[{"data":1,"prerenderedAt":103874},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-prebytek-spotrebitele-vyrobce":1626,"course-stats-imek":6077,"course-topics-imek":6081,"backlinks-prebytek-spotrebitele-vyrobce":103852,"related-prebytek-spotrebitele-vyrobce":103867},{"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":6076},{"id":1628,"title":820,"body":1629,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":6061,"navigation":664,"path":6062,"seo":6063,"sources":6064,"stem":6065,"tags":6066,"type":6074,"updated":677,"__hash__":6075},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":1630,"toc":6038},[1631,1634,1716,1770,1773,1776,2057,2136,2145,2147,2166,2170,2247,2345,2349,2667,2761,2763,2782,2786,2860,2947,2950,3127,3132,3134,3559,3561,3565,3569,3823,3873,3975,4044,4047,4083,4269,4331,4461,4540,4652,4689,4894,4913,4932,4997,5002,5005,5050,5053,5173,5219,5221,5225,5573,5575,5579,5857,5859,5863,5899,5906,5979,5981,5985],[12,1632,820],{"id":1633},"přebytek-spotřebitele-a-výrobce",[1635,1636,1637],"blockquote",{},[724,1638,1639,1642,1643,1646,1647,1665,1666,1646,1669,1686,1687,1711,1712,1715],{},[883,1640,1641],{},"!abstract"," TL;DR\n",[38,1644,1645],{},"Přebytek spotřebitele"," (",[883,1648,1650],{"className":1649},[886],[888,1651,1652],{"xmlns":890},[892,1653,1654,1662],{},[895,1655,1656,1659],{},[898,1657,1658],{},"C",[898,1660,1661],{},"S",[902,1663,1664],{"encoding":904},"CS",") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,1667,1668],{},"Přebytek výrobce",[883,1670,1672],{"className":1671},[886],[888,1673,1674],{"xmlns":890},[892,1675,1676,1683],{},[895,1677,1678,1681],{},[898,1679,1680],{},"P",[898,1682,1661],{},[902,1684,1685],{"encoding":904},"PS",") 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 ",[883,1688,1690],{"className":1689},[886],[888,1691,1692],{"xmlns":890},[892,1693,1694,1708],{},[895,1695,1696,1698,1700,1704,1706],{},[898,1697,1658],{},[898,1699,1661],{},[1701,1702,1703],"mo",{},"+",[898,1705,1680],{},[898,1707,1661],{},[902,1709,1710],{"encoding":904},"CS + PS"," měří ",[38,1713,1714],{},"celkový blahobyt trhu",".",[724,1717,1718,1646,1720,1343,1723,1738,1739,1646,1742,1343,1745,1760,1761,1765,1766,1715],{},[38,1719,1645],{},[614,1721,1722],{},"consumer surplus",[883,1724,1726],{"className":1725},[886],[888,1727,1728],{"xmlns":890},[892,1729,1730,1736],{},[895,1731,1732,1734],{},[898,1733,1658],{},[898,1735,1661],{},[902,1737,1664],{"encoding":904},") a ",[38,1740,1741],{},"přebytek výrobce",[614,1743,1744],{},"producer surplus",[883,1746,1748],{"className":1747},[886],[888,1749,1750],{"xmlns":890},[892,1751,1752,1758],{},[895,1753,1754,1756],{},[898,1755,1680],{},[898,1757,1661],{},[902,1759,1685],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,1762,1764],{"className":1763,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,1767,1769],{"className":1768,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[1771,1772],"hr",{},[115,1774,1241],{"id":1775},"úvod",[724,1777,1778,1779,1809,1810,1834,1835,1856,1857,1889,1890,1922,1923,1951,1952,1955,1956,1959,1960,1995,1996,2020,2021,1715],{},"Je dána funkce poptávky ",[883,1780,1782],{"className":1781},[886],[888,1783,1784],{"xmlns":890},[892,1785,1786,1806],{},[895,1787,1788,1790,1793,1796,1800,1803],{},[898,1789,1680],{},[1701,1791,1792],{},"=",[898,1794,1795],{},"D",[1701,1797,1799],{"stretchy":1798},"false","(",[898,1801,1802],{},"Q",[1701,1804,1805],{"stretchy":1798},")",[902,1807,1808],{"encoding":904},"P = D(Q)",", resp. funkce nabídky ",[883,1811,1813],{"className":1812},[886],[888,1814,1815],{"xmlns":890},[892,1816,1817,1831],{},[895,1818,1819,1821,1823,1825,1827,1829],{},[898,1820,1680],{},[1701,1822,1792],{},[898,1824,1661],{},[1701,1826,1799],{"stretchy":1798},[898,1828,1802],{},[1701,1830,1805],{"stretchy":1798},[902,1832,1833],{"encoding":904},"P = S(Q)",". Pro pevně zadané množství ",[883,1836,1838],{"className":1837},[886],[888,1839,1840],{"xmlns":890},[892,1841,1842,1853],{},[895,1843,1844],{},[1845,1846,1847,1849],"msub",{},[898,1848,1802],{},[1850,1851,1852],"mn",{},"0",[902,1854,1855],{"encoding":904},"Q_0"," je odpovídající cena ",[883,1858,1860],{"className":1859},[886],[888,1861,1862],{"xmlns":890},[892,1863,1864,1886],{},[895,1865,1866,1872,1874,1876,1878,1884],{},[1845,1867,1868,1870],{},[898,1869,1680],{},[1850,1871,1852],{},[1701,1873,1792],{},[898,1875,1795],{},[1701,1877,1799],{"stretchy":1798},[1845,1879,1880,1882],{},[898,1881,1802],{},[1850,1883,1852],{},[1701,1885,1805],{"stretchy":1798},[902,1887,1888],{"encoding":904},"P_0 = D(Q_0)"," (resp. ",[883,1891,1893],{"className":1892},[886],[888,1894,1895],{"xmlns":890},[892,1896,1897,1919],{},[895,1898,1899,1905,1907,1909,1911,1917],{},[1845,1900,1901,1903],{},[898,1902,1680],{},[1850,1904,1852],{},[1701,1906,1792],{},[898,1908,1661],{},[1701,1910,1799],{"stretchy":1798},[1845,1912,1913,1915],{},[898,1914,1802],{},[1850,1916,1852],{},[1701,1918,1805],{"stretchy":1798},[902,1920,1921],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,1924,1926],{"className":1925},[886],[888,1927,1928],{"xmlns":890},[892,1929,1930,1948],{},[895,1931,1932,1938,1942],{},[1845,1933,1934,1936],{},[898,1935,1680],{},[1850,1937,1852],{},[1939,1940,1941],"mtext",{}," ",[1845,1943,1944,1946],{},[898,1945,1802],{},[1850,1947,1852],{},[902,1949,1950],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,1953,1954],{},"výdaje spotřebitele",", nebo ",[38,1957,1958],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,1961,1963],{"className":1962},[886],[888,1964,1965],{"xmlns":890},[892,1966,1967,1992],{},[895,1968,1969,1971,1973,1979,1981,1984,1986],{},[1850,1970,1852],{},[1939,1972,1941],{},[1845,1974,1975,1977],{},[898,1976,1802],{},[1850,1978,1852],{},[1939,1980,1941],{},[898,1982,1983],{},"A",[1939,1985,1941],{},[1845,1987,1988,1990],{},[898,1989,1680],{},[1850,1991,1852],{},[902,1993,1994],{"encoding":904},"0\\,Q_0\\,A\\,P_0"," v rovině ",[883,1997,1999],{"className":1998},[886],[888,2000,2001],{"xmlns":890},[892,2002,2003,2017],{},[895,2004,2005,2007,2009,2013,2015],{},[1701,2006,1799],{"stretchy":1798},[898,2008,1802],{},[1701,2010,2012],{"separator":2011},"true",",",[898,2014,1680],{},[1701,2016,1805],{"stretchy":1798},[902,2018,2019],{"encoding":904},"(Q, P)",", kde ",[883,2022,2024],{"className":2023},[886],[888,2025,2026],{"xmlns":890},[892,2027,2028,2054],{},[895,2029,2030,2032,2034,2037,2043,2045,2051],{},[898,2031,1983],{},[1701,2033,1792],{},[1701,2035,2036],{"stretchy":1798},"[",[1845,2038,2039,2041],{},[898,2040,1802],{},[1850,2042,1852],{},[1701,2044,2012],{"separator":2011},[1845,2046,2047,2049],{},[898,2048,1680],{},[1850,2050,1852],{},[1701,2052,2053],{"stretchy":1798},"]",[902,2055,2056],{"encoding":904},"A = [Q_0, P_0]",[1635,2058,2059,2065,2125],{},[724,2060,2061,2064],{},[883,2062,2063],{},"!info"," Intuice",[120,2066,2067,2097],{},[123,2068,2069,2070,2073,2074,2077,2078,2096],{},"Za jednotky zboží nakoupené ",[38,2071,2072],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,2075,2076],{},"více"," než ",[883,2079,2081],{"className":2080},[886],[888,2082,2083],{"xmlns":890},[892,2084,2085,2093],{},[895,2086,2087],{},[1845,2088,2089,2091],{},[898,2090,1680],{},[1850,2092,1852],{},[902,2094,2095],{"encoding":904},"P_0"," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,2098,2099,2100,2102,2103,2106,2107,2124],{},"Za jednotky zboží prodané ",[38,2101,2072],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,2104,2105],{},"nižší"," cenu než ",[883,2108,2110],{"className":2109},[886],[888,2111,2112],{"xmlns":890},[892,2113,2114,2122],{},[895,2115,2116],{},[1845,2117,2118,2120],{},[898,2119,1680],{},[1850,2121,1852],{},[902,2123,2095],{"encoding":904}," — rozdíl je jeho přebytek.",[724,2126,2127,2128,2131,2132,2135],{},"Přebytek je tedy rozdíl mezi ",[614,2129,2130],{},"ochotou"," (platit \u002F prodávat) a ",[614,2133,2134],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,2137,2138],{},[2139,2140],"img",{"alt":2141,"className":2142,"src":2144},"imek-prebytky-cs-ps",[210,2143],"wikilink-broken","\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[1771,2146],{},[115,2148,2150,2151,1805],{"id":2149},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,2152,2154],{"className":2153},[886],[888,2155,2156],{"xmlns":890},[892,2157,2158,2164],{},[895,2159,2160,2162],{},[898,2161,1658],{},[898,2163,1661],{},[902,2165,1664],{"encoding":904},[198,2167,2169],{"id":2168},"definice-vzorec-214","Definice (vzorec 2.14)",[724,2171,2172,2173,2196,2197,2214,2215,2246],{},"Pro poptávku ",[883,2174,2176],{"className":2175},[886],[888,2177,2178],{"xmlns":890},[892,2179,2180,2194],{},[895,2181,2182,2184,2186,2188,2190,2192],{},[898,2183,1680],{},[1701,2185,1792],{},[898,2187,1795],{},[1701,2189,1799],{"stretchy":1798},[898,2191,1802],{},[1701,2193,1805],{"stretchy":1798},[902,2195,1808],{"encoding":904}," a pevně zadané ",[883,2198,2200],{"className":2199},[886],[888,2201,2202],{"xmlns":890},[892,2203,2204,2212],{},[895,2205,2206],{},[1845,2207,2208,2210],{},[898,2209,1802],{},[1850,2211,1852],{},[902,2213,1855],{"encoding":904}," s cenou ",[883,2216,2218],{"className":2217},[886],[888,2219,2220],{"xmlns":890},[892,2221,2222,2244],{},[895,2223,2224,2230,2232,2234,2236,2242],{},[1845,2225,2226,2228],{},[898,2227,1680],{},[1850,2229,1852],{},[1701,2231,1792],{},[898,2233,1795],{},[1701,2235,1799],{"stretchy":1798},[1845,2237,2238,2240],{},[898,2239,1802],{},[1850,2241,1852],{},[1701,2243,1805],{"stretchy":1798},[902,2245,1888],{"encoding":904},":",[883,2248,2250],{"className":2249},[886],[888,2251,2253],{"xmlns":890,"display":2252},"block",[892,2254,2255,2342],{},[2256,2257,2259],"mtable",{"width":2258},"100%",[2260,2261,2262,2266,2335,2337],"mtr",{},[2263,2264],"mtd",{"width":2265},"50%",[2263,2267,2268],{},[895,2269,2270,2272,2274,2276,2282,2284,2286,2300,2302,2304,2306,2308,2310,2313,2315,2318,2324,2326,2332],{},[898,2271,1658],{},[898,2273,1661],{},[1701,2275,1799],{"stretchy":1798},[1845,2277,2278,2280],{},[898,2279,1802],{},[1850,2281,1852],{},[1701,2283,1805],{"stretchy":1798},[1701,2285,1792],{},[2287,2288,2289,2292,2294],"msubsup",{},[1701,2290,2291],{},"∫",[1850,2293,1852],{},[1845,2295,2296,2298],{},[898,2297,1802],{},[1850,2299,1852],{},[898,2301,1795],{},[1701,2303,1799],{"stretchy":1798},[898,2305,1802],{},[1701,2307,1805],{"stretchy":1798},[1939,2309,1941],{},[898,2311,2312],{},"d",[898,2314,1802],{},[1701,2316,2317],{},"−",[1845,2319,2320,2322],{},[898,2321,1680],{},[1850,2323,1852],{},[1939,2325,1941],{},[1845,2327,2328,2330],{},[898,2329,1802],{},[1850,2331,1852],{},[898,2333,1715],{"mathvariant":2334},"normal",[2263,2336],{"width":2265},[2263,2338,2339],{},[1939,2340,2341],{},"(2.14)",[902,2343,2344],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[198,2346,2348],{"id":2347},"geometrická-interpretace","Geometrická interpretace",[120,2350,2351,2444,2507],{},[123,2352,2353,2394,2395,2421,2422,2425,2426,2443],{},[883,2354,2356],{"className":2355},[886],[888,2357,2358],{"xmlns":890},[892,2359,2360,2391],{},[895,2361,2362],{},[2363,2364,2365,2377,2379,2381,2383,2385,2387,2389],"mstyle",{"scriptlevel":1852,"displaystyle":2011},[2287,2366,2367,2369,2371],{},[1701,2368,2291],{},[1850,2370,1852],{},[1845,2372,2373,2375],{},[898,2374,1802],{},[1850,2376,1852],{},[898,2378,1795],{},[1701,2380,1799],{"stretchy":1798},[898,2382,1802],{},[1701,2384,1805],{"stretchy":1798},[1939,2386,1941],{},[898,2388,2312],{},[898,2390,1802],{},[902,2392,2393],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,2396,2398],{"className":2397},[886],[888,2399,2400],{"xmlns":890},[892,2401,2402,2418],{},[895,2403,2404,2406,2408,2410,2416],{},[1701,2405,2036],{"stretchy":1798},[1850,2407,1852],{},[1701,2409,2012],{"separator":2011},[1845,2411,2412,2414],{},[898,2413,1802],{},[1850,2415,1852],{},[1701,2417,2053],{"stretchy":1798},[902,2419,2420],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,2423,2424],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,2427,2429],{"className":2428},[886],[888,2430,2431],{"xmlns":890},[892,2432,2433,2441],{},[895,2434,2435],{},[1845,2436,2437,2439],{},[898,2438,1802],{},[1850,2440,1852],{},[902,2442,1855],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,2445,2446,2472,2473,2506],{},[883,2447,2449],{"className":2448},[886],[888,2450,2451],{"xmlns":890},[892,2452,2453,2469],{},[895,2454,2455,2461,2463],{},[1845,2456,2457,2459],{},[898,2458,1680],{},[1850,2460,1852],{},[1939,2462,1941],{},[1845,2464,2465,2467],{},[898,2466,1802],{},[1850,2468,1852],{},[902,2470,2471],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,2474,2476],{"className":2475},[886],[888,2477,2478],{"xmlns":890},[892,2479,2480,2504],{},[895,2481,2482,2484,2486,2492,2494,2496,2498],{},[1850,2483,1852],{},[1939,2485,1941],{},[1845,2487,2488,2490],{},[898,2489,1802],{},[1850,2491,1852],{},[1939,2493,1941],{},[898,2495,1983],{},[1939,2497,1941],{},[1845,2499,2500,2502],{},[898,2501,1680],{},[1850,2503,1852],{},[902,2505,1994],{"encoding":904},").",[123,2508,2509,2524,2525,2547,2548,2573,2574,2020,2601,2633,2634,1715],{},[883,2510,2512],{"className":2511},[886],[888,2513,2514],{"xmlns":890},[892,2515,2516,2522],{},[895,2517,2518,2520],{},[898,2519,1658],{},[898,2521,1661],{},[902,2523,1664],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,2526,2528],{"className":2527},[886],[888,2529,2530],{"xmlns":890},[892,2531,2532,2544],{},[895,2533,2534,2536,2538],{},[898,2535,1680],{},[1701,2537,1792],{},[1845,2539,2540,2542],{},[898,2541,1680],{},[1850,2543,1852],{},[902,2545,2546],{"encoding":904},"P = P_0"," v pásu ",[883,2549,2551],{"className":2550},[886],[888,2552,2553],{"xmlns":890},[892,2554,2555,2571],{},[895,2556,2557,2559,2561,2563,2569],{},[1701,2558,2036],{"stretchy":1798},[1850,2560,1852],{},[1701,2562,2012],{"separator":2011},[1845,2564,2565,2567],{},[898,2566,1802],{},[1850,2568,1852],{},[1701,2570,2053],{"stretchy":1798},[902,2572,2420],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,2575,2577],{"className":2576},[886],[888,2578,2579],{"xmlns":890},[892,2580,2581,2598],{},[895,2582,2583,2589,2591,2594,2596],{},[1845,2584,2585,2587],{},[898,2586,1680],{},[1850,2588,1852],{},[1939,2590,1941],{},[898,2592,2593],{},"B",[1939,2595,1941],{},[898,2597,1983],{},[902,2599,2600],{"encoding":904},"P_0\\,B\\,A",[883,2602,2604],{"className":2603},[886],[888,2605,2606],{"xmlns":890},[892,2607,2608,2630],{},[895,2609,2610,2612,2614,2616,2618,2620,2622,2624,2626,2628],{},[898,2611,2593],{},[1701,2613,1792],{},[1701,2615,2036],{"stretchy":1798},[1850,2617,1852],{},[1701,2619,2012],{"separator":2011},[898,2621,1795],{},[1701,2623,1799],{"stretchy":1798},[1850,2625,1852],{},[1701,2627,1805],{"stretchy":1798},[1701,2629,2053],{"stretchy":1798},[902,2631,2632],{"encoding":904},"B = [0, D(0)]"," a ",[883,2635,2637],{"className":2636},[886],[888,2638,2639],{"xmlns":890},[892,2640,2641,2665],{},[895,2642,2643,2645,2647,2649,2655,2657,2663],{},[898,2644,1983],{},[1701,2646,1792],{},[1701,2648,2036],{"stretchy":1798},[1845,2650,2651,2653],{},[898,2652,1802],{},[1850,2654,1852],{},[1701,2656,2012],{"separator":2011},[1845,2658,2659,2661],{},[898,2660,1680],{},[1850,2662,1852],{},[1701,2664,2053],{"stretchy":1798},[902,2666,2056],{"encoding":904},[724,2668,2669],{},[614,2670,2671,2672,2685,2686,2719,2720,2745,2746,1715],{},"Obrázek 2.24: Křivka poptávky ",[883,2673,2675],{"className":2674},[886],[888,2676,2677],{"xmlns":890},[892,2678,2679,2683],{},[895,2680,2681],{},[898,2682,1795],{},[902,2684,1795],{"encoding":904},", bod ",[883,2687,2689],{"className":2688},[886],[888,2690,2691],{"xmlns":890},[892,2692,2693,2717],{},[895,2694,2695,2697,2699,2701,2707,2709,2715],{},[898,2696,1983],{},[1701,2698,1792],{},[1701,2700,2036],{"stretchy":1798},[1845,2702,2703,2705],{},[898,2704,1802],{},[1850,2706,1852],{},[1701,2708,2012],{"separator":2011},[1845,2710,2711,2713],{},[898,2712,1680],{},[1850,2714,1852],{},[1701,2716,2053],{"stretchy":1798},[902,2718,2056],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,2721,2723],{"className":2722},[886],[888,2724,2725],{"xmlns":890},[892,2726,2727,2743],{},[895,2728,2729,2735,2737,2739,2741],{},[1845,2730,2731,2733],{},[898,2732,1680],{},[1850,2734,1852],{},[1939,2736,1941],{},[898,2738,2593],{},[1939,2740,1941],{},[898,2742,1983],{},[902,2744,2600],{"encoding":904}," představuje ",[883,2747,2749],{"className":2748},[886],[888,2750,2751],{"xmlns":890},[892,2752,2753,2759],{},[895,2754,2755,2757],{},[898,2756,1658],{},[898,2758,1661],{},[902,2760,1664],{"encoding":904},[1771,2762],{},[115,2764,2766,2767,1805],{"id":2765},"přebytek-výrobce-psps","Přebytek výrobce (",[883,2768,2770],{"className":2769},[886],[888,2771,2772],{"xmlns":890},[892,2773,2774,2780],{},[895,2775,2776,2778],{},[898,2777,1680],{},[898,2779,1661],{},[902,2781,1685],{"encoding":904},[198,2783,2785],{"id":2784},"definice-vzorec-215","Definice (vzorec 2.15)",[724,2787,2788,2789,2196,2812,2214,2829,2246],{},"Analogicky — pro nabídku ",[883,2790,2792],{"className":2791},[886],[888,2793,2794],{"xmlns":890},[892,2795,2796,2810],{},[895,2797,2798,2800,2802,2804,2806,2808],{},[898,2799,1680],{},[1701,2801,1792],{},[898,2803,1661],{},[1701,2805,1799],{"stretchy":1798},[898,2807,1802],{},[1701,2809,1805],{"stretchy":1798},[902,2811,1833],{"encoding":904},[883,2813,2815],{"className":2814},[886],[888,2816,2817],{"xmlns":890},[892,2818,2819,2827],{},[895,2820,2821],{},[1845,2822,2823,2825],{},[898,2824,1802],{},[1850,2826,1852],{},[902,2828,1855],{"encoding":904},[883,2830,2832],{"className":2831},[886],[888,2833,2834],{"xmlns":890},[892,2835,2836,2858],{},[895,2837,2838,2844,2846,2848,2850,2856],{},[1845,2839,2840,2842],{},[898,2841,1680],{},[1850,2843,1852],{},[1701,2845,1792],{},[898,2847,1661],{},[1701,2849,1799],{"stretchy":1798},[1845,2851,2852,2854],{},[898,2853,1802],{},[1850,2855,1852],{},[1701,2857,1805],{"stretchy":1798},[902,2859,1921],{"encoding":904},[883,2861,2863],{"className":2862},[886],[888,2864,2865],{"xmlns":890,"display":2252},[892,2866,2867,2944],{},[2256,2868,2869],{"width":2258},[2260,2870,2871,2873,2937,2939],{},[2263,2872],{"width":2265},[2263,2874,2875],{},[895,2876,2877,2879,2881,2883,2889,2891,2893,2899,2901,2907,2909,2921,2923,2925,2927,2929,2931,2933,2935],{},[898,2878,1680],{},[898,2880,1661],{},[1701,2882,1799],{"stretchy":1798},[1845,2884,2885,2887],{},[898,2886,1802],{},[1850,2888,1852],{},[1701,2890,1805],{"stretchy":1798},[1701,2892,1792],{},[1845,2894,2895,2897],{},[898,2896,1680],{},[1850,2898,1852],{},[1939,2900,1941],{},[1845,2902,2903,2905],{},[898,2904,1802],{},[1850,2906,1852],{},[1701,2908,2317],{},[2287,2910,2911,2913,2915],{},[1701,2912,2291],{},[1850,2914,1852],{},[1845,2916,2917,2919],{},[898,2918,1802],{},[1850,2920,1852],{},[898,2922,1661],{},[1701,2924,1799],{"stretchy":1798},[898,2926,1802],{},[1701,2928,1805],{"stretchy":1798},[1939,2930,1941],{},[898,2932,2312],{},[898,2934,1802],{},[898,2936,1715],{"mathvariant":2334},[2263,2938],{"width":2265},[2263,2940,2941],{},[1939,2942,2943],{},"(2.15)",[902,2945,2946],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[198,2948,2348],{"id":2949},"geometrická-interpretace-1",[120,2951,2952,3001,3062],{},[123,2953,2954,2979,2980,2983,2984,1715],{},[883,2955,2957],{"className":2956},[886],[888,2958,2959],{"xmlns":890},[892,2960,2961,2977],{},[895,2962,2963,2969,2971],{},[1845,2964,2965,2967],{},[898,2966,1680],{},[1850,2968,1852],{},[1939,2970,1941],{},[1845,2972,2973,2975],{},[898,2974,1802],{},[1850,2976,1852],{},[902,2978,2471],{"encoding":904}," — ",[38,2981,2982],{},"tržba"," výrobce