{"className":33543},[886],[888,33545,33546],{"xmlns":890},[892,33547,33548,33568],{},[895,33549,33550,33552,33554,33560,33562],{},[2138,33551,23794],{},[2005,33553,2007],{},[2281,33555,33556,33558],{},[898,33557,2797],{},[2138,33559,2140],{},[898,33561,4680],{"mathvariant":2385},[2281,33563,33564,33566],{},[898,33565,2797],{},[2138,33567,2287],{},[902,33569,33570],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,33572,33574],{"className":33573},[886],[888,33575,33576],{"xmlns":890},[892,33577,33578,33596],{},[895,33579,33580,33586,33588,33590],{},[2281,33581,33582,33584],{},[898,33583,2797],{},[2138,33585,2140],{},[2005,33587,2007],{},[2138,33589,23794],{},[2281,33591,33592,33594],{},[898,33593,2797],{},[2138,33595,2287],{},[902,33597,33598],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,33601,33603],{"className":33602},[886],[888,33604,33605],{"xmlns":890},[892,33606,33607,33659],{},[895,33608,33609,33623,33625,33627,33633,33645,33647,33649,33655,33657],{},[9172,33610,33611,33613,33615],{},[898,33612,2797],{},[2138,33614,2287],{},[895,33616,33617,33619,33621],{},[2138,33618,2287],{},[898,33620,4680],{"mathvariant":2385},[2138,33622,2140],{},[2005,33624,2014],{"stretchy":2013},[2138,33626,23794],{},[2281,33628,33629,33631],{},[898,33630,2797],{},[2138,33632,2287],{},[2133,33634,33635,33637],{},[2005,33636,2020],{"stretchy":2013},[895,33638,33639,33641,33643],{},[2138,33640,2287],{},[898,33642,4680],{"mathvariant":2385},[2138,33644,2140],{},[2005,33646,2007],{},[2138,33648,5015],{},[2281,33650,33651,33653],{},[898,33652,2797],{},[2138,33654,2287],{},[2005,33656,2007],{},[2138,33658,2140],{},[902,33660,33661],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,33663,33664,1343,33688],{},[883,33665,33667],{"className":33666},[886],[888,33668,33669],{"xmlns":890},[892,33670,33671,33685],{},[895,33672,33673,33681,33683],{},[9172,33674,33675,33677,33679],{},[898,33676,2797],{},[2138,33678,2287],{},[2005,33680,4360],{},[2005,33682,2007],{},[2138,33684,2360],{},[902,33686,33687],{"encoding":904},"Q_1^* = 4",[883,33689,33691],{"className":33690},[886],[888,33692,33693],{"xmlns":890},[892,33694,33695,33709],{},[895,33696,33697,33705,33707],{},[9172,33698,33699,33701,33703],{},[898,33700,2797],{},[2138,33702,2140],{},[2005,33704,4360],{},[2005,33706,2007],{},[2138,33708,2287],{},[902,33710,33711],{"encoding":904},"Q_2^* = 1",[883,33713,33715],{"className":33714},[886],[888,33716,33717],{"xmlns":890},[892,33718,33719,33731],{},[895,33720,33721,33727,33729],{},[2133,33722,33723,33725],{},[898,33724,16450],{},[2005,33726,4360],{},[2005,33728,2007],{},[2138,33730,2287],{},[902,33732,33733],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,33736,33738],{"className":33737},[886],[888,33739,33740],{"xmlns":890},[892,33741,33742,33770],{},[895,33743,33744,33750,33752,33754,33756,33758,33760,33762,33764,33766,33768],{},[2133,33745,33746,33748],{},[898,33747,1868],{},[2005,33749,4360],{},[2005,33751,2007],{},[2138,33753,23794],{},[2005,33755,3185],{},[2138,33757,2360],{},[2005,33759,2104],{},[2138,33761,2287],{},[2005,33763,3185],{},[2138,33765,2287],{},[2005,33767,2007],{},[2138,33769,2140],{},[902,33771,33772],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,33774,33775,33778,33779,1343,33845,1343,33911,33977,33978,34015,34016,34038,34039,1644],{},[614,33776,33777],{},"Ověření postačující podmínky"," (6.26): ",[883,33780,33782],{"className":33781},[886],[888,33783,33784],{"xmlns":890},[892,33785,33786,33842],{},[895,33787,33788,33800,33802,33804,33812,33828],{},[9172,33789,33790,33792,33794],{},[898,33791,900],{},[2138,33793,2912],{},[895,33795,33796,33798],{},[2005,33797,2387],{"mathvariant":2385},[2005,33799,2387],{"mathvariant":2385},[2005,33801,2007],{},[2005,33803,2234],{},[2334,33805,33806],{"scriptlevel":2336,"displaystyle":2013},[2338,33807,33808,33810],{},[2138,33809,2287],{},[2138,33811,2360],{},[9172,33813,33814,33816,33818],{},[898,33815,2797],{},[2138,33817,2287],{},[895,33819,33820,33822,33824,33826],{},[2005,33821,2234],{},[2138,33823,2182],{},[898,33825,4680],{"mathvariant":2385},[2138,33827,2140],{},[9172,33829,33830,33832,33834],{},[898,33831,2797],{},[2138,33833,2140],{},[895,33835,33836,33838,33840],{},[2138,33837,2287],{},[898,33839,4680],{"mathvariant":2385},[2138,33841,2140],{},[902,33843,33844],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,33846,33848],{"className":33847},[886],[888,33849,33850],{"xmlns":890},[892,33851,33852,33908],{},[895,33853,33854,33866,33868,33870,33878,33892],{},[9172,33855,33856,33858,33860],{},[898,33857,900],{},[2138,33859,32551],{},[895,33861,33862,33864],{},[2005,33863,2387],{"mathvariant":2385},[2005,33865,2387],{"mathvariant":2385},[2005,33867,2007],{},[2005,33869,2234],{},[2334,33871,33872],{"scriptlevel":2336,"displaystyle":2013},[2338,33873,33874,33876],{},[2138,33875,2287],{},[2138,33877,2360],{},[9172,33879,33880,33882,33884],{},[898,33881,2797],{},[2138,33883,2287],{},[895,33885,33886,33888,33890],{},[2138,33887,2287],{},[898,33889,4680],{"mathvariant":2385},[2138,33891,2140],{},[9172,33893,33894,33896,33898],{},[898,33895,2797],{},[2138,33897,2140],{},[895,33899,33900,33902,33904,33906],{},[2005,33901,2234],{},[2138,33903,2182],{},[898,33905,4680],{"mathvariant":2385},[2138,33907,2140],{},[902,33909,33910],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,33912,33914],{"className":33913},[886],[888,33915,33916],{"xmlns":890},[892,33917,33918,33974],{},[895,33919,33920,33932,33934,33942,33958],{},[9172,33921,33922,33924,33926],{},[898,33923,900],{},[2138,33925,3517],{},[895,33927,33928,33930],{},[2005,33929,2387],{"mathvariant":2385},[2005,33931,2387],{"mathvariant":2385},[2005,33933,2007],{},[2334,33935,33936],{"scriptlevel":2336,"displaystyle":2013},[2338,33937,33938,33940],{},[2138,33939,2287],{},[2138,33941,2360],{},[9172,33943,33944,33946,33948],{},[898,33945,2797],{},[2138,33947,2287],{},[895,33949,33950,33952,33954,33956],{},[2005,33951,2234],{},[2138,33953,2287],{},[898,33955,4680],{"mathvariant":2385},[2138,33957,2140],{},[9172,33959,33960,33962,33964],{},[898,33961,2797],{},[2138,33963,2140],{},[895,33965,33966,33968,33970,33972],{},[2005,33967,2234],{},[2138,33969,2287],{},[898,33971,4680],{"mathvariant":2385},[2138,33973,2140],{},[902,33975,33976],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,33979,33981],{"className":33980},[886],[888,33982,33983],{"xmlns":890},[892,33984,33985,34012],{},[895,33986,33987,33989,33991,33993,33995,33997,33999,34001,34003,34005,34008,34010],{},[898,33988,1860],{},[2005,33990,2014],{"stretchy":2013},[2138,33992,2360],{},[2005,33994,2295],{"separator":2294},[2138,33996,2287],{},[2005,33998,2295],{"separator":2294},[2138,34000,2287],{},[2005,34002,2020],{"stretchy":2013},[2005,34004,2007],{},[2138,34006,34007],{},"0,28125",[2005,34009,3416],{},[2138,34011,2336],{},[902,34013,34014],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,34017,34019],{"className":34018},[886],[888,34020,34021],{"xmlns":890},[892,34022,34023,34035],{},[895,34024,34025,34027,34029,34031,34033],{},[2005,34026,2495],{"stretchy":2013},[2138,34028,2360],{},[2005,34030,2295],{"separator":2294},[2138,34032,2287],{},[2005,34034,2510],{"stretchy":2013},[902,34036,34037],{"encoding":904},"[4, 1]"," je vázané ",[38,34040,3783],{},[115,34042,34044],{"id":34043},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,34046,34047],{},"Obecně:",[883,34049,34051],{"className":34050},[886],[888,34052,34053],{"xmlns":890,"display":28071},[892,34054,34055,34150],{},[20760,34056,34057],{"width":28076},[20765,34058,34059,34061,34143,34145],{},[20768,34060],{"width":28081},[20768,34062,34063],{},[895,34064,34065,34071,34073,34079,34081,34087,34089,34095,34097,34099,34101,34103,34105,34111,34113,34119,34121,34127,34129,34135,34137,34139,34141],{},[2281,34066,34067,34069],{},[898,34068,2797],{},[2138,34070,2287],{},[2005,34072,2007],{},[2281,34074,34075,34077],{},[898,34076,1860],{},[2138,34078,2287],{},[2005,34080,2014],{"stretchy":2013},[2281,34082,34083,34085],{},[898,34084,3946],{},[2138,34086,2287],{},[2005,34088,2295],{"separator":2294},[2281,34090,34091,34093],{},[898,34092,3946],{},[2138,34094,2140],{},[2005,34096,2295],{"separator":2294},[898,34098,900],{},[2005,34100,2020],{"stretchy":2013},[2005,34102,2295],{"separator":2294},[5884,34104],{"width":15290},[2281,34106,34107,34109],{},[898,34108,2797],{},[2138,34110,2140],{},[2005,34112,2007],{},[2281,34114,34115,34117],{},[898,34116,1860],{},[2138,34118,2140],{},[2005,34120,2014],{"stretchy":2013},[2281,34122,34123,34125],{},[898,34124,3946],{},[2138,34126,2287],{},[2005,34128,2295],{"separator":2294},[2281,34130,34131,34133],{},[898,34132,3946],{},[2138,34134,2140],{},[2005,34136,2295],{"separator":2294},[898,34138,900],{},[2005,34140,2020],{"stretchy":2013},[2005,34142,2295],{"separator":2294},[20768,34144],{"width":28081},[20768,34146,34147],{},[2297,34148,34149],{},"(6.27)",[902,34151,34152],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,34154,34156],{"className":34155},[886],[888,34157,34158],{"xmlns":890,"display":28071},[892,34159,34160,34207],{},[20760,34161,34162],{"width":28076},[20765,34163,34164,34166,34200,34202],{},[20768,34165],{"width":28081},[20768,34167,34168],{},[895,34169,34170,34172,34174,34176,34178,34184,34186,34192,34194,34196,34198],{},[898,34171,16450],{},[2005,34173,2007],{},[898,34175,16450],{},[2005,34177,2014],{"stretchy":2013},[2281,34179,34180,34182],{},[898,34181,3946],{},[2138,34183,2287],{},[2005,34185,2295],{"separator":2294},[2281,34187,34188,34190],{},[898,34189,3946],{},[2138,34191,2140],{},[2005,34193,2295],{"separator":2294},[898,34195,900],{},[2005,34197,2020],{"stretchy":2013},[898,34199,1644],{"mathvariant":2385},[20768,34201],{"width":28081},[20768,34203,34204],{},[2297,34205,34206],{},"(6.28)",[902,34208,34209],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,34211,34212,34213,2212,34216,34229,34230,34243],{},"Hicksova poptávka závisí na ",[38,34214,34215],{},"hladině užitečnosti",[883,34217,34219],{"className":34218},[886],[888,34220,34221],{"xmlns":890},[892,34222,34223,34227],{},[895,34224,34225],{},[898,34226,900],{},[902,34228,900],{"encoding":904}," (nikoli na důchodu ",[883,34231,34233],{"className":34232},[886],[888,34234,34235],{"xmlns":890},[892,34236,34237,34241],{},[895,34238,34239],{},[898,34240,9134],{},[902,34242,9134],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,34245,34247,34248],{"id":34246},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,34249,34251],{"className":34250},[886],[888,34252,34253],{"xmlns":890},[892,34254,34255,34289],{},[895,34256,34257,34259,34261,34275],{},[898,34258,900],{},[2005,34260,2007],{},[9172,34262,34263,34265,34267],{},[898,34264,2797],{},[2138,34266,2287],{},[895,34268,34269,34271,34273],{},[2138,34270,2287],{},[898,34272,4680],{"mathvariant":2385},[2138,34274,2140],{},[9172,34276,34277,34279,34281],{},[898,34278,2797],{},[2138,34280,2140],{},[895,34282,34283,34285,34287],{},[2138,34284,2287],{},[898,34286,4680],{"mathvariant":2385},[2138,34288,2140],{},[902,34290,33164],{"encoding":904},[724,34292,34293,34323],{},[883,34294,34296],{"className":34295},[886],[888,34297,34298],{"xmlns":890},[892,34299,34300,34320],{},[895,34301,34302,34308,34310,34316,34318],{},[2281,34303,34304,34306],{},[898,34305,3946],{},[2138,34307,2287],{},[2005,34309,2295],{"separator":2294},[2281,34311,34312,34314],{},[898,34313,3946],{},[2138,34315,2140],{},[2005,34317,2295],{"separator":2294},[898,34319,900],{},[902,34321,34322],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,34325,34327],{"className":34326},[886],[888,34328,34329],{"xmlns":890,"display":28071},[892,34330,34331,34405],{},[895,34332,34333,34335,34337,34343,34349,34351,34357,34363,34365,34367,34369,34371,34373,34387,34401,34403],{},[898,34334,9801],{"mathvariant":28553},[2005,34336,2007],{},[2281,34338,34339,34341],{},[898,34340,3946],{},[2138,34342,2287],{},[2281,34344,34345,34347],{},[898,34346,2797],{},[2138,34348,2287],{},[2005,34350,2104],{},[2281,34352,34353,34355],{},[898,34354,3946],{},[2138,34356,2140],{},[2281,34358,34359,34361],{},[898,34360,2797],{},[2138,34362,2140],{},[2005,34364,2104],{},[898,34366,16450],{},[2005,34368,2014],{"stretchy":2013},[898,34370,900],{},[2005,34372,2234],{},[9172,34374,34375,34377,34379],{},[898,34376,2797],{},[2138,34378,2287],{},[895,34380,34381,34383,34385],{},[2138,34382,2287],{},[898,34384,4680],{"mathvariant":2385},[2138,34386,2140],{},[9172,34388,34389,34391,34393],{},[898,34390,2797],{},[2138,34392,2140],{},[895,34394,34395,34397,34399],{},[2138,34396,2287],{},[898,34398,4680],{"mathvariant":2385},[2138,34400,2140],{},[2005,34402,2020],{"stretchy":2013},[898,34404,1644],{"mathvariant":2385},[902,34406,34407],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,34409,30436],{},[883,34411,34413],{"className":34412},[886],[888,34414,34415],{"xmlns":890,"display":28071},[892,34416,34417,34639],{},[20760,34418,34419,34499,34579],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,34420,34421,34433],{},[20768,34422,34423],{},[2334,34424,34425],{"scriptlevel":2336,"displaystyle":2294},[9172,34426,34427,34429,34431],{},[898,34428,9801],{"mathvariant":28553},[2138,34430,2287],{},[2005,34432,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,34434,34435],{},[2334,34436,34437],{"scriptlevel":2336,"displaystyle":2294},[895,34438,34439,34441,34443,34449,34451,34453,34455,34463,34479,34493,34495,34497],{},[895,34440],{},[2005,34442,2007],{},[2281,34444,34445,34447],{},[898,34446,3946],{},[2138,34448,2287],{},[2005,34450,2234],{},[898,34452,16450],{},[2005,34454,3185],{},[2334,34456,34457],{"scriptlevel":2336,"displaystyle":2013},[2338,34458,34459,34461],{},[2138,34460,2287],{},[2138,34462,2140],{},[9172,34464,34465,34467,34469],{},[898,34466,2797],{},[2138,34468,2287],{},[895,34470,34471,34473,34475,34477],{},[2005,34472,2234],{},[2138,34474,2287],{},[898,34476,4680],{"mathvariant":2385},[2138,34478,2140],{},[9172,34480,34481,34483,34485],{},[898,34482,2797],{},[2138,34484,2140],{},[895,34486,34487,34489,34491],{},[2138,34488,2287],{},[898,34490,4680],{"mathvariant":2385},[2138,34492,2140],{},[2005,34494,2007],{},[2138,34496,2336],{},[2005,34498,2295],{"separator":2294},[20765,34500,34501,34513],{},[20768,34502,34503],{},[2334,34504,34505],{"scriptlevel":2336,"displaystyle":2294},[9172,34506,34507,34509,34511],{},[898,34508,9801],{"mathvariant":28553},[2138,34510,2140],{},[2005,34512,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,34514,34515],{},[2334,34516,34517],{"scriptlevel":2336,"displaystyle":2294},[895,34518,34519,34521,34523,34529,34531,34533,34535,34543,34557,34573,34575,34577],{},[895,34520],{},[2005,34522,2007],{},[2281,34524,34525,34527],{},[898,34526,3946],{},[2138,34528,2140],{},[2005,34530,2234],{},[898,34532,16450],{},[2005,34534,3185],{},[2334,34536,34537],{"scriptlevel":2336,"displaystyle":2013},[2338,34538,34539,34541],{},[2138,34540,2287],{},[2138,34542,2140],{},[9172,34544,34545,34547,34549],{},[898,34546,2797],{},[2138,34548,2287],{},[895,34550,34551,34553,34555],{},[2138,34552,2287],{},[898,34554,4680],{"mathvariant":2385},[2138,34556,2140],{},[9172,34558,34559,34561,34563],{},[898,34560,2797],{},[2138,34562,2140],{},[895,34564,34565,34567,34569,34571],{},[2005,34566,2234],{},[2138,34568,2287],{},[898,34570,4680],{"mathvariant":2385},[2138,34572,2140],{},[2005,34574,2007],{},[2138,34576,2336],{},[2005,34578,2295],{"separator":2294},[20765,34580,34581,34593],{},[20768,34582,34583],{},[2334,34584,34585],{"scriptlevel":2336,"displaystyle":2294},[9172,34586,34587,34589,34591],{},[898,34588,9801],{"mathvariant":28553},[898,34590,16450],{},[2005,34592,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[20768,34594,34595],{},[2334,34596,34597],{"scriptlevel":2336,"displaystyle":2294},[895,34598,34599,34601,34603,34605,34607,34621,34635,34637],{},[895,34600],{},[2005,34602,2007],{},[898,34604,900],{},[2005,34606,2234],{},[9172,34608,34609,34611,34613],{},[898,34610,2797],{},[2138,34612,2287],{},[895,34614,34615,34617,34619],{},[2138,34616,2287],{},[898,34618,4680],{"mathvariant":2385},[2138,34620,2140],{},[9172,34622,34623,34625,34627],{},[898,34624,2797],{},[2138,34626,2140],{},[895,34628,34629,34631,34633],{},[2138,34630,2287],{},[898,34632,4680],{"mathvariant":2385},[2138,34634,2140],{},[2005,34636,2007],{},[2138,34638,12466],{},[902,34640,34641],{"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}",[724,34643,34644,34645,34715,34716,34774],{},"Podílem rovnic: ",[883,34646,34648],{"className":34647},[886],[888,34649,34650],{"xmlns":890},[892,34651,34652,34712],{},[895,34653,34654,34660,34662,34668,34670,34676,34678,34684,34686,34692,34698,34700,34706],{},[2281,34655,34656,34658],{},[898,34657,3946],{},[2138,34659,2287],{},[898,34661,4680],{"mathvariant":2385},[2281,34663,34664,34666],{},[898,34665,3946],{},[2138,34667,2140],{},[2005,34669,2007],{},[2281,34671,34672,34674],{},[898,34673,2797],{},[2138,34675,2140],{},[898,34677,4680],{"mathvariant":2385},[2281,34679,34680,34682],{},[898,34681,2797],{},[2138,34683,2287],{},[2005,34685,3996],{},[2281,34687,34688,34690],{},[898,34689,3946],{},[2138,34691,2287],{},[2281,34693,34694,34696],{},[898,34695,2797],{},[2138,34697,2287],{},[2005,34699,2007],{},[2281,34701,34702,34704],{},[898,34703,3946],{},[2138,34705,2140],{},[2281,34707,34708,34710],{},[898,34709,2797],{},[2138,34711,2140],{},[902,34713,34714],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,34717,34719],{"className":34718},[886],[888,34720,34721],{"xmlns":890},[892,34722,34723,34771],{},[895,34724,34725,34727,34729,34735,34741,34743,34749,34755,34757,34759,34765],{},[898,34726,1868],{},[2005,34728,2007],{},[2281,34730,34731,34733],{},[898,34732,3946],{},[2138,34734,2287],{},[2281,34736,34737,34739],{},[898,34738,2797],{},[2138,34740,2287],{},[2005,34742,2104],{},[2281,34744,34745,34747],{},[898,34746,3946],{},[2138,34748,2140],{},[2281,34750,34751,34753],{},[898,34752,2797],{},[2138,34754,2140],{},[2005,34756,2007],{},[2138,34758,2140],{},[2281,34760,34761,34763],{},[898,34762,3946],{},[2138,34764,2287],{},[2281,34766,34767,34769],{},[898,34768,2797],{},[2138,34770,2287],{},[902,34772,34773],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,34776,34778],{"className":34777},[886],[888,34779,34780],{"xmlns":890,"display":28071},[892,34781,34782,34849],{},[20760,34783,34784],{"width":28076},[20765,34785,34786,34788,34842,34844],{},[20768,34787],{"width":28081},[20768,34789,34790],{},[895,34791,34792,34798,34800,34814,34816,34818,34824,34826,34840],{},[2281,34793,34794,34796],{},[898,34795,2797],{},[2138,34797,2287],{},[2005,34799,2007],{},[2338,34801,34802,34804],{},[898,34803,1868],{},[895,34805,34806,34808],{},[2138,34807,2140],{},[2281,34809,34810,34812],{},[898,34811,3946],{},[2138,34813,2287],{},[2005,34815,2295],{"separator":2294},[5884,34817],{"width":15290},[2281,34819,34820,34822],{},[898,34821,2797],{},[2138,34823,2140],{},[2005,34825,2007],{},[2338,34827,34828,34830],{},[898,34829,1868],{},[895,34831,34832,34834],{},[2138,34833,2140],{},[2281,34835,34836,34838],{},[898,34837,3946],{},[2138,34839,2140],{},[898,34841,1644],{"mathvariant":2385},[20768,34843],{"width":28081},[20768,34845,34846],{},[2297,34847,34848],{},"(6.29)",[902,34850,34851],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,34853,34854,34855,17583,34937,34973],{},"Ze třetí rovnice ",[883,34856,34858],{"className":34857},[886],[888,34859,34860],{"xmlns":890},[892,34861,34862,34934],{},[895,34863,34864,34866,34868,34906,34908],{},[898,34865,900],{},[2005,34867,2007],{},[8123,34869,34870],{},[895,34871,34872,34888,34890],{},[2334,34873,34874],{"scriptlevel":2336,"displaystyle":2013},[2338,34875,34876,34878],{},[898,34877,1868],{},[895,34879,34880,34882],{},[2138,34881,2140],{},[2281,34883,34884,34886],{},[898,34885,3946],{},[2138,34887,2287],{},[2005,34889,3185],{},[2334,34891,34892],{"scriptlevel":2336,"displaystyle":2013},[2338,34893,34894,34896],{},[898,34895,1868],{},[895,34897,34898,34900],{},[2138,34899,2140],{},[2281,34901,34902,34904],{},[898,34903,3946],{},[2138,34905,2140],{},[2005,34907,2007],{},[2334,34909,34910],{"scriptlevel":2336,"displaystyle":2013},[2338,34911,34912,34914],{},[898,34913,1868],{},[895,34915,34916,34918],{},[2138,34917,2140],{},[8123,34919,34920],{},[895,34921,34922,34928],{},[2281,34923,34924,34926],{},[898,34925,3946],{},[2138,34927,2287],{},[2281,34929,34930,34932],{},[898,34931,3946],{},[2138,34933,2140],{},[902,34935,34936],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,34938,34940],{"className":34939},[886],[888,34941,34942],{"xmlns":890},[892,34943,34944,34970],{},[895,34945,34946,34948,34950,34952,34954],{},[898,34947,1868],{},[2005,34949,2007],{},[2138,34951,2140],{},[898,34953,900],{},[8123,34955,34956],{},[895,34957,34958,34964],{},[2281,34959,34960,34962],{},[898,34961,3946],{},[2138,34963,2287],{},[2281,34965,34966,34968],{},[898,34967,3946],{},[2138,34969,2140],{},[902,34971,34972],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,34975,34977],{"className":34976},[886],[888,34978,34979],{"xmlns":890,"display":28071},[892,34980,34981,35126],{},[20760,34982,34983],{"width":28076},[20765,34984,34985,34987,35119,35121],{},[20768,34986],{"width":28081},[20768,34988,34989],{},[12838,34990,34991],{"notation":12840},[2334,34992,34993],{"scriptlevel":2336,"displaystyle":2013},[2334,34994,34995],{"scriptlevel":2336,"displaystyle":2013},[2334,34996,34997],{"scriptlevel":2336,"displaystyle":2294},[895,34998,34999,35001,35007,35009,35011,35027,35029,35035,35037,35043,35045,35051,35053,35055,35057,35059,35061,35067,35069,35071,35087,35089,35095,35097,35103,35105,35111,35113,35115,35117],{},[2297,35000,3993],{},[2281,35002,35003,35005],{},[898,35004,2797],{},[2138,35006,2287],{},[2005,35008,2007],{},[898,35010,900],{},[8123,35012,35013],{},[2338,35014,35015,35021],{},[2281,35016,35017,35019],{},[898,35018,3946],{},[2138,35020,2140],{},[2281,35022,35023,35025],{},[898,35024,3946],{},[2138,35026,2287],{},[2005,35028,2007],{},[2281,35030,35031,35033],{},[898,35032,1860],{},[2138,35034,2287],{},[2005,35036,2014],{"stretchy":2013},[2281,35038,35039,35041],{},[898,35040,3946],{},[2138,35042,2287],{},[2005,35044,2295],{"separator":2294},[2281,35046,35047,35049],{},[898,35048,3946],{},[2138,35050,2140],{},[2005,35052,2295],{"separator":2294},[898,35054,900],{},[2005,35056,2020],{"stretchy":2013},[2005,35058,2295],{"separator":2294},[5884,35060],{"width":15290},[2281,35062,35063,35065],{},[898,35064,2797],{},[2138,35066,2140],{},[2005,35068,2007],{},[898,35070,900],{},[8123,35072,35073],{},[2338,35074,35075,35081],{},[2281,35076,35077,35079],{},[898,35078,3946],{},[2138,35080,2287],{},[2281,35082,35083,35085],{},[898,35084,3946],{},[2138,35086,2140],{},[2005,35088,2007],{},[2281,35090,35091,35093],{},[898,35092,1860],{},[2138,35094,2140],{},[2005,35096,2014],{"stretchy":2013},[2281,35098,35099,35101],{},[898,35100,3946],{},[2138,35102,2287],{},[2005,35104,2295],{"separator":2294},[2281,35106,35107,35109],{},[898,35108,3946],{},[2138,35110,2140],{},[2005,35112,2295],{"separator":2294},[898,35114,900],{},[2005,35116,2020],{"stretchy":2013},[2297,35118,3993],{},[20768,35120],{"width":28081},[20768,35122,35123],{},[2297,35124,35125],{},"(6.30)",[902,35127,35128],{"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}",[115,35130,35132],{"id":35131},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,35134,35135,35136,35149,35150,35167,35168,35181,35182,35199,35200,35203,35204,35243,35244,35273],{},"Primární (max ",[883,35137,35139],{"className":35138},[886],[888,35140,35141],{"xmlns":890},[892,35142,35143,35147],{},[895,35144,35145],{},[898,35146,900],{},[902,35148,900],{"encoding":904}," při rozpočtu ",[883,35151,35153],{"className":35152},[886],[888,35154,35155],{"xmlns":890},[892,35156,35157,35165],{},[895,35158,35159],{},[2133,35160,35161,35163],{},[898,35162,9134],{},[2005,35164,4360],{},[902,35166,28033],{"encoding":904},") a duální (min ",[883,35169,35171],{"className":35170},[886],[888,35172,35173],{"xmlns":890},[892,35174,35175,35179],{},[895,35176,35177],{},[898,35178,1868],{},[902,35180,1868],{"encoding":904}," při užitečnosti ",[883,35183,35185],{"className":35184},[886],[888,35186,35187],{"xmlns":890},[892,35188,35189,35197],{},[895,35190,35191],{},[2133,35192,35193,35195],{},[898,35194,900],{},[2005,35196,4360],{},[902,35198,27967],{"encoding":904},") úloha jsou ",[38,35201,35202],{},"ekvivalentní",": mají tentýž bod optima ",[883,35205,35207],{"className":35206},[886],[888,35208,35209],{"xmlns":890},[892,35210,35211,35241],{},[895,35212,35213,35219,35221,35229,35231,35239],{},[2133,35214,35215,35217],{},[898,35216,2797],{},[2005,35218,4360],{},[2005,35220,2495],{"stretchy":2013},[9172,35222,35223,35225,35227],{},[898,35224,2797],{},[2138,35226,2287],{},[2005,35228,4360],{},[2005,35230,2295],{"separator":2294},[9172,35232,35233,35235,35237],{},[898,35234,2797],{},[2138,35236,2140],{},[2005,35238,4360],{},[2005,35240,2510],{"stretchy":2013},[902,35242,28332],{"encoding":904}," a v obou platí ",[883,35245,35247],{"className":35246},[886],[888,35248,35249],{"xmlns":890},[892,35250,35251,35271],{},[895,35252,35253,35255,35257,35263,35265],{},[2297,35254,10607],{},[2005,35256,2007],{},[2281,35258,35259,35261],{},[898,35260,3946],{},[2138,35262,2287],{},[898,35264,4680],{"mathvariant":2385},[2281,35266,35267,35269],{},[898,35268,3946],{},[2138,35270,2140],{},[902,35272,28003],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,35275,35276],{},[2568,35277],{"alt":35278,"className":35279,"src":35280},"imek-primarni-vs-dualni",[210,2572],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,35282,35283,35394],{},[123,35284,35285,35288,35289,35302,35303,35343,35344,1644],{},[38,35286,35287],{},"Primární"," (Marshall): zadáno ",[883,35290,35292],{"className":35291},[886],[888,35293,35294],{"xmlns":890},[892,35295,35296,35300],{},[895,35297,35298],{},[898,35299,9134],{},[902,35301,9134],{"encoding":904},", hledáme maximální ",[883,35304,35306],{"className":35305},[886],[888,35307,35308],{"xmlns":890},[892,35309,35310,35340],{},[895,35311,35312,35318,35320,35326,35328,35334,35336,35338],{},[2133,35313,35314,35316],{},[898,35315,900],{},[2005,35317,4360],{},[2005,35319,2014],{"stretchy":2013},[2281,35321,35322,35324],{},[898,35323,3946],{},[2138,35325,2287],{},[2005,35327,2295],{"separator":2294},[2281,35329,35330,35332],{},[898,35331,3946],{},[2138,35333,2140],{},[2005,35335,2295],{"separator":2294},[898,35337,9134],{},[2005,35339,2020],{"stretchy":2013},[902,35341,35342],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,35345,35347],{"className":35346},[886],[888,35348,35349],{"xmlns":890},[892,35350,35351,35391],{},[895,35352,35353,35359,35361,35369,35371,35377,35379,35385,35387,35389],{},[2281,35354,35355,35357],{},[898,35356,2797],{},[898,35358,17797],{},[2005,35360,2007],{},[9172,35362,35363,35365,35367],{},[898,35364,1860],{},[898,35366,17797],{},[898,35368,2826],{},[2005,35370,2014],{"stretchy":2013},[2281,35372,35373,35375],{},[898,35374,3946],{},[2138,35376,2287],{},[2005,35378,2295],{"separator":2294},[2281,35380,35381,35383],{},[898,35382,3946],{},[2138,35384,2140],{},[2005,35386,2295],{"separator":2294},[898,35388,9134],{},[2005,35390,2020],{"stretchy":2013},[902,35392,35393],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,35395,35396,35399,35400,35413,35414,35343,35454,1644],{},[38,35397,35398],{},"Duální"," (Hicks): zadáno ",[883,35401,35403],{"className":35402},[886],[888,35404,35405],{"xmlns":890},[892,35406,35407,35411],{},[895,35408,35409],{},[898,35410,900],{},[902,35412,900],{"encoding":904},", hledáme minimální ",[883,35415,35417],{"className":35416},[886],[888,35418,35419],{"xmlns":890},[892,35420,35421,35451],{},[895,35422,35423,35429,35431,35437,35439,35445,35447,35449],{},[2133,35424,35425,35427],{},[898,35426,1868],{},[2005,35428,4360],{},[2005,35430,2014],{"stretchy":2013},[2281,35432,35433,35435],{},[898,35434,3946],{},[2138,35436,2287],{},[2005,35438,2295],{"separator":2294},[2281,35440,35441,35443],{},[898,35442,3946],{},[2138,35444,2140],{},[2005,35446,2295],{"separator":2294},[898,35448,900],{},[2005,35450,2020],{"stretchy":2013},[902,35452,35453],{"encoding":904},"E^*(P_1, P_2, U)",[883,35455,35457],{"className":35456},[886],[888,35458,35459],{"xmlns":890},[892,35460,35461,35502],{},[895,35462,35463,35469,35471,35480,35482,35488,35490,35496,35498,35500],{},[2281,35464,35465,35467],{},[898,35466,2797],{},[898,35468,17797],{},[2005,35470,2007],{},[9172,35472,35473,35475,35477],{},[898,35474,1860],{},[898,35476,17797],{},[898,35478,35479],{},"H",[2005,35481,2014],{"stretchy":2013},[2281,35483,35484,35486],{},[898,35485,3946],{},[2138,35487,2287],{},[2005,35489,2295],{"separator":2294},[2281,35491,35492,35494],{},[898,35493,3946],{},[2138,35495,2140],{},[2005,35497,2295],{"separator":2294},[898,35499,900],{},[2005,35501,2020],{"stretchy":2013},[902,35503,35504],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,35506,35507,35508,35511,35512,35515],{},"Proč se studují obě? Marshallova poptávka je ",[38,35509,35510],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,35513,35514],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,35517,35519],{"id":35518},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,35521,35523],{"id":35522},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,35525,35526,35529,35530,35562,35563,35601,35602,35628],{},[38,35527,35528],{},"6.8"," Jsou dány užitečnost ",[883,35531,35533],{"className":35532},[886],[888,35534,35535],{"xmlns":890},[892,35536,35537,35559],{},[895,35538,35539,35541,35543,35551],{},[898,35540,900],{},[2005,35542,2007],{},[9172,35544,35545,35547,35549],{},[898,35546,2797],{},[2138,35548,2287],{},[2138,35550,5015],{},[9172,35552,35553,35555,35557],{},[898,35554,2797],{},[2138,35556,2140],{},[2138,35558,5015],{},[902,35560,35561],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,35564,35566],{"className":35565},[886],[888,35567,35568],{"xmlns":890},[892,35569,35570,35598],{},[895,35571,35572,35580,35582,35584,35586,35594,35596],{},[9172,35573,35574,35576,35578],{},[898,35575,3946],{},[2138,35577,2287],{},[2005,35579,4360],{},[2005,35581,2007],{},[2138,35583,2360],{},[2005,35585,2295],{"separator":2294},[9172,35587,35588,35590,35592],{},[898,35589,3946],{},[2138,35591,2140],{},[2005,35593,4360],{},[2005,35595,2007],{},[2138,35597,2871],{},[902,35599,35600],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,35603,35605],{"className":35604},[886],[888,35606,35607],{"xmlns":890},[892,35608,35609,35625],{},[895,35610,35611,35617,35619],{},[2281,35612,35613,35615],{},[898,35614,2797],{},[2138,35616,2287],{},[2005,35618,2295],{"separator":2294},[2281,35620,35621,35623],{},[898,35622,2797],{},[2138,35624,2140],{},[902,35626,35627],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,35630,35631,35634,35635,35677,35678,35709,35710,35732,35733,1644],{},[38,35632,35633],{},"6.9"," Jsou dány rozpočtové omezení ",[883,35636,35638],{"className":35637},[886],[888,35639,35640],{"xmlns":890},[892,35641,35642,35674],{},[895,35643,35644,35646,35648,35654,35660,35662,35668],{},[898,35645,9134],{},[2005,35647,2007],{},[2281,35649,35650,35652],{},[898,35651,3946],{},[2138,35653,2287],{},[2281,35655,35656,35658],{},[898,35657,2797],{},[2138,35659,2287],{},[2005,35661,2104],{},[2281,35663,35664,35666],{},[898,35665,3946],{},[2138,35667,2140],{},[2281,35669,35670,35672],{},[898,35671,2797],{},[2138,35673,2140],{},[902,35675,35676],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,35679,35681],{"className":35680},[886],[888,35682,35683],{"xmlns":890},[892,35684,35685,35707],{},[895,35686,35687,35689,35691,35699],{},[898,35688,900],{},[2005,35690,2007],{},[9172,35692,35693,35695,35697],{},[898,35694,2797],{},[2138,35696,2287],{},[2138,35698,5015],{},[9172,35700,35701,35703,35705],{},[898,35702,2797],{},[2138,35704,2140],{},[2138,35706,5015],{},[902,35708,35561],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,35711,35713],{"className":35712},[886],[888,35714,35715],{"xmlns":890},[892,35716,35717,35729],{},[895,35718,35719,35725,35727],{},[2133,35720,35721,35723],{},[898,35722,9134],{},[2005,35724,4360],{},[2005,35726,2007],{},[2138,35728,15116],{},[902,35730,35731],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,35734,35736],{"className":35735},[886],[888,35737,35738],{"xmlns":890},[892,35739,35740,35768],{},[895,35741,35742,35750,35752,35754,35756,35764,35766],{},[9172,35743,35744,35746,35748],{},[898,35745,3946],{},[2138,35747,2287],{},[2005,35749,4360],{},[2005,35751,2007],{},[2138,35753,2237],{},[2005,35755,2295],{"separator":2294},[9172,35757,35758,35760,35762],{},[898,35759,3946],{},[2138,35761,2140],{},[2005,35763,4360],{},[2005,35765,2007],{},[2138,35767,2871],{},[902,35769,35770],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,35772,35773,35776,35777,21600,35809,35839,35840,1644],{},[38,35774,35775],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,35778,35780],{"className":35779},[886],[888,35781,35782],{"xmlns":890},[892,35783,35784,35806],{},[895,35785,35786,35788,35790,35798],{},[898,35787,900],{},[2005,35789,2007],{},[9172,35791,35792,35794,35796],{},[898,35793,2797],{},[2138,35795,2287],{},[898,35797,207],{},[9172,35799,35800,35802,35804],{},[898,35801,2797],{},[2138,35803,2140],{},[898,35805,2107],{},[902,35807,35808],{"encoding":904},"U = Q_1^a Q_2^b",[883,35810,35812],{"className":35811},[886],[888,35813,35814],{"xmlns":890},[892,35815,35816,35836],{},[895,35817,35818,35820,35822,35824,35826,35828,35830,35832,35834],{},[898,35819,207],{},[2005,35821,2295],{"separator":2294},[898,35823,2107],{},[2005,35825,6512],{},[2005,35827,5330],{"stretchy":2013},[2138,35829,2336],{},[2005,35831,2295],{"separator":2294},[2138,35833,2287],{},[2005,35835,5347],{"stretchy":2013},[902,35837,35838],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,35841,35843],{"className":35842},[886],[888,35844,35845],{"xmlns":890},[892,35846,35847,35879],{},[895,35848,35849,35851,35853,35859,35865,35867,35873],{},[898,35850,9134],{},[2005,35852,2007],{},[2281,35854,35855,35857],{},[898,35856,3946],{},[2138,35858,2287],{},[2281,35860,35861,35863],{},[898,35862,2797],{},[2138,35864,2287],{},[2005,35866,2104],{},[2281,35868,35869,35871],{},[898,35870,3946],{},[2138,35872,2140],{},[2281,35874,35875,35877],{},[898,35876,2797],{},[2138,35878,2140],{},[902,35880,35676],{"encoding":904},[724,35882,35883,35886,35887,21600,35921,35839,35939,1644],{},[38,35884,35885],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,35888,35890],{"className":35889},[886],[888,35891,35892],{"xmlns":890},[892,35893,35894,35918],{},[895,35895,35896,35898,35900,35908,35910],{},[898,35897,900],{},[2005,35899,2007],{},[9172,35901,35902,35904,35906],{},[898,35903,2797],{},[2138,35905,2287],{},[898,35907,207],{},[2005,35909,2104],{},[9172,35911,35912,35914,35916],{},[898,35913,2797],{},[2138,35915,2140],{},[898,35917,207],{},[902,35919,35920],{"encoding":904},"U = Q_1^a + Q_2^a",[883,35922,35924],{"className":35923},[886],[888,35925,35926],{"xmlns":890},[892,35927,35928,35936],{},[895,35929,35930,35932,35934],{},[898,35931,207],{},[2005,35933,3379],{"mathvariant":2385},[2138,35935,2336],{},[902,35937,35938],{"encoding":904},"a \\neq 0",[883,35940,35942],{"className":35941},[886],[888,35943,35944],{"xmlns":890},[892,35945,35946,35978],{},[895,35947,35948,35950,35952,35958,35964,35966,35972],{},[898,35949,9134],{},[2005,35951,2007],{},[2281,35953,35954,35956],{},[898,35955,3946],{},[2138,35957,2287],{},[2281,35959,35960,35962],{},[898,35961,2797],{},[2138,35963,2287],{},[2005,35965,2104],{},[2281,35967,35968,35970],{},[898,35969,3946],{},[2138,35971,2140],{},[2281,35973,35974,35976],{},[898,35975,2797],{},[2138,35977,2140],{},[902,35979,35676],{"encoding":904},[198,35981,35983],{"id":35982},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,35985,35986,35529,35989,1343,36016,36038,36039,1343,36062,36086,36087,36112,36113,1644],{},[38,35987,35988],{},"6.12",[883,35990,35992],{"className":35991},[886],[888,35993,35994],{"xmlns":890},[892,35995,35996,36014],{},[895,35997,35998,36000,36002,36008],{},[898,35999,900],{},[2005,36001,2007],{},[2281,36003,36004,36006],{},[898,36005,2797],{},[2138,36007,2287],{},[2281,36009,36010,36012],{},[898,36011,2797],{},[2138,36013,2140],{},[902,36015,30231],{"encoding":904},[883,36017,36019],{"className":36018},[886],[888,36020,36021],{"xmlns":890},[892,36022,36023,36035],{},[895,36024,36025,36031,36033],{},[2133,36026,36027,36029],{},[898,36028,900],{},[2005,36030,4360],{},[2005,36032,2007],{},[2138,36034,2871],{},[902,36036,36037],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,36040,36042],{"className":36041},[886],[888,36043,36044],{"xmlns":890},[892,36045,36046,36060],{},[895,36047,36048,36056,36058],{},[9172,36049,36050,36052,36054],{},[898,36051,3946],{},[2138,36053,2287],{},[2005,36055,4360],{},[2005,36057,2007],{},[2138,36059,2140],{},[902,36061,30304],{"encoding":904},[883,36063,36065],{"className":36064},[886],[888,36066,36067],{"xmlns":890},[892,36068,36069,36083],{},[895,36070,36071,36079,36081],{},[9172,36072,36073,36075,36077],{},[898,36074,3946],{},[2138,36076,2140],{},[2005,36078,4360],{},[2005,36080,2007],{},[2138,36082,2360],{},[902,36084,36085],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,36088,36090],{"className":36089},[886],[888,36091,36092],{"xmlns":890},[892,36093,36094,36110],{},[895,36095,36096,36102,36104],{},[2281,36097,36098,36100],{},[898,36099,2797],{},[2138,36101,2287],{},[2005,36103,2295],{"separator":2294},[2281,36105,36106,36108],{},[898,36107,2797],{},[2138,36109,2140],{},[902,36111,35627],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,36114,36116],{"className":36115},[886],[888,36117,36118],{"xmlns":890},[892,36119,36120,36140],{},[895,36121,36122,36124,36126,36132,36134],{},[898,36123,900],{},[2005,36125,2007],{},[2281,36127,36128,36130],{},[898,36129,2797],{},[2138,36131,2287],{},[2005,36133,3185],{},[2281,36135,36136,36138],{},[898,36137,2797],{},[2138,36139,2140],{},[902,36141,36142],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,36144,36145,36148,36149,36190,36191,36213,36214,1644],{},[38,36146,36147],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,36150,36152],{"className":36151},[886],[888,36153,36154],{"xmlns":890},[892,36155,36156,36188],{},[895,36157,36158,36160,36162,36168,36174,36176,36182],{},[898,36159,1868],{},[2005,36161,2007],{},[2281,36163,36164,36166],{},[898,36165,3946],{},[2138,36167,2287],{},[2281,36169,36170,36172],{},[898,36171,2797],{},[2138,36173,2287],{},[2005,36175,2104],{},[2281,36177,36178,36180],{},[898,36179,3946],{},[2138,36181,2140],{},[2281,36183,36184,36186],{},[898,36185,2797],{},[2138,36187,2140],{},[902,36189,27948],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,36192,36194],{"className":36193},[886],[888,36195,36196],{"xmlns":890},[892,36197,36198,36210],{},[895,36199,36200,36206,36208],{},[2133,36201,36202,36204],{},[898,36203,900],{},[2005,36205,4360],{},[2005,36207,2007],{},[2138,36209,5010],{},[902,36211,36212],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,36215,36217],{"className":36216},[886],[888,36218,36219],{"xmlns":890},[892,36220,36221,36250],{},[895,36222,36223,36231,36233,36235,36237,36245,36247],{},[9172,36224,36225,36227,36229],{},[898,36226,3946],{},[2138,36228,2287],{},[2005,36230,4360],{},[2005,36232,2007],{},[2138,36234,9041],{},[2005,36236,2295],{"separator":2294},[9172,36238,36239,36241,36243],{},[898,36240,3946],{},[2138,36242,2140],{},[2005,36244,4360],{},[2005,36246,2007],{},[2138,36248,36249],{},"15",[902,36251,36252],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,36254,15726],{"id":15725},[120,36256,36257,36314,36353,36373,36408,36462,36467,36473,36569,36614],{},[123,36258,36259,2212,36262,36311,36312,1644],{},[38,36260,36261],{},"Rozpočtové omezení (budget constraint)",[883,36263,36265],{"className":36264},[886],[888,36266,36267],{"xmlns":890},[892,36268,36269,36309],{},[895,36270,36271,36277,36279,36287,36293,36295,36303],{},[2133,36272,36273,36275],{},[898,36274,9134],{},[2005,36276,4360],{},[2005,36278,2007],{},[9172,36280,36281,36283,36285],{},[898,36282,3946],{},[2138,36284,2287],{},[2005,36286,4360],{},[2281,36288,36289,36291],{},[898,36290,2797],{},[2138,36292,2287],{},[2005,36294,2104],{},[9172,36296,36297,36299,36301],{},[898,36298,3946],{},[2138,36300,2140],{},[2005,36302,4360],{},[2281,36304,36305,36307],{},[898,36306,2797],{},[2138,36308,2140],{},[902,36310,17305],{"encoding":904}," — (6.12); ",[38,36313,28141],{},[123,36315,36316,36319,36320,1644],{},[38,36317,36318],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,36321,36323],{"className":36322},[886],[888,36324,36325],{"xmlns":890},[892,36326,36327,36351],{},[895,36328,36329,36331,36333,36341,36343],{},[2297,36330,10607],{},[2005,36332,2007],{},[9172,36334,36335,36337,36339],{},[898,36336,3946],{},[2138,36338,2287],{},[2005,36340,4360],{},[898,36342,4680],{"mathvariant":2385},[9172,36344,36345,36347,36349],{},[898,36346,3946],{},[2138,36348,2140],{},[2005,36350,4360],{},[902,36352,28984],{"encoding":904},[123,36354,36355,36370,36371,1644],{},[38,36356,29128,36357],{},[883,36358,36360],{"className":36359},[886],[888,36361,36362],{"xmlns":890},[892,36363,36364,36368],{},[895,36365,36366],{},[898,36367,16450],{},[902,36369,16503],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,36372,29150],{},[123,36374,36375,36378,36379,1644],{},[38,36376,36377],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,36380,36382],{"className":36381},[886],[888,36383,36384],{"xmlns":890},[892,36385,36386,36406],{},[895,36387,36388,36390,36392,36398,36400],{},[2297,36389,10607],{},[2005,36391,2007],{},[2281,36393,36394,36396],{},[898,36395,3946],{},[2138,36397,2287],{},[898,36399,4680],{"mathvariant":2385},[2281,36401,36402,36404],{},[898,36403,3946],{},[2138,36405,2140],{},[902,36407,28003],{"encoding":904},[123,36409,36410,7021,36413,36461],{},[38,36411,36412],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,36414,36416],{"className":36415},[886],[888,36417,36418],{"xmlns":890},[892,36419,36420,36458],{},[895,36421,36422,36428,36430,36436,36438,36444,36446,36452,36454,36456],{},[2281,36423,36424,36426],{},[898,36425,2797],{},[898,36427,17797],{},[2005,36429,2007],{},[2281,36431,36432,36434],{},[898,36433,1860],{},[898,36435,17797],{},[2005,36437,2014],{"stretchy":2013},[2281,36439,36440,36442],{},[898,36441,3946],{},[2138,36443,2287],{},[2005,36445,2295],{"separator":2294},[2281,36447,36448,36450],{},[898,36449,3946],{},[2138,36451,2140],{},[2005,36453,2295],{"separator":2294},[898,36455,9134],{},[2005,36457,2020],{"stretchy":2013},[902,36459,36460],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,36463,36464,36466],{},[38,36465,31732],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,36468,36469,36472],{},[38,36470,36471],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,36474,36475,7021,36477,36524,36525,36568],{},[38,36476,34044],{},[883,36478,36480],{"className":36479},[886],[888,36481,36482],{"xmlns":890},[892,36483,36484,36522],{},[895,36485,36486,36492,36494,36500,36502,36508,36510,36516,36518,36520],{},[2281,36487,36488,36490],{},[898,36489,2797],{},[898,36491,17797],{},[2005,36493,2007],{},[2281,36495,36496,36498],{},[898,36497,1860],{},[898,36499,17797],{},[2005,36501,2014],{"stretchy":2013},[2281,36503,36504,36506],{},[898,36505,3946],{},[2138,36507,2287],{},[2005,36509,2295],{"separator":2294},[2281,36511,36512,36514],{},[898,36513,3946],{},[2138,36515,2140],{},[2005,36517,2295],{"separator":2294},[898,36519,900],{},[2005,36521,2020],{"stretchy":2013},[902,36523,17830],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,36526,36528],{"className":36527},[886],[888,36529,36530],{"xmlns":890},[892,36531,36532,36566],{},[895,36533,36534,36536,36538,36552],{},[898,36535,900],{},[2005,36537,2007],{},[9172,36539,36540,36542,36544],{},[898,36541,2797],{},[2138,36543,2287],{},[895,36545,36546,36548,36550],{},[2138,36547,2287],{},[898,36549,4680],{"mathvariant":2385},[2138,36551,2140],{},[9172,36553,36554,36556,36558],{},[898,36555,2797],{},[2138,36557,2140],{},[895,36559,36560,36562,36564],{},[2138,36561,2287],{},[898,36563,4680],{"mathvariant":2385},[2138,36565,2140],{},[902,36567,33164],{"encoding":904},": (6.30).",[123,36570,36571,36613],{},[38,36572,36573,36574],{},"Bod dotyku ",[883,36575,36577],{"className":36576},[886],[888,36578,36579],{"xmlns":890},[892,36580,36581,36611],{},[895,36582,36583,36589,36591,36599,36601,36609],{},[2133,36584,36585,36587],{},[898,36586,2797],{},[2005,36588,4360],{},[2005,36590,2495],{"stretchy":2013},[9172,36592,36593,36595,36597],{},[898,36594,2797],{},[2138,36596,2287],{},[2005,36598,4360],{},[2005,36600,2295],{"separator":2294},[9172,36602,36603,36605,36607],{},[898,36604,2797],{},[2138,36606,2140],{},[2005,36608,4360],{},[2005,36610,2510],{"stretchy":2013},[902,36612,28332],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,36615,36616,36619,36620,36633,36634,36647],{},[38,36617,36618],{},"Dualita"," — ekvivalence max ",[883,36621,36623],{"className":36622},[886],[888,36624,36625],{"xmlns":890},[892,36626,36627,36631],{},[895,36628,36629],{},[898,36630,900],{},[902,36632,900],{"encoding":904}," a min ",[883,36635,36637],{"className":36636},[886],[888,36638,36639],{"xmlns":890},[892,36640,36641,36645],{},[895,36642,36643],{},[898,36644,1868],{},[902,36646,1868],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,36649,3800],{"id":3799},[120,36651,36652,36675,36691,36704,36715],{},[123,36653,36654,2212,36657,36660,36661,36674],{},[38,36655,36656],{},"Teorie před optimalizací:",[207,36658,880],{"className":36659,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,36662,36664],{"className":36663},[886],[888,36665,36666],{"xmlns":890},[892,36667,36668,36672],{},[895,36669,36670],{},[898,36671,900],{},[902,36673,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,36676,36677,2212,36680,36683,36684,36687,36688,1644],{},[38,36678,36679],{},"Matematický aparát:",[207,36681,793],{"className":36682,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,36685,784],{"className":36686,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,36689,2366],{"className":36690,"dataFsResolvedFilePath":764,"href":765},[210],[123,36692,36693,2212,36696,36699,36700,36703],{},[38,36694,36695],{},"Paralely:",[207,36697,11092],{"className":36698,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,36701,11946],{"className":36702,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,36705,36706,2212,36709,1343,36712],{},[38,36707,36708],{},"Přednášky:",[207,36710,1094],{"className":36711,"dataFsResolvedFilePath":838,"href":839},[210],[207,36713,1101],{"className":36714,"dataFsResolvedFilePath":868,"href":869},[210],[123,36716,36717,2212,36719],{},[38,36718,16210],{},[207,36720,16214],{"className":36721,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":36723},[36724,36725,36726,36731,36732,36733,36735,36738,36741,36743,36744,36746,36747,36751,36752],{"id":12011,"depth":642,"text":12012},{"id":28011,"depth":642,"text":28012},{"id":28409,"depth":642,"text":28410,"children":36727},[36728,36729],{"id":28529,"depth":649,"text":28530},{"id":29110,"depth":649,"text":36730},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":29572,"depth":642,"text":29573},{"id":29883,"depth":642,"text":29884},{"id":30202,"depth":642,"text":36734},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":30975,"depth":642,"text":30976,"children":36736},[36737],{"id":31731,"depth":649,"text":31732},{"id":31911,"depth":642,"text":31912,"children":36739},[36740],{"id":32168,"depth":649,"text":32169},{"id":33119,"depth":642,"text":36742},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":34043,"depth":642,"text":34044},{"id":34246,"depth":642,"text":36745},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":35131,"depth":642,"text":35132},{"id":35518,"depth":642,"text":35519,"children":36748},[36749,36750],{"id":35522,"depth":649,"text":35523},{"id":35982,"depth":649,"text":35983},{"id":15725,"depth":642,"text":15726},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":27772,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,36759,1144,9779,36760,36761,36762],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":36765,"title":802,"body":36766,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":50819,"navigation":664,"path":50820,"seo":50821,"sources":50822,"stem":50823,"tags":50824,"type":3865,"updated":677,"__hash__":50830},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":36767,"toc":50775},[36768,36771,36797,36801,36808,36960,36974,36977,36979,37066,37070,37106,37179,37200,37325,37335,37348,37352,37357,37387,37449,37458,37462,37524,37531,37552,37670,37748,37752,37755,37814,37929,37934,37966,38028,38076,38131,38135,38156,38180,38228,38232,38244,38248,38358,38362,38378,38419,38430,38589,38599,38604,38608,38730,38740,38747,38751,38829,38840,38920,38926,38933,39072,39079,39082,39139,39143,39221,39267,39311,39317,39430,39434,39437,39632,39636,39873,39876,40030,40183,40185,40187,40267,40270,40375,40444,40453,40457,40460,40521,40530,40534,40567,40645,40684,40688,40737,40791,40795,40824,40853,40905,40912,40966,41044,41048,41091,41158,41202,41306,41325,41327,41331,41439,41443,41511,41560,41567,41652,41656,41728,41733,41781,41970,41974,41979,42155,42160,42219,42324,42328,42355,42359,42366,42530,42617,42622,42624,42627,42727,42877,42949,43023,43025,43029,43043,43047,43180,43235,43347,43424,43428,43485,43588,43647,43808,43812,43887,43959,44057,44115,44209,44262,44283,44337,44342,44420,44468,44555,44593,44681,44834,44870,44924,44927,44929,44931,44980,44987,44995,45082,45091,45178,45185,45187,45191,45416,45418,45422,45426,45495,45546,45749,45755,45766,45834,45840,46262,46266,46330,46354,46550,46556,46570,46638,46641,46681,46905,46973,47275,47684,47761,47927,47933,47936,48011,48464,48515,48921,49026,49689,49692,49769,49777,49851,49882,49884,49888,49932,49934,49936,49940,50170,50174,50265,50270,50364,50369,50542,50546,50664,50669,50718,50720,50722],[12,36769,802],{"id":36770},"poptávka-nabídka-a-tržní-rovnováha",[3876,36772,36773],{},[724,36774,36775,36777,36778,36781,36782,36785,36786,36789,36790,36792,36793,36796],{},[883,36776,4164],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,36779,36780],{},"poptávka",") a výrobce (",[38,36783,36784],{},"nabídka","), jejich interakci v ",[38,36787,36788],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,36791,17984],{},"). Uzavírá ji pojem ",[38,36794,36795],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,36798,36800],{"id":36799},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,36802,36803,36804,36807],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,36805,36806],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,36809,36810,36827,36869,36885],{},[123,36811,36812,36813,36826],{},"cena ",[883,36814,36816],{"className":36815},[886],[888,36817,36818],{"xmlns":890},[892,36819,36820,36824],{},[895,36821,36822],{},[898,36823,3946],{},[902,36825,3946],{"encoding":904}," zkoumaného zboží,",[123,36828,36829,36830,2295],{},"ceny alternativních zboží ",[883,36831,36833],{"className":36832},[886],[888,36834,36835],{"xmlns":890},[892,36836,36837,36866],{},[895,36838,36839,36845,36847,36853,36855,36857,36859],{},[2281,36840,36841,36843],{},[898,36842,3946],{},[2138,36844,2287],{},[2005,36846,2295],{"separator":2294},[2281,36848,36849,36851],{},[898,36850,3946],{},[2138,36852,2140],{},[2005,36854,2295],{"separator":2294},[2005,36856,9652],{},[2005,36858,2295],{"separator":2294},[2281,36860,36861,36863],{},[898,36862,3946],{},[898,36864,36865],{},"n",[902,36867,36868],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,36870,36871,36872,2295],{},"důchod ",[883,36873,36875],{"className":36874},[886],[888,36876,36877],{"xmlns":890},[892,36878,36879,36883],{},[895,36880,36881],{},[898,36882,9134],{},[902,36884,9134],{"encoding":904},[123,36886,36887,36888,36901,36902,36915,36916,36929,36930,36944,36945,36959],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,36889,36891],{"className":36890},[886],[888,36892,36893],{"xmlns":890},[892,36894,36895,36899],{},[895,36896,36897],{},[898,36898,9801],{},[902,36900,9801],{"encoding":904},", kapitál ",[883,36903,36905],{"className":36904},[886],[888,36906,36907],{"xmlns":890},[892,36908,36909,36913],{},[895,36910,36911],{},[898,36912,9806],{},[902,36914,9806],{"encoding":904},", půda ",[883,36917,36919],{"className":36918},[886],[888,36920,36921],{"xmlns":890},[892,36922,36923,36927],{},[895,36924,36925],{},[898,36926,1868],{},[902,36928,1868],{"encoding":904},"), technologie, počet výrobců ",[883,36931,36933],{"className":36932},[886],[888,36934,36935],{"xmlns":890},[892,36936,36937,36942],{},[895,36938,36939],{},[898,36940,36941],{},"O",[902,36943,36941],{"encoding":904},", počasí ",[883,36946,36948],{"className":36947},[886],[888,36949,36950],{"xmlns":890},[892,36951,36952,36957],{},[895,36953,36954],{},[898,36955,36956],{},"W",[902,36958,36956],{"encoding":904}," atd.",[724,36961,36962,36963,36966,36967,36970,36971,1644],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,36964,36965],{},"ceteris paribus","), hovoříme o ",[38,36968,36969],{},"jednofaktorovém modelu","; jinak jde o model ",[38,36972,36973],{},"vícefaktorový",[36975,36976],"hr",{},[115,36978,13167],{"id":36780},[3876,36980,36981],{},[724,36982,36983,36985,36986,36999,37000,37013,37014,37017,37018,37041,37042,1644],{},[883,36984,4164],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,36987,36989],{"className":36988},[886],[888,36990,36991],{"xmlns":890},[892,36992,36993,36997],{},[895,36994,36995],{},[898,36996,2797],{},[902,36998,2797],{"encoding":904}," na ceně ",[883,37001,37003],{"className":37002},[886],[888,37004,37005],{"xmlns":890},[892,37006,37007,37011],{},[895,37008,37009],{},[898,37010,3946],{},[902,37012,3946],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,37015,37016],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,37019,37021],{"className":37020},[886],[888,37022,37023],{"xmlns":890},[892,37024,37025,37039],{},[895,37026,37027,37029,37031,37033,37035,37037],{},[898,37028,2797],{},[2005,37030,2007],{},[898,37032,1860],{},[2005,37034,2014],{"stretchy":2013},[898,37036,3946],{},[2005,37038,2020],{"stretchy":2013},[902,37040,4200],{"encoding":904}," a jeho lineární verzí ",[883,37043,37045],{"className":37044},[886],[888,37046,37047],{"xmlns":890},[892,37048,37049,37063],{},[895,37050,37051,37053,37055,37057,37059,37061],{},[898,37052,3946],{},[2005,37054,2007],{},[898,37056,207],{},[898,37058,2797],{},[2005,37060,2104],{},[898,37062,2107],{},[902,37064,37065],{"encoding":904},"P = aQ + b",[198,37067,37069],{"id":37068},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,37071,37072,37073,37086,37087,37100,37101,10030,37103,3159],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,37074,37076],{"className":37075},[886],[888,37077,37078],{"xmlns":890},[892,37079,37080,37084],{},[895,37081,37082],{},[898,37083,2797],{},[902,37085,2797],{"encoding":904}," závisí na ceně ",[883,37088,37090],{"className":37089},[886],[888,37091,37092],{"xmlns":890},[892,37093,37094,37098],{},[895,37095,37096],{},[898,37097,3946],{},[902,37099,3946],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,37102,28007],{},[614,37104,37105],{},"demand function",[883,37107,37109],{"className":37108},[886],[888,37110,37111],{"xmlns":890,"display":28071},[892,37112,37113,37176],{},[20760,37114,37115],{"width":28076},[20765,37116,37117,37119,37169,37171],{},[20768,37118],{"width":28081},[20768,37120,37121],{},[895,37122,37123,37125,37127,37129,37131,37133,37135,37141,37143,37149,37151,37153,37155,37161,37163,37165,37167],{},[898,37124,2797],{},[2005,37126,2007],{},[898,37128,1860],{},[2005,37130,2014],{"stretchy":2013},[898,37132,3946],{},[2005,37134,2295],{"separator":2294},[2281,37136,37137,37139],{},[898,37138,3946],{},[2138,37140,2287],{},[2005,37142,2295],{"separator":2294},[2281,37144,37145,37147],{},[898,37146,3946],{},[2138,37148,2140],{},[2005,37150,2295],{"separator":2294},[2005,37152,9652],{},[2005,37154,2295],{"separator":2294},[2281,37156,37157,37159],{},[898,37158,3946],{},[898,37160,36865],{},[2005,37162,2295],{"separator":2294},[898,37164,9134],{},[2005,37166,2020],{"stretchy":2013},[898,37168,1644],{"mathvariant":2385},[20768,37170],{"width":28081},[20768,37172,37173],{},[2297,37174,37175],{},"(2.1)",[902,37177,37178],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,37180,37181,37182,37185,37186,37199],{},"Důležitou vlastností je ",[38,37183,37184],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,37187,37189],{"className":37188},[886],[888,37190,37191],{"xmlns":890},[892,37192,37193,37197],{},[895,37194,37195],{},[898,37196,12047],{},[902,37198,12047],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,37201,37203],{"className":37202},[886],[888,37204,37205],{"xmlns":890,"display":28071},[892,37206,37207,37322],{},[20760,37208,37209],{"width":28076},[20765,37210,37211,37213,37315,37317],{},[20768,37212],{"width":28081},[20768,37214,37215],{},[895,37216,37217,37219,37221,37223,37225,37227,37229,37231,37233,37239,37241,37243,37249,37251,37253,37255,37257,37263,37265,37267,37269,37271,37273,37275,37277,37279,37281,37287,37289,37295,37297,37299,37301,37307,37309,37311,37313],{},[898,37218,2797],{},[2005,37220,2007],{},[898,37222,1860],{},[2005,37224,2014],{"stretchy":2013},[898,37226,12047],{},[898,37228,3946],{},[2005,37230,2295],{"separator":2294},[898,37232,12047],{},[2281,37234,37235,37237],{},[898,37236,3946],{},[2138,37238,2287],{},[2005,37240,2295],{"separator":2294},[898,37242,12047],{},[2281,37244,37245,37247],{},[898,37246,3946],{},[2138,37248,2140],{},[2005,37250,2295],{"separator":2294},[2005,37252,9652],{},[2005,37254,2295],{"separator":2294},[898,37256,12047],{},[2281,37258,37259,37261],{},[898,37260,3946],{},[898,37262,36865],{},[2005,37264,2295],{"separator":2294},[898,37266,12047],{},[898,37268,9134],{},[2005,37270,2020],{"stretchy":2013},[2005,37272,2007],{},[898,37274,1860],{},[2005,37276,2014],{"stretchy":2013},[898,37278,3946],{},[2005,37280,2295],{"separator":2294},[2281,37282,37283,37285],{},[898,37284,3946],{},[2138,37286,2287],{},[2005,37288,2295],{"separator":2294},[2281,37290,37291,37293],{},[898,37292,3946],{},[2138,37294,2140],{},[2005,37296,2295],{"separator":2294},[2005,37298,9652],{},[2005,37300,2295],{"separator":2294},[2281,37302,37303,37305],{},[898,37304,3946],{},[898,37306,36865],{},[2005,37308,2295],{"separator":2294},[898,37310,9134],{},[2005,37312,2020],{"stretchy":2013},[898,37314,1644],{"mathvariant":2385},[20768,37316],{"width":28081},[20768,37318,37319],{},[2297,37320,37321],{},"(2.2)",[902,37323,37324],{"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}",[3876,37326,37327],{},[724,37328,37329,37331,37332,1644],{},[883,37330,4418],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,37333,37334],{},"v jednofaktorových modelech neplatí",[724,37336,37337,37338,1343,37341,3894,37344,37347],{},"Rozlišuje se poptávka ",[38,37339,37340],{},"individuální",[38,37342,37343],{},"tržní",[38,37345,37346],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,37349,37351],{"id":37350},"jednofaktorové-modely","Jednofaktorové modely",[37353,37354,37356],"h4",{"id":37355},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,37358,37359,37360,37373,37374,2713],{},"Poptávané množství ",[883,37361,37363],{"className":37362},[886],[888,37364,37365],{"xmlns":890},[892,37366,37367,37371],{},[895,37368,37369],{},[898,37370,2797],{},[902,37372,2797],{"encoding":904}," závisí pouze na ceně ",[883,37375,37377],{"className":37376},[886],[888,37378,37379],{"xmlns":890},[892,37380,37381,37385],{},[895,37382,37383],{},[898,37384,3946],{},[902,37386,3946],{"encoding":904},[883,37388,37390],{"className":37389},[886],[888,37391,37392],{"xmlns":890,"display":28071},[892,37393,37394,37446],{},[20760,37395,37396],{"width":28076},[20765,37397,37398,37400,37439,37441],{},[20768,37399],{"width":28081},[20768,37401,37402],{},[895,37403,37404,37406,37408,37410,37412,37414,37416,37418,37420,37423,37425,37427,37429,37431,37433,37435,37437],{},[898,37405,2797],{},[2005,37407,2007],{},[898,37409,1860],{},[2005,37411,2014],{"stretchy":2013},[898,37413,3946],{},[2005,37415,2020],{"stretchy":2013},[2005,37417,2295],{"separator":2294},[5884,37419],{"width":5886},[2297,37421,37422],{},"resp.",[5884,37424],{"width":5886},[898,37426,3946],{},[2005,37428,2007],{},[898,37430,1860],{},[2005,37432,2014],{"stretchy":2013},[898,37434,2797],{},[2005,37436,2020],{"stretchy":2013},[898,37438,1644],{"mathvariant":2385},[20768,37440],{"width":28081},[20768,37442,37443],{},[2297,37444,37445],{},"(2.3)",[902,37447,37448],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,37450,37451,37452,10030,37455,3927],{},"Graf této funkce se nazývá ",[38,37453,37454],{},"křivka poptávky",[614,37456,37457],{},"demand curve",[37353,37459,37461],{"id":37460},"zákon-klesající-poptávky","Zákon klesající poptávky",[3876,37463,37464],{},[724,37465,37466],{},[38,37467,37468,37469,37482,37483,37496,37497,37482,37510,37523],{},"Roste-li cena ",[883,37470,37472],{"className":37471},[886],[888,37473,37474],{"xmlns":890},[892,37475,37476,37480],{},[895,37477,37478],{},[898,37479,3946],{},[902,37481,3946],{"encoding":904},", pak množství ",[883,37484,37486],{"className":37485},[886],[888,37487,37488],{"xmlns":890},[892,37489,37490,37494],{},[895,37491,37492],{},[898,37493,2797],{},[902,37495,2797],{"encoding":904}," klesá; klesá-li cena ",[883,37498,37500],{"className":37499},[886],[888,37501,37502],{"xmlns":890},[892,37503,37504,37508],{},[895,37505,37506],{},[898,37507,3946],{},[902,37509,3946],{"encoding":904},[883,37511,37513],{"className":37512},[886],[888,37514,37515],{"xmlns":890},[892,37516,37517,37521],{},[895,37518,37519],{},[898,37520,2797],{},[902,37522,2797],{"encoding":904}," roste.",[724,37525,37526,37527,37530],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,37528,37529],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[3876,37532,37533,37538],{},[724,37534,37535,37537],{},[883,37536,4164],{}," Intuice — proč zákon platí",[120,37539,37540,37546],{},[123,37541,37542,37545],{},[38,37543,37544],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,37547,37548,37551],{},[38,37549,37550],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,37553,37554,37555,37568,37569,37582,37583,37609,37610,37636,37637,8108,37663,37666,37667,1644],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,37556,37558],{"className":37557},[886],[888,37559,37560],{"xmlns":890},[892,37561,37562,37566],{},[895,37563,37564],{},[898,37565,3946],{},[902,37567,3946],{"encoding":904}," se vynáší na svislou osu, množství ",[883,37570,37572],{"className":37571},[886],[888,37573,37574],{"xmlns":890},[892,37575,37576,37580],{},[895,37577,37578],{},[898,37579,2797],{},[902,37581,2797],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,37584,37586],{"className":37585},[886],[888,37587,37588],{"xmlns":890},[892,37589,37590,37606],{},[895,37591,37592,37594,37596,37598,37604],{},[2005,37593,2495],{"stretchy":2013},[2138,37595,2336],{},[2005,37597,2295],{"separator":2294},[2281,37599,37600,37602],{},[898,37601,3946],{},[2138,37603,2336],{},[2005,37605,2510],{"stretchy":2013},[902,37607,37608],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,37611,37613],{"className":37612},[886],[888,37614,37615],{"xmlns":890},[892,37616,37617,37633],{},[895,37618,37619,37621,37627,37629,37631],{},[2005,37620,2495],{"stretchy":2013},[2281,37622,37623,37625],{},[898,37624,2797],{},[2138,37626,2336],{},[2005,37628,2295],{"separator":2294},[2138,37630,2336],{},[2005,37632,2510],{"stretchy":2013},[902,37634,37635],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,37638,37640],{"className":37639},[886],[888,37641,37642],{"xmlns":890},[892,37643,37644,37660],{},[895,37645,37646,37648,37650,37652,37658],{},[2005,37647,2014],{"stretchy":2013},[2138,37649,2336],{},[2005,37651,2295],{"separator":2294},[2281,37653,37654,37656],{},[898,37655,3946],{},[2138,37657,2336],{},[2005,37659,2020],{"stretchy":2013},[902,37661,37662],{"encoding":904},"(0, P_0)",[38,37664,37665],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,37668,37669],{},"konvexní",[724,37671,37672],{},[614,37673,37674,37675,37697,37698,3894,37723,1644],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,37676,37678],{"className":37677},[886],[888,37679,37680],{"xmlns":890},[892,37681,37682,37694],{},[895,37683,37684,37686,37688,37690,37692],{},[2005,37685,2014],{"stretchy":2013},[898,37687,2797],{},[2005,37689,2295],{"separator":2294},[898,37691,3946],{},[2005,37693,2020],{"stretchy":2013},[902,37695,37696],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,37699,37701],{"className":37700},[886],[888,37702,37703],{"xmlns":890},[892,37704,37705,37721],{},[895,37706,37707,37709,37711,37713,37719],{},[2005,37708,2495],{"stretchy":2013},[2138,37710,2336],{},[2005,37712,2295],{"separator":2294},[2281,37714,37715,37717],{},[898,37716,3946],{},[2138,37718,2336],{},[2005,37720,2510],{"stretchy":2013},[902,37722,37608],{"encoding":904},[883,37724,37726],{"className":37725},[886],[888,37727,37728],{"xmlns":890},[892,37729,37730,37746],{},[895,37731,37732,37734,37740,37742,37744],{},[2005,37733,2495],{"stretchy":2013},[2281,37735,37736,37738],{},[898,37737,2797],{},[2138,37739,2336],{},[2005,37741,2295],{"separator":2294},[2138,37743,2336],{},[2005,37745,2510],{"stretchy":2013},[902,37747,37635],{"encoding":904},[37353,37749,37751],{"id":37750},"lineární-model-poptávky","Lineární model poptávky",[724,37753,37754],{},"Nejjednodušší závislostí je",[883,37756,37758],{"className":37757},[886],[888,37759,37760],{"xmlns":890,"display":28071},[892,37761,37762,37811],{},[20760,37763,37764],{"width":28076},[20765,37765,37766,37768,37804,37806],{},[20768,37767],{"width":28081},[20768,37769,37770],{},[895,37771,37772,37774,37776,37778,37780,37782,37784,37786,37788,37790,37792,37794,37796,37798,37800,37802],{},[898,37773,3946],{},[2005,37775,2007],{},[898,37777,207],{},[898,37779,2797],{},[2005,37781,2104],{},[898,37783,2107],{},[2005,37785,2295],{"separator":2294},[5884,37787],{"width":5886},[898,37789,207],{},[2005,37791,3455],{},[2138,37793,2336],{},[2005,37795,2295],{"separator":2294},[2297,37797,2299],{},[898,37799,2107],{},[2005,37801,3416],{},[2138,37803,12466],{},[20768,37805],{"width":28081},[20768,37807,37808],{},[2297,37809,37810],{},"(2.4)",[902,37812,37813],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,37815,37816,37817,21600,37853,3894,37877,8043,37903,37925,37926,1644],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,37818,37820],{"className":37819},[886],[888,37821,37822],{"xmlns":890},[892,37823,37824,37850],{},[895,37825,37826,37828,37830,37838,37840,37842],{},[898,37827,2797],{},[2005,37829,2007],{},[2334,37831,37832],{"scriptlevel":2336,"displaystyle":2013},[2338,37833,37834,37836],{},[2138,37835,2287],{},[898,37837,207],{},[898,37839,3946],{},[2005,37841,2234],{},[2334,37843,37844],{"scriptlevel":2336,"displaystyle":2013},[2338,37845,37846,37848],{},[898,37847,2107],{},[898,37849,207],{},[902,37851,37852],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,37854,37856],{"className":37855},[886],[888,37857,37858],{"xmlns":890},[892,37859,37860,37874],{},[895,37861,37862,37870,37872],{},[2334,37863,37864],{"scriptlevel":2336,"displaystyle":2013},[2338,37865,37866,37868],{},[2138,37867,2287],{},[898,37869,207],{},[2005,37871,3455],{},[2138,37873,2336],{},[902,37875,37876],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,37878,37880],{"className":37879},[886],[888,37881,37882],{"xmlns":890},[892,37883,37884,37900],{},[895,37885,37886,37888,37896,37898],{},[2005,37887,2234],{},[2334,37889,37890],{"scriptlevel":2336,"displaystyle":2013},[2338,37891,37892,37894],{},[898,37893,2107],{},[898,37895,207],{},[2005,37897,3416],{},[2138,37899,2336],{},[902,37901,37902],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,37904,37906],{"className":37905},[886],[888,37907,37908],{"xmlns":890},[892,37909,37910,37922],{},[895,37911,37912,37914,37916,37918,37920],{},[2005,37913,2014],{"stretchy":2013},[2138,37915,2336],{},[2005,37917,2295],{"separator":2294},[898,37919,2107],{},[2005,37921,2020],{"stretchy":2013},[902,37923,37924],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,37927,37928],{},"nedokonalé konkurenci",[37930,37931,37933],"h5",{"id":37932},"příklad-21","Příklad 2.1",[724,37935,37936,37939,37940,1644],{},[38,37937,37938],{},"Zadání:"," Lineární poptávka ",[883,37941,37943],{"className":37942},[886],[888,37944,37945],{"xmlns":890},[892,37946,37947,37963],{},[895,37948,37949,37951,37953,37955,37957,37959,37961],{},[898,37950,3946],{},[2005,37952,2007],{},[2005,37954,2234],{},[2138,37956,2140],{},[898,37958,2797],{},[2005,37960,2104],{},[2138,37962,3134],{},[902,37964,37965],{"encoding":904},"P = -2Q + 60",[724,37967,37968,37971,37972,37994,37995,1644],{},[38,37969,37970],{},"Řešení:"," Reálné cenové rozpětí je ",[883,37973,37975],{"className":37974},[886],[888,37976,37977],{"xmlns":890},[892,37978,37979,37991],{},[895,37980,37981,37983,37985,37987,37989],{},[2005,37982,2014],{"stretchy":2013},[2138,37984,2336],{},[2005,37986,2295],{"separator":2294},[2138,37988,3134],{},[2005,37990,2020],{"stretchy":2013},[902,37992,37993],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,37996,37998],{"className":37997},[886],[888,37999,38000],{"xmlns":890},[892,38001,38002,38025],{},[895,38003,38004,38006,38008,38010,38018,38020,38022],{},[898,38005,2797],{},[2005,38007,2007],{},[2005,38009,2234],{},[2334,38011,38012],{"scriptlevel":2336,"displaystyle":2013},[2338,38013,38014,38016],{},[2138,38015,2287],{},[2138,38017,2140],{},[898,38019,3946],{},[2005,38021,2104],{},[2138,38023,38024],{},"30",[902,38026,38027],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,38029,38030,38053],{},[19,38031,38032],{},[22,38033,38034,38049,38051],{},[25,38035,38036],{},[883,38037,38039],{"className":38038},[886],[888,38040,38041],{"xmlns":890},[892,38042,38043,38047],{},[895,38044,38045],{},[898,38046,3946],{},[902,38048,3946],{"encoding":904},[25,38050,5217],{},[25,38052,9041],{},[30,38054,38055],{},[22,38056,38057,38072,38074],{},[35,38058,38059],{},[883,38060,38062],{"className":38061},[886],[888,38063,38064],{"xmlns":890},[892,38065,38066,38070],{},[895,38067,38068],{},[898,38069,2797],{},[902,38071,2797],{"encoding":904},[35,38073,2871],{},[35,38075,9041],{},[724,38077,38078],{},[614,38079,38080,38081,3894,38103,1644],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,38082,38084],{"className":38083},[886],[888,38085,38086],{"xmlns":890},[892,38087,38088,38100],{},[895,38089,38090,38092,38094,38096,38098],{},[2005,38091,2495],{"stretchy":2013},[2138,38093,2336],{},[2005,38095,2295],{"separator":2294},[898,38097,2107],{},[2005,38099,2510],{"stretchy":2013},[902,38101,38102],{"encoding":904},"[0, b]",[883,38104,38106],{"className":38105},[886],[888,38107,38108],{"xmlns":890},[892,38109,38110,38128],{},[895,38111,38112,38114,38116,38118,38120,38122,38124,38126],{},[2005,38113,2495],{"stretchy":2013},[2005,38115,2234],{},[898,38117,2107],{},[898,38119,4680],{"mathvariant":2385},[898,38121,207],{},[2005,38123,2295],{"separator":2294},[2138,38125,2336],{},[2005,38127,2510],{"stretchy":2013},[902,38129,38130],{"encoding":904},"[-b\u002Fa, 0]",[37353,38132,38134],{"id":38133},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,38136,38137,38138,38155],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,38139,38141],{"className":38140},[886],[888,38142,38143],{"xmlns":890},[892,38144,38145,38153],{},[895,38146,38147],{},[2133,38148,38149,38151],{},[898,38150,3946],{},[2005,38152,4360],{},[902,38154,4410],{"encoding":904},", je funkce poptávky konstantní:",[883,38157,38159],{"className":38158},[886],[888,38160,38161],{"xmlns":890,"display":28071},[892,38162,38163,38177],{},[895,38164,38165,38167,38169,38175],{},[898,38166,3946],{},[2005,38168,2007],{},[2133,38170,38171,38173],{},[898,38172,3946],{},[2005,38174,4360],{},[898,38176,1644],{"mathvariant":2385},[902,38178,38179],{"encoding":904},"P = P^*.",[724,38181,38182],{},[614,38183,38184,38185,38206,38207,1644],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,38186,38188],{"className":38187},[886],[888,38189,38190],{"xmlns":890},[892,38191,38192,38204],{},[895,38193,38194,38196,38198,38200,38202],{},[2005,38195,2014],{"stretchy":2013},[898,38197,2797],{},[2005,38199,2295],{"separator":2294},[898,38201,3946],{},[2005,38203,2020],{"stretchy":2013},[902,38205,37696],{"encoding":904}," na úrovni ",[883,38208,38210],{"className":38209},[886],[888,38211,38212],{"xmlns":890},[892,38213,38214,38226],{},[895,38215,38216,38218,38220],{},[898,38217,3946],{},[2005,38219,2007],{},[2133,38221,38222,38224],{},[898,38223,3946],{},[2005,38225,4360],{},[902,38227,4363],{"encoding":904},[37353,38229,38231],{"id":38230},"giffenův-statek","Giffenův statek",[724,38233,38234,38235,38237,38238,38240,38241,1644],{},"Existují zboží, u nichž je křivka poptávky ",[38,38236,13663],{}," — tzv. ",[38,38239,38231],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,38242,38243],{},"podřadnému zboží",[37930,38245,38247],{"id":38246},"příklad-22","Příklad 2.2",[724,38249,38250,38253,38254,38272,38273,38295,38296,38314,38315,38333,38334,38357],{},[38,38251,38252],{},"Zadání a popis:"," Křivka ",[883,38255,38257],{"className":38256},[886],[888,38258,38259],{"xmlns":890},[892,38260,38261,38269],{},[895,38262,38263],{},[2281,38264,38265,38267],{},[898,38266,1860],{},[2138,38268,2287],{},[902,38270,38271],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,38274,38276],{"className":38275},[886],[888,38277,38278],{"xmlns":890},[892,38279,38280,38292],{},[895,38281,38282,38284,38286,38288,38290],{},[2005,38283,2014],{"stretchy":2013},[2138,38285,2336],{},[2005,38287,2295],{"separator":2294},[2138,38289,36249],{},[2005,38291,2020],{"stretchy":2013},[902,38293,38294],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,38297,38299],{"className":38298},[886],[888,38300,38301],{"xmlns":890},[892,38302,38303,38311],{},[895,38304,38305],{},[2281,38306,38307,38309],{},[898,38308,2797],{},[2138,38310,2336],{},[902,38312,38313],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,38316,38318],{"className":38317},[886],[888,38319,38320],{"xmlns":890},[892,38321,38322,38330],{},[895,38323,38324],{},[2281,38325,38326,38328],{},[898,38327,1860],{},[2138,38329,2140],{},[902,38331,38332],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,38335,38337],{"className":38336},[886],[888,38338,38339],{"xmlns":890},[892,38340,38341,38354],{},[895,38342,38343,38345,38347,38349,38352],{},[2005,38344,2495],{"stretchy":2013},[2138,38346,2336],{},[2005,38348,2295],{"separator":2294},[2138,38350,38351],{},"21",[2005,38353,2510],{"stretchy":2013},[902,38355,38356],{"encoding":904},"[0, 21]"," centů.",[198,38359,38361],{"id":38360},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,38363,38364,38365,2713],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,38366,38368],{"className":38367},[886],[888,38369,38370],{"xmlns":890},[892,38371,38372,38376],{},[895,38373,38374],{},[898,38375,9134],{},[902,38377,9134],{"encoding":904},[883,38379,38381],{"className":38380},[886],[888,38382,38383],{"xmlns":890,"display":28071},[892,38384,38385,38416],{},[20760,38386,38387],{"width":28076},[20765,38388,38389,38391,38409,38411],{},[20768,38390],{"width":28081},[20768,38392,38393],{},[895,38394,38395,38397,38399,38401,38403,38405,38407],{},[898,38396,2797],{},[2005,38398,2007],{},[898,38400,1868],{},[2005,38402,2014],{"stretchy":2013},[898,38404,9134],{},[2005,38406,2020],{"stretchy":2013},[898,38408,1644],{"mathvariant":2385},[20768,38410],{"width":28081},[20768,38412,38413],{},[2297,38414,38415],{},"(2.5)",[902,38417,38418],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,38420,38421,38422,38425,38426,38429],{},"Funkce se nazývá ",[38,38423,38424],{},"Engelova",", její graf ",[38,38427,38428],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,38431,38432,38564],{},[123,38433,38434,7021,38437,38450,38451,38464,38465,38482,38483],{},[38,38435,38436],{},"Normální (superior) zboží",[883,38438,38440],{"className":38439},[886],[888,38441,38442],{"xmlns":890},[892,38443,38444,38448],{},[895,38445,38446],{},[898,38447,2797],{},[902,38449,2797],{"encoding":904}," roste s ",[883,38452,38454],{"className":38453},[886],[888,38455,38456],{"xmlns":890},[892,38457,38458,38462],{},[895,38459,38460],{},[898,38461,9134],{},[902,38463,9134],{"encoding":904},", nepřesáhne hodnotu ",[883,38466,38468],{"className":38467},[886],[888,38469,38470],{"xmlns":890},[892,38471,38472,38480],{},[895,38473,38474],{},[2281,38475,38476,38478],{},[898,38477,2797],{},[2138,38479,2336],{},[902,38481,38313],{"encoding":904},":\n",[120,38484,38485,38517],{},[123,38486,38487,38490,38491,38494,38495,1644],{},[38,38488,38489],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,38492,38493],{},"konkávní"," křivka, autonomní spotřeba ",[883,38496,38498],{"className":38497},[886],[888,38499,38500],{"xmlns":890},[892,38501,38502,38514],{},[895,38503,38504,38510,38512],{},[2281,38505,38506,38508],{},[898,38507,2797],{},[2138,38509,2287],{},[2005,38511,3416],{},[2138,38513,2336],{},[902,38515,38516],{"encoding":904},"Q_1 > 0",[123,38518,38519,38522,38523,38541,38542,38544,38545,2212,38562,1644],{},[38,38520,38521],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,38524,38526],{"className":38525},[886],[888,38527,38528],{"xmlns":890},[892,38529,38530,38538],{},[895,38531,38532],{},[2281,38533,38534,38536],{},[898,38535,9134],{},[2138,38537,2287],{},[902,38539,38540],{"encoding":904},"Y_1",", křivka je nejprve ",[38,38543,37669],{}," a od ",[883,38546,38548],{"className":38547},[886],[888,38549,38550],{"xmlns":890},[892,38551,38552,38560],{},[895,38553,38554],{},[2281,38555,38556,38558],{},[898,38557,9134],{},[2138,38559,2287],{},[902,38561,38540],{"encoding":904},[38,38563,38493],{},[123,38565,38566,38569,38570,38588],{},[38,38567,38568],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,38571,38573],{"className":38572},[886],[888,38574,38575],{"xmlns":890},[892,38576,38577,38585],{},[895,38578,38579],{},[2281,38580,38581,38583],{},[898,38582,9134],{},[2138,38584,2336],{},[902,38586,38587],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,38590,38591,38592,38595,38596,3927],{},"Mírou citlivosti je ",[614,38593,38594],{},"důchodová elasticita"," (viz ",[207,38597,1753],{"className":38598,"dataFsResolvedFilePath":848,"href":849},[210],[724,38600,38601],{},[614,38602,38603],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[37353,38605,38607],{"id":38606},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[3876,38609,38610,38681,38724],{},[724,38611,38612,38614,38615,2212,38618,2212,38631,5675,38633,38646,38647,38650,38651,1644],{},[883,38613,4418],{}," Pozor — nezbytné ≠ podřadné\n",[38,38616,38617],{},"Nezbytné zboží:",[883,38619,38621],{"className":38620},[886],[888,38622,38623],{"xmlns":890},[892,38624,38625,38629],{},[895,38626,38627],{},[898,38628,2797],{},[902,38630,2797],{"encoding":904},[38,38632,7328],{},[883,38634,38636],{"className":38635},[886],[888,38637,38638],{"xmlns":890},[892,38639,38640,38644],{},[895,38641,38642],{},[898,38643,9134],{},[902,38645,9134],{"encoding":904},", ale ",[38,38648,38649],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,38652,38654],{"className":38653},[886],[888,38655,38656],{"xmlns":890},[892,38657,38658,38678],{},[895,38659,38660,38666,38668,38670,38672,38674,38676],{},[2281,38661,38662,38664],{},[898,38663,1868],{},[898,38665,9134],{},[2005,38667,6512],{},[2005,38669,2014],{"stretchy":2013},[2138,38671,2336],{},[2005,38673,2295],{"separator":2294},[2138,38675,2287],{},[2005,38677,2020],{"stretchy":2013},[902,38679,38680],{"encoding":904},"E_Y \\in (0, 1)",[724,38682,38683,2212,38686,2212,38699,38701,38702,1644],{},[38,38684,38685],{},"Podřadné zboží:",[883,38687,38689],{"className":38688},[886],[888,38690,38691],{"xmlns":890},[892,38692,38693,38697],{},[895,38694,38695],{},[898,38696,2797],{},[902,38698,2797],{"encoding":904},[38,38700,7348],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,38703,38705],{"className":38704},[886],[888,38706,38707],{"xmlns":890},[892,38708,38709,38721],{},[895,38710,38711,38717,38719],{},[2281,38712,38713,38715],{},[898,38714,1868],{},[898,38716,9134],{},[2005,38718,3455],{},[2138,38720,2336],{},[902,38722,38723],{"encoding":904},"E_Y \u003C 0",[724,38725,38726,38727,1644],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,38728,38729],{},"méně kusů, ne jen proporčně méně",[724,38731,38732,38735,38736,38739],{},[38,38733,38734],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,38737,38738],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,38741,38742],{},[2568,38743],{"alt":38744,"className":38745,"src":38746},"imek-engelovy-krivky-3typy",[210,2572],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[37930,38748,38750],{"id":38749},"české-příklady","České příklady",[16,38752,38753,38763],{},[19,38754,38755],{},[22,38756,38757,38760],{},[25,38758,38759],{},"Podřadné",[25,38761,38762],{},"Nahradí se za",[30,38764,38765,38773,38781,38789,38797,38805,38813,38821],{},[22,38766,38767,38770],{},[35,38768,38769],{},"Instantní polévky, ramen",[35,38771,38772],{},"Čerstvé jídlo, restaurace",[22,38774,38775,38778],{},[35,38776,38777],{},"MHD (autobus, tramvaj)",[35,38779,38780],{},"Vlastní auto, Uber, taxi",[22,38782,38783,38786],{},[35,38784,38785],{},"Mražené polotovary, pizza z mrazáku",[35,38787,38788],{},"Čerstvé suroviny, hotovky",[22,38790,38791,38794],{},[35,38792,38793],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,38795,38796],{},"Značkové produkty",[22,38798,38799,38802],{},[35,38800,38801],{},"Paštika Májka, obyčejný měkký salám",[35,38803,38804],{},"Kvalitní uzeniny, šunka od kosti",[22,38806,38807,38810],{},[35,38808,38809],{},"Second hand oblečení",[35,38811,38812],{},"Nové oblečení, značky",[22,38814,38815,38818],{},[35,38816,38817],{},"Krabicové víno, nejlevnější pivo",[35,38819,38820],{},"Lahvové víno, řemeslná piva",[22,38822,38823,38826],{},[35,38824,38825],{},"Ojetá auta nižších tříd",[35,38827,38828],{},"Nová auta, prémiové značky",[3876,38830,38831],{},[724,38832,38833,38835,38836,38839],{},[883,38834,4578],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,38837,38838],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,38841,38842,38845,38846,10030,38849,38871,38872,10030,38875,38896,38897,38915,38916,38919],{},[38,38843,38844],{},"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 ",[38,38847,38848],{},"luxus",[883,38850,38852],{"className":38851},[886],[888,38853,38854],{"xmlns":890},[892,38855,38856,38868],{},[895,38857,38858,38864,38866],{},[2281,38859,38860,38862],{},[898,38861,1868],{},[898,38863,9134],{},[2005,38865,3416],{},[2138,38867,2287],{},[902,38869,38870],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,38873,38874],{},"podřadné",[883,38876,38878],{"className":38877},[886],[888,38879,38880],{"xmlns":890},[892,38881,38882,38894],{},[895,38883,38884,38890,38892],{},[2281,38885,38886,38888],{},[898,38887,1868],{},[898,38889,9134],{},[2005,38891,3455],{},[2138,38893,2336],{},[902,38895,38723],{"encoding":904},"). Proto je ",[883,38898,38900],{"className":38899},[886],[888,38901,38902],{"xmlns":890},[892,38903,38904,38912],{},[895,38905,38906],{},[2281,38907,38908,38910],{},[898,38909,1868],{},[898,38911,9134],{},[902,38913,38914],{"encoding":904},"E_Y"," vždy ",[38,38917,38918],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,38921,38922,38923,38925],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,38924,38231],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,38927,38929,38930,2020],{"id":38928},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,38931,38932],{},"shift of demand",[724,38934,38935,38936,38954,38955,38972,38973,38986,38987,2694,39000,39022,39023,39040,39041,39067,39068,39071],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,38937,38939],{"className":38938},[886],[888,38940,38941],{"xmlns":890},[892,38942,38943,38951],{},[895,38944,38945],{},[2281,38946,38947,38949],{},[898,38948,3946],{},[2138,38950,2336],{},[902,38952,38953],{"encoding":904},"P_0"," odpovídá množství ",[883,38956,38958],{"className":38957},[886],[888,38959,38960],{"xmlns":890},[892,38961,38962,38970],{},[895,38963,38964],{},[2281,38965,38966,38968],{},[898,38967,2797],{},[2138,38969,2336],{},[902,38971,38313],{"encoding":904}," na křivce ",[883,38974,38976],{"className":38975},[886],[888,38977,38978],{"xmlns":890},[892,38979,38980,38984],{},[895,38981,38982],{},[898,38983,1860],{},[902,38985,1860],{"encoding":904},"; vzroste-li důchod z ",[883,38988,38990],{"className":38989},[886],[888,38991,38992],{"xmlns":890},[892,38993,38994,38998],{},[895,38995,38996],{},[898,38997,9134],{},[902,38999,9134],{"encoding":904},[883,39001,39003],{"className":39002},[886],[888,39004,39005],{"xmlns":890},[892,39006,39007,39019],{},[895,39008,39009,39015,39017],{},[2281,39010,39011,39013],{},[898,39012,9134],{},[2138,39014,2287],{},[2005,39016,3416],{},[898,39018,9134],{},[902,39020,39021],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,39024,39026],{"className":39025},[886],[888,39027,39028],{"xmlns":890},[892,39029,39030,39038],{},[895,39031,39032],{},[2281,39033,39034,39036],{},[898,39035,3946],{},[2138,39037,2336],{},[902,39039,38953],{"encoding":904}," odpovídá vyšší ",[883,39042,39044],{"className":39043},[886],[888,39045,39046],{"xmlns":890},[892,39047,39048,39064],{},[895,39049,39050,39056,39058],{},[2281,39051,39052,39054],{},[898,39053,2797],{},[2138,39055,2287],{},[2005,39057,3416],{},[2281,39059,39060,39062],{},[898,39061,2797],{},[2138,39063,2336],{},[902,39065,39066],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,39069,39070],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,39073,39074],{},[2568,39075],{"alt":39076,"className":39077,"src":39078},"imek-posun-vs-pohyb-po-krivce",[210,2572],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,39080,39081],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,39083,39084],{},[614,39085,39086,39087,14017,39117,39138],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,39088,39090],{"className":39089},[886],[888,39091,39092],{"xmlns":890},[892,39093,39094,39114],{},[895,39095,39096,39102,39104,39106,39108],{},[2281,39097,39098,39100],{},[898,39099,1860],{},[2138,39101,2140],{},[2005,39103,2295],{"separator":2294},[898,39105,1860],{},[2005,39107,2295],{"separator":2294},[2281,39109,39110,39112],{},[898,39111,1860],{},[2138,39113,2287],{},[902,39115,39116],{"encoding":904},"D_2, D, D_1",[883,39118,39120],{"className":39119},[886],[888,39121,39122],{"xmlns":890},[892,39123,39124,39136],{},[895,39125,39126,39128,39130,39132,39134],{},[2005,39127,2014],{"stretchy":2013},[898,39129,2797],{},[2005,39131,2295],{"separator":2294},[898,39133,3946],{},[2005,39135,2020],{"stretchy":2013},[902,39137,37696],{"encoding":904},", šipky naznačují posuny.",[37930,39140,39142],{"id":39141},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,39144,39145,39147,39148,39171,39172,39189,39190,39207,39208,1644],{},[38,39146,37938],{}," Poptávce ",[883,39149,39151],{"className":39150},[886],[888,39152,39153],{"xmlns":890},[892,39154,39155,39169],{},[895,39156,39157,39159,39161,39163,39165,39167],{},[898,39158,3946],{},[2005,39160,2007],{},[898,39162,1860],{},[2005,39164,2014],{"stretchy":2013},[898,39166,2797],{},[2005,39168,2020],{"stretchy":2013},[902,39170,4646],{"encoding":904}," odpovídá ceně ",[883,39173,39175],{"className":39174},[886],[888,39176,39177],{"xmlns":890},[892,39178,39179,39187],{},[895,39180,39181],{},[2281,39182,39183,39185],{},[898,39184,3946],{},[2138,39186,2336],{},[902,39188,38953],{"encoding":904}," množství ",[883,39191,39193],{"className":39192},[886],[888,39194,39195],{"xmlns":890},[892,39196,39197,39205],{},[895,39198,39199],{},[2281,39200,39201,39203],{},[898,39202,2797],{},[2138,39204,2336],{},[902,39206,38313],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,39209,39211],{"className":39210},[886],[888,39212,39213],{"xmlns":890},[892,39214,39215,39219],{},[895,39216,39217],{},[898,39218,2783],{},[902,39220,2783],{"encoding":904},[724,39222,39223,39225,39226,39243,39244,39266],{},[38,39224,37970],{}," Kupující nakupuje množství ",[883,39227,39229],{"className":39228},[886],[888,39230,39231],{"xmlns":890},[892,39232,39233,39241],{},[895,39234,39235],{},[2281,39236,39237,39239],{},[898,39238,2797],{},[2138,39240,2287],{},[902,39242,29007],{"encoding":904},", které odpovídá ceně ",[883,39245,39247],{"className":39246},[886],[888,39248,39249],{"xmlns":890},[892,39250,39251,39263],{},[895,39252,39253,39259,39261],{},[2281,39254,39255,39257],{},[898,39256,3946],{},[2138,39258,2336],{},[2005,39260,2104],{},[898,39262,2783],{},[902,39264,39265],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,39268,39270],{"className":39269},[886],[888,39271,39272],{"xmlns":890,"display":28071},[892,39273,39274,39308],{},[895,39275,39276,39278,39280,39286,39288,39290,39292,39294,39296,39298,39300,39302,39304,39306],{},[898,39277,3946],{},[2005,39279,2007],{},[2281,39281,39282,39284],{},[898,39283,1860],{},[2138,39285,2287],{},[2005,39287,2014],{"stretchy":2013},[898,39289,2797],{},[2005,39291,2020],{"stretchy":2013},[2005,39293,2007],{},[898,39295,1860],{},[2005,39297,2014],{"stretchy":2013},[898,39299,2797],{},[2005,39301,2020],{"stretchy":2013},[2005,39303,2234],{},[898,39305,2783],{},[2005,39307,2295],{"separator":2294},[902,39309,39310],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,39312,39313,39314,1644],{},"tj. dojde k ",[38,39315,39316],{},"posunu poptávky doleva",[724,39318,39319],{},[614,39320,39321,39322,39343,39344,1343,39361,1343,39374,39395,39396,3894,39413,1644],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,39323,39325],{"className":39324},[886],[888,39326,39327],{"xmlns":890},[892,39328,39329,39341],{},[895,39330,39331,39333,39335,39337,39339],{},[2005,39332,2014],{"stretchy":2013},[898,39334,2797],{},[2005,39336,2295],{"separator":2294},[898,39338,3946],{},[2005,39340,2020],{"stretchy":2013},[902,39342,37696],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,39345,39347],{"className":39346},[886],[888,39348,39349],{"xmlns":890},[892,39350,39351,39359],{},[895,39352,39353],{},[2281,39354,39355,39357],{},[898,39356,3946],{},[2138,39358,2336],{},[902,39360,38953],{"encoding":904},[883,39362,39364],{"className":39363},[886],[888,39365,39366],{"xmlns":890},[892,39367,39368,39372],{},[895,39369,39370],{},[898,39371,2783],{},[902,39373,2783],{"encoding":904},[883,39375,39377],{"className":39376},[886],[888,39378,39379],{"xmlns":890},[892,39380,39381,39393],{},[895,39382,39383,39389,39391],{},[2281,39384,39385,39387],{},[898,39386,3946],{},[2138,39388,2336],{},[2005,39390,2104],{},[898,39392,2783],{},[902,39394,39265],{"encoding":904},"; na vodorovné ",[883,39397,39399],{"className":39398},[886],[888,39400,39401],{"xmlns":890},[892,39402,39403,39411],{},[895,39404,39405],{},[2281,39406,39407,39409],{},[898,39408,2797],{},[2138,39410,2287],{},[902,39412,29007],{"encoding":904},[883,39414,39416],{"className":39415},[886],[888,39417,39418],{"xmlns":890},[892,39419,39420,39428],{},[895,39421,39422],{},[2281,39423,39424,39426],{},[898,39425,2797],{},[2138,39427,2336],{},[902,39429,38313],{"encoding":904},[198,39431,39433],{"id":39432},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,39435,39436],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,39438,39440],{"className":39439},[886],[888,39441,39442],{"xmlns":890,"display":28071},[892,39443,39444,39629],{},[20760,39445,39446],{"width":28076},[20765,39447,39448,39450,39622,39624],{},[20768,39449],{"width":28081},[20768,39451,39452],{},[20760,39453,39454,39538],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,39455,39456,39466],{},[20768,39457,39458],{},[2334,39459,39460],{"scriptlevel":2336,"displaystyle":2294},[2281,39461,39462,39464],{},[898,39463,2797],{},[2138,39465,2287],{},[20768,39467,39468],{},[2334,39469,39470],{"scriptlevel":2336,"displaystyle":2294},[895,39471,39472,39474,39476,39482,39484,39490,39492,39498,39500,39502,39508,39510,39516,39522,39524,39530,39536],{},[895,39473],{},[2005,39475,2007],{},[2281,39477,39478,39480],{},[898,39479,1860],{},[2138,39481,2287],{},[2005,39483,2014],{"stretchy":2013},[2281,39485,39486,39488],{},[898,39487,3946],{},[2138,39489,2287],{},[2005,39491,2295],{"separator":2294},[2281,39493,39494,39496],{},[898,39495,3946],{},[2138,39497,2140],{},[2005,39499,2020],{"stretchy":2013},[2005,39501,2007],{},[2281,39503,39504,39506],{},[898,39505,207],{},[2138,39507,2287],{},[2005,39509,2104],{},[2281,39511,39512,39514],{},[898,39513,2107],{},[2138,39515,2287],{},[2281,39517,39518,39520],{},[898,39519,3946],{},[2138,39521,2287],{},[2005,39523,2104],{},[2281,39525,39526,39528],{},[898,39527,2151],{},[2138,39529,2287],{},[2281,39531,39532,39534],{},[898,39533,3946],{},[2138,39535,2140],{},[2005,39537,2295],{"separator":2294},[20765,39539,39540,39550],{},[20768,39541,39542],{},[2334,39543,39544],{"scriptlevel":2336,"displaystyle":2294},[2281,39545,39546,39548],{},[898,39547,2797],{},[2138,39549,2140],{},[20768,39551,39552],{},[2334,39553,39554],{"scriptlevel":2336,"displaystyle":2294},[895,39555,39556,39558,39560,39566,39568,39574,39576,39582,39584,39586,39592,39594,39600,39606,39608,39614,39620],{},[895,39557],{},[2005,39559,2007],{},[2281,39561,39562,39564],{},[898,39563,1860],{},[2138,39565,2140],{},[2005,39567,2014],{"stretchy":2013},[2281,39569,39570,39572],{},[898,39571,3946],{},[2138,39573,2287],{},[2005,39575,2295],{"separator":2294},[2281,39577,39578,39580],{},[898,39579,3946],{},[2138,39581,2140],{},[2005,39583,2020],{"stretchy":2013},[2005,39585,2007],{},[2281,39587,39588,39590],{},[898,39589,207],{},[2138,39591,2140],{},[2005,39593,2104],{},[2281,39595,39596,39598],{},[898,39597,2107],{},[2138,39599,2140],{},[2281,39601,39602,39604],{},[898,39603,3946],{},[2138,39605,2287],{},[2005,39607,2104],{},[2281,39609,39610,39612],{},[898,39611,2151],{},[2138,39613,2140],{},[2281,39615,39616,39618],{},[898,39617,3946],{},[2138,39619,2140],{},[898,39621,1644],{"mathvariant":2385},[20768,39623],{"width":28081},[20768,39625,39626],{},[2297,39627,39628],{},"(2.6)",[902,39630,39631],{"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}",[37353,39633,39635],{"id":39634},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,39637,39638,39685,39732],{},[123,39639,39640,1343,39662,39684],{},[883,39641,39643],{"className":39642},[886],[888,39644,39645],{"xmlns":890},[892,39646,39647,39659],{},[895,39648,39649,39655,39657],{},[2281,39650,39651,39653],{},[898,39652,207],{},[2138,39654,2287],{},[2005,39656,3416],{},[2138,39658,2336],{},[902,39660,39661],{"encoding":904},"a_1 > 0",[883,39663,39665],{"className":39664},[886],[888,39666,39667],{"xmlns":890},[892,39668,39669,39681],{},[895,39670,39671,39677,39679],{},[2281,39672,39673,39675],{},[898,39674,207],{},[2138,39676,2140],{},[2005,39678,3416],{},[2138,39680,2336],{},[902,39682,39683],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,39686,39687,1343,39709,39731],{},[883,39688,39690],{"className":39689},[886],[888,39691,39692],{"xmlns":890},[892,39693,39694,39706],{},[895,39695,39696,39702,39704],{},[2281,39697,39698,39700],{},[898,39699,2107],{},[2138,39701,2287],{},[2005,39703,3455],{},[2138,39705,2336],{},[902,39707,39708],{"encoding":904},"b_1 \u003C 0",[883,39710,39712],{"className":39711},[886],[888,39713,39714],{"xmlns":890},[892,39715,39716,39728],{},[895,39717,39718,39724,39726],{},[2281,39719,39720,39722],{},[898,39721,2151],{},[2138,39723,2140],{},[2005,39725,3455],{},[2138,39727,2336],{},[902,39729,39730],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,39733,39734,39735,1343,39752,39770,39771],{},"zkřížené koeficienty ",[883,39736,39738],{"className":39737},[886],[888,39739,39740],{"xmlns":890},[892,39741,39742,39750],{},[895,39743,39744],{},[2281,39745,39746,39748],{},[898,39747,2151],{},[2138,39749,2287],{},[902,39751,29804],{"encoding":904},[883,39753,39755],{"className":39754},[886],[888,39756,39757],{"xmlns":890},[892,39758,39759,39767],{},[895,39760,39761],{},[2281,39762,39763,39765],{},[898,39764,2107],{},[2138,39766,2140],{},[902,39768,39769],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,39772,39773,39823],{},[123,39774,39775,39778,39779,1343,39801,2295],{},[38,39776,39777],{},"substituty"," (máslo vs. margarín): ",[883,39780,39782],{"className":39781},[886],[888,39783,39784],{"xmlns":890},[892,39785,39786,39798],{},[895,39787,39788,39794,39796],{},[2281,39789,39790,39792],{},[898,39791,2151],{},[2138,39793,2287],{},[2005,39795,3416],{},[2138,39797,2336],{},[902,39799,39800],{"encoding":904},"c_1 > 0",[883,39802,39804],{"className":39803},[886],[888,39805,39806],{"xmlns":890},[892,39807,39808,39820],{},[895,39809,39810,39816,39818],{},[2281,39811,39812,39814],{},[898,39813,2107],{},[2138,39815,2140],{},[2005,39817,3416],{},[2138,39819,2336],{},[902,39821,39822],{"encoding":904},"b_2 > 0",[123,39824,39825,39828,39829,1343,39851,1644],{},[38,39826,39827],{},"komplementy"," (auto vs. benzín): ",[883,39830,39832],{"className":39831},[886],[888,39833,39834],{"xmlns":890},[892,39835,39836,39848],{},[895,39837,39838,39844,39846],{},[2281,39839,39840,39842],{},[898,39841,2151],{},[2138,39843,2287],{},[2005,39845,3455],{},[2138,39847,2336],{},[902,39849,39850],{"encoding":904},"c_1 \u003C 0",[883,39852,39854],{"className":39853},[886],[888,39855,39856],{"xmlns":890},[892,39857,39858,39870],{},[895,39859,39860,39866,39868],{},[2281,39861,39862,39864],{},[898,39863,2107],{},[2138,39865,2140],{},[2005,39867,3455],{},[2138,39869,2336],{},[902,39871,39872],{"encoding":904},"b_2 \u003C 0",[724,39874,39875],{},"Schematicky:",[724,39877,39878,39881],{},[38,39879,39880],{},"Substituty",[883,39882,39884],{"className":39883},[886],[888,39885,39886],{"xmlns":890},[892,39887,39888,40027],{},[895,39889,39890,39896,39898,39913,39915,39935,39937,39957,39959,39961,39967,39969,39983,39985,40005,40007],{},[2281,39891,39892,39894],{},[898,39893,2797],{},[2138,39895,2287],{},[2005,39897,2007],{},[898,39899,39900],{},[39901,39902,39903,39911],"munder",{},[2005,39904,39905],{},[2281,39906,39907,39909],{},[898,39908,207],{},[2138,39910,2287],{},[2005,39912,2104],{"lspace":2386,"rspace":2386},[2005,39914,2104],{},[898,39916,39917],{},[39901,39918,39919,39933],{},[2005,39920,39921,39927],{},[2281,39922,39923,39925],{},[898,39924,2107],{},[2138,39926,2287],{},[2281,39928,39929,39931],{},[898,39930,3946],{},[2138,39932,2287],{},[2005,39934,2234],{"lspace":2386,"rspace":2386},[2005,39936,2104],{},[898,39938,39939],{},[39901,39940,39941,39955],{},[2005,39942,39943,39949],{},[2281,39944,39945,39947],{},[898,39946,2151],{},[2138,39948,2287],{},[2281,39950,39951,39953],{},[898,39952,3946],{},[2138,39954,2140],{},[2005,39956,2104],{"lspace":2386,"rspace":2386},[2005,39958,2295],{"separator":2294},[5884,39960],{"width":5886},[2281,39962,39963,39965],{},[898,39964,2797],{},[2138,39966,2140],{},[2005,39968,2007],{},[898,39970,39971],{},[39901,39972,39973,39981],{},[2005,39974,39975],{},[2281,39976,39977,39979],{},[898,39978,207],{},[2138,39980,2140],{},[2005,39982,2104],{"lspace":2386,"rspace":2386},[2005,39984,2104],{},[898,39986,39987],{},[39901,39988,39989,40003],{},[2005,39990,39991,39997],{},[2281,39992,39993,39995],{},[898,39994,2107],{},[2138,39996,2140],{},[2281,39998,39999,40001],{},[898,40000,3946],{},[2138,40002,2287],{},[2005,40004,2104],{"lspace":2386,"rspace":2386},[2005,40006,2104],{},[898,40008,40009],{},[39901,40010,40011,40025],{},[2005,40012,40013,40019],{},[2281,40014,40015,40017],{},[898,40016,2151],{},[2138,40018,2140],{},[2281,40020,40021,40023],{},[898,40022,3946],{},[2138,40024,2140],{},[2005,40026,2234],{"lspace":2386,"rspace":2386},[902,40028,40029],{"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}",[724,40031,40032,40035],{},[38,40033,40034],{},"Komplementy",[883,40036,40038],{"className":40037},[886],[888,40039,40040],{"xmlns":890},[892,40041,40042,40180],{},[895,40043,40044,40050,40052,40066,40068,40088,40090,40110,40112,40114,40120,40122,40136,40138,40158,40160],{},[2281,40045,40046,40048],{},[898,40047,2797],{},[2138,40049,2287],{},[2005,40051,2007],{},[898,40053,40054],{},[39901,40055,40056,40064],{},[2005,40057,40058],{},[2281,40059,40060,40062],{},[898,40061,207],{},[2138,40063,2287],{},[2005,40065,2104],{"lspace":2386,"rspace":2386},[2005,40067,2104],{},[898,40069,40070],{},[39901,40071,40072,40086],{},[2005,40073,40074,40080],{},[2281,40075,40076,40078],{},[898,40077,2107],{},[2138,40079,2287],{},[2281,40081,40082,40084],{},[898,40083,3946],{},[2138,40085,2287],{},[2005,40087,2234],{"lspace":2386,"rspace":2386},[2005,40089,2104],{},[898,40091,40092],{},[39901,40093,40094,40108],{},[2005,40095,40096,40102],{},[2281,40097,40098,40100],{},[898,40099,2151],{},[2138,40101,2287],{},[2281,40103,40104,40106],{},[898,40105,3946],{},[2138,40107,2140],{},[2005,40109,2234],{"lspace":2386,"rspace":2386},[2005,40111,2295],{"separator":2294},[5884,40113],{"width":5886},[2281,40115,40116,40118],{},[898,40117,2797],{},[2138,40119,2140],{},[2005,40121,2007],{},[898,40123,40124],{},[39901,40125,40126,40134],{},[2005,40127,40128],{},[2281,40129,40130,40132],{},[898,40131,207],{},[2138,40133,2140],{},[2005,40135,2104],{"lspace":2386,"rspace":2386},[2005,40137,2104],{},[898,40139,40140],{},[39901,40141,40142,40156],{},[2005,40143,40144,40150],{},[2281,40145,40146,40148],{},[898,40147,2107],{},[2138,40149,2140],{},[2281,40151,40152,40154],{},[898,40153,3946],{},[2138,40155,2287],{},[2005,40157,2234],{"lspace":2386,"rspace":2386},[2005,40159,2104],{},[898,40161,40162],{},[39901,40163,40164,40178],{},[2005,40165,40166,40172],{},[2281,40167,40168,40170],{},[898,40169,2151],{},[2138,40171,2140],{},[2281,40173,40174,40176],{},[898,40175,3946],{},[2138,40177,2140],{},[2005,40179,2234],{"lspace":2386,"rspace":2386},[902,40181,40182],{"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}",[36975,40184],{},[115,40186,13131],{"id":36784},[3876,40188,40189],{},[724,40190,40191,40193,40194,36999,40207,37013,40220,40223,40224,5675,40248,40266],{},[883,40192,4164],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,40195,40197],{"className":40196},[886],[888,40198,40199],{"xmlns":890},[892,40200,40201,40205],{},[895,40202,40203],{},[898,40204,2797],{},[902,40206,2797],{"encoding":904},[883,40208,40210],{"className":40209},[886],[888,40211,40212],{"xmlns":890},[892,40213,40214,40218],{},[895,40215,40216],{},[898,40217,3946],{},[902,40219,3946],{"encoding":904},[38,40221,40222],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,40225,40227],{"className":40226},[886],[888,40228,40229],{"xmlns":890},[892,40230,40231,40245],{},[895,40232,40233,40235,40237,40239,40241,40243],{},[898,40234,3946],{},[2005,40236,2007],{},[898,40238,2151],{},[898,40240,2797],{},[2005,40242,2104],{},[898,40244,2203],{},[902,40246,40247],{"encoding":904},"P = cQ + d",[883,40249,40251],{"className":40250},[886],[888,40252,40253],{"xmlns":890},[892,40254,40255,40263],{},[895,40256,40257,40259,40261],{},[898,40258,2151],{},[2005,40260,3416],{},[2138,40262,2336],{},[902,40264,40265],{"encoding":904},"c > 0"," je standardní aproximací.",[198,40268,37069],{"id":40269},"obecný-vícefaktorový-model-1",[724,40271,40272,10030,40275,40278,40279,40292,40293,36901,40306,36915,40319,40332,40333,40347,40348,36944,40361,40374],{},[38,40273,40274],{},"Nabízené množství",[614,40276,40277],{},"quantity supplied",") závisí na ceně ",[883,40280,40282],{"className":40281},[886],[888,40283,40284],{"xmlns":890},[892,40285,40286,40290],{},[895,40287,40288],{},[898,40289,3946],{},[902,40291,3946],{"encoding":904},", cenách výrobních faktorů (práce ",[883,40294,40296],{"className":40295},[886],[888,40297,40298],{"xmlns":890},[892,40299,40300,40304],{},[895,40301,40302],{},[898,40303,9801],{},[902,40305,9801],{"encoding":904},[883,40307,40309],{"className":40308},[886],[888,40310,40311],{"xmlns":890},[892,40312,40313,40317],{},[895,40314,40315],{},[898,40316,9806],{},[902,40318,9806],{"encoding":904},[883,40320,40322],{"className":40321},[886],[888,40323,40324],{"xmlns":890},[892,40325,40326,40330],{},[895,40327,40328],{},[898,40329,1868],{},[902,40331,1868],{"encoding":904},"), očekávání ",[883,40334,40336],{"className":40335},[886],[888,40337,40338],{"xmlns":890},[892,40339,40340,40345],{},[895,40341,40342],{},[898,40343,40344],{},"V",[902,40346,40344],{"encoding":904},", počtu výrobců ",[883,40349,40351],{"className":40350},[886],[888,40352,40353],{"xmlns":890},[892,40354,40355,40359],{},[895,40356,40357],{},[898,40358,36941],{},[902,40360,36941],{"encoding":904},[883,40362,40364],{"className":40363},[886],[888,40365,40366],{"xmlns":890},[892,40367,40368,40372],{},[895,40369,40370],{},[898,40371,36956],{},[902,40373,36956],{"encoding":904}," a dalších:",[883,40376,40378],{"className":40377},[886],[888,40379,40380],{"xmlns":890,"display":28071},[892,40381,40382,40441],{},[20760,40383,40384],{"width":28076},[20765,40385,40386,40388,40434,40436],{},[20768,40387],{"width":28081},[20768,40389,40390],{},[895,40391,40392,40394,40396,40398,40400,40402,40404,40406,40408,40410,40412,40414,40416,40418,40420,40422,40424,40426,40428,40430,40432],{},[898,40393,2797],{},[2005,40395,2007],{},[898,40397,8679],{},[2005,40399,2014],{"stretchy":2013},[898,40401,3946],{},[2005,40403,2295],{"separator":2294},[898,40405,9801],{},[2005,40407,2295],{"separator":2294},[898,40409,9806],{},[2005,40411,2295],{"separator":2294},[898,40413,1868],{},[2005,40415,2295],{"separator":2294},[898,40417,40344],{},[2005,40419,2295],{"separator":2294},[898,40421,36941],{},[2005,40423,2295],{"separator":2294},[898,40425,36956],{},[2005,40427,2295],{"separator":2294},[2005,40429,9652],{},[2005,40431,2020],{"stretchy":2013},[898,40433,1644],{"mathvariant":2385},[20768,40435],{"width":28081},[20768,40437,40438],{},[2297,40439,40440],{},"(2.7)",[902,40442,40443],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,40445,38421,40446,10030,40449,40452],{},[38,40447,40448],{},"funkce nabídky",[614,40450,40451],{},"supply function",") v širším slova smyslu.",[198,40454,40456],{"id":40455},"jednofaktorový-model","Jednofaktorový model",[724,40458,40459],{},"V nejpřirozenějším jednofaktorovém modelu",[883,40461,40463],{"className":40462},[886],[888,40464,40465],{"xmlns":890,"display":28071},[892,40466,40467,40518],{},[20760,40468,40469],{"width":28076},[20765,40470,40471,40473,40511,40513],{},[20768,40472],{"width":28081},[20768,40474,40475],{},[895,40476,40477,40479,40481,40483,40485,40487,40489,40491,40493,40495,40497,40499,40501,40503,40505,40507,40509],{},[898,40478,2797],{},[2005,40480,2007],{},[898,40482,8679],{},[2005,40484,2014],{"stretchy":2013},[898,40486,3946],{},[2005,40488,2020],{"stretchy":2013},[2005,40490,2295],{"separator":2294},[5884,40492],{"width":5886},[2297,40494,37422],{},[5884,40496],{"width":5886},[898,40498,3946],{},[2005,40500,2007],{},[898,40502,8679],{},[2005,40504,2014],{"stretchy":2013},[898,40506,2797],{},[2005,40508,2020],{"stretchy":2013},[898,40510,1644],{"mathvariant":2385},[20768,40512],{"width":28081},[20768,40514,40515],{},[2297,40516,40517],{},"(2.8)",[902,40519,40520],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,40522,40523,40524,10030,40527,3927],{},"Graf je ",[38,40525,40526],{},"křivka nabídky",[614,40528,40529],{},"supply curve",[37353,40531,40533],{"id":40532},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[3876,40535,40536],{},[724,40537,40538],{},[38,40539,37468,40540,40553,40554,37523],{},[883,40541,40543],{"className":40542},[886],[888,40544,40545],{"xmlns":890},[892,40546,40547,40551],{},[895,40548,40549],{},[898,40550,3946],{},[902,40552,3946],{"encoding":904},", pak nabízené množství ",[883,40555,40557],{"className":40556},[886],[888,40558,40559],{"xmlns":890},[892,40560,40561,40565],{},[895,40562,40563],{},[898,40564,2797],{},[902,40566,2797],{"encoding":904},[724,40568,40569,40570,40595,40596,40626,40627,40644],{},"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 ",[883,40571,40573],{"className":40572},[886],[888,40574,40575],{"xmlns":890},[892,40576,40577,40593],{},[895,40578,40579,40581,40583,40585,40591],{},[2005,40580,2495],{"stretchy":2013},[2138,40582,2336],{},[2005,40584,2295],{"separator":2294},[2281,40586,40587,40589],{},[898,40588,3946],{},[2138,40590,2336],{},[2005,40592,2510],{"stretchy":2013},[902,40594,37608],{"encoding":904}," na svislé ose (případně z ",[883,40597,40599],{"className":40598},[886],[888,40600,40601],{"xmlns":890},[892,40602,40603,40623],{},[895,40604,40605,40607,40613,40615,40621],{},[2005,40606,2495],{"stretchy":2013},[2281,40608,40609,40611],{},[898,40610,2797],{},[2138,40612,2287],{},[2005,40614,2295],{"separator":2294},[2281,40616,40617,40619],{},[898,40618,3946],{},[2138,40620,2287],{},[2005,40622,2510],{"stretchy":2013},[902,40624,40625],{"encoding":904},"[Q_1, P_1]","), kde ",[883,40628,40630],{"className":40629},[886],[888,40631,40632],{"xmlns":890},[892,40633,40634,40642],{},[895,40635,40636],{},[2281,40637,40638,40640],{},[898,40639,3946],{},[2138,40641,2336],{},[902,40643,38953],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,40646,40647],{},[614,40648,40649,40650,3726,40663,1644],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,40651,40653],{"className":40652},[886],[888,40654,40655],{"xmlns":890},[892,40656,40657,40661],{},[895,40658,40659],{},[898,40660,8679],{},[902,40662,8679],{"encoding":904},[883,40664,40666],{"className":40665},[886],[888,40667,40668],{"xmlns":890},[892,40669,40670,40682],{},[895,40671,40672,40674,40676,40678,40680],{},[2005,40673,2014],{"stretchy":2013},[898,40675,2797],{},[2005,40677,2295],{"separator":2294},[898,40679,3946],{},[2005,40681,2020],{"stretchy":2013},[902,40683,37696],{"encoding":904},[37353,40685,40687],{"id":40686},"lineární-model-nabídky","Lineární model nabídky",[883,40689,40691],{"className":40690},[886],[888,40692,40693],{"xmlns":890,"display":28071},[892,40694,40695,40734],{},[20760,40696,40697],{"width":28076},[20765,40698,40699,40701,40727,40729],{},[20768,40700],{"width":28081},[20768,40702,40703],{},[895,40704,40705,40707,40709,40711,40713,40715,40717,40719,40721,40723,40725],{},[898,40706,3946],{},[2005,40708,2007],{},[898,40710,2151],{},[898,40712,2797],{},[2005,40714,2104],{},[898,40716,2203],{},[2005,40718,2295],{"separator":2294},[5884,40720],{"width":5886},[898,40722,2151],{},[2005,40724,3416],{},[2138,40726,12466],{},[20768,40728],{"width":28081},[20768,40730,40731],{},[2297,40732,40733],{},"(2.9)",[902,40735,40736],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,40738,40739,40740,40776,40777,40790],{},"Alternativně ",[883,40741,40743],{"className":40742},[886],[888,40744,40745],{"xmlns":890},[892,40746,40747,40773],{},[895,40748,40749,40751,40753,40761,40763,40765],{},[898,40750,2797],{},[2005,40752,2007],{},[2334,40754,40755],{"scriptlevel":2336,"displaystyle":2013},[2338,40756,40757,40759],{},[2138,40758,2287],{},[898,40760,2151],{},[898,40762,3946],{},[2005,40764,2234],{},[2334,40766,40767],{"scriptlevel":2336,"displaystyle":2013},[2338,40768,40769,40771],{},[898,40770,2203],{},[898,40772,2151],{},[902,40774,40775],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,40778,40780],{"className":40779},[886],[888,40781,40782],{"xmlns":890},[892,40783,40784,40788],{},[895,40785,40786],{},[898,40787,3946],{},[902,40789,3946],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[37930,40792,40794],{"id":40793},"příklad-25","Příklad 2.5",[724,40796,40797,40799,40800,1644],{},[38,40798,37938],{}," Lineární nabídka ",[883,40801,40803],{"className":40802},[886],[888,40804,40805],{"xmlns":890},[892,40806,40807,40821],{},[895,40808,40809,40811,40813,40815,40817,40819],{},[898,40810,3946],{},[2005,40812,2007],{},[2138,40814,5015],{},[898,40816,2797],{},[2005,40818,2104],{},[2138,40820,5010],{},[902,40822,40823],{"encoding":904},"P = 0{,}5Q + 25",[724,40825,40826,40828,40829,1644],{},[38,40827,37970],{}," Alternativní tvar ",[883,40830,40832],{"className":40831},[886],[888,40833,40834],{"xmlns":890},[892,40835,40836,40850],{},[895,40837,40838,40840,40842,40844,40846,40848],{},[898,40839,2797],{},[2005,40841,2007],{},[2138,40843,2140],{},[898,40845,3946],{},[2005,40847,2234],{},[2138,40849,3128],{},[902,40851,40852],{"encoding":904},"Q = 2P - 50",[16,40854,40855,40880],{},[19,40856,40857],{},[22,40858,40859,40874,40876,40878],{},[25,40860,40861],{},[883,40862,40864],{"className":40863},[886],[888,40865,40866],{"xmlns":890},[892,40867,40868,40872],{},[895,40869,40870],{},[898,40871,3946],{},[902,40873,3946],{"encoding":904},[25,40875,38024],{},[25,40877,15044],{},[25,40879,5217],{},[30,40881,40882],{},[22,40883,40884,40899,40901,40903],{},[35,40885,40886],{},[883,40887,40889],{"className":40888},[886],[888,40890,40891],{"xmlns":890},[892,40892,40893,40897],{},[895,40894,40895],{},[898,40896,2797],{},[902,40898,2797],{"encoding":904},[35,40900,2871],{},[35,40902,9041],{},[35,40904,38024],{},[198,40906,40908,40909,2020],{"id":40907},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,40910,40911],{},"shift of supply",[724,40913,40914,40915,40918,40919,40936,40937,40962,40963,1644],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,40916,40917],{},"doprava",": při stejné ceně ",[883,40920,40922],{"className":40921},[886],[888,40923,40924],{"xmlns":890},[892,40925,40926,40934],{},[895,40927,40928],{},[2281,40929,40930,40932],{},[898,40931,3946],{},[2138,40933,2336],{},[902,40935,38953],{"encoding":904}," vyrobí výrobce větší ",[883,40938,40940],{"className":40939},[886],[888,40941,40942],{"xmlns":890},[892,40943,40944,40960],{},[895,40945,40946,40952,40954],{},[2281,40947,40948,40950],{},[898,40949,2797],{},[2138,40951,2287],{},[2005,40953,3416],{},[2281,40955,40956,40958],{},[898,40957,2797],{},[2138,40959,2336],{},[902,40961,39066],{"encoding":904},"); zdražení vstupů posune křivku ",[38,40964,40965],{},"doleva",[724,40967,40968],{},[614,40969,40970,40971,40984,40985,41003,41004,41022,41023,1644],{},"Obrázek 2.11: Původní ",[883,40972,40974],{"className":40973},[886],[888,40975,40976],{"xmlns":890},[892,40977,40978,40982],{},[895,40979,40980],{},[898,40981,8679],{},[902,40983,8679],{"encoding":904},", posunuté ",[883,40986,40988],{"className":40987},[886],[888,40989,40990],{"xmlns":890},[892,40991,40992,41000],{},[895,40993,40994],{},[2281,40995,40996,40998],{},[898,40997,8679],{},[2138,40999,2287],{},[902,41001,41002],{"encoding":904},"S_1"," (doprava) a ",[883,41005,41007],{"className":41006},[886],[888,41008,41009],{"xmlns":890},[892,41010,41011,41019],{},[895,41012,41013],{},[2281,41014,41015,41017],{},[898,41016,8679],{},[2138,41018,2140],{},[902,41020,41021],{"encoding":904},"S_2"," (doleva) v ",[883,41024,41026],{"className":41025},[886],[888,41027,41028],{"xmlns":890},[892,41029,41030,41042],{},[895,41031,41032,41034,41036,41038,41040],{},[2005,41033,2014],{"stretchy":2013},[898,41035,2797],{},[2005,41037,2295],{"separator":2294},[898,41039,3946],{},[2005,41041,2020],{"stretchy":2013},[902,41043,37696],{"encoding":904},[37930,41045,41047],{"id":41046},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,41049,41050,41052,41053,41077,41078,1644],{},[38,41051,37938],{}," Nabídka ",[883,41054,41056],{"className":41055},[886],[888,41057,41058],{"xmlns":890},[892,41059,41060,41074],{},[895,41061,41062,41064,41066,41068,41070,41072],{},[898,41063,3946],{},[2005,41065,2007],{},[898,41067,8679],{},[2005,41069,2014],{"stretchy":2013},[898,41071,2797],{},[2005,41073,2020],{"stretchy":2013},[902,41075,41076],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,41079,41081],{"className":41080},[886],[888,41082,41083],{"xmlns":890},[892,41084,41085,41089],{},[895,41086,41087],{},[898,41088,2783],{},[902,41090,2783],{"encoding":904},[724,41092,41093,41095,41096,41109,41110,41128,41129,41157],{},[38,41094,37970],{}," Spotřebitel zaplatí ",[883,41097,41099],{"className":41098},[886],[888,41100,41101],{"xmlns":890},[892,41102,41103,41107],{},[895,41104,41105],{},[898,41106,3946],{},[902,41108,3946],{"encoding":904},", výrobce obdrží ",[883,41111,41113],{"className":41112},[886],[888,41114,41115],{"xmlns":890},[892,41116,41117,41125],{},[895,41118,41119,41121,41123],{},[898,41120,3946],{},[2005,41122,2234],{},[898,41124,2783],{},[902,41126,41127],{"encoding":904},"P - T",". Z podmínky ",[883,41130,41132],{"className":41131},[886],[888,41133,41134],{"xmlns":890},[892,41135,41136,41154],{},[895,41137,41138,41140,41142,41144,41146,41148,41150,41152],{},[898,41139,3946],{},[2005,41141,2234],{},[898,41143,2783],{},[2005,41145,2007],{},[898,41147,8679],{},[2005,41149,2014],{"stretchy":2013},[898,41151,2797],{},[2005,41153,2020],{"stretchy":2013},[902,41155,41156],{"encoding":904},"P - T = S(Q)"," plyne",[883,41159,41161],{"className":41160},[886],[888,41162,41163],{"xmlns":890,"display":28071},[892,41164,41165,41199],{},[895,41166,41167,41169,41171,41177,41179,41181,41183,41185,41187,41189,41191,41193,41195,41197],{},[898,41168,3946],{},[2005,41170,2007],{},[2281,41172,41173,41175],{},[898,41174,8679],{},[2138,41176,2287],{},[2005,41178,2014],{"stretchy":2013},[898,41180,2797],{},[2005,41182,2020],{"stretchy":2013},[2005,41184,2007],{},[898,41186,8679],{},[2005,41188,2014],{"stretchy":2013},[898,41190,2797],{},[2005,41192,2020],{"stretchy":2013},[2005,41194,2104],{},[898,41196,2783],{},[898,41198,1644],{"mathvariant":2385},[902,41200,41201],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,41203,41204,41205,41218,41219,2212,41232,41235,41236,3894,41256,8108,41274,1644],{},"Křivka ",[883,41206,41208],{"className":41207},[886],[888,41209,41210],{"xmlns":890},[892,41211,41212,41216],{},[895,41213,41214],{},[898,41215,8679],{},[902,41217,8679],{"encoding":904}," se tedy posune o ",[883,41220,41222],{"className":41221},[886],[888,41223,41224],{"xmlns":890},[892,41225,41226,41230],{},[895,41227,41228],{},[898,41229,2783],{},[902,41231,2783],{"encoding":904},[38,41233,41234],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,41237,41239],{"className":41238},[886],[888,41240,41241],{"xmlns":890},[892,41242,41243,41253],{},[895,41244,41245,41247,41249,41251],{},[898,41246,3946],{},[2005,41248,2007],{},[2138,41250,2140],{},[898,41252,2797],{},[902,41254,41255],{"encoding":904},"P = 2Q",[883,41257,41259],{"className":41258},[886],[888,41260,41261],{"xmlns":890},[892,41262,41263,41271],{},[895,41264,41265,41267,41269],{},[898,41266,2783],{},[2005,41268,2007],{},[2138,41270,2244],{},[902,41272,41273],{"encoding":904},"T = 6",[883,41275,41277],{"className":41276},[886],[888,41278,41279],{"xmlns":890},[892,41280,41281,41303],{},[895,41282,41283,41289,41291,41293,41295,41297,41299,41301],{},[2281,41284,41285,41287],{},[898,41286,8679],{},[2138,41288,2287],{},[2005,41290,2713],{},[898,41292,3946],{},[2005,41294,2007],{},[2138,41296,2140],{},[898,41298,2797],{},[2005,41300,2104],{},[2138,41302,2244],{},[902,41304,41305],{"encoding":904},"S_1: P = 2Q + 6",[724,41307,41308],{},[614,41309,41310,41311,41324],{},"Obrázek 2.12: Posun nabídky o ",[883,41312,41314],{"className":41313},[886],[888,41315,41316],{"xmlns":890},[892,41317,41318,41322],{},[895,41319,41320],{},[898,41321,2783],{},[902,41323,2783],{"encoding":904}," svisle nahoru.",[36975,41326],{},[115,41328,41330],{"id":41329},"tržní-rovnováha","Tržní rovnováha",[3876,41332,41333],{},[724,41334,41335,41337,41338,2212,41341,41373,41374,1343,41397,41420,41421,41424,41425,41438],{},[883,41336,4164],{}," TL;DR\nV ",[38,41339,41340],{},"rovnovážném bodě",[883,41342,41344],{"className":41343},[886],[888,41345,41346],{"xmlns":890},[892,41347,41348,41370],{},[895,41349,41350,41352,41354,41360,41362,41368],{},[898,41351,1868],{},[2005,41353,2495],{"stretchy":2013},[2133,41355,41356,41358],{},[898,41357,2797],{},[898,41359,1868],{},[2005,41361,2295],{"separator":2294},[2133,41363,41364,41366],{},[898,41365,3946],{},[898,41367,1868],{},[2005,41369,2510],{"stretchy":2013},[902,41371,41372],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,41375,41377],{"className":41376},[886],[888,41378,41379],{"xmlns":890},[892,41380,41381,41395],{},[895,41382,41383,41385,41387,41389,41391,41393],{},[898,41384,3946],{},[2005,41386,2007],{},[898,41388,1860],{},[2005,41390,2014],{"stretchy":2013},[898,41392,2797],{},[2005,41394,2020],{"stretchy":2013},[902,41396,4646],{"encoding":904},[883,41398,41400],{"className":41399},[886],[888,41401,41402],{"xmlns":890},[892,41403,41404,41418],{},[895,41405,41406,41408,41410,41412,41414,41416],{},[898,41407,3946],{},[2005,41409,2007],{},[898,41411,8679],{},[2005,41413,2014],{"stretchy":2013},[898,41415,2797],{},[2005,41417,2020],{"stretchy":2013},[902,41419,41076],{"encoding":904},". Čtyři ",[38,41422,41423],{},"pravidla komparativní statiky"," popisují, jak se ",[883,41426,41428],{"className":41427},[886],[888,41429,41430],{"xmlns":890},[892,41431,41432,41436],{},[895,41433,41434],{},[898,41435,1868],{},[902,41437,1868],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,41440,41442],{"id":41441},"definice","Definice",[724,41444,41445,10030,41447,41450,41451,2212,41454,41472,41473,41504,41505,10030,41508,3927],{},[38,41446,41330],{},[614,41448,41449],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,41452,41453],{},"rovnovážné ceně",[883,41455,41457],{"className":41456},[886],[888,41458,41459],{"xmlns":890},[892,41460,41461,41469],{},[895,41462,41463],{},[2133,41464,41465,41467],{},[898,41466,3946],{},[898,41468,1868],{},[902,41470,41471],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,41474,41476],{"className":41475},[886],[888,41477,41478],{"xmlns":890},[892,41479,41480,41502],{},[895,41481,41482,41484,41486,41492,41494,41500],{},[898,41483,1868],{},[2005,41485,2495],{"stretchy":2013},[2133,41487,41488,41490],{},[898,41489,2797],{},[898,41491,1868],{},[2005,41493,2295],{"separator":2294},[2133,41495,41496,41498],{},[898,41497,3946],{},[898,41499,1868],{},[2005,41501,2510],{"stretchy":2013},[902,41503,41372],{"encoding":904}," se nazývá ",[38,41506,41507],{},"rovnovážný bod",[614,41509,41510],{},"equilibrium point",[724,41512,41513,41514,1343,41537,1644],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,41515,41517],{"className":41516},[886],[888,41518,41519],{"xmlns":890},[892,41520,41521,41535],{},[895,41522,41523,41525,41527,41529,41531,41533],{},[898,41524,3946],{},[2005,41526,2007],{},[898,41528,1860],{},[2005,41530,2014],{"stretchy":2013},[898,41532,2797],{},[2005,41534,2020],{"stretchy":2013},[902,41536,4646],{"encoding":904},[883,41538,41540],{"className":41539},[886],[888,41541,41542],{"xmlns":890},[892,41543,41544,41558],{},[895,41545,41546,41548,41550,41552,41554,41556],{},[898,41547,3946],{},[2005,41549,2007],{},[898,41551,8679],{},[2005,41553,2014],{"stretchy":2013},[898,41555,2797],{},[2005,41557,2020],{"stretchy":2013},[902,41559,41076],{"encoding":904},[724,41561,41562],{},[2568,41563],{"alt":41564,"className":41565,"src":41566},"imek-poptavka-nabidka-rovnovaha",[210,2572],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,41568,41569],{},[614,41570,41571,41572,41585,41586,14017,41599,41620,41621,1644],{},"Obrázek 2.13: Klesající ",[883,41573,41575],{"className":41574},[886],[888,41576,41577],{"xmlns":890},[892,41578,41579,41583],{},[895,41580,41581],{},[898,41582,1860],{},[902,41584,1860],{"encoding":904}," a rostoucí ",[883,41587,41589],{"className":41588},[886],[888,41590,41591],{"xmlns":890},[892,41592,41593,41597],{},[895,41594,41595],{},[898,41596,8679],{},[902,41598,8679],{"encoding":904},[883,41600,41602],{"className":41601},[886],[888,41603,41604],{"xmlns":890},[892,41605,41606,41618],{},[895,41607,41608,41610,41612,41614,41616],{},[2005,41609,2014],{"stretchy":2013},[898,41611,2797],{},[2005,41613,2295],{"separator":2294},[898,41615,3946],{},[2005,41617,2020],{"stretchy":2013},[902,41619,37696],{"encoding":904}," protínající se v ",[883,41622,41624],{"className":41623},[886],[888,41625,41626],{"xmlns":890},[892,41627,41628,41650],{},[895,41629,41630,41632,41634,41640,41642,41648],{},[898,41631,1868],{},[2005,41633,2495],{"stretchy":2013},[2133,41635,41636,41638],{},[898,41637,2797],{},[898,41639,1868],{},[2005,41641,2295],{"separator":2294},[2133,41643,41644,41646],{},[898,41645,3946],{},[898,41647,1868],{},[2005,41649,2510],{"stretchy":2013},[902,41651,41372],{"encoding":904},[198,41653,41655],{"id":41654},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,41657,41658,41660,41661,41695,41696,1644],{},[38,41659,37938],{}," Poptávka ",[883,41662,41664],{"className":41663},[886],[888,41665,41666],{"xmlns":890},[892,41667,41668,41692],{},[895,41669,41670,41672,41674,41676,41682,41684,41686,41688,41690],{},[898,41671,3946],{},[2005,41673,2007],{},[2005,41675,2234],{},[2133,41677,41678,41680],{},[898,41679,2797],{},[2138,41681,2140],{},[2005,41683,2234],{},[2138,41685,2871],{},[898,41687,2797],{},[2005,41689,2104],{},[2138,41691,8809],{},[902,41693,41694],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,41697,41699],{"className":41698},[886],[888,41700,41701],{"xmlns":890},[892,41702,41703,41725],{},[895,41704,41705,41707,41709,41715,41717,41719,41721,41723],{},[898,41706,3946],{},[2005,41708,2007],{},[2133,41710,41711,41713],{},[898,41712,2797],{},[2138,41714,2140],{},[2005,41716,2104],{},[2138,41718,22952],{},[898,41720,2797],{},[2005,41722,2104],{},[2138,41724,32551],{},[902,41726,41727],{"encoding":904},"P = Q^2 + 14Q + 22",[724,41729,41730,41732],{},[38,41731,37970],{}," Z