za prodané množství ",[883,2985,2987],{"className":2986},[886],[888,2988,2989],{"xmlns":890},[892,2990,2991,2999],{},[895,2992,2993],{},[1845,2994,2995,2997],{},[898,2996,1802],{},[1850,2998,1852],{},[902,3000,1855],{"encoding":904},[123,3002,3003,3043,3044,3061],{},[883,3004,3006],{"className":3005},[886],[888,3007,3008],{"xmlns":890},[892,3009,3010,3040],{},[895,3011,3012],{},[2363,3013,3014,3026,3028,3030,3032,3034,3036,3038],{"scriptlevel":1852,"displaystyle":2011},[2287,3015,3016,3018,3020],{},[1701,3017,2291],{},[1850,3019,1852],{},[1845,3021,3022,3024],{},[898,3023,1802],{},[1850,3025,1852],{},[898,3027,1661],{},[1701,3029,1799],{"stretchy":1798},[898,3031,1802],{},[1701,3033,1805],{"stretchy":1798},[1939,3035,1941],{},[898,3037,2312],{},[898,3039,1802],{},[902,3041,3042],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,3045,3047],{"className":3046},[886],[888,3048,3049],{"xmlns":890},[892,3050,3051,3059],{},[895,3052,3053],{},[1845,3054,3055,3057],{},[898,3056,1802],{},[1850,3058,1852],{},[902,3060,1855],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,3063,3064,3079,3080,3101,3102,1715],{},[883,3065,3067],{"className":3066},[886],[888,3068,3069],{"xmlns":890},[892,3070,3071,3077],{},[895,3072,3073,3075],{},[898,3074,1680],{},[898,3076,1661],{},[902,3078,1685],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,3081,3083],{"className":3082},[886],[888,3084,3085],{"xmlns":890},[892,3086,3087,3099],{},[895,3088,3089,3091,3093],{},[898,3090,1680],{},[1701,3092,1792],{},[1845,3094,3095,3097],{},[898,3096,1680],{},[1850,3098,1852],{},[902,3100,2546],{"encoding":904}," a křivkou nabídky v pásu ",[883,3103,3105],{"className":3104},[886],[888,3106,3107],{"xmlns":890},[892,3108,3109,3125],{},[895,3110,3111,3113,3115,3117,3123],{},[1701,3112,2036],{"stretchy":1798},[1850,3114,1852],{},[1701,3116,2012],{"separator":2011},[1845,3118,3119,3121],{},[898,3120,1802],{},[1850,3122,1852],{},[1701,3124,2053],{"stretchy":1798},[902,3126,2420],{"encoding":904},[724,3128,3129],{},[614,3130,3131],{},"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.",[1771,3133],{},[1635,3135,3136,3142],{},[724,3137,3138,3141],{},[883,3139,3140],{},"!tip"," Postup výpočtu CS a PS",[152,3143,3144,3277,3388,3418,3552],{},[123,3145,3146,3147,3164,3165,3196,3197,3228,3229,1715],{},"Zjisti (nebo si zvol) množství ",[883,3148,3150],{"className":3149},[886],[888,3151,3152],{"xmlns":890},[892,3153,3154,3162],{},[895,3155,3156],{},[1845,3157,3158,3160],{},[898,3159,1802],{},[1850,3161,1852],{},[902,3163,1855],{"encoding":904}," a odpovídající cenu ",[883,3166,3168],{"className":3167},[886],[888,3169,3170],{"xmlns":890},[892,3171,3172,3194],{},[895,3173,3174,3180,3182,3184,3186,3192],{},[1845,3175,3176,3178],{},[898,3177,1680],{},[1850,3179,1852],{},[1701,3181,1792],{},[898,3183,1795],{},[1701,3185,1799],{"stretchy":1798},[1845,3187,3188,3190],{},[898,3189,1802],{},[1850,3191,1852],{},[1701,3193,1805],{"stretchy":1798},[902,3195,1888],{"encoding":904}," resp. ",[883,3198,3200],{"className":3199},[886],[888,3201,3202],{"xmlns":890},[892,3203,3204,3226],{},[895,3205,3206,3212,3214,3216,3218,3224],{},[1845,3207,3208,3210],{},[898,3209,1680],{},[1850,3211,1852],{},[1701,3213,1792],{},[898,3215,1661],{},[1701,3217,1799],{"stretchy":1798},[1845,3219,3220,3222],{},[898,3221,1802],{},[1850,3223,1852],{},[1701,3225,1805],{"stretchy":1798},[902,3227,1921],{"encoding":904},". V rovnováze platí ",[883,3230,3232],{"className":3231},[886],[888,3233,3234],{"xmlns":890},[892,3235,3236,3274],{},[895,3237,3238,3240,3242,3250,3252,3254,3256,3258,3264,3266,3268],{},[898,3239,1795],{},[1701,3241,1799],{"stretchy":1798},[3243,3244,3245,3247],"msup",{},[898,3246,1802],{},[898,3248,3249],{},"E",[1701,3251,1805],{"stretchy":1798},[1701,3253,1792],{},[898,3255,1661],{},[1701,3257,1799],{"stretchy":1798},[3243,3259,3260,3262],{},[898,3261,1802],{},[898,3263,3249],{},[1701,3265,1805],{"stretchy":1798},[1701,3267,1792],{},[3243,3269,3270,3272],{},[898,3271,1680],{},[898,3273,3249],{},[902,3275,3276],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,3278,3279,3280,3318,3319,3334,3335,3318,3373,2506],{},"Spočti určitý integrál ",[883,3281,3283],{"className":3282},[886],[888,3284,3285],{"xmlns":890},[892,3286,3287,3315],{},[895,3288,3289,3301,3303,3305,3307,3309,3311,3313],{},[2287,3290,3291,3293,3295],{},[1701,3292,2291],{},[1850,3294,1852],{},[1845,3296,3297,3299],{},[898,3298,1802],{},[1850,3300,1852],{},[898,3302,1795],{},[1701,3304,1799],{"stretchy":1798},[898,3306,1802],{},[1701,3308,1805],{"stretchy":1798},[1939,3310,1941],{},[898,3312,2312],{},[898,3314,1802],{},[902,3316,3317],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ"," (pro ",[883,3320,3322],{"className":3321},[886],[888,3323,3324],{"xmlns":890},[892,3325,3326,3332],{},[895,3327,3328,3330],{},[898,3329,1658],{},[898,3331,1661],{},[902,3333,1664],{"encoding":904},") nebo ",[883,3336,3338],{"className":3337},[886],[888,3339,3340],{"xmlns":890},[892,3341,3342,3370],{},[895,3343,3344,3356,3358,3360,3362,3364,3366,3368],{},[2287,3345,3346,3348,3350],{},[1701,3347,2291],{},[1850,3349,1852],{},[1845,3351,3352,3354],{},[898,3353,1802],{},[1850,3355,1852],{},[898,3357,1661],{},[1701,3359,1799],{"stretchy":1798},[898,3361,1802],{},[1701,3363,1805],{"stretchy":1798},[1939,3365,1941],{},[898,3367,2312],{},[898,3369,1802],{},[902,3371,3372],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,3374,3376],{"className":3375},[886],[888,3377,3378],{"xmlns":890},[892,3379,3380,3386],{},[895,3381,3382,3384],{},[898,3383,1680],{},[898,3385,1661],{},[902,3387,1685],{"encoding":904},[123,3389,3390,3391,1715],{},"Sestav obdélník ",[883,3392,3394],{"className":3393},[886],[888,3395,3396],{"xmlns":890},[892,3397,3398,3415],{},[895,3399,3400,3406,3409],{},[1845,3401,3402,3404],{},[898,3403,1680],{},[1850,3405,1852],{},[1701,3407,3408],{},"⋅",[1845,3410,3411,3413],{},[898,3412,1802],{},[1850,3414,1852],{},[902,3416,3417],{"encoding":904},"P_0 \\cdot Q_0",[123,3419,3420,3421],{},"Dosaď:\n",[120,3422,3423,3488],{},[123,3424,3425,3483,3484,3487],{},[883,3426,3428],{"className":3427},[886],[888,3429,3430],{"xmlns":890},[892,3431,3432,3480],{},[895,3433,3434,3436,3438,3440,3452,3454,3456,3458,3460,3462,3464,3466,3468,3474],{},[898,3435,1658],{},[898,3437,1661],{},[1701,3439,1792],{},[2287,3441,3442,3444,3446],{},[1701,3443,2291],{},[1850,3445,1852],{},[1845,3447,3448,3450],{},[898,3449,1802],{},[1850,3451,1852],{},[898,3453,1795],{},[1701,3455,1799],{"stretchy":1798},[898,3457,1802],{},[1701,3459,1805],{"stretchy":1798},[1939,3461,1941],{},[898,3463,2312],{},[898,3465,1802],{},[1701,3467,2317],{},[1845,3469,3470,3472],{},[898,3471,1680],{},[1850,3473,1852],{},[1845,3475,3476,3478],{},[898,3477,1802],{},[1850,3479,1852],{},[902,3481,3482],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,3485,3486],{},"mínus"," obdélník)",[123,3489,3490,3548,3549,3551],{},[883,3491,3493],{"className":3492},[886],[888,3494,3495],{"xmlns":890},[892,3496,3497,3545],{},[895,3498,3499,3501,3503,3505,3511,3517,3519,3531,3533,3535,3537,3539,3541,3543],{},[898,3500,1680],{},[898,3502,1661],{},[1701,3504,1792],{},[1845,3506,3507,3509],{},[898,3508,1680],{},[1850,3510,1852],{},[1845,3512,3513,3515],{},[898,3514,1802],{},[1850,3516,1852],{},[1701,3518,2317],{},[2287,3520,3521,3523,3525],{},[1701,3522,2291],{},[1850,3524,1852],{},[1845,3526,3527,3529],{},[898,3528,1802],{},[1850,3530,1852],{},[898,3532,1661],{},[1701,3534,1799],{"stretchy":1798},[898,3536,1802],{},[1701,3538,1805],{"stretchy":1798},[1939,3540,1941],{},[898,3542,2312],{},[898,3544,1802],{},[902,3546,3547],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,3550,3486],{}," integrál)",[123,3553,3554,3555,3558],{},"Kontrola znaménka: obě hodnoty musí být ",[38,3556,3557],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[1771,3560],{},[115,3562,3564],{"id":3563},"příklady","Příklady",[198,3566,3568],{"id":3567},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1635,3570,3571],{},[724,3572,3573,3576,3577,3602,3603,3628,3629,1343,3650,1343,3669,1343,3688,3707,3708,3789,3790,3808,3809,3822],{},[883,3574,3575],{},"!example"," Zadání\nJsou dány poptávka ",[883,3578,3580],{"className":3579},[886],[888,3581,3582],{"xmlns":890},[892,3583,3584,3599],{},[895,3585,3586,3588,3590,3592,3594,3596],{},[898,3587,1680],{},[1701,3589,1792],{},[898,3591,207],{},[898,3593,1802],{},[1701,3595,1703],{},[898,3597,3598],{},"b",[902,3600,3601],{"encoding":904},"P = aQ + b"," a nabídka ",[883,3604,3606],{"className":3605},[886],[888,3607,3608],{"xmlns":890},[892,3609,3610,3625],{},[895,3611,3612,3614,3616,3619,3621,3623],{},[898,3613,1680],{},[1701,3615,1792],{},[898,3617,3618],{},"c",[898,3620,1802],{},[1701,3622,1703],{},[898,3624,2312],{},[902,3626,3627],{"encoding":904},"P = cQ + d"," s hodnotami ",[883,3630,3632],{"className":3631},[886],[888,3633,3634],{"xmlns":890},[892,3635,3636,3647],{},[895,3637,3638,3640,3642,3644],{},[898,3639,207],{},[1701,3641,1792],{},[1701,3643,2317],{},[1850,3645,3646],{},"3",[902,3648,3649],{"encoding":904},"a = -3",[883,3651,3653],{"className":3652},[886],[888,3654,3655],{"xmlns":890},[892,3656,3657,3666],{},[895,3658,3659,3661,3663],{},[898,3660,3598],{},[1701,3662,1792],{},[1850,3664,3665],{},"40",[902,3667,3668],{"encoding":904},"b = 40",[883,3670,3672],{"className":3671},[886],[888,3673,3674],{"xmlns":890},[892,3675,3676,3685],{},[895,3677,3678,3680,3682],{},[898,3679,3618],{},[1701,3681,1792],{},[1850,3683,3684],{},"0,5",[902,3686,3687],{"encoding":904},"c = 0{,}5",[883,3689,3691],{"className":3690},[886],[888,3692,3693],{"xmlns":890},[892,3694,3695,3704],{},[895,3696,3697,3699,3701],{},[898,3698,2312],{},[1701,3700,1792],{},[1850,3702,3703],{},"10",[902,3705,3706],{"encoding":904},"d = 10",".