rovnosti",[883,41734,41736],{"className":41735},[886],[888,41737,41738],{"xmlns":890,"display":28071},[892,41739,41740,41778],{},[895,41741,41742,41744,41750,41752,41754,41756,41758,41760,41762,41768,41770,41772,41774,41776],{},[2005,41743,2234],{},[2133,41745,41746,41748],{},[898,41747,2797],{},[2138,41749,2140],{},[2005,41751,2234],{},[2138,41753,2871],{},[898,41755,2797],{},[2005,41757,2104],{},[2138,41759,8809],{},[2005,41761,2007],{},[2133,41763,41764,41766],{},[898,41765,2797],{},[2138,41767,2140],{},[2005,41769,2104],{},[2138,41771,22952],{},[898,41773,2797],{},[2005,41775,2104],{},[2138,41777,32551],{},[902,41779,41780],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,41782,41783,41784,41819,41820,41853,41854,41871,41872,41885,41886,1343,41908,41945,41946,1644],{},"dostaneme ",[883,41785,41787],{"className":41786},[886],[888,41788,41789],{"xmlns":890},[892,41790,41791,41816],{},[895,41792,41793,41795,41801,41803,41806,41808,41810,41812,41814],{},[2138,41794,2140],{},[2133,41796,41797,41799],{},[898,41798,2797],{},[2138,41800,2140],{},[2005,41802,2104],{},[2138,41804,41805],{},"24",[898,41807,2797],{},[2005,41809,2234],{},[2138,41811,5623],{},[2005,41813,2007],{},[2138,41815,2336],{},[902,41817,41818],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,41821,41823],{"className":41822},[886],[888,41824,41825],{"xmlns":890},[892,41826,41827,41850],{},[895,41828,41829,41835,41837,41839,41841,41843,41846,41848],{},[2133,41830,41831,41833],{},[898,41832,2797],{},[2138,41834,2140],{},[2005,41836,2104],{},[2138,41838,3517],{},[898,41840,2797],{},[2005,41842,2234],{},[2138,41844,41845],{},"64",[2005,41847,2007],{},[2138,41849,2336],{},[902,41851,41852],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,41855,41857],{"className":41856},[886],[888,41858,41859],{"xmlns":890},[892,41860,41861,41868],{},[895,41862,41863,41865],{},[2005,41864,2234],{},[2138,41866,41867],{},"16",[902,41869,41870],{"encoding":904},"-16"," (nevyhovuje) a ",[883,41873,41875],{"className":41874},[886],[888,41876,41877],{"xmlns":890},[892,41878,41879,41883],{},[895,41880,41881],{},[2138,41882,2360],{},[902,41884,2360],{"encoding":904},". Tedy ",[883,41887,41889],{"className":41888},[886],[888,41890,41891],{"xmlns":890},[892,41892,41893,41905],{},[895,41894,41895,41901,41903],{},[2133,41896,41897,41899],{},[898,41898,2797],{},[898,41900,1868],{},[2005,41902,2007],{},[2138,41904,2360],{},[902,41906,41907],{"encoding":904},"Q^E = 4",[883,41909,41911],{"className":41910},[886],[888,41912,41913],{"xmlns":890},[892,41914,41915,41942],{},[895,41916,41917,41923,41925,41927,41929,41931,41933,41935,41937,41939],{},[2133,41918,41919,41921],{},[898,41920,3946],{},[898,41922,1868],{},[2005,41924,2007],{},[2005,41926,2234],{},[2138,41928,41867],{},[2005,41930,2234],{},[2138,41932,5217],{},[2005,41934,2104],{},[2138,41936,8809],{},[2005,41938,2007],{},[2138,41940,41941],{},"94",[902,41943,41944],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,41947,41949],{"className":41948},[886],[888,41950,41951],{"xmlns":890},[892,41952,41953,41967],{},[895,41954,41955,41957,41959,41961,41963,41965],{},[898,41956,1868],{},[2005,41958,2495],{"stretchy":2013},[2138,41960,2360],{},[2005,41962,2295],{"separator":2294},[2138,41964,41941],{},[2005,41966,2510],{"stretchy":2013},[902,41968,41969],{"encoding":904},"E[4, 94]",[198,41971,41973],{"id":41972},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,41975,41976,41978],{},[38,41977,37938],{}," Poptávky a nabídky dvou zboží",[883,41980,41982],{"className":41981},[886],[888,41983,41984],{"xmlns":890,"display":28071},[892,41985,41986,42152],{},[20760,41987,41990,42078],{"rowspacing":20762,"columnalign":41988,"columnspacing":41989},"right left right left","0em 1em 0em",[20765,41991,41992,42002,42034,42044],{},[20768,41993,41994],{},[2334,41995,41996],{"scriptlevel":2336,"displaystyle":2294},[2281,41997,41998,42000],{},[898,41999,2797],{},[2138,42001,2287],{},[20768,42003,42004],{},[2334,42005,42006],{"scriptlevel":2336,"displaystyle":2294},[895,42007,42008,42010,42012,42014,42016,42018,42024,42026,42032],{},[895,42009],{},[2005,42011,2007],{},[2138,42013,5217],{},[2005,42015,2234],{},[2138,42017,2237],{},[2281,42019,42020,42022],{},[898,42021,3946],{},[2138,42023,2287],{},[2005,42025,2234],{},[2281,42027,42028,42030],{},[898,42029,3946],{},[2138,42031,2140],{},[2005,42033,2295],{"separator":2294},[20768,42035,42036],{},[2334,42037,42038],{"scriptlevel":2336,"displaystyle":2294},[2281,42039,42040,42042],{},[898,42041,2797],{},[2138,42043,2140],{},[20768,42045,42046],{},[2334,42047,42048],{"scriptlevel":2336,"displaystyle":2294},[895,42049,42050,42052,42054,42056,42058,42060,42066,42068,42070,42076],{},[895,42051],{},[2005,42053,2007],{},[2138,42055,3128],{},[2005,42057,2234],{},[2138,42059,2140],{},[2281,42061,42062,42064],{},[898,42063,3946],{},[2138,42065,2287],{},[2005,42067,2234],{},[2138,42069,2360],{},[2281,42071,42072,42074],{},[898,42073,3946],{},[2138,42075,2140],{},[2005,42077,2295],{"separator":2294},[20765,42079,42080,42090,42116,42126],{},[20768,42081,42082],{},[2334,42083,42084],{"scriptlevel":2336,"displaystyle":2294},[2281,42085,42086,42088],{},[898,42087,2797],{},[2138,42089,2287],{},[20768,42091,42092],{},[2334,42093,42094],{"scriptlevel":2336,"displaystyle":2294},[895,42095,42096,42098,42100,42102,42104,42106,42108,42114],{},[895,42097],{},[2005,42099,2007],{},[2005,42101,2234],{},[2138,42103,2182],{},[2005,42105,2104],{},[2138,42107,2360],{},[2281,42109,42110,42112],{},[898,42111,3946],{},[2138,42113,2287],{},[2005,42115,2295],{"separator":2294},[20768,42117,42118],{},[2334,42119,42120],{"scriptlevel":2336,"displaystyle":2294},[2281,42121,42122,42124],{},[898,42123,2797],{},[2138,42125,2140],{},[20768,42127,42128],{},[2334,42129,42130],{"scriptlevel":2336,"displaystyle":2294},[895,42131,42132,42134,42136,42138,42140,42142,42144,42150],{},[895,42133],{},[2005,42135,2007],{},[2005,42137,2234],{},[2138,42139,24206],{},[2005,42141,2104],{},[2138,42143,2182],{},[2281,42145,42146,42148],{},[898,42147,3946],{},[2138,42149,2140],{},[898,42151,1644],{"mathvariant":2385},[902,42153,42154],{"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}",[724,42156,42157,42159],{},[38,42158,37970],{}," Z rovností poptávek a nabídek dostaneme",[883,42161,42163],{"className":42162},[886],[888,42164,42165],{"xmlns":890,"display":28071},[892,42166,42167,42216],{},[895,42168,42169,42171,42177,42179,42185,42187,42189,42191,42193,42195,42201,42203,42205,42211,42213],{},[2138,42170,4008],{},[2281,42172,42173,42175],{},[898,42174,3946],{},[2138,42176,2287],{},[2005,42178,2104],{},[2281,42180,42181,42183],{},[898,42182,3946],{},[2138,42184,2140],{},[2005,42186,2007],{},[2138,42188,21209],{},[2005,42190,2295],{"separator":2294},[5884,42192],{"width":5886},[2138,42194,2140],{},[2281,42196,42197,42199],{},[898,42198,3946],{},[2138,42200,2287],{},[2005,42202,2104],{},[2138,42204,24206],{},[2281,42206,42207,42209],{},[898,42208,3946],{},[2138,42210,2140],{},[2005,42212,2007],{},[2138,42214,42215],{},"57.",[902,42217,42218],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,42220,42221,42222,1343,42246,42270,42271,1343,42296,42320,42321,42323],{},"Řešením je ",[883,42223,42225],{"className":42224},[886],[888,42226,42227],{"xmlns":890},[892,42228,42229,42243],{},[895,42230,42231,42239,42241],{},[9172,42232,42233,42235,42237],{},[898,42234,3946],{},[2138,42236,2287],{},[898,42238,1868],{},[2005,42240,2007],{},[2138,42242,2360],{},[902,42244,42245],{"encoding":904},"P_1^E = 4",[883,42247,42249],{"className":42248},[886],[888,42250,42251],{"xmlns":890},[892,42252,42253,42267],{},[895,42254,42255,42263,42265],{},[9172,42256,42257,42259,42261],{},[898,42258,3946],{},[2138,42260,2140],{},[898,42262,1868],{},[2005,42264,2007],{},[2138,42266,24206],{},[902,42268,42269],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,42272,42274],{"className":42273},[886],[888,42275,42276],{"xmlns":890},[892,42277,42278,42293],{},[895,42279,42280,42288,42290],{},[9172,42281,42282,42284,42286],{},[898,42283,2797],{},[2138,42285,2287],{},[898,42287,1868],{},[2005,42289,2007],{},[2138,42291,42292],{},"13",[902,42294,42295],{"encoding":904},"Q_1^E = 13",[883,42297,42299],{"className":42298},[886],[888,42300,42301],{"xmlns":890},[892,42302,42303,42317],{},[895,42304,42305,42313,42315],{},[9172,42306,42307,42309,42311],{},[898,42308,2797],{},[2138,42310,2140],{},[898,42312,1868],{},[2005,42314,2007],{},[2138,42316,22952],{},[902,42318,42319],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,42322,39827],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,42325,42327],{"id":42326},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,42329,42330,42331,42348,42349,10030,42352,3927],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,42332,42334],{"className":42333},[886],[888,42335,42336],{"xmlns":890},[892,42337,42338,42346],{},[895,42339,42340],{},[2133,42341,42342,42344],{},[898,42343,3946],{},[898,42345,1868],{},[902,42347,41471],{"encoding":904},"; mechanismus popisuje ",[38,42350,42351],{},"teorém pavučiny",[614,42353,42354],{},"cobweb model",[198,42356,42358],{"id":42357},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,42360,42361],{},[2568,42362],{"alt":42363,"className":42364,"src":42365},"imek-komparativni-statika-4pripady",[210,2572],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[3876,42367,42368,42409,42449,42489],{},[724,42369,42370,42373,42374,6196,42391,1644],{},[38,42371,42372],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,42375,42377],{"className":42376},[886],[888,42378,42379],{"xmlns":890},[892,42380,42381,42389],{},[895,42382,42383],{},[2133,42384,42385,42387],{},[898,42386,3946],{},[898,42388,1868],{},[902,42390,41471],{"encoding":904},[883,42392,42394],{"className":42393},[886],[888,42395,42396],{"xmlns":890},[892,42397,42398,42406],{},[895,42399,42400],{},[2133,42401,42402,42404],{},[898,42403,2797],{},[898,42405,1868],{},[902,42407,42408],{"encoding":904},"Q^E",[724,42410,42411,42414,42415,6196,42432,1644],{},[38,42412,42413],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,42416,42418],{"className":42417},[886],[888,42419,42420],{"xmlns":890},[892,42421,42422,42430],{},[895,42423,42424],{},[2133,42425,42426,42428],{},[898,42427,3946],{},[898,42429,1868],{},[902,42431,41471],{"encoding":904},[883,42433,42435],{"className":42434},[886],[888,42436,42437],{"xmlns":890},[892,42438,42439,42447],{},[895,42440,42441],{},[2133,42442,42443,42445],{},[898,42444,2797],{},[898,42446,1868],{},[902,42448,42408],{"encoding":904},[724,42450,42451,42454,42455,9361,42472,1644],{},[38,42452,42453],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,42456,42458],{"className":42457},[886],[888,42459,42460],{"xmlns":890},[892,42461,42462,42470],{},[895,42463,42464],{},[2133,42465,42466,42468],{},[898,42467,3946],{},[898,42469,1868],{},[902,42471,41471],{"encoding":904},[883,42473,42475],{"className":42474},[886],[888,42476,42477],{"xmlns":890},[892,42478,42479,42487],{},[895,42480,42481],{},[2133,42482,42483,42485],{},[898,42484,2797],{},[898,42486,1868],{},[902,42488,42408],{"encoding":904},[724,42490,42491,42494,42495,42512,42513,1644],{},[38,42492,42493],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,42496,42498],{"className":42497},[886],[888,42499,42500],{"xmlns":890},[892,42501,42502,42510],{},[895,42503,42504],{},[2133,42505,42506,42508],{},[898,42507,3946],{},[898,42509,1868],{},[902,42511,41471],{"encoding":904},", pokles ",[883,42514,42516],{"className":42515},[886],[888,42517,42518],{"xmlns":890},[892,42519,42520,42528],{},[895,42521,42522],{},[2133,42523,42524,42526],{},[898,42525,2797],{},[898,42527,1868],{},[902,42529,42408],{"encoding":904},[16,42531,42532,42577],{},[19,42533,42534],{},[22,42535,42536,42539,42558],{},[25,42537,42538],{},"Změna",[25,42540,42541],{},[883,42542,42544],{"className":42543},[886],[888,42545,42546],{"xmlns":890},[892,42547,42548,42556],{},[895,42549,42550],{},[2133,42551,42552,42554],{},[898,42553,3946],{},[898,42555,1868],{},[902,42557,41471],{"encoding":904},[25,42559,42560],{},[883,42561,42563],{"className":42562},[886],[888,42564,42565],{"xmlns":890},[892,42566,42567,42575],{},[895,42568,42569],{},[2133,42570,42571,42573],{},[898,42572,2797],{},[898,42574,1868],{},[902,42576,42408],{"encoding":904},[30,42578,42579,42589,42599,42608],{},[22,42580,42581,42584,42587],{},[35,42582,42583],{},"Růst poptávky",[35,42585,42586],{},"↑",[35,42588,42586],{},[22,42590,42591,42594,42597],{},[35,42592,42593],{},"Pokles poptávky",[35,42595,42596],{},"↓",[35,42598,42596],{},[22,42600,42601,42604,42606],{},[35,42602,42603],{},"Růst nabídky",[35,42605,42596],{},[35,42607,42586],{},[22,42609,42610,42613,42615],{},[35,42611,42612],{},"Pokles nabídky",[35,42614,42586],{},[35,42616,42596],{},[724,42618,42619],{},[614,42620,42621],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[36975,42623],{},[115,42625,811],{"id":42626},"zdanění-trhu",[3876,42628,42629,42718],{},[724,42630,42631,42633,42634,42647,42648,2935,42661,42664,42665,36781,42688,42713,42714,42717],{},[883,42632,4164],{}," TL;DR\nJednotková daň ",[883,42635,42637],{"className":42636},[886],[888,42638,42639],{"xmlns":890},[892,42640,42641,42645],{},[895,42642,42643],{},[898,42644,2783],{},[902,42646,2783],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,42649,42651],{"className":42650},[886],[888,42652,42653],{"xmlns":890},[892,42654,42655,42659],{},[895,42656,42657],{},[898,42658,2783],{},[902,42660,2783],{"encoding":904},[38,42662,42663],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,42666,42668],{"className":42667},[886],[888,42669,42670],{"xmlns":890},[892,42671,42672,42685],{},[895,42673,42674],{},[2281,42675,42676,42678],{},[898,42677,2783],{},[895,42679,42680,42683],{},[898,42681,42682],{},"s",[898,42684,724],{},[902,42686,42687],{"encoding":904},"T_{sp}",[883,42689,42691],{"className":42690},[886],[888,42692,42693],{"xmlns":890},[892,42694,42695,42710],{},[895,42696,42697],{},[2281,42698,42699,42701],{},[898,42700,2783],{},[895,42702,42703,42706,42708],{},[898,42704,42705],{},"v",[898,42707,2003],{},[898,42709,12047],{},[902,42711,42712],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,42715,42716],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,42719,42720],{},[614,42721,42722,42723,1644],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,42724,42726],{"className":42725,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,42728,42729,42730,42733,42734,42760,42761,42764,42765,42791,42792,42809,42810,42850,42851,3894,42864,1644],{},"Existují dvě formy zdanění — daň uložená ",[38,42731,42732],{},"výrobci"," (posun nabídky ",[883,42735,42737],{"className":42736},[886],[888,42738,42739],{"xmlns":890},[892,42740,42741,42757],{},[895,42742,42743,42749,42751,42753,42755],{},[2281,42744,42745,42747],{},[898,42746,8679],{},[2138,42748,2287],{},[2005,42750,2007],{},[898,42752,8679],{},[2005,42754,2104],{},[898,42756,2783],{},[902,42758,42759],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,42762,42763],{},"spotřebiteli"," (posun poptávky ",[883,42766,42768],{"className":42767},[886],[888,42769,42770],{"xmlns":890},[892,42771,42772,42788],{},[895,42773,42774,42780,42782,42784,42786],{},[2281,42775,42776,42778],{},[898,42777,1860],{},[2138,42779,2140],{},[2005,42781,2007],{},[898,42783,1860],{},[2005,42785,2234],{},[898,42787,2783],{},[902,42789,42790],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,42793,42795],{"className":42794},[886],[888,42796,42797],{"xmlns":890},[892,42798,42799,42807],{},[895,42800,42801],{},[2133,42802,42803,42805],{},[898,42804,2797],{},[898,42806,1868],{},[902,42808,42408],{"encoding":904}," klesá a vzniká rozklad daně ",[883,42811,42813],{"className":42812},[886],[888,42814,42815],{"xmlns":890},[892,42816,42817,42847],{},[895,42818,42819,42821,42823,42833,42835],{},[898,42820,2783],{},[2005,42822,2007],{},[2281,42824,42825,42827],{},[898,42826,2783],{},[895,42828,42829,42831],{},[898,42830,42682],{},[898,42832,724],{},[2005,42834,2104],{},[2281,42836,42837,42839],{},[898,42838,2783],{},[895,42840,42841,42843,42845],{},[898,42842,42705],{},[898,42844,2003],{},[898,42846,12047],{},[902,42848,42849],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,42852,42854],{"className":42853},[886],[888,42855,42856],{"xmlns":890},[892,42857,42858,42862],{},[895,42859,42860],{},[898,42861,1860],{},[902,42863,1860],{"encoding":904},[883,42865,42867],{"className":42866},[886],[888,42868,42869],{"xmlns":890},[892,42870,42871,42875],{},[895,42872,42873],{},[898,42874,8679],{},[902,42876,8679],{"encoding":904},[724,42878,42879,42880,42883,42884,3894,42914,42948],{},"Zásadním výsledkem kapitoly je ",[38,42881,42882],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,42885,42887],{"className":42886},[886],[888,42888,42889],{"xmlns":890},[892,42890,42891,42911],{},[895,42892,42893,42901,42903],{},[9172,42894,42895,42897,42899],{},[898,42896,2797],{},[2138,42898,2287],{},[898,42900,1868],{},[2005,42902,2007],{},[9172,42904,42905,42907,42909],{},[898,42906,2797],{},[2138,42908,2140],{},[898,42910,1868],{},[902,42912,42913],{"encoding":904},"Q_1^E = Q_2^E",[883,42915,42917],{"className":42916},[886],[888,42918,42919],{"xmlns":890},[892,42920,42921,42945],{},[895,42922,42923,42931,42933,42935,42937],{},[9172,42924,42925,42927,42929],{},[898,42926,3946],{},[2138,42928,2287],{},[898,42930,1868],{},[2005,42932,2234],{},[898,42934,2783],{},[2005,42936,2007],{},[9172,42938,42939,42941,42943],{},[898,42940,3946],{},[2138,42942,2140],{},[898,42944,1868],{},[902,42946,42947],{"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.",[724,42950,42951,42952,42955,42956,42982,42983,43011,43012,43015,43016,43019,43020,1644],{},"Podrobný výklad, Příklady ",[38,42953,42954],{},"2.9"," (daň výrobci, ",[883,42957,42959],{"className":42958},[886],[888,42960,42961],{"xmlns":890},[892,42962,42963,42979],{},[895,42964,42965,42975,42977],{},[2281,42966,42967,42969],{},[898,42968,2783],{},[895,42970,42971,42973],{},[898,42972,42682],{},[898,42974,724],{},[2005,42976,2007],{},[2138,42978,2140],{},[902,42980,42981],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,42984,42986],{"className":42985},[886],[888,42987,42988],{"xmlns":890},[892,42989,42990,43008],{},[895,42991,42992,43004,43006],{},[2281,42993,42994,42996],{},[898,42995,2783],{},[895,42997,42998,43000,43002],{},[898,42999,42705],{},[898,43001,2003],{},[898,43003,12047],{},[2005,43005,2007],{},[2138,43007,2360],{},[902,43009,43010],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,43013,43014],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,43017,43018],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,43021,42726],{"className":43022,"dataFsResolvedFilePath":809,"href":810},[210],[36975,43024],{},[115,43026,43028],{"id":43027},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[3876,43030,43031],{},[724,43032,43033,43035,43036,43039,43040,43042],{},[883,43034,4164],{}," TL;DR\nMultiplikátory jsou ",[38,43037,43038],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,43041,36965],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,43044,43046],{"id":43045},"redukovaný-tvar","Redukovaný tvar",[724,43048,43049,43050,10030,43073,1343,43091,12134,43108,10030,43131,43148,43149,43179],{},"Pro lineární model ",[883,43051,43053],{"className":43052},[886],[888,43054,43055],{"xmlns":890},[892,43056,43057,43071],{},[895,43058,43059,43061,43063,43065,43067,43069],{},[898,43060,3946],{},[2005,43062,2007],{},[898,43064,207],{},[898,43066,2797],{},[2005,43068,2104],{},[898,43070,2107],{},[902,43072,37065],{"encoding":904},[883,43074,43076],{"className":43075},[886],[888,43077,43078],{"xmlns":890},[892,43079,43080,43088],{},[895,43081,43082,43084,43086],{},[898,43083,207],{},[2005,43085,3455],{},[2138,43087,2336],{},[902,43089,43090],{"encoding":904},"a \u003C 0",[883,43092,43094],{"className":43093},[886],[888,43095,43096],{"xmlns":890},[892,43097,43098,43106],{},[895,43099,43100,43102,43104],{},[898,43101,2107],{},[2005,43103,3416],{},[2138,43105,2336],{},[902,43107,18820],{"encoding":904},[883,43109,43111],{"className":43110},[886],[888,43112,43113],{"xmlns":890},[892,43114,43115,43129],{},[895,43116,43117,43119,43121,43123,43125,43127],{},[898,43118,3946],{},[2005,43120,2007],{},[898,43122,2151],{},[898,43124,2797],{},[2005,43126,2104],{},[898,43128,2203],{},[902,43130,40247],{"encoding":904},[883,43132,43134],{"className":43133},[886],[888,43135,43136],{"xmlns":890},[892,43137,43138,43146],{},[895,43139,43140,43142,43144],{},[898,43141,2151],{},[2005,43143,3416],{},[2138,43145,2336],{},[902,43147,40265],{"encoding":904},") dává podmínka rovnováhy ",[883,43150,43152],{"className":43151},[886],[888,43153,43154],{"xmlns":890},[892,43155,43156,43176],{},[895,43157,43158,43160,43162,43164,43166,43168,43170,43172,43174],{},[898,43159,207],{},[898,43161,2797],{},[2005,43163,2104],{},[898,43165,2107],{},[2005,43167,2007],{},[898,43169,2151],{},[898,43171,2797],{},[2005,43173,2104],{},[898,43175,2203],{},[902,43177,43178],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,43181,43183],{"className":43182},[886],[888,43184,43185],{"xmlns":890,"display":28071},[892,43186,43187,43232],{},[20760,43188,43189],{"width":28076},[20765,43190,43191,43193,43225,43227],{},[20768,43192],{"width":28081},[20768,43194,43195],{},[895,43196,43197,43203,43205,43223],{},[2133,43198,43199,43201],{},[898,43200,2797],{},[898,43202,1868],{},[2005,43204,2007],{},[2338,43206,43207,43215],{},[895,43208,43209,43211,43213],{},[898,43210,2107],{},[2005,43212,2234],{},[898,43214,2203],{},[895,43216,43217,43219,43221],{},[898,43218,2151],{},[2005,43220,2234],{},[898,43222,207],{},[898,43224,1644],{"mathvariant":2385},[20768,43226],{"width":28081},[20768,43228,43229],{},[2297,43230,43231],{},"(2.10)",[902,43233,43234],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,43236,43237,43238,10030,43240,43243,43244,43261,43262,2212,43265,43291,43292,43305,43306,43324,43325,3927],{},"Vztah (2.10) je ",[38,43239,20960],{},[614,43241,43242],{},"reduced form",") pro ",[883,43245,43247],{"className":43246},[886],[888,43248,43249],{"xmlns":890},[892,43250,43251,43259],{},[895,43252,43253],{},[2133,43254,43255,43257],{},[898,43256,2797],{},[898,43258,1868],{},[902,43260,42408],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,43263,43264],{},"parametrů",[883,43266,43268],{"className":43267},[886],[888,43269,43270],{"xmlns":890},[892,43271,43272,43288],{},[895,43273,43274,43276,43278,43280,43282,43284,43286],{},[898,43275,207],{},[2005,43277,2295],{"separator":2294},[898,43279,2107],{},[2005,43281,2295],{"separator":2294},[898,43283,2151],{},[2005,43285,2295],{"separator":2294},[898,43287,2203],{},[902,43289,43290],{"encoding":904},"a, b, c, d",". Aby ",[883,43293,43295],{"className":43294},[886],[888,43296,43297],{"xmlns":890},[892,43298,43299,43303],{},[895,43300,43301],{},[898,43302,1868],{},[902,43304,1868],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,43307,43309],{"className":43308},[886],[888,43310,43311],{"xmlns":890},[892,43312,43313,43321],{},[895,43314,43315,43317,43319],{},[898,43316,2107],{},[2005,43318,3416],{},[898,43320,2203],{},[902,43322,43323],{"encoding":904},"b > d"," (neboť ",[883,43326,43328],{"className":43327},[886],[888,43329,43330],{"xmlns":890},[892,43331,43332,43344],{},[895,43333,43334,43336,43338,43340,43342],{},[898,43335,2151],{},[2005,43337,2234],{},[898,43339,207],{},[2005,43341,3416],{},[2138,43343,2336],{},[902,43345,43346],{"encoding":904},"c - a > 0",[724,43348,43349],{},[614,43350,43351,43352,43365,43366,43379,43380,18654,43393,41945,43410,43423],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,43353,43355],{"className":43354},[886],[888,43356,43357],{"xmlns":890},[892,43358,43359,43363],{},[895,43360,43361],{},[898,43362,2107],{},[902,43364,2107],{"encoding":904}," na ose ",[883,43367,43369],{"className":43368},[886],[888,43370,43371],{"xmlns":890},[892,43372,43373,43377],{},[895,43374,43375],{},[898,43376,3946],{},[902,43378,3946],{"encoding":904},") a nabídka (úsek ",[883,43381,43383],{"className":43382},[886],[888,43384,43385],{"xmlns":890},[892,43386,43387,43391],{},[895,43388,43389],{},[898,43390,2203],{},[902,43392,2203],{"encoding":904},[883,43394,43396],{"className":43395},[886],[888,43397,43398],{"xmlns":890},[892,43399,43400,43408],{},[895,43401,43402,43404,43406],{},[898,43403,2107],{},[2005,43405,3416],{},[898,43407,2203],{},[902,43409,43323],{"encoding":904},[883,43411,43413],{"className":43412},[886],[888,43414,43415],{"xmlns":890},[892,43416,43417,43421],{},[895,43418,43419],{},[898,43420,1868],{},[902,43422,1868],{"encoding":904}," v 1. kvadrantu.",[198,43425,43427],{"id":43426},"definice-multiplikátorů","Definice multiplikátorů",[724,43429,43430,43431,43456,43457,43470,43471,43484],{},"V komparativní statice jsou ",[883,43432,43434],{"className":43433},[886],[888,43435,43436],{"xmlns":890},[892,43437,43438,43454],{},[895,43439,43440,43442,43444,43446,43448,43450,43452],{},[898,43441,207],{},[2005,43443,2295],{"separator":2294},[898,43445,2107],{},[2005,43447,2295],{"separator":2294},[898,43449,2151],{},[2005,43451,2295],{"separator":2294},[898,43453,2203],{},[902,43455,43290],{"encoding":904}," exogenní proměnné a ",[883,43458,43460],{"className":43459},[886],[888,43461,43462],{"xmlns":890},[892,43463,43464,43468],{},[895,43465,43466],{},[898,43467,2797],{},[902,43469,2797],{"encoding":904}," endogenní. Přibližná změna ",[883,43472,43474],{"className":43473},[886],[888,43475,43476],{"xmlns":890},[892,43477,43478,43482],{},[895,43479,43480],{},[898,43481,2797],{},[902,43483,2797],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,43486,43488],{"className":43487},[886],[888,43489,43490],{"xmlns":890,"display":28071},[892,43491,43492,43585],{},[20760,43493,43494],{"width":28076},[20765,43495,43496,43498,43578,43580],{},[20768,43497],{"width":28081},[20768,43499,43500],{},[895,43501,43502,43504,43506,43508,43510,43512,43514,43522,43524,43526,43528,43530,43538,43540,43542,43544,43546,43554,43556,43558,43560,43562,43570,43572,43574,43576],{},[898,43503,2897],{"mathvariant":2385},[898,43505,2797],{},[2005,43507,2739],{},[898,43509,2203],{},[898,43511,2797],{},[2005,43513,2007],{},[9172,43515,43516,43518,43520],{},[898,43517,2797],{},[898,43519,207],{},[2005,43521,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,43523,2995],{},[898,43525,2203],{},[898,43527,207],{},[2005,43529,2104],{},[9172,43531,43532,43534,43536],{},[898,43533,2797],{},[898,43535,2107],{},[2005,43537,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,43539,2995],{},[898,43541,2203],{},[898,43543,2107],{},[2005,43545,2104],{},[9172,43547,43548,43550,43552],{},[898,43549,2797],{},[898,43551,2151],{},[2005,43553,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,43555,2995],{},[898,43557,2203],{},[898,43559,2151],{},[2005,43561,2104],{},[9172,43563,43564,43566,43568],{},[898,43565,2797],{},[898,43567,2203],{},[2005,43569,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,43571,2995],{},[898,43573,2203],{},[898,43575,2203],{},[898,43577,1644],{"mathvariant":2385},[20768,43579],{"width":28081},[20768,43581,43582],{},[2297,43583,43584],{},"(2.11)",[902,43586,43587],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,43589,43590,43591,43641,43642,10030,43644,3159],{},"Parciální derivace ",[883,43592,43594],{"className":43593},[886],[888,43595,43596],{"xmlns":890},[892,43597,43598,43638],{},[895,43599,43600,43608,43610,43618,43620,43628,43630],{},[9172,43601,43602,43604,43606],{},[898,43603,2797],{},[898,43605,207],{},[2005,43607,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43609,2295],{"separator":2294},[9172,43611,43612,43614,43616],{},[898,43613,2797],{},[898,43615,2107],{},[2005,43617,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43619,2295],{"separator":2294},[9172,43621,43622,43624,43626],{},[898,43623,2797],{},[898,43625,2151],{},[2005,43627,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43629,2295],{"separator":2294},[9172,43631,43632,43634,43636],{},[898,43633,2797],{},[898,43635,2203],{},[2005,43637,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,43639,43640],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,43643,17984],{},[614,43645,43646],{},"multipliers",[883,43648,43650],{"className":43649},[886],[888,43651,43652],{"xmlns":890,"display":28071},[892,43653,43654,43805],{},[20760,43655,43656],{"width":28076},[20765,43657,43658,43660,43798,43800],{},[20768,43659],{"width":28081},[20768,43661,43662],{},[895,43663,43664,43672,43674,43700,43702,43704,43712,43714,43726,43728,43730,43738,43740,43742,43768,43770,43772,43780,43782,43784,43796],{},[9172,43665,43666,43668,43670],{},[898,43667,2797],{},[898,43669,207],{},[2005,43671,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43673,2007],{},[2338,43675,43676,43684],{},[895,43677,43678,43680,43682],{},[898,43679,2107],{},[2005,43681,2234],{},[898,43683,2203],{},[895,43685,43686,43688,43690,43692,43694],{},[2005,43687,2014],{"stretchy":2013},[898,43689,2151],{},[2005,43691,2234],{},[898,43693,207],{},[2133,43695,43696,43698],{},[2005,43697,2020],{"stretchy":2013},[2138,43699,2140],{},[2005,43701,2295],{"separator":2294},[5884,43703],{"width":15290},[9172,43705,43706,43708,43710],{},[898,43707,2797],{},[898,43709,2107],{},[2005,43711,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43713,2007],{},[2338,43715,43716,43718],{},[2138,43717,2287],{},[895,43719,43720,43722,43724],{},[898,43721,2151],{},[2005,43723,2234],{},[898,43725,207],{},[2005,43727,2295],{"separator":2294},[5884,43729],{"width":15290},[9172,43731,43732,43734,43736],{},[898,43733,2797],{},[898,43735,2151],{},[2005,43737,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43739,2007],{},[2005,43741,2234],{},[2338,43743,43744,43752],{},[895,43745,43746,43748,43750],{},[898,43747,2107],{},[2005,43749,2234],{},[898,43751,2203],{},[895,43753,43754,43756,43758,43760,43762],{},[2005,43755,2014],{"stretchy":2013},[898,43757,2151],{},[2005,43759,2234],{},[898,43761,207],{},[2133,43763,43764,43766],{},[2005,43765,2020],{"stretchy":2013},[2138,43767,2140],{},[2005,43769,2295],{"separator":2294},[5884,43771],{"width":15290},[9172,43773,43774,43776,43778],{},[898,43775,2797],{},[898,43777,2203],{},[2005,43779,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43781,2007],{},[2005,43783,2234],{},[2338,43785,43786,43788],{},[2138,43787,2287],{},[895,43789,43790,43792,43794],{},[898,43791,2151],{},[2005,43793,2234],{},[898,43795,207],{},[898,43797,1644],{"mathvariant":2385},[20768,43799],{"width":28081},[20768,43801,43802],{},[2297,43803,43804],{},"(2.12)",[902,43806,43807],{"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}",[198,43809,43811],{"id":43810},"znaménka-a-interpretace","Znaménka a interpretace",[724,43813,43814,43815,1343,43832,1343,43849,1343,43866,43883,43884,3159],{},"Za podmínek ",[883,43816,43818],{"className":43817},[886],[888,43819,43820],{"xmlns":890},[892,43821,43822,43830],{},[895,43823,43824,43826,43828],{},[898,43825,207],{},[2005,43827,3455],{},[2138,43829,2336],{},[902,43831,43090],{"encoding":904},[883,43833,43835],{"className":43834},[886],[888,43836,43837],{"xmlns":890},[892,43838,43839,43847],{},[895,43840,43841,43843,43845],{},[898,43842,2107],{},[2005,43844,3416],{},[2138,43846,2336],{},[902,43848,18820],{"encoding":904},[883,43850,43852],{"className":43851},[886],[888,43853,43854],{"xmlns":890},[892,43855,43856,43864],{},[895,43857,43858,43860,43862],{},[898,43859,2151],{},[2005,43861,3416],{},[2138,43863,2336],{},[902,43865,40265],{"encoding":904},[883,43867,43869],{"className":43868},[886],[888,43870,43871],{"xmlns":890},[892,43872,43873,43881],{},[895,43874,43875,43877,43879],{},[898,43876,2107],{},[2005,43878,3416],{},[898,43880,2203],{},[902,43882,43323],{"encoding":904}," platí (znaménka se ",[38,43885,43886],{},"nemění",[883,43888,43890],{"className":43889},[886],[888,43891,43892],{"xmlns":890,"display":28071},[892,43893,43894,43956],{},[895,43895,43896,43904,43906,43908,43910,43912,43920,43922,43924,43926,43928,43936,43938,43940,43942,43944,43952,43954],{},[9172,43897,43898,43900,43902],{},[898,43899,2797],{},[898,43901,207],{},[2005,43903,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43905,3416],{},[2138,43907,2336],{},[2005,43909,2295],{"separator":2294},[5884,43911],{"width":5886},[9172,43913,43914,43916,43918],{},[898,43915,2797],{},[898,43917,2107],{},[2005,43919,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43921,3416],{},[2138,43923,2336],{},[2005,43925,2295],{"separator":2294},[5884,43927],{"width":5886},[9172,43929,43930,43932,43934],{},[898,43931,2797],{},[898,43933,2151],{},[2005,43935,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43937,3455],{},[2138,43939,2336],{},[2005,43941,2295],{"separator":2294},[5884,43943],{"width":5886},[9172,43945,43946,43948,43950],{},[898,43947,2797],{},[898,43949,2203],{},[2005,43951,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,43953,3455],{},[2138,43955,12466],{},[902,43957,43958],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,43960,43961,44020],{},[123,43962,43963,2212,43966,43986,43987,44004,44005,1343,44018,1644],{},[38,43964,43965],{},"Kvantitativní smysl:",[883,43967,43969],{"className":43968},[886],[888,43970,43971],{"xmlns":890},[892,43972,43973,43983],{},[895,43974,43975],{},[9172,43976,43977,43979,43981],{},[898,43978,2797],{},[898,43980,2017],{},[2005,43982,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,43984,43985],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,43988,43990],{"className":43989},[886],[888,43991,43992],{"xmlns":890},[892,43993,43994,44002],{},[895,43995,43996],{},[2133,43997,43998,44000],{},[898,43999,2797],{},[898,44001,1868],{},[902,44003,42408],{"encoding":904}," při jednotkové změně parametru ",[883,44006,44008],{"className":44007},[886],[888,44009,44010],{"xmlns":890},[892,44011,44012,44016],{},[895,44013,44014],{},[898,44015,2017],{},[902,44017,2017],{"encoding":904},[614,44019,36965],{},[123,44021,44022,44025,44026,44043,44044,1644],{},[38,44023,44024],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,44027,44029],{"className":44028},[886],[888,44030,44031],{"xmlns":890},[892,44032,44033,44041],{},[895,44034,44035],{},[2133,44036,44037,44039],{},[898,44038,2797],{},[898,44040,1868],{},[902,44042,42408],{"encoding":904}," na růst ",[883,44045,44047],{"className":44046},[886],[888,44048,44049],{"xmlns":890},[892,44050,44051,44055],{},[895,44052,44053],{},[898,44054,2017],{},[902,44056,2017],{"encoding":904},[724,44058,44059,44060,44073,44074,43324,44091,3927],{},"Např. růst ",[883,44061,44063],{"className":44062},[886],[888,44064,44065],{"xmlns":890},[892,44066,44067,44071],{},[895,44068,44069],{},[898,44070,2151],{},[902,44072,2151],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,44075,44077],{"className":44076},[886],[888,44078,44079],{"xmlns":890},[892,44080,44081,44089],{},[895,44082,44083],{},[2133,44084,44085,44087],{},[898,44086,2797],{},[898,44088,1868],{},[902,44090,42408],{"encoding":904},[883,44092,44094],{"className":44093},[886],[888,44095,44096],{"xmlns":890},[892,44097,44098,44112],{},[895,44099,44100,44108,44110],{},[9172,44101,44102,44104,44106],{},[898,44103,2797],{},[898,44105,2151],{},[2005,44107,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,44109,3455],{},[2138,44111,2336],{},[902,44113,44114],{"encoding":904},"Q'_c \u003C 0",[724,44116,44117],{},[614,44118,44119,44120,44140,44141,44165,44166,44188,44189,1644],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,44121,44123],{"className":44122},[886],[888,44124,44125],{"xmlns":890},[892,44126,44127,44137],{},[895,44128,44129,44131,44133,44135],{},[898,44130,2151],{},[898,44132,2797],{},[2005,44134,2104],{},[898,44136,2203],{},[902,44138,44139],{"encoding":904},"cQ + d"," na strmější ",[883,44142,44144],{"className":44143},[886],[888,44145,44146],{"xmlns":890},[892,44147,44148,44162],{},[895,44149,44150,44156,44158,44160],{},[2281,44151,44152,44154],{},[898,44153,2151],{},[2138,44155,2287],{},[898,44157,2797],{},[2005,44159,2104],{},[898,44161,2203],{},[902,44163,44164],{"encoding":904},"c_1 Q + d"," (při ",[883,44167,44169],{"className":44168},[886],[888,44170,44171],{"xmlns":890},[892,44172,44173,44185],{},[895,44174,44175,44181,44183],{},[2281,44176,44177,44179],{},[898,44178,2151],{},[2138,44180,2287],{},[2005,44182,3416],{},[898,44184,2151],{},[902,44186,44187],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,44190,44192],{"className":44191},[886],[888,44193,44194],{"xmlns":890},[892,44195,44196,44206],{},[895,44197,44198,44204],{},[2133,44199,44200,44202],{},[898,44201,2797],{},[898,44203,1868],{},[2005,44205,42596],{},[902,44207,44208],{"encoding":904},"Q^E \\downarrow",[724,44210,44211,44212,44244,44245,1644],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,44213,44215],{"className":44214},[886],[888,44216,44217],{"xmlns":890},[892,44218,44219,44241],{},[895,44220,44221,44223,44225,44227,44235,44237,44239],{},[898,44222,2897],{"mathvariant":2385},[898,44224,2797],{},[2005,44226,2739],{},[9172,44228,44229,44231,44233],{},[898,44230,2797],{},[898,44232,2107],{},[2005,44234,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,44236,2995],{},[898,44238,2203],{},[898,44240,2107],{},[902,44242,44243],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,44246,44248],{"className":44247},[886],[888,44249,44250],{"xmlns":890},[892,44251,44252,44260],{},[895,44253,44254],{},[2133,44255,44256,44258],{},[898,44257,3946],{},[898,44259,1868],{},[902,44261,41471],{"encoding":904},[198,44263,44265,44266],{"id":44264},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,44267,44269],{"className":44268},[886],[888,44270,44271],{"xmlns":890},[892,44272,44273,44281],{},[895,44274,44275],{},[2133,44276,44277,44279],{},[898,44278,2797],{},[898,44280,1868],{},[902,44282,42408],{"encoding":904},[724,44284,44285,41660,44287,41695,44313,1644],{},[38,44286,37938],{},[883,44288,44290],{"className":44289},[886],[888,44291,44292],{"xmlns":890},[892,44293,44294,44310],{},[895,44295,44296,44298,44300,44302,44304,44306,44308],{},[898,44297,3946],{},[2005,44299,2007],{},[2005,44301,2234],{},[2138,44303,2182],{},[898,44305,2797],{},[2005,44307,2104],{},[2138,44309,5217],{},[902,44311,44312],{"encoding":904},"P = -3Q + 40",[883,44314,44316],{"className":44315},[886],[888,44317,44318],{"xmlns":890},[892,44319,44320,44334],{},[895,44321,44322,44324,44326,44328,44330,44332],{},[898,44323,3946],{},[2005,44325,2007],{},[2138,44327,5015],{},[898,44329,2797],{},[2005,44331,2104],{},[2138,44333,2871],{},[902,44335,44336],{"encoding":904},"P = 0{,}5Q + 10",[724,44338,44339,44341],{},[38,44340,37970],{}," Rovnovážné množství",[883,44343,44345],{"className":44344},[886],[888,44346,44347],{"xmlns":890,"display":28071},[892,44348,44349,44417],{},[895,44350,44351,44357,44359,44377,44379,44403,44405,44412,44414],{},[2133,44352,44353,44355],{},[898,44354,2797],{},[898,44356,1868],{},[2005,44358,2007],{},[2338,44360,44361,44369],{},[895,44362,44363,44365,44367],{},[898,44364,2107],{},[2005,44366,2234],{},[898,44368,2203],{},[895,44370,44371,44373,44375],{},[898,44372,2151],{},[2005,44374,2234],{},[898,44376,207],{},[2005,44378,2007],{},[2338,44380,44381,44389],{},[895,44382,44383,44385,44387],{},[2138,44384,5217],{},[2005,44386,2234],{},[2138,44388,2871],{},[895,44390,44391,44393,44395,44397,44399,44401],{},[2138,44392,5015],{},[2005,44394,2234],{},[2005,44396,2014],{"stretchy":2013},[2005,44398,2234],{},[2138,44400,2182],{},[2005,44402,2020],{"stretchy":2013},[2005,44404,2007],{},[2338,44406,44407,44409],{},[2138,44408,38024],{},[2138,44410,44411],{},"3,5",[2005,44413,2739],{},[2138,44415,44416],{},"8,571.",[902,44418,44419],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,44421,44422,44467],{},[38,44423,44424,44425,2680,44438,2694,44452,44466],{},"(a) Změna ",[883,44426,44428],{"className":44427},[886],[888,44429,44430],{"xmlns":890},[892,44431,44432,44436],{},[895,44433,44434],{},[898,44435,2151],{},[902,44437,2151],{"encoding":904},[883,44439,44441],{"className":44440},[886],[888,44442,44443],{"xmlns":890},[892,44444,44445,44449],{},[895,44446,44447],{},[2138,44448,5015],{},[902,44450,44451],{"encoding":904},"0{,}5",[883,44453,44455],{"className":44454},[886],[888,44456,44457],{"xmlns":890},[892,44458,44459,44463],{},[895,44460,44461],{},[2138,44462,19327],{},[902,44464,44465],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,44469,44471],{"className":44470},[886],[888,44472,44473],{"xmlns":890,"display":28071},[892,44474,44475,44552],{},[895,44476,44477,44485,44487,44489,44491,44493,44495,44521,44523,44525,44527,44529,44531,44541,44543,44545,44547,44549],{},[9172,44478,44479,44481,44483],{},[898,44480,2797],{},[898,44482,2151],{},[2005,44484,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,44486,2995],{},[898,44488,2203],{},[898,44490,2151],{},[2005,44492,2007],{},[2005,44494,2234],{},[2338,44496,44497,44505],{},[895,44498,44499,44501,44503],{},[898,44500,2107],{},[2005,44502,2234],{},[898,44504,2203],{},[895,44506,44507,44509,44511,44513,44515],{},[2005,44508,2014],{"stretchy":2013},[898,44510,2151],{},[2005,44512,2234],{},[898,44514,207],{},[2133,44516,44517,44519],{},[2005,44518,2020],{"stretchy":2013},[2138,44520,2140],{},[2297,44522,2995],{},[898,44524,2203],{},[898,44526,2151],{},[2005,44528,2007],{},[2005,44530,2234],{},[2338,44532,44533,44535],{},[2138,44534,38024],{},[2133,44536,44537,44539],{},[2138,44538,44411],{},[2138,44540,2140],{},[2005,44542,3185],{},[2138,44544,2802],{},[2005,44546,2739],{},[2005,44548,2234],{},[2138,44550,44551],{},"0,245.",[902,44553,44554],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,44556,44557,44558,1644],{},"Nové rovnovážné množství ",[883,44559,44561],{"className":44560},[886],[888,44562,44563],{"xmlns":890},[892,44564,44565,44590],{},[895,44566,44567,44575,44577,44580,44582,44585,44587],{},[9172,44568,44569,44571,44573],{},[898,44570,2797],{},[2138,44572,2287],{},[898,44574,1868],{},[2005,44576,2739],{},[2138,44578,44579],{},"8,571",[2005,44581,2234],{},[2138,44583,44584],{},"0,245",[2005,44586,2007],{},[2138,44588,44589],{},"8,326",[902,44591,44592],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,44594,44595,44680],{},[38,44596,44597,44598,1343,44618,1343,44640,1343,44660,1644],{},"(b) Současné změny ",[883,44599,44601],{"className":44600},[886],[888,44602,44603],{"xmlns":890},[892,44604,44605,44615],{},[895,44606,44607,44609,44611,44613],{},[898,44608,2203],{},[898,44610,207],{},[2005,44612,2007],{},[2138,44614,5015],{},[902,44616,44617],{"encoding":904},"da = 0{,}5",[883,44619,44621],{"className":44620},[886],[888,44622,44623],{"xmlns":890},[892,44624,44625,44637],{},[895,44626,44627,44629,44631,44633,44635],{},[898,44628,2203],{},[898,44630,2107],{},[2005,44632,2007],{},[2005,44634,2234],{},[2138,44636,2237],{},[902,44638,44639],{"encoding":904},"db = -5",[883,44641,44643],{"className":44642},[886],[888,44644,44645],{"xmlns":890},[892,44646,44647,44657],{},[895,44648,44649,44651,44653,44655],{},[898,44650,2203],{},[898,44652,2151],{},[2005,44654,2007],{},[2138,44656,2802],{},[902,44658,44659],{"encoding":904},"dc = 0{,}1",[883,44661,44663],{"className":44662},[886],[888,44664,44665],{"xmlns":890},[892,44666,44667,44677],{},[895,44668,44669,44671,44673,44675],{},[898,44670,2203],{},[898,44672,2203],{},[2005,44674,2007],{},[2138,44676,2287],{},[902,44678,44679],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,44682,44684],{"className":44683},[886],[888,44685,44686],{"xmlns":890,"display":28071},[892,44687,44688,44831],{},[20760,44689,44690,44772,44808],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,44691,44692,44702],{},[20768,44693,44694],{},[2334,44695,44696],{"scriptlevel":2336,"displaystyle":2294},[895,44697,44698,44700],{},[898,44699,2897],{"mathvariant":2385},[898,44701,2797],{},[20768,44703,44704],{},[2334,44705,44706],{"scriptlevel":2336,"displaystyle":2294},[895,44707,44708,44710,44712,44722,44724,44726,44728,44734,44736,44738,44740,44742,44744,44746,44756,44758,44760,44762,44768,44770],{},[895,44709],{},[2005,44711,2739],{},[2338,44713,44714,44716],{},[2138,44715,38024],{},[2133,44717,44718,44720],{},[2138,44719,44411],{},[2138,44721,2140],{},[2005,44723,3185],{},[2138,44725,5015],{},[2005,44727,2104],{},[2338,44729,44730,44732],{},[2138,44731,2287],{},[2138,44733,44411],{},[2005,44735,3185],{},[2005,44737,2014],{"stretchy":2013},[2005,44739,2234],{},[2138,44741,2237],{},[2005,44743,2020],{"stretchy":2013},[2005,44745,2234],{},[2338,44747,44748,44750],{},[2138,44749,38024],{},[2133,44751,44752,44754],{},[2138,44753,44411],{},[2138,44755,2140],{},[2005,44757,3185],{},[2138,44759,2802],{},[2005,44761,2234],{},[2338,44763,44764,44766],{},[2138,44765,2287],{},[2138,44767,44411],{},[2005,44769,3185],{},[2138,44771,2287],{},[20765,44773,44774,44780],{},[20768,44775,44776],{},[2334,44777,44778],{"scriptlevel":2336,"displaystyle":2294},[895,44779],{},[20768,44781,44782],{},[2334,44783,44784],{"scriptlevel":2336,"displaystyle":2294},[895,44785,44786,44788,44790,44793,44795,44798,44800,44803,44805],{},[895,44787],{},[2005,44789,2007],{},[2138,44791,44792],{},"1,2245",[2005,44794,2234],{},[2138,44796,44797],{},"1,4286",[2005,44799,2234],{},[2138,44801,44802],{},"0,2449",[2005,44804,2234],{},[2138,44806,44807],{},"0,2857",[20765,44809,44810,44816],{},[20768,44811,44812],{},[2334,44813,44814],{"scriptlevel":2336,"displaystyle":2294},[895,44815],{},[20768,44817,44818],{},[2334,44819,44820],{"scriptlevel":2336,"displaystyle":2294},[895,44821,44822,44824,44826,44828],{},[895,44823],{},[2005,44825,2739],{},[2005,44827,2234],{},[2138,44829,44830],{},"0,735.",[902,44832,44833],{"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}",[724,44835,30070,44836,1644],{},[883,44837,44839],{"className":44838},[886],[888,44840,44841],{"xmlns":890},[892,44842,44843,44867],{},[895,44844,44845,44853,44855,44857,44859,44862,44864],{},[9172,44846,44847,44849,44851],{},[898,44848,2797],{},[2138,44850,2287],{},[898,44852,1868],{},[2005,44854,2739],{},[2138,44856,44579],{},[2005,44858,2234],{},[2138,44860,44861],{},"0,735",[2005,44863,2007],{},[2138,44865,44866],{},"7,836",[902,44868,44869],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[3876,44871,44872],{},[724,44873,44874,44876,44877,44900,44901,44923],{},[883,44875,4418],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,44878,44880],{"className":44879},[886],[888,44881,44882],{"xmlns":890},[892,44883,44884,44897],{},[895,44885,44886,44888,44890,44892,44894],{},[898,44887,2897],{"mathvariant":2385},[898,44889,2797],{},[2005,44891,2739],{},[2005,44893,2234],{},[2138,44895,44896],{},"2,69",[902,44898,44899],{"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 ",[883,44902,44904],{"className":44903},[886],[888,44905,44906],{"xmlns":890},[892,44907,44908,44920],{},[895,44909,44910,44912,44914,44916,44918],{},[898,44911,2897],{"mathvariant":2385},[898,44913,2797],{},[2005,44915,2739],{},[2005,44917,2234],{},[2138,44919,44861],{},[902,44921,44922],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,44925,44926],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[36975,44928],{},[115,44930,820],{"id":11789},[3876,44932,44933],{},[724,44934,44935,3883,44937,10030,44940,12134,44956,10030,44959,44975,44976,1644],{},[883,44936,4164],{},[38,44938,44939],{},"Přebytek spotřebitele",[883,44941,44943],{"className":44942},[886],[888,44944,44945],{"xmlns":890},[892,44946,44947,44953],{},[895,44948,44949,44951],{},[898,44950,1852],{},[898,44952,8679],{},[902,44954,44955],{"encoding":904},"CS",[38,44957,44958],{},"přebytek výrobce",[883,44960,44962],{"className":44961},[886],[888,44963,44964],{"xmlns":890},[892,44965,44966,44972],{},[895,44967,44968,44970],{},[898,44969,3946],{},[898,44971,8679],{},[902,44973,44974],{"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 ",[207,44977,44979],{"className":44978,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,44981,44982],{},[2568,44983],{"alt":44984,"className":44985,"src":44986},"imek-prebytky-cs-ps",[210,2572],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,44988,44989,10030,44991,44994],{},[38,44990,44939],{},[614,44992,44993],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,44996,44998],{"className":44997},[886],[888,44999,45000],{"xmlns":890,"display":28071},[892,45001,45002,45079],{},[20760,45003,45004],{"width":28076},[20765,45005,45006,45008,45072,45074],{},[20768,45007],{"width":28081},[20768,45009,45010],{},[895,45011,45012,45014,45016,45018,45024,45026,45028,45040,45042,45044,45046,45048,45050,45052,45054,45056,45062,45064,45070],{},[898,45013,1852],{},[898,45015,8679],{},[2005,45017,2014],{"stretchy":2013},[2281,45019,45020,45022],{},[898,45021,2797],{},[2138,45023,2336],{},[2005,45025,2020],{"stretchy":2013},[2005,45027,2007],{},[9172,45029,45030,45032,45034],{},[2005,45031,11174],{},[2138,45033,2336],{},[2281,45035,45036,45038],{},[898,45037,2797],{},[2138,45039,2336],{},[898,45041,1860],{},[2005,45043,2014],{"stretchy":2013},[898,45045,2797],{},[2005,45047,2020],{"stretchy":2013},[2297,45049,2995],{},[898,45051,2203],{},[898,45053,2797],{},[2005,45055,2234],{},[2281,45057,45058,45060],{},[898,45059,3946],{},[2138,45061,2336],{},[2297,45063,2995],{},[2281,45065,45066,45068],{},[898,45067,2797],{},[2138,45069,2336],{},[898,45071,1644],{"mathvariant":2385},[20768,45073],{"width":28081},[20768,45075,45076],{},[2297,45077,45078],{},"(2.14)",[902,45080,45081],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,45083,45084,10030,45087,45090],{},[38,45085,45086],{},"Přebytek výrobce",[614,45088,45089],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,45092,45094],{"className":45093},[886],[888,45095,45096],{"xmlns":890,"display":28071},[892,45097,45098,45175],{},[20760,45099,45100],{"width":28076},[20765,45101,45102,45104,45168,45170],{},[20768,45103],{"width":28081},[20768,45105,45106],{},[895,45107,45108,45110,45112,45114,45120,45122,45124,45130,45132,45138,45140,45152,45154,45156,45158,45160,45162,45164,45166],{},[898,45109,3946],{},[898,45111,8679],{},[2005,45113,2014],{"stretchy":2013},[2281,45115,45116,45118],{},[898,45117,2797],{},[2138,45119,2336],{},[2005,45121,2020],{"stretchy":2013},[2005,45123,2007],{},[2281,45125,45126,45128],{},[898,45127,3946],{},[2138,45129,2336],{},[2297,45131,2995],{},[2281,45133,45134,45136],{},[898,45135,2797],{},[2138,45137,2336],{},[2005,45139,2234],{},[9172,45141,45142,45144,45146],{},[2005,45143,11174],{},[2138,45145,2336],{},[2281,45147,45148,45150],{},[898,45149,2797],{},[2138,45151,2336],{},[898,45153,8679],{},[2005,45155,2014],{"stretchy":2013},[898,45157,2797],{},[2005,45159,2020],{"stretchy":2013},[2297,45161,2995],{},[898,45163,2203],{},[898,45165,2797],{},[898,45167,1644],{"mathvariant":2385},[20768,45169],{"width":28081},[20768,45171,45172],{},[2297,45173,45174],{},"(2.15)",[902,45176,45177],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,45179,45180,45181,1644],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,45182,45184],{"className":45183,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[36975,45186],{},[115,45188,45190],{"id":45189},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,45192,45193,45224,45229,45235,45263,45269,45298,45304,45384,45410],{},[123,45194,45195,45197,45198,45223],{},[38,45196,37933],{}," — lineární poptávka ",[883,45199,45201],{"className":45200},[886],[888,45202,45203],{"xmlns":890},[892,45204,45205,45221],{},[895,45206,45207,45209,45211,45213,45215,45217,45219],{},[898,45208,3946],{},[2005,45210,2007],{},[2005,45212,2234],{},[2138,45214,2140],{},[898,45216,2797],{},[2005,45218,2104],{},[2138,45220,3134],{},[902,45222,37965],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,45225,45226,45228],{},[38,45227,38247],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,45230,45231,45234],{},[38,45232,45233],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,45236,45237,45239,45240,1644],{},[38,45238,40794],{}," — lineární nabídka ",[883,45241,45243],{"className":45242},[886],[888,45244,45245],{"xmlns":890},[892,45246,45247,45261],{},[895,45248,45249,45251,45253,45255,45257,45259],{},[898,45250,3946],{},[2005,45252,2007],{},[2138,45254,5015],{},[898,45256,2797],{},[2005,45258,2104],{},[2138,45260,5010],{},[902,45262,40823],{"encoding":904},[123,45264,45265,45268],{},[38,45266,45267],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,45270,45271,45274,45275,1644],{},[38,45272,45273],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,45276,45278],{"className":45277},[886],[888,45279,45280],{"xmlns":890},[892,45281,45282,45296],{},[895,45283,45284,45286,45288,45290,45292,45294],{},[898,45285,1868],{},[2005,45287,2495],{"stretchy":2013},[2138,45289,2360],{},[2005,45291,2295],{"separator":2294},[2138,45293,41941],{},[2005,45295,2510],{"stretchy":2013},[902,45297,41969],{"encoding":904},[123,45299,45300,45303],{},[38,45301,45302],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,45305,45306,45309,45310,45327,45328,1343,45353,45380,45381,2959],{},[38,45307,45308],{},"Příklad 2.9"," — daň ",[883,45311,45313],{"className":45312},[886],[888,45314,45315],{"xmlns":890},[892,45316,45317,45325],{},[895,45318,45319,45321,45323],{},[898,45320,2783],{},[2005,45322,2007],{},[2138,45324,2244],{},[902,45326,41273],{"encoding":904}," na výrobce; rozklad ",[883,45329,45331],{"className":45330},[886],[888,45332,45333],{"xmlns":890},[892,45334,45335,45351],{},[895,45336,45337,45347,45349],{},[2281,45338,45339,45341],{},[898,45340,2783],{},[895,45342,45343,45345],{},[898,45344,42682],{},[898,45346,724],{},[2005,45348,2007],{},[2138,45350,2140],{},[902,45352,42981],{"encoding":904},[883,45354,45356],{"className":45355},[886],[888,45357,45358],{"xmlns":890},[892,45359,45360,45378],{},[895,45361,45362,45374,45376],{},[2281,45363,45364,45366],{},[898,45365,2783],{},[895,45367,45368,45370,45372],{},[898,45369,42705],{},[898,45371,2003],{},[898,45373,12047],{},[2005,45375,2007],{},[2138,45377,2360],{},[902,45379,43010],{"encoding":904},". (Viz ",[207,45382,42726],{"className":45383,"dataFsResolvedFilePath":809,"href":810},[210],[123,45385,45386,45309,45389,45406,45407,2959],{},[38,45387,45388],{},"Příklad 2.10",[883,45390,45392],{"className":45391},[886],[888,45393,45394],{"xmlns":890},[892,45395,45396,45404],{},[895,45397,45398,45400,45402],{},[898,45399,2783],{},[2005,45401,2007],{},[2138,45403,2244],{},[902,45405,41273],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,45408,42726],{"className":45409,"dataFsResolvedFilePath":809,"href":810},[210],[123,45411,45412,45415],{},[38,45413,45414],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[36975,45417],{},[115,45419,45421],{"id":45420},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,45423,45425],{"id":45424},"základní-analýza-poptávky","Základní analýza poptávky",[724,45427,45428,45431,45432,45467,45468,45494],{},[38,45429,45430],{},"2.1"," Je dána poptávka ",[883,45433,45435],{"className":45434},[886],[888,45436,45437],{"xmlns":890},[892,45438,45439,45464],{},[895,45440,45441,45443,45445,45447,45449,45451,45453,45455,45458,45460,45462],{},[898,45442,2797],{},[2005,45444,2007],{},[898,45446,1860],{},[2005,45448,2014],{"stretchy":2013},[898,45450,3946],{},[2005,45452,2020],{"stretchy":2013},[2005,45454,2007],{},[2138,45456,45457],{},"75",[2005,45459,2234],{},[2138,45461,2237],{},[898,45463,3946],{},[902,45465,45466],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,45469,45471],{"className":45470},[886],[888,45472,45473],{"xmlns":890},[892,45474,45475,45491],{},[895,45476,45477,45479,45481,45483,45485,45487,45489],{},[2138,45478,2336],{},[2005,45480,2295],{"separator":2294},[2138,45482,2237],{},[2005,45484,2295],{"separator":2294},[2138,45486,2871],{},[2005,45488,2295],{"separator":2294},[2138,45490,36249],{},[902,45492,45493],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,45496,45497,45500,45501,45519,45520,3159],{},[38,45498,45499],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,45502,45504],{"className":45503},[886],[888,45505,45506],{"xmlns":890},[892,45507,45508,45516],{},[895,45509,45510,45512,45514],{},[898,45511,3946],{},[2005,45513,2295],{"separator":2294},[898,45515,2797],{},[902,45517,45518],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,45521,45523],{"className":45522},[886],[888,45524,45525],{"xmlns":890},[892,45526,45527,45543],{},[895,45528,45529,45531,45533,45535,45537,45539,45541],{},[898,45530,207],{},[2005,45532,2295],{"separator":2294},[898,45534,2107],{},[2005,45536,2295],{"separator":2294},[898,45538,2151],{},[2005,45540,3416],{},[2138,45542,2336],{},[902,45544,45545],{"encoding":904},"a, b, c > 0",[120,45547,45548,45581,45612,45647,45678,45713],{},[123,45549,45550,45551],{},"(a) ",[883,45552,45554],{"className":45553},[886],[888,45555,45556],{"xmlns":890},[892,45557,45558,45578],{},[895,45559,45560,45562,45564],{},[898,45561,2797],{},[2005,45563,2007],{},[2334,45565,45566],{"scriptlevel":2336,"displaystyle":2294},[2338,45567,45568,45570],{},[898,45569,207],{},[895,45571,45572,45574,45576],{},[898,45573,3946],{},[2005,45575,2104],{},[898,45577,2151],{},[902,45579,45580],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,45582,45583,45584],{},"(b) ",[883,45585,45587],{"className":45586},[886],[888,45588,45589],{"xmlns":890},[892,45590,45591,45609],{},[895,45592,45593,45595,45597],{},[898,45594,2797],{},[2005,45596,2007],{},[8123,45598,45599],{},[895,45600,45601,45603,45605,45607],{},[898,45602,207],{},[2005,45604,2234],{},[898,45606,2107],{},[898,45608,2797],{},[902,45610,45611],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,45613,45614,45615],{},"(c) ",[883,45616,45618],{"className":45617},[886],[888,45619,45620],{"xmlns":890},[892,45621,45622,45644],{},[895,45623,45624,45626,45628],{},[898,45625,2797],{},[2005,45627,2007],{},[2334,45629,45630],{"scriptlevel":2336,"displaystyle":2294},[2338,45631,45632,45642],{},[895,45633,45634,45636,45638],{},[898,45635,207],{},[2005,45637,2234],{},[8123,45639,45640],{},[898,45641,3946],{},[898,45643,2107],{},[902,45645,45646],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,45648,45649,45650],{},"(d) ",[883,45651,45653],{"className":45652},[886],[888,45654,45655],{"xmlns":890},[892,45656,45657,45675],{},[895,45658,45659,45661,45663,45665,45667,45669],{},[898,45660,3946],{},[2005,45662,2007],{},[898,45664,207],{},[2005,45666,2234],{},[898,45668,2107],{},[2133,45670,45671,45673],{},[898,45672,2797],{},[2138,45674,2140],{},[902,45676,45677],{"encoding":904},"P = a - bQ^2",[123,45679,45680,45681],{},"(e) ",[883,45682,45684],{"className":45683},[886],[888,45685,45686],{"xmlns":890},[892,45687,45688,45710],{},[895,45689,45690,45692,45694,45696,45706,45708],{},[898,45691,2797],{},[2005,45693,2007],{},[898,45695,2107],{},[2133,45697,45698,45700],{},[898,45699,3946],{},[895,45701,45702,45704],{},[2005,45703,2234],{},[898,45705,207],{},[2005,45707,2104],{},[898,45709,2151],{},[902,45711,45712],{"encoding":904},"Q = bP^{-a} + c",[123,45714,45715,45716],{},"(f) ",[883,45717,45719],{"className":45718},[886],[888,45720,45721],{"xmlns":890},[892,45722,45723,45746],{},[895,45724,45725,45727,45729,45731,45733],{},[898,45726,2797],{},[2005,45728,2007],{},[898,45730,207],{},[2005,45732,3185],{},[2133,45734,45735,45738],{},[898,45736,45737],{},"e",[895,45739,45740,45742,45744],{},[2005,45741,2234],{},[898,45743,2107],{},[898,45745,3946],{},[902,45747,45748],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,45750,45751,45754],{},[38,45752,45753],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,45756,45757,45760,45763],{},[123,45758,45759],{},"(a) Cena substitutu.",[123,45761,45762],{},"(b) Cena komplementu.",[123,45764,45765],{},"(c) Výdaje na reklamu.",[724,45767,45768,45431,45770,45804,45805,45833],{},[38,45769,24647],{},[883,45771,45773],{"className":45772},[886],[888,45774,45775],{"xmlns":890},[892,45776,45777,45801],{},[895,45778,45779,45781,45783,45785,45787,45789,45791,45793,45795,45797,45799],{},[898,45780,3946],{},[2005,45782,2007],{},[898,45784,1860],{},[2005,45786,2014],{"stretchy":2013},[898,45788,2797],{},[2005,45790,2020],{"stretchy":2013},[2005,45792,2007],{},[2138,45794,3517],{},[2005,45796,2234],{},[2138,45798,2140],{},[898,45800,2797],{},[902,45802,45803],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,45806,45808],{"className":45807},[886],[888,45809,45810],{"xmlns":890},[892,45811,45812,45830],{},[895,45813,45814,45816,45818,45824,45826,45828],{},[898,45815,3946],{},[2005,45817,2007],{},[2133,45819,45820,45822],{},[898,45821,1860],{},[2005,45823,4360],{},[2005,45825,2014],{"stretchy":2013},[898,45827,2797],{},[2005,45829,2020],{"stretchy":2013},[902,45831,45832],{"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.",[724,45835,45836,45839],{},[38,45837,45838],{},"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:",[120,45841,45842,45926,46002,46088,46176],{},[123,45843,45550,45844,1343,45884,1644],{},[883,45845,45847],{"className":45846},[886],[888,45848,45849],{"xmlns":890},[892,45850,45851,45881],{},[895,45852,45853,45859,45861,45863,45865,45867,45873,45875],{},[2281,45854,45855,45857],{},[898,45856,1844],{},[2138,45858,2287],{},[2005,45860,2007],{},[2138,45862,9041],{},[2005,45864,2234],{},[2138,45866,2360],{},[2281,45868,45869,45871],{},[898,45870,1836],{},[2138,45872,2287],{},[2005,45874,2104],{},[2281,45876,45877,45879],{},[898,45878,1836],{},[2138,45880,2140],{},[902,45882,45883],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,45885,45887],{"className":45886},[886],[888,45888,45889],{"xmlns":890},[892,45890,45891,45923],{},[895,45892,45893,45899,45901,45903,45905,45907,45913,45915,45917],{},[2281,45894,45895,45897],{},[898,45896,1844],{},[2138,45898,2140],{},[2005,45900,2007],{},[2138,45902,2871],{},[2005,45904,2104],{},[2138,45906,2140],{},[2281,45908,45909,45911],{},[898,45910,1836],{},[2138,45912,2287],{},[2005,45914,2234],{},[2138,45916,2360],{},[2281,45918,45919,45921],{},[898,45920,1836],{},[2138,45922,2140],{},[902,45924,45925],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,45927,45583,45928,1343,45970,1644],{},[883,45929,45931],{"className":45930},[886],[888,45932,45933],{"xmlns":890},[892,45934,45935,45967],{},[895,45936,45937,45943,45945,45947,45949,45951,45957,45959,45961],{},[2281,45938,45939,45941],{},[898,45940,1844],{},[2138,45942,2287],{},[2005,45944,2007],{},[2138,45946,3128],{},[2005,45948,2234],{},[2138,45950,2871],{},[2281,45952,45953,45955],{},[898,45954,1836],{},[2138,45956,2287],{},[2005,45958,2234],{},[2138,45960,2244],{},[2281,45962,45963,45965],{},[898,45964,1836],{},[2138,45966,2140],{},[902,45968,45969],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,45971,45973],{"className":45972},[886],[888,45974,45975],{"xmlns":890},[892,45976,45977,45999],{},[895,45978,45979,45985,45987,45989,45991,45993],{},[2281,45980,45981,45983],{},[898,45982,1844],{},[2138,45984,2140],{},[2005,45986,2007],{},[2138,45988,36249],{},[2005,45990,2234],{},[2138,45992,2871],{},[2281,45994,45995,45997],{},[898,45996,1836],{},[2138,45998,2140],{},[902,46000,46001],{"encoding":904},"B_2 = 15 - 10A_2",[123,46003,45614,46004,1343,46046,1644],{},[883,46005,46007],{"className":46006},[886],[888,46008,46009],{"xmlns":890},[892,46010,46011,46043],{},[895,46012,46013,46019,46021,46023,46025,46027,46033,46035,46037],{},[2281,46014,46015,46017],{},[898,46016,1844],{},[2138,46018,2287],{},[2005,46020,2007],{},[2138,46022,38024],{},[2005,46024,2234],{},[2138,46026,2140],{},[2281,46028,46029,46031],{},[898,46030,1836],{},[2138,46032,2287],{},[2005,46034,2234],{},[2138,46036,2360],{},[2281,46038,46039,46041],{},[898,46040,1836],{},[2138,46042,2140],{},[902,46044,46045],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,46047,46049],{"className":46048},[886],[888,46050,46051],{"xmlns":890},[892,46052,46053,46085],{},[895,46054,46055,46061,46063,46065,46067,46069,46075,46077,46079],{},[2281,46056,46057,46059],{},[898,46058,1844],{},[2138,46060,2140],{},[2005,46062,2007],{},[2138,46064,36249],{},[2005,46066,2104],{},[2138,46068,2140],{},[2281,46070,46071,46073],{},[898,46072,1836],{},[2138,46074,2287],{},[2005,46076,2234],{},[2138,46078,2140],{},[2281,46080,46081,46083],{},[898,46082,1836],{},[2138,46084,2140],{},[902,46086,46087],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,46089,45649,46090,1343,46134,1644],{},[883,46091,46093],{"className":46092},[886],[888,46094,46095],{"xmlns":890},[892,46096,46097,46131],{},[895,46098,46099,46105,46107,46109,46111,46113,46115,46121,46123,46125],{},[2281,46100,46101,46103],{},[898,46102,1844],{},[2138,46104,2287],{},[2005,46106,2007],{},[2005,46108,2234],{},[2138,46110,9041],{},[2005,46112,2234],{},[2138,46114,2140],{},[2281,46116,46117,46119],{},[898,46118,1836],{},[2138,46120,2287],{},[2005,46122,2104],{},[2138,46124,2182],{},[2281,46126,46127,46129],{},[898,46128,1836],{},[2138,46130,2140],{},[902,46132,46133],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,46135,46137],{"className":46136},[886],[888,46138,46139],{"xmlns":890},[892,46140,46141,46173],{},[895,46142,46143,46149,46151,46153,46155,46157,46163,46165,46167],{},[2281,46144,46145,46147],{},[898,46146,1844],{},[2138,46148,2140],{},[2005,46150,2007],{},[2138,46152,2871],{},[2005,46154,2104],{},[2138,46156,2140],{},[2281,46158,46159,46161],{},[898,46160,1836],{},[2138,46162,2287],{},[2005,46164,2234],{},[2138,46166,2140],{},[2281,46168,46169,46171],{},[898,46170,1836],{},[2138,46172,2140],{},[902,46174,46175],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,46177,45680,46178,1343,46220,1644],{},[883,46179,46181],{"className":46180},[886],[888,46182,46183],{"xmlns":890},[892,46184,46185,46217],{},[895,46186,46187,46193,46195,46197,46199,46201,46207,46209,46211],{},[2281,46188,46189,46191],{},[898,46190,1844],{},[2138,46192,2287],{},[2005,46194,2007],{},[2138,46196,9041],{},[2005,46198,2104],{},[2138,46200,2140],{},[2281,46202,46203,46205],{},[898,46204,1836],{},[2138,46206,2287],{},[2005,46208,2104],{},[2138,46210,2360],{},[2281,46212,46213,46215],{},[898,46214,1836],{},[2138,46216,2140],{},[902,46218,46219],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,46221,46223],{"className":46222},[886],[888,46224,46225],{"xmlns":890},[892,46226,46227,46259],{},[895,46228,46229,46235,46237,46239,46241,46243,46249,46251,46253],{},[2281,46230,46231,46233],{},[898,46232,1844],{},[2138,46234,2140],{},[2005,46236,2007],{},[2138,46238,5217],{},[2005,46240,2234],{},[2138,46242,2182],{},[2281,46244,46245,46247],{},[898,46246,1836],{},[2138,46248,2287],{},[2005,46250,2104],{},[2138,46252,2237],{},[2281,46254,46255,46257],{},[898,46256,1836],{},[2138,46258,2140],{},[902,46260,46261],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,46263,46265],{"id":46264},"základní-analýza-nabídky","Základní analýza nabídky",[724,46267,46268,46271,46272,46306,46307,46329],{},[38,46269,46270],{},"2.6"," Je dána nabídka ",[883,46273,46275],{"className":46274},[886],[888,46276,46277],{"xmlns":890},[892,46278,46279,46303],{},[895,46280,46281,46283,46285,46287,46289,46291,46293,46295,46297,46299,46301],{},[898,46282,3946],{},[2005,46284,2007],{},[898,46286,8679],{},[2005,46288,2014],{"stretchy":2013},[898,46290,2797],{},[2005,46292,2020],{"stretchy":2013},[2005,46294,2007],{},[2138,46296,9041],{},[2005,46298,2104],{},[2138,46300,2847],{},[898,46302,2797],{},[902,46304,46305],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,46308,46310],{"className":46309},[886],[888,46311,46312],{"xmlns":890},[892,46313,46314,46326],{},[895,46315,46316,46318,46320,46322,46324],{},[2138,46317,5010],{},[2005,46319,2295],{"separator":2294},[2138,46321,38024],{},[2005,46323,2295],{"separator":2294},[2138,46325,15044],{},[902,46327,46328],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,46331,46332,46335,46336,46353],{},[38,46333,46334],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,46337,46339],{"className":46338},[886],[888,46340,46341],{"xmlns":890},[892,46342,46343,46351],{},[895,46344,46345,46347,46349],{},[898,46346,3946],{},[2005,46348,2295],{"separator":2294},[898,46350,2797],{},[902,46352,45518],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,46355,46356,46382,46410,46443,46477,46513],{},[123,46357,45550,46358],{},[883,46359,46361],{"className":46360},[886],[888,46362,46363],{"xmlns":890},[892,46364,46365,46379],{},[895,46366,46367,46369,46371,46373,46375,46377],{},[898,46368,3946],{},[2005,46370,2007],{},[2138,46372,38024],{},[2005,46374,2104],{},[2138,46376,2140],{},[898,46378,2797],{},[902,46380,46381],{"encoding":904},"P = 30 + 2Q",[123,46383,45583,46384],{},[883,46385,46387],{"className":46386},[886],[888,46388,46389],{"xmlns":890},[892,46390,46391,46407],{},[895,46392,46393,46395,46397,46399,46401,46403,46405],{},[898,46394,2797],{},[2005,46396,2007],{},[2005,46398,2234],{},[2138,46400,2182],{},[2005,46402,2104],{},[2138,46404,3517],{},[898,46406,3946],{},[902,46408,46409],{"encoding":904},"Q = -3 + 12P",[123,46411,45614,46412],{},[883,46413,46415],{"className":46414},[886],[888,46416,46417],{"xmlns":890},[892,46418,46419,46441],{},[895,46420,46421,46423,46425,46431,46433,46435,46437,46439],{},[898,46422,3946],{},[2005,46424,2007],{},[2133,46426,46427,46429],{},[898,46428,2797],{},[2138,46430,2140],{},[2005,46432,2104],{},[2138,46434,22952],{},[898,46436,2797],{},[2005,46438,2104],{},[2138,46440,32551],{},[902,46442,41727],{"encoding":904},[123,46444,45649,46445],{},[883,46446,46448],{"className":46447},[886],[888,46449,46450],{"xmlns":890},[892,46451,46452,46474],{},[895,46453,46454,46456,46458,46464,46466,46468,46470,46472],{},[898,46455,3946],{},[2005,46457,2007],{},[2133,46459,46460,46462],{},[898,46461,2797],{},[2138,46463,2140],{},[2005,46465,2104],{},[2138,46467,2140],{},[898,46469,2797],{},[2005,46471,2104],{},[2138,46473,3517],{},[902,46475,46476],{"encoding":904},"P = Q^2 + 2Q + 12",[123,46478,45680,46479],{},[883,46480,46482],{"className":46481},[886],[888,46483,46484],{"xmlns":890},[892,46485,46486,46510],{},[895,46487,46488,46490,46492,46494,46496,46498,46500,46502,46504],{},[898,46489,2797],{},[2005,46491,2007],{},[2138,46493,8809],{},[2005,46495,2104],{},[2138,46497,2237],{},[898,46499,3946],{},[2005,46501,2104],{},[2138,46503,2802],{},[2133,46505,46506,46508],{},[898,46507,3946],{},[2138,46509,2140],{},[902,46511,46512],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,46514,45715,46515],{},[883,46516,46518],{"className":46517},[886],[888,46519,46520],{"xmlns":890},[892,46521,46522,46547],{},[895,46523,46524,46526,46528,46530,46532,46534,46536,46538,46541],{},[898,46525,2797],{},[2005,46527,2007],{},[2138,46529,24206],{},[2005,46531,2104],{},[2138,46533,2802],{},[898,46535,3946],{},[2005,46537,2104],{},[2138,46539,46540],{},"0,004",[2133,46542,46543,46545],{},[898,46544,3946],{},[2138,46546,2140],{},[902,46548,46549],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,46551,46552,46555],{},[38,46553,46554],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,46557,46558,46561,46564,46567],{},[123,46559,46560],{},"(a) Sníží ceny surovin — vstupů.",[123,46562,46563],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,46565,46566],{},"(c) Zvýší ceny všech energií.",[123,46568,46569],{},"(d) Sníží daňové odvody státu.",[724,46571,46572,46271,46574,46608,46609,46637],{},[38,46573,42954],{},[883,46575,46577],{"className":46576},[886],[888,46578,46579],{"xmlns":890},[892,46580,46581,46605],{},[895,46582,46583,46585,46587,46589,46591,46593,46595,46597,46599,46601,46603],{},[898,46584,3946],{},[2005,46586,2007],{},[898,46588,8679],{},[2005,46590,2014],{"stretchy":2013},[898,46592,2797],{},[2005,46594,2020],{"stretchy":2013},[2005,46596,2007],{},[2138,46598,5015],{},[898,46600,2797],{},[2005,46602,2104],{},[2138,46604,36249],{},[902,46606,46607],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,46610,46612],{"className":46611},[886],[888,46613,46614],{"xmlns":890},[892,46615,46616,46634],{},[895,46617,46618,46620,46622,46628,46630,46632],{},[898,46619,3946],{},[2005,46621,2007],{},[2133,46623,46624,46626],{},[898,46625,8679],{},[2005,46627,4360],{},[2005,46629,2014],{"stretchy":2013},[898,46631,2797],{},[2005,46633,2020],{"stretchy":2013},[902,46635,46636],{"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.",[198,46639,41330],{"id":46640},"tržní-rovnováha-1",[724,46642,46643,46645,46646,46663,46664,2713],{},[38,46644,43014],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,46647,46649],{"className":46648},[886],[888,46650,46651],{"xmlns":890},[892,46652,46653,46661],{},[895,46654,46655],{},[2133,46656,46657,46659],{},[898,46658,2797],{},[898,46660,1868],{},[902,46662,42408],{"encoding":904}," a rovnovážnou cenu ",[883,46665,46667],{"className":46666},[886],[888,46668,46669],{"xmlns":890},[892,46670,46671,46679],{},[895,46672,46673],{},[2133,46674,46675,46677],{},[898,46676,3946],{},[898,46678,1868],{},[902,46680,41471],{"encoding":904},[120,46682,46683,46736,46787,46846],{},[123,46684,45550,46685,1343,46712,1644],{},[883,46686,46688],{"className":46687},[886],[888,46689,46690],{"xmlns":890},[892,46691,46692,46709],{},[895,46693,46694,46696,46698,46700,46702,46704,46706],{},[898,46695,3946],{},[2005,46697,2007],{},[2005,46699,2234],{},[2138,46701,2237],{},[898,46703,2797],{},[2005,46705,2104],{},[2138,46707,46708],{},"80",[902,46710,46711],{"encoding":904},"P = -5Q + 80",[883,46713,46715],{"className":46714},[886],[888,46716,46717],{"xmlns":890},[892,46718,46719,46733],{},[895,46720,46721,46723,46725,46727,46729,46731],{},[898,46722,3946],{},[2005,46724,2007],{},[2138,46726,2140],{},[898,46728,2797],{},[2005,46730,2104],{},[2138,46732,2871],{},[902,46734,46735],{"encoding":904},"P = 2Q + 10",[123,46737,45583,46738,1343,46764,1644],{},[883,46739,46741],{"className":46740},[886],[888,46742,46743],{"xmlns":890},[892,46744,46745,46761],{},[895,46746,46747,46749,46751,46753,46755,46757,46759],{},[898,46748,2797],{},[2005,46750,2007],{},[2005,46752,2234],{},[2138,46754,5015],{},[898,46756,3946],{},[2005,46758,2104],{},[2138,46760,5010],{},[902,46762,46763],{"encoding":904},"Q = -0{,}5P + 25",[883,46765,46767],{"className":46766},[886],[888,46768,46769],{"xmlns":890},[892,46770,46771,46785],{},[895,46772,46773,46775,46777,46779,46781,46783],{},[898,46774,2797],{},[2005,46776,2007],{},[2138,46778,2140],{},[898,46780,3946],{},[2005,46782,2234],{},[2138,46784,3128],{},[902,46786,40852],{"encoding":904},[123,46788,45614,46789,1343,46815,1644],{},[883,46790,46792],{"className":46791},[886],[888,46793,46794],{"xmlns":890},[892,46795,46796,46812],{},[895,46797,46798,46800,46802,46804,46806,46808,46810],{},[898,46799,3946],{},[2005,46801,2007],{},[2005,46803,2234],{},[2138,46805,2360],{},[898,46807,2797],{},[2005,46809,2104],{},[2138,46811,4055],{},[902,46813,46814],{"encoding":904},"P = -4Q + 120",[883,46816,46818],{"className":46817},[886],[888,46819,46820],{"xmlns":890},[892,46821,46822,46843],{},[895,46823,46824,46826,46828,46836,46838,46840],{},[898,46825,3946],{},[2005,46827,2007],{},[2334,46829,46830],{"scriptlevel":2336,"displaystyle":2013},[2338,46831,46832,46834],{},[2138,46833,2287],{},[2138,46835,2182],{},[898,46837,2797],{},[2005,46839,2104],{},[2138,46841,46842],{},"29",[902,46844,46845],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,46847,45649,46848,1343,46877,1644],{},[883,46849,46851],{"className":46850},[886],[888,46852,46853],{"xmlns":890},[892,46854,46855,46874],{},[895,46856,46857,46859,46861,46863,46869,46871],{},[898,46858,3946],{},[2005,46860,2007],{},[2005,46862,2234],{},[2133,46864,46865,46867],{},[898,46866,2797],{},[2138,46868,2140],{},[2005,46870,2104],{},[2138,46872,46873],{},"52",[902,46875,46876],{"encoding":904},"P = -Q^2 + 52",[883,46878,46880],{"className":46879},[886],[888,46881,46882],{"xmlns":890},[892,46883,46884,46902],{},[895,46885,46886,46888,46890,46892,46898,46900],{},[898,46887,3946],{},[2005,46889,2007],{},[2138,46891,2140],{},[2133,46893,46894,46896],{},[898,46895,2797],{},[2138,46897,2140],{},[2005,46899,2104],{},[2138,46901,2871],{},[902,46903,46904],{"encoding":904},"P = 2Q^2 + 10",[724,46906,46907,46910,46911,46941,46942,46972],{},[38,46908,46909],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,46912,46914],{"className":46913},[886],[888,46915,46916],{"xmlns":890},[892,46917,46918,46938],{},[895,46919,46920,46928,46930],{},[9172,46921,46922,46924,46926],{},[898,46923,2797],{},[2138,46925,2287],{},[898,46927,1868],{},[2005,46929,2295],{"separator":2294},[9172,46931,46932,46934,46936],{},[898,46933,2797],{},[2138,46935,2140],{},[898,46937,1868],{},[902,46939,46940],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,46943,46945],{"className":46944},[886],[888,46946,46947],{"xmlns":890},[892,46948,46949,46969],{},[895,46950,46951,46959,46961],{},[9172,46952,46953,46955,46957],{},[898,46954,3946],{},[2138,46956,2287],{},[898,46958,1868],{},[2005,46960,2295],{"separator":2294},[9172,46962,46963,46965,46967],{},[898,46964,3946],{},[2138,46966,2140],{},[898,46968,1868],{},[902,46970,46971],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,46974,46975,47127],{},[123,46976,45550,46977,1343,47017,1343,47059,1343,47093,1644],{},[883,46978,46980],{"className":46979},[886],[888,46981,46982],{"xmlns":890},[892,46983,46984,47014],{},[895,46985,46986,46992,46994,46996,46998,47000,47006,47008],{},[2281,46987,46988,46990],{},[898,46989,2797],{},[2138,46991,2287],{},[2005,46993,2007],{},[2138,46995,2871],{},[2005,46997,2234],{},[2138,46999,2140],{},[2281,47001,47002,47004],{},[898,47003,3946],{},[2138,47005,2287],{},[2005,47007,2104],{},[2281,47009,47010,47012],{},[898,47011,3946],{},[2138,47013,2140],{},[902,47015,47016],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,47018,47020],{"className":47019},[886],[888,47021,47022],{"xmlns":890},[892,47023,47024,47056],{},[895,47025,47026,47032,47034,47036,47038,47040,47046,47048,47050],{},[2281,47027,47028,47030],{},[898,47029,2797],{},[2138,47031,2140],{},[2005,47033,2007],{},[2138,47035,2237],{},[2005,47037,2104],{},[2138,47039,2140],{},[2281,47041,47042,47044],{},[898,47043,3946],{},[2138,47045,2287],{},[2005,47047,2234],{},[2138,47049,2140],{},[2281,47051,47052,47054],{},[898,47053,3946],{},[2138,47055,2140],{},[902,47057,47058],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,47060,47062],{"className":47061},[886],[888,47063,47064],{"xmlns":890},[892,47065,47066,47090],{},[895,47067,47068,47074,47076,47078,47080,47082,47084],{},[2281,47069,47070,47072],{},[898,47071,2797],{},[2138,47073,2287],{},[2005,47075,2007],{},[2005,47077,2234],{},[2138,47079,2182],{},[2005,47081,2104],{},[2138,47083,2140],{},[2281,47085,47086,47088],{},[898,47087,3946],{},[2138,47089,2287],{},[902,47091,47092],{"encoding":904},"Q_1 = -3 + 2P_1",[883,47094,47096],{"className":47095},[886],[888,47097,47098],{"xmlns":890},[892,47099,47100,47124],{},[895,47101,47102,47108,47110,47112,47114,47116,47118],{},[2281,47103,47104,47106],{},[898,47105,2797],{},[2138,47107,2140],{},[2005,47109,2007],{},[2005,47111,2234],{},[2138,47113,2140],{},[2005,47115,2104],{},[2138,47117,2182],{},[2281,47119,47120,47122],{},[898,47121,3946],{},[2138,47123,2140],{},[902,47125,47126],{"encoding":904},"Q_2 = -2 + 3P_2",[123,47128,45583,47129,1343,47169,1343,47211,1343,47243,1644],{},[883,47130,47132],{"className":47131},[886],[888,47133,47134],{"xmlns":890},[892,47135,47136,47166],{},[895,47137,47138,47144,47146,47148,47150,47152,47158,47160],{},[2281,47139,47140,47142],{},[898,47141,2797],{},[2138,47143,2287],{},[2005,47145,2007],{},[2138,47147,3098],{},[2005,47149,2234],{},[2138,47151,2140],{},[2281,47153,47154,47156],{},[898,47155,3946],{},[2138,47157,2287],{},[2005,47159,2104],{},[2281,47161,47162,47164],{},[898,47163,3946],{},[2138,47165,2140],{},[902,47167,47168],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,47170,47172],{"className":47171},[886],[888,47173,47174],{"xmlns":890},[892,47175,47176,47208],{},[895,47177,47178,47184,47186,47188,47190,47192,47198,47200,47202],{},[2281,47179,47180,47182],{},[898,47181,2797],{},[2138,47183,2140],{},[2005,47185,2007],{},[2138,47187,2237],{},[2005,47189,2104],{},[2138,47191,2140],{},[2281,47193,47194,47196],{},[898,47195,3946],{},[2138,47197,2287],{},[2005,47199,2234],{},[2138,47201,2182],{},[2281,47203,47204,47206],{},[898,47205,3946],{},[2138,47207,2140],{},[902,47209,47210],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,47212,47214],{"className":47213},[886],[888,47215,47216],{"xmlns":890},[892,47217,47218,47240],{},[895,47219,47220,47226,47228,47230,47232,47234],{},[2281,47221,47222,47224],{},[898,47223,2797],{},[2138,47225,2287],{},[2005,47227,2007],{},[2005,47229,2234],{},[2138,47231,2871],{},[2005,47233,2104],{},[2281,47235,47236,47238],{},[898,47237,3946],{},[2138,47239,2287],{},[902,47241,47242],{"encoding":904},"Q_1 = -10 + P_1",[883,47244,47246],{"className":47245},[886],[888,47247,47248],{"xmlns":890},[892,47249,47250,47272],{},[895,47251,47252,47258,47260,47262,47264,47266],{},[2281,47253,47254,47256],{},[898,47255,2797],{},[2138,47257,2140],{},[2005,47259,2007],{},[2138,47261,2237],{},[2005,47263,2104],{},[2138,47265,2244],{},[2281,47267,47268,47270],{},[898,47269,3946],{},[2138,47271,2140],{},[902,47273,47274],{"encoding":904},"Q_2 = 5 + 6P_2",[724,47276,47277,47280,47281,1343,47329,1343,47375,47425,47426,1343,47458,1343,47492,21600,47526,3894,47544,47562,47563,47576,47577,47603,47604,46941,47644,1644],{},[38,47278,47279],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,47282,47284],{"className":47283},[886],[888,47285,47286],{"xmlns":890},[892,47287,47288,47326],{},[895,47289,47290,47296,47298,47300,47302,47308,47310,47312,47318,47320],{},[2281,47291,47292,47294],{},[898,47293,2797],{},[2138,47295,2287],{},[2005,47297,2007],{},[2138,47299,36249],{},[2005,47301,2234],{},[2281,47303,47304,47306],{},[898,47305,3946],{},[2138,47307,2287],{},[2005,47309,2104],{},[2138,47311,2140],{},[2281,47313,47314,47316],{},[898,47315,3946],{},[2138,47317,2140],{},[2005,47319,2104],{},[2281,47321,47322,47324],{},[898,47323,3946],{},[2138,47325,2182],{},[902,47327,47328],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,47330,47332],{"className":47331},[886],[888,47333,47334],{"xmlns":890},[892,47335,47336,47372],{},[895,47337,47338,47344,47346,47348,47350,47356,47358,47364,47366],{},[2281,47339,47340,47342],{},[898,47341,2797],{},[2138,47343,2140],{},[2005,47345,2007],{},[2138,47347,4008],{},[2005,47349,2104],{},[2281,47351,47352,47354],{},[898,47353,3946],{},[2138,47355,2287],{},[2005,47357,2234],{},[2281,47359,47360,47362],{},[898,47361,3946],{},[2138,47363,2140],{},[2005,47365,2234],{},[2281,47367,47368,47370],{},[898,47369,3946],{},[2138,47371,2182],{},[902,47373,47374],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,47376,47378],{"className":47377},[886],[888,47379,47380],{"xmlns":890},[892,47381,47382,47422],{},[895,47383,47384,47390,47392,47394,47396,47398,47404,47406,47412,47414,47416],{},[2281,47385,47386,47388],{},[898,47387,2797],{},[2138,47389,2182],{},[2005,47391,2007],{},[2138,47393,5591],{},[2005,47395,2104],{},[2138,47397,2140],{},[2281,47399,47400,47402],{},[898,47401,3946],{},[2138,47403,2287],{},[2005,47405,2234],{},[2281,47407,47408,47410],{},[898,47409,3946],{},[2138,47411,2140],{},[2005,47413,2234],{},[2138,47415,2360],{},[2281,47417,47418,47420],{},[898,47419,3946],{},[2138,47421,2182],{},[902,47423,47424],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,47427,47429],{"className":47428},[886],[888,47430,47431],{"xmlns":890},[892,47432,47433,47455],{},[895,47434,47435,47441,47443,47445,47447,47449],{},[2281,47436,47437,47439],{},[898,47438,2797],{},[2138,47440,2287],{},[2005,47442,2007],{},[2005,47444,2234],{},[2138,47446,24206],{},[2005,47448,2104],{},[2281,47450,47451,47453],{},[898,47452,3946],{},[2138,47454,2287],{},[902,47456,47457],{"encoding":904},"Q_1 = -7 + P_1",[883,47459,47461],{"className":47460},[886],[888,47462,47463],{"xmlns":890},[892,47464,47465,47489],{},[895,47466,47467,47473,47475,47477,47479,47481,47483],{},[2281,47468,47469,47471],{},[898,47470,2797],{},[2138,47472,2140],{},[2005,47474,2007],{},[2005,47476,2234],{},[2138,47478,2360],{},[2005,47480,2104],{},[2138,47482,2360],{},[2281,47484,47485,47487],{},[898,47486,3946],{},[2138,47488,2140],{},[902,47490,47491],{"encoding":904},"Q_2 = -4 + 4P_2",[883,47493,47495],{"className":47494},[886],[888,47496,47497],{"xmlns":890},[892,47498,47499,47523],{},[895,47500,47501,47507,47509,47511,47513,47515,47517],{},[2281,47502,47503,47505],{},[898,47504,2797],{},[2138,47506,2182],{},[2005,47508,2007],{},[2005,47510,2234],{},[2138,47512,2237],{},[2005,47514,2104],{},[2138,47516,2140],{},[2281,47518,47519,47521],{},[898,47520,3946],{},[2138,47522,2182],{},[902,47524,47525],{"encoding":904},"Q_3 = -5 + 2P_3",[883,47527,47529],{"className":47528},[886],[888,47530,47531],{"xmlns":890},[892,47532,47533,47541],{},[895,47534,47535],{},[2281,47536,47537,47539],{},[898,47538,2797],{},[898,47540,17797],{},[902,47542,47543],{"encoding":904},"Q_i",[883,47545,47547],{"className":47546},[886],[888,47548,47549],{"xmlns":890},[892,47550,47551,47559],{},[895,47552,47553],{},[2281,47554,47555,47557],{},[898,47556,3946],{},[898,47558,17797],{},[902,47560,47561],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,47564,47566],{"className":47565},[886],[888,47567,47568],{"xmlns":890},[892,47569,47570,47574],{},[895,47571,47572],{},[898,47573,17797],{},[902,47575,17797],{"encoding":904},"-tého zboží, ",[883,47578,47580],{"className":47579},[886],[888,47581,47582],{"xmlns":890},[892,47583,47584,47600],{},[895,47585,47586,47588,47590,47592,47594,47596,47598],{},[898,47587,17797],{},[2005,47589,2007],{},[2138,47591,2287],{},[2005,47593,2295],{"separator":2294},[2138,47595,2140],{},[2005,47597,2295],{"separator":2294},[2138,47599,2182],{},[902,47601,47602],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,47605,47607],{"className":47606},[886],[888,47608,47609],{"xmlns":890},[892,47610,47611,47641],{},[895,47612,47613,47621,47623,47631,47633],{},[9172,47614,47615,47617,47619],{},[898,47616,2797],{},[2138,47618,2287],{},[898,47620,1868],{},[2005,47622,2295],{"separator":2294},[9172,47624,47625,47627,47629],{},[898,47626,2797],{},[2138,47628,2140],{},[898,47630,1868],{},[2005,47632,2295],{"separator":2294},[9172,47634,47635,47637,47639],{},[898,47636,2797],{},[2138,47638,2182],{},[898,47640,1868],{},[902,47642,47643],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,47645,47647],{"className":47646},[886],[888,47648,47649],{"xmlns":890},[892,47650,47651,47681],{},[895,47652,47653,47661,47663,47671,47673],{},[9172,47654,47655,47657,47659],{},[898,47656,3946],{},[2138,47658,2287],{},[898,47660,1868],{},[2005,47662,2295],{"separator":2294},[9172,47664,47665,47667,47669],{},[898,47666,3946],{},[2138,47668,2140],{},[898,47670,1868],{},[2005,47672,2295],{"separator":2294},[9172,47674,47675,47677,47679],{},[898,47676,3946],{},[2138,47678,2182],{},[898,47680,1868],{},[902,47682,47683],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,47685,47686,47689,47690,47726,47727,1644],{},[38,47687,47688],{},"2.13"," Jsou dány poptávka ",[883,47691,47693],{"className":47692},[886],[888,47694,47695],{"xmlns":890},[892,47696,47697,47723],{},[895,47698,47699,47701,47703,47705,47707,47709,47711,47713,47715,47717,47719,47721],{},[898,47700,3946],{},[2005,47702,2007],{},[898,47704,1860],{},[2005,47706,2014],{"stretchy":2013},[898,47708,2797],{},[2005,47710,2020],{"stretchy":2013},[2005,47712,2007],{},[2005,47714,2234],{},[2138,47716,2360],{},[898,47718,2797],{},[2005,47720,2104],{},[2138,47722,46708],{},[902,47724,47725],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,47728,47730],{"className":47729},[886],[888,47731,47732],{"xmlns":890},[892,47733,47734,47758],{},[895,47735,47736,47738,47740,47742,47744,47746,47748,47750,47752,47754,47756],{},[898,47737,3946],{},[2005,47739,2007],{},[898,47741,8679],{},[2005,47743,2014],{"stretchy":2013},[898,47745,2797],{},[2005,47747,2020],{"stretchy":2013},[2005,47749,2007],{},[2138,47751,2182],{},[898,47753,2797],{},[2005,47755,2104],{},[2138,47757,2871],{},[902,47759,47760],{"encoding":904},"P = S(Q) = 3Q + 10",[120,47762,47763,47800,47864,47924],{},[123,47764,47765,47766,46663,47783,1644],{},"(a) Určete rovnovážné množství ",[883,47767,47769],{"className":47768},[886],[888,47770,47771],{"xmlns":890},[892,47772,47773,47781],{},[895,47774,47775],{},[2133,47776,47777,47779],{},[898,47778,2797],{},[898,47780,1868],{},[902,47782,42408],{"encoding":904},[883,47784,47786],{"className":47785},[886],[888,47787,47788],{"xmlns":890},[892,47789,47790,47798],{},[895,47791,47792],{},[2133,47793,47794,47796],{},[898,47795,3946],{},[898,47797,1868],{},[902,47799,41471],{"encoding":904},[123,47801,47802,47803,47821,47822,47842,47843,47863],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,47804,47806],{"className":47805},[886],[888,47807,47808],{"xmlns":890},[892,47809,47810,47818],{},[895,47811,47812,47814,47816],{},[898,47813,2783],{},[2005,47815,2007],{},[2138,47817,24206],{},[902,47819,47820],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,47823,47825],{"className":47824},[886],[888,47826,47827],{"xmlns":890},[892,47828,47829,47839],{},[895,47830,47831],{},[9172,47832,47833,47835,47837],{},[898,47834,2797],{},[2138,47836,2287],{},[898,47838,1868],{},[902,47840,47841],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,47844,47846],{"className":47845},[886],[888,47847,47848],{"xmlns":890},[892,47849,47850,47860],{},[895,47851,47852],{},[9172,47853,47854,47856,47858],{},[898,47855,3946],{},[2138,47857,2287],{},[898,47859,1868],{},[902,47861,47862],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,47865,47866,47867,47821,47884,47842,47904,47863],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,47868,47870],{"className":47869},[886],[888,47871,47872],{"xmlns":890},[892,47873,47874,47882],{},[895,47875,47876,47878,47880],{},[898,47877,2783],{},[2005,47879,2007],{},[2138,47881,24206],{},[902,47883,47820],{"encoding":904},[883,47885,47887],{"className":47886},[886],[888,47888,47889],{"xmlns":890},[892,47890,47891,47901],{},[895,47892,47893],{},[9172,47894,47895,47897,47899],{},[898,47896,2797],{},[2138,47898,2140],{},[898,47900,1868],{},[902,47902,47903],{"encoding":904},"Q_2^E",[883,47905,47907],{"className":47906},[886],[888,47908,47909],{"xmlns":890},[892,47910,47911,47921],{},[895,47912,47913],{},[9172,47914,47915,47917,47919],{},[898,47916,3946],{},[2138,47918,2140],{},[898,47920,1868],{},[902,47922,47923],{"encoding":904},"P_2^E",[123,47925,47926],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,47928,47929,47930,1644],{},"Viz též ",[207,47931,42726],{"className":47932,"dataFsResolvedFilePath":809,"href":810},[210],[198,47934,43028],{"id":47935},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,47937,47938,47689,47941,47726,47977,1644],{},[38,47939,47940],{},"2.14",[883,47942,47944],{"className":47943},[886],[888,47945,47946],{"xmlns":890},[892,47947,47948,47974],{},[895,47949,47950,47952,47954,47956,47958,47960,47962,47964,47966,47968,47970,47972],{},[898,47951,3946],{},[2005,47953,2007],{},[898,47955,207],{},[898,47957,2797],{},[2005,47959,2104],{},[898,47961,2107],{},[2005,47963,2007],{},[2005,47965,2234],{},[2138,47967,2140],{},[898,47969,2797],{},[2005,47971,2104],{},[2138,47973,3128],{},[902,47975,47976],{"encoding":904},"P = aQ + b = -2Q + 50",[883,47978,47980],{"className":47979},[886],[888,47981,47982],{"xmlns":890},[892,47983,47984,48008],{},[895,47985,47986,47988,47990,47992,47994,47996,47998,48000,48002,48004,48006],{},[898,47987,3946],{},[2005,47989,2007],{},[898,47991,2151],{},[898,47993,2797],{},[2005,47995,2104],{},[898,47997,2203],{},[2005,47999,2007],{},[2138,48001,19327],{},[898,48003,2797],{},[2005,48005,2104],{},[2138,48007,9041],{},[902,48009,48010],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,48012,48013,48049,48052,48138,48191,48271,48325],{},[123,48014,47765,48015,46663,48032,1644],{},[883,48016,48018],{"className":48017},[886],[888,48019,48020],{"xmlns":890},[892,48021,48022,48030],{},[895,48023,48024],{},[2133,48025,48026,48028],{},[898,48027,2797],{},[898,48029,1868],{},[902,48031,42408],{"encoding":904},[883,48033,48035],{"className":48034},[886],[888,48036,48037],{"xmlns":890},[892,48038,48039,48047],{},[895,48040,48041],{},[2133,48042,48043,48045],{},[898,48044,3946],{},[898,48046,1868],{},[902,48048,41471],{"encoding":904},[123,48050,48051],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,48053,48054,48055,48072,48073,2680,48086,2694,48102,48118,48119,1644],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,48056,48058],{"className":48057},[886],[888,48059,48060],{"xmlns":890},[892,48061,48062,48070],{},[895,48063,48064],{},[2133,48065,48066,48068],{},[898,48067,2797],{},[898,48069,1868],{},[902,48071,42408],{"encoding":904}," odpovídající změně ",[883,48074,48076],{"className":48075},[886],[888,48077,48078],{"xmlns":890},[892,48079,48080,48084],{},[895,48081,48082],{},[898,48083,207],{},[902,48085,207],{"encoding":904},[883,48087,48089],{"className":48088},[886],[888,48090,48091],{"xmlns":890},[892,48092,48093,48099],{},[895,48094,48095,48097],{},[2005,48096,2234],{},[2138,48098,2140],{},[902,48100,48101],{"encoding":904},"-2",[883,48103,48105],{"className":48104},[886],[888,48106,48107],{"xmlns":890},[892,48108,48109,48115],{},[895,48110,48111,48113],{},[2005,48112,2234],{},[2138,48114,2182],{},[902,48116,48117],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48120,48122],{"className":48121},[886],[888,48123,48124],{"xmlns":890},[892,48125,48126,48136],{},[895,48127,48128],{},[9172,48129,48130,48132,48134],{},[898,48131,2797],{},[2138,48133,2287],{},[898,48135,1868],{},[902,48137,47841],{"encoding":904},[123,48139,48140,48141,48072,48158,48171,48172,1644],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,48142,48144],{"className":48143},[886],[888,48145,48146],{"xmlns":890},[892,48147,48148,48156],{},[895,48149,48150],{},[2133,48151,48152,48154],{},[898,48153,2797],{},[898,48155,1868],{},[902,48157,42408],{"encoding":904},[883,48159,48161],{"className":48160},[886],[888,48162,48163],{"xmlns":890},[892,48164,48165,48169],{},[895,48166,48167],{},[898,48168,2107],{},[902,48170,2107],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48173,48175],{"className":48174},[886],[888,48176,48177],{"xmlns":890},[892,48178,48179,48189],{},[895,48180,48181],{},[9172,48182,48183,48185,48187],{},[898,48184,2797],{},[2138,48186,2140],{},[898,48188,1868],{},[902,48190,47903],{"encoding":904},[123,48192,48193,48194,48072,48211,2680,48224,2694,48237,48118,48251,1644],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,48195,48197],{"className":48196},[886],[888,48198,48199],{"xmlns":890},[892,48200,48201,48209],{},[895,48202,48203],{},[2133,48204,48205,48207],{},[898,48206,2797],{},[898,48208,1868],{},[902,48210,42408],{"encoding":904},[883,48212,48214],{"className":48213},[886],[888,48215,48216],{"xmlns":890},[892,48217,48218,48222],{},[895,48219,48220],{},[898,48221,2151],{},[902,48223,2151],{"encoding":904},[883,48225,48227],{"className":48226},[886],[888,48228,48229],{"xmlns":890},[892,48230,48231,48235],{},[895,48232,48233],{},[2138,48234,19327],{},[902,48236,44465],{"encoding":904},[883,48238,48240],{"className":48239},[886],[888,48241,48242],{"xmlns":890},[892,48243,48244,48248],{},[895,48245,48246],{},[2138,48247,14595],{},[902,48249,48250],{"encoding":904},"0{,}8",[883,48252,48254],{"className":48253},[886],[888,48255,48256],{"xmlns":890},[892,48257,48258,48268],{},[895,48259,48260],{},[9172,48261,48262,48264,48266],{},[898,48263,2797],{},[2138,48265,2182],{},[898,48267,1868],{},[902,48269,48270],{"encoding":904},"Q_3^E",[123,48272,48273,48274,48072,48291,48304,48305,1644],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,48275,48277],{"className":48276},[886],[888,48278,48279],{"xmlns":890},[892,48280,48281,48289],{},[895,48282,48283],{},[2133,48284,48285,48287],{},[898,48286,2797],{},[898,48288,1868],{},[902,48290,42408],{"encoding":904},[883,48292,48294],{"className":48293},[886],[888,48295,48296],{"xmlns":890},[892,48297,48298,48302],{},[895,48299,48300],{},[898,48301,2203],{},[902,48303,2203],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,48306,48308],{"className":48307},[886],[888,48309,48310],{"xmlns":890},[892,48311,48312,48322],{},[895,48313,48314],{},[9172,48315,48316,48318,48320],{},[898,48317,2797],{},[2138,48319,2360],{},[898,48321,1868],{},[902,48323,48324],{"encoding":904},"Q_4^E",[123,48326,48327,48328,48345,48346,48359,48360,21426,48373,1343,48388,21426,48401,3894,48415,21426,48428,48443,48444,1644],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,48329,48331],{"className":48330},[886],[888,48332,48333],{"xmlns":890},[892,48334,48335,48343],{},[895,48336,48337],{},[2133,48338,48339,48341],{},[898,48340,2797],{},[898,48342,1868],{},[902,48344,42408],{"encoding":904}," odpovídající změnám ",[883,48347,48349],{"className":48348},[886],[888,48350,48351],{"xmlns":890},[892,48352,48353,48357],{},[895,48354,48355],{},[898,48356,207],{},[902,48358,207],{"encoding":904}," o 1, ",[883,48361,48363],{"className":48362},[886],[888,48364,48365],{"xmlns":890},[892,48366,48367,48371],{},[895,48368,48369],{},[898,48370,2107],{},[902,48372,2107],{"encoding":904},[883,48374,48376],{"className":48375},[886],[888,48377,48378],{"xmlns":890},[892,48379,48380,48386],{},[895,48381,48382,48384],{},[2005,48383,2234],{},[2138,48385,2871],{},[902,48387,19461],{"encoding":904},[883,48389,48391],{"className":48390},[886],[888,48392,48393],{"xmlns":890},[892,48394,48395,48399],{},[895,48396,48397],{},[898,48398,2151],{},[902,48400,2151],{"encoding":904},[883,48402,48404],{"className":48403},[886],[888,48405,48406],{"xmlns":890},[892,48407,48408,48412],{},[895,48409,48410],{},[2138,48411,2802],{},[902,48413,48414],{"encoding":904},"0{,}1",[883,48416,48418],{"className":48417},[886],[888,48419,48420],{"xmlns":890},[892,48421,48422,48426],{},[895,48423,48424],{},[898,48425,2203],{},[902,48427,2203],{"encoding":904},[883,48429,48431],{"className":48430},[886],[888,48432,48433],{"xmlns":890},[892,48434,48435,48441],{},[895,48436,48437,48439],{},[2005,48438,2234],{},[2138,48440,2871],{},[902,48442,19461],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,48445,48447],{"className":48446},[886],[888,48448,48449],{"xmlns":890},[892,48450,48451,48461],{},[895,48452,48453],{},[9172,48454,48455,48457,48459],{},[898,48456,2797],{},[2138,48458,2237],{},[898,48460,1868],{},[902,48462,48463],{"encoding":904},"Q_5^E",[724,48465,48466,47689,48469,47726,48492,1644],{},[38,48467,48468],{},"2.15",[883,48470,48472],{"className":48471},[886],[888,48473,48474],{"xmlns":890},[892,48475,48476,48490],{},[895,48477,48478,48480,48482,48484,48486,48488],{},[898,48479,3946],{},[2005,48481,2007],{},[898,48483,207],{},[898,48485,2797],{},[2005,48487,2104],{},[898,48489,2107],{},[902,48491,37065],{"encoding":904},[883,48493,48495],{"className":48494},[886],[888,48496,48497],{"xmlns":890},[892,48498,48499,48513],{},[895,48500,48501,48503,48505,48507,48509,48511],{},[898,48502,3946],{},[2005,48504,2007],{},[898,48506,2151],{},[898,48508,2797],{},[2005,48510,2104],{},[898,48512,2203],{},[902,48514,40247],{"encoding":904},[120,48516,48517,48592,48609,48718,48771,48825],{},[123,48518,48519,48520,48533,48534,48559,48560,48591],{},"(a) Odvoďte redukovaný tvar pro ",[883,48521,48523],{"className":48522},[886],[888,48524,48525],{"xmlns":890},[892,48526,48527,48531],{},[895,48528,48529],{},[898,48530,3946],{},[902,48532,3946],{"encoding":904},". Stanovte podmínky pro ",[883,48535,48537],{"className":48536},[886],[888,48538,48539],{"xmlns":890},[892,48540,48541,48557],{},[895,48542,48543,48545,48547,48549,48551,48553,48555],{},[898,48544,207],{},[2005,48546,2295],{"separator":2294},[898,48548,2107],{},[2005,48550,2295],{"separator":2294},[898,48552,2151],{},[2005,48554,2295],{"separator":2294},[898,48556,2203],{},[902,48558,43290],{"encoding":904}," tak, aby rovnovážný bod ",[883,48561,48563],{"className":48562},[886],[888,48564,48565],{"xmlns":890},[892,48566,48567,48589],{},[895,48568,48569,48571,48573,48579,48581,48587],{},[898,48570,1868],{},[2005,48572,2495],{"stretchy":2013},[2133,48574,48575,48577],{},[898,48576,2797],{},[898,48578,1868],{},[2005,48580,2295],{"separator":2294},[2133,48582,48583,48585],{},[898,48584,3946],{},[898,48586,1868],{},[2005,48588,2510],{"stretchy":2013},[902,48590,41372],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,48593,48594,48595,48608],{},"(b) Vypočtěte multiplikátory pro ",[883,48596,48598],{"className":48597},[886],[888,48599,48600],{"xmlns":890},[892,48601,48602,48606],{},[895,48603,48604],{},[898,48605,3946],{},[902,48607,3946],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,48610,48611,48612,1343,48632,1343,48650,1343,48668,48686,48687,48704,48705,1644],{},"(c) Pro hodnoty parametrů ",[883,48613,48615],{"className":48614},[886],[888,48616,48617],{"xmlns":890},[892,48618,48619,48629],{},[895,48620,48621,48623,48625,48627],{},[898,48622,207],{},[2005,48624,2007],{},[2005,48626,2234],{},[2138,48628,2140],{},[902,48630,48631],{"encoding":904},"a = -2",[883,48633,48635],{"className":48634},[886],[888,48636,48637],{"xmlns":890},[892,48638,48639,48647],{},[895,48640,48641,48643,48645],{},[898,48642,2107],{},[2005,48644,2007],{},[2138,48646,5217],{},[902,48648,48649],{"encoding":904},"b = 40",[883,48651,48653],{"className":48652},[886],[888,48654,48655],{"xmlns":890},[892,48656,48657,48665],{},[895,48658,48659,48661,48663],{},[898,48660,2151],{},[2005,48662,2007],{},[2138,48664,5015],{},[902,48666,48667],{"encoding":904},"c = 0{,}5",[883,48669,48671],{"className":48670},[886],[888,48672,48673],{"xmlns":890},[892,48674,48675,48683],{},[895,48676,48677,48679,48681],{},[898,48678,2203],{},[2005,48680,2007],{},[2138,48682,2871],{},[902,48684,48685],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,48688,48690],{"className":48689},[886],[888,48691,48692],{"xmlns":890},[892,48693,48694,48702],{},[895,48695,48696],{},[2133,48697,48698,48700],{},[898,48699,3946],{},[898,48701,1868],{},[902,48703,41471],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,48706,48708],{"className":48707},[886],[888,48709,48710],{"xmlns":890},[892,48711,48712,48716],{},[895,48713,48714],{},[898,48715,3946],{},[902,48717,3946],{"encoding":904},[123,48719,48720,48721,48072,48738,48751,48752,1644],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,48722,48724],{"className":48723},[886],[888,48725,48726],{"xmlns":890},[892,48727,48728,48736],{},[895,48729,48730],{},[2133,48731,48732,48734],{},[898,48733,3946],{},[898,48735,1868],{},[902,48737,41471],{"encoding":904},[883,48739,48741],{"className":48740},[886],[888,48742,48743],{"xmlns":890},[892,48744,48745,48749],{},[895,48746,48747],{},[898,48748,207],{},[902,48750,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,48753,48755],{"className":48754},[886],[888,48756,48757],{"xmlns":890},[892,48758,48759,48769],{},[895,48760,48761],{},[9172,48762,48763,48765,48767],{},[898,48764,3946],{},[2138,48766,2287],{},[898,48768,1868],{},[902,48770,47862],{"encoding":904},[123,48772,48773,48774,48791,48792,48805,48806,1644],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,48775,48777],{"className":48776},[886],[888,48778,48779],{"xmlns":890},[892,48780,48781,48789],{},[895,48782,48783],{},[2133,48784,48785,48787],{},[898,48786,3946],{},[898,48788,1868],{},[902,48790,41471],{"encoding":904}," odpovídající poklesu ",[883,48793,48795],{"className":48794},[886],[888,48796,48797],{"xmlns":890},[892,48798,48799,48803],{},[895,48800,48801],{},[898,48802,207],{},[902,48804,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,48807,48809],{"className":48808},[886],[888,48810,48811],{"xmlns":890},[892,48812,48813,48823],{},[895,48814,48815],{},[9172,48816,48817,48819,48821],{},[898,48818,3946],{},[2138,48820,2140],{},[898,48822,1868],{},[902,48824,47923],{"encoding":904},[123,48826,48827,48828,48345,48845,48858,48859,2694,48872,3894,48887,48900,48901,1644],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,48829,48831],{"className":48830},[886],[888,48832,48833],{"xmlns":890},[892,48834,48835,48843],{},[895,48836,48837],{},[2133,48838,48839,48841],{},[898,48840,3946],{},[898,48842,1868],{},[902,48844,41471],{"encoding":904},[883,48846,48848],{"className":48847},[886],[888,48849,48850],{"xmlns":890},[892,48851,48852,48856],{},[895,48853,48854],{},[898,48855,207],{},[902,48857,207],{"encoding":904}," na 35, ",[883,48860,48862],{"className":48861},[886],[888,48863,48864],{"xmlns":890},[892,48865,48866,48870],{},[895,48867,48868],{},[898,48869,2151],{},[902,48871,2151],{"encoding":904},[883,48873,48875],{"className":48874},[886],[888,48876,48877],{"xmlns":890},[892,48878,48879,48884],{},[895,48880,48881],{},[2138,48882,48883],{},"0,7",[902,48885,48886],{"encoding":904},"0{,}7",[883,48888,48890],{"className":48889},[886],[888,48891,48892],{"xmlns":890},[892,48893,48894,48898],{},[895,48895,48896],{},[898,48897,2203],{},[902,48899,2203],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,48902,48904],{"className":48903},[886],[888,48905,48906],{"xmlns":890},[892,48907,48908,48918],{},[895,48909,48910],{},[9172,48911,48912,48914,48916],{},[898,48913,3946],{},[2138,48915,2182],{},[898,48917,1868],{},[902,48919,48920],{"encoding":904},"P_3^E",[724,48922,48923,47689,48926,47726,48954,21600,48982,3894,49008,1644],{},[38,48924,48925],{},"2.16",[883,48927,48929],{"className":48928},[886],[888,48930,48931],{"xmlns":890},[892,48932,48933,48951],{},[895,48934,48935,48937,48939,48941,48943,48945],{},[898,48936,3946],{},[2005,48938,2007],{},[898,48940,207],{},[2005,48942,2104],{},[898,48944,2107],{},[2133,48946,48947,48949],{},[898,48948,2797],{},[2138,48950,2140],{},[902,48952,48953],{"encoding":904},"P = a + bQ^2",[883,48955,48957],{"className":48956},[886],[888,48958,48959],{"xmlns":890},[892,48960,48961,48979],{},[895,48962,48963,48965,48967,48969,48971,48973],{},[898,48964,3946],{},[2005,48966,2007],{},[898,48968,2151],{},[2005,48970,2104],{},[898,48972,2203],{},[2133,48974,48975,48977],{},[898,48976,2797],{},[2138,48978,2140],{},[902,48980,48981],{"encoding":904},"P = c + dQ^2",[883,48983,48985],{"className":48984},[886],[888,48986,48987],{"xmlns":890},[892,48988,48989,49005],{},[895,48990,48991,48993,48995,48997,48999,49001,49003],{},[898,48992,207],{},[2005,48994,2295],{"separator":2294},[898,48996,2151],{},[2005,48998,2295],{"separator":2294},[898,49000,2203],{},[2005,49002,3416],{},[2138,49004,2336],{},[902,49006,49007],{"encoding":904},"a, c, d > 0",[883,49009,49011],{"className":49010},[886],[888,49012,49013],{"xmlns":890},[892,49014,49015,49023],{},[895,49016,49017,49019,49021],{},[898,49018,2107],{},[2005,49020,3455],{},[2138,49022,2336],{},[902,49024,49025],{"encoding":904},"b \u003C 0",[120,49027,49028,49076,49092,49199,49251,49303,49412,49428,49527,49580],{},[123,49029,48519,49030,49043,49044,49075],{},[883,49031,49033],{"className":49032},[886],[888,49034,49035],{"xmlns":890},[892,49036,49037,49041],{},[895,49038,49039],{},[898,49040,2797],{},[902,49042,2797],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,49045,49047],{"className":49046},[886],[888,49048,49049],{"xmlns":890},[892,49050,49051,49073],{},[895,49052,49053,49055,49057,49063,49065,49071],{},[898,49054,1868],{},[2005,49056,2495],{"stretchy":2013},[2133,49058,49059,49061],{},[898,49060,2797],{},[898,49062,1868],{},[2005,49064,2295],{"separator":2294},[2133,49066,49067,49069],{},[898,49068,3946],{},[898,49070,1868],{},[2005,49072,2510],{"stretchy":2013},[902,49074,41372],{"encoding":904}," patřil do 1. kvadrantu.",[123,49077,48594,49078,49091],{},[883,49079,49081],{"className":49080},[886],[888,49082,49083],{"xmlns":890},[892,49084,49085,49089],{},[895,49086,49087],{},[898,49088,2797],{},[902,49090,2797],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,49093,48611,49094,1343,49112,1343,49132,1343,49150,49168,49169,48704,49186,1644],{},[883,49095,49097],{"className":49096},[886],[888,49098,49099],{"xmlns":890},[892,49100,49101,49109],{},[895,49102,49103,49105,49107],{},[898,49104,207],{},[2005,49106,2007],{},[2138,49108,3098],{},[902,49110,49111],{"encoding":904},"a = 100",[883,49113,49115],{"className":49114},[886],[888,49116,49117],{"xmlns":890},[892,49118,49119,49129],{},[895,49120,49121,49123,49125,49127],{},[898,49122,2107],{},[2005,49124,2007],{},[2005,49126,2234],{},[2138,49128,2287],{},[902,49130,49131],{"encoding":904},"b = -1",[883,49133,49135],{"className":49134},[886],[888,49136,49137],{"xmlns":890},[892,49138,49139,49147],{},[895,49140,49141,49143,49145],{},[898,49142,2151],{},[2005,49144,2007],{},[2138,49146,9041],{},[902,49148,49149],{"encoding":904},"c = 20",[883,49151,49153],{"className":49152},[886],[888,49154,49155],{"xmlns":890},[892,49156,49157,49165],{},[895,49158,49159,49161,49163],{},[898,49160,2203],{},[2005,49162,2007],{},[2138,49164,2287],{},[902,49166,49167],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,49170,49172],{"className":49171},[886],[888,49173,49174],{"xmlns":890},[892,49175,49176,49184],{},[895,49177,49178],{},[2133,49179,49180,49182],{},[898,49181,2797],{},[898,49183,1868],{},[902,49185,42408],{"encoding":904},[883,49187,49189],{"className":49188},[886],[888,49190,49191],{"xmlns":890},[892,49192,49193,49197],{},[895,49194,49195],{},[898,49196,2797],{},[902,49198,2797],{"encoding":904},[123,49200,48140,49201,48072,49218,49231,49232,1644],{},[883,49202,49204],{"className":49203},[886],[888,49205,49206],{"xmlns":890},[892,49207,49208,49216],{},[895,49209,49210],{},[2133,49211,49212,49214],{},[898,49213,2797],{},[898,49215,1868],{},[902,49217,42408],{"encoding":904},[883,49219,49221],{"className":49220},[886],[888,49222,49223],{"xmlns":890},[892,49224,49225,49229],{},[895,49226,49227],{},[898,49228,207],{},[902,49230,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49233,49235],{"className":49234},[886],[888,49236,49237],{"xmlns":890},[892,49238,49239,49249],{},[895,49240,49241],{},[9172,49242,49243,49245,49247],{},[898,49244,2797],{},[2138,49246,2287],{},[898,49248,1868],{},[902,49250,47841],{"encoding":904},[123,49252,48193,49253,48072,49270,49283,49284,1644],{},[883,49254,49256],{"className":49255},[886],[888,49257,49258],{"xmlns":890},[892,49259,49260,49268],{},[895,49261,49262],{},[2133,49263,49264,49266],{},[898,49265,2797],{},[898,49267,1868],{},[902,49269,42408],{"encoding":904},[883,49271,49273],{"className":49272},[886],[888,49274,49275],{"xmlns":890},[892,49276,49277,49281],{},[895,49278,49279],{},[898,49280,2151],{},[902,49282,2151],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,49285,49287],{"className":49286},[886],[888,49288,49289],{"xmlns":890},[892,49290,49291,49301],{},[895,49292,49293],{},[9172,49294,49295,49297,49299],{},[898,49296,2797],{},[2138,49298,2140],{},[898,49300,1868],{},[902,49302,47903],{"encoding":904},[123,49304,48273,49305,48345,49322,49335,49336,2694,49349,49364,49365,49378,49379,49392,49393,1644],{},[883,49306,49308],{"className":49307},[886],[888,49309,49310],{"xmlns":890},[892,49311,49312,49320],{},[895,49313,49314],{},[2133,49315,49316,49318],{},[898,49317,2797],{},[898,49319,1868],{},[902,49321,42408],{"encoding":904},[883,49323,49325],{"className":49324},[886],[888,49326,49327],{"xmlns":890},[892,49328,49329,49333],{},[895,49330,49331],{},[898,49332,207],{},[902,49334,207],{"encoding":904}," na 110, poklesu ",[883,49337,49339],{"className":49338},[886],[888,49340,49341],{"xmlns":890},[892,49342,49343,49347],{},[895,49344,49345],{},[898,49346,2107],{},[902,49348,2107],{"encoding":904},[883,49350,49352],{"className":49351},[886],[888,49353,49354],{"xmlns":890},[892,49355,49356,49362],{},[895,49357,49358,49360],{},[2005,49359,2234],{},[2138,49361,2140],{},[902,49363,48101],{"encoding":904},", růstu ",[883,49366,49368],{"className":49367},[886],[888,49369,49370],{"xmlns":890},[892,49371,49372,49376],{},[895,49373,49374],{},[898,49375,2151],{},[902,49377,2151],{"encoding":904}," na 25 a růstu ",[883,49380,49382],{"className":49381},[886],[888,49383,49384],{"xmlns":890},[892,49385,49386,49390],{},[895,49387,49388],{},[898,49389,2203],{},[902,49391,2203],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,49394,49396],{"className":49395},[886],[888,49397,49398],{"xmlns":890},[892,49399,49400,49410],{},[895,49401,49402],{},[9172,49403,49404,49406,49408],{},[898,49405,2797],{},[2138,49407,2182],{},[898,49409,1868],{},[902,49411,48270],{"encoding":904},[123,49413,49414,49415,49091],{},"(i) Vypočtěte multiplikátory pro ",[883,49416,49418],{"className":49417},[886],[888,49419,49420],{"xmlns":890},[892,49421,49422,49426],{},[895,49423,49424],{},[898,49425,3946],{},[902,49427,3946],{"encoding":904},[123,49429,49430,49431,48704,49448,49461,49462,48072,49479,2694,49492,49507,49508,1644],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,49432,49434],{"className":49433},[886],[888,49435,49436],{"xmlns":890},[892,49437,49438,49446],{},[895,49439,49440],{},[2133,49441,49442,49444],{},[898,49443,3946],{},[898,49445,1868],{},[902,49447,41471],{"encoding":904},[883,49449,49451],{"className":49450},[886],[888,49452,49453],{"xmlns":890},[892,49454,49455,49459],{},[895,49456,49457],{},[898,49458,3946],{},[902,49460,3946],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,49463,49465],{"className":49464},[886],[888,49466,49467],{"xmlns":890},[892,49468,49469,49477],{},[895,49470,49471],{},[2133,49472,49473,49475],{},[898,49474,3946],{},[898,49476,1868],{},[902,49478,41471],{"encoding":904},[883,49480,49482],{"className":49481},[886],[888,49483,49484],{"xmlns":890},[892,49485,49486,49490],{},[895,49487,49488],{},[898,49489,207],{},[902,49491,207],{"encoding":904},[883,49493,49495],{"className":49494},[886],[888,49496,49497],{"xmlns":890},[892,49498,49499,49505],{},[895,49500,49501,49503],{},[2005,49502,2234],{},[2138,49504,2182],{},[902,49506,48117],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49509,49511],{"className":49510},[886],[888,49512,49513],{"xmlns":890},[892,49514,49515,49525],{},[895,49516,49517],{},[9172,49518,49519,49521,49523],{},[898,49520,3946],{},[2138,49522,2287],{},[898,49524,1868],{},[902,49526,47862],{"encoding":904},[123,49528,49529,49530,48072,49547,49560,49561,1644],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,49531,49533],{"className":49532},[886],[888,49534,49535],{"xmlns":890},[892,49536,49537,49545],{},[895,49538,49539],{},[2133,49540,49541,49543],{},[898,49542,3946],{},[898,49544,1868],{},[902,49546,41471],{"encoding":904},[883,49548,49550],{"className":49549},[886],[888,49551,49552],{"xmlns":890},[892,49553,49554,49558],{},[895,49555,49556],{},[898,49557,207],{},[902,49559,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49562,49564],{"className":49563},[886],[888,49565,49566],{"xmlns":890},[892,49567,49568,49578],{},[895,49569,49570],{},[9172,49571,49572,49574,49576],{},[898,49573,3946],{},[2138,49575,2140],{},[898,49577,1868],{},[902,49579,47923],{"encoding":904},[123,49581,49582,49583,48791,49600,49613,49614,2694,49627,49364,49642,49655,49656,49669,49670,1644],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,49584,49586],{"className":49585},[886],[888,49587,49588],{"xmlns":890},[892,49589,49590,49598],{},[895,49591,49592],{},[2133,49593,49594,49596],{},[898,49595,3946],{},[898,49597,1868],{},[902,49599,41471],{"encoding":904},[883,49601,49603],{"className":49602},[886],[888,49604,49605],{"xmlns":890},[892,49606,49607,49611],{},[895,49608,49609],{},[898,49610,207],{},[902,49612,207],{"encoding":904}," na 90, poklesu ",[883,49615,49617],{"className":49616},[886],[888,49618,49619],{"xmlns":890},[892,49620,49621,49625],{},[895,49622,49623],{},[898,49624,2107],{},[902,49626,2107],{"encoding":904},[883,49628,49630],{"className":49629},[886],[888,49631,49632],{"xmlns":890},[892,49633,49634,49640],{},[895,49635,49636,49638],{},[2005,49637,2234],{},[2138,49639,2182],{},[902,49641,48117],{"encoding":904},[883,49643,49645],{"className":49644},[886],[888,49646,49647],{"xmlns":890},[892,49648,49649,49653],{},[895,49650,49651],{},[898,49652,2151],{},[902,49654,2151],{"encoding":904}," na 30 a růstu ",[883,49657,49659],{"className":49658},[886],[888,49660,49661],{"xmlns":890},[892,49662,49663,49667],{},[895,49664,49665],{},[898,49666,2203],{},[902,49668,2203],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,49671,49673],{"className":49672},[886],[888,49674,49675],{"xmlns":890},[892,49676,49677,49687],{},[895,49678,49679],{},[9172,49680,49681,49683,49685],{},[898,49682,3946],{},[2138,49684,2182],{},[898,49686,1868],{},[902,49688,48920],{"encoding":904},[198,49690,820],{"id":49691},"přebytek-spotřebitele-a-výrobce-1",[724,49693,49694,47689,49697,47726,49733,1644],{},[38,49695,49696],{},"2.17",[883,49698,49700],{"className":49699},[886],[888,49701,49702],{"xmlns":890},[892,49703,49704,49730],{},[895,49705,49706,49708,49710,49712,49714,49716,49718,49720,49722,49724],{},[898,49707,3946],{},[2005,49709,2007],{},[898,49711,1860],{},[2005,49713,2014],{"stretchy":2013},[898,49715,2797],{},[2005,49717,2020],{"stretchy":2013},[2005,49719,2007],{},[2138,49721,15044],{},[2005,49723,2234],{},[2133,49725,49726,49728],{},[898,49727,2797],{},[2138,49729,2140],{},[902,49731,49732],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,49734,49736],{"className":49735},[886],[888,49737,49738],{"xmlns":890},[892,49739,49740,49766],{},[895,49741,49742,49744,49746,49748,49750,49752,49754,49756,49758,49760],{},[898,49743,3946],{},[2005,49745,2007],{},[898,49747,8679],{},[2005,49749,2014],{"stretchy":2013},[898,49751,2797],{},[2005,49753,2020],{"stretchy":2013},[2005,49755,2007],{},[2138,49757,2182],{},[2005,49759,2104],{},[2133,49761,49762,49764],{},[898,49763,2797],{},[2138,49765,2140],{},[902,49767,49768],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,49770,49771,49774],{},[123,49772,49773],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,49775,49776],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,49778,49779,47689,49782,47726,49816,1644],{},[38,49780,49781],{},"2.18",[883,49783,49785],{"className":49784},[886],[888,49786,49787],{"xmlns":890},[892,49788,49789,49813],{},[895,49790,49791,49793,49795,49797,49799,49801,49803,49805,49807,49809,49811],{},[898,49792,3946],{},[2005,49794,2007],{},[898,49796,1860],{},[2005,49798,2014],{"stretchy":2013},[898,49800,2797],{},[2005,49802,2020],{"stretchy":2013},[2005,49804,2007],{},[2138,49806,3715],{},[2005,49808,2234],{},[2138,49810,2140],{},[898,49812,2797],{},[902,49814,49815],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,49817,49819],{"className":49818},[886],[888,49820,49821],{"xmlns":890},[892,49822,49823,49849],{},[895,49824,49825,49827,49829,49831,49833,49835,49837,49839,49841,49843],{},[898,49826,3946],{},[2005,49828,2007],{},[898,49830,8679],{},[2005,49832,2014],{"stretchy":2013},[898,49834,2797],{},[2005,49836,2020],{"stretchy":2013},[2005,49838,2007],{},[2138,49840,2182],{},[2005,49842,2104],{},[2133,49844,49845,49847],{},[898,49846,2797],{},[2138,49848,2140],{},[902,49850,49768],{"encoding":904},[120,49852,49853,49873,49876,49879],{},[123,49854,49855,49856,1644],{},"(a) Vypočtěte rovnovážné množství ",[883,49857,49859],{"className":49858},[886],[888,49860,49861],{"xmlns":890},[892,49862,49863,49871],{},[895,49864,49865],{},[2133,49866,49867,49869],{},[898,49868,2797],{},[898,49870,1868],{},[902,49872,42408],{"encoding":904},[123,49874,49875],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,49877,49878],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,49880,49881],{},"(c) Graficky interpretujte.",[36975,49883],{},[115,49885,49887],{"id":49886},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,49889,49890,49893,49896,49899,49902,49905,49908,49911,49914,49917,49920,49923,49926,49929],{},[123,49891,49892],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,49894,49895],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,49897,49898],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,49900,49901],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,49903,49904],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,49906,49907],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,49909,49910],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,49912,49913],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,49915,49916],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,49918,49919],{},"K čemu slouží multiplikátory?",[123,49921,49922],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,49924,49925],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,49927,49928],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,49930,49931],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[36975,49933],{},[115,49935,15726],{"id":15725},[724,49937,49938],{},[38,49939,13167],{},[120,49941,49942,49977,49982,50012,50017,50080,50106,50111,50141,50150,50157,50163],{},[123,49943,49944,10030,49947,18654,49950,2212,49952,1343,49975],{},[38,49945,49946],{},"Poptávané množství",[614,49948,49949],{},"quantity demanded",[38,49951,28007],{},[883,49953,49955],{"className":49954},[886],[888,49956,49957],{"xmlns":890},[892,49958,49959,49973],{},[895,49960,49961,49963,49965,49967,49969,49971],{},[898,49962,2797],{},[2005,49964,2007],{},[898,49966,1860],{},[2005,49968,2014],{"stretchy":2013},[898,49970,3946],{},[2005,49972,2020],{"stretchy":2013},[902,49974,4200],{"encoding":904},[38,49976,37454],{},[123,49978,49979,49981],{},[38,49980,37461],{}," — substituční + důchodový efekt",[123,49983,49984,2212,49987],{},[38,49985,49986],{},"Reálné cenové rozpětí",[883,49988,49990],{"className":49989},[886],[888,49991,49992],{"xmlns":890},[892,49993,49994,50010],{},[895,49995,49996,49998,50000,50002,50008],{},[2005,49997,2014],{"stretchy":2013},[2138,49999,2336],{},[2005,50001,2295],{"separator":2294},[2281,50003,50004,50006],{},[898,50005,3946],{},[2138,50007,2336],{},[2005,50009,2020],{"stretchy":2013},[902,50011,37662],{"encoding":904},[123,50013,50014,11101],{},[38,50015,50016],{},"Homogenita poptávky",[123,50018,50019,2212,50022,1343,50045,1343,50062,50079],{},[38,50020,50021],{},"Lineární poptávka",[883,50023,50025],{"className":50024},[886],[888,50026,50027],{"xmlns":890},[892,50028,50029,50043],{},[895,50030,50031,50033,50035,50037,50039,50041],{},[898,50032,3946],{},[2005,50034,2007],{},[898,50036,207],{},[898,50038,2797],{},[2005,50040,2104],{},[898,50042,2107],{},[902,50044,37065],{"encoding":904},[883,50046,50048],{"className":50047},[886],[888,50049,50050],{"xmlns":890},[892,50051,50052,50060],{},[895,50053,50054,50056,50058],{},[898,50055,207],{},[2005,50057,3455],{},[2138,50059,2336],{},[902,50061,43090],{"encoding":904},[883,50063,50065],{"className":50064},[886],[888,50066,50067],{"xmlns":890},[892,50068,50069,50077],{},[895,50070,50071,50073,50075],{},[898,50072,2107],{},[2005,50074,3416],{},[2138,50076,2336],{},[902,50078,18820],{"encoding":904}," — nedokonalá konkurence",[123,50081,50082,7021,50085],{},[38,50083,50084],{},"Dokonalá konkurence",[883,50086,50088],{"className":50087},[886],[888,50089,50090],{"xmlns":890},[892,50091,50092,50104],{},[895,50093,50094,50096,50098],{},[898,50095,3946],{},[2005,50097,2007],{},[2133,50099,50100,50102],{},[898,50101,3946],{},[2005,50103,4360],{},[902,50105,4363],{"encoding":904},[123,50107,50108,50110],{},[38,50109,38231],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,50112,50113,2212,50115,1343,50139],{},[38,50114,31732],{},[883,50116,50118],{"className":50117},[886],[888,50119,50120],{"xmlns":890},[892,50121,50122,50136],{},[895,50123,50124,50126,50128,50130,50132,50134],{},[898,50125,2797],{},[2005,50127,2007],{},[898,50129,1868],{},[2005,50131,2014],{"stretchy":2013},[898,50133,9134],{},[2005,50135,2020],{"stretchy":2013},[902,50137,50138],{"encoding":904},"Q = E(Y)",[38,50140,38428],{},[123,50142,50143,50146,50147,50149],{},[38,50144,50145],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,50148,38874],{}," zboží",[123,50151,50152,3894,50154,50156],{},[38,50153,39880],{},[38,50155,39827],{}," — znaménka zkřížených koeficientů",[123,50158,50159,50162],{},[38,50160,50161],{},"Dvoukomoditní trh"," (2.6)",[123,50164,50165,10030,50168,2020],{},[38,50166,50167],{},"Posun poptávky",[614,50169,38932],{},[724,50171,50172],{},[38,50173,13131],{},[120,50175,50176,50209,50213,50258],{},[123,50177,50178,10030,50180,18654,50182,2212,50184,1343,50207],{},[38,50179,40274],{},[614,50181,40277],{},[38,50183,40448],{},[883,50185,50187],{"className":50186},[886],[888,50188,50189],{"xmlns":890},[892,50190,50191,50205],{},[895,50192,50193,50195,50197,50199,50201,50203],{},[898,50194,2797],{},[2005,50196,2007],{},[898,50198,8679],{},[2005,50200,2014],{"stretchy":2013},[898,50202,3946],{},[2005,50204,2020],{"stretchy":2013},[902,50206,8688],{"encoding":904},[38,50208,40526],{},[123,50210,50211],{},[38,50212,40533],{},[123,50214,50215,2212,50218,1343,50241],{},[38,50216,50217],{},"Lineární nabídka",[883,50219,50221],{"className":50220},[886],[888,50222,50223],{"xmlns":890},[892,50224,50225,50239],{},[895,50226,50227,50229,50231,50233,50235,50237],{},[898,50228,3946],{},[2005,50230,2007],{},[898,50232,2151],{},[898,50234,2797],{},[2005,50236,2104],{},[898,50238,2203],{},[902,50240,40247],{"encoding":904},[883,50242,50244],{"className":50243},[886],[888,50245,50246],{"xmlns":890},[892,50247,50248,50256],{},[895,50249,50250,50252,50254],{},[898,50251,2151],{},[2005,50253,3416],{},[2138,50255,2336],{},[902,50257,40265],{"encoding":904},[123,50259,50260,10030,50263,2020],{},[38,50261,50262],{},"Posun nabídky",[614,50264,40911],{},[724,50266,50267],{},[38,50268,50269],{},"Rovnováha a komparativní statika",[120,50271,50272,50351,50357],{},[123,50273,50274,10030,50276,18654,50278,2212,50281,1343,50298,2212,50301,1343,50318,2212,50320],{},[38,50275,41330],{},[614,50277,41449],{},[38,50279,50280],{},"rovnovážná