\nRovnovážné množství:\n",[883,3709,3711],{"className":3710},[886],[888,3712,3713],{"xmlns":890},[892,3714,3715,3786],{},[895,3716,3717,3723,3725,3744,3746,3770,3772,3780,3783],{},[3243,3718,3719,3721],{},[898,3720,1802],{},[898,3722,3249],{},[1701,3724,1792],{},[3726,3727,3728,3736],"mfrac",{},[895,3729,3730,3732,3734],{},[898,3731,3598],{},[1701,3733,2317],{},[898,3735,2312],{},[895,3737,3738,3740,3742],{},[898,3739,3618],{},[1701,3741,2317],{},[898,3743,207],{},[1701,3745,1792],{},[3726,3747,3748,3756],{},[895,3749,3750,3752,3754],{},[1850,3751,3665],{},[1701,3753,2317],{},[1850,3755,3703],{},[895,3757,3758,3760,3762,3764,3766,3768],{},[1850,3759,3684],{},[1701,3761,2317],{},[1701,3763,1799],{"stretchy":1798},[1701,3765,2317],{},[1850,3767,3646],{},[1701,3769,1805],{"stretchy":1798},[1701,3771,1792],{},[3726,3773,3774,3777],{},[1850,3775,3776],{},"30",[1850,3778,3779],{},"3,5",[1701,3781,3782],{},"≐",[1850,3784,3785],{},"8,571.",[902,3787,3788],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,3791,3793],{"className":3792},[886],[888,3794,3795],{"xmlns":890},[892,3796,3797,3805],{},[895,3798,3799],{},[3243,3800,3801,3803],{},[898,3802,1802],{},[898,3804,3249],{},[902,3806,3807],{"encoding":904},"Q^E"," (a) při změně samotného parametru ",[883,3810,3812],{"className":3811},[886],[888,3813,3814],{"xmlns":890},[892,3815,3816,3820],{},[895,3817,3818],{},[898,3819,3618],{},[902,3821,3618],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,3824,3825],{},[38,3826,3827,3828,3841,3842,3856,3857,3872],{},"Řešení (a) — změna ",[883,3829,3831],{"className":3830},[886],[888,3832,3833],{"xmlns":890},[892,3834,3835,3839],{},[895,3836,3837],{},[898,3838,3618],{},[902,3840,3618],{"encoding":904}," z ",[883,3843,3845],{"className":3844},[886],[888,3846,3847],{"xmlns":890},[892,3848,3849,3853],{},[895,3850,3851],{},[1850,3852,3684],{},[902,3854,3855],{"encoding":904},"0{,}5"," na ",[883,3858,3860],{"className":3859},[886],[888,3861,3862],{"xmlns":890},[892,3863,3864,3869],{},[895,3865,3866],{},[1850,3867,3868],{},"0,6",[902,3870,3871],{"encoding":904},"0{,}6",", ceteris paribus.",[724,3874,3875,3876,3942,3943,2246],{},"Pomocí vzorce (2.13) pro ",[883,3877,3879],{"className":3878},[886],[888,3880,3881],{"xmlns":890},[892,3882,3883,3939],{},[895,3884,3885,3906,3908,3910],{},[2363,3886,3887],{"scriptlevel":1852,"displaystyle":2011},[3726,3888,3889,3900],{},[895,3890,3891,3894],{},[898,3892,3893],{"mathvariant":2334},"∂",[3243,3895,3896,3898],{},[898,3897,1802],{},[898,3899,3249],{},[895,3901,3902,3904],{},[898,3903,3893],{"mathvariant":2334},[898,3905,3618],{},[1701,3907,1792],{},[1701,3909,2317],{},[2363,3911,3912],{"scriptlevel":1852,"displaystyle":2011},[3726,3913,3914,3922],{},[895,3915,3916,3918,3920],{},[898,3917,3598],{},[1701,3919,2317],{},[898,3921,2312],{},[895,3923,3924,3926,3928,3930,3932],{},[1701,3925,1799],{"stretchy":1798},[898,3927,3618],{},[1701,3929,2317],{},[898,3931,207],{},[3243,3933,3934,3936],{},[1701,3935,1805],{"stretchy":1798},[1850,3937,3938],{},"2",[902,3940,3941],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,3944,3946],{"className":3945},[886],[888,3947,3948],{"xmlns":890},[892,3949,3950,3972],{},[895,3951,3952,3954],{},[1701,3953,2317],{},[2363,3955,3956],{"scriptlevel":1852,"displaystyle":2011},[3726,3957,3958,3964],{},[3243,3959,3960,3962],{},[898,3961,1802],{},[898,3963,3249],{},[895,3965,3966,3968,3970],{},[898,3967,3618],{},[1701,3969,2317],{},[898,3971,207],{},[902,3973,3974],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,3976,3978],{"className":3977},[886],[888,3979,3980],{"xmlns":890,"display":2252},[892,3981,3982,4041],{},[895,3983,3984,3986,3992,3994,3996,4012,4014,4016,4018,4020,4022,4029,4031,4034,4036,4038],{},[898,3985,2312],{},[3243,3987,3988,3990],{},[898,3989,1802],{},[898,3991,3249],{},[1701,3993,1792],{},[1701,3995,2317],{},[3726,3997,3998,4004],{},[3243,3999,4000,4002],{},[898,4001,1802],{},[898,4003,3249],{},[895,4005,4006,4008,4010],{},[898,4007,3618],{},[1701,4009,2317],{},[898,4011,207],{},[1939,4013,1941],{},[898,4015,2312],{},[898,4017,3618],{},[1701,4019,1792],{},[1701,4021,2317],{},[3726,4023,4024,4027],{},[1850,4025,4026],{},"8,571",[1850,4028,3779],{},[1701,4030,3408],{},[1850,4032,4033],{},"0,1",[1701,4035,3782],{},[1701,4037,2317],{},[1850,4039,4040],{},"0,245.",[902,4042,4043],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,4045,4046],{},"Nové rovnovážné množství:",[883,4048,4050],{"className":4049},[886],[888,4051,4052],{"xmlns":890,"display":2252},[892,4053,4054,4080],{},[895,4055,4056,4065,4068,4070,4072,4075,4077],{},[2287,4057,4058,4060,4063],{},[898,4059,1802],{},[1850,4061,4062],{},"1",[898,4064,3249],{},[1701,4066,4067],{},"≈",[1850,4069,4026],{},[1701,4071,2317],{},[1850,4073,4074],{},"0,245",[1701,4076,1792],{},[1850,4078,4079],{},"8,326.",[902,4081,4082],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,4084,4085,4088,4089,1343,4117,1343,4140,1343,4162,4185,4186,1343,4206,1343,4229,1343,4249,1715],{},[38,4086,4087],{},"Řešení (b) — současná změna všech parametrů:"," ",[883,4090,4092],{"className":4091},[886],[888,4093,4094],{"xmlns":890},[892,4095,4096,4114],{},[895,4097,4098,4100,4102,4104,4106,4109,4111],{},[898,4099,207],{},[1701,4101,2246],{},[1701,4103,2317],{},[1850,4105,3646],{},[1701,4107,4108],{},"→",[1701,4110,2317],{},[1850,4112,4113],{},"2,5",[902,4115,4116],{"encoding":904},"a: -3 \\to -2{,}5",[883,4118,4120],{"className":4119},[886],[888,4121,4122],{"xmlns":890},[892,4123,4124,4137],{},[895,4125,4126,4128,4130,4132,4134],{},[898,4127,3598],{},[1701,4129,2246],{},[1850,4131,3665],{},[1701,4133,4108],{},[1850,4135,4136],{},"35",[902,4138,4139],{"encoding":904},"b: 40 \\to 35",[883,4141,4143],{"className":4142},[886],[888,4144,4145],{"xmlns":890},[892,4146,4147,4159],{},[895,4148,4149,4151,4153,4155,4157],{},[898,4150,3618],{},[1701,4152,2246],{},[1850,4154,3684],{},[1701,4156,4108],{},[1850,4158,3868],{},[902,4160,4161],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,4163,4165],{"className":4164},[886],[888,4166,4167],{"xmlns":890},[892,4168,4169,4182],{},[895,4170,4171,4173,4175,4177,4179],{},[898,4172,2312],{},[1701,4174,2246],{},[1850,4176,3703],{},[1701,4178,4108],{},[1850,4180,4181],{},"11",[902,4183,4184],{"encoding":904},"d: 10 \\to 11",", tedy ",[883,4187,4189],{"className":4188},[886],[888,4190,4191],{"xmlns":890},[892,4192,4193,4203],{},[895,4194,4195,4197,4199,4201],{},[898,4196,2312],{},[898,4198,207],{},[1701,4200,1792],{},[1850,4202,3684],{},[902,4204,4205],{"encoding":904},"da = 0{,}5",[883,4207,4209],{"className":4208},[886],[888,4210,4211],{"xmlns":890},[892,4212,4213,4226],{},[895,4214,4215,4217,4219,4221,4223],{},[898,4216,2312],{},[898,4218,3598],{},[1701,4220,1792],{},[1701,4222,2317],{},[1850,4224,4225],{},"5",[902,4227,4228],{"encoding":904},"db = -5",[883,4230,4232],{"className":4231},[886],[888,4233,4234],{"xmlns":890},[892,4235,4236,4246],{},[895,4237,4238,4240,4242,4244],{},[898,4239,2312],{},[898,4241,3618],{},[1701,4243,1792],{},[1850,4245,4033],{},[902,4247,4248],{"encoding":904},"dc = 0{,}1",[883,4250,4252],{"className":4251},[886],[888,4253,4254],{"xmlns":890},[892,4255,4256,4266],{},[895,4257,4258,4260,4262,4264],{},[898,4259,2312],{},[898,4261,2312],{},[1701,4263,1792],{},[1850,4265,4062],{},[902,4267,4268],{"encoding":904},"dd = 1",[724,4270,4271,4272,4330],{},"Totální diferenciál ",[883,4273,4275],{"className":4274},[886],[888,4276,4277],{"xmlns":890},[892,4278,4279,4327],{},[895,4280,4281,4287,4289,4291,4293,4295,4297,4299,4301,4303,4305,4307],{},[3243,4282,4283,4285],{},[898,4284,1802],{},[898,4286,3249],{},[1701,4288,1799],{"stretchy":1798},[898,4290,207],{},[1701,4292,2012],{"separator":2011},[898,4294,3598],{},[1701,4296,2012],{"separator":2011},[898,4298,3618],{},[1701,4300,2012],{"separator":2011},[898,4302,2312],{},[1701,4304,1805],{"stretchy":1798},[1701,4306,1792],{},[2363,4308,4309],{"scriptlevel":1852,"displaystyle":2011},[3726,4310,4311,4319],{},[895,4312,4313,4315,4317],{},[898,4314,3598],{},[1701,4316,2317],{},[898,4318,2312],{},[895,4320,4321,4323,4325],{},[898,4322,3618],{},[1701,4324,2317],{},[898,4326,207],{},[902,4328,4329],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,4332,4334],{"className":4333},[886],[888,4335,4336],{"xmlns":890,"display":2252},[892,4337,4338,4458],{},[895,4339,4340,4342,4348,4350,4376,4378,4380,4382,4384,4396,4398,4400,4402,4404,4430,4432,4434,4436,4438,4450,4452,4454,4456],{},[898,4341,2312],{},[3243,4343,4344,4346],{},[898,4345,1802],{},[898,4347,3249],{},[1701,4349,1792],{},[3726,4351,4352,4360],{},[895,4353,4354,4356,4358],{},[898,4355,3598],{},[1701,4357,2317],{},[898,4359,2312],{},[895,4361,4362,4364,4366,4368,4370],{},[1701,4363,1799],{"stretchy":1798},[898,4365,3618],{},[1701,4367,2317],{},[898,4369,207],{},[3243,4371,4372,4374],{},[1701,4373,1805],{"stretchy":1798},[1850,4375,3938],{},[1939,4377,1941],{},[898,4379,2312],{},[898,4381,207],{},[1701,4383,1703],{},[3726,4385,4386,4388],{},[1850,4387,4062],{},[895,4389,4390,4392,4394],{},[898,4391,3618],{},[1701,4393,2317],{},[898,4395,207],{},[1939,4397,1941],{},[898,4399,2312],{},[898,4401,3598],{},[1701,4403,2317],{},[3726,4405,4406,4414],{},[895,4407,4408,4410,4412],{},[898,4409,3598],{},[1701,4411,2317],{},[898,4413,2312],{},[895,4415,4416,4418,4420,4422,4424],{},[1701,4417,1799],{"stretchy":1798},[898,4419,3618],{},[1701,4421,2317],{},[898,4423,207],{},[3243,4425,4426,4428],{},[1701,4427,1805],{"stretchy":1798},[1850,4429,3938],{},[1939,4431,1941],{},[898,4433,2312],{},[898,4435,3618],{},[1701,4437,2317],{},[3726,4439,4440,4442],{},[1850,4441,4062],{},[895,4443,4444,4446,4448],{},[898,4445,3618],{},[1701,4447,2317],{},[898,4449,207],{},[1939,4451,1941],{},[898,4453,2312],{},[898,4455,2312],{},[898,4457,1715],{"mathvariant":2334},[902,4459,4460],{"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.",[724,4462,4463,4464,1343,4486,1343,4517,4539],{},"Dosazením číselných hodnot (",[883,4465,4467],{"className":4466},[886],[888,4468,4469],{"xmlns":890},[892,4470,4471,4483],{},[895,4472,4473,4475,4477,4479,4481],{},[898,4474,3618],{},[1701,4476,2317],{},[898,4478,207],{},[1701,4480,1792],{},[1850,4482,3779],{},[902,4484,4485],{"encoding":904},"c - a = 3{,}5",[883,4487,4489],{"className":4488},[886],[888,4490,4491],{"xmlns":890},[892,4492,4493,4514],{},[895,4494,4495,4497,4499,4501,4503,4509,4511],{},[1701,4496,1799],{"stretchy":1798},[898,4498,3618],{},[1701,4500,2317],{},[898,4502,207],{},[3243,4504,4505,4507],{},[1701,4506,1805],{"stretchy":1798},[1850,4508,3938],{},[1701,4510,1792],{},[1850,4512,4513],{},"12,25",[902,4515,4516],{"encoding":904},"(c-a)^2 = 12{,}25",[883,4518,4520],{"className":4519},[886],[888,4521,4522],{"xmlns":890},[892,4523,4524,4536],{},[895,4525,4526,4528,4530,4532,4534],{},[898,4527,3598],{},[1701,4529,2317],{},[898,4531,2312],{},[1701,4533,1792],{},[1850,4535,3776],{},[902,4537,4538],{"encoding":904},"b - d = 30","):",[883,4541,4543],{"className":4542},[886],[888,4544,4545],{"xmlns":890,"display":2252},[892,4546,4547,4649],{},[895,4548,4549,4551,4557,4559,4567,4569,4571,4573,4575,4583,4585,4587,4589,4591,4593,4601,4603,4605,4607,4609,4617,4619,4621,4623,4625,4628,4630,4633,4635,4637,4639,4642,4644,4646],{},[898,4550,2312],{},[3243,4552,4553,4555],{},[898,4554,1802],{},[898,4556,3249],{},[1701,4558,4067],{},[2363,4560,4561],{"scriptlevel":1852,"displaystyle":1798},[3726,4562,4563,4565],{},[1850,4564,3776],{},[1850,4566,4513],{},[1701,4568,1799],{"stretchy":1798},[1850,4570,3684],{},[1701,4572,1805],{"stretchy":1798},[1701,4574,1703],{},[2363,4576,4577],{"scriptlevel":1852,"displaystyle":1798},[3726,4578,4579,4581],{},[1850,4580,4062],{},[1850,4582,3779],{},[1701,4584,1799],{"stretchy":1798},[1701,4586,2317],{},[1850,4588,4225],{},[1701,4590,1805],{"stretchy":1798},[1701,4592,2317],{},[2363,4594,4595],{"scriptlevel":1852,"displaystyle":1798},[3726,4596,4597,4599],{},[1850,4598,3776],{},[1850,4600,4513],{},[1701,4602,1799],{"stretchy":1798},[1850,4604,4033],{},[1701,4606,1805],{"stretchy":1798},[1701,4608,2317],{},[2363,4610,4611],{"scriptlevel":1852,"displaystyle":1798},[3726,4612,4613,4615],{},[1850,4614,4062],{},[1850,4616,3779],{},[1701,4618,1799],{"stretchy":1798},[1850,4620,4062],{},[1701,4622,1805],{"stretchy":1798},[1701,4624,3782],{},[1850,4626,4627],{},"1,224",[1701,4629,2317],{},[1850,4631,4632],{},"1,429",[1701,4634,2317],{},[1850,4636,4074],{},[1701,4638,2317],{},[1850,4640,4641],{},"0,286",[1701,4643,3782],{},[1701,4645,2317],{},[1850,4647,4648],{},"0,735.",[902,4650,4651],{"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.",[724,4653,4654,4655,1715],{},"Tedy ",[883,4656,4658],{"className":4657},[886],[888,4659,4660],{"xmlns":890},[892,4661,4662,4686],{},[895,4663,4664,4672,4674,4676,4678,4681,4683],{},[2287,4665,4666,4668,4670],{},[898,4667,1802],{},[1850,4669,4062],{},[898,4671,3249],{},[1701,4673,4067],{},[1850,4675,4026],{},[1701,4677,2317],{},[1850,4679,4680],{},"0,735",[1701,4682,3782],{},[1850,4684,4685],{},"7,836",[902,4687,4688],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1635,4690,4691],{},[724,4692,4693,4696,4697,4721,4722,4748,4749,4752,4753,4852,4853,4876,4877,4893],{},[883,4694,4695],{},"!warning"," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,4698,4700],{"className":4699},[886],[888,4701,4702],{"xmlns":890},[892,4703,4704,4718],{},[895,4705,4706,4709,4711,4713,4715],{},[898,4707,4708],{"mathvariant":2334},"Δ",[898,4710,1802],{},[1701,4712,4067],{},[1701,4714,2317],{},[1850,4716,4717],{},"2,69",[902,4719,4720],{"encoding":904},"\\Delta Q \\approx -2{,}69",", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,4723,4725],{"className":4724},[886],[888,4726,4727],{"xmlns":890},[892,4728,4729,4745],{},[895,4730,4731,4733,4739,4741,4743],{},[898,4732,2312],{},[3243,4734,4735,4737],{},[898,4736,1802],{},[898,4738,3249],{},[1701,4740,3782],{},[1701,4742,2317],{},[1850,4744,4680],{},[902,4746,4747],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,4750,4751],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,4754,4756],{"className":4755},[886],[888,4757,4758],{"xmlns":890},[892,4759,4760,4849],{},[895,4761,4762,4770,4772,4808,4810,4834,4836,4844,4846],{},[2287,4763,4764,4766,4768],{},[898,4765,1802],{},[1850,4767,4062],{},[898,4769,3249],{},[1701,4771,1792],{},[3726,4773,4774,4792],{},[895,4775,4776,4784,4786],{},[3243,4777,4778,4780],{},[898,4779,3598],{},[1701,4781,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},"0em","′",[1701,4785,2317],{},[3243,4787,4788,4790],{},[898,4789,2312],{},[1701,4791,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[895,4793,4794,4800,4802],{},[3243,4795,4796,4798],{},[898,4797,3618],{},[1701,4799,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,4801,2317],{},[3243,4803,4804,4806],{},[898,4805,207],{},[1701,4807,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,4809,1792],{},[3726,4811,4812,4820],{},[895,4813,4814,4816,4818],{},[1850,4815,4136],{},[1701,4817,2317],{},[1850,4819,4181],{},[895,4821,4822,4824,4826,4828,4830,4832],{},[1850,4823,3868],{},[1701,4825,2317],{},[1701,4827,1799],{"stretchy":1798},[1701,4829,2317],{},[1850,4831,4113],{},[1701,4833,1805],{"stretchy":1798},[1701,4835,1792],{},[3726,4837,4838,4841],{},[1850,4839,4840],{},"24",[1850,4842,4843],{},"3,1",[1701,4845,3782],{},[1850,4847,4848],{},"7,742",[902,4850,4851],{"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 ",[883,4854,4856],{"className":4855},[886],[888,4857,4858],{"xmlns":890},[892,4859,4860,4873],{},[895,4861,4862,4864,4866,4868,4870],{},[898,4863,4708],{"mathvariant":2334},[898,4865,1802],{},[1701,4867,3782],{},[1701,4869,2317],{},[1850,4871,4872],{},"0,829",[902,4874,4875],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,4878,4880],{"className":4879},[886],[888,4881,4882],{"xmlns":890},[892,4883,4884,4890],{},[895,4885,4886,4888],{},[1701,4887,2317],{},[1850,4889,4717],{},[902,4891,4892],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,4895,4896],{},[614,4897,4898,4899,4912],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,4900,4902],{"className":4901},[886],[888,4903,4904],{"xmlns":890},[892,4905,4906,4910],{},[895,4907,4908],{},[898,4909,1802],{},[902,4911,1802],{"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.",[198,4914,4916,4917],{"id":4915},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,4918,4920],{"className":4919},[886],[888,4921,4922],{"xmlns":890},[892,4923,4924,4930],{},[895,4925,4926,4928],{},[898,4927,1680],{},[898,4929,1661],{},[902,4931,1685],{"encoding":904},[1635,4933,4934],{},[724,4935,4936,4938,4939,4973,4974,4996],{},[883,4937,3575],{}," Zadání\nPro nabídku ",[883,4940,4942],{"className":4941},[886],[888,4943,4944],{"xmlns":890},[892,4945,4946,4970],{},[895,4947,4948,4950,4952,4954,4956,4958,4960,4962,4964,4966,4968],{},[898,4949,1680],{},[1701,4951,1792],{},[898,4953,1661],{},[1701,4955,1799],{"stretchy":1798},[898,4957,1802],{},[1701,4959,1805],{"stretchy":1798},[1701,4961,1792],{},[1850,4963,3703],{},[1701,4965,1703],{},[1850,4967,3938],{},[898,4969,1802],{},[902,4971,4972],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,4975,4977],{"className":4976},[886],[888,4978,4979],{"xmlns":890},[892,4980,4981,4993],{},[895,4982,4983,4989,4991],{},[1845,4984,4985,4987],{},[898,4986,1802],{},[1850,4988,1852],{},[1701,4990,1792],{},[1850,4992,3703],{},[902,4994,4995],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,4998,4999],{},[38,5000,5001],{},"Řešení.",[724,5003,5004],{},"Odpovídající cena:",[883,5006,5008],{"className":5007},[886],[888,5009,5010],{"xmlns":890,"display":2252},[892,5011,5012,5047],{},[895,5013,5014,5020,5022,5024,5026,5028,5030,5032,5034,5036,5038,5040,5042,5044],{},[1845,5015,5016,5018],{},[898,5017,1680],{},[1850,5019,1852],{},[1701,5021,1792],{},[898,5023,1661],{},[1701,5025,1799],{"stretchy":1798},[1850,5027,3703],{},[1701,5029,1805],{"stretchy":1798},[1701,5031,1792],{},[1850,5033,3703],{},[1701,5035,1703],{},[1850,5037,3938],{},[1701,5039,3408],{},[1850,5041,3703],{},[1701,5043,1792],{},[1850,5045,5046],{},"30.",[902,5048,5049],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,5051,5052],{},"Dle