cena",[883,50282,50284],{"className":50283},[886],[888,50285,50286],{"xmlns":890},[892,50287,50288,50296],{},[895,50289,50290],{},[2133,50291,50292,50294],{},[898,50293,3946],{},[898,50295,1868],{},[902,50297,41471],{"encoding":904},[38,50299,50300],{},"rovnovážné množství",[883,50302,50304],{"className":50303},[886],[888,50305,50306],{"xmlns":890},[892,50307,50308,50316],{},[895,50309,50310],{},[2133,50311,50312,50314],{},[898,50313,2797],{},[898,50315,1868],{},[902,50317,42408],{"encoding":904},[38,50319,41507],{},[883,50321,50323],{"className":50322},[886],[888,50324,50325],{"xmlns":890},[892,50326,50327,50349],{},[895,50328,50329,50331,50333,50339,50341,50347],{},[898,50330,1868],{},[2005,50332,2495],{"stretchy":2013},[2133,50334,50335,50337],{},[898,50336,2797],{},[898,50338,1868],{},[2005,50340,2295],{"separator":2294},[2133,50342,50343,50345],{},[898,50344,3946],{},[898,50346,1868],{},[2005,50348,2510],{"stretchy":2013},[902,50350,41372],{"encoding":904},[123,50352,50353,50356],{},[38,50354,50355],{},"Pravidla 1–4"," komparativní statiky",[123,50358,50359,10030,50362,2020],{},[38,50360,50361],{},"Teorém pavučiny",[614,50363,42354],{},[724,50365,50366],{},[38,50367,50368],{},"Zdanění",[120,50370,50371,50427,50475],{},[123,50372,50373,50375,50376,50401,50402,2020],{},[38,50374,50368],{}," — daň výrobci (",[883,50377,50379],{"className":50378},[886],[888,50380,50381],{"xmlns":890},[892,50382,50383,50399],{},[895,50384,50385,50391,50393,50395,50397],{},[2281,50386,50387,50389],{},[898,50388,8679],{},[2138,50390,2287],{},[2005,50392,2007],{},[898,50394,8679],{},[2005,50396,2104],{},[898,50398,2783],{},[902,50400,42759],{"encoding":904},") vs. daň spotřebiteli (",[883,50403,50405],{"className":50404},[886],[888,50406,50407],{"xmlns":890},[892,50408,50409,50425],{},[895,50410,50411,50417,50419,50421,50423],{},[2281,50412,50413,50415],{},[898,50414,1860],{},[2138,50416,2140],{},[2005,50418,2007],{},[898,50420,1860],{},[2005,50422,2234],{},[898,50424,2783],{},[902,50426,42790],{"encoding":904},[123,50428,50429,2212,50431,1343,50452],{},[38,50430,42663],{},[883,50432,50434],{"className":50433},[886],[888,50435,50436],{"xmlns":890},[892,50437,50438,50450],{},[895,50439,50440],{},[2281,50441,50442,50444],{},[898,50443,2783],{},[895,50445,50446,50448],{},[898,50447,42682],{},[898,50449,724],{},[902,50451,42687],{"encoding":904},[883,50453,50455],{"className":50454},[886],[888,50456,50457],{"xmlns":890},[892,50458,50459,50473],{},[895,50460,50461],{},[2281,50462,50463,50465],{},[898,50464,2783],{},[895,50466,50467,50469,50471],{},[898,50468,42705],{},[898,50470,2003],{},[898,50472,12047],{},[902,50474,42712],{"encoding":904},[123,50476,50477,2212,50480,1343,50509],{},[38,50478,50479],{},"Ekvivalence zdanění",[883,50481,50483],{"className":50482},[886],[888,50484,50485],{"xmlns":890},[892,50486,50487,50507],{},[895,50488,50489,50497,50499],{},[9172,50490,50491,50493,50495],{},[898,50492,2797],{},[2138,50494,2287],{},[898,50496,1868],{},[2005,50498,2007],{},[9172,50500,50501,50503,50505],{},[898,50502,2797],{},[2138,50504,2140],{},[898,50506,1868],{},[902,50508,42913],{"encoding":904},[883,50510,50512],{"className":50511},[886],[888,50513,50514],{"xmlns":890},[892,50515,50516,50540],{},[895,50517,50518,50526,50528,50530,50532],{},[9172,50519,50520,50522,50524],{},[898,50521,3946],{},[2138,50523,2287],{},[898,50525,1868],{},[2005,50527,2234],{},[898,50529,2783],{},[2005,50531,2007],{},[9172,50533,50534,50536,50538],{},[898,50535,3946],{},[2138,50537,2140],{},[898,50539,1868],{},[902,50541,42947],{"encoding":904},[724,50543,50544],{},[38,50545,26413],{},[120,50547,50548,50594,50625,50630,50636,50643],{},[123,50549,50550,2212,50552],{},[38,50551,43046],{},[883,50553,50555],{"className":50554},[886],[888,50556,50557],{"xmlns":890},[892,50558,50559,50591],{},[895,50560,50561,50567,50569,50571,50573,50575,50577,50579,50581,50583,50585,50587,50589],{},[2133,50562,50563,50565],{},[898,50564,2797],{},[898,50566,1868],{},[2005,50568,2007],{},[2005,50570,2014],{"stretchy":2013},[898,50572,2107],{},[2005,50574,2234],{},[898,50576,2203],{},[2005,50578,2020],{"stretchy":2013},[898,50580,4680],{"mathvariant":2385},[2005,50582,2014],{"stretchy":2013},[898,50584,2151],{},[2005,50586,2234],{},[898,50588,207],{},[2005,50590,2020],{"stretchy":2013},[902,50592,50593],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,50595,50596,2212,50599,50624],{},[38,50597,50598],{},"Parametry",[883,50600,50602],{"className":50601},[886],[888,50603,50604],{"xmlns":890},[892,50605,50606,50622],{},[895,50607,50608,50610,50612,50614,50616,50618,50620],{},[898,50609,207],{},[2005,50611,2295],{"separator":2294},[898,50613,2107],{},[2005,50615,2295],{"separator":2294},[898,50617,2151],{},[2005,50619,2295],{"separator":2294},[898,50621,2203],{},[902,50623,43290],{"encoding":904}," — exogenní proměnné",[123,50626,50627],{},[38,50628,50629],{},"Endogenní \u002F exogenní proměnná",[123,50631,50632,50635],{},[38,50633,50634],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,50637,50638,1343,50641],{},[38,50639,50640],{},"Komparativní statika",[38,50642,36965],{},[123,50644,50645,2212,50647,50663],{},[38,50646,2963],{},[883,50648,50650],{"className":50649},[886],[888,50651,50652],{"xmlns":890},[892,50653,50654,50660],{},[895,50655,50656,50658],{},[898,50657,2203],{},[898,50659,2797],{},[902,50661,50662],{"encoding":904},"dQ"," (2.11)",[724,50665,50666],{},[38,50667,50668],{},"Přebytky a ostatní",[120,50670,50671,50709],{},[123,50672,50673,2212,50675,50690,50691,2212,50693,50708],{},[38,50674,44939],{},[883,50676,50678],{"className":50677},[886],[888,50679,50680],{"xmlns":890},[892,50681,50682,50688],{},[895,50683,50684,50686],{},[898,50685,1852],{},[898,50687,8679],{},[902,50689,44955],{"encoding":904}," (2.14), ",[38,50692,44958],{},[883,50694,50696],{"className":50695},[886],[888,50697,50698],{"xmlns":890},[892,50699,50700,50706],{},[895,50701,50702,50704],{},[898,50703,3946],{},[898,50705,8679],{},[902,50707,44974],{"encoding":904}," (2.15)",[123,50710,50711,1343,50714,50717],{},[38,50712,50713],{},"Homo economicus",[38,50715,50716],{},"Marshallova formulace"," (1890)",[36975,50719],{},[115,50721,3800],{"id":3799},[120,50723,50724,50759,50768],{},[123,50725,50726,2212,50729,50732,50733,1343,50736,50739,50740,50743,50744,50747,50748,50751,50752,50755,50756],{},[38,50727,50728],{},"Související témata:",[207,50730,811],{"className":50731,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,50734,820],{"className":50735,"dataFsResolvedFilePath":818,"href":819},[210],[207,50737,2366],{"className":50738,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,50741,775],{"className":50742,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,50745,784],{"className":50746,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,50749,793],{"className":50750,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,50753,3836],{"className":50754,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,50757,3831],{"className":50758,"dataFsResolvedFilePath":827,"href":828},[210],[123,50760,50761,2212,50764],{},[38,50762,50763],{},"Shrnutí přednášek:",[207,50765,50767],{"className":50766,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,50769,50770,2212,50772],{},[38,50771,16210],{},[207,50773,16214],{"className":50774,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":50776},[50777,50778,50786,50792,50799,50800,50807,50808,50809,50816,50817,50818],{"id":36799,"depth":642,"text":36800},{"id":36780,"depth":642,"text":13167,"children":50779},[50780,50781,50782,50783,50785],{"id":37068,"depth":649,"text":37069},{"id":37350,"depth":649,"text":37351},{"id":38360,"depth":649,"text":38361},{"id":38928,"depth":649,"text":50784},"Posun poptávky (shift of demand)",{"id":39432,"depth":649,"text":39433},{"id":36784,"depth":642,"text":13131,"children":50787},[50788,50789,50790],{"id":40269,"depth":649,"text":37069},{"id":40455,"depth":649,"text":40456},{"id":40907,"depth":649,"text":50791},"Posun nabídky (shift of supply)",{"id":41329,"depth":642,"text":41330,"children":50793},[50794,50795,50796,50797,50798],{"id":41441,"depth":649,"text":41442},{"id":41654,"depth":649,"text":41655},{"id":41972,"depth":649,"text":41973},{"id":42326,"depth":649,"text":42327},{"id":42357,"depth":649,"text":42358},{"id":42626,"depth":642,"text":811},{"id":43027,"depth":642,"text":43028,"children":50801},[50802,50803,50804,50805],{"id":43045,"depth":649,"text":43046},{"id":43426,"depth":649,"text":43427},{"id":43810,"depth":649,"text":43811},{"id":44264,"depth":649,"text":50806},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":11789,"depth":642,"text":820},{"id":45189,"depth":642,"text":45190},{"id":45420,"depth":642,"text":45421,"children":50810},[50811,50812,50813,50814,50815],{"id":45424,"depth":649,"text":45425},{"id":46264,"depth":649,"text":46265},{"id":46640,"depth":649,"text":41330},{"id":47935,"depth":649,"text":43028},{"id":49691,"depth":649,"text":820},{"id":49886,"depth":642,"text":49887},{"id":15725,"depth":642,"text":15726},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,50825,50826,50827,17890,50828,50829],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":50832,"title":820,"body":50833,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":55112,"navigation":664,"path":55113,"seo":55114,"sources":55115,"stem":55116,"tags":55117,"type":3865,"updated":677,"__hash__":55122},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":50834,"toc":55090},[50835,50837,50905,50955,50957,50960,51218,51294,51299,51301,51320,51324,51400,51485,51487,51801,51894,51896,51915,51919,51993,52078,52081,52257,52262,52264,52684,52686,52690,52694,52930,52974,53074,53140,53143,53176,53352,53414,53544,53622,53733,53767,53965,53984,54003,54068,54072,54075,54120,54123,54241,54287,54289,54293,54641,54643,54645,54923,54925,54929,54964,54971,55044,55046,55048],[12,50836,820],{"id":11789},[3876,50838,50839],{},[724,50840,50841,3883,50843,10030,50845,50860,50861,10030,50863,50878,50879,50901,50902,1644],{},[883,50842,3882],{},[38,50844,44939],{},[883,50846,50848],{"className":50847},[886],[888,50849,50850],{"xmlns":890},[892,50851,50852,50858],{},[895,50853,50854,50856],{},[898,50855,1852],{},[898,50857,8679],{},[902,50859,44955],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,50862,45086],{},[883,50864,50866],{"className":50865},[886],[888,50867,50868],{"xmlns":890},[892,50869,50870,50876],{},[895,50871,50872,50874],{},[898,50873,3946],{},[898,50875,8679],{},[902,50877,44974],{"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 ",[883,50880,50882],{"className":50881},[886],[888,50883,50884],{"xmlns":890},[892,50885,50886,50898],{},[895,50887,50888,50890,50892,50894,50896],{},[898,50889,1852],{},[898,50891,8679],{},[2005,50893,2104],{},[898,50895,3946],{},[898,50897,8679],{},[902,50899,50900],{"encoding":904},"CS + PS"," měří ",[38,50903,50904],{},"celkový blahobyt trhu",[724,50906,50907,10030,50909,1343,50911,12134,50926,10030,50928,1343,50930,50945,50946,50950,50951,1644],{},[38,50908,44939],{},[614,50910,44993],{},[883,50912,50914],{"className":50913},[886],[888,50915,50916],{"xmlns":890},[892,50917,50918,50924],{},[895,50919,50920,50922],{},[898,50921,1852],{},[898,50923,8679],{},[902,50925,44955],{"encoding":904},[38,50927,44958],{},[614,50929,45089],{},[883,50931,50933],{"className":50932},[886],[888,50934,50935],{"xmlns":890},[892,50936,50937,50943],{},[895,50938,50939,50941],{},[898,50940,3946],{},[898,50942,8679],{},[902,50944,44974],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,50947,50949],{"className":50948,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,50952,50954],{"className":50953,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[36975,50956],{},[115,50958,1241],{"id":50959},"úvod",[724,50961,50962,50963,50986,50987,51010,51011,51028,51029,3919,51061,51093,51094,51120,51121,51124,51125,51128,51129,14017,51163,21600,51184,1644],{},"Je dána funkce poptávky ",[883,50964,50966],{"className":50965},[886],[888,50967,50968],{"xmlns":890},[892,50969,50970,50984],{},[895,50971,50972,50974,50976,50978,50980,50982],{},[898,50973,3946],{},[2005,50975,2007],{},[898,50977,1860],{},[2005,50979,2014],{"stretchy":2013},[898,50981,2797],{},[2005,50983,2020],{"stretchy":2013},[902,50985,4646],{"encoding":904},", resp. funkce nabídky ",[883,50988,50990],{"className":50989},[886],[888,50991,50992],{"xmlns":890},[892,50993,50994,51008],{},[895,50995,50996,50998,51000,51002,51004,51006],{},[898,50997,3946],{},[2005,50999,2007],{},[898,51001,8679],{},[2005,51003,2014],{"stretchy":2013},[898,51005,2797],{},[2005,51007,2020],{"stretchy":2013},[902,51009,41076],{"encoding":904},". Pro pevně zadané množství ",[883,51012,51014],{"className":51013},[886],[888,51015,51016],{"xmlns":890},[892,51017,51018,51026],{},[895,51019,51020],{},[2281,51021,51022,51024],{},[898,51023,2797],{},[2138,51025,2336],{},[902,51027,38313],{"encoding":904}," je odpovídající cena ",[883,51030,51032],{"className":51031},[886],[888,51033,51034],{"xmlns":890},[892,51035,51036,51058],{},[895,51037,51038,51044,51046,51048,51050,51056],{},[2281,51039,51040,51042],{},[898,51041,3946],{},[2138,51043,2336],{},[2005,51045,2007],{},[898,51047,1860],{},[2005,51049,2014],{"stretchy":2013},[2281,51051,51052,51054],{},[898,51053,2797],{},[2138,51055,2336],{},[2005,51057,2020],{"stretchy":2013},[902,51059,51060],{"encoding":904},"P_0 = D(Q_0)",[883,51062,51064],{"className":51063},[886],[888,51065,51066],{"xmlns":890},[892,51067,51068,51090],{},[895,51069,51070,51076,51078,51080,51082,51088],{},[2281,51071,51072,51074],{},[898,51073,3946],{},[2138,51075,2336],{},[2005,51077,2007],{},[898,51079,8679],{},[2005,51081,2014],{"stretchy":2013},[2281,51083,51084,51086],{},[898,51085,2797],{},[2138,51087,2336],{},[2005,51089,2020],{"stretchy":2013},[902,51091,51092],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,51095,51097],{"className":51096},[886],[888,51098,51099],{"xmlns":890},[892,51100,51101,51117],{},[895,51102,51103,51109,51111],{},[2281,51104,51105,51107],{},[898,51106,3946],{},[2138,51108,2336],{},[2297,51110,2995],{},[2281,51112,51113,51115],{},[898,51114,2797],{},[2138,51116,2336],{},[902,51118,51119],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,51122,51123],{},"výdaje spotřebitele",", nebo ",[38,51126,51127],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,51130,51132],{"className":51131},[886],[888,51133,51134],{"xmlns":890},[892,51135,51136,51160],{},[895,51137,51138,51140,51142,51148,51150,51152,51154],{},[2138,51139,2336],{},[2297,51141,2995],{},[2281,51143,51144,51146],{},[898,51145,2797],{},[2138,51147,2336],{},[2297,51149,2995],{},[898,51151,1836],{},[2297,51153,2995],{},[2281,51155,51156,51158],{},[898,51157,3946],{},[2138,51159,2336],{},[902,51161,51162],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,51164,51166],{"className":51165},[886],[888,51167,51168],{"xmlns":890},[892,51169,51170,51182],{},[895,51171,51172,51174,51176,51178,51180],{},[2005,51173,2014],{"stretchy":2013},[898,51175,2797],{},[2005,51177,2295],{"separator":2294},[898,51179,3946],{},[2005,51181,2020],{"stretchy":2013},[902,51183,37696],{"encoding":904},[883,51185,51187],{"className":51186},[886],[888,51188,51189],{"xmlns":890},[892,51190,51191,51215],{},[895,51192,51193,51195,51197,51199,51205,51207,51213],{},[898,51194,1836],{},[2005,51196,2007],{},[2005,51198,2495],{"stretchy":2013},[2281,51200,51201,51203],{},[898,51202,2797],{},[2138,51204,2336],{},[2005,51206,2295],{"separator":2294},[2281,51208,51209,51211],{},[898,51210,3946],{},[2138,51212,2336],{},[2005,51214,2510],{"stretchy":2013},[902,51216,51217],{"encoding":904},"A = [Q_0, P_0]",[3876,51219,51220,51225,51283],{},[724,51221,51222,51224],{},[883,51223,4164],{}," Intuice",[120,51226,51227,51255],{},[123,51228,51229,51230,51233,51234,51236,51237,51254],{},"Za jednotky zboží nakoupené ",[38,51231,51232],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,51235,25275],{}," než ",[883,51238,51240],{"className":51239},[886],[888,51241,51242],{"xmlns":890},[892,51243,51244,51252],{},[895,51245,51246],{},[2281,51247,51248,51250],{},[898,51249,3946],{},[2138,51251,2336],{},[902,51253,38953],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,51256,51257,51258,51260,51261,51264,51265,51282],{},"Za jednotky zboží prodané ",[38,51259,51232],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,51262,51263],{},"nižší"," cenu než ",[883,51266,51268],{"className":51267},[886],[888,51269,51270],{"xmlns":890},[892,51271,51272,51280],{},[895,51273,51274],{},[2281,51275,51276,51278],{},[898,51277,3946],{},[2138,51279,2336],{},[902,51281,38953],{"encoding":904}," — rozdíl je jeho přebytek.",[724,51284,51285,51286,51289,51290,51293],{},"Přebytek je tedy rozdíl mezi ",[614,51287,51288],{},"ochotou"," (platit \u002F prodávat) a ",[614,51291,51292],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,51295,51296],{},[2568,51297],{"alt":44984,"className":51298,"src":44986},[210,2572],[36975,51300],{},[115,51302,51304,51305,2020],{"id":51303},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,51306,51308],{"className":51307},[886],[888,51309,51310],{"xmlns":890},[892,51311,51312,51318],{},[895,51313,51314,51316],{},[898,51315,1852],{},[898,51317,8679],{},[902,51319,44955],{"encoding":904},[198,51321,51323],{"id":51322},"definice-vzorec-214","Definice (vzorec 2.14)",[724,51325,51326,51327,51350,51351,51368,51369,2713],{},"Pro poptávku ",[883,51328,51330],{"className":51329},[886],[888,51331,51332],{"xmlns":890},[892,51333,51334,51348],{},[895,51335,51336,51338,51340,51342,51344,51346],{},[898,51337,3946],{},[2005,51339,2007],{},[898,51341,1860],{},[2005,51343,2014],{"stretchy":2013},[898,51345,2797],{},[2005,51347,2020],{"stretchy":2013},[902,51349,4646],{"encoding":904}," a pevně zadané ",[883,51352,51354],{"className":51353},[886],[888,51355,51356],{"xmlns":890},[892,51357,51358,51366],{},[895,51359,51360],{},[2281,51361,51362,51364],{},[898,51363,2797],{},[2138,51365,2336],{},[902,51367,38313],{"encoding":904}," s cenou ",[883,51370,51372],{"className":51371},[886],[888,51373,51374],{"xmlns":890},[892,51375,51376,51398],{},[895,51377,51378,51384,51386,51388,51390,51396],{},[2281,51379,51380,51382],{},[898,51381,3946],{},[2138,51383,2336],{},[2005,51385,2007],{},[898,51387,1860],{},[2005,51389,2014],{"stretchy":2013},[2281,51391,51392,51394],{},[898,51393,2797],{},[2138,51395,2336],{},[2005,51397,2020],{"stretchy":2013},[902,51399,51060],{"encoding":904},[883,51401,51403],{"className":51402},[886],[888,51404,51405],{"xmlns":890,"display":28071},[892,51406,51407,51483],{},[20760,51408,51409],{"width":28076},[20765,51410,51411,51413,51477,51479],{},[20768,51412],{"width":28081},[20768,51414,51415],{},[895,51416,51417,51419,51421,51423,51429,51431,51433,51445,51447,51449,51451,51453,51455,51457,51459,51461,51467,51469,51475],{},[898,51418,1852],{},[898,51420,8679],{},[2005,51422,2014],{"stretchy":2013},[2281,51424,51425,51427],{},[898,51426,2797],{},[2138,51428,2336],{},[2005,51430,2020],{"stretchy":2013},[2005,51432,2007],{},[9172,51434,51435,51437,51439],{},[2005,51436,11174],{},[2138,51438,2336],{},[2281,51440,51441,51443],{},[898,51442,2797],{},[2138,51444,2336],{},[898,51446,1860],{},[2005,51448,2014],{"stretchy":2013},[898,51450,2797],{},[2005,51452,2020],{"stretchy":2013},[2297,51454,2995],{},[898,51456,2203],{},[898,51458,2797],{},[2005,51460,2234],{},[2281,51462,51463,51465],{},[898,51464,3946],{},[2138,51466,2336],{},[2297,51468,2995],{},[2281,51470,51471,51473],{},[898,51472,2797],{},[2138,51474,2336],{},[898,51476,1644],{"mathvariant":2385},[20768,51478],{"width":28081},[20768,51480,51481],{},[2297,51482,45078],{},[902,51484,45081],{"encoding":904},[198,51486,2453],{"id":2452},[120,51488,51489,51581,51643],{},[123,51490,51491,51531,51532,51558,51559,51562,51563,51580],{},[883,51492,51494],{"className":51493},[886],[888,51495,51496],{"xmlns":890},[892,51497,51498,51528],{},[895,51499,51500],{},[2334,51501,51502,51514,51516,51518,51520,51522,51524,51526],{"scriptlevel":2336,"displaystyle":2294},[9172,51503,51504,51506,51508],{},[2005,51505,11174],{},[2138,51507,2336],{},[2281,51509,51510,51512],{},[898,51511,2797],{},[2138,51513,2336],{},[898,51515,1860],{},[2005,51517,2014],{"stretchy":2013},[898,51519,2797],{},[2005,51521,2020],{"stretchy":2013},[2297,51523,2995],{},[898,51525,2203],{},[898,51527,2797],{},[902,51529,51530],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,51533,51535],{"className":51534},[886],[888,51536,51537],{"xmlns":890},[892,51538,51539,51555],{},[895,51540,51541,51543,51545,51547,51553],{},[2005,51542,2495],{"stretchy":2013},[2138,51544,2336],{},[2005,51546,2295],{"separator":2294},[2281,51548,51549,51551],{},[898,51550,2797],{},[2138,51552,2336],{},[2005,51554,2510],{"stretchy":2013},[902,51556,51557],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,51560,51561],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,51564,51566],{"className":51565},[886],[888,51567,51568],{"xmlns":890},[892,51569,51570,51578],{},[895,51571,51572],{},[2281,51573,51574,51576],{},[898,51575,2797],{},[2138,51577,2336],{},[902,51579,38313],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,51582,51583,51609,51610,3927],{},[883,51584,51586],{"className":51585},[886],[888,51587,51588],{"xmlns":890},[892,51589,51590,51606],{},[895,51591,51592,51598,51600],{},[2281,51593,51594,51596],{},[898,51595,3946],{},[2138,51597,2336],{},[2297,51599,2995],{},[2281,51601,51602,51604],{},[898,51603,2797],{},[2138,51605,2336],{},[902,51607,51608],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,51611,51613],{"className":51612},[886],[888,51614,51615],{"xmlns":890},[892,51616,51617,51641],{},[895,51618,51619,51621,51623,51629,51631,51633,51635],{},[2138,51620,2336],{},[2297,51622,2995],{},[2281,51624,51625,51627],{},[898,51626,2797],{},[2138,51628,2336],{},[2297,51630,2995],{},[898,51632,1836],{},[2297,51634,2995],{},[2281,51636,51637,51639],{},[898,51638,3946],{},[2138,51640,2336],{},[902,51642,51162],{"encoding":904},[123,51644,51645,51660,51661,51683,51684,51709,51710,21600,51736,3894,51768,1644],{},[883,51646,51648],{"className":51647},[886],[888,51649,51650],{"xmlns":890},[892,51651,51652,51658],{},[895,51653,51654,51656],{},[898,51655,1852],{},[898,51657,8679],{},[902,51659,44955],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,51662,51664],{"className":51663},[886],[888,51665,51666],{"xmlns":890},[892,51667,51668,51680],{},[895,51669,51670,51672,51674],{},[898,51671,3946],{},[2005,51673,2007],{},[2281,51675,51676,51678],{},[898,51677,3946],{},[2138,51679,2336],{},[902,51681,51682],{"encoding":904},"P = P_0"," v pásu ",[883,51685,51687],{"className":51686},[886],[888,51688,51689],{"xmlns":890},[892,51690,51691,51707],{},[895,51692,51693,51695,51697,51699,51705],{},[2005,51694,2495],{"stretchy":2013},[2138,51696,2336],{},[2005,51698,2295],{"separator":2294},[2281,51700,51701,51703],{},[898,51702,2797],{},[2138,51704,2336],{},[2005,51706,2510],{"stretchy":2013},[902,51708,51557],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,51711,51713],{"className":51712},[886],[888,51714,51715],{"xmlns":890},[892,51716,51717,51733],{},[895,51718,51719,51725,51727,51729,51731],{},[2281,51720,51721,51723],{},[898,51722,3946],{},[2138,51724,2336],{},[2297,51726,2995],{},[898,51728,1844],{},[2297,51730,2995],{},[898,51732,1836],{},[902,51734,51735],{"encoding":904},"P_0\\,B\\,A",[883,51737,51739],{"className":51738},[886],[888,51740,51741],{"xmlns":890},[892,51742,51743,51765],{},[895,51744,51745,51747,51749,51751,51753,51755,51757,51759,51761,51763],{},[898,51746,1844],{},[2005,51748,2007],{},[2005,51750,2495],{"stretchy":2013},[2138,51752,2336],{},[2005,51754,2295],{"separator":2294},[898,51756,1860],{},[2005,51758,2014],{"stretchy":2013},[2138,51760,2336],{},[2005,51762,2020],{"stretchy":2013},[2005,51764,2510],{"stretchy":2013},[902,51766,51767],{"encoding":904},"B = [0, D(0)]",[883,51769,51771],{"className":51770},[886],[888,51772,51773],{"xmlns":890},[892,51774,51775,51799],{},[895,51776,51777,51779,51781,51783,51789,51791,51797],{},[898,51778,1836],{},[2005,51780,2007],{},[2005,51782,2495],{"stretchy":2013},[2281,51784,51785,51787],{},[898,51786,2797],{},[2138,51788,2336],{},[2005,51790,2295],{"separator":2294},[2281,51792,51793,51795],{},[898,51794,3946],{},[2138,51796,2336],{},[2005,51798,2510],{"stretchy":2013},[902,51800,51217],{"encoding":904},[724,51802,51803],{},[614,51804,51805,51806,51819,51820,51853,51854,29147,51879,1644],{},"Obrázek 2.24: Křivka poptávky ",[883,51807,51809],{"className":51808},[886],[888,51810,51811],{"xmlns":890},[892,51812,51813,51817],{},[895,51814,51815],{},[898,51816,1860],{},[902,51818,1860],{"encoding":904},", bod ",[883,51821,51823],{"className":51822},[886],[888,51824,51825],{"xmlns":890},[892,51826,51827,51851],{},[895,51828,51829,51831,51833,51835,51841,51843,51849],{},[898,51830,1836],{},[2005,51832,2007],{},[2005,51834,2495],{"stretchy":2013},[2281,51836,51837,51839],{},[898,51838,2797],{},[2138,51840,2336],{},[2005,51842,2295],{"separator":2294},[2281,51844,51845,51847],{},[898,51846,3946],{},[2138,51848,2336],{},[2005,51850,2510],{"stretchy":2013},[902,51852,51217],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,51855,51857],{"className":51856},[886],[888,51858,51859],{"xmlns":890},[892,51860,51861,51877],{},[895,51862,51863,51869,51871,51873,51875],{},[2281,51864,51865,51867],{},[898,51866,3946],{},[2138,51868,2336],{},[2297,51870,2995],{},[898,51872,1844],{},[2297,51874,2995],{},[898,51876,1836],{},[902,51878,51735],{"encoding":904},[883,51880,51882],{"className":51881},[886],[888,51883,51884],{"xmlns":890},[892,51885,51886,51892],{},[895,51887,51888,51890],{},[898,51889,1852],{},[898,51891,8679],{},[902,51893,44955],{"encoding":904},[36975,51895],{},[115,51897,51899,51900,2020],{"id":51898},"přebytek-výrobce-psps","Přebytek výrobce (",[883,51901,51903],{"className":51902},[886],[888,51904,51905],{"xmlns":890},[892,51906,51907,51913],{},[895,51908,51909,51911],{},[898,51910,3946],{},[898,51912,8679],{},[902,51914,44974],{"encoding":904},[198,51916,51918],{"id":51917},"definice-vzorec-215","Definice (vzorec 2.15)",[724,51920,51921,51922,51350,51945,51368,51962,2713],{},"Analogicky — pro nabídku ",[883,51923,51925],{"className":51924},[886],[888,51926,51927],{"xmlns":890},[892,51928,51929,51943],{},[895,51930,51931,51933,51935,51937,51939,51941],{},[898,51932,3946],{},[2005,51934,2007],{},[898,51936,8679],{},[2005,51938,2014],{"stretchy":2013},[898,51940,2797],{},[2005,51942,2020],{"stretchy":2013},[902,51944,41076],{"encoding":904},[883,51946,51948],{"className":51947},[886],[888,51949,51950],{"xmlns":890},[892,51951,51952,51960],{},[895,51953,51954],{},[2281,51955,51956,51958],{},[898,51957,2797],{},[2138,51959,2336],{},[902,51961,38313],{"encoding":904},[883,51963,51965],{"className":51964},[886],[888,51966,51967],{"xmlns":890},[892,51968,51969,51991],{},[895,51970,51971,51977,51979,51981,51983,51989],{},[2281,51972,51973,51975],{},[898,51974,3946],{},[2138,51976,2336],{},[2005,51978,2007],{},[898,51980,8679],{},[2005,51982,2014],{"stretchy":2013},[2281,51984,51985,51987],{},[898,51986,2797],{},[2138,51988,2336],{},[2005,51990,2020],{"stretchy":2013},[902,51992,51092],{"encoding":904},[883,51994,51996],{"className":51995},[886],[888,51997,51998],{"xmlns":890,"display":28071},[892,51999,52000,52076],{},[20760,52001,52002],{"width":28076},[20765,52003,52004,52006,52070,52072],{},[20768,52005],{"width":28081},[20768,52007,52008],{},[895,52009,52010,52012,52014,52016,52022,52024,52026,52032,52034,52040,52042,52054,52056,52058,52060,52062,52064,52066,52068],{},[898,52011,3946],{},[898,52013,8679],{},[2005,52015,2014],{"stretchy":2013},[2281,52017,52018,52020],{},[898,52019,2797],{},[2138,52021,2336],{},[2005,52023,2020],{"stretchy":2013},[2005,52025,2007],{},[2281,52027,52028,52030],{},[898,52029,3946],{},[2138,52031,2336],{},[2297,52033,2995],{},[2281,52035,52036,52038],{},[898,52037,2797],{},[2138,52039,2336],{},[2005,52041,2234],{},[9172,52043,52044,52046,52048],{},[2005,52045,11174],{},[2138,52047,2336],{},[2281,52049,52050,52052],{},[898,52051,2797],{},[2138,52053,2336],{},[898,52055,8679],{},[2005,52057,2014],{"stretchy":2013},[898,52059,2797],{},[2005,52061,2020],{"stretchy":2013},[2297,52063,2995],{},[898,52065,2203],{},[898,52067,2797],{},[898,52069,1644],{"mathvariant":2385},[20768,52071],{"width":28081},[20768,52073,52074],{},[2297,52075,45174],{},[902,52077,45177],{"encoding":904},[198,52079,2453],{"id":52080},"geometrická-interpretace-1",[120,52082,52083,52131,52192],{},[123,52084,52085,7021,52110,52113,52114,1644],{},[883,52086,52088],{"className":52087},[886],[888,52089,52090],{"xmlns":890},[892,52091,52092,52108],{},[895,52093,52094,52100,52102],{},[2281,52095,52096,52098],{},[898,52097,3946],{},[2138,52099,2336],{},[2297,52101,2995],{},[2281,52103,52104,52106],{},[898,52105,2797],{},[2138,52107,2336],{},[902,52109,51608],{"encoding":904},[38,52111,52112],{},"tržba"," výrobce za prodané množství ",[883,52115,52117],{"className":52116},[886],[888,52118,52119],{"xmlns":890},[892,52120,52121,52129],{},[895,52122,52123],{},[2281,52124,52125,52127],{},[898,52126,2797],{},[2138,52128,2336],{},[902,52130,38313],{"encoding":904},[123,52132,52133,52173,52174,52191],{},[883,52134,52136],{"className":52135},[886],[888,52137,52138],{"xmlns":890},[892,52139,52140,52170],{},[895,52141,52142],{},[2334,52143,52144,52156,52158,52160,52162,52164,52166,52168],{"scriptlevel":2336,"displaystyle":2294},[9172,52145,52146,52148,52150],{},[2005,52147,11174],{},[2138,52149,2336],{},[2281,52151,52152,52154],{},[898,52153,2797],{},[2138,52155,2336],{},[898,52157,8679],{},[2005,52159,2014],{"stretchy":2013},[898,52161,2797],{},[2005,52163,2020],{"stretchy":2013},[2297,52165,2995],{},[898,52167,2203],{},[898,52169,2797],{},[902,52171,52172],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,52175,52177],{"className":52176},[886],[888,52178,52179],{"xmlns":890},[892,52180,52181,52189],{},[895,52182,52183],{},[2281,52184,52185,52187],{},[898,52186,2797],{},[2138,52188,2336],{},[902,52190,38313],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,52193,52194,52209,52210,52231,52232,1644],{},[883,52195,52197],{"className":52196},[886],[888,52198,52199],{"xmlns":890},[892,52200,52201,52207],{},[895,52202,52203,52205],{},[898,52204,3946],{},[898,52206,8679],{},[902,52208,44974],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,52211,52213],{"className":52212},[886],[888,52214,52215],{"xmlns":890},[892,52216,52217,52229],{},[895,52218,52219,52221,52223],{},[898,52220,3946],{},[2005,52222,2007],{},[2281,52224,52225,52227],{},[898,52226,3946],{},[2138,52228,2336],{},[902,52230,51682],{"encoding":904}," a křivkou nabídky v pásu ",[883,52233,52235],{"className":52234},[886],[888,52236,52237],{"xmlns":890},[892,52238,52239,52255],{},[895,52240,52241,52243,52245,52247,52253],{},[2005,52242,2495],{"stretchy":2013},[2138,52244,2336],{},[2005,52246,2295],{"separator":2294},[2281,52248,52249,52251],{},[898,52250,2797],{},[2138,52252,2336],{},[2005,52254,2510],{"stretchy":2013},[902,52256,51557],{"encoding":904},[724,52258,52259],{},[614,52260,52261],{},"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.",[36975,52263],{},[3876,52265,52266,52271],{},[724,52267,52268,52270],{},[883,52269,4578],{}," Postup výpočtu CS a PS",[152,52272,52273,52404,52514,52543,52677],{},[123,52274,52275,52276,52293,52294,52325,52326,52357,52358,1644],{},"Zjisti (nebo si zvol) množství ",[883,52277,52279],{"className":52278},[886],[888,52280,52281],{"xmlns":890},[892,52282,52283,52291],{},[895,52284,52285],{},[2281,52286,52287,52289],{},[898,52288,2797],{},[2138,52290,2336],{},[902,52292,38313],{"encoding":904}," a odpovídající cenu ",[883,52295,52297],{"className":52296},[886],[888,52298,52299],{"xmlns":890},[892,52300,52301,52323],{},[895,52302,52303,52309,52311,52313,52315,52321],{},[2281,52304,52305,52307],{},[898,52306,3946],{},[2138,52308,2336],{},[2005,52310,2007],{},[898,52312,1860],{},[2005,52314,2014],{"stretchy":2013},[2281,52316,52317,52319],{},[898,52318,2797],{},[2138,52320,2336],{},[2005,52322,2020],{"stretchy":2013},[902,52324,51060],{"encoding":904}," resp. ",[883,52327,52329],{"className":52328},[886],[888,52330,52331],{"xmlns":890},[892,52332,52333,52355],{},[895,52334,52335,52341,52343,52345,52347,52353],{},[2281,52336,52337,52339],{},[898,52338,3946],{},[2138,52340,2336],{},[2005,52342,2007],{},[898,52344,8679],{},[2005,52346,2014],{"stretchy":2013},[2281,52348,52349,52351],{},[898,52350,2797],{},[2138,52352,2336],{},[2005,52354,2020],{"stretchy":2013},[902,52356,51092],{"encoding":904},". V rovnováze platí ",[883,52359,52361],{"className":52360},[886],[888,52362,52363],{"xmlns":890},[892,52364,52365,52401],{},[895,52366,52367,52369,52371,52377,52379,52381,52383,52385,52391,52393,52395],{},[898,52368,1860],{},[2005,52370,2014],{"stretchy":2013},[2133,52372,52373,52375],{},[898,52374,2797],{},[898,52376,1868],{},[2005,52378,2020],{"stretchy":2013},[2005,52380,2007],{},[898,52382,8679],{},[2005,52384,2014],{"stretchy":2013},[2133,52386,52387,52389],{},[898,52388,2797],{},[898,52390,1868],{},[2005,52392,2020],{"stretchy":2013},[2005,52394,2007],{},[2133,52396,52397,52399],{},[898,52398,3946],{},[898,52400,1868],{},[902,52402,52403],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,52405,52406,52407,20132,52445,52460,52461,20132,52499,3927],{},"Spočti určitý integrál ",[883,52408,52410],{"className":52409},[886],[888,52411,52412],{"xmlns":890},[892,52413,52414,52442],{},[895,52415,52416,52428,52430,52432,52434,52436,52438,52440],{},[9172,52417,52418,52420,52422],{},[2005,52419,11174],{},[2138,52421,2336],{},[2281,52423,52424,52426],{},[898,52425,2797],{},[2138,52427,2336],{},[898,52429,1860],{},[2005,52431,2014],{"stretchy":2013},[898,52433,2797],{},[2005,52435,2020],{"stretchy":2013},[2297,52437,2995],{},[898,52439,2203],{},[898,52441,2797],{},[902,52443,52444],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,52446,52448],{"className":52447},[886],[888,52449,52450],{"xmlns":890},[892,52451,52452,52458],{},[895,52453,52454,52456],{},[898,52455,1852],{},[898,52457,8679],{},[902,52459,44955],{"encoding":904},") nebo ",[883,52462,52464],{"className":52463},[886],[888,52465,52466],{"xmlns":890},[892,52467,52468,52496],{},[895,52469,52470,52482,52484,52486,52488,52490,52492,52494],{},[9172,52471,52472,52474,52476],{},[2005,52473,11174],{},[2138,52475,2336],{},[2281,52477,52478,52480],{},[898,52479,2797],{},[2138,52481,2336],{},[898,52483,8679],{},[2005,52485,2014],{"stretchy":2013},[898,52487,2797],{},[2005,52489,2020],{"stretchy":2013},[2297,52491,2995],{},[898,52493,2203],{},[898,52495,2797],{},[902,52497,52498],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,52500,52502],{"className":52501},[886],[888,52503,52504],{"xmlns":890},[892,52505,52506,52512],{},[895,52507,52508,52510],{},[898,52509,3946],{},[898,52511,8679],{},[902,52513,44974],{"encoding":904},[123,52515,52516,52517,1644],{},"Sestav obdélník ",[883,52518,52520],{"className":52519},[886],[888,52521,52522],{"xmlns":890},[892,52523,52524,52540],{},[895,52525,52526,52532,52534],{},[2281,52527,52528,52530],{},[898,52529,3946],{},[2138,52531,2336],{},[2005,52533,3185],{},[2281,52535,52536,52538],{},[898,52537,2797],{},[2138,52539,2336],{},[902,52541,52542],{"encoding":904},"P_0 \\cdot Q_0",[123,52544,52545,52546],{},"Dosaď:\n",[120,52547,52548,52613],{},[123,52549,52550,52608,52609,52612],{},[883,52551,52553],{"className":52552},[886],[888,52554,52555],{"xmlns":890},[892,52556,52557,52605],{},[895,52558,52559,52561,52563,52565,52577,52579,52581,52583,52585,52587,52589,52591,52593,52599],{},[898,52560,1852],{},[898,52562,8679],{},[2005,52564,2007],{},[9172,52566,52567,52569,52571],{},[2005,52568,11174],{},[2138,52570,2336],{},[2281,52572,52573,52575],{},[898,52574,2797],{},[2138,52576,2336],{},[898,52578,1860],{},[2005,52580,2014],{"stretchy":2013},[898,52582,2797],{},[2005,52584,2020],{"stretchy":2013},[2297,52586,2995],{},[898,52588,2203],{},[898,52590,2797],{},[2005,52592,2234],{},[2281,52594,52595,52597],{},[898,52596,3946],{},[2138,52598,2336],{},[2281,52600,52601,52603],{},[898,52602,2797],{},[2138,52604,2336],{},[902,52606,52607],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,52610,52611],{},"mínus"," obdélník)",[123,52614,52615,52673,52674,52676],{},[883,52616,52618],{"className":52617},[886],[888,52619,52620],{"xmlns":890},[892,52621,52622,52670],{},[895,52623,52624,52626,52628,52630,52636,52642,52644,52656,52658,52660,52662,52664,52666,52668],{},[898,52625,3946],{},[898,52627,8679],{},[2005,52629,2007],{},[2281,52631,52632,52634],{},[898,52633,3946],{},[2138,52635,2336],{},[2281,52637,52638,52640],{},[898,52639,2797],{},[2138,52641,2336],{},[2005,52643,2234],{},[9172,52645,52646,52648,52650],{},[2005,52647,11174],{},[2138,52649,2336],{},[2281,52651,52652,52654],{},[898,52653,2797],{},[2138,52655,2336],{},[898,52657,8679],{},[2005,52659,2014],{"stretchy":2013},[898,52661,2797],{},[2005,52663,2020],{"stretchy":2013},[2297,52665,2995],{},[898,52667,2203],{},[898,52669,2797],{},[902,52671,52672],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,52675,52611],{}," integrál)",[123,52678,52679,52680,52683],{},"Kontrola znaménka: obě hodnoty musí být ",[38,52681,52682],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[36975,52685],{},[115,52687,52689],{"id":52688},"příklady","Příklady",[198,52691,52693],{"id":52692},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[3876,52695,52696],{},[724,52697,52698,52701,52702,47726,52725,52748,52749,1343,52769,1343,52786,1343,52803,52820,52821,52897,52898,52915,52916,52929],{},[883,52699,52700],{},"!example"," Zadání\nJsou dány poptávka ",[883,52703,52705],{"className":52704},[886],[888,52706,52707],{"xmlns":890},[892,52708,52709,52723],{},[895,52710,52711,52713,52715,52717,52719,52721],{},[898,52712,3946],{},[2005,52714,2007],{},[898,52716,207],{},[898,52718,2797],{},[2005,52720,2104],{},[898,52722,2107],{},[902,52724,37065],{"encoding":904},[883,52726,52728],{"className":52727},[886],[888,52729,52730],{"xmlns":890},[892,52731,52732,52746],{},[895,52733,52734,52736,52738,52740,52742,52744],{},[898,52735,3946],{},[2005,52737,2007],{},[898,52739,2151],{},[898,52741,2797],{},[2005,52743,2104],{},[898,52745,2203],{},[902,52747,40247],{"encoding":904}," s hodnotami ",[883,52750,52752],{"className":52751},[886],[888,52753,52754],{"xmlns":890},[892,52755,52756,52766],{},[895,52757,52758,52760,52762,52764],{},[898,52759,207],{},[2005,52761,2007],{},[2005,52763,2234],{},[2138,52765,2182],{},[902,52767,52768],{"encoding":904},"a = -3",[883,52770,52772],{"className":52771},[886],[888,52773,52774],{"xmlns":890},[892,52775,52776,52784],{},[895,52777,52778,52780,52782],{},[898,52779,2107],{},[2005,52781,2007],{},[2138,52783,5217],{},[902,52785,48649],{"encoding":904},[883,52787,52789],{"className":52788},[886],[888,52790,52791],{"xmlns":890},[892,52792,52793,52801],{},[895,52794,52795,52797,52799],{},[898,52796,2151],{},[2005,52798,2007],{},[2138,52800,5015],{},[902,52802,48667],{"encoding":904},[883,52804,52806],{"className":52805},[886],[888,52807,52808],{"xmlns":890},[892,52809,52810,52818],{},[895,52811,52812,52814,52816],{},[898,52813,2203],{},[2005,52815,2007],{},[2138,52817,2871],{},[902,52819,48685],{"encoding":904},".\nRovnovážné množství:\n",[883,52822,52824],{"className":52823},[886],[888,52825,52826],{"xmlns":890},[892,52827,52828,52894],{},[895,52829,52830,52836,52838,52856,52858,52882,52884,52890,52892],{},[2133,52831,52832,52834],{},[898,52833,2797],{},[898,52835,1868],{},[2005,52837,2007],{},[2338,52839,52840,52848],{},[895,52841,52842,52844,52846],{},[898,52843,2107],{},[2005,52845,2234],{},[898,52847,2203],{},[895,52849,52850,52852,52854],{},[898,52851,2151],{},[2005,52853,2234],{},[898,52855,207],{},[2005,52857,2007],{},[2338,52859,52860,52868],{},[895,52861,52862,52864,52866],{},[2138,52863,5217],{},[2005,52865,2234],{},[2138,52867,2871],{},[895,52869,52870,52872,52874,52876,52878,52880],{},[2138,52871,5015],{},[2005,52873,2234],{},[2005,52875,2014],{"stretchy":2013},[2005,52877,2234],{},[2138,52879,2182],{},[2005,52881,2020],{"stretchy":2013},[2005,52883,2007],{},[2338,52885,52886,52888],{},[2138,52887,38024],{},[2138,52889,44411],{},[2005,52891,5906],{},[2138,52893,44416],{},[902,52895,52896],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,52899,52901],{"className":52900},[886],[888,52902,52903],{"xmlns":890},[892,52904,52905,52913],{},[895,52906,52907],{},[2133,52908,52909,52911],{},[898,52910,2797],{},[898,52912,1868],{},[902,52914,42408],{"encoding":904}," (a) při změně samotného parametru ",[883,52917,52919],{"className":52918},[886],[888,52920,52921],{"xmlns":890},[892,52922,52923,52927],{},[895,52924,52925],{},[898,52926,2151],{},[902,52928,2151],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,52931,52932],{},[38,52933,52934,52935,2680,52948,2694,52961,9301],{},"Řešení (a) — změna ",[883,52936,52938],{"className":52937},[886],[888,52939,52940],{"xmlns":890},[892,52941,52942,52946],{},[895,52943,52944],{},[898,52945,2151],{},[902,52947,2151],{"encoding":904},[883,52949,52951],{"className":52950},[886],[888,52952,52953],{"xmlns":890},[892,52954,52955,52959],{},[895,52956,52957],{},[2138,52958,5015],{},[902,52960,44451],{"encoding":904},[883,52962,52964],{"className":52963},[886],[888,52965,52966],{"xmlns":890},[892,52967,52968,52972],{},[895,52969,52970],{},[2138,52971,19327],{},[902,52973,44465],{"encoding":904},[724,52975,52976,52977,53041,53042,2713],{},"Pomocí vzorce (2.13) pro ",[883,52978,52980],{"className":52979},[886],[888,52981,52982],{"xmlns":890},[892,52983,52984,53038],{},[895,52985,52986,53006,53008,53010],{},[2334,52987,52988],{"scriptlevel":2336,"displaystyle":2294},[2338,52989,52990,53000],{},[895,52991,52992,52994],{},[898,52993,9877],{"mathvariant":2385},[2133,52995,52996,52998],{},[898,52997,2797],{},[898,52999,1868],{},[895,53001,53002,53004],{},[898,53003,9877],{"mathvariant":2385},[898,53005,2151],{},[2005,53007,2007],{},[2005,53009,2234],{},[2334,53011,53012],{"scriptlevel":2336,"displaystyle":2294},[2338,53013,53014,53022],{},[895,53015,53016,53018,53020],{},[898,53017,2107],{},[2005,53019,2234],{},[898,53021,2203],{},[895,53023,53024,53026,53028,53030,53032],{},[2005,53025,2014],{"stretchy":2013},[898,53027,2151],{},[2005,53029,2234],{},[898,53031,207],{},[2133,53033,53034,53036],{},[2005,53035,2020],{"stretchy":2013},[2138,53037,2140],{},[902,53039,53040],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,53043,53045],{"className":53044},[886],[888,53046,53047],{"xmlns":890},[892,53048,53049,53071],{},[895,53050,53051,53053],{},[2005,53052,2234],{},[2334,53054,53055],{"scriptlevel":2336,"displaystyle":2294},[2338,53056,53057,53063],{},[2133,53058,53059,53061],{},[898,53060,2797],{},[898,53062,1868],{},[895,53064,53065,53067,53069],{},[898,53066,2151],{},[2005,53068,2234],{},[898,53070,207],{},[902,53072,53073],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,53075,53077],{"className":53076},[886],[888,53078,53079],{"xmlns":890,"display":28071},[892,53080,53081,53137],{},[895,53082,53083,53085,53091,53093,53095,53111,53113,53115,53117,53119,53121,53127,53129,53131,53133,53135],{},[898,53084,2203],{},[2133,53086,53087,53089],{},[898,53088,2797],{},[898,53090,1868],{},[2005,53092,2007],{},[2005,53094,2234],{},[2338,53096,53097,53103],{},[2133,53098,53099,53101],{},[898,53100,2797],{},[898,53102,1868],{},[895,53104,53105,53107,53109],{},[898,53106,2151],{},[2005,53108,2234],{},[898,53110,207],{},[2297,53112,2995],{},[898,53114,2203],{},[898,53116,2151],{},[2005,53118,2007],{},[2005,53120,2234],{},[2338,53122,53123,53125],{},[2138,53124,44579],{},[2138,53126,44411],{},[2005,53128,3185],{},[2138,53130,2802],{},[2005,53132,5906],{},[2005,53134,2234],{},[2138,53136,44551],{},[902,53138,53139],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,53141,53142],{},"Nové rovnovážné množství:",[883,53144,53146],{"className":53145},[886],[888,53147,53148],{"xmlns":890,"display":28071},[892,53149,53150,53173],{},[895,53151,53152,53160,53162,53164,53166,53168,53170],{},[9172,53153,53154,53156,53158],{},[898,53155,2797],{},[2138,53157,2287],{},[898,53159,1868],{},[2005,53161,2739],{},[2138,53163,44579],{},[2005,53165,2234],{},[2138,53167,44584],{},[2005,53169,2007],{},[2138,53171,53172],{},"8,326.",[902,53174,53175],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,53177,53178,2212,53181,1343,53208,1343,53230,1343,53252,5595,53274,1343,53293,1343,53314,1343,53333,1644],{},[38,53179,53180],{},"Řešení (b) — současná změna všech parametrů:",[883,53182,53184],{"className":53183},[886],[888,53185,53186],{"xmlns":890},[892,53187,53188,53205],{},[895,53189,53190,53192,53194,53196,53198,53200,53202],{},[898,53191,207],{},[2005,53193,2713],{},[2005,53195,2234],{},[2138,53197,2182],{},[2005,53199,3131],{},[2005,53201,2234],{},[2138,53203,53204],{},"2,5",[902,53206,53207],{"encoding":904},"a: -3 \\to -2{,}5",[883,53209,53211],{"className":53210},[886],[888,53212,53213],{"xmlns":890},[892,53214,53215,53227],{},[895,53216,53217,53219,53221,53223,53225],{},[898,53218,2107],{},[2005,53220,2713],{},[2138,53222,5217],{},[2005,53224,3131],{},[2138,53226,15044],{},[902,53228,53229],{"encoding":904},"b: 40 \\to 35",[883,53231,53233],{"className":53232},[886],[888,53234,53235],{"xmlns":890},[892,53236,53237,53249],{},[895,53238,53239,53241,53243,53245,53247],{},[898,53240,2151],{},[2005,53242,2713],{},[2138,53244,5015],{},[2005,53246,3131],{},[2138,53248,19327],{},[902,53250,53251],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,53253,53255],{"className":53254},[886],[888,53256,53257],{"xmlns":890},[892,53258,53259,53271],{},[895,53260,53261,53263,53265,53267,53269],{},[898,53262,2203],{},[2005,53264,2713],{},[2138,53266,2871],{},[2005,53268,3131],{},[2138,53270,2912],{},[902,53272,53273],{"encoding":904},"d: 10 \\to 11",[883,53275,53277],{"className":53276},[886],[888,53278,53279],{"xmlns":890},[892,53280,53281,53291],{},[895,53282,53283,53285,53287,53289],{},[898,53284,2203],{},[898,53286,207],{},[2005,53288,2007],{},[2138,53290,5015],{},[902,53292,44617],{"encoding":904},[883,53294,53296],{"className":53295},[886],[888,53297,53298],{"xmlns":890},[892,53299,53300,53312],{},[895,53301,53302,53304,53306,53308,53310],{},[898,53303,2203],{},[898,53305,2107],{},[2005,53307,2007],{},[2005,53309,2234],{},[2138,53311,2237],{},[902,53313,44639],{"encoding":904},[883,53315,53317],{"className":53316},[886],[888,53318,53319],{"xmlns":890},[892,53320,53321,53331],{},[895,53322,53323,53325,53327,53329],{},[898,53324,2203],{},[898,53326,2151],{},[2005,53328,2007],{},[2138,53330,2802],{},[902,53332,44659],{"encoding":904},[883,53334,53336],{"className":53335},[886],[888,53337,53338],{"xmlns":890},[892,53339,53340,53350],{},[895,53341,53342,53344,53346,53348],{},[898,53343,2203],{},[898,53345,2203],{},[2005,53347,2007],{},[2138,53349,2287],{},[902,53351,44679],{"encoding":904},[724,53353,53354,53355,53413],{},"Totální diferenciál ",[883,53356,53358],{"className":53357},[886],[888,53359,53360],{"xmlns":890},[892,53361,53362,53410],{},[895,53363,53364,53370,53372,53374,53376,53378,53380,53382,53384,53386,53388,53390],{},[2133,53365,53366,53368],{},[898,53367,2797],{},[898,53369,1868],{},[2005,53371,2014],{"stretchy":2013},[898,53373,207],{},[2005,53375,2295],{"separator":2294},[898,53377,2107],{},[2005,53379,2295],{"separator":2294},[898,53381,2151],{},[2005,53383,2295],{"separator":2294},[898,53385,2203],{},[2005,53387,2020],{"stretchy":2013},[2005,53389,2007],{},[2334,53391,53392],{"scriptlevel":2336,"displaystyle":2294},[2338,53393,53394,53402],{},[895,53395,53396,53398,53400],{},[898,53397,2107],{},[2005,53399,2234],{},[898,53401,2203],{},[895,53403,53404,53406,53408],{},[898,53405,2151],{},[2005,53407,2234],{},[898,53409,207],{},[902,53411,53412],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,53415,53417],{"className":53416},[886],[888,53418,53419],{"xmlns":890,"display":28071},[892,53420,53421,53541],{},[895,53422,53423,53425,53431,53433,53459,53461,53463,53465,53467,53479,53481,53483,53485,53487,53513,53515,53517,53519,53521,53533,53535,53537,53539],{},[898,53424,2203],{},[2133,53426,53427,53429],{},[898,53428,2797],{},[898,53430,1868],{},[2005,53432,2007],{},[2338,53434,53435,53443],{},[895,53436,53437,53439,53441],{},[898,53438,2107],{},[2005,53440,2234],{},[898,53442,2203],{},[895,53444,53445,53447,53449,53451,53453],{},[2005,53446,2014],{"stretchy":2013},[898,53448,2151],{},[2005,53450,2234],{},[898,53452,207],{},[2133,53454,53455,53457],{},[2005,53456,2020],{"stretchy":2013},[2138,53458,2140],{},[2297,53460,2995],{},[898,53462,2203],{},[898,53464,207],{},[2005,53466,2104],{},[2338,53468,53469,53471],{},[2138,53470,2287],{},[895,53472,53473,53475,53477],{},[898,53474,2151],{},[2005,53476,2234],{},[898,53478,207],{},[2297,53480,2995],{},[898,53482,2203],{},[898,53484,2107],{},[2005,53486,2234],{},[2338,53488,53489,53497],{},[895,53490,53491,53493,53495],{},[898,53492,2107],{},[2005,53494,2234],{},[898,53496,2203],{},[895,53498,53499,53501,53503,53505,53507],{},[2005,53500,2014],{"stretchy":2013},[898,53502,2151],{},[2005,53504,2234],{},[898,53506,207],{},[2133,53508,53509,53511],{},[2005,53510,2020],{"stretchy":2013},[2138,53512,2140],{},[2297,53514,2995],{},[898,53516,2203],{},[898,53518,2151],{},[2005,53520,2234],{},[2338,53522,53523,53525],{},[2138,53524,2287],{},[895,53526,53527,53529,53531],{},[898,53528,2151],{},[2005,53530,2234],{},[898,53532,207],{},[2297,53534,2995],{},[898,53536,2203],{},[898,53538,2203],{},[898,53540,1644],{"mathvariant":2385},[902,53542,53543],{"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.",[724,53545,53546,53547,1343,53569,1343,53600,3159],{},"Dosazením číselných hodnot (",[883,53548,53550],{"className":53549},[886],[888,53551,53552],{"xmlns":890},[892,53553,53554,53566],{},[895,53555,53556,53558,53560,53562,53564],{},[898,53557,2151],{},[2005,53559,2234],{},[898,53561,207],{},[2005,53563,2007],{},[2138,53565,44411],{},[902,53567,53568],{"encoding":904},"c - a = 3{,}5",[883,53570,53572],{"className":53571},[886],[888,53573,53574],{"xmlns":890},[892,53575,53576,53597],{},[895,53577,53578,53580,53582,53584,53586,53592,53594],{},[2005,53579,2014],{"stretchy":2013},[898,53581,2151],{},[2005,53583,2234],{},[898,53585,207],{},[2133,53587,53588,53590],{},[2005,53589,2020],{"stretchy":2013},[2138,53591,2140],{},[2005,53593,2007],{},[2138,53595,53596],{},"12,25",[902,53598,53599],{"encoding":904},"(c-a)^2 = 12{,}25",[883,53601,53603],{"className":53602},[886],[888,53604,53605],{"xmlns":890},[892,53606,53607,53619],{},[895,53608,53609,53611,53613,53615,53617],{},[898,53610,2107],{},[2005,53612,2234],{},[898,53614,2203],{},[2005,53616,2007],{},[2138,53618,38024],{},[902,53620,53621],{"encoding":904},"b - d = 30",[883,53623,53625],{"className":53624},[886],[888,53626,53627],{"xmlns":890,"display":28071},[892,53628,53629,53730],{},[895,53630,53631,53633,53639,53641,53649,53651,53653,53655,53657,53665,53667,53669,53671,53673,53675,53683,53685,53687,53689,53691,53699,53701,53703,53705,53707,53710,53712,53715,53717,53719,53721,53724,53726,53728],{},[898,53632,2203],{},[2133,53634,53635,53637],{},[898,53636,2797],{},[898,53638,1868],{},[2005,53640,2739],{},[2334,53642,53643],{"scriptlevel":2336,"displaystyle":2013},[2338,53644,53645,53647],{},[2138,53646,38024],{},[2138,53648,53596],{},[2005,53650,2014],{"stretchy":2013},[2138,53652,5015],{},[2005,53654,2020],{"stretchy":2013},[2005,53656,2104],{},[2334,53658,53659],{"scriptlevel":2336,"displaystyle":2013},[2338,53660,53661,53663],{},[2138,53662,2287],{},[2138,53664,44411],{},[2005,53666,2014],{"stretchy":2013},[2005,53668,2234],{},[2138,53670,2237],{},[2005,53672,2020],{"stretchy":2013},[2005,53674,2234],{},[2334,53676,53677],{"scriptlevel":2336,"displaystyle":2013},[2338,53678,53679,53681],{},[2138,53680,38024],{},[2138,53682,53596],{},[2005,53684,2014],{"stretchy":2013},[2138,53686,2802],{},[2005,53688,2020],{"stretchy":2013},[2005,53690,2234],{},[2334,53692,53693],{"scriptlevel":2336,"displaystyle":2013},[2338,53694,53695,53697],{},[2138,53696,2287],{},[2138,53698,44411],{},[2005,53700,2014],{"stretchy":2013},[2138,53702,2287],{},[2005,53704,2020],{"stretchy":2013},[2005,53706,5906],{},[2138,53708,53709],{},"1,224",[2005,53711,2234],{},[2138,53713,53714],{},"1,429",[2005,53716,2234],{},[2138,53718,44584],{},[2005,53720,2234],{},[2138,53722,53723],{},"0,286",[2005,53725,5906],{},[2005,53727,2234],{},[2138,53729,44830],{},[902,53731,53732],{"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.",[724,53734,30070,53735,1644],{},[883,53736,53738],{"className":53737},[886],[888,53739,53740],{"xmlns":890},[892,53741,53742,53764],{},[895,53743,53744,53752,53754,53756,53758,53760,53762],{},[9172,53745,53746,53748,53750],{},[898,53747,2797],{},[2138,53749,2287],{},[898,53751,1868],{},[2005,53753,2739],{},[2138,53755,44579],{},[2005,53757,2234],{},[2138,53759,44861],{},[2005,53761,5906],{},[2138,53763,44866],{},[902,53765,53766],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[3876,53768,53769],{},[724,53770,53771,53773,53774,53795,53796,53822,53823,53826,53827,53923,53924,53947,53948,53964],{},[883,53772,4418],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,53775,53777],{"className":53776},[886],[888,53778,53779],{"xmlns":890},[892,53780,53781,53793],{},[895,53782,53783,53785,53787,53789,53791],{},[898,53784,2897],{"mathvariant":2385},[898,53786,2797],{},[2005,53788,2739],{},[2005,53790,2234],{},[2138,53792,44896],{},[902,53794,44899],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,53797,53799],{"className":53798},[886],[888,53800,53801],{"xmlns":890},[892,53802,53803,53819],{},[895,53804,53805,53807,53813,53815,53817],{},[898,53806,2203],{},[2133,53808,53809,53811],{},[898,53810,2797],{},[898,53812,1868],{},[2005,53814,5906],{},[2005,53816,2234],{},[2138,53818,44861],{},[902,53820,53821],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,53824,53825],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,53828,53830],{"className":53829},[886],[888,53831,53832],{"xmlns":890},[892,53833,53834,53920],{},[895,53835,53836,53844,53846,53880,53882,53906,53908,53915,53917],{},[9172,53837,53838,53840,53842],{},[898,53839,2797],{},[2138,53841,2287],{},[898,53843,1868],{},[2005,53845,2007],{},[2338,53847,53848,53864],{},[895,53849,53850,53856,53858],{},[2133,53851,53852,53854],{},[898,53853,2107],{},[2005,53855,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,53857,2234],{},[2133,53859,53860,53862],{},[898,53861,2203],{},[2005,53863,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[895,53865,53866,53872,53874],{},[2133,53867,53868,53870],{},[898,53869,2151],{},[2005,53871,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,53873,2234],{},[2133,53875,53876,53878],{},[898,53877,207],{},[2005,53879,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,53881,2007],{},[2338,53883,53884,53892],{},[895,53885,53886,53888,53890],{},[2138,53887,15044],{},[2005,53889,2234],{},[2138,53891,2912],{},[895,53893,53894,53896,53898,53900,53902,53904],{},[2138,53895,19327],{},[2005,53897,2234],{},[2005,53899,2014],{"stretchy":2013},[2005,53901,2234],{},[2138,53903,53204],{},[2005,53905,2020],{"stretchy":2013},[2005,53907,2007],{},[2338,53909,53910,53912],{},[2138,53911,41805],{},[2138,53913,53914],{},"3,1",[2005,53916,5906],{},[2138,53918,53919],{},"7,742",[902,53921,53922],{"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 ",[883,53925,53927],{"className":53926},[886],[888,53928,53929],{"xmlns":890},[892,53930,53931,53944],{},[895,53932,53933,53935,53937,53939,53941],{},[898,53934,2897],{"mathvariant":2385},[898,53936,2797],{},[2005,53938,5906],{},[2005,53940,2234],{},[2138,53942,53943],{},"0,829",[902,53945,53946],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,53949,53951],{"className":53950},[886],[888,53952,53953],{"xmlns":890},[892,53954,53955,53961],{},[895,53956,53957,53959],{},[2005,53958,2234],{},[2138,53960,44896],{},[902,53962,53963],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,53966,53967],{},[614,53968,53969,53970,53983],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,53971,53973],{"className":53972},[886],[888,53974,53975],{"xmlns":890},[892,53976,53977,53981],{},[895,53978,53979],{},[898,53980,2797],{},[902,53982,2797],{"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.",[198,53985,53987,53988],{"id":53986},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,53989,53991],{"className":53990},[886],[888,53992,53993],{"xmlns":890},[892,53994,53995,54001],{},[895,53996,53997,53999],{},[898,53998,3946],{},[898,54000,8679],{},[902,54002,44974],{"encoding":904},[3876,54004,54005],{},[724,54006,54007,54009,54010,54044,54045,54067],{},[883,54008,52700],{}," Zadání\nPro nabídku ",[883,54011,54013],{"className":54012},[886],[888,54014,54015],{"xmlns":890},[892,54016,54017,54041],{},[895,54018,54019,54021,54023,54025,54027,54029,54031,54033,54035,54037,54039],{},[898,54020,3946],{},[2005,54022,2007],{},[898,54024,8679],{},[2005,54026,2014],{"stretchy":2013},[898,54028,2797],{},[2005,54030,2020],{"stretchy":2013},[2005,54032,2007],{},[2138,54034,2871],{},[2005,54036,2104],{},[2138,54038,2140],{},[898,54040,2797],{},[902,54042,54043],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,54046,54048],{"className":54047},[886],[888,54049,54050],{"xmlns":890},[892,54051,54052,54064],{},[895,54053,54054,54060,54062],{},[2281,54055,54056,54058],{},[898,54057,2797],{},[2138,54059,2336],{},[2005,54061,2007],{},[2138,54063,2871],{},[902,54065,54066],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,54069,54070],{},[38,54071,22776],{},[724,54073,54074],{},"Odpovídající cena:",[883,54076,54078],{"className":54077},[886],[888,54079,54080],{"xmlns":890,"display":28071},[892,54081,54082,54117],{},[895,54083,54084,54090,54092,54094,54096,54098,54100,54102,54104,54106,54108,54110,54112,54114],{},[2281,54085,54086,54088],{},[898,54087,3946],{},[2138,54089,2336],{},[2005,54091,2007],{},[898,54093,8679],{},[2005,54095,2014],{"stretchy":2013},[2138,54097,2871],{},[2005,54099,2020],{"stretchy":2013},[2005,54101,2007],{},[2138,54103,2871],{},[2005,54105,2104],{},[2138,54107,2140],{},[2005,54109,3185],{},[2138,54111,2871],{},[2005,54113,2007],{},[2138,54115,54116],{},"30.",[902,54118,54119],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,54121,54122],{},"Dle vzorce (2.15):",[883,54124,54126],{"className":54125},[886],[888,54127,54128],{"xmlns":890,"display":28071},[892,54129,54130,54238],{},[895,54131,54132,54134,54136,54138,54140,54142,54144,54150,54156,54158,54166,54168,54170,54172,54174,54176,54178,54180,54182,54184,54186,54188,54190,54192,54194,54197,54199,54201,54203,54209,54217,54219,54221,54223,54225,54227,54229,54231,54233,54235],{},[898,54133,3946],{},[898,54135,8679],{},[2005,54137,2014],{"stretchy":2013},[2138,54139,2871],{},[2005,54141,2020],{"stretchy":2013},[2005,54143,2007],{},[2281,54145,54146,54148],{},[898,54147,3946],{},[2138,54149,2336],{},[2281,54151,54152,54154],{},[898,54153,2797],{},[2138,54155,2336],{},[2005,54157,2234],{},[9172,54159,54160,54162,54164],{},[2005,54161,11174],{},[2138,54163,2336],{},[2138,54165,2871],{},[2005,54167,2014],{"stretchy":2013},[2138,54169,2871],{},[2005,54171,2104],{},[2138,54173,2140],{},[898,54175,2797],{},[2005,54177,2020],{"stretchy":2013},[2297,54179,2995],{},[898,54181,2203],{},[898,54183,2797],{},[2005,54185,2007],{},[2138,54187,2871],{},[2005,54189,3185],{},[2138,54191,38024],{},[2005,54193,2234],{},[2005,54195,2495],{"fence":2013,"stretchy":2294,"minsize":54196,"maxsize":54196},"1.8em",[2138,54198,2871],{},[898,54200,2797],{},[2005,54202,2104],{},[2133,54204,54205,54207],{},[898,54206,2797],{},[2138,54208,2140],{},[9172,54210,54211,54213,54215],{},[2005,54212,2510],{"fence":2013,"stretchy":2294,"minsize":54196,"maxsize":54196},[2138,54214,2336],{},[2138,54216,2871],{},[2005,54218,2007],{},[2138,54220,30086],{},[2005,54222,2234],{},[2005,54224,2014],{"stretchy":2013},[2138,54226,3098],{},[2005,54228,2104],{},[2138,54230,3098],{},[2005,54232,2020],{"stretchy":2013},[2005,54234,2007],{},[2138,54236,54237],{},"100.",[902,54239,54240],{"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.",[724,54242,54243,54244,54265,54266,54286],{},"Přebytek výrobce při množství ",[883,54245,54247],{"className":54246},[886],[888,54248,54249],{"xmlns":890},[892,54250,54251,54263],{},[895,54252,54253,54259,54261],{},[2281,54254,54255,54257],{},[898,54256,2797],{},[2138,54258,2336],{},[2005,54260,2007],{},[2138,54262,2871],{},[902,54264,54066],{"encoding":904}," je tedy ",[883,54267,54269],{"className":54268},[886],[888,54270,54271],{"xmlns":890},[892,54272,54273,54283],{},[895,54274,54275,54277,54279,54281],{},[898,54276,3946],{},[898,54278,8679],{},[2005,54280,2007],{},[2138,54282,3098],{},[902,54284,54285],{"encoding":904},"PS = 100"," (peněžních jednotek).",[36975,54288],{},[115,54290,54292],{"id":54291},"cheat-sheet","Cheat sheet",[16,54294,54295,54308],{},[19,54296,54297],{},[22,54298,54299,54302,54305],{},[25,54300,54301],{},"Veličina",[25,54303,54304],{},"Vzorec",[25,54306,54307],{},"Geometrie",[30,54309,54310,54428,54542,54610],{},[22,54311,54312,54340,54396],{},[35,54313,54314],{},[883,54315,54317],{"className":54316},[886],[888,54318,54319],{"xmlns":890},[892,54320,54321,54337],{},[895,54322,54323,54325,54327,54329,54335],{},[898,54324,1852],{},[898,54326,8679],{},[2005,54328,2014],{"stretchy":2013},[2281,54330,54331,54333],{},[898,54332,2797],{},[2138,54334,2336],{},[2005,54336,2020],{"stretchy":2013},[902,54338,54339],{"encoding":904},"CS(Q_0)",[35,54341,54342],{},[883,54343,54345],{"className":54344},[886],[888,54346,54347],{"xmlns":890},[892,54348,54349,54393],{},[895,54350,54351],{},[2334,54352,54353,54365,54367,54369,54371,54373,54375,54377,54379,54381,54387],{"scriptlevel":2336,"displaystyle":2294},[9172,54354,54355,54357,54359],{},[2005,54356,11174],{},[2138,54358,2336],{},[2281,54360,54361,54363],{},[898,54362,2797],{},[2138,54364,2336],{},[898,54366,1860],{},[2005,54368,2014],{"stretchy":2013},[898,54370,2797],{},[2005,54372,2020],{"stretchy":2013},[2297,54374,2995],{},[898,54376,2203],{},[898,54378,2797],{},[2005,54380,2234],{},[2281,54382,54383,54385],{},[898,54384,3946],{},[2138,54386,2336],{},[2281,54388,54389,54391],{},[898,54390,2797],{},[2138,54392,2336],{},[902,54394,54395],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,54397,54398,54399,54402,54403,54406,54407],{},"plocha ",[38,54400,54401],{},"pod"," křivkou poptávky, ",[38,54404,54405],{},"nad"," čárou ",[883,54408,54410],{"className":54409},[886],[888,54411,54412],{"xmlns":890},[892,54413,54414,54426],{},[895,54415,54416,54418,54420],{},[898,54417,3946],{},[2005,54419,2007],{},[2281,54421,54422,54424],{},[898,54423,3946],{},[2138,54425,2336],{},[902,54427,51682],{"encoding":904},[22,54429,54430,54458,54514],{},[35,54431,54432],{},[883,54433,54435],{"className":54434},[886],[888,54436,54437],{"xmlns":890},[892,54438,54439,54455],{},[895,54440,54441,54443,54445,54447,54453],{},[898,54442,3946],{},[898,54444,8679],{},[2005,54446,2014],{"stretchy":2013},[2281,54448,54449,54451],{},[898,54450,2797],{},[2138,54452,2336],{},[2005,54454,2020],{"stretchy":2013},[902,54456,54457],{"encoding":904},"PS(Q_0)",[35,54459,54460],{},[883,54461,54463],{"className":54462},[886],[888,54464,54465],{"xmlns":890},[892,54466,54467,54511],{},[895,54468,54469],{},[2334,54470,54471,54477,54483,54485,54497,54499,54501,54503,54505,54507,54509],{"scriptlevel":2336,"displaystyle":2294},[2281,54472,54473,54475],{},[898,54474,3946],{},[2138,54476,2336],{},[2281,54478,54479,54481],{},[898,54480,2797],{},[2138,54482,2336],{},[2005,54484,2234],{},[9172,54486,54487,54489,54491],{},[2005,54488,11174],{},[2138,54490,2336],{},[2281,54492,54493,54495],{},[898,54494,2797],{},[2138,54496,2336],{},[898,54498,8679],{},[2005,54500,2014],{"stretchy":2013},[898,54502,2797],{},[2005,54504,2020],{"stretchy":2013},[2297,54506,2995],{},[898,54508,2203],{},[898,54510,2797],{},[902,54512,54513],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,54515,54398,54516,54518,54519,54406,54521],{},[38,54517,54405],{}," křivkou nabídky, ",[38,54520,54401],{},[883,54522,54524],{"className":54523},[886],[888,54525,54526],{"xmlns":890},[892,54527,54528,54540],{},[895,54529,54530,54532,54534],{},[898,54531,3946],{},[2005,54533,2007],{},[2281,54535,54536,54538],{},[898,54537,3946],{},[2138,54539,2336],{},[902,54541,51682],{"encoding":904},[22,54543,54544,54547,54574],{},[35,54545,54546],{},"Výdaje \u002F tržby",[35,54548,54549],{},[883,54550,54552],{"className":54551},[886],[888,54553,54554],{"xmlns":890},[892,54555,54556,54572],{},[895,54557,54558,54564,54566],{},[2281,54559,54560,54562],{},[898,54561,3946],{},[2138,54563,2336],{},[2005,54565,3185],{},[2281,54567,54568,54570],{},[898,54569,2797],{},[2138,54571,2336],{},[902,54573,52542],{"encoding":904},[35,54575,54576,54577],{},"obdélník ",[883,54578,54580],{"className":54579},[886],[888,54581,54582],{"xmlns":890},[892,54583,54584,54608],{},[895,54585,54586,54588,54590,54596,54598,54600,54602],{},[2138,54587,2336],{},[2297,54589,2995],{},[2281,54591,54592,54594],{},[898,54593,2797],{},[2138,54595,2336],{},[2297,54597,2995],{},[898,54599,1836],{},[2297,54601,2995],{},[2281,54603,54604,54606],{},[898,54605,3946],{},[2138,54607,2336],{},[902,54609,51162],{"encoding":904},[22,54611,54612,54615,54638],{},[35,54613,54614],{},"Celkový přebytek",[35,54616,54617],{},[883,54618,54620],{"className":54619},[886],[888,54621,54622],{"xmlns":890},[892,54623,54624,54636],{},[895,54625,54626,54628,54630,54632,54634],{},[898,54627,1852],{},[898,54629,8679],{},[2005,54631,2104],{},[898,54633,3946],{},[898,54635,8679],{},[902,54637,50900],{"encoding":904},[35,54639,54640],{},"součet obou ploch v rovnováze",[36975,54642],{},[115,54644,15726],{"id":15725},[120,54646,54647,54669,54691,54735,54779,54842,54870],{},[123,54648,54649,10030,54651,1343,54666,54668],{},[38,54650,44939],{},[883,54652,54654],{"className":54653},[886],[888,54655,54656],{"xmlns":890},[892,54657,54658,54664],{},[895,54659,54660,54662],{},[898,54661,1852],{},[898,54663,8679],{},[902,54665,44955],{"encoding":904},[614,54667,44993],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,54670,54671,10030,54673,1343,54688,54690],{},[38,54672,45086],{},[883,54674,54676],{"className":54675},[886],[888,54677,54678],{"xmlns":890},[892,54679,54680,54686],{},[895,54681,54682,54684],{},[898,54683,3946],{},[898,54685,8679],{},[902,54687,44974],{"encoding":904},[614,54689,45089],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,54692,54693,7021,54696,1644],{},[38,54694,54695],{},"Ochota platit",[883,54697,54699],{"className":54698},[886],[888,54700,54701],{"xmlns":890},[892,54702,54703,54733],{},[895,54704,54705],{},[2334,54706,54707,54719,54721,54723,54725,54727,54729,54731],{"scriptlevel":2336,"displaystyle":2294},[9172,54708,54709,54711,54713],{},[2005,54710,11174],{},[2138,54712,2336],{},[2281,54714,54715,54717],{},[898,54716,2797],{},[2138,54718,2336],{},[898,54720,1860],{},[2005,54722,2014],{"stretchy":2013},[898,54724,2797],{},[2005,54726,2020],{"stretchy":2013},[2297,54728,2995],{},[898,54730,2203],{},[898,54732,2797],{},[902,54734,51530],{"encoding":904},[123,54736,54737,7021,54740,1644],{},[38,54738,54739],{},"Minimální cena výrobce",[883,54741,54743],{"className":54742},[886],[888,54744,54745],{"xmlns":890},[892,54746,54747,54777],{},[895,54748,54749],{},[2334,54750,54751,54763,54765,54767,54769,54771,54773,54775],{"scriptlevel":2336,"displaystyle":2294},[9172,54752,54753,54755,54757],{},[2005,54754,11174],{},[2138,54756,2336],{},[2281,54758,54759,54761],{},[898,54760,2797],{},[2138,54762,2336],{},[898,54764,8679],{},[2005,54766,2014],{"stretchy":2013},[898,54768,2797],{},[2005,54770,2020],{"stretchy":2013},[2297,54772,2995],{},[898,54774,2203],{},[898,54776,2797],{},[902,54778,52172],{"encoding":904},[123,54780,54781,7021,54784,52673,54809,3927],{},[38,54782,54783],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,54785,54787],{"className":54786},[886],[888,54788,54789],{"xmlns":890},[892,54790,54791,54807],{},[895,54792,54793,54799,54801],{},[2281,54794,54795,54797],{},[898,54796,3946],{},[2138,54798,2336],{},[2297,54800,2995],{},[2281,54802,54803,54805],{},[898,54804,2797],{},[2138,54806,2336],{},[902,54808,51608],{"encoding":904},[883,54810,54812],{"className":54811},[886],[888,54813,54814],{"xmlns":890},[892,54815,54816,54840],{},[895,54817,54818,54820,54822,54828,54830,54832,54834],{},[2138,54819,2336],{},[2297,54821,2995],{},[2281,54823,54824,54826],{},[898,54825,2797],{},[2138,54827,2336],{},[2297,54829,2995],{},[898,54831,1836],{},[2297,54833,2995],{},[2281,54835,54836,54838],{},[898,54837,3946],{},[2138,54839,2336],{},[902,54841,51162],{"encoding":904},[123,54843,54844,54847,54848,54869],{},[38,54845,54846],{},"Celkový přebytek trhu"," — součet ",[883,54849,54851],{"className":54850},[886],[888,54852,54853],{"xmlns":890},[892,54854,54855,54867],{},[895,54856,54857,54859,54861,54863,54865],{},[898,54858,1852],{},[898,54860,8679],{},[2005,54862,2104],{},[898,54864,3946],{},[898,54866,8679],{},[902,54868,50900],{"encoding":904}," v rovnovážném bodě.",[123,54871,54872,54874,54875,1343,54888,54901,54902,1644],{},[38,54873,2453],{}," — plochy ohraničené křivkami ",[883,54876,54878],{"className":54877},[886],[888,54879,54880],{"xmlns":890},[892,54881,54882,54886],{},[895,54883,54884],{},[898,54885,1860],{},[902,54887,1860],{"encoding":904},[883,54889,54891],{"className":54890},[886],[888,54892,54893],{"xmlns":890},[892,54894,54895,54899],{},[895,54896,54897],{},[898,54898,8679],{},[902,54900,8679],{"encoding":904}," a přímkou ",[883,54903,54905],{"className":54904},[886],[888,54906,54907],{"xmlns":890},[892,54908,54909,54921],{},[895,54910,54911,54913,54915],{},[898,54912,3946],{},[2005,54914,2007],{},[2281,54916,54917,54919],{},[898,54918,3946],{},[2138,54920,2336],{},[902,54922,51682],{"encoding":904},[36975,54924],{},[115,54926,54928],{"id":54927},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,54930,54931,54932,54945,54946,54963],{},"Uvalení jednotkové daně ",[883,54933,54935],{"className":54934},[886],[888,54936,54937],{"xmlns":890},[892,54938,54939,54943],{},[895,54940,54941],{},[898,54942,2783],{},[902,54944,2783],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,54947,54949],{"className":54948},[886],[888,54950,54951],{"xmlns":890},[892,54952,54953,54961],{},[895,54954,54955],{},[2133,54956,54957,54959],{},[898,54958,2797],{},[898,54960,1868],{},[902,54962,42408],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,54965,54966],{},[2568,54967],{"alt":54968,"className":54969,"src":54970},"imek-prebytky-s-dani-deadweight",[210,2572],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,54972,54973,54974,54989,54990,55005,55006,52673,55009,55033,55034,10030,55037,55040,55041,1644],{},"Přebytek spotřebitele ",[883,54975,54977],{"className":54976},[886],[888,54978,54979],{"xmlns":890},[892,54980,54981,54987],{},[895,54982,54983,54985],{},[898,54984,1852],{},[898,54986,8679],{},[902,54988,44955],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,54991,54993],{"className":54992},[886],[888,54994,54995],{"xmlns":890},[892,54996,54997,55003],{},[895,54998,54999,55001],{},[898,55000,3946],{},[898,55002,8679],{},[902,55004,44974],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,55007,55008],{},"daňový příjem",[883,55010,55012],{"className":55011},[886],[888,55013,55014],{"xmlns":890},[892,55015,55016,55030],{},[895,55017,55018,55020,55022],{},[898,55019,2783],{},[2005,55021,3185],{},[9172,55023,55024,55026,55028],{},[898,55025,2797],{},[2138,55027,2287],{},[898,55029,1868],{},[902,55031,55032],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,55035,55036],{},"mrtvá ztráta",[614,55038,55039],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,55042,811],{"className":55043,"dataFsResolvedFilePath":809,"href":810},[210],[36975,55045],{},[115,55047,3800],{"id":3799},[120,55049,55050,55057,55069,55076,55083],{},[123,55051,55052,2212,55054],{},[38,55053,16228],{},[207,55055,802],{"className":55056,"dataFsResolvedFilePath":800,"href":801},[210],[123,55058,55059,2212,55061,55064,55065,55068],{},[38,55060,36679],{},[207,55062,775],{"className":55063,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,55066,2366],{"className":55067,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,55070,55071,2212,55073],{},[38,55072,16238],{},[207,55074,3831],{"className":55075,"dataFsResolvedFilePath":827,"href":828},[210],[123,55077,55078,2212,55080],{},[38,55079,50763],{},[207,55081,50767],{"className":55082,"dataFsResolvedFilePath":745,"href":746},[210],[123,55084,55085,2212,55087],{},[38,55086,16210],{},[207,55088,16214],{"className":55089,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":55091},[55092,55093,55098,55103,55108,55109,55110,55111],{"id":50959,"depth":642,"text":1241},{"id":51303,"depth":642,"text":55094,"children":55095},"Přebytek spotřebitele (CSCS)",[55096,55097],{"id":51322,"depth":649,"text":51323},{"id":2452,"depth":649,"text":2453},{"id":51898,"depth":642,"text":55099,"children":55100},"Přebytek výrobce (PSPS)",[55101,55102],{"id":51917,"depth":649,"text":51918},{"id":52080,"depth":649,"text":2453},{"id":52688,"depth":642,"text":52689,"children":55104},[55105,55106],{"id":52692,"depth":649,"text":52693},{"id":53986,"depth":649,"text":55107},"Příklad 2.13 — numerický výpočet PSPS",{"id":54291,"depth":642,"text":54292},{"id":15725,"depth":642,"text":15726},{"id":54927,"depth":642,"text":54928},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,50829,55118,55119,11994,16246,55120,55121],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":55124,"title":55125,"body":55126,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":74455,"navigation":664,"path":74456,"seo":74457,"sources":74458,"stem":74459,"tags":74460,"type":3865,"updated":677,"__hash__":74466},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":55127,"toc":74419},[55128,55131,55317,55319,55410,55415,55741,55745,55752,55756,55801,55868,55899,55949,55984,55988,56047,56052,56118,56236,56338,56342,56365,56443,56486,56490,56519,56586,56592,56706,56710,56790,56827,56879,57077,57141,57228,57232,57235,57314,57317,57435,57454,57519,57523,57615,57683,57724,57778,57846,57883,57887,57945,57975,58186,58258,58310,58476,58569,58604,58608,58612,58649,58714,58769,58773,58796,58885,58989,59058,59062,59159,59272,59328,59382,59440,59501,59504,59540,59605,59635,59864,59922,59956,59960,59987,60066,60180,60201,60280,60282,60390,60394,60532,60854,60858,60861,60865,60914,60918,61172,61324,61331,61404,61588,61593,61936,61940,61963,61965,61986,62045,62055,62104,62246,62320,62415,62530,62628,62746,62750,62819,62824,62936,63081,63132,63244,63286,63290,63310,63371,63398,63460,63464,63486,63555,63835,63842,63872,63879,64072,64076,64154,64159,64235,64238,64326,64402,64469,64518,64621,64694,64815,65166,65279,65381,65385,65388,65395,65398,65434,65493,65502,65651,65875,65879,65942,66121,66213,66268,66272,66328,66398,66450,66471,66552,66555,66630,66674,66678,66719,66762,66788,66792,66863,66959,67021,67073,67176,67254,67277,67306,67310,67476,67593,67665,67980,68140,68144,68195,68257,68292,68322,68422,68464,68633,68638,68734,68772,68776,68895,69196,69198,69233,69237,69241,69369,69501,69823,70011,70089,70093,70398,70511,70657,70842,70948,71180,71295,71377,71496,71594,71635,71639,71694,71838,71992,72152,72245,72439,72751,72882,73011,73015,73087,73129,73180,73182,74377,74379],[12,55129,55125],{"id":55130},"příjem-náklady-zisk-a-nabídka-firmy",[3876,55132,55133],{},[724,55134,55135,3883,55137,2212,55140,55155,55156,2212,55159,55174,55175,2212,55178,55206,55207,55229,55230,55254,55255,55277,55278,55281,55282,55298,55299,1644],{},[883,55136,3882],{},[38,55138,55139],{},"Příjem",[883,55141,55143],{"className":55142},[886],[888,55144,55145],{"xmlns":890},[892,55146,55147,55153],{},[895,55148,55149,55151],{},[898,55150,2783],{},[898,55152,4003],{},[902,55154,4103],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,55157,55158],{},"náklady",[883,55160,55162],{"className":55161},[886],[888,55163,55164],{"xmlns":890},[892,55165,55166,55172],{},[895,55167,55168,55170],{},[898,55169,2783],{},[898,55171,1852],{},[902,55173,3251],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,55176,55177],{},"zisk",[883,55179,55181],{"className":55180},[886],[888,55182,55183],{"xmlns":890},[892,55184,55185,55203],{},[895,55186,55187,55189,55191,55193,55195,55197,55199,55201],{},[898,55188,3946],{},[898,55190,4003],{},[2005,55192,2007],{},[898,55194,2783],{},[898,55196,4003],{},[2005,55198,2234],{},[898,55200,2783],{},[898,55202,1852],{},[902,55204,55205],{"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: ",[883,55208,55210],{"className":55209},[886],[888,55211,55212],{"xmlns":890},[892,55213,55214,55226],{},[895,55215,55216,55218,55220,55222,55224],{},[898,55217,1836],{},[898,55219,1852],{},[2005,55221,2007],{},[898,55223,2826],{},[898,55225,1852],{},[902,55227,55228],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,55231,55233],{"className":55232},[886],[888,55234,55235],{"xmlns":890},[892,55236,55237,55251],{},[895,55238,55239,55241,55243,55245,55247,55249],{},[898,55240,1836],{},[898,55242,40344],{},[898,55244,1852],{},[2005,55246,2007],{},[898,55248,2826],{},[898,55250,1852],{},[902,55252,55253],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,55256,55258],{"className":55257},[886],[888,55259,55260],{"xmlns":890},[892,55261,55262,55274],{},[895,55263,55264,55266,55268,55270,55272],{},[898,55265,2826],{},[898,55267,4003],{},[2005,55269,2007],{},[898,55271,2826],{},[898,55273,1852],{},[902,55275,55276],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,55279,55280],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,55283,55285],{"className":55284},[886],[888,55286,55287],{"xmlns":890},[892,55288,55289,55295],{},[895,55290,55291,55293],{},[898,55292,2826],{},[898,55294,1852],{},[902,55296,55297],{"encoding":904},"MC"," nad bodem minima ",[883,55300,55302],{"className":55301},[886],[888,55303,55304],{"xmlns":890},[892,55305,55306,55314],{},[895,55307,55308,55310,55312],{},[898,55309,1836],{},[898,55311,40344],{},[898,55313,1852],{},[902,55315,55316],{"encoding":904},"AVC",[115,55318,1241],{"id":50959},[724,55320,55321,55322,55325,55326,55328,55329,1343,55332,1343,55335,55337,55338,55341,55342,55345,55346,55349,55350,2680,55365,1348,55380,2680,55395,3927],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,55323,55324],{},"příjmem"," (revenue) a ",[38,55327,55158],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,55330,55331],{},"zisku",[38,55333,55334],{},"bodů zvratu",[38,55336,1980],{}," a konstrukcí ",[38,55339,55340],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,55343,1145],{"className":55344,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,55347,11135],{"className":55348,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,55351,55353],{"className":55352},[886],[888,55354,55355],{"xmlns":890},[892,55356,55357,55363],{},[895,55358,55359,55361],{},[898,55360,2783],{},[898,55362,4003],{},[902,55364,4103],{"encoding":904},[883,55366,55368],{"className":55367},[886],[888,55369,55370],{"xmlns":890},[892,55371,55372,55378],{},[895,55373,55374,55376],{},[898,55375,2826],{},[898,55377,4003],{},[902,55379,6640],{"encoding":904},[883,55381,55383],{"className":55382},[886],[888,55384,55385],{"xmlns":890},[892,55386,55387,55393],{},[895,55388,55389,55391],{},[898,55390,2783],{},[898,55392,1852],{},[902,55394,3251],{"encoding":904},[883,55396,55398],{"className":55397},[886],[888,55399,55400],{"xmlns":890},[892,55401,55402,55408],{},[895,55403,55404,55406],{},[898,55405,2826],{},[898,55407,1852],{},[902,55409,55297],{"encoding":904},[724,55411,55412],{},[38,55413,55414],{},"Cílové znalosti:",[120,55416,55417,55581,55584,55587,55680,55727,55734],{},[123,55418,55419,55420,1343,55435,1343,55451,3894,55466,1343,55481,1343,55497,1343,55515,1343,55533,1343,55550,1343,55566,8431],{},"odvodit a interpretovat funkce ",[883,55421,55423],{"className":55422},[886],[888,55424,55425],{"xmlns":890},[892,55426,55427,55433],{},[895,55428,55429,55431],{},[898,55430,2783],{},[898,55432,4003],{},[902,55434,4103],{"encoding":904},[883,55436,55438],{"className":55437},[886],[888,55439,55440],{"xmlns":890},[892,55441,55442,55448],{},[895,55443,55444,55446],{},[898,55445,1836],{},[898,55447,4003],{},[902,55449,55450],{"encoding":904},"AR",[883,55452,55454],{"className":55453},[886],[888,55455,55456],{"xmlns":890},[892,55457,55458,55464],{},[895,55459,55460,55462],{},[898,55461,2826],{},[898,55463,4003],{},[902,55465,6640],{"encoding":904},[883,55467,55469],{"className":55468},[886],[888,55470,55471],{"xmlns":890},[892,55472,55473,55479],{},[895,55474,55475,55477],{},[898,55476,2783],{},[898,55478,1852],{},[902,55480,3251],{"encoding":904},[883,55482,55484],{"className":55483},[886],[888,55485,55486],{"xmlns":890},[892,55487,55488,55494],{},[895,55489,55490,55492],{},[898,55491,1876],{},[898,55493,1852],{},[902,55495,55496],{"encoding":904},"FC",[883,55498,55500],{"className":55499},[886],[888,55501,55502],{"xmlns":890},[892,55503,55504,55512],{},[895,55505,55506,55508,55510],{},[898,55507,2783],{},[898,55509,40344],{},[898,55511,1852],{},[902,55513,55514],{"encoding":904},"TVC",[883,55516,55518],{"className":55517},[886],[888,55519,55520],{"xmlns":890},[892,55521,55522,55530],{},[895,55523,55524,55526,55528],{},[898,55525,1836],{},[898,55527,1876],{},[898,55529,1852],{},[902,55531,55532],{"encoding":904},"AFC",[883,55534,55536],{"className":55535},[886],[888,55537,55538],{"xmlns":890},[892,55539,55540,55548],{},[895,55541,55542,55544,55546],{},[898,55543,1836],{},[898,55545,40344],{},[898,55547,1852],{},[902,55549,55316],{"encoding":904},[883,55551,55553],{"className":55552},[886],[888,55554,55555],{"xmlns":890},[892,55556,55557,55563],{},[895,55558,55559,55561],{},[898,55560,1836],{},[898,55562,1852],{},[902,55564,55565],{"encoding":904},"AC",[883,55567,55569],{"className":55568},[886],[888,55570,55571],{"xmlns":890},[892,55572,55573,55579],{},[895,55574,55575,55577],{},[898,55576,2826],{},[898,55578,1852],{},[902,55580,55297],{"encoding":904},[123,55582,55583],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,55585,55586],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,55588,55589,55590,55593,55594,41819,55636,8431],{},"osvojit si ",[38,55591,55592],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,55595,55597],{"className":55596},[886],[888,55598,55599],{"xmlns":890},[892,55600,55601,55633],{},[895,55602,55603,55605,55607,55609,55615,55617,55619,55621,55623,55625,55631],{},[898,55604,1836],{},[898,55606,1852],{},[2005,55608,2014],{"stretchy":2013},[2281,55610,55611,55613],{},[898,55612,2797],{},[2138,55614,2336],{},[2005,55616,2020],{"stretchy":2013},[2005,55618,2007],{},[898,55620,2826],{},[898,55622,1852],{},[2005,55624,2014],{"stretchy":2013},[2281,55626,55627,55629],{},[898,55628,2797],{},[2138,55630,2336],{},[2005,55632,2020],{"stretchy":2013},[902,55634,55635],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,55637,55639],{"className":55638},[886],[888,55640,55641],{"xmlns":890},[892,55642,55643,55677],{},[895,55644,55645,55647,55649,55651,55653,55659,55661,55663,55665,55667,55669,55675],{},[898,55646,1836],{},[898,55648,40344],{},[898,55650,1852],{},[2005,55652,2014],{"stretchy":2013},[2281,55654,55655,55657],{},[898,55656,2797],{},[2138,55658,2336],{},[2005,55660,2020],{"stretchy":2013},[2005,55662,2007],{},[898,55664,2826],{},[898,55666,1852],{},[2005,55668,2014],{"stretchy":2013},[2281,55670,55671,55673],{},[898,55672,2797],{},[2138,55674,2336],{},[2005,55676,2020],{"stretchy":2013},[902,55678,55679],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,55681,55589,55682,55593,55685,8431],{},[38,55683,55684],{},"princip maximalizace zisku",[883,55686,55688],{"className":55687},[886],[888,55689,55690],{"xmlns":890},[892,55691,55692,55724],{},[895,55693,55694,55696,55698,55700,55706,55708,55710,55712,55714,55716,55722],{},[898,55695,2826],{},[898,55697,4003],{},[2005,55699,2014],{"stretchy":2013},[2281,55701,55702,55704],{},[898,55703,2797],{},[2138,55705,2336],{},[2005,55707,2020],{"stretchy":2013},[2005,55709,2007],{},[898,55711,2826],{},[898,55713,1852],{},[2005,55715,2014],{"stretchy":2013},[2281,55717,55718,55720],{},[898,55719,2797],{},[2138,55721,2336],{},[2005,55723,2020],{"stretchy":2013},[902,55725,55726],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,55728,55729,55730,55733],{},"stanovit ",[38,55731,55732],{},"body zvratu"," a interval zisku;",[123,55735,55736,55737,55740],{},"zkonstruovat ",[38,55738,55739],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,55742,55744],{"id":55743},"příjem-firmy","Příjem firmy",[724,55746,55747],{},[2568,55748],{"alt":55749,"className":55750,"src":55751},"imek-ar-mr-dvojnasobny-sklon",[210,2572],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,55753,55755],{"id":55754},"celkový-příjem","Celkový příjem",[724,55757,55758,55759,10030,55774,55777,55778,29949],{},"Celkový příjem ",[883,55760,55762],{"className":55761},[886],[888,55763,55764],{"xmlns":890},[892,55765,55766,55772],{},[895,55767,55768,55770],{},[898,55769,2783],{},[898,55771,4003],{},[902,55773,4103],{"encoding":904},[38,55775,55776],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,55779,55781],{"className":55780},[886],[888,55782,55783],{"xmlns":890},[892,55784,55785,55799],{},[895,55786,55787,55789,55791,55793,55795,55797],{},[898,55788,3946],{},[2005,55790,2007],{},[898,55792,1860],{},[2005,55794,2014],{"stretchy":2013},[898,55796,2797],{},[2005,55798,2020],{"stretchy":2013},[902,55800,4646],{"encoding":904},[883,55802,55804],{"className":55803},[886],[888,55805,55806],{"xmlns":890,"display":28071},[892,55807,55808,55865],{},[20760,55809,55810],{"width":28076},[20765,55811,55812,55814,55858,55860],{},[20768,55813],{"width":28081},[20768,55815,55816],{},[895,55817,55818,55820,55822,55824,55826,55828,55830,55832,55834,55836,55838,55840,55842,55844,55846,55848,55850,55852,55854,55856],{},[898,55819,2783],{},[898,55821,4003],{},[2005,55823,2007],{},[898,55825,2783],{},[898,55827,4003],{},[2005,55829,2014],{"stretchy":2013},[898,55831,2797],{},[2005,55833,2020],{"stretchy":2013},[2005,55835,2007],{},[898,55837,3946],{},[2005,55839,3185],{},[898,55841,2797],{},[2005,55843,2007],{},[898,55845,1860],{},[2005,55847,2014],{"stretchy":2013},[898,55849,2797],{},[2005,55851,2020],{"stretchy":2013},[2005,55853,3185],{},[898,55855,2797],{},[898,55857,1644],{"mathvariant":2385},[20768,55859],{"width":28081},[20768,55861,55862],{},[2297,55863,55864],{},"(3.1)",[902,55866,55867],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,55869,55870,55871,55874,55875,55898],{},"Graf funkce se nazývá ",[38,55872,55873],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,55876,55878],{"className":55877},[886],[888,55879,55880],{"xmlns":890},[892,55881,55882,55896],{},[895,55883,55884,55886,55888,55890,55892,55894],{},[898,55885,3946],{},[2005,55887,2007],{},[898,55889,207],{},[898,55891,2797],{},[2005,55893,2104],{},[898,55895,2107],{},[902,55897,37065],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,55900,55902],{"className":55901},[886],[888,55903,55904],{"xmlns":890,"display":28071},[892,55905,55906,55946],{},[895,55907,55908,55910,55912,55914,55916,55918,55920,55922,55924,55926,55928,55930,55932,55938,55940,55942,55944],{},[898,55909,2783],{},[898,55911,4003],{},[2005,55913,2007],{},[898,55915,2797],{},[2005,55917,2014],{"stretchy":2013},[898,55919,207],{},[898,55921,2797],{},[2005,55923,2104],{},[898,55925,2107],{},[2005,55927,2020],{"stretchy":2013},[2005,55929,2007],{},[898,55931,207],{},[2133,55933,55934,55936],{},[898,55935,2797],{},[2138,55937,2140],{},[2005,55939,2104],{},[898,55941,2107],{},[898,55943,2797],{},[2005,55945,2295],{"separator":2294},[902,55947,55948],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,55950,55951,55952,55965,55966,55983],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,55953,55955],{"className":55954},[886],[888,55956,55957],{"xmlns":890},[892,55958,55959,55963],{},[895,55960,55961],{},[898,55962,900],{},[902,55964,900],{"encoding":904}," (jelikož ",[883,55967,55969],{"className":55968},[886],[888,55970,55971],{"xmlns":890},[892,55972,55973,55981],{},[895,55974,55975,55977,55979],{},[898,55976,207],{},[2005,55978,3455],{},[2138,55980,2336],{},[902,55982,43090],{"encoding":904},") procházející počátkem.",[37353,55985,55987],{"id":55986},"příklad-31","Příklad 3.1",[724,55989,55990,55993,55994,56030,56031,56046],{},[38,55991,55992],{},"Zadání."," Pro poptávku ",[883,55995,55997],{"className":55996},[886],[888,55998,55999],{"xmlns":890},[892,56000,56001,56027],{},[895,56002,56003,56005,56007,56009,56011,56013,56015,56017,56019,56021,56023,56025],{},[898,56004,3946],{},[2005,56006,2007],{},[898,56008,1860],{},[2005,56010,2014],{"stretchy":2013},[898,56012,2797],{},[2005,56014,2020],{"stretchy":2013},[2005,56016,2007],{},[2005,56018,2234],{},[2138,56020,2140],{},[898,56022,2797],{},[2005,56024,2104],{},[2138,56026,3098],{},[902,56028,56029],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,56032,56034],{"className":56033},[886],[888,56035,56036],{"xmlns":890},[892,56037,56038,56044],{},[895,56039,56040,56042],{},[898,56041,2783],{},[898,56043,4003],{},[902,56045,4103],{"encoding":904}," a charakterizujte jeho křivku.",[724,56048,56049,56051],{},[38,56050,22776],{}," Celkový příjem je",[883,56053,56055],{"className":56054},[886],[888,56056,56057],{"xmlns":890,"display":28071},[892,56058,56059,56115],{},[895,56060,56061,56063,56065,56067,56069,56071,56073,56075,56077,56079,56081,56083,56085,56087,56089,56091,56093,56095,56097,56099,56101,56107,56109,56111,56113],{},[898,56062,2783],{},[898,56064,4003],{},[2005,56066,2007],{},[898,56068,2783],{},[898,56070,4003],{},[2005,56072,2014],{"stretchy":2013},[898,56074,2797],{},[2005,56076,2020],{"stretchy":2013},[2005,56078,2007],{},[898,56080,2797],{},[2005,56082,2014],{"stretchy":2013},[2005,56084,2234],{},[2138,56086,2140],{},[898,56088,2797],{},[2005,56090,2104],{},[2138,56092,3098],{},[2005,56094,2020],{"stretchy":2013},[2005,56096,2007],{},[2005,56098,2234],{},[2138,56100,2140],{},[2133,56102,56103,56105],{},[898,56104,2797],{},[2138,56106,2140],{},[2005,56108,2104],{},[2138,56110,3098],{},[898,56112,2797],{},[898,56114,1644],{"mathvariant":2385},[902,56116,56117],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,56119,56120,56121,3894,56143,56165,56166,56184,56185,1644],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,56122,56124],{"className":56123},[886],[888,56125,56126],{"xmlns":890},[892,56127,56128,56140],{},[895,56129,56130,56136,56138],{},[2281,56131,56132,56134],{},[898,56133,2797],{},[2138,56135,2287],{},[2005,56137,2007],{},[2138,56139,2336],{},[902,56141,56142],{"encoding":904},"Q_1 = 0",[883,56144,56146],{"className":56145},[886],[888,56147,56148],{"xmlns":890},[892,56149,56150,56162],{},[895,56151,56152,56158,56160],{},[2281,56153,56154,56156],{},[898,56155,2797],{},[2138,56157,2140],{},[2005,56159,2007],{},[2138,56161,3128],{},[902,56163,56164],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,56167,56169],{"className":56168},[886],[888,56170,56171],{"xmlns":890},[892,56172,56173,56181],{},[895,56174,56175,56177,56179],{},[898,56176,2797],{},[2005,56178,2007],{},[2138,56180,5010],{},[902,56182,56183],{"encoding":904},"Q = 25"," ve výši ",[883,56186,56188],{"className":56187},[886],[888,56189,56190],{"xmlns":890},[892,56191,56192,56233],{},[895,56193,56194,56196,56206,56208,56210,56212,56214,56217,56219,56221,56223,56225,56227,56229,56231],{},[898,56195,2783],{},[2281,56197,56198,56200,56203],{},[898,56199,4003],{},[898,56201,56202],{},"max",[2005,56204,56205],{},"⁡",[2005,56207,2007],{},[2005,56209,2234],{},[2138,56211,2140],{},[2005,56213,3185],{},[2138,56215,56216],{},"625",[2005,56218,2104],{},[2138,56220,3098],{},[2005,56222,3185],{},[2138,56224,5010],{},[2005,56226,2007],{},[2138,56228,2287],{},[2297,56230,2995],{},[2138,56232,30748],{},[902,56234,56235],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,56237,56238],{},[614,56239,56240,56241,56275,56276,3894,56289,56302,56303,2633,56321,1644],{},"Obrázek 3.1: Parabola ",[883,56242,56244],{"className":56243},[886],[888,56245,56246],{"xmlns":890},[892,56247,56248,56272],{},[895,56249,56250,56252,56254,56256,56258,56260,56266,56268,56270],{},[898,56251,2783],{},[898,56253,4003],{},[2005,56255,2007],{},[2005,56257,2234],{},[2138,56259,2140],{},[2133,56261,56262,56264],{},[898,56263,2797],{},[2138,56265,2140],{},[2005,56267,2104],{},[2138,56269,3098],{},[898,56271,2797],{},[902,56273,56274],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,56277,56279],{"className":56278},[886],[888,56280,56281],{"xmlns":890},[892,56282,56283,56287],{},[895,56284,56285],{},[2138,56286,2336],{},[902,56288,2336],{"encoding":904},[883,56290,56292],{"className":56291},[886],[888,56293,56294],{"xmlns":890},[892,56295,56296,56300],{},[895,56297,56298],{},[2138,56299,3128],{},[902,56301,3128],{"encoding":904}," a maximem ",[883,56304,56306],{"className":56305},[886],[888,56307,56308],{"xmlns":890},[892,56309,56310,56318],{},[895,56311,56312,56314,56316],{},[2138,56313,2287],{},[2297,56315,2995],{},[2138,56317,30748],{},[902,56319,56320],{"encoding":904},"1\\,250",[883,56322,56324],{"className":56323},[886],[888,56325,56326],{"xmlns":890},[892,56327,56328,56336],{},[895,56329,56330,56332,56334],{},[898,56331,2797],{},[2005,56333,2007],{},[2138,56335,5010],{},[902,56337,56183],{"encoding":904},[198,56339,56341],{"id":56340},"průměrný-příjem","Průměrný příjem",[724,56343,56344,2212,56346,10030,56361,56364],{},[38,56345,56341],{},[883,56347,56349],{"className":56348},[886],[888,56350,56351],{"xmlns":890},[892,56352,56353,56359],{},[895,56354,56355,56357],{},[898,56356,1836],{},[898,56358,4003],{},[902,56360,55450],{"encoding":904},[38,56362,56363],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,56366,56368],{"className":56367},[886],[888,56369,56370],{"xmlns":890,"display":28071},[892,56371,56372,56440],{},[895,56373,56374,56376,56378,56380,56382,56384,56386,56388,56390,56392,56408,56410,56428,56430,56432,56434,56436,56438],{},[898,56375,1836],{},[898,56377,4003],{},[2005,56379,2007],{},[898,56381,1836],{},[898,56383,4003],{},[2005,56385,2014],{"stretchy":2013},[898,56387,2797],{},[2005,56389,2020],{"stretchy":2013},[2005,56391,2007],{},[2338,56393,56394,56406],{},[895,56395,56396,56398,56400,56402,56404],{},[898,56397,2783],{},[898,56399,4003],{},[2005,56401,2014],{"stretchy":2013},[898,56403,2797],{},[2005,56405,2020],{"stretchy":2013},[898,56407,2797],{},[2005,56409,2007],{},[2338,56411,56412,56426],{},[895,56413,56414,56416,56418,56420,56422,56424],{},[898,56415,2797],{},[2297,56417,2995],{},[898,56419,1860],{},[2005,56421,2014],{"stretchy":2013},[898,56423,2797],{},[2005,56425,2020],{"stretchy":2013},[898,56427,2797],{},[2005,56429,2007],{},[898,56431,1860],{},[2005,56433,2014],{"stretchy":2013},[898,56435,2797],{},[2005,56437,2020],{"stretchy":2013},[898,56439,1644],{"mathvariant":2385},[902,56441,56442],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[3876,56444,56445],{},[724,56446,56447,56450,56451,1343,56454,1644],{},[883,56448,56449],{},"!note"," Klíčové pozorování\n",[38,56452,56453],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,56455,56457],{"className":56456},[886],[888,56458,56459],{"xmlns":890},[892,56460,56461,56483],{},[895,56462,56463,56465,56467,56469,56471,56473,56475,56477,56479,56481],{},[898,56464,1836],{},[898,56466,4003],{},[2005,56468,2014],{"stretchy":2013},[898,56470,2797],{},[2005,56472,2020],{"stretchy":2013},[2005,56474,2007],{},[898,56476,1860],{},[2005,56478,2014],{"stretchy":2013},[898,56480,2797],{},[2005,56482,2020],{"stretchy":2013},[902,56484,56485],{"encoding":904},"AR(Q) = D(Q)",[198,56487,56489],{"id":56488},"mezní-příjem","Mezní příjem",[724,56491,56492,56493,2212,56496,10030,56511,56514,56515,56518],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,56494,56495],{},"mezní příjem",[883,56497,56499],{"className":56498},[886],[888,56500,56501],{"xmlns":890},[892,56502,56503,56509],{},[895,56504,56505,56507],{},[898,56506,2826],{},[898,56508,4003],{},[902,56510,6640],{"encoding":904},[38,56512,56513],{},"marginal revenue","), definovaný jako ",[207,56516,1145],{"className":56517,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,56520,56522],{"className":56521},[886],[888,56523,56524],{"xmlns":890,"display":28071},[892,56525,56526,56583],{},[20760,56527,56528],{"width":28076},[20765,56529,56530,56532,56576,56578],{},[20768,56531],{"width":28081},[20768,56533,56534],{},[895,56535,56536,56538,56540,56542,56558,56560,56562,56568,56570,56572,56574],{},[898,56537,2826],{},[898,56539,4003],{},[2005,56541,2007],{},[2338,56543,56544,56552],{},[895,56545,56546,56548,56550],{},[898,56547,2203],{"mathvariant":2385},[898,56549,2783],{},[898,56551,4003],{},[895,56553,56554,56556],{},[898,56555,2203],{"mathvariant":2385},[898,56557,2797],{},[2005,56559,2007],{},[898,56561,2783],{},[2133,56563,56564,56566],{},[898,56565,4003],{},[2005,56567,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,56569,2014],{"stretchy":2013},[898,56571,2797],{},[2005,56573,2020],{"stretchy":2013},[898,56575,1644],{"mathvariant":2385},[20768,56577],{"width":28081},[20768,56579,56580],{},[2297,56581,56582],{},"(3.2)",[902,56584,56585],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,56587,56588,56589,56591],{},"Mezní příjem udává ",[38,56590,2605],{}," celkového příjmu vzhledem k množství.",[3876,56593,56594],{},[724,56595,56596,56598,56599,56625,56626,56643,56644,1644],{},[883,56597,4164],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,56600,56602],{"className":56601},[886],[888,56603,56604],{"xmlns":890},[892,56605,56606,56622],{},[895,56607,56608,56610,56612,56614,56620],{},[898,56609,2826],{},[898,56611,4003],{},[2005,56613,2014],{"stretchy":2013},[2133,56615,56616,56618],{},[898,56617,2797],{},[2005,56619,4360],{},[2005,56621,2020],{"stretchy":2013},[902,56623,56624],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,56627,56629],{"className":56628},[886],[888,56630,56631],{"xmlns":890},[892,56632,56633,56641],{},[895,56634,56635],{},[2133,56636,56637,56639],{},[898,56638,2797],{},[2005,56640,4360],{},[902,56642,29849],{"encoding":904},". Jinak řečeno: ",[883,56645,56647],{"className":56646},[886],[888,56648,56649],{"xmlns":890},[892,56650,56651,56703],{},[895,56652,56653,56655,56657,56659,56665,56667,56669,56671,56673,56675,56681,56683,56685,56687,56689,56691,56693,56695,56701],{},[898,56654,2826],{},[898,56656,4003],{},[2005,56658,2014],{"stretchy":2013},[2133,56660,56661,56663],{},[898,56662,2797],{},[2005,56664,4360],{},[2005,56666,2020],{"stretchy":2013},[2005,56668,2739],{},[898,56670,2783],{},[898,56672,4003],{},[2005,56674,2014],{"stretchy":2013},[2133,56676,56677,56679],{},[898,56678,2797],{},[2005,56680,4360],{},[2005,56682,2104],{},[2138,56684,2287],{},[2005,56686,2020],{"stretchy":2013},[2005,56688,2234],{},[898,56690,2783],{},[898,56692,4003],{},[2005,56694,2014],{"stretchy":2013},[2133,56696,56697,56699],{},[898,56698,2797],{},[2005,56700,4360],{},[2005,56702,2020],{"stretchy":2013},[902,56704,56705],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[37353,56707,56709],{"id":56708},"příklad-32","Příklad 3.2",[724,56711,56712,55993,56714,56030,56748,56763,56764,1644],{},[38,56713,55992],{},[883,56715,56717],{"className":56716},[886],[888,56718,56719],{"xmlns":890},[892,56720,56721,56745],{},[895,56722,56723,56725,56727,56729,56731,56733,56735,56737,56739,56741,56743],{},[898,56724,3946],{},[2005,56726,2007],{},[898,56728,1860],{},[2005,56730,2014],{"stretchy":2013},[898,56732,2797],{},[2005,56734,2020],{"stretchy":2013},[2005,56736,2007],{},[2138,56738,3098],{},[2005,56740,2234],{},[2138,56742,2140],{},[898,56744,2797],{},[902,56746,56747],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,56749,56751],{"className":56750},[886],[888,56752,56753],{"xmlns":890},[892,56754,56755,56761],{},[895,56756,56757,56759],{},[898,56758,2826],{},[898,56760,4003],{},[902,56762,6640],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,56765,56767],{"className":56766},[886],[888,56768,56769],{"xmlns":890},[892,56770,56771,56787],{},[895,56772,56773,56775,56777,56779,56781,56783,56785],{},[898,56774,2797],{},[2005,56776,2007],{},[2138,56778,36249],{},[2005,56780,2295],{"separator":2294},[2138,56782,41867],{},[2005,56784,2295],{"separator":2294},[2138,56786,9041],{},[902,56788,56789],{"encoding":904},"Q = 15, 16, 20",[724,56791,56792,2212,56794,56826],{},[38,56793,22776],{},[883,56795,56797],{"className":56796},[886],[888,56798,56799],{"xmlns":890},[892,56800,56801,56823],{},[895,56802,56803,56805,56807,56809,56811,56813,56815,56817],{},[898,56804,2783],{},[898,56806,4003],{},[2005,56808,2007],{},[2138,56810,3098],{},[898,56812,2797],{},[2005,56814,2234],{},[2138,56816,2140],{},[2133,56818,56819,56821],{},[898,56820,2797],{},[2138,56822,2140],{},[902,56824,56825],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,56828,56830],{"className":56829},[886],[888,56831,56832],{"xmlns":890,"display":28071},[892,56833,56834,56876],{},[895,56835,56836,56838,56840,56842,56844,56846,56848,56850,56852,56858,56864,56866,56868,56870,56872,56874],{},[898,56837,2826],{},[898,56839,4003],{},[2005,56841,2007],{},[2005,56843,2014],{"stretchy":2013},[2138,56845,3098],{},[898,56847,2797],{},[2005,56849,2234],{},[2138,56851,2140],{},[2133,56853,56854,56856],{},[898,56855,2797],{},[2138,56857,2140],{},[2133,56859,56860,56862],{},[2005,56861,2020],{"stretchy":2013},[2005,56863,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,56865,2007],{},[2138,56867,3098],{},[2005,56869,2234],{},[2138,56871,2360],{},[898,56873,2797],{},[898,56875,1644],{"mathvariant":2385},[902,56877,56878],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,56880,9669,56881,8108,56899,56925,56926,4364,56939,56954,56955,56968,56969,21426,56982,4364,56995,57010,57011,57024,57025,57056,57057,57076],{},[883,56882,56884],{"className":56883},[886],[888,56885,56886],{"xmlns":890},[892,56887,56888,56896],{},[895,56889,56890,56892,56894],{},[898,56891,2797],{},[2005,56893,2007],{},[2138,56895,36249],{},[902,56897,56898],{"encoding":904},"Q = 15",[883,56900,56902],{"className":56901},[886],[888,56903,56904],{"xmlns":890},[892,56905,56906,56922],{},[895,56907,56908,56910,56912,56914,56916,56918,56920],{},[898,56909,2826],{},[898,56911,4003],{},[2005,56913,2014],{"stretchy":2013},[2138,56915,36249],{},[2005,56917,2020],{"stretchy":2013},[2005,56919,2007],{},[2138,56921,5217],{},[902,56923,56924],{"encoding":904},"MR(15) = 40",": při množství ",[883,56927,56929],{"className":56928},[886],[888,56930,56931],{"xmlns":890},[892,56932,56933,56937],{},[895,56934,56935],{},[2138,56936,36249],{},[902,56938,36249],{"encoding":904},[883,56940,56942],{"className":56941},[886],[888,56943,56944],{"xmlns":890},[892,56945,56946,56952],{},[895,56947,56948,56950],{},[898,56949,2783],{},[898,56951,4003],{},[902,56953,4103],{"encoding":904}," mění asi ",[883,56956,56958],{"className":56957},[886],[888,56959,56960],{"xmlns":890},[892,56961,56962,56966],{},[895,56963,56964],{},[2138,56965,5217],{},[902,56967,5217],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,56970,56972],{"className":56971},[886],[888,56973,56974],{"xmlns":890},[892,56975,56976,56980],{},[895,56977,56978],{},[898,56979,2797],{},[902,56981,2797],{"encoding":904},[883,56983,56985],{"className":56984},[886],[888,56986,56987],{"xmlns":890},[892,56988,56989,56993],{},[895,56990,56991],{},[2138,56992,2287],{},[902,56994,2287],{"encoding":904},[883,56996,56998],{"className":56997},[886],[888,56999,57000],{"xmlns":890},[892,57001,57002,57008],{},[895,57003,57004,57006],{},[898,57005,2783],{},[898,57007,4003],{},[902,57009,4103],{"encoding":904}," zvýší přibližně o ",[883,57012,57014],{"className":57013},[886],[888,57015,57016],{"xmlns":890},[892,57017,57018,57022],{},[895,57019,57020],{},[2138,57021,5217],{},[902,57023,5217],{"encoding":904},", tj. ze skutečné hodnoty ",[883,57026,57028],{"className":57027},[886],[888,57029,57030],{"xmlns":890},[892,57031,57032,57053],{},[895,57033,57034,57036,57038,57040,57042,57044,57046,57048,57050],{},[898,57035,2783],{},[898,57037,4003],{},[2005,57039,2014],{"stretchy":2013},[2138,57041,36249],{},[2005,57043,2020],{"stretchy":2013},[2005,57045,2007],{},[2138,57047,2287],{},[2297,57049,2995],{},[2138,57051,57052],{},"050",[902,57054,57055],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,57058,57060],{"className":57059},[886],[888,57061,57062],{"xmlns":890},[892,57063,57064,57073],{},[895,57065,57066,57068,57070],{},[2138,57067,2287],{},[2297,57069,2995],{},[2138,57071,57072],{},"090",[902,57074,57075],{"encoding":904},"1\\,090",". Skutečná změna je",[883,57078,57080],{"className":57079},[886],[888,57081,57082],{"xmlns":890,"display":28071},[892,57083,57084,57138],{},[895,57085,57086,57088,57090,57092,57094,57096,57098,57100,57102,57104,57106,57108,57110,57112,57114,57116,57118,57120,57122,57125,57127,57129,57131,57133,57135],{},[898,57087,2897],{"mathvariant":2385},[898,57089,2783],{},[898,57091,4003],{},[2005,57093,2007],{},[898,57095,2783],{},[898,57097,4003],{},[2005,57099,2014],{"stretchy":2013},[2138,57101,41867],{},[2005,57103,2020],{"stretchy":2013},[2005,57105,2234],{},[898,57107,2783],{},[898,57109,4003],{},[2005,57111,2014],{"stretchy":2013},[2138,57113,36249],{},[2005,57115,2020],{"stretchy":2013},[2005,57117,2007],{},[2138,57119,2287],{},[2297,57121,2995],{},[2138,57123,57124],{},"088",[2005,57126,2234],{},[2138,57128,2287],{},[2297,57130,2995],{},[2138,57132,57052],{},[2005,57134,2007],{},[2138,57136,57137],{},"38.",[902,57139,57140],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,57142,57143,57144,1343,57170,2935,57196,57211,57212,57227],{},"Podobně ",[883,57145,57147],{"className":57146},[886],[888,57148,57149],{"xmlns":890},[892,57150,57151,57167],{},[895,57152,57153,57155,57157,57159,57161,57163,57165],{},[898,57154,2826],{},[898,57156,4003],{},[2005,57158,2014],{"stretchy":2013},[2138,57160,41867],{},[2005,57162,2020],{"stretchy":2013},[2005,57164,2007],{},[2138,57166,5571],{},[902,57168,57169],{"encoding":904},"MR(16) = 36",[883,57171,57173],{"className":57172},[886],[888,57174,57175],{"xmlns":890},[892,57176,57177,57193],{},[895,57178,57179,57181,57183,57185,57187,57189,57191],{},[898,57180,2826],{},[898,57182,4003],{},[2005,57184,2014],{"stretchy":2013},[2138,57186,9041],{},[2005,57188,2020],{"stretchy":2013},[2005,57190,2007],{},[2138,57192,9041],{},[902,57194,57195],{"encoding":904},"MR(20) = 20",[883,57197,57199],{"className":57198},[886],[888,57200,57201],{"xmlns":890},[892,57202,57203,57209],{},[895,57204,57205,57207],{},[898,57206,2826],{},[898,57208,4003],{},[902,57210,6640],{"encoding":904}," je klesající funkce — rychlost změny ",[883,57213,57215],{"className":57214},[886],[888,57216,57217],{"xmlns":890},[892,57218,57219,57225],{},[895,57220,57221,57223],{},[898,57222,2783],{},[898,57224,4003],{},[902,57226,4103],{"encoding":904}," s růstem množství klesá.",[198,57229,57231],{"id":57230},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,57233,57234],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,57236,57238],{"className":57237},[886],[888,57239,57240],{"xmlns":890,"display":28071},[892,57241,57242,57311],{},[20760,57243,57244],{"width":28076},[20765,57245,57246,57248,57304,57306],{},[20768,57247],{"width":28081},[20768,57249,57250],{},[895,57251,57252,57254,57256,57258,57260,57262,57264,57266,57268,57270,57272,57274,57276,57278,57284,57286,57288,57290,57292,57294,57296,57298,57300,57302],{},[898,57253,2897],{"mathvariant":2385},[898,57255,2783],{},[898,57257,4003],{},[2297,57259,3993],{},[2005,57261,2739],{},[2297,57263,3993],{},[898,57265,2203],{"mathvariant":2385},[898,57267,2783],{},[898,57269,4003],{},[2005,57271,2007],{},[2005,57273,2014],{"stretchy":2013},[898,57275,2783],{},[898,57277,4003],{},[2133,57279,57280,57282],{},[2005,57281,2020],{"stretchy":2013},[2005,57283,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,57285,2995],{},[898,57287,2203],{"mathvariant":2385},[898,57289,2797],{},[2005,57291,2007],{},[898,57293,2826],{},[898,57295,4003],{},[2297,57297,2995],{},[898,57299,2203],{"mathvariant":2385},[898,57301,2797],{},[2005,57303,2295],{"separator":2294},[20768,57305],{"width":28081},[20768,57307,57308],{},[2297,57309,57310],{},"(3.3)",[902,57312,57313],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,57315,57316],{},"schematicky:",[883,57318,57320],{"className":57319},[886],[888,57321,57322],{"xmlns":890,"display":28071},[892,57323,57324,57432],{},[895,57325,57326,57364,57366,57368,57370,57399,57402,57430],{},[895,57327,57328,57331,57337,57340,57346,57349,57355,57361],{},[2297,57329,57330],{},"zm",[8392,57332,57333,57335],{"accent":2294},[2297,57334,45737],{},[2005,57336,25063],{},[2297,57338,57339],{},"na celkov",[8392,57341,57342,57344],{"accent":2294},[2297,57343,45737],{},[2005,57345,24982],{},[2297,57347,57348],{},"ho p",[8392,57350,57351,57353],{"accent":2294},[2297,57352,12047],{},[2005,57354,25063],{},[8392,57356,57357,57359],{"accent":2294},[2297,57358,25051],{},[2005,57360,24982],{},[2297,57362,57363],{},"jmu",[2297,57365,3993],{},[2005,57367,2739],{},[2297,57369,3993],{},[895,57371,57372,57375,57381,57384,57390,57396],{},[2297,57373,57374],{},"mezn",[8392,57376,57377,57379],{"accent":2294},[2297,57378,25051],{},[2005,57380,24982],{},[2297,57382,57383],{}," p",[8392,57385,57386,57388],{"accent":2294},[2297,57387,12047],{},[2005,57389,25063],{},[8392,57391,57392,57394],{"accent":2294},[2297,57393,25051],{},[2005,57395,24982],{},[2297,57397,57398],{},"jem",[2005,57400,57401],{},"×",[895,57403,57404,57406,57412,57415,57421,57424],{},[2297,57405,57330],{},[8392,57407,57408,57410],{"accent":2294},[2297,57409,45737],{},[2005,57411,25063],{},[2297,57413,57414],{},"na mno",[8392,57416,57417,57419],{"accent":2294},[2297,57418,9600],{},[2005,57420,25063],{},[2297,57422,57423],{},"stv",[8392,57425,57426,57428],{"accent":2294},[2297,57427,25051],{},[2005,57429,24982],{},[898,57431,1644],{"mathvariant":2385},[902,57433,57434],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,57436,57437,57438,57453],{},"Pro porovnání skutečná změna ",[883,57439,57441],{"className":57440},[886],[888,57442,57443],{"xmlns":890},[892,57444,57445,57451],{},[895,57446,57447,57449],{},[898,57448,2783],{},[898,57450,4003],{},[902,57452,4103],{"encoding":904}," je",[883,57455,57457],{"className":57456},[886],[888,57458,57459],{"xmlns":890,"display":28071},[892,57460,57461,57516],{},[20760,57462,57463],{"width":28076},[20765,57464,57465,57467,57509,57511],{},[20768,57466],{"width":28081},[20768,57468,57469],{},[895,57470,57471,57473,57475,57477,57479,57481,57483,57485,57487,57489,57491,57493,57495,57497,57499,57501,57503,57505,57507],{},[898,57472,2897],{"mathvariant":2385},[898,57474,2783],{},[898,57476,4003],{},[2005,57478,2007],{},[898,57480,2783],{},[898,57482,4003],{},[2005,57484,2014],{"stretchy":2013},[898,57486,2797],{},[2005,57488,2104],{},[898,57490,2203],{"mathvariant":2385},[898,57492,2797],{},[2005,57494,2020],{"stretchy":2013},[2005,57496,2234],{},[898,57498,2783],{},[898,57500,4003],{},[2005,57502,2014],{"stretchy":2013},[898,57504,2797],{},[2005,57506,2020],{"stretchy":2013},[898,57508,1644],{"mathvariant":2385},[20768,57510],{"width":28081},[20768,57512,57513],{},[2297,57514,57515],{},"(3.4)",[902,57517,57518],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[37353,57520,57522],{"id":57521},"příklad-33","Příklad 3.3",[724,57524,57525,57527,57528,57558,57559,2666,57574,2680,57587,2694,57600,57614],{},[38,57526,55992],{}," Pro ",[883,57529,57531],{"className":57530},[886],[888,57532,57533],{"xmlns":890},[892,57534,57535,57555],{},[895,57536,57537,57539,57541,57543,57545,57547,57549],{},[898,57538,2783],{},[898,57540,4003],{},[2005,57542,2007],{},[2138,57544,3098],{},[898,57546,2797],{},[2005,57548,2234],{},[2133,57550,57551,57553],{},[898,57552,2797],{},[2138,57554,2140],{},[902,57556,57557],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,57560,57562],{"className":57561},[886],[888,57563,57564],{"xmlns":890},[892,57565,57566,57572],{},[895,57567,57568,57570],{},[898,57569,2783],{},[898,57571,4003],{},[902,57573,4103],{"encoding":904},[883,57575,57577],{"className":57576},[886],[888,57578,57579],{"xmlns":890},[892,57580,57581,57585],{},[895,57582,57583],{},[898,57584,2797],{},[902,57586,2797],{"encoding":904},[883,57588,57590],{"className":57589},[886],[888,57591,57592],{"xmlns":890},[892,57593,57594,57598],{},[895,57595,57596],{},[2138,57597,3134],{},[902,57599,3134],{"encoding":904},[883,57601,57603],{"className":57602},[886],[888,57604,57605],{"xmlns":890},[892,57606,57607,57612],{},[895,57608,57609],{},[2138,57610,57611],{},"63",[902,57613,57611],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,57616,57617,2212,57619,57644,57645,1343,57663,2713],{},[38,57618,22776],{},[883,57620,57622],{"className":57621},[886],[888,57623,57624],{"xmlns":890},[892,57625,57626,57642],{},[895,57627,57628,57630,57632,57634,57636,57638,57640],{},[898,57629,2826],{},[898,57631,4003],{},[2005,57633,2007],{},[2138,57635,3098],{},[2005,57637,2234],{},[2138,57639,2140],{},[898,57641,2797],{},[902,57643,11441],{"encoding":904},", tedy při ",[883,57646,57648],{"className":57647},[886],[888,57649,57650],{"xmlns":890},[892,57651,57652,57660],{},[895,57653,57654,57656,57658],{},[898,57655,2797],{},[2005,57657,2007],{},[2138,57659,3134],{},[902,57661,57662],{"encoding":904},"Q = 60",[883,57664,57666],{"className":57665},[886],[888,57667,57668],{"xmlns":890},[892,57669,57670,57680],{},[895,57671,57672,57674,57676,57678],{},[898,57673,2203],{"mathvariant":2385},[898,57675,2797],{},[2005,57677,2007],{},[2138,57679,2182],{},[902,57681,57682],{"encoding":904},"\\mathrm{d}Q = 3",[883,57684,57686],{"className":57685},[886],[888,57687,57688],{"xmlns":890,"display":28071},[892,57689,57690,57721],{},[895,57691,57692,57694,57696,57698,57700,57702,57704,57706,57708,57710,57712,57714,57716,57718],{},[898,57693,2203],{"mathvariant":2385},[898,57695,2783],{},[898,57697,4003],{},[2005,57699,2007],{},[2005,57701,2014],{"stretchy":2013},[2138,57703,3098],{},[2005,57705,2234],{},[2138,57707,4055],{},[2005,57709,2020],{"stretchy":2013},[2005,57711,3185],{},[2138,57713,2182],{},[2005,57715,2007],{},[2005,57717,2234],{},[2138,57719,57720],{},"60.",[902,57722,57723],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,57725,57726,57727,57757,57758,57777],{},"Celkový příjem klesne z ",[883,57728,57730],{"className":57729},[886],[888,57731,57732],{"xmlns":890},[892,57733,57734,57754],{},[895,57735,57736,57738,57740,57742,57744,57746,57748,57750,57752],{},[898,57737,2783],{},[898,57739,4003],{},[2005,57741,2014],{"stretchy":2013},[2138,57743,3134],{},[2005,57745,2020],{"stretchy":2013},[2005,57747,2007],{},[2138,57749,2140],{},[2297,57751,2995],{},[2138,57753,20148],{},[902,57755,57756],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,57759,57761],{"className":57760},[886],[888,57762,57763],{"xmlns":890},[892,57764,57765,57774],{},[895,57766,57767,57769,57771],{},[2138,57768,2140],{},[2297,57770,2995],{},[2138,57772,57773],{},"340",[902,57775,57776],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,57779,57781],{"className":57780},[886],[888,57782,57783],{"xmlns":890,"display":28071},[892,57784,57785,57843],{},[895,57786,57787,57789,57791,57793,57795,57797,57799,57801,57803,57805,57807,57809,57811,57813,57815,57817,57819,57821,57823,57826,57828,57830,57832,57834,57836,57838,57841],{},[898,57788,2897],{"mathvariant":2385},[898,57790,2783],{},[898,57792,4003],{},[2005,57794,2007],{},[898,57796,2783],{},[898,57798,4003],{},[2005,57800,2014],{"stretchy":2013},[2138,57802,57611],{},[2005,57804,2020],{"stretchy":2013},[2005,57806,2234],{},[898,57808,2783],{},[898,57810,4003],{},[2005,57812,2014],{"stretchy":2013},[2138,57814,3134],{},[2005,57816,2020],{"stretchy":2013},[2005,57818,2007],{},[2138,57820,2140],{},[2297,57822,2995],{},[2138,57824,57825],{},"331",[2005,57827,2234],{},[2138,57829,2140],{},[2297,57831,2995],{},[2138,57833,20148],{},[2005,57835,2007],{},[2005,57837,2234],{},[2138,57839,57840],{},"69",[2005,57842,2295],{"separator":2294},[902,57844,57845],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,57847,57848,57849,57864,57865,1644],{},"tj. ",[883,57850,57852],{"className":57851},[886],[888,57853,57854],{"xmlns":890},[892,57855,57856,57862],{},[895,57857,57858,57860],{},[898,57859,2783],{},[898,57861,4003],{},[902,57863,4103],{"encoding":904}," klesne na ",[883,57866,57868],{"className":57867},[886],[888,57869,57870],{"xmlns":890},[892,57871,57872,57880],{},[895,57873,57874,57876,57878],{},[2138,57875,2140],{},[2297,57877,2995],{},[2138,57879,57825],{},[902,57881,57882],{"encoding":904},"2\\,331",[198,57884,57886],{"id":57885},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,57888,57889,57890,10399,57913,31585],{},"Obecně pro lineární poptávku ",[883,57891,57893],{"className":57892},[886],[888,57894,57895],{"xmlns":890},[892,57896,57897,57911],{},[895,57898,57899,57901,57903,57905,57907,57909],{},[898,57900,3946],{},[2005,57902,2007],{},[898,57904,207],{},[898,57906,2797],{},[2005,57908,2104],{},[898,57910,2107],{},[902,57912,37065],{"encoding":904},[883,57914,57916],{"className":57915},[886],[888,57917,57918],{"xmlns":890},[892,57919,57920,57942],{},[895,57921,57922,57924,57926,57928,57930,57936,57938,57940],{},[898,57923,2783],{},[898,57925,4003],{},[2005,57927,2007],{},[898,57929,207],{},[2133,57931,57932,57934],{},[898,57933,2797],{},[2138,57935,2140],{},[2005,57937,2104],{},[898,57939,2107],{},[898,57941,2797],{},[902,57943,57944],{"encoding":904},"TR = aQ^2 + bQ",[883,57946,57948],{"className":57947},[886],[888,57949,57950],{"xmlns":890,"display":28071},[892,57951,57952,57972],{},[895,57953,57954,57956,57958,57960,57962,57964,57966,57968,57970],{},[898,57955,2826],{},[898,57957,4003],{},[2005,57959,2007],{},[2138,57961,2140],{},[898,57963,207],{},[898,57965,2797],{},[2005,57967,2104],{},[898,57969,2107],{},[898,57971,1644],{"mathvariant":2385},[902,57973,57974],{"encoding":904},"MR = 2aQ + b.",[724,57976,57977,57978,57993,57994,58009,58010,58023,58024,10030,58027,58043,58044,58057,58058,58073,58074,58089,58090,58105,58106,2633,58119,58149,58150,58169,58170,58185],{},"Křivky ",[883,57979,57981],{"className":57980},[886],[888,57982,57983],{"xmlns":890},[892,57984,57985,57991],{},[895,57986,57987,57989],{},[898,57988,2826],{},[898,57990,4003],{},[902,57992,6640],{"encoding":904}," a poptávky (resp. ",[883,57995,57997],{"className":57996},[886],[888,57998,57999],{"xmlns":890},[892,58000,58001,58007],{},[895,58002,58003,58005],{},[898,58004,1836],{},[898,58006,4003],{},[902,58008,55450],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,58011,58013],{"className":58012},[886],[888,58014,58015],{"xmlns":890},[892,58016,58017,58021],{},[895,58018,58019],{},[898,58020,2107],{},[902,58022,2107],{"encoding":904},", přičemž ",[38,58025,58026],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,58028,58030],{"className":58029},[886],[888,58031,58032],{"xmlns":890},[892,58033,58034,58040],{},[895,58035,58036,58038],{},[2138,58037,2140],{},[898,58039,207],{},[902,58041,58042],{"encoding":904},"2a"," vs. ",[883,58045,58047],{"className":58046},[886],[888,58048,58049],{"xmlns":890},[892,58050,58051,58055],{},[895,58052,58053],{},[898,58054,207],{},[902,58056,207],{"encoding":904},", obrázek 3.2). ",[883,58059,58061],{"className":58060},[886],[888,58062,58063],{"xmlns":890},[892,58064,58065,58071],{},[895,58066,58067,58069],{},[898,58068,2826],{},[898,58070,4003],{},[902,58072,6640],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,58075,58077],{"className":58076},[886],[888,58078,58079],{"xmlns":890},[892,58080,58081,58087],{},[895,58082,58083,58085],{},[898,58084,2783],{},[898,58086,4003],{},[902,58088,4103],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,58091,58093],{"className":58092},[886],[888,58094,58095],{"xmlns":890},[892,58096,58097,58103],{},[895,58098,58099,58101],{},[898,58100,2826],{},[898,58102,4003],{},[902,58104,6640],{"encoding":904}," osu ",[883,58107,58109],{"className":58108},[886],[888,58110,58111],{"xmlns":890},[892,58112,58113,58117],{},[895,58114,58115],{},[898,58116,2797],{},[902,58118,2797],{"encoding":904},[883,58120,58122],{"className":58121},[886],[888,58123,58124],{"xmlns":890},[892,58125,58126,58146],{},[895,58127,58128,58130,58132,58134],{},[898,58129,2797],{},[2005,58131,2007],{},[2005,58133,2234],{},[2334,58135,58136],{"scriptlevel":2336,"displaystyle":2013},[2338,58137,58138,58140],{},[898,58139,2107],{},[895,58141,58142,58144],{},[2138,58143,2140],{},[898,58145,207],{},[902,58147,58148],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,58151,58153],{"className":58152},[886],[888,58154,58155],{"xmlns":890},[892,58156,58157,58167],{},[895,58158,58159,58161,58163,58165],{},[898,58160,2826],{},[898,58162,4003],{},[2005,58164,2007],{},[2138,58166,2336],{},[902,58168,7090],{"encoding":904},", a dále ",[883,58171,58173],{"className":58172},[886],[888,58174,58175],{"xmlns":890},[892,58176,58177,58183],{},[895,58178,58179,58181],{},[898,58180,2783],{},[898,58182,4003],{},[902,58184,4103],{"encoding":904}," klesá.",[724,58187,58188,58189,58195,58196,58228,58229,58257],{},"V případě ",[38,58190,58191],{},[207,58192,58194],{"className":58193,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,58197,58199],{"className":58198},[886],[888,58200,58201],{"xmlns":890},[892,58202,58203,58225],{},[895,58204,58205,58207,58209,58211,58213,58215,58217,58219],{},[898,58206,3946],{},[2005,58208,2007],{},[898,58210,1860],{},[2005,58212,2014],{"stretchy":2013},[898,58214,2797],{},[2005,58216,2020],{"stretchy":2013},[2005,58218,2007],{},[2133,58220,58221,58223],{},[898,58222,3946],{},[2005,58224,4360],{},[902,58226,58227],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,58230,58232],{"className":58231},[886],[888,58233,58234],{"xmlns":890},[892,58235,58236,58254],{},[895,58237,58238,58240,58242,58244,58246,58248],{},[898,58239,2783],{},[898,58241,4003],{},[2005,58243,2007],{},[898,58245,2797],{},[2005,58247,3185],{},[2133,58249,58250,58252],{},[898,58251,3946],{},[2005,58253,4360],{},[902,58255,58256],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,58259,58261],{"className":58260},[886],[888,58262,58263],{"xmlns":890,"display":28071},[892,58264,58265,58307],{},[895,58266,58267,58269,58271,58273,58275,58277,58279,58285,58287,58289,58303,58305],{},[898,58268,2826],{},[898,58270,4003],{},[2005,58272,2007],{},[898,58274,1836],{},[898,58276,4003],{},[2005,58278,2007],{},[2133,58280,58281,58283],{},[898,58282,3946],{},[2005,58284,4360],{},[5884,58286],{"width":15290},[2005,58288,2014],{"stretchy":2013},[895,58290,58291,58294,58300],{},[2297,58292,58293],{},"obr",[8392,58295,58296,58298],{"accent":2294},[2297,58297,207],{},[2005,58299,24982],{},[2297,58301,58302],{},"zek 3.4",[2005,58304,2020],{"stretchy":2013},[898,58306,1644],{"mathvariant":2385},[902,58308,58309],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,58311,58312],{},[614,58313,58314,58315,3894,58341,58369,58370,58383,58384,58399,58400,3726,58413,1343,58439,3726,58454,1644],{},"Obrázek 3.2: Přímky ",[883,58316,58318],{"className":58317},[886],[888,58319,58320],{"xmlns":890},[892,58321,58322,58338],{},[895,58323,58324,58326,58328,58330,58332,58334,58336],{},[898,58325,1836],{},[898,58327,4003],{},[2005,58329,2007],{},[898,58331,207],{},[898,58333,2797],{},[2005,58335,2104],{},[898,58337,2107],{},[902,58339,58340],{"encoding":904},"AR = aQ + b",[883,58342,58344],{"className":58343},[886],[888,58345,58346],{"xmlns":890},[892,58347,58348,58366],{},[895,58349,58350,58352,58354,58356,58358,58360,58362,58364],{},[898,58351,2826],{},[898,58353,4003],{},[2005,58355,2007],{},[2138,58357,2140],{},[898,58359,207],{},[898,58361,2797],{},[2005,58363,2104],{},[898,58365,2107],{},[902,58367,58368],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,58371,58373],{"className":58372},[886],[888,58374,58375],{"xmlns":890},[892,58376,58377,58381],{},[895,58378,58379],{},[898,58380,2107],{},[902,58382,2107],{"encoding":904}," se svislou osou, ",[883,58385,58387],{"className":58386},[886],[888,58388,58389],{"xmlns":890},[892,58390,58391,58397],{},[895,58392,58393,58395],{},[898,58394,2826],{},[898,58396,4003],{},[902,58398,6640],{"encoding":904}," protíná osu ",[883,58401,58403],{"className":58402},[886],[888,58404,58405],{"xmlns":890},[892,58406,58407,58411],{},[895,58408,58409],{},[898,58410,2797],{},[902,58412,2797],{"encoding":904},[883,58414,58416],{"className":58415},[886],[888,58417,58418],{"xmlns":890},[892,58419,58420,58436],{},[895,58421,58422,58424],{},[2005,58423,2234],{},[2334,58425,58426],{"scriptlevel":2336,"displaystyle":2013},[2338,58427,58428,58430],{},[898,58429,2107],{},[895,58431,58432,58434],{},[2138,58433,2140],{},[898,58435,207],{},[902,58437,58438],{"encoding":904},"-\\tfrac{b}{2a}",[883,58440,58442],{"className":58441},[886],[888,58443,58444],{"xmlns":890},[892,58445,58446,58452],{},[895,58447,58448,58450],{},[898,58449,1836],{},[898,58451,4003],{},[902,58453,55450],{"encoding":904},[883,58455,58457],{"className":58456},[886],[888,58458,58459],{"xmlns":890},[892,58460,58461,58473],{},[895,58462,58463,58465],{},[2005,58464,2234],{},[2334,58466,58467],{"scriptlevel":2336,"displaystyle":2013},[2338,58468,58469,58471],{},[898,58470,2107],{},[898,58472,207],{},[902,58474,58475],{"encoding":904},"-\\tfrac{b}{a}",[724,58477,58478],{},[614,58479,58480,58481,58512,58513,58542,58543,1644],{},"Obrázek 