vzorce (2.15):",[883,5054,5056],{"className":5055},[886],[888,5057,5058],{"xmlns":890,"display":2252},[892,5059,5060,5170],{},[895,5061,5062,5064,5066,5068,5070,5072,5074,5080,5086,5088,5096,5098,5100,5102,5104,5106,5108,5110,5112,5114,5116,5118,5120,5122,5124,5127,5129,5131,5133,5139,5147,5149,5152,5154,5156,5159,5161,5163,5165,5167],{},[898,5063,1680],{},[898,5065,1661],{},[1701,5067,1799],{"stretchy":1798},[1850,5069,3703],{},[1701,5071,1805],{"stretchy":1798},[1701,5073,1792],{},[1845,5075,5076,5078],{},[898,5077,1680],{},[1850,5079,1852],{},[1845,5081,5082,5084],{},[898,5083,1802],{},[1850,5085,1852],{},[1701,5087,2317],{},[2287,5089,5090,5092,5094],{},[1701,5091,2291],{},[1850,5093,1852],{},[1850,5095,3703],{},[1701,5097,1799],{"stretchy":1798},[1850,5099,3703],{},[1701,5101,1703],{},[1850,5103,3938],{},[898,5105,1802],{},[1701,5107,1805],{"stretchy":1798},[1939,5109,1941],{},[898,5111,2312],{},[898,5113,1802],{},[1701,5115,1792],{},[1850,5117,3703],{},[1701,5119,3408],{},[1850,5121,3776],{},[1701,5123,2317],{},[1701,5125,2036],{"fence":1798,"stretchy":2011,"minsize":5126,"maxsize":5126},"1.8em",[1850,5128,3703],{},[898,5130,1802],{},[1701,5132,1703],{},[3243,5134,5135,5137],{},[898,5136,1802],{},[1850,5138,3938],{},[2287,5140,5141,5143,5145],{},[1701,5142,2053],{"fence":1798,"stretchy":2011,"minsize":5126,"maxsize":5126},[1850,5144,1852],{},[1850,5146,3703],{},[1701,5148,1792],{},[1850,5150,5151],{},"300",[1701,5153,2317],{},[1701,5155,1799],{"stretchy":1798},[1850,5157,5158],{},"100",[1701,5160,1703],{},[1850,5162,5158],{},[1701,5164,1805],{"stretchy":1798},[1701,5166,1792],{},[1850,5168,5169],{},"100.",[902,5171,5172],{"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.",[724,5174,5175,5176,5197,5198,5218],{},"Přebytek výrobce při množství ",[883,5177,5179],{"className":5178},[886],[888,5180,5181],{"xmlns":890},[892,5182,5183,5195],{},[895,5184,5185,5191,5193],{},[1845,5186,5187,5189],{},[898,5188,1802],{},[1850,5190,1852],{},[1701,5192,1792],{},[1850,5194,3703],{},[902,5196,4995],{"encoding":904}," je tedy ",[883,5199,5201],{"className":5200},[886],[888,5202,5203],{"xmlns":890},[892,5204,5205,5215],{},[895,5206,5207,5209,5211,5213],{},[898,5208,1680],{},[898,5210,1661],{},[1701,5212,1792],{},[1850,5214,5158],{},[902,5216,5217],{"encoding":904},"PS = 100"," (peněžních jednotek).",[1771,5220],{},[115,5222,5224],{"id":5223},"cheat-sheet","Cheat sheet",[16,5226,5227,5240],{},[19,5228,5229],{},[22,5230,5231,5234,5237],{},[25,5232,5233],{},"Veličina",[25,5235,5236],{},"Vzorec",[25,5238,5239],{},"Geometrie",[30,5241,5242,5360,5474,5542],{},[22,5243,5244,5272,5328],{},[35,5245,5246],{},[883,5247,5249],{"className":5248},[886],[888,5250,5251],{"xmlns":890},[892,5252,5253,5269],{},[895,5254,5255,5257,5259,5261,5267],{},[898,5256,1658],{},[898,5258,1661],{},[1701,5260,1799],{"stretchy":1798},[1845,5262,5263,5265],{},[898,5264,1802],{},[1850,5266,1852],{},[1701,5268,1805],{"stretchy":1798},[902,5270,5271],{"encoding":904},"CS(Q_0)",[35,5273,5274],{},[883,5275,5277],{"className":5276},[886],[888,5278,5279],{"xmlns":890},[892,5280,5281,5325],{},[895,5282,5283],{},[2363,5284,5285,5297,5299,5301,5303,5305,5307,5309,5311,5313,5319],{"scriptlevel":1852,"displaystyle":2011},[2287,5286,5287,5289,5291],{},[1701,5288,2291],{},[1850,5290,1852],{},[1845,5292,5293,5295],{},[898,5294,1802],{},[1850,5296,1852],{},[898,5298,1795],{},[1701,5300,1799],{"stretchy":1798},[898,5302,1802],{},[1701,5304,1805],{"stretchy":1798},[1939,5306,1941],{},[898,5308,2312],{},[898,5310,1802],{},[1701,5312,2317],{},[1845,5314,5315,5317],{},[898,5316,1680],{},[1850,5318,1852],{},[1845,5320,5321,5323],{},[898,5322,1802],{},[1850,5324,1852],{},[902,5326,5327],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,5329,5330,5331,5334,5335,5338,5339],{},"plocha ",[38,5332,5333],{},"pod"," křivkou poptávky, ",[38,5336,5337],{},"nad"," čárou ",[883,5340,5342],{"className":5341},[886],[888,5343,5344],{"xmlns":890},[892,5345,5346,5358],{},[895,5347,5348,5350,5352],{},[898,5349,1680],{},[1701,5351,1792],{},[1845,5353,5354,5356],{},[898,5355,1680],{},[1850,5357,1852],{},[902,5359,2546],{"encoding":904},[22,5361,5362,5390,5446],{},[35,5363,5364],{},[883,5365,5367],{"className":5366},[886],[888,5368,5369],{"xmlns":890},[892,5370,5371,5387],{},[895,5372,5373,5375,5377,5379,5385],{},[898,5374,1680],{},[898,5376,1661],{},[1701,5378,1799],{"stretchy":1798},[1845,5380,5381,5383],{},[898,5382,1802],{},[1850,5384,1852],{},[1701,5386,1805],{"stretchy":1798},[902,5388,5389],{"encoding":904},"PS(Q_0)",[35,5391,5392],{},[883,5393,5395],{"className":5394},[886],[888,5396,5397],{"xmlns":890},[892,5398,5399,5443],{},[895,5400,5401],{},[2363,5402,5403,5409,5415,5417,5429,5431,5433,5435,5437,5439,5441],{"scriptlevel":1852,"displaystyle":2011},[1845,5404,5405,5407],{},[898,5406,1680],{},[1850,5408,1852],{},[1845,5410,5411,5413],{},[898,5412,1802],{},[1850,5414,1852],{},[1701,5416,2317],{},[2287,5418,5419,5421,5423],{},[1701,5420,2291],{},[1850,5422,1852],{},[1845,5424,5425,5427],{},[898,5426,1802],{},[1850,5428,1852],{},[898,5430,1661],{},[1701,5432,1799],{"stretchy":1798},[898,5434,1802],{},[1701,5436,1805],{"stretchy":1798},[1939,5438,1941],{},[898,5440,2312],{},[898,5442,1802],{},[902,5444,5445],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,5447,5330,5448,5450,5451,5338,5453],{},[38,5449,5337],{}," křivkou nabídky, ",[38,5452,5333],{},[883,5454,5456],{"className":5455},[886],[888,5457,5458],{"xmlns":890},[892,5459,5460,5472],{},[895,5461,5462,5464,5466],{},[898,5463,1680],{},[1701,5465,1792],{},[1845,5467,5468,5470],{},[898,5469,1680],{},[1850,5471,1852],{},[902,5473,2546],{"encoding":904},[22,5475,5476,5479,5506],{},[35,5477,5478],{},"Výdaje \u002F tržby",[35,5480,5481],{},[883,5482,5484],{"className":5483},[886],[888,5485,5486],{"xmlns":890},[892,5487,5488,5504],{},[895,5489,5490,5496,5498],{},[1845,5491,5492,5494],{},[898,5493,1680],{},[1850,5495,1852],{},[1701,5497,3408],{},[1845,5499,5500,5502],{},[898,5501,1802],{},[1850,5503,1852],{},[902,5505,3417],{"encoding":904},[35,5507,5508,5509],{},"obdélník ",[883,5510,5512],{"className":5511},[886],[888,5513,5514],{"xmlns":890},[892,5515,5516,5540],{},[895,5517,5518,5520,5522,5528,5530,5532,5534],{},[1850,5519,1852],{},[1939,5521,1941],{},[1845,5523,5524,5526],{},[898,5525,1802],{},[1850,5527,1852],{},[1939,5529,1941],{},[898,5531,1983],{},[1939,5533,1941],{},[1845,5535,5536,5538],{},[898,5537,1680],{},[1850,5539,1852],{},[902,5541,1994],{"encoding":904},[22,5543,5544,5547,5570],{},[35,5545,5546],{},"Celkový přebytek",[35,5548,5549],{},[883,5550,5552],{"className":5551},[886],[888,5553,5554],{"xmlns":890},[892,5555,5556,5568],{},[895,5557,5558,5560,5562,5564,5566],{},[898,5559,1658],{},[898,5561,1661],{},[1701,5563,1703],{},[898,5565,1680],{},[898,5567,1661],{},[902,5569,1710],{"encoding":904},[35,5571,5572],{},"součet obou ploch v rovnováze",[1771,5574],{},[115,5576,5578],{"id":5577},"klíčové-pojmy","Klíčové pojmy",[120,5580,5581,5603,5625,5669,5713,5776,5804],{},[123,5582,5583,1646,5585,1343,5600,5602],{},[38,5584,1645],{},[883,5586,5588],{"className":5587},[886],[888,5589,5590],{"xmlns":890},[892,5591,5592,5598],{},[895,5593,5594,5596],{},[898,5595,1658],{},[898,5597,1661],{},[902,5599,1664],{"encoding":904},[614,5601,1722],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,5604,5605,1646,5607,1343,5622,5624],{},[38,5606,1668],{},[883,5608,5610],{"className":5609},[886],[888,5611,5612],{"xmlns":890},[892,5613,5614,5620],{},[895,5615,5616,5618],{},[898,5617,1680],{},[898,5619,1661],{},[902,5621,1685],{"encoding":904},[614,5623,1744],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,5626,5627,2979,5630,1715],{},[38,5628,5629],{},"Ochota platit",[883,5631,5633],{"className":5632},[886],[888,5634,5635],{"xmlns":890},[892,5636,5637,5667],{},[895,5638,5639],{},[2363,5640,5641,5653,5655,5657,5659,5661,5663,5665],{"scriptlevel":1852,"displaystyle":2011},[2287,5642,5643,5645,5647],{},[1701,5644,2291],{},[1850,5646,1852],{},[1845,5648,5649,5651],{},[898,5650,1802],{},[1850,5652,1852],{},[898,5654,1795],{},[1701,5656,1799],{"stretchy":1798},[898,5658,1802],{},[1701,5660,1805],{"stretchy":1798},[1939,5662,1941],{},[898,5664,2312],{},[898,5666,1802],{},[902,5668,2393],{"encoding":904},[123,5670,5671,2979,5674,1715],{},[38,5672,5673],{},"Minimální cena výrobce",[883,5675,5677],{"className":5676},[886],[888,5678,5679],{"xmlns":890},[892,5680,5681,5711],{},[895,5682,5683],{},[2363,5684,5685,5697,5699,5701,5703,5705,5707,5709],{"scriptlevel":1852,"displaystyle":2011},[2287,5686,5687,5689,5691],{},[1701,5688,2291],{},[1850,5690,1852],{},[1845,5692,5693,5695],{},[898,5694,1802],{},[1850,5696,1852],{},[898,5698,1661],{},[1701,5700,1799],{"stretchy":1798},[898,5702,1802],{},[1701,5704,1805],{"stretchy":1798},[1939,5706,1941],{},[898,5708,2312],{},[898,5710,1802],{},[902,5712,3042],{"encoding":904},[123,5714,5715,2979,5718,3548,5743,2506],{},[38,5716,5717],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,5719,5721],{"className":5720},[886],[888,5722,5723],{"xmlns":890},[892,5724,5725,5741],{},[895,5726,5727,5733,5735],{},[1845,5728,5729,5731],{},[898,5730,1680],{},[1850,5732,1852],{},[1939,5734,1941],{},[1845,5736,5737,5739],{},[898,5738,1802],{},[1850,5740,1852],{},[902,5742,2471],{"encoding":904},[883,5744,5746],{"className":5745},[886],[888,5747,5748],{"xmlns":890},[892,5749,5750,5774],{},[895,5751,5752,5754,5756,5762,5764,5766,5768],{},[1850,5753,1852],{},[1939,5755,1941],{},[1845,5757,5758,5760],{},[898,5759,1802],{},[1850,5761,1852],{},[1939,5763,1941],{},[898,5765,1983],{},[1939,5767,1941],{},[1845,5769,5770,5772],{},[898,5771,1680],{},[1850,5773,1852],{},[902,5775,1994],{"encoding":904},[123,5777,5778,5781,5782,5803],{},[38,5779,5780],{},"Celkový