3.3: Parabola ",[883,58482,58484],{"className":58483},[886],[888,58485,58486],{"xmlns":890},[892,58487,58488,58510],{},[895,58489,58490,58492,58494,58496,58498,58504,58506,58508],{},[898,58491,2783],{},[898,58493,4003],{},[2005,58495,2007],{},[898,58497,207],{},[2133,58499,58500,58502],{},[898,58501,2797],{},[2138,58503,2140],{},[2005,58505,2104],{},[898,58507,2107],{},[898,58509,2797],{},[902,58511,57944],{"encoding":904}," s maximem v ",[883,58514,58516],{"className":58515},[886],[888,58517,58518],{"xmlns":890},[892,58519,58520,58540],{},[895,58521,58522,58524,58526,58528],{},[898,58523,2797],{},[2005,58525,2007],{},[2005,58527,2234],{},[2334,58529,58530],{"scriptlevel":2336,"displaystyle":2013},[2338,58531,58532,58534],{},[898,58533,2107],{},[895,58535,58536,58538],{},[2138,58537,2140],{},[898,58539,207],{},[902,58541,58148],{"encoding":904}," a nulou v ",[883,58544,58546],{"className":58545},[886],[888,58547,58548],{"xmlns":890},[892,58549,58550,58566],{},[895,58551,58552,58554,58556,58558],{},[898,58553,2797],{},[2005,58555,2007],{},[2005,58557,2234],{},[2334,58559,58560],{"scriptlevel":2336,"displaystyle":2013},[2338,58561,58562,58564],{},[898,58563,2107],{},[898,58565,207],{},[902,58567,58568],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,58570,58571],{},[614,58572,58573,58574,1644],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,58575,58577],{"className":58576},[886],[888,58578,58579],{"xmlns":890},[892,58580,58581,58601],{},[895,58582,58583,58585,58587,58589,58591,58593,58595],{},[898,58584,1836],{},[898,58586,4003],{},[2005,58588,2007],{},[898,58590,2826],{},[898,58592,4003],{},[2005,58594,2007],{},[2133,58596,58597,58599],{},[898,58598,3946],{},[2005,58600,4360],{},[902,58602,58603],{"encoding":904},"AR = MR = P^*",[115,58605,58607],{"id":58606},"náklady-firmy","Náklady firmy",[198,58609,58611],{"id":58610},"celkové-náklady","Celkové náklady",[724,58613,58614,2212,58616,10030,58631,58634,58635,58648],{},[38,58615,58611],{},[883,58617,58619],{"className":58618},[886],[888,58620,58621],{"xmlns":890},[892,58622,58623,58629],{},[895,58624,58625,58627],{},[898,58626,2783],{},[898,58628,1852],{},[902,58630,3251],{"encoding":904},[38,58632,58633],{},"total cost",") jsou veškeré náklady na realizaci ",[883,58636,58638],{"className":58637},[886],[888,58639,58640],{"xmlns":890},[892,58641,58642,58646],{},[895,58643,58644],{},[898,58645,2797],{},[902,58647,2797],{"encoding":904}," jednotek produkce:",[883,58650,58652],{"className":58651},[886],[888,58653,58654],{"xmlns":890,"display":28071},[892,58655,58656,58711],{},[20760,58657,58658],{"width":28076},[20765,58659,58660,58662,58704,58706],{},[20768,58661],{"width":28081},[20768,58663,58664],{},[895,58665,58666,58668,58670,58672,58674,58676,58678,58680,58682,58684,58686,58688,58690,58692,58694,58696,58698,58700,58702],{},[898,58667,2783],{},[898,58669,1852],{},[2005,58671,2007],{},[898,58673,2783],{},[898,58675,1852],{},[2005,58677,2014],{"stretchy":2013},[898,58679,2797],{},[2005,58681,2020],{"stretchy":2013},[2005,58683,2007],{},[898,58685,1876],{},[898,58687,1852],{},[2005,58689,2104],{},[898,58691,2783],{},[898,58693,40344],{},[898,58695,1852],{},[2005,58697,2014],{"stretchy":2013},[898,58699,2797],{},[2005,58701,2020],{"stretchy":2013},[2005,58703,2295],{"separator":2294},[20768,58705],{"width":28081},[20768,58707,58708],{},[2297,58709,58710],{},"(3.5)",[902,58712,58713],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,58715,4316,58716,58731,58732,10030,58735,12134,58738,58731,58762,10030,58765,58768],{},[883,58717,58719],{"className":58718},[886],[888,58720,58721],{"xmlns":890},[892,58722,58723,58729],{},[895,58724,58725,58727],{},[898,58726,1876],{},[898,58728,1852],{},[902,58730,55496],{"encoding":904}," jsou ",[38,58733,58734],{},"fixní náklady",[38,58736,58737],{},"fixed cost",[883,58739,58741],{"className":58740},[886],[888,58742,58743],{"xmlns":890},[892,58744,58745,58759],{},[895,58746,58747,58749,58751,58753,58755,58757],{},[898,58748,2783],{},[898,58750,40344],{},[898,58752,1852],{},[2005,58754,2014],{"stretchy":2013},[898,58756,2797],{},[2005,58758,2020],{"stretchy":2013},[902,58760,58761],{"encoding":904},"TVC(Q)",[38,58763,58764],{},"celkové variabilní náklady",[38,58766,58767],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,58770,58772],{"id":58771},"průměrné-náklady","Průměrné náklady",[724,58774,58775,2212,58777,10030,58792,58795],{},[38,58776,58772],{},[883,58778,58780],{"className":58779},[886],[888,58781,58782],{"xmlns":890},[892,58783,58784,58790],{},[895,58785,58786,58788],{},[898,58787,1836],{},[898,58789,1852],{},[902,58791,55565],{"encoding":904},[38,58793,58794],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,58797,58799],{"className":58798},[886],[888,58800,58801],{"xmlns":890,"display":28071},[892,58802,58803,58882],{},[20760,58804,58805],{"width":28076},[20765,58806,58807,58809,58875,58877],{},[20768,58808],{"width":28081},[20768,58810,58811],{},[895,58812,58813,58815,58817,58819,58821,58823,58825,58827,58829,58831,58841,58843,58853,58855,58873],{},[898,58814,1836],{},[898,58816,1852],{},[2005,58818,2007],{},[898,58820,1836],{},[898,58822,1852],{},[2005,58824,2014],{"stretchy":2013},[898,58826,2797],{},[2005,58828,2020],{"stretchy":2013},[2005,58830,2007],{},[2338,58832,58833,58839],{},[895,58834,58835,58837],{},[898,58836,2783],{},[898,58838,1852],{},[898,58840,2797],{},[2005,58842,2007],{},[2338,58844,58845,58851],{},[895,58846,58847,58849],{},[898,58848,1876],{},[898,58850,1852],{},[898,58852,2797],{},[2005,58854,2104],{},[2338,58856,58857,58871],{},[895,58858,58859,58861,58863,58865,58867,58869],{},[898,58860,2783],{},[898,58862,40344],{},[898,58864,1852],{},[2005,58866,2014],{"stretchy":2013},[898,58868,2797],{},[2005,58870,2020],{"stretchy":2013},[898,58872,2797],{},[2005,58874,2295],{"separator":2294},[20768,58876],{"width":28081},[20768,58878,58879],{},[2297,58880,58881],{},"(3.6)",[902,58883,58884],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,58886,4316,58887,58731,58911,2212,58914,10030,58931,12134,58934,58731,58966,2212,58969,10030,58986,3159],{},[883,58888,58890],{"className":58889},[886],[888,58891,58892],{"xmlns":890},[892,58893,58894,58908],{},[895,58895,58896],{},[2334,58897,58898],{"scriptlevel":2336,"displaystyle":2013},[2338,58899,58900,58906],{},[895,58901,58902,58904],{},[898,58903,1876],{},[898,58905,1852],{},[898,58907,2797],{},[902,58909,58910],{"encoding":904},"\\tfrac{FC}{Q}",[38,58912,58913],{},"průměrné fixní náklady",[883,58915,58917],{"className":58916},[886],[888,58918,58919],{"xmlns":890},[892,58920,58921,58929],{},[895,58922,58923,58925,58927],{},[898,58924,1836],{},[898,58926,1876],{},[898,58928,1852],{},[902,58930,55532],{"encoding":904},[38,58932,58933],{},"average fixed cost",[883,58935,58937],{"className":58936},[886],[888,58938,58939],{"xmlns":890},[892,58940,58941,58963],{},[895,58942,58943],{},[2334,58944,58945],{"scriptlevel":2336,"displaystyle":2013},[2338,58946,58947,58961],{},[895,58948,58949,58951,58953,58955,58957,58959],{},[898,58950,2783],{},[898,58952,40344],{},[898,58954,1852],{},[2005,58956,2014],{"stretchy":2013},[898,58958,2797],{},[2005,58960,2020],{"stretchy":2013},[898,58962,2797],{},[902,58964,58965],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,58967,58968],{},"průměrné variabilní náklady",[883,58970,58972],{"className":58971},[886],[888,58973,58974],{"xmlns":890},[892,58975,58976,58984],{},[895,58977,58978,58980,58982],{},[898,58979,1836],{},[898,58981,40344],{},[898,58983,1852],{},[902,58985,55316],{"encoding":904},[38,58987,58988],{},"average variable cost",[883,58990,58992],{"className":58991},[886],[888,58993,58994],{"xmlns":890,"display":28071},[892,58995,58996,59055],{},[20760,58997,58998],{"width":28076},[20765,58999,59000,59002,59048,59050],{},[20768,59001],{"width":28081},[20768,59003,59004],{},[895,59005,59006,59008,59010,59012,59014,59016,59018,59020,59022,59024,59026,59028,59046],{},[898,59007,1836],{},[898,59009,40344],{},[898,59011,1852],{},[2005,59013,2007],{},[898,59015,1836],{},[898,59017,40344],{},[898,59019,1852],{},[2005,59021,2014],{"stretchy":2013},[898,59023,2797],{},[2005,59025,2020],{"stretchy":2013},[2005,59027,2007],{},[2338,59029,59030,59044],{},[895,59031,59032,59034,59036,59038,59040,59042],{},[898,59033,2783],{},[898,59035,40344],{},[898,59037,1852],{},[2005,59039,2014],{"stretchy":2013},[898,59041,2797],{},[2005,59043,2020],{"stretchy":2013},[898,59045,2797],{},[898,59047,1644],{"mathvariant":2385},[20768,59049],{"width":28081},[20768,59051,59052],{},[2297,59053,59054],{},"(3.7)",[902,59056,59057],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[37353,59059,59061],{"id":59060},"příklad-34","Příklad 3.4",[724,59063,59064,57527,59066,3894,59091,56030,59115,3894,59130,59145,59146,1644],{},[38,59065,55992],{},[883,59067,59069],{"className":59068},[886],[888,59070,59071],{"xmlns":890},[892,59072,59073,59088],{},[895,59074,59075,59077,59079,59081,59083,59085],{},[898,59076,1876],{},[898,59078,1852],{},[2005,59080,2007],{},[2138,59082,2287],{},[2297,59084,2995],{},[2138,59086,59087],{},"000",[902,59089,59090],{"encoding":904},"FC = 1\\,000",[883,59092,59094],{"className":59093},[886],[888,59095,59096],{"xmlns":890},[892,59097,59098,59112],{},[895,59099,59100,59102,59104,59106,59108,59110],{},[898,59101,2783],{},[898,59103,40344],{},[898,59105,1852],{},[2005,59107,2007],{},[2138,59109,2360],{},[898,59111,2797],{},[902,59113,59114],{"encoding":904},"TVC = 4Q",[883,59116,59118],{"className":59117},[886],[888,59119,59120],{"xmlns":890},[892,59121,59122,59128],{},[895,59123,59124,59126],{},[898,59125,2783],{},[898,59127,1852],{},[902,59129,3251],{"encoding":904},[883,59131,59133],{"className":59132},[886],[888,59134,59135],{"xmlns":890},[892,59136,59137,59143],{},[895,59138,59139,59141],{},[898,59140,1836],{},[898,59142,1852],{},[902,59144,55565],{"encoding":904}," a jejich chování s rostoucím ",[883,59147,59149],{"className":59148},[886],[888,59150,59151],{"xmlns":890},[892,59152,59153,59157],{},[895,59154,59155],{},[898,59156,2797],{},[902,59158,2797],{"encoding":904},[724,59160,59161,2212,59163,3894,59193,59229,59230,4364,59243,59258,59259,2713],{},[38,59162,22776],{},[883,59164,59166],{"className":59165},[886],[888,59167,59168],{"xmlns":890},[892,59169,59170,59190],{},[895,59171,59172,59174,59176,59178,59180,59182,59184,59186,59188],{},[898,59173,2783],{},[898,59175,1852],{},[2005,59177,2007],{},[2138,59179,2287],{},[2297,59181,2995],{},[2138,59183,59087],{},[2005,59185,2104],{},[2138,59187,2360],{},[898,59189,2797],{},[902,59191,59192],{"encoding":904},"TC = 1\\,000 + 4Q",[883,59194,59196],{"className":59195},[886],[888,59197,59198],{"xmlns":890},[892,59199,59200,59226],{},[895,59201,59202,59204,59206,59208,59222,59224],{},[898,59203,1836],{},[898,59205,1852],{},[2005,59207,2007],{},[2334,59209,59210],{"scriptlevel":2336,"displaystyle":2013},[2338,59211,59212,59220],{},[895,59213,59214,59216,59218],{},[2138,59215,2287],{},[2297,59217,2995],{},[2138,59219,59087],{},[898,59221,2797],{},[2005,59223,2104],{},[2138,59225,2360],{},[902,59227,59228],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,59231,59233],{"className":59232},[886],[888,59234,59235],{"xmlns":890},[892,59236,59237,59241],{},[895,59238,59239],{},[898,59240,2797],{},[902,59242,2797],{"encoding":904},[883,59244,59246],{"className":59245},[886],[888,59247,59248],{"xmlns":890},[892,59249,59250,59256],{},[895,59251,59252,59254],{},[898,59253,1836],{},[898,59255,1852],{},[902,59257,55565],{"encoding":904}," blíží ",[883,59260,59262],{"className":59261},[886],[888,59263,59264],{"xmlns":890},[892,59265,59266,59270],{},[895,59267,59268],{},[2138,59269,2360],{},[902,59271,2360],{"encoding":904},[883,59273,59275],{"className":59274},[886],[888,59276,59277],{"xmlns":890,"display":28071},[892,59278,59279,59325],{},[895,59280,59281,59298,59320,59322],{},[39901,59282,59283,59290],{},[895,59284,59285,59288],{},[898,59286,59287],{},"lim",[2005,59289,56205],{},[895,59291,59292,59294,59296],{},[898,59293,2797],{},[2005,59295,3131],{},[898,59297,6303],{"mathvariant":2385},[895,59299,59300,59302,59314,59316,59318],{},[2005,59301,2014],{"fence":2294},[2338,59303,59304,59312],{},[895,59305,59306,59308,59310],{},[2138,59307,2287],{},[2297,59309,2995],{},[2138,59311,59087],{},[898,59313,2797],{},[2005,59315,2104],{},[2138,59317,2360],{},[2005,59319,2020],{"fence":2294},[2005,59321,2007],{},[2138,59323,59324],{},"4.",[902,59326,59327],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,59329,59330,59368,59369,1644],{},[883,59331,59333],{"className":59332},[886],[888,59334,59335],{"xmlns":890},[892,59336,59337,59365],{},[895,59338,59339,59341,59343,59345,59347,59361,59363],{},[898,59340,1836],{},[898,59342,1876],{},[898,59344,1852],{},[2005,59346,2007],{},[2334,59348,59349],{"scriptlevel":2336,"displaystyle":2013},[2338,59350,59351,59359],{},[895,59352,59353,59355,59357],{},[2138,59354,2287],{},[2297,59356,2995],{},[2138,59358,59087],{},[898,59360,2797],{},[2005,59362,3131],{},[2138,59364,2336],{},[902,59366,59367],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,59370,59372],{"className":59371},[886],[888,59373,59374],{"xmlns":890},[892,59375,59376,59380],{},[895,59377,59378],{},[898,59379,2797],{},[902,59381,2797],{"encoding":904},[724,59383,59384],{},[614,59385,59386,59387,59416,59417,1644],{},"Obrázek 3.5: Přímka ",[883,59388,59390],{"className":59389},[886],[888,59391,59392],{"xmlns":890},[892,59393,59394,59414],{},[895,59395,59396,59398,59400,59402,59404,59406,59408,59410,59412],{},[898,59397,2783],{},[898,59399,1852],{},[2005,59401,2007],{},[2138,59403,2287],{},[2297,59405,2995],{},[2138,59407,59087],{},[2005,59409,2104],{},[2138,59411,2360],{},[898,59413,2797],{},[902,59415,59192],{"encoding":904}," protínající svislou osu ve výši ",[883,59418,59420],{"className":59419},[886],[888,59421,59422],{"xmlns":890},[892,59423,59424,59438],{},[895,59425,59426,59428,59430,59432,59434,59436],{},[898,59427,1876],{},[898,59429,1852],{},[2005,59431,2007],{},[2138,59433,2287],{},[2297,59435,2995],{},[2138,59437,59087],{},[902,59439,59090],{"encoding":904},[724,59441,59442],{},[614,59443,59444,59445,59480,59481,1644],{},"Obrázek 3.6: Hyperbola ",[883,59446,59448],{"className":59447},[886],[888,59449,59450],{"xmlns":890},[892,59451,59452,59478],{},[895,59453,59454,59456,59458,59460,59474,59476],{},[898,59455,1836],{},[898,59457,1852],{},[2005,59459,2007],{},[2334,59461,59462],{"scriptlevel":2336,"displaystyle":2013},[2338,59463,59464,59472],{},[895,59465,59466,59468,59470],{},[2138,59467,2287],{},[2297,59469,2995],{},[2138,59471,59087],{},[898,59473,2797],{},[2005,59475,2104],{},[2138,59477,2360],{},[902,59479,59228],{"encoding":904}," s vodorovnou asymptotou ",[883,59482,59484],{"className":59483},[886],[888,59485,59486],{"xmlns":890},[892,59487,59488,59498],{},[895,59489,59490,59492,59494,59496],{},[898,59491,1836],{},[898,59493,1852],{},[2005,59495,2007],{},[2138,59497,2360],{},[902,59499,59500],{"encoding":904},"AC = 4",[724,59502,59503],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,59505,59507],{"className":59506},[886],[888,59508,59509],{"xmlns":890,"display":28071},[892,59510,59511,59537],{},[895,59512,59513,59515,59517,59519,59521,59523,59525,59527,59529,59531,59533,59535],{},[898,59514,2783],{},[898,59516,40344],{},[898,59518,1852],{},[2005,59520,2007],{},[898,59522,2797],{},[2005,59524,3185],{},[898,59526,40344],{},[898,59528,1852],{},[2005,59530,2014],{"stretchy":2013},[898,59532,2797],{},[2005,59534,2020],{"stretchy":2013},[2005,59536,2295],{"separator":2294},[902,59538,59539],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,59541,4316,59542,58731,59570,59573,59574,59604],{},[883,59543,59545],{"className":59544},[886],[888,59546,59547],{"xmlns":890},[892,59548,59549,59567],{},[895,59550,59551,59553,59555,59557,59559,59561,59563,59565],{},[898,59552,40344],{},[898,59554,1852],{},[2005,59556,2007],{},[898,59558,40344],{},[898,59560,1852],{},[2005,59562,2014],{"stretchy":2013},[898,59564,2797],{},[2005,59566,2020],{"stretchy":2013},[902,59568,59569],{"encoding":904},"VC = VC(Q)",[38,59571,59572],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,59575,59577],{"className":59576},[886],[888,59578,59579],{"xmlns":890},[892,59580,59581,59601],{},[895,59582,59583,59585,59587,59589,59591,59593,59595,59597,59599],{},[898,59584,2783],{},[898,59586,40344],{},[898,59588,1852],{},[2005,59590,2014],{"stretchy":2013},[898,59592,2797],{},[2005,59594,2020],{"stretchy":2013},[2005,59596,2007],{},[898,59598,207],{},[898,59600,2797],{},[902,59602,59603],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,59606,59608],{"className":59607},[886],[888,59609,59610],{"xmlns":890,"display":28071},[892,59611,59612,59632],{},[895,59613,59614,59616,59618,59620,59622,59624,59626,59628,59630],{},[898,59615,2783],{},[898,59617,1852],{},[2005,59619,2007],{},[898,59621,1876],{},[898,59623,1852],{},[2005,59625,2104],{},[898,59627,207],{},[898,59629,2797],{},[898,59631,1644],{"mathvariant":2385},[902,59633,59634],{"encoding":904},"TC = FC + aQ.",[724,59636,59637,59638,59653,59654,59669,59670,59693,59694,59728,59729,59480,59742,59755,59756,3894,59804,59848,59849,1644],{},"Křivkou ",[883,59639,59641],{"className":59640},[886],[888,59642,59643],{"xmlns":890},[892,59644,59645,59651],{},[895,59646,59647,59649],{},[898,59648,2783],{},[898,59650,1852],{},[902,59652,3251],{"encoding":904}," je přímka se svislým průsečíkem ",[883,59655,59657],{"className":59656},[886],[888,59658,59659],{"xmlns":890},[892,59660,59661,59667],{},[895,59662,59663,59665],{},[898,59664,1876],{},[898,59666,1852],{},[902,59668,55496],{"encoding":904}," a sklonem ",[883,59671,59673],{"className":59672},[886],[888,59674,59675],{"xmlns":890},[892,59676,59677,59690],{},[895,59678,59679,59682,59684,59686,59688],{},[898,59680,59681],{},"tan",[2005,59683,56205],{},[898,59685,18868],{},[2005,59687,2007],{},[898,59689,207],{},[902,59691,59692],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,59695,59697],{"className":59696},[886],[888,59698,59699],{"xmlns":890},[892,59700,59701,59725],{},[895,59702,59703,59705,59707,59709,59721,59723],{},[898,59704,1836],{},[898,59706,1852],{},[2005,59708,2007],{},[2334,59710,59711],{"scriptlevel":2336,"displaystyle":2013},[2338,59712,59713,59719],{},[895,59714,59715,59717],{},[898,59716,1876],{},[898,59718,1852],{},[898,59720,2797],{},[2005,59722,2104],{},[898,59724,207],{},[902,59726,59727],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,59730,59732],{"className":59731},[886],[888,59733,59734],{"xmlns":890},[892,59735,59736,59740],{},[895,59737,59738],{},[898,59739,9801],{},[902,59741,9801],{"encoding":904},[883,59743,59745],{"className":59744},[886],[888,59746,59747],{"xmlns":890},[892,59748,59749,59753],{},[895,59750,59751],{},[898,59752,207],{},[902,59754,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,59757,59759],{"className":59758},[886],[888,59760,59761],{"xmlns":890},[892,59762,59763,59801],{},[895,59764,59765,59785,59797,59799],{},[2281,59766,59767,59773],{},[895,59768,59769,59771],{},[898,59770,59287],{},[2005,59772,56205],{},[895,59774,59775,59777,59779],{},[898,59776,2797],{},[2005,59778,3131],{},[2133,59780,59781,59783],{},[2138,59782,2336],{},[2005,59784,2104],{},[2334,59786,59787],{"scriptlevel":2336,"displaystyle":2013},[2338,59788,59789,59795],{},[895,59790,59791,59793],{},[898,59792,1876],{},[898,59794,1852],{},[898,59796,2797],{},[2005,59798,2007],{},[898,59800,6303],{"mathvariant":2385},[902,59802,59803],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,59805,59807],{"className":59806},[886],[888,59808,59809],{"xmlns":890},[892,59810,59811,59845],{},[895,59812,59813,59829,59841,59843],{},[2281,59814,59815,59821],{},[895,59816,59817,59819],{},[898,59818,59287],{},[2005,59820,56205],{},[895,59822,59823,59825,59827],{},[898,59824,2797],{},[2005,59826,3131],{},[898,59828,6303],{"mathvariant":2385},[2334,59830,59831],{"scriptlevel":2336,"displaystyle":2013},[2338,59832,59833,59839],{},[895,59834,59835,59837],{},[898,59836,1876],{},[898,59838,1852],{},[898,59840,2797],{},[2005,59842,2007],{},[2138,59844,2336],{},[902,59846,59847],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,59850,59852],{"className":59851},[886],[888,59853,59854],{"xmlns":890},[892,59855,59856,59862],{},[895,59857,59858,59860],{},[898,59859,1836],{},[898,59861,1852],{},[902,59863,55565],{"encoding":904},[724,59865,59866],{},[614,59867,59868,59869,59884,59885,59900,59901,1644],{},"Obrázek 3.7: Přímka ",[883,59870,59872],{"className":59871},[886],[888,59873,59874],{"xmlns":890},[892,59875,59876,59882],{},[895,59877,59878,59880],{},[898,59879,2783],{},[898,59881,1852],{},[902,59883,3251],{"encoding":904}," s osovým průsečíkem ve výši ",[883,59886,59888],{"className":59887},[886],[888,59889,59890],{"xmlns":890},[892,59891,59892,59898],{},[895,59893,59894,59896],{},[898,59895,1876],{},[898,59897,1852],{},[902,59899,55496],{"encoding":904}," a se sklonem ",[883,59902,59904],{"className":59903},[886],[888,59905,59906],{"xmlns":890},[892,59907,59908,59920],{},[895,59909,59910,59912,59914,59916,59918],{},[898,59911,59681],{},[2005,59913,56205],{},[898,59915,18868],{},[2005,59917,2007],{},[898,59919,207],{},[902,59921,59692],{"encoding":904},[724,59923,59924],{},[614,59925,59926,59927,59942,59943,1644],{},"Obrázek 3.8: Klesající hyperbola ",[883,59928,59930],{"className":59929},[886],[888,59931,59932],{"xmlns":890},[892,59933,59934,59940],{},[895,59935,59936,59938],{},[898,59937,1836],{},[898,59939,1852],{},[902,59941,55565],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,59944,59946],{"className":59945},[886],[888,59947,59948],{"xmlns":890},[892,59949,59950,59954],{},[895,59951,59952],{},[898,59953,207],{},[902,59955,207],{"encoding":904},[198,59957,59959],{"id":59958},"mezní-náklady","Mezní náklady",[724,59961,59962,2212,59964,10030,59979,59982,59983,59986],{},[38,59963,59959],{},[883,59965,59967],{"className":59966},[886],[888,59968,59969],{"xmlns":890},[892,59970,59971,59977],{},[895,59972,59973,59975],{},[898,59974,2826],{},[898,59976,1852],{},[902,59978,55297],{"encoding":904},[38,59980,59981],{},"marginal cost",") jsou ",[207,59984,1145],{"className":59985,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,59988,59990],{"className":59989},[886],[888,59991,59992],{"xmlns":890,"display":28071},[892,59993,59994,60063],{},[20760,59995,59996],{"width":28076},[20765,59997,59998,60000,60056,60058],{},[20768,59999],{"width":28081},[20768,60001,60002],{},[895,60003,60004,60006,60008,60010,60012,60014,60016,60018,60020,60022,60038,60040,60042,60048,60050,60052,60054],{},[898,60005,2826],{},[898,60007,1852],{},[2005,60009,2007],{},[898,60011,2826],{},[898,60013,1852],{},[2005,60015,2014],{"stretchy":2013},[898,60017,2797],{},[2005,60019,2020],{"stretchy":2013},[2005,60021,2007],{},[2338,60023,60024,60032],{},[895,60025,60026,60028,60030],{},[898,60027,2203],{"mathvariant":2385},[898,60029,2783],{},[898,60031,1852],{},[895,60033,60034,60036],{},[898,60035,2203],{"mathvariant":2385},[898,60037,2797],{},[2005,60039,2007],{},[898,60041,2783],{},[2133,60043,60044,60046],{},[898,60045,1852],{},[2005,60047,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,60049,2014],{"stretchy":2013},[898,60051,2797],{},[2005,60053,2020],{"stretchy":2013},[898,60055,1644],{"mathvariant":2385},[20768,60057],{"width":28081},[20768,60059,60060],{},[2297,60061,60062],{},"(3.8)",[902,60064,60065],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[3876,60067,60068],{},[724,60069,60070,60072,60073,60099,60100,60117,60118,1644],{},[883,60071,4164],{}," Intuice — „kolik stojí další kus\"\n",[883,60074,60076],{"className":60075},[886],[888,60077,60078],{"xmlns":890},[892,60079,60080,60096],{},[895,60081,60082,60084,60086,60088,60094],{},[898,60083,2826],{},[898,60085,1852],{},[2005,60087,2014],{"stretchy":2013},[2133,60089,60090,60092],{},[898,60091,2797],{},[2005,60093,4360],{},[2005,60095,2020],{"stretchy":2013},[902,60097,60098],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,60101,60103],{"className":60102},[886],[888,60104,60105],{"xmlns":890},[892,60106,60107,60115],{},[895,60108,60109],{},[2133,60110,60111,60113],{},[898,60112,2797],{},[2005,60114,4360],{},[902,60116,29849],{"encoding":904},". Formálně ",[883,60119,60121],{"className":60120},[886],[888,60122,60123],{"xmlns":890},[892,60124,60125,60177],{},[895,60126,60127,60129,60131,60133,60139,60141,60143,60145,60147,60149,60155,60157,60159,60161,60163,60165,60167,60169,60175],{},[898,60128,2826],{},[898,60130,1852],{},[2005,60132,2014],{"stretchy":2013},[2133,60134,60135,60137],{},[898,60136,2797],{},[2005,60138,4360],{},[2005,60140,2020],{"stretchy":2013},[2005,60142,2739],{},[898,60144,2783],{},[898,60146,1852],{},[2005,60148,2014],{"stretchy":2013},[2133,60150,60151,60153],{},[898,60152,2797],{},[2005,60154,4360],{},[2005,60156,2104],{},[2138,60158,2287],{},[2005,60160,2020],{"stretchy":2013},[2005,60162,2234],{},[898,60164,2783],{},[898,60166,1852],{},[2005,60168,2014],{"stretchy":2013},[2133,60170,60171,60173],{},[898,60172,2797],{},[2005,60174,4360],{},[2005,60176,2020],{"stretchy":2013},[902,60178,60179],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,60181,60182,60183,2713],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,60184,60186],{"className":60185},[886],[888,60187,60188],{"xmlns":890},[892,60189,60190,60198],{},[895,60191,60192,60194,60196],{},[898,60193,2897],{"mathvariant":2385},[898,60195,2783],{},[898,60197,1852],{},[902,60199,60200],{"encoding":904},"\\Delta TC",[883,60202,60204],{"className":60203},[886],[888,60205,60206],{"xmlns":890,"display":28071},[892,60207,60208,60277],{},[20760,60209,60210],{"width":28076},[20765,60211,60212,60214,60270,60272],{},[20768,60213],{"width":28081},[20768,60215,60216],{},[895,60217,60218,60220,60222,60224,60226,60228,60230,60232,60234,60236,60238,60240,60242,60244,60250,60252,60254,60256,60258,60260,60262,60264,60266,60268],{},[898,60219,2897],{"mathvariant":2385},[898,60221,2783],{},[898,60223,1852],{},[2297,60225,3993],{},[2005,60227,2739],{},[2297,60229,3993],{},[898,60231,2203],{"mathvariant":2385},[898,60233,2783],{},[898,60235,1852],{},[2005,60237,2007],{},[2005,60239,2014],{"stretchy":2013},[898,60241,2783],{},[898,60243,1852],{},[2133,60245,60246,60248],{},[2005,60247,2020],{"stretchy":2013},[2005,60249,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,60251,2995],{},[898,60253,2203],{"mathvariant":2385},[898,60255,2797],{},[2005,60257,2007],{},[898,60259,2826],{},[898,60261,1852],{},[2297,60263,2995],{},[898,60265,2203],{"mathvariant":2385},[898,60267,2797],{},[2005,60269,2295],{"separator":2294},[20768,60271],{"width":28081},[20768,60273,60274],{},[2297,60275,60276],{},"(3.9)",[902,60278,60279],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,60281,57316],{},[883,60283,60285],{"className":60284},[886],[888,60286,60287],{"xmlns":890,"display":28071},[892,60288,60289,60387],{},[895,60290,60291,60329,60331,60333,60335,60357,60359,60385],{},[895,60292,60293,60295,60301,60303,60309,60312,60318,60321],{},[2297,60294,57330],{},[8392,60296,60297,60299],{"accent":2294},[2297,60298,45737],{},[2005,60300,25063],{},[2297,60302,57339],{},[8392,60304,60305,60307],{"accent":2294},[2297,60306,2003],{},[2005,60308,24982],{},[2297,60310,60311],{},"ch n",[8392,60313,60314,60316],{"accent":2294},[2297,60315,207],{},[2005,60317,24982],{},[2297,60319,60320],{},"klad",[8392,60322,60323,60326],{"accent":2294},[2297,60324,60325],{},"u",[2005,60327,60328],{},"˚",[2297,60330,3993],{},[2005,60332,2739],{},[2297,60334,3993],{},[895,60336,60337,60339,60345,60348,60354],{},[2297,60338,57374],{},[8392,60340,60341,60343],{"accent":2294},[2297,60342,25051],{},[2005,60344,24982],{},[2297,60346,60347],{}," n",[8392,60349,60350,60352],{"accent":2294},[2297,60351,207],{},[2005,60353,24982],{},[2297,60355,60356],{},"klady",[2005,60358,57401],{},[895,60360,60361,60363,60369,60371,60377,60379],{},[2297,60362,57330],{},[8392,60364,60365,60367],{"accent":2294},[2297,60366,45737],{},[2005,60368,25063],{},[2297,60370,57414],{},[8392,60372,60373,60375],{"accent":2294},[2297,60374,9600],{},[2005,60376,25063],{},[2297,60378,57423],{},[8392,60380,60381,60383],{"accent":2294},[2297,60382,25051],{},[2005,60384,24982],{},[898,60386,1644],{"mathvariant":2385},[902,60388,60389],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[37353,60391,60393],{"id":60392},"příklad-35","Příklad 3.5",[724,60395,60396,57527,60398,56030,60434,60449,60450,60465,60466,2680,60479,2694,60492,60505,60506,2694,60519,1644],{},[38,60397,55992],{},[883,60399,60401],{"className":60400},[886],[888,60402,60403],{"xmlns":890},[892,60404,60405,60431],{},[895,60406,60407,60409,60411,60413,60415,60417,60419,60421,60423,60425],{},[898,60408,2783],{},[898,60410,1852],{},[2005,60412,2007],{},[2138,60414,8383],{},[2005,60416,2104],{},[2138,60418,2244],{},[898,60420,2797],{},[2005,60422,2104],{},[2138,60424,2140],{},[2133,60426,60427,60429],{},[898,60428,2797],{},[2138,60430,2140],{},[902,60432,60433],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,60435,60437],{"className":60436},[886],[888,60438,60439],{"xmlns":890},[892,60440,60441,60447],{},[895,60442,60443,60445],{},[898,60444,2826],{},[898,60446,1852],{},[902,60448,55297],{"encoding":904}," a odhadněte změny ",[883,60451,60453],{"className":60452},[886],[888,60454,60455],{"xmlns":890},[892,60456,60457,60463],{},[895,60458,60459,60461],{},[898,60460,2783],{},[898,60462,1852],{},[902,60464,3251],{"encoding":904}," při změnách ",[883,60467,60469],{"className":60468},[886],[888,60470,60471],{"xmlns":890},[892,60472,60473,60477],{},[895,60474,60475],{},[898,60476,2797],{},[902,60478,2797],{"encoding":904},[883,60480,60482],{"className":60481},[886],[888,60483,60484],{"xmlns":890},[892,60485,60486,60490],{},[895,60487,60488],{},[2138,60489,36249],{},[902,60491,36249],{"encoding":904},[883,60493,60495],{"className":60494},[886],[888,60496,60497],{"xmlns":890},[892,60498,60499,60503],{},[895,60500,60501],{},[2138,60502,41867],{},[902,60504,41867],{"encoding":904}," a z ",[883,60507,60509],{"className":60508},[886],[888,60510,60511],{"xmlns":890},[892,60512,60513,60517],{},[895,60514,60515],{},[2138,60516,36249],{},[902,60518,36249],{"encoding":904},[883,60520,60522],{"className":60521},[886],[888,60523,60524],{"xmlns":890},[892,60525,60526,60530],{},[895,60527,60528],{},[2138,60529,3517],{},[902,60531,3517],{"encoding":904},[724,60533,60534,2212,60536,2935,60562,1343,60589,60616,60617,60632,60633,60648,60649,60676,60677,60697,60698,20537,60719,60775,60776,2680,60789,2694,60802,8108,60815,1644],{},[38,60535,22776],{},[883,60537,60539],{"className":60538},[886],[888,60540,60541],{"xmlns":890},[892,60542,60543,60559],{},[895,60544,60545,60547,60549,60551,60553,60555,60557],{},[898,60546,2826],{},[898,60548,1852],{},[2005,60550,2007],{},[2138,60552,2244],{},[2005,60554,2104],{},[2138,60556,2360],{},[898,60558,2797],{},[902,60560,60561],{"encoding":904},"MC = 6 + 4Q",[883,60563,60565],{"className":60564},[886],[888,60566,60567],{"xmlns":890},[892,60568,60569,60586],{},[895,60570,60571,60573,60575,60577,60579,60581,60583],{},[898,60572,2826],{},[898,60574,1852],{},[2005,60576,2014],{"stretchy":2013},[2138,60578,36249],{},[2005,60580,2020],{"stretchy":2013},[2005,60582,2007],{},[2138,60584,60585],{},"66",[902,60587,60588],{"encoding":904},"MC(15) = 66",[883,60590,60592],{"className":60591},[886],[888,60593,60594],{"xmlns":890},[892,60595,60596,60613],{},[895,60597,60598,60600,60602,60604,60606,60608,60610],{},[898,60599,2826],{},[898,60601,1852],{},[2005,60603,2014],{"stretchy":2013},[2138,60605,9041],{},[2005,60607,2020],{"stretchy":2013},[2005,60609,2007],{},[2138,60611,60612],{},"86",[902,60614,60615],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,60618,60620],{"className":60619},[886],[888,60621,60622],{"xmlns":890},[892,60623,60624,60630],{},[895,60625,60626,60628],{},[898,60627,2783],{},[898,60629,1852],{},[902,60631,3251],{"encoding":904}," zvyšuje (",[883,60634,60636],{"className":60635},[886],[888,60637,60638],{"xmlns":890},[892,60639,60640,60646],{},[895,60641,60642,60644],{},[898,60643,2826],{},[898,60645,1852],{},[902,60647,55297],{"encoding":904}," je rostoucí). Z ",[883,60650,60652],{"className":60651},[886],[888,60653,60654],{"xmlns":890},[892,60655,60656,60673],{},[895,60657,60658,60660,60662,60664,60666,60668,60670],{},[898,60659,2783],{},[898,60661,1852],{},[2005,60663,2014],{"stretchy":2013},[2138,60665,36249],{},[2005,60667,2020],{"stretchy":2013},[2005,60669,2007],{},[2138,60671,60672],{},"740",[902,60674,60675],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,60678,60680],{"className":60679},[886],[888,60681,60682],{"xmlns":890},[892,60683,60684,60694],{},[895,60685,60686,60688,60690,60692],{},[898,60687,2203],{"mathvariant":2385},[898,60689,2797],{},[2005,60691,2007],{},[2138,60693,2287],{},[902,60695,60696],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,60699,60701],{"className":60700},[886],[888,60702,60703],{"xmlns":890},[892,60704,60705,60716],{},[895,60706,60707,60709,60711,60713],{},[898,60708,2783],{},[898,60710,1852],{},[2005,60712,2739],{},[2138,60714,60715],{},"806",[902,60717,60718],{"encoding":904},"TC \\approx 806",[883,60720,60722],{"className":60721},[886],[888,60723,60724],{"xmlns":890},[892,60725,60726,60772],{},[895,60727,60728,60730,60732,60734,60736,60738,60740,60742,60744,60746,60748,60750,60752,60754,60756,60758,60760,60763,60765,60767,60769],{},[898,60729,2897],{"mathvariant":2385},[898,60731,2783],{},[898,60733,1852],{},[2005,60735,2007],{},[898,60737,2783],{},[898,60739,1852],{},[2005,60741,2014],{"stretchy":2013},[2138,60743,41867],{},[2005,60745,2020],{"stretchy":2013},[2005,60747,2234],{},[898,60749,2783],{},[898,60751,1852],{},[2005,60753,2014],{"stretchy":2013},[2138,60755,36249],{},[2005,60757,2020],{"stretchy":2013},[2005,60759,2007],{},[2138,60761,60762],{},"808",[2005,60764,2234],{},[2138,60766,60672],{},[2005,60768,2007],{},[2138,60770,60771],{},"68",[902,60773,60774],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,60777,60779],{"className":60778},[886],[888,60780,60781],{"xmlns":890},[892,60782,60783,60787],{},[895,60784,60785],{},[898,60786,2797],{},[902,60788,2797],{"encoding":904},[883,60790,60792],{"className":60791},[886],[888,60793,60794],{"xmlns":890},[892,60795,60796,60800],{},[895,60797,60798],{},[2138,60799,36249],{},[902,60801,36249],{"encoding":904},[883,60803,60805],{"className":60804},[886],[888,60806,60807],{"xmlns":890},[892,60808,60809,60813],{},[895,60810,60811],{},[2138,60812,3517],{},[902,60814,3517],{"encoding":904},[883,60816,60818],{"className":60817},[886],[888,60819,60820],{"xmlns":890},[892,60821,60822,60851],{},[895,60823,60824,60826,60828,60830,60832,60834,60836,60838,60840,60842,60844,60846,60848],{},[898,60825,2897],{"mathvariant":2385},[898,60827,2783],{},[898,60829,1852],{},[2005,60831,2739],{},[2138,60833,60585],{},[2005,60835,3185],{},[2005,60837,2014],{"stretchy":2013},[2005,60839,2234],{},[2138,60841,2182],{},[2005,60843,2020],{"stretchy":2013},[2005,60845,2007],{},[2005,60847,2234],{},[2138,60849,60850],{},"198",[902,60852,60853],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,60855,60857],{"id":60856},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,60859,60860],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[37353,60862,60864],{"id":60863},"příklad-36","Příklad 3.6",[724,60866,60867,57527,60869,60913],{},[38,60868,55992],{},[883,60870,60872],{"className":60871},[886],[888,60873,60874],{"xmlns":890},[892,60875,60876,60910],{},[895,60877,60878,60880,60882,60884,60886,60888,60890,60892,60894,60896,60902,60904],{},[898,60879,2783],{},[898,60881,1852],{},[2005,60883,2007],{},[2138,60885,3098],{},[2005,60887,2104],{},[2138,60889,5010],{},[898,60891,2797],{},[2005,60893,2234],{},[2138,60895,2237],{},[2133,60897,60898,60900],{},[898,60899,2797],{},[2138,60901,2140],{},[2005,60903,2104],{},[2133,60905,60906,60908],{},[898,60907,2797],{},[2138,60909,2182],{},[902,60911,60912],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,60915,60916],{},[38,60917,22776],{},[883,60919,60921],{"className":60920},[886],[888,60922,60923],{"xmlns":890,"display":28071},[892,60924,60925,61169],{},[20760,60926,60927,60953,61001,61035,61077,61127],{"rowspacing":20762,"columnalign":20763,"columnspacing":2386},[20765,60928,60929,60939],{},[20768,60930,60931],{},[2334,60932,60933],{"scriptlevel":2336,"displaystyle":2294},[895,60934,60935,60937],{},[898,60936,1876],{},[898,60938,1852],{},[20768,60940,60941],{},[2334,60942,60943],{"scriptlevel":2336,"displaystyle":2294},[895,60944,60945,60947,60949,60951],{},[895,60946],{},[2005,60948,2007],{},[2138,60950,3098],{},[2005,60952,2295],{"separator":2294},[20765,60954,60955,60967],{},[20768,60956,60957],{},[2334,60958,60959],{"scriptlevel":2336,"displaystyle":2294},[895,60960,60961,60963,60965],{},[898,60962,2783],{},[898,60964,40344],{},[898,60966,1852],{},[20768,60968,60969],{},[2334,60970,60971],{"scriptlevel":2336,"displaystyle":2294},[895,60972,60973,60975,60977,60979,60981,60983,60985,60991,60993,60999],{},[895,60974],{},[2005,60976,2007],{},[2138,60978,5010],{},[898,60980,2797],{},[2005,60982,2234],{},[2138,60984,2237],{},[2133,60986,60987,60989],{},[898,60988,2797],{},[2138,60990,2140],{},[2005,60992,2104],{},[2133,60994,60995,60997],{},[898,60996,2797],{},[2138,60998,2182],{},[2005,61000,2295],{"separator":2294},[20765,61002,61003,61015],{},[20768,61004,61005],{},[2334,61006,61007],{"scriptlevel":2336,"displaystyle":2294},[895,61008,61009,61011,61013],{},[898,61010,1836],{},[898,61012,1876],{},[898,61014,1852],{},[20768,61016,61017],{},[2334,61018,61019],{"scriptlevel":2336,"displaystyle":2294},[895,61020,61021,61023,61025,61033],{},[895,61022],{},[2005,61024,2007],{},[2334,61026,61027],{"scriptlevel":2336,"displaystyle":2013},[2338,61028,61029,61031],{},[2138,61030,3098],{},[898,61032,2797],{},[2005,61034,2295],{"separator":2294},[20765,61036,61037,61049],{},[20768,61038,61039],{},[2334,61040,61041],{"scriptlevel":2336,"displaystyle":2294},[895,61042,61043,61045,61047],{},[898,61044,1836],{},[898,61046,40344],{},[898,61048,1852],{},[20768,61050,61051],{},[2334,61052,61053],{"scriptlevel":2336,"displaystyle":2294},[895,61054,61055,61057,61059,61061,61063,61065,61067,61069,61075],{},[895,61056],{},[2005,61058,2007],{},[2138,61060,5010],{},[2005,61062,2234],{},[2138,61064,2237],{},[898,61066,2797],{},[2005,61068,2104],{},[2133,61070,61071,61073],{},[898,61072,2797],{},[2138,61074,2140],{},[2005,61076,2295],{"separator":2294},[20765,61078,61079,61089],{},[20768,61080,61081],{},[2334,61082,61083],{"scriptlevel":2336,"displaystyle":2294},[895,61084,61085,61087],{},[898,61086,1836],{},[898,61088,1852],{},[20768,61090,61091],{},[2334,61092,61093],{"scriptlevel":2336,"displaystyle":2294},[895,61094,61095,61097,61099,61107,61109,61111,61113,61115,61117,61119,61125],{},[895,61096],{},[2005,61098,2007],{},[2334,61100,61101],{"scriptlevel":2336,"displaystyle":2013},[2338,61102,61103,61105],{},[2138,61104,3098],{},[898,61106,2797],{},[2005,61108,2104],{},[2138,61110,5010],{},[2005,61112,2234],{},[2138,61114,2237],{},[898,61116,2797],{},[2005,61118,2104],{},[2133,61120,61121,61123],{},[898,61122,2797],{},[2138,61124,2140],{},[2005,61126,2295],{"separator":2294},[20765,61128,61129,61139],{},[20768,61130,61131],{},[2334,61132,61133],{"scriptlevel":2336,"displaystyle":2294},[895,61134,61135,61137],{},[898,61136,2826],{},[898,61138,1852],{},[20768,61140,61141],{},[2334,61142,61143],{"scriptlevel":2336,"displaystyle":2294},[895,61144,61145,61147,61149,61151,61153,61155,61157,61159,61161,61167],{},[895,61146],{},[2005,61148,2007],{},[2138,61150,5010],{},[2005,61152,2234],{},[2138,61154,2871],{},[898,61156,2797],{},[2005,61158,2104],{},[2138,61160,2182],{},[2133,61162,61163,61165],{},[898,61164,2797],{},[2138,61166,2140],{},[898,61168,1644],{"mathvariant":2385},[902,61170,61171],{"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}",[724,61173,61174,61175,15798,61190,15798,61205,61220,61221,61236,61237,1343,61255,61236,61272,1343,61290,61236,61305,61323],{},"Význačné body ",[883,61176,61178],{"className":61177},[886],[888,61179,61180],{"xmlns":890},[892,61181,61182,61187],{},[895,61183,61184],{},[2138,61185,61186],{},"1,67",[902,61188,61189],{"encoding":904},"1{,}67",[883,61191,61193],{"className":61192},[886],[888,61194,61195],{"xmlns":890},[892,61196,61197,61202],{},[895,61198,61199],{},[2138,61200,61201],{},"2,50",[902,61203,61204],{"encoding":904},"2{,}50",[883,61206,61208],{"className":61207},[886],[888,61209,61210],{"xmlns":890},[892,61211,61212,61217],{},[895,61213,61214],{},[2138,61215,61216],{},"4,73",[902,61218,61219],{"encoding":904},"4{,}73"," odpovídají: ",[883,61222,61224],{"className":61223},[886],[888,61225,61226],{"xmlns":890},[892,61227,61228,61234],{},[895,61229,61230,61232],{},[898,61231,2826],{},[898,61233,1852],{},[902,61235,55297],{"encoding":904}," minimum v ",[883,61238,61240],{"className":61239},[886],[888,61241,61242],{"xmlns":890},[892,61243,61244,61252],{},[895,61245,61246,61248,61250],{},[898,61247,2797],{},[2005,61249,5906],{},[2138,61251,61186],{},[902,61253,61254],{"encoding":904},"Q \\doteq 1{,}67",[883,61256,61258],{"className":61257},[886],[888,61259,61260],{"xmlns":890},[892,61261,61262,61270],{},[895,61263,61264,61266,61268],{},[898,61265,1836],{},[898,61267,40344],{},[898,61269,1852],{},[902,61271,55316],{"encoding":904},[883,61273,61275],{"className":61274},[886],[888,61276,61277],{"xmlns":890},[892,61278,61279,61287],{},[895,61280,61281,61283,61285],{},[898,61282,2797],{},[2005,61284,2007],{},[2138,61286,61201],{},[902,61288,61289],{"encoding":904},"Q = 2{,}50",[883,61291,61293],{"className":61292},[886],[888,61294,61295],{"xmlns":890},[892,61296,61297,61303],{},[895,61298,61299,61301],{},[898,61300,1836],{},[898,61302,1852],{},[902,61304,55565],{"encoding":904},[883,61306,61308],{"className":61307},[886],[888,61309,61310],{"xmlns":890},[892,61311,61312,61320],{},[895,61313,61314,61316,61318],{},[898,61315,2797],{},[2005,61317,5906],{},[2138,61319,61216],{},[902,61321,61322],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,61325,61326],{},[2568,61327],{"alt":61328,"className":61329,"src":61330},"imek-ac-avc-mc",[210,2572],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,61332,61333],{},[614,61334,61335,61336,3894,61351,61368,61369,15798,61388,61403],{},"Obrázek 3.9: Kubické křivky ",[883,61337,61339],{"className":61338},[886],[888,61340,61341],{"xmlns":890},[892,61342,61343,61349],{},[895,61344,61345,61347],{},[898,61346,2783],{},[898,61348,1852],{},[902,61350,3251],{"encoding":904},[883,61352,61354],{"className":61353},[886],[888,61355,61356],{"xmlns":890},[892,61357,61358,61366],{},[895,61359,61360,61362,61364],{},[898,61361,2783],{},[898,61363,40344],{},[898,61365,1852],{},[902,61367,55514],{"encoding":904}," rostoucí od bodu ",[883,61370,61372],{"className":61371},[886],[888,61373,61374],{"xmlns":890},[892,61375,61376,61386],{},[895,61377,61378,61380,61382,61384],{},[898,61379,1876],{},[898,61381,1852],{},[2005,61383,2007],{},[2138,61385,3098],{},[902,61387,11638],{"encoding":904},[883,61389,61391],{"className":61390},[886],[888,61392,61393],{"xmlns":890},[892,61394,61395,61401],{},[895,61396,61397,61399],{},[898,61398,1876],{},[898,61400,1852],{},[902,61402,55496],{"encoding":904}," je vodorovná přímka.",[724,61405,61406],{},[614,61407,61408,61409,1343,61424,1343,61441,29206,61456,61469,61470,2935,61487,61502,61503,6196,61520,61535,61536,26194,61549,1343,61562,1343,61575,1644],{},"Obrázek 3.10: Křivky ",[883,61410,61412],{"className":61411},[886],[888,61413,61414],{"xmlns":890},[892,61415,61416,61422],{},[895,61417,61418,61420],{},[898,61419,1836],{},[898,61421,1852],{},[902,61423,55565],{"encoding":904},[883,61425,61427],{"className":61426},[886],[888,61428,61429],{"xmlns":890},[892,61430,61431,61439],{},[895,61432,61433,61435,61437],{},[898,61434,1836],{},[898,61436,40344],{},[898,61438,1852],{},[902,61440,55316],{"encoding":904},[883,61442,61444],{"className":61443},[886],[888,61445,61446],{"xmlns":890},[892,61447,61448,61454],{},[895,61449,61450,61452],{},[898,61451,2826],{},[898,61453,1852],{},[902,61455,55297],{"encoding":904},[883,61457,61459],{"className":61458},[886],[888,61460,61461],{"xmlns":890},[892,61462,61463,61467],{},[895,61464,61465],{},[898,61466,900],{},[902,61468,900],{"encoding":904}," a klesající hyperbola ",[883,61471,61473],{"className":61472},[886],[888,61474,61475],{"xmlns":890},[892,61476,61477,61485],{},[895,61478,61479,61481,61483],{},[898,61480,1836],{},[898,61482,1876],{},[898,61484,1852],{},[902,61486,55532],{"encoding":904},[883,61488,61490],{"className":61489},[886],[888,61491,61492],{"xmlns":890},[892,61493,61494,61500],{},[895,61495,61496,61498],{},[898,61497,2826],{},[898,61499,1852],{},[902,61501,55297],{"encoding":904}," protíná ",[883,61504,61506],{"className":61505},[886],[888,61507,61508],{"xmlns":890},[892,61509,61510,61518],{},[895,61511,61512,61514,61516],{},[898,61513,1836],{},[898,61515,40344],{},[898,61517,1852],{},[902,61519,55316],{"encoding":904},[883,61521,61523],{"className":61522},[886],[888,61524,61525],{"xmlns":890},[892,61526,61527,61533],{},[895,61528,61529,61531],{},[898,61530,1836],{},[898,61532,1852],{},[902,61534,55565],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,61537,61539],{"className":61538},[886],[888,61540,61541],{"xmlns":890},[892,61542,61543,61547],{},[895,61544,61545],{},[898,61546,2797],{},[902,61548,2797],{"encoding":904},[883,61550,61552],{"className":61551},[886],[888,61553,61554],{"xmlns":890},[892,61555,61556,61560],{},[895,61557,61558],{},[2138,61559,61186],{},[902,61561,61189],{"encoding":904},[883,61563,61565],{"className":61564},[886],[888,61566,61567],{"xmlns":890},[892,61568,61569,61573],{},[895,61570,61571],{},[2138,61572,61201],{},[902,61574,61204],{"encoding":904},[883,61576,61578],{"className":61577},[886],[888,61579,61580],{"xmlns":890},[892,61581,61582,61586],{},[895,61583,61584],{},[2138,61585,61216],{},[902,61587,61219],{"encoding":904},[724,61589,61590],{},[38,61591,61592],{},"Standardní vlastnosti:",[120,61594,61595,61630,61694,61762,61812,61832],{},[123,61596,61597,3894,61612,61629],{},[883,61598,61600],{"className":61599},[886],[888,61601,61602],{"xmlns":890},[892,61603,61604,61610],{},[895,61605,61606,61608],{},[898,61607,2783],{},[898,61609,1852],{},[902,61611,3251],{"encoding":904},[883,61613,61615],{"className":61614},[886],[888,61616,61617],{"xmlns":890},[892,61618,61619,61627],{},[895,61620,61621,61623,61625],{},[898,61622,2783],{},[898,61624,40344],{},[898,61626,1852],{},[902,61628,55514],{"encoding":904}," jsou kubické funkce;",[123,61631,61632,1343,61647,1343,61664,61679,61680,61693],{},[883,61633,61635],{"className":61634},[886],[888,61636,61637],{"xmlns":890},[892,61638,61639,61645],{},[895,61640,61641,61643],{},[898,61642,1836],{},[898,61644,1852],{},[902,61646,55565],{"encoding":904},[883,61648,61650],{"className":61649},[886],[888,61651,61652],{"xmlns":890},[892,61653,61654,61662],{},[895,61655,61656,61658,61660],{},[898,61657,1836],{},[898,61659,40344],{},[898,61661,1852],{},[902,61663,55316],{"encoding":904},[883,61665,61667],{"className":61666},[886],[888,61668,61669],{"xmlns":890},[892,61670,61671,61677],{},[895,61672,61673,61675],{},[898,61674,2826],{},[898,61676,1852],{},[902,61678,55297],{"encoding":904}," jsou křivky tvaru ",[883,61681,61683],{"className":61682},[886],[888,61684,61685],{"xmlns":890},[892,61686,61687,61691],{},[895,61688,61689],{},[898,61690,900],{},[902,61692,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,61695,61696,61711,61712,1343,61729,61746,61747,8431],{},[883,61697,61699],{"className":61698},[886],[888,61700,61701],{"xmlns":890},[892,61702,61703,61709],{},[895,61704,61705,61707],{},[898,61706,2826],{},[898,61708,1852],{},[902,61710,55297],{"encoding":904}," nabývá minima před ",[883,61713,61715],{"className":61714},[886],[888,61716,61717],{"xmlns":890},[892,61718,61719,61727],{},[895,61720,61721,61723,61725],{},[898,61722,1836],{},[898,61724,40344],{},[898,61726,1852],{},[902,61728,55316],{"encoding":904},[883,61730,61732],{"className":61731},[886],[888,61733,61734],{"xmlns":890},[892,61735,61736,61744],{},[895,61737,61738,61740,61742],{},[898,61739,1836],{},[898,61741,40344],{},[898,61743,1852],{},[902,61745,55316],{"encoding":904}," před ",[883,61748,61750],{"className":61749},[886],[888,61751,61752],{"xmlns":890},[892,61753,61754,61760],{},[895,61755,61756,61758],{},[898,61757,1836],{},[898,61759,1852],{},[902,61761,55565],{"encoding":904},[123,61763,61764,61502,61779,3894,61794,61811],{},[883,61765,61767],{"className":61766},[886],[888,61768,61769],{"xmlns":890},[892,61770,61771,61777],{},[895,61772,61773,61775],{},[898,61774,2826],{},[898,61776,1852],{},[902,61778,55297],{"encoding":904},[883,61780,61782],{"className":61781},[886],[888,61783,61784],{"xmlns":890},[892,61785,61786,61792],{},[895,61787,61788,61790],{},[898,61789,1836],{},[898,61791,1852],{},[902,61793,55565],{"encoding":904},[883,61795,61797],{"className":61796},[886],[888,61798,61799],{"xmlns":890},[892,61800,61801,61809],{},[895,61802,61803,61805,61807],{},[898,61804,1836],{},[898,61806,40344],{},[898,61808,1852],{},[902,61810,55316],{"encoding":904}," zdola právě v jejich minimech;",[123,61813,61814,61831],{},[883,61815,61817],{"className":61816},[886],[888,61818,61819],{"xmlns":890},[892,61820,61821,61829],{},[895,61822,61823,61825,61827],{},[898,61824,1836],{},[898,61826,1876],{},[898,61828,1852],{},[902,61830,55532],{"encoding":904}," je hyperbola, stále klesající;",[123,61833,61834,61866,61867,3894,61882,61899,61900,61913,61914,3927],{},[883,61835,61837],{"className":61836},[886],[888,61838,61839],{"xmlns":890},[892,61840,61841,61863],{},[895,61842,61843,61845,61847,61849,61851,61853,61855,61857,61859,61861],{},[898,61844,1836],{},[898,61846,1852],{},[2005,61848,2007],{},[898,61850,1836],{},[898,61852,1876],{},[898,61854,1852],{},[2005,61856,2104],{},[898,61858,1836],{},[898,61860,40344],{},[898,61862,1852],{},[902,61864,61865],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,61868,61870],{"className":61869},[886],[888,61871,61872],{"xmlns":890},[892,61873,61874,61880],{},[895,61875,61876,61878],{},[898,61877,1836],{},[898,61879,1852],{},[902,61881,55565],{"encoding":904},[883,61883,61885],{"className":61884},[886],[888,61886,61887],{"xmlns":890},[892,61888,61889,61897],{},[895,61890,61891,61893,61895],{},[898,61892,1836],{},[898,61894,40344],{},[898,61896,1852],{},[902,61898,55316],{"encoding":904}," klesá s rostoucím ",[883,61901,61903],{"className":61902},[886],[888,61904,61905],{"xmlns":890},[892,61906,61907,61911],{},[895,61908,61909],{},[898,61910,2797],{},[902,61912,2797],{"encoding":904}," (protože ",[883,61915,61917],{"className":61916},[886],[888,61918,61919],{"xmlns":890},[892,61920,61921,61933],{},[895,61922,61923,61925,61927,61929,61931],{},[898,61924,1836],{},[898,61926,1876],{},[898,61928,1852],{},[2005,61930,3131],{},[2138,61932,2336],{},[902,61934,61935],{"encoding":904},"AFC \\to 0",[115,61937,61939],{"id":61938},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,61941,61942,61943,61946,61947,61962],{},"Častou optimalizační úlohou je ",[38,61944,61945],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,61948,61950],{"className":61949},[886],[888,61951,61952],{"xmlns":890},[892,61953,61954,61960],{},[895,61955,61956,61958],{},[898,61957,1836],{},[898,61959,1852],{},[902,61961,55565],{"encoding":904}," minimální.",[198,61964,16419],{"id":16418},[724,61966,61967,61968,61985],{},"Mají-li průměrné náklady minimum v bodě ",[883,61969,61971],{"className":61970},[886],[888,61972,61973],{"xmlns":890},[892,61974,61975,61983],{},[895,61976,61977],{},[2281,61978,61979,61981],{},[898,61980,2797],{},[2138,61982,2336],{},[902,61984,38313],{"encoding":904},", pak platí",[883,61987,61989],{"className":61988},[886],[888,61990,61991],{"xmlns":890,"display":28071},[892,61992,61993,62042],{},[20760,61994,61995],{"width":28076},[20765,61996,61997,61999,62035,62037],{},[20768,61998],{"width":28081},[20768,62000,62001],{},[895,62002,62003,62005,62007,62009,62015,62017,62019,62021,62023,62025,62031,62033],{},[898,62004,1836],{},[898,62006,1852],{},[2005,62008,2014],{"stretchy":2013},[2281,62010,62011,62013],{},[898,62012,2797],{},[2138,62014,2336],{},[2005,62016,2020],{"stretchy":2013},[2005,62018,2007],{},[898,62020,2826],{},[898,62022,1852],{},[2005,62024,2014],{"stretchy":2013},[2281,62026,62027,62029],{},[898,62028,2797],{},[2138,62030,2336],{},[2005,62032,2020],{"stretchy":2013},[898,62034,1644],{"mathvariant":2385},[20768,62036],{"width":28081},[20768,62038,62039],{},[2297,62040,62041],{},"(3.10)",[902,62043,62044],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[3876,62046,62047],{},[724,62048,62049,62051,62052],{},[883,62050,56449],{}," Princip\n",[38,62053,62054],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,62056,62057,62060,62061,62103],{},[38,62058,62059],{},"Odvození."," Z ",[883,62062,62064],{"className":62063},[886],[888,62065,62066],{"xmlns":890},[892,62067,62068,62100],{},[895,62069,62070,62072,62074,62076,62078,62080,62082],{},[898,62071,1836],{},[898,62073,1852],{},[2005,62075,2014],{"stretchy":2013},[898,62077,2797],{},[2005,62079,2020],{"stretchy":2013},[2005,62081,2007],{},[2334,62083,62084],{"scriptlevel":2336,"displaystyle":2013},[2338,62085,62086,62098],{},[895,62087,62088,62090,62092,62094,62096],{},[898,62089,2783],{},[898,62091,1852],{},[2005,62093,2014],{"stretchy":2013},[898,62095,2797],{},[2005,62097,2020],{"stretchy":2013},[898,62099,2797],{},[902,62101,62102],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,62105,62107],{"className":62106},[886],[888,62108,62109],{"xmlns":890,"display":28071},[892,62110,62111,62243],{},[895,62112,62113,62115,62121,62123,62125,62127,62129,62169,62171,62211,62213,62241],{},[898,62114,1836],{},[2133,62116,62117,62119],{},[898,62118,1852],{},[2005,62120,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,62122,2014],{"stretchy":2013},[898,62124,2797],{},[2005,62126,2020],{"stretchy":2013},[2005,62128,2007],{},[2338,62130,62131,62163],{},[895,62132,62133,62135,62141,62143,62145,62147,62149,62151,62153,62155,62157,62159,62161],{},[898,62134,2783],{},[2133,62136,62137,62139],{},[898,62138,1852],{},[2005,62140,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,62142,2014],{"stretchy":2013},[898,62144,2797],{},[2005,62146,2020],{"stretchy":2013},[2005,62148,3185],{},[898,62150,2797],{},[2005,62152,2234],{},[898,62154,2783],{},[898,62156,1852],{},[2005,62158,2014],{"stretchy":2013},[898,62160,2797],{},[2005,62162,2020],{"stretchy":2013},[2133,62164,62165,62167],{},[898,62166,2797],{},[2138,62168,2140],{},[2005,62170,2007],{},[2338,62172,62173,62205],{},[895,62174,62175,62177,62179,62181,62183,62185,62187,62189,62191,62193,62195,62197,62199,62201,62203],{},[898,62176,2826],{},[898,62178,1852],{},[2005,62180,2014],{"stretchy":2013},[898,62182,2797],{},[2005,62184,2020],{"stretchy":2013},[2005,62186,3185],{},[898,62188,2797],{},[2005,62190,2234],{},[898,62192,1836],{},[898,62194,1852],{},[2005,62196,2014],{"stretchy":2013},[898,62198,2797],{},[2005,62200,2020],{"stretchy":2013},[2005,62202,3185],{},[898,62204,2797],{},[2133,62206,62207,62209],{},[898,62208,2797],{},[2138,62210,2140],{},[2005,62212,2007],{},[2338,62214,62215,62239],{},[895,62216,62217,62219,62221,62223,62225,62227,62229,62231,62233,62235,62237],{},[898,62218,2826],{},[898,62220,1852],{},[2005,62222,2014],{"stretchy":2013},[898,62224,2797],{},[2005,62226,2020],{"stretchy":2013},[2005,62228,2234],{},[898,62230,1836],{},[898,62232,1852],{},[2005,62234,2014],{"stretchy":2013},[898,62236,2797],{},[2005,62238,2020],{"stretchy":2013},[898,62240,2797],{},[898,62242,1644],{"mathvariant":2385},[902,62244,62245],{"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}.",[724,62247,62248,62249,2633,62264,8108,62286,56826],{},"Nutnou podmínkou minima ",[883,62250,62252],{"className":62251},[886],[888,62253,62254],{"xmlns":890},[892,62255,62256,62262],{},[895,62257,62258,62260],{},[898,62259,1836],{},[898,62261,1852],{},[902,62263,55565],{"encoding":904},[883,62265,62267],{"className":62266},[886],[888,62268,62269],{"xmlns":890},[892,62270,62271,62283],{},[895,62272,62273,62279,62281],{},[2281,62274,62275,62277],{},[898,62276,2797],{},[2138,62278,2336],{},[2005,62280,3416],{},[2138,62282,2336],{},[902,62284,62285],{"encoding":904},"Q_0 > 0",[883,62287,62289],{"className":62288},[886],[888,62290,62291],{"xmlns":890},[892,62292,62293,62317],{},[895,62294,62295,62297,62303,62305,62311,62313,62315],{},[898,62296,1836],{},[2133,62298,62299,62301],{},[898,62300,1852],{},[2005,62302,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,62304,2014],{"stretchy":2013},[2281,62306,62307,62309],{},[898,62308,2797],{},[2138,62310,2336],{},[2005,62312,2020],{"stretchy":2013},[2005,62314,2007],{},[2138,62316,2336],{},[902,62318,62319],{"encoding":904},"AC'(Q_0) = 0",[883,62321,62323],{"className":62322},[886],[888,62324,62325],{"xmlns":890,"display":28071},[892,62326,62327,62412],{},[895,62328,62329,62369,62371,62373,62375,62378,62380,62382,62384,62386,62392,62394,62396,62398,62400,62402,62408,62410],{},[2338,62330,62331,62363],{},[895,62332,62333,62335,62337,62339,62345,62347,62349,62351,62353,62355,62361],{},[898,62334,2826],{},[898,62336,1852],{},[2005,62338,2014],{"stretchy":2013},[2281,62340,62341,62343],{},[898,62342,2797],{},[2138,62344,2336],{},[2005,62346,2020],{"stretchy":2013},[2005,62348,2234],{},[898,62350,1836],{},[898,62352,1852],{},[2005,62354,2014],{"stretchy":2013},[2281,62356,62357,62359],{},[898,62358,2797],{},[2138,62360,2336],{},[2005,62362,2020],{"stretchy":2013},[2281,62364,62365,62367],{},[898,62366,2797],{},[2138,62368,2336],{},[2005,62370,2007],{},[2138,62372,2336],{},[5884,62374],{"width":15290},[2005,62376,62377],{},"⟺",[5884,62379],{"width":15290},[898,62381,2826],{},[898,62383,1852],{},[2005,62385,2014],{"stretchy":2013},[2281,62387,62388,62390],{},[898,62389,2797],{},[2138,62391,2336],{},[2005,62393,2020],{"stretchy":2013},[2005,62395,2007],{},[898,62397,1836],{},[898,62399,1852],{},[2005,62401,2014],{"stretchy":2013},[2281,62403,62404,62406],{},[898,62405,2797],{},[2138,62407,2336],{},[2005,62409,2020],{"stretchy":2013},[898,62411,1644],{"mathvariant":2385},[902,62413,62414],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,62416,62417,2212,62420,61502,62435,62450,62451,62466,62467,8108,62484,62506,62507,62529],{},[38,62418,62419],{},"Geometrická interpretace.",[883,62421,62423],{"className":62422},[886],[888,62424,62425],{"xmlns":890},[892,62426,62427,62433],{},[895,62428,62429,62431],{},[898,62430,2826],{},[898,62432,1852],{},[902,62434,55297],{"encoding":904},[883,62436,62438],{"className":62437},[886],[888,62439,62440],{"xmlns":890},[892,62441,62442,62448],{},[895,62443,62444,62446],{},[898,62445,1836],{},[898,62447,1852],{},[902,62449,55565],{"encoding":904}," právě v bodě minima ",[883,62452,62454],{"className":62453},[886],[888,62455,62456],{"xmlns":890},[892,62457,62458,62464],{},[895,62459,62460,62462],{},[898,62461,1836],{},[898,62463,1852],{},[902,62465,55565],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,62468,62470],{"className":62469},[886],[888,62471,62472],{"xmlns":890},[892,62473,62474,62482],{},[895,62475,62476],{},[2281,62477,62478,62480],{},[898,62479,2797],{},[2138,62481,2336],{},[902,62483,38313],{"encoding":904},[883,62485,62487],{"className":62486},[886],[888,62488,62489],{"xmlns":890},[892,62490,62491,62503],{},[895,62492,62493,62495,62497,62499,62501],{},[898,62494,2826],{},[898,62496,1852],{},[2005,62498,3455],{},[898,62500,1836],{},[898,62502,1852],{},[902,62504,62505],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,62508,62510],{"className":62509},[886],[888,62511,62512],{"xmlns":890},[892,62513,62514,62526],{},[895,62515,62516,62518,62520,62522,62524],{},[898,62517,2826],{},[898,62519,1852],{},[2005,62521,3416],{},[898,62523,1836],{},[898,62525,1852],{},[902,62527,62528],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,62531,62532,62533,62575,62576,62593,62594,1644],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,62534,62536],{"className":62535},[886],[888,62537,62538],{"xmlns":890},[892,62539,62540,62572],{},[895,62541,62542,62544,62546,62548,62554,62556,62558,62560,62562,62564,62570],{},[898,62543,1836],{},[898,62545,1852],{},[2005,62547,2014],{"stretchy":2013},[2281,62549,62550,62552],{},[898,62551,2797],{},[2138,62553,2336],{},[2005,62555,2020],{"stretchy":2013},[2005,62557,2007],{},[898,62559,2826],{},[898,62561,1852],{},[2005,62563,2014],{"stretchy":2013},[2281,62565,62566,62568],{},[898,62567,2797],{},[2138,62569,2336],{},[2005,62571,2020],{"stretchy":2013},[902,62573,62574],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,62577,62579],{"className":62578},[886],[888,62580,62581],{"xmlns":890},[892,62582,62583,62591],{},[895,62584,62585],{},[2281,62586,62587,62589],{},[898,62588,2797],{},[2138,62590,2336],{},[902,62592,38313],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,62595,62597],{"className":62596},[886],[888,62598,62599],{"xmlns":890},[892,62600,62601,62625],{},[895,62602,62603,62605,62607,62609,62611,62613,62615,62617,62619,62621,62623],{},[898,62604,1836],{},[898,62606,1852],{},[2005,62608,2014],{"stretchy":2013},[898,62610,2797],{},[2005,62612,2020],{"stretchy":2013},[2005,62614,2007],{},[898,62616,2826],{},[898,62618,1852],{},[2005,62620,2014],{"stretchy":2013},[898,62622,2797],{},[2005,62624,2020],{"stretchy":2013},[902,62626,62627],{"encoding":904},"AC(Q) = MC(Q)",[3876,62629,62630],{},[724,62631,62632,62634,62635,10399,62653,62674,62675,10399,62678,62699,62700,62715,62716,58043,62731,3927],{},[883,62633,4418],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,62636,62637,62638],{},"minimum ",[883,62639,62641],{"className":62640},[886],[888,62642,62643],{"xmlns":890},[892,62644,62645,62651],{},[895,62646,62647,62649],{},[898,62648,1836],{},[898,62650,1852],{},[902,62652,55565],{"encoding":904},[883,62654,62656],{"className":62655},[886],[888,62657,62658],{"xmlns":890},[892,62659,62660,62672],{},[895,62661,62662,62664,62666,62668,62670],{},[898,62663,1836],{},[898,62665,1852],{},[2005,62667,2007],{},[898,62669,2826],{},[898,62671,1852],{},[902,62673,55228],{"encoding":904},", pro ",[38,62676,62677],{},"maximum zisku",[883,62679,62681],{"className":62680},[886],[888,62682,62683],{"xmlns":890},[892,62684,62685,62697],{},[895,62686,62687,62689,62691,62693,62695],{},[898,62688,2826],{},[898,62690,4003],{},[2005,62692,2007],{},[898,62694,2826],{},[898,62696,1852],{},[902,62698,55276],{"encoding":904},". Obě podmínky využívají ",[883,62701,62703],{"className":62702},[886],[888,62704,62705],{"xmlns":890},[892,62706,62707,62713],{},[895,62708,62709,62711],{},[898,62710,2826],{},[898,62712,1852],{},[902,62714,55297],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,62717,62719],{"className":62718},[886],[888,62720,62721],{"xmlns":890},[892,62722,62723,62729],{},[895,62724,62725,62727],{},[898,62726,1836],{},[898,62728,1852],{},[902,62730,55565],{"encoding":904},[883,62732,62734],{"className":62733},[886],[888,62735,62736],{"xmlns":890},[892,62737,62738,62744],{},[895,62739,62740,62742],{},[898,62741,2826],{},[898,62743,4003],{},[902,62745,6640],{"encoding":904},[37353,62747,62749],{"id":62748},"příklad-37","Příklad 3.7",[724,62751,62752,57527,62754,62788,62789,62802,62803,62818],{},[38,62753,55992],{},[883,62755,62757],{"className":62756},[886],[888,62758,62759],{"xmlns":890},[892,62760,62761,62785],{},[895,62762,62763,62765,62767,62769,62775,62777,62779,62781,62783],{},[898,62764,2783],{},[898,62766,1852],{},[2005,62768,2007],{},[2133,62770,62771,62773],{},[898,62772,2797],{},[2138,62774,2140],{},[2005,62776,2104],{},[2138,62778,2182],{},[898,62780,2797],{},[2005,62782,2104],{},[2138,62784,5571],{},[902,62786,62787],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,62790,62792],{"className":62791},[886],[888,62793,62794],{"xmlns":890},[892,62795,62796,62800],{},[895,62797,62798],{},[898,62799,2797],{},[902,62801,2797],{"encoding":904}," minimalizující ",[883,62804,62806],{"className":62805},[886],[888,62807,62808],{"xmlns":890},[892,62809,62810,62816],{},[895,62811,62812,62814],{},[898,62813,1836],{},[898,62815,1852],{},[902,62817,55565],{"encoding":904}," a ověřte princip (3.10).",[724,62820,62821,62823],{},[38,62822,22776],{}," Přímý výpočet:",[883,62825,62827],{"className":62826},[886],[888,62828,62829],{"xmlns":890,"display":28071},[892,62830,62831,62933],{},[895,62832,62833,62835,62837,62839,62861,62863,62865,62867,62869,62871,62877,62879,62881,62883,62885,62887,62893,62895,62897,62899,62909,62911,62931],{},[898,62834,1836],{},[898,62836,1852],{},[2005,62838,2007],{},[2338,62840,62841,62859],{},[895,62842,62843,62849,62851,62853,62855,62857],{},[2133,62844,62845,62847],{},[898,62846,2797],{},[2138,62848,2140],{},[2005,62850,2104],{},[2138,62852,2182],{},[898,62854,2797],{},[2005,62856,2104],{},[2138,62858,5571],{},[898,62860,2797],{},[2005,62862,2007],{},[898,62864,2797],{},[2005,62866,2104],{},[2138,62868,2182],{},[2005,62870,2104],{},[2338,62872,62873,62875],{},[2138,62874,5571],{},[898,62876,2797],{},[2005,62878,2295],{"separator":2294},[5884,62880],{"width":5886},[2005,62882,2014],{"stretchy":2013},[898,62884,1836],{},[898,62886,1852],{},[2133,62888,62889,62891],{},[2005,62890,2020],{"stretchy":2013},[2005,62892,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,62894,2007],{},[2138,62896,2287],{},[2005,62898,2234],{},[2338,62900,62901,62903],{},[2138,62902,5571],{},[2133,62904,62905,62907],{},[898,62906,2797],{},[2138,62908,2140],{},[2005,62910,2007],{},[2338,62912,62913,62925],{},[895,62914,62915,62921,62923],{},[2133,62916,62917,62919],{},[898,62918,2797],{},[2138,62920,2140],{},[2005,62922,2234],{},[2138,62924,5571],{},[2133,62926,62927,62929],{},[898,62928,2797],{},[2138,62930,2140],{},[898,62932,1644],{"mathvariant":2385},[902,62934,62935],{"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}.",[724,62937,62938,62978,62979,63003,63004,63054,63055,1644],{},[883,62939,62941],{"className":62940},[886],[888,62942,62943],{"xmlns":890},[892,62944,62945,62975],{},[895,62946,62947,62949,62951,62953,62959,62961,62963,62965,62971,62973],{},[2005,62948,2014],{"stretchy":2013},[898,62950,1836],{},[898,62952,1852],{},[2133,62954,62955,62957],{},[2005,62956,2020],{"stretchy":2013},[2005,62958,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,62960,2007],{},[2138,62962,2336],{},[2005,62964,3996],{},[2281,62966,62967,62969],{},[898,62968,2797],{},[2138,62970,2287],{},[2005,62972,2007],{},[2138,62974,2244],{},[902,62976,62977],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,62980,62982],{"className":62981},[886],[888,62983,62984],{"xmlns":890},[892,62985,62986,63000],{},[895,62987,62988,62994,62996,62998],{},[2281,62989,62990,62992],{},[898,62991,2797],{},[2138,62993,2140],{},[2005,62995,2007],{},[2005,62997,2234],{},[2138,62999,2244],{},[902,63001,63002],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,63005,63007],{"className":63006},[886],[888,63008,63009],{"xmlns":890},[892,63010,63011,63051],{},[895,63012,63013,63015,63017,63019,63029,63031,63033,63035,63037,63045,63047,63049],{},[2005,63014,2014],{"stretchy":2013},[898,63016,1836],{},[898,63018,1852],{},[2133,63020,63021,63023],{},[2005,63022,2020],{"stretchy":2013},[895,63024,63025,63027],{},[2005,63026,2387],{"mathvariant":2385},[2005,63028,2387],{"mathvariant":2385},[2005,63030,2014],{"stretchy":2013},[2138,63032,2244],{},[2005,63034,2020],{"stretchy":2013},[2005,63036,2007],{},[2334,63038,63039],{"scriptlevel":2336,"displaystyle":2013},[2338,63040,63041,63043],{},[2138,63042,2287],{},[2138,63044,2182],{},[2005,63046,3416],{},[2138,63048,2336],{},[2005,63050,3996],{},[902,63052,63053],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,63056,63058],{"className":63057},[886],[888,63059,63060],{"xmlns":890},[892,63061,63062,63078],{},[895,63063,63064,63066,63068,63070,63072,63074,63076],{},[898,63065,1836],{},[898,63067,1852],{},[2005,63069,2014],{"stretchy":2013},[2138,63071,2244],{},[2005,63073,2020],{"stretchy":2013},[2005,63075,2007],{},[2138,63077,36249],{},[902,63079,63080],{"encoding":904},"AC(6) = 15",[724,63082,63083,63084,63110,63111,2713],{},"Pomocí principu: ",[883,63085,63087],{"className":63086},[886],[888,63088,63089],{"xmlns":890},[892,63090,63091,63107],{},[895,63092,63093,63095,63097,63099,63101,63103,63105],{},[898,63094,2826],{},[898,63096,1852],{},[2005,63098,2007],{},[2138,63100,2140],{},[898,63102,2797],{},[2005,63104,2104],{},[2138,63106,2182],{},[902,63108,63109],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,63112,63114],{"className":63113},[886],[888,63115,63116],{"xmlns":890},[892,63117,63118,63130],{},[895,63119,63120,63122,63124,63126,63128],{},[898,63121,1836],{},[898,63123,1852],{},[2005,63125,2007],{},[898,63127,2826],{},[898,63129,1852],{},[902,63131,55228],{"encoding":904},[883,63133,63135],{"className":63134},[886],[888,63136,63137],{"xmlns":890,"display":28071},[892,63138,63139,63241],{},[895,63140,63141,63163,63165,63167,63169,63171,63173,63175,63177,63179,63185,63187,63189,63191,63193,63195,63197,63199,63205,63207,63209,63211,63213,63215,63217,63223,63225,63227,63229,63231,63233,63235,63237,63239],{},[2338,63142,63143,63161],{},[895,63144,63145,63151,63153,63155,63157,63159],{},[2133,63146,63147,63149],{},[898,63148,2797],{},[2138,63150,2140],{},[2005,63152,2104],{},[2138,63154,2182],{},[898,63156,2797],{},[2005,63158,2104],{},[2138,63160,5571],{},[898,63162,2797],{},[2005,63164,2007],{},[2138,63166,2140],{},[898,63168,2797],{},[2005,63170,2104],{},[2138,63172,2182],{},[2297,63174,3993],{},[2005,63176,3996],{},[2297,63178,3993],{},[2133,63180,63181,63183],{},[898,63182,2797],{},[2138,63184,2140],{},[2005,63186,2104],{},[2138,63188,2182],{},[898,63190,2797],{},[2005,63192,2104],{},[2138,63194,5571],{},[2005,63196,2007],{},[2138,63198,2140],{},[2133,63200,63201,63203],{},[898,63202,2797],{},[2138,63204,2140],{},[2005,63206,2104],{},[2138,63208,2182],{},[898,63210,2797],{},[2297,63212,3993],{},[2005,63214,3996],{},[2297,63216,3993],{},[2133,63218,63219,63221],{},[898,63220,2797],{},[2138,63222,2140],{},[2005,63224,2007],{},[2138,63226,5571],{},[2297,63228,3993],{},[2005,63230,3996],{},[2297,63232,3993],{},[898,63234,2797],{},[2005,63236,2007],{},[2138,63238,2244],{},[2005,63240,2295],{"separator":2294},[902,63242,63243],{"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,",[724,63245,63246,63247,63285],{},"a ",[883,63248,63250],{"className":63249},[886],[888,63251,63252],{"xmlns":890},[892,63253,63254,63282],{},[895,63255,63256,63258,63260,63262,63264,63266,63268,63270,63272,63274,63276,63278,63280],{},[898,63257,1836],{},[898,63259,1852],{},[2005,63261,2014],{"stretchy":2013},[2138,63263,2244],{},[2005,63265,2020],{"stretchy":2013},[2005,63267,2007],{},[898,63269,2826],{},[898,63271,1852],{},[2005,63273,2014],{"stretchy":2013},[2138,63275,2244],{},[2005,63277,2020],{"stretchy":2013},[2005,63279,2007],{},[2138,63281,36249],{},[902,63283,63284],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,63287,63289],{"id":63288},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,63291,63292,63293,2713],{},"Analogicky pro ",[883,63294,63296],{"className":63295},[886],[888,63297,63298],{"xmlns":890},[892,63299,63300,63308],{},[895,63301,63302,63304,63306],{},[898,63303,1836],{},[898,63305,40344],{},[898,63307,1852],{},[902,63309,55316],{"encoding":904},[883,63311,63313],{"className":63312},[886],[888,63314,63315],{"xmlns":890,"display":28071},[892,63316,63317,63368],{},[20760,63318,63319],{"width":28076},[20765,63320,63321,63323,63361,63363],{},[20768,63322],{"width":28081},[20768,63324,63325],{},[895,63326,63327,63329,63331,63333,63335,63341,63343,63345,63347,63349,63351,63357,63359],{},[898,63328,1836],{},[898,63330,40344],{},[898,63332,1852],{},[2005,63334,2014],{"stretchy":2013},[2281,63336,63337,63339],{},[898,63338,2797],{},[2138,63340,2336],{},[2005,63342,2020],{"stretchy":2013},[2005,63344,2007],{},[898,63346,2826],{},[898,63348,1852],{},[2005,63350,2014],{"stretchy":2013},[2281,63352,63353,63355],{},[898,63354,2797],{},[2138,63356,2336],{},[2005,63358,2020],{"stretchy":2013},[898,63360,1644],{"mathvariant":2385},[20768,63362],{"width":28081},[20768,63364,63365],{},[2297,63366,63367],{},"(3.11)",[902,63369,63370],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[3876,63372,63373],{},[724,63374,63375,62051,63377],{},[883,63376,56449],{},[38,63378,63379,63380,63397],{},"V bodě minima průměrných variabilních nákladů se ",[883,63381,63383],{"className":63382},[886],[888,63384,63385],{"xmlns":890},[892,63386,63387,63395],{},[895,63388,63389,63391,63393],{},[898,63390,1836],{},[898,63392,40344],{},[898,63394,1852],{},[902,63396,55316],{"encoding":904}," rovnají mezním nákladům.",[724,63399,63400,63401,63423,63424,1644],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,63402,63404],{"className":63403},[886],[888,63405,63406],{"xmlns":890},[892,63407,63408,63420],{},[895,63409,63410,63416,63418],{},[2281,63411,63412,63414],{},[898,63413,2797],{},[2138,63415,2336],{},[2005,63417,2007],{},[2138,63419,53204],{},[902,63421,63422],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,63425,63427],{"className":63426},[886],[888,63428,63429],{"xmlns":890},[892,63430,63431,63457],{},[895,63432,63433,63435,63437,63439,63441,63443,63445,63447,63449,63451,63453,63455],{},[898,63434,1836],{},[898,63436,40344],{},[898,63438,1852],{},[2005,63440,2014],{"stretchy":2013},[898,63442,2797],{},[2005,63444,2020],{"stretchy":2013},[2005,63446,2007],{},[898,63448,2826],{},[898,63450,1852],{},[2005,63452,2014],{"stretchy":2013},[898,63454,2797],{},[2005,63456,2020],{"stretchy":2013},[902,63458,63459],{"encoding":904},"AVC(Q) = MC(Q)",[115,63461,63463],{"id":63462},"zisk-a-body-zvratu","Zisk a body zvratu",[724,63465,63466,2212,63469,63485],{},[38,63467,63468],{},"Zisk",[883,63470,63472],{"className":63471},[886],[888,63473,63474],{"xmlns":890},[892,63475,63476,63482],{},[895,63477,63478,63480],{},[898,63479,3946],{},[898,63481,4003],{},[902,63483,63484],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,63487,63489],{"className":63488},[886],[888,63490,63491],{"xmlns":890,"display":28071},[892,63492,63493,63552],{},[20760,63494,63495],{"width":28076},[20765,63496,63497,63499,63545,63547],{},[20768,63498],{"width":28081},[20768,63500,63501],{},[895,63502,63503,63505,63507,63509,63511,63513,63515,63517,63519,63521,63523,63525,63527,63529,63531,63533,63535,63537,63539,63541,63543],{},[898,63504,3946],{},[898,63506,4003],{},[2005,63508,2007],{},[898,63510,3946],{},[898,63512,4003],{},[2005,63514,2014],{"stretchy":2013},[898,63516,2797],{},[2005,63518,2020],{"stretchy":2013},[2005,63520,2007],{},[898,63522,2783],{},[898,63524,4003],{},[2005,63526,2014],{"stretchy":2013},[898,63528,2797],{},[2005,63530,2020],{"stretchy":2013},[2005,63532,2234],{},[898,63534,2783],{},[898,63536,1852],{},[2005,63538,2014],{"stretchy":2013},[898,63540,2797],{},[2005,63542,2020],{"stretchy":2013},[898,63544,1644],{"mathvariant":2385},[20768,63546],{"width":28081},[20768,63548,63549],{},[2297,63550,63551],{},"(3.12)",[902,63553,63554],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,63556,63557,63558,3894,63573,43641,63588,63590,63591,63594,63595,63611,63612,63627,63628,63643,63644,1343,63657,63670,63671,1343,63689,63707,63708,10030,63711,63714,63715,1348,63737,8108,63759,63781,63782,8108,63812,63834],{},"Body rovnosti ",[883,63559,63561],{"className":63560},[886],[888,63562,63563],{"xmlns":890},[892,63564,63565,63571],{},[895,63566,63567,63569],{},[898,63568,2783],{},[898,63570,4003],{},[902,63572,4103],{"encoding":904},[883,63574,63576],{"className":63575},[886],[888,63577,63578],{"xmlns":890},[892,63579,63580,63586],{},[895,63581,63582,63584],{},[898,63583,2783],{},[898,63585,1852],{},[902,63587,3251],{"encoding":904},[38,63589,55732],{}," (též vyrovnání, ",[614,63592,63593],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,63596,63598],{"className":63597},[886],[888,63599,63600],{"xmlns":890},[892,63601,63602,63608],{},[895,63603,63604,63606],{},[898,63605,40344],{},[898,63607,1852],{},[902,63609,63610],{"encoding":904},"VC",") je ",[883,63613,63615],{"className":63614},[886],[888,63616,63617],{"xmlns":890},[892,63618,63619,63625],{},[895,63620,63621,63623],{},[898,63622,2783],{},[898,63624,4003],{},[902,63626,4103],{"encoding":904}," kvadratická a ",[883,63629,63631],{"className":63630},[886],[888,63632,63633],{"xmlns":890},[892,63634,63635,63641],{},[895,63636,63637,63639],{},[898,63638,2783],{},[898,63640,1852],{},[902,63642,3251],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,63645,63647],{"className":63646},[886],[888,63648,63649],{"xmlns":890},[892,63650,63651,63655],{},[895,63652,63653],{},[898,63654,1836],{},[902,63656,1836],{"encoding":904},[883,63658,63660],{"className":63659},[886],[888,63661,63662],{"xmlns":890},[892,63663,63664,63668],{},[895,63665,63666],{},[898,63667,1844],{},[902,63669,1844],{"encoding":904}," odpovídajících množstvím ",[883,63672,63674],{"className":63673},[886],[888,63675,63676],{"xmlns":890},[892,63677,63678,63686],{},[895,63679,63680],{},[2281,63681,63682,63684],{},[898,63683,2797],{},[898,63685,1836],{},[902,63687,63688],{"encoding":904},"Q_A",[883,63690,63692],{"className":63691},[886],[888,63693,63694],{"xmlns":890},[892,63695,63696,63704],{},[895,63697,63698],{},[2281,63699,63700,63702],{},[898,63701,2797],{},[898,63703,1844],{},[902,63705,63706],{"encoding":904},"Q_B"," — firma je na ",[38,63709,63710],{},"prahu rentability",[614,63712,63713],{},"break even","). Pro ",[883,63716,63718],{"className":63717},[886],[888,63719,63720],{"xmlns":890},[892,63721,63722,63734],{},[895,63723,63724,63726,63728],{},[898,63725,2797],{},[2005,63727,3455],{},[2281,63729,63730,63732],{},[898,63731,2797],{},[898,63733,1836],{},[902,63735,63736],{"encoding":904},"Q \u003C Q_A",[883,63738,63740],{"className":63739},[886],[888,63741,63742],{"xmlns":890},[892,63743,63744,63756],{},[895,63745,63746,63748,63750],{},[898,63747,2797],{},[2005,63749,3416],{},[2281,63751,63752,63754],{},[898,63753,2797],{},[898,63755,1844],{},[902,63757,63758],{"encoding":904},"Q > Q_B",[883,63760,63762],{"className":63761},[886],[888,63763,63764],{"xmlns":890},[892,63765,63766,63778],{},[895,63767,63768,63770,63772,63774,63776],{},[898,63769,2783],{},[898,63771,1852],{},[2005,63773,3416],{},[898,63775,2783],{},[898,63777,4003],{},[902,63779,63780],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,63783,63785],{"className":63784},[886],[888,63786,63787],{"xmlns":890},[892,63788,63789,63809],{},[895,63790,63791,63797,63799,63801,63803],{},[2281,63792,63793,63795],{},[898,63794,2797],{},[898,63796,1836],{},[2005,63798,3455],{},[898,63800,2797],{},[2005,63802,3455],{},[2281,63804,63805,63807],{},[898,63806,2797],{},[898,63808,1844],{},[902,63810,63811],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,63813,63815],{"className":63814},[886],[888,63816,63817],{"xmlns":890},[892,63818,63819,63831],{},[895,63820,63821,63823,63825,63827,63829],{},[898,63822,2783],{},[898,63824,4003],{},[2005,63826,3416],{},[898,63828,2783],{},[898,63830,1852],{},[902,63832,63833],{"encoding":904},"TR > TC"," (zisk).",[3876,63836,63837],{},[724,63838,63839,63841],{},[883,63840,4164],{}," 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.",[724,63843,63844,63845,63871],{},"Body zvratu jsou řešení rovnice ",[883,63846,63848],{"className":63847},[886],[888,63849,63850],{"xmlns":890},[892,63851,63852,63868],{},[895,63853,63854,63856,63858,63860,63862,63864,63866],{},[898,63855,3946],{},[898,63857,4003],{},[2005,63859,2014],{"stretchy":2013},[898,63861,2797],{},[2005,63863,2020],{"stretchy":2013},[2005,63865,2007],{},[2138,63867,2336],{},[902,63869,63870],{"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.",[724,63873,63874],{},[2568,63875],{"alt":63876,"className":63877,"src":63878},"imek-tr-tc-body-zvratu",[210,2572],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,63880,63881],{},[614,63882,63883,63884,63899,63900,63915,63916,3894,63929,43365,63942,63955,63956,3894,63973,63990,63991,64011,64012,3894,64027,6479,64042,64071],{},"Obrázek 3.11: Body zvratu — křivky ",[883,63885,63887],{"className":63886},[886],[888,63888,63889],{"xmlns":890},[892,63890,63891,63897],{},[895,63892,63893,63895],{},[898,63894,2783],{},[898,63896,4003],{},[902,63898,4103],{"encoding":904}," (obrácená parabola) a ",[883,63901,63903],{"className":63902},[886],[888,63904,63905],{"xmlns":890},[892,63906,63907,63913],{},[895,63908,63909,63911],{},[898,63910,2783],{},[898,63912,1852],{},[902,63914,3251],{"encoding":904}," (přímka) se protínají v bodech ",[883,63917,63919],{"className":63918},[886],[888,63920,63921],{"xmlns":890},[892,63922,63923,63927],{},[895,63924,63925],{},[898,63926,1836],{},[902,63928,1836],{"encoding":904},[883,63930,63932],{"className":63931},[886],[888,63933,63934],{"xmlns":890},[892,63935,63936,63940],{},[895,63937,63938],{},[898,63939,1844],{},[902,63941,1844],{"encoding":904},[883,63943,63945],{"className":63944},[886],[888,63946,63947],{"xmlns":890},[892,63948,63949,63953],{},[895,63950,63951],{},[898,63952,2797],{},[902,63954,2797],{"encoding":904}," v hodnotách ",[883,63957,63959],{"className":63958},[886],[888,63960,63961],{"xmlns":890},[892,63962,63963,63971],{},[895,63964,63965],{},[2281,63966,63967,63969],{},[898,63968,2797],{},[898,63970,1836],{},[902,63972,63688],{"encoding":904},[883,63974,63976],{"className":63975},[886],[888,63977,63978],{"xmlns":890},[892,63979,63980,63988],{},[895,63981,63982],{},[2281,63983,63984,63986],{},[898,63985,2797],{},[898,63987,1844],{},[902,63989,63706],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,63992,63994],{"className":63993},[886],[888,63995,63996],{"xmlns":890},[892,63997,63998,64008],{},[895,63999,64000],{},[2281,64001,64002,64004,64006],{},[898,64003,2797],{},[898,64005,56202],{},[2005,64007,56205],{},[902,64009,64010],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,64013,64015],{"className":64014},[886],[888,64016,64017],{"xmlns":890},[892,64018,64019,64025],{},[895,64020,64021,64023],{},[898,64022,2783],{},[898,64024,4003],{},[902,64026,4103],{"encoding":904},[883,64028,64030],{"className":64029},[886],[888,64031,64032],{"xmlns":890},[892,64033,64034,64040],{},[895,64035,64036,64038],{},[898,64037,2783],{},[898,64039,1852],{},[902,64041,3251],{"encoding":904},[883,64043,64045],{"className":64044},[886],[888,64046,64047],{"xmlns":890},[892,64048,64049,64069],{},[895,64050,64051,64057,64059,64061,64063],{},[2281,64052,64053,64055],{},[898,64054,2797],{},[898,64056,1836],{},[2005,64058,3455],{},[898,64060,2797],{},[2005,64062,3455],{},[2281,64064,64065,64067],{},[898,64066,2797],{},[898,64068,1844],{},[902,64070,63811],{"encoding":904}," vyznačuje zisk.",[37353,64073,64075],{"id":64074},"příklad-38","Příklad 3.8",[724,64077,64078,64080,64081,1343,64101,1343,64127,64153],{},[38,64079,55992],{}," Dáno ",[883,64082,64084],{"className":64083},[886],[888,64085,64086],{"xmlns":890},[892,64087,64088,64098],{},[895,64089,64090,64092,64094,64096],{},[898,64091,1876],{},[898,64093,1852],{},[2005,64095,2007],{},[2138,64097,2360],{},[902,64099,64100],{"encoding":904},"FC = 4",[883,64102,64104],{"className":64103},[886],[888,64105,64106],{"xmlns":890},[892,64107,64108,64124],{},[895,64109,64110,64112,64114,64116,64118],{},[898,64111,2783],{},[898,64113,40344],{},[898,64115,1852],{},[2005,64117,2007],{},[2133,64119,64120,64122],{},[898,64121,2797],{},[2138,64123,2140],{},[902,64125,64126],{"encoding":904},"TVC = Q^2",[883,64128,64130],{"className":64129},[886],[888,64131,64132],{"xmlns":890},[892,64133,64134,64150],{},[895,64135,64136,64138,64140,64142,64144,64146,64148],{},[898,64137,3946],{},[2005,64139,2007],{},[2005,64141,2234],{},[2138,64143,2140],{},[898,64145,2797],{},[2005,64147,2104],{},[2138,64149,4008],{},[902,64151,64152],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,64155,64156,64158],{},[38,64157,22776],{}," Celkové náklady a příjem:",[883,64160,64162],{"className":64161},[886],[888,64163,64164],{"xmlns":890,"display":28071},[892,64165,64166,64232],{},[895,64167,64168,64170,64172,64174,64176,64178,64184,64186,64188,64190,64192,64194,64196,64198,64200,64202,64204,64206,64208,64210,64212,64214,64216,64218,64224,64226,64228,64230],{},[898,64169,2783],{},[898,64171,1852],{},[2005,64173,2007],{},[2138,64175,2360],{},[2005,64177,2104],{},[2133,64179,64180,64182],{},[898,64181,2797],{},[2138,64183,2140],{},[2005,64185,2295],{"separator":2294},[5884,64187],{"width":5886},[898,64189,2783],{},[898,64191,4003],{},[2005,64193,2007],{},[898,64195,2797],{},[2005,64197,3185],{},[2005,64199,2014],{"stretchy":2013},[2005,64201,2234],{},[2138,64203,2140],{},[898,64205,2797],{},[2005,64207,2104],{},[2138,64209,4008],{},[2005,64211,2020],{"stretchy":2013},[2005,64213,2007],{},[2005,64215,2234],{},[2138,64217,2140],{},[2133,64219,64220,64222],{},[898,64221,2797],{},[2138,64223,2140],{},[2005,64225,2104],{},[2138,64227,4008],{},[898,64229,2797],{},[898,64231,1644],{"mathvariant":2385},[902,64233,64234],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,64236,64237],{},"Zisk dle (3.12):",[883,64239,64241],{"className":64240},[886],[888,64242,64243],{"xmlns":890,"display":28071},[892,64244,64245,64323],{},[895,64246,64247,64249,64251,64253,64255,64257,64259,64261,64263,64265,64267,64269,64271,64277,64279,64281,64283,64285,64287,64289,64291,64293,64299,64301,64303,64305,64307,64313,64315,64317,64319,64321],{},[898,64248,3946],{},[898,64250,4003],{},[2005,64252,2007],{},[898,64254,2783],{},[898,64256,4003],{},[2005,64258,2234],{},[898,64260,2783],{},[898,64262,1852],{},[2005,64264,2007],{},[2005,64266,2014],{"stretchy":2013},[2005,64268,2234],{},[2138,64270,2140],{},[2133,64272,64273,64275],{},[898,64274,2797],{},[2138,64276,2140],{},[2005,64278,2104],{},[2138,64280,4008],{},[898,64282,2797],{},[2005,64284,2020],{"stretchy":2013},[2005,64286,2234],{},[2005,64288,2014],{"stretchy":2013},[2138,64290,2360],{},[2005,64292,2104],{},[2133,64294,64295,64297],{},[898,64296,2797],{},[2138,64298,2140],{},[2005,64300,2020],{"stretchy":2013},[2005,64302,2007],{},[2005,64304,2234],{},[2138,64306,2182],{},[2133,64308,64309,64311],{},[898,64310,2797],{},[2138,64312,2140],{},[2005,64314,2104],{},[2138,64316,4008],{},[898,64318,2797],{},[2005,64320,2234],{},[2138,64322,59324],{},[902,64324,64325],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,64327,64328,64331,64332,17583,64368,2713],{},[38,64329,64330],{},"Body zvratu"," jsou kořeny rovnice ",[883,64333,64335],{"className":64334},[886],[888,64336,64337],{"xmlns":890},[892,64338,64339,64365],{},[895,64340,64341,64343,64345,64351,64353,64355,64357,64359,64361,64363],{},[2005,64342,2234],{},[2138,64344,2182],{},[2133,64346,64347,64349],{},[898,64348,2797],{},[2138,64350,2140],{},[2005,64352,2104],{},[2138,64354,4008],{},[898,64356,2797],{},[2005,64358,2234],{},[2138,64360,2360],{},[2005,64362,2007],{},[2138,64364,2336],{},[902,64366,64367],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,64369,64371],{"className":64370},[886],[888,64372,64373],{"xmlns":890},[892,64374,64375,64399],{},[895,64376,64377,64379,64385,64387,64389,64391,64393,64395,64397],{},[2138,64378,2182],{},[2133,64380,64381,64383],{},[898,64382,2797],{},[2138,64384,2140],{},[2005,64386,2234],{},[2138,64388,4008],{},[898,64390,2797],{},[2005,64392,2104],{},[2138,64394,2360],{},[2005,64396,2007],{},[2138,64398,2336],{},[902,64400,64401],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,64403,64405],{"className":64404},[886],[888,64406,64407],{"xmlns":890,"display":28071},[892,64408,64409,64466],{},[895,64410,64411,64423,64425,64448,64450,64464],{},[2281,64412,64413,64415],{},[898,64414,2797],{},[895,64416,64417,64419,64421],{},[2138,64418,2287],{},[2005,64420,2295],{"separator":2294},[2138,64422,2140],{},[2005,64424,2007],{},[2338,64426,64427,64446],{},[895,64428,64429,64431,64434],{},[2138,64430,4008],{},[2005,64432,64433],{},"±",[8123,64435,64436],{},[895,64437,64438,64441,64443],{},[2138,64439,64440],{},"81",[2005,64442,2234],{},[2138,64444,64445],{},"48",[2138,64447,2244],{},[2005,64449,2007],{},[2338,64451,64452,64462],{},[895,64453,64454,64456,64458],{},[2138,64455,4008],{},[2005,64457,64433],{},[8123,64459,64460],{},[2138,64461,8957],{},[2138,64463,2244],{},[2005,64465,2295],{"separator":2294},[902,64467,64468],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,64470,64471,64472,3894,64495,1644],{},"numericky ",[883,64473,64475],{"className":64474},[886],[888,64476,64477],{"xmlns":890},[892,64478,64479,64492],{},[895,64480,64481,64487,64489],{},[2281,64482,64483,64485],{},[898,64484,2797],{},[2138,64486,2287],{},[2005,64488,5906],{},[2138,64490,64491],{},"0,543",[902,64493,64494],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,64496,64498],{"className":64497},[886],[888,64499,64500],{"xmlns":890},[892,64501,64502,64515],{},[895,64503,64504,64510,64512],{},[2281,64505,64506,64508],{},[898,64507,2797],{},[2138,64509,2140],{},[2005,64511,5906],{},[2138,64513,64514],{},"2,457",[902,64516,64517],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,64519,64520,2212,64523,7558,64568,17583,64602,64620],{},[38,64521,64522],{},"Maximum zisku.",[883,64524,64526],{"className":64525},[886],[888,64527,64528],{"xmlns":890},[892,64529,64530,64565],{},[895,64531,64532,64534,64540,64542,64544,64546,64548,64550,64552,64554,64556,64558,64560,64562],{},[898,64533,3946],{},[2133,64535,64536,64538],{},[898,64537,4003],{},[2005,64539,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,64541,2007],{},[2005,64543,2234],{},[2138,64545,2244],{},[898,64547,2797],{},[2005,64549,2104],{},[2138,64551,4008],{},[2005,64553,2007],{},[2138,64555,2336],{},[2005,64557,3996],{},[898,64559,2797],{},[2005,64561,2007],{},[2138,64563,64564],{},"1,5",[902,64566,64567],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,64569,64571],{"className":64570},[886],[888,64572,64573],{"xmlns":890},[892,64574,64575,64599],{},[895,64576,64577,64579,64589,64591,64593,64595,64597],{},[898,64578,3946],{},[2133,64580,64581,64583],{},[898,64582,4003],{},[895,64584,64585,64587],{},[2005,64586,2387],{"mathvariant":2385},[2005,64588,2387],{"mathvariant":2385},[2005,64590,2007],{},[2005,64592,2234],{},[2138,64594,2244],{},[2005,64596,3455],{},[2138,64598,2336],{},[902,64600,64601],{"encoding":904},"PR'' = -6 \u003C 0",[883,64603,64605],{"className":64604},[886],[888,64606,64607],{"xmlns":890},[892,64608,64609,64617],{},[895,64610,64611,64613,64615],{},[898,64612,2797],{},[2005,64614,2007],{},[2138,64616,64564],{},[902,64618,64619],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,64622,64624],{"className":64623},[886],[888,64625,64626],{"xmlns":890,"display":28071},[892,64627,64628,64691],{},[895,64629,64630,64632,64634,64636,64638,64640,64642,64644,64646,64648,64650,64652,64658,64660,64662,64664,64666,64668,64670,64672,64674,64677,64679,64682,64684,64686,64688],{},[898,64631,3946],{},[898,64633,4003],{},[2005,64635,2014],{"stretchy":2013},[2138,64637,64564],{},[2005,64639,2020],{"stretchy":2013},[2005,64641,2007],{},[2005,64643,2234],{},[2138,64645,2182],{},[2005,64647,3185],{},[2005,64649,2014],{"stretchy":2013},[2138,64651,64564],{},[2133,64653,64654,64656],{},[2005,64655,2020],{"stretchy":2013},[2138,64657,2140],{},[2005,64659,2104],{},[2138,64661,4008],{},[2005,64663,3185],{},[2138,64665,64564],{},[2005,64667,2234],{},[2138,64669,2360],{},[2005,64671,2007],{},[2005,64673,2234],{},[2138,64675,64676],{},"6,75",[2005,64678,2104],{},[2138,64680,64681],{},"13,5",[2005,64683,2234],{},[2138,64685,2360],{},[2005,64687,2007],{},[2138,64689,64690],{},"2,75.",[902,64692,64693],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,64695,64696,64697,1343,64742,64795,64796,64814],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,64698,64700],{"className":64699},[886],[888,64701,64702],{"xmlns":890},[892,64703,64704,64739],{},[895,64705,64706,64708,64714,64716,64718,64720,64722,64724,64726,64728,64730,64732,64734,64736],{},[898,64707,2783],{},[2133,64709,64710,64712],{},[898,64711,4003],{},[2005,64713,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,64715,2007],{},[2005,64717,2234],{},[2138,64719,2360],{},[898,64721,2797],{},[2005,64723,2104],{},[2138,64725,4008],{},[2005,64727,2007],{},[2138,64729,2336],{},[2005,64731,3996],{},[898,64733,2797],{},[2005,64735,2007],{},[2138,64737,64738],{},"2,25",[902,64740,64741],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,64743,64745],{"className":64744},[886],[888,64746,64747],{"xmlns":890},[892,64748,64749,64792],{},[895,64750,64751,64753,64761,64763,64765,64767,64769,64771,64773,64779,64781,64783,64785,64787,64789],{},[898,64752,2783],{},[2281,64754,64755,64757,64759],{},[898,64756,4003],{},[898,64758,56202],{},[2005,64760,56205],{},[2005,64762,2007],{},[2005,64764,2234],{},[2138,64766,2140],{},[2005,64768,3185],{},[2005,64770,2014],{"stretchy":2013},[2138,64772,64738],{},[2133,64774,64775,64777],{},[2005,64776,2020],{"stretchy":2013},[2138,64778,2140],{},[2005,64780,2104],{},[2138,64782,4008],{},[2005,64784,3185],{},[2138,64786,64738],{},[2005,64788,2007],{},[2138,64790,64791],{},"10,125",[902,64793,64794],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,64797,64799],{"className":64798},[886],[888,64800,64801],{"xmlns":890},[892,64802,64803,64811],{},[895,64804,64805,64807,64809],{},[898,64806,2797],{},[2005,64808,2007],{},[2138,64810,64738],{},[902,64812,64813],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[3876,64816,64817],{},[724,64818,64819,64821,64822,1343,64844,64866,64867,1343,64884,64905,64906,64938,64939,64977,64978,2680,64996,65013,65014,3894,65042,65076,65077,7691,65115,3894,65139,1644],{},[883,64820,4418],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,64823,64825],{"className":64824},[886],[888,64826,64827],{"xmlns":890},[892,64828,64829,64841],{},[895,64830,64831,64837,64839],{},[2281,64832,64833,64835],{},[898,64834,2797],{},[2138,64836,2287],{},[2005,64838,2007],{},[2138,64840,5015],{},[902,64842,64843],{"encoding":904},"Q_1 = 0{,}5",[883,64845,64847],{"className":64846},[886],[888,64848,64849],{"xmlns":890},[892,64850,64851,64863],{},[895,64852,64853,64859,64861],{},[2281,64854,64855,64857],{},[898,64856,2797],{},[2138,64858,2140],{},[2005,64860,2007],{},[2138,64862,2360],{},[902,64864,64865],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,64868,64870],{"className":64869},[886],[888,64871,64872],{"xmlns":890},[892,64873,64874,64882],{},[895,64875,64876,64878,64880],{},[898,64877,2797],{},[2005,64879,2007],{},[2138,64881,64738],{},[902,64883,64813],{"encoding":904},[883,64885,64887],{"className":64886},[886],[888,64888,64889],{"xmlns":890},[892,64890,64891,64902],{},[895,64892,64893,64895,64897,64899],{},[898,64894,3946],{},[898,64896,4003],{},[2005,64898,2007],{},[2138,64900,64901],{},"6,125",[902,64903,64904],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,64907,64909],{"className":64908},[886],[888,64910,64911],{"xmlns":890},[892,64912,64913,64935],{},[895,64914,64915,64917,64923,64925,64927,64929,64931,64933],{},[898,64916,3946],{},[2133,64918,64919,64921],{},[898,64920,4003],{},[2005,64922,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,64924,2007],{},[2005,64926,2234],{},[2138,64928,2360],{},[898,64930,2797],{},[2005,64932,2104],{},[2138,64934,4008],{},[902,64936,64937],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,64940,64942],{"className":64941},[886],[888,64943,64944],{"xmlns":890},[892,64945,64946,64974],{},[895,64947,64948,64950,64952,64954,64956,64958,64964,64966,64968,64970,64972],{},[898,64949,3946],{},[898,64951,4003],{},[2005,64953,2007],{},[2005,64955,2234],{},[2138,64957,2140],{},[2133,64959,64960,64962],{},[898,64961,2797],{},[2138,64963,2140],{},[2005,64965,2104],{},[2138,64967,4008],{},[898,64969,2797],{},[2005,64971,2234],{},[2138,64973,2360],{},[902,64975,64976],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,64979,64981],{"className":64980},[886],[888,64982,64983],{"xmlns":890},[892,64984,64985,64993],{},[895,64986,64987],{},[2133,64988,64989,64991],{},[898,64990,2797],{},[2138,64992,2140],{},[902,64994,64995],{"encoding":904},"Q^2",[883,64997,64999],{"className":64998},[886],[888,65000,65001],{"xmlns":890},[892,65002,65003,65011],{},[895,65004,65005,65007,65009],{},[898,65006,2783],{},[898,65008,40344],{},[898,65010,1852],{},[902,65012,55514],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,65015,65017],{"className":65016},[886],[888,65018,65019],{"xmlns":890},[892,65020,65021,65039],{},[895,65022,65023,65025,65027,65029,65031,65033],{},[898,65024,2783],{},[898,65026,1852],{},[2005,65028,2007],{},[2138,65030,2360],{},[2005,65032,2104],{},[2133,65034,65035,65037],{},[898,65036,2797],{},[2138,65038,2140],{},[902,65040,65041],{"encoding":904},"TC = 4 + Q^2",[883,65043,65045],{"className":65044},[886],[888,65046,65047],{"xmlns":890},[892,65048,65049,65073],{},[895,65050,65051,65053,65055,65057,65059,65061,65067,65069,65071],{},[898,65052,2783],{},[898,65054,4003],{},[2005,65056,2007],{},[2005,65058,2234],{},[2138,65060,2140],{},[2133,65062,65063,65065],{},[898,65064,2797],{},[2138,65066,2140],{},[2005,65068,2104],{},[2138,65070,4008],{},[898,65072,2797],{},[902,65074,65075],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,65078,65080],{"className":65079},[886],[888,65081,65082],{"xmlns":890},[892,65083,65084,65112],{},[895,65085,65086,65088,65090,65092,65094,65096,65102,65104,65106,65108,65110],{},[898,65087,3946],{},[898,65089,4003],{},[2005,65091,2007],{},[2005,65093,2234],{},[2138,65095,2182],{},[2133,65097,65098,65100],{},[898,65099,2797],{},[2138,65101,2140],{},[2005,65103,2104],{},[2138,65105,4008],{},[898,65107,2797],{},[2005,65109,2234],{},[2138,65111,2360],{},[902,65113,65114],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,65116,65118],{"className":65117},[886],[888,65119,65120],{"xmlns":890},[892,65121,65122,65136],{},[895,65123,65124,65132,65134],{},[2281,65125,65126,65128,65130],{},[898,65127,2797],{},[898,65129,56202],{},[2005,65131,56205],{},[2005,65133,2007],{},[2138,65135,64564],{},[902,65137,65138],{"encoding":904},"Q_{\\max} = 1{,}5",[883,65140,65142],{"className":65141},[886],[888,65143,65144],{"xmlns":890},[892,65145,65146,65163],{},[895,65147,65148,65150,65158,65160],{},[898,65149,3946],{},[2281,65151,65152,65154,65156],{},[898,65153,4003],{},[898,65155,56202],{},[2005,65157,56205],{},[2005,65159,2007],{},[2138,65161,65162],{},"2,75",[902,65164,65165],{"encoding":904},"PR_{\\max} = 2{,}75",[724,65167,65168],{},[614,65169,65170,65171,65198,65199,65232,65233,1343,65256,1644],{},"Obrázek 3.12: Graf ",[883,65172,65174],{"className":65173},[886],[888,65175,65176],{"xmlns":890},[892,65177,65178,65196],{},[895,65179,65180,65182,65184,65186,65188,65190],{},[898,65181,2783],{},[898,65183,1852],{},[2005,65185,2007],{},[2138,65187,2360],{},[2005,65189,2104],{},[2133,65191,65192,65194],{},[898,65193,2797],{},[2138,65195,2140],{},[902,65197,65041],{"encoding":904}," (parabola) a ",[883,65200,65202],{"className":65201},[886],[888,65203,65204],{"xmlns":890},[892,65205,65206,65230],{},[895,65207,65208,65210,65212,65214,65216,65218,65224,65226,65228],{},[898,65209,2783],{},[898,65211,4003],{},[2005,65213,2007],{},[2005,65215,2234],{},[2138,65217,2140],{},[2133,65219,65220,65222],{},[898,65221,2797],{},[2138,65223,2140],{},[2005,65225,2104],{},[2138,65227,4008],{},[898,65229,2797],{},[902,65231,65075],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,65234,65236],{"className":65235},[886],[888,65237,65238],{"xmlns":890},[892,65239,65240,65253],{},[895,65241,65242,65248,65250],{},[2281,65243,65244,65246],{},[898,65245,2797],{},[2138,65247,2287],{},[2005,65249,5906],{},[2138,65251,65252],{},"0,54",[902,65254,65255],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,65257,65259],{"className":65258},[886],[888,65260,65261],{"xmlns":890},[892,65262,65263,65276],{},[895,65264,65265,65271,65273],{},[2281,65266,65267,65269],{},[898,65268,2797],{},[2138,65270,2140],{},[2005,65272,5906],{},[2138,65274,65275],{},"2,46",[902,65277,65278],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,65280,65281],{},[614,65282,65283,65284,58512,65321,65338,65339,1343,65360,1644],{},"Obrázek 3.13: Graf zisku ",[883,65285,65287],{"className":65286},[886],[888,65288,65289],{"xmlns":890},[892,65290,65291,65319],{},[895,65292,65293,65295,65297,65299,65301,65303,65309,65311,65313,65315,65317],{},[898,65294,3946],{},[898,65296,4003],{},[2005,65298,2007],{},[2005,65300,2234],{},[2138,65302,2182],{},[2133,65304,65305,65307],{},[898,65306,2797],{},[2138,65308,2140],{},[2005,65310,2104],{},[2138,65312,4008],{},[898,65314,2797],{},[2005,65316,2234],{},[2138,65318,2360],{},[902,65320,65114],{"encoding":904},[883,65322,65324],{"className":65323},[886],[888,65325,65326],{"xmlns":890},[892,65327,65328,65336],{},[895,65329,65330,65332,65334],{},[898,65331,2797],{},[2005,65333,2007],{},[2138,65335,64564],{},[902,65337,64619],{"encoding":904}," a nulami ",[883,65340,65342],{"className":65341},[886],[888,65343,65344],{"xmlns":890},[892,65345,65346,65358],{},[895,65347,65348,65354,65356],{},[2281,65349,65350,65352],{},[898,65351,2797],{},[2138,65353,2287],{},[2005,65355,5906],{},[2138,65357,65252],{},[902,65359,65255],{"encoding":904},[883,65361,65363],{"className":65362},[886],[888,65364,65365],{"xmlns":890},[892,65366,65367,65379],{},[895,65368,65369,65375,65377],{},[2281,65370,65371,65373],{},[898,65372,2797],{},[2138,65374,2140],{},[2005,65376,5906],{},[2138,65378,65275],{},[902,65380,65278],{"encoding":904},[115,65382,65384],{"id":65383},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,65386,65387],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,65389,65390],{},[2568,65391],{"alt":65392,"className":65393,"src":65394},"imek-max-zisku-dva-pohledy",[210,2572],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,65396,16419],{"id":65397},"princip-1",[724,65399,65400,65401,2633,65416,65433],{},"Má-li zisk ",[883,65402,65404],{"className":65403},[886],[888,65405,65406],{"xmlns":890},[892,65407,65408,65414],{},[895,65409,65410,65412],{},[898,65411,3946],{},[898,65413,4003],{},[902,65415,63484],{"encoding":904},[883,65417,65419],{"className":65418},[886],[888,65420,65421],{"xmlns":890},[892,65422,65423,65431],{},[895,65424,65425],{},[2281,65426,65427,65429],{},[898,65428,2797],{},[2138,65430,2336],{},[902,65432,38313],{"encoding":904}," maximum, pak platí",[883,65435,65437],{"className":65436},[886],[888,65438,65439],{"xmlns":890,"display":28071},[892,65440,65441,65490],{},[20760,65442,65443],{"width":28076},[20765,65444,65445,65447,65483,65485],{},[20768,65446],{"width":28081},[20768,65448,65449],{},[895,65450,65451,65453,65455,65457,65463,65465,65467,65469,65471,65473,65479,65481],{},[898,65452,2826],{},[898,65454,4003],{},[2005,65456,2014],{"stretchy":2013},[2281,65458,65459,65461],{},[898,65460,2797],{},[2138,65462,2336],{},[2005,65464,2020],{"stretchy":2013},[2005,65466,2007],{},[898,65468,2826],{},[898,65470,1852],{},[2005,65472,2014],{"stretchy":2013},[2281,65474,65475,65477],{},[898,65476,2797],{},[2138,65478,2336],{},[2005,65480,2020],{"stretchy":2013},[898,65482,1644],{"mathvariant":2385},[20768,65484],{"width":28081},[20768,65486,65487],{},[2297,65488,65489],{},"(3.13)",[902,65491,65492],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[3876,65494,65495],{},[724,65496,65497,62051,65499],{},[883,65498,56449],{},[38,65500,65501],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,65503,65504,65507,65508,8108,65535,17583,65609,1644],{},[38,65505,65506],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,65509,65511],{"className":65510},[886],[888,65512,65513],{"xmlns":890},[892,65514,65515,65533],{},[895,65516,65517,65519,65521,65523,65525,65527,65529,65531],{},[898,65518,3946],{},[898,65520,4003],{},[2005,65522,2007],{},[898,65524,2783],{},[898,65526,4003],{},[2005,65528,2234],{},[898,65530,2783],{},[898,65532,1852],{},[902,65534,55205],{"encoding":904},[883,65536,65538],{"className":65537},[886],[888,65539,65540],{"xmlns":890},[892,65541,65542,65606],{},[895,65543,65544,65546,65552,65554,65560,65562,65564,65566,65572,65574,65580,65582,65584,65586,65592,65594,65600,65602,65604],{},[898,65545,3946],{},[2133,65547,65548,65550],{},[898,65549,4003],{},[2005,65551,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,65553,2014],{"stretchy":2013},[2281,65555,65556,65558],{},[898,65557,2797],{},[2138,65559,2336],{},[2005,65561,2020],{"stretchy":2013},[2005,65563,2007],{},[898,65565,2783],{},[2133,65567,65568,65570],{},[898,65569,4003],{},[2005,65571,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,65573,2014],{"stretchy":2013},[2281,65575,65576,65578],{},[898,65577,2797],{},[2138,65579,2336],{},[2005,65581,2020],{"stretchy":2013},[2005,65583,2234],{},[898,65585,2783],{},[2133,65587,65588,65590],{},[898,65589,1852],{},[2005,65591,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,65593,2014],{"stretchy":2013},[2281,65595,65596,65598],{},[898,65597,2797],{},[2138,65599,2336],{},[2005,65601,2020],{"stretchy":2013},[2005,65603,2007],{},[2138,65605,2336],{},[902,65607,65608],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,65610,65612],{"className":65611},[886],[888,65613,65614],{"xmlns":890},[892,65615,65616,65648],{},[895,65617,65618,65620,65622,65624,65630,65632,65634,65636,65638,65640,65646],{},[898,65619,2826],{},[898,65621,4003],{},[2005,65623,2014],{"stretchy":2013},[2281,65625,65626,65628],{},[898,65627,2797],{},[2138,65629,2336],{},[2005,65631,2020],{"stretchy":2013},[2005,65633,2007],{},[898,65635,2826],{},[898,65637,1852],{},[2005,65639,2014],{"stretchy":2013},[2281,65641,65642,65644],{},[898,65643,2797],{},[2138,65645,2336],{},[2005,65647,2020],{"stretchy":2013},[902,65649,65650],{"encoding":904},"MR(Q_0) = MC(Q_0)",[3876,65652,65653,65658],{},[724,65654,65655,65657],{},[883,65656,4578],{}," Postup — jak najít maximum zisku",[152,65659,65660,65724,65779,65816,65844],{},[123,65661,65662,65663,3894,65678,65693,65694,3927],{},"Sestavte ",[883,65664,65666],{"className":65665},[886],[888,65667,65668],{"xmlns":890},[892,65669,65670,65676],{},[895,65671,65672,65674],{},[898,65673,2783],{},[898,65675,4003],{},[902,65677,4103],{"encoding":904},[883,65679,65681],{"className":65680},[886],[888,65682,65683],{"xmlns":890},[892,65684,65685,65691],{},[895,65686,65687,65689],{},[898,65688,2783],{},[898,65690,1852],{},[902,65692,3251],{"encoding":904}," ze zadání (typicky ",[883,65695,65697],{"className":65696},[886],[888,65698,65699],{"xmlns":890},[892,65700,65701,65721],{},[895,65702,65703,65705,65707,65709,65711,65713,65715,65717,65719],{},[898,65704,2783],{},[898,65706,4003],{},[2005,65708,2007],{},[898,65710,3946],{},[2005,65712,2014],{"stretchy":2013},[898,65714,2797],{},[2005,65716,2020],{"stretchy":2013},[2005,65718,3185],{},[898,65720,2797],{},[902,65722,65723],{"encoding":904},"TR = P(Q) \\cdot Q",[123,65725,65726,65727,3894,65753,1644],{},"Vypočtěte ",[883,65728,65730],{"className":65729},[886],[888,65731,65732],{"xmlns":890},[892,65733,65734,65750],{},[895,65735,65736,65738,65740,65742,65744],{},[898,65737,2826],{},[898,65739,4003],{},[2005,65741,2007],{},[898,65743,2783],{},[2133,65745,65746,65748],{},[898,65747,4003],{},[2005,65749,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,65751,65752],{"encoding":904},"MR = TR'",[883,65754,65756],{"className":65755},[886],[888,65757,65758],{"xmlns":890},[892,65759,65760,65776],{},[895,65761,65762,65764,65766,65768,65770],{},[898,65763,2826],{},[898,65765,1852],{},[2005,65767,2007],{},[898,65769,2783],{},[2133,65771,65772,65774],{},[898,65773,1852],{},[2005,65775,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,65777,65778],{"encoding":904},"MC = TC'",[123,65780,65781,65782,1644],{},"Řešte rovnici ",[883,65783,65785],{"className":65784},[886],[888,65786,65787],{"xmlns":890},[892,65788,65789,65813],{},[895,65790,65791,65793,65795,65797,65799,65801,65803,65805,65807,65809,65811],{},[898,65792,2826],{},[898,65794,4003],{},[2005,65796,2014],{"stretchy":2013},[898,65798,2797],{},[2005,65800,2020],{"stretchy":2013},[2005,65802,2007],{},[898,65804,2826],{},[898,65806,1852],{},[2005,65808,2014],{"stretchy":2013},[898,65810,2797],{},[2005,65812,2020],{"stretchy":2013},[902,65814,65815],{"encoding":904},"MR(Q) = MC(Q)",[123,65817,65818,65819,65843],{},"Ověřte druhou derivaci ",[883,65820,65822],{"className":65821},[886],[888,65823,65824],{"xmlns":890},[892,65825,65826,65840],{},[895,65827,65828,65830],{},[898,65829,3946],{},[2133,65831,65832,65834],{},[898,65833,4003],{},[895,65835,65836,65838],{},[2005,65837,2387],{"mathvariant":2385},[2005,65839,2387],{"mathvariant":2385},[902,65841,65842],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,65845,65846,65847,65874],{},"Dosaďte do ",[883,65848,65850],{"className":65849},[886],[888,65851,65852],{"xmlns":890},[892,65853,65854,65872],{},[895,65855,65856,65858,65860,65862,65864,65866,65868,65870],{},[898,65857,3946],{},[898,65859,4003],{},[2005,65861,2007],{},[898,65863,2783],{},[898,65865,4003],{},[2005,65867,2234],{},[898,65869,2783],{},[898,65871,1852],{},[902,65873,55205],{"encoding":904}," pro hodnotu maxima.",[37353,65876,65878],{"id":65877},"příklad-39","Příklad 3.9",[724,65880,65881,55993,65883,3894,65905,65941],{},[38,65882,55992],{},[883,65884,65886],{"className":65885},[886],[888,65887,65888],{"xmlns":890},[892,65889,65890,65902],{},[895,65891,65892,65894,65896,65898,65900],{},[898,65893,3946],{},[2005,65895,2007],{},[2138,65897,38024],{},[2005,65899,2234],{},[898,65901,2797],{},[902,65903,65904],{"encoding":904},"P = 30 - Q",[883,65906,65908],{"className":65907},[886],[888,65909,65910],{"xmlns":890},[892,65911,65912,65938],{},[895,65913,65914,65916,65918,65920,65922,65928,65930,65932,65934,65936],{},[898,65915,2783],{},[898,65917,1852],{},[2005,65919,2007],{},[2138,65921,5015],{},[2133,65923,65924,65926],{},[898,65925,2797],{},[2138,65927,2140],{},[2005,65929,2104],{},[2138,65931,2244],{},[898,65933,2797],{},[2005,65935,2104],{},[2138,65937,24206],{},[902,65939,65940],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,65943,65944,2212,65946,1343,65976,66014,66015,15798,66059,66093,66094,1644],{},[38,65945,22776],{},[883,65947,65949],{"className":65948},[886],[888,65950,65951],{"xmlns":890},[892,65952,65953,65973],{},[895,65954,65955,65957,65959,65961,65963,65965,65967],{},[898,65956,2783],{},[898,65958,4003],{},[2005,65960,2007],{},[2138,65962,38024],{},[898,65964,2797],{},[2005,65966,2234],{},[2133,65968,65969,65971],{},[898,65970,2797],{},[2138,65972,2140],{},[902,65974,65975],{"encoding":904},"TR = 30Q - Q^2",[883,65977,65979],{"className":65978},[886],[888,65980,65981],{"xmlns":890},[892,65982,65983,66011],{},[895,65984,65985,65987,65989,65991,65993,65995,66001,66003,66005,66007,66009],{},[898,65986,3946],{},[898,65988,4003],{},[2005,65990,2007],{},[2005,65992,2234],{},[2138,65994,64564],{},[2133,65996,65997,65999],{},[898,65998,2797],{},[2138,66000,2140],{},[2005,66002,2104],{},[2138,66004,41805],{},[898,66006,2797],{},[2005,66008,2234],{},[2138,66010,24206],{},[902,66012,66013],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,66016,66018],{"className":66017},[886],[888,66019,66020],{"xmlns":890},[892,66021,66022,66056],{},[895,66023,66024,66026,66032,66034,66036,66038,66040,66042,66044,66046,66048,66050,66052,66054],{},[898,66025,3946],{},[2133,66027,66028,66030],{},[898,66029,4003],{},[2005,66031,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,66033,2007],{},[2005,66035,2234],{},[2138,66037,2182],{},[898,66039,2797],{},[2005,66041,2104],{},[2138,66043,41805],{},[2005,66045,2007],{},[2138,66047,2336],{},[2005,66049,3996],{},[898,66051,2797],{},[2005,66053,2007],{},[2138,66055,5591],{},[902,66057,66058],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,66060,66062],{"className":66061},[886],[888,66063,66064],{"xmlns":890},[892,66065,66066,66090],{},[895,66067,66068,66070,66080,66082,66084,66086,66088],{},[898,66069,3946],{},[2133,66071,66072,66074],{},[898,66073,4003],{},[895,66075,66076,66078],{},[2005,66077,2387],{"mathvariant":2385},[2005,66079,2387],{"mathvariant":2385},[2005,66081,2007],{},[2005,66083,2234],{},[2138,66085,2182],{},[2005,66087,3455],{},[2138,66089,2336],{},[902,66091,66092],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,66095,66097],{"className":66096},[886],[888,66098,66099],{"xmlns":890},[892,66100,66101,66118],{},[895,66102,66103,66105,66107,66109,66111,66113,66115],{},[898,66104,3946],{},[898,66106,4003],{},[2005,66108,2014],{"stretchy":2013},[2138,66110,5591],{},[2005,66112,2020],{"stretchy":2013},[2005,66114,2007],{},[2138,66116,66117],{},"89",[902,66119,66120],{"encoding":904},"PR(8) = 89",[724,66122,66123,66124,1343,66150,15798,66174,66212],{},"Ověření principu: ",[883,66125,66127],{"className":66126},[886],[888,66128,66129],{"xmlns":890},[892,66130,66131,66147],{},[895,66132,66133,66135,66137,66139,66141,66143,66145],{},[898,66134,2826],{},[898,66136,4003],{},[2005,66138,2007],{},[2138,66140,38024],{},[2005,66142,2234],{},[2138,66144,2140],{},[898,66146,2797],{},[902,66148,66149],{"encoding":904},"MR = 30 - 2Q",[883,66151,66153],{"className":66152},[886],[888,66154,66155],{"xmlns":890},[892,66156,66157,66171],{},[895,66158,66159,66161,66163,66165,66167,66169],{},[898,66160,2826],{},[898,66162,1852],{},[2005,66164,2007],{},[898,66166,2797],{},[2005,66168,2104],{},[2138,66170,2244],{},[902,66172,66173],{"encoding":904},"MC = Q + 6",[883,66175,66177],{"className":66176},[886],[888,66178,66179],{"xmlns":890},[892,66180,66181,66209],{},[895,66182,66183,66185,66187,66189,66191,66193,66195,66197,66199,66201,66203,66205,66207],{},[898,66184,2826],{},[898,66186,4003],{},[2005,66188,2014],{"stretchy":2013},[2138,66190,5591],{},[2005,66192,2020],{"stretchy":2013},[2005,66194,2007],{},[2138,66196,22952],{},[2005,66198,2007],{},[898,66200,2826],{},[898,66202,1852],{},[2005,66204,2014],{"stretchy":2013},[2138,66206,5591],{},[2005,66208,2020],{"stretchy":2013},[902,66210,66211],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,66214,66215,66216,66249,66250,66267],{},"V řadě případů — má-li rovnice ",[883,66217,66219],{"className":66218},[886],[888,66220,66221],{"xmlns":890},[892,66222,66223,66247],{},[895,66224,66225,66227,66229,66231,66233,66235,66237,66239,66241,66243,66245],{},[898,66226,2826],{},[898,66228,4003],{},[2005,66230,2014],{"stretchy":2013},[898,66232,2797],{},[2005,66234,2020],{"stretchy":2013},[2005,66236,2007],{},[898,66238,2826],{},[898,66240,1852],{},[2005,66242,2014],{"stretchy":2013},[898,66244,2797],{},[2005,66246,2020],{"stretchy":2013},[902,66248,65815],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,66251,66253],{"className":66252},[886],[888,66254,66255],{"xmlns":890},[892,66256,66257,66265],{},[895,66258,66259],{},[2281,66260,66261,66263],{},[898,66262,2797],{},[2138,66264,2336],{},[902,66266,38313],{"encoding":904}," — není třeba provádět test druhé derivace.",[37353,66269,66271],{"id":66270},"příklad-310","Příklad 3.10",[724,66273,66274,66276,66277,66281,66282,66295,66296,66327],{},[38,66275,55992],{}," Firma vyrábí minipočítače v ",[207,66278,66280],{"className":66279,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,66283,66285],{"className":66284},[886],[888,66286,66287],{"xmlns":890},[892,66288,66289,66293],{},[895,66290,66291],{},[2138,66292,15197],{},[902,66294,15197],{"encoding":904}," EUR\u002Fks. ",[883,66297,66299],{"className":66298},[886],[888,66300,66301],{"xmlns":890},[892,66302,66303,66324],{},[895,66304,66305,66307,66309,66311,66313,66315,66318],{},[898,66306,2783],{},[898,66308,1852],{},[2005,66310,2007],{},[2138,66312,3128],{},[2005,66314,2104],{},[2138,66316,66317],{},"28",[2133,66319,66320,66322],{},[898,66321,2797],{},[2138,66323,2140],{},[902,66325,66326],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,66329,66330,2212,66332,1343,66354,1343,66374,66397],{},[38,66331,22776],{},[883,66333,66335],{"className":66334},[886],[888,66336,66337],{"xmlns":890},[892,66338,66339,66351],{},[895,66340,66341,66343,66345,66347,66349],{},[898,66342,2783],{},[898,66344,4003],{},[2005,66346,2007],{},[2138,66348,15197],{},[898,66350,2797],{},[902,66352,66353],{"encoding":904},"TR = 900Q",[883,66355,66357],{"className":66356},[886],[888,66358,66359],{"xmlns":890},[892,66360,66361,66371],{},[895,66362,66363,66365,66367,66369],{},[898,66364,2826],{},[898,66366,4003],{},[2005,66368,2007],{},[2138,66370,15197],{},[902,66372,66373],{"encoding":904},"MR = 900",[883,66375,66377],{"className":66376},[886],[888,66378,66379],{"xmlns":890},[892,66380,66381,66394],{},[895,66382,66383,66385,66387,66389,66392],{},[898,66384,2826],{},[898,66386,1852],{},[2005,66388,2007],{},[2138,66390,66391],{},"56",[898,66393,2797],{},[902,66395,66396],{"encoding":904},"MC = 56Q",". Z principu:",[883,66399,66401],{"className":66400},[886],[888,66402,66403],{"xmlns":890,"display":28071},[892,66404,66405,66447],{},[895,66406,66407,66409,66411,66413,66415,66417,66419,66421,66423,66425,66433,66435,66438,66440,66442,66444],{},[2138,66408,15197],{},[2005,66410,2007],{},[2138,66412,66391],{},[898,66414,2797],{},[2297,66416,3993],{},[2005,66418,3996],{},[2297,66420,3993],{},[898,66422,2797],{},[2005,66424,2007],{},[2334,66426,66427],{"scriptlevel":2336,"displaystyle":2013},[2338,66428,66429,66431],{},[2138,66430,15197],{},[2138,66432,66391],{},[2005,66434,5906],{},[2138,66436,66437],{},"16,07",[2297,66439,3993],{},[2005,66441,2739],{},[2297,66443,3993],{},[2138,66445,66446],{},"16.",[902,66448,66449],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,66451,66452,66453,2713],{},"Zisk při ",[883,66454,66456],{"className":66455},[886],[888,66457,66458],{"xmlns":890},[892,66459,66460,66468],{},[895,66461,66462,66464,66466],{},[898,66463,2797],{},[2005,66465,2007],{},[2138,66467,41867],{},[902,66469,66470],{"encoding":904},"Q = 16",[883,66472,66474],{"className":66473},[886],[888,66475,66476],{"xmlns":890,"display":28071},[892,66477,66478,66549],{},[895,66479,66480,66482,66484,66486,66488,66490,66492,66494,66496,66498,66500,66502,66504,66506,66508,66510,66516,66518,66520,66522,66524,66526,66528,66530,66532,66535,66537,66539,66541,66544,66547],{},[898,66481,3946],{},[898,66483,4003],{},[2005,66485,2014],{"stretchy":2013},[2138,66487,41867],{},[2005,66489,2020],{"stretchy":2013},[2005,66491,2007],{},[2138,66493,15197],{},[2005,66495,3185],{},[2138,66497,41867],{},[2005,66499,2234],{},[2005,66501,2014],{"stretchy":2013},[2138,66503,3128],{},[2005,66505,2104],{},[2138,66507,66317],{},[2005,66509,3185],{},[2133,66511,66512,66514],{},[2138,66513,41867],{},[2138,66515,2140],{},[2005,66517,2020],{"stretchy":2013},[2005,66519,2007],{},[2138,66521,22952],{},[2297,66523,2995],{},[2138,66525,20148],{},[2005,66527,2234],{},[2138,66529,24206],{},[2297,66531,2995],{},[2138,66533,66534],{},"218",[2005,66536,2007],{},[2138,66538,24206],{},[2297,66540,2995],{},[2138,66542,66543],{},"182",[2297,66545,66546],{}," EUR",[898,66548,1644],{"mathvariant":2385},[902,66550,66551],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,66553,66554],{},"Pro srovnání při původních 30 ks:",[883,66556,66558],{"className":66557},[886],[888,66559,66560],{"xmlns":890,"display":28071},[892,66561,66562,66627],{},[895,66563,66564,66566,66568,66570,66572,66574,66576,66578,66580,66582,66584,66586,66588,66590,66592,66594,66596,66598,66600,66603,66605,66607,66609,66611,66613,66615,66617,66619,66621,66623,66625],{},[898,66565,3946],{},[898,66567,4003],{},[2005,66569,2014],{"stretchy":2013},[2138,66571,38024],{},[2005,66573,2020],{"stretchy":2013},[2005,66575,2007],{},[2138,66577,15197],{},[2005,66579,3185],{},[2138,66581,38024],{},[2005,66583,2234],{},[2005,66585,2014],{"stretchy":2013},[2138,66587,3128],{},[2005,66589,2104],{},[2138,66591,66317],{},[2005,66593,3185],{},[2138,66595,15197],{},[2005,66597,2020],{"stretchy":2013},[2005,66599,2007],{},[2138,66601,66602],{},"27",[2297,66604,2995],{},[2138,66606,59087],{},[2005,66608,2234],{},[2138,66610,5010],{},[2297,66612,2995],{},[2138,66614,30748],{},[2005,66616,2007],{},[2138,66618,2287],{},[2297,66620,2995],{},[2138,66622,23748],{},[2297,66624,66546],{},[898,66626,1644],{"mathvariant":2385},[902,66628,66629],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,66631,66632,66635,66636,66654,66655,66673],{},[38,66633,66634],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,66637,66639],{"className":66638},[886],[888,66640,66641],{"xmlns":890},[892,66642,66643,66651],{},[895,66644,66645,66647,66649],{},[2138,66646,24206],{},[2297,66648,2995],{},[2138,66650,66543],{},[902,66652,66653],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,66656,66658],{"className":66657},[886],[888,66659,66660],{"xmlns":890},[892,66661,66662,66670],{},[895,66663,66664,66666,66668],{},[2138,66665,2287],{},[2297,66667,2995],{},[2138,66669,23748],{},[902,66671,66672],{"encoding":904},"1\\,750"," EUR.",[198,66675,66677],{"id":66676},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,66679,66680,66681,62575,66694,66718],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,66682,66684],{"className":66683},[886],[888,66685,66686],{"xmlns":890},[892,66687,66688,66692],{},[895,66689,66690],{},[898,66691,3946],{},[902,66693,3946],{"encoding":904},[883,66695,66697],{"className":66696},[886],[888,66698,66699],{"xmlns":890},[892,66700,66701,66715],{},[895,66702,66703,66705,66707,66709,66711,66713],{},[898,66704,2783],{},[898,66706,4003],{},[2005,66708,2007],{},[898,66710,3946],{},[2005,66712,3185],{},[898,66714,2797],{},[902,66716,66717],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,66720,66722],{"className":66721},[886],[888,66723,66724],{"xmlns":890,"display":28071},[892,66725,66726,66759],{},[20760,66727,66728],{"width":28076},[20765,66729,66730,66732,66752,66754],{},[20768,66731],{"width":28081},[20768,66733,66734],{},[895,66735,66736,66738,66740,66742,66744,66746,66748,66750],{},[898,66737,3946],{},[2005,66739,2007],{},[898,66741,2826],{},[898,66743,1852],{},[2005,66745,2014],{"stretchy":2013},[898,66747,2797],{},[2005,66749,2020],{"stretchy":2013},[898,66751,1644],{"mathvariant":2385},[20768,66753],{"width":28081},[20768,66755,66756],{},[2297,66757,66758],{},"(3.14)",[902,66760,66761],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,66763,66764,66765,1644],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,66766,66768],{"className":66767},[886],[888,66769,66770],{"xmlns":890},[892,66771,66772,66786],{},[895,66773,66774,66776],{},[898,66775,3946],{},[2133,66777,66778,66780],{},[898,66779,4003],{},[895,66781,66782,66784],{},[2005,66783,2387],{"mathvariant":2385},[2005,66785,2387],{"mathvariant":2385},[902,66787,65842],{"encoding":904},[37353,66789,66791],{"id":66790},"příklad-311","Příklad 3.11",[724,66793,66794,57527,66796,66843,66844,66862],{},[38,66795,55992],{},[883,66797,66799],{"className":66798},[886],[888,66800,66801],{"xmlns":890},[892,66802,66803,66840],{},[895,66804,66805,66807,66809,66811,66814,66820,66822,66824,66830,66832,66834,66836,66838],{},[898,66806,2783],{},[898,66808,1852],{},[2005,66810,2007],{},[2138,66812,66813],{},"0,04",[2133,66815,66816,66818],{},[898,66817,2797],{},[2138,66819,2182],{},[2005,66821,2234],{},[2138,66823,22551],{},[2133,66825,66826,66828],{},[898,66827,2797],{},[2138,66829,2140],{},[2005,66831,2104],{},[2138,66833,2871],{},[898,66835,2797],{},[2005,66837,2104],{},[2138,66839,2237],{},[902,66841,66842],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,66845,66847],{"className":66846},[886],[888,66848,66849],{"xmlns":890},[892,66850,66851,66859],{},[895,66852,66853,66855,66857],{},[898,66854,3946],{},[2005,66856,2007],{},[2138,66858,2360],{},[902,66860,66861],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,66864,66865,66867,66868,17583,66910,66944,66945,2713],{},[38,66866,22776],{}," Z (3.14): ",[883,66869,66871],{"className":66870},[886],[888,66872,66873],{"xmlns":890},[892,66874,66875,66907],{},[895,66876,66877,66879,66881,66883,66886,66892,66894,66897,66899,66901,66903,66905],{},[898,66878,2826],{},[898,66880,1852],{},[2005,66882,2007],{},[2138,66884,66885],{},"0,12",[2133,66887,66888,66890],{},[898,66889,2797],{},[2138,66891,2140],{},[2005,66893,2234],{},[2138,66895,66896],{},"1,8",[898,66898,2797],{},[2005,66900,2104],{},[2138,66902,2871],{},[2005,66904,2007],{},[2138,66906,2360],{},[902,66908,66909],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,66911,66913],{"className":66912},[886],[888,66914,66915],{"xmlns":890},[892,66916,66917,66941],{},[895,66918,66919,66921,66927,66929,66931,66933,66935,66937,66939],{},[2138,66920,66885],{},[2133,66922,66923,66925],{},[898,66924,2797],{},[2138,66926,2140],{},[2005,66928,2234],{},[2138,66930,66896],{},[898,66932,2797],{},[2005,66934,2104],{},[2138,66936,2244],{},[2005,66938,2007],{},[2138,66940,2336],{},[902,66942,66943],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,66946,66948],{"className":66947},[886],[888,66949,66950],{"xmlns":890},[892,66951,66952,66956],{},[895,66953,66954],{},[2138,66955,66885],{},[902,66957,66958],{"encoding":904},"0{,}12",[883,66960,66962],{"className":66961},[886],[888,66963,66964],{"xmlns":890,"display":28071},[892,66965,66966,67018],{},[895,66967,66968,66974,66976,66978,66980,66982,66984,66986,66988,66990,66992,66994,67000,67002,67004,67006,67008,67014,67016],{},[2133,66969,66970,66972],{},[898,66971,2797],{},[2138,66973,2140],{},[2005,66975,2234],{},[2138,66977,36249],{},[898,66979,2797],{},[2005,66981,2104],{},[2138,66983,3128],{},[2005,66985,2007],{},[2138,66987,2336],{},[2297,66989,3993],{},[2005,66991,3996],{},[2297,66993,3993],{},[2281,66995,66996,66998],{},[898,66997,2797],{},[2138,66999,2287],{},[2005,67001,2007],{},[2138,67003,2237],{},[2005,67005,2295],{"separator":2294},[2297,67007,3993],{},[2281,67009,67010,67012],{},[898,67011,2797],{},[2138,67013,2140],{},[2005,67015,2007],{},[2138,67017,19334],{},[902,67019,67020],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,67022,67023,67024,2713],{},"Dále ",[883,67025,67027],{"className":67026},[886],[888,67028,67029],{"xmlns":890},[892,67030,67031,67070],{},[895,67032,67033,67035,67045,67047,67049,67051,67057,67059,67061,67064,67066,67068],{},[898,67034,3946],{},[2133,67036,67037,67039],{},[898,67038,4003],{},[895,67040,67041,67043],{},[2005,67042,2387],{"mathvariant":2385},[2005,67044,2387],{"mathvariant":2385},[2005,67046,2007],{},[2005,67048,2234],{},[898,67050,2826],{},[2133,67052,67053,67055],{},[898,67054,1852],{},[2005,67056,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,67058,2007],{},[2005,67060,2234],{},[2138,67062,67063],{},"0,24",[898,67065,2797],{},[2005,67067,2104],{},[2138,67069,66896],{},[902,67071,67072],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,67074,67075,67125],{},[123,67076,67077,67121,67122,67124],{},[883,67078,67080],{"className":67079},[886],[888,67081,67082],{"xmlns":890},[892,67083,67084,67118],{},[895,67085,67086,67088,67098,67100,67102,67104,67106,67108,67110,67112,67114,67116],{},[898,67087,3946],{},[2133,67089,67090,67092],{},[898,67091,4003],{},[895,67093,67094,67096],{},[2005,67095,2387],{"mathvariant":2385},[2005,67097,2387],{"mathvariant":2385},[2005,67099,2014],{"stretchy":2013},[2138,67101,2237],{},[2005,67103,2020],{"stretchy":2013},[2005,67105,2007],{},[2138,67107,19327],{},[2005,67109,3416],{},[2138,67111,2336],{},[2297,67113,3993],{},[2005,67115,3996],{},[2297,67117,3993],{},[902,67119,67120],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,67123,3783],{}," zisku (minimalizace ztráty);",[123,67126,67127,67121,67173,67175],{},[883,67128,67130],{"className":67129},[886],[888,67131,67132],{"xmlns":890},[892,67133,67134,67170],{},[895,67135,67136,67138,67148,67150,67152,67154,67156,67158,67160,67162,67164,67166,67168],{},[898,67137,3946],{},[2133,67139,67140,67142],{},[898,67141,4003],{},[895,67143,67144,67146],{},[2005,67145,2387],{"mathvariant":2385},[2005,67147,2387],{"mathvariant":2385},[2005,67149,2014],{"stretchy":2013},[2138,67151,2871],{},[2005,67153,2020],{"stretchy":2013},[2005,67155,2007],{},[2005,67157,2234],{},[2138,67159,19327],{},[2005,67161,3455],{},[2138,67163,2336],{},[2297,67165,3993],{},[2005,67167,3996],{},[2297,67169,3993],{},[902,67171,67172],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,67174,3725],{}," zisku, avšak",[883,67177,67179],{"className":67178},[886],[888,67180,67181],{"xmlns":890,"display":28071},[892,67182,67183,67251],{},[895,67184,67185,67187,67189,67191,67193,67195,67197,67199,67201,67203,67205,67207,67209,67211,67213,67215,67217,67219,67221,67223,67225,67227,67229,67231,67233,67235,67237,67239,67241,67243,67245,67247,67249],{},[898,67186,3946],{},[898,67188,4003],{},[2005,67190,2014],{"stretchy":2013},[2138,67192,2871],{},[2005,67194,2020],{"stretchy":2013},[2005,67196,2007],{},[2138,67198,2360],{},[2005,67200,3185],{},[2138,67202,2871],{},[2005,67204,2234],{},[2005,67206,2014],{"stretchy":2013},[2138,67208,66813],{},[2005,67210,3185],{},[2138,67212,2287],{},[2297,67214,2995],{},[2138,67216,59087],{},[2005,67218,2234],{},[2138,67220,22551],{},[2005,67222,3185],{},[2138,67224,3098],{},[2005,67226,2104],{},[2138,67228,3098],{},[2005,67230,2104],{},[2138,67232,2237],{},[2005,67234,2020],{"stretchy":2013},[2005,67236,2007],{},[2138,67238,5217],{},[2005,67240,2234],{},[2138,67242,21186],{},[2005,67244,2007],{},[2005,67246,2234],{},[2138,67248,36249],{},[2005,67250,2295],{"separator":2294},[902,67252,67253],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,67255,67256,67257,1644],{},"tj. ztráta větší než ",[883,67258,67260],{"className":67259},[886],[888,67261,67262],{"xmlns":890},[892,67263,67264,67274],{},[895,67265,67266,67268,67270,67272],{},[898,67267,1876],{},[898,67269,1852],{},[2005,67271,2007],{},[2138,67273,2237],{},[902,67275,67276],{"encoding":904},"FC = 5",[724,67278,67279,67282,67283,67286,67287,1644],{},[38,67280,67281],{},"Závěr:"," firma by měla ",[38,67284,67285],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,67288,67290],{"className":67289},[886],[888,67291,67292],{"xmlns":890},[892,67293,67294,67304],{},[895,67295,67296,67298,67300,67302],{},[898,67297,1876],{},[898,67299,1852],{},[2005,67301,2007],{},[2138,67303,2237],{},[902,67305,67276],{"encoding":904},[115,67307,67309],{"id":67308},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,67311,67312,67313,67315,67316,67331,67332,67345,67346,67372,67373,67386,67387,67404,67405,2633,67422,67425,67426,67446,67447,67462,67463,2713],{},"Důležitým završením analýzy je konstrukce ",[38,67314,55280],{},". S nabízeným množstvím rostou mezní náklady ",[883,67317,67319],{"className":67318},[886],[888,67320,67321],{"xmlns":890},[892,67322,67323,67329],{},[895,67324,67325,67327],{},[898,67326,2826],{},[898,67328,1852],{},[902,67330,55297],{"encoding":904}," a tyto určují cenu ",[883,67333,67335],{"className":67334},[886],[888,67336,67337],{"xmlns":890},[892,67338,67339,67343],{},[895,67340,67341],{},[898,67342,3946],{},[902,67344,3946],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,67347,67349],{"className":67348},[886],[888,67350,67351],{"xmlns":890},[892,67352,67353,67369],{},[895,67354,67355,67357,67359,67361,67363,67365,67367],{},[898,67356,3946],{},[2005,67358,2007],{},[898,67360,2826],{},[898,67362,1852],{},[2005,67364,2014],{"stretchy":2013},[898,67366,2797],{},[2005,67368,2020],{"stretchy":2013},[902,67370,67371],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,67374,67376],{"className":67375},[886],[888,67377,67378],{"xmlns":890},[892,67379,67380,67384],{},[895,67381,67382],{},[898,67383,3946],{},[902,67385,3946],{"encoding":904}," však nemůže být nižší než ",[883,67388,67390],{"className":67389},[886],[888,67391,67392],{"xmlns":890},[892,67393,67394,67402],{},[895,67395,67396],{},[2133,67397,67398,67400],{},[898,67399,3946],{},[2005,67401,4360],{},[902,67403,4410],{"encoding":904}," odpovídající množství ",[883,67406,67408],{"className":67407},[886],[888,67409,67410],{"xmlns":890},[892,67411,67412,67420],{},[895,67413,67414],{},[2133,67415,67416,67418],{},[898,67417,2797],{},[2005,67419,4360],{},[902,67421,29849],{"encoding":904},[38,67423,67424],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,67427,67429],{"className":67428},[886],[888,67430,67431],{"xmlns":890},[892,67432,67433,67443],{},[895,67434,67435,67437],{},[2138,67436,2336],{},[2133,67438,67439,67441],{},[898,67440,2797],{},[2005,67442,4360],{},[902,67444,67445],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,67448,67450],{"className":67449},[886],[888,67451,67452],{"xmlns":890},[892,67453,67454,67460],{},[895,67455,67456,67458],{},[898,67457,2826],{},[898,67459,1852],{},[902,67461,55297],{"encoding":904}," nad bodem ",[883,67464,67466],{"className":67465},[886],[888,67467,67468],{"xmlns":890},[892,67469,67470,67474],{},[895,67471,67472],{},[898,67473,1836],{},[902,67475,1836],{"encoding":904},[883,67477,67479],{"className":67478},[886],[888,67480,67481],{"xmlns":890,"display":28071},[892,67482,67483,67590],{},[20760,67484,67485],{"width":28076},[20765,67486,67487,67489,67583,67585],{},[20768,67488],{"width":28081},[20768,67490,67491],{},[895,67492,67493,67495,67497,67499,67501,67503,67505,67507],{},[898,67494,3946],{},[2005,67496,2007],{},[898,67498,8679],{},[2005,67500,2014],{"stretchy":2013},[898,67502,2797],{},[2005,67504,2020],{"stretchy":2013},[2005,67506,2007],{},[895,67508,67509,67512],{},[2005,67510,67511],{"fence":2294},"{",[20760,67513,67516,67555],{"rowspacing":67514,"columnalign":67515,"columnspacing":15290},"0.36em","left left",[20765,67517,67518,67534],{},[20768,67519,67520],{},[2334,67521,67522],{"scriptlevel":2336,"displaystyle":2013},[895,67523,67524,67526,67528,67530,67532],{},[898,67525,2826],{},[898,67527,1852],{},[2005,67529,2014],{"stretchy":2013},[898,67531,2797],{},[2005,67533,2020],{"stretchy":2013},[20768,67535,67536],{},[2334,67537,67538],{"scriptlevel":2336,"displaystyle":2013},[895,67539,67540,67543,67545,67547,67553],{},[2297,67541,67542],{},"pro ",[898,67544,2797],{},[2005,67546,4491],{},[2133,67548,67549,67551],{},[898,67550,2797],{},[2005,67552,4360],{},[2005,67554,2295],{"separator":2294},[20765,67556,67557,67563],{},[20768,67558,67559],{},[2334,67560,67561],{"scriptlevel":2336,"displaystyle":2013},[2138,67562,2336],{},[20768,67564,67565],{},[2334,67566,67567],{"scriptlevel":2336,"displaystyle":2013},[895,67568,67569,67571,67573,67575,67581],{},[2297,67570,67542],{},[898,67572,2797],{},[2005,67574,3455],{},[2133,67576,67577,67579],{},[898,67578,2797],{},[2005,67580,4360],{},[2005,67582,2295],{"separator":2294},[20768,67584],{"width":28081},[20768,67586,67587],{},[2297,67588,67589],{},"(3.15)",[902,67591,67592],{"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}",[724,67594,4316,67595,67612,67613,67630,67631,41504,67661,67664],{},[883,67596,67598],{"className":67597},[886],[888,67599,67600],{"xmlns":890},[892,67601,67602,67610],{},[895,67603,67604],{},[2133,67605,67606,67608],{},[898,67607,2797],{},[2005,67609,4360],{},[902,67611,29849],{"encoding":904}," je bod minima ",[883,67614,67616],{"className":67615},[886],[888,67617,67618],{"xmlns":890},[892,67619,67620,67628],{},[895,67621,67622,67624,67626],{},[898,67623,1836],{},[898,67625,40344],{},[898,67627,1852],{},[902,67629,55316],{"encoding":904},". Bod ",[883,67632,67634],{"className":67633},[886],[888,67635,67636],{"xmlns":890},[892,67637,67638,67658],{},[895,67639,67640,67642,67648,67650,67656],{},[2005,67641,2014],{"stretchy":2013},[2133,67643,67644,67646],{},[898,67645,2797],{},[2005,67647,4360],{},[2005,67649,2295],{"separator":2294},[2133,67651,67652,67654],{},[898,67653,3946],{},[2005,67655,4360],{},[2005,67657,2020],{"stretchy":2013},[902,67659,67660],{"encoding":904},"(Q^*, P^*)",[38,67662,67663],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[3876,67666,67667,67672],{},[724,67668,67669,67671],{},[883,67670,4578],{}," Postup — jak odvodit nabídku firmy",[152,67673,67674,67723,67818,67873,67944],{},[123,67675,67676,67677,3894,67699,1644],{},"Ze zadaných nákladů určete ",[883,67678,67680],{"className":67679},[886],[888,67681,67682],{"xmlns":890},[892,67683,67684,67696],{},[895,67685,67686,67688,67690,67692,67694],{},[898,67687,2826],{},[898,67689,1852],{},[2005,67691,2014],{"stretchy":2013},[898,67693,2797],{},[2005,67695,2020],{"stretchy":2013},[902,67697,67698],{"encoding":904},"MC(Q)",[883,67700,67702],{"className":67701},[886],[888,67703,67704],{"xmlns":890},[892,67705,67706,67720],{},[895,67707,67708,67710,67712,67714,67716,67718],{},[898,67709,1836],{},[898,67711,40344],{},[898,67713,1852],{},[2005,67715,2014],{"stretchy":2013},[898,67717,2797],{},[2005,67719,2020],{"stretchy":2013},[902,67721,67722],{"encoding":904},"AVC(Q)",[123,67724,67725,67726,67743,67744,67761,67762,67794,67795,3927],{},"Najděte ",[883,67727,67729],{"className":67728},[886],[888,67730,67731],{"xmlns":890},[892,67732,67733,67741],{},[895,67734,67735],{},[2133,67736,67737,67739],{},[898,67738,2797],{},[2005,67740,4360],{},[902,67742,29849],{"encoding":904}," jako bod minima ",[883,67745,67747],{"className":67746},[886],[888,67748,67749],{"xmlns":890},[892,67750,67751,67759],{},[895,67752,67753,67755,67757],{},[898,67754,1836],{},[898,67756,40344],{},[898,67758,1852],{},[902,67760,55316],{"encoding":904}," (řešením ",[883,67763,67765],{"className":67764},[886],[888,67766,67767],{"xmlns":890},[892,67768,67769,67791],{},[895,67770,67771,67773,67775,67781,67783,67785,67787,67789],{},[898,67772,1836],{},[898,67774,40344],{},[2133,67776,67777,67779],{},[898,67778,1852],{},[2005,67780,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,67782,2014],{"stretchy":2013},[898,67784,2797],{},[2005,67786,2020],{"stretchy":2013},[2005,67788,2007],{},[2138,67790,2336],{},[902,67792,67793],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,67796,67798],{"className":67797},[886],[888,67799,67800],{"xmlns":890},[892,67801,67802,67816],{},[895,67803,67804,67806,67808,67810,67812,67814],{},[898,67805,1836],{},[898,67807,40344],{},[898,67809,1852],{},[2005,67811,2007],{},[898,67813,2826],{},[898,67815,1852],{},[902,67817,55253],{"encoding":904},[123,67819,65726,67820,67872],{},[883,67821,67823],{"className":67822},[886],[888,67824,67825],{"xmlns":890},[892,67826,67827,67869],{},[895,67828,67829,67835,67837,67839,67841,67843,67849,67851,67853,67855,67857,67859,67861,67867],{},[2133,67830,67831,67833],{},[898,67832,3946],{},[2005,67834,4360],{},[2005,67836,2007],{},[898,67838,2826],{},[898,67840,1852],{},[2005,67842,2014],{"stretchy":2013},[2133,67844,67845,67847],{},[898,67846,2797],{},[2005,67848,4360],{},[2005,67850,2020],{"stretchy":2013},[2005,67852,2007],{},[898,67854,1836],{},[898,67856,40344],{},[898,67858,1852],{},[2005,67860,2014],{"stretchy":2013},[2133,67862,67863,67865],{},[898,67864,2797],{},[2005,67866,4360],{},[2005,67868,2020],{"stretchy":2013},[902,67870,67871],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,67874,67875,67876,6479,67908,67930,67931,1644],{},"Zapište nabídku: ",[883,67877,67879],{"className":67878},[886],[888,67880,67881],{"xmlns":890},[892,67882,67883,67905],{},[895,67884,67885,67887,67889,67891,67893,67895,67897,67899,67901,67903],{},[898,67886,8679],{},[2005,67888,2014],{"stretchy":2013},[898,67890,2797],{},[2005,67892,2020],{"stretchy":2013},[2005,67894,2007],{},[898,67896,2826],{},[898,67898,1852],{},[2005,67900,2014],{"stretchy":2013},[898,67902,2797],{},[2005,67904,2020],{"stretchy":2013},[902,67906,67907],{"encoding":904},"S(Q) = MC(Q)",[883,67909,67911],{"className":67910},[886],[888,67912,67913],{"xmlns":890},[892,67914,67915,67927],{},[895,67916,67917,67919,67921],{},[898,67918,2797],{},[2005,67920,4491],{},[2133,67922,67923,67925],{},[898,67924,2797],{},[2005,67926,4360],{},[902,67928,67929],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,67932,67934],{"className":67933},[886],[888,67935,67936],{"xmlns":890},[892,67937,67938,67942],{},[895,67939,67940],{},[2138,67941,2336],{},[902,67943,2336],{"encoding":904},[123,67945,67946,67947,67979],{},"V případě potřeby vyjádřete inverzi ",[883,67948,67950],{"className":67949},[886],[888,67951,67952],{"xmlns":890},[892,67953,67954,67976],{},[895,67955,67956,67958,67960,67970,67972,67974],{},[898,67957,2797],{},[2005,67959,2007],{},[2133,67961,67962,67964],{},[898,67963,8679],{},[895,67965,67966,67968],{},[2005,67967,2234],{},[2138,67969,2287],{},[2005,67971,2014],{"stretchy":2013},[898,67973,3946],{},[2005,67975,2020],{"stretchy":2013},[902,67977,67978],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,67981,67982],{},[614,67983,67984,67985,1343,68000,3894,68017,29206,68032,68045,68046,68071,68072,68085,68086,68103,68104,68121,68122,68139],{},"Obrázek 3.14: Křivky ",[883,67986,67988],{"className":67987},[886],[888,67989,67990],{"xmlns":890},[892,67991,67992,67998],{},[895,67993,67994,67996],{},[898,67995,1836],{},[898,67997,1852],{},[902,67999,55565],{"encoding":904},[883,68001,68003],{"className":68002},[886],[888,68004,68005],{"xmlns":890},[892,68006,68007,68015],{},[895,68008,68009,68011,68013],{},[898,68010,1836],{},[898,68012,40344],{},[898,68014,1852],{},[902,68016,55316],{"encoding":904},[883,68018,68020],{"className":68019},[886],[888,68021,68022],{"xmlns":890},[892,68023,68024,68030],{},[895,68025,68026,68028],{},[898,68027,2826],{},[898,68029,1852],{},[902,68031,55297],{"encoding":904},[883,68033,68035],{"className":68034},[886],[888,68036,68037],{"xmlns":890},[892,68038,68039,68043],{},[895,68040,68041],{},[898,68042,900],{},[902,68044,900],{"encoding":904},"; křivka nabídky ",[883,68047,68049],{"className":68048},[886],[888,68050,68051],{"xmlns":890},[892,68052,68053,68069],{},[895,68054,68055,68057,68059,68061,68063,68065,68067],{},[898,68056,3946],{},[2005,68058,2007],{},[898,68060,2826],{},[898,68062,1852],{},[2005,68064,2014],{"stretchy":2013},[898,68066,2797],{},[2005,68068,2020],{"stretchy":2013},[902,68070,67371],{"encoding":904}," začíná v bodě ",[883,68073,68075],{"className":68074},[886],[888,68076,68077],{"xmlns":890},[892,68078,68079,68083],{},[895,68080,68081],{},[898,68082,1836],{},[902,68084,1836],{"encoding":904}," odpovídajícím minimu ",[883,68087,68089],{"className":68088},[886],[888,68090,68091],{"xmlns":890},[892,68092,68093,68101],{},[895,68094,68095,68097,68099],{},[898,68096,1836],{},[898,68098,40344],{},[898,68100,1852],{},[902,68102,55316],{"encoding":904}," při ceně ",[883,68105,68107],{"className":68106},[886],[888,68108,68109],{"xmlns":890},[892,68110,68111,68119],{},[895,68112,68113],{},[2133,68114,68115,68117],{},[898,68116,3946],{},[2005,68118,4360],{},[902,68120,4410],{"encoding":904}," (minimální cena nabídky); pod ",[883,68123,68125],{"className":68124},[886],[888,68126,68127],{"xmlns":890},[892,68128,68129,68137],{},[895,68130,68131],{},[2133,68132,68133,68135],{},[898,68134,2797],{},[2005,68136,4360],{},[902,68138,29849],{"encoding":904}," je nabídka nulová.",[37353,68141,68143],{"id":68142},"příklad-312","Příklad 3.12",[724,68145,68146,57527,68148,68194],{},[38,68147,55992],{},[883,68149,68151],{"className":68150},[886],[888,68152,68153],{"xmlns":890},[892,68154,68155,68191],{},[895,68156,68157,68159,68161,68163,68165,68171,68173,68175,68181,68183,68185,68187,68189],{},[898,68158,2783],{},[898,68160,1852],{},[2005,68162,2007],{},[2138,68164,2802],{},[2133,68166,68167,68169],{},[898,68168,2797],{},[2138,68170,2182],{},[2005,68172,2234],{},[2138,68174,2140],{},[2133,68176,68177,68179],{},[898,68178,2797],{},[2138,68180,2140],{},[2005,68182,2104],{},[2138,68184,36249],{},[898,68186,2797],{},[2005,68188,2104],{},[2138,68190,2871],{},[902,68192,68193],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,68196,68197,2212,68199,68236,68237,2713],{},[38,68198,22776],{},[883,68200,68202],{"className":68201},[886],[888,68203,68204],{"xmlns":890},[892,68205,68206,68233],{},[895,68207,68208,68210,68212,68214,68217,68223,68225,68227,68229,68231],{},[898,68209,2826],{},[898,68211,1852],{},[2005,68213,2007],{},[2138,68215,68216],{},"0,3",[2133,68218,68219,68221],{},[898,68220,2797],{},[2138,68222,2140],{},[2005,68224,2234],{},[2138,68226,2360],{},[898,68228,2797],{},[2005,68230,2104],{},[2138,68232,36249],{},[902,68234,68235],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,68238,68240],{"className":68239},[886],[888,68241,68242],{"xmlns":890},[892,68243,68244,68254],{},[895,68245,68246,68248,68250,68252],{},[898,68247,3946],{},[2005,68249,2007],{},[898,68251,2826],{},[898,68253,1852],{},[902,68255,68256],{"encoding":904},"P = MC",[883,68258,68260],{"className":68259},[886],[888,68261,68262],{"xmlns":890,"display":28071},[892,68263,68264,68289],{},[895,68265,68266,68268,68270,68272,68278,68280,68282,68284,68286],{},[898,68267,3946],{},[2005,68269,2007],{},[2138,68271,68216],{},[2133,68273,68274,68276],{},[898,68275,2797],{},[2138,68277,2140],{},[2005,68279,2234],{},[2138,68281,2360],{},[898,68283,2797],{},[2005,68285,2104],{},[2138,68287,68288],{},"15.",[902,68290,68291],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,68293,68294,68295,5388,68308,68321],{},"Vyjádření ",[883,68296,68298],{"className":68297},[886],[888,68299,68300],{"xmlns":890},[892,68301,68302,68306],{},[895,68303,68304],{},[898,68305,2797],{},[902,68307,2797],{"encoding":904},[883,68309,68311],{"className":68310},[886],[888,68312,68313],{"xmlns":890},[892,68314,68315,68319],{},[895,68316,68317],{},[898,68318,3946],{},[902,68320,3946],{"encoding":904}," doplněním na čtverec:",[883,68323,68325],{"className":68324},[886],[888,68326,68327],{"xmlns":890,"display":28071},[892,68328,68329,68419],{},[895,68330,68331,68333,68335,68337,68375,68377,68379,68401,68403,68417],{},[898,68332,3946],{},[2005,68334,2007],{},[2138,68336,68216],{},[895,68338,68339,68341,68363,68365,68373],{},[2005,68340,2014],{"fence":2294},[2133,68342,68343,68361],{},[895,68344,68345,68347,68349,68351,68359],{},[2005,68346,2014],{"fence":2294},[898,68348,2797],{},[2005,68350,2234],{},[2334,68352,68353],{"scriptlevel":2336,"displaystyle":2013},[2338,68354,68355,68357],{},[2138,68356,9041],{},[2138,68358,2182],{},[2005,68360,2020],{"fence":2294},[2138,68362,2140],{},[2005,68364,2104],{},[2334,68366,68367],{"scriptlevel":2336,"displaystyle":2013},[2338,68368,68369,68371],{},[2138,68370,3128],{},[2138,68372,4008],{},[2005,68374,2020],{"fence":2294},[2005,68376,2295],{"separator":2294},[5884,68378],{"width":5886},[2133,68380,68381,68399],{},[895,68382,68383,68385,68387,68389,68397],{},[2005,68384,2014],{"fence":2294},[898,68386,2797],{},[2005,68388,2234],{},[2334,68390,68391],{"scriptlevel":2336,"displaystyle":2013},[2338,68392,68393,68395],{},[2138,68394,9041],{},[2138,68396,2182],{},[2005,68398,2020],{"fence":2294},[2138,68400,2140],{},[2005,68402,2007],{},[2338,68404,68405,68415],{},[895,68406,68407,68409,68411,68413],{},[2138,68408,38024],{},[898,68410,3946],{},[2005,68412,2234],{},[2138,68414,3128],{},[2138,68416,4008],{},[2005,68418,2295],{"separator":2294},[902,68420,68421],{"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},",[883,68423,68425],{"className":68424},[886],[888,68426,68427],{"xmlns":890,"display":28071},[892,68428,68429,68461],{},[895,68430,68431,68433,68435,68441,68443,68459],{},[898,68432,2797],{},[2005,68434,2007],{},[2338,68436,68437,68439],{},[2138,68438,9041],{},[2138,68440,2182],{},[2005,68442,2104],{},[2338,68444,68445,68457],{},[8123,68446,68447],{},[895,68448,68449,68451,68453,68455],{},[2138,68450,38024],{},[898,68452,3946],{},[2005,68454,2234],{},[2138,68456,3128],{},[2138,68458,2182],{},[898,68460,1644],{"mathvariant":2385},[902,68462,68463],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,68465,67023,68466,1343,68504,1343,68552,68586,68587,1644],{},[883,68467,68469],{"className":68468},[886],[888,68470,68471],{"xmlns":890},[892,68472,68473,68501],{},[895,68474,68475,68477,68479,68481,68483,68485,68491,68493,68495,68497,68499],{},[898,68476,1836],{},[898,68478,40344],{},[898,68480,1852],{},[2005,68482,2007],{},[2138,68484,2802],{},[2133,68486,68487,68489],{},[898,68488,2797],{},[2138,68490,2140],{},[2005,68492,2234],{},[2138,68494,2140],{},[898,68496,2797],{},[2005,68498,2104],{},[2138,68500,36249],{},[902,68502,68503],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,68505,68507],{"className":68506},[886],[888,68508,68509],{"xmlns":890},[892,68510,68511,68549],{},[895,68512,68513,68515,68517,68523,68525,68527,68529,68531,68533,68535,68537,68539,68545,68547],{},[898,68514,1836],{},[898,68516,40344],{},[2133,68518,68519,68521],{},[898,68520,1852],{},[2005,68522,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,68524,2007],{},[2138,68526,2847],{},[898,68528,2797],{},[2005,68530,2234],{},[2138,68532,2140],{},[2005,68534,2007],{},[2138,68536,2336],{},[2005,68538,3996],{},[2133,68540,68541,68543],{},[898,68542,2797],{},[2005,68544,4360],{},[2005,68546,2007],{},[2138,68548,2871],{},[902,68550,68551],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,68553,68555],{"className":68554},[886],[888,68556,68557],{"xmlns":890},[892,68558,68559,68583],{},[895,68560,68561,68563,68565,68575,68577,68579,68581],{},[898,68562,1836],{},[898,68564,40344],{},[2133,68566,68567,68569],{},[898,68568,1852],{},[895,68570,68571,68573],{},[2005,68572,2387],{"mathvariant":2385},[2005,68574,2387],{"mathvariant":2385},[2005,68576,2007],{},[2138,68578,2847],{},[2005,68580,3416],{},[2138,68582,2336],{},[902,68584,68585],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,68588,68590],{"className":68589},[886],[888,68591,68592],{"xmlns":890},[892,68593,68594,68630],{},[895,68595,68596,68602,68604,68606,68608,68610,68612,68614,68616,68618,68620,68622,68624,68626,68628],{},[2133,68597,68598,68600],{},[898,68599,3946],{},[2005,68601,4360],{},[2005,68603,2007],{},[898,68605,2826],{},[898,68607,1852],{},[2005,68609,2014],{"stretchy":2013},[2138,68611,2871],{},[2005,68613,2020],{"stretchy":2013},[2005,68615,2007],{},[2138,68617,38024],{},[2005,68619,2234],{},[2138,68621,5217],{},[2005,68623,2104],{},[2138,68625,36249],{},[2005,68627,2007],{},[2138,68629,2237],{},[902,68631,68632],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,68634,68635],{},[38,68636,68637],{},"Závěr.",[883,68639,68641],{"className":68640},[886],[888,68642,68643],{"xmlns":890,"display":28071},[892,68644,68645,68731],{},[895,68646,68647,68649,68651,68653,68655,68657,68659,68661],{},[898,68648,3946],{},[2005,68650,2007],{},[898,68652,8679],{},[2005,68654,2014],{"stretchy":2013},[898,68656,2797],{},[2005,68658,2020],{"stretchy":2013},[2005,68660,2007],{},[895,68662,68663,68665],{},[2005,68664,67511],{"fence":2294},[20760,68666,68667,68709],{"rowspacing":67514,"columnalign":67515,"columnspacing":15290},[20765,68668,68669,68693],{},[20768,68670,68671],{},[2334,68672,68673],{"scriptlevel":2336,"displaystyle":2013},[895,68674,68675,68677,68683,68685,68687,68689,68691],{},[2138,68676,68216],{},[2133,68678,68679,68681],{},[898,68680,2797],{},[2138,68682,2140],{},[2005,68684,2234],{},[2138,68686,2360],{},[898,68688,2797],{},[2005,68690,2104],{},[2138,68692,36249],{},[20768,68694,68695],{},[2334,68696,68697],{"scriptlevel":2336,"displaystyle":2013},[895,68698,68699,68701,68703,68705,68707],{},[2297,68700,67542],{},[898,68702,2797],{},[2005,68704,4491],{},[2138,68706,2871],{},[2005,68708,2295],{"separator":2294},[20765,68710,68711,68717],{},[20768,68712,68713],{},[2334,68714,68715],{"scriptlevel":2336,"displaystyle":2013},[2138,68716,2336],{},[20768,68718,68719],{},[2334,68720,68721],{"scriptlevel":2336,"displaystyle":2013},[895,68722,68723,68725,68727,68729],{},[2297,68724,67542],{},[898,68726,2797],{},[2005,68728,3455],{},[2138,68730,19334],{},[902,68732,68733],{"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}",[724,68735,68736],{},[614,68737,68738,68739,68754,68755,1644],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,68740,68742],{"className":68741},[886],[888,68743,68744],{"xmlns":890},[892,68745,68746,68752],{},[895,68747,68748,68750],{},[898,68749,2826],{},[898,68751,1852],{},[902,68753,55297],{"encoding":904}," ležící nad minimem ",[883,68756,68758],{"className":68757},[886],[888,68759,68760],{"xmlns":890},[892,68761,68762,68770],{},[895,68763,68764,68766,68768],{},[898,68765,1836],{},[898,68767,40344],{},[898,68769,1852],{},[902,68771,55316],{"encoding":904},[115,68773,68775],{"id":68774},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,68777,68778,68779,68783,68784,68799,68800,68820,68821,3894,68824,68827,68828,68830,68831,19951,68853,68855,68856,3894,68858,58731,68861,2212,68864,41819,68879,68894],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,68780,68782],{"className":68781,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,68785,68787],{"className":68786},[886],[888,68788,68789],{"xmlns":890},[892,68790,68791,68797],{},[895,68792,68793,68795],{},[898,68794,2783],{},[898,68796,4003],{},[902,68798,4103],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,68801,68803],{"className":68802},[886],[888,68804,68805],{"xmlns":890},[892,68806,68807,68817],{},[895,68808,68809,68811,68813,68815],{},[898,68810,2783],{},[898,68812,4003],{},[898,68814,4680],{"mathvariant":2385},[898,68816,2797],{},[902,68818,68819],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,68822,68823],{},"fixních",[38,68825,68826],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,68829,64330],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,68832,68834],{"className":68833},[886],[888,68835,68836],{"xmlns":890},[892,68837,68838,68850],{},[895,68839,68840,68842,68844,68846,68848],{},[898,68841,2783],{},[898,68843,4003],{},[2005,68845,2234],{},[898,68847,2783],{},[898,68849,1852],{},[902,68851,68852],{"encoding":904},"TR - TC",[38,68854,55177],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,68857,56489],{},[38,68859,68860],{},"mezní náklady",[207,68862,1145],{"className":68863,"dataFsResolvedFilePath":764,"href":765},[210],[883,68865,68867],{"className":68866},[886],[888,68868,68869],{"xmlns":890},[892,68870,68871,68877],{},[895,68872,68873,68875],{},[898,68874,2783],{},[898,68876,4003],{},[902,68878,4103],{"encoding":904},[883,68880,68882],{"className":68881},[886],[888,68883,68884],{"xmlns":890},[892,68885,68886,68892],{},[895,68887,68888,68890],{},[898,68889,2783],{},[898,68891,1852],{},[902,68893,3251],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,68896,68897,68959,69025,69087],{},[123,68898,68899,68902,68903,10399,68918,1644],{},[38,68900,68901],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,68904,68906],{"className":68905},[886],[888,68907,68908],{"xmlns":890},[892,68909,68910,68916],{},[895,68911,68912,68914],{},[898,68913,1836],{},[898,68915,1852],{},[902,68917,55565],{"encoding":904},[883,68919,68921],{"className":68920},[886],[888,68922,68923],{"xmlns":890},[892,68924,68925,68957],{},[895,68926,68927,68929,68931,68933,68939,68941,68943,68945,68947,68949,68955],{},[898,68928,1836],{},[898,68930,1852],{},[2005,68932,2014],{"stretchy":2013},[2281,68934,68935,68937],{},[898,68936,2797],{},[2138,68938,2336],{},[2005,68940,2020],{"stretchy":2013},[2005,68942,2007],{},[898,68944,2826],{},[898,68946,1852],{},[2005,68948,2014],{"stretchy":2013},[2281,68950,68951,68953],{},[898,68952,2797],{},[2138,68954,2336],{},[2005,68956,2020],{"stretchy":2013},[902,68958,62574],{"encoding":904},[123,68960,68961,68902,68964,10399,68981,1644],{},[38,68962,68963],{},"Princip minimalizace průměrných variabilních nákladů:",[883,68965,68967],{"className":68966},[886],[888,68968,68969],{"xmlns":890},[892,68970,68971,68979],{},[895,68972,68973,68975,68977],{},[898,68974,1836],{},[898,68976,40344],{},[898,68978,1852],{},[902,68980,55316],{"encoding":904},[883,68982,68984],{"className":68983},[886],[888,68985,68986],{"xmlns":890},[892,68987,68988,69022],{},[895,68989,68990,68992,68994,68996,68998,69004,69006,69008,69010,69012,69014,69020],{},[898,68991,1836],{},[898,68993,40344],{},[898,68995,1852],{},[2005,68997,2014],{"stretchy":2013},[2281,68999,69000,69002],{},[898,69001,2797],{},[2138,69003,2336],{},[2005,69005,2020],{"stretchy":2013},[2005,69007,2007],{},[898,69009,2826],{},[898,69011,1852],{},[2005,69013,2014],{"stretchy":2013},[2281,69015,69016,69018],{},[898,69017,2797],{},[2138,69019,2336],{},[2005,69021,2020],{"stretchy":2013},[902,69023,69024],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,69026,69027,69030,69031,10399,69046,1644],{},[38,69028,69029],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,69032,69034],{"className":69033},[886],[888,69035,69036],{"xmlns":890},[892,69037,69038,69044],{},[895,69039,69040,69042],{},[898,69041,3946],{},[898,69043,4003],{},[902,69045,63484],{"encoding":904},[883,69047,69049],{"className":69048},[886],[888,69050,69051],{"xmlns":890},[892,69052,69053,69085],{},[895,69054,69055,69057,69059,69061,69067,69069,69071,69073,69075,69077,69083],{},[898,69056,2826],{},[898,69058,4003],{},[2005,69060,2014],{"stretchy":2013},[2281,69062,69063,69065],{},[898,69064,2797],{},[2138,69066,2336],{},[2005,69068,2020],{"stretchy":2013},[2005,69070,2007],{},[898,69072,2826],{},[898,69074,1852],{},[2005,69076,2014],{"stretchy":2013},[2281,69078,69079,69081],{},[898,69080,2797],{},[2138,69082,2336],{},[2005,69084,2020],{"stretchy":2013},[902,69086,65650],{"encoding":904},[123,69088,69089,2212,69092,6479,69128,67930,69149,21600,69162,67612,69179,1644],{},[38,69090,69091],{},"Funkce nabídky firmy:",[883,69093,69095],{"className":69094},[886],[888,69096,69097],{"xmlns":890},[892,69098,69099,69125],{},[895,69100,69101,69103,69105,69107,69109,69111,69113,69115,69117,69119,69121,69123],{},[898,69102,3946],{},[2005,69104,2007],{},[898,69106,8679],{},[2005,69108,2014],{"stretchy":2013},[898,69110,2797],{},[2005,69112,2020],{"stretchy":2013},[2005,69114,2007],{},[898,69116,2826],{},[898,69118,1852],{},[2005,69120,2014],{"stretchy":2013},[898,69122,2797],{},[2005,69124,2020],{"stretchy":2013},[902,69126,69127],{"encoding":904},"P = S(Q) = MC(Q)",[883,69129,69131],{"className":69130},[886],[888,69132,69133],{"xmlns":890},[892,69134,69135,69147],{},[895,69136,69137,69139,69141],{},[898,69138,2797],{},[2005,69140,4491],{},[2133,69142,69143,69145],{},[898,69144,2797],{},[2005,69146,4360],{},[902,69148,67929],{"encoding":904},[883,69150,69152],{"className":69151},[886],[888,69153,69154],{"xmlns":890},[892,69155,69156,69160],{},[895,69157,69158],{},[2138,69159,2336],{},[902,69161,2336],{"encoding":904},[883,69163,69165],{"className":69164},[886],[888,69166,69167],{"xmlns":890},[892,69168,69169,69177],{},[895,69170,69171],{},[2133,69172,69173,69175],{},[898,69174,2797],{},[2005,69176,4360],{},[902,69178,29849],{"encoding":904},[883,69180,69182],{"className":69181},[886],[888,69183,69184],{"xmlns":890},[892,69185,69186,69194],{},[895,69187,69188,69190,69192],{},[898,69189,1836],{},[898,69191,40344],{},[898,69193,1852],{},[902,69195,55316],{"encoding":904},[115,69197,49887],{"id":49886},[152,69199,69200,69203,69206,69209,69212,69215,69218,69221,69224,69227,69230],{},[123,69201,69202],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,69204,69205],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,69207,69208],{},"Jak se vypočte mezní příjem a co udává?",[123,69210,69211],{},"Z jakých složek se skládají celkové náklady?",[123,69213,69214],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,69216,69217],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,69219,69220],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,69222,69223],{},"Jak se vypočte zisk?",[123,69225,69226],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,69228,69229],{},"Co jsou body zvratu? Jak se najdou?",[123,69231,69232],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,69234,69236],{"id":69235},"úlohy-31328","Úlohy 3.1–3.28",[198,69238,69240],{"id":69239},"příjem-3135","Příjem (3.1–3.5)",[724,69242,69243,45431,69246,69274,69275,69290,69291,69306,69307,69322,69323,1343,69338,1343,69353,69368],{},[38,69244,69245],{},"3.1",[883,69247,69249],{"className":69248},[886],[888,69250,69251],{"xmlns":890},[892,69252,69253,69271],{},[895,69254,69255,69257,69259,69261,69263,69265,69267,69269],{},[898,69256,3946],{},[2005,69258,2007],{},[898,69260,1860],{},[2005,69262,2014],{"stretchy":2013},[898,69264,2797],{},[2005,69266,2020],{"stretchy":2013},[2005,69268,2007],{},[2138,69270,3098],{},[902,69272,69273],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,69276,69278],{"className":69277},[886],[888,69279,69280],{"xmlns":890},[892,69281,69282,69288],{},[895,69283,69284,69286],{},[898,69285,2783],{},[898,69287,4003],{},[902,69289,4103],{"encoding":904},", průměrný příjem ",[883,69292,69294],{"className":69293},[886],[888,69295,69296],{"xmlns":890},[892,69297,69298,69304],{},[895,69299,69300,69302],{},[898,69301,1836],{},[898,69303,4003],{},[902,69305,55450],{"encoding":904}," a mezní příjem ",[883,69308,69310],{"className":69309},[886],[888,69311,69312],{"xmlns":890},[892,69313,69314,69320],{},[895,69315,69316,69318],{},[898,69317,2826],{},[898,69319,4003],{},[902,69321,6640],{"encoding":904},". (c) Vypočtěte ",[883,69324,69326],{"className":69325},[886],[888,69327,69328],{"xmlns":890},[892,69329,69330,69336],{},[895,69331,69332,69334],{},[898,69333,2783],{},[898,69335,4003],{},[902,69337,4103],{"encoding":904},[883,69339,69341],{"className":69340},[886],[888,69342,69343],{"xmlns":890},[892,69344,69345,69351],{},[895,69346,69347,69349],{},[898,69348,1836],{},[898,69350,4003],{},[902,69352,55450],{"encoding":904},[883,69354,69356],{"className":69355},[886],[888,69357,69358],{"xmlns":890},[892,69359,69360,69366],{},[895,69361,69362,69364],{},[898,69363,2826],{},[898,69365,4003],{},[902,69367,6640],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69370,69371,45431,69374,69274,69410,69290,69425,69306,69440,69322,69455,1343,69470,1343,69485,69500],{},[38,69372,69373],{},"3.2",[883,69375,69377],{"className":69376},[886],[888,69378,69379],{"xmlns":890},[892,69380,69381,69407],{},[895,69382,69383,69385,69387,69389,69391,69393,69395,69397,69399,69401,69403,69405],{},[898,69384,3946],{},[2005,69386,2007],{},[898,69388,1860],{},[2005,69390,2014],{"stretchy":2013},[898,69392,2797],{},[2005,69394,2020],{"stretchy":2013},[2005,69396,2007],{},[2005,69398,2234],{},[2138,69400,5015],{},[898,69402,2797],{},[2005,69404,2104],{},[2138,69406,9041],{},[902,69408,69409],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,69411,69413],{"className":69412},[886],[888,69414,69415],{"xmlns":890},[892,69416,69417,69423],{},[895,69418,69419,69421],{},[898,69420,2783],{},[898,69422,4003],{},[902,69424,4103],{"encoding":904},[883,69426,69428],{"className":69427},[886],[888,69429,69430],{"xmlns":890},[892,69431,69432,69438],{},[895,69433,69434,69436],{},[898,69435,1836],{},[898,69437,4003],{},[902,69439,55450],{"encoding":904},[883,69441,69443],{"className":69442},[886],[888,69444,69445],{"xmlns":890},[892,69446,69447,69453],{},[895,69448,69449,69451],{},[898,69450,2826],{},[898,69452,4003],{},[902,69454,6640],{"encoding":904},[883,69456,69458],{"className":69457},[886],[888,69459,69460],{"xmlns":890},[892,69461,69462,69468],{},[895,69463,69464,69466],{},[898,69465,2783],{},[898,69467,4003],{},[902,69469,4103],{"encoding":904},[883,69471,69473],{"className":69472},[886],[888,69474,69475],{"xmlns":890},[892,69476,69477,69483],{},[895,69478,69479,69481],{},[898,69480,1836],{},[898,69482,4003],{},[902,69484,55450],{"encoding":904},[883,69486,69488],{"className":69487},[886],[888,69489,69490],{"xmlns":890},[892,69491,69492,69498],{},[895,69493,69494,69496],{},[898,69495,2826],{},[898,69497,4003],{},[902,69499,6640],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,69502,69503,45431,69506,69543,69544,69290,69559,69306,69574,69589,69590,6479,69605,69631,69632,69647,69648,1343,69663,6479,69678,69631,69703,69718,69719,69732,69733,69748,69749,69764,69765,1343,69778,1343,69793,1343,69808,1644],{},[38,69504,69505],{},"3.3",[883,69507,69509],{"className":69508},[886],[888,69510,69511],{"xmlns":890},[892,69512,69513,69540],{},[895,69514,69515,69517,69519,69521,69523,69525,69527,69529,69532,69534],{},[898,69516,3946],{},[2005,69518,2007],{},[898,69520,1860],{},[2005,69522,2014],{"stretchy":2013},[898,69524,2797],{},[2005,69526,2020],{"stretchy":2013},[2005,69528,2007],{},[2138,69530,69531],{},"1200",[2005,69533,2234],{},[2133,69535,69536,69538],{},[898,69537,2797],{},[2138,69539,2140],{},[902,69541,69542],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,69545,69547],{"className":69546},[886],[888,69548,69549],{"xmlns":890},[892,69550,69551,69557],{},[895,69552,69553,69555],{},[898,69554,2783],{},[898,69556,4003],{},[902,69558,4103],{"encoding":904},[883,69560,69562],{"className":69561},[886],[888,69563,69564],{"xmlns":890},[892,69565,69566,69572],{},[895,69567,69568,69570],{},[898,69569,1836],{},[898,69571,4003],{},[902,69573,55450],{"encoding":904},[883,69575,69577],{"className":69576},[886],[888,69578,69579],{"xmlns":890},[892,69580,69581,69587],{},[895,69582,69583,69585],{},[898,69584,2826],{},[898,69586,4003],{},[902,69588,6640],{"encoding":904},". (b) Vypočtěte ",[883,69591,69593],{"className":69592},[886],[888,69594,69595],{"xmlns":890},[892,69596,69597,69603],{},[895,69598,69599,69601],{},[898,69600,2783],{},[898,69602,4003],{},[902,69604,4103],{"encoding":904},[883,69606,69608],{"className":69607},[886],[888,69609,69610],{"xmlns":890},[892,69611,69612,69628],{},[895,69613,69614,69616,69618,69620,69622,69624,69626],{},[898,69615,2797],{},[2005,69617,2007],{},[2138,69619,2871],{},[2005,69621,2295],{"separator":2294},[2138,69623,9041],{},[2005,69625,2295],{"separator":2294},[2138,69627,38024],{},[902,69629,69630],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,69633,69635],{"className":69634},[886],[888,69636,69637],{"xmlns":890},[892,69638,69639,69645],{},[895,69640,69641,69643],{},[898,69642,2783],{},[898,69644,4003],{},[902,69646,4103],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,69649,69651],{"className":69650},[886],[888,69652,69653],{"xmlns":890},[892,69654,69655,69661],{},[895,69656,69657,69659],{},[898,69658,1836],{},[898,69660,4003],{},[902,69662,55450],{"encoding":904},[883,69664,69666],{"className":69665},[886],[888,69667,69668],{"xmlns":890},[892,69669,69670,69676],{},[895,69671,69672,69674],{},[898,69673,2826],{},[898,69675,4003],{},[902,69677,6640],{"encoding":904},[883,69679,69681],{"className":69680},[886],[888,69682,69683],{"xmlns":890},[892,69684,69685,69701],{},[895,69686,69687,69689,69691,69693,69695,69697,69699],{},[898,69688,2797],{},[2005,69690,2007],{},[2138,69692,2871],{},[2005,69694,2295],{"separator":2294},[2138,69696,9041],{},[2005,69698,2295],{"separator":2294},[2138,69700,38024],{},[902,69702,69630],{"encoding":904},[883,69704,69706],{"className":69705},[886],[888,69707,69708],{"xmlns":890},[892,69709,69710,69716],{},[895,69711,69712,69714],{},[898,69713,2826],{},[898,69715,4003],{},[902,69717,6640],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,69720,69722],{"className":69721},[886],[888,69723,69724],{"xmlns":890},[892,69725,69726,69730],{},[895,69727,69728],{},[898,69729,2797],{},[902,69731,2797],{"encoding":904},", které maximalizuje ",[883,69734,69736],{"className":69735},[886],[888,69737,69738],{"xmlns":890},[892,69739,69740,69746],{},[895,69741,69742,69744],{},[898,69743,2783],{},[898,69745,4003],{},[902,69747,4103],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,69750,69752],{"className":69751},[886],[888,69753,69754],{"xmlns":890},[892,69755,69756,69762],{},[895,69757,69758,69760],{},[898,69759,2783],{},[898,69761,4003],{},[902,69763,4103],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,69766,69768],{"className":69767},[886],[888,69769,69770],{"xmlns":890},[892,69771,69772,69776],{},[895,69773,69774],{},[898,69775,1860],{},[902,69777,1860],{"encoding":904},[883,69779,69781],{"className":69780},[886],[888,69782,69783],{"xmlns":890},[892,69784,69785,69791],{},[895,69786,69787,69789],{},[898,69788,2783],{},[898,69790,4003],{},[902,69792,4103],{"encoding":904},[883,69794,69796],{"className":69795},[886],[888,69797,69798],{"xmlns":890},[892,69799,69800,69806],{},[895,69801,69802,69804],{},[898,69803,1836],{},[898,69805,4003],{},[902,69807,55450],{"encoding":904},[883,69809,69811],{"className":69810},[886],[888,69812,69813],{"xmlns":890},[892,69814,69815,69821],{},[895,69816,69817,69819],{},[898,69818,2826],{},[898,69820,4003],{},[902,69822,6640],{"encoding":904},[724,69824,69825,69828,69829,69859,69860,69875,69876,10162,69889,1343,69907,1343,69924,69942,69943,69965,69966,69981,69982,69995,69996,1644],{},[38,69826,69827],{},"3.4"," Je dán celkový příjem ",[883,69830,69832],{"className":69831},[886],[888,69833,69834],{"xmlns":890},[892,69835,69836,69856],{},[895,69837,69838,69840,69842,69844,69846,69848,69850],{},[898,69839,2783],{},[898,69841,4003],{},[2005,69843,2007],{},[2138,69845,69531],{},[898,69847,2797],{},[2005,69849,2234],{},[2133,69851,69852,69854],{},[898,69853,2797],{},[2138,69855,2182],{},[902,69857,69858],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,69861,69863],{"className":69862},[886],[888,69864,69865],{"xmlns":890},[892,69866,69867,69873],{},[895,69868,69869,69871],{},[898,69870,2783],{},[898,69872,4003],{},[902,69874,4103],{"encoding":904}," vzhledem ke ",[883,69877,69879],{"className":69878},[886],[888,69880,69881],{"xmlns":890},[892,69882,69883,69887],{},[895,69884,69885],{},[898,69886,2797],{},[902,69888,2797],{"encoding":904},[883,69890,69892],{"className":69891},[886],[888,69893,69894],{"xmlns":890},[892,69895,69896,69904],{},[895,69897,69898,69900,69902],{},[898,69899,2797],{},[2005,69901,2007],{},[2138,69903,2237],{},[902,69905,69906],{"encoding":904},"Q = 5",[883,69908,69910],{"className":69909},[886],[888,69911,69912],{"xmlns":890},[892,69913,69914,69922],{},[895,69915,69916,69918,69920],{},[898,69917,2797],{},[2005,69919,2007],{},[2138,69921,5591],{},[902,69923,5594],{"encoding":904},[883,69925,69927],{"className":69926},[886],[888,69928,69929],{"xmlns":890},[892,69930,69931,69939],{},[895,69932,69933,69935,69937],{},[898,69934,2797],{},[2005,69936,2007],{},[2138,69938,3517],{},[902,69940,69941],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,69944,69946],{"className":69945},[886],[888,69947,69948],{"xmlns":890},[892,69949,69950,69962],{},[895,69951,69952,69954,69956,69958,69960],{},[898,69953,2826],{},[898,69955,4003],{},[2005,69957,2014],{"stretchy":2013},[2138,69959,2871],{},[2005,69961,2020],{"stretchy":2013},[902,69963,69964],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,69967,69969],{"className":69968},[886],[888,69970,69971],{"xmlns":890},[892,69972,69973,69979],{},[895,69974,69975,69977],{},[898,69976,2783],{},[898,69978,4003],{},[902,69980,4103],{"encoding":904},", jestliže se ",[883,69983,69985],{"className":69984},[886],[888,69986,69987],{"xmlns":890},[892,69988,69989,69993],{},[895,69990,69991],{},[898,69992,2797],{},[902,69994,2797],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,69997,69999],{"className":69998},[886],[888,70000,70001],{"xmlns":890},[892,70002,70003,70009],{},[895,70004,70005,70007],{},[898,70006,2783],{},[898,70008,4003],{},[902,70010,4103],{"encoding":904},[724,70012,70013,70016,70017,70043,70044,70059,70060,69981,70075,70088],{},[38,70014,70015],{},"3.5"," Je dán mezní příjem ",[883,70018,70020],{"className":70019},[886],[888,70021,70022],{"xmlns":890},[892,70023,70024,70040],{},[895,70025,70026,70028,70030,70032,70034,70036,70038],{},[898,70027,2826],{},[898,70029,4003],{},[2005,70031,2007],{},[2005,70033,2234],{},[898,70035,2797],{},[2005,70037,2104],{},[2138,70039,9041],{},[902,70041,70042],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,70045,70047],{"className":70046},[886],[888,70048,70049],{"xmlns":890},[892,70050,70051,70057],{},[895,70052,70053,70055],{},[898,70054,2783],{},[898,70056,4003],{},[902,70058,4103],{"encoding":904},". (b) Vypočtěte změnu ",[883,70061,70063],{"className":70062},[886],[888,70064,70065],{"xmlns":890},[892,70066,70067,70073],{},[895,70068,70069,70071],{},[898,70070,2783],{},[898,70072,4003],{},[902,70074,4103],{"encoding":904},[883,70076,70078],{"className":70077},[886],[888,70079,70080],{"xmlns":890},[892,70081,70082,70086],{},[895,70083,70084],{},[898,70085,2797],{},[902,70087,2797],{"encoding":904}," změní z 8 na 12.",[198,70090,70092],{"id":70091},"náklady-36316","Náklady (3.6–3.16)",[724,70094,70095,70098,70099,70139,70140,70155,70156,70173,70174,70191,70192,70207,70208,70223,70224,69589,70239,1343,70254,1343,70271,1343,70288,1343,70303,1343,70318,6479,70333,70351,70352,1343,70367,1343,70382,70397],{},[38,70096,70097],{},"3.6"," Jsou dány celkové náklady ",[883,70100,70102],{"className":70101},[886],[888,70103,70104],{"xmlns":890},[892,70105,70106,70136],{},[895,70107,70108,70110,70112,70114,70116,70118,70120,70122,70124],{},[898,70109,2783],{},[898,70111,1852],{},[2005,70113,2007],{},[2138,70115,3098],{},[2005,70117,2104],{},[2138,70119,2140],{},[898,70121,2797],{},[2005,70123,2104],{},[2334,70125,70126],{"scriptlevel":2336,"displaystyle":2013},[2338,70127,70128,70134],{},[2133,70129,70130,70132],{},[898,70131,2797],{},[2138,70133,2140],{},[2138,70135,2871],{},[902,70137,70138],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,70141,70143],{"className":70142},[886],[888,70144,70145],{"xmlns":890},[892,70146,70147,70153],{},[895,70148,70149,70151],{},[898,70150,1876],{},[898,70152,1852],{},[902,70154,55496],{"encoding":904},", celkové variabilní náklady ",[883,70157,70159],{"className":70158},[886],[888,70160,70161],{"xmlns":890},[892,70162,70163,70171],{},[895,70164,70165,70167,70169],{},[898,70166,2783],{},[898,70168,40344],{},[898,70170,1852],{},[902,70172,55514],{"encoding":904},", průměrné variabilní náklady ",[883,70175,70177],{"className":70176},[886],[888,70178,70179],{"xmlns":890},[892,70180,70181,70189],{},[895,70182,70183,70185,70187],{},[898,70184,1836],{},[898,70186,40344],{},[898,70188,1852],{},[902,70190,55316],{"encoding":904},", variabilní náklady na jednotku ",[883,70193,70195],{"className":70194},[886],[888,70196,70197],{"xmlns":890},[892,70198,70199,70205],{},[895,70200,70201,70203],{},[898,70202,40344],{},[898,70204,1852],{},[902,70206,63610],{"encoding":904},", průměrné náklady ",[883,70209,70211],{"className":70210},[886],[888,70212,70213],{"xmlns":890},[892,70214,70215,70221],{},[895,70216,70217,70219],{},[898,70218,1836],{},[898,70220,1852],{},[902,70222,55565],{"encoding":904}," a mezní náklady ",[883,70225,70227],{"className":70226},[886],[888,70228,70229],{"xmlns":890},[892,70230,70231,70237],{},[895,70232,70233,70235],{},[898,70234,2826],{},[898,70236,1852],{},[902,70238,55297],{"encoding":904},[883,70240,70242],{"className":70241},[886],[888,70243,70244],{"xmlns":890},[892,70245,70246,70252],{},[895,70247,70248,70250],{},[898,70249,2783],{},[898,70251,1852],{},[902,70253,3251],{"encoding":904},[883,70255,70257],{"className":70256},[886],[888,70258,70259],{"xmlns":890},[892,70260,70261,70269],{},[895,70262,70263,70265,70267],{},[898,70264,2783],{},[898,70266,40344],{},[898,70268,1852],{},[902,70270,55514],{"encoding":904},[883,70272,70274],{"className":70273},[886],[888,70275,70276],{"xmlns":890},[892,70277,70278,70286],{},[895,70279,70280,70282,70284],{},[898,70281,1836],{},[898,70283,40344],{},[898,70285,1852],{},[902,70287,55316],{"encoding":904},[883,70289,70291],{"className":70290},[886],[888,70292,70293],{"xmlns":890},[892,70294,70295,70301],{},[895,70296,70297,70299],{},[898,70298,40344],{},[898,70300,1852],{},[902,70302,63610],{"encoding":904},[883,70304,70306],{"className":70305},[886],[888,70307,70308],{"xmlns":890},[892,70309,70310,70316],{},[895,70311,70312,70314],{},[898,70313,1836],{},[898,70315,1852],{},[902,70317,55565],{"encoding":904},[883,70319,70321],{"className":70320},[886],[888,70322,70323],{"xmlns":890},[892,70324,70325,70331],{},[895,70326,70327,70329],{},[898,70328,2826],{},[898,70330,1852],{},[902,70332,55297],{"encoding":904},[883,70334,70336],{"className":70335},[886],[888,70337,70338],{"xmlns":890},[892,70339,70340,70348],{},[895,70341,70342,70344,70346],{},[898,70343,2797],{},[2005,70345,2007],{},[2138,70347,3128],{},[902,70349,70350],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,70353,70355],{"className":70354},[886],[888,70356,70357],{"xmlns":890},[892,70358,70359,70365],{},[895,70360,70361,70363],{},[898,70362,2783],{},[898,70364,1852],{},[902,70366,3251],{"encoding":904},[883,70368,70370],{"className":70369},[886],[888,70371,70372],{"xmlns":890},[892,70373,70374,70380],{},[895,70375,70376,70378],{},[898,70377,1836],{},[898,70379,1852],{},[902,70381,55565],{"encoding":904},[883,70383,70385],{"className":70384},[886],[888,70386,70387],{"xmlns":890},[892,70388,70389,70395],{},[895,70390,70391,70393],{},[898,70392,2826],{},[898,70394,1852],{},[902,70396,55297],{"encoding":904}," rostou, resp. klesají.",[724,70399,70400,70403,70404,70223,70434,70449,70450,70465,70466,1343,70481,1343,70496,1644],{},[38,70401,70402],{},"3.7"," Jsou dány průměrné náklady ",[883,70405,70407],{"className":70406},[886],[888,70408,70409],{"xmlns":890},[892,70410,70411,70431],{},[895,70412,70413,70415,70417,70419,70427,70429],{},[898,70414,1836],{},[898,70416,1852],{},[2005,70418,2007],{},[2334,70420,70421],{"scriptlevel":2336,"displaystyle":2013},[2338,70422,70423,70425],{},[2138,70424,3098],{},[898,70426,2797],{},[2005,70428,2104],{},[2138,70430,9041],{},[902,70432,70433],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,70435,70437],{"className":70436},[886],[888,70438,70439],{"xmlns":890},[892,70440,70441,70447],{},[895,70442,70443,70445],{},[898,70444,2826],{},[898,70446,1852],{},[902,70448,55297],{"encoding":904},". (a) Určete celkové náklady ",[883,70451,70453],{"className":70452},[886],[888,70454,70455],{"xmlns":890},[892,70456,70457,70463],{},[895,70458,70459,70461],{},[898,70460,2783],{},[898,70462,1852],{},[902,70464,3251],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,70467,70469],{"className":70468},[886],[888,70470,70471],{"xmlns":890},[892,70472,70473,70479],{},[895,70474,70475,70477],{},[898,70476,1836],{},[898,70478,1852],{},[902,70480,55565],{"encoding":904},[883,70482,70484],{"className":70483},[886],[888,70485,70486],{"xmlns":890},[892,70487,70488,70494],{},[895,70489,70490,70492],{},[898,70491,2783],{},[898,70493,1852],{},[902,70495,3251],{"encoding":904},[883,70497,70499],{"className":70498},[886],[888,70500,70501],{"xmlns":890},[892,70502,70503,70509],{},[895,70504,70505,70507],{},[898,70506,2826],{},[898,70508,1852],{},[902,70510,55297],{"encoding":904},[724,70512,70513,70098,70516,70560,70561,1343,70578,1343,70593,1343,70610,1343,70625,1343,70642,1644],{},[38,70514,70515],{},"3.8",[883,70517,70519],{"className":70518},[886],[888,70520,70521],{"xmlns":890},[892,70522,70523,70557],{},[895,70524,70525,70527,70529,70531,70533,70535,70537,70539,70541,70543,70549,70551],{},[898,70526,2783],{},[898,70528,1852],{},[2005,70530,2007],{},[2138,70532,46708],{},[2005,70534,2104],{},[2138,70536,38024],{},[898,70538,2797],{},[2005,70540,2234],{},[2138,70542,2244],{},[2133,70544,70545,70547],{},[898,70546,2797],{},[2138,70548,2140],{},[2005,70550,2104],{},[2133,70552,70553,70555],{},[898,70554,2797],{},[2138,70556,2182],{},[902,70558,70559],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,70562,70564],{"className":70563},[886],[888,70565,70566],{"xmlns":890},[892,70567,70568,70576],{},[895,70569,70570,70572,70574],{},[898,70571,2783],{},[898,70573,40344],{},[898,70575,1852],{},[902,70577,55514],{"encoding":904},[883,70579,70581],{"className":70580},[886],[888,70582,70583],{"xmlns":890},[892,70584,70585,70591],{},[895,70586,70587,70589],{},[898,70588,1876],{},[898,70590,1852],{},[902,70592,55496],{"encoding":904},[883,70594,70596],{"className":70595},[886],[888,70597,70598],{"xmlns":890},[892,70599,70600,70608],{},[895,70601,70602,70604,70606],{},[898,70603,1836],{},[898,70605,40344],{},[898,70607,1852],{},[902,70609,55316],{"encoding":904},[883,70611,70613],{"className":70612},[886],[888,70614,70615],{"xmlns":890},[892,70616,70617,70623],{},[895,70618,70619,70621],{},[898,70620,1836],{},[898,70622,1852],{},[902,70624,55565],{"encoding":904},[883,70626,70628],{"className":70627},[886],[888,70629,70630],{"xmlns":890},[892,70631,70632,70640],{},[895,70633,70634,70636,70638],{},[898,70635,1836],{},[898,70637,1876],{},[898,70639,1852],{},[902,70641,55532],{"encoding":904},[883,70643,70645],{"className":70644},[886],[888,70646,70647],{"xmlns":890},[892,70648,70649,70655],{},[895,70650,70651,70653],{},[898,70652,2826],{},[898,70654,1852],{},[902,70656,55297],{"encoding":904},[724,70658,70659,70098,70662,70692,70693,69875,70708,6479,70721,1343,70739,1343,70757,69942,70775,69965,70797,70812,70813,70826,70827,1644],{},[38,70660,70661],{},"3.9",[883,70663,70665],{"className":70664},[886],[888,70666,70667],{"xmlns":890},[892,70668,70669,70689],{},[895,70670,70671,70673,70675,70677,70679,70681,70683],{},[898,70672,2783],{},[898,70674,1852],{},[2005,70676,2007],{},[2138,70678,15116],{},[2005,70680,2104],{},[2138,70682,19327],{},[2133,70684,70685,70687],{},[898,70686,2797],{},[2138,70688,2140],{},[902,70690,70691],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,70694,70696],{"className":70695},[886],[888,70697,70698],{"xmlns":890},[892,70699,70700,70706],{},[895,70701,70702,70704],{},[898,70703,2783],{},[898,70705,1852],{},[902,70707,3251],{"encoding":904},[883,70709,70711],{"className":70710},[886],[888,70712,70713],{"xmlns":890},[892,70714,70715,70719],{},[895,70716,70717],{},[898,70718,2797],{},[902,70720,2797],{"encoding":904},[883,70722,70724],{"className":70723},[886],[888,70725,70726],{"xmlns":890},[892,70727,70728,70736],{},[895,70729,70730,70732,70734],{},[898,70731,2797],{},[2005,70733,2007],{},[2138,70735,2871],{},[902,70737,70738],{"encoding":904},"Q = 10",[883,70740,70742],{"className":70741},[886],[888,70743,70744],{"xmlns":890},[892,70745,70746,70754],{},[895,70747,70748,70750,70752],{},[898,70749,2797],{},[2005,70751,2007],{},[2138,70753,9041],{},[902,70755,70756],{"encoding":904},"Q = 20",[883,70758,70760],{"className":70759},[886],[888,70761,70762],{"xmlns":890},[892,70763,70764,70772],{},[895,70765,70766,70768,70770],{},[898,70767,2797],{},[2005,70769,2007],{},[2138,70771,38024],{},[902,70773,70774],{"encoding":904},"Q = 30",[883,70776,70778],{"className":70777},[886],[888,70779,70780],{"xmlns":890},[892,70781,70782,70794],{},[895,70783,70784,70786,70788,70790,70792],{},[898,70785,2826],{},[898,70787,1852],{},[2005,70789,2014],{"stretchy":2013},[2138,70791,36249],{},[2005,70793,2020],{"stretchy":2013},[902,70795,70796],{"encoding":904},"MC(15)",[883,70798,70800],{"className":70799},[886],[888,70801,70802],{"xmlns":890},[892,70803,70804,70810],{},[895,70805,70806,70808],{},[898,70807,2783],{},[898,70809,1852],{},[902,70811,3251],{"encoding":904}," v důsledku změny ",[883,70814,70816],{"className":70815},[886],[888,70817,70818],{"xmlns":890},[892,70819,70820,70824],{},[895,70821,70822],{},[898,70823,2797],{},[902,70825,2797],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,70828,70830],{"className":70829},[886],[888,70831,70832],{"xmlns":890},[892,70833,70834,70840],{},[895,70835,70836,70838],{},[898,70837,2783],{},[898,70839,1852],{},[902,70841,3251],{"encoding":904},[724,70843,70844,70847,70848,70449,70884,70899,70900,70059,70919,70812,70934,70947],{},[38,70845,70846],{},"3.10"," Jsou dány mezní náklady ",[883,70849,70851],{"className":70850},[886],[888,70852,70853],{"xmlns":890},[892,70854,70855,70881],{},[895,70856,70857,70859,70861,70863,70865,70867,70869,70871,70873,70875],{},[898,70858,2826],{},[898,70860,1852],{},[2005,70862,2007],{},[2138,70864,3134],{},[2005,70866,2234],{},[2138,70868,41867],{},[898,70870,2797],{},[2005,70872,2104],{},[2138,70874,64564],{},[2133,70876,70877,70879],{},[898,70878,2797],{},[2138,70880,2140],{},[902,70882,70883],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,70885,70887],{"className":70886},[886],[888,70888,70889],{"xmlns":890},[892,70890,70891,70897],{},[895,70892,70893,70895],{},[898,70894,2783],{},[898,70896,1852],{},[902,70898,3251],{"encoding":904},", jestliže fixní náklady ",[883,70901,70903],{"className":70902},[886],[888,70904,70905],{"xmlns":890},[892,70906,70907,70917],{},[895,70908,70909,70911,70913,70915],{},[898,70910,1876],{},[898,70912,1852],{},[2005,70914,2007],{},[2138,70916,3098],{},[902,70918,11638],{"encoding":904},[883,70920,70922],{"className":70921},[886],[888,70923,70924],{"xmlns":890},[892,70925,70926,70932],{},[895,70927,70928,70930],{},[898,70929,2783],{},[898,70931,1852],{},[902,70933,3251],{"encoding":904},[883,70935,70937],{"className":70936},[886],[888,70938,70939],{"xmlns":890},[892,70940,70941,70945],{},[895,70942,70943],{},[898,70944,2797],{},[902,70946,2797],{"encoding":904}," z 15 na 20.",[724,70949,70950,70098,70953,70996,70997,71010,71011,71026,71027,71042,71043,71010,71056,71026,71073,71090,71091,71010,71104,71026,71119,71134,71135,71155,71156,71179],{},[38,70951,70952],{},"3.11",[883,70954,70956],{"className":70955},[886],[888,70957,70958],{"xmlns":890},[892,70959,70960,70994],{},[895,70961,70962,70964,70966,70968,70970,70972,70974,70976,70978,70980,70986,70988],{},[898,70963,2783],{},[898,70965,1852],{},[2005,70967,2007],{},[2138,70969,3098],{},[2005,70971,2104],{},[2138,70973,5010],{},[898,70975,2797],{},[2005,70977,2234],{},[2138,70979,2237],{},[2133,70981,70982,70984],{},[898,70983,2797],{},[2138,70985,2140],{},[2005,70987,2104],{},[2133,70989,70990,70992],{},[898,70991,2797],{},[2138,70993,2182],{},[902,70995,60912],{"encoding":904},". (a) Určete ",[883,70998,71000],{"className":70999},[886],[888,71001,71002],{"xmlns":890},[892,71003,71004,71008],{},[895,71005,71006],{},[898,71007,2797],{},[902,71009,2797],{"encoding":904},", které minimalizuje ",[883,71012,71014],{"className":71013},[886],[888,71015,71016],{"xmlns":890},[892,71017,71018,71024],{},[895,71019,71020,71022],{},[898,71021,2826],{},[898,71023,1852],{},[902,71025,55297],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,71028,71030],{"className":71029},[886],[888,71031,71032],{"xmlns":890},[892,71033,71034,71040],{},[895,71035,71036,71038],{},[898,71037,2826],{},[898,71039,1852],{},[902,71041,55297],{"encoding":904},". (b) Určete ",[883,71044,71046],{"className":71045},[886],[888,71047,71048],{"xmlns":890},[892,71049,71050,71054],{},[895,71051,71052],{},[898,71053,2797],{},[902,71055,2797],{"encoding":904},[883,71057,71059],{"className":71058},[886],[888,71060,71061],{"xmlns":890},[892,71062,71063,71071],{},[895,71064,71065,71067,71069],{},[898,71066,1836],{},[898,71068,40344],{},[898,71070,1852],{},[902,71072,55316],{"encoding":904},[883,71074,71076],{"className":71075},[886],[888,71077,71078],{"xmlns":890},[892,71079,71080,71088],{},[895,71081,71082,71084,71086],{},[898,71083,1836],{},[898,71085,40344],{},[898,71087,1852],{},[902,71089,55316],{"encoding":904},". (c) Určete ",[883,71092,71094],{"className":71093},[886],[888,71095,71096],{"xmlns":890},[892,71097,71098,71102],{},[895,71099,71100],{},[898,71101,2797],{},[902,71103,2797],{"encoding":904},[883,71105,71107],{"className":71106},[886],[888,71108,71109],{"xmlns":890},[892,71110,71111,71117],{},[895,71112,71113,71115],{},[898,71114,1836],{},[898,71116,1852],{},[902,71118,55565],{"encoding":904},[883,71120,71122],{"className":71121},[886],[888,71123,71124],{"xmlns":890},[892,71125,71126,71132],{},[895,71127,71128,71130],{},[898,71129,1836],{},[898,71131,1852],{},[902,71133,55565],{"encoding":904}," (rada: hledaný kořen ",[883,71136,71138],{"className":71137},[886],[888,71139,71140],{"xmlns":890},[892,71141,71142,71152],{},[895,71143,71144,71146],{},[898,71145,1836],{},[2133,71147,71148,71150],{},[898,71149,1852],{},[2005,71151,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,71153,71154],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,71157,71159],{"className":71158},[886],[888,71160,71161],{"xmlns":890},[892,71162,71163,71176],{},[895,71164,71165,71167,71170,71172,71174],{},[2005,71166,2014],{"stretchy":2013},[2138,71168,71169],{},"4,7",[2005,71171,8431],{"separator":2294},[2138,71173,5285],{},[2005,71175,2020],{"stretchy":2013},[902,71177,71178],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,71181,71182,71185,71186,2633,71214,71231,71232,21600,71273,71294],{},[38,71183,71184],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,71187,71189],{"className":71188},[886],[888,71190,71191],{"xmlns":890},[892,71192,71193,71211],{},[895,71194,71195,71197,71199,71201,71203,71205,71207,71209],{},[898,71196,1836],{},[898,71198,1852],{},[2005,71200,2007],{},[898,71202,1836],{},[898,71204,1852],{},[2005,71206,2014],{"stretchy":2013},[898,71208,2797],{},[2005,71210,2020],{"stretchy":2013},[902,71212,71213],{"encoding":904},"AC = AC(Q)",[883,71215,71217],{"className":71216},[886],[888,71218,71219],{"xmlns":890},[892,71220,71221,71229],{},[895,71222,71223],{},[2281,71224,71225,71227],{},[898,71226,2797],{},[2138,71228,2336],{},[902,71230,38313],{"encoding":904}," minimum, pak platí ",[883,71233,71235],{"className":71234},[886],[888,71236,71237],{"xmlns":890},[892,71238,71239,71271],{},[895,71240,71241,71243,71245,71247,71253,71255,71257,71259,71261,71263,71269],{},[898,71242,1836],{},[898,71244,1852],{},[2005,71246,2014],{"stretchy":2013},[2281,71248,71249,71251],{},[898,71250,2797],{},[2138,71252,2336],{},[2005,71254,2020],{"stretchy":2013},[2005,71256,2007],{},[898,71258,2826],{},[898,71260,1852],{},[2005,71262,2014],{"stretchy":2013},[2281,71264,71265,71267],{},[898,71266,2797],{},[2138,71268,2336],{},[2005,71270,2020],{"stretchy":2013},[902,71272,62574],{"encoding":904},[883,71274,71276],{"className":71275},[886],[888,71277,71278],{"xmlns":890},[892,71279,71280,71292],{},[895,71281,71282,71284,71286,71288,71290],{},[898,71283,2826],{},[898,71285,1852],{},[2005,71287,2014],{"stretchy":2013},[898,71289,2797],{},[2005,71291,2020],{"stretchy":2013},[902,71293,67698],{"encoding":904}," jsou mezní náklady.",[724,71296,71297,70098,71300,70560,71334,71010,71347,71026,71362,1644],{},[38,71298,71299],{},"3.13",[883,71301,71303],{"className":71302},[886],[888,71304,71305],{"xmlns":890},[892,71306,71307,71331],{},[895,71308,71309,71311,71313,71315,71321,71323,71325,71327,71329],{},[898,71310,2783],{},[898,71312,1852],{},[2005,71314,2007],{},[2133,71316,71317,71319],{},[898,71318,2797],{},[2138,71320,2140],{},[2005,71322,2104],{},[2138,71324,2140],{},[898,71326,2797],{},[2005,71328,2104],{},[2138,71330,5010],{},[902,71332,71333],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,71335,71337],{"className":71336},[886],[888,71338,71339],{"xmlns":890},[892,71340,71341,71345],{},[895,71342,71343],{},[898,71344,2797],{},[902,71346,2797],{"encoding":904},[883,71348,71350],{"className":71349},[886],[888,71351,71352],{"xmlns":890},[892,71353,71354,71360],{},[895,71355,71356,71358],{},[898,71357,1836],{},[898,71359,1852],{},[902,71361,55565],{"encoding":904},[883,71363,71365],{"className":71364},[886],[888,71366,71367],{"xmlns":890},[892,71368,71369,71375],{},[895,71370,71371,71373],{},[898,71372,1836],{},[898,71374,1852],{},[902,71376,55565],{"encoding":904},[724,71378,71379,71382,71383,2633,71415,71231,71432,21600,71475,71294],{},[38,71380,71381],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,71384,71386],{"className":71385},[886],[888,71387,71388],{"xmlns":890},[892,71389,71390,71412],{},[895,71391,71392,71394,71396,71398,71400,71402,71404,71406,71408,71410],{},[898,71393,1836],{},[898,71395,40344],{},[898,71397,1852],{},[2005,71399,2007],{},[898,71401,1836],{},[898,71403,40344],{},[898,71405,1852],{},[2005,71407,2014],{"stretchy":2013},[898,71409,2797],{},[2005,71411,2020],{"stretchy":2013},[902,71413,71414],{"encoding":904},"AVC = AVC(Q)",[883,71416,71418],{"className":71417},[886],[888,71419,71420],{"xmlns":890},[892,71421,71422,71430],{},[895,71423,71424],{},[2281,71425,71426,71428],{},[898,71427,2797],{},[2138,71429,2336],{},[902,71431,38313],{"encoding":904},[883,71433,71435],{"className":71434},[886],[888,71436,71437],{"xmlns":890},[892,71438,71439,71473],{},[895,71440,71441,71443,71445,71447,71449,71455,71457,71459,71461,71463,71465,71471],{},[898,71442,1836],{},[898,71444,40344],{},[898,71446,1852],{},[2005,71448,2014],{"stretchy":2013},[2281,71450,71451,71453],{},[898,71452,2797],{},[2138,71454,2336],{},[2005,71456,2020],{"stretchy":2013},[2005,71458,2007],{},[898,71460,2826],{},[898,71462,1852],{},[2005,71464,2014],{"stretchy":2013},[2281,71466,71467,71469],{},[898,71468,2797],{},[2138,71470,2336],{},[2005,71472,2020],{"stretchy":2013},[902,71474,69024],{"encoding":904},[883,71476,71478],{"className":71477},[886],[888,71479,71480],{"xmlns":890},[892,71481,71482,71494],{},[895,71483,71484,71486,71488,71490,71492],{},[898,71485,2826],{},[898,71487,1852],{},[2005,71489,2014],{"stretchy":2013},[898,71491,2797],{},[2005,71493,2020],{"stretchy":2013},[902,71495,67698],{"encoding":904},[724,71497,71498,70098,71501,70560,71547,71010,71560,71026,71577,1644],{},[38,71499,71500],{},"3.15",[883,71502,71504],{"className":71503},[886],[888,71505,71506],{"xmlns":890},[892,71507,71508,71544],{},[895,71509,71510,71512,71514,71516,71518,71520,71522,71524,71526,71528,71534,71536,71538],{},[898,71511,2783],{},[898,71513,1852],{},[2005,71515,2007],{},[2138,71517,3128],{},[2005,71519,2104],{},[2138,71521,36249],{},[898,71523,2797],{},[2005,71525,2234],{},[2138,71527,2140],{},[2133,71529,71530,71532],{},[898,71531,2797],{},[2138,71533,2140],{},[2005,71535,2104],{},[2138,71537,2847],{},[2133,71539,71540,71542],{},[898,71541,2797],{},[2138,71543,2182],{},[902,71545,71546],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,71548,71550],{"className":71549},[886],[888,71551,71552],{"xmlns":890},[892,71553,71554,71558],{},[895,71555,71556],{},[898,71557,2797],{},[902,71559,2797],{"encoding":904},[883,71561,71563],{"className":71562},[886],[888,71564,71565],{"xmlns":890},[892,71566,71567,71575],{},[895,71568,71569,71571,71573],{},[898,71570,1836],{},[898,71572,40344],{},[898,71574,1852],{},[902,71576,55316],{"encoding":904},[883,71578,71580],{"className":71579},[886],[888,71581,71582],{"xmlns":890},[892,71583,71584,71592],{},[895,71585,71586,71588,71590],{},[898,71587,1836],{},[898,71589,40344],{},[898,71591,1852],{},[902,71593,55316],{"encoding":904},[724,71595,71596,71599,71600,71613,71614,71634],{},[38,71597,71598],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,71601,71603],{"className":71602},[886],[888,71604,71605],{"xmlns":890},[892,71606,71607,71611],{},[895,71608,71609],{},[898,71610,2017],{},[902,71612,2017],{"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 ",[883,71615,71617],{"className":71616},[886],[888,71618,71619],{"xmlns":890},[892,71620,71621,71631],{},[895,71622,71623,71625,71627,71629],{},[2138,71624,2871],{},[2297,71626,2995],{},[2138,71628,59087],{},[898,71630,2017],{},[902,71632,71633],{"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.",[198,71636,71638],{"id":71637},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,71640,71641,71644,71645,3894,71667,71693],{},[38,71642,71643],{},"3.17"," Jsou dány ",[883,71646,71648],{"className":71647},[886],[888,71649,71650],{"xmlns":890},[892,71651,71652,71664],{},[895,71653,71654,71656,71658,71660,71662],{},[898,71655,2783],{},[898,71657,4003],{},[2005,71659,2007],{},[2138,71661,2871],{},[898,71663,2797],{},[902,71665,71666],{"encoding":904},"TR = 10Q",[883,71668,71670],{"className":71669},[886],[888,71671,71672],{"xmlns":890},[892,71673,71674,71690],{},[895,71675,71676,71678,71680,71682,71684,71686,71688],{},[898,71677,2783],{},[898,71679,1852],{},[2005,71681,2007],{},[2138,71683,3098],{},[2005,71685,2104],{},[2138,71687,2237],{},[898,71689,2797],{},[902,71691,71692],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,71695,71696,71699,71700,6196,71715,71730,71731,1343,71753,21600,71780,71802,71803,71837],{},[38,71697,71698],{},"3.18"," Odvoďte, že jestliže ",[883,71701,71703],{"className":71702},[886],[888,71704,71705],{"xmlns":890},[892,71706,71707,71713],{},[895,71708,71709,71711],{},[898,71710,2783],{},[898,71712,4003],{},[902,71714,4103],{"encoding":904},[883,71716,71718],{"className":71717},[886],[888,71719,71720],{"xmlns":890},[892,71721,71722,71728],{},[895,71723,71724,71726],{},[898,71725,2783],{},[898,71727,1852],{},[902,71729,3251],{"encoding":904}," jsou lineární tvaru ",[883,71732,71734],{"className":71733},[886],[888,71735,71736],{"xmlns":890},[892,71737,71738,71750],{},[895,71739,71740,71742,71744,71746,71748],{},[898,71741,2783],{},[898,71743,4003],{},[2005,71745,2007],{},[898,71747,724],{},[898,71749,2797],{},[902,71751,71752],{"encoding":904},"TR = pQ",[883,71754,71756],{"className":71755},[886],[888,71757,71758],{"xmlns":890},[892,71759,71760,71777],{},[895,71761,71762,71764,71766,71768,71771,71773,71775],{},[898,71763,2783],{},[898,71765,1852],{},[2005,71767,2007],{},[898,71769,71770],{},"m",[2005,71772,2104],{},[898,71774,36865],{},[898,71776,2797],{},[902,71778,71779],{"encoding":904},"TC = m + nQ",[883,71781,71783],{"className":71782},[886],[888,71784,71785],{"xmlns":890},[892,71786,71787,71799],{},[895,71788,71789,71791,71793,71795,71797],{},[898,71790,71770],{},[2005,71792,2295],{"separator":2294},[898,71794,36865],{},[2005,71796,2295],{"separator":2294},[898,71798,724],{},[902,71800,71801],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,71804,71806],{"className":71805},[886],[888,71807,71808],{"xmlns":890},[892,71809,71810,71834],{},[895,71811,71812,71818,71820],{},[2133,71813,71814,71816],{},[898,71815,2797],{},[2005,71817,4360],{},[2005,71819,2007],{},[2334,71821,71822],{"scriptlevel":2336,"displaystyle":2013},[2338,71823,71824,71826],{},[898,71825,71770],{},[895,71827,71828,71830,71832],{},[898,71829,724],{},[2005,71831,2234],{},[898,71833,36865],{},[902,71835,71836],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,71839,71840,71644,71843,3894,71877,70996,71903,71916,71917,69748,71932,71947,71948,69732,71961,69748,71976,71991],{},[38,71841,71842],{},"3.19",[883,71844,71846],{"className":71845},[886],[888,71847,71848],{"xmlns":890},[892,71849,71850,71874],{},[895,71851,71852,71854,71856,71858,71860,71862,71868,71870,71872],{},[898,71853,2783],{},[898,71855,4003],{},[2005,71857,2007],{},[2005,71859,2234],{},[2138,71861,2140],{},[2133,71863,71864,71866],{},[898,71865,2797],{},[2138,71867,2140],{},[2005,71869,2104],{},[2138,71871,22952],{},[898,71873,2797],{},[902,71875,71876],{"encoding":904},"TR = -2Q^2 + 14Q",[883,71878,71880],{"className":71879},[886],[888,71881,71882],{"xmlns":890},[892,71883,71884,71900],{},[895,71885,71886,71888,71890,71892,71894,71896,71898],{},[898,71887,2783],{},[898,71889,1852],{},[2005,71891,2007],{},[2138,71893,2140],{},[898,71895,2797],{},[2005,71897,2104],{},[2138,71899,2871],{},[902,71901,71902],{"encoding":904},"TC = 2Q + 10",[883,71904,71906],{"className":71905},[886],[888,71907,71908],{"xmlns":890},[892,71909,71910,71914],{},[895,71911,71912],{},[898,71913,2797],{},[902,71915,2797],{"encoding":904},", které maximalizuje zisk ",[883,71918,71920],{"className":71919},[886],[888,71921,71922],{"xmlns":890},[892,71923,71924,71930],{},[895,71925,71926,71928],{},[898,71927,3946],{},[898,71929,4003],{},[902,71931,63484],{"encoding":904},[883,71933,71935],{"className":71934},[886],[888,71936,71937],{"xmlns":890},[892,71938,71939,71945],{},[895,71940,71941,71943],{},[898,71942,3946],{},[898,71944,4003],{},[902,71946,63484],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,71949,71951],{"className":71950},[886],[888,71952,71953],{"xmlns":890},[892,71954,71955,71959],{},[895,71956,71957],{},[898,71958,2797],{},[902,71960,2797],{"encoding":904},[883,71962,71964],{"className":71963},[886],[888,71965,71966],{"xmlns":890},[892,71967,71968,71974],{},[895,71969,71970,71972],{},[898,71971,2783],{},[898,71973,4003],{},[902,71975,4103],{"encoding":904},[883,71977,71979],{"className":71978},[886],[888,71980,71981],{"xmlns":890},[892,71982,71983,71989],{},[895,71984,71985,71987],{},[898,71986,2783],{},[898,71988,4003],{},[902,71990,4103],{"encoding":904},". (d) Graficky interpretujte.",[724,71993,71994,47689,71997,1343,72023,1343,72042,70996,72062,71916,72075,69748,72090,72105,72106,72128,72129,71179],{},[38,71995,71996],{},"3.20",[883,71998,72000],{"className":71999},[886],[888,72001,72002],{"xmlns":890},[892,72003,72004,72020],{},[895,72005,72006,72008,72010,72012,72014],{},[898,72007,3946],{},[2005,72009,2007],{},[2138,72011,20148],{},[2005,72013,2234],{},[2133,72015,72016,72018],{},[898,72017,2797],{},[2138,72019,2140],{},[902,72021,72022],{"encoding":904},"P = 400 - Q^2",[883,72024,72026],{"className":72025},[886],[888,72027,72028],{"xmlns":890},[892,72029,72030,72040],{},[895,72031,72032,72034,72036,72038],{},[898,72033,1876],{},[898,72035,1852],{},[2005,72037,2007],{},[2138,72039,3098],{},[902,72041,11638],{"encoding":904},[883,72043,72045],{"className":72044},[886],[888,72046,72047],{"xmlns":890},[892,72048,72049,72059],{},[895,72050,72051,72053,72055,72057],{},[898,72052,2826],{},[898,72054,1852],{},[2005,72056,2007],{},[2138,72058,9041],{},[902,72060,72061],{"encoding":904},"MC = 20",[883,72063,72065],{"className":72064},[886],[888,72066,72067],{"xmlns":890},[892,72068,72069,72073],{},[895,72070,72071],{},[898,72072,2797],{},[902,72074,2797],{"encoding":904},[883,72076,72078],{"className":72077},[886],[888,72079,72080],{"xmlns":890},[892,72081,72082,72088],{},[895,72083,72084,72086],{},[898,72085,3946],{},[898,72087,4003],{},[902,72089,63484],{"encoding":904},[883,72091,72093],{"className":72092},[886],[888,72094,72095],{"xmlns":890},[892,72096,72097,72103],{},[895,72098,72099,72101],{},[898,72100,3946],{},[898,72102,4003],{},[902,72104,63484],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,72107,72109],{"className":72108},[886],[888,72110,72111],{"xmlns":890},[892,72112,72113,72125],{},[895,72114,72115,72117,72119,72121,72123],{},[2005,72116,2014],{"stretchy":2013},[2138,72118,2336],{},[2005,72120,2295],{"separator":2294},[2138,72122,2287],{},[2005,72124,2020],{"stretchy":2013},[902,72126,72127],{"encoding":904},"(0, 1)",", druhý do ",[883,72130,72132],{"className":72131},[886],[888,72133,72134],{"xmlns":890},[892,72135,72136,72149],{},[895,72137,72138,72140,72143,72145,72147],{},[2005,72139,2014],{"stretchy":2013},[2138,72141,72142],{},"19",[2005,72144,2295],{"separator":2294},[2138,72146,9041],{},[2005,72148,2020],{"stretchy":2013},[902,72150,72151],{"encoding":904},"(19, 20)",[724,72153,72154,72157,72158,2633,72186,72203,72204,1644],{},[38,72155,72156],{},"3.21"," Dokažte, že má-li zisk ",[883,72159,72161],{"className":72160},[886],[888,72162,72163],{"xmlns":890},[892,72164,72165,72183],{},[895,72166,72167,72169,72171,72173,72175,72177,72179,72181],{},[898,72168,3946],{},[898,72170,4003],{},[2005,72172,2007],{},[898,72174,3946],{},[898,72176,4003],{},[2005,72178,2014],{"stretchy":2013},[898,72180,2797],{},[2005,72182,2020],{"stretchy":2013},[902,72184,72185],{"encoding":904},"PR = PR(Q)",[883,72187,72189],{"className":72188},[886],[888,72190,72191],{"xmlns":890},[892,72192,72193,72201],{},[895,72194,72195],{},[2281,72196,72197,72199],{},[898,72198,2797],{},[2138,72200,2336],{},[902,72202,38313],{"encoding":904}," maximum, pak platí ",[883,72205,72207],{"className":72206},[886],[888,72208,72209],{"xmlns":890},[892,72210,72211,72243],{},[895,72212,72213,72215,72217,72219,72225,72227,72229,72231,72233,72235,72241],{},[898,72214,2826],{},[898,72216,4003],{},[2005,72218,2014],{"stretchy":2013},[2281,72220,72221,72223],{},[898,72222,2797],{},[2138,72224,2336],{},[2005,72226,2020],{"stretchy":2013},[2005,72228,2007],{},[898,72230,2826],{},[898,72232,1852],{},[2005,72234,2014],{"stretchy":2013},[2281,72236,72237,72239],{},[898,72238,2797],{},[2138,72240,2336],{},[2005,72242,2020],{"stretchy":2013},[902,72244,65650],{"encoding":904},[724,72246,72247,72250,72251,3894,72266,56030,72281,71916,72294,72309,72310,1343,72337,72374,72375,1343,72402,1644],{},[38,72248,72249],{},"3.22"," Pro zadané ",[883,72252,72254],{"className":72253},[886],[888,72255,72256],{"xmlns":890},[892,72257,72258,72264],{},[895,72259,72260,72262],{},[898,72261,2826],{},[898,72263,4003],{},[902,72265,6640],{"encoding":904},[883,72267,72269],{"className":72268},[886],[888,72270,72271],{"xmlns":890},[892,72272,72273,72279],{},[895,72274,72275,72277],{},[898,72276,2826],{},[898,72278,1852],{},[902,72280,55297],{"encoding":904},[883,72282,72284],{"className":72283},[886],[888,72285,72286],{"xmlns":890},[892,72287,72288,72292],{},[895,72289,72290],{},[898,72291,2797],{},[902,72293,2797],{"encoding":904},[883,72295,72297],{"className":72296},[886],[888,72298,72299],{"xmlns":890},[892,72300,72301,72307],{},[895,72302,72303,72305],{},[898,72304,3946],{},[898,72306,4003],{},[902,72308,63484],{"encoding":904},". (a) ",[883,72311,72313],{"className":72312},[886],[888,72314,72315],{"xmlns":890},[892,72316,72317,72334],{},[895,72318,72319,72321,72323,72325,72328,72330,72332],{},[898,72320,2826],{},[898,72322,4003],{},[2005,72324,2007],{},[2138,72326,72327],{},"236",[2005,72329,2234],{},[2138,72331,41867],{},[898,72333,2797],{},[902,72335,72336],{"encoding":904},"MR = 236 - 16Q",[883,72338,72340],{"className":72339},[886],[888,72341,72342],{"xmlns":890},[892,72343,72344,72371],{},[895,72345,72346,72348,72350,72352,72354,72360,72362,72365,72367,72369],{},[898,72347,2826],{},[898,72349,1852],{},[2005,72351,2007],{},[2138,72353,2182],{},[2133,72355,72356,72358],{},[898,72357,2797],{},[2138,72359,2140],{},[2005,72361,2234],{},[2138,72363,72364],{},"32",[898,72366,2797],{},[2005,72368,2104],{},[2138,72370,5750],{},[902,72372,72373],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,72376,72378],{"className":72377},[886],[888,72379,72380],{"xmlns":890},[892,72381,72382,72399],{},[895,72383,72384,72386,72388,72390,72393,72395,72397],{},[898,72385,2826],{},[898,72387,4003],{},[2005,72389,2007],{},[2138,72391,72392],{},"280",[2005,72394,2234],{},[2138,72396,9041],{},[898,72398,2797],{},[902,72400,72401],{"encoding":904},"MR = 280 - 20Q",[883,72403,72405],{"className":72404},[886],[888,72406,72407],{"xmlns":890},[892,72408,72409,72436],{},[895,72410,72411,72413,72415,72417,72420,72426,72428,72430,72432,72434],{},[898,72412,2826],{},[898,72414,1852],{},[2005,72416,2007],{},[2138,72418,72419],{},"1,6",[2133,72421,72422,72424],{},[898,72423,2797],{},[2138,72425,2140],{},[2005,72427,2234],{},[2138,72429,36249],{},[898,72431,2797],{},[2005,72433,2104],{},[2138,72435,3134],{},[902,72437,72438],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,72440,72441,72250,72444,3894,72459,56030,72474,69732,72487,69748,72502,72309,72517,1343,72548,72374,72584,1343,72616,72660,72661,1343,72693,1644],{},[38,72442,72443],{},"3.23",[883,72445,72447],{"className":72446},[886],[888,72448,72449],{"xmlns":890},[892,72450,72451,72457],{},[895,72452,72453,72455],{},[898,72454,2783],{},[898,72456,4003],{},[902,72458,4103],{"encoding":904},[883,72460,72462],{"className":72461},[886],[888,72463,72464],{"xmlns":890},[892,72465,72466,72472],{},[895,72467,72468,72470],{},[898,72469,2783],{},[898,72471,1852],{},[902,72473,3251],{"encoding":904},[883,72475,72477],{"className":72476},[886],[888,72478,72479],{"xmlns":890},[892,72480,72481,72485],{},[895,72482,72483],{},[898,72484,2797],{},[902,72486,2797],{"encoding":904},[883,72488,72490],{"className":72489},[886],[888,72491,72492],{"xmlns":890},[892,72493,72494,72500],{},[895,72495,72496,72498],{},[898,72497,3946],{},[898,72499,4003],{},[902,72501,63484],{"encoding":904},[883,72503,72505],{"className":72504},[886],[888,72506,72507],{"xmlns":890},[892,72508,72509,72515],{},[895,72510,72511,72513],{},[898,72512,3946],{},[898,72514,4003],{},[902,72516,63484],{"encoding":904},[883,72518,72520],{"className":72519},[886],[888,72521,72522],{"xmlns":890},[892,72523,72524,72545],{},[895,72525,72526,72528,72530,72532,72535,72537,72539],{},[898,72527,2783],{},[898,72529,4003],{},[2005,72531,2007],{},[2138,72533,72534],{},"125",[898,72536,2797],{},[2005,72538,2234],{},[2133,72540,72541,72543],{},[898,72542,2797],{},[2138,72544,2140],{},[902,72546,72547],{"encoding":904},"TR = 125Q - Q^2",[883,72549,72551],{"className":72550},[886],[888,72552,72553],{"xmlns":890},[892,72554,72555,72581],{},[895,72556,72557,72559,72561,72563,72565,72567,72569,72571,72573,72575],{},[898,72558,2783],{},[898,72560,1852],{},[2005,72562,2007],{},[2138,72564,15116],{},[2005,72566,2104],{},[2138,72568,2237],{},[898,72570,2797],{},[2005,72572,2104],{},[2138,72574,5015],{},[2133,72576,72577,72579],{},[898,72578,2797],{},[2138,72580,2140],{},[902,72582,72583],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,72585,72587],{"className":72586},[886],[888,72588,72589],{"xmlns":890},[892,72590,72591,72613],{},[895,72592,72593,72595,72597,72599,72601,72603,72605,72607],{},[898,72594,2783],{},[898,72596,4003],{},[2005,72598,2007],{},[2138,72600,9041],{},[898,72602,2797],{},[2005,72604,2234],{},[2138,72606,2140],{},[2133,72608,72609,72611],{},[898,72610,2797],{},[2138,72612,2140],{},[902,72614,72615],{"encoding":904},"TR = 20Q - 2Q^2",[883,72617,72619],{"className":72618},[886],[888,72620,72621],{"xmlns":890},[892,72622,72623,72657],{},[895,72624,72625,72627,72629,72631,72633,72635,72637,72639,72641,72643,72649,72651],{},[898,72626,2783],{},[898,72628,1852],{},[2005,72630,2007],{},[2138,72632,2140],{},[2005,72634,2104],{},[2138,72636,9041],{},[898,72638,2797],{},[2005,72640,2234],{},[2138,72642,5591],{},[2133,72644,72645,72647],{},[898,72646,2797],{},[2138,72648,2140],{},[2005,72650,2104],{},[2133,72652,72653,72655],{},[898,72654,2797],{},[2138,72656,2182],{},[902,72658,72659],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,72662,72664],{"className":72663},[886],[888,72665,72666],{"xmlns":890},[892,72667,72668,72690],{},[895,72669,72670,72672,72674,72676,72678,72680,72682,72684],{},[898,72671,2783],{},[898,72673,4003],{},[2005,72675,2007],{},[2138,72677,2360],{},[898,72679,2797],{},[2005,72681,2234],{},[2138,72683,23794],{},[2133,72685,72686,72688],{},[898,72687,2797],{},[2138,72689,2140],{},[902,72691,72692],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,72694,72696],{"className":72695},[886],[888,72697,72698],{"xmlns":890},[892,72699,72700,72748],{},[895,72701,72702,72704,72706,72708,72710,72712,72714,72716,72718,72734,72736],{},[898,72703,2783],{},[898,72705,1852],{},[2005,72707,2007],{},[2138,72709,2360],{},[2005,72711,2104],{},[2138,72713,2140],{},[898,72715,2797],{},[2005,72717,2234],{},[2334,72719,72720],{"scriptlevel":2336,"displaystyle":2013},[2338,72721,72722,72732],{},[895,72723,72724,72726],{},[2138,72725,2182],{},[2133,72727,72728,72730],{},[898,72729,2797],{},[2138,72731,2140],{},[2138,72733,2871],{},[2005,72735,2104],{},[2334,72737,72738],{"scriptlevel":2336,"displaystyle":2013},[2338,72739,72740,72746],{},[2133,72741,72742,72744],{},[898,72743,2797],{},[2138,72745,2182],{},[2138,72747,9041],{},[902,72749,72750],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,72752,72753,72756,72757,72787,72788,72820,72821,21600,72851,72881],{},[38,72754,72755],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,72758,72760],{"className":72759},[886],[888,72761,72762],{"xmlns":890},[892,72763,72764,72784],{},[895,72765,72766,72772,72774,72776,72778],{},[2281,72767,72768,72770],{},[898,72769,3946],{},[2138,72771,2287],{},[2005,72773,2007],{},[2138,72775,15116],{},[2005,72777,2234],{},[2281,72779,72780,72782],{},[898,72781,2797],{},[2138,72783,2287],{},[902,72785,72786],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,72789,72791],{"className":72790},[886],[888,72792,72793],{"xmlns":890},[892,72794,72795,72817],{},[895,72796,72797,72803,72805,72807,72809,72811],{},[2281,72798,72799,72801],{},[898,72800,3946],{},[2138,72802,2140],{},[2005,72804,2007],{},[2138,72806,30086],{},[2005,72808,2234],{},[2138,72810,64564],{},[2281,72812,72813,72815],{},[898,72814,2797],{},[2138,72816,2140],{},[902,72818,72819],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,72822,72824],{"className":72823},[886],[888,72825,72826],{"xmlns":890},[892,72827,72828,72848],{},[895,72829,72830,72832,72834,72836,72838,72840,72842,72844,72846],{},[898,72831,2783],{},[898,72833,1852],{},[2005,72835,2007],{},[2138,72837,3128],{},[2297,72839,2995],{},[2138,72841,59087],{},[2005,72843,2104],{},[2138,72845,9041],{},[898,72847,2797],{},[902,72849,72850],{"encoding":904},"TC = 50\\,000 + 20Q",[883,72852,72854],{"className":72853},[886],[888,72855,72856],{"xmlns":890},[892,72857,72858,72878],{},[895,72859,72860,72862,72864,72870,72872],{},[898,72861,2797],{},[2005,72863,2007],{},[2281,72865,72866,72868],{},[898,72867,2797],{},[2138,72869,2287],{},[2005,72871,2104],{},[2281,72873,72874,72876],{},[898,72875,2797],{},[2138,72877,2140],{},[902,72879,72880],{"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.",[724,72883,72884,72887,72888,72918,72919,72820,72951,21600,72981,73010],{},[38,72885,72886],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,72889,72891],{"className":72890},[886],[888,72892,72893],{"xmlns":890},[892,72894,72895,72915],{},[895,72896,72897,72903,72905,72907,72909],{},[2281,72898,72899,72901],{},[898,72900,3946],{},[2138,72902,2287],{},[2005,72904,2007],{},[2138,72906,30086],{},[2005,72908,2234],{},[2281,72910,72911,72913],{},[898,72912,2797],{},[2138,72914,2287],{},[902,72916,72917],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,72920,72922],{"className":72921},[886],[888,72923,72924],{"xmlns":890},[892,72925,72926,72948],{},[895,72927,72928,72934,72936,72938,72940,72942],{},[2281,72929,72930,72932],{},[898,72931,3946],{},[2138,72933,2140],{},[2005,72935,2007],{},[2138,72937,8383],{},[2005,72939,2234],{},[2138,72941,5015],{},[2281,72943,72944,72946],{},[898,72945,2797],{},[2138,72947,2140],{},[902,72949,72950],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,72952,72954],{"className":72953},[886],[888,72955,72956],{"xmlns":890},[892,72957,72958,72978],{},[895,72959,72960,72962,72964,72966,72968,72970,72972,72974,72976],{},[898,72961,2783],{},[898,72963,1852],{},[2005,72965,2007],{},[2138,72967,2237],{},[2297,72969,2995],{},[2138,72971,59087],{},[2005,72973,2104],{},[2138,72975,3098],{},[898,72977,2797],{},[902,72979,72980],{"encoding":904},"TC = 5\\,000 + 100Q",[883,72982,72984],{"className":72983},[886],[888,72985,72986],{"xmlns":890},[892,72987,72988,73008],{},[895,72989,72990,72992,72994,73000,73002],{},[898,72991,2797],{},[2005,72993,2007],{},[2281,72995,72996,72998],{},[898,72997,2797],{},[2138,72999,2287],{},[2005,73001,2104],{},[2281,73003,73004,73006],{},[898,73005,2797],{},[2138,73007,2140],{},[902,73009,72880],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,73012,73014],{"id":73013},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,73016,73017,73020,73021,73068,73069,73086],{},[38,73018,73019],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,73022,73024],{"className":73023},[886],[888,73025,73026],{"xmlns":890},[892,73027,73028,73065],{},[895,73029,73030,73032,73034,73036,73038,73041,73047,73049,73052,73058,73060,73063],{},[898,73031,2783],{},[898,73033,40344],{},[898,73035,1852],{},[2005,73037,2007],{},[2138,73039,73040],{},"0,85",[2133,73042,73043,73045],{},[898,73044,2797],{},[2138,73046,2182],{},[2005,73048,2234],{},[2138,73050,73051],{},"11,9",[2133,73053,73054,73056],{},[898,73055,2797],{},[2138,73057,2140],{},[2005,73059,2104],{},[2138,73061,73062],{},"102",[898,73064,2797],{},[902,73066,73067],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,73070,73072],{"className":73071},[886],[888,73073,73074],{"xmlns":890},[892,73075,73076,73084],{},[895,73077,73078],{},[2133,73079,73080,73082],{},[898,73081,3946],{},[2005,73083,4360],{},[902,73085,4410],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,73088,73089,70847,73092,73128],{},[38,73090,73091],{},"3.27",[883,73093,73095],{"className":73094},[886],[888,73096,73097],{"xmlns":890},[892,73098,73099,73125],{},[895,73100,73101,73103,73105,73107,73109,73115,73117,73119,73121,73123],{},[898,73102,2826],{},[898,73104,1852],{},[2005,73106,2007],{},[2138,73108,2931],{},[2133,73110,73111,73113],{},[898,73112,2797],{},[2138,73114,2140],{},[2005,73116,2234],{},[2138,73118,64445],{},[898,73120,2797],{},[2005,73122,2104],{},[2138,73124,30748],{},[902,73126,73127],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,73130,73131,70098,73134,73128],{},[38,73132,73133],{},"3.28",[883,73135,73137],{"className":73136},[886],[888,73138,73139],{"xmlns":890},[892,73140,73141,73177],{},[895,73142,73143,73145,73147,73149,73151,73157,73159,73161,73167,73169,73171,73173,73175],{},[898,73144,2783],{},[898,73146,1852],{},[2005,73148,2007],{},[2138,73150,5015],{},[2133,73152,73153,73155],{},[898,73154,2797],{},[2138,73156,2182],{},[2005,73158,2234],{},[2138,73160,24206],{},[2133,73162,73163,73165],{},[898,73164,2797],{},[2138,73166,2140],{},[2005,73168,2104],{},[2138,73170,3134],{},[898,73172,2797],{},[2005,73174,2104],{},[2138,73176,15116],{},[902,73178,73179],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,73181,15726],{"id":15725},[120,73183,73184,73212,73257,73329,73394,73434,73526,73632,73672,73786,73879,73943,73975,74035,74041,74105,74154,74208,74316,74371],{},[123,73185,73186,2212,73188,73211],{},[38,73187,55755],{},[883,73189,73191],{"className":73190},[886],[888,73192,73193],{"xmlns":890},[892,73194,73195,73209],{},[895,73196,73197,73199,73201,73203,73205,73207],{},[898,73198,2783],{},[898,73200,4003],{},[2005,73202,2007],{},[898,73204,3946],{},[2005,73206,3185],{},[898,73208,2797],{},[902,73210,66717],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,73213,73214,2212,73216,73256],{},[38,73215,56341],{},[883,73217,73219],{"className":73218},[886],[888,73220,73221],{"xmlns":890},[892,73222,73223,73253],{},[895,73224,73225,73227,73229,73231,73243,73245,73247,73249,73251],{},[898,73226,1836],{},[898,73228,4003],{},[2005,73230,2007],{},[2334,73232,73233],{"scriptlevel":2336,"displaystyle":2013},[2338,73234,73235,73241],{},[895,73236,73237,73239],{},[898,73238,2783],{},[898,73240,4003],{},[898,73242,2797],{},[2005,73244,2007],{},[898,73246,1860],{},[2005,73248,2014],{"stretchy":2013},[898,73250,2797],{},[2005,73252,2020],{"stretchy":2013},[902,73254,73255],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,73258,73259,2212,73261,73297,73298,73313,73314,1644],{},[38,73260,56489],{},[883,73262,73264],{"className":73263},[886],[888,73265,73266],{"xmlns":890},[892,73267,73268,73294],{},[895,73269,73270,73272,73274,73276],{},[898,73271,2826],{},[898,73273,4003],{},[2005,73275,2007],{},[2334,73277,73278],{"scriptlevel":2336,"displaystyle":2013},[2338,73279,73280,73288],{},[895,73281,73282,73284,73286],{},[898,73283,2203],{"mathvariant":2385},[898,73285,2783],{},[898,73287,4003],{},[895,73289,73290,73292],{},[898,73291,2203],{"mathvariant":2385},[898,73293,2797],{},[902,73295,73296],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,73299,73301],{"className":73300},[886],[888,73302,73303],{"xmlns":890},[892,73304,73305,73311],{},[895,73306,73307,73309],{},[898,73308,2783],{},[898,73310,4003],{},[902,73312,4103],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,73315,73317],{"className":73316},[886],[888,73318,73319],{"xmlns":890},[892,73320,73321,73327],{},[895,73322,73323,73325],{},[898,73324,1836],{},[898,73326,4003],{},[902,73328,55450],{"encoding":904},[123,73330,73331,2212,73334,1343,73364,1644],{},[38,73332,73333],{},"Diferenciál příjmu\u002Fnákladů",[883,73335,73337],{"className":73336},[886],[888,73338,73339],{"xmlns":890},[892,73340,73341,73361],{},[895,73342,73343,73345,73347,73349,73351,73353,73355,73357,73359],{},[898,73344,2897],{"mathvariant":2385},[898,73346,2783],{},[898,73348,4003],{},[2005,73350,2739],{},[898,73352,2826],{},[898,73354,4003],{},[2297,73356,2995],{},[898,73358,2203],{"mathvariant":2385},[898,73360,2797],{},[902,73362,73363],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,73365,73367],{"className":73366},[886],[888,73368,73369],{"xmlns":890},[892,73370,73371,73391],{},[895,73372,73373,73375,73377,73379,73381,73383,73385,73387,73389],{},[898,73374,2897],{"mathvariant":2385},[898,73376,2783],{},[898,73378,1852],{},[2005,73380,2739],{},[898,73382,2826],{},[898,73384,1852],{},[2297,73386,2995],{},[898,73388,2203],{"mathvariant":2385},[898,73390,2797],{},[902,73392,73393],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,73395,73396,2212,73398,1644],{},[38,73397,58611],{},[883,73399,73401],{"className":73400},[886],[888,73402,73403],{"xmlns":890},[892,73404,73405,73431],{},[895,73406,73407,73409,73411,73413,73415,73417,73419,73421,73423,73425,73427,73429],{},[898,73408,2783],{},[898,73410,1852],{},[2005,73412,2007],{},[898,73414,1876],{},[898,73416,1852],{},[2005,73418,2104],{},[898,73420,2783],{},[898,73422,40344],{},[898,73424,1852],{},[2005,73426,2014],{"stretchy":2013},[898,73428,2797],{},[2005,73430,2020],{"stretchy":2013},[902,73432,73433],{"encoding":904},"TC = FC + TVC(Q)",[123,73435,73436,2212,73439,1343,73454,2212,73456,1343,73479,2212,73482,1644],{},[38,73437,73438],{},"Fixní náklady",[883,73440,73442],{"className":73441},[886],[888,73443,73444],{"xmlns":890},[892,73445,73446,73452],{},[895,73447,73448,73450],{},[898,73449,1876],{},[898,73451,1852],{},[902,73453,55496],{"encoding":904},[38,73455,58764],{},[883,73457,73459],{"className":73458},[886],[888,73460,73461],{"xmlns":890},[892,73462,73463,73477],{},[895,73464,73465,73467,73469,73471,73473,73475],{},[898,73466,2783],{},[898,73468,40344],{},[898,73470,1852],{},[2005,73472,2014],{"stretchy":2013},[898,73474,2797],{},[2005,73476,2020],{"stretchy":2013},[902,73478,58761],{"encoding":904},[38,73480,73481],{},"variabilní náklady na jednotku",[883,73483,73485],{"className":73484},[886],[888,73486,73487],{"xmlns":890},[892,73488,73489,73523],{},[895,73490,73491,73493,73495,73497,73499,73501,73503],{},[898,73492,40344],{},[898,73494,1852],{},[2005,73496,2014],{"stretchy":2013},[898,73498,2797],{},[2005,73500,2020],{"stretchy":2013},[2005,73502,2007],{},[2334,73504,73505],{"scriptlevel":2336,"displaystyle":2013},[2338,73506,73507,73521],{},[895,73508,73509,73511,73513,73515,73517,73519],{},[898,73510,2783],{},[898,73512,40344],{},[898,73514,1852],{},[2005,73516,2014],{"stretchy":2013},[898,73518,2797],{},[2005,73520,2020],{"stretchy":2013},[898,73522,2797],{},[902,73524,73525],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,73527,73528,2212,73530,1343,73560,2212,73563,1343,73595,2212,73598,1644],{},[38,73529,58772],{},[883,73531,73533],{"className":73532},[886],[888,73534,73535],{"xmlns":890},[892,73536,73537,73557],{},[895,73538,73539,73541,73543,73545],{},[898,73540,1836],{},[898,73542,1852],{},[2005,73544,2007],{},[2334,73546,73547],{"scriptlevel":2336,"displaystyle":2013},[2338,73548,73549,73555],{},[895,73550,73551,73553],{},[898,73552,2783],{},[898,73554,1852],{},[898,73556,2797],{},[902,73558,73559],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,73561,73562],{},"průměrné fixní",[883,73564,73566],{"className":73565},[886],[888,73567,73568],{"xmlns":890},[892,73569,73570,73592],{},[895,73571,73572,73574,73576,73578,73580],{},[898,73573,1836],{},[898,73575,1876],{},[898,73577,1852],{},[2005,73579,2007],{},[2334,73581,73582],{"scriptlevel":2336,"displaystyle":2013},[2338,73583,73584,73590],{},[895,73585,73586,73588],{},[898,73587,1876],{},[898,73589,1852],{},[898,73591,2797],{},[902,73593,73594],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,73596,73597],{},"průměrné variabilní",[883,73599,73601],{"className":73600},[886],[888,73602,73603],{"xmlns":890},[892,73604,73605,73629],{},[895,73606,73607,73609,73611,73613,73615],{},[898,73608,1836],{},[898,73610,40344],{},[898,73612,1852],{},[2005,73614,2007],{},[2334,73616,73617],{"scriptlevel":2336,"displaystyle":2013},[2338,73618,73619,73627],{},[895,73620,73621,73623,73625],{},[898,73622,2783],{},[898,73624,40344],{},[898,73626,1852],{},[898,73628,2797],{},[902,73630,73631],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,73633,73634,2212,73636,1644],{},[38,73635,59959],{},[883,73637,73639],{"className":73638},[886],[888,73640,73641],{"xmlns":890},[892,73642,73643,73669],{},[895,73644,73645,73647,73649,73651],{},[898,73646,2826],{},[898,73648,1852],{},[2005,73650,2007],{},[2334,73652,73653],{"scriptlevel":2336,"displaystyle":2013},[2338,73654,73655,73663],{},[895,73656,73657,73659,73661],{},[898,73658,2203],{"mathvariant":2385},[898,73660,2783],{},[898,73662,1852],{},[895,73664,73665,73667],{},[898,73666,2203],{"mathvariant":2385},[898,73668,2797],{},[902,73670,73671],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,73673,73674,2212,73676,73724,73725,73738,73739,1343,73754,1343,73771,1644],{},[38,73675,60857],{},[883,73677,73679],{"className":73678},[886],[888,73680,73681],{"xmlns":890},[892,73682,73683,73721],{},[895,73684,73685,73687,73689,73691,73693,73695,73697,73699,73701,73703,73705,73711,73713,73715],{},[898,73686,2783],{},[898,73688,1852],{},[2005,73690,2007],{},[898,73692,1876],{},[898,73694,1852],{},[2005,73696,2104],{},[898,73698,207],{},[898,73700,2797],{},[2005,73702,2104],{},[898,73704,2107],{},[2133,73706,73707,73709],{},[898,73708,2797],{},[2138,73710,2140],{},[2005,73712,2104],{},[898,73714,2151],{},[2133,73716,73717,73719],{},[898,73718,2797],{},[2138,73720,2182],{},[902,73722,73723],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,73726,73728],{"className":73727},[886],[888,73729,73730],{"xmlns":890},[892,73731,73732,73736],{},[895,73733,73734],{},[898,73735,900],{},[902,73737,900],{"encoding":904},"-průběhem ",[883,73740,73742],{"className":73741},[886],[888,73743,73744],{"xmlns":890},[892,73745,73746,73752],{},[895,73747,73748,73750],{},[898,73749,1836],{},[898,73751,1852],{},[902,73753,55565],{"encoding":904},[883,73755,73757],{"className":73756},[886],[888,73758,73759],{"xmlns":890},[892,73760,73761,73769],{},[895,73762,73763,73765,73767],{},[898,73764,1836],{},[898,73766,40344],{},[898,73768,1852],{},[902,73770,55316],{"encoding":904},[883,73772,73774],{"className":73773},[886],[888,73775,73776],{"xmlns":890},[892,73777,73778,73784],{},[895,73779,73780,73782],{},[898,73781,2826],{},[898,73783,1852],{},[902,73785,55297],{"encoding":904},[123,73787,73788,73790,73791,10399,73806,73847,73848,61502,73863,73878],{},[38,73789,61939],{},": v bodě minima ",[883,73792,73794],{"className":73793},[886],[888,73795,73796],{"xmlns":890},[892,73797,73798,73804],{},[895,73799,73800,73802],{},[898,73801,1836],{},[898,73803,1852],{},[902,73805,55565],{"encoding":904},[883,73807,73809],{"className":73808},[886],[888,73810,73811],{"xmlns":890},[892,73812,73813,73845],{},[895,73814,73815,73817,73819,73821,73827,73829,73831,73833,73835,73837,73843],{},[898,73816,1836],{},[898,73818,1852],{},[2005,73820,2014],{"stretchy":2013},[2281,73822,73823,73825],{},[898,73824,2797],{},[2138,73826,2336],{},[2005,73828,2020],{"stretchy":2013},[2005,73830,2007],{},[898,73832,2826],{},[898,73834,1852],{},[2005,73836,2014],{"stretchy":2013},[2281,73838,73839,73841],{},[898,73840,2797],{},[2138,73842,2336],{},[2005,73844,2020],{"stretchy":2013},[902,73846,62574],{"encoding":904},"; geometricky ",[883,73849,73851],{"className":73850},[886],[888,73852,73853],{"xmlns":890},[892,73854,73855,73861],{},[895,73856,73857,73859],{},[898,73858,2826],{},[898,73860,1852],{},[902,73862,55297],{"encoding":904},[883,73864,73866],{"className":73865},[886],[888,73867,73868],{"xmlns":890},[892,73869,73870,73876],{},[895,73871,73872,73874],{},[898,73873,1836],{},[898,73875,1852],{},[902,73877,55565],{"encoding":904}," v jejím minimu.",[123,73880,73881,73790,73883,10399,73900,1644],{},[38,73882,63289],{},[883,73884,73886],{"className":73885},[886],[888,73887,73888],{"xmlns":890},[892,73889,73890,73898],{},[895,73891,73892,73894,73896],{},[898,73893,1836],{},[898,73895,40344],{},[898,73897,1852],{},[902,73899,55316],{"encoding":904},[883,73901,73903],{"className":73902},[886],[888,73904,73905],{"xmlns":890},[892,73906,73907,73941],{},[895,73908,73909,73911,73913,73915,73917,73923,73925,73927,73929,73931,73933,73939],{},[898,73910,1836],{},[898,73912,40344],{},[898,73914,1852],{},[2005,73916,2014],{"stretchy":2013},[2281,73918,73919,73921],{},[898,73920,2797],{},[2138,73922,2336],{},[2005,73924,2020],{"stretchy":2013},[2005,73926,2007],{},[898,73928,2826],{},[898,73930,1852],{},[2005,73932,2014],{"stretchy":2013},[2281,73934,73935,73937],{},[898,73936,2797],{},[2138,73938,2336],{},[2005,73940,2020],{"stretchy":2013},[902,73942,69024],{"encoding":904},[123,73944,73945,2212,73947,73974],{},[38,73946,63468],{},[883,73948,73950],{"className":73949},[886],[888,73951,73952],{"xmlns":890},[892,73953,73954,73972],{},[895,73955,73956,73958,73960,73962,73964,73966,73968,73970],{},[898,73957,3946],{},[898,73959,4003],{},[2005,73961,2007],{},[898,73963,2783],{},[898,73965,4003],{},[2005,73967,2234],{},[898,73969,2783],{},[898,73971,1852],{},[902,73973,55205],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,73976,73977,10030,73979,73981,73982,74008,74009,74034],{},[38,73978,64330],{},[614,73980,63593],{},") — hodnoty ",[883,73983,73985],{"className":73984},[886],[888,73986,73987],{"xmlns":890},[892,73988,73989,74005],{},[895,73990,73991,73997,73999],{},[2281,73992,73993,73995],{},[898,73994,2797],{},[898,73996,1836],{},[2005,73998,2295],{"separator":2294},[2281,74000,74001,74003],{},[898,74002,2797],{},[898,74004,1844],{},[902,74006,74007],{"encoding":904},"Q_A, Q_B"," splňující ",[883,74010,74012],{"className":74011},[886],[888,74013,74014],{"xmlns":890},[892,74015,74016,74032],{},[895,74017,74018,74020,74022,74024,74026,74028,74030],{},[898,74019,3946],{},[898,74021,4003],{},[2005,74023,2014],{"stretchy":2013},[898,74025,2797],{},[2005,74027,2020],{"stretchy":2013},[2005,74029,2007],{},[2138,74031,2336],{},[902,74033,63870],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,74036,74037,74040],{},[38,74038,74039],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,74042,74043,74045,74046,10399,74063,74104],{},[38,74044,65384],{}," — v bodě maxima zisku ",[883,74047,74049],{"className":74048},[886],[888,74050,74051],{"xmlns":890},[892,74052,74053,74061],{},[895,74054,74055],{},[2281,74056,74057,74059],{},[898,74058,2797],{},[2138,74060,2336],{},[902,74062,38313],{"encoding":904},[883,74064,74066],{"className":74065},[886],[888,74067,74068],{"xmlns":890},[892,74069,74070,74102],{},[895,74071,74072,74074,74076,74078,74084,74086,74088,74090,74092,74094,74100],{},[898,74073,2826],{},[898,74075,4003],{},[2005,74077,2014],{"stretchy":2013},[2281,74079,74080,74082],{},[898,74081,2797],{},[2138,74083,2336],{},[2005,74085,2020],{"stretchy":2013},[2005,74087,2007],{},[898,74089,2826],{},[898,74091,1852],{},[2005,74093,2014],{"stretchy":2013},[2281,74095,74096,74098],{},[898,74097,2797],{},[2138,74099,2336],{},[2005,74101,2020],{"stretchy":2013},[902,74103,65650],{"encoding":904}," (3.13).",[123,74106,74107,20307,74109,10399,74128,74153],{},[38,74108,66677],{},[883,74110,74112],{"className":74111},[886],[888,74113,74114],{"xmlns":890},[892,74115,74116,74125],{},[895,74117,74118,74120,74122],{},[898,74119,3946],{},[2005,74121,2007],{},[2297,74123,74124],{},"konst",[902,74126,74127],{"encoding":904},"P = \\text{konst}",[883,74129,74131],{"className":74130},[886],[888,74132,74133],{"xmlns":890},[892,74134,74135,74151],{},[895,74136,74137,74139,74141,74143,74145,74147,74149],{},[898,74138,3946],{},[2005,74140,2007],{},[898,74142,2826],{},[898,74144,1852],{},[2005,74146,2014],{"stretchy":2013},[898,74148,2797],{},[2005,74150,2020],{"stretchy":2013},[902,74152,67371],{"encoding":904}," (3.14).",[123,74155,74156,74159,74160,74189,74190,74207],{},[38,74157,74158],{},"Shutdown point"," — bod ",[883,74161,74163],{"className":74162},[886],[888,74164,74165],{"xmlns":890},[892,74166,74167,74187],{},[895,74168,74169,74171,74177,74179,74185],{},[2005,74170,2014],{"stretchy":2013},[2133,74172,74173,74175],{},[898,74174,2797],{},[2005,74176,4360],{},[2005,74178,2295],{"separator":2294},[2133,74180,74181,74183],{},[898,74182,3946],{},[2005,74184,4360],{},[2005,74186,2020],{"stretchy":2013},[902,74188,67660],{"encoding":904}," v minimu ",[883,74191,74193],{"className":74192},[886],[888,74194,74195],{"xmlns":890},[892,74196,74197,74205],{},[895,74198,74199,74201,74203],{},[898,74200,1836],{},[898,74202,40344],{},[898,74204,1852],{},[902,74206,55316],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,74209,74210,2212,74213,6479,74248,67930,74269,74282,74283,74298,74299,1644],{},[38,74211,74212],{},"Funkce nabídky firmy",[883,74214,74216],{"className":74215},[886],[888,74217,74218],{"xmlns":890},[892,74219,74220,74246],{},[895,74221,74222,74224,74226,74228,74230,74232,74234,74236,74238,74240,74242,74244],{},[898,74223,3946],{},[2005,74225,2007],{},[898,74227,8679],{},[2005,74229,2014],{"stretchy":2013},[898,74231,2797],{},[2005,74233,2020],{"stretchy":2013},[2005,74235,2007],{},[898,74237,2826],{},[898,74239,1852],{},[2005,74241,2014],{"stretchy":2013},[898,74243,2797],{},[2005,74245,2020],{"stretchy":2013},[902,74247,69127],{"encoding":904},[883,74249,74251],{"className":74250},[886],[888,74252,74253],{"xmlns":890},[892,74254,74255,74267],{},[895,74256,74257,74259,74261],{},[898,74258,2797],{},[2005,74260,4491],{},[2133,74262,74263,74265],{},[898,74264,2797],{},[2005,74266,4360],{},[902,74268,67929],{"encoding":904},[883,74270,74272],{"className":74271},[886],[888,74273,74274],{"xmlns":890},[892,74275,74276,74280],{},[895,74277,74278],{},[2138,74279,2336],{},[902,74281,2336],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,74284,74286],{"className":74285},[886],[888,74287,74288],{"xmlns":890},[892,74289,74290,74296],{},[895,74291,74292,74294],{},[898,74293,2826],{},[898,74295,1852],{},[902,74297,55297],{"encoding":904}," nad minimem ",[883,74300,74302],{"className":74301},[886],[888,74303,74304],{"xmlns":890},[892,74305,74306,74314],{},[895,74307,74308,74310,74312],{},[898,74309,1836],{},[898,74311,40344],{},[898,74313,1852],{},[902,74315,55316],{"encoding":904},[123,74317,74318,7021,74320,74341,74342,1644],{},[38,74319,50084],{},[883,74321,74323],{"className":74322},[886],[888,74324,74325],{"xmlns":890},[892,74326,74327,74339],{},[895,74328,74329,74331,74333],{},[898,74330,3946],{},[2005,74332,2007],{},[2133,74334,74335,74337],{},[898,74336,3946],{},[2005,74338,4360],{},[902,74340,4363],{"encoding":904}," konstantní ⇒ ",[883,74343,74345],{"className":74344},[886],[888,74346,74347],{"xmlns":890},[892,74348,74349,74369],{},[895,74350,74351,74353,74355,74357,74359,74361,74363],{},[898,74352,1836],{},[898,74354,4003],{},[2005,74356,2007],{},[898,74358,2826],{},[898,74360,4003],{},[2005,74362,2007],{},[2133,74364,74365,74367],{},[898,74366,3946],{},[2005,74368,4360],{},[902,74370,58603],{"encoding":904},[123,74372,74373,74376],{},[38,74374,74375],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,74378,3800],{"id":3799},[120,74380,74381,74400,74412],{},[123,74382,74383,2212,74385,1343,74388,1343,74391,1343,74394,1343,74397],{},[38,74384,50728],{},[207,74386,11946],{"className":74387,"dataFsResolvedFilePath":800,"href":801},[210],[207,74389,3836],{"className":74390,"dataFsResolvedFilePath":848,"href":849},[210],[207,74392,2366],{"className":74393,"dataFsResolvedFilePath":764,"href":765},[210],[207,74395,775],{"className":74396,"dataFsResolvedFilePath":773,"href":774},[210],[207,74398,859],{"className":74399,"dataFsResolvedFilePath":857,"href":858},[210],[123,74401,74402,2212,74404,1343,74408],{},[38,74403,36708],{},[207,74405,74407],{"className":74406,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,74409,74411],{"className":74410,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,74413,74414,2212,74416],{},[38,74415,16210],{},[207,74417,16214],{"className":74418,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":74420},[74421,74422,74429,74435,74439,74440,74444,74445,74446,74447,74453,74454],{"id":50959,"depth":642,"text":1241},{"id":55743,"depth":642,"text":55744,"children":74423},[74424,74425,74426,74427,74428],{"id":55754,"depth":649,"text":55755},{"id":56340,"depth":649,"text":56341},{"id":56488,"depth":649,"text":56489},{"id":57230,"depth":649,"text":57231},{"id":57885,"depth":649,"text":57886},{"id":58606,"depth":642,"text":58607,"children":74430},[74431,74432,74433,74434],{"id":58610,"depth":649,"text":58611},{"id":58771,"depth":649,"text":58772},{"id":59958,"depth":649,"text":59959},{"id":60856,"depth":649,"text":60857},{"id":61938,"depth":642,"text":61939,"children":74436},[74437,74438],{"id":16418,"depth":649,"text":16419},{"id":63288,"depth":649,"text":63289},{"id":63462,"depth":642,"text":63463},{"id":65383,"depth":642,"text":65384,"children":74441},[74442,74443],{"id":65397,"depth":649,"text":16419},{"id":66676,"depth":649,"text":66677},{"id":67308,"depth":642,"text":67309},{"id":68774,"depth":642,"text":68775},{"id":49886,"depth":642,"text":49887},{"id":69235,"depth":642,"text":69236,"children":74448},[74449,74450,74451,74452],{"id":69239,"depth":649,"text":69240},{"id":70091,"depth":649,"text":70092},{"id":71637,"depth":649,"text":71638},{"id":73013,"depth":649,"text":73014},{"id":15725,"depth":642,"text":15726},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":55125,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,74461,74462,55177,74463,74464,74465],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":74468,"title":74469,"body":74470,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":86567,"navigation":664,"path":86568,"seo":86569,"sources":86570,"stem":86571,"tags":86572,"type":3865,"updated":677,"__hash__":86578},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":74471,"toc":86524},[74472,74475,74831,74835,74838,74906,74958,74968,74972,75006,75047,75071,75094,75123,75190,75297,75340,75397,75472,75517,75521,75529,75537,75540,75805,75856,75936,76006,76029,76057,76102,76124,76128,76135,76184,76210,76361,76364,76401,76564,76672,76676,76713,76788,76857,76976,77098,77179,77185,77226,77299,77392,77396,77432,77520,77634,77739,77824,77964,77968,78016,78061,78067,78071,78074,78125,78175,78182,78248,78381,78426,78430,78451,78830,78925,78942,78996,79000,79082,79166,79336,79339,79382,79449,79523,79527,79532,79601,79609,79618,79696,79762,79767,79862,79905,79910,79958,79963,80011,80129,80212,80250,80353,80412,80553,80557,80600,80673,80697,80751,80758,80760,80805,80850,80861,80866,80902,80964,80987,80996,81097,81164,81237,81244,81335,81397,81433,81490,81549,81734,81830,81834,81838,81917,81922,82046,82132,82138,82248,82285,82376,82474,82477,82481,82547,82584,82706,82758,82762,82790,82842,82916,83021,83045,83104,83108,83126,83269,83417,83419,83454,83458,83460,83550,83680,83806,83898,83973,83977,84093,84197,84387,84423,84517,84523,84636,84939,84945,85063,85162,85238,85240,86402,86404],[12,74473,74469],{"id":74474},"produkce-produkční-funkce-cobb-douglas-mrts",[3876,74476,74477],{},[724,74478,74479,3883,74481,74483,74484,36901,74497,74510,74511,16383,74524,10030,74526,74550,74551,2212,74553,3894,74587,2212,74590,74618,74619,10399,74639,74669,74670,10030,74673,74701,74702,74705,74706,74736,74737,74767,74768,2212,74771,74811,74812,74830],{},[883,74480,3882],{},[38,74482,859],{}," popisuje vztah mezi vstupy (práce ",[883,74485,74487],{"className":74486},[886],[888,74488,74489],{"xmlns":890},[892,74490,74491,74495],{},[895,74492,74493],{},[898,74494,9801],{},[902,74496,9801],{"encoding":904},[883,74498,74500],{"className":74499},[886],[888,74501,74502],{"xmlns":890},[892,74503,74504,74508],{},[895,74505,74506],{},[898,74507,9806],{},[902,74509,9806],{"encoding":904},") a výstupem ",[883,74512,74514],{"className":74513},[886],[888,74515,74516],{"xmlns":890},[892,74517,74518,74522],{},[895,74519,74520],{},[898,74521,2797],{},[902,74523,2797],{"encoding":904},[38,74525,36969],{},[883,74527,74529],{"className":74528},[886],[888,74530,74531],{"xmlns":890},[892,74532,74533,74547],{},[895,74534,74535,74537,74539,74541,74543,74545],{},[898,74536,2797],{},[2005,74538,2007],{},[898,74540,2797],{},[2005,74542,2014],{"stretchy":2013},[898,74544,9801],{},[2005,74546,2020],{"stretchy":2013},[902,74548,74549],{"encoding":904},"Q = Q(L)",") studujeme ",[614,74552,10029],{},[883,74554,74556],{"className":74555},[886],[888,74557,74558],{"xmlns":890},[892,74559,74560,74584],{},[895,74561,74562,74564,74570,74572,74578,74580,74582],{},[898,74563,2826],{},[2281,74565,74566,74568],{},[898,74567,3946],{},[898,74569,9801],{},[2005,74571,2007],{},[2133,74573,74574,74576],{},[898,74575,2797],{},[2005,74577,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,74579,2014],{"stretchy":2013},[898,74581,9801],{},[2005,74583,2020],{"stretchy":2013},[902,74585,74586],{"encoding":904},"MP_L = Q'(L)",[614,74588,74589],{},"průměrný produkt",[883,74591,74593],{"className":74592},[886],[888,74594,74595],{"xmlns":890},[892,74596,74597,74615],{},[895,74598,74599,74601,74607,74609,74611,74613],{},[898,74600,1836],{},[2281,74602,74603,74605],{},[898,74604,3946],{},[898,74606,9801],{},[2005,74608,2007],{},[898,74610,2797],{},[898,74612,4680],{"mathvariant":2385},[898,74614,9801],{},[902,74616,74617],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,74620,74622],{"className":74621},[886],[888,74623,74624],{"xmlns":890},[892,74625,74626,74636],{},[895,74627,74628,74630],{},[898,74629,1836],{},[2281,74631,74632,74634],{},[898,74633,3946],{},[898,74635,9801],{},[902,74637,74638],{"encoding":904},"AP_L",[883,74640,74642],{"className":74641},[886],[888,74643,74644],{"xmlns":890},[892,74645,74646,74666],{},[895,74647,74648,74650,74656,74658,74660],{},[898,74649,2826],{},[2281,74651,74652,74654],{},[898,74653,3946],{},[898,74655,9801],{},[2005,74657,2007],{},[898,74659,1836],{},[2281,74661,74662,74664],{},[898,74663,3946],{},[898,74665,9801],{},[902,74667,74668],{"encoding":904},"MP_L = AP_L",". Ve ",[38,74671,74672],{},"dvoufaktorovém modelu",[883,74674,74676],{"className":74675},[886],[888,74677,74678],{"xmlns":890},[892,74679,74680,74698],{},[895,74681,74682,74684,74686,74688,74690,74692,74694,74696],{},[898,74683,2797],{},[2005,74685,2007],{},[898,74687,2797],{},[2005,74689,2014],{"stretchy":2013},[898,74691,9801],{},[2005,74693,2295],{"separator":2294},[898,74695,9806],{},[2005,74697,2020],{"stretchy":2013},[902,74699,74700],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,74703,74704],{},"Cobb-Douglasovy"," funkce ",[883,74707,74709],{"className":74708},[886],[888,74710,74711],{"xmlns":890},[892,74712,74713,74733],{},[895,74714,74715,74717,74719,74721,74727],{},[898,74716,2797],{},[2005,74718,2007],{},[898,74720,1836],{},[2133,74722,74723,74725],{},[898,74724,9801],{},[898,74726,207],{},[2133,74728,74729,74731],{},[898,74730,9806],{},[898,74732,2107],{},[902,74734,74735],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,74738,74740],{"className":74739},[886],[888,74741,74742],{"xmlns":890},[892,74743,74744,74764],{},[895,74745,74746,74748,74754,74756,74758],{},[898,74747,2826],{},[2281,74749,74750,74752],{},[898,74751,3946],{},[898,74753,9801],{},[2005,74755,2295],{"separator":2294},[898,74757,2826],{},[2281,74759,74760,74762],{},[898,74761,3946],{},[898,74763,9806],{},[902,74765,74766],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,74769,74770],{},"mezní míru technické substituce",[883,74772,74774],{"className":74773},[886],[888,74775,74776],{"xmlns":890},[892,74777,74778,74808],{},[895,74779,74780,74782,74784,74786,74788,74790,74792,74798,74800,74802],{},[898,74781,2826],{},[898,74783,4003],{},[898,74785,2783],{},[898,74787,8679],{},[2005,74789,2007],{},[898,74791,2826],{},[2281,74793,74794,74796],{},[898,74795,3946],{},[898,74797,9801],{},[898,74799,4680],{"mathvariant":2385},[898,74801,2826],{},[2281,74803,74804,74806],{},[898,74805,3946],{},[898,74807,9806],{},[902,74809,74810],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,74813,74815],{"className":74814},[886],[888,74816,74817],{"xmlns":890},[892,74818,74819,74827],{},[895,74820,74821,74823,74825],{},[898,74822,207],{},[2005,74824,2104],{},[898,74826,2107],{},[902,74828,74829],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,74832,74834],{"id":74833},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,74836,74837],{},"Po prostudování kapitoly 5 student umí:",[120,74839,74840,74846,74856,74862,74868,74873,74879,74889,74894,74900],{},[123,74841,74842,74843,2295],{},"popsat ",[38,74844,74845],{},"jednofaktorový model produkce",[123,74847,74848,74849,3894,74852,74855],{},"vypočítat ",[38,74850,74851],{},"mezní",[38,74853,74854],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,74857,74858,74859,2295],{},"charakterizovat průběh ",[38,74860,74861],{},"křivky produkce",[123,74863,74864,74865,2295],{},"formulovat ",[38,74866,74867],{},"princip maximalizace průměrného produktu práce",[123,74869,74842,74870,2295],{},[38,74871,74872],{},"dvoufaktorový model produkce",[123,74874,74875,74876,2295],{},"uvést tvar ",[38,74877,74878],{},"Cobb–Douglasových produkčních funkcí",[123,74880,74881,74882,1343,74884,1343,74886,2295],{},"vyložit, co jsou ",[38,74883,24618],{},[38,74885,13663],{},[38,74887,74888],{},"klesající výnosy z rozsahu",[123,74890,74848,74891,74855],{},[38,74892,74893],{},"mezní produkty práce a kapitálu",[123,74895,74896,74897,2295],{},"najít ",[38,74898,74899],{},"izokvanty",[123,74901,74848,74902,74905],{},[38,74903,74904],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,74907,74908,74909,74912,74913,74916,74917,2212,74920,1343,74933,2212,74936,3894,74949,74952,74953,74955,74956,1644],{},"Každý proces produkce je určován ",[38,74910,74911],{},"faktory"," (též ",[38,74914,74915],{},"vstupy",") produkce. K hlavním patří ",[38,74918,74919],{},"práce",[883,74921,74923],{"className":74922},[886],[888,74924,74925],{"xmlns":890},[892,74926,74927,74931],{},[895,74928,74929],{},[898,74930,9801],{},[902,74932,9801],{"encoding":904},[38,74934,74935],{},"kapitál",[883,74937,74939],{"className":74938},[886],[888,74940,74941],{"xmlns":890},[892,74942,74943,74947],{},[895,74944,74945],{},[898,74946,9806],{},[902,74948,9806],{"encoding":904},[38,74950,74951],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,74954,36969],{}," (produkce závisí jen na práci); v opačném případě o ",[38,74957,74672],{},[724,74959,74960,74961,1343,74964,74967],{},"Související matematický aparát: ",[207,74962,2366],{"className":74963,"dataFsResolvedFilePath":764,"href":765},[210],[207,74965,784],{"className":74966,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,74969,74971],{"id":74970},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,74973,74974,74975,74988,74989,75002,75003],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,74976,74978],{"className":74977},[886],[888,74979,74980],{"xmlns":890},[892,74981,74982,74986],{},[895,74983,74984],{},[898,74985,2797],{},[902,74987,2797],{"encoding":904}," na práci ",[883,74990,74992],{"className":74991},[886],[888,74993,74994],{"xmlns":890},[892,74995,74996,75000],{},[895,74997,74998],{},[898,74999,9801],{},[902,75001,9801],{"encoding":904}," vyjadřuje ",[38,75004,75005],{},"produkční funkce",[883,75007,75009],{"className":75008},[886],[888,75010,75011],{"xmlns":890,"display":28071},[892,75012,75013,75044],{},[20760,75014,75015],{"width":28076},[20765,75016,75017,75019,75037,75039],{},[20768,75018],{"width":28081},[20768,75020,75021],{},[895,75022,75023,75025,75027,75029,75031,75033,75035],{},[898,75024,2797],{},[2005,75026,2007],{},[898,75028,2797],{},[2005,75030,2014],{"stretchy":2013},[898,75032,9801],{},[2005,75034,2020],{"stretchy":2013},[2005,75036,2295],{"separator":2294},[20768,75038],{"width":28081},[20768,75040,75041],{},[2297,75042,75043],{},"(5.1)",[902,75045,75046],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,75048,75049,75050,10030,75053,75056,75057,75070],{},"jejíž graf se nazývá ",[38,75051,75052],{},"křivka produkce",[614,75054,75055],{},"production curve","). Práce ",[883,75058,75060],{"className":75059},[886],[888,75061,75062],{"xmlns":890},[892,75063,75064,75068],{},[895,75065,75066],{},[898,75067,9801],{},[902,75069,9801],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,75072,75074,75075,2020],{"id":75073},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,75076,75078],{"className":75077},[886],[888,75079,75080],{"xmlns":890},[892,75081,75082,75092],{},[895,75083,75084,75086],{},[898,75085,2826],{},[2281,75087,75088,75090],{},[898,75089,3946],{},[898,75091,9801],{},[902,75093,10050],{"encoding":904},[724,75095,75096,10030,75099,75102,75103,75122],{},[38,75097,75098],{},"Mezní produkt práce",[614,75100,75101],{},"marginal product of labour",") ",[883,75104,75106],{"className":75105},[886],[888,75107,75108],{"xmlns":890},[892,75109,75110,75120],{},[895,75111,75112,75114],{},[898,75113,2826],{},[2281,75115,75116,75118],{},[898,75117,3946],{},[898,75119,9801],{},[902,75121,10050],{"encoding":904}," je derivace produkce podle práce:",[883,75124,75126],{"className":75125},[886],[888,75127,75128],{"xmlns":890,"display":28071},[892,75129,75130,75187],{},[20760,75131,75132],{"width":28076},[20765,75133,75134,75136,75180,75182],{},[20768,75135],{"width":28081},[20768,75137,75138],{},[895,75139,75140,75142,75148,75150,75164,75166,75172,75174,75176,75178],{},[898,75141,2826],{},[2281,75143,75144,75146],{},[898,75145,3946],{},[898,75147,9801],{},[2005,75149,2007],{},[2338,75151,75152,75158],{},[895,75153,75154,75156],{},[898,75155,2203],{},[898,75157,2797],{},[895,75159,75160,75162],{},[898,75161,2203],{},[898,75163,9801],{},[2005,75165,2007],{},[2133,75167,75168,75170],{},[898,75169,2797],{},[2005,75171,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,75173,2014],{"stretchy":2013},[898,75175,9801],{},[2005,75177,2020],{"stretchy":2013},[898,75179,1644],{"mathvariant":2385},[20768,75181],{"width":28081},[20768,75183,75184],{},[2297,75185,75186],{},"(5.2)",[902,75188,75189],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,75191,75192,75193,19951,75211,75239,75240,75257,75258,2694,75275,3927],{},"Pro pevnou hodnotu ",[883,75194,75196],{"className":75195},[886],[888,75197,75198],{"xmlns":890},[892,75199,75200,75208],{},[895,75201,75202],{},[2133,75203,75204,75206],{},[898,75205,9801],{},[2005,75207,4360],{},[902,75209,75210],{"encoding":904},"L^*",[883,75212,75214],{"className":75213},[886],[888,75215,75216],{"xmlns":890},[892,75217,75218,75236],{},[895,75219,75220,75226,75228,75234],{},[2133,75221,75222,75224],{},[898,75223,2797],{},[2005,75225,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,75227,2014],{"stretchy":2013},[2133,75229,75230,75232],{},[898,75231,9801],{},[2005,75233,4360],{},[2005,75235,2020],{"stretchy":2013},[902,75237,75238],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,75241,75243],{"className":75242},[886],[888,75244,75245],{"xmlns":890},[892,75246,75247,75255],{},[895,75248,75249],{},[2133,75250,75251,75253],{},[898,75252,9801],{},[2005,75254,4360],{},[902,75256,75210],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,75259,75261],{"className":75260},[886],[888,75262,75263],{"xmlns":890},[892,75264,75265,75273],{},[895,75266,75267],{},[2133,75268,75269,75271],{},[898,75270,9801],{},[2005,75272,4360],{},[902,75274,75210],{"encoding":904},[883,75276,75278],{"className":75277},[886],[888,75279,75280],{"xmlns":890},[892,75281,75282,75294],{},[895,75283,75284,75290,75292],{},[2133,75285,75286,75288],{},[898,75287,9801],{},[2005,75289,4360],{},[2005,75291,2104],{},[2138,75293,2287],{},[902,75295,75296],{"encoding":904},"L^*+1",[3876,75298,75299],{},[724,75300,75301,18030,75303,75322,75323,75326,75327,1644],{},[883,75302,4164],{},[883,75304,75306],{"className":75305},[886],[888,75307,75308],{"xmlns":890},[892,75309,75310,75320],{},[895,75311,75312,75314],{},[898,75313,2826],{},[2281,75315,75316,75318],{},[898,75317,3946],{},[898,75319,9801],{},[902,75321,10050],{"encoding":904}," odpovídá na otázku „",[38,75324,75325],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,75328,75330],{"className":75329},[886],[888,75331,75332],{"xmlns":890},[892,75333,75334,75338],{},[895,75335,75336],{},[898,75337,9801],{},[902,75339,9801],{"encoding":904},[724,75341,75342,75345,75346,75362,75363,2694,75376,75396],{},[38,75343,75344],{},"Přibližná změna produkce"," pro změnu práce o ",[883,75347,75349],{"className":75348},[886],[888,75350,75351],{"xmlns":890},[892,75352,75353,75359],{},[895,75354,75355,75357],{},[898,75356,2203],{},[898,75358,9801],{},[902,75360,75361],{"encoding":904},"dL"," (z ",[883,75364,75366],{"className":75365},[886],[888,75367,75368],{"xmlns":890},[892,75369,75370,75374],{},[895,75371,75372],{},[898,75373,9801],{},[902,75375,9801],{"encoding":904},[883,75377,75379],{"className":75378},[886],[888,75380,75381],{"xmlns":890},[892,75382,75383,75393],{},[895,75384,75385,75387,75389,75391],{},[898,75386,9801],{},[2005,75388,2104],{},[898,75390,2203],{},[898,75392,9801],{},[902,75394,75395],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,75398,75400],{"className":75399},[886],[888,75401,75402],{"xmlns":890,"display":28071},[892,75403,75404,75469],{},[20760,75405,75406],{"width":28076},[20765,75407,75408,75410,75462,75464],{},[20768,75409],{"width":28081},[20768,75411,75412],{},[895,75413,75414,75416,75418,75420,75422,75424,75426,75432,75434,75436,75438,75440,75442,75444,75446,75448,75454,75456,75458,75460],{},[898,75415,2897],{"mathvariant":2385},[898,75417,2797],{},[2005,75419,2739],{},[898,75421,2203],{},[898,75423,2797],{},[2005,75425,2007],{},[2133,75427,75428,75430],{},[898,75429,2797],{},[2005,75431,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,75433,2014],{"stretchy":2013},[898,75435,9801],{},[2005,75437,2020],{"stretchy":2013},[2297,75439,2995],{},[898,75441,2203],{},[898,75443,9801],{},[2005,75445,2007],{},[898,75447,2826],{},[2281,75449,75450,75452],{},[898,75451,3946],{},[898,75453,9801],{},[2297,75455,2995],{},[898,75457,2203],{},[898,75459,9801],{},[898,75461,1644],{"mathvariant":2385},[20768,75463],{"width":28081},[20768,75465,75466],{},[2297,75467,75468],{},"(5.3)",[902,75470,75471],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,75473,75474,75475,1644],{},"Skutečná změna je ",[883,75476,75478],{"className":75477},[886],[888,75479,75480],{"xmlns":890},[892,75481,75482,75514],{},[895,75483,75484,75486,75488,75490,75492,75494,75496,75498,75500,75502,75504,75506,75508,75510,75512],{},[898,75485,2897],{"mathvariant":2385},[898,75487,2797],{},[2005,75489,2007],{},[898,75491,2797],{},[2005,75493,2014],{"stretchy":2013},[898,75495,9801],{},[2005,75497,2104],{},[898,75499,2203],{},[898,75501,9801],{},[2005,75503,2020],{"stretchy":2013},[2005,75505,2234],{},[898,75507,2797],{},[2005,75509,2014],{"stretchy":2013},[898,75511,9801],{},[2005,75513,2020],{"stretchy":2013},[902,75515,75516],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,75518,75520],{"id":75519},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,75522,75523,10030,75526,3159],{},[38,75524,75525],{},"Zákon klesajících výnosů",[614,75527,75528],{},"law of diminishing marginal productivity",[3876,75530,75531],{},[724,75532,75533,75534,75536],{},"Roste-li postupně některý ze vstupů (",[614,75535,36965],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,75538,75539],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,75541,75542,75543,2212,75564,75583,75584,75634,75635,75637,75638,2212,75658,75677,75678,75634,75710,2935,75712,75731,75732,21600,75749,75783,75784,8108,75801,75804],{},"1° ",[38,75544,75545,75546,2713],{},"Do bodu ",[883,75547,75549],{"className":75548},[886],[888,75550,75551],{"xmlns":890},[892,75552,75553,75561],{},[895,75554,75555],{},[2281,75556,75557,75559],{},[898,75558,9801],{},[2138,75560,2336],{},[902,75562,75563],{"encoding":904},"L_0",[883,75565,75567],{"className":75566},[886],[888,75568,75569],{"xmlns":890},[892,75570,75571,75581],{},[895,75572,75573,75575],{},[898,75574,2826],{},[2281,75576,75577,75579],{},[898,75578,3946],{},[898,75580,9801],{},[902,75582,10050],{"encoding":904}," roste, tj. ",[883,75585,75587],{"className":75586},[886],[888,75588,75589],{"xmlns":890},[892,75590,75591,75631],{},[895,75592,75593,75595,75597,75603,75609,75611,75621,75623,75625,75627,75629],{},[2005,75594,2014],{"stretchy":2013},[898,75596,2826],{},[2281,75598,75599,75601],{},[898,75600,3946],{},[898,75602,9801],{},[2133,75604,75605,75607],{},[2005,75606,2020],{"stretchy":2013},[2005,75608,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,75610,2007],{},[2133,75612,75613,75615],{},[898,75614,2797],{},[895,75616,75617,75619],{},[2005,75618,2387],{"mathvariant":2385},[2005,75620,2387],{"mathvariant":2385},[2005,75622,2014],{"stretchy":2013},[898,75624,9801],{},[2005,75626,2020],{"stretchy":2013},[2005,75628,3416],{},[2138,75630,2336],{},[902,75632,75633],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,75636,37669],{},".