přebytek trhu"," — součet ",[883,5783,5785],{"className":5784},[886],[888,5786,5787],{"xmlns":890},[892,5788,5789,5801],{},[895,5790,5791,5793,5795,5797,5799],{},[898,5792,1658],{},[898,5794,1661],{},[1701,5796,1703],{},[898,5798,1680],{},[898,5800,1661],{},[902,5802,1710],{"encoding":904}," v rovnovážném bodě.",[123,5805,5806,5808,5809,1343,5822,5835,5836,1715],{},[38,5807,2348],{}," — plochy ohraničené křivkami ",[883,5810,5812],{"className":5811},[886],[888,5813,5814],{"xmlns":890},[892,5815,5816,5820],{},[895,5817,5818],{},[898,5819,1795],{},[902,5821,1795],{"encoding":904},[883,5823,5825],{"className":5824},[886],[888,5826,5827],{"xmlns":890},[892,5828,5829,5833],{},[895,5830,5831],{},[898,5832,1661],{},[902,5834,1661],{"encoding":904}," a přímkou ",[883,5837,5839],{"className":5838},[886],[888,5840,5841],{"xmlns":890},[892,5842,5843,5855],{},[895,5844,5845,5847,5849],{},[898,5846,1680],{},[1701,5848,1792],{},[1845,5850,5851,5853],{},[898,5852,1680],{},[1850,5854,1852],{},[902,5856,2546],{"encoding":904},[1771,5858],{},[115,5860,5862],{"id":5861},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,5864,5865,5866,5880,5881,5898],{},"Uvalení jednotkové daně ",[883,5867,5869],{"className":5868},[886],[888,5870,5871],{"xmlns":890},[892,5872,5873,5878],{},[895,5874,5875],{},[898,5876,5877],{},"T",[902,5879,5877],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,5882,5884],{"className":5883},[886],[888,5885,5886],{"xmlns":890},[892,5887,5888,5896],{},[895,5889,5890],{},[3243,5891,5892,5894],{},[898,5893,1802],{},[898,5895,3249],{},[902,5897,3807],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,5900,5901],{},[2139,5902],{"alt":5903,"className":5904,"src":5905},"imek-prebytky-s-dani-deadweight",[210,2143],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,5907,5908,5909,5924,5925,5940,5941,3548,5944,5968,5969,1646,5972,5975,5976,1715],{},"Přebytek spotřebitele ",[883,5910,5912],{"className":5911},[886],[888,5913,5914],{"xmlns":890},[892,5915,5916,5922],{},[895,5917,5918,5920],{},[898,5919,1658],{},[898,5921,1661],{},[902,5923,1664],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,5926,5928],{"className":5927},[886],[888,5929,5930],{"xmlns":890},[892,5931,5932,5938],{},[895,5933,5934,5936],{},[898,5935,1680],{},[898,5937,1661],{},[902,5939,1685],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,5942,5943],{},"daňový příjem",[883,5945,5947],{"className":5946},[886],[888,5948,5949],{"xmlns":890},[892,5950,5951,5965],{},[895,5952,5953,5955,5957],{},[898,5954,5877],{},[1701,5956,3408],{},[2287,5958,5959,5961,5963],{},[898,5960,1802],{},[1850,5962,4062],{},[898,5964,3249],{},[902,5966,5967],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,5970,5971],{},"mrtvá ztráta",[614,5973,5974],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,5977,811],{"className":5978,"dataFsResolvedFilePath":809,"href":810},[210],[1771,5980],{},[115,5982,5984],{"id":5983},"navigace","Navigace",[120,5986,5987,5995,6009,6018,6027],{},[123,5988,5989,4088,5992],{},[38,5990,5991],{},"Nadřazené téma:",[207,5993,802],{"className":5994,"dataFsResolvedFilePath":800,"href":801},[210],[123,5996,5997,4088,6000,6003,6004,6008],{},[38,5998,5999],{},"Matematický aparát:",[207,6001,775],{"className":6002,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,6005,6007],{"className":6006,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace"," (monotonie křivek)",[123,6010,6011,4088,6014],{},[38,6012,6013],{},"Související:",[207,6015,6017],{"className":6016,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk",[123,6019,6020,4088,6023],{},[38,6021,6022],{},"Shrnutí přednášek:",[207,6024,6026],{"className":6025,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,6028,6029,4088,6032],{},[38,6030,6031],{},"Kurz:",[207,6033,6037],{"className":6034,"dataFsResolvedFilePath":6035,"href":6036},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",{"title":641,"searchDepth":642,"depth":642,"links":6039},[6040,6041,6046,6051,6056,6057,6058,6059],{"id":1775,"depth":642,"text":1241},{"id":2149,"depth":642,"text":6042,"children":6043},"Přebytek spotřebitele (CSCS)",[6044,6045],{"id":2168,"depth":649,"text":2169},{"id":2347,"depth":649,"text":2348},{"id":2765,"depth":642,"text":6047,"children":6048},"Přebytek výrobce (PSPS)",[6049,6050],{"id":2784,"depth":649,"text":2785},{"id":2949,"depth":649,"text":2348},{"id":3563,"depth":642,"text":3564,"children":6052},[6053,6054],{"id":3567,"depth":649,"text":3568},{"id":4915,"depth":649,"text":6055},"Příklad 2.13 — numerický výpočet PSPS",{"id":5223,"depth":642,"text":5224},{"id":5577,"depth":642,"text":5578},{"id":5861,"depth":642,"text":5862},{"id":5983,"depth":642,"text":5984},"2026-04-22",{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,6067,6068,6069,6070,6071,6072,6073],"prebytek","cs","ps","integral","poptavka-nabidka","spotrebitel","vyrobce","topic","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs","topics",{"zapisku":1625,"topics":6078,"summaries":6079,"outputs":6080},15,5,1,[6082,7938,13626,15181,16050,20324,21931,31802,40789,54810,58864,78208,90320,99279,99567],{"id":6083,"title":6084,"body":6085,"course":1128,"courses":659,"created":1129,"description":7927,"extension":661,"meta":7928,"navigation":664,"path":7929,"seo":7930,"sources":7931,"stem":7932,"tags":7933,"type":6074,"updated":677,"__hash__":7937},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":6086,"toc":7910},[6087,6090,6109,6113,6192,6195,6318,6464,6466,6546,6548,6607,6657,6664,6668,6801,6851,6855,6895,6963,7032,7040,7044,7082,7154,7158,7236,7284,7328,7332,7336,7406,7410,7460,7539,7546,7549,7602,7872,7874],[12,6088,6084],{"id":6089},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,6091,6092,6093,6097,6098,6101,6102,6105,6106,1715],{},"Matematický aparát kurzu ",[207,6094,6096],{"className":6095,"dataFsResolvedFilePath":6035,"href":6036},[210],"ImeK",". Bez derivace se neobejdou ",[38,6099,6100],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,6103,6104],{},"maximalizace zisku"," ani ",[38,6107,6108],{},"minimalizace nákladů",[115,6110,6112],{"id":6111},"funkce-a-polynomy","Funkce a polynomy",[724,6114,6115,6116,6143,6144,6157,6158,6171,6172,1715],{},"Funkce jedné proměnné ",[883,6117,6119],{"className":6118},[886],[888,6120,6121],{"xmlns":890},[892,6122,6123,6140],{},[895,6124,6125,6128,6130,6133,6135,6138],{},[898,6126,6127],{},"y",[1701,6129,1792],{},[898,6131,6132],{},"f",[1701,6134,1799],{"stretchy":1798},[898,6136,6137],{},"x",[1701,6139,1805],{"stretchy":1798},[902,6141,6142],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,6145,6147],{"className":6146},[886],[888,6148,6149],{"xmlns":890},[892,6150,6151,6155],{},[895,6152,6153],{},[898,6154,6137],{},[902,6156,6137],{"encoding":904}," (nezávislá) → ",[883,6159,6161],{"className":6160},[886],[888,6162,6163],{"xmlns":890},[892,6164,6165,6169],{},[895,6166,6167],{},[898,6168,6127],{},[902,6170,6127],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,6173,6175],{"className":6174},[886],[888,6176,6177],{"xmlns":890},[892,6178,6179,6189],{},[895,6180,6181,6183,6185,6187],{},[898,6182,6132],{},[1701,6184,1799],{"stretchy":1798},[898,6186,207],{},[1701,6188,1805],{"stretchy":1798},[902,6190,6191],{"encoding":904},"f(a)",[724,6193,6194],{},"Polynomy:",[120,6196,6197,6228,6268],{},[123,6198,6199],{},[152,6200,6201],{},[123,6202,6203,6204],{},"stupně: ",[883,6205,6207],{"className":6206},[886],[888,6208,6209],{"xmlns":890},[892,6210,6211,6225],{},[895,6212,6213,6215,6217,6219,6221,6223],{},[898,6214,6127],{},[1701,6216,1792],{},[898,6218,207],{},[898,6220,6137],{},[1701,6222,1703],{},[898,6224,3598],{},[902,6226,6227],{"encoding":904},"y = ax + b",[123,6229,6230],{},[152,6231,6232],{"start":642},[123,6233,6203,6234],{},[883,6235,6237],{"className":6236},[886],[888,6238,6239],{"xmlns":890},[892,6240,6241,6265],{},[895,6242,6243,6245,6247,6249,6255,6257,6259,6261,6263],{},[898,6244,6127],{},[1701,6246,1792],{},[898,6248,207],{},[3243,6250,6251,6253],{},[898,6252,6137],{},[1850,6254,3938],{},[1701,6256,1703],{},[898,6258,3598],{},[898,6260,6137],{},[1701,6262,1703],{},[898,6264,3618],{},[902,6266,6267],{"encoding":904},"y = ax^2 + bx + c",[123,6269,6270],{},[152,6271,6272],{"start":649},[123,6273,6203,6274],{},[883,6275,6277],{"className":6276},[886],[888,6278,6279],{"xmlns":890},[892,6280,6281,6315],{},[895,6282,6283,6285,6287,6289,6295,6297,6299,6305,6307,6309,6311,6313],{},[898,6284,6127],{},[1701,6286,1792],{},[898,6288,207],{},[3243,6290,6291,6293],{},[898,6292,6137],{},[1850,6294,3646],{},[1701,6296,1703],{},[898,6298,3598],{},[3243,6300,6301,6303],{},[898,6302,6137],{},[1850,6304,3938],{},[1701,6306,1703],{},[898,6308,3618],{},[898,6310,6137],{},[1701,6312,1703],{},[898,6314,2312],{},[902,6316,6317],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,6319,6320,4088,6323,6378,6379,6416,6417,1715],{},[38,6321,6322],{},"Příklad