\n2° ",[38,75639,75640,75641,2713],{},"Od bodu ",[883,75642,75644],{"className":75643},[886],[888,75645,75646],{"xmlns":890},[892,75647,75648,75656],{},[895,75649,75650],{},[2281,75651,75652,75654],{},[898,75653,9801],{},[2138,75655,2336],{},[902,75657,75563],{"encoding":904},[883,75659,75661],{"className":75660},[886],[888,75662,75663],{"xmlns":890},[892,75664,75665,75675],{},[895,75666,75667,75669],{},[898,75668,2826],{},[2281,75670,75671,75673],{},[898,75672,3946],{},[898,75674,9801],{},[902,75676,10050],{"encoding":904}," klesá, ",[883,75679,75681],{"className":75680},[886],[888,75682,75683],{"xmlns":890},[892,75684,75685,75707],{},[895,75686,75687,75697,75699,75701,75703,75705],{},[2133,75688,75689,75691],{},[898,75690,2797],{},[895,75692,75693,75695],{},[2005,75694,2387],{"mathvariant":2385},[2005,75696,2387],{"mathvariant":2385},[2005,75698,2014],{"stretchy":2013},[898,75700,9801],{},[2005,75702,2020],{"stretchy":2013},[2005,75704,3455],{},[2138,75706,2336],{},[902,75708,75709],{"encoding":904},"Q''(L) \u003C 0",[38,75711,38493],{},[883,75713,75715],{"className":75714},[886],[888,75716,75717],{"xmlns":890},[892,75718,75719,75729],{},[895,75720,75721,75723],{},[898,75722,2826],{},[2281,75724,75725,75727],{},[898,75726,3946],{},[898,75728,9801],{},[902,75730,10050],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,75733,75735],{"className":75734},[886],[888,75736,75737],{"xmlns":890},[892,75738,75739,75747],{},[895,75740,75741],{},[2281,75742,75743,75745],{},[898,75744,9801],{},[2138,75746,2287],{},[902,75748,13218],{"encoding":904},[883,75750,75752],{"className":75751},[886],[888,75753,75754],{"xmlns":890},[892,75755,75756,75780],{},[895,75757,75758,75760,75766,75768,75774,75776,75778],{},[898,75759,2826],{},[2281,75761,75762,75764],{},[898,75763,3946],{},[898,75765,9801],{},[2005,75767,2014],{"stretchy":2013},[2281,75769,75770,75772],{},[898,75771,9801],{},[2138,75773,2287],{},[2005,75775,2020],{"stretchy":2013},[2005,75777,2007],{},[2138,75779,2336],{},[902,75781,75782],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,75785,75787],{"className":75786},[886],[888,75788,75789],{"xmlns":890},[892,75790,75791,75799],{},[895,75792,75793],{},[2281,75794,75795,75797],{},[898,75796,9801],{},[2138,75798,2336],{},[902,75800,75563],{"encoding":904},[38,75802,75803],{},"inflexním bodem"," produkční funkce.",[724,75806,75807,75808,10399,75825,1644],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,75809,75811],{"className":75810},[886],[888,75812,75813],{"xmlns":890},[892,75814,75815,75823],{},[895,75816,75817],{},[2281,75818,75819,75821],{},[898,75820,9801],{},[2138,75822,2336],{},[902,75824,75563],{"encoding":904},[883,75826,75828],{"className":75827},[886],[888,75829,75830],{"xmlns":890},[892,75831,75832,75854],{},[895,75833,75834,75844,75846,75848,75850,75852],{},[2133,75835,75836,75838],{},[898,75837,2797],{},[895,75839,75840,75842],{},[2005,75841,2387],{"mathvariant":2385},[2005,75843,2387],{"mathvariant":2385},[2005,75845,2014],{"stretchy":2013},[898,75847,9801],{},[2005,75849,2020],{"stretchy":2013},[2005,75851,3455],{},[2138,75853,2336],{},[902,75855,75709],{"encoding":904},[724,75857,75858,2212,75861,5675,75901,1343,75918,75935],{},[38,75859,75860],{},"Typický polynom třetího stupně:",[883,75862,75864],{"className":75863},[886],[888,75865,75866],{"xmlns":890},[892,75867,75868,75898],{},[895,75869,75870,75872,75874,75876,75878,75880,75882,75888,75890,75892],{},[898,75871,2797],{},[2005,75873,2014],{"stretchy":2013},[898,75875,9801],{},[2005,75877,2020],{"stretchy":2013},[2005,75879,2007],{},[898,75881,207],{},[2133,75883,75884,75886],{},[898,75885,9801],{},[2138,75887,2182],{},[2005,75889,2104],{},[898,75891,2107],{},[2133,75893,75894,75896],{},[898,75895,9801],{},[2138,75897,2140],{},[902,75899,75900],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,75902,75904],{"className":75903},[886],[888,75905,75906],{"xmlns":890},[892,75907,75908,75916],{},[895,75909,75910,75912,75914],{},[898,75911,207],{},[2005,75913,3455],{},[2138,75915,2336],{},[902,75917,43090],{"encoding":904},[883,75919,75921],{"className":75920},[886],[888,75922,75923],{"xmlns":890},[892,75924,75925,75933],{},[895,75926,75927,75929,75931],{},[898,75928,2107],{},[2005,75930,3416],{},[2138,75932,2336],{},[902,75934,18820],{"encoding":904},". Pak",[883,75937,75939],{"className":75938},[886],[888,75940,75941],{"xmlns":890,"display":28071},[892,75942,75943,76003],{},[895,75944,75945,75951,75953,75955,75963,75971,75973,75975,75981,75983,75985,75993,76001],{},[2281,75946,75947,75949],{},[898,75948,9801],{},[2138,75950,2336],{},[2005,75952,2007],{},[2005,75954,2234],{},[2334,75956,75957],{"scriptlevel":2336,"displaystyle":2013},[2338,75958,75959,75961],{},[2138,75960,2287],{},[2138,75962,2182],{},[2334,75964,75965],{"scriptlevel":2336,"displaystyle":2013},[2338,75966,75967,75969],{},[898,75968,2107],{},[898,75970,207],{},[2005,75972,2295],{"separator":2294},[5884,75974],{"width":5886},[2281,75976,75977,75979],{},[898,75978,9801],{},[2138,75980,2287],{},[2005,75982,2007],{},[2005,75984,2234],{},[2334,75986,75987],{"scriptlevel":2336,"displaystyle":2013},[2338,75988,75989,75991],{},[2138,75990,2140],{},[2138,75992,2182],{},[2334,75994,75995],{"scriptlevel":2336,"displaystyle":2013},[2338,75996,75997,75999],{},[898,75998,2107],{},[898,76000,207],{},[898,76002,1644],{"mathvariant":2385},[902,76004,76005],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,76007,76009,76010,2020],{"id":76008},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,76011,76013],{"className":76012},[886],[888,76014,76015],{"xmlns":890},[892,76016,76017,76027],{},[895,76018,76019,76021],{},[898,76020,1836],{},[2281,76022,76023,76025],{},[898,76024,3946],{},[898,76026,9801],{},[902,76028,74638],{"encoding":904},[724,76030,76031,10030,76034,75102,76037,76056],{},[38,76032,76033],{},"Průměrný produkt práce",[614,76035,76036],{},"average product of labour",[883,76038,76040],{"className":76039},[886],[888,76041,76042],{"xmlns":890},[892,76043,76044,76054],{},[895,76045,76046,76048],{},[898,76047,1836],{},[2281,76049,76050,76052],{},[898,76051,3946],{},[898,76053,9801],{},[902,76055,74638],{"encoding":904}," je podíl produkce a práce:",[883,76058,76060],{"className":76059},[886],[888,76061,76062],{"xmlns":890,"display":28071},[892,76063,76064,76099],{},[20760,76065,76066],{"width":28076},[20765,76067,76068,76070,76092,76094],{},[20768,76069],{"width":28081},[20768,76071,76072],{},[895,76073,76074,76076,76082,76084,76090],{},[898,76075,1836],{},[2281,76077,76078,76080],{},[898,76079,3946],{},[898,76081,9801],{},[2005,76083,2007],{},[2338,76085,76086,76088],{},[898,76087,2797],{},[898,76089,9801],{},[898,76091,1644],{"mathvariant":2385},[20768,76093],{"width":28081},[20768,76095,76096],{},[2297,76097,76098],{},"(5.4)",[902,76100,76101],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,76103,76104,76105,1644],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,76106,76108],{"className":76107},[886],[888,76109,76110],{"xmlns":890},[892,76111,76112,76122],{},[895,76113,76114,76116],{},[898,76115,1836],{},[2281,76117,76118,76120],{},[898,76119,3946],{},[898,76121,9801],{},[902,76123,74638],{"encoding":904},[115,76125,76127],{"id":76126},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,76129,76130],{},[2568,76131],{"alt":76132,"className":76133,"src":76134},"imek-q-mpl-apl-tripanel",[210,2572],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[3876,76136,76137],{},[724,76138,76139,76142,76143,2633,76162,76179,76180],{},[38,76140,76141],{},"Princip:"," Má-li ",[883,76144,76146],{"className":76145},[886],[888,76147,76148],{"xmlns":890},[892,76149,76150,76160],{},[895,76151,76152,76154],{},[898,76153,1836],{},[2281,76155,76156,76158],{},[898,76157,3946],{},[898,76159,9801],{},[902,76161,74638],{"encoding":904},[883,76163,76165],{"className":76164},[886],[888,76166,76167],{"xmlns":890},[892,76168,76169,76177],{},[895,76170,76171],{},[2281,76172,76173,76175],{},[898,76174,9801],{},[2138,76176,2336],{},[902,76178,75563],{"encoding":904}," maximum, pak platí\n",[883,76181,76183],{"className":76182,"title":4208,"style":4209},[4207],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,76185,76186,76187,76190,76191,2212,76195,1644],{},"Slovně: ",[38,76188,76189],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,76192,76194],{"className":76193,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,76196,76198],{"className":76197},[886],[888,76199,76200],{"xmlns":890},[892,76201,76202,76208],{},[895,76203,76204,76206],{},[898,76205,1836],{},[898,76207,1852],{},[902,76209,55565],{"encoding":904},[3876,76211,76212,76236],{},[724,76213,76214,76216,76217],{},[883,76215,4578],{}," Postup — jak najít max ",[883,76218,76220],{"className":76219},[886],[888,76221,76222],{"xmlns":890},[892,76223,76224,76234],{},[895,76225,76226,76228],{},[898,76227,1836],{},[2281,76229,76230,76232],{},[898,76231,3946],{},[898,76233,9801],{},[902,76235,74638],{"encoding":904},[152,76237,76238,76276,76358],{},[123,76239,76240,76241,76275],{},"Napište ",[883,76242,76244],{"className":76243},[886],[888,76245,76246],{"xmlns":890},[892,76247,76248,76272],{},[895,76249,76250,76252,76258,76260,76262,76264,76266,76268,76270],{},[898,76251,1836],{},[2281,76253,76254,76256],{},[898,76255,3946],{},[898,76257,9801],{},[2005,76259,2007],{},[898,76261,2797],{},[2005,76263,2014],{"stretchy":2013},[898,76265,9801],{},[2005,76267,2020],{"stretchy":2013},[898,76269,4680],{"mathvariant":2385},[898,76271,9801],{},[902,76273,76274],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,76277,76278,76279,76311,76312,76315,76316,1644],{},"Položte ",[883,76280,76282],{"className":76281},[886],[888,76283,76284],{"xmlns":890},[892,76285,76286,76308],{},[895,76287,76288,76290,76292,76298,76304,76306],{},[2005,76289,2014],{"stretchy":2013},[898,76291,1836],{},[2281,76293,76294,76296],{},[898,76295,3946],{},[898,76297,9801],{},[2133,76299,76300,76302],{},[2005,76301,2020],{"stretchy":2013},[2005,76303,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,76305,2007],{},[2138,76307,2336],{},[902,76309,76310],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,76313,76314],{},"Zkratka:"," můžete rovnou řešit ",[883,76317,76319],{"className":76318},[886],[888,76320,76321],{"xmlns":890},[892,76322,76323,76355],{},[895,76324,76325,76327,76333,76335,76337,76339,76341,76343,76349,76351,76353],{},[898,76326,2826],{},[2281,76328,76329,76331],{},[898,76330,3946],{},[898,76332,9801],{},[2005,76334,2014],{"stretchy":2013},[898,76336,9801],{},[2005,76338,2020],{"stretchy":2013},[2005,76340,2007],{},[898,76342,1836],{},[2281,76344,76345,76347],{},[898,76346,3946],{},[898,76348,9801],{},[2005,76350,2014],{"stretchy":2013},[898,76352,9801],{},[2005,76354,2020],{"stretchy":2013},[902,76356,76357],{"encoding":904},"MP_L(L) = AP_L(L)",[123,76359,76360],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,76362,65506],{"id":76363},"odvození",[724,76365,76366,76367,76400],{},"Z ",[883,76368,76370],{"className":76369},[886],[888,76371,76372],{"xmlns":890},[892,76373,76374,76398],{},[895,76375,76376,76378,76384,76386,76388,76390,76392,76394,76396],{},[898,76377,1836],{},[2281,76379,76380,76382],{},[898,76381,3946],{},[898,76383,9801],{},[2005,76385,2007],{},[898,76387,2797],{},[2005,76389,2014],{"stretchy":2013},[898,76391,9801],{},[2005,76393,2020],{"stretchy":2013},[898,76395,4680],{"mathvariant":2385},[898,76397,9801],{},[902,76399,76274],{"encoding":904}," a derivace podílu:",[883,76402,76404],{"className":76403},[886],[888,76405,76406],{"xmlns":890,"display":28071},[892,76407,76408,76561],{},[895,76409,76410,76412,76414,76420,76426,76428,76430,76432,76434,76474,76476,76482,76516,76518,76524,76527,76529,76535,76537,76539,76541,76543,76545,76551,76553,76555,76557,76559],{},[2005,76411,2014],{"stretchy":2013},[898,76413,1836],{},[2281,76415,76416,76418],{},[898,76417,3946],{},[898,76419,9801],{},[2133,76421,76422,76424],{},[2005,76423,2020],{"stretchy":2013},[2005,76425,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,76427,2014],{"stretchy":2013},[898,76429,9801],{},[2005,76431,2020],{"stretchy":2013},[2005,76433,2007],{},[2338,76435,76436,76468],{},[895,76437,76438,76444,76446,76448,76450,76452,76454,76456,76458,76460,76462,76464,76466],{},[2133,76439,76440,76442],{},[898,76441,2797],{},[2005,76443,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,76445,2014],{"stretchy":2013},[898,76447,9801],{},[2005,76449,2020],{"stretchy":2013},[2005,76451,3185],{},[898,76453,9801],{},[2005,76455,2234],{},[898,76457,2797],{},[2005,76459,2014],{"stretchy":2013},[898,76461,9801],{},[2005,76463,2020],{"stretchy":2013},[2005,76465,3185],{},[2138,76467,2287],{},[2133,76469,76470,76472],{},[898,76471,9801],{},[2138,76473,2140],{},[2005,76475,2007],{},[2338,76477,76478,76480],{},[2138,76479,2287],{},[898,76481,9801],{},[895,76483,76484,76486,76492,76494,76496,76498,76500,76514],{},[2005,76485,2014],{"fence":2294},[2133,76487,76488,76490],{},[898,76489,2797],{},[2005,76491,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,76493,2014],{"stretchy":2013},[898,76495,9801],{},[2005,76497,2020],{"stretchy":2013},[2005,76499,2234],{},[2338,76501,76502,76512],{},[895,76503,76504,76506,76508,76510],{},[898,76505,2797],{},[2005,76507,2014],{"stretchy":2013},[898,76509,9801],{},[2005,76511,2020],{"stretchy":2013},[898,76513,9801],{},[2005,76515,2020],{"fence":2294},[2005,76517,2007],{},[2338,76519,76520,76522],{},[2138,76521,2287],{},[898,76523,9801],{},[2005,76525,2014],{"fence":2294,"stretchy":2294,"minsize":76526,"maxsize":76526},"1.2em",[898,76528,2826],{},[2281,76530,76531,76533],{},[898,76532,3946],{},[898,76534,9801],{},[2005,76536,2014],{"stretchy":2013},[898,76538,9801],{},[2005,76540,2020],{"stretchy":2013},[2005,76542,2234],{},[898,76544,1836],{},[2281,76546,76547,76549],{},[898,76548,3946],{},[898,76550,9801],{},[2005,76552,2014],{"stretchy":2013},[898,76554,9801],{},[2005,76556,2020],{"stretchy":2013},[2005,76558,2020],{"fence":2294,"stretchy":2294,"minsize":76526,"maxsize":76526},[898,76560,1644],{"mathvariant":2385},[902,76562,76563],{"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).",[724,76565,9669,76566,8108,76588,76671],{},[883,76567,76569],{"className":76568},[886],[888,76570,76571],{"xmlns":890},[892,76572,76573,76585],{},[895,76574,76575,76581,76583],{},[2281,76576,76577,76579],{},[898,76578,9801],{},[2138,76580,2336],{},[2005,76582,3416],{},[2138,76584,2336],{},[902,76586,76587],{"encoding":904},"L_0 > 0",[883,76589,76591],{"className":76590},[886],[888,76592,76593],{"xmlns":890},[892,76594,76595,76668],{},[895,76596,76597,76599,76601,76607,76613,76615,76621,76623,76625,76627,76630,76632,76638,76640,76646,76648,76650,76652,76658,76660,76666],{},[2005,76598,2014],{"stretchy":2013},[898,76600,1836],{},[2281,76602,76603,76605],{},[898,76604,3946],{},[898,76606,9801],{},[2133,76608,76609,76611],{},[2005,76610,2020],{"stretchy":2013},[2005,76612,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,76614,2014],{"stretchy":2013},[2281,76616,76617,76619],{},[898,76618,9801],{},[2138,76620,2336],{},[2005,76622,2020],{"stretchy":2013},[2005,76624,2007],{},[2138,76626,2336],{},[2005,76628,76629],{},"⇔",[898,76631,2826],{},[2281,76633,76634,76636],{},[898,76635,3946],{},[898,76637,9801],{},[2005,76639,2014],{"stretchy":2013},[2281,76641,76642,76644],{},[898,76643,9801],{},[2138,76645,2336],{},[2005,76647,2020],{"stretchy":2013},[2005,76649,2007],{},[898,76651,1836],{},[2281,76653,76654,76656],{},[898,76655,3946],{},[898,76657,9801],{},[2005,76659,2014],{"stretchy":2013},[2281,76661,76662,76664],{},[898,76663,9801],{},[2138,76665,2336],{},[2005,76667,2020],{"stretchy":2013},[902,76669,76670],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,76673,76675],{"id":76674},"příklad-51","Příklad 5.1",[724,76677,76678,76679,1644],{},"Je dána produkce ",[883,76680,76682],{"className":76681},[886],[888,76683,76684],{"xmlns":890},[892,76685,76686,76710],{},[895,76687,76688,76690,76692,76694,76700,76702,76704],{},[898,76689,2797],{},[2005,76691,2007],{},[2138,76693,2244],{},[2133,76695,76696,76698],{},[898,76697,9801],{},[2138,76699,2140],{},[2005,76701,2234],{},[2138,76703,2847],{},[2133,76705,76706,76708],{},[898,76707,9801],{},[2138,76709,2182],{},[902,76711,76712],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,76714,76715,57527,76718,76768,76769,1644],{},[38,76716,76717],{},"(a)",[883,76719,76721],{"className":76720},[886],[888,76722,76723],{"xmlns":890},[892,76724,76725,76765],{},[895,76726,76727,76729,76731,76733,76735,76737,76739,76741,76743,76745,76747,76749,76751,76753,76755,76757,76759,76761,76763],{},[898,76728,9801],{},[2005,76730,2007],{},[2138,76732,2140],{},[2005,76734,2295],{"separator":2294},[2138,76736,2237],{},[2005,76738,2295],{"separator":2294},[2138,76740,5591],{},[2005,76742,2295],{"separator":2294},[2138,76744,2871],{},[2005,76746,2295],{"separator":2294},[2138,76748,22952],{},[2005,76750,2295],{"separator":2294},[2138,76752,3715],{},[2005,76754,2295],{"separator":2294},[2138,76756,9041],{},[2005,76758,2295],{"separator":2294},[2138,76760,38351],{},[2005,76762,2295],{"separator":2294},[2138,76764,5010],{},[902,76766,76767],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,76770,76772],{"className":76771},[886],[888,76773,76774],{"xmlns":890},[892,76775,76776,76786],{},[895,76777,76778,76780],{},[898,76779,2826],{},[2281,76781,76782,76784],{},[898,76783,3946],{},[898,76785,9801],{},[902,76787,10050],{"encoding":904},[724,76789,76790,76791,34973],{},"Podle (5.2): ",[883,76792,76794],{"className":76793},[886],[888,76795,76796],{"xmlns":890},[892,76797,76798,76854],{},[895,76799,76800,76802,76808,76810,76816,76818,76820,76822,76824,76826,76828,76830,76832,76838,76840,76842,76844,76846,76848,76850,76852],{},[898,76801,2826],{},[2281,76803,76804,76806],{},[898,76805,3946],{},[898,76807,9801],{},[2005,76809,2007],{},[2133,76811,76812,76814],{},[898,76813,2797],{},[2005,76815,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,76817,2014],{"stretchy":2013},[898,76819,9801],{},[2005,76821,2020],{"stretchy":2013},[2005,76823,2007],{},[2138,76825,3517],{},[898,76827,9801],{},[2005,76829,2234],{},[2138,76831,19327],{},[2133,76833,76834,76836],{},[898,76835,9801],{},[2138,76837,2140],{},[2005,76839,2007],{},[898,76841,9801],{},[2005,76843,2014],{"stretchy":2013},[2138,76845,3517],{},[2005,76847,2234],{},[2138,76849,19327],{},[898,76851,9801],{},[2005,76853,2020],{"stretchy":2013},[902,76855,76856],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,76858,76859,76896],{},[19,76860,76861],{},[22,76862,76863,76878,76880,76882,76884,76886,76888,76890,76892,76894],{},[25,76864,76865],{},[883,76866,76868],{"className":76867},[886],[888,76869,76870],{"xmlns":890},[892,76871,76872,76876],{},[895,76873,76874],{},[898,76875,9801],{},[902,76877,9801],{"encoding":904},[25,76879,2140],{},[25,76881,2237],{},[25,76883,5591],{},[25,76885,2871],{},[25,76887,22952],{},[25,76889,3715],{},[25,76891,9041],{},[25,76893,38351],{},[25,76895,5010],{},[30,76897,76898],{},[22,76899,76900,76921,76924,76927,76930,76932,76935,76937,76939,76958],{},[35,76901,76902],{},[883,76903,76905],{"className":76904},[886],[888,76906,76907],{"xmlns":890},[892,76908,76909,76919],{},[895,76910,76911,76913],{},[898,76912,2826],{},[2281,76914,76915,76917],{},[898,76916,3946],{},[898,76918,9801],{},[902,76920,10050],{"encoding":904},[35,76922,76923],{},"21,6",[35,76925,76926],{},"45",[35,76928,76929],{},"57,6",[35,76931,3134],{},[35,76933,76934],{},"50,4",[35,76936,76923],{},[35,76938,2336],{},[35,76940,76941],{},[883,76942,76944],{"className":76943},[886],[888,76945,76946],{"xmlns":890},[892,76947,76948,76955],{},[895,76949,76950,76952],{},[2005,76951,2234],{},[2138,76953,76954],{},"12,6",[902,76956,76957],{"encoding":904},"-12{,}6",[35,76959,76960],{},[883,76961,76963],{"className":76962},[886],[888,76964,76965],{"xmlns":890},[892,76966,76967,76973],{},[895,76968,76969,76971],{},[2005,76970,2234],{},[2138,76972,45457],{},[902,76974,76975],{"encoding":904},"-75",[724,76977,76978,76997,76998,77016,77017,77034,77035,77053,77054,77078,77079,77097],{},[883,76979,76981],{"className":76980},[886],[888,76982,76983],{"xmlns":890},[892,76984,76985,76995],{},[895,76986,76987,76989],{},[898,76988,2826],{},[2281,76990,76991,76993],{},[898,76992,3946],{},[898,76994,9801],{},[902,76996,10050],{"encoding":904}," nabývá maxima pro ",[883,76999,77001],{"className":77000},[886],[888,77002,77003],{"xmlns":890},[892,77004,77005,77013],{},[895,77006,77007,77009,77011],{},[898,77008,9801],{},[2005,77010,2007],{},[2138,77012,2871],{},[902,77014,77015],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,77018,77020],{"className":77019},[886],[888,77021,77022],{"xmlns":890},[892,77023,77024,77032],{},[895,77025,77026,77028,77030],{},[898,77027,9801],{},[2005,77029,2007],{},[2138,77031,2871],{},[902,77033,77015],{"encoding":904}," přírůstky klesají, v ",[883,77036,77038],{"className":77037},[886],[888,77039,77040],{"xmlns":890},[892,77041,77042,77050],{},[895,77043,77044,77046,77048],{},[898,77045,9801],{},[2005,77047,2007],{},[2138,77049,9041],{},[902,77051,77052],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,77055,77057],{"className":77056},[886],[888,77058,77059],{"xmlns":890},[892,77060,77061,77075],{},[895,77062,77063,77065,77067,77069,77071,77073],{},[898,77064,2797],{},[2005,77066,2014],{"stretchy":2013},[2138,77068,9041],{},[2005,77070,2020],{"stretchy":2013},[2005,77072,2007],{},[2138,77074,23863],{},[902,77076,77077],{"encoding":904},"Q(20) = 800","), od ",[883,77080,77082],{"className":77081},[886],[888,77083,77084],{"xmlns":890},[892,77085,77086,77094],{},[895,77087,77088,77090,77092],{},[898,77089,9801],{},[2005,77091,3416],{},[2138,77093,9041],{},[902,77095,77096],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,77099,77100],{},[614,77101,77102,77103,77143,77144,2633,77162,1644],{},"Obrázek 5.1 — graf produkce ",[883,77104,77106],{"className":77105},[886],[888,77107,77108],{"xmlns":890},[892,77109,77110,77140],{},[895,77111,77112,77114,77116,77118,77120,77122,77124,77130,77132,77134],{},[898,77113,2797],{},[2005,77115,2014],{"stretchy":2013},[898,77117,9801],{},[2005,77119,2020],{"stretchy":2013},[2005,77121,2007],{},[2138,77123,2244],{},[2133,77125,77126,77128],{},[898,77127,9801],{},[2138,77129,2140],{},[2005,77131,2234],{},[2138,77133,2847],{},[2133,77135,77136,77138],{},[898,77137,9801],{},[2138,77139,2182],{},[902,77141,77142],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,77145,77147],{"className":77146},[886],[888,77148,77149],{"xmlns":890},[892,77150,77151,77159],{},[895,77152,77153,77155,77157],{},[898,77154,2797],{},[2005,77156,2007],{},[2138,77158,23863],{},[902,77160,77161],{"encoding":904},"Q = 800",[883,77163,77165],{"className":77164},[886],[888,77166,77167],{"xmlns":890},[892,77168,77169,77177],{},[895,77170,77171,77173,77175],{},[898,77172,9801],{},[2005,77174,2007],{},[2138,77176,9041],{},[902,77178,77052],{"encoding":904},[724,77180,77181,77184],{},[38,77182,77183],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,77186,77187,77188,1343,77206,2713],{},"Podle (5.3) s ",[883,77189,77191],{"className":77190},[886],[888,77192,77193],{"xmlns":890},[892,77194,77195,77203],{},[895,77196,77197,77199,77201],{},[898,77198,9801],{},[2005,77200,2007],{},[2138,77202,2244],{},[902,77204,77205],{"encoding":904},"L = 6",[883,77207,77209],{"className":77208},[886],[888,77210,77211],{"xmlns":890},[892,77212,77213,77223],{},[895,77214,77215,77217,77219,77221],{},[898,77216,2203],{},[898,77218,9801],{},[2005,77220,2007],{},[2138,77222,2182],{},[902,77224,77225],{"encoding":904},"dL = 3",[883,77227,77229],{"className":77228},[886],[888,77230,77231],{"xmlns":890,"display":28071},[892,77232,77233,77296],{},[895,77234,77235,77237,77239,77241,77243,77249,77251,77253,77255,77257,77259,77261,77263,77265,77267,77269,77271,77273,77275,77277,77279,77281,77283,77285,77287,77289,77291,77293],{},[898,77236,2203],{},[898,77238,2797],{},[2005,77240,2007],{},[898,77242,2826],{},[2281,77244,77245,77247],{},[898,77246,3946],{},[898,77248,9801],{},[2005,77250,2014],{"stretchy":2013},[2138,77252,2244],{},[2005,77254,2020],{"stretchy":2013},[2005,77256,3185],{},[2138,77258,2182],{},[2005,77260,2007],{},[2005,77262,2014],{"stretchy":2013},[2138,77264,3517],{},[2005,77266,3185],{},[2138,77268,2244],{},[2005,77270,2234],{},[2138,77272,19327],{},[2005,77274,3185],{},[2138,77276,5571],{},[2005,77278,2020],{"stretchy":2013},[2005,77280,3185],{},[2138,77282,2182],{},[2005,77284,2007],{},[2138,77286,76934],{},[2005,77288,3185],{},[2138,77290,2182],{},[2005,77292,2007],{},[2138,77294,77295],{},"151,2.",[902,77297,77298],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,77300,77301,77302,57757,77327,77341,77342,1644],{},"Produkce vzroste z ",[883,77303,77305],{"className":77304},[886],[888,77306,77307],{"xmlns":890},[892,77308,77309,77324],{},[895,77310,77311,77313,77315,77317,77319,77321],{},[898,77312,2797],{},[2005,77314,2014],{"stretchy":2013},[2138,77316,2244],{},[2005,77318,2020],{"stretchy":2013},[2005,77320,2007],{},[2138,77322,77323],{},"172,8",[902,77325,77326],{"encoding":904},"Q(6) = 172{,}8",[883,77328,77330],{"className":77329},[886],[888,77331,77332],{"xmlns":890},[892,77333,77334,77339],{},[895,77335,77336],{},[2138,77337,77338],{},"324",[902,77340,77338],{"encoding":904},". Skutečná hodnota: ",[883,77343,77345],{"className":77344},[886],[888,77346,77347],{"xmlns":890},[892,77348,77349,77389],{},[895,77350,77351,77353,77355,77357,77359,77361,77363,77365,77367,77369,77371,77373,77375,77377,77380,77382,77384,77386],{},[898,77352,2897],{"mathvariant":2385},[898,77354,2797],{},[2005,77356,2007],{},[898,77358,2797],{},[2005,77360,2014],{"stretchy":2013},[2138,77362,4008],{},[2005,77364,2020],{"stretchy":2013},[2005,77366,2234],{},[898,77368,2797],{},[2005,77370,2014],{"stretchy":2013},[2138,77372,2244],{},[2005,77374,2020],{"stretchy":2013},[2005,77376,2007],{},[2138,77378,77379],{},"340,2",[2005,77381,2234],{},[2138,77383,77323],{},[2005,77385,2007],{},[2138,77387,77388],{},"167,4",[902,77390,77391],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,77393,77395],{"id":77394},"příklad-52","Příklad 5.2",[724,77397,77398,77399,1644],{},"Ověříme princip (5.5) pro ",[883,77400,77402],{"className":77401},[886],[888,77403,77404],{"xmlns":890},[892,77405,77406,77430],{},[895,77407,77408,77410,77412,77414,77420,77422,77424],{},[898,77409,2797],{},[2005,77411,2007],{},[2138,77413,2244],{},[2133,77415,77416,77418],{},[898,77417,9801],{},[2138,77419,2140],{},[2005,77421,2234],{},[2138,77423,2847],{},[2133,77425,77426,77428],{},[898,77427,9801],{},[2138,77429,2182],{},[902,77431,76712],{"encoding":904},[883,77433,77435],{"className":77434},[886],[888,77436,77437],{"xmlns":890,"display":28071},[892,77438,77439,77517],{},[895,77440,77441,77443,77449,77451,77457,77459,77461,77463,77465,77467,77473,77475,77477,77479,77487,77489,77491,77493,77495,77497,77499,77501,77503,77505,77507,77513,77515],{},[898,77442,1836],{},[2281,77444,77445,77447],{},[898,77446,3946],{},[898,77448,9801],{},[2005,77450,2007],{},[2338,77452,77453,77455],{},[898,77454,2797],{},[898,77456,9801],{},[2005,77458,2007],{},[2138,77460,2244],{},[898,77462,9801],{},[2005,77464,2234],{},[2138,77466,2847],{},[2133,77468,77469,77471],{},[898,77470,9801],{},[2138,77472,2140],{},[2005,77474,2295],{"separator":2294},[5884,77476],{"width":15290},[898,77478,1836],{},[9172,77480,77481,77483,77485],{},[898,77482,3946],{},[898,77484,9801],{},[2005,77486,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,77488,2007],{},[2138,77490,2244],{},[2005,77492,2234],{},[2138,77494,19277],{},[898,77496,9801],{},[2005,77498,2007],{},[2138,77500,2336],{},[2297,77502,3993],{},[2005,77504,3996],{},[2297,77506,3993],{},[2281,77508,77509,77511],{},[898,77510,9801],{},[2138,77512,2336],{},[2005,77514,2007],{},[2138,77516,68288],{},[902,77518,77519],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,77521,77522,77558,77559,77577,77578,1644],{},[883,77523,77525],{"className":77524},[886],[888,77526,77527],{"xmlns":890},[892,77528,77529,77555],{},[895,77530,77531,77533,77545,77547,77549,77551,77553],{},[898,77532,1836],{},[9172,77534,77535,77537,77539],{},[898,77536,3946],{},[898,77538,9801],{},[895,77540,77541,77543],{},[2005,77542,2387],{"mathvariant":2385},[2005,77544,2387],{"mathvariant":2385},[2005,77546,2007],{},[2005,77548,2234],{},[2138,77550,19277],{},[2005,77552,3455],{},[2138,77554,2336],{},[902,77556,77557],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,77560,77562],{"className":77561},[886],[888,77563,77564],{"xmlns":890},[892,77565,77566,77574],{},[895,77567,77568,77570,77572],{},[898,77569,9801],{},[2005,77571,2007],{},[2138,77573,36249],{},[902,77575,77576],{"encoding":904},"L = 15"," je maximum, ",[883,77579,77581],{"className":77580},[886],[888,77582,77583],{"xmlns":890},[892,77584,77585,77631],{},[895,77586,77587,77589,77595,77597,77599,77601,77603,77605,77607,77609,77611,77613,77615,77618,77620,77623,77625,77627,77629],{},[898,77588,1836],{},[2281,77590,77591,77593],{},[898,77592,3946],{},[898,77594,9801],{},[2005,77596,2014],{"stretchy":2013},[2138,77598,36249],{},[2005,77600,2020],{"stretchy":2013},[2005,77602,2007],{},[2138,77604,2244],{},[2005,77606,3185],{},[2138,77608,36249],{},[2005,77610,2234],{},[2138,77612,2847],{},[2005,77614,3185],{},[2138,77616,77617],{},"225",[2005,77619,2007],{},[2138,77621,77622],{},"90",[2005,77624,2234],{},[2138,77626,76926],{},[2005,77628,2007],{},[2138,77630,76926],{},[902,77632,77633],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,77635,77636,41885,77692,77738],{},[883,77637,77639],{"className":77638},[886],[888,77640,77641],{"xmlns":890},[892,77642,77643,77689],{},[895,77644,77645,77647,77653,77655,77657,77659,77661,77663,77665,77667,77669,77671,77673,77675,77677,77680,77682,77685,77687],{},[898,77646,2826],{},[2281,77648,77649,77651],{},[898,77650,3946],{},[898,77652,9801],{},[2005,77654,2014],{"stretchy":2013},[2138,77656,36249],{},[2005,77658,2020],{"stretchy":2013},[2005,77660,2007],{},[2138,77662,3517],{},[2005,77664,3185],{},[2138,77666,36249],{},[2005,77668,2234],{},[2138,77670,19327],{},[2005,77672,3185],{},[2138,77674,77617],{},[2005,77676,2007],{},[2138,77678,77679],{},"180",[2005,77681,2234],{},[2138,77683,77684],{},"135",[2005,77686,2007],{},[2138,77688,76926],{},[902,77690,77691],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,77693,77695],{"className":77694},[886],[888,77696,77697],{"xmlns":890},[892,77698,77699,77735],{},[895,77700,77701,77703,77709,77711,77713,77715,77717,77719,77725,77727,77729,77731,77733],{},[898,77702,2826],{},[2281,77704,77705,77707],{},[898,77706,3946],{},[898,77708,9801],{},[2005,77710,2014],{"stretchy":2013},[2138,77712,36249],{},[2005,77714,2020],{"stretchy":2013},[2005,77716,2007],{},[898,77718,1836],{},[2281,77720,77721,77723],{},[898,77722,3946],{},[898,77724,9801],{},[2005,77726,2014],{"stretchy":2013},[2138,77728,36249],{},[2005,77730,2020],{"stretchy":2013},[2005,77732,2007],{},[2138,77734,76926],{},[902,77736,77737],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,77740,77741,77744,77745,17583,77774,1644],{},[38,77742,77743],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,77746,77748],{"className":77747},[886],[888,77749,77750],{"xmlns":890},[892,77751,77752,77772],{},[895,77753,77754,77756,77762,77764,77766],{},[898,77755,2826],{},[2281,77757,77758,77760],{},[898,77759,3946],{},[898,77761,9801],{},[2005,77763,2007],{},[898,77765,1836],{},[2281,77767,77768,77770],{},[898,77769,3946],{},[898,77771,9801],{},[902,77773,74668],{"encoding":904},[883,77775,77777],{"className":77776},[886],[888,77778,77779],{"xmlns":890},[892,77780,77781,77821],{},[895,77782,77783,77785,77787,77789,77791,77797,77799,77801,77803,77805,77807,77813,77815,77817,77819],{},[2138,77784,3517],{},[898,77786,9801],{},[2005,77788,2234],{},[2138,77790,19327],{},[2133,77792,77793,77795],{},[898,77794,9801],{},[2138,77796,2140],{},[2005,77798,2007],{},[2138,77800,2244],{},[898,77802,9801],{},[2005,77804,2234],{},[2138,77806,2847],{},[2133,77808,77809,77811],{},[898,77810,9801],{},[2138,77812,2140],{},[2005,77814,3996],{},[898,77816,9801],{},[2005,77818,2007],{},[2138,77820,36249],{},[902,77822,77823],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,77825,77826],{},[614,77827,77828,77829,77848,77849,12134,77867,77886,77887,77905,77906,77923,77924,77943,77944,77963],{},"Obrázek 5.3 — křivky ",[883,77830,77832],{"className":77831},[886],[888,77833,77834],{"xmlns":890},[892,77835,77836,77846],{},[895,77837,77838,77840],{},[898,77839,2826],{},[2281,77841,77842,77844],{},[898,77843,3946],{},[898,77845,9801],{},[902,77847,10050],{"encoding":904}," (max 60 při ",[883,77850,77852],{"className":77851},[886],[888,77853,77854],{"xmlns":890},[892,77855,77856,77864],{},[895,77857,77858,77860,77862],{},[898,77859,9801],{},[2005,77861,2007],{},[2138,77863,2871],{},[902,77865,77866],{"encoding":904},"L=10",[883,77868,77870],{"className":77869},[886],[888,77871,77872],{"xmlns":890},[892,77873,77874,77884],{},[895,77875,77876,77878],{},[898,77877,1836],{},[2281,77879,77880,77882],{},[898,77881,3946],{},[898,77883,9801],{},[902,77885,74638],{"encoding":904}," (max 45 při ",[883,77888,77890],{"className":77889},[886],[888,77891,77892],{"xmlns":890},[892,77893,77894,77902],{},[895,77895,77896,77898,77900],{},[898,77897,9801],{},[2005,77899,2007],{},[2138,77901,36249],{},[902,77903,77904],{"encoding":904},"L=15","), průsečík v ",[883,77907,77909],{"className":77908},[886],[888,77910,77911],{"xmlns":890},[892,77912,77913,77921],{},[895,77914,77915,77917,77919],{},[898,77916,9801],{},[2005,77918,2007],{},[2138,77920,36249],{},[902,77922,77576],{"encoding":904},". Nalevo od 15 leží ",[883,77925,77927],{"className":77926},[886],[888,77928,77929],{"xmlns":890},[892,77930,77931,77941],{},[895,77932,77933,77935],{},[898,77934,2826],{},[2281,77936,77937,77939],{},[898,77938,3946],{},[898,77940,9801],{},[902,77942,10050],{"encoding":904}," nad ",[883,77945,77947],{"className":77946},[886],[888,77948,77949],{"xmlns":890},[892,77950,77951,77961],{},[895,77952,77953,77955],{},[898,77954,1836],{},[2281,77956,77957,77959],{},[898,77958,3946],{},[898,77960,9801],{},[902,77962,74638],{"encoding":904},", napravo pod ní.",[115,77965,77967],{"id":77966},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,77969,77970,77971,2694,77984,2212,77987,6196,78000,2212,78003,2713],{},"V dvoufaktorovém modelu závisí produkce ",[883,77972,77974],{"className":77973},[886],[888,77975,77976],{"xmlns":890},[892,77977,77978,77982],{},[895,77979,77980],{},[898,77981,2797],{},[902,77983,2797],{"encoding":904},[38,77985,77986],{},"práci",[883,77988,77990],{"className":77989},[886],[888,77991,77992],{"xmlns":890},[892,77993,77994,77998],{},[895,77995,77996],{},[898,77997,9801],{},[902,77999,9801],{"encoding":904},[38,78001,78002],{},"kapitálu",[883,78004,78006],{"className":78005},[886],[888,78007,78008],{"xmlns":890},[892,78009,78010,78014],{},[895,78011,78012],{},[898,78013,9806],{},[902,78015,9806],{"encoding":904},[883,78017,78019],{"className":78018},[886],[888,78020,78021],{"xmlns":890,"display":28071},[892,78022,78023,78058],{},[20760,78024,78025],{"width":28076},[20765,78026,78027,78029,78051,78053],{},[20768,78028],{"width":28081},[20768,78030,78031],{},[895,78032,78033,78035,78037,78039,78041,78043,78045,78047,78049],{},[898,78034,2797],{},[2005,78036,2007],{},[898,78038,2797],{},[2005,78040,2014],{"stretchy":2013},[898,78042,9801],{},[2005,78044,2295],{"separator":2294},[898,78046,9806],{},[2005,78048,2020],{"stretchy":2013},[898,78050,1644],{"mathvariant":2385},[20768,78052],{"width":28081},[20768,78054,78055],{},[2297,78056,78057],{},"(5.6)",[902,78059,78060],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,78062,78063,78064,78066],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,78065,75005],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,78068,78070],{"id":78069},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,78072,78073],{},"Široce používané produkční funkce mají tvar",[883,78075,78077],{"className":78076},[886],[888,78078,78079],{"xmlns":890,"display":28071},[892,78080,78081,78122],{},[20760,78082,78083],{"width":28076},[20765,78084,78085,78087,78115,78117],{},[20768,78086],{"width":28081},[20768,78088,78089],{},[895,78090,78091,78093,78095,78097,78099,78105,78107,78113],{},[898,78092,2797],{},[2005,78094,2007],{},[898,78096,1836],{},[2297,78098,2995],{},[2133,78100,78101,78103],{},[898,78102,9801],{},[898,78104,207],{},[2297,78106,2995],{},[2133,78108,78109,78111],{},[898,78110,9806],{},[898,78112,2107],{},[2005,78114,2295],{"separator":2294},[20768,78116],{"width":28081},[20768,78118,78119],{},[2297,78120,78121],{},"(5.7)",[902,78123,78124],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,78126,4316,78127,78149,78150,78152,78153,1644],{},[883,78128,78130],{"className":78129},[886],[888,78131,78132],{"xmlns":890},[892,78133,78134,78146],{},[895,78135,78136,78138,78140,78142,78144],{},[898,78137,1836],{},[2005,78139,2295],{"separator":2294},[898,78141,207],{},[2005,78143,2295],{"separator":2294},[898,78145,2107],{},[902,78147,78148],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,78151,74704],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,78154,78156],{"className":78155},[886],[888,78157,78158],{"xmlns":890},[892,78159,78160,78172],{},[895,78161,78162,78164,78166,78168,78170],{},[898,78163,207],{},[2005,78165,2295],{"separator":2294},[898,78167,2107],{},[2005,78169,3455],{},[2138,78171,2287],{},[902,78173,78174],{"encoding":904},"a, b \u003C 1",[724,78176,78177],{},[2568,78178],{"alt":78179,"className":78180,"src":78181},"imek-vynosy-z-rozsahu-3typy",[210,2572],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,78183,78184,78185,78188,78189,2694,78202,78218,78219,2694,78232,2713],{},"Reflektují ekonomickou zákonitost, že ",[38,78186,78187],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,78190,78192],{"className":78191},[886],[888,78193,78194],{"xmlns":890},[892,78195,78196,78200],{},[895,78197,78198],{},[898,78199,9801],{},[902,78201,9801],{"encoding":904},[883,78203,78205],{"className":78204},[886],[888,78206,78207],{"xmlns":890},[892,78208,78209,78215],{},[895,78210,78211,78213],{},[898,78212,12047],{},[898,78214,9801],{},[902,78216,78217],{"encoding":904},"rL"," a kapitál z ",[883,78220,78222],{"className":78221},[886],[888,78223,78224],{"xmlns":890},[892,78225,78226,78230],{},[895,78227,78228],{},[898,78229,9806],{},[902,78231,9806],{"encoding":904},[883,78233,78235],{"className":78234},[886],[888,78236,78237],{"xmlns":890},[892,78238,78239,78245],{},[895,78240,78241,78243],{},[898,78242,12047],{},[898,78244,9806],{},[902,78246,78247],{"encoding":904},"rK",[883,78249,78251],{"className":78250},[886],[888,78252,78253],{"xmlns":890,"display":28071},[892,78254,78255,78378],{},[20760,78256,78257],{"width":28076},[20765,78258,78259,78261,78371,78373],{},[20768,78260],{"width":28081},[20768,78262,78263],{},[895,78264,78265,78267,78269,78271,78273,78275,78277,78279,78281,78283,78285,78287,78289,78291,78297,78299,78301,78303,78309,78311,78313,78315,78327,78329,78335,78341,78343,78355,78357,78359,78361,78363,78365,78367,78369],{},[898,78266,2797],{},[2005,78268,2014],{"stretchy":2013},[898,78270,12047],{},[898,78272,9801],{},[2005,78274,2295],{"separator":2294},[898,78276,12047],{},[898,78278,9806],{},[2005,78280,2020],{"stretchy":2013},[2005,78282,2007],{},[898,78284,1836],{},[2005,78286,2014],{"stretchy":2013},[898,78288,12047],{},[898,78290,9801],{},[2133,78292,78293,78295],{},[2005,78294,2020],{"stretchy":2013},[898,78296,207],{},[2005,78298,2014],{"stretchy":2013},[898,78300,12047],{},[898,78302,9806],{},[2133,78304,78305,78307],{},[2005,78306,2020],{"stretchy":2013},[898,78308,2107],{},[2005,78310,2007],{},[898,78312,1836],{},[2297,78314,2995],{},[2133,78316,78317,78319],{},[898,78318,12047],{},[895,78320,78321,78323,78325],{},[898,78322,207],{},[2005,78324,2104],{},[898,78326,2107],{},[2297,78328,2995],{},[2133,78330,78331,78333],{},[898,78332,9801],{},[898,78334,207],{},[2133,78336,78337,78339],{},[898,78338,9806],{},[898,78340,2107],{},[2005,78342,2007],{},[2133,78344,78345,78347],{},[898,78346,12047],{},[895,78348,78349,78351,78353],{},[898,78350,207],{},[2005,78352,2104],{},[898,78354,2107],{},[2297,78356,2995],{},[898,78358,2797],{},[2005,78360,2014],{"stretchy":2013},[898,78362,9801],{},[2005,78364,2295],{"separator":2294},[898,78366,9806],{},[2005,78368,2020],{"stretchy":2013},[898,78370,1644],{"mathvariant":2385},[20768,78372],{"width":28081},[20768,78374,78375],{},[2297,78376,78377],{},"(5.8)",[902,78379,78380],{"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}",[724,78382,78383,78384],{},"Volně: ",[38,78385,78386,78387,78400,78401,78425],{},"změní-li se vstupy ",[883,78388,78390],{"className":78389},[886],[888,78391,78392],{"xmlns":890},[892,78393,78394,78398],{},[895,78395,78396],{},[898,78397,12047],{},[902,78399,12047],{"encoding":904},"-krát, změní se výstup ",[883,78402,78404],{"className":78403},[886],[888,78405,78406],{"xmlns":890},[892,78407,78408,78422],{},[895,78409,78410],{},[2133,78411,78412,78414],{},[898,78413,12047],{},[895,78415,78416,78418,78420],{},[898,78417,207],{},[2005,78419,2104],{},[898,78421,2107],{},[902,78423,78424],{"encoding":904},"r^{a+b}","-krát.",[198,78427,78429],{"id":78428},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,78431,78432,78433,78450],{},"Součet exponentů ",[883,78434,78436],{"className":78435},[886],[888,78437,78438],{"xmlns":890},[892,78439,78440,78448],{},[895,78441,78442,78444,78446],{},[898,78443,207],{},[2005,78445,2104],{},[898,78447,2107],{},[902,78449,74829],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,78452,78453,78482],{},[19,78454,78455],{},[22,78456,78457,78460,78463,78480],{},[25,78458,78459],{},"Typ",[25,78461,78462],{},"Podmínka",[25,78464,78465,78466,78479],{},"Chování produkce při ",[883,78467,78469],{"className":78468},[886],[888,78470,78471],{"xmlns":890},[892,78472,78473,78477],{},[895,78474,78475],{},[898,78476,12047],{},[902,78478,12047],{"encoding":904},"-násobném zvýšení vstupů",[25,78481,3078],{},[30,78483,78484,78595,78710],{},[22,78485,78486,78494,78518,78551],{},[35,78487,75542,78488,10030,78491,2020],{},[38,78489,78490],{},"Konstantní",[614,78492,78493],{},"constant returns",[35,78495,78496],{},[883,78497,78499],{"className":78498},[886],[888,78500,78501],{"xmlns":890},[892,78502,78503,78515],{},[895,78504,78505,78507,78509,78511,78513],{},[898,78506,207],{},[2005,78508,2104],{},[898,78510,2107],{},[2005,78512,2007],{},[2138,78514,2287],{},[902,78516,78517],{"encoding":904},"a+b = 1",[35,78519,78520,78533,78534,2212,78537,78550],{},[883,78521,78523],{"className":78522},[886],[888,78524,78525],{"xmlns":890},[892,78526,78527,78531],{},[895,78528,78529],{},[898,78530,2797],{},[902,78532,2797],{"encoding":904}," vzroste ",[38,78535,78536],{},"přesně",[883,78538,78540],{"className":78539},[886],[888,78541,78542],{"xmlns":890},[892,78543,78544,78548],{},[895,78545,78546],{},[898,78547,12047],{},[902,78549,12047],{"encoding":904},"-krát",[35,78552,78553],{},[883,78554,78556],{"className":78555},[886],[888,78557,78558],{"xmlns":890},[892,78559,78560,78592],{},[895,78561,78562,78564,78566,78568,78580],{},[898,78563,2797],{},[2005,78565,2007],{},[2138,78567,2140],{},[2133,78569,78570,78572],{},[898,78571,9801],{},[895,78573,78574,78576,78578],{},[2138,78575,2287],{},[898,78577,4680],{"mathvariant":2385},[2138,78579,2360],{},[2133,78581,78582,78584],{},[898,78583,9806],{},[895,78585,78586,78588,78590],{},[2138,78587,2182],{},[898,78589,4680],{"mathvariant":2385},[2138,78591,2360],{},[902,78593,78594],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,78596,78597,78606,78630,78660],{},[35,78598,78599,78600,10030,78603,2020],{},"2° ",[38,78601,78602],{},"Rostoucí",[614,78604,78605],{},"increasing returns",[35,78607,78608],{},[883,78609,78611],{"className":78610},[886],[888,78612,78613],{"xmlns":890},[892,78614,78615,78627],{},[895,78616,78617,78619,78621,78623,78625],{},[898,78618,207],{},[2005,78620,2104],{},[898,78622,2107],{},[2005,78624,3416],{},[2138,78626,2287],{},[902,78628,78629],{"encoding":904},"a+b > 1",[35,78631,78632,78533,78645,51236,78647,78550],{},[883,78633,78635],{"className":78634},[886],[888,78636,78637],{"xmlns":890},[892,78638,78639,78643],{},[895,78640,78641],{},[898,78642,2797],{},[902,78644,2797],{"encoding":904},[38,78646,25275],{},[883,78648,78650],{"className":78649},[886],[888,78651,78652],{"xmlns":890},[892,78653,78654,78658],{},[895,78655,78656],{},[898,78657,12047],{},[902,78659,12047],{"encoding":904},[35,78661,78662,10030,78688,2020],{},[883,78663,78665],{"className":78664},[886],[888,78666,78667],{"xmlns":890},[892,78668,78669,78685],{},[895,78670,78671,78673,78675,78677,78679],{},[898,78672,2797],{},[2005,78674,2007],{},[2138,78676,24206],{},[898,78678,9801],{},[2133,78680,78681,78683],{},[898,78682,9806],{},[2138,78684,2140],{},[902,78686,78687],{"encoding":904},"Q = 7LK^2",[883,78689,78691],{"className":78690},[886],[888,78692,78693],{"xmlns":890},[892,78694,78695,78707],{},[895,78696,78697,78699,78701,78703,78705],{},[898,78698,207],{},[2005,78700,2104],{},[898,78702,2107],{},[2005,78704,2007],{},[2138,78706,2182],{},[902,78708,78709],{"encoding":904},"a+b = 3",[22,78711,78712,78721,78745,78776],{},[35,78713,78714,78715,10030,78718,2020],{},"3° ",[38,78716,78717],{},"Klesající",[614,78719,78720],{},"decreasing returns",[35,78722,78723],{},[883,78724,78726],{"className":78725},[886],[888,78727,78728],{"xmlns":890},[892,78729,78730,78742],{},[895,78731,78732,78734,78736,78738,78740],{},[898,78733,207],{},[2005,78735,2104],{},[898,78737,2107],{},[2005,78739,3455],{},[2138,78741,2287],{},[902,78743,78744],{"encoding":904},"a+b \u003C 1",[35,78746,78747,78533,78760,51236,78763,78550],{},[883,78748,78750],{"className":78749},[886],[888,78751,78752],{"xmlns":890},[892,78753,78754,78758],{},[895,78755,78756],{},[898,78757,2797],{},[902,78759,2797],{"encoding":904},[38,78761,78762],{},"méně",[883,78764,78766],{"className":78765},[886],[888,78767,78768],{"xmlns":890},[892,78769,78770,78774],{},[895,78771,78772],{},[898,78773,12047],{},[902,78775,12047],{"encoding":904},[35,78777,78778,10030,78808,2020],{},[883,78779,78781],{"className":78780},[886],[888,78782,78783],{"xmlns":890},[892,78784,78785,78805],{},[895,78786,78787,78789,78791,78793,78799],{},[898,78788,2797],{},[2005,78790,2007],{},[2138,78792,2871],{},[2133,78794,78795,78797],{},[898,78796,9801],{},[2138,78798,68216],{},[2133,78800,78801,78803],{},[898,78802,9806],{},[2138,78804,5015],{},[902,78806,78807],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,78809,78811],{"className":78810},[886],[888,78812,78813],{"xmlns":890},[892,78814,78815,78827],{},[895,78816,78817,78819,78821,78823,78825],{},[898,78818,207],{},[2005,78820,2104],{},[898,78822,2107],{},[2005,78824,2007],{},[2138,78826,14595],{},[902,78828,78829],{"encoding":904},"a+b = 0{,}8",[3876,78831,78832],{},[724,78833,78834,78836,78837,78854,78855,78858,78859,2212,78862,78898,78899,78921,78922,1644],{},[883,78835,4418],{}," Pozor\nSoučet ",[883,78838,78840],{"className":78839},[886],[888,78841,78842],{"xmlns":890},[892,78843,78844,78852],{},[895,78845,78846,78848,78850],{},[898,78847,207],{},[2005,78849,2104],{},[898,78851,2107],{},[902,78853,74829],{"encoding":904}," neudává velikost produkce, ale ",[38,78856,78857],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,78860,78861],{},"ryzí Cobb-Douglas",[883,78863,78865],{"className":78864},[886],[888,78866,78867],{"xmlns":890},[892,78868,78869,78895],{},[895,78870,78871,78873,78875,78877,78883],{},[898,78872,2797],{},[2005,78874,2007],{},[898,78876,1836],{},[2133,78878,78879,78881],{},[898,78880,9801],{},[898,78882,207],{},[2133,78884,78885,78887],{},[898,78886,9806],{},[895,78888,78889,78891,78893],{},[2138,78890,2287],{},[2005,78892,2234],{},[898,78894,207],{},[902,78896,78897],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,78900,78902],{"className":78901},[886],[888,78903,78904],{"xmlns":890},[892,78905,78906,78918],{},[895,78907,78908,78910,78912,78914,78916],{},[898,78909,2107],{},[2005,78911,2007],{},[2138,78913,2287],{},[2005,78915,2234],{},[898,78917,207],{},[902,78919,78920],{"encoding":904},"b = 1-a",", tedy vždy ",[38,78923,78924],{},"konstantní výnosy z rozsahu",[198,78926,78928,78929],{"id":78927},"parametr-efektivity-aa","Parametr efektivity ",[883,78930,78932],{"className":78931},[886],[888,78933,78934],{"xmlns":890},[892,78935,78936,78940],{},[895,78937,78938],{},[898,78939,1836],{},[902,78941,1836],{"encoding":904},[724,78943,78944,78945,78958,78959,78972,78973,78991,78992,78995],{},"Konstanta ",[883,78946,78948],{"className":78947},[886],[888,78949,78950],{"xmlns":890},[892,78951,78952,78956],{},[895,78953,78954],{},[898,78955,1836],{},[902,78957,1836],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,78960,78962],{"className":78961},[886],[888,78963,78964],{"xmlns":890},[892,78965,78966,78970],{},[895,78967,78968],{},[898,78969,2797],{},[902,78971,2797],{"encoding":904}," při pevně zadaných ",[883,78974,78976],{"className":78975},[886],[888,78977,78978],{"xmlns":890},[892,78979,78980,78988],{},[895,78981,78982,78984,78986],{},[898,78983,9801],{},[2005,78985,2295],{"separator":2294},[898,78987,9806],{},[902,78989,78990],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,78993,78994],{},"parametr efektivity"," — indikátor stavu technologie.",[198,78997,78999],{"id":78998},"příklad-53","Příklad 5.3",[724,79001,79002,79003,78898,79045,79047,79048,1644],{},"Produkční funkce ",[883,79004,79006],{"className":79005},[886],[888,79007,79008],{"xmlns":890},[892,79009,79010,79042],{},[895,79011,79012,79014,79016,79018,79030],{},[898,79013,2797],{},[2005,79015,2007],{},[2138,79017,2140],{},[2133,79019,79020,79022],{},[898,79021,9801],{},[895,79023,79024,79026,79028],{},[2138,79025,2287],{},[898,79027,4680],{"mathvariant":2385},[2138,79029,2360],{},[2133,79031,79032,79034],{},[898,79033,9806],{},[895,79035,79036,79038,79040],{},[2138,79037,2182],{},[898,79039,4680],{"mathvariant":2385},[2138,79041,2360],{},[902,79043,79044],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,79046,24618],{}," výnosy z rozsahu, neboť ",[883,79049,79051],{"className":79050},[886],[888,79052,79053],{"xmlns":890},[892,79054,79055,79079],{},[895,79056,79057,79065,79067,79075,79077],{},[2334,79058,79059],{"scriptlevel":2336,"displaystyle":2013},[2338,79060,79061,79063],{},[2138,79062,2287],{},[2138,79064,2360],{},[2005,79066,2104],{},[2334,79068,79069],{"scriptlevel":2336,"displaystyle":2013},[2338,79070,79071,79073],{},[2138,79072,2182],{},[2138,79074,2360],{},[2005,79076,2007],{},[2138,79078,2287],{},[902,79080,79081],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,79083,79084,79085,6196,79098,79111,79112,2212,79125,79165],{},"Změní-li se ",[883,79086,79088],{"className":79087},[886],[888,79089,79090],{"xmlns":890},[892,79091,79092,79096],{},[895,79093,79094],{},[898,79095,9801],{},[902,79097,9801],{"encoding":904},[883,79099,79101],{"className":79100},[886],[888,79102,79103],{"xmlns":890},[892,79104,79105,79109],{},[895,79106,79107],{},[898,79108,9806],{},[902,79110,9806],{"encoding":904}," čtyřnásobně, změní se ",[883,79113,79115],{"className":79114},[886],[888,79116,79117],{"xmlns":890},[892,79118,79119,79123],{},[895,79120,79121],{},[898,79122,2797],{},[902,79124,2797],{"encoding":904},[883,79126,79128],{"className":79127},[886],[888,79129,79130],{"xmlns":890},[892,79131,79132,79162],{},[895,79133,79134,79154,79156],{},[2133,79135,79136,79138],{},[2138,79137,2360],{},[895,79139,79140,79142,79144,79146,79148,79150,79152],{},[2138,79141,2287],{},[898,79143,4680],{"mathvariant":2385},[2138,79145,2360],{},[2005,79147,2104],{},[2138,79149,2182],{},[898,79151,4680],{"mathvariant":2385},[2138,79153,2360],{},[2005,79155,2007],{},[2133,79157,79158,79160],{},[2138,79159,2360],{},[2138,79161,2287],{},[902,79163,79164],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,79167,79169],{"className":79168},[886],[888,79170,79171],{"xmlns":890,"display":28071},[892,79172,79173,79333],{},[895,79174,79175,79177,79179,79181,79183,79185,79187,79189,79191,79193,79195,79197,79199,79201,79213,79215,79217,79219,79231,79233,79235,79237,79257,79269,79281,79283,79285,79287,79289,79301,79313,79315,79317,79319,79321,79323,79325,79327,79329,79331],{},[898,79176,2797],{},[2005,79178,2014],{"stretchy":2013},[2138,79180,2360],{},[898,79182,9801],{},[2005,79184,2295],{"separator":2294},[2138,79186,2360],{},[898,79188,9806],{},[2005,79190,2020],{"stretchy":2013},[2005,79192,2007],{},[2138,79194,2140],{},[2005,79196,2014],{"stretchy":2013},[2138,79198,2360],{},[898,79200,9801],{},[2133,79202,79203,79205],{},[2005,79204,2020],{"stretchy":2013},[895,79206,79207,79209,79211],{},[2138,79208,2287],{},[898,79210,4680],{"mathvariant":2385},[2138,79212,2360],{},[2005,79214,2014],{"stretchy":2013},[2138,79216,2360],{},[898,79218,9806],{},[2133,79220,79221,79223],{},[2005,79222,2020],{"stretchy":2013},[895,79224,79225,79227,79229],{},[2138,79226,2182],{},[898,79228,4680],{"mathvariant":2385},[2138,79230,2360],{},[2005,79232,2007],{},[2138,79234,2140],{},[2005,79236,3185],{},[2133,79238,79239,79241],{},[2138,79240,2360],{},[895,79242,79243,79245,79247,79249,79251,79253,79255],{},[2138,79244,2287],{},[898,79246,4680],{"mathvariant":2385},[2138,79248,2360],{},[2005,79250,2104],{},[2138,79252,2182],{},[898,79254,4680],{"mathvariant":2385},[2138,79256,2360],{},[2133,79258,79259,79261],{},[898,79260,9801],{},[895,79262,79263,79265,79267],{},[2138,79264,2287],{},[898,79266,4680],{"mathvariant":2385},[2138,79268,2360],{},[2133,79270,79271,79273],{},[898,79272,9806],{},[895,79274,79275,79277,79279],{},[2138,79276,2182],{},[898,79278,4680],{"mathvariant":2385},[2138,79280,2360],{},[2005,79282,2007],{},[2138,79284,2360],{},[2005,79286,3185],{},[2138,79288,2140],{},[2133,79290,79291,79293],{},[898,79292,9801],{},[895,79294,79295,79297,79299],{},[2138,79296,2287],{},[898,79298,4680],{"mathvariant":2385},[2138,79300,2360],{},[2133,79302,79303,79305],{},[898,79304,9806],{},[895,79306,79307,79309,79311],{},[2138,79308,2182],{},[898,79310,4680],{"mathvariant":2385},[2138,79312,2360],{},[2005,79314,2007],{},[2138,79316,2360],{},[2297,79318,2995],{},[898,79320,2797],{},[2005,79322,2014],{"stretchy":2013},[898,79324,9801],{},[2005,79326,2295],{"separator":2294},[898,79328,9806],{},[2005,79330,2020],{"stretchy":2013},[898,79332,1644],{"mathvariant":2385},[902,79334,79335],{"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).",[198,79337,79338],{"id":37184},"Homogenita",[724,79340,79341,79342,8108,79365,79381],{},"Funkce ",[883,79343,79345],{"className":79344},[886],[888,79346,79347],{"xmlns":890},[892,79348,79349,79363],{},[895,79350,79351,79353,79355,79357,79359,79361],{},[898,79352,2797],{},[2005,79354,2014],{"stretchy":2013},[898,79356,9801],{},[2005,79358,2295],{"separator":2294},[898,79360,9806],{},[2005,79362,2020],{"stretchy":2013},[902,79364,10002],{"encoding":904},[38,79366,79367,79368],{},"homogenní stupně ",[883,79369,79371],{"className":79370},[886],[888,79372,79373],{"xmlns":890},[892,79374,79375,79379],{},[895,79376,79377],{},[898,79378,36865],{},[902,79380,36865],{"encoding":904},", jestliže",[883,79383,79385],{"className":79384},[886],[888,79386,79387],{"xmlns":890,"display":28071},[892,79388,79389,79446],{},[20760,79390,79391],{"width":28076},[20765,79392,79393,79395,79439,79441],{},[20768,79394],{"width":28081},[20768,79396,79397],{},[895,79398,79399,79401,79403,79405,79407,79409,79411,79413,79415,79417,79423,79425,79427,79429,79431,79433,79435,79437],{},[898,79400,2797],{},[2005,79402,2014],{"stretchy":2013},[898,79404,12047],{},[898,79406,9801],{},[2005,79408,2295],{"separator":2294},[898,79410,12047],{},[898,79412,9806],{},[2005,79414,2020],{"stretchy":2013},[2005,79416,2007],{},[2133,79418,79419,79421],{},[898,79420,12047],{},[898,79422,36865],{},[2297,79424,2995],{},[898,79426,2797],{},[2005,79428,2014],{"stretchy":2013},[898,79430,9801],{},[2005,79432,2295],{"separator":2294},[898,79434,9806],{},[2005,79436,2020],{"stretchy":2013},[2005,79438,2295],{"separator":2294},[20768,79440],{"width":28081},[20768,79442,79443],{},[2297,79444,79445],{},"(5.10)",[902,79447,79448],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,79450,4316,79451,79469,79470,79488,79489,43641,79502,79505,79506,1644],{},[883,79452,79454],{"className":79453},[886],[888,79455,79456],{"xmlns":890},[892,79457,79458,79466],{},[895,79459,79460,79462,79464],{},[898,79461,36865],{},[2005,79463,4491],{},[2138,79465,2336],{},[902,79467,79468],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,79471,79473],{"className":79472},[886],[888,79474,79475],{"xmlns":890},[892,79476,79477,79485],{},[895,79478,79479,79481,79483],{},[898,79480,12047],{},[2005,79482,3416],{},[2138,79484,2336],{},[902,79486,79487],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,79490,79492],{"className":79491},[886],[888,79493,79494],{"xmlns":890},[892,79495,79496,79500],{},[895,79497,79498],{},[2138,79499,2287],{},[902,79501,2287],{"encoding":904},[38,79503,79504],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,79507,79509],{"className":79508},[886],[888,79510,79511],{"xmlns":890},[892,79512,79513,79521],{},[895,79514,79515,79517,79519],{},[898,79516,207],{},[2005,79518,2104],{},[898,79520,2107],{},[902,79522,74829],{"encoding":904},[115,79524,79526],{"id":79525},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,79528,79529],{},[38,79530,79531],{},"Ryzí Cobb-Douglasovy funkce:",[883,79533,79535],{"className":79534},[886],[888,79536,79537],{"xmlns":890,"display":28071},[892,79538,79539,79598],{},[20760,79540,79541],{"width":28076},[20765,79542,79543,79545,79591,79593],{},[20768,79544],{"width":28081},[20768,79546,79547],{},[895,79548,79549,79551,79553,79555,79557,79563,79565,79577,79579,79581,79583,79585,79587,79589],{},[898,79550,2797],{},[2005,79552,2007],{},[898,79554,1836],{},[2297,79556,2995],{},[2133,79558,79559,79561],{},[898,79560,9801],{},[898,79562,207],{},[2297,79564,2995],{},[2133,79566,79567,79569],{},[898,79568,9806],{},[895,79570,79571,79573,79575],{},[2138,79572,2287],{},[2005,79574,2234],{},[898,79576,207],{},[2005,79578,2295],{"separator":2294},[5884,79580],{"width":15290},[2138,79582,2336],{},[2005,79584,3455],{},[898,79586,207],{},[2005,79588,3455],{},[2138,79590,13266],{},[20768,79592],{"width":28081},[20768,79594,79595],{},[2297,79596,79597],{},"(5.9)",[902,79599,79600],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,79602,79603,79604,79606,79607,1644],{},"Mají vždy ",[38,79605,78924],{}," a jsou ",[38,79608,79504],{},[724,79610,79611,10030,79614,79617],{},[38,79612,79613],{},"CES produkční funkce",[614,79615,79616],{},"Constant Elasticity of Substitution",", 1961):",[883,79619,79621],{"className":79620},[886],[888,79622,79623],{"xmlns":890,"display":28071},[892,79624,79625,79693],{},[895,79626,79627,79629,79631,79633,79691],{},[898,79628,2797],{},[2005,79630,2007],{},[898,79632,1836],{},[2133,79634,79635,79679],{},[895,79636,79637,79639,79641,79643,79645,79647,79649,79651,79661,79663,79665,79667,79677],{},[2005,79638,2495],{"fence":2294},[2005,79640,2014],{"stretchy":2013},[2138,79642,2287],{},[2005,79644,2234],{},[898,79646,207],{},[2005,79648,2020],{"stretchy":2013},[2297,79650,2995],{},[2133,79652,79653,79655],{},[898,79654,9801],{},[895,79656,79657,79659],{},[2005,79658,2234],{},[898,79660,2107],{},[2005,79662,2104],{},[898,79664,207],{},[2297,79666,2995],{},[2133,79668,79669,79671],{},[898,79670,9806],{},[895,79672,79673,79675],{},[2005,79674,2234],{},[898,79676,2107],{},[2005,79678,2510],{"fence":2294},[895,79680,79681,79683],{},[2005,79682,2234],{},[2334,79684,79685],{"scriptlevel":2336,"displaystyle":2013},[2338,79686,79687,79689],{},[2138,79688,2287],{},[898,79690,2107],{},[2005,79692,2295],{"separator":2294},[902,79694,79695],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,79697,4316,79698,1343,79716,1343,79737,79761],{},[883,79699,79701],{"className":79700},[886],[888,79702,79703],{"xmlns":890},[892,79704,79705,79713],{},[895,79706,79707,79709,79711],{},[898,79708,1836],{},[2005,79710,3416],{},[2138,79712,2336],{},[902,79714,79715],{"encoding":904},"A > 0",[883,79717,79719],{"className":79718},[886],[888,79720,79721],{"xmlns":890},[892,79722,79723,79735],{},[895,79724,79725,79727,79729,79731,79733],{},[2138,79726,2336],{},[2005,79728,3455],{},[898,79730,207],{},[2005,79732,3455],{},[2138,79734,2287],{},[902,79736,18842],{"encoding":904},[883,79738,79740],{"className":79739},[886],[888,79741,79742],{"xmlns":890},[892,79743,79744,79758],{},[895,79745,79746,79748,79750,79752,79754,79756],{},[2005,79747,2234],{},[2138,79749,2287],{},[2005,79751,3455],{},[898,79753,2107],{},[2005,79755,3379],{"mathvariant":2385},[2138,79757,2336],{},[902,79759,79760],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,79763,79764],{},[38,79765,79766],{},"Další typy:",[120,79768,79769,79811],{},[123,79770,79771,2212,79774,79810],{},[38,79772,79773],{},"Lineární:",[883,79775,79777],{"className":79776},[886],[888,79778,79779],{"xmlns":890},[892,79780,79781,79807],{},[895,79782,79783,79785,79787,79789,79791,79793,79795,79797,79799,79801,79803,79805],{},[898,79784,2797],{},[2005,79786,2014],{"stretchy":2013},[898,79788,9801],{},[2005,79790,2295],{"separator":2294},[898,79792,9806],{},[2005,79794,2020],{"stretchy":2013},[2005,79796,2007],{},[898,79798,207],{},[898,79800,9801],{},[2005,79802,2104],{},[898,79804,2107],{},[898,79806,9806],{},[902,79808,79809],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,79812,79813,2212,79816,79861],{},[38,79814,79815],{},"Leontiefova:",[883,79817,79819],{"className":79818},[886],[888,79820,79821],{"xmlns":890},[892,79822,79823,79858],{},[895,79824,79825,79827,79829,79831,79833,79835,79837,79839,79842,79844,79846,79848,79850,79852,79854,79856],{},[898,79826,2797],{},[2005,79828,2014],{"stretchy":2013},[898,79830,9801],{},[2005,79832,2295],{"separator":2294},[898,79834,9806],{},[2005,79836,2020],{"stretchy":2013},[2005,79838,2007],{},[898,79840,79841],{},"min",[2005,79843,56205],{},[2005,79845,2014],{"stretchy":2013},[898,79847,207],{},[898,79849,9801],{},[2005,79851,2295],{"separator":2294},[898,79853,2107],{},[898,79855,9806],{},[2005,79857,2020],{"stretchy":2013},[902,79859,79860],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,79863,79865,79866,1343,79885,79904],{"id":79864},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,79867,79869],{"className":79868},[886],[888,79870,79871],{"xmlns":890},[892,79872,79873,79883],{},[895,79874,79875,79877],{},[898,79876,2826],{},[2281,79878,79879,79881],{},[898,79880,3946],{},[898,79882,9801],{},[902,79884,10050],{"encoding":904},[883,79886,79888],{"className":79887},[886],[888,79889,79890],{"xmlns":890},[892,79891,79892,79902],{},[895,79893,79894,79896],{},[898,79895,2826],{},[2281,79897,79898,79900],{},[898,79899,3946],{},[898,79901,9806],{},[902,79903,10095],{"encoding":904}," a totální diferenciál",[724,79906,79907],{},[38,79908,79909],{},"Mezní produkt práce:",[883,79911,79913],{"className":79912},[886],[888,79914,79915],{"xmlns":890,"display":28071},[892,79916,79917,79955],{},[895,79918,79919,79921,79927,79929,79937,79939,79953],{},[898,79920,2826],{},[2281,79922,79923,79925],{},[898,79924,3946],{},[898,79926,9801],{},[2005,79928,2007],{},[9172,79930,79931,79933,79935],{},[898,79932,2797],{},[898,79934,9801],{},[2005,79936,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,79938,2007],{},[2338,79940,79941,79947],{},[895,79942,79943,79945],{},[898,79944,9877],{"mathvariant":2385},[898,79946,2797],{},[895,79948,79949,79951],{},[898,79950,9877],{"mathvariant":2385},[898,79952,9801],{},[898,79954,1644],{"mathvariant":2385},[902,79956,79957],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,79959,79960],{},[38,79961,79962],{},"Mezní produkt kapitálu:",[883,79964,79966],{"className":79965},[886],[888,79967,79968],{"xmlns":890,"display":28071},[892,79969,79970,80008],{},[895,79971,79972,79974,79980,79982,79990,79992,80006],{},[898,79973,2826],{},[2281,79975,79976,79978],{},[898,79977,3946],{},[898,79979,9806],{},[2005,79981,2007],{},[9172,79983,79984,79986,79988],{},[898,79985,2797],{},[898,79987,9806],{},[2005,79989,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,79991,2007],{},[2338,79993,79994,80000],{},[895,79995,79996,79998],{},[898,79997,9877],{"mathvariant":2385},[898,79999,2797],{},[895,80001,80002,80004],{},[898,80003,9877],{"mathvariant":2385},[898,80005,9806],{},[898,80007,1644],{"mathvariant":2385},[902,80009,80010],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,80012,80013,80043,80044,80065,80066,80084,80085,80098,80099,1644],{},[883,80014,80016],{"className":80015},[886],[888,80017,80018],{"xmlns":890},[892,80019,80020,80040],{},[895,80021,80022,80024,80030,80032,80034,80036,80038],{},[898,80023,2826],{},[2281,80025,80026,80028],{},[898,80027,3946],{},[898,80029,9801],{},[2005,80031,2014],{"stretchy":2013},[898,80033,207],{},[2005,80035,2295],{"separator":2294},[898,80037,2107],{},[2005,80039,2020],{"stretchy":2013},[902,80041,80042],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,80045,80047],{"className":80046},[886],[888,80048,80049],{"xmlns":890},[892,80050,80051,80063],{},[895,80052,80053,80055,80057,80059,80061],{},[2005,80054,2495],{"stretchy":2013},[898,80056,207],{},[2005,80058,2295],{"separator":2294},[898,80060,2107],{},[2005,80062,2510],{"stretchy":2013},[902,80064,10828],{"encoding":904}," (na hladině ",[883,80067,80069],{"className":80068},[886],[888,80070,80071],{"xmlns":890},[892,80072,80073,80081],{},[895,80074,80075,80077,80079],{},[898,80076,9806],{},[2005,80078,2007],{},[898,80080,2107],{},[902,80082,80083],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,80086,80088],{"className":80087},[886],[888,80089,80090],{"xmlns":890},[892,80091,80092,80096],{},[895,80093,80094],{},[898,80095,9801],{},[902,80097,9801],{"encoding":904},". Analogicky ",[883,80100,80102],{"className":80101},[886],[888,80103,80104],{"xmlns":890},[892,80105,80106,80126],{},[895,80107,80108,80110,80116,80118,80120,80122,80124],{},[898,80109,2826],{},[2281,80111,80112,80114],{},[898,80113,3946],{},[898,80115,9806],{},[2005,80117,2014],{"stretchy":2013},[898,80119,207],{},[2005,80121,2295],{"separator":2294},[898,80123,2107],{},[2005,80125,2020],{"stretchy":2013},[902,80127,80128],{"encoding":904},"MP_K(a, b)",[3876,80130,80131,80135],{},[724,80132,80133,51224],{},[883,80134,4164],{},[120,80136,80137,80175],{},[123,80138,80139,26194,80158],{},[883,80140,80142],{"className":80141},[886],[888,80143,80144],{"xmlns":890},[892,80145,80146,80156],{},[895,80147,80148,80150],{},[898,80149,2826],{},[2281,80151,80152,80154],{},[898,80153,3946],{},[898,80155,9801],{},[902,80157,10050],{"encoding":904},[614,80159,80160,80161,80174],{},"„o kolik vzroste ",[883,80162,80164],{"className":80163},[886],[888,80165,80166],{"xmlns":890},[892,80167,80168,80172],{},[895,80169,80170],{},[898,80171,2797],{},[902,80173,2797],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,80176,80177,26194,80196],{},[883,80178,80180],{"className":80179},[886],[888,80181,80182],{"xmlns":890},[892,80183,80184,80194],{},[895,80185,80186,80188],{},[898,80187,2826],{},[2281,80189,80190,80192],{},[898,80191,3946],{},[898,80193,9806],{},[902,80195,10095],{"encoding":904},[614,80197,80160,80198,80211],{},[883,80199,80201],{"className":80200},[886],[888,80202,80203],{"xmlns":890},[892,80204,80205,80209],{},[895,80206,80207],{},[898,80208,2797],{},[902,80210,2797],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,80213,80214,80217,80218,80233,80234,2713],{},[38,80215,80216],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,80219,80221],{"className":80220},[886],[888,80222,80223],{"xmlns":890},[892,80224,80225,80231],{},[895,80226,80227,80229],{},[898,80228,2203],{},[898,80230,9801],{},[902,80232,75361],{"encoding":904}," a kapitálu o ",[883,80235,80237],{"className":80236},[886],[888,80238,80239],{"xmlns":890},[892,80240,80241,80247],{},[895,80242,80243,80245],{},[898,80244,2203],{},[898,80246,9806],{},[902,80248,80249],{"encoding":904},"dK",[883,80251,80253],{"className":80252},[886],[888,80254,80255],{"xmlns":890,"display":28071},[892,80256,80257,80350],{},[20760,80258,80259],{"width":28076},[20765,80260,80261,80263,80343,80345],{},[20768,80262],{"width":28081},[20768,80264,80265],{},[895,80266,80267,80269,80271,80273,80275,80277,80279,80287,80289,80291,80293,80295,80303,80305,80307,80309,80311,80313,80319,80321,80323,80325,80327,80329,80335,80337,80339,80341],{},[898,80268,2897],{"mathvariant":2385},[898,80270,2797],{},[2005,80272,2739],{},[898,80274,2203],{},[898,80276,2797],{},[2005,80278,2007],{},[9172,80280,80281,80283,80285],{},[898,80282,2797],{},[898,80284,9801],{},[2005,80286,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,80288,2995],{},[898,80290,2203],{},[898,80292,9801],{},[2005,80294,2104],{},[9172,80296,80297,80299,80301],{},[898,80298,2797],{},[898,80300,9806],{},[2005,80302,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2297,80304,2995],{},[898,80306,2203],{},[898,80308,9806],{},[2005,80310,2007],{},[898,80312,2826],{},[2281,80314,80315,80317],{},[898,80316,3946],{},[898,80318,9801],{},[2297,80320,2995],{},[898,80322,2203],{},[898,80324,9801],{},[2005,80326,2104],{},[898,80328,2826],{},[2281,80330,80331,80333],{},[898,80332,3946],{},[898,80334,9806],{},[2297,80336,2995],{},[898,80338,2203],{},[898,80340,9806],{},[898,80342,1644],{"mathvariant":2385},[20768,80344],{"width":28081},[20768,80346,80347],{},[2297,80348,80349],{},"(5.11)",[902,80351,80352],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,80354,80355,80356,1644],{},"Skutečná změna: ",[883,80357,80359],{"className":80358},[886],[888,80360,80361],{"xmlns":890},[892,80362,80363,80409],{},[895,80364,80365,80367,80369,80371,80373,80375,80377,80379,80381,80383,80385,80387,80389,80391,80393,80395,80397,80399,80401,80403,80405,80407],{},[898,80366,2897],{"mathvariant":2385},[898,80368,2797],{},[2005,80370,2007],{},[898,80372,2797],{},[2005,80374,2014],{"stretchy":2013},[898,80376,9801],{},[2005,80378,2104],{},[898,80380,2203],{},[898,80382,9801],{},[2005,80384,2295],{"separator":2294},[898,80386,9806],{},[2005,80388,2104],{},[898,80390,2203],{},[898,80392,9806],{},[2005,80394,2020],{"stretchy":2013},[2005,80396,2234],{},[898,80398,2797],{},[2005,80400,2014],{"stretchy":2013},[898,80402,9801],{},[2005,80404,2295],{"separator":2294},[898,80406,9806],{},[2005,80408,2020],{"stretchy":2013},[902,80410,80411],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,80413,80414,80416,80417,80435,80436,80449,80450,80469,80470,80502,80503,80535,80536,1644],{},[38,80415,75525],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,80418,80420],{"className":80419},[886],[888,80421,80422],{"xmlns":890},[892,80423,80424,80432],{},[895,80425,80426],{},[2281,80427,80428,80430],{},[898,80429,9806],{},[2138,80431,2336],{},[902,80433,80434],{"encoding":904},"K_0"," se od jistého ",[883,80437,80439],{"className":80438},[886],[888,80440,80441],{"xmlns":890},[892,80442,80443,80447],{},[895,80444,80445],{},[898,80446,9801],{},[902,80448,9801],{"encoding":904}," stane ",[883,80451,80453],{"className":80452},[886],[888,80454,80455],{"xmlns":890},[892,80456,80457,80467],{},[895,80458,80459,80461],{},[898,80460,2826],{},[2281,80462,80463,80465],{},[898,80464,3946],{},[898,80466,9801],{},[902,80468,10050],{"encoding":904}," klesající (",[883,80471,80473],{"className":80472},[886],[888,80474,80475],{"xmlns":890},[892,80476,80477,80499],{},[895,80478,80479,80495,80497],{},[9172,80480,80481,80483,80489],{},[898,80482,2797],{},[895,80484,80485,80487],{},[898,80486,9801],{},[898,80488,9801],{},[895,80490,80491,80493],{},[2005,80492,2387],{"mathvariant":2385},[2005,80494,2387],{"mathvariant":2385},[2005,80496,3455],{},[2138,80498,2336],{},[902,80500,80501],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,80504,80506],{"className":80505},[886],[888,80507,80508],{"xmlns":890},[892,80509,80510,80532],{},[895,80511,80512,80528,80530],{},[9172,80513,80514,80516,80522],{},[898,80515,2797],{},[895,80517,80518,80520],{},[898,80519,9806],{},[898,80521,9806],{},[895,80523,80524,80526],{},[2005,80525,2387],{"mathvariant":2385},[2005,80527,2387],{"mathvariant":2385},[2005,80529,3455],{},[2138,80531,2336],{},[902,80533,80534],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,80537,80539],{"className":80538},[886],[888,80540,80541],{"xmlns":890},[892,80542,80543,80551],{},[895,80544,80545],{},[2281,80546,80547,80549],{},[898,80548,9801],{},[2138,80550,2336],{},[902,80552,75563],{"encoding":904},[115,80554,80556],{"id":80555},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,80558,80559,80562,80563,80586,80587,29949],{},[38,80560,80561],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,80564,80566],{"className":80565},[886],[888,80567,80568],{"xmlns":890},[892,80569,80570,80584],{},[895,80571,80572,80574,80576,80578,80580,80582],{},[898,80573,2797],{},[2005,80575,2014],{"stretchy":2013},[898,80577,9801],{},[2005,80579,2295],{"separator":2294},[898,80581,9806],{},[2005,80583,2020],{"stretchy":2013},[902,80585,10002],{"encoding":904}," stupně ",[883,80588,80590],{"className":80589},[886],[888,80591,80592],{"xmlns":890},[892,80593,80594,80598],{},[895,80595,80596],{},[898,80597,36865],{},[902,80599,36865],{"encoding":904},[883,80601,80603],{"className":80602},[886],[888,80604,80605],{"xmlns":890,"display":28071},[892,80606,80607,80670],{},[20760,80608,80609],{"width":28076},[20765,80610,80611,80613,80663,80665],{},[20768,80612],{"width":28081},[20768,80614,80615],{},[895,80616,80617,80619,80621,80629,80631,80633,80635,80643,80645,80647,80649,80651,80653,80655,80657,80659,80661],{},[898,80618,9801],{},[2297,80620,2995],{},[9172,80622,80623,80625,80627],{},[898,80624,2797],{},[898,80626,9801],{},[2005,80628,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,80630,2104],{},[898,80632,9806],{},[2297,80634,2995],{},[9172,80636,80637,80639,80641],{},[898,80638,2797],{},[898,80640,9806],{},[2005,80642,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,80644,2007],{},[898,80646,36865],{},[2297,80648,2995],{},[898,80650,2797],{},[2005,80652,2014],{"stretchy":2013},[898,80654,9801],{},[2005,80656,2295],{"separator":2294},[898,80658,9806],{},[2005,80660,2020],{"stretchy":2013},[898,80662,1644],{"mathvariant":2385},[20768,80664],{"width":28081},[20768,80666,80667],{},[2297,80668,80669],{},"(5.12)",[902,80671,80672],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,80674,80675,80696],{},[38,80676,80677,80678],{},"Speciální případ ",[883,80679,80681],{"className":80680},[886],[888,80682,80683],{"xmlns":890},[892,80684,80685,80693],{},[895,80686,80687,80689,80691],{},[898,80688,36865],{},[2005,80690,2007],{},[2138,80692,2287],{},[902,80694,80695],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,80698,80700],{"className":80699},[886],[888,80701,80702],{"xmlns":890,"display":28071},[892,80703,80704,80748],{},[895,80705,80706,80708,80710,80712,80718,80720,80722,80724,80726,80732,80734,80736,80738,80740,80742,80744,80746],{},[898,80707,9801],{},[2005,80709,3185],{},[898,80711,2826],{},[2281,80713,80714,80716],{},[898,80715,3946],{},[898,80717,9801],{},[2005,80719,2104],{},[898,80721,9806],{},[2005,80723,3185],{},[898,80725,2826],{},[2281,80727,80728,80730],{},[898,80729,3946],{},[898,80731,9806],{},[2005,80733,2007],{},[898,80735,2797],{},[2005,80737,2014],{"stretchy":2013},[898,80739,9801],{},[2005,80741,2295],{"separator":2294},[898,80743,9806],{},[2005,80745,2020],{"stretchy":2013},[898,80747,1644],{"mathvariant":2385},[902,80749,80750],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,80752,80753,80754,80757],{},"Slovně — ",[38,80755,80756],{},"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).",[115,80759,9784],{"id":74899},[724,80761,80762,10030,80764,80767,80768,80790,80791,2713],{},[38,80763,9784],{},[614,80765,80766],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,80769,80771],{"className":80770},[886],[888,80772,80773],{"xmlns":890},[892,80774,80775,80787],{},[895,80776,80777,80779,80781,80783,80785],{},[2005,80778,2495],{"stretchy":2013},[898,80780,9801],{},[2005,80782,2295],{"separator":2294},[898,80784,9806],{},[2005,80786,2510],{"stretchy":2013},[902,80788,80789],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,80792,80794],{"className":80793},[886],[888,80795,80796],{"xmlns":890},[892,80797,80798,80803],{},[895,80799,80800],{},[898,80801,80802],{},"q",[902,80804,80802],{"encoding":904},[883,80806,80808],{"className":80807},[886],[888,80809,80810],{"xmlns":890,"display":28071},[892,80811,80812,80847],{},[20760,80813,80814],{"width":28076},[20765,80815,80816,80818,80840,80842],{},[20768,80817],{"width":28081},[20768,80819,80820],{},[895,80821,80822,80824,80826,80828,80830,80832,80834,80836,80838],{},[898,80823,2797],{},[2005,80825,2014],{"stretchy":2013},[898,80827,9801],{},[2005,80829,2295],{"separator":2294},[898,80831,9806],{},[2005,80833,2020],{"stretchy":2013},[2005,80835,2007],{},[898,80837,80802],{},[898,80839,1644],{"mathvariant":2385},[20768,80841],{"width":28081},[20768,80843,80844],{},[2297,80845,80846],{},"(5.13)",[902,80848,80849],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,80851,80852,80853,80856,80857,3927],{},"Jsou to ",[38,80854,80855],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,80858,80860],{"className":80859,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,80862,80863],{},[38,80864,80865],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,80867,80868,80873,80878,80883],{},[123,80869,80870,80872],{},[38,80871,12525],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,80874,80875,80877],{},[38,80876,37669],{}," (úloha 5.14);",[123,80879,80880,8431],{},[38,80881,80882],{},"neprotínají se",[123,80884,80885,80886,4364,80899,1644],{},"s rostoucím ",[883,80887,80889],{"className":80888},[886],[888,80890,80891],{"xmlns":890},[892,80892,80893,80897],{},[895,80894,80895],{},[898,80896,80802],{},[902,80898,80802],{"encoding":904},[38,80900,80901],{},"vzdalují od počátku",[724,80903,80904],{},[614,80905,80906,80907,80929,80930,1644],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,80908,80910],{"className":80909},[886],[888,80911,80912],{"xmlns":890},[892,80913,80914,80926],{},[895,80915,80916,80918,80920,80922,80924],{},[2005,80917,2014],{"stretchy":2013},[898,80919,9801],{},[2005,80921,2295],{"separator":2294},[898,80923,9806],{},[2005,80925,2020],{"stretchy":2013},[902,80927,80928],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,80931,80933],{"className":80932},[886],[888,80934,80935],{"xmlns":890},[892,80936,80937,80961],{},[895,80938,80939,80945,80947,80953,80955],{},[2281,80940,80941,80943],{},[898,80942,80802],{},[2138,80944,2287],{},[2005,80946,3455],{},[2281,80948,80949,80951],{},[898,80950,80802],{},[2138,80952,2336],{},[2005,80954,3455],{},[2281,80956,80957,80959],{},[898,80958,80802],{},[2138,80960,2140],{},[902,80962,80963],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,80965,80967,80968,2020],{"id":80966},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,80969,80971],{"className":80970},[886],[888,80972,80973],{"xmlns":890},[892,80974,80975,80985],{},[895,80976,80977,80979,80981,80983],{},[898,80978,2826],{},[898,80980,4003],{},[898,80982,2783],{},[898,80984,8679],{},[902,80986,10603],{"encoding":904},[724,80988,80989,10030,80992,80995],{},[38,80990,80991],{},"Mezní míra technické substituce",[614,80993,80994],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,80997,80999],{"className":80998},[886],[888,81000,81001],{"xmlns":890,"display":28071},[892,81002,81003,81094],{},[20760,81004,81005],{"width":28076},[20765,81006,81007,81009,81087,81089],{},[20768,81008],{"width":28081},[20768,81010,81011],{},[895,81012,81013,81015,81017,81019,81021,81023,81025,81027,81029,81031,81033,81035,81037,81039,81041,81043,81065,81067,81085],{},[898,81014,2826],{},[898,81016,4003],{},[898,81018,2783],{},[898,81020,8679],{},[2005,81022,2007],{},[898,81024,2826],{},[898,81026,4003],{},[898,81028,2783],{},[898,81030,8679],{},[2005,81032,2014],{"stretchy":2013},[898,81034,9801],{},[2005,81036,2295],{"separator":2294},[898,81038,9806],{},[2005,81040,2020],{"stretchy":2013},[2005,81042,2007],{},[2338,81044,81045,81055],{},[895,81046,81047,81049],{},[898,81048,2826],{},[2281,81050,81051,81053],{},[898,81052,3946],{},[898,81054,9801],{},[895,81056,81057,81059],{},[898,81058,2826],{},[2281,81060,81061,81063],{},[898,81062,3946],{},[898,81064,9806],{},[2005,81066,2007],{},[2338,81068,81069,81077],{},[9172,81070,81071,81073,81075],{},[898,81072,2797],{},[898,81074,9801],{},[2005,81076,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,81078,81079,81081,81083],{},[898,81080,2797],{},[898,81082,9806],{},[2005,81084,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[898,81086,1644],{"mathvariant":2385},[20768,81088],{"width":28081},[20768,81090,81091],{},[2297,81092,81093],{},"(5.14)",[902,81095,81096],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,81098,81099,2212,81101,81131,81132,81163],{},[38,81100,9222],{},[883,81102,81104],{"className":81103},[886],[888,81105,81106],{"xmlns":890},[892,81107,81108,81128],{},[895,81109,81110,81112,81114,81116,81118,81120,81122,81124,81126],{},[898,81111,2826],{},[898,81113,4003],{},[898,81115,2783],{},[898,81117,8679],{},[2005,81119,2014],{"stretchy":2013},[898,81121,9801],{},[2005,81123,2295],{"separator":2294},[898,81125,9806],{},[2005,81127,2020],{"stretchy":2013},[902,81129,81130],{"encoding":904},"MRTS(L, K)"," udává, ",[38,81133,81134,81135,81148,81149,81162],{},"o kolik se musí přibližně změnit kapitál ",[883,81136,81138],{"className":81137},[886],[888,81139,81140],{"xmlns":890},[892,81141,81142,81146],{},[895,81143,81144],{},[898,81145,9806],{},[902,81147,9806],{"encoding":904},", jestliže se práce ",[883,81150,81152],{"className":81151},[886],[888,81153,81154],{"xmlns":890},[892,81155,81156,81160],{},[895,81157,81158],{},[898,81159,9801],{},[902,81161,9801],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[3876,81165,81166],{},[724,81167,81168,18030,81170,81189,81190,81227,81228,81231,81232,81236],{},[883,81169,4164],{},[883,81171,81173],{"className":81172},[886],[888,81174,81175],{"xmlns":890},[892,81176,81177,81187],{},[895,81178,81179,81181,81183,81185],{},[898,81180,2826],{},[898,81182,4003],{},[898,81184,2783],{},[898,81186,8679],{},[902,81188,10603],{"encoding":904}," říká: ",[614,81191,81192,81193,81212,81213,81226],{},"„jednu jednotku práce musím nahradit přibližně ",[883,81194,81196],{"className":81195},[886],[888,81197,81198],{"xmlns":890},[892,81199,81200,81210],{},[895,81201,81202,81204,81206,81208],{},[898,81203,2826],{},[898,81205,4003],{},[898,81207,2783],{},[898,81209,8679],{},[902,81211,10603],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,81214,81216],{"className":81215},[886],[888,81217,81218],{"xmlns":890},[892,81219,81220,81224],{},[895,81221,81222],{},[898,81223,2797],{},[902,81225,2797],{"encoding":904}," zůstala stejná.\""," Je to ",[38,81229,81230],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,81233,81235],{"className":81234,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,81238,81239],{},[2568,81240],{"alt":81241,"className":81242,"src":81243},"imek-izokvanty-mrts",[210,2572],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,81245,81246,81249,81250,8108,81280,81302,81303,3159],{},[38,81247,81248],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,81251,81253],{"className":81252},[886],[888,81254,81255],{"xmlns":890},[892,81256,81257,81277],{},[895,81258,81259,81261,81267,81269,81275],{},[2005,81260,2495],{"stretchy":2013},[2281,81262,81263,81265],{},[898,81264,9801],{},[2138,81266,2336],{},[2005,81268,2295],{"separator":2294},[2281,81270,81271,81273],{},[898,81272,9806],{},[2138,81274,2336],{},[2005,81276,2510],{"stretchy":2013},[902,81278,81279],{"encoding":904},"[L_0, K_0]",[883,81281,81283],{"className":81282},[886],[888,81284,81285],{"xmlns":890},[892,81286,81287,81299],{},[895,81288,81289,81291,81293,81295,81297],{},[2005,81290,2234],{},[898,81292,2826],{},[898,81294,4003],{},[898,81296,2783],{},[898,81298,8679],{},[902,81300,81301],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,81304,81306],{"className":81305},[886],[888,81307,81308],{"xmlns":890},[892,81309,81310,81332],{},[895,81311,81312,81314,81316,81318,81320,81322,81324,81326],{},[898,81313,2797],{},[2005,81315,2014],{"stretchy":2013},[898,81317,9801],{},[2005,81319,2295],{"separator":2294},[898,81321,9806],{},[2005,81323,2020],{"stretchy":2013},[2005,81325,2007],{},[2281,81327,81328,81330],{},[898,81329,80802],{},[2138,81331,2336],{},[902,81333,81334],{"encoding":904},"Q(L,K) = q_0",[883,81336,81338],{"className":81337},[886],[888,81339,81340],{"xmlns":890,"display":28071},[892,81341,81342,81394],{},[895,81343,81344,81358,81360,81362,81380,81382,81384,81386,81388,81390,81392],{},[2338,81345,81346,81352],{},[895,81347,81348,81350],{},[898,81349,2203],{},[898,81351,9806],{},[895,81353,81354,81356],{},[898,81355,2203],{},[898,81357,9801],{},[2005,81359,2007],{},[2005,81361,2234],{},[2338,81363,81364,81372],{},[9172,81365,81366,81368,81370],{},[898,81367,2797],{},[898,81369,9801],{},[2005,81371,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,81373,81374,81376,81378],{},[898,81375,2797],{},[898,81377,9806],{},[2005,81379,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,81381,2007],{},[2005,81383,2234],{},[898,81385,2826],{},[898,81387,4003],{},[898,81389,2783],{},[898,81391,8679],{},[898,81393,1644],{"mathvariant":2385},[902,81395,81396],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,81398,81399,81400,81415,81416,81432],{},"Změní-li se práce o ",[883,81401,81403],{"className":81402},[886],[888,81404,81405],{"xmlns":890},[892,81406,81407,81413],{},[895,81408,81409,81411],{},[898,81410,2203],{},[898,81412,9801],{},[902,81414,75361],{"encoding":904},", lze pro odhad změny kapitálu ",[883,81417,81419],{"className":81418},[886],[888,81420,81421],{"xmlns":890},[892,81422,81423,81429],{},[895,81424,81425,81427],{},[898,81426,2897],{"mathvariant":2385},[898,81428,9806],{},[902,81430,81431],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,81434,81436],{"className":81435},[886],[888,81437,81438],{"xmlns":890,"display":28071},[892,81439,81440,81487],{},[20760,81441,81442],{"width":28076},[20765,81443,81444,81446,81480,81482],{},[20768,81445],{"width":28081},[20768,81447,81448],{},[895,81449,81450,81452,81454,81456,81458,81460,81462,81464,81466,81468,81470,81472,81474,81476,81478],{},[898,81451,2897],{"mathvariant":2385},[898,81453,9806],{},[2005,81455,2739],{},[898,81457,2203],{},[898,81459,9806],{},[2005,81461,2007],{},[2005,81463,2234],{},[898,81465,2826],{},[898,81467,4003],{},[898,81469,2783],{},[898,81471,8679],{},[2297,81473,2995],{},[898,81475,2203],{},[898,81477,9801],{},[2005,81479,2295],{"separator":2294},[20768,81481],{"width":28081},[20768,81483,81484],{},[2297,81485,81486],{},"(5.15)",[902,81488,81489],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,81491,81493],{"className":81492},[886],[888,81494,81495],{"xmlns":890,"display":28071},[892,81496,81497,81546],{},[20760,81498,81499],{"width":28076},[20765,81500,81501,81503,81539,81541],{},[20768,81502],{"width":28081},[20768,81504,81505],{},[895,81506,81507,81509,81511,81513,81531,81533,81535,81537],{},[898,81508,2203],{},[898,81510,9801],{},[2005,81512,2007],{},[2338,81514,81515,81521],{},[895,81516,81517,81519],{},[2005,81518,2234],{},[2138,81520,2287],{},[895,81522,81523,81525,81527,81529],{},[898,81524,2826],{},[898,81526,4003],{},[898,81528,2783],{},[898,81530,8679],{},[2297,81532,2995],{},[898,81534,2203],{},[898,81536,9806],{},[898,81538,1644],{"mathvariant":2385},[20768,81540],{"width":28081},[20768,81542,81543],{},[2297,81544,81545],{},"(5.16)",[902,81547,81548],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[3876,81550,81551,81575],{},[724,81552,81553,81555,81556],{},[883,81554,4578],{}," Postup — jak spočítat ",[883,81557,81559],{"className":81558},[886],[888,81560,81561],{"xmlns":890},[892,81562,81563,81573],{},[895,81564,81565,81567,81569,81571],{},[898,81566,2826],{},[898,81568,4003],{},[898,81570,2783],{},[898,81572,8679],{},[902,81574,10603],{"encoding":904},[152,81576,81577,81618,81661,81693],{},[123,81578,81579,81580,3894,81599,1644],{},"Vypočtěte parciální derivace ",[883,81581,81583],{"className":81582},[886],[888,81584,81585],{"xmlns":890},[892,81586,81587,81597],{},[895,81588,81589],{},[9172,81590,81591,81593,81595],{},[898,81592,2797],{},[898,81594,9801],{},[2005,81596,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,81598,10026],{"encoding":904},[883,81600,81602],{"className":81601},[886],[888,81603,81604],{"xmlns":890},[892,81605,81606,81616],{},[895,81607,81608],{},[9172,81609,81610,81612,81614],{},[898,81611,2797],{},[898,81613,9806],{},[2005,81615,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,81617,10072],{"encoding":904},[123,81619,65846,81620,81660],{},[883,81621,81623],{"className":81622},[886],[888,81624,81625],{"xmlns":890},[892,81626,81627,81657],{},[895,81628,81629,81631,81633,81635,81637,81639,81647,81649],{},[898,81630,2826],{},[898,81632,4003],{},[898,81634,2783],{},[898,81636,8679],{},[2005,81638,2007],{},[9172,81640,81641,81643,81645],{},[898,81642,2797],{},[898,81644,9801],{},[2005,81646,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[898,81648,4680],{"mathvariant":2385},[9172,81650,81651,81653,81655],{},[898,81652,2797],{},[898,81654,9806],{},[2005,81656,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,81658,81659],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,81662,81663,81664,1644],{},"Případně dosaďte konkrétní ",[883,81665,81667],{"className":81666},[886],[888,81668,81669],{"xmlns":890},[892,81670,81671,81691],{},[895,81672,81673,81675,81681,81683,81689],{},[2005,81674,2495],{"stretchy":2013},[2281,81676,81677,81679],{},[898,81678,9801],{},[2138,81680,2336],{},[2005,81682,2295],{"separator":2294},[2281,81684,81685,81687],{},[898,81686,9806],{},[2138,81688,2336],{},[2005,81690,2510],{"stretchy":2013},[902,81692,81279],{"encoding":904},[123,81694,81695,81696,81730,81731,81733],{},"Pro odhad substituce použijte ",[883,81697,81699],{"className":81698},[886],[888,81700,81701],{"xmlns":890},[892,81702,81703,81727],{},[895,81704,81705,81707,81709,81711,81713,81715,81717,81719,81721,81723,81725],{},[898,81706,2897],{"mathvariant":2385},[898,81708,9806],{},[2005,81710,2739],{},[2005,81712,2234],{},[898,81714,2826],{},[898,81716,4003],{},[898,81718,2783],{},[898,81720,8679],{},[2005,81722,3185],{},[898,81724,2897],{"mathvariant":2385},[898,81726,9801],{},[902,81728,81729],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,81732,52611],{}," — substituce, ne doplnění).",[724,81735,81736],{},[614,81737,81738,81739,81771,81772,2633,81785,15798,81814,81829],{},"Obrázek 5.7 — izokvanta ",[883,81740,81742],{"className":81741},[886],[888,81743,81744],{"xmlns":890},[892,81745,81746,81768],{},[895,81747,81748,81754,81756,81758,81760,81762,81764,81766],{},[2281,81749,81750,81752],{},[898,81751,80802],{},[2138,81753,2336],{},[2005,81755,2007],{},[898,81757,2797],{},[2005,81759,2014],{"stretchy":2013},[898,81761,9801],{},[2005,81763,2295],{"separator":2294},[898,81765,9806],{},[2005,81767,2020],{"stretchy":2013},[902,81769,81770],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,81773,81775],{"className":81774},[886],[888,81776,81777],{"xmlns":890},[892,81778,81779,81783],{},[895,81780,81781],{},[898,81782,18861],{},[902,81784,18861],{"encoding":904},[883,81786,81788],{"className":81787},[886],[888,81789,81790],{"xmlns":890},[892,81791,81792,81812],{},[895,81793,81794,81796,81802,81804,81810],{},[2005,81795,2495],{"stretchy":2013},[2281,81797,81798,81800],{},[898,81799,9801],{},[2138,81801,2336],{},[2005,81803,2295],{"separator":2294},[2281,81805,81806,81808],{},[898,81807,9806],{},[2138,81809,2336],{},[2005,81811,2510],{"stretchy":2013},[902,81813,81279],{"encoding":904},[883,81815,81817],{"className":81816},[886],[888,81818,81819],{"xmlns":890},[892,81820,81821,81827],{},[895,81822,81823,81825],{},[898,81824,2897],{"mathvariant":2385},[898,81826,9806],{},[902,81828,81431],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,81831,81833],{"id":81832},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,81835,81837],{"id":81836},"příklad-54","Příklad 5.4",[724,81839,76678,81840,1343,81882,1343,81899,1644],{},[883,81841,81843],{"className":81842},[886],[888,81844,81845],{"xmlns":890},[892,81846,81847,81879],{},[895,81848,81849,81851,81853,81855,81867],{},[898,81850,2797],{},[2005,81852,2007],{},[2138,81854,36249],{},[2133,81856,81857,81859],{},[898,81858,9801],{},[895,81860,81861,81863,81865],{},[2138,81862,2287],{},[898,81864,4680],{"mathvariant":2385},[2138,81866,2140],{},[2133,81868,81869,81871],{},[898,81870,9806],{},[895,81872,81873,81875,81877],{},[2138,81874,2287],{},[898,81876,4680],{"mathvariant":2385},[2138,81878,2182],{},[902,81880,81881],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,81883,81885],{"className":81884},[886],[888,81886,81887],{"xmlns":890},[892,81888,81889,81897],{},[895,81890,81891,81893,81895],{},[898,81892,9801],{},[2005,81894,2007],{},[2138,81896,9041],{},[902,81898,77052],{"encoding":904},[883,81900,81902],{"className":81901},[886],[888,81903,81904],{"xmlns":890},[892,81905,81906,81914],{},[895,81907,81908,81910,81912],{},[898,81909,9806],{},[2005,81911,2007],{},[2138,81913,3098],{},[902,81915,81916],{"encoding":904},"K = 100",[724,81918,81919],{},[38,81920,81921],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,81923,81925],{"className":81924},[886],[888,81926,81927],{"xmlns":890,"display":28071},[892,81928,81929,82043],{},[895,81930,81931,81933,81939,81941,81949,81951,81959,81973,81985,81987,81989,81991,81997,81999,82001,82003,82005,82007,82009,82017,82019,82029,82031,82038,82040],{},[898,81932,2826],{},[2281,81934,81935,81937],{},[898,81936,3946],{},[898,81938,9801],{},[2005,81940,2007],{},[9172,81942,81943,81945,81947],{},[898,81944,2797],{},[898,81946,9801],{},[2005,81948,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,81950,2007],{},[2334,81952,81953],{"scriptlevel":2336,"displaystyle":2013},[2338,81954,81955,81957],{},[2138,81956,36249],{},[2138,81958,2140],{},[2133,81960,81961,81963],{},[898,81962,9801],{},[895,81964,81965,81967,81969,81971],{},[2005,81966,2234],{},[2138,81968,2287],{},[898,81970,4680],{"mathvariant":2385},[2138,81972,2140],{},[2133,81974,81975,81977],{},[898,81976,9806],{},[895,81978,81979,81981,81983],{},[2138,81980,2287],{},[898,81982,4680],{"mathvariant":2385},[2138,81984,2182],{},[2005,81986,2295],{"separator":2294},[5884,81988],{"width":15290},[898,81990,2826],{},[2281,81992,81993,81995],{},[898,81994,3946],{},[898,81996,9801],{},[2005,81998,2014],{"stretchy":2013},[2138,82000,9041],{},[2005,82002,2295],{"separator":2294},[2138,82004,3098],{},[2005,82006,2020],{"stretchy":2013},[2005,82008,2007],{},[2334,82010,82011],{"scriptlevel":2336,"displaystyle":2013},[2338,82012,82013,82015],{},[2138,82014,36249],{},[2138,82016,2140],{},[2005,82018,3185],{},[2334,82020,82021],{"scriptlevel":2336,"displaystyle":2013},[2338,82022,82023,82025],{},[2138,82024,2287],{},[8123,82026,82027],{},[2138,82028,9041],{},[2005,82030,3185],{},[82032,82033,82034,82036],"mroot",{},[2138,82035,3098],{},[2138,82037,2182],{},[2005,82039,2739],{},[2138,82041,82042],{},"7,153.",[902,82044,82045],{"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.",[724,82047,82048,82049,44165,82071,10238,82088,82109,82110,82131],{},"Přibližná změna při ",[883,82050,82052],{"className":82051},[886],[888,82053,82054],{"xmlns":890},[892,82055,82056,82068],{},[895,82057,82058,82060,82062,82064,82066],{},[898,82059,9801],{},[2005,82061,2713],{},[2138,82063,9041],{},[2005,82065,3131],{},[2138,82067,38351],{},[902,82069,82070],{"encoding":904},"L: 20 \\to 21",[883,82072,82074],{"className":82073},[886],[888,82075,82076],{"xmlns":890},[892,82077,82078,82086],{},[895,82079,82080,82082,82084],{},[898,82081,9806],{},[2005,82083,2007],{},[2138,82085,3098],{},[902,82087,81916],{"encoding":904},[883,82089,82091],{"className":82090},[886],[888,82092,82093],{"xmlns":890},[892,82094,82095,82106],{},[895,82096,82097,82099,82101,82103],{},[898,82098,2897],{"mathvariant":2385},[898,82100,2797],{},[2005,82102,2739],{},[2138,82104,82105],{},"7,153",[902,82107,82108],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,82111,82113],{"className":82112},[886],[888,82114,82115],{"xmlns":890},[892,82116,82117,82128],{},[895,82118,82119,82121,82123,82125],{},[898,82120,2897],{"mathvariant":2385},[898,82122,2797],{},[2005,82124,2739],{},[2138,82126,82127],{},"26,888",[902,82129,82130],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,82133,82134,82137],{},[38,82135,82136],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,82139,82141],{"className":82140},[886],[888,82142,82143],{"xmlns":890,"display":28071},[892,82144,82145,82245],{},[895,82146,82147,82149,82155,82157,82165,82167,82169,82181,82195,82197,82199,82201,82207,82209,82211,82213,82215,82217,82219,82221,82225,82227,82240,82242],{},[898,82148,2826],{},[2281,82150,82151,82153],{},[898,82152,3946],{},[898,82154,9806],{},[2005,82156,2007],{},[9172,82158,82159,82161,82163],{},[898,82160,2797],{},[898,82162,9806],{},[2005,82164,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,82166,2007],{},[2138,82168,2237],{},[2133,82170,82171,82173],{},[898,82172,9801],{},[895,82174,82175,82177,82179],{},[2138,82176,2287],{},[898,82178,4680],{"mathvariant":2385},[2138,82180,2140],{},[2133,82182,82183,82185],{},[898,82184,9806],{},[895,82186,82187,82189,82191,82193],{},[2005,82188,2234],{},[2138,82190,2140],{},[898,82192,4680],{"mathvariant":2385},[2138,82194,2182],{},[2005,82196,2295],{"separator":2294},[5884,82198],{"width":15290},[898,82200,2826],{},[2281,82202,82203,82205],{},[898,82204,3946],{},[898,82206,9806],{},[2005,82208,2014],{"stretchy":2013},[2138,82210,9041],{},[2005,82212,2295],{"separator":2294},[2138,82214,3098],{},[2005,82216,2020],{"stretchy":2013},[2005,82218,2007],{},[2138,82220,2237],{},[8123,82222,82223],{},[2138,82224,9041],{},[2005,82226,3185],{},[2334,82228,82229],{"scriptlevel":2336,"displaystyle":2013},[2338,82230,82231,82233],{},[2138,82232,2287],{},[82032,82234,82235,82238],{},[2138,82236,82237],{},"10000",[2138,82239,2182],{},[2005,82241,2739],{},[2138,82243,82244],{},"4,525.",[902,82246,82247],{"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.",[724,82249,82250,82251,2694,82268,3927],{},"Produkce poklesne přibližně o 4,525 (z ",[883,82252,82254],{"className":82253},[886],[888,82255,82256],{"xmlns":890},[892,82257,82258,82265],{},[895,82259,82260,82262],{},[2005,82261,2739],{},[2138,82263,82264],{},"905,126",[902,82266,82267],{"encoding":904},"\\approx 905{,}126",[883,82269,82271],{"className":82270},[886],[888,82272,82273],{"xmlns":890},[892,82274,82275,82282],{},[895,82276,82277,82279],{},[2005,82278,2739],{},[2138,82280,82281],{},"900,601",[902,82283,82284],{"encoding":904},"\\approx 900{,}601",[724,82286,82287,3138,82334,1343,82356,3927],{},[38,82288,82289,82290,3894,82312],{},"(c) Změna ",[883,82291,82293],{"className":82292},[886],[888,82294,82295],{"xmlns":890},[892,82296,82297,82309],{},[895,82298,82299,82301,82303,82305,82307],{},[898,82300,9801],{},[2005,82302,2713],{},[2138,82304,9041],{},[2005,82306,3131],{},[2138,82308,36249],{},[902,82310,82311],{"encoding":904},"L: 20 \\to 15",[883,82313,82315],{"className":82314},[886],[888,82316,82317],{"xmlns":890},[892,82318,82319,82331],{},[895,82320,82321,82323,82325,82327,82329],{},[898,82322,9806],{},[2005,82324,2713],{},[2138,82326,3098],{},[2005,82328,3131],{},[2138,82330,8809],{},[902,82332,82333],{"encoding":904},"K: 100 \\to 150",[883,82335,82337],{"className":82336},[886],[888,82338,82339],{"xmlns":890},[892,82340,82341,82353],{},[895,82342,82343,82345,82347,82349,82351],{},[898,82344,2203],{},[898,82346,9801],{},[2005,82348,2007],{},[2005,82350,2234],{},[2138,82352,2237],{},[902,82354,82355],{"encoding":904},"dL = -5",[883,82357,82359],{"className":82358},[886],[888,82360,82361],{"xmlns":890},[892,82362,82363,82373],{},[895,82364,82365,82367,82369,82371],{},[898,82366,2203],{},[898,82368,9806],{},[2005,82370,2007],{},[2138,82372,3128],{},[902,82374,82375],{"encoding":904},"dK = 50",[883,82377,82379],{"className":82378},[886],[888,82380,82381],{"xmlns":890,"display":28071},[892,82382,82383,82471],{},[895,82384,82385,82387,82389,82391,82393,82399,82401,82403,82405,82407,82409,82411,82413,82415,82417,82419,82421,82423,82429,82431,82433,82435,82437,82439,82441,82443,82445,82447,82449,82451,82453,82455,82457,82459,82462,82464,82466,82468],{},[898,82386,2203],{},[898,82388,2797],{},[2005,82390,2007],{},[898,82392,2826],{},[2281,82394,82395,82397],{},[898,82396,3946],{},[898,82398,9801],{},[2005,82400,2014],{"stretchy":2013},[2138,82402,9041],{},[2005,82404,2295],{"separator":2294},[2138,82406,3098],{},[2005,82408,2020],{"stretchy":2013},[2005,82410,3185],{},[2005,82412,2014],{"stretchy":2013},[2005,82414,2234],{},[2138,82416,2237],{},[2005,82418,2020],{"stretchy":2013},[2005,82420,2104],{},[898,82422,2826],{},[2281,82424,82425,82427],{},[898,82426,3946],{},[898,82428,9806],{},[2005,82430,2014],{"stretchy":2013},[2138,82432,9041],{},[2005,82434,2295],{"separator":2294},[2138,82436,3098],{},[2005,82438,2020],{"stretchy":2013},[2005,82440,3185],{},[2138,82442,3128],{},[2005,82444,2007],{},[2138,82446,82105],{},[2005,82448,3185],{},[2005,82450,2014],{"stretchy":2013},[2005,82452,2234],{},[2138,82454,2237],{},[2005,82456,2020],{"stretchy":2013},[2005,82458,2104],{},[2138,82460,82461],{},"4,525",[2005,82463,3185],{},[2138,82465,3128],{},[2005,82467,2739],{},[2138,82469,82470],{},"190,485.",[902,82472,82473],{"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.",[724,82475,82476],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,82478,82480],{"id":82479},"příklad-55","Příklad 5.5",[724,82482,82483,82484,82520,82521,1644],{},"Pro produkci ",[883,82485,82487],{"className":82486},[886],[888,82488,82489],{"xmlns":890},[892,82490,82491,82517],{},[895,82492,82493,82495,82497,82499,82501,82503,82505,82507,82513],{},[898,82494,2797],{},[2005,82496,2014],{"stretchy":2013},[898,82498,9801],{},[2005,82500,2295],{"separator":2294},[898,82502,9806],{},[2005,82504,2020],{"stretchy":2013},[2005,82506,2007],{},[82032,82508,82509,82511],{},[898,82510,9801],{},[2138,82512,2182],{},[8123,82514,82515],{},[898,82516,9806],{},[902,82518,82519],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,82522,82524],{"className":82523},[886],[888,82525,82526],{"xmlns":890},[892,82527,82528,82544],{},[895,82529,82530,82536,82540,82542],{},[82032,82531,82532,82534],{},[898,82533,9801],{},[2138,82535,2182],{},[8123,82537,82538],{},[898,82539,9806],{},[2005,82541,2007],{},[898,82543,80802],{},[902,82545,82546],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,82548,82549,82550,1644],{},"Umocněním na druhou: ",[883,82551,82553],{"className":82552},[886],[888,82554,82555],{"xmlns":890},[892,82556,82557,82581],{},[895,82558,82559,82561,82563,82569,82571],{},[898,82560,9806],{},[2005,82562,2007],{},[2133,82564,82565,82567],{},[898,82566,80802],{},[2138,82568,2140],{},[898,82570,4680],{"mathvariant":2385},[82032,82572,82573,82579],{},[2133,82574,82575,82577],{},[898,82576,9801],{},[2138,82578,2140],{},[2138,82580,2182],{},[902,82582,82583],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,82585,82586,82626,82666],{},[123,82587,82588],{},[883,82589,82591],{"className":82590},[886],[888,82592,82593],{"xmlns":890},[892,82594,82595,82623],{},[895,82596,82597,82599,82601,82603,82605,82607,82609,82611,82613],{},[898,82598,80802],{},[2005,82600,2007],{},[2138,82602,2287],{},[2005,82604,3996],{},[898,82606,9806],{},[2005,82608,2007],{},[2138,82610,2287],{},[898,82612,4680],{"mathvariant":2385},[82032,82614,82615,82621],{},[2133,82616,82617,82619],{},[898,82618,9801],{},[2138,82620,2140],{},[2138,82622,2182],{},[902,82624,82625],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,82627,82628],{},[883,82629,82631],{"className":82630},[886],[888,82632,82633],{"xmlns":890},[892,82634,82635,82663],{},[895,82636,82637,82639,82641,82643,82645,82647,82649,82651,82653],{},[898,82638,80802],{},[2005,82640,2007],{},[2138,82642,2140],{},[2005,82644,3996],{},[898,82646,9806],{},[2005,82648,2007],{},[2138,82650,2360],{},[898,82652,4680],{"mathvariant":2385},[82032,82654,82655,82661],{},[2133,82656,82657,82659],{},[898,82658,9801],{},[2138,82660,2140],{},[2138,82662,2182],{},[902,82664,82665],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,82667,82668],{},[883,82669,82671],{"className":82670},[886],[888,82672,82673],{"xmlns":890},[892,82674,82675,82703],{},[895,82676,82677,82679,82681,82683,82685,82687,82689,82691,82693],{},[898,82678,80802],{},[2005,82680,2007],{},[2138,82682,2182],{},[2005,82684,3996],{},[898,82686,9806],{},[2005,82688,2007],{},[2138,82690,4008],{},[898,82692,4680],{"mathvariant":2385},[82032,82694,82695,82701],{},[2133,82696,82697,82699],{},[898,82698,9801],{},[2138,82700,2140],{},[2138,82702,2182],{},[902,82704,82705],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,82707,82708],{},[614,82709,82710,82711,6479,82732,1644],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,82712,82714],{"className":82713},[886],[888,82715,82716],{"xmlns":890},[892,82717,82718,82730],{},[895,82719,82720,82722,82724,82726,82728],{},[2005,82721,2014],{"stretchy":2013},[898,82723,9801],{},[2005,82725,2295],{"separator":2294},[898,82727,9806],{},[2005,82729,2020],{"stretchy":2013},[902,82731,80928],{"encoding":904},[883,82733,82735],{"className":82734},[886],[888,82736,82737],{"xmlns":890},[892,82738,82739,82755],{},[895,82740,82741,82743,82745,82747,82749,82751,82753],{},[898,82742,80802],{},[2005,82744,2007],{},[2138,82746,2287],{},[2005,82748,2295],{"separator":2294},[2138,82750,2140],{},[2005,82752,2295],{"separator":2294},[2138,82754,2182],{},[902,82756,82757],{"encoding":904},"q = 1, 2, 3",[198,82759,82761],{"id":82760},"příklad-56","Příklad 5.6",[724,82763,76678,82764,1644],{},[883,82765,82767],{"className":82766},[886],[888,82768,82769],{"xmlns":890},[892,82770,82771,82787],{},[895,82772,82773,82775,82777,82779,82781,82783],{},[898,82774,2797],{},[2005,82776,2007],{},[2138,82778,2140],{},[898,82780,9801],{},[2005,82782,2104],{},[8123,82784,82785],{},[898,82786,9806],{},[902,82788,82789],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,82791,82793],{"className":82792},[886],[888,82794,82795],{"xmlns":890,"display":28071},[892,82796,82797,82839],{},[895,82798,82799,82801,82807,82809,82811,82813,82815,82817,82823,82825,82837],{},[898,82800,2826],{},[2281,82802,82803,82805],{},[898,82804,3946],{},[898,82806,9801],{},[2005,82808,2007],{},[2138,82810,2140],{},[2005,82812,2295],{"separator":2294},[5884,82814],{"width":5886},[898,82816,2826],{},[2281,82818,82819,82821],{},[898,82820,3946],{},[898,82822,9806],{},[2005,82824,2007],{},[2338,82826,82827,82829],{},[2138,82828,2287],{},[895,82830,82831,82833],{},[2138,82832,2140],{},[8123,82834,82835],{},[898,82836,9806],{},[898,82838,1644],{"mathvariant":2385},[902,82840,82841],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,82843,82845],{"className":82844},[886],[888,82846,82847],{"xmlns":890,"display":28071},[892,82848,82849,82913],{},[895,82850,82851,82853,82855,82857,82859,82861,82883,82885,82903,82905,82907,82911],{},[898,82852,2826],{},[898,82854,4003],{},[898,82856,2783],{},[898,82858,8679],{},[2005,82860,2007],{},[2338,82862,82863,82873],{},[895,82864,82865,82867],{},[898,82866,2826],{},[2281,82868,82869,82871],{},[898,82870,3946],{},[898,82872,9801],{},[895,82874,82875,82877],{},[898,82876,2826],{},[2281,82878,82879,82881],{},[898,82880,3946],{},[898,82882,9806],{},[2005,82884,2007],{},[2338,82886,82887,82889],{},[2138,82888,2140],{},[2334,82890,82891],{"scriptlevel":2336,"displaystyle":2013},[2338,82892,82893,82895],{},[2138,82894,2287],{},[895,82896,82897,82899],{},[2138,82898,2140],{},[8123,82900,82901],{},[898,82902,9806],{},[2005,82904,2007],{},[2138,82906,2360],{},[8123,82908,82909],{},[898,82910,9806],{},[898,82912,1644],{"mathvariant":2385},[902,82914,82915],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,82917,82918,82919,82962,82963,83002,83003,1644],{},"Například ",[883,82920,82922],{"className":82921},[886],[888,82923,82924],{"xmlns":890},[892,82925,82926,82959],{},[895,82927,82928,82930,82932,82934,82936,82938,82940,82942,82944,82946,82948,82950,82954,82956],{},[898,82929,2826],{},[898,82931,4003],{},[898,82933,2783],{},[898,82935,8679],{},[2005,82937,2014],{"stretchy":2013},[2138,82939,2360],{},[2005,82941,2295],{"separator":2294},[2138,82943,24206],{},[2005,82945,2020],{"stretchy":2013},[2005,82947,2007],{},[2138,82949,2360],{},[8123,82951,82952],{},[2138,82953,24206],{},[2005,82955,2739],{},[2138,82957,82958],{},"10,58",[902,82960,82961],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,82964,82966],{"className":82965},[886],[888,82967,82968],{"xmlns":890},[892,82969,82970,82999],{},[895,82971,82972,82974,82976,82978,82980,82982,82984,82986,82988,82990,82994,82996],{},[898,82973,2797],{},[2005,82975,2014],{"stretchy":2013},[2138,82977,2360],{},[2005,82979,2295],{"separator":2294},[2138,82981,24206],{},[2005,82983,2020],{"stretchy":2013},[2005,82985,2007],{},[2138,82987,5591],{},[2005,82989,2104],{},[8123,82991,82992],{},[2138,82993,24206],{},[2005,82995,2739],{},[2138,82997,82998],{},"10,646",[902,83000,83001],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,83004,83006],{"className":83005},[886],[888,83007,83008],{"xmlns":890},[892,83009,83010,83018],{},[895,83011,83012,83014],{},[2138,83013,2360],{},[8123,83015,83016],{},[2138,83017,24206],{},[902,83019,83020],{"encoding":904},"4\\sqrt{7}",[724,83022,83023,83024,83044],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,83025,83027],{"className":83026},[886],[888,83028,83029],{"xmlns":890},[892,83030,83031,83041],{},[895,83032,83033,83035,83037,83039],{},[898,83034,2203],{},[898,83036,9801],{},[2005,83038,2007],{},[2138,83040,2140],{},[902,83042,83043],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,83046,83048],{"className":83047},[886],[888,83049,83050],{"xmlns":890,"display":28071},[892,83051,83052,83101],{},[895,83053,83054,83056,83058,83060,83062,83064,83066,83068,83070,83072,83074,83076,83078,83080,83082,83084,83086,83088,83090,83094,83096,83098],{},[898,83055,2203],{},[898,83057,9806],{},[2005,83059,2007],{},[2005,83061,2234],{},[898,83063,2826],{},[898,83065,4003],{},[898,83067,2783],{},[898,83069,8679],{},[2005,83071,2014],{"stretchy":2013},[2138,83073,2360],{},[2005,83075,2295],{"separator":2294},[2138,83077,24206],{},[2005,83079,2020],{"stretchy":2013},[2005,83081,3185],{},[2138,83083,2140],{},[2005,83085,2007],{},[2005,83087,2234],{},[2138,83089,5591],{},[8123,83091,83092],{},[2138,83093,24206],{},[2005,83095,2739],{},[2005,83097,2234],{},[2138,83099,83100],{},"21,17.",[902,83102,83103],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,83105,83107],{"id":83106},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,83109,83110,83111,1343,83113,3894,83115,83117,83118,83121,83122,83125],{},"Hlavními faktory produkce jsou ",[38,83112,74919],{},[38,83114,74935],{},[38,83116,74951],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,83119,83120],{},"jednofaktorový"," (pouze práce) a ",[38,83123,83124],{},"dvoufaktorový"," (práce + kapitál) model.",[724,83127,83128,83129,83132,83133,83135,83136,83138,83139,26194,83142,83161,83162,83179,83180,83197,83198,83220,83221,4364,83240,1644],{},"V ",[38,83130,83131],{},"1F modelu"," se definuje ",[38,83134,10029],{}," (derivace produkce podle práce) a ",[38,83137,74854],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,83140,83141],{},"zákonu klesajících výnosů",[883,83143,83145],{"className":83144},[886],[888,83146,83147],{"xmlns":890},[892,83148,83149,83159],{},[895,83150,83151,83153],{},[898,83152,2826],{},[2281,83154,83155,83157],{},[898,83156,3946],{},[898,83158,9801],{},[902,83160,10050],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,83163,83165],{"className":83164},[886],[888,83166,83167],{"xmlns":890},[892,83168,83169,83177],{},[895,83170,83171],{},[2281,83172,83173,83175],{},[898,83174,9801],{},[2138,83176,2336],{},[902,83178,75563],{"encoding":904}," klesá a v bodě ",[883,83181,83183],{"className":83182},[886],[888,83184,83185],{"xmlns":890},[892,83186,83187,83195],{},[895,83188,83189],{},[2281,83190,83191,83193],{},[898,83192,9801],{},[2138,83194,2287],{},[902,83196,13218],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,83199,83200,83201],{},"princip maximalizace ",[883,83202,83204],{"className":83203},[886],[888,83205,83206],{"xmlns":890},[892,83207,83208,83218],{},[895,83209,83210,83212],{},[898,83211,1836],{},[2281,83213,83214,83216],{},[898,83215,3946],{},[898,83217,9801],{},[902,83219,74638],{"encoding":904},": v bodě maxima ",[883,83222,83224],{"className":83223},[886],[888,83225,83226],{"xmlns":890},[892,83227,83228,83238],{},[895,83229,83230,83232],{},[898,83231,1836],{},[2281,83233,83234,83236],{},[898,83235,3946],{},[898,83237,9801],{},[902,83239,74638],{"encoding":904},[883,83241,83243],{"className":83242},[886],[888,83244,83245],{"xmlns":890},[892,83246,83247,83267],{},[895,83248,83249,83251,83257,83259,83261],{},[898,83250,2826],{},[2281,83252,83253,83255],{},[898,83254,3946],{},[898,83256,9801],{},[2005,83258,2007],{},[898,83260,1836],{},[2281,83262,83263,83265],{},[898,83264,3946],{},[898,83266,9801],{},[902,83268,74668],{"encoding":904},[724,83270,83271,83272,83275,83276,2212,83279,83308,83309,83326,83327,83330,83331,83360,83361,83363,83364,8108,83394,83416],{},"Ve ",[38,83273,83274],{},"2F modelu"," se obvykle používají ",[38,83277,83278],{},"Cobb-Douglasovy funkce",[883,83280,83282],{"className":83281},[886],[888,83283,83284],{"xmlns":890},[892,83285,83286,83306],{},[895,83287,83288,83290,83292,83294,83300],{},[898,83289,2797],{},[2005,83291,2007],{},[898,83293,1836],{},[2133,83295,83296,83298],{},[898,83297,9801],{},[898,83299,207],{},[2133,83301,83302,83304],{},[898,83303,9806],{},[898,83305,2107],{},[902,83307,74735],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,83310,83312],{"className":83311},[886],[888,83313,83314],{"xmlns":890},[892,83315,83316,83324],{},[895,83317,83318,83320,83322],{},[898,83319,207],{},[2005,83321,2104],{},[898,83323,2107],{},[902,83325,74829],{"encoding":904}," rozlišujeme ",[38,83328,83329],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,83332,83334],{"className":83333},[886],[888,83335,83336],{"xmlns":890},[892,83337,83338,83358],{},[895,83339,83340,83342,83348,83350,83352],{},[898,83341,2826],{},[2281,83343,83344,83346],{},[898,83345,3946],{},[898,83347,9801],{},[2005,83349,2295],{"separator":2294},[898,83351,2826],{},[2281,83353,83354,83356],{},[898,83355,3946],{},[898,83357,9806],{},[902,83359,74766],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,83362,9784],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,83365,83367],{"className":83366},[886],[888,83368,83369],{"xmlns":890},[892,83370,83371,83391],{},[895,83372,83373,83375,83381,83383,83385],{},[898,83374,2826],{},[2281,83376,83377,83379],{},[898,83378,3946],{},[898,83380,9801],{},[898,83382,4680],{"mathvariant":2385},[898,83384,2826],{},[2281,83386,83387,83389],{},[898,83388,3946],{},[898,83390,9806],{},[902,83392,83393],{"encoding":904},"MP_L\u002FMP_K",[38,83395,83396,83397,2020],{},"mezní míra technické substituce (",[883,83398,83400],{"className":83399},[886],[888,83401,83402],{"xmlns":890},[892,83403,83404,83414],{},[895,83405,83406,83408,83410,83412],{},[898,83407,2826],{},[898,83409,4003],{},[898,83411,2783],{},[898,83413,8679],{},[902,83415,10603],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,83418,49887],{"id":49886},[152,83420,83421,83424,83427,83430,83433,83436,83439,83442,83445,83448,83451],{},[123,83422,83423],{},"Jaké jsou faktory produkce?",[123,83425,83426],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,83428,83429],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,83431,83432],{},"Co udává mezní produkt práce?",[123,83434,83435],{},"Co musí respektovat průběh křivky produkce?",[123,83437,83438],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,83440,83441],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,83443,83444],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,83446,83447],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,83449,83450],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,83452,83453],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,83455,83457],{"id":83456},"úlohy-51517","Úlohy 5.1–5.17",[198,83459,40456],{"id":40455},[724,83461,83462,83465,83466,83488,83489,1343,83509,1343,83529,83549],{},[38,83463,83464],{},"5.1"," Je dána produkce ",[883,83467,83469],{"className":83468},[886],[888,83470,83471],{"xmlns":890},[892,83472,83473,83485],{},[895,83474,83475,83477,83479,83481],{},[898,83476,2797],{},[2005,83478,2007],{},[2138,83480,2871],{},[8123,83482,83483],{},[898,83484,9801],{},[902,83486,83487],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,83490,83492],{"className":83491},[886],[888,83493,83494],{"xmlns":890},[892,83495,83496,83506],{},[895,83497,83498,83500,83502,83504],{},[898,83499,2797],{},[2005,83501,2014],{"stretchy":2013},[2138,83503,2287],{},[2005,83505,2020],{"stretchy":2013},[902,83507,83508],{"encoding":904},"Q(1)",[883,83510,83512],{"className":83511},[886],[888,83513,83514],{"xmlns":890},[892,83515,83516,83526],{},[895,83517,83518,83520,83522,83524],{},[898,83519,2797],{},[2005,83521,2014],{"stretchy":2013},[2138,83523,2360],{},[2005,83525,2020],{"stretchy":2013},[902,83527,83528],{"encoding":904},"Q(4)",[883,83530,83532],{"className":83531},[886],[888,83533,83534],{"xmlns":890},[892,83535,83536,83546],{},[895,83537,83538,83540,83542,83544],{},[898,83539,2797],{},[2005,83541,2014],{"stretchy":2013},[2138,83543,4008],{},[2005,83545,2020],{"stretchy":2013},[902,83547,83548],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,83551,83552,83465,83555,83591,83592,83605,83606,83625,83626,83652,83653,2694,83666,83679],{},[38,83553,83554],{},"5.2",[883,83556,83558],{"className":83557},[886],[888,83559,83560],{"xmlns":890},[892,83561,83562,83588],{},[895,83563,83564,83566,83568,83570,83572,83578,83580,83582],{},[898,83565,2797],{},[2005,83567,2007],{},[2005,83569,2234],{},[2138,83571,2802],{},[2133,83573,83574,83576],{},[898,83575,9801],{},[2138,83577,2182],{},[2005,83579,2104],{},[2138,83581,4008],{},[2133,83583,83584,83586],{},[898,83585,9801],{},[2138,83587,2140],{},[902,83589,83590],{"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 ",[883,83593,83595],{"className":83594},[886],[888,83596,83597],{"xmlns":890},[892,83598,83599,83603],{},[895,83600,83601],{},[898,83602,9801],{},[902,83604,9801],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,83607,83609],{"className":83608},[886],[888,83610,83611],{"xmlns":890},[892,83612,83613,83623],{},[895,83614,83615,83617],{},[898,83616,2826],{},[2281,83618,83619,83621],{},[898,83620,3946],{},[898,83622,9801],{},[902,83624,10050],{"encoding":904},". (f) Vypočtěte ",[883,83627,83629],{"className":83628},[886],[888,83630,83631],{"xmlns":890},[892,83632,83633,83649],{},[895,83634,83635,83637,83643,83645,83647],{},[898,83636,2826],{},[2281,83638,83639,83641],{},[898,83640,3946],{},[898,83642,9801],{},[2005,83644,2014],{"stretchy":2013},[2138,83646,2871],{},[2005,83648,2020],{"stretchy":2013},[902,83650,83651],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,83654,83656],{"className":83655},[886],[888,83657,83658],{"xmlns":890},[892,83659,83660,83664],{},[895,83661,83662],{},[2138,83663,2871],{},[902,83665,2871],{"encoding":904},[883,83667,83669],{"className":83668},[886],[888,83670,83671],{"xmlns":890},[892,83672,83673,83677],{},[895,83674,83675],{},[2138,83676,42292],{},[902,83678,42292],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,83681,83682,83685,83686,83708,83709,83737,83738,83769,83770,1644],{},[38,83683,83684],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,83687,83689],{"className":83688},[886],[888,83690,83691],{"xmlns":890},[892,83692,83693,83705],{},[895,83694,83695,83697,83699,83701],{},[898,83696,2797],{},[2005,83698,2007],{},[2138,83700,15116],{},[8123,83702,83703],{},[898,83704,9801],{},[902,83706,83707],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,83710,83712],{"className":83711},[886],[888,83713,83714],{"xmlns":890},[892,83715,83716,83734],{},[895,83717,83718,83720,83722,83724,83728,83730,83732],{},[898,83719,2797],{},[2005,83721,2007],{},[2138,83723,30086],{},[8123,83725,83726],{},[898,83727,9801],{},[2005,83729,2234],{},[2138,83731,2360],{},[898,83733,9801],{},[902,83735,83736],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,83739,83741],{"className":83740},[886],[888,83742,83743],{"xmlns":890},[892,83744,83745,83766],{},[895,83746,83747,83749,83751,83753,83755,83757,83760],{},[898,83748,2797],{},[2005,83750,2007],{},[2138,83752,3128],{},[898,83754,9801],{},[2005,83756,2234],{},[2138,83758,83759],{},"0,01",[2133,83761,83762,83764],{},[898,83763,9801],{},[2138,83765,2140],{},[902,83767,83768],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,83771,83773],{"className":83772},[886],[888,83774,83775],{"xmlns":890},[892,83776,83777,83803],{},[895,83778,83779,83781,83783,83785,83787,83793,83795,83797],{},[898,83780,2797],{},[2005,83782,2007],{},[2005,83784,2234],{},[2138,83786,68216],{},[2133,83788,83789,83791],{},[898,83790,9801],{},[2138,83792,2182],{},[2005,83794,2104],{},[2138,83796,4008],{},[2133,83798,83799,83801],{},[898,83800,9801],{},[2138,83802,2140],{},[902,83804,83805],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,83807,83808,83811,83812,2633,83831,72203,83848,1644],{},[38,83809,83810],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,83813,83815],{"className":83814},[886],[888,83816,83817],{"xmlns":890},[892,83818,83819,83829],{},[895,83820,83821,83823],{},[898,83822,1836],{},[2281,83824,83825,83827],{},[898,83826,3946],{},[898,83828,9801],{},[902,83830,74638],{"encoding":904},[883,83832,83834],{"className":83833},[886],[888,83835,83836],{"xmlns":890},[892,83837,83838,83846],{},[895,83839,83840],{},[2281,83841,83842,83844],{},[898,83843,9801],{},[2138,83845,2336],{},[902,83847,75563],{"encoding":904},[883,83849,83851],{"className":83850},[886],[888,83852,83853],{"xmlns":890},[892,83854,83855,83895],{},[895,83856,83857,83859,83865,83867,83873,83875,83877,83879,83885,83887,83893],{},[898,83858,1836],{},[2281,83860,83861,83863],{},[898,83862,3946],{},[898,83864,9801],{},[2005,83866,2014],{"stretchy":2013},[2281,83868,83869,83871],{},[898,83870,9801],{},[2138,83872,2336],{},[2005,83874,2020],{"stretchy":2013},[2005,83876,2007],{},[898,83878,2826],{},[2281,83880,83881,83883],{},[898,83882,3946],{},[898,83884,9801],{},[2005,83886,2014],{"stretchy":2013},[2281,83888,83889,83891],{},[898,83890,9801],{},[2138,83892,2336],{},[2005,83894,2020],{"stretchy":2013},[902,83896,83897],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,83899,83900,83465,83903,21600,83939,83952,83953,83972],{},[38,83901,83902],{},"5.5",[883,83904,83906],{"className":83905},[886],[888,83907,83908],{"xmlns":890},[892,83909,83910,83936],{},[895,83911,83912,83914,83916,83918,83920,83926,83928,83930],{},[898,83913,2797],{},[2005,83915,2007],{},[2005,83917,2234],{},[2138,83919,2847],{},[2133,83921,83922,83924],{},[898,83923,9801],{},[2138,83925,2182],{},[2005,83927,2104],{},[2138,83929,3517],{},[2133,83931,83932,83934],{},[898,83933,9801],{},[2138,83935,2140],{},[902,83937,83938],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,83940,83942],{"className":83941},[886],[888,83943,83944],{"xmlns":890},[892,83945,83946,83950],{},[895,83947,83948],{},[898,83949,9801],{},[902,83951,9801],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,83954,83956],{"className":83955},[886],[888,83957,83958],{"xmlns":890},[892,83959,83960,83970],{},[895,83961,83962,83964],{},[898,83963,1836],{},[2281,83965,83966,83968],{},[898,83967,3946],{},[898,83969,9801],{},[902,83971,74638],{"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.",[198,83974,83976],{"id":83975},"dvoufaktorový-model","Dvoufaktorový model",[724,83978,83979,83982,83983,83708,84009,83737,84051,1644],{},[38,83980,83981],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,83984,83986],{"className":83985},[886],[888,83987,83988],{"xmlns":890},[892,83989,83990,84006],{},[895,83991,83992,83994,83996,83998,84000],{},[898,83993,2797],{},[2005,83995,2007],{},[2138,83997,24206],{},[898,83999,9801],{},[2133,84001,84002,84004],{},[898,84003,9806],{},[2138,84005,2140],{},[902,84007,84008],{"encoding":904},"Q = 7 L K^{2}",[883,84010,84012],{"className":84011},[886],[888,84013,84014],{"xmlns":890},[892,84015,84016,84048],{},[895,84017,84018,84020,84022,84024,84036],{},[898,84019,2797],{},[2005,84021,2007],{},[2138,84023,3128],{},[2133,84025,84026,84028],{},[898,84027,9801],{},[895,84029,84030,84032,84034],{},[2138,84031,2140],{},[898,84033,4680],{"mathvariant":2385},[2138,84035,2182],{},[2133,84037,84038,84040],{},[898,84039,9806],{},[895,84041,84042,84044,84046],{},[2138,84043,2287],{},[898,84045,4680],{"mathvariant":2385},[2138,84047,2182],{},[902,84049,84050],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,84052,84054],{"className":84053},[886],[888,84055,84056],{"xmlns":890},[892,84057,84058,84090],{},[895,84059,84060,84062,84064,84066,84078],{},[898,84061,2797],{},[2005,84063,2007],{},[2138,84065,3715],{},[2133,84067,84068,84070],{},[898,84069,9801],{},[895,84071,84072,84074,84076],{},[2138,84073,2182],{},[898,84075,4680],{"mathvariant":2385},[2138,84077,2237],{},[2133,84079,84080,84082],{},[898,84081,9806],{},[895,84083,84084,84086,84088],{},[2138,84085,2140],{},[898,84087,4680],{"mathvariant":2385},[2138,84089,2237],{},[902,84091,84092],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,84094,84095,83465,84098,84140,84141,1343,84159,84178,84179,84196],{},[38,84096,84097],{},"5.7",[883,84099,84101],{"className":84100},[886],[888,84102,84103],{"xmlns":890},[892,84104,84105,84137],{},[895,84106,84107,84109,84111,84113,84125],{},[898,84108,2797],{},[2005,84110,2007],{},[2138,84112,2871],{},[2133,84114,84115,84117],{},[898,84116,9801],{},[895,84118,84119,84121,84123],{},[2138,84120,2287],{},[898,84122,4680],{"mathvariant":2385},[2138,84124,2140],{},[2133,84126,84127,84129],{},[898,84128,9806],{},[895,84130,84131,84133,84135],{},[2138,84132,2287],{},[898,84134,4680],{"mathvariant":2385},[2138,84136,2140],{},[902,84138,84139],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,84142,84144],{"className":84143},[886],[888,84145,84146],{"xmlns":890},[892,84147,84148,84156],{},[895,84149,84150,84152,84154],{},[898,84151,9801],{},[2005,84153,2007],{},[2138,84155,20148],{},[902,84157,84158],{"encoding":904},"L = 400",[883,84160,84162],{"className":84161},[886],[888,84163,84164],{"xmlns":890},[892,84165,84166,84175],{},[895,84167,84168,84170,84172],{},[898,84169,9806],{},[2005,84171,2007],{},[2138,84173,84174],{},"17576",[902,84176,84177],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,84180,84182],{"className":84181},[886],[888,84183,84184],{"xmlns":890},[892,84185,84186,84194],{},[895,84187,84188,84190,84192],{},[898,84189,9801],{},[2005,84191,2295],{"separator":2294},[898,84193,9806],{},[902,84195,78990],{"encoding":904}," zdvojnásobí.",[724,84198,84199,84202,84203,84140,84234,1343,84252,69589,84270,84300,84301,84331,84332,2694,84345,84359,84360,2694,84373,84386],{},[38,84200,84201],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,84204,84206],{"className":84205},[886],[888,84207,84208],{"xmlns":890},[892,84209,84210,84231],{},[895,84211,84212,84214,84216,84219,84225],{},[898,84213,2797],{},[2005,84215,2007],{},[2138,84217,84218],{},"1,01",[2133,84220,84221,84223],{},[898,84222,9801],{},[2138,84224,23735],{},[2133,84226,84227,84229],{},[898,84228,9806],{},[2138,84230,23794],{},[902,84232,84233],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,84235,84237],{"className":84236},[886],[888,84238,84239],{"xmlns":890},[892,84240,84241,84249],{},[895,84242,84243,84245,84247],{},[898,84244,9801],{},[2005,84246,2007],{},[2138,84248,30748],{},[902,84250,84251],{"encoding":904},"L = 250",[883,84253,84255],{"className":84254},[886],[888,84256,84257],{"xmlns":890},[892,84258,84259,84267],{},[895,84260,84261,84263,84265],{},[898,84262,9806],{},[2005,84264,2007],{},[2138,84266,2790],{},[902,84268,84269],{"encoding":904},"K = 1000",[883,84271,84273],{"className":84272},[886],[888,84274,84275],{"xmlns":890},[892,84276,84277,84297],{},[895,84278,84279,84281,84287,84289,84291,84293,84295],{},[898,84280,2826],{},[2281,84282,84283,84285],{},[898,84284,3946],{},[898,84286,9801],{},[2005,84288,2014],{"stretchy":2013},[2138,84290,30748],{},[2005,84292,2295],{"separator":2294},[2138,84294,2790],{},[2005,84296,2020],{"stretchy":2013},[902,84298,84299],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,84302,84304],{"className":84303},[886],[888,84305,84306],{"xmlns":890},[892,84307,84308,84328],{},[895,84309,84310,84312,84318,84320,84322,84324,84326],{},[898,84311,2826],{},[2281,84313,84314,84316],{},[898,84315,3946],{},[898,84317,9806],{},[2005,84319,2014],{"stretchy":2013},[2138,84321,30748],{},[2005,84323,2295],{"separator":2294},[2138,84325,2790],{},[2005,84327,2020],{"stretchy":2013},[902,84329,84330],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,84333,84335],{"className":84334},[886],[888,84336,84337],{"xmlns":890},[892,84338,84339,84343],{},[895,84340,84341],{},[898,84342,9801],{},[902,84344,9801],{"encoding":904},[883,84346,84348],{"className":84347},[886],[888,84349,84350],{"xmlns":890},[892,84351,84352,84357],{},[895,84353,84354],{},[2138,84355,84356],{},"260",[902,84358,84356],{"encoding":904}," a současném poklesu ",[883,84361,84363],{"className":84362},[886],[888,84364,84365],{"xmlns":890},[892,84366,84367,84371],{},[895,84368,84369],{},[898,84370,9806],{},[902,84372,9806],{"encoding":904},[883,84374,84376],{"className":84375},[886],[888,84377,84378],{"xmlns":890},[892,84379,84380,84384],{},[895,84381,84382],{},[2138,84383,15197],{},[902,84385,15197],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,84388,84389,84392,84393,1644],{},[38,84390,84391],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,84394,84396],{"className":84395},[886],[888,84397,84398],{"xmlns":890},[892,84399,84400,84420],{},[895,84401,84402,84404,84406,84408,84414],{},[898,84403,2797],{},[2005,84405,2007],{},[2138,84407,2871],{},[2133,84409,84410,84412],{},[898,84411,9801],{},[2138,84413,68216],{},[2133,84415,84416,84418],{},[898,84417,9806],{},[2138,84419,5015],{},[902,84421,84422],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,84424,84425,84428,84429,80586,84452,10399,84465,10030,84515,3927],{},[38,84426,84427],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,84430,84432],{"className":84431},[886],[888,84433,84434],{"xmlns":890},[892,84435,84436,84450],{},[895,84437,84438,84440,84442,84444,84446,84448],{},[898,84439,2797],{},[2005,84441,2014],{"stretchy":2013},[898,84443,9801],{},[2005,84445,2295],{"separator":2294},[898,84447,9806],{},[2005,84449,2020],{"stretchy":2013},[902,84451,10002],{"encoding":904},[883,84453,84455],{"className":84454},[886],[888,84456,84457],{"xmlns":890},[892,84458,84459,84463],{},[895,84460,84461],{},[898,84462,36865],{},[902,84464,36865],{"encoding":904},[883,84466,84468],{"className":84467},[886],[888,84469,84470],{"xmlns":890},[892,84471,84472,84512],{},[895,84473,84474,84476,84484,84486,84488,84496,84498,84500,84502,84504,84506,84508,84510],{},[898,84475,9801],{},[9172,84477,84478,84480,84482],{},[898,84479,2797],{},[898,84481,9801],{},[2005,84483,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,84485,2104],{},[898,84487,9806],{},[9172,84489,84490,84492,84494],{},[898,84491,2797],{},[898,84493,9806],{},[2005,84495,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,84497,2007],{},[898,84499,36865],{},[898,84501,2797],{},[2005,84503,2014],{"stretchy":2013},[898,84505,9801],{},[2005,84507,2295],{"separator":2294},[898,84509,9806],{},[2005,84511,2020],{"stretchy":2013},[902,84513,84514],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,84516,80561],{},[724,84518,84519,84522],{},[38,84520,84521],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,84524,84525,83465,84528,84568,84569,1343,84591,1343,84613,84635],{},[38,84526,84527],{},"5.12",[883,84529,84531],{"className":84530},[886],[888,84532,84533],{"xmlns":890},[892,84534,84535,84565],{},[895,84536,84537,84539,84541,84553],{},[898,84538,2797],{},[2005,84540,2007],{},[2133,84542,84543,84545],{},[898,84544,9801],{},[895,84546,84547,84549,84551],{},[2138,84548,2287],{},[898,84550,4680],{"mathvariant":2385},[2138,84552,2182],{},[2133,84554,84555,84557],{},[898,84556,9806],{},[895,84558,84559,84561,84563],{},[2138,84560,2287],{},[898,84562,4680],{"mathvariant":2385},[2138,84564,2360],{},[902,84566,84567],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,84570,84572],{"className":84571},[886],[888,84573,84574],{"xmlns":890},[892,84575,84576,84588],{},[895,84577,84578,84584,84586],{},[2281,84579,84580,84582],{},[898,84581,80802],{},[2138,84583,2336],{},[2005,84585,2007],{},[2138,84587,2287],{},[902,84589,84590],{"encoding":904},"q_0 = 1",[883,84592,84594],{"className":84593},[886],[888,84595,84596],{"xmlns":890},[892,84597,84598,84610],{},[895,84599,84600,84606,84608],{},[2281,84601,84602,84604],{},[898,84603,80802],{},[2138,84605,2287],{},[2005,84607,2007],{},[2138,84609,2140],{},[902,84611,84612],{"encoding":904},"q_1 = 2",[883,84614,84616],{"className":84615},[886],[888,84617,84618],{"xmlns":890},[892,84619,84620,84632],{},[895,84621,84622,84628,84630],{},[2281,84623,84624,84626],{},[898,84625,80802],{},[2138,84627,2140],{},[2005,84629,2007],{},[2138,84631,2182],{},[902,84633,84634],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,84637,84638,83465,84641,84681,84682,1343,84710,1343,84738,1343,84766,1343,84795,1343,84824,1343,84853,1343,84882,1343,84911,1644],{},[38,84639,84640],{},"5.13",[883,84642,84644],{"className":84643},[886],[888,84645,84646],{"xmlns":890},[892,84647,84648,84678],{},[895,84649,84650,84652,84654,84666],{},[898,84651,2797],{},[2005,84653,2007],{},[2133,84655,84656,84658],{},[898,84657,9801],{},[895,84659,84660,84662,84664],{},[2138,84661,2287],{},[898,84663,4680],{"mathvariant":2385},[2138,84665,2182],{},[2133,84667,84668,84670],{},[898,84669,9806],{},[895,84671,84672,84674,84676],{},[2138,84673,2287],{},[898,84675,4680],{"mathvariant":2385},[2138,84677,2140],{},[902,84679,84680],{"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): ",[883,84683,84685],{"className":84684},[886],[888,84686,84687],{"xmlns":890},[892,84688,84689,84707],{},[895,84690,84691,84697,84699,84701,84703,84705],{},[2281,84692,84693,84695],{},[898,84694,1836],{},[2138,84696,2287],{},[2005,84698,2495],{"stretchy":2013},[2138,84700,2287],{},[2005,84702,8431],{"separator":2294},[2138,84704,2287],{},[2005,84706,2510],{"stretchy":2013},[902,84708,84709],{"encoding":904},"A_1[1; 1]",[883,84711,84713],{"className":84712},[886],[888,84714,84715],{"xmlns":890},[892,84716,84717,84735],{},[895,84718,84719,84725,84727,84729,84731,84733],{},[2281,84720,84721,84723],{},[898,84722,1836],{},[2138,84724,2140],{},[2005,84726,2495],{"stretchy":2013},[2138,84728,2287],{},[2005,84730,8431],{"separator":2294},[2138,84732,5591],{},[2005,84734,2510],{"stretchy":2013},[902,84736,84737],{"encoding":904},"A_2[1; 8]",[883,84739,84741],{"className":84740},[886],[888,84742,84743],{"xmlns":890},[892,84744,84745,84763],{},[895,84746,84747,84753,84755,84757,84759,84761],{},[2281,84748,84749,84751],{},[898,84750,1836],{},[2138,84752,2182],{},[2005,84754,2495],{"stretchy":2013},[2138,84756,2287],{},[2005,84758,8431],{"separator":2294},[2138,84760,66602],{},[2005,84762,2510],{"stretchy":2013},[902,84764,84765],{"encoding":904},"A_3[1; 27]",[883,84767,84769],{"className":84768},[886],[888,84770,84771],{"xmlns":890},[892,84772,84773,84792],{},[895,84774,84775,84781,84783,84785,84787,84790],{},[2281,84776,84777,84779],{},[898,84778,1836],{},[2138,84780,2360],{},[2005,84782,2495],{"stretchy":2013},[2138,84784,2140],{},[2005,84786,8431],{"separator":2294},[2138,84788,84789],{},"0,353",[2005,84791,2510],{"stretchy":2013},[902,84793,84794],{"encoding":904},"A_4[2; 0{,}353]",[883,84796,84798],{"className":84797},[886],[888,84799,84800],{"xmlns":890},[892,84801,84802,84821],{},[895,84803,84804,84810,84812,84814,84816,84819],{},[2281,84805,84806,84808],{},[898,84807,1836],{},[2138,84809,2237],{},[2005,84811,2495],{"stretchy":2013},[2138,84813,2140],{},[2005,84815,8431],{"separator":2294},[2138,84817,84818],{},"2,828",[2005,84820,2510],{"stretchy":2013},[902,84822,84823],{"encoding":904},"A_5[2; 2{,}828]",[883,84825,84827],{"className":84826},[886],[888,84828,84829],{"xmlns":890},[892,84830,84831,84850],{},[895,84832,84833,84839,84841,84843,84845,84848],{},[2281,84834,84835,84837],{},[898,84836,1836],{},[2138,84838,2244],{},[2005,84840,2495],{"stretchy":2013},[2138,84842,2140],{},[2005,84844,8431],{"separator":2294},[2138,84846,84847],{},"9,545",[2005,84849,2510],{"stretchy":2013},[902,84851,84852],{"encoding":904},"A_6[2; 9{,}545]",[883,84854,84856],{"className":84855},[886],[888,84857,84858],{"xmlns":890},[892,84859,84860,84879],{},[895,84861,84862,84868,84870,84872,84874,84877],{},[2281,84863,84864,84866],{},[898,84865,1836],{},[2138,84867,24206],{},[2005,84869,2495],{"stretchy":2013},[2138,84871,64564],{},[2005,84873,8431],{"separator":2294},[2138,84875,84876],{},"0,544",[2005,84878,2510],{"stretchy":2013},[902,84880,84881],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,84883,84885],{"className":84884},[886],[888,84886,84887],{"xmlns":890},[892,84888,84889,84908],{},[895,84890,84891,84897,84899,84901,84903,84906],{},[2281,84892,84893,84895],{},[898,84894,1836],{},[2138,84896,5591],{},[2005,84898,2495],{"stretchy":2013},[2138,84900,64564],{},[2005,84902,8431],{"separator":2294},[2138,84904,84905],{},"14,696",[2005,84907,2510],{"stretchy":2013},[902,84909,84910],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,84912,84914],{"className":84913},[886],[888,84915,84916],{"xmlns":890},[892,84917,84918,84936],{},[895,84919,84920,84926,84928,84930,84932,84934],{},[2281,84921,84922,84924],{},[898,84923,1836],{},[2138,84925,4008],{},[2005,84927,2495],{"stretchy":2013},[2138,84929,2140],{},[2005,84931,8431],{"separator":2294},[2138,84933,2237],{},[2005,84935,2510],{"stretchy":2013},[902,84937,84938],{"encoding":904},"A_9[2; 5]",[724,84940,84941,84944],{},[38,84942,84943],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,84946,84947,84950,84951,84981,84982,84995,84996,85009,85010,69322,85029,85048,85049,1644],{},[38,84948,84949],{},"5.15"," Produkce firmy je dána vztahem ",[883,84952,84954],{"className":84953},[886],[888,84955,84956],{"xmlns":890},[892,84957,84958,84978],{},[895,84959,84960,84962,84964,84966,84972],{},[898,84961,2797],{},[2005,84963,2007],{},[2138,84965,2140],{},[2133,84967,84968,84970],{},[898,84969,9801],{},[2138,84971,5015],{},[2133,84973,84974,84976],{},[898,84975,9806],{},[2138,84977,23794],{},[902,84979,84980],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,84983,84985],{"className":84984},[886],[888,84986,84987],{"xmlns":890},[892,84988,84989,84993],{},[895,84990,84991],{},[2138,84992,3098],{},[902,84994,3098],{"encoding":904}," pracovníků a disponuje-li ",[883,84997,84999],{"className":84998},[886],[888,85000,85001],{"xmlns":890},[892,85002,85003,85007],{},[895,85004,85005],{},[2138,85006,64440],{},[902,85008,64440],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,85011,85013],{"className":85012},[886],[888,85014,85015],{"xmlns":890},[892,85016,85017,85027],{},[895,85018,85019,85021,85023,85025],{},[898,85020,2826],{},[898,85022,4003],{},[898,85024,2783],{},[898,85026,8679],{},[902,85028,10603],{"encoding":904},[883,85030,85032],{"className":85031},[886],[888,85033,85034],{"xmlns":890},[892,85035,85036,85046],{},[895,85037,85038,85040,85042,85044],{},[898,85039,2826],{},[898,85041,4003],{},[898,85043,2783],{},[898,85045,8679],{},[902,85047,10603],{"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 ",[883,85050,85052],{"className":85051},[886],[888,85053,85054],{"xmlns":890},[892,85055,85056,85061],{},[895,85057,85058],{},[2138,85059,85060],{},"95",[902,85062,85060],{"encoding":904},[724,85064,85065,83465,85068,70996,85100,85119,85120,85133,85134,85147,85148,85161],{},[38,85066,85067],{},"5.16",[883,85069,85071],{"className":85070},[886],[888,85072,85073],{"xmlns":890},[892,85074,85075,85097],{},[895,85076,85077,85079,85081,85087,85089,85091],{},[898,85078,2797],{},[2005,85080,2007],{},[2133,85082,85083,85085],{},[898,85084,9806],{},[2138,85086,2140],{},[2005,85088,2104],{},[2138,85090,2140],{},[2133,85092,85093,85095],{},[898,85094,9801],{},[2138,85096,2140],{},[902,85098,85099],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,85101,85103],{"className":85102},[886],[888,85104,85105],{"xmlns":890},[892,85106,85107,85117],{},[895,85108,85109,85111,85113,85115],{},[898,85110,2826],{},[898,85112,4003],{},[898,85114,2783],{},[898,85116,8679],{},[902,85118,10603],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,85121,85123],{"className":85122},[886],[888,85124,85125],{"xmlns":890},[892,85126,85127,85131],{},[895,85128,85129],{},[2138,85130,3128],{},[902,85132,3128],{"encoding":904}," pracovníky a ",[883,85135,85137],{"className":85136},[886],[888,85138,85139],{"xmlns":890},[892,85140,85141,85145],{},[895,85142,85143],{},[2138,85144,77622],{},[902,85146,77622],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,85149,85151],{"className":85150},[886],[888,85152,85153],{"xmlns":890},[892,85154,85155,85159],{},[895,85156,85157],{},[2138,85158,46708],{},[902,85160,46708],{"encoding":904}," jednotek.",[724,85163,85164,85167,85168,10399,85198,1644],{},[38,85165,85166],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,85169,85171],{"className":85170},[886],[888,85172,85173],{"xmlns":890},[892,85174,85175,85195],{},[895,85176,85177,85179,85181,85183,85189],{},[898,85178,2797],{},[2005,85180,2007],{},[898,85182,1836],{},[2133,85184,85185,85187],{},[898,85186,9801],{},[898,85188,207],{},[2133,85190,85191,85193],{},[898,85192,9806],{},[898,85194,2107],{},[902,85196,85197],{"encoding":904},"Q = A L^{a} K^{b}",[883,85199,85201],{"className":85200},[886],[888,85202,85203],{"xmlns":890},[892,85204,85205,85235],{},[895,85206,85207,85209,85211,85213,85215,85217,85225,85227],{},[898,85208,2826],{},[898,85210,4003],{},[898,85212,2783],{},[898,85214,8679],{},[2005,85216,2007],{},[2334,85218,85219],{"scriptlevel":2336,"displaystyle":2013},[2338,85220,85221,85223],{},[898,85222,207],{},[898,85224,2107],{},[2005,85226,3185],{},[2334,85228,85229],{"scriptlevel":2336,"displaystyle":2013},[2338,85230,85231,85233],{},[898,85232,9806],{},[898,85234,9801],{},[902,85236,85237],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,85239,15726],{"id":15725},[120,85241,85242,85275,85302,85311,85361,85392,85445,85468,85523,85596,85674,85717,85749,85782,85823,85895,85956,86022,86039,86112,86178,86230,86286,86320,86363],{},[123,85243,85244,85247,85248,36901,85261,85274],{},[38,85245,85246],{},"Faktory (vstupy) produkce:"," práce ",[883,85249,85251],{"className":85250},[886],[888,85252,85253],{"xmlns":890},[892,85254,85255,85259],{},[895,85256,85257],{},[898,85258,9801],{},[902,85260,9801],{"encoding":904},[883,85262,85264],{"className":85263},[886],[888,85265,85266],{"xmlns":890},[892,85267,85268,85272],{},[895,85269,85270],{},[898,85271,9806],{},[902,85273,9806],{"encoding":904},", půda.",[123,85276,85277,7021,85279,1644],{},[38,85278,40456],{},[883,85280,85282],{"className":85281},[886],[888,85283,85284],{"xmlns":890},[892,85285,85286,85300],{},[895,85287,85288,85290,85292,85294,85296,85298],{},[898,85289,2797],{},[2005,85291,2007],{},[898,85293,2797],{},[2005,85295,2014],{"stretchy":2013},[898,85297,9801],{},[2005,85299,2020],{"stretchy":2013},[902,85301,74549],{"encoding":904},[123,85303,85304,10030,85306,12134,85309,1644],{},[38,85305,859],{},[614,85307,85308],{},"production function",[38,85310,75052],{},[123,85312,85313,2212,85315,1644],{},[38,85314,75098],{},[883,85316,85318],{"className":85317},[886],[888,85319,85320],{"xmlns":890},[892,85321,85322,85358],{},[895,85323,85324,85326,85332,85334,85336,85338,85340,85342,85344,85346,85352,85354,85356],{},[898,85325,2826],{},[2281,85327,85328,85330],{},[898,85329,3946],{},[898,85331,9801],{},[2005,85333,2007],{},[898,85335,2203],{},[898,85337,2797],{},[898,85339,4680],{"mathvariant":2385},[898,85341,2203],{},[898,85343,9801],{},[2005,85345,2007],{},[2133,85347,85348,85350],{},[898,85349,2797],{},[2005,85351,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,85353,2014],{"stretchy":2013},[898,85355,9801],{},[2005,85357,2020],{"stretchy":2013},[902,85359,85360],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,85362,85363,2212,85365,1644],{},[38,85364,76033],{},[883,85366,85368],{"className":85367},[886],[888,85369,85370],{"xmlns":890},[892,85371,85372,85390],{},[895,85373,85374,85376,85382,85384,85386,85388],{},[898,85375,1836],{},[2281,85377,85378,85380],{},[898,85379,3946],{},[898,85381,9801],{},[2005,85383,2007],{},[898,85385,2797],{},[898,85387,4680],{"mathvariant":2385},[898,85389,9801],{},[902,85391,74617],{"encoding":904},[123,85393,85394,85396,85397,10399,85414,1644],{},[38,85395,75520],{}," — od určitého ",[883,85398,85400],{"className":85399},[886],[888,85401,85402],{"xmlns":890},[892,85403,85404,85412],{},[895,85405,85406],{},[2281,85407,85408,85410],{},[898,85409,9801],{},[2138,85411,2336],{},[902,85413,75563],{"encoding":904},[883,85415,85417],{"className":85416},[886],[888,85418,85419],{"xmlns":890},[892,85420,85421,85443],{},[895,85422,85423,85433,85435,85437,85439,85441],{},[2133,85424,85425,85427],{},[898,85426,2797],{},[895,85428,85429,85431],{},[2005,85430,2387],{"mathvariant":2385},[2005,85432,2387],{"mathvariant":2385},[2005,85434,2014],{"stretchy":2013},[898,85436,9801],{},[2005,85438,2020],{"stretchy":2013},[2005,85440,3455],{},[2138,85442,2336],{},[902,85444,75709],{"encoding":904},[123,85446,85447,2212,85450,85467],{},[38,85448,85449],{},"Inflexní bod",[883,85451,85453],{"className":85452},[886],[888,85454,85455],{"xmlns":890},[892,85456,85457,85465],{},[895,85458,85459],{},[2281,85460,85461,85463],{},[898,85462,9801],{},[2138,85464,2336],{},[902,85466,75563],{"encoding":904}," — přechod z konvexity do konkavity.",[123,85469,85470,2212,85473,7021,85490,1644],{},[38,85471,85472],{},"Bod maxima produkce",[883,85474,85476],{"className":85475},[886],[888,85477,85478],{"xmlns":890},[892,85479,85480,85488],{},[895,85481,85482],{},[2281,85483,85484,85486],{},[898,85485,9801],{},[2138,85487,2287],{},[902,85489,13218],{"encoding":904},[883,85491,85493],{"className":85492},[886],[888,85494,85495],{"xmlns":890},[892,85496,85497,85521],{},[895,85498,85499,85501,85507,85509,85515,85517,85519],{},[898,85500,2826],{},[2281,85502,85503,85505],{},[898,85504,3946],{},[898,85506,9801],{},[2005,85508,2014],{"stretchy":2013},[2281,85510,85511,85513],{},[898,85512,9801],{},[2138,85514,2287],{},[2005,85516,2020],{"stretchy":2013},[2005,85518,2007],{},[2138,85520,2336],{},[902,85522,75782],{"encoding":904},[123,85524,85525,85547,85548,10399,85567,1644],{},[38,85526,85527,85528],{},"Princip maximalizace ",[883,85529,85531],{"className":85530},[886],[888,85532,85533],{"xmlns":890},[892,85534,85535,85545],{},[895,85536,85537,85539],{},[898,85538,1836],{},[2281,85540,85541,85543],{},[898,85542,3946],{},[898,85544,9801],{},[902,85546,74638],{"encoding":904}," — v bodě maxima ",[883,85549,85551],{"className":85550},[886],[888,85552,85553],{"xmlns":890},[892,85554,85555,85565],{},[895,85556,85557,85559],{},[898,85558,1836],{},[2281,85560,85561,85563],{},[898,85562,3946],{},[898,85564,9801],{},[902,85566,74638],{"encoding":904},[883,85568,85570],{"className":85569},[886],[888,85571,85572],{"xmlns":890},[892,85573,85574,85594],{},[895,85575,85576,85578,85584,85586,85588],{},[898,85577,2826],{},[2281,85579,85580,85582],{},[898,85581,3946],{},[898,85583,9801],{},[2005,85585,2007],{},[898,85587,1836],{},[2281,85589,85590,85592],{},[898,85591,3946],{},[898,85593,9801],{},[902,85595,74668],{"encoding":904},[123,85597,85598,2212,85601,1343,85640,1343,85657,1644],{},[38,85599,85600],{},"Polynomiální produkční funkce",[883,85602,85604],{"className":85603},[886],[888,85605,85606],{"xmlns":890},[892,85607,85608,85638],{},[895,85609,85610,85612,85614,85616,85618,85620,85622,85628,85630,85632],{},[898,85611,2797],{},[2005,85613,2014],{"stretchy":2013},[898,85615,9801],{},[2005,85617,2020],{"stretchy":2013},[2005,85619,2007],{},[898,85621,207],{},[2133,85623,85624,85626],{},[898,85625,9801],{},[2138,85627,2182],{},[2005,85629,2104],{},[898,85631,2107],{},[2133,85633,85634,85636],{},[898,85635,9801],{},[2138,85637,2140],{},[902,85639,75900],{"encoding":904},[883,85641,85643],{"className":85642},[886],[888,85644,85645],{"xmlns":890},[892,85646,85647,85655],{},[895,85648,85649,85651,85653],{},[898,85650,207],{},[2005,85652,3455],{},[2138,85654,2336],{},[902,85656,43090],{"encoding":904},[883,85658,85660],{"className":85659},[886],[888,85661,85662],{"xmlns":890},[892,85663,85664,85672],{},[895,85665,85666,85668,85670],{},[898,85667,2107],{},[2005,85669,3416],{},[2138,85671,2336],{},[902,85673,18820],{"encoding":904},[123,85675,85676,2212,85679,1644],{},[38,85677,85678],{},"Diferenciál produkce",[883,85680,85682],{"className":85681},[886],[888,85683,85684],{"xmlns":890},[892,85685,85686,85714],{},[895,85687,85688,85690,85692,85694,85696,85698,85700,85702,85708,85710,85712],{},[898,85689,2897],{"mathvariant":2385},[898,85691,2797],{},[2005,85693,2739],{},[898,85695,2203],{},[898,85697,2797],{},[2005,85699,2007],{},[898,85701,2826],{},[2281,85703,85704,85706],{},[898,85705,3946],{},[898,85707,9801],{},[2297,85709,2995],{},[898,85711,2203],{},[898,85713,9801],{},[902,85715,85716],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,85718,85719,7021,85721,1644],{},[38,85720,83976],{},[883,85722,85724],{"className":85723},[886],[888,85725,85726],{"xmlns":890},[892,85727,85728,85746],{},[895,85729,85730,85732,85734,85736,85738,85740,85742,85744],{},[898,85731,2797],{},[2005,85733,2007],{},[898,85735,2797],{},[2005,85737,2014],{"stretchy":2013},[898,85739,9801],{},[2005,85741,2295],{"separator":2294},[898,85743,9806],{},[2005,85745,2020],{"stretchy":2013},[902,85747,85748],{"encoding":904},"Q = Q(L, K)",[123,85750,85751,7021,85753,1644],{},[38,85752,78070],{},[883,85754,85756],{"className":85755},[886],[888,85757,85758],{"xmlns":890},[892,85759,85760,85780],{},[895,85761,85762,85764,85766,85768,85774],{},[898,85763,2797],{},[2005,85765,2007],{},[898,85767,1836],{},[2133,85769,85770,85772],{},[898,85771,9801],{},[898,85773,207],{},[2133,85775,85776,85778],{},[898,85777,9806],{},[898,85779,2107],{},[902,85781,74735],{"encoding":904},[123,85783,85784,7021,85787,85822],{},[38,85785,85786],{},"Ryzí Cobb-Douglas",[883,85788,85790],{"className":85789},[886],[888,85791,85792],{"xmlns":890},[892,85793,85794,85820],{},[895,85795,85796,85798,85800,85802,85808],{},[898,85797,2797],{},[2005,85799,2007],{},[898,85801,1836],{},[2133,85803,85804,85806],{},[898,85805,9801],{},[898,85807,207],{},[2133,85809,85810,85812],{},[898,85811,9806],{},[895,85813,85814,85816,85818],{},[2138,85815,2287],{},[2005,85817,2234],{},[898,85819,207],{},[902,85821,78897],{"encoding":904}," (konstantní výnosy).",[123,85824,85825,7021,85827,1644],{},[38,85826,79613],{},[883,85828,85830],{"className":85829},[886],[888,85831,85832],{"xmlns":890},[892,85833,85834,85892],{},[895,85835,85836,85838,85840,85842,85844,85846,85848,85850,85852,85854,85864,85866,85868,85878],{},[898,85837,2797],{},[2005,85839,2007],{},[898,85841,1836],{},[2005,85843,2495],{"stretchy":2013},[2005,85845,2014],{"stretchy":2013},[2138,85847,2287],{},[2005,85849,2234],{},[898,85851,207],{},[2005,85853,2020],{"stretchy":2013},[2133,85855,85856,85858],{},[898,85857,9801],{},[895,85859,85860,85862],{},[2005,85861,2234],{},[898,85863,2107],{},[2005,85865,2104],{},[898,85867,207],{},[2133,85869,85870,85872],{},[898,85871,9806],{},[895,85873,85874,85876],{},[2005,85875,2234],{},[898,85877,2107],{},[2133,85879,85880,85882],{},[2005,85881,2510],{"stretchy":2013},[895,85883,85884,85886,85888,85890],{},[2005,85885,2234],{},[2138,85887,2287],{},[898,85889,4680],{"mathvariant":2385},[898,85891,2107],{},[902,85893,85894],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,85896,85897,10030,85900,12134,85922,10030,85925,85955],{},[38,85898,85899],{},"Lineární",[883,85901,85903],{"className":85902},[886],[888,85904,85905],{"xmlns":890},[892,85906,85907,85919],{},[895,85908,85909,85911,85913,85915,85917],{},[898,85910,207],{},[898,85912,9801],{},[2005,85914,2104],{},[898,85916,2107],{},[898,85918,9806],{},[902,85920,85921],{"encoding":904},"aL + bK",[38,85923,85924],{},"Leontiefova",[883,85926,85928],{"className":85927},[886],[888,85929,85930],{"xmlns":890},[892,85931,85932,85952],{},[895,85933,85934,85936,85938,85940,85942,85944,85946,85948,85950],{},[898,85935,79841],{},[2005,85937,56205],{},[2005,85939,2014],{"stretchy":2013},[898,85941,207],{},[898,85943,9801],{},[2005,85945,2295],{"separator":2294},[898,85947,2107],{},[898,85949,9806],{},[2005,85951,2020],{"stretchy":2013},[902,85953,85954],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,85957,85958,7021,85974,1644],{},[38,85959,85960,85961],{},"Homogenita stupně ",[883,85962,85964],{"className":85963},[886],[888,85965,85966],{"xmlns":890},[892,85967,85968,85972],{},[895,85969,85970],{},[898,85971,36865],{},[902,85973,36865],{"encoding":904},[883,85975,85977],{"className":85976},[886],[888,85978,85979],{"xmlns":890},[892,85980,85981,86019],{},[895,85982,85983,85985,85987,85989,85991,85993,85995,85997,85999,86001,86007,86009,86011,86013,86015,86017],{},[898,85984,2797],{},[2005,85986,2014],{"stretchy":2013},[898,85988,12047],{},[898,85990,9801],{},[2005,85992,2295],{"separator":2294},[898,85994,12047],{},[898,85996,9806],{},[2005,85998,2020],{"stretchy":2013},[2005,86000,2007],{},[2133,86002,86003,86005],{},[898,86004,12047],{},[898,86006,36865],{},[898,86008,2797],{},[2005,86010,2014],{"stretchy":2013},[898,86012,9801],{},[2005,86014,2295],{"separator":2294},[898,86016,9806],{},[2005,86018,2020],{"stretchy":2013},[902,86020,86021],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,86023,86024,78995],{},[38,86025,78928,86026],{},[883,86027,86029],{"className":86028},[886],[888,86030,86031],{"xmlns":890},[892,86032,86033,86037],{},[895,86034,86035],{},[898,86036,1836],{},[902,86038,1836],{"encoding":904},[123,86040,86041,86043,86044,86066,86067,86089,86090,3927],{},[38,86042,78429],{}," — konstantní (",[883,86045,86047],{"className":86046},[886],[888,86048,86049],{"xmlns":890},[892,86050,86051,86063],{},[895,86052,86053,86055,86057,86059,86061],{},[898,86054,207],{},[2005,86056,2104],{},[898,86058,2107],{},[2005,86060,2007],{},[2138,86062,2287],{},[902,86064,86065],{"encoding":904},"a+b=1","), rostoucí (",[883,86068,86070],{"className":86069},[886],[888,86071,86072],{"xmlns":890},[892,86073,86074,86086],{},[895,86075,86076,86078,86080,86082,86084],{},[898,86077,207],{},[2005,86079,2104],{},[898,86081,2107],{},[2005,86083,3416],{},[2138,86085,2287],{},[902,86087,86088],{"encoding":904},"a+b>1","), klesající (",[883,86091,86093],{"className":86092},[886],[888,86094,86095],{"xmlns":890},[892,86096,86097,86109],{},[895,86098,86099,86101,86103,86105,86107],{},[898,86100,207],{},[2005,86102,2104],{},[898,86104,2107],{},[2005,86106,3455],{},[2138,86108,2287],{},[902,86110,86111],{"encoding":904},"a+b\u003C1",[123,86113,86114,2212,86116,1343,86146,2212,86148,1644],{},[38,86115,75098],{},[883,86117,86119],{"className":86118},[886],[888,86120,86121],{"xmlns":890},[892,86122,86123,86143],{},[895,86124,86125,86127,86133,86135],{},[898,86126,2826],{},[2281,86128,86129,86131],{},[898,86130,3946],{},[898,86132,9801],{},[2005,86134,2007],{},[9172,86136,86137,86139,86141],{},[898,86138,2797],{},[898,86140,9801],{},[2005,86142,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,86144,86145],{"encoding":904},"MP_L = Q'_L",[38,86147,78002],{},[883,86149,86151],{"className":86150},[886],[888,86152,86153],{"xmlns":890},[892,86154,86155,86175],{},[895,86156,86157,86159,86165,86167],{},[898,86158,2826],{},[2281,86160,86161,86163],{},[898,86162,3946],{},[898,86164,9806],{},[2005,86166,2007],{},[9172,86168,86169,86171,86173],{},[898,86170,2797],{},[898,86172,9806],{},[2005,86174,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,86176,86177],{"encoding":904},"MP_K = Q'_K",[123,86179,86180,2212,86182,1644],{},[38,86181,80216],{},[883,86183,86185],{"className":86184},[886],[888,86186,86187],{"xmlns":890},[892,86188,86189,86227],{},[895,86190,86191,86193,86195,86197,86199,86205,86207,86209,86211,86213,86215,86221,86223,86225],{},[898,86192,2203],{},[898,86194,2797],{},[2005,86196,2007],{},[898,86198,2826],{},[2281,86200,86201,86203],{},[898,86202,3946],{},[898,86204,9801],{},[2297,86206,2995],{},[898,86208,2203],{},[898,86210,9801],{},[2005,86212,2104],{},[898,86214,2826],{},[2281,86216,86217,86219],{},[898,86218,3946],{},[898,86220,9806],{},[2297,86222,2995],{},[898,86224,2203],{},[898,86226,9806],{},[902,86228,86229],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,86231,86232,7021,86234,1644],{},[38,86233,80561],{},[883,86235,86237],{"className":86236},[886],[888,86238,86239],{"xmlns":890},[892,86240,86241,86283],{},[895,86242,86243,86245,86253,86255,86257,86265,86267,86269,86271,86273,86275,86277,86279,86281],{},[898,86244,9801],{},[9172,86246,86247,86249,86251],{},[898,86248,2797],{},[898,86250,9801],{},[2005,86252,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,86254,2104],{},[898,86256,9806],{},[9172,86258,86259,86261,86263],{},[898,86260,2797],{},[898,86262,9806],{},[2005,86264,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,86266,2007],{},[898,86268,36865],{},[2297,86270,2995],{},[898,86272,2797],{},[2005,86274,2014],{"stretchy":2013},[898,86276,9801],{},[2005,86278,2295],{"separator":2294},[898,86280,9806],{},[2005,86282,2020],{"stretchy":2013},[902,86284,86285],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,86287,86288,86291,86292,1644],{},[38,86289,86290],{},"Izokvanta"," — křivka ",[883,86293,86295],{"className":86294},[886],[888,86296,86297],{"xmlns":890},[892,86298,86299,86317],{},[895,86300,86301,86303,86305,86307,86309,86311,86313,86315],{},[898,86302,2797],{},[2005,86304,2014],{"stretchy":2013},[898,86306,9801],{},[2005,86308,2295],{"separator":2294},[898,86310,9806],{},[2005,86312,2020],{"stretchy":2013},[2005,86314,2007],{},[898,86316,80802],{},[902,86318,86319],{"encoding":904},"Q(L, K) = q",[123,86321,86322,2212,86324,1644],{},[38,86323,80991],{},[883,86325,86327],{"className":86326},[886],[888,86328,86329],{"xmlns":890},[892,86330,86331,86361],{},[895,86332,86333,86335,86337,86339,86341,86343,86345,86351,86353,86355],{},[898,86334,2826],{},[898,86336,4003],{},[898,86338,2783],{},[898,86340,8679],{},[2005,86342,2007],{},[898,86344,2826],{},[2281,86346,86347,86349],{},[898,86348,3946],{},[898,86350,9801],{},[898,86352,4680],{"mathvariant":2385},[898,86354,2826],{},[2281,86356,86357,86359],{},[898,86358,3946],{},[898,86360,9806],{},[902,86362,74810],{"encoding":904},[123,86364,86365,2212,86368,1644],{},[38,86366,86367],{},"Substituční vztah",[883,86369,86371],{"className":86370},[886],[888,86372,86373],{"xmlns":890},[892,86374,86375,86399],{},[895,86376,86377,86379,86381,86383,86385,86387,86389,86391,86393,86395,86397],{},[898,86378,2897],{"mathvariant":2385},[898,86380,9806],{},[2005,86382,2739],{},[2005,86384,2234],{},[898,86386,2826],{},[898,86388,4003],{},[898,86390,2783],{},[898,86392,8679],{},[2297,86394,2995],{},[898,86396,2203],{},[898,86398,9801],{},[902,86400,86401],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,86403,3800],{"id":3799},[120,86405,86406,86503,86510,86517],{},[123,86407,86408,2212,86410,86413,86414,1343,86417,86420,86421,86424,86425,86444,86445,18654,86464,86467,86468,86487,86488,3927],{},[38,86409,50728],{},[207,86411,784],{"className":86412,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,86415,2366],{"className":86416,"dataFsResolvedFilePath":764,"href":765},[210],[207,86418,793],{"className":86419,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,86422,880],{"className":86423,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,86426,86428],{"className":86427},[886],[888,86429,86430],{"xmlns":890},[892,86431,86432,86442],{},[895,86433,86434,86436,86438,86440],{},[898,86435,2826],{},[898,86437,4003],{},[898,86439,2783],{},[898,86441,8679],{},[902,86443,10603],{"encoding":904}," ↔ ",[883,86446,86448],{"className":86447},[886],[888,86449,86450],{"xmlns":890},[892,86451,86452,86462],{},[895,86453,86454,86456,86458,86460],{},[898,86455,2826],{},[898,86457,4003],{},[898,86459,1852],{},[898,86461,8679],{},[902,86463,10607],{"encoding":904},[207,86465,3831],{"className":86466,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,86469,86471],{"className":86470},[886],[888,86472,86473],{"xmlns":890},[892,86474,86475,86485],{},[895,86476,86477,86479],{},[898,86478,1836],{},[2281,86480,86481,86483],{},[898,86482,3946],{},[898,86484,9801],{},[902,86486,74638],{"encoding":904}," ↔ min ",[883,86489,86491],{"className":86490},[886],[888,86492,86493],{"xmlns":890},[892,86494,86495,86501],{},[895,86496,86497,86499],{},[898,86498,1836],{},[898,86500,1852],{},[902,86502,55565],{"encoding":904},[123,86504,86505,2212,86507,1644],{},[38,86506,3807],{},[207,86508,3836],{"className":86509,"dataFsResolvedFilePath":848,"href":849},[210],[123,86511,86512,2212,86514,1644],{},[38,86513,16219],{},[207,86515,1094],{"className":86516,"dataFsResolvedFilePath":838,"href":839},[210],[123,86518,86519,2212,86521,1644],{},[38,86520,16210],{},[207,86522,16214],{"className":86523,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":86525},[86526,86527,86528,86532,86534,86539,86540,86547,86548,86550,86551,86552,86554,86559,86560,86561,86565,86566],{"id":74833,"depth":642,"text":74834},{"id":74970,"depth":642,"text":74971},{"id":75073,"depth":642,"text":86529,"children":86530},"Mezní produkt práce (MPLMP_L)",[86531],{"id":75519,"depth":649,"text":75520},{"id":76008,"depth":642,"text":86533},"Průměrný produkt práce (APLAP_L)",{"id":76126,"depth":642,"text":76127,"children":86535},[86536,86537,86538],{"id":76363,"depth":649,"text":65506},{"id":76674,"depth":649,"text":76675},{"id":77394,"depth":649,"text":77395},{"id":77966,"depth":642,"text":77967},{"id":78069,"depth":642,"text":78070,"children":86541},[86542,86543,86545,86546],{"id":78428,"depth":649,"text":78429},{"id":78927,"depth":649,"text":86544},"Parametr efektivity AA",{"id":78998,"depth":649,"text":78999},{"id":37184,"depth":649,"text":79338},{"id":79525,"depth":642,"text":79526},{"id":79864,"depth":642,"text":86549},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":80555,"depth":642,"text":80556},{"id":74899,"depth":642,"text":9784},{"id":80966,"depth":642,"text":86553},"Mezní míra technické substituce (MRTSMRTS)",{"id":81832,"depth":642,"text":81833,"children":86555},[86556,86557,86558],{"id":81836,"depth":649,"text":81837},{"id":82479,"depth":649,"text":82480},{"id":82760,"depth":649,"text":82761},{"id":83106,"depth":642,"text":83107},{"id":49886,"depth":642,"text":49887},{"id":83456,"depth":642,"text":83457,"children":86562},[86563,86564],{"id":40455,"depth":649,"text":40456},{"id":83975,"depth":649,"text":83976},{"id":15725,"depth":642,"text":15726},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Fprodukce",{"title":74469,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,1756,86573,86574,86575,74899,86576,86577],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":86580,"title":86581,"body":86582,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":95528,"navigation":664,"path":95529,"seo":95530,"sources":95531,"stem":95532,"tags":95533,"type":3865,"updated":677,"__hash__":95536},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":86583,"toc":95502},[86584,86587,86589,86786,86795,86799,86802,86854,86858,86870,86874,86877,86894,87017,87023,87167,87177,87181,87216,87254,87302,87359,87419,87461,88037,88041,88124,88233,88326,88584,88587,88640,88751,88833,88837,88848,89081,89136,89142,89182,89245,89256,89447,89553,89706,89754,89759,89873,89911,90037,90083,90110,90187,90262,90342,90472,90533,90621,90625,90628,90697,90780,90787,90847,91157,91161,91167,91220,91236,91287,91425,91501,91614,91931,91935,91942,92102,92161,92165,92187,92284,92405,92519,92542,92605,92662,92914,92922,92926,92933,93187,93237,93293,93296,93460,93464,93562,93564,93596,93600,93733,93975,94159,94327,94634,94767,94954,94966,94968,95403,95405],[12,86585,86581],{"id":86586},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,86588,12012],{"id":12011},[724,86590,86591,2212,86593,86624,86625,86628,86629,86659,86660,86678,86679,86719,86720,86723,86724,86737,86738,28258,86741,86754,86755,86768,86769,86782,86783,1644],{},[38,86592,880],{},[883,86594,86596],{"className":86595},[886],[888,86597,86598],{"xmlns":890},[892,86599,86600,86622],{},[895,86601,86602,86604,86606,86612,86614,86620],{},[898,86603,900],{},[2005,86605,2014],{"stretchy":2013},[2281,86607,86608,86610],{},[898,86609,2797],{},[2138,86611,2287],{},[2005,86613,2295],{"separator":2294},[2281,86615,86616,86618],{},[898,86617,2797],{},[2138,86619,2140],{},[2005,86621,2020],{"stretchy":2013},[902,86623,16350],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,86626,86627],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,86630,86632],{"className":86631},[886],[888,86633,86634],{"xmlns":890},[892,86635,86636,86656],{},[895,86637,86638,86640,86646,86648],{},[898,86639,2826],{},[2281,86641,86642,86644],{},[898,86643,900],{},[898,86645,17797],{},[2005,86647,2007],{},[9172,86649,86650,86652,86654],{},[898,86651,900],{},[898,86653,17797],{},[2005,86655,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,86657,86658],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,86661,86663],{"className":86662},[886],[888,86664,86665],{"xmlns":890},[892,86666,86667,86675],{},[895,86668,86669,86671,86673],{},[898,86670,900],{},[2005,86672,2007],{},[898,86674,2151],{},[902,86676,86677],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,86680,86682],{"className":86681},[886],[888,86683,86684],{"xmlns":890},[892,86685,86686,86716],{},[895,86687,86688,86690,86692,86694,86696,86698,86700,86706,86708,86710],{},[898,86689,2826],{},[898,86691,4003],{},[898,86693,1852],{},[898,86695,8679],{},[2005,86697,2007],{},[898,86699,2826],{},[2281,86701,86702,86704],{},[898,86703,900],{},[2138,86705,2287],{},[898,86707,4680],{"mathvariant":2385},[898,86709,2826],{},[2281,86711,86712,86714],{},[898,86713,900],{},[2138,86715,2140],{},[902,86717,86718],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,86721,86722],{},"teorii užitečnosti"," — funkce ",[883,86725,86727],{"className":86726},[886],[888,86728,86729],{"xmlns":890},[892,86730,86731,86735],{},[895,86732,86733],{},[898,86734,900],{},[902,86736,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,86739,86740],{},"Optimalizaci spotřebitele",[883,86742,86744],{"className":86743},[886],[888,86745,86746],{"xmlns":890},[892,86747,86748,86752],{},[895,86749,86750],{},[898,86751,900],{},[902,86753,900],{"encoding":904}," při rozpočtu, min ",[883,86756,86758],{"className":86757},[886],[888,86759,86760],{"xmlns":890},[892,86761,86762,86766],{},[895,86763,86764],{},[898,86765,1868],{},[902,86767,1868],{"encoding":904}," při dané ",[883,86770,86772],{"className":86771},[886],[888,86773,86774],{"xmlns":890},[892,86775,86776,86780],{},[895,86777,86778],{},[898,86779,900],{},[902,86781,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,86784,913],{"className":86785,"dataFsResolvedFilePath":911,"href":912},[210],[724,86787,86788,86789,86791,86792,1644],{},"Kapitola 6 knihy ",[614,86790,16214],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,86793,36759],{"className":86794,"dataFsResolvedFilePath":911,"href":912},[210],[115,86796,86798],{"id":86797},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,86800,86801],{},"Po prostudování této kapitoly byste měli umět:",[120,86803,86804,86809,86818,86823,86826,86832,86838,86841,86847],{},[123,86805,86806,86807,2295],{},"vyložit, co se rozumí termínem ",[38,86808,1759],{},[123,86810,86811,86812,3894,86815,2295],{},"definovat pojmy ",[38,86813,86814],{},"svazek zboží",[38,86816,86817],{},"funkce užitečnosti",[123,86819,74848,86820,74855],{},[38,86821,86822],{},"mezní užitečnosti",[123,86824,86825],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,86827,74875,86828,86831],{},[38,86829,86830],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,86833,74896,86834,86837],{},[38,86835,86836],{},"křivky užitečnosti"," (indiferenční křivky),",[123,86839,86840],{},"vyjmenovat jejich základní vlastnosti,",[123,86842,74848,86843,86846],{},[38,86844,86845],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,86848,86849,86850,86853],{},"řešit ",[38,86851,86852],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,86855,86857],{"id":86856},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,86859,86860,86861,86865,86866,86869],{},"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 ",[207,86862,86864],{"className":86863,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,86867,86868],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,86871,86873],{"id":86872},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,86875,86876],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,86878,86879,86885],{},[123,86880,86881,86884],{},[38,86882,86883],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,86886,86887,86890,86891,86893],{},[38,86888,86889],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,86892,86627],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[3876,86895,86896],{},[724,86897,86898,86900,86901,86904,86905,2212,86918,86921,86922,3894,86935,86954,86955,1343,86981,87008,87009,87012,87013,87016],{},[883,86899,4418],{}," Pozor — ordinalisté užitečnost ",[38,86902,86903],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,86906,86908],{"className":86907},[886],[888,86909,86910],{"xmlns":890},[892,86911,86912,86916],{},[895,86913,86914],{},[898,86915,900],{},[902,86917,900],{"encoding":904},[38,86919,86920],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,86923,86925],{"className":86924},[886],[888,86926,86927],{"xmlns":890},[892,86928,86929,86933],{},[895,86930,86931],{},[898,86932,900],{},[902,86934,900],{"encoding":904},[883,86936,86938],{"className":86937},[886],[888,86939,86940],{"xmlns":890},[892,86941,86942,86951],{},[895,86943,86944],{},[8392,86945,86946,86948],{"accent":2294},[898,86947,900],{},[2005,86949,86950],{},"~",[902,86952,86953],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,86956,86958],{"className":86957},[886],[888,86959,86960],{"xmlns":890},[892,86961,86962,86978],{},[895,86963,86964,86970,86972],{},[8392,86965,86966,86968],{"accent":2294},[898,86967,900],{},[2005,86969,86950],{},[2005,86971,2007],{},[2133,86973,86974,86976],{},[898,86975,900],{},[2138,86977,2140],{},[902,86979,86980],{"encoding":904},"\\tilde U = U^2",[883,86982,86984],{"className":86983},[886],[888,86985,86986],{"xmlns":890},[892,86987,86988,87005],{},[895,86989,86990,86996,86998,87001,87003],{},[8392,86991,86992,86994],{"accent":2294},[898,86993,900],{},[2005,86995,86950],{},[2005,86997,2007],{},[898,86999,87000],{},"ln",[2005,87002,56205],{},[898,87004,900],{},[902,87006,87007],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,87010,87011],{},"porovnání"," mezi svazky a ",[38,87014,87015],{},"poměry"," mezních veličin.",[724,87018,87019,87020,2713],{},"Ordinalistický přístup vychází z ",[38,87021,87022],{},"pěti hlavních předpokladů",[152,87024,87025,87031,87037,87155,87161],{},[123,87026,87027,87030],{},[38,87028,87029],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,87032,87033,87036],{},[38,87034,87035],{},"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.",[123,87038,87039,87042,87043,61746,87056,87069,87070,61746,87083,2935,87096,87099,87100,3894,87119,62575,87137,1644],{},[38,87040,87041],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,87044,87046],{"className":87045},[886],[888,87047,87048],{"xmlns":890},[892,87049,87050,87054],{},[895,87051,87052],{},[898,87053,1836],{},[902,87055,1836],{"encoding":904},[883,87057,87059],{"className":87058},[886],[888,87060,87061],{"xmlns":890},[892,87062,87063,87067],{},[895,87064,87065],{},[898,87066,1844],{},[902,87068,1844],{"encoding":904},", nebude jindy preferovat ",[883,87071,87073],{"className":87072},[886],[888,87074,87075],{"xmlns":890},[892,87076,87077,87081],{},[895,87078,87079],{},[898,87080,1844],{},[902,87082,1844],{"encoding":904},[883,87084,87086],{"className":87085},[886],[888,87087,87088],{"xmlns":890},[892,87089,87090,87094],{},[895,87091,87092],{},[898,87093,1836],{},[902,87095,1836],{"encoding":904},[38,87097,87098],{},"Tranzitivita",": pokud ",[883,87101,87103],{"className":87102},[886],[888,87104,87105],{"xmlns":890},[892,87106,87107,87116],{},[895,87108,87109,87111,87114],{},[898,87110,1836],{},[2005,87112,87113],{},"≻",[898,87115,1844],{},[902,87117,87118],{"encoding":904},"A \\succ B",[883,87120,87122],{"className":87121},[886],[888,87123,87124],{"xmlns":890},[892,87125,87126,87134],{},[895,87127,87128,87130,87132],{},[898,87129,1844],{},[2005,87131,87113],{},[898,87133,1852],{},[902,87135,87136],{"encoding":904},"B \\succ C",[883,87138,87140],{"className":87139},[886],[888,87141,87142],{"xmlns":890},[892,87143,87144,87152],{},[895,87145,87146,87148,87150],{},[898,87147,1836],{},[2005,87149,87113],{},[898,87151,1852],{},[902,87153,87154],{"encoding":904},"A \\succ C",[123,87156,87157,87160],{},[38,87158,87159],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,87162,87163,87166],{},[38,87164,87165],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,87168,87169,87170,87173,87174,1644],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,87171,87172],{},"preference"," a na příbuzné ",[614,87175,87176],{},"funkci užitečnosti",[115,87178,87180],{"id":87179},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,87182,87183,87184,87197,87198,87201,87202,87215],{},"Uvažujme ",[883,87185,87187],{"className":87186},[886],[888,87188,87189],{"xmlns":890},[892,87190,87191,87195],{},[895,87192,87193],{},[898,87194,36865],{},[902,87196,36865],{"encoding":904}," různých zboží. ",[38,87199,87200],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,87203,87205],{"className":87204},[886],[888,87206,87207],{"xmlns":890},[892,87208,87209,87213],{},[895,87210,87211],{},[898,87212,36865],{},[902,87214,36865],{"encoding":904},"-tice",[724,87217,87218],{},[883,87219,87221],{"className":87220},[886],[888,87222,87223],{"xmlns":890},[892,87224,87225,87251],{},[895,87226,87227,87229,87235,87237,87239,87241,87247,87249],{},[2005,87228,2014],{"stretchy":2013},[2281,87230,87231,87233],{},[898,87232,2797],{},[2138,87234,2287],{},[2005,87236,2295],{"separator":2294},[2005,87238,9652],{},[2005,87240,2295],{"separator":2294},[2281,87242,87243,87245],{},[898,87244,2797],{},[898,87246,36865],{},[2005,87248,2020],{"stretchy":2013},[2005,87250,2295],{"separator":2294},[902,87252,87253],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,87255,4316,87256,87273,87274,87287,87288,87291,87292,87295,87296,87299,87300,2713],{},[883,87257,87259],{"className":87258},[886],[888,87260,87261],{"xmlns":890},[892,87262,87263,87271],{},[895,87264,87265],{},[2281,87266,87267,87269],{},[898,87268,2797],{},[898,87270,17797],{},[902,87272,47543],{"encoding":904}," značí množství ",[883,87275,87277],{"className":87276},[886],[888,87278,87279],{"xmlns":890},[892,87280,87281,87285],{},[895,87282,87283],{},[898,87284,17797],{},[902,87286,17797],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,87289,87290],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,87293,87294],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,87297,87298],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,87301,87176],{},[883,87303,87305],{"className":87304},[886],[888,87306,87307],{"xmlns":890,"display":28071},[892,87308,87309,87356],{},[20760,87310,87311],{"width":28076},[20765,87312,87313,87315,87349,87351],{},[20768,87314],{"width":28081},[20768,87316,87317],{},[895,87318,87319,87321,87323,87325,87327,87333,87335,87337,87339,87345,87347],{},[898,87320,900],{},[2005,87322,2007],{},[898,87324,900],{},[2005,87326,2014],{"stretchy":2013},[2281,87328,87329,87331],{},[898,87330,2797],{},[2138,87332,2287],{},[2005,87334,2295],{"separator":2294},[2005,87336,9652],{},[2005,87338,2295],{"separator":2294},[2281,87340,87341,87343],{},[898,87342,2797],{},[898,87344,36865],{},[2005,87346,2020],{"stretchy":2013},[2005,87348,2295],{"separator":2294},[20768,87350],{"width":28081},[20768,87352,87353],{},[2297,87354,87355],{},"(6.1)",[902,87357,87358],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,87360,4316,87361,87391,87392,87414,87415,87418],{},[883,87362,87364],{"className":87363},[886],[888,87365,87366],{"xmlns":890},[892,87367,87368,87388],{},[895,87369,87370,87376,87378,87380,87382],{},[2281,87371,87372,87374],{},[898,87373,2797],{},[2138,87375,2287],{},[2005,87377,2295],{"separator":2294},[2005,87379,9652],{},[2005,87381,2295],{"separator":2294},[2281,87383,87384,87386],{},[898,87385,2797],{},[898,87387,36865],{},[902,87389,87390],{"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 ",[883,87393,87395],{"className":87394},[886],[888,87396,87397],{"xmlns":890},[892,87398,87399,87411],{},[895,87400,87401,87403,87405],{},[898,87402,900],{},[2005,87404,2295],{"separator":2294},[8392,87406,87407,87409],{"accent":2294},[898,87408,900],{},[2005,87410,86950],{},[902,87412,87413],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,87416,87417],{},"monotónní transformace"," zachovávající pořadí.",[724,87420,87421,87422,7021,87425,1644],{},"Dále se omezíme na funkce pro ",[38,87423,87424],{},"dvě zboží",[883,87426,87428],{"className":87427},[886],[888,87429,87430],{"xmlns":890},[892,87431,87432,87458],{},[895,87433,87434,87436,87438,87440,87442,87448,87450,87456],{},[898,87435,900],{},[2005,87437,2007],{},[898,87439,900],{},[2005,87441,2014],{"stretchy":2013},[2281,87443,87444,87446],{},[898,87445,2797],{},[2138,87447,2287],{},[2005,87449,2295],{"separator":2294},[2281,87451,87452,87454],{},[898,87453,2797],{},[2138,87455,2140],{},[2005,87457,2020],{"stretchy":2013},[902,87459,87460],{"encoding":904},"U = U(Q_1, Q_2)",[3876,87462,87463,87538],{},[724,87464,87465,87467,87468,2713],{},[883,87466,52700],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,87469,87471],{"className":87470},[886],[888,87472,87473],{"xmlns":890},[892,87474,87475,87535],{},[895,87476,87477,87479,87481,87483,87485,87491,87493,87499,87501,87507,87509,87511,87513],{},[898,87478,900],{},[2005,87480,2007],{},[898,87482,900],{},[2005,87484,2014],{"stretchy":2013},[2281,87486,87487,87489],{},[898,87488,2797],{},[2138,87490,2287],{},[2005,87492,2295],{"separator":2294},[2281,87494,87495,87497],{},[898,87496,2797],{},[2138,87498,2140],{},[2005,87500,2295],{"separator":2294},[2281,87502,87503,87505],{},[898,87504,2797],{},[2138,87506,2182],{},[2005,87508,2020],{"stretchy":2013},[2005,87510,2007],{},[2138,87512,2140],{},[8123,87514,87515],{},[895,87516,87517,87523,87529],{},[2281,87518,87519,87521],{},[898,87520,2797],{},[2138,87522,2287],{},[2281,87524,87525,87527],{},[898,87526,2797],{},[2138,87528,2140],{},[2281,87530,87531,87533],{},[898,87532,2797],{},[2138,87534,2182],{},[902,87536,87537],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,87539,87540,87733],{},[123,87541,87542,87543,87569,87570,12944,87596,3894,87655,5595,87715,8431],{},"svazek ",[883,87544,87546],{"className":87545},[886],[888,87547,87548],{"xmlns":890},[892,87549,87550,87566],{},[895,87551,87552,87554,87556,87558,87560,87562,87564],{},[2005,87553,2014],{"stretchy":2013},[2138,87555,41867],{},[2005,87557,2295],{"separator":2294},[2138,87559,2360],{},[2005,87561,2295],{"separator":2294},[2138,87563,41845],{},[2005,87565,2020],{"stretchy":2013},[902,87567,87568],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,87571,87573],{"className":87572},[886],[888,87574,87575],{"xmlns":890},[892,87576,87577,87593],{},[895,87578,87579,87581,87583,87585,87587,87589,87591],{},[2005,87580,2014],{"stretchy":2013},[2138,87582,4008],{},[2005,87584,2295],{"separator":2294},[2138,87586,4008],{},[2005,87588,2295],{"separator":2294},[2138,87590,66602],{},[2005,87592,2020],{"stretchy":2013},[902,87594,87595],{"encoding":904},"(9, 9, 27)",[883,87597,87599],{"className":87598},[886],[888,87600,87601],{"xmlns":890},[892,87602,87603,87652],{},[895,87604,87605,87607,87609,87611,87613,87615,87617,87619,87621,87623,87625,87639,87641,87643,87648,87650],{},[898,87606,900],{},[2005,87608,2014],{"stretchy":2013},[2138,87610,41867],{},[2005,87612,2295],{"separator":2294},[2138,87614,2360],{},[2005,87616,2295],{"separator":2294},[2138,87618,41845],{},[2005,87620,2020],{"stretchy":2013},[2005,87622,2007],{},[2138,87624,2140],{},[8123,87626,87627],{},[895,87628,87629,87631,87633,87635,87637],{},[2138,87630,41867],{},[2005,87632,3185],{},[2138,87634,2360],{},[2005,87636,3185],{},[2138,87638,41845],{},[2005,87640,2007],{},[2138,87642,2140],{},[8123,87644,87645],{},[2138,87646,87647],{},"4096",[2005,87649,2007],{},[2138,87651,5623],{},[902,87653,87654],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,87656,87658],{"className":87657},[886],[888,87659,87660],{"xmlns":890},[892,87661,87662,87712],{},[895,87663,87664,87666,87668,87670,87672,87674,87676,87678,87680,87682,87684,87698,87700,87702,87707,87709],{},[898,87665,900],{},[2005,87667,2014],{"stretchy":2013},[2138,87669,4008],{},[2005,87671,2295],{"separator":2294},[2138,87673,4008],{},[2005,87675,2295],{"separator":2294},[2138,87677,66602],{},[2005,87679,2020],{"stretchy":2013},[2005,87681,2007],{},[2138,87683,2140],{},[8123,87685,87686],{},[895,87687,87688,87690,87692,87694,87696],{},[2138,87689,4008],{},[2005,87691,3185],{},[2138,87693,4008],{},[2005,87695,3185],{},[2138,87697,66602],{},[2005,87699,2007],{},[2138,87701,2140],{},[8123,87703,87704],{},[2138,87705,87706],{},"2187",[2005,87708,5906],{},[2138,87710,87711],{},"93,53",[902,87713,87714],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,87716,87718],{"className":87717},[886],[888,87719,87720],{"xmlns":890},[892,87721,87722,87730],{},[895,87723,87724,87726,87728],{},[2138,87725,5623],{},[2005,87727,3416],{},[2138,87729,87711],{},[902,87731,87732],{"encoding":904},"128 > 93{,}53",[123,87734,87735,87736,3894,87762,87788,87789,3894,87829,87870,87871,87917,87918,3894,87944,2853,87970,3894,87988,88006,88007,1644],{},"svazky ",[883,87737,87739],{"className":87738},[886],[888,87740,87741],{"xmlns":890},[892,87742,87743,87759],{},[895,87744,87745,87747,87749,87751,87753,87755,87757],{},[2005,87746,2014],{"stretchy":2013},[2138,87748,2360],{},[2005,87750,2295],{"separator":2294},[2138,87752,5591],{},[2005,87754,2295],{"separator":2294},[2138,87756,2140],{},[2005,87758,2020],{"stretchy":2013},[902,87760,87761],{"encoding":904},"(4, 8, 2)",[883,87763,87765],{"className":87764},[886],[888,87766,87767],{"xmlns":890},[892,87768,87769,87785],{},[895,87770,87771,87773,87775,87777,87779,87781,87783],{},[2005,87772,2014],{"stretchy":2013},[2138,87774,41845],{},[2005,87776,2295],{"separator":2294},[2138,87778,2287],{},[2005,87780,2295],{"separator":2294},[2138,87782,2360],{},[2005,87784,2020],{"stretchy":2013},[902,87786,87787],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,87790,87792],{"className":87791},[886],[888,87793,87794],{"xmlns":890},[892,87795,87796,87826],{},[895,87797,87798,87800,87802,87804,87806,87808,87810,87812,87814,87816,87818,87822,87824],{},[898,87799,900],{},[2005,87801,2014],{"stretchy":2013},[2138,87803,2360],{},[2005,87805,2295],{"separator":2294},[2138,87807,5591],{},[2005,87809,2295],{"separator":2294},[2138,87811,2140],{},[2005,87813,2020],{"stretchy":2013},[2005,87815,2007],{},[2138,87817,2140],{},[8123,87819,87820],{},[2138,87821,41845],{},[2005,87823,2007],{},[2138,87825,41867],{},[902,87827,87828],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,87830,87832],{"className":87831},[886],[888,87833,87834],{"xmlns":890},[892,87835,87836,87867],{},[895,87837,87838,87840,87842,87844,87846,87848,87850,87852,87854,87856,87858,87863,87865],{},[898,87839,900],{},[2005,87841,2014],{"stretchy":2013},[2138,87843,41845],{},[2005,87845,2295],{"separator":2294},[2138,87847,2287],{},[2005,87849,2295],{"separator":2294},[2138,87851,2360],{},[2005,87853,2020],{"stretchy":2013},[2005,87855,2007],{},[2138,87857,2140],{},[8123,87859,87860],{},[2138,87861,87862],{},"256",[2005,87864,2007],{},[2138,87866,72364],{},[902,87868,87869],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,87872,87874],{"className":87873},[886],[888,87875,87876],{"xmlns":890},[892,87877,87878,87914],{},[895,87879,87880,87882,87884,87886,87888,87890,87892,87894,87896,87898,87900,87902,87904,87906,87908,87910,87912],{},[898,87881,900],{},[2005,87883,2014],{"stretchy":2013},[2138,87885,2360],{},[2005,87887,2295],{"separator":2294},[2138,87889,5591],{},[2005,87891,2295],{"separator":2294},[2138,87893,2140],{},[2005,87895,2020],{"stretchy":2013},[2005,87897,2007],{},[898,87899,900],{},[2005,87901,2014],{"stretchy":2013},[2138,87903,41845],{},[2005,87905,2295],{"separator":2294},[2138,87907,2287],{},[2005,87909,2295],{"separator":2294},[2138,87911,2360],{},[2005,87913,2020],{"stretchy":2013},[902,87915,87916],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,87919,87921],{"className":87920},[886],[888,87922,87923],{"xmlns":890},[892,87924,87925,87941],{},[895,87926,87927,87929,87931,87933,87935,87937,87939],{},[2138,87928,2360],{},[2005,87930,3185],{},[2138,87932,5591],{},[2005,87934,3185],{},[2138,87936,2140],{},[2005,87938,2007],{},[2138,87940,41845],{},[902,87942,87943],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,87945,87947],{"className":87946},[886],[888,87948,87949],{"xmlns":890},[892,87950,87951,87967],{},[895,87952,87953,87955,87957,87959,87961,87963,87965],{},[2138,87954,41845],{},[2005,87956,3185],{},[2138,87958,2287],{},[2005,87960,3185],{},[2138,87962,2360],{},[2005,87964,2007],{},[2138,87966,87862],{},[902,87968,87969],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,87971,87973],{"className":87972},[886],[888,87974,87975],{"xmlns":890},[892,87976,87977,87985],{},[895,87978,87979,87981,87983],{},[898,87980,900],{},[2005,87982,2007],{},[2138,87984,41867],{},[902,87986,87987],{"encoding":904},"U = 16",[883,87989,87991],{"className":87990},[886],[888,87992,87993],{"xmlns":890},[892,87994,87995,88003],{},[895,87996,87997,87999,88001],{},[898,87998,900],{},[2005,88000,2007],{},[2138,88002,72364],{},[902,88004,88005],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,88008,88010],{"className":88009},[886],[888,88011,88012],{"xmlns":890},[892,88013,88014,88034],{},[895,88015,88016,88022,88028],{},[2281,88017,88018,88020],{},[898,88019,2797],{},[2138,88021,2287],{},[2281,88023,88024,88026],{},[898,88025,2797],{},[2138,88027,2140],{},[2281,88029,88030,88032],{},[898,88031,2797],{},[2138,88033,2182],{},[902,88035,88036],{"encoding":904},"Q_1 Q_2 Q_3",[115,88038,88040],{"id":88039},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,88042,88043,88044,8108,88079,2212,88082,41819,88099,10030,88116,88119,88120,88123],{},"Pro funkci užitečnosti ",[883,88045,88047],{"className":88046},[886],[888,88048,88049],{"xmlns":890},[892,88050,88051,88077],{},[895,88052,88053,88055,88057,88059,88061,88067,88069,88075],{},[898,88054,900],{},[2005,88056,2007],{},[898,88058,900],{},[2005,88060,2014],{"stretchy":2013},[2281,88062,88063,88065],{},[898,88064,2797],{},[2138,88066,2287],{},[2005,88068,2295],{"separator":2294},[2281,88070,88071,88073],{},[898,88072,2797],{},[2138,88074,2140],{},[2005,88076,2020],{"stretchy":2013},[902,88078,87460],{"encoding":904},[38,88080,88081],{},"mezní užitečnost",[883,88083,88085],{"className":88084},[886],[888,88086,88087],{"xmlns":890},[892,88088,88089,88097],{},[895,88090,88091],{},[2281,88092,88093,88095],{},[898,88094,2797],{},[2138,88096,2287],{},[902,88098,29007],{"encoding":904},[883,88100,88102],{"className":88101},[886],[888,88103,88104],{"xmlns":890},[892,88105,88106,88114],{},[895,88107,88108],{},[2281,88109,88110,88112],{},[898,88111,2797],{},[2138,88113,2140],{},[902,88115,29026],{"encoding":904},[38,88117,88118],{},"marginal utility",") parciální ",[207,88121,1145],{"className":88122,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,88125,88127],{"className":88126},[886],[888,88128,88129],{"xmlns":890,"display":28071},[892,88130,88131,88230],{},[20760,88132,88133],{"width":28076},[20765,88134,88135,88137,88223,88225],{},[20768,88136],{"width":28081},[20768,88138,88139],{},[895,88140,88141,88143,88149,88151,88159,88161,88179,88181,88183,88185,88191,88193,88201,88203,88221],{},[898,88142,2826],{},[2281,88144,88145,88147],{},[898,88146,900],{},[2138,88148,2287],{},[2005,88150,2007],{},[9172,88152,88153,88155,88157],{},[898,88154,900],{},[2138,88156,2287],{},[2005,88158,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,88160,2007],{},[2338,88162,88163,88169],{},[895,88164,88165,88167],{},[898,88166,9877],{"mathvariant":2385},[898,88168,900],{},[895,88170,88171,88173],{},[898,88172,9877],{"mathvariant":2385},[2281,88174,88175,88177],{},[898,88176,2797],{},[2138,88178,2287],{},[2005,88180,2295],{"separator":2294},[5884,88182],{"width":15290},[898,88184,2826],{},[2281,88186,88187,88189],{},[898,88188,900],{},[2138,88190,2140],{},[2005,88192,2007],{},[9172,88194,88195,88197,88199],{},[898,88196,900],{},[2138,88198,2140],{},[2005,88200,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,88202,2007],{},[2338,88204,88205,88211],{},[895,88206,88207,88209],{},[898,88208,9877],{"mathvariant":2385},[898,88210,900],{},[895,88212,88213,88215],{},[898,88214,9877],{"mathvariant":2385},[2281,88216,88217,88219],{},[898,88218,2797],{},[2138,88220,2140],{},[898,88222,1644],{"mathvariant":2385},[20768,88224],{"width":28081},[20768,88226,88227],{},[2297,88228,88229],{},"(6.2)",[902,88231,88232],{"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}",[724,88234,88235,88236,88270,88271,88301,88302,2212,88305,1644],{},"Pro pevné ",[883,88237,88239],{"className":88238},[886],[888,88240,88241],{"xmlns":890},[892,88242,88243,88267],{},[895,88244,88245,88251,88253,88255,88257,88263,88265],{},[2281,88246,88247,88249],{},[898,88248,2797],{},[2138,88250,2287],{},[2005,88252,2007],{},[898,88254,207],{},[2005,88256,2295],{"separator":2294},[2281,88258,88259,88261],{},[898,88260,2797],{},[2138,88262,2140],{},[2005,88264,2007],{},[898,88266,2107],{},[902,88268,88269],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,88272,88274],{"className":88273},[886],[888,88275,88276],{"xmlns":890},[892,88277,88278,88298],{},[895,88279,88280,88282,88288,88290,88292,88294,88296],{},[898,88281,2826],{},[2281,88283,88284,88286],{},[898,88285,900],{},[2138,88287,2287],{},[2005,88289,2014],{"stretchy":2013},[898,88291,207],{},[2005,88293,2295],{"separator":2294},[898,88295,2107],{},[2005,88297,2020],{"stretchy":2013},[902,88299,88300],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,88303,88304],{},"v bodě (na hladině)",[883,88306,88308],{"className":88307},[886],[888,88309,88310],{"xmlns":890},[892,88311,88312,88324],{},[895,88313,88314,88316,88318,88320,88322],{},[2005,88315,2495],{"stretchy":2013},[898,88317,207],{},[2005,88319,2295],{"separator":2294},[898,88321,2107],{},[2005,88323,2510],{"stretchy":2013},[902,88325,10828],{"encoding":904},[3876,88327,88328],{},[724,88329,88330,88332,88333,88363,88392,88393,2619,88406,2633,88423,88444,88445,2680,88462,2694,88475,88492,88493,88515,88516,88545,88546,6479,88566,88583],{},[883,88331,4164],{}," Intuice — co říká ",[883,88334,88336],{"className":88335},[886],[888,88337,88338],{"xmlns":890},[892,88339,88340,88360],{},[895,88341,88342,88344,88350,88352,88354,88356,88358],{},[898,88343,2826],{},[2281,88345,88346,88348],{},[898,88347,900],{},[2138,88349,2287],{},[2005,88351,2014],{"stretchy":2013},[898,88353,207],{},[2005,88355,2295],{"separator":2294},[898,88357,2107],{},[2005,88359,2020],{"stretchy":2013},[902,88361,88362],{"encoding":904},"MU_1(a,b)",[883,88364,88366],{"className":88365},[886],[888,88367,88368],{"xmlns":890},[892,88369,88370,88390],{},[895,88371,88372,88374,88380,88382,88384,88386,88388],{},[898,88373,2826],{},[2281,88375,88376,88378],{},[898,88377,900],{},[2138,88379,2287],{},[2005,88381,2014],{"stretchy":2013},[898,88383,207],{},[2005,88385,2295],{"separator":2294},[898,88387,2107],{},[2005,88389,2020],{"stretchy":2013},[902,88391,88300],{"encoding":904}," je rychlost změny ",[883,88394,88396],{"className":88395},[886],[888,88397,88398],{"xmlns":890},[892,88399,88400,88404],{},[895,88401,88402],{},[898,88403,900],{},[902,88405,900],{"encoding":904},[883,88407,88409],{"className":88408},[886],[888,88410,88411],{"xmlns":890},[892,88412,88413,88421],{},[895,88414,88415],{},[2281,88416,88417,88419],{},[898,88418,2797],{},[2138,88420,2287],{},[902,88422,29007],{"encoding":904},[883,88424,88426],{"className":88425},[886],[888,88427,88428],{"xmlns":890},[892,88429,88430,88442],{},[895,88431,88432,88434,88436,88438,88440],{},[2005,88433,2495],{"stretchy":2013},[898,88435,207],{},[2005,88437,2295],{"separator":2294},[898,88439,2107],{},[2005,88441,2510],{"stretchy":2013},[902,88443,10828],{"encoding":904},". Přibližně: změní-li se ",[883,88446,88448],{"className":88447},[886],[888,88449,88450],{"xmlns":890},[892,88451,88452,88460],{},[895,88453,88454],{},[2281,88455,88456,88458],{},[898,88457,2797],{},[2138,88459,2287],{},[902,88461,29007],{"encoding":904},[883,88463,88465],{"className":88464},[886],[888,88466,88467],{"xmlns":890},[892,88468,88469,88473],{},[895,88470,88471],{},[898,88472,207],{},[902,88474,207],{"encoding":904},[883,88476,88478],{"className":88477},[886],[888,88479,88480],{"xmlns":890},[892,88481,88482,88490],{},[895,88483,88484,88486,88488],{},[898,88485,207],{},[2005,88487,2104],{},[2138,88489,2287],{},[902,88491,2712],{"encoding":904}," při pevném ",[883,88494,88496],{"className":88495},[886],[888,88497,88498],{"xmlns":890},[892,88499,88500,88512],{},[895,88501,88502,88508,88510],{},[2281,88503,88504,88506],{},[898,88505,2797],{},[2138,88507,2140],{},[2005,88509,2007],{},[898,88511,2107],{},[902,88513,88514],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,88517,88519],{"className":88518},[886],[888,88520,88521],{"xmlns":890},[892,88522,88523,88543],{},[895,88524,88525,88527,88533,88535,88537,88539,88541],{},[898,88526,2826],{},[2281,88528,88529,88531],{},[898,88530,900],{},[2138,88532,2287],{},[2005,88534,2014],{"stretchy":2013},[898,88536,207],{},[2005,88538,2295],{"separator":2294},[898,88540,2107],{},[2005,88542,2020],{"stretchy":2013},[902,88544,88300],{"encoding":904},". Stejně tak ",[883,88547,88549],{"className":88548},[886],[888,88550,88551],{"xmlns":890},[892,88552,88553,88563],{},[895,88554,88555,88557],{},[898,88556,2826],{},[2281,88558,88559,88561],{},[898,88560,900],{},[2138,88562,2140],{},[902,88564,88565],{"encoding":904},"MU_2",[883,88567,88569],{"className":88568},[886],[888,88570,88571],{"xmlns":890},[892,88572,88573,88581],{},[895,88574,88575],{},[2281,88576,88577,88579],{},[898,88578,2797],{},[2138,88580,2140],{},[902,88582,29026],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,88585,80216],{"id":88586},"totální-diferenciál",[724,88588,88589,88590,48345,88606,88636,88637,2713],{},"Přibližnou změnu užitečnosti ",[883,88591,88593],{"className":88592},[886],[888,88594,88595],{"xmlns":890},[892,88596,88597,88603],{},[895,88598,88599,88601],{},[898,88600,2897],{"mathvariant":2385},[898,88602,900],{},[902,88604,88605],{"encoding":904},"\\Delta U",[883,88607,88609],{"className":88608},[886],[888,88610,88611],{"xmlns":890},[892,88612,88613,88633],{},[895,88614,88615,88617,88623,88625,88627],{},[898,88616,2203],{"mathvariant":2385},[2281,88618,88619,88621],{},[898,88620,2797],{},[2138,88622,2287],{},[2005,88624,2295],{"separator":2294},[898,88626,2203],{"mathvariant":2385},[2281,88628,88629,88631],{},[898,88630,2797],{},[2138,88632,2140],{},[902,88634,88635],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,88638,88639],{},"totálního diferenciálu",[883,88641,88643],{"className":88642},[886],[888,88644,88645],{"xmlns":890,"display":28071},[892,88646,88647,88748],{},[20760,88648,88649],{"width":28076},[20765,88650,88651,88653,88741,88743],{},[20768,88652],{"width":28081},[20768,88654,88655],{},[895,88656,88657,88659,88661,88663,88665,88667,88669,88677,88679,88685,88687,88695,88697,88703,88705,88707,88713,88715,88721,88723,88725,88731,88733,88739],{},[898,88658,2897],{"mathvariant":2385},[898,88660,900],{},[2005,88662,2739],{},[898,88664,2203],{"mathvariant":2385},[898,88666,900],{},[2005,88668,2007],{},[9172,88670,88671,88673,88675],{},[898,88672,900],{},[2138,88674,2287],{},[2005,88676,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[898,88678,2203],{"mathvariant":2385},[2281,88680,88681,88683],{},[898,88682,2797],{},[2138,88684,2287],{},[2005,88686,2104],{},[9172,88688,88689,88691,88693],{},[898,88690,900],{},[2138,88692,2140],{},[2005,88694,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[898,88696,2203],{"mathvariant":2385},[2281,88698,88699,88701],{},[898,88700,2797],{},[2138,88702,2140],{},[2005,88704,2007],{},[898,88706,2826],{},[2281,88708,88709,88711],{},[898,88710,900],{},[2138,88712,2287],{},[898,88714,2203],{"mathvariant":2385},[2281,88716,88717,88719],{},[898,88718,2797],{},[2138,88720,2287],{},[2005,88722,2104],{},[898,88724,2826],{},[2281,88726,88727,88729],{},[898,88728,900],{},[2138,88730,2140],{},[898,88732,2203],{"mathvariant":2385},[2281,88734,88735,88737],{},[898,88736,2797],{},[2138,88738,2140],{},[898,88740,1644],{"mathvariant":2385},[20768,88742],{"width":28081},[20768,88744,88745],{},[2297,88746,88747],{},"(6.3)",[902,88749,88750],{"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}",[724,88752,75474,88753,1644],{},[883,88754,88756],{"className":88755},[886],[888,88757,88758],{"xmlns":890},[892,88759,88760,88830],{},[895,88761,88762,88764,88766,88768,88770,88772,88778,88780,88782,88788,88790,88796,88798,88800,88806,88808,88810,88812,88814,88820,88822,88828],{},[898,88763,2897],{"mathvariant":2385},[898,88765,900],{},[2005,88767,2007],{},[898,88769,900],{},[2005,88771,2014],{"stretchy":2013},[2281,88773,88774,88776],{},[898,88775,2797],{},[2138,88777,2287],{},[2005,88779,2104],{},[898,88781,2203],{"mathvariant":2385},[2281,88783,88784,88786],{},[898,88785,2797],{},[2138,88787,2287],{},[2005,88789,2295],{"separator":2294},[2281,88791,88792,88794],{},[898,88793,2797],{},[2138,88795,2140],{},[2005,88797,2104],{},[898,88799,2203],{"mathvariant":2385},[2281,88801,88802,88804],{},[898,88803,2797],{},[2138,88805,2140],{},[2005,88807,2020],{"stretchy":2013},[2005,88809,2234],{},[898,88811,900],{},[2005,88813,2014],{"stretchy":2013},[2281,88815,88816,88818],{},[898,88817,2797],{},[2138,88819,2287],{},[2005,88821,2295],{"separator":2294},[2281,88823,88824,88826],{},[898,88825,2797],{},[2138,88827,2140],{},[2005,88829,2020],{"stretchy":2013},[902,88831,88832],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,88834,88836],{"id":88835},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,88838,88839,88840,88843,88844,88847],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,88841,88842],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,88845,88846],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,88849,88850,88853,88854,41819,88880,88906,88907,1343,88939,88971,88972,3894,89026,89080],{},[38,88851,88852],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,88855,88857],{"className":88856},[886],[888,88858,88859],{"xmlns":890},[892,88860,88861,88877],{},[895,88862,88863,88869,88871],{},[2281,88864,88865,88867],{},[898,88866,2797],{},[2138,88868,2140],{},[2005,88870,2007],{},[2281,88872,88873,88875],{},[898,88874,207],{},[2138,88876,2336],{},[902,88878,88879],{"encoding":904},"Q_2 = a_0",[883,88881,88883],{"className":88882},[886],[888,88884,88885],{"xmlns":890},[892,88886,88887,88903],{},[895,88888,88889,88895,88897],{},[2281,88890,88891,88893],{},[898,88892,2797],{},[2138,88894,2287],{},[2005,88896,2007],{},[2281,88898,88899,88901],{},[898,88900,2107],{},[2138,88902,2336],{},[902,88904,88905],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,88908,88910],{"className":88909},[886],[888,88911,88912],{"xmlns":890},[892,88913,88914,88936],{},[895,88915,88916,88918,88920,88926,88928,88934],{},[898,88917,900],{},[2005,88919,2014],{"stretchy":2013},[2281,88921,88922,88924],{},[898,88923,2797],{},[2138,88925,2287],{},[2005,88927,2295],{"separator":2294},[2281,88929,88930,88932],{},[898,88931,207],{},[2138,88933,2336],{},[2005,88935,2020],{"stretchy":2013},[902,88937,88938],{"encoding":904},"U(Q_1, a_0)",[883,88940,88942],{"className":88941},[886],[888,88943,88944],{"xmlns":890},[892,88945,88946,88968],{},[895,88947,88948,88950,88952,88958,88960,88966],{},[898,88949,900],{},[2005,88951,2014],{"stretchy":2013},[2281,88953,88954,88956],{},[898,88955,2107],{},[2138,88957,2336],{},[2005,88959,2295],{"separator":2294},[2281,88961,88962,88964],{},[898,88963,2797],{},[2138,88965,2140],{},[2005,88967,2020],{"stretchy":2013},[902,88969,88970],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,88973,88975],{"className":88974},[886],[888,88976,88977],{"xmlns":890},[892,88978,88979,89023],{},[895,88980,88981,89019,89021],{},[2334,88982,88983],{"scriptlevel":2336,"displaystyle":2294},[2338,88984,88985,89009],{},[895,88986,88987,88989,88991,88993,88999,89001,89007],{},[898,88988,2203],{"mathvariant":2385},[898,88990,900],{},[2005,88992,2014],{"stretchy":2013},[2281,88994,88995,88997],{},[898,88996,2797],{},[2138,88998,2287],{},[2005,89000,2295],{"separator":2294},[2281,89002,89003,89005],{},[898,89004,207],{},[2138,89006,2336],{},[2005,89008,2020],{"stretchy":2013},[895,89010,89011,89013],{},[898,89012,2203],{"mathvariant":2385},[2281,89014,89015,89017],{},[898,89016,2797],{},[2138,89018,2287],{},[2005,89020,3416],{},[2138,89022,2336],{},[902,89024,89025],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,89027,89029],{"className":89028},[886],[888,89030,89031],{"xmlns":890},[892,89032,89033,89077],{},[895,89034,89035,89073,89075],{},[2334,89036,89037],{"scriptlevel":2336,"displaystyle":2294},[2338,89038,89039,89063],{},[895,89040,89041,89043,89045,89047,89053,89055,89061],{},[898,89042,2203],{"mathvariant":2385},[898,89044,900],{},[2005,89046,2014],{"stretchy":2013},[2281,89048,89049,89051],{},[898,89050,2107],{},[2138,89052,2336],{},[2005,89054,2295],{"separator":2294},[2281,89056,89057,89059],{},[898,89058,2797],{},[2138,89060,2140],{},[2005,89062,2020],{"stretchy":2013},[895,89064,89065,89067],{},[898,89066,2203],{"mathvariant":2385},[2281,89068,89069,89071],{},[898,89070,2797],{},[2138,89072,2140],{},[2005,89074,3416],{},[2138,89076,2336],{},[902,89078,89079],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,89082,89084],{"className":89083},[886],[888,89085,89086],{"xmlns":890,"display":28071},[892,89087,89088,89133],{},[20760,89089,89090],{"width":28076},[20765,89091,89092,89094,89126,89128],{},[20768,89093],{"width":28081},[20768,89095,89096],{},[895,89097,89098,89106,89108,89110,89112,89114,89122,89124],{},[9172,89099,89100,89102,89104],{},[898,89101,900],{},[2138,89103,2287],{},[2005,89105,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,89107,3416],{},[2138,89109,2336],{},[2005,89111,2295],{"separator":2294},[5884,89113],{"width":15290},[9172,89115,89116,89118,89120],{},[898,89117,900],{},[2138,89119,2140],{},[2005,89121,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,89123,3416],{},[2138,89125,12466],{},[20768,89127],{"width":28081},[20768,89129,89130],{},[2297,89131,89132],{},"(6.4)",[902,89134,89135],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,89137,89138,89139,89141],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,89140,52682],{}," — užitečnost roste s množstvím každého zboží.",[724,89143,89144,89147,89148,89178,89179,2713],{},[38,89145,89146],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,89149,89151],{"className":89150},[886],[888,89152,89153],{"xmlns":890},[892,89154,89155,89175],{},[895,89156,89157,89165,89167],{},[9172,89158,89159,89161,89163],{},[898,89160,900],{},[2138,89162,2287],{},[2005,89164,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,89166,2295],{"separator":2294},[9172,89168,89169,89171,89173],{},[898,89170,900],{},[2138,89172,2140],{},[2005,89174,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,89176,89177],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,89180,89181],{},"záporné",[883,89183,89185],{"className":89184},[886],[888,89186,89187],{"xmlns":890,"display":28071},[892,89188,89189,89242],{},[20760,89190,89191],{"width":28076},[20765,89192,89193,89195,89235,89237],{},[20768,89194],{"width":28081},[20768,89196,89197],{},[895,89198,89199,89211,89213,89215,89217,89219,89231,89233],{},[9172,89200,89201,89203,89205],{},[898,89202,900],{},[2138,89204,2912],{},[895,89206,89207,89209],{},[2005,89208,2387],{"mathvariant":2385},[2005,89210,2387],{"mathvariant":2385},[2005,89212,3455],{},[2138,89214,2336],{},[2005,89216,2295],{"separator":2294},[5884,89218],{"width":15290},[9172,89220,89221,89223,89225],{},[898,89222,900],{},[2138,89224,32551],{},[895,89226,89227,89229],{},[2005,89228,2387],{"mathvariant":2385},[2005,89230,2387],{"mathvariant":2385},[2005,89232,3455],{},[2138,89234,12466],{},[20768,89236],{"width":28081},[20768,89238,89239],{},[2297,89240,89241],{},"(6.5)",[902,89243,89244],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,89246,89247,89248,89251,89252,1644],{},"Podmínka (6.5) je známa jako ",[38,89249,89250],{},"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 ",[207,89253,89255],{"className":89254,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,89257,89258,89259,3894,89291,89323,89324,3894,89350,89376,89377,89405,89406,3894,89408,89410,89411,89446],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,89260,89262],{"className":89261},[886],[888,89263,89264],{"xmlns":890},[892,89265,89266,89288],{},[895,89267,89268,89270,89272,89278,89280,89286],{},[898,89269,900],{},[2005,89271,2014],{"stretchy":2013},[2281,89273,89274,89276],{},[898,89275,2797],{},[2138,89277,2287],{},[2005,89279,2295],{"separator":2294},[2281,89281,89282,89284],{},[898,89283,2107],{},[2138,89285,2336],{},[2005,89287,2020],{"stretchy":2013},[902,89289,89290],{"encoding":904},"U(Q_1, b_0)",[883,89292,89294],{"className":89293},[886],[888,89295,89296],{"xmlns":890},[892,89297,89298,89320],{},[895,89299,89300,89302,89304,89310,89312,89318],{},[898,89301,900],{},[2005,89303,2014],{"stretchy":2013},[2281,89305,89306,89308],{},[898,89307,207],{},[2138,89309,2336],{},[2005,89311,2295],{"separator":2294},[2281,89313,89314,89316],{},[898,89315,2797],{},[2138,89317,2140],{},[2005,89319,2020],{"stretchy":2013},[902,89321,89322],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,89325,89327],{"className":89326},[886],[888,89328,89329],{"xmlns":890},[892,89330,89331,89347],{},[895,89332,89333,89335,89337,89339,89345],{},[2005,89334,2014],{"stretchy":2013},[898,89336,900],{},[2005,89338,2295],{"separator":2294},[2281,89340,89341,89343],{},[898,89342,2797],{},[2138,89344,2287],{},[2005,89346,2020],{"stretchy":2013},[902,89348,89349],{"encoding":904},"(U, Q_1)",[883,89351,89353],{"className":89352},[886],[888,89354,89355],{"xmlns":890},[892,89356,89357,89373],{},[895,89358,89359,89361,89363,89365,89371],{},[2005,89360,2014],{"stretchy":2013},[898,89362,900],{},[2005,89364,2295],{"separator":2294},[2281,89366,89367,89369],{},[898,89368,2797],{},[2138,89370,2140],{},[2005,89372,2020],{"stretchy":2013},[902,89374,89375],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,89378,89380],{"className":89379},[886],[888,89381,89382],{"xmlns":890},[892,89383,89384,89402],{},[895,89385,89386,89388,89390,89392,89394,89396,89398,89400],{},[898,89387,900],{},[2005,89389,2014],{"stretchy":2013},[2138,89391,2336],{},[2005,89393,2295],{"separator":2294},[2138,89395,2336],{},[2005,89397,2020],{"stretchy":2013},[2005,89399,2007],{},[2138,89401,2336],{},[902,89403,89404],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,89407,13663],{},[38,89409,38493],{},". Typický tvar grafu ",[883,89412,89414],{"className":89413},[886],[888,89415,89416],{"xmlns":890},[892,89417,89418,89444],{},[895,89419,89420,89422,89424,89426,89428,89434,89436,89442],{},[898,89421,900],{},[2005,89423,2007],{},[898,89425,900],{},[2005,89427,2014],{"stretchy":2013},[2281,89429,89430,89432],{},[898,89431,2797],{},[2138,89433,2287],{},[2005,89435,2295],{"separator":2294},[2281,89437,89438,89440],{},[898,89439,2797],{},[2138,89441,2140],{},[2005,89443,2020],{"stretchy":2013},[902,89445,87460],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,89448,89449],{},[614,89450,89451,89452,88492,89480,89501,89502,88492,89530,89552],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,89453,89455],{"className":89454},[886],[888,89456,89457],{"xmlns":890},[892,89458,89459,89477],{},[895,89460,89461,89463,89465,89471,89473,89475],{},[898,89462,900],{},[2005,89464,2014],{"stretchy":2013},[2281,89466,89467,89469],{},[898,89468,2797],{},[2138,89470,2287],{},[2005,89472,2295],{"separator":2294},[898,89474,2107],{},[2005,89476,2020],{"stretchy":2013},[902,89478,89479],{"encoding":904},"U(Q_1, b)",[883,89481,89483],{"className":89482},[886],[888,89484,89485],{"xmlns":890},[892,89486,89487,89499],{},[895,89488,89489,89495,89497],{},[2281,89490,89491,89493],{},[898,89492,2797],{},[2138,89494,2140],{},[2005,89496,2007],{},[898,89498,2107],{},[902,89500,88514],{"encoding":904}," (vlevo) a ",[883,89503,89505],{"className":89504},[886],[888,89506,89507],{"xmlns":890},[892,89508,89509,89527],{},[895,89510,89511,89513,89515,89517,89519,89525],{},[898,89512,900],{},[2005,89514,2014],{"stretchy":2013},[898,89516,207],{},[2005,89518,2295],{"separator":2294},[2281,89520,89521,89523],{},[898,89522,2797],{},[2138,89524,2140],{},[2005,89526,2020],{"stretchy":2013},[902,89528,89529],{"encoding":904},"U(a, Q_2)",[883,89531,89533],{"className":89532},[886],[888,89534,89535],{"xmlns":890},[892,89536,89537,89549],{},[895,89538,89539,89545,89547],{},[2281,89540,89541,89543],{},[898,89542,2797],{},[2138,89544,2287],{},[2005,89546,2007],{},[898,89548,207],{},[902,89550,89551],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,89554,89555],{},[614,89556,89557,89558,89593,89594,89624,89625,3894,89648,89670,89671,1644],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,89559,89561],{"className":89560},[886],[888,89562,89563],{"xmlns":890},[892,89564,89565,89591],{},[895,89566,89567,89569,89571,89573,89575,89581,89583,89589],{},[898,89568,900],{},[2005,89570,2007],{},[898,89572,900],{},[2005,89574,2014],{"stretchy":2013},[2281,89576,89577,89579],{},[898,89578,2797],{},[2138,89580,2287],{},[2005,89582,2295],{"separator":2294},[2281,89584,89585,89587],{},[898,89586,2797],{},[2138,89588,2140],{},[2005,89590,2020],{"stretchy":2013},[902,89592,87460],{"encoding":904}," nad rovinou ",[883,89595,89597],{"className":89596},[886],[888,89598,89599],{"xmlns":890},[892,89600,89601,89621],{},[895,89602,89603,89605,89611,89613,89619],{},[2005,89604,2014],{"stretchy":2013},[2281,89606,89607,89609],{},[898,89608,2797],{},[2138,89610,2287],{},[2005,89612,2295],{"separator":2294},[2281,89614,89615,89617],{},[898,89616,2797],{},[2138,89618,2140],{},[2005,89620,2020],{"stretchy":2013},[902,89622,89623],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,89626,89628],{"className":89627},[886],[888,89629,89630],{"xmlns":890},[892,89631,89632,89645],{},[895,89633,89634,89640,89642],{},[2281,89635,89636,89638],{},[898,89637,2797],{},[2138,89639,2287],{},[2005,89641,2007],{},[2297,89643,89644],{},"const",[902,89646,89647],{"encoding":904},"Q_1 = \\text{const}",[883,89649,89651],{"className":89650},[886],[888,89652,89653],{"xmlns":890},[892,89654,89655,89667],{},[895,89656,89657,89663,89665],{},[2281,89658,89659,89661],{},[898,89660,2797],{},[2138,89662,2140],{},[2005,89664,2007],{},[2297,89666,89644],{},[902,89668,89669],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,89672,89674],{"className":89673},[886],[888,89675,89676],{"xmlns":890},[892,89677,89678,89704],{},[895,89679,89680,89682,89684,89690,89692,89698,89700,89702],{},[898,89681,900],{},[2005,89683,2014],{"stretchy":2013},[2281,89685,89686,89688],{},[898,89687,2797],{},[2138,89689,2287],{},[2005,89691,2295],{"separator":2294},[2281,89693,89694,89696],{},[898,89695,2797],{},[2138,89697,2140],{},[2005,89699,2020],{"stretchy":2013},[2005,89701,2007],{},[898,89703,2151],{},[902,89705,9774],{"encoding":904},[198,89707,89709,89710],{"id":89708},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,89711,89713],{"className":89712},[886],[888,89714,89715],{"xmlns":890},[892,89716,89717,89751],{},[895,89718,89719,89721,89723,89737],{},[898,89720,900],{},[2005,89722,2007],{},[9172,89724,89725,89727,89729],{},[898,89726,2797],{},[2138,89728,2287],{},[895,89730,89731,89733,89735],{},[2138,89732,2287],{},[898,89734,4680],{"mathvariant":2385},[2138,89736,2140],{},[9172,89738,89739,89741,89743],{},[898,89740,2797],{},[2138,89742,2140],{},[895,89744,89745,89747,89749],{},[2138,89746,2287],{},[898,89748,4680],{"mathvariant":2385},[2138,89750,2182],{},[902,89752,89753],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,89755,89756],{},[38,89757,89758],{},"Ověření (6.4) a (6.5).",[883,89760,89762],{"className":89761},[886],[888,89763,89764],{"xmlns":890,"display":28071},[892,89765,89766,89870],{},[895,89767,89768,89776,89778,89786,89802,89816,89818,89820,89828,89830,89838,89852,89868],{},[9172,89769,89770,89772,89774],{},[898,89771,900],{},[2138,89773,2287],{},[2005,89775,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,89777,2007],{},[2334,89779,89780],{"scriptlevel":2336,"displaystyle":2013},[2338,89781,89782,89784],{},[2138,89783,2287],{},[2138,89785,2140],{},[9172,89787,89788,89790,89792],{},[898,89789,2797],{},[2138,89791,2287],{},[895,89793,89794,89796,89798,89800],{},[2005,89795,2234],{},[2138,89797,2287],{},[898,89799,4680],{"mathvariant":2385},[2138,89801,2140],{},[9172,89803,89804,89806,89808],{},[898,89805,2797],{},[2138,89807,2140],{},[895,89809,89810,89812,89814],{},[2138,89811,2287],{},[898,89813,4680],{"mathvariant":2385},[2138,89815,2182],{},[2005,89817,2295],{"separator":2294},[5884,89819],{"width":15290},[9172,89821,89822,89824,89826],{},[898,89823,900],{},[2138,89825,2140],{},[2005,89827,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,89829,2007],{},[2334,89831,89832],{"scriptlevel":2336,"displaystyle":2013},[2338,89833,89834,89836],{},[2138,89835,2287],{},[2138,89837,2182],{},[9172,89839,89840,89842,89844],{},[898,89841,2797],{},[2138,89843,2287],{},[895,89845,89846,89848,89850],{},[2138,89847,2287],{},[898,89849,4680],{"mathvariant":2385},[2138,89851,2140],{},[9172,89853,89854,89856,89858],{},[898,89855,2797],{},[2138,89857,2140],{},[895,89859,89860,89862,89864,89866],{},[2005,89861,2234],{},[2138,89863,2140],{},[898,89865,4680],{"mathvariant":2385},[2138,89867,2182],{},[2005,89869,2295],{"separator":2294},[902,89871,89872],{"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},",[724,89874,89875,89876,89910],{},"zřejmě ",[883,89877,89879],{"className":89878},[886],[888,89880,89881],{"xmlns":890},[892,89882,89883,89907],{},[895,89884,89885,89893,89895,89903,89905],{},[9172,89886,89887,89889,89891],{},[898,89888,900],{},[2138,89890,2287],{},[2005,89892,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,89894,2295],{"separator":2294},[9172,89896,89897,89899,89901],{},[898,89898,900],{},[2138,89900,2140],{},[2005,89902,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,89904,3416],{},[2138,89906,2336],{},[902,89908,89909],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,89912,89914],{"className":89913},[886],[888,89915,89916],{"xmlns":890,"display":28071},[892,89917,89918,90034],{},[895,89919,89920,89932,89934,89936,89944,89960,89974,89976,89978,89990,89992,89994,90002,90016,90032],{},[9172,89921,89922,89924,89926],{},[898,89923,900],{},[2138,89925,2912],{},[895,89927,89928,89930],{},[2005,89929,2387],{"mathvariant":2385},[2005,89931,2387],{"mathvariant":2385},[2005,89933,2007],{},[2005,89935,2234],{},[2334,89937,89938],{"scriptlevel":2336,"displaystyle":2013},[2338,89939,89940,89942],{},[2138,89941,2287],{},[2138,89943,2360],{},[9172,89945,89946,89948,89950],{},[898,89947,2797],{},[2138,89949,2287],{},[895,89951,89952,89954,89956,89958],{},[2005,89953,2234],{},[2138,89955,2182],{},[898,89957,4680],{"mathvariant":2385},[2138,89959,2140],{},[9172,89961,89962,89964,89966],{},[898,89963,2797],{},[2138,89965,2140],{},[895,89967,89968,89970,89972],{},[2138,89969,2287],{},[898,89971,4680],{"mathvariant":2385},[2138,89973,2182],{},[2005,89975,2295],{"separator":2294},[5884,89977],{"width":15290},[9172,89979,89980,89982,89984],{},[898,89981,900],{},[2138,89983,32551],{},[895,89985,89986,89988],{},[2005,89987,2387],{"mathvariant":2385},[2005,89989,2387],{"mathvariant":2385},[2005,89991,2007],{},[2005,89993,2234],{},[2334,89995,89996],{"scriptlevel":2336,"displaystyle":2013},[2338,89997,89998,90000],{},[2138,89999,2140],{},[2138,90001,4008],{},[9172,90003,90004,90006,90008],{},[898,90005,2797],{},[2138,90007,2287],{},[895,90009,90010,90012,90014],{},[2138,90011,2287],{},[898,90013,4680],{"mathvariant":2385},[2138,90015,2140],{},[9172,90017,90018,90020,90022],{},[898,90019,2797],{},[2138,90021,2140],{},[895,90023,90024,90026,90028,90030],{},[2005,90025,2234],{},[2138,90027,2237],{},[898,90029,4680],{"mathvariant":2385},[2138,90031,2182],{},[2005,90033,2295],{"separator":2294},[902,90035,90036],{"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},",[724,90038,90039,90040,90082],{},"opět ",[883,90041,90043],{"className":90042},[886],[888,90044,90045],{"xmlns":890},[892,90046,90047,90079],{},[895,90048,90049,90061,90063,90075,90077],{},[9172,90050,90051,90053,90055],{},[898,90052,900],{},[2138,90054,2912],{},[895,90056,90057,90059],{},[2005,90058,2387],{"mathvariant":2385},[2005,90060,2387],{"mathvariant":2385},[2005,90062,2295],{"separator":2294},[9172,90064,90065,90067,90069],{},[898,90066,900],{},[2138,90068,32551],{},[895,90070,90071,90073],{},[2005,90072,2387],{"mathvariant":2385},[2005,90074,2387],{"mathvariant":2385},[2005,90076,3455],{},[2138,90078,2336],{},[902,90080,90081],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,90084,90085],{},[38,90086,90087,90088,1644],{},"(a) Mezní užitečnosti v bodě ",[883,90089,90091],{"className":90090},[886],[888,90092,90093],{"xmlns":890},[892,90094,90095,90107],{},[895,90096,90097,90099,90101,90103,90105],{},[2005,90098,2495],{"stretchy":2013},[2138,90100,3098],{},[2005,90102,2295],{"separator":2294},[2138,90104,8383],{},[2005,90106,2510],{"stretchy":2013},[902,90108,90109],{"encoding":904},"[100, 200]",[883,90111,90113],{"className":90112},[886],[888,90114,90115],{"xmlns":890,"display":28071},[892,90116,90117,90184],{},[895,90118,90119,90121,90127,90129,90131,90133,90135,90137,90139,90147,90149,90163,90165,90177,90179,90182],{},[898,90120,2826],{},[2281,90122,90123,90125],{},[898,90124,900],{},[2138,90126,2287],{},[2005,90128,2014],{"stretchy":2013},[2138,90130,3098],{},[2005,90132,2295],{"separator":2294},[2138,90134,8383],{},[2005,90136,2020],{"stretchy":2013},[2005,90138,2007],{},[2334,90140,90141],{"scriptlevel":2336,"displaystyle":2013},[2338,90142,90143,90145],{},[2138,90144,2287],{},[2138,90146,2140],{},[2005,90148,3185],{},[2133,90150,90151,90153],{},[2138,90152,3098],{},[895,90154,90155,90157,90159,90161],{},[2005,90156,2234],{},[2138,90158,2287],{},[898,90160,4680],{"mathvariant":2385},[2138,90162,2140],{},[2005,90164,3185],{},[2133,90166,90167,90169],{},[2138,90168,8383],{},[895,90170,90171,90173,90175],{},[2138,90172,2287],{},[898,90174,4680],{"mathvariant":2385},[2138,90176,2182],{},[2005,90178,5906],{},[2138,90180,90181],{},"0,4204",[2005,90183,2295],{"separator":2294},[902,90185,90186],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,90188,90190],{"className":90189},[886],[888,90191,90192],{"xmlns":890,"display":28071},[892,90193,90194,90259],{},[895,90195,90196,90198,90204,90206,90208,90210,90212,90214,90216,90224,90226,90238,90240,90254,90256],{},[898,90197,2826],{},[2281,90199,90200,90202],{},[898,90201,900],{},[2138,90203,2140],{},[2005,90205,2014],{"stretchy":2013},[2138,90207,3098],{},[2005,90209,2295],{"separator":2294},[2138,90211,8383],{},[2005,90213,2020],{"stretchy":2013},[2005,90215,2007],{},[2334,90217,90218],{"scriptlevel":2336,"displaystyle":2013},[2338,90219,90220,90222],{},[2138,90221,2287],{},[2138,90223,2182],{},[2005,90225,3185],{},[2133,90227,90228,90230],{},[2138,90229,3098],{},[895,90231,90232,90234,90236],{},[2138,90233,2287],{},[898,90235,4680],{"mathvariant":2385},[2138,90237,2140],{},[2005,90239,3185],{},[2133,90241,90242,90244],{},[2138,90243,8383],{},[895,90245,90246,90248,90250,90252],{},[2005,90247,2234],{},[2138,90249,2140],{},[898,90251,4680],{"mathvariant":2385},[2138,90253,2182],{},[2005,90255,5906],{},[2138,90257,90258],{},"0,63067.",[902,90260,90261],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,90263,90264,2212,90266,90301,90302,90323,90324,90341],{},[614,90265,9222],{},[883,90267,90269],{"className":90268},[886],[888,90270,90271],{"xmlns":890},[892,90272,90273,90298],{},[895,90274,90275,90277,90283,90285,90287,90289,90291,90293,90295],{},[898,90276,2826],{},[2281,90278,90279,90281],{},[898,90280,900],{},[2138,90282,2140],{},[2005,90284,2014],{"stretchy":2013},[2138,90286,3098],{},[2005,90288,2295],{"separator":2294},[2138,90290,8383],{},[2005,90292,2020],{"stretchy":2013},[2005,90294,5906],{},[2138,90296,90297],{},"0,63067",[902,90299,90300],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,90303,90305],{"className":90304},[886],[888,90306,90307],{"xmlns":890},[892,90308,90309,90321],{},[895,90310,90311,90313,90315,90317,90319],{},[2005,90312,2495],{"stretchy":2013},[2138,90314,3098],{},[2005,90316,2295],{"separator":2294},[2138,90318,8383],{},[2005,90320,2510],{"stretchy":2013},[902,90322,90109],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,90325,90327],{"className":90326},[886],[888,90328,90329],{"xmlns":890},[892,90330,90331,90339],{},[895,90332,90333],{},[2281,90334,90335,90337],{},[898,90336,2797],{},[2138,90338,2140],{},[902,90340,29026],{"encoding":904}," přibližně o 0,63067.",[724,90343,90344,90363,90364,39189,90385,90402,90403,90429,90430,90447,90448,3159],{},[38,90345,90346,90347,90362],{},"(b) Odhad změny ",[883,90348,90350],{"className":90349},[886],[888,90351,90352],{"xmlns":890},[892,90353,90354,90360],{},[895,90355,90356,90358],{},[898,90357,2897],{"mathvariant":2385},[898,90359,900],{},[902,90361,88605],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,90365,90367],{"className":90366},[886],[888,90368,90369],{"xmlns":890},[892,90370,90371,90383],{},[895,90372,90373,90375,90377,90379,90381],{},[2005,90374,2495],{"stretchy":2013},[2138,90376,3098],{},[2005,90378,2295],{"separator":2294},[2138,90380,8383],{},[2005,90382,2510],{"stretchy":2013},[902,90384,90109],{"encoding":904},[883,90386,90388],{"className":90387},[886],[888,90389,90390],{"xmlns":890},[892,90391,90392,90400],{},[895,90393,90394],{},[2281,90395,90396,90398],{},[898,90397,2797],{},[2138,90399,2287],{},[902,90401,29007],{"encoding":904}," na 98 (tj. ",[883,90404,90406],{"className":90405},[886],[888,90407,90408],{"xmlns":890},[892,90409,90410,90426],{},[895,90411,90412,90414,90420,90422,90424],{},[898,90413,2203],{"mathvariant":2385},[2281,90415,90416,90418],{},[898,90417,2797],{},[2138,90419,2287],{},[2005,90421,2007],{},[2005,90423,2234],{},[2138,90425,2140],{},[902,90427,90428],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,90431,90433],{"className":90432},[886],[888,90434,90435],{"xmlns":890},[892,90436,90437,90445],{},[895,90438,90439],{},[2281,90440,90441,90443],{},[898,90442,2797],{},[2138,90444,2140],{},[902,90446,29026],{"encoding":904}," o 3 (tj. ",[883,90449,90451],{"className":90450},[886],[888,90452,90453],{"xmlns":890},[892,90454,90455,90469],{},[895,90456,90457,90459,90465,90467],{},[898,90458,2203],{"mathvariant":2385},[2281,90460,90461,90463],{},[898,90462,2797],{},[2138,90464,2140],{},[2005,90466,2007],{},[2138,90468,2182],{},[902,90470,90471],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,90473,90475],{"className":90474},[886],[888,90476,90477],{"xmlns":890,"display":28071},[892,90478,90479,90530],{},[895,90480,90481,90483,90485,90487,90489,90491,90493,90495,90497,90499,90501,90503,90505,90507,90509,90511,90513,90515,90517,90520,90522,90525,90527],{},[898,90482,2897],{"mathvariant":2385},[898,90484,900],{},[2005,90486,2739],{},[898,90488,2203],{"mathvariant":2385},[898,90490,900],{},[2005,90492,2007],{},[2138,90494,90181],{},[2005,90496,3185],{},[2005,90498,2014],{"stretchy":2013},[2005,90500,2234],{},[2138,90502,2140],{},[2005,90504,2020],{"stretchy":2013},[2005,90506,2104],{},[2138,90508,90297],{},[2005,90510,3185],{},[2138,90512,2182],{},[2005,90514,2007],{},[2005,90516,2234],{},[2138,90518,90519],{},"0,8408",[2005,90521,2104],{},[2138,90523,90524],{},"1,89201",[2005,90526,5906],{},[2138,90528,90529],{},"1,05.",[902,90531,90532],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,90534,90535,90536,90539,90540,90591,90592,1644],{},"Užitečnost se tedy zvýší přibližně o ",[38,90537,90538],{},"1,05",". Skutečná změna je ",[883,90541,90543],{"className":90542},[886],[888,90544,90545],{"xmlns":890},[892,90546,90547,90588],{},[895,90548,90549,90551,90553,90555,90557,90559,90562,90564,90567,90569,90571,90573,90575,90577,90579,90581,90583,90585],{},[898,90550,2897],{"mathvariant":2385},[898,90552,900],{},[2005,90554,2007],{},[898,90556,900],{},[2005,90558,2014],{"stretchy":2013},[2138,90560,90561],{},"98",[2005,90563,2295],{"separator":2294},[2138,90565,90566],{},"203",[2005,90568,2020],{"stretchy":2013},[2005,90570,2234],{},[898,90572,900],{},[2005,90574,2014],{"stretchy":2013},[2138,90576,3098],{},[2005,90578,2295],{"separator":2294},[2138,90580,8383],{},[2005,90582,2020],{"stretchy":2013},[2005,90584,5906],{},[2138,90586,90587],{},"1,031",[902,90589,90590],{"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 ",[883,90593,90595],{"className":90594},[886],[888,90596,90597],{"xmlns":890},[892,90598,90599,90619],{},[895,90600,90601,90603,90609,90611,90613],{},[898,90602,2203],{"mathvariant":2385},[2281,90604,90605,90607],{},[898,90606,2797],{},[2138,90608,2287],{},[2005,90610,2295],{"separator":2294},[898,90612,2203],{"mathvariant":2385},[2281,90614,90615,90617],{},[898,90616,2797],{},[2138,90618,2140],{},[902,90620,88635],{"encoding":904},[115,90622,90624],{"id":90623},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,90626,90627],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,90629,90631],{"className":90630},[886],[888,90632,90633],{"xmlns":890,"display":28071},[892,90634,90635,90694],{},[20760,90636,90637],{"width":28076},[20765,90638,90639,90641,90687,90689],{},[20768,90640],{"width":28081},[20768,90642,90643],{},[895,90644,90645,90647,90649,90655,90657,90663,90665,90667,90675,90677,90685],{},[898,90646,900],{},[2005,90648,2014],{"stretchy":2013},[2281,90650,90651,90653],{},[898,90652,2797],{},[2138,90654,2287],{},[2005,90656,2295],{"separator":2294},[2281,90658,90659,90661],{},[898,90660,2797],{},[2138,90662,2140],{},[2005,90664,2020],{"stretchy":2013},[2005,90666,2007],{},[9172,90668,90669,90671,90673],{},[898,90670,2797],{},[2138,90672,2287],{},[898,90674,207],{},[2005,90676,3185],{},[9172,90678,90679,90681,90683],{},[898,90680,2797],{},[2138,90682,2140],{},[898,90684,2107],{},[2005,90686,2295],{"separator":2294},[20768,90688],{"width":28081},[20768,90690,90691],{},[2297,90692,90693],{},"(6.6)",[902,90695,90696],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,90698,4316,90699,90717,90718,90720,90721,90725,90726,90756,90757,90779],{},[883,90700,90702],{"className":90701},[886],[888,90703,90704],{"xmlns":890},[892,90705,90706,90714],{},[895,90707,90708,90710,90712],{},[898,90709,207],{},[2005,90711,2295],{"separator":2294},[898,90713,2107],{},[902,90715,90716],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,90719,74704],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,90722,90724],{"className":90723,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,90727,90729],{"className":90728},[886],[888,90730,90731],{"xmlns":890},[892,90732,90733,90753],{},[895,90734,90735,90737,90739,90741,90743,90745,90747,90749,90751],{},[898,90736,207],{},[2005,90738,2295],{"separator":2294},[898,90740,2107],{},[2005,90742,6512],{},[2005,90744,2014],{"stretchy":2013},[2138,90746,2336],{},[2005,90748,2295],{"separator":2294},[2138,90750,2287],{},[2005,90752,2020],{"stretchy":2013},[902,90754,90755],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,90758,90760],{"className":90759},[886],[888,90761,90762],{"xmlns":890},[892,90763,90764,90776],{},[895,90765,90766,90768,90770,90772,90774],{},[898,90767,2107],{},[2005,90769,2007],{},[2138,90771,2287],{},[2005,90773,2234],{},[898,90775,207],{},[902,90777,90778],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,90781,90782],{},[2568,90783],{"alt":90784,"className":90785,"src":90786},"imek-cobb-douglas-3d-plus-ic",[210,2572],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,90788,90790],{"className":90789},[886],[888,90791,90792],{"xmlns":890,"display":28071},[892,90793,90794,90844],{},[895,90795,90796,90798,90800,90806,90808,90814,90816,90818,90826,90828,90842],{},[898,90797,900],{},[2005,90799,2014],{"stretchy":2013},[2281,90801,90802,90804],{},[898,90803,2797],{},[2138,90805,2287],{},[2005,90807,2295],{"separator":2294},[2281,90809,90810,90812],{},[898,90811,2797],{},[2138,90813,2140],{},[2005,90815,2020],{"stretchy":2013},[2005,90817,2007],{},[9172,90819,90820,90822,90824],{},[898,90821,2797],{},[2138,90823,2287],{},[898,90825,207],{},[2005,90827,3185],{},[9172,90829,90830,90832,90834],{},[898,90831,2797],{},[2138,90833,2140],{},[895,90835,90836,90838,90840],{},[2138,90837,2287],{},[2005,90839,2234],{},[898,90841,207],{},[898,90843,1644],{"mathvariant":2385},[902,90845,90846],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[3876,90848,90849,90898,91020,91154],{},[724,90850,90851,90853,90854],{},[883,90852,52700],{}," Příklad 6.3 — ověření vlastností pro ",[883,90855,90857],{"className":90856},[886],[888,90858,90859],{"xmlns":890},[892,90860,90861,90895],{},[895,90862,90863,90865,90867,90881],{},[898,90864,900],{},[2005,90866,2007],{},[9172,90868,90869,90871,90873],{},[898,90870,2797],{},[2138,90872,2287],{},[895,90874,90875,90877,90879],{},[2138,90876,2287],{},[898,90878,4680],{"mathvariant":2385},[2138,90880,2360],{},[9172,90882,90883,90885,90887],{},[898,90884,2797],{},[2138,90886,2140],{},[895,90888,90889,90891,90893],{},[2138,90890,2182],{},[898,90892,4680],{"mathvariant":2385},[2138,90894,2360],{},[902,90896,90897],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,90899,90901],{"className":90900},[886],[888,90902,90903],{"xmlns":890,"display":28071},[892,90904,90905,91017],{},[895,90906,90907,90915,90917,90925,90941,90955,90957,90959,90961,90963,90971,90973,90981,90995,91011,91013,91015],{},[9172,90908,90909,90911,90913],{},[898,90910,900],{},[2138,90912,2287],{},[2005,90914,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,90916,2007],{},[2334,90918,90919],{"scriptlevel":2336,"displaystyle":2013},[2338,90920,90921,90923],{},[2138,90922,2287],{},[2138,90924,2360],{},[9172,90926,90927,90929,90931],{},[898,90928,2797],{},[2138,90930,2287],{},[895,90932,90933,90935,90937,90939],{},[2005,90934,2234],{},[2138,90936,2182],{},[898,90938,4680],{"mathvariant":2385},[2138,90940,2360],{},[9172,90942,90943,90945,90947],{},[898,90944,2797],{},[2138,90946,2140],{},[895,90948,90949,90951,90953],{},[2138,90950,2182],{},[898,90952,4680],{"mathvariant":2385},[2138,90954,2360],{},[2005,90956,3416],{},[2138,90958,2336],{},[2005,90960,2295],{"separator":2294},[5884,90962],{"width":15290},[9172,90964,90965,90967,90969],{},[898,90966,900],{},[2138,90968,2140],{},[2005,90970,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,90972,2007],{},[2334,90974,90975],{"scriptlevel":2336,"displaystyle":2013},[2338,90976,90977,90979],{},[2138,90978,2182],{},[2138,90980,2360],{},[9172,90982,90983,90985,90987],{},[898,90984,2797],{},[2138,90986,2287],{},[895,90988,90989,90991,90993],{},[2138,90990,2287],{},[898,90992,4680],{"mathvariant":2385},[2138,90994,2360],{},[9172,90996,90997,90999,91001],{},[898,90998,2797],{},[2138,91000,2140],{},[895,91002,91003,91005,91007,91009],{},[2005,91004,2234],{},[2138,91006,2287],{},[898,91008,4680],{"mathvariant":2385},[2138,91010,2360],{},[2005,91012,3416],{},[2138,91014,2336],{},[2005,91016,2295],{"separator":2294},[902,91018,91019],{"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,",[883,91021,91023],{"className":91022},[886],[888,91024,91025],{"xmlns":890,"display":28071},[892,91026,91027,91151],{},[895,91028,91029,91041,91043,91045,91053,91069,91083,91085,91087,91089,91091,91103,91105,91107,91115,91129,91145,91147,91149],{},[9172,91030,91031,91033,91035],{},[898,91032,900],{},[2138,91034,2912],{},[895,91036,91037,91039],{},[2005,91038,2387],{"mathvariant":2385},[2005,91040,2387],{"mathvariant":2385},[2005,91042,2007],{},[2005,91044,2234],{},[2334,91046,91047],{"scriptlevel":2336,"displaystyle":2013},[2338,91048,91049,91051],{},[2138,91050,2182],{},[2138,91052,41867],{},[9172,91054,91055,91057,91059],{},[898,91056,2797],{},[2138,91058,2287],{},[895,91060,91061,91063,91065,91067],{},[2005,91062,2234],{},[2138,91064,24206],{},[898,91066,4680],{"mathvariant":2385},[2138,91068,2360],{},[9172,91070,91071,91073,91075],{},[898,91072,2797],{},[2138,91074,2140],{},[895,91076,91077,91079,91081],{},[2138,91078,2182],{},[898,91080,4680],{"mathvariant":2385},[2138,91082,2360],{},[2005,91084,3455],{},[2138,91086,2336],{},[2005,91088,2295],{"separator":2294},[5884,91090],{"width":15290},[9172,91092,91093,91095,91097],{},[898,91094,900],{},[2138,91096,32551],{},[895,91098,91099,91101],{},[2005,91100,2387],{"mathvariant":2385},[2005,91102,2387],{"mathvariant":2385},[2005,91104,2007],{},[2005,91106,2234],{},[2334,91108,91109],{"scriptlevel":2336,"displaystyle":2013},[2338,91110,91111,91113],{},[2138,91112,2182],{},[2138,91114,41867],{},[9172,91116,91117,91119,91121],{},[898,91118,2797],{},[2138,91120,2287],{},[895,91122,91123,91125,91127],{},[2138,91124,2287],{},[898,91126,4680],{"mathvariant":2385},[2138,91128,2360],{},[9172,91130,91131,91133,91135],{},[898,91132,2797],{},[2138,91134,2140],{},[895,91136,91137,91139,91141,91143],{},[2005,91138,2234],{},[2138,91140,2237],{},[898,91142,4680],{"mathvariant":2385},[2138,91144,2360],{},[2005,91146,3455],{},[2138,91148,2336],{},[2005,91150,2295],{"separator":2294},[902,91152,91153],{"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,",[724,91155,91156],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,91158,91160],{"id":91159},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,91162,91163,91166],{},[38,91164,91165],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,91168,91170],{"className":91169},[886],[888,91171,91172],{"xmlns":890,"display":28071},[892,91173,91174,91217],{},[20760,91175,91176],{"width":28076},[20765,91177,91178,91180,91210,91212],{},[20768,91179],{"width":28081},[20768,91181,91182],{},[895,91183,91184,91186,91188,91194,91196,91202,91204,91206,91208],{},[898,91185,900],{},[2005,91187,2014],{"stretchy":2013},[2281,91189,91190,91192],{},[898,91191,2797],{},[2138,91193,2287],{},[2005,91195,2295],{"separator":2294},[2281,91197,91198,91200],{},[898,91199,2797],{},[2138,91201,2140],{},[2005,91203,2020],{"stretchy":2013},[2005,91205,2007],{},[898,91207,2151],{},[2005,91209,2295],{"separator":2294},[20768,91211],{"width":28081},[20768,91213,91214],{},[2297,91215,91216],{},"(6.7)",[902,91218,91219],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,91221,4316,91222,91235],{},[883,91223,91225],{"className":91224},[886],[888,91226,91227],{"xmlns":890},[892,91228,91229,91233],{},[895,91230,91231],{},[898,91232,2151],{},[902,91234,2151],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,91237,91239],{"className":91238},[886],[888,91240,91241],{"xmlns":890,"display":28071},[892,91242,91243,91284],{},[20760,91244,91245],{"width":28076},[20765,91246,91247,91249,91277,91279],{},[20768,91248],{"width":28081},[20768,91250,91251],{},[895,91252,91253,91261,91263,91271,91273,91275],{},[9172,91254,91255,91257,91259],{},[898,91256,2797],{},[2138,91258,2287],{},[898,91260,207],{},[2005,91262,3185],{},[9172,91264,91265,91267,91269],{},[898,91266,2797],{},[2138,91268,2140],{},[898,91270,2107],{},[2005,91272,2007],{},[898,91274,2151],{},[898,91276,1644],{"mathvariant":2385},[20768,91278],{"width":28081},[20768,91280,91281],{},[2297,91282,91283],{},"(6.8)",[902,91285,91286],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,91288,91289,91290,4364,91320,2212,91323,91336,91337,91372,91373,91390,91391,91420,91421,91424],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,91291,91293],{"className":91292},[886],[888,91294,91295],{"xmlns":890},[892,91296,91297,91317],{},[895,91298,91299,91301,91307,91309,91315],{},[2005,91300,2495],{"stretchy":2013},[2281,91302,91303,91305],{},[898,91304,2797],{},[2138,91306,2287],{},[2005,91308,2295],{"separator":2294},[2281,91310,91311,91313],{},[898,91312,2797],{},[2138,91314,2140],{},[2005,91316,2510],{"stretchy":2013},[902,91318,91319],{"encoding":904},"[Q_1, Q_2]",[38,91321,91322],{},"stejnou úrovní uspokojení",[883,91324,91326],{"className":91325},[886],[888,91327,91328],{"xmlns":890},[892,91329,91330,91334],{},[895,91331,91332],{},[898,91333,2151],{},[902,91335,2151],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,91338,91340],{"className":91339},[886],[888,91341,91342],{"xmlns":890},[892,91343,91344,91370],{},[895,91345,91346,91348,91350,91352,91354,91360,91362,91368],{},[898,91347,900],{},[2005,91349,2007],{},[898,91351,900],{},[2005,91353,2014],{"stretchy":2013},[2281,91355,91356,91358],{},[898,91357,2797],{},[2138,91359,2287],{},[2005,91361,2295],{"separator":2294},[2281,91363,91364,91366],{},[898,91365,2797],{},[2138,91367,2140],{},[2005,91369,2020],{"stretchy":2013},[902,91371,87460],{"encoding":904}," s rovinami ",[883,91374,91376],{"className":91375},[886],[888,91377,91378],{"xmlns":890},[892,91379,91380,91388],{},[895,91381,91382,91384,91386],{},[898,91383,900],{},[2005,91385,2007],{},[898,91387,2151],{},[902,91389,86677],{"encoding":904}," rovnoběžnými s rovinou ",[883,91392,91394],{"className":91393},[886],[888,91395,91396],{"xmlns":890},[892,91397,91398,91418],{},[895,91399,91400,91402,91408,91410,91416],{},[2005,91401,2014],{"stretchy":2013},[2281,91403,91404,91406],{},[898,91405,2797],{},[2138,91407,2287],{},[2005,91409,2295],{"separator":2294},[2281,91411,91412,91414],{},[898,91413,2797],{},[2138,91415,2140],{},[2005,91417,2020],{"stretchy":2013},[902,91419,89623],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,91422,91423],{},"izokvantami"," produkčních funkcí.",[724,91426,91427],{},[614,91428,91429,91430,89501,91448,91466,91467,1644],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,91431,91433],{"className":91432},[886],[888,91434,91435],{"xmlns":890},[892,91436,91437,91445],{},[895,91438,91439,91441,91443],{},[898,91440,207],{},[2005,91442,3455],{},[898,91444,2107],{},[902,91446,91447],{"encoding":904},"a \u003C b",[883,91449,91451],{"className":91450},[886],[888,91452,91453],{"xmlns":890},[892,91454,91455,91463],{},[895,91456,91457,91459,91461],{},[898,91458,207],{},[2005,91460,3416],{},[898,91462,2107],{},[902,91464,91465],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,91468,91470],{"className":91469},[886],[888,91471,91472],{"xmlns":890},[892,91473,91474,91498],{},[895,91475,91476,91482,91484,91490,91492],{},[2281,91477,91478,91480],{},[898,91479,2151],{},[2138,91481,2336],{},[2005,91483,3455],{},[2281,91485,91486,91488],{},[898,91487,2151],{},[2138,91489,2287],{},[2005,91491,3455],{},[2281,91493,91494,91496],{},[898,91495,2151],{},[2138,91497,2140],{},[902,91499,91500],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,91502,91503],{},[614,91504,91505,91506,91535,91536,91594,91595,91613],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,91507,91509],{"className":91508},[886],[888,91510,91511],{"xmlns":890},[892,91512,91513,91533],{},[895,91514,91515,91517,91523,91525,91531],{},[2005,91516,2014],{"stretchy":2013},[2281,91518,91519,91521],{},[898,91520,2797],{},[2138,91522,2287],{},[2005,91524,2295],{"separator":2294},[2281,91526,91527,91529],{},[898,91528,2797],{},[2138,91530,2140],{},[2005,91532,2020],{"stretchy":2013},[902,91534,89623],{"encoding":904},"; body ",[883,91537,91539],{"className":91538},[886],[888,91540,91541],{"xmlns":890},[892,91542,91543,91591],{},[895,91544,91545,91547,91549,91551,91557,91559,91565,91567,91569,91571,91573,91575,91581,91583,91589],{},[898,91546,1836],{},[2005,91548,2007],{},[2005,91550,2495],{"stretchy":2013},[2281,91552,91553,91555],{},[898,91554,207],{},[2138,91556,2287],{},[2005,91558,2295],{"separator":2294},[2281,91560,91561,91563],{},[898,91562,207],{},[2138,91564,2140],{},[2005,91566,2510],{"stretchy":2013},[2005,91568,2295],{"separator":2294},[898,91570,1844],{},[2005,91572,2007],{},[2005,91574,2495],{"stretchy":2013},[2281,91576,91577,91579],{},[898,91578,2107],{},[2138,91580,2287],{},[2005,91582,2295],{"separator":2294},[2281,91584,91585,91587],{},[898,91586,2107],{},[2138,91588,2140],{},[2005,91590,2510],{"stretchy":2013},[902,91592,91593],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,91596,91598],{"className":91597},[886],[888,91599,91600],{"xmlns":890},[892,91601,91602,91610],{},[895,91603,91604,91606,91608],{},[898,91605,1852],{},[2005,91607,2295],{"separator":2294},[898,91609,1860],{},[902,91611,91612],{"encoding":904},"C, D"," na vyšší hladině.",[3876,91615,91616],{},[724,91617,91618,91620,91621,91683,91684,91728,91729,91763,91764,26194,91782,91763,91836,26194,91854,91930],{},[883,91619,52700],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,91622,91624],{"className":91623},[886],[888,91625,91626],{"xmlns":890},[892,91627,91628,91680],{},[895,91629,91630,91632,91634,91640,91642,91648,91650,91652,91666],{},[898,91631,900],{},[2005,91633,2014],{"stretchy":2013},[2281,91635,91636,91638],{},[898,91637,2797],{},[2138,91639,2287],{},[2005,91641,2295],{"separator":2294},[2281,91643,91644,91646],{},[898,91645,2797],{},[2138,91647,2140],{},[2005,91649,2020],{"stretchy":2013},[2005,91651,2007],{},[9172,91653,91654,91656,91658],{},[898,91655,2797],{},[2138,91657,2287],{},[895,91659,91660,91662,91664],{},[2138,91661,2287],{},[898,91663,4680],{"mathvariant":2385},[2138,91665,2360],{},[9172,91667,91668,91670,91672],{},[898,91669,2797],{},[2138,91671,2140],{},[895,91673,91674,91676,91678],{},[2138,91675,2182],{},[898,91677,4680],{"mathvariant":2385},[2138,91679,2360],{},[902,91681,91682],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,91685,91687],{"className":91686},[886],[888,91688,91689],{"xmlns":890},[892,91690,91691,91725],{},[895,91692,91693,91707,91721,91723],{},[9172,91694,91695,91697,91699],{},[898,91696,2797],{},[2138,91698,2287],{},[895,91700,91701,91703,91705],{},[2138,91702,2287],{},[898,91704,4680],{"mathvariant":2385},[2138,91706,2360],{},[9172,91708,91709,91711,91713],{},[898,91710,2797],{},[2138,91712,2140],{},[895,91714,91715,91717,91719],{},[2138,91716,2182],{},[898,91718,4680],{"mathvariant":2385},[2138,91720,2360],{},[2005,91722,2007],{},[898,91724,2151],{},[902,91726,91727],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,91730,91732],{"className":91731},[886],[888,91733,91734],{"xmlns":890},[892,91735,91736,91760],{},[895,91737,91738,91744,91752,91754],{},[2281,91739,91740,91742],{},[898,91741,2797],{},[2138,91743,2287],{},[9172,91745,91746,91748,91750],{},[898,91747,2797],{},[2138,91749,2140],{},[2138,91751,2182],{},[2005,91753,2007],{},[2133,91755,91756,91758],{},[898,91757,2151],{},[2138,91759,2360],{},[902,91761,91762],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,91765,91767],{"className":91766},[886],[888,91768,91769],{"xmlns":890},[892,91770,91771,91779],{},[895,91772,91773,91775,91777],{},[898,91774,2151],{},[2005,91776,2007],{},[2138,91778,2287],{},[902,91780,91781],{"encoding":904},"c = 1",[883,91783,91785],{"className":91784},[886],[888,91786,91787],{"xmlns":890},[892,91788,91789,91833],{},[895,91790,91791,91797,91799,91815,91817],{},[2281,91792,91793,91795],{},[898,91794,2797],{},[2138,91796,2140],{},[2005,91798,2007],{},[9172,91800,91801,91803,91805],{},[898,91802,2797],{},[2138,91804,2287],{},[895,91806,91807,91809,91811,91813],{},[2005,91808,2234],{},[2138,91810,2287],{},[898,91812,4680],{"mathvariant":2385},[2138,91814,2182],{},[2005,91816,2007],{},[2334,91818,91819],{"scriptlevel":2336,"displaystyle":2294},[2338,91820,91821,91823],{},[2138,91822,2287],{},[82032,91824,91825,91831],{},[2281,91826,91827,91829],{},[898,91828,2797],{},[2138,91830,2287],{},[2138,91832,2182],{},[902,91834,91835],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,91837,91839],{"className":91838},[886],[888,91840,91841],{"xmlns":890},[892,91842,91843,91851],{},[895,91844,91845,91847,91849],{},[898,91846,2151],{},[2005,91848,2007],{},[2138,91850,2140],{},[902,91852,91853],{"encoding":904},"c = 2",[883,91855,91857],{"className":91856},[886],[888,91858,91859],{"xmlns":890},[892,91860,91861,91927],{},[895,91862,91863,91869,91871,91883,91885,91901,91903],{},[2281,91864,91865,91867],{},[898,91866,2797],{},[2138,91868,2140],{},[2005,91870,2007],{},[2133,91872,91873,91875],{},[2138,91874,2140],{},[895,91876,91877,91879,91881],{},[2138,91878,2360],{},[898,91880,4680],{"mathvariant":2385},[2138,91882,2182],{},[2005,91884,3185],{},[9172,91886,91887,91889,91891],{},[898,91888,2797],{},[2138,91890,2287],{},[895,91892,91893,91895,91897,91899],{},[2005,91894,2234],{},[2138,91896,2287],{},[898,91898,4680],{"mathvariant":2385},[2138,91900,2182],{},[2005,91902,2007],{},[2334,91904,91905],{"scriptlevel":2336,"displaystyle":2294},[2338,91906,91907,91917],{},[895,91908,91909,91911],{},[2138,91910,2140],{},[82032,91912,91913,91915],{},[2138,91914,2140],{},[2138,91916,2182],{},[82032,91918,91919,91925],{},[2281,91920,91921,91923],{},[898,91922,2797],{},[2138,91924,2287],{},[2138,91926,2182],{},[902,91928,91929],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,91932,91934],{"id":91933},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,91936,91937],{},[2568,91938],{"alt":91939,"className":91940,"src":91941},"imek-ic-4vlastnosti-anotovane",[210,2572],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[3876,91943,91944,91953,92000,92044,92050,92056],{},[724,91945,91946,91948,91949,91952],{},[883,91947,4418],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,91950,91951],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,91954,91955],{},[883,91956,91958],{"className":91957},[886],[888,91959,91960],{"xmlns":890},[892,91961,91962,91997],{},[895,91963,91964,91967,91969,91971,91973,91975,91993,91995],{},[898,91965,91966],{"mathvariant":2385},"tg",[2005,91968,56205],{},[898,91970,18868],{},[2005,91972,2007],{},[2005,91974,2234],{},[2338,91976,91977,91985],{},[9172,91978,91979,91981,91983],{},[898,91980,900],{},[2138,91982,2287],{},[2005,91984,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,91986,91987,91989,91991],{},[898,91988,900],{},[2138,91990,2140],{},[2005,91992,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,91994,3455],{},[2138,91996,2336],{},[902,91998,91999],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,92001,92002,92003,92043],{},"(derivace implicitně zadané funkce ",[883,92004,92006],{"className":92005},[886],[888,92007,92008],{"xmlns":890},[892,92009,92010,92040],{},[895,92011,92012,92014,92016,92022,92024,92030,92032,92034,92036,92038],{},[898,92013,900],{},[2005,92015,2014],{"stretchy":2013},[2281,92017,92018,92020],{},[898,92019,2797],{},[2138,92021,2287],{},[2005,92023,2295],{"separator":2294},[2281,92025,92026,92028],{},[898,92027,2797],{},[2138,92029,2140],{},[2005,92031,2020],{"stretchy":2013},[2005,92033,2234],{},[898,92035,2151],{},[2005,92037,2007],{},[2138,92039,2336],{},[902,92041,92042],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,92045,92046,92049],{},[38,92047,92048],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,92051,92052,92055],{},[38,92053,92054],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,92057,92058,92061,92062,92080,92081,92097,92098,92101],{},[38,92059,92060],{},"4° Konvexní."," Pro každé dva body ",[883,92063,92065],{"className":92064},[886],[888,92066,92067],{"xmlns":890},[892,92068,92069,92077],{},[895,92070,92071,92073,92075],{},[898,92072,1836],{},[2005,92074,2295],{"separator":2294},[898,92076,1844],{},[902,92078,92079],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,92082,92084],{"className":92083},[886],[888,92085,92086],{"xmlns":890},[892,92087,92088,92094],{},[895,92089,92090,92092],{},[898,92091,1836],{},[898,92093,1844],{},[902,92095,92096],{"encoding":904},"AB"," ve ",[38,92099,92100],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,92103,92104],{},[614,92105,92106,92107,92142,92143,1644],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,92108,92110],{"className":92109},[886],[888,92111,92112],{"xmlns":890},[892,92113,92114,92140],{},[895,92115,92116,92118,92120,92126,92128,92134,92136,92138],{},[898,92117,900],{},[2005,92119,2014],{"stretchy":2013},[2281,92121,92122,92124],{},[898,92123,2797],{},[2138,92125,2287],{},[2005,92127,2295],{"separator":2294},[2281,92129,92130,92132],{},[898,92131,2797],{},[2138,92133,2140],{},[2005,92135,2020],{"stretchy":2013},[2005,92137,2007],{},[898,92139,2151],{},[902,92141,9774],{"encoding":904}," s tečnou se sklonem ",[883,92144,92146],{"className":92145},[886],[888,92147,92148],{"xmlns":890},[892,92149,92150,92158],{},[895,92151,92152,92154,92156],{},[898,92153,91966],{"mathvariant":2385},[2005,92155,56205],{},[898,92157,18868],{},[902,92159,92160],{"encoding":904},"\\operatorname{tg}\\alpha",[115,92162,92164],{"id":92163},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,92166,92167,2212,92170,10030,92183,92186],{},[38,92168,92169],{},"Mezní míra komoditní substituce",[883,92171,92173],{"className":92172},[886],[888,92174,92175],{"xmlns":890},[892,92176,92177,92181],{},[895,92178,92179],{},[2297,92180,10607],{},[902,92182,28243],{"encoding":904},[38,92184,92185],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,92188,92190],{"className":92189},[886],[888,92191,92192],{"xmlns":890,"display":28071},[892,92193,92194,92281],{},[20760,92195,92196],{"width":28076},[20765,92197,92198,92200,92274,92276],{},[20768,92199],{"width":28081},[20768,92201,92202],{},[895,92203,92204,92206,92208,92210,92212,92218,92220,92226,92228,92230,92252,92254,92272],{},[2297,92205,10607],{},[2005,92207,2007],{},[2297,92209,10607],{},[2005,92211,2014],{"stretchy":2013},[2281,92213,92214,92216],{},[898,92215,2797],{},[2138,92217,2287],{},[2005,92219,2295],{"separator":2294},[2281,92221,92222,92224],{},[898,92223,2797],{},[2138,92225,2140],{},[2005,92227,2020],{"stretchy":2013},[2005,92229,2007],{},[2338,92231,92232,92242],{},[895,92233,92234,92236],{},[898,92235,2826],{},[2281,92237,92238,92240],{},[898,92239,900],{},[2138,92241,2287],{},[895,92243,92244,92246],{},[898,92245,2826],{},[2281,92247,92248,92250],{},[898,92249,900],{},[2138,92251,2140],{},[2005,92253,2007],{},[2338,92255,92256,92264],{},[9172,92257,92258,92260,92262],{},[898,92259,900],{},[2138,92261,2287],{},[2005,92263,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,92265,92266,92268,92270],{},[898,92267,900],{},[2138,92269,2140],{},[2005,92271,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[898,92273,1644],{"mathvariant":2385},[20768,92275],{"width":28081},[20768,92277,92278],{},[2297,92279,92280],{},"(6.9)",[902,92282,92283],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,92285,92286,92287,92321,92322,92354,92355,92390,92391,92404],{},"Geometricky: ",[883,92288,92290],{"className":92289},[886],[888,92291,92292],{"xmlns":890},[892,92293,92294,92318],{},[895,92295,92296,92298],{},[2005,92297,2234],{},[2334,92299,92300],{"scriptlevel":2336,"displaystyle":2013},[2338,92301,92302,92310],{},[9172,92303,92304,92306,92308],{},[898,92305,900],{},[2138,92307,2287],{},[2005,92309,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,92311,92312,92314,92316],{},[898,92313,900],{},[2138,92315,2140],{},[2005,92317,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,92319,92320],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,92323,92325],{"className":92324},[886],[888,92326,92327],{"xmlns":890},[892,92328,92329,92351],{},[895,92330,92331,92337,92339,92341,92343,92349],{},[2281,92332,92333,92335],{},[898,92334,2797],{},[2138,92336,2140],{},[2005,92338,2007],{},[898,92340,2010],{},[2005,92342,2014],{"stretchy":2013},[2281,92344,92345,92347],{},[898,92346,2797],{},[2138,92348,2287],{},[2005,92350,2020],{"stretchy":2013},[902,92352,92353],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,92356,92358],{"className":92357},[886],[888,92359,92360],{"xmlns":890},[892,92361,92362,92388],{},[895,92363,92364,92366,92368,92374,92376,92382,92384,92386],{},[898,92365,900],{},[2005,92367,2014],{"stretchy":2013},[2281,92369,92370,92372],{},[898,92371,2797],{},[2138,92373,2287],{},[2005,92375,2295],{"separator":2294},[2281,92377,92378,92380],{},[898,92379,2797],{},[2138,92381,2140],{},[2005,92383,2020],{"stretchy":2013},[2005,92385,2007],{},[898,92387,2151],{},[902,92389,9774],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,92392,92394],{"className":92393},[886],[888,92395,92396],{"xmlns":890},[892,92397,92398,92402],{},[895,92399,92400],{},[2297,92401,10607],{},[902,92403,28243],{"encoding":904}," chápeme jako velikost kompenzace.",[3876,92406,92407],{},[724,92408,92409,92411,92412,8108,92444,92482,92483,92500,92501,92518],{},[883,92410,4164],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,92413,92415],{"className":92414},[886],[888,92416,92417],{"xmlns":890},[892,92418,92419,92441],{},[895,92420,92421,92423,92425,92431,92433,92439],{},[2297,92422,10607],{},[2005,92424,2014],{"stretchy":2013},[2281,92426,92427,92429],{},[898,92428,2797],{},[2138,92430,2287],{},[2005,92432,2295],{"separator":2294},[2281,92434,92435,92437],{},[898,92436,2797],{},[2138,92438,2140],{},[2005,92440,2020],{"stretchy":2013},[902,92442,92443],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,92445,92446,92447,29008,92464,92481],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,92448,92450],{"className":92449},[886],[888,92451,92452],{"xmlns":890},[892,92453,92454,92462],{},[895,92455,92456],{},[2281,92457,92458,92460],{},[898,92459,2797],{},[2138,92461,2287],{},[902,92463,29007],{"encoding":904},[883,92465,92467],{"className":92466},[886],[888,92468,92469],{"xmlns":890},[892,92470,92471,92479],{},[895,92472,92473],{},[2281,92474,92475,92477],{},[898,92476,2797],{},[2138,92478,2140],{},[902,92480,29026],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,92484,92486],{"className":92485},[886],[888,92487,92488],{"xmlns":890},[892,92489,92490,92498],{},[895,92491,92492],{},[2281,92493,92494,92496],{},[898,92495,2797],{},[2138,92497,2140],{},[902,92499,29026],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,92502,92504],{"className":92503},[886],[888,92505,92506],{"xmlns":890},[892,92507,92508,92516],{},[895,92509,92510],{},[2281,92511,92512,92514],{},[898,92513,2797],{},[2138,92515,2287],{},[902,92517,29007],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,92520,92521,92522,29949],{},"Pro obecnou změnu ",[883,92523,92525],{"className":92524},[886],[888,92526,92527],{"xmlns":890},[892,92528,92529,92539],{},[895,92530,92531,92533],{},[898,92532,2203],{"mathvariant":2385},[2281,92534,92535,92537],{},[898,92536,2797],{},[2138,92538,2287],{},[902,92540,92541],{"encoding":904},"\\mathrm{d} Q_1",[883,92543,92545],{"className":92544},[886],[888,92546,92547],{"xmlns":890,"display":28071},[892,92548,92549,92602],{},[20760,92550,92551],{"width":28076},[20765,92552,92553,92555,92595,92597],{},[20768,92554],{"width":28081},[20768,92556,92557],{},[895,92558,92559,92561,92567,92569,92571,92577,92579,92581,92583,92585,92587,92593],{},[898,92560,2897],{"mathvariant":2385},[2281,92562,92563,92565],{},[898,92564,2797],{},[2138,92566,2140],{},[2005,92568,2739],{},[898,92570,2203],{"mathvariant":2385},[2281,92572,92573,92575],{},[898,92574,2797],{},[2138,92576,2140],{},[2005,92578,2007],{},[2005,92580,2234],{},[2297,92582,10607],{},[2005,92584,3185],{},[898,92586,2203],{"mathvariant":2385},[2281,92588,92589,92591],{},[898,92590,2797],{},[2138,92592,2287],{},[2005,92594,2295],{"separator":2294},[20768,92596],{"width":28081},[20768,92598,92599],{},[2297,92600,92601],{},"(6.10)",[902,92603,92604],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,92606,92608],{"className":92607},[886],[888,92609,92610],{"xmlns":890,"display":28071},[892,92611,92612,92659],{},[20760,92613,92614],{"width":28076},[20765,92615,92616,92618,92652,92654],{},[20768,92617],{"width":28081},[20768,92619,92620],{},[895,92621,92622,92624,92630,92632,92634,92640,92642,92644,92650],{},[898,92623,2203],{"mathvariant":2385},[2281,92625,92626,92628],{},[898,92627,2797],{},[2138,92629,2287],{},[2005,92631,2007],{},[2005,92633,2234],{},[2338,92635,92636,92638],{},[2138,92637,2287],{},[2297,92639,10607],{},[2297,92641,2995],{},[898,92643,2203],{"mathvariant":2385},[2281,92645,92646,92648],{},[898,92647,2797],{},[2138,92649,2140],{},[898,92651,1644],{"mathvariant":2385},[20768,92653],{"width":28081},[20768,92655,92656],{},[2297,92657,92658],{},"(6.11)",[902,92660,92661],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[3876,92663,92664,92730,92847],{},[724,92665,92666,92668,92669,29949],{},[883,92667,52700],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,92670,92672],{"className":92671},[886],[888,92673,92674],{"xmlns":890},[892,92675,92676,92728],{},[895,92677,92678,92680,92682,92688,92690,92696,92698,92700,92714],{},[898,92679,900],{},[2005,92681,2014],{"stretchy":2013},[2281,92683,92684,92686],{},[898,92685,2797],{},[2138,92687,2287],{},[2005,92689,2295],{"separator":2294},[2281,92691,92692,92694],{},[898,92693,2797],{},[2138,92695,2140],{},[2005,92697,2020],{"stretchy":2013},[2005,92699,2007],{},[9172,92701,92702,92704,92706],{},[898,92703,2797],{},[2138,92705,2287],{},[895,92707,92708,92710,92712],{},[2138,92709,2287],{},[898,92711,4680],{"mathvariant":2385},[2138,92713,2140],{},[9172,92715,92716,92718,92720],{},[898,92717,2797],{},[2138,92719,2140],{},[895,92721,92722,92724,92726],{},[2138,92723,2287],{},[898,92725,4680],{"mathvariant":2385},[2138,92727,2140],{},[902,92729,29948],{"encoding":904},[724,92731,92732],{},[883,92733,92735],{"className":92734},[886],[888,92736,92737],{"xmlns":890},[892,92738,92739,92845],{},[895,92740,92741,92743,92745,92827,92829,92843],{},[2297,92742,10607],{},[2005,92744,2007],{},[2338,92746,92747,92787],{},[895,92748,92749,92757,92773],{},[2334,92750,92751],{"scriptlevel":2336,"displaystyle":2013},[2338,92752,92753,92755],{},[2138,92754,2287],{},[2138,92756,2140],{},[9172,92758,92759,92761,92763],{},[898,92760,2797],{},[2138,92762,2287],{},[895,92764,92765,92767,92769,92771],{},[2005,92766,2234],{},[2138,92768,2287],{},[898,92770,4680],{"mathvariant":2385},[2138,92772,2140],{},[9172,92774,92775,92777,92779],{},[898,92776,2797],{},[2138,92778,2140],{},[895,92780,92781,92783,92785],{},[2138,92782,2287],{},[898,92784,4680],{"mathvariant":2385},[2138,92786,2140],{},[895,92788,92789,92797,92811],{},[2334,92790,92791],{"scriptlevel":2336,"displaystyle":2013},[2338,92792,92793,92795],{},[2138,92794,2287],{},[2138,92796,2140],{},[9172,92798,92799,92801,92803],{},[898,92800,2797],{},[2138,92802,2287],{},[895,92804,92805,92807,92809],{},[2138,92806,2287],{},[898,92808,4680],{"mathvariant":2385},[2138,92810,2140],{},[9172,92812,92813,92815,92817],{},[898,92814,2797],{},[2138,92816,2140],{},[895,92818,92819,92821,92823,92825],{},[2005,92820,2234],{},[2138,92822,2287],{},[898,92824,4680],{"mathvariant":2385},[2138,92826,2140],{},[2005,92828,2007],{},[2338,92830,92831,92837],{},[2281,92832,92833,92835],{},[898,92834,2797],{},[2138,92836,2140],{},[2281,92838,92839,92841],{},[898,92840,2797],{},[2138,92842,2287],{},[898,92844,1644],{"mathvariant":2385},[902,92846,30067],{"encoding":904},[724,92848,30070,92849,2935,92892,30118,92894,92913],{},[883,92850,92852],{"className":92851},[886],[888,92853,92854],{"xmlns":890},[892,92855,92856,92890],{},[895,92857,92858,92860,92862,92864,92866,92868,92870,92872,92880,92882],{},[2297,92859,10607],{},[2005,92861,2014],{"stretchy":2013},[2138,92863,30086],{},[2005,92865,2295],{"separator":2294},[2138,92867,15116],{},[2005,92869,2020],{"stretchy":2013},[2005,92871,2007],{},[2334,92873,92874],{"scriptlevel":2336,"displaystyle":2013},[2338,92875,92876,92878],{},[2138,92877,15116],{},[2138,92879,30086],{},[2005,92881,2007],{},[2334,92883,92884],{"scriptlevel":2336,"displaystyle":2013},[2338,92885,92886,92888],{},[2138,92887,2237],{},[2138,92889,2182],{},[902,92891,30115],{"encoding":904},[614,92893,9222],{},[883,92895,92897],{"className":92896},[886],[888,92898,92899],{"xmlns":890},[892,92900,92901,92911],{},[895,92902,92903],{},[2334,92904,92905],{"scriptlevel":2336,"displaystyle":2013},[2338,92906,92907,92909],{},[2138,92908,2237],{},[2138,92910,2182],{},[902,92912,30138],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,92915,92916,92917,92921],{},"(Paralelou je ",[207,92918,92920],{"className":92919,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,92923,92925],{"id":92924},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,92927,92928,92929,92932],{},"Rámcově se v kapitole 6 studují ",[38,92930,92931],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,92934,92935,93071],{},[123,92936,92937,92939,92940,10162,92971,2212,92974,93023,93024,1644],{},[38,92938,28257],{}," — maximalizace ",[883,92941,92943],{"className":92942},[886],[888,92944,92945],{"xmlns":890},[892,92946,92947,92969],{},[895,92948,92949,92951,92953,92959,92961,92967],{},[898,92950,900],{},[2005,92952,2014],{"stretchy":2013},[2281,92954,92955,92957],{},[898,92956,2797],{},[2138,92958,2287],{},[2005,92960,2295],{"separator":2294},[2281,92962,92963,92965],{},[898,92964,2797],{},[2138,92966,2140],{},[2005,92968,2020],{"stretchy":2013},[902,92970,16350],{"encoding":904},[38,92972,92973],{},"rozpočtovém omezení",[883,92975,92977],{"className":92976},[886],[888,92978,92979],{"xmlns":890},[892,92980,92981,93021],{},[895,92982,92983,92989,92991,92999,93005,93007,93015],{},[2133,92984,92985,92987],{},[898,92986,9134],{},[2005,92988,4360],{},[2005,92990,2007],{},[9172,92992,92993,92995,92997],{},[898,92994,3946],{},[2138,92996,2287],{},[2005,92998,4360],{},[2281,93000,93001,93003],{},[898,93002,2797],{},[2138,93004,2287],{},[2005,93006,2104],{},[9172,93008,93009,93011,93013],{},[898,93010,3946],{},[2138,93012,2140],{},[2005,93014,4360],{},[2281,93016,93017,93019],{},[898,93018,2797],{},[2138,93020,2140],{},[902,93022,17305],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,93025,93027],{"className":93026},[886],[888,93028,93029],{"xmlns":890},[892,93030,93031,93069],{},[895,93032,93033,93039,93041,93047,93049,93055,93057,93063,93065,93067],{},[2281,93034,93035,93037],{},[898,93036,2797],{},[898,93038,17797],{},[2005,93040,2007],{},[2281,93042,93043,93045],{},[898,93044,1860],{},[898,93046,17797],{},[2005,93048,2014],{"stretchy":2013},[2281,93050,93051,93053],{},[898,93052,3946],{},[2138,93054,2287],{},[2005,93056,2295],{"separator":2294},[2281,93058,93059,93061],{},[898,93060,3946],{},[2138,93062,2140],{},[2005,93064,2295],{"separator":2294},[898,93066,9134],{},[2005,93068,2020],{"stretchy":2013},[902,93070,36460],{"encoding":904},[123,93072,93073,27906,93076,27949,93122,93139,93140,1644],{},[38,93074,93075],{},"Duální úloha",[883,93077,93079],{"className":93078},[886],[888,93080,93081],{"xmlns":890},[892,93082,93083,93119],{},[895,93084,93085,93087,93089,93097,93103,93105,93113],{},[898,93086,1868],{},[2005,93088,2007],{},[9172,93090,93091,93093,93095],{},[898,93092,3946],{},[2138,93094,2287],{},[2005,93096,4360],{},[2281,93098,93099,93101],{},[898,93100,2797],{},[2138,93102,2287],{},[2005,93104,2104],{},[9172,93106,93107,93109,93111],{},[898,93108,3946],{},[2138,93110,2140],{},[2005,93112,4360],{},[2281,93114,93115,93117],{},[898,93116,2797],{},[2138,93118,2140],{},[902,93120,93121],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,93123,93125],{"className":93124},[886],[888,93126,93127],{"xmlns":890},[892,93128,93129,93137],{},[895,93130,93131],{},[2133,93132,93133,93135],{},[898,93134,900],{},[2005,93136,4360],{},[902,93138,27967],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,93141,93143],{"className":93142},[886],[888,93144,93145],{"xmlns":890},[892,93146,93147,93185],{},[895,93148,93149,93155,93157,93163,93165,93171,93173,93179,93181,93183],{},[2281,93150,93151,93153],{},[898,93152,2797],{},[898,93154,17797],{},[2005,93156,2007],{},[2281,93158,93159,93161],{},[898,93160,1860],{},[898,93162,17797],{},[2005,93164,2014],{"stretchy":2013},[2281,93166,93167,93169],{},[898,93168,3946],{},[2138,93170,2287],{},[2005,93172,2295],{"separator":2294},[2281,93174,93175,93177],{},[898,93176,3946],{},[2138,93178,2140],{},[2005,93180,2295],{"separator":2294},[898,93182,900],{},[2005,93184,2020],{"stretchy":2013},[902,93186,17830],{"encoding":904},[724,93188,93189,93190,93193,93194,2212,93197,93236],{},"Obě úlohy se řeší ",[207,93191,27972],{"className":93192,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,93195,93196],{},"tentýž bod dotyku",[883,93198,93200],{"className":93199},[886],[888,93201,93202],{"xmlns":890},[892,93203,93204,93234],{},[895,93205,93206,93212,93214,93222,93224,93232],{},[2133,93207,93208,93210],{},[898,93209,2797],{},[2005,93211,4360],{},[2005,93213,2495],{"stretchy":2013},[9172,93215,93216,93218,93220],{},[898,93217,2797],{},[2138,93219,2287],{},[2005,93221,4360],{},[2005,93223,2295],{"separator":2294},[9172,93225,93226,93228,93230],{},[898,93227,2797],{},[2138,93229,2140],{},[2005,93231,4360],{},[2005,93233,2510],{"stretchy":2013},[902,93235,28332],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,93238,93240],{"className":93239},[886],[888,93241,93242],{"xmlns":890,"display":28071},[892,93243,93244,93290],{},[895,93245,93246,93248,93250,93268,93270,93288],{},[2297,93247,10607],{},[2005,93249,2007],{},[2338,93251,93252,93260],{},[9172,93253,93254,93256,93258],{},[898,93255,900],{},[2138,93257,2287],{},[2005,93259,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[9172,93261,93262,93264,93266],{},[898,93263,900],{},[2138,93265,2140],{},[2005,93267,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,93269,2007],{},[2338,93271,93272,93280],{},[9172,93273,93274,93276,93278],{},[898,93275,3946],{},[2138,93277,2287],{},[2005,93279,4360],{},[9172,93281,93282,93284,93286],{},[898,93283,3946],{},[2138,93285,2140],{},[2005,93287,4360],{},[898,93289,1644],{"mathvariant":2385},[902,93291,93292],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,93294,93295],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[3876,93297,93298],{},[724,93299,93300,93302,93303,93306,93307,93310,93311,93338,93339,93373,93374,93408,93409,93452,93453,93456,93457,1644],{},[883,93301,4164],{}," Pro detailní postup viz ",[207,93304,36759],{"className":93305,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,93308,93309],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,93312,93314],{"className":93313},[886],[888,93315,93316],{"xmlns":890},[892,93317,93318,93336],{},[895,93319,93320,93322,93324,93330],{},[898,93321,900],{},[2005,93323,2007],{},[2281,93325,93326,93328],{},[898,93327,2797],{},[2138,93329,2287],{},[2281,93331,93332,93334],{},[898,93333,2797],{},[2138,93335,2140],{},[902,93337,30231],{"encoding":904}," s výsledkem ",[883,93340,93342],{"className":93341},[886],[888,93343,93344],{"xmlns":890},[892,93345,93346,93370],{},[895,93347,93348,93354,93356,93358,93360,93366,93368],{},[2281,93349,93350,93352],{},[898,93351,2797],{},[2138,93353,2287],{},[2005,93355,2007],{},[2138,93357,5010],{},[2005,93359,2295],{"separator":2294},[2281,93361,93362,93364],{},[898,93363,2797],{},[2138,93365,2140],{},[2005,93367,2007],{},[2138,93369,2871],{},[902,93371,93372],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,93375,93377],{"className":93376},[886],[888,93378,93379],{"xmlns":890},[892,93380,93381,93405],{},[895,93382,93383,93389,93391,93393,93395,93401,93403],{},[2281,93384,93385,93387],{},[898,93386,2797],{},[2138,93388,2287],{},[2005,93390,2007],{},[2138,93392,2360],{},[2005,93394,2295],{"separator":2294},[2281,93396,93397,93399],{},[898,93398,2797],{},[2138,93400,2140],{},[2005,93402,2007],{},[2138,93404,2287],{},[902,93406,93407],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,93410,93412],{"className":93411},[886],[888,93413,93414],{"xmlns":890},[892,93415,93416,93450],{},[895,93417,93418,93420,93422,93436],{},[898,93419,900],{},[2005,93421,2007],{},[9172,93423,93424,93426,93428],{},[898,93425,2797],{},[2138,93427,2287],{},[895,93429,93430,93432,93434],{},[2138,93431,2287],{},[898,93433,4680],{"mathvariant":2385},[2138,93435,2140],{},[9172,93437,93438,93440,93442],{},[898,93439,2797],{},[2138,93441,2140],{},[895,93443,93444,93446,93448],{},[2138,93445,2287],{},[898,93447,4680],{"mathvariant":2385},[2138,93449,2140],{},[902,93451,33164],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,93454,93455],{},"6.8–6.13"," jsou na stránce ",[207,93458,27772],{"className":93459,"dataFsResolvedFilePath":911,"href":912},[210],[115,93461,93463],{"id":93462},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,93465,93466,93467,93480,93481,93483,93484,93486,93487,93489,93490,93492,93493,93495,93496,93498,93499,2212,93501,93536,93537,93550,93551,93554,93555,93558,93559,1644],{},"Každá ",[883,93468,93470],{"className":93469},[886],[888,93471,93472],{"xmlns":890},[892,93473,93474,93478],{},[895,93475,93476],{},[898,93477,36865],{},[902,93479,36865],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,93482,86814],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,93485,87298],{}," a současně ",[38,93488,86817],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,93491,86822],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,93494,52682],{}," (6.4) a druhé parciální derivace ",[38,93497,89181],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,93500,9737],{},[883,93502,93504],{"className":93503},[886],[888,93505,93506],{"xmlns":890},[892,93507,93508,93534],{},[895,93509,93510,93512,93514,93520,93522,93528,93530,93532],{},[898,93511,900],{},[2005,93513,2014],{"stretchy":2013},[2281,93515,93516,93518],{},[898,93517,2797],{},[2138,93519,2287],{},[2005,93521,2295],{"separator":2294},[2281,93523,93524,93526],{},[898,93525,2797],{},[2138,93527,2140],{},[2005,93529,2020],{"stretchy":2013},[2005,93531,2007],{},[898,93533,2151],{},[902,93535,9774],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,93538,93540],{"className":93539},[886],[888,93541,93542],{"xmlns":890},[892,93543,93544,93548],{},[895,93545,93546],{},[2297,93547,10607],{},[902,93549,28243],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,93552,93553],{},"maximalizace užitečnosti"," a duální ",[38,93556,93557],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,93560,36759],{"className":93561,"dataFsResolvedFilePath":911,"href":912},[210],[115,93563,49887],{"id":49886},[152,93565,93566,93569,93572,93575,93578,93581,93584,93587,93590,93593],{},[123,93567,93568],{},"Co se zahrnuje pod termín užitečnost?",[123,93570,93571],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,93573,93574],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,93576,93577],{},"Jak se vypočítá mezní užitečnost?",[123,93579,93580],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,93582,93583],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,93585,93586],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,93588,93589],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,93591,93592],{},"Proč mají křivky užitečnosti záporný sklon?",[123,93594,93595],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,93597,93599],{"id":93598},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,93601,93602,93605,93606,83488,93648,1343,93676,1343,93704,93732],{},[38,93603,93604],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,93607,93609],{"className":93608},[886],[888,93610,93611],{"xmlns":890},[892,93612,93613,93645],{},[895,93614,93615,93617,93619,93625,93627,93629,93635,93637,93639],{},[898,93616,900],{},[2005,93618,2007],{},[2281,93620,93621,93623],{},[898,93622,2797],{},[2138,93624,2287],{},[2005,93626,2104],{},[2138,93628,64564],{},[2281,93630,93631,93633],{},[898,93632,2797],{},[2138,93634,2140],{},[2005,93636,2104],{},[2138,93638,2140],{},[2281,93640,93641,93643],{},[898,93642,2797],{},[2138,93644,2182],{},[902,93646,93647],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,93649,93651],{"className":93650},[886],[888,93652,93653],{"xmlns":890},[892,93654,93655,93673],{},[895,93656,93657,93659,93661,93663,93665,93667,93669,93671],{},[898,93658,900],{},[2005,93660,2014],{"stretchy":2013},[2138,93662,2360],{},[2005,93664,2295],{"separator":2294},[2138,93666,2140],{},[2005,93668,2295],{"separator":2294},[2138,93670,2140],{},[2005,93672,2020],{"stretchy":2013},[902,93674,93675],{"encoding":904},"U(4, 2, 2)",[883,93677,93679],{"className":93678},[886],[888,93680,93681],{"xmlns":890},[892,93682,93683,93701],{},[895,93684,93685,93687,93689,93691,93693,93695,93697,93699],{},[898,93686,900],{},[2005,93688,2014],{"stretchy":2013},[2138,93690,2287],{},[2005,93692,2295],{"separator":2294},[2138,93694,2360],{},[2005,93696,2295],{"separator":2294},[2138,93698,2140],{},[2005,93700,2020],{"stretchy":2013},[902,93702,93703],{"encoding":904},"U(1, 4, 2)",[883,93705,93707],{"className":93706},[886],[888,93708,93709],{"xmlns":890},[892,93710,93711,93729],{},[895,93712,93713,93715,93717,93719,93721,93723,93725,93727],{},[898,93714,900],{},[2005,93716,2014],{"stretchy":2013},[2138,93718,2140],{},[2005,93720,2295],{"separator":2294},[2138,93722,2182],{},[2005,93724,2295],{"separator":2294},[2138,93726,2287],{},[2005,93728,2020],{"stretchy":2013},[902,93730,93731],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,93734,93735,93738,93739,93791,93792,1343,93818,1343,93844,1343,93870,1343,93896,1343,93922,1343,93948,93974],{},[38,93736,93737],{},"6.2"," Je dána užitečnost ",[883,93740,93742],{"className":93741},[886],[888,93743,93744],{"xmlns":890},[892,93745,93746,93788],{},[895,93747,93748,93750,93752,93754,93768,93782],{},[898,93749,900],{},[2005,93751,2007],{},[2138,93753,2140],{},[9172,93755,93756,93758,93760],{},[898,93757,2797],{},[2138,93759,2287],{},[895,93761,93762,93764,93766],{},[2138,93763,2287],{},[898,93765,4680],{"mathvariant":2385},[2138,93767,2182],{},[9172,93769,93770,93772,93774],{},[898,93771,2797],{},[2138,93773,2140],{},[895,93775,93776,93778,93780],{},[2138,93777,2287],{},[898,93779,4680],{"mathvariant":2385},[2138,93781,2140],{},[2281,93783,93784,93786],{},[898,93785,2797],{},[2138,93787,2182],{},[902,93789,93790],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,93793,93795],{"className":93794},[886],[888,93796,93797],{"xmlns":890},[892,93798,93799,93815],{},[895,93800,93801,93803,93805,93807,93809,93811,93813],{},[2005,93802,2014],{"stretchy":2013},[2138,93804,5571],{},[2005,93806,2295],{"separator":2294},[2138,93808,66602],{},[2005,93810,2295],{"separator":2294},[2138,93812,2871],{},[2005,93814,2020],{"stretchy":2013},[902,93816,93817],{"encoding":904},"(36, 27, 10)",[883,93819,93821],{"className":93820},[886],[888,93822,93823],{"xmlns":890},[892,93824,93825,93841],{},[895,93826,93827,93829,93831,93833,93835,93837,93839],{},[2005,93828,2014],{"stretchy":2013},[2138,93830,41845],{},[2005,93832,2295],{"separator":2294},[2138,93834,5591],{},[2005,93836,2295],{"separator":2294},[2138,93838,9041],{},[2005,93840,2020],{"stretchy":2013},[902,93842,93843],{"encoding":904},"(64, 8, 20)",[883,93845,93847],{"className":93846},[886],[888,93848,93849],{"xmlns":890},[892,93850,93851,93867],{},[895,93852,93853,93855,93857,93859,93861,93863,93865],{},[2005,93854,2014],{"stretchy":2013},[2138,93856,5010],{},[2005,93858,2295],{"separator":2294},[2138,93860,41845],{},[2005,93862,2295],{"separator":2294},[2138,93864,5591],{},[2005,93866,2020],{"stretchy":2013},[902,93868,93869],{"encoding":904},"(25, 64, 8)",[883,93871,93873],{"className":93872},[886],[888,93874,93875],{"xmlns":890},[892,93876,93877,93893],{},[895,93878,93879,93881,93883,93885,93887,93889,93891],{},[2005,93880,2014],{"stretchy":2013},[2138,93882,2360],{},[2005,93884,2295],{"separator":2294},[2138,93886,72534],{},[2005,93888,2295],{"separator":2294},[2138,93890,2244],{},[2005,93892,2020],{"stretchy":2013},[902,93894,93895],{"encoding":904},"(4, 125, 6)",[883,93897,93899],{"className":93898},[886],[888,93900,93901],{"xmlns":890},[892,93902,93903,93919],{},[895,93904,93905,93907,93909,93911,93913,93915,93917],{},[2005,93906,2014],{"stretchy":2013},[2138,93908,4008],{},[2005,93910,2295],{"separator":2294},[2138,93912,5217],{},[2005,93914,2295],{"separator":2294},[2138,93916,3517],{},[2005,93918,2020],{"stretchy":2013},[902,93920,93921],{"encoding":904},"(9, 40, 12)",[883,93923,93925],{"className":93924},[886],[888,93926,93927],{"xmlns":890},[892,93928,93929,93945],{},[895,93930,93931,93933,93935,93937,93939,93941,93943],{},[2005,93932,2014],{"stretchy":2013},[2138,93934,4008],{},[2005,93936,2295],{"separator":2294},[2138,93938,41845],{},[2005,93940,2295],{"separator":2294},[2138,93942,2237],{},[2005,93944,2020],{"stretchy":2013},[902,93946,93947],{"encoding":904},"(9, 64, 5)",[883,93949,93951],{"className":93950},[886],[888,93952,93953],{"xmlns":890},[892,93954,93955,93971],{},[895,93956,93957,93959,93961,93963,93965,93967,93969],{},[2005,93958,2014],{"stretchy":2013},[2138,93960,41845],{},[2005,93962,2295],{"separator":2294},[2138,93964,5591],{},[2005,93966,2295],{"separator":2294},[2138,93968,2871],{},[2005,93970,2020],{"stretchy":2013},[902,93972,93973],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,93976,93977,93738,93980,94023,94024,94058,94059,6479,94089,94122,94123,94140,94141,94158],{},[38,93978,93979],{},"6.3",[883,93981,93983],{"className":93982},[886],[888,93984,93985],{"xmlns":890},[892,93986,93987,94021],{},[895,93988,93989,93991,93993,94007],{},[898,93990,900],{},[2005,93992,2007],{},[9172,93994,93995,93997,93999],{},[898,93996,2797],{},[2138,93998,2287],{},[895,94000,94001,94003,94005],{},[2138,94002,2287],{},[898,94004,4680],{"mathvariant":2385},[2138,94006,2140],{},[9172,94008,94009,94011,94013],{},[898,94010,2797],{},[2138,94012,2140],{},[895,94014,94015,94017,94019],{},[2138,94016,2287],{},[898,94018,4680],{"mathvariant":2385},[2138,94020,2140],{},[902,94022,33164],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,94025,94027],{"className":94026},[886],[888,94028,94029],{"xmlns":890},[892,94030,94031,94055],{},[895,94032,94033,94039,94041,94043,94045,94051,94053],{},[2281,94034,94035,94037],{},[898,94036,2797],{},[2138,94038,2287],{},[2005,94040,2007],{},[2138,94042,3128],{},[2005,94044,2295],{"separator":2294},[2281,94046,94047,94049],{},[898,94048,2797],{},[2138,94050,2140],{},[2005,94052,2007],{},[2138,94054,46708],{},[902,94056,94057],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,94060,94062],{"className":94061},[886],[888,94063,94064],{"xmlns":890},[892,94065,94066,94086],{},[895,94067,94068,94070,94076,94078,94080],{},[898,94069,2826],{},[2281,94071,94072,94074],{},[898,94073,900],{},[2138,94075,2287],{},[2005,94077,2295],{"separator":2294},[898,94079,2826],{},[2281,94081,94082,94084],{},[898,94083,900],{},[2138,94085,2140],{},[902,94087,94088],{"encoding":904},"MU_1, MU_2",[883,94090,94092],{"className":94091},[886],[888,94093,94094],{"xmlns":890},[892,94095,94096,94120],{},[895,94097,94098,94104,94106,94108,94110,94116,94118],{},[2281,94099,94100,94102],{},[898,94101,2797],{},[2138,94103,2287],{},[2005,94105,2007],{},[2138,94107,3128],{},[2005,94109,2295],{"separator":2294},[2281,94111,94112,94114],{},[898,94113,2797],{},[2138,94115,2140],{},[2005,94117,2007],{},[2138,94119,46708],{},[902,94121,94057],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,94124,94126],{"className":94125},[886],[888,94127,94128],{"xmlns":890},[892,94129,94130,94138],{},[895,94131,94132],{},[2281,94133,94134,94136],{},[898,94135,2797],{},[2138,94137,2287],{},[902,94139,29007],{"encoding":904}," na 60 a poklesu ",[883,94142,94144],{"className":94143},[886],[888,94145,94146],{"xmlns":890},[892,94147,94148,94156],{},[895,94149,94150],{},[2281,94151,94152,94154],{},[898,94153,2797],{},[2138,94155,2140],{},[902,94157,29026],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,94160,94161,94164,94165,94226,94227,1644],{},[38,94162,94163],{},"6.4"," Je dána funkce ",[883,94166,94168],{"className":94167},[886],[888,94169,94170],{"xmlns":890},[892,94171,94172,94224],{},[895,94173,94174,94176,94178,94184,94186,94192,94194,94196,94210],{},[898,94175,900],{},[2005,94177,2014],{"stretchy":2013},[2281,94179,94180,94182],{},[898,94181,2797],{},[2138,94183,2287],{},[2005,94185,2295],{"separator":2294},[2281,94187,94188,94190],{},[898,94189,2797],{},[2138,94191,2140],{},[2005,94193,2020],{"stretchy":2013},[2005,94195,2007],{},[9172,94197,94198,94200,94202],{},[898,94199,2797],{},[2138,94201,2287],{},[895,94203,94204,94206,94208],{},[2138,94205,2287],{},[898,94207,4680],{"mathvariant":2385},[2138,94209,2140],{},[9172,94211,94212,94214,94216],{},[898,94213,2797],{},[2138,94215,2140],{},[895,94217,94218,94220,94222],{},[2138,94219,2287],{},[898,94221,4680],{"mathvariant":2385},[2138,94223,2140],{},[902,94225,29948],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,94228,94230],{"className":94229},[886],[888,94231,94232],{"xmlns":890},[892,94233,94234,94324],{},[895,94235,94236,94238,94240,94246,94248,94250,94252,94254,94256,94258,94264,94266,94268,94270,94272,94274,94276,94278,94280,94286,94288,94290,94292,94294,94296,94298,94304,94306,94308,94310,94312,94314,94316,94322],{},[898,94237,900],{},[2005,94239,2014],{"stretchy":2013},[2281,94241,94242,94244],{},[898,94243,2797],{},[2138,94245,2287],{},[2005,94247,2295],{"separator":2294},[2138,94249,2287],{},[2005,94251,2020],{"stretchy":2013},[2005,94253,2295],{"separator":2294},[898,94255,900],{},[2005,94257,2014],{"stretchy":2013},[2281,94259,94260,94262],{},[898,94261,2797],{},[2138,94263,2287],{},[2005,94265,2295],{"separator":2294},[2138,94267,2140],{},[2005,94269,2020],{"stretchy":2013},[2005,94271,2295],{"separator":2294},[898,94273,900],{},[2005,94275,2014],{"stretchy":2013},[2138,94277,2287],{},[2005,94279,2295],{"separator":2294},[2281,94281,94282,94284],{},[898,94283,2797],{},[2138,94285,2140],{},[2005,94287,2020],{"stretchy":2013},[2005,94289,2295],{"separator":2294},[898,94291,900],{},[2005,94293,2014],{"stretchy":2013},[2138,94295,2140],{},[2005,94297,2295],{"separator":2294},[2281,94299,94300,94302],{},[898,94301,2797],{},[2138,94303,2140],{},[2005,94305,2020],{"stretchy":2013},[2005,94307,2295],{"separator":2294},[898,94309,900],{},[2005,94311,2014],{"stretchy":2013},[2138,94313,2182],{},[2005,94315,2295],{"separator":2294},[2281,94317,94318,94320],{},[898,94319,2797],{},[2138,94321,2140],{},[2005,94323,2020],{"stretchy":2013},[902,94325,94326],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,94328,94329,93738,94332,94376,94377,94485,94486,1343,94511,1343,94536,94578,94579,1343,94608,94633],{},[38,94330,94331],{},"6.5",[883,94333,94335],{"className":94334},[886],[888,94336,94337],{"xmlns":890},[892,94338,94339,94373],{},[895,94340,94341,94343,94345,94359],{},[898,94342,900],{},[2005,94344,2007],{},[9172,94346,94347,94349,94351],{},[898,94348,2797],{},[2138,94350,2287],{},[895,94352,94353,94355,94357],{},[2138,94354,2140],{},[898,94356,4680],{"mathvariant":2385},[2138,94358,2182],{},[9172,94360,94361,94363,94365],{},[898,94362,2797],{},[2138,94364,2140],{},[895,94366,94367,94369,94371],{},[2138,94368,2287],{},[898,94370,4680],{"mathvariant":2385},[2138,94372,2182],{},[902,94374,94375],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,94378,94380],{"className":94379},[886],[888,94381,94382],{"xmlns":890},[892,94383,94384,94482],{},[895,94385,94386,94388,94390,94396,94398,94404,94406,94408,94410,94412,94414,94416,94422,94424,94426,94428,94430,94432,94434,94440,94442,94444,94446,94448,94450,94452,94454,94456,94462,94464,94466,94468,94470,94472,94474,94480],{},[898,94387,900],{},[2005,94389,2014],{"stretchy":2013},[2281,94391,94392,94394],{},[898,94393,2797],{},[2138,94395,2287],{},[2005,94397,2295],{"separator":2294},[2281,94399,94400,94402],{},[898,94401,2797],{},[2138,94403,2140],{},[2005,94405,2020],{"stretchy":2013},[2005,94407,2007],{},[2138,94409,2140],{},[2005,94411,2295],{"separator":2294},[898,94413,900],{},[2005,94415,2014],{"stretchy":2013},[2281,94417,94418,94420],{},[898,94419,2797],{},[2138,94421,2287],{},[2005,94423,2295],{"separator":2294},[2138,94425,2182],{},[2005,94427,2020],{"stretchy":2013},[2005,94429,2295],{"separator":2294},[898,94431,900],{},[2005,94433,2014],{"stretchy":2013},[2281,94435,94436,94438],{},[898,94437,2797],{},[2138,94439,2287],{},[2005,94441,2295],{"separator":2294},[2138,94443,2140],{},[2005,94445,2020],{"stretchy":2013},[2005,94447,2295],{"separator":2294},[898,94449,900],{},[2005,94451,2014],{"stretchy":2013},[2138,94453,2140],{},[2005,94455,2295],{"separator":2294},[2281,94457,94458,94460],{},[898,94459,2797],{},[2138,94461,2140],{},[2005,94463,2020],{"stretchy":2013},[2005,94465,2295],{"separator":2294},[898,94467,900],{},[2005,94469,2014],{"stretchy":2013},[2138,94471,2182],{},[2005,94473,2295],{"separator":2294},[2281,94475,94476,94478],{},[898,94477,2797],{},[2138,94479,2140],{},[2005,94481,2020],{"stretchy":2013},[902,94483,94484],{"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 ",[883,94487,94489],{"className":94488},[886],[888,94490,94491],{"xmlns":890},[892,94492,94493,94508],{},[895,94494,94495,94497,94499,94501,94503,94506],{},[898,94496,1836],{},[2005,94498,2495],{"stretchy":2013},[2138,94500,64564],{},[2005,94502,8431],{"separator":2294},[2138,94504,94505],{},"3,555",[2005,94507,2510],{"stretchy":2013},[902,94509,94510],{"encoding":904},"A[1{,}5; 3{,}555]",[883,94512,94514],{"className":94513},[886],[888,94515,94516],{"xmlns":890},[892,94517,94518,94533],{},[895,94519,94520,94522,94524,94526,94528,94531],{},[898,94521,1844],{},[2005,94523,2495],{"stretchy":2013},[2138,94525,53204],{},[2005,94527,8431],{"separator":2294},[2138,94529,94530],{},"1,28",[2005,94532,2510],{"stretchy":2013},[902,94534,94535],{"encoding":904},"B[2{,}5; 1{,}28]",[883,94537,94539],{"className":94538},[886],[888,94540,94541],{"xmlns":890},[892,94542,94543,94575],{},[895,94544,94545,94547,94549,94551,94553,94555,94557,94563,94565,94567,94569,94571,94573],{},[898,94546,1852],{},[2005,94548,2495],{"stretchy":2013},[2138,94550,2140],{},[2005,94552,8431],{"separator":2294},[898,94554,900],{},[2005,94556,2014],{"stretchy":2013},[2281,94558,94559,94561],{},[898,94560,2797],{},[2138,94562,2287],{},[2005,94564,2295],{"separator":2294},[2138,94566,2182],{},[2005,94568,2020],{"stretchy":2013},[2005,94570,2007],{},[2138,94572,2182],{},[2005,94574,2510],{"stretchy":2013},[902,94576,94577],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,94580,94582],{"className":94581},[886],[888,94583,94584],{"xmlns":890},[892,94585,94586,94605],{},[895,94587,94588,94590,94592,94594,94596,94598,94600,94603],{},[898,94589,1860],{},[2005,94591,2495],{"stretchy":2013},[2138,94593,2182],{},[2005,94595,8431],{"separator":2294},[2138,94597,2287],{},[2005,94599,8431],{"separator":2294},[2138,94601,94602],{},"0,832",[2005,94604,2510],{"stretchy":2013},[902,94606,94607],{"encoding":904},"D[3; 1; 0{,}832]",[883,94609,94611],{"className":94610},[886],[888,94612,94613],{"xmlns":890},[892,94614,94615,94630],{},[895,94616,94617,94619,94621,94623,94625,94628],{},[898,94618,1868],{},[2005,94620,2495],{"stretchy":2013},[2138,94622,53204],{},[2005,94624,8431],{"separator":2294},[2138,94626,94627],{},"4,32",[2005,94629,2510],{"stretchy":2013},[902,94631,94632],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,94635,94636,93738,94639,94682,94683,6479,94696,94730,94731,94748,94749,94766],{},[38,94637,94638],{},"6.6",[883,94640,94642],{"className":94641},[886],[888,94643,94644],{"xmlns":890},[892,94645,94646,94680],{},[895,94647,94648,94650,94652,94666],{},[898,94649,900],{},[2005,94651,2007],{},[9172,94653,94654,94656,94658],{},[898,94655,2797],{},[2138,94657,2287],{},[895,94659,94660,94662,94664],{},[2138,94661,2140],{},[898,94663,4680],{"mathvariant":2385},[2138,94665,2182],{},[9172,94667,94668,94670,94672],{},[898,94669,2797],{},[2138,94671,2140],{},[895,94673,94674,94676,94678],{},[2138,94675,2287],{},[898,94677,4680],{"mathvariant":2385},[2138,94679,2182],{},[902,94681,94375],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,94684,94686],{"className":94685},[886],[888,94687,94688],{"xmlns":890},[892,94689,94690,94694],{},[895,94691,94692],{},[2297,94693,10607],{},[902,94695,28243],{"encoding":904},[883,94697,94699],{"className":94698},[886],[888,94700,94701],{"xmlns":890},[892,94702,94703,94727],{},[895,94704,94705,94711,94713,94715,94717,94723,94725],{},[2281,94706,94707,94709],{},[898,94708,2797],{},[2138,94710,2287],{},[2005,94712,2007],{},[2138,94714,3098],{},[2005,94716,2295],{"separator":2294},[2281,94718,94719,94721],{},[898,94720,2797],{},[2138,94722,2140],{},[2005,94724,2007],{},[2138,94726,8383],{},[902,94728,94729],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,94732,94734],{"className":94733},[886],[888,94735,94736],{"xmlns":890},[892,94737,94738,94746],{},[895,94739,94740],{},[2281,94741,94742,94744],{},[898,94743,2797],{},[2138,94745,2287],{},[902,94747,29007],{"encoding":904},", poklesne-li ",[883,94750,94752],{"className":94751},[886],[888,94753,94754],{"xmlns":890},[892,94755,94756,94764],{},[895,94757,94758],{},[2281,94759,94760,94762],{},[898,94761,2797],{},[2138,94763,2140],{},[902,94765,29026],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,94768,94769,94772,94773,94790,94791,94808,94809,94841,94842,94867,94868,94881,94882,1343,94906,1343,94930,1644],{},[38,94770,94771],{},"6.7"," Míra uspokojení z nákupu množství ",[883,94774,94776],{"className":94775},[886],[888,94777,94778],{"xmlns":890},[892,94779,94780,94788],{},[895,94781,94782],{},[2281,94783,94784,94786],{},[898,94785,2797],{},[2138,94787,2287],{},[902,94789,29007],{"encoding":904}," nealko nápojů a množství ",[883,94792,94794],{"className":94793},[886],[888,94795,94796],{"xmlns":890},[892,94797,94798,94806],{},[895,94799,94800],{},[2281,94801,94802,94804],{},[898,94803,2797],{},[2138,94805,2140],{},[902,94807,29026],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,94810,94812],{"className":94811},[886],[888,94813,94814],{"xmlns":890},[892,94815,94816,94838],{},[895,94817,94818,94820,94822],{},[898,94819,900],{},[2005,94821,2007],{},[8123,94823,94824],{},[895,94825,94826,94832],{},[2281,94827,94828,94830],{},[898,94829,2797],{},[2138,94831,2287],{},[2281,94833,94834,94836],{},[898,94835,2797],{},[2138,94837,2140],{},[902,94839,94840],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,94843,94845],{"className":94844},[886],[888,94846,94847],{"xmlns":890},[892,94848,94849,94865],{},[895,94850,94851,94857,94859],{},[2281,94852,94853,94855],{},[898,94854,2797],{},[2138,94856,2287],{},[2005,94858,2295],{"separator":2294},[2281,94860,94861,94863],{},[898,94862,2797],{},[2138,94864,2140],{},[902,94866,35627],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,94869,94871],{"className":94870},[886],[888,94872,94873],{"xmlns":890},[892,94874,94875,94879],{},[895,94876,94877],{},[2297,94878,10607],{},[902,94880,28243],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,94883,94885],{"className":94884},[886],[888,94886,94887],{"xmlns":890},[892,94888,94889,94903],{},[895,94890,94891,94893,94895,94897,94899,94901],{},[2297,94892,10607],{},[2005,94894,2014],{"stretchy":2013},[2138,94896,2237],{},[2005,94898,2295],{"separator":2294},[2138,94900,9041],{},[2005,94902,2020],{"stretchy":2013},[902,94904,94905],{"encoding":904},"\\text{MRCS}(5, 20)",[883,94907,94909],{"className":94908},[886],[888,94910,94911],{"xmlns":890},[892,94912,94913,94927],{},[895,94914,94915,94917,94919,94921,94923,94925],{},[2297,94916,10607],{},[2005,94918,2014],{"stretchy":2013},[2138,94920,9041],{},[2005,94922,2295],{"separator":2294},[2138,94924,2237],{},[2005,94926,2020],{"stretchy":2013},[902,94928,94929],{"encoding":904},"\\text{MRCS}(20, 5)",[883,94931,94933],{"className":94932},[886],[888,94934,94935],{"xmlns":890},[892,94936,94937,94951],{},[895,94938,94939,94941,94943,94945,94947,94949],{},[2297,94940,10607],{},[2005,94942,2014],{"stretchy":2013},[2138,94944,2140],{},[2005,94946,2295],{"separator":2294},[2138,94948,3128],{},[2005,94950,2020],{"stretchy":2013},[902,94952,94953],{"encoding":904},"\\text{MRCS}(2, 50)",[3876,94955,94956],{},[724,94957,94958,94960,94961,1644],{},[883,94959,4578],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,94962,94965],{"className":94963,"dataFsResolvedFilePath":911,"href":94964},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,94967,15726],{"id":15725},[120,94969,94970,94976,94981,94987,95040,95050,95096,95151,95214,95271,95326,95365],{},[123,94971,94972,94975],{},[38,94973,94974],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,94977,94978,94980],{},[38,94979,86873],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,94982,94983,94986],{},[38,94984,94985],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,94988,94989,94991,94992,95005,95006,1644],{},[38,94990,87200],{}," — uspořádaná ",[883,94993,94995],{"className":94994},[886],[888,94996,94997],{"xmlns":890},[892,94998,94999,95003],{},[895,95000,95001],{},[898,95002,36865],{},[902,95004,36865],{"encoding":904},"-tice ",[883,95007,95009],{"className":95008},[886],[888,95010,95011],{"xmlns":890},[892,95012,95013,95037],{},[895,95014,95015,95017,95023,95025,95027,95029,95035],{},[2005,95016,2014],{"stretchy":2013},[2281,95018,95019,95021],{},[898,95020,2797],{},[2138,95022,2287],{},[2005,95024,2295],{"separator":2294},[2005,95026,9652],{},[2005,95028,2295],{"separator":2294},[2281,95030,95031,95033],{},[898,95032,2797],{},[898,95034,36865],{},[2005,95036,2020],{"stretchy":2013},[902,95038,95039],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,95041,95042,95045,95046,95049],{},[38,95043,95044],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,95047,95048],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,95051,95052,2212,95055,95095],{},[38,95053,95054],{},"Funkce užitečnosti",[883,95056,95058],{"className":95057},[886],[888,95059,95060],{"xmlns":890},[892,95061,95062,95092],{},[895,95063,95064,95066,95068,95070,95072,95078,95080,95082,95084,95090],{},[898,95065,900],{},[2005,95067,2007],{},[898,95069,900],{},[2005,95071,2014],{"stretchy":2013},[2281,95073,95074,95076],{},[898,95075,2797],{},[2138,95077,2287],{},[2005,95079,2295],{"separator":2294},[2005,95081,9652],{},[2005,95083,2295],{"separator":2294},[2281,95085,95086,95088],{},[898,95087,2797],{},[898,95089,36865],{},[2005,95091,2020],{"stretchy":2013},[902,95093,95094],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,95097,95098,2212,95101,95130,95131,2212,95134,95150],{},[38,95099,95100],{},"Mezní užitečnost",[883,95102,95104],{"className":95103},[886],[888,95105,95106],{"xmlns":890},[892,95107,95108,95128],{},[895,95109,95110,95112,95118,95120],{},[898,95111,2826],{},[2281,95113,95114,95116],{},[898,95115,900],{},[898,95117,17797],{},[2005,95119,2007],{},[9172,95121,95122,95124,95126],{},[898,95123,900],{},[898,95125,17797],{},[2005,95127,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[902,95129,86658],{"encoding":904}," — vzorec (6.2); ",[38,95132,95133],{},"totální diferenciál",[883,95135,95137],{"className":95136},[886],[888,95138,95139],{"xmlns":890},[892,95140,95141,95147],{},[895,95142,95143,95145],{},[898,95144,2203],{"mathvariant":2385},[898,95146,900],{},[902,95148,95149],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,95152,95153,95155,95156,95180,95181,95213],{},[38,95154,88836],{}," — (6.4) ",[883,95157,95159],{"className":95158},[886],[888,95160,95161],{"xmlns":890},[892,95162,95163,95177],{},[895,95164,95165,95173,95175],{},[9172,95166,95167,95169,95171],{},[898,95168,900],{},[898,95170,17797],{},[2005,95172,2387],{"mathvariant":2385,"lspace":2386,"rspace":2386},[2005,95174,3416],{},[2138,95176,2336],{},[902,95178,95179],{"encoding":904},"U'_i > 0",", (6.5) ",[883,95182,95184],{"className":95183},[886],[888,95185,95186],{"xmlns":890},[892,95187,95188,95210],{},[895,95189,95190,95206,95208],{},[9172,95191,95192,95194,95200],{},[898,95193,900],{},[895,95195,95196,95198],{},[898,95197,17797],{},[898,95199,17797],{},[895,95201,95202,95204],{},[2005,95203,2387],{"mathvariant":2385},[2005,95205,2387],{"mathvariant":2385},[2005,95207,3455],{},[2138,95209,2336],{},[902,95211,95212],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,95215,95216,2212,95218,95249,95250,1644],{},[38,95217,90624],{},[883,95219,95221],{"className":95220},[886],[888,95222,95223],{"xmlns":890},[892,95224,95225,95247],{},[895,95226,95227,95229,95231,95239],{},[898,95228,900],{},[2005,95230,2007],{},[9172,95232,95233,95235,95237],{},[898,95234,2797],{},[2138,95236,2287],{},[898,95238,207],{},[9172,95240,95241,95243,95245],{},[898,95242,2797],{},[2138,95244,2140],{},[898,95246,2107],{},[902,95248,35808],{"encoding":904}," — (6.6), speciálně ",[883,95251,95253],{"className":95252},[886],[888,95254,95255],{"xmlns":890},[892,95256,95257,95269],{},[895,95258,95259,95261,95263,95265,95267],{},[898,95260,2107],{},[2005,95262,2007],{},[2138,95264,2287],{},[2005,95266,2234],{},[898,95268,207],{},[902,95270,90778],{"encoding":904},[123,95272,95273,2212,95276,95311,95312,95325],{},[38,95274,95275],{},"Křivky užitečnosti (indiferenční)",[883,95277,95279],{"className":95278},[886],[888,95280,95281],{"xmlns":890},[892,95282,95283,95309],{},[895,95284,95285,95287,95289,95295,95297,95303,95305,95307],{},[898,95286,900],{},[2005,95288,2014],{"stretchy":2013},[2281,95290,95291,95293],{},[898,95292,2797],{},[2138,95294,2287],{},[2005,95296,2295],{"separator":2294},[2281,95298,95299,95301],{},[898,95300,2797],{},[2138,95302,2140],{},[2005,95304,2020],{"stretchy":2013},[2005,95306,2007],{},[898,95308,2151],{},[902,95310,9774],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,95313,95315],{"className":95314},[886],[888,95316,95317],{"xmlns":890},[892,95318,95319,95323],{},[895,95320,95321],{},[898,95322,900],{},[902,95324,900],{"encoding":904},", konvexní.",[123,95327,95328,2212,95330,95364],{},[38,95329,92169],{},[883,95331,95333],{"className":95332},[886],[888,95334,95335],{"xmlns":890},[892,95336,95337,95361],{},[895,95338,95339,95341,95343,95345,95351,95353,95355],{},[2297,95340,10607],{},[2005,95342,2007],{},[898,95344,2826],{},[2281,95346,95347,95349],{},[898,95348,900],{},[2138,95350,2287],{},[898,95352,4680],{"mathvariant":2385},[898,95354,2826],{},[2281,95356,95357,95359],{},[898,95358,900],{},[2138,95360,2140],{},[902,95362,95363],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,95366,95367,2212,95370,9775,95399,95402],{},[38,95368,95369],{},"Podmínka optimality",[883,95371,95373],{"className":95372},[886],[888,95374,95375],{"xmlns":890},[892,95376,95377,95397],{},[895,95378,95379,95381,95383,95389,95391],{},[2297,95380,10607],{},[2005,95382,2007],{},[2281,95384,95385,95387],{},[898,95386,3946],{},[2138,95388,2287],{},[898,95390,4680],{"mathvariant":2385},[2281,95392,95393,95395],{},[898,95394,3946],{},[2138,95396,2140],{},[902,95398,28003],{"encoding":904},[207,95400,36759],{"className":95401,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,95404,3800],{"id":3799},[120,95406,95407,95444,95485,95495],{},[123,95408,95409,2212,95412,95415,95416,95429,95430,95443],{},[38,95410,95411],{},"Navazující téma:",[207,95413,913],{"className":95414,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,95417,95419],{"className":95418},[886],[888,95420,95421],{"xmlns":890},[892,95422,95423,95427],{},[895,95424,95425],{},[898,95426,900],{},[902,95428,900],{"encoding":904},", min ",[883,95431,95433],{"className":95432},[886],[888,95434,95435],{"xmlns":890},[892,95436,95437,95441],{},[895,95438,95439],{},[898,95440,1868],{},[902,95442,1868],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,95445,95446,2212,95449,11097,95452,86413,95455,95458,95459,95462,95463,18654,95481,95484],{},[38,95447,95448],{},"Související pojmy:",[207,95450,784],{"className":95451,"dataFsResolvedFilePath":782,"href":783},[210],[207,95453,2366],{"className":95454,"dataFsResolvedFilePath":764,"href":765},[210],[207,95456,11092],{"className":95457,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,95460,11946],{"className":95461,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,95464,95466],{"className":95465},[886],[888,95467,95468],{"xmlns":890},[892,95469,95470,95478],{},[895,95471,95472],{},[2281,95473,95474,95476],{},[898,95475,1860],{},[898,95477,17797],{},[902,95479,95480],{"encoding":904},"D_i",[207,95482,793],{"className":95483,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,95486,95487,2212,95489,1343,95492],{},[38,95488,36708],{},[207,95490,1094],{"className":95491,"dataFsResolvedFilePath":838,"href":839},[210],[207,95493,1101],{"className":95494,"dataFsResolvedFilePath":868,"href":869},[210],[123,95496,95497,2212,95499],{},[38,95498,16210],{},[207,95500,16214],{"className":95501,"dataFsResolvedFilePath":1641,"href":1642},[210],{"title":641,"searchDepth":642,"depth":642,"links":95503},[95504,95505,95506,95509,95510,95513,95517,95518,95521,95522,95523,95524,95525,95526,95527],{"id":12011,"depth":642,"text":12012},{"id":86797,"depth":642,"text":86798},{"id":86856,"depth":642,"text":86857,"children":95507},[95508],{"id":86872,"depth":649,"text":86873},{"id":87179,"depth":642,"text":87180},{"id":88039,"depth":642,"text":88040,"children":95511},[95512],{"id":88586,"depth":649,"text":80216},{"id":88835,"depth":642,"text":88836,"children":95514},[95515],{"id":89708,"depth":649,"text":95516},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":90623,"depth":642,"text":90624},{"id":91159,"depth":642,"text":91160,"children":95519},[95520],{"id":91933,"depth":649,"text":91934},{"id":92163,"depth":642,"text":92164},{"id":92924,"depth":642,"text":92925},{"id":93462,"depth":642,"text":93463},{"id":49886,"depth":642,"text":49887},{"id":93598,"depth":642,"text":93599},{"id":15725,"depth":642,"text":15726},{"id":3799,"depth":642,"text":3800},{},"\u002Ftopics\u002Fuzitecnost",{"title":86581,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,9779,95534,86575,11127,95535],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":95538,"title":757,"body":95539,"course":1128,"courses":659,"created":1129,"description":95812,"extension":661,"meta":95813,"navigation":664,"path":95814,"seo":95815,"sources":95816,"stem":95817,"tags":95818,"type":3865,"updated":677,"__hash__":95824},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":95540,"toc":95804},[95541,95544,95551,95558,95562,95572,95574,95608,95612,95655,95658,95716,95720,95750,95754,95775,95777],[12,95542,757],{"id":95543},"základy-matematické-ekonomie",[724,95545,95546,95547,95550],{},"Úvodní pojmy a princip modelování v ",[207,95548,16387],{"className":95549,"dataFsResolvedFilePath":1641,"href":1642},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,95552,95553],{},[2568,95554],{"alt":95555,"className":95556,"src":95557},"imek-model-promenne",[210,2572],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,95559,95561],{"id":95560},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,95563,95564,95567,95568,95571],{},[38,95565,95566],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,95569,95570],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,95573,15726],{"id":15725},[120,95575,95576,95582,95588,95594,95603],{},[123,95577,95578,95581],{},[38,95579,95580],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,95583,95584,95587],{},[38,95585,95586],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,95589,95590,95593],{},[38,95591,95592],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,95595,95596,7021,95599,95602],{},[38,95597,95598],{},"Ceteris paribus",[614,95600,95601],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,95604,95605,95607],{},[38,95606,50640],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,95609,95611],{"id":95610},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,95613,95614,95654],{},[883,95615,95617],{"className":95616},[886],[888,95618,95619],{"xmlns":890},[892,95620,95621,95651],{},[895,95622,95623,95625,95627,95629,95631,95633,95635,95637,95639,95641,95643,95645,95647,95649],{},[898,95624,2797],{},[2005,95626,2007],{},[898,95628,1860],{},[2005,95630,2014],{"stretchy":2013},[898,95632,3946],{},[2005,95634,2295],{"separator":2294},[898,95636,9134],{},[2005,95638,2295],{"separator":2294},[898,95640,18301],{},[2005,95642,2295],{"separator":2294},[898,95644,900],{},[2005,95646,2295],{"separator":2294},[2005,95648,9652],{},[2005,95650,2020],{"stretchy":2013},[902,95652,95653],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,95656,95657],{},"Zjednodušení:",[120,95659,95660,95688],{},[123,95661,95662,2212,95665],{},[38,95663,95664],{},"Jednofaktorový model:",[883,95666,95668],{"className":95667},[886],[888,95669,95670],{"xmlns":890},[892,95671,95672,95686],{},[895,95673,95674,95676,95678,95680,95682,95684],{},[898,95675,2797],{},[2005,95677,2007],{},[898,95679,1860],{},[2005,95681,2014],{"stretchy":2013},[898,95683,3946],{},[2005,95685,2020],{"stretchy":2013},[902,95687,4200],{"encoding":904},[123,95689,95690,2212,95693],{},[38,95691,95692],{},"Inverzní zápis:",[883,95694,95696],{"className":95695},[886],[888,95697,95698],{"xmlns":890},[892,95699,95700,95714],{},[895,95701,95702,95704,95706,95708,95710,95712],{},[898,95703,3946],{},[2005,95705,2007],{},[898,95707,1860],{},[2005,95709,2014],{"stretchy":2013},[898,95711,2797],{},[2005,95713,2020],{"stretchy":2013},[902,95715,4646],{"encoding":904},[115,95717,95719],{"id":95718},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,95721,95722,95731],{},[123,95723,95724,95727,95728,3927],{},[38,95725,95726],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,95729,16246],{"className":95730,"dataFsResolvedFilePath":800,"href":801},[210],[123,95732,95733,95736,95737,95740,95741,95744,95745,95749],{},[38,95734,95735],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,95738,1145],{"className":95739,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,95742,16259],{"className":95743,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,95746,95748],{"className":95747,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,95751,95753],{"id":95752},"konvence-z-přednášek","Konvence z přednášek",[120,95755,95756,95763,95769],{},[123,95757,95758,95759,95762],{},"Symbol ",[95760,95761,2739],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,95764,95765,95766,1644],{},"Numerické výsledky ",[38,95767,95768],{},"na 3 desetinná místa",[123,95770,3904,95771,95774],{},[614,95772,95773],{},"jednotková změna"," má standardní význam (změna o 1).",[115,95776,3800],{"id":3799},[120,95778,95779,95784,95792],{},[123,95780,95781,95783],{},[38,95782,3807],{}," —",[123,95785,95786,2212,95788],{},[38,95787,3815],{},[207,95789,95791],{"className":95790,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,95793,95794,2212,95796,1343,95800],{},[38,95795,3823],{},[207,95797,95799],{"className":95798,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,95801,95803],{"className":95802,"dataFsResolvedFilePath":1641,"href":1642},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":95805},[95806,95807,95808,95809,95810,95811],{"id":95560,"depth":642,"text":95561},{"id":15725,"depth":642,"text":15726},{"id":95610,"depth":642,"text":95611},{"id":95718,"depth":642,"text":95719},{"id":95752,"depth":642,"text":95753},{"id":3799,"depth":642,"text":3800},"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":95812},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,95819,95820,95821,95822,95823],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":95826,"title":95827,"body":95828,"course":1128,"courses":659,"created":9562,"description":641,"extension":661,"meta":100100,"navigation":664,"path":100101,"seo":100102,"sources":100103,"stem":100104,"tags":100105,"type":3865,"updated":677,"__hash__":100109},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":95829,"toc":100083},[95830,95833,95927,95931,95953,95967,96019,96021,96025,96088,96131,96150,96313,96412,96415,96482,96486,96615,96654,96684,96796,96841,96907,96960,97036,97092,97094,97098,97162,97206,97226,97387,97390,97474,97571,97574,97640,97644,97693,97719,97824,97888,97893,97989,98036,98038,98041,98063,98105,98112,98145,98147,98218,98272,98381,98385,98474,98550,98814,98852,98854,98858,98861,98868,99179,99182,99240,99420,99449,99451,99455,99461,99599,99608,99610,99612,100037,100039,100041],[12,95831,95827],{"id":95832},"zdanění-trhu-dopady-daně-na-rovnováhu",[3876,95834,95835],{},[724,95836,95837,42633,95839,95852,95853,95856,95857,95859,95860,95863,95864,95885,95886,95909,95910,95913,95914,1644],{},[883,95838,4164],{},[883,95840,95842],{"className":95841},[886],[888,95843,95844],{"xmlns":890},[892,95845,95846,95850],{},[895,95847,95848],{},[898,95849,2783],{},[902,95851,2783],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,95854,95855],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,95858,86864],{}," (je-li uložena spotřebiteli). Výsledné ",[38,95861,95862],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,95865,95867],{"className":95866},[886],[888,95868,95869],{"xmlns":890},[892,95870,95871,95883],{},[895,95872,95873],{},[2281,95874,95875,95877],{},[898,95876,2783],{},[895,95878,95879,95881],{},[898,95880,42682],{},[898,95882,724],{},[902,95884,42687],{"encoding":904}," (spotřebitel) a ",[883,95887,95889],{"className":95888},[886],[888,95890,95891],{"xmlns":890},[892,95892,95893,95907],{},[895,95894,95895],{},[2281,95896,95897,95899],{},[898,95898,2783],{},[895,95900,95901,95903,95905],{},[898,95902,42705],{},[898,95904,2003],{},[898,95906,12047],{},[902,95908,42712],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,95911,95912],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,95915,95917],{"className":95916},[886],[888,95918,95919],{"xmlns":890},[892,95920,95921,95925],{},[895,95922,95923],{},[898,95924,2783],{},[902,95926,2783],{"encoding":904},[115,95928,95930],{"id":95929},"dvě-formy-zdanění","Dvě formy zdanění",[724,95932,95933,95934,95952],{},"Uvažujme jednotkovou daň ",[883,95935,95937],{"className":95936},[886],[888,95938,95939],{"xmlns":890},[892,95940,95941,95949],{},[895,95942,95943,95945,95947],{},[898,95944,2783],{},[2005,95946,3416],{},[2138,95948,2336],{},[902,95950,95951],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,95954,95955,95961],{},[123,95956,95957,95960],{},[38,95958,95959],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,95962,95963,95966],{},[38,95964,95965],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,95968,95969,95970,95983,95984,95987,95988,1644],{},"V obou případech dochází k posunu jedné z křivek o ",[883,95971,95973],{"className":95972},[886],[888,95974,95975],{"xmlns":890},[892,95976,95977,95981],{},[895,95978,95979],{},[898,95980,2783],{},[902,95982,2783],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,95985,95986],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,95989,95991],{"className":95990},[886],[888,95992,95993],{"xmlns":890},[892,95994,95995,96017],{},[895,95996,95997,95999,96001,96007,96009,96015],{},[898,95998,1868],{},[2005,96000,2495],{"stretchy":2013},[2133,96002,96003,96005],{},[898,96004,2797],{},[898,96006,1868],{},[2005,96008,2295],{"separator":2294},[2133,96010,96011,96013],{},[898,96012,3946],{},[898,96014,1868],{},[2005,96016,2510],{"stretchy":2013},[902,96018,41372],{"encoding":904},[36975,96020],{},[115,96022,96024],{"id":96023},"daň-uložená-výrobci","Daň uložená výrobci",[724,96026,96027,96028,96041,96042,96059,96060,96087],{},"Je-li daň ",[883,96029,96031],{"className":96030},[886],[888,96032,96033],{"xmlns":890},[892,96034,96035,96039],{},[895,96036,96037],{},[898,96038,2783],{},[902,96040,2783],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,96043,96045],{"className":96044},[886],[888,96046,96047],{"xmlns":890},[892,96048,96049,96057],{},[895,96050,96051,96053,96055],{},[898,96052,3946],{},[2005,96054,2234],{},[898,96056,2783],{},[902,96058,41127],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,96061,96063],{"className":96062},[886],[888,96064,96065],{"xmlns":890},[892,96066,96067,96085],{},[895,96068,96069,96071,96073,96075,96077,96079,96081,96083],{},[898,96070,3946],{},[2005,96072,2234],{},[898,96074,2783],{},[2005,96076,2007],{},[898,96078,8679],{},[2005,96080,2014],{"stretchy":2013},[898,96082,2797],{},[2005,96084,2020],{"stretchy":2013},[902,96086,41156],{"encoding":904}," nová funkce nabídky:",[883,96089,96091],{"className":96090},[886],[888,96092,96093],{"xmlns":890,"display":28071},[892,96094,96095,96129],{},[895,96096,96097,96099,96101,96107,96109,96111,96113,96115,96117,96119,96121,96123,96125,96127],{},[898,96098,3946],{},[2005,96100,2007],{},[2281,96102,96103,96105],{},[898,96104,8679],{},[2138,96106,2287],{},[2005,96108,2014],{"stretchy":2013},[898,96110,2797],{},[2005,96112,2020],{"stretchy":2013},[2005,96114,2007],{},[898,96116,8679],{},[2005,96118,2014],{"stretchy":2013},[898,96120,2797],{},[2005,96122,2020],{"stretchy":2013},[2005,96124,2104],{},[898,96126,2783],{},[898,96128,1644],{"mathvariant":2385},[902,96130,41201],{"encoding":904},[724,96132,96133,96134,2212,96147,96149],{},"Nabídka se tedy posouvá o ",[883,96135,96137],{"className":96136},[886],[888,96138,96139],{"xmlns":890},[892,96140,96141,96145],{},[895,96142,96143],{},[898,96144,2783],{},[902,96146,2783],{"encoding":904},[38,96148,41234],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,96151,96152,96153,96193,96194,3894,96222,96250,96251,96270,96271,96295,96296,3927],{},"Nový rovnovážný bod ",[883,96154,96156],{"className":96155},[886],[888,96157,96158],{"xmlns":890},[892,96159,96160,96190],{},[895,96161,96162,96168,96170,96178,96180,96188],{},[2281,96163,96164,96166],{},[898,96165,1868],{},[2138,96167,2287],{},[2005,96169,2495],{"stretchy":2013},[9172,96171,96172,96174,96176],{},[898,96173,2797],{},[2138,96175,2287],{},[898,96177,1868],{},[2005,96179,2295],{"separator":2294},[9172,96181,96182,96184,96186],{},[898,96183,3946],{},[2138,96185,2287],{},[898,96187,1868],{},[2005,96189,2510],{"stretchy":2013},[902,96191,96192],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,96195,96197],{"className":96196},[886],[888,96198,96199],{"xmlns":890},[892,96200,96201,96219],{},[895,96202,96203,96211,96213],{},[9172,96204,96205,96207,96209],{},[898,96206,2797],{},[2138,96208,2287],{},[898,96210,1868],{},[2005,96212,3455],{},[2133,96214,96215,96217],{},[898,96216,2797],{},[898,96218,1868],{},[902,96220,96221],{"encoding":904},"Q_1^E \u003C Q^E",[883,96223,96225],{"className":96224},[886],[888,96226,96227],{"xmlns":890},[892,96228,96229,96247],{},[895,96230,96231,96239,96241],{},[9172,96232,96233,96235,96237],{},[898,96234,3946],{},[2138,96236,2287],{},[898,96238,1868],{},[2005,96240,3416],{},[2133,96242,96243,96245],{},[898,96244,3946],{},[898,96246,1868],{},[902,96248,96249],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,96252,96254],{"className":96253},[886],[888,96255,96256],{"xmlns":890},[892,96257,96258,96268],{},[895,96259,96260],{},[9172,96261,96262,96264,96266],{},[898,96263,3946],{},[2138,96265,2287],{},[898,96267,1868],{},[902,96269,47862],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,96272,96274],{"className":96273},[886],[888,96275,96276],{"xmlns":890},[892,96277,96278,96292],{},[895,96279,96280,96288,96290],{},[9172,96281,96282,96284,96286],{},[898,96283,3946],{},[2138,96285,2287],{},[898,96287,1868],{},[2005,96289,2234],{},[898,96291,2783],{},[902,96293,96294],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,96297,96299],{"className":96298},[886],[888,96300,96301],{"xmlns":890},[892,96302,96303,96311],{},[895,96304,96305],{},[2133,96306,96307,96309],{},[898,96308,3946],{},[898,96310,1868],{},[902,96312,41471],{"encoding":904},[724,96314,96315],{},[614,96316,96317,96318,96348,96349,96362,96363,5675,96380,96393,96394,1644],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,96319,96321],{"className":96320},[886],[888,96322,96323],{"xmlns":890},[892,96324,96325,96345],{},[895,96326,96327,96329,96331,96337,96339,96341,96343],{},[898,96328,8679],{},[2005,96330,3131],{},[2281,96332,96333,96335],{},[898,96334,8679],{},[2138,96336,2287],{},[2005,96338,2007],{},[898,96340,8679],{},[2005,96342,2104],{},[898,96344,2783],{},[902,96346,96347],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,96350,96352],{"className":96351},[886],[888,96353,96354],{"xmlns":890},[892,96355,96356,96360],{},[895,96357,96358],{},[898,96359,2783],{},[902,96361,2783],{"encoding":904},". Průsečík ",[883,96364,96366],{"className":96365},[886],[888,96367,96368],{"xmlns":890},[892,96369,96370,96378],{},[895,96371,96372],{},[2281,96373,96374,96376],{},[898,96375,8679],{},[2138,96377,2287],{},[902,96379,41002],{"encoding":904},[883,96381,96383],{"className":96382},[886],[888,96384,96385],{"xmlns":890},[892,96386,96387,96391],{},[895,96388,96389],{},[898,96390,1860],{},[902,96392,1860],{"encoding":904}," je nový rovnovážný bod ",[883,96395,96397],{"className":96396},[886],[888,96398,96399],{"xmlns":890},[892,96400,96401,96409],{},[895,96402,96403],{},[2281,96404,96405,96407],{},[898,96406,1868],{},[2138,96408,2287],{},[902,96410,96411],{"encoding":904},"E_1",[198,96413,45308],{"id":96414},"příklad-29",[724,96416,96417,41660,96419,41695,96443,96463,96464,96481],{},[38,96418,37938],{},[883,96420,96422],{"className":96421},[886],[888,96423,96424],{"xmlns":890},[892,96425,96426,96440],{},[895,96427,96428,96430,96432,96434,96436,96438],{},[898,96429,3946],{},[2005,96431,2007],{},[2138,96433,3517],{},[2005,96435,2234],{},[2138,96437,2140],{},[898,96439,2797],{},[902,96441,96442],{"encoding":904},"P = 12 - 2Q",[883,96444,96446],{"className":96445},[886],[888,96447,96448],{"xmlns":890},[892,96449,96450,96460],{},[895,96451,96452,96454,96456,96458],{},[898,96453,3946],{},[2005,96455,2007],{},[2138,96457,2360],{},[898,96459,2797],{},[902,96461,96462],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,96465,96467],{"className":96466},[886],[888,96468,96469],{"xmlns":890},[892,96470,96471,96479],{},[895,96472,96473,96475,96477],{},[898,96474,2783],{},[2005,96476,2007],{},[2138,96478,2244],{},[902,96480,41273],{"encoding":904}," Kč.",[724,96483,96484],{},[38,96485,37970],{},[724,96487,96488,96491,96492,5575,96518,5595,96538,1343,96560,96590,96591,1644],{},[614,96489,96490],{},"Bez daně."," Z rovnosti ",[883,96493,96495],{"className":96494},[886],[888,96496,96497],{"xmlns":890},[892,96498,96499,96515],{},[895,96500,96501,96503,96505,96507,96509,96511,96513],{},[2138,96502,3517],{},[2005,96504,2234],{},[2138,96506,2140],{},[898,96508,2797],{},[2005,96510,2007],{},[2138,96512,2360],{},[898,96514,2797],{},[902,96516,96517],{"encoding":904},"12 - 2Q = 4Q",[883,96519,96521],{"className":96520},[886],[888,96522,96523],{"xmlns":890},[892,96524,96525,96535],{},[895,96526,96527,96529,96531,96533],{},[2138,96528,2244],{},[898,96530,2797],{},[2005,96532,2007],{},[2138,96534,3517],{},[902,96536,96537],{"encoding":904},"6Q = 12",[883,96539,96541],{"className":96540},[886],[888,96542,96543],{"xmlns":890},[892,96544,96545,96557],{},[895,96546,96547,96553,96555],{},[2133,96548,96549,96551],{},[898,96550,2797],{},[898,96552,1868],{},[2005,96554,2007],{},[2138,96556,2140],{},[902,96558,96559],{"encoding":904},"Q^E = 2",[883,96561,96563],{"className":96562},[886],[888,96564,96565],{"xmlns":890},[892,96566,96567,96587],{},[895,96568,96569,96575,96577,96579,96581,96583,96585],{},[2133,96570,96571,96573],{},[898,96572,3946],{},[898,96574,1868],{},[2005,96576,2007],{},[2138,96578,2360],{},[2005,96580,3185],{},[2138,96582,2140],{},[2005,96584,2007],{},[2138,96586,5591],{},[902,96588,96589],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,96592,96594],{"className":96593},[886],[888,96595,96596],{"xmlns":890},[892,96597,96598,96612],{},[895,96599,96600,96602,96604,96606,96608,96610],{},[898,96601,1868],{},[2005,96603,2495],{"stretchy":2013},[2138,96605,2140],{},[2005,96607,2295],{"separator":2294},[2138,96609,5591],{},[2005,96611,2510],{"stretchy":2013},[902,96613,96614],{"encoding":904},"E[2, 8]",[724,96616,96617,96620,96621,96653],{},[614,96618,96619],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,96622,96624],{"className":96623},[886],[888,96625,96626],{"xmlns":890},[892,96627,96628,96650],{},[895,96629,96630,96636,96638,96640,96642,96644,96646,96648],{},[2281,96631,96632,96634],{},[898,96633,8679],{},[2138,96635,2287],{},[2005,96637,2713],{},[898,96639,3946],{},[2005,96641,2007],{},[2138,96643,2360],{},[898,96645,2797],{},[2005,96647,2104],{},[2138,96649,2244],{},[902,96651,96652],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,96655,96657],{"className":96656},[886],[888,96658,96659],{"xmlns":890,"display":28071},[892,96660,96661,96681],{},[895,96662,96663,96665,96667,96669,96671,96673,96675,96677,96679],{},[2138,96664,3517],{},[2005,96666,2234],{},[2138,96668,2140],{},[898,96670,2797],{},[2005,96672,2007],{},[2138,96674,2360],{},[898,96676,2797],{},[2005,96678,2104],{},[2138,96680,2244],{},[902,96682,96683],{"encoding":904},"12 - 2Q = 4Q + 6",[724,96685,96686,96687,5595,96707,1343,96731,96767,96768,1644],{},"plyne ",[883,96688,96690],{"className":96689},[886],[888,96691,96692],{"xmlns":890},[892,96693,96694,96704],{},[895,96695,96696,96698,96700,96702],{},[2138,96697,2244],{},[898,96699,2797],{},[2005,96701,2007],{},[2138,96703,2244],{},[902,96705,96706],{"encoding":904},"6Q = 6",[883,96708,96710],{"className":96709},[886],[888,96711,96712],{"xmlns":890},[892,96713,96714,96728],{},[895,96715,96716,96724,96726],{},[9172,96717,96718,96720,96722],{},[898,96719,2797],{},[2138,96721,2287],{},[898,96723,1868],{},[2005,96725,2007],{},[2138,96727,2287],{},[902,96729,96730],{"encoding":904},"Q_1^E = 1",[883,96732,96734],{"className":96733},[886],[888,96735,96736],{"xmlns":890},[892,96737,96738,96764],{},[895,96739,96740,96748,96750,96752,96754,96756,96758,96760,96762],{},[9172,96741,96742,96744,96746],{},[898,96743,3946],{},[2138,96745,2287],{},[898,96747,1868],{},[2005,96749,2007],{},[2138,96751,2360],{},[2005,96753,3185],{},[2138,96755,2287],{},[2005,96757,2104],{},[2138,96759,2244],{},[2005,96761,2007],{},[2138,96763,2871],{},[902,96765,96766],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,96769,96771],{"className":96770},[886],[888,96772,96773],{"xmlns":890},[892,96774,96775,96793],{},[895,96776,96777,96783,96785,96787,96789,96791],{},[2281,96778,96779,96781],{},[898,96780,1868],{},[2138,96782,2287],{},[2005,96784,2495],{"stretchy":2013},[2138,96786,2287],{},[2005,96788,2295],{"separator":2294},[2138,96790,2871],{},[2005,96792,2510],{"stretchy":2013},[902,96794,96795],{"encoding":904},"E_1[1, 10]",[724,96797,96798,96801,96802,96826,96827,96840],{},[614,96799,96800],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,96803,96805],{"className":96804},[886],[888,96806,96807],{"xmlns":890},[892,96808,96809,96823],{},[895,96810,96811,96819,96821],{},[9172,96812,96813,96815,96817],{},[898,96814,3946],{},[2138,96816,2287],{},[898,96818,1868],{},[2005,96820,2007],{},[2138,96822,2871],{},[902,96824,96825],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,96828,96830],{"className":96829},[886],[888,96831,96832],{"xmlns":890},[892,96833,96834,96838],{},[895,96835,96836],{},[2138,96837,5591],{},[902,96839,5591],{"encoding":904},", navýšení je",[883,96842,96844],{"className":96843},[886],[888,96845,96846],{"xmlns":890,"display":28071},[892,96847,96848,96904],{},[895,96849,96850,96860,96862,96870,96872,96878,96880,96882,96884,96886,96888,96890,96892,96902],{},[2281,96851,96852,96854],{},[898,96853,2783],{},[895,96855,96856,96858],{},[898,96857,42682],{},[898,96859,724],{},[2005,96861,2007],{},[9172,96863,96864,96866,96868],{},[898,96865,3946],{},[2138,96867,2287],{},[898,96869,1868],{},[2005,96871,2234],{},[2133,96873,96874,96876],{},[898,96875,3946],{},[898,96877,1868],{},[2005,96879,2007],{},[2138,96881,2871],{},[2005,96883,2234],{},[2138,96885,5591],{},[2005,96887,2007],{},[2138,96889,2140],{},[2297,96891,2299],{},[895,96893,96894,96896],{},[2297,96895,9806],{},[8392,96897,96898,96900],{"accent":2294},[2297,96899,2151],{},[2005,96901,25063],{},[898,96903,1644],{"mathvariant":2385},[902,96905,96906],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,96908,96909,96910,96826,96946,96959],{},"Výrobci zůstává čistá cena ",[883,96911,96913],{"className":96912},[886],[888,96914,96915],{"xmlns":890},[892,96916,96917,96943],{},[895,96918,96919,96927,96929,96931,96933,96935,96937,96939,96941],{},[9172,96920,96921,96923,96925],{},[898,96922,3946],{},[2138,96924,2287],{},[898,96926,1868],{},[2005,96928,2234],{},[898,96930,2783],{},[2005,96932,2007],{},[2138,96934,2871],{},[2005,96936,2234],{},[2138,96938,2244],{},[2005,96940,2007],{},[2138,96942,2360],{},[902,96944,96945],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,96947,96949],{"className":96948},[886],[888,96950,96951],{"xmlns":890},[892,96952,96953,96957],{},[895,96954,96955],{},[2138,96956,5591],{},[902,96958,5591],{"encoding":904},", pokles je",[883,96961,96963],{"className":96962},[886],[888,96964,96965],{"xmlns":890,"display":28071},[892,96966,96967,97033],{},[895,96968,96969,96981,96983,96989,96991,96993,97001,97003,97005,97007,97009,97011,97013,97015,97017,97019,97021,97031],{},[2281,96970,96971,96973],{},[898,96972,2783],{},[895,96974,96975,96977,96979],{},[898,96976,42705],{},[898,96978,2003],{},[898,96980,12047],{},[2005,96982,2007],{},[2133,96984,96985,96987],{},[898,96986,3946],{},[898,96988,1868],{},[2005,96990,2234],{},[2005,96992,2014],{"stretchy":2013},[9172,96994,96995,96997,96999],{},[898,96996,3946],{},[2138,96998,2287],{},[898,97000,1868],{},[2005,97002,2234],{},[898,97004,2783],{},[2005,97006,2020],{"stretchy":2013},[2005,97008,2007],{},[2138,97010,5591],{},[2005,97012,2234],{},[2138,97014,2360],{},[2005,97016,2007],{},[2138,97018,2360],{},[2297,97020,2299],{},[895,97022,97023,97025],{},[2297,97024,9806],{},[8392,97026,97027,97029],{"accent":2294},[2297,97028,2151],{},[2005,97030,25063],{},[898,97032,1644],{"mathvariant":2385},[902,97034,97035],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,97037,97038,97039,97091],{},"Kontrola: ",[883,97040,97042],{"className":97041},[886],[888,97043,97044],{"xmlns":890},[892,97045,97046,97088],{},[895,97047,97048,97058,97060,97072,97074,97076,97078,97080,97082,97084,97086],{},[2281,97049,97050,97052],{},[898,97051,2783],{},[895,97053,97054,97056],{},[898,97055,42682],{},[898,97057,724],{},[2005,97059,2104],{},[2281,97061,97062,97064],{},[898,97063,2783],{},[895,97065,97066,97068,97070],{},[898,97067,42705],{},[898,97069,2003],{},[898,97071,12047],{},[2005,97073,2007],{},[2138,97075,2140],{},[2005,97077,2104],{},[2138,97079,2360],{},[2005,97081,2007],{},[2138,97083,2244],{},[2005,97085,2007],{},[898,97087,2783],{},[902,97089,97090],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[36975,97093],{},[115,97095,97097],{"id":97096},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,97099,96027,97100,97113,97114,97132,97133,97161],{},[883,97101,97103],{"className":97102},[886],[888,97104,97105],{"xmlns":890},[892,97106,97107,97111],{},[895,97108,97109],{},[898,97110,2783],{},[902,97112,2783],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,97115,97117],{"className":97116},[886],[888,97118,97119],{"xmlns":890},[892,97120,97121,97129],{},[895,97122,97123,97125,97127],{},[898,97124,3946],{},[2005,97126,2104],{},[898,97128,2783],{},[902,97130,97131],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,97134,97136],{"className":97135},[886],[888,97137,97138],{"xmlns":890},[892,97139,97140,97158],{},[895,97141,97142,97144,97146,97148,97150,97152,97154,97156],{},[898,97143,3946],{},[2005,97145,2104],{},[898,97147,2783],{},[2005,97149,2007],{},[898,97151,1860],{},[2005,97153,2014],{"stretchy":2013},[898,97155,2797],{},[2005,97157,2020],{"stretchy":2013},[902,97159,97160],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,97163,97165],{"className":97164},[886],[888,97166,97167],{"xmlns":890,"display":28071},[892,97168,97169,97203],{},[895,97170,97171,97173,97175,97181,97183,97185,97187,97189,97191,97193,97195,97197,97199,97201],{},[898,97172,3946],{},[2005,97174,2007],{},[2281,97176,97177,97179],{},[898,97178,1860],{},[2138,97180,2140],{},[2005,97182,2014],{"stretchy":2013},[898,97184,2797],{},[2005,97186,2020],{"stretchy":2013},[2005,97188,2007],{},[898,97190,1860],{},[2005,97192,2014],{"stretchy":2013},[898,97194,2797],{},[2005,97196,2020],{"stretchy":2013},[2005,97198,2234],{},[898,97200,2783],{},[898,97202,1644],{"mathvariant":2385},[902,97204,97205],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,97207,97208,97209,2212,97222,97225],{},"Poptávka se tedy posouvá o ",[883,97210,97212],{"className":97211},[886],[888,97213,97214],{"xmlns":890},[892,97215,97216,97220],{},[895,97217,97218],{},[898,97219,2783],{},[902,97221,2783],{"encoding":904},[38,97223,97224],{},"svisle dolů",". Nabídka se nemění.",[724,97227,96152,97228,96193,97268,3894,97296,97324,97325,97344,97345,97369,97370,3927],{},[883,97229,97231],{"className":97230},[886],[888,97232,97233],{"xmlns":890},[892,97234,97235,97265],{},[895,97236,97237,97243,97245,97253,97255,97263],{},[2281,97238,97239,97241],{},[898,97240,1868],{},[2138,97242,2140],{},[2005,97244,2495],{"stretchy":2013},[9172,97246,97247,97249,97251],{},[898,97248,2797],{},[2138,97250,2140],{},[898,97252,1868],{},[2005,97254,2295],{"separator":2294},[9172,97256,97257,97259,97261],{},[898,97258,3946],{},[2138,97260,2140],{},[898,97262,1868],{},[2005,97264,2510],{"stretchy":2013},[902,97266,97267],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,97269,97271],{"className":97270},[886],[888,97272,97273],{"xmlns":890},[892,97274,97275,97293],{},[895,97276,97277,97285,97287],{},[9172,97278,97279,97281,97283],{},[898,97280,2797],{},[2138,97282,2140],{},[898,97284,1868],{},[2005,97286,3455],{},[2133,97288,97289,97291],{},[898,97290,2797],{},[898,97292,1868],{},[902,97294,97295],{"encoding":904},"Q_2^E \u003C Q^E",[883,97297,97299],{"className":97298},[886],[888,97300,97301],{"xmlns":890},[892,97302,97303,97321],{},[895,97304,97305,97313,97315],{},[9172,97306,97307,97309,97311],{},[898,97308,3946],{},[2138,97310,2140],{},[898,97312,1868],{},[2005,97314,3455],{},[2133,97316,97317,97319],{},[898,97318,3946],{},[898,97320,1868],{},[902,97322,97323],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,97326,97328],{"className":97327},[886],[888,97329,97330],{"xmlns":890},[892,97331,97332,97342],{},[895,97333,97334],{},[9172,97335,97336,97338,97340],{},[898,97337,3946],{},[2138,97339,2140],{},[898,97341,1868],{},[902,97343,47923],{"encoding":904},", spotřebitel platí celkem ",[883,97346,97348],{"className":97347},[886],[888,97349,97350],{"xmlns":890},[892,97351,97352,97366],{},[895,97353,97354,97362,97364],{},[9172,97355,97356,97358,97360],{},[898,97357,3946],{},[2138,97359,2140],{},[898,97361,1868],{},[2005,97363,2104],{},[898,97365,2783],{},[902,97367,97368],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,97371,97373],{"className":97372},[886],[888,97374,97375],{"xmlns":890},[892,97376,97377,97385],{},[895,97378,97379],{},[2133,97380,97381,97383],{},[898,97382,3946],{},[898,97384,1868],{},[902,97386,41471],{"encoding":904},[724,97388,97389],{},"Daňové břemeno:",[883,97391,97393],{"className":97392},[886],[888,97394,97395],{"xmlns":890,"display":28071},[892,97396,97397,97471],{},[895,97398,97399,97409,97411,97413,97421,97423,97425,97427,97429,97435,97437,97439,97451,97453,97459,97461,97469],{},[2281,97400,97401,97403],{},[898,97402,2783],{},[895,97404,97405,97407],{},[898,97406,42682],{},[898,97408,724],{},[2005,97410,2007],{},[2005,97412,2014],{"stretchy":2013},[9172,97414,97415,97417,97419],{},[898,97416,3946],{},[2138,97418,2140],{},[898,97420,1868],{},[2005,97422,2104],{},[898,97424,2783],{},[2005,97426,2020],{"stretchy":2013},[2005,97428,2234],{},[2133,97430,97431,97433],{},[898,97432,3946],{},[898,97434,1868],{},[2005,97436,2295],{"separator":2294},[5884,97438],{"width":5886},[2281,97440,97441,97443],{},[898,97442,2783],{},[895,97444,97445,97447,97449],{},[898,97446,42705],{},[898,97448,2003],{},[898,97450,12047],{},[2005,97452,2007],{},[2133,97454,97455,97457],{},[898,97456,3946],{},[898,97458,1868],{},[2005,97460,2234],{},[9172,97462,97463,97465,97467],{},[898,97464,3946],{},[2138,97466,2140],{},[898,97468,1868],{},[898,97470,1644],{"mathvariant":2385},[902,97472,97473],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,97475,97476],{},[614,97477,97478,97479,97509,97510,96362,97523,5675,97540,96393,97553,1644],{},"Obrázek 2.19: Posun ",[883,97480,97482],{"className":97481},[886],[888,97483,97484],{"xmlns":890},[892,97485,97486,97506],{},[895,97487,97488,97490,97492,97498,97500,97502,97504],{},[898,97489,1860],{},[2005,97491,3131],{},[2281,97493,97494,97496],{},[898,97495,1860],{},[2138,97497,2140],{},[2005,97499,2007],{},[898,97501,1860],{},[2005,97503,2234],{},[898,97505,2783],{},[902,97507,97508],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,97511,97513],{"className":97512},[886],[888,97514,97515],{"xmlns":890},[892,97516,97517,97521],{},[895,97518,97519],{},[898,97520,2783],{},[902,97522,2783],{"encoding":904},[883,97524,97526],{"className":97525},[886],[888,97527,97528],{"xmlns":890},[892,97529,97530,97538],{},[895,97531,97532],{},[2281,97533,97534,97536],{},[898,97535,1860],{},[2138,97537,2140],{},[902,97539,38332],{"encoding":904},[883,97541,97543],{"className":97542},[886],[888,97544,97545],{"xmlns":890},[892,97546,97547,97551],{},[895,97548,97549],{},[898,97550,8679],{},[902,97552,8679],{"encoding":904},[883,97554,97556],{"className":97555},[886],[888,97557,97558],{"xmlns":890},[892,97559,97560,97568],{},[895,97561,97562],{},[2281,97563,97564,97566],{},[898,97565,1868],{},[2138,97567,2140],{},[902,97569,97570],{"encoding":904},"E_2",[198,97572,45388],{"id":97573},"příklad-210",[724,97575,97576,97578,97579,41695,97602,97621,97622,97639],{},[38,97577,37938],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,97580,97582],{"className":97581},[886],[888,97583,97584],{"xmlns":890},[892,97585,97586,97600],{},[895,97587,97588,97590,97592,97594,97596,97598],{},[898,97589,3946],{},[2005,97591,2007],{},[2138,97593,3517],{},[2005,97595,2234],{},[2138,97597,2140],{},[898,97599,2797],{},[902,97601,96442],{"encoding":904},[883,97603,97605],{"className":97604},[886],[888,97606,97607],{"xmlns":890},[892,97608,97609,97619],{},[895,97610,97611,97613,97615,97617],{},[898,97612,3946],{},[2005,97614,2007],{},[2138,97616,2360],{},[898,97618,2797],{},[902,97620,96462],{"encoding":904},". Daň ",[883,97623,97625],{"className":97624},[886],[888,97626,97627],{"xmlns":890},[892,97628,97629,97637],{},[895,97630,97631,97633,97635],{},[898,97632,2783],{},[2005,97634,2007],{},[2138,97636,2244],{},[902,97638,41273],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,97641,97642],{},[38,97643,37970],{},[724,97645,97646,97647,96653],{},"Nová poptávka je ",[883,97648,97650],{"className":97649},[886],[888,97651,97652],{"xmlns":890},[892,97653,97654,97690],{},[895,97655,97656,97662,97664,97666,97668,97670,97672,97674,97676,97678,97680,97682,97684,97686,97688],{},[2281,97657,97658,97660],{},[898,97659,1860],{},[2138,97661,2140],{},[2005,97663,2713],{},[898,97665,3946],{},[2005,97667,2007],{},[2138,97669,3517],{},[2005,97671,2234],{},[2138,97673,2140],{},[898,97675,2797],{},[2005,97677,2234],{},[2138,97679,2244],{},[2005,97681,2007],{},[2138,97683,2244],{},[2005,97685,2234],{},[2138,97687,2140],{},[898,97689,2797],{},[902,97691,97692],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,97694,97696],{"className":97695},[886],[888,97697,97698],{"xmlns":890,"display":28071},[892,97699,97700,97716],{},[895,97701,97702,97704,97706,97708,97710,97712,97714],{},[2138,97703,2244],{},[2005,97705,2234],{},[2138,97707,2140],{},[898,97709,2797],{},[2005,97711,2007],{},[2138,97713,2360],{},[898,97715,2797],{},[902,97717,97718],{"encoding":904},"6 - 2Q = 4Q",[724,97720,96686,97721,5595,97740,1343,97764,96767,97796,1644],{},[883,97722,97724],{"className":97723},[886],[888,97725,97726],{"xmlns":890},[892,97727,97728,97738],{},[895,97729,97730,97732,97734,97736],{},[2138,97731,2244],{},[898,97733,2797],{},[2005,97735,2007],{},[2138,97737,2244],{},[902,97739,96706],{"encoding":904},[883,97741,97743],{"className":97742},[886],[888,97744,97745],{"xmlns":890},[892,97746,97747,97761],{},[895,97748,97749,97757,97759],{},[9172,97750,97751,97753,97755],{},[898,97752,2797],{},[2138,97754,2140],{},[898,97756,1868],{},[2005,97758,2007],{},[2138,97760,2287],{},[902,97762,97763],{"encoding":904},"Q_2^E = 1",[883,97765,97767],{"className":97766},[886],[888,97768,97769],{"xmlns":890},[892,97770,97771,97793],{},[895,97772,97773,97781,97783,97785,97787,97789,97791],{},[9172,97774,97775,97777,97779],{},[898,97776,3946],{},[2138,97778,2140],{},[898,97780,1868],{},[2005,97782,2007],{},[2138,97784,2360],{},[2005,97786,3185],{},[2138,97788,2287],{},[2005,97790,2007],{},[2138,97792,2360],{},[902,97794,97795],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,97797,97799],{"className":97798},[886],[888,97800,97801],{"xmlns":890},[892,97802,97803,97821],{},[895,97804,97805,97811,97813,97815,97817,97819],{},[2281,97806,97807,97809],{},[898,97808,1868],{},[2138,97810,2140],{},[2005,97812,2495],{"stretchy":2013},[2138,97814,2287],{},[2005,97816,2295],{"separator":2294},[2138,97818,2360],{},[2005,97820,2510],{"stretchy":2013},[902,97822,97823],{"encoding":904},"E_2[1, 4]",[724,97825,97826,97827,97863,97864,96481],{},"Spotřebitel platí celkem ",[883,97828,97830],{"className":97829},[886],[888,97831,97832],{"xmlns":890},[892,97833,97834,97860],{},[895,97835,97836,97844,97846,97848,97850,97852,97854,97856,97858],{},[9172,97837,97838,97840,97842],{},[898,97839,3946],{},[2138,97841,2140],{},[898,97843,1868],{},[2005,97845,2104],{},[898,97847,2783],{},[2005,97849,2007],{},[2138,97851,2360],{},[2005,97853,2104],{},[2138,97855,2244],{},[2005,97857,2007],{},[2138,97859,2871],{},[902,97861,97862],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,97865,97867],{"className":97866},[886],[888,97868,97869],{"xmlns":890},[892,97870,97871,97885],{},[895,97872,97873,97881,97883],{},[9172,97874,97875,97877,97879],{},[898,97876,3946],{},[2138,97878,2140],{},[898,97880,1868],{},[2005,97882,2007],{},[2138,97884,2360],{},[902,97886,97887],{"encoding":904},"P_2^E = 4",[724,97889,97890],{},[614,97891,97892],{},"Rozklad daňového břemene:",[883,97894,97896],{"className":97895},[886],[888,97897,97898],{"xmlns":890,"display":28071},[892,97899,97900,97986],{},[895,97901,97902,97912,97914,97916,97918,97920,97922,97924,97926,97928,97930,97932,97934,97944,97946,97948,97960,97962,97964,97966,97968,97970,97972,97974,97984],{},[2281,97903,97904,97906],{},[898,97905,2783],{},[895,97907,97908,97910],{},[898,97909,42682],{},[898,97911,724],{},[2005,97913,2007],{},[2005,97915,2014],{"stretchy":2013},[2138,97917,2360],{},[2005,97919,2104],{},[2138,97921,2244],{},[2005,97923,2020],{"stretchy":2013},[2005,97925,2234],{},[2138,97927,5591],{},[2005,97929,2007],{},[2138,97931,2140],{},[2297,97933,2299],{},[895,97935,97936,97938],{},[2297,97937,9806],{},[8392,97939,97940,97942],{"accent":2294},[2297,97941,2151],{},[2005,97943,25063],{},[2005,97945,2295],{"separator":2294},[5884,97947],{"width":5886},[2281,97949,97950,97952],{},[898,97951,2783],{},[895,97953,97954,97956,97958],{},[898,97955,42705],{},[898,97957,2003],{},[898,97959,12047],{},[2005,97961,2007],{},[2138,97963,5591],{},[2005,97965,2234],{},[2138,97967,2360],{},[2005,97969,2007],{},[2138,97971,2360],{},[2297,97973,2299],{},[895,97975,97976,97978],{},[2297,97977,9806],{},[8392,97979,97980,97982],{"accent":2294},[2297,97981,2151],{},[2005,97983,25063],{},[898,97985,1644],{"mathvariant":2385},[902,97987,97988],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,97990,97991,97992,1644],{},"Opět ",[883,97993,97995],{"className":97994},[886],[888,97996,97997],{"xmlns":890},[892,97998,97999,98033],{},[895,98000,98001,98011,98013,98025,98027,98029,98031],{},[2281,98002,98003,98005],{},[898,98004,2783],{},[895,98006,98007,98009],{},[898,98008,42682],{},[898,98010,724],{},[2005,98012,2104],{},[2281,98014,98015,98017],{},[898,98016,2783],{},[895,98018,98019,98021,98023],{},[898,98020,42705],{},[898,98022,2003],{},[898,98024,12047],{},[2005,98026,2007],{},[2138,98028,2244],{},[2005,98030,2007],{},[898,98032,2783],{},[902,98034,98035],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[36975,98037],{},[115,98039,42663],{"id":98040},"daňové-břemeno",[724,98042,98043,10030,98045,98048,98049,98062],{},[38,98044,42663],{},[614,98046,98047],{},"tax burden",") je rozdělení zaplacené daně ",[883,98050,98052],{"className":98051},[886],[888,98053,98054],{"xmlns":890},[892,98055,98056,98060],{},[895,98057,98058],{},[898,98059,2783],{},[902,98061,2783],{"encoding":904}," mezi spotřebitele a výrobce:",[883,98064,98066],{"className":98065},[886],[888,98067,98068],{"xmlns":890,"display":28071},[892,98069,98070,98102],{},[895,98071,98072,98074,98076,98086,98088,98100],{},[898,98073,2783],{},[2005,98075,2007],{},[2281,98077,98078,98080],{},[898,98079,2783],{},[895,98081,98082,98084],{},[898,98083,42682],{},[898,98085,724],{},[2005,98087,2104],{},[2281,98089,98090,98092],{},[898,98091,2783],{},[895,98093,98094,98096,98098],{},[898,98095,42705],{},[898,98097,2003],{},[898,98099,12047],{},[898,98101,1644],{"mathvariant":2385},[902,98103,98104],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,98106,98107],{},[2568,98108],{"alt":98109,"className":98110,"src":98111},"imek-dan-rozklad-bremene-sklony",[210,2572],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[3876,98113,98114],{},[724,98115,98116,98118,98119,3894,98132,1644],{},[883,98117,4164],{}," 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 ",[883,98120,98122],{"className":98121},[886],[888,98123,98124],{"xmlns":890},[892,98125,98126,98130],{},[895,98127,98128],{},[898,98129,1860],{},[902,98131,1860],{"encoding":904},[883,98133,98135],{"className":98134},[886],[888,98136,98137],{"xmlns":890},[892,98138,98139,98143],{},[895,98140,98141],{},[898,98142,8679],{},[902,98144,8679],{"encoding":904},[198,98146,2453],{"id":2452},[724,98148,98149,98150,98171,98172,98185,98186,98203,98204,98217],{},"V grafu ",[883,98151,98153],{"className":98152},[886],[888,98154,98155],{"xmlns":890},[892,98156,98157,98169],{},[895,98158,98159,98161,98163,98165,98167],{},[2005,98160,2014],{"stretchy":2013},[898,98162,2797],{},[2005,98164,2295],{"separator":2294},[898,98166,3946],{},[2005,98168,2020],{"stretchy":2013},[902,98170,37696],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,98173,98175],{"className":98174},[886],[888,98176,98177],{"xmlns":890},[892,98178,98179,98183],{},[895,98180,98181],{},[898,98182,2783],{},[902,98184,2783],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,98187,98189],{"className":98188},[886],[888,98190,98191],{"xmlns":890},[892,98192,98193,98201],{},[895,98194,98195],{},[2133,98196,98197,98199],{},[898,98198,3946],{},[898,98200,1868],{},[902,98202,41471],{"encoding":904},", rozdělí se úsečka ",[883,98205,98207],{"className":98206},[886],[888,98208,98209],{"xmlns":890},[892,98210,98211,98215],{},[895,98212,98213],{},[898,98214,2783],{},[902,98216,2783],{"encoding":904}," na dvě části:",[120,98219,98220,98245],{},[123,98221,98222,98223,98244],{},"horní část odpovídá ",[883,98224,98226],{"className":98225},[886],[888,98227,98228],{"xmlns":890},[892,98229,98230,98242],{},[895,98231,98232],{},[2281,98233,98234,98236],{},[898,98235,2783],{},[895,98237,98238,98240],{},[898,98239,42682],{},[898,98241,724],{},[902,98243,42687],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,98246,98247,98248,98271],{},"dolní část odpovídá ",[883,98249,98251],{"className":98250},[886],[888,98252,98253],{"xmlns":890},[892,98254,98255,98269],{},[895,98256,98257],{},[2281,98258,98259,98261],{},[898,98260,2783],{},[895,98262,98263,98265,98267],{},[898,98264,42705],{},[898,98266,2003],{},[898,98268,12047],{},[902,98270,42712],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,98273,98274],{},[614,98275,98276,98277,2694,98290,98311,98312,98335,98336,3894,98357,98380],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,98278,98280],{"className":98279},[886],[888,98281,98282],{"xmlns":890},[892,98283,98284,98288],{},[895,98285,98286],{},[898,98287,2783],{},[902,98289,2783],{"encoding":904},[883,98291,98293],{"className":98292},[886],[888,98294,98295],{"xmlns":890},[892,98296,98297,98309],{},[895,98298,98299],{},[2281,98300,98301,98303],{},[898,98302,2783],{},[895,98304,98305,98307],{},[898,98306,42682],{},[898,98308,724],{},[902,98310,42687],{"encoding":904}," (nahoře) a ",[883,98313,98315],{"className":98314},[886],[888,98316,98317],{"xmlns":890},[892,98318,98319,98333],{},[895,98320,98321],{},[2281,98322,98323,98325],{},[898,98324,2783],{},[895,98326,98327,98329,98331],{},[898,98328,42705],{},[898,98330,2003],{},[898,98332,12047],{},[902,98334,42712],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,98337,98339],{"className":98338},[886],[888,98340,98341],{"xmlns":890},[892,98342,98343,98355],{},[895,98344,98345],{},[2281,98346,98347,98349],{},[898,98348,2783],{},[895,98350,98351,98353],{},[898,98352,42682],{},[898,98354,724],{},[902,98356,42687],{"encoding":904},[883,98358,98360],{"className":98359},[886],[888,98361,98362],{"xmlns":890},[892,98363,98364,98378],{},[895,98365,98366],{},[2281,98367,98368,98370],{},[898,98369,2783],{},[895,98371,98372,98374,98376],{},[898,98373,42705],{},[898,98375,2003],{},[898,98377,12047],{},[902,98379,42712],{"encoding":904}," je v obou případech stejná.",[198,98382,98384],{"id":98383},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,98386,98387,98388,98391,98392,10030,98415,98432,98433,10030,98456,98473],{},"Platí obecně: ",[38,98389,98390],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,98393,98395],{"className":98394},[886],[888,98396,98397],{"xmlns":890},[892,98398,98399,98413],{},[895,98400,98401,98403,98405,98407,98409,98411],{},[898,98402,3946],{},[2005,98404,2007],{},[898,98406,207],{},[898,98408,2797],{},[2005,98410,2104],{},[898,98412,2107],{},[902,98414,37065],{"encoding":904},[883,98416,98418],{"className":98417},[886],[888,98419,98420],{"xmlns":890},[892,98421,98422,98430],{},[895,98423,98424,98426,98428],{},[898,98425,207],{},[2005,98427,3455],{},[2138,98429,2336],{},[902,98431,43090],{"encoding":904},") a lineární nabídku ",[883,98434,98436],{"className":98435},[886],[888,98437,98438],{"xmlns":890},[892,98439,98440,98454],{},[895,98441,98442,98444,98446,98448,98450,98452],{},[898,98443,3946],{},[2005,98445,2007],{},[898,98447,2151],{},[898,98449,2797],{},[2005,98451,2104],{},[898,98453,2203],{},[902,98455,40247],{"encoding":904},[883,98457,98459],{"className":98458},[886],[888,98460,98461],{"xmlns":890},[892,98462,98463,98471],{},[895,98464,98465,98467,98469],{},[898,98466,2151],{},[2005,98468,3416],{},[2138,98470,2336],{},[902,98472,40265],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,98475,98477],{"className":98476},[886],[888,98478,98479],{"xmlns":890,"display":28071},[892,98480,98481,98547],{},[895,98482,98483,98507,98509,98519,98521,98545],{},[2338,98484,98485,98495],{},[2281,98486,98487,98489],{},[898,98488,2783],{},[895,98490,98491,98493],{},[898,98492,42682],{},[898,98494,724],{},[2281,98496,98497,98499],{},[898,98498,2783],{},[895,98500,98501,98503,98505],{},[898,98502,42705],{},[898,98504,2003],{},[898,98506,12047],{},[2005,98508,2007],{},[2338,98510,98511,98513],{},[898,98512,2151],{},[895,98514,98515,98517],{},[2005,98516,2234],{},[898,98518,207],{},[2005,98520,2007],{},[2338,98522,98523,98535],{},[895,98524,98525,98528,98531,98533],{},[898,98526,98527],{"mathvariant":2385},"∣",[2297,98529,98530],{},"sklon ",[898,98532,8679],{},[898,98534,98527],{"mathvariant":2385},[895,98536,98537,98539,98541,98543],{},[898,98538,98527],{"mathvariant":2385},[2297,98540,98530],{},[898,98542,1860],{},[898,98544,98527],{"mathvariant":2385},[898,98546,1644],{"mathvariant":2385},[902,98548,98549],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[3876,98551,98552,98557],{},[724,98553,98554,98556],{},[883,98555,4578],{}," Postup výpočtu rozkladu",[152,98558,98559,98594,98647,98726],{},[123,98560,98561,98562,98593],{},"Spočti rovnovážný bod ",[883,98563,98565],{"className":98564},[886],[888,98566,98567],{"xmlns":890},[892,98568,98569,98591],{},[895,98570,98571,98573,98575,98581,98583,98589],{},[898,98572,1868],{},[2005,98574,2495],{"stretchy":2013},[2133,98576,98577,98579],{},[898,98578,2797],{},[898,98580,1868],{},[2005,98582,2295],{"separator":2294},[2133,98584,98585,98587],{},[898,98586,3946],{},[898,98588,1868],{},[2005,98590,2510],{"stretchy":2013},[902,98592,41372],{"encoding":904}," bez daně.",[123,98595,98596,98597,1348,98622,3927],{},"Urči posunutou křivku (",[883,98598,98600],{"className":98599},[886],[888,98601,98602],{"xmlns":890},[892,98603,98604,98620],{},[895,98605,98606,98612,98614,98616,98618],{},[2281,98607,98608,98610],{},[898,98609,8679],{},[2138,98611,2287],{},[2005,98613,2007],{},[898,98615,8679],{},[2005,98617,2104],{},[898,98619,2783],{},[902,98621,42759],{"encoding":904},[883,98623,98625],{"className":98624},[886],[888,98626,98627],{"xmlns":890},[892,98628,98629,98645],{},[895,98630,98631,98637,98639,98641,98643],{},[2281,98632,98633,98635],{},[898,98634,1860],{},[2138,98636,2140],{},[2005,98638,2007],{},[898,98640,1860],{},[2005,98642,2234],{},[898,98644,2783],{},[902,98646,42790],{"encoding":904},[123,98648,98649,98650,3919,98669,12134,98688,3919,98707,3927],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,98651,98653],{"className":98652},[886],[888,98654,98655],{"xmlns":890},[892,98656,98657,98667],{},[895,98658,98659],{},[9172,98660,98661,98663,98665],{},[898,98662,2797],{},[2138,98664,2287],{},[898,98666,1868],{},[902,98668,47841],{"encoding":904},[883,98670,98672],{"className":98671},[886],[888,98673,98674],{"xmlns":890},[892,98675,98676,98686],{},[895,98677,98678],{},[9172,98679,98680,98682,98684],{},[898,98681,2797],{},[2138,98683,2140],{},[898,98685,1868],{},[902,98687,47903],{"encoding":904},[883,98689,98691],{"className":98690},[886],[888,98692,98693],{"xmlns":890},[892,98694,98695,98705],{},[895,98696,98697],{},[9172,98698,98699,98701,98703],{},[898,98700,3946],{},[2138,98702,2287],{},[898,98704,1868],{},[902,98706,47862],{"encoding":904},[883,98708,98710],{"className":98709},[886],[888,98711,98712],{"xmlns":890},[892,98713,98714,98724],{},[895,98715,98716],{},[9172,98717,98718,98720,98722],{},[898,98719,3946],{},[2138,98721,2140],{},[898,98723,1868],{},[902,98725,47923],{"encoding":904},[123,98727,98728,98729,3894,98750,98773,98774,1644],{},"Dopočítej ",[883,98730,98732],{"className":98731},[886],[888,98733,98734],{"xmlns":890},[892,98735,98736,98748],{},[895,98737,98738],{},[2281,98739,98740,98742],{},[898,98741,2783],{},[895,98743,98744,98746],{},[898,98745,42682],{},[898,98747,724],{},[902,98749,42687],{"encoding":904},[883,98751,98753],{"className":98752},[886],[888,98754,98755],{"xmlns":890},[892,98756,98757,98771],{},[895,98758,98759],{},[2281,98760,98761,98763],{},[898,98762,2783],{},[895,98764,98765,98767,98769],{},[898,98766,42705],{},[898,98768,2003],{},[898,98770,12047],{},[902,98772,42712],{"encoding":904}," z definice, vždy ověř ",[883,98775,98777],{"className":98776},[886],[888,98778,98779],{"xmlns":890},[892,98780,98781,98811],{},[895,98782,98783,98793,98795,98807,98809],{},[2281,98784,98785,98787],{},[898,98786,2783],{},[895,98788,98789,98791],{},[898,98790,42682],{},[898,98792,724],{},[2005,98794,2104],{},[2281,98796,98797,98799],{},[898,98798,2783],{},[895,98800,98801,98803,98805],{},[898,98802,42705],{},[898,98804,2003],{},[898,98806,12047],{},[2005,98808,2007],{},[898,98810,2783],{},[902,98812,98813],{"encoding":904},"T_{sp} + T_{vyr} = T",[3876,98815,98816],{},[724,98817,98818,98820,98821,98824,98825,3894,98838,98851],{},[883,98819,4418],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,98822,98823],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,98826,98828],{"className":98827},[886],[888,98829,98830],{"xmlns":890},[892,98831,98832,98836],{},[895,98833,98834],{},[898,98835,1860],{},[902,98837,1860],{"encoding":904},[883,98839,98841],{"className":98840},[886],[888,98842,98843],{"xmlns":890},[892,98844,98845,98849],{},[895,98846,98847],{},[898,98848,8679],{},[902,98850,8679],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[36975,98853],{},[115,98855,98857],{"id":98856},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,98859,98860],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,98862,98863],{},[2568,98864],{"alt":98865,"className":98866,"src":98867},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2572],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,98869,98870,98882],{},[19,98871,98872],{},[22,98873,98874,98876,98879],{},[25,98875,54301],{},[25,98877,98878],{},"(a) daň výrobci",[25,98880,98881],{},"(b) daň spotřebiteli",[30,98883,98884,98939,99006,99066],{},[22,98885,98886,98889,98914],{},[35,98887,98888],{},"Rovnovážné množství",[35,98890,98891],{},[883,98892,98894],{"className":98893},[886],[888,98895,98896],{"xmlns":890},[892,98897,98898,98912],{},[895,98899,98900,98908,98910],{},[9172,98901,98902,98904,98906],{},[898,98903,2797],{},[2138,98905,2287],{},[898,98907,1868],{},[2005,98909,2007],{},[2138,98911,2287],{},[902,98913,96730],{"encoding":904},[35,98915,98916],{},[883,98917,98919],{"className":98918},[886],[888,98920,98921],{"xmlns":890},[892,98922,98923,98937],{},[895,98924,98925,98933,98935],{},[9172,98926,98927,98929,98931],{},[898,98928,2797],{},[2138,98930,2140],{},[898,98932,1868],{},[2005,98934,2007],{},[2138,98936,2287],{},[902,98938,97763],{"encoding":904},[22,98940,98941,98944,98969],{},[35,98942,98943],{},"Cena placená spotřebitelem",[35,98945,98946],{},[883,98947,98949],{"className":98948},[886],[888,98950,98951],{"xmlns":890},[892,98952,98953,98967],{},[895,98954,98955,98963,98965],{},[9172,98956,98957,98959,98961],{},[898,98958,3946],{},[2138,98960,2287],{},[898,98962,1868],{},[2005,98964,2007],{},[2138,98966,2871],{},[902,98968,96825],{"encoding":904},[35,98970,98971],{},[883,98972,98974],{"className":98973},[886],[888,98975,98976],{"xmlns":890},[892,98977,98978,99004],{},[895,98979,98980,98988,98990,98992,98994,98996,98998,99000,99002],{},[9172,98981,98982,98984,98986],{},[898,98983,3946],{},[2138,98985,2140],{},[898,98987,1868],{},[2005,98989,2104],{},[898,98991,2783],{},[2005,98993,2007],{},[2138,98995,2360],{},[2005,98997,2104],{},[2138,98999,2244],{},[2005,99001,2007],{},[2138,99003,2871],{},[902,99005,97862],{"encoding":904},[22,99007,99008,99011,99041],{},[35,99009,99010],{},"Cena přijímaná výrobcem",[35,99012,99013],{},[883,99014,99016],{"className":99015},[886],[888,99017,99018],{"xmlns":890},[892,99019,99020,99038],{},[895,99021,99022,99030,99032,99034,99036],{},[9172,99023,99024,99026,99028],{},[898,99025,3946],{},[2138,99027,2287],{},[898,99029,1868],{},[2005,99031,2234],{},[898,99033,2783],{},[2005,99035,2007],{},[2138,99037,2360],{},[902,99039,99040],{"encoding":904},"P_1^E - T = 4",[35,99042,99043],{},[883,99044,99046],{"className":99045},[886],[888,99047,99048],{"xmlns":890},[892,99049,99050,99064],{},[895,99051,99052,99060,99062],{},[9172,99053,99054,99056,99058],{},[898,99055,3946],{},[2138,99057,2140],{},[898,99059,1868],{},[2005,99061,2007],{},[2138,99063,2360],{},[902,99065,97887],{"encoding":904},[22,99067,99068,99071,99125],{},[35,99069,99070],{},"Rozklad břemene",[35,99072,99073,1343,99098],{},[883,99074,99076],{"className":99075},[886],[888,99077,99078],{"xmlns":890},[892,99079,99080,99096],{},[895,99081,99082,99092,99094],{},[2281,99083,99084,99086],{},[898,99085,2783],{},[895,99087,99088,99090],{},[898,99089,42682],{},[898,99091,724],{},[2005,99093,2007],{},[2138,99095,2140],{},[902,99097,42981],{"encoding":904},[883,99099,99101],{"className":99100},[886],[888,99102,99103],{"xmlns":890},[892,99104,99105,99123],{},[895,99106,99107,99119,99121],{},[2281,99108,99109,99111],{},[898,99110,2783],{},[895,99112,99113,99115,99117],{},[898,99114,42705],{},[898,99116,2003],{},[898,99118,12047],{},[2005,99120,2007],{},[2138,99122,2360],{},[902,99124,43010],{"encoding":904},[35,99126,99127,1343,99152],{},[883,99128,99130],{"className":99129},[886],[888,99131,99132],{"xmlns":890},[892,99133,99134,99150],{},[895,99135,99136,99146,99148],{},[2281,99137,99138,99140],{},[898,99139,2783],{},[895,99141,99142,99144],{},[898,99143,42682],{},[898,99145,724],{},[2005,99147,2007],{},[2138,99149,2140],{},[902,99151,42981],{"encoding":904},[883,99153,99155],{"className":99154},[886],[888,99156,99157],{"xmlns":890},[892,99158,99159,99177],{},[895,99160,99161,99173,99175],{},[2281,99162,99163,99165],{},[898,99164,2783],{},[895,99166,99167,99169,99171],{},[898,99168,42705],{},[898,99170,2003],{},[898,99172,12047],{},[2005,99174,2007],{},[2138,99176,2360],{},[902,99178,43010],{"encoding":904},[724,99180,99181],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,99183,99185],{"className":99184},[886],[888,99186,99187],{"xmlns":890,"display":28071},[892,99188,99189,99237],{},[895,99190,99191,99199,99201,99209,99211,99213,99221,99223,99225,99227,99235],{},[9172,99192,99193,99195,99197],{},[898,99194,2797],{},[2138,99196,2287],{},[898,99198,1868],{},[2005,99200,2007],{},[9172,99202,99203,99205,99207],{},[898,99204,2797],{},[2138,99206,2140],{},[898,99208,1868],{},[2005,99210,2295],{"separator":2294},[5884,99212],{"width":5886},[9172,99214,99215,99217,99219],{},[898,99216,3946],{},[2138,99218,2287],{},[898,99220,1868],{},[2005,99222,2234],{},[898,99224,2783],{},[2005,99226,2007],{},[9172,99228,99229,99231,99233],{},[898,99230,3946],{},[2138,99232,2140],{},[898,99234,1868],{},[898,99236,1644],{"mathvariant":2385},[902,99238,99239],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[3876,99241,99242,99261,99415],{},[724,99243,99244,99246,99247,99260],{},[883,99245,4578],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,99248,99250],{"className":99249},[886],[888,99251,99252],{"xmlns":890},[892,99253,99254,99258],{},[895,99255,99256],{},[898,99257,2783],{},[902,99259,2783],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,99262,99263,99295,99331,99368],{},[123,99264,99265,99266,2295],{},"rovnovážná množství obou režimů, ",[883,99267,99269],{"className":99268},[886],[888,99270,99271],{"xmlns":890},[892,99272,99273,99293],{},[895,99274,99275,99283,99285],{},[9172,99276,99277,99279,99281],{},[898,99278,2797],{},[2138,99280,2287],{},[898,99282,1868],{},[2005,99284,2007],{},[9172,99286,99287,99289,99291],{},[898,99288,2797],{},[2138,99290,2140],{},[898,99292,1868],{},[902,99294,42913],{"encoding":904},[123,99296,99297,99298,2295],{},"čistá cena přijímaná výrobcem, ",[883,99299,99301],{"className":99300},[886],[888,99302,99303],{"xmlns":890},[892,99304,99305,99329],{},[895,99306,99307,99315,99317,99319,99321],{},[9172,99308,99309,99311,99313],{},[898,99310,3946],{},[2138,99312,2287],{},[898,99314,1868],{},[2005,99316,2234],{},[898,99318,2783],{},[2005,99320,2007],{},[9172,99322,99323,99325,99327],{},[898,99324,3946],{},[2138,99326,2140],{},[898,99328,1868],{},[902,99330,42947],{"encoding":904},[123,99332,99333,99334,2295],{},"celková cena placená spotřebitelem, ",[883,99335,99337],{"className":99336},[886],[888,99338,99339],{"xmlns":890},[892,99340,99341,99365],{},[895,99342,99343,99351,99353,99361,99363],{},[9172,99344,99345,99347,99349],{},[898,99346,3946],{},[2138,99348,2287],{},[898,99350,1868],{},[2005,99352,2007],{},[9172,99354,99355,99357,99359],{},[898,99356,3946],{},[2138,99358,2140],{},[898,99360,1868],{},[2005,99362,2104],{},[898,99364,2783],{},[902,99366,99367],{"encoding":904},"P_1^E = P_2^E + T",[123,99369,99370,99371,3894,99392,1644],{},"rozklad daňového břemene ",[883,99372,99374],{"className":99373},[886],[888,99375,99376],{"xmlns":890},[892,99377,99378,99390],{},[895,99379,99380],{},[2281,99381,99382,99384],{},[898,99383,2783],{},[895,99385,99386,99388],{},[898,99387,42682],{},[898,99389,724],{},[902,99391,42687],{"encoding":904},[883,99393,99395],{"className":99394},[886],[888,99396,99397],{"xmlns":890},[892,99398,99399,99413],{},[895,99400,99401],{},[2281,99402,99403,99405],{},[898,99404,2783],{},[895,99406,99407,99409,99411],{},[898,99408,42705],{},[898,99410,2003],{},[898,99412,12047],{},[902,99414,42712],{"encoding":904},[724,99416,99417,99418,1644],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,99419,35202],{},[724,99421,99422,99423,3894,99436,3927],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,99424,99426],{"className":99425},[886],[888,99427,99428],{"xmlns":890},[892,99429,99430,99434],{},[895,99431,99432],{},[898,99433,1860],{},[902,99435,1860],{"encoding":904},[883,99437,99439],{"className":99438},[886],[888,99440,99441],{"xmlns":890},[892,99442,99443,99447],{},[895,99444,99445],{},[898,99446,8679],{},[902,99448,8679],{"encoding":904},[36975,99450],{},[115,99452,99454],{"id":99453},"úlohy","Úlohy",[724,99456,99457,99458,3159],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,99459,16246],{"className":99460,"dataFsResolvedFilePath":800,"href":801},[210],[120,99462,99463,99493,99524],{},[123,99464,99465,99468,99469,99492],{},[38,99466,99467],{},"Úloha 2.4"," — Poptávka ",[883,99470,99472],{"className":99471},[886],[888,99473,99474],{"xmlns":890},[892,99475,99476,99490],{},[895,99477,99478,99480,99482,99484,99486,99488],{},[898,99479,3946],{},[2005,99481,2007],{},[2138,99483,3517],{},[2005,99485,2234],{},[2138,99487,2140],{},[898,99489,2797],{},[902,99491,96442],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,99494,99495,99498,99499,99523],{},[38,99496,99497],{},"Úloha 2.9"," — Nabídka ",[883,99500,99502],{"className":99501},[886],[888,99503,99504],{"xmlns":890},[892,99505,99506,99520],{},[895,99507,99508,99510,99512,99514,99516,99518],{},[898,99509,3946],{},[2005,99511,2007],{},[2138,99513,5015],{},[898,99515,2797],{},[2005,99517,2104],{},[2138,99519,36249],{},[902,99521,99522],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,99525,99526,99529,99530,3894,99556,99580,99581,99598],{},[38,99527,99528],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,99531,99533],{"className":99532},[886],[888,99534,99535],{"xmlns":890},[892,99536,99537,99553],{},[895,99538,99539,99541,99543,99545,99547,99549,99551],{},[898,99540,3946],{},[2005,99542,2007],{},[2005,99544,2234],{},[2138,99546,2360],{},[898,99548,2797],{},[2005,99550,2104],{},[2138,99552,46708],{},[902,99554,99555],{"encoding":904},"P = -4Q + 80",[883,99557,99559],{"className":99558},[886],[888,99560,99561],{"xmlns":890},[892,99562,99563,99577],{},[895,99564,99565,99567,99569,99571,99573,99575],{},[898,99566,3946],{},[2005,99568,2007],{},[2138,99570,2182],{},[898,99572,2797],{},[2005,99574,2104],{},[2138,99576,2871],{},[902,99578,99579],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,99582,99584],{"className":99583},[886],[888,99585,99586],{"xmlns":890},[892,99587,99588,99596],{},[895,99589,99590,99592,99594],{},[898,99591,2783],{},[2005,99593,2007],{},[2138,99595,24206],{},[902,99597,47820],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,99600,99601,99602,99604,99605,99607],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,99603,45233],{}," (posun poptávky při zdanění kupujícího) a ",[38,99606,45267],{}," (posun nabídky při zdanění výrobce).",[36975,99609],{},[115,99611,15726],{"id":15725},[120,99613,99614,99633,99691,99748,99831,99877,99920,99965,100031],{},[123,99615,99616,2212,99619,99632],{},[38,99617,99618],{},"Jednotková daň",[883,99620,99622],{"className":99621},[886],[888,99623,99624],{"xmlns":890},[892,99625,99626,99630],{},[895,99627,99628],{},[898,99629,2783],{},[902,99631,2783],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,99634,99635,99637,99638,99676,99677,99690],{},[38,99636,96024],{}," — posun nabídky ",[883,99639,99641],{"className":99640},[886],[888,99642,99643],{"xmlns":890},[892,99644,99645,99673],{},[895,99646,99647,99653,99655,99657,99659,99661,99663,99665,99667,99669,99671],{},[2281,99648,99649,99651],{},[898,99650,8679],{},[2138,99652,2287],{},[2005,99654,2014],{"stretchy":2013},[898,99656,2797],{},[2005,99658,2020],{"stretchy":2013},[2005,99660,2007],{},[898,99662,8679],{},[2005,99664,2014],{"stretchy":2013},[898,99666,2797],{},[2005,99668,2020],{"stretchy":2013},[2005,99670,2104],{},[898,99672,2783],{},[902,99674,99675],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,99678,99680],{"className":99679},[886],[888,99681,99682],{"xmlns":890},[892,99683,99684,99688],{},[895,99685,99686],{},[898,99687,2783],{},[902,99689,2783],{"encoding":904}," svisle nahoru)",[123,99692,99693,99695,99696,99676,99734,99747],{},[38,99694,97097],{}," — posun poptávky ",[883,99697,99699],{"className":99698},[886],[888,99700,99701],{"xmlns":890},[892,99702,99703,99731],{},[895,99704,99705,99711,99713,99715,99717,99719,99721,99723,99725,99727,99729],{},[2281,99706,99707,99709],{},[898,99708,1860],{},[2138,99710,2140],{},[2005,99712,2014],{"stretchy":2013},[898,99714,2797],{},[2005,99716,2020],{"stretchy":2013},[2005,99718,2007],{},[898,99720,1860],{},[2005,99722,2014],{"stretchy":2013},[898,99724,2797],{},[2005,99726,2020],{"stretchy":2013},[2005,99728,2234],{},[898,99730,2783],{},[902,99732,99733],{"encoding":904},"D_2(Q) = D(Q) - T",[883,99735,99737],{"className":99736},[886],[888,99738,99739],{"xmlns":890},[892,99740,99741,99745],{},[895,99742,99743],{},[898,99744,2783],{},[902,99746,2783],{"encoding":904}," svisle dolů)",[123,99749,99750,7021,99753,41819,99792],{},[38,99751,99752],{},"Rovnovážný bod s daní",[883,99754,99756],{"className":99755},[886],[888,99757,99758],{"xmlns":890},[892,99759,99760,99790],{},[895,99761,99762,99768,99770,99778,99780,99788],{},[2281,99763,99764,99766],{},[898,99765,1868],{},[2138,99767,2287],{},[2005,99769,2495],{"stretchy":2013},[9172,99771,99772,99774,99776],{},[898,99773,2797],{},[2138,99775,2287],{},[898,99777,1868],{},[2005,99779,2295],{"separator":2294},[9172,99781,99782,99784,99786],{},[898,99783,3946],{},[2138,99785,2287],{},[898,99787,1868],{},[2005,99789,2510],{"stretchy":2013},[902,99791,96192],{"encoding":904},[883,99793,99795],{"className":99794},[886],[888,99796,99797],{"xmlns":890},[892,99798,99799,99829],{},[895,99800,99801,99807,99809,99817,99819,99827],{},[2281,99802,99803,99805],{},[898,99804,1868],{},[2138,99806,2140],{},[2005,99808,2495],{"stretchy":2013},[9172,99810,99811,99813,99815],{},[898,99812,2797],{},[2138,99814,2140],{},[898,99816,1868],{},[2005,99818,2295],{"separator":2294},[9172,99820,99821,99823,99825],{},[898,99822,3946],{},[2138,99824,2140],{},[898,99826,1868],{},[2005,99828,2510],{"stretchy":2013},[902,99830,97267],{"encoding":904},[123,99832,99833,10030,99835,99837,99838],{},[38,99834,42663],{},[614,99836,98047],{},") — rozklad ",[883,99839,99841],{"className":99840},[886],[888,99842,99843],{"xmlns":890},[892,99844,99845,99875],{},[895,99846,99847,99849,99851,99861,99863],{},[898,99848,2783],{},[2005,99850,2007],{},[2281,99852,99853,99855],{},[898,99854,2783],{},[895,99856,99857,99859],{},[898,99858,42682],{},[898,99860,724],{},[2005,99862,2104],{},[2281,99864,99865,99867],{},[898,99866,2783],{},[895,99868,99869,99871,99873],{},[898,99870,42705],{},[898,99872,2003],{},[898,99874,12047],{},[902,99876,42849],{"encoding":904},[123,99878,99879,99902,99903,2020],{},[38,99880,99881],{},[883,99882,99884],{"className":99883},[886],[888,99885,99886],{"xmlns":890},[892,99887,99888,99900],{},[895,99889,99890],{},[2281,99891,99892,99894],{},[898,99893,2783],{},[895,99895,99896,99898],{},[898,99897,42682],{},[898,99899,724],{},[902,99901,42687],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,99904,99906],{"className":99905},[886],[888,99907,99908],{"xmlns":890},[892,99909,99910,99918],{},[895,99911,99912],{},[2133,99913,99914,99916],{},[898,99915,3946],{},[898,99917,1868],{},[902,99919,41471],{"encoding":904},[123,99921,99922,99947,99948,2020],{},[38,99923,99924],{},[883,99925,99927],{"className":99926},[886],[888,99928,99929],{"xmlns":890},[892,99930,99931,99945],{},[895,99932,99933],{},[2281,99934,99935,99937],{},[898,99936,2783],{},[895,99938,99939,99941,99943],{},[898,99940,42705],{},[898,99942,2003],{},[898,99944,12047],{},[902,99946,42712],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,99949,99951],{"className":99950},[886],[888,99952,99953],{"xmlns":890},[892,99954,99955,99963],{},[895,99956,99957],{},[2133,99958,99959,99961],{},[898,99960,3946],{},[898,99962,1868],{},[902,99964,41471],{"encoding":904},[123,99966,99967,7021,99969,1343,99998],{},[38,99968,50479],{},[883,99970,99972],{"className":99971},[886],[888,99973,99974],{"xmlns":890},[892,99975,99976,99996],{},[895,99977,99978,99986,99988],{},[9172,99979,99980,99982,99984],{},[898,99981,2797],{},[2138,99983,2287],{},[898,99985,1868],{},[2005,99987,2007],{},[9172,99989,99990,99992,99994],{},[898,99991,2797],{},[2138,99993,2140],{},[898,99995,1868],{},[902,99997,42913],{"encoding":904},[883,99999,100001],{"className":100000},[886],[888,100002,100003],{"xmlns":890},[892,100004,100005,100029],{},[895,100006,100007,100015,100017,100019,100021],{},[9172,100008,100009,100011,100013],{},[898,100010,3946],{},[2138,100012,2287],{},[898,100014,1868],{},[2005,100016,2234],{},[898,100018,2783],{},[2005,100020,2007],{},[9172,100022,100023,100025,100027],{},[898,100024,3946],{},[2138,100026,2140],{},[898,100028,1868],{},[902,100030,42947],{"encoding":904},[123,100032,100033,100036],{},[38,100034,100035],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[36975,100038],{},[115,100040,3800],{"id":3799},[120,100042,100043,100051,100069,100076],{},[123,100044,100045,2212,100048],{},[38,100046,100047],{},"Kontext (hub):",[207,100049,802],{"className":100050,"dataFsResolvedFilePath":800,"href":801},[210],[123,100052,100053,2212,100055,100058,100059,18654,100061,100064,100065,100068],{},[38,100054,50728],{},[207,100056,820],{"className":100057,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,100060,55039],{},[207,100062,2366],{"className":100063,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,100066,3836],{"className":100067,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran 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ské matematiky, mikroekonomie a makroekonomie na bakalářské úrovni. ## Přehled zdrojů - \u003C\u003Cimek-detail-predmetu>> — sylabus a administrativní informace - KS 1. blok — 57 stran, matematic …",[],1777154975534]