rozkladu:",[883,6324,6326],{"className":6325},[886],[888,6327,6328],{"xmlns":890},[892,6329,6330,6375],{},[895,6331,6332,6334,6336,6342,6344,6346,6348,6350,6353,6355,6357,6359,6361,6363,6365,6367,6369,6371,6373],{},[898,6333,6127],{},[1701,6335,1792],{},[3243,6337,6338,6340],{},[898,6339,6137],{},[1850,6341,3938],{},[1701,6343,2317],{},[1850,6345,4225],{},[898,6347,6137],{},[1701,6349,1703],{},[1850,6351,6352],{},"6",[1701,6354,1792],{},[1701,6356,1799],{"stretchy":1798},[898,6358,6137],{},[1701,6360,2317],{},[1850,6362,3938],{},[1701,6364,1805],{"stretchy":1798},[1701,6366,1799],{"stretchy":1798},[898,6368,6137],{},[1701,6370,2317],{},[1850,6372,3646],{},[1701,6374,1805],{"stretchy":1798},[902,6376,6377],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,6380,6382],{"className":6381},[886],[888,6383,6384],{"xmlns":890},[892,6385,6386,6413],{},[895,6387,6388,6394,6396,6398,6400,6403,6409,6411],{},[1845,6389,6390,6392],{},[898,6391,6137],{},[1850,6393,4062],{},[1701,6395,1792],{},[1850,6397,3938],{},[1701,6399,2012],{"separator":2011},[1939,6401,6402],{}," ",[1845,6404,6405,6407],{},[898,6406,6137],{},[1850,6408,3938],{},[1701,6410,1792],{},[1850,6412,3646],{},[902,6414,6415],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,6418,6420],{"className":6419},[886],[888,6421,6422],{"xmlns":890},[892,6423,6424,6461],{},[895,6425,6426,6428,6430,6432,6434,6436,6444,6450,6452],{},[898,6427,6127],{},[1701,6429,1792],{},[1701,6431,1799],{"stretchy":1798},[898,6433,6137],{},[1701,6435,2317],{},[2363,6437,6438],{"scriptlevel":1852,"displaystyle":1798},[3726,6439,6440,6442],{},[1850,6441,4225],{},[1850,6443,3938],{},[3243,6445,6446,6448],{},[1701,6447,1805],{"stretchy":1798},[1850,6449,3938],{},[1701,6451,2317],{},[2363,6453,6454],{"scriptlevel":1852,"displaystyle":1798},[3726,6455,6456,6458],{},[1850,6457,4062],{},[1850,6459,6460],{},"4",[902,6462,6463],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,6465,6007],{"id":1145},[724,6467,6468,6469,1348,6493,6521,6522,1715],{},"Označení ",[883,6470,6472],{"className":6471},[886],[888,6473,6474],{"xmlns":890},[892,6475,6476,6490],{},[895,6477,6478,6484,6486,6488],{},[3243,6479,6480,6482],{},[898,6481,6132],{},[1701,6483,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,6485,1799],{"stretchy":1798},[898,6487,6137],{},[1701,6489,1805],{"stretchy":1798},[902,6491,6492],{"encoding":904},"f'(x)",[883,6494,6496],{"className":6495},[886],[888,6497,6498],{"xmlns":890},[892,6499,6500,6518],{},[895,6501,6502],{},[2363,6503,6504],{"scriptlevel":1852,"displaystyle":2011},[3726,6505,6506,6512],{},[895,6507,6508,6510],{},[898,6509,2312],{},[898,6511,6127],{},[895,6513,6514,6516],{},[898,6515,2312],{},[898,6517,6137],{},[902,6519,6520],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,6523,6525],{"className":6524},[886],[888,6526,6527],{"xmlns":890},[892,6528,6529,6543],{},[895,6530,6531,6537,6539,6541],{},[3243,6532,6533,6535],{},[898,6534,6132],{},[1701,6536,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,6538,1799],{"stretchy":1798},[898,6540,207],{},[1701,6542,1805],{"stretchy":1798},[902,6544,6545],{"encoding":904},"f'(a)",[198,6547,2348],{"id":2347},[724,6549,6550,6573,6574,6577,6578,6606],{},[883,6551,6553],{"className":6552},[886],[888,6554,6555],{"xmlns":890},[892,6556,6557,6571],{},[895,6558,6559,6565,6567,6569],{},[3243,6560,6561,6563],{},[898,6562,6132],{},[1701,6564,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,6566,1799],{"stretchy":1798},[898,6568,207],{},[1701,6570,1805],{"stretchy":1798},[902,6572,6545],{"encoding":904}," = ",[38,6575,6576],{},"sklon tečny"," ke grafu funkce v bodě ",[883,6579,6581],{"className":6580},[886],[888,6582,6583],{"xmlns":890},[892,6584,6585,6603],{},[895,6586,6587,6589,6591,6593,6595,6597,6599,6601],{},[1701,6588,2036],{"stretchy":1798},[898,6590,207],{},[1701,6592,2012],{"separator":2011},[898,6594,6132],{},[1701,6596,1799],{"stretchy":1798},[898,6598,207],{},[1701,6600,1805],{"stretchy":1798},[1701,6602,2053],{"stretchy":1798},[902,6604,6605],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,6608,6609],{},[883,6610,6612],{"className":6611},[886],[888,6613,6614],{"xmlns":890},[892,6615,6616,6654],{},[895,6617,6618,6620,6622,6624,6626,6628,6630,6632,6638,6640,6642,6644,6646,6648,6650,6652],{},[898,6619,6127],{},[1701,6621,2317],{},[898,6623,6132],{},[1701,6625,1799],{"stretchy":1798},[898,6627,207],{},[1701,6629,1805],{"stretchy":1798},[1701,6631,1792],{},[3243,6633,6634,6636],{},[898,6635,6132],{},[1701,6637,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,6639,1799],{"stretchy":1798},[898,6641,207],{},[1701,6643,1805],{"stretchy":1798},[1701,6645,1799],{"stretchy":1798},[898,6647,6137],{},[1701,6649,2317],{},[898,6651,207],{},[1701,6653,1805],{"stretchy":1798},[902,6655,6656],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,6658,6659],{},[2139,6660],{"alt":6661,"className":6662,"src":6663},"imek-derivace-tecna",[210,2143],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,6665,6667],{"id":6666},"inženýrská-interpretace","Inženýrská interpretace",[724,6669,6670,6573,6693,4088,6696,6709,6710,6723,6724,6742,6743,6756,6757,3841,6770,3856,6783,2246],{},[883,6671,6673],{"className":6672},[886],[888,6674,6675],{"xmlns":890},[892,6676,6677,6691],{},[895,6678,6679,6685,6687,6689],{},[3243,6680,6681,6683],{},[898,6682,6132],{},[1701,6684,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,6686,1799],{"stretchy":1798},[898,6688,207],{},[1701,6690,1805],{"stretchy":1798},[902,6692,6545],{"encoding":904},[38,6694,6695],{},"rychlost změny",[883,6697,6699],{"className":6698},[886],[888,6700,6701],{"xmlns":890},[892,6702,6703,6707],{},[895,6704,6705],{},[898,6706,6127],{},[902,6708,6127],{"encoding":904}," vzhledem k ",[883,6711,6713],{"className":6712},[886],[888,6714,6715],{"xmlns":890},[892,6716,6717,6721],{},[895,6718,6719],{},[898,6720,6137],{},[902,6722,6137],{"encoding":904}," v bodě ",[883,6725,6727],{"className":6726},[886],[888,6728,6729],{"xmlns":890},[892,6730,6731,6739],{},[895,6732,6733,6735,6737],{},[898,6734,6137],{},[1701,6736,1792],{},[898,6738,207],{},[902,6740,6741],{"encoding":904},"x = a","; přibližná změna ",[883,6744,6746],{"className":6745},[886],[888,6747,6748],{"xmlns":890},[892,6749,6750,6754],{},[895,6751,6752],{},[898,6753,6127],{},[902,6755,6127],{"encoding":904}," při změně ",[883,6758,6760],{"className":6759},[886],[888,6761,6762],{"xmlns":890},[892,6763,6764,6768],{},[895,6765,6766],{},[898,6767,6137],{},[902,6769,6137],{"encoding":904},[883,6771,6773],{"className":6772},[886],[888,6774,6775],{"xmlns":890},[892,6776,6777,6781],{},[895,6778,6779],{},[898,6780,207],{},[902,6782,207],{"encoding":904},[883,6784,6786],{"className":6785},[886],[888,6787,6788],{"xmlns":890},[892,6789,6790,6798],{},[895,6791,6792,6794,6796],{},[898,6793,207],{},[1701,6795,1703],{},[1850,6797,4062],{},[902,6799,6800],{"encoding":904},"a+1",[724,6802,6803],{},[883,6804,6806],{"className":6805},[886],[888,6807,6808],{"xmlns":890},[892,6809,6810,6848],{},[895,6811,6812,6814,6816,6818,6820,6822,6824,6826,6828,6830,6832,6834,6836,6842,6844,6846],{},[898,6813,6132],{},[1701,6815,1799],{"stretchy":1798},[898,6817,207],{},[1701,6819,1703],{},[1850,6821,4062],{},[1701,6823,1805],{"stretchy":1798},[1701,6825,4067],{},[898,6827,6132],{},[1701,6829,1799],{"stretchy":1798},[898,6831,207],{},[1701,6833,1805],{"stretchy":1798},[1701,6835,1703],{},[3243,6837,6838,6840],{},[898,6839,6132],{},[1701,6841,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,6843,1799],{"stretchy":1798},[898,6845,207],{},[1701,6847,1805],{"stretchy":1798},[902,6849,6850],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,6852,6854],{"id":6853},"příklad-mezní-náklady","Příklad — mezní náklady",[724,6856,6857,6858,1715],{},"Celkové náklady ",[883,6859,6861],{"className":6860},[886],[888,6862,6863],{"xmlns":890},[892,6864,6865,6892],{},[895,6866,6867,6869,6871,6873,6876,6878,6880,6882,6884,6886],{},[898,6868,5877],{},[898,6870,1658],{},[1701,6872,1792],{},[1850,6874,6875],{},"1000",[1701,6877,1703],{},[1850,6879,3938],{},[898,6881,1802],{},[1701,6883,1703],{},[1850,6885,4033],{},[3243,6887,6888,6890],{},[898,6889,1802],{},[1850,6891,3938],{},[902,6893,6894],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,6896,6897,6898,6936,6937,1715],{},"Mezní náklady: ",[883,6899,6901],{"className":6900},[886],[888,6902,6903],{"xmlns":890},[892,6904,6905,6933],{},[895,6906,6907,6910,6912,6914,6916,6922,6924,6926,6928,6931],{},[898,6908,6909],{},"M",[898,6911,1658],{},[1701,6913,1792],{},[898,6915,5877],{},[3243,6917,6918,6920],{},[898,6919,1658],{},[1701,6921,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,6923,1792],{},[1850,6925,3938],{},[1701,6927,1703],{},[1850,6929,6930],{},"0,2",[898,6932,1802],{},[902,6934,6935],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,6938,6940],{"className":6939},[886],[888,6941,6942],{"xmlns":890},[892,6943,6944,6960],{},[895,6945,6946,6948,6950,6952,6954,6956,6958],{},[898,6947,6909],{},[898,6949,1658],{},[1701,6951,1799],{"stretchy":1798},[1850,6953,3703],{},[1701,6955,1805],{"stretchy":1798},[1701,6957,1792],{},[1850,6959,6460],{},[902,6961,6962],{"encoding":904},"MC(10) = 4",[724,6964,6965,4088,6968,7015,7016,4088,7019,1715],{},[38,6966,6967],{},"Skutečný přírůstek:",[883,6969,6971],{"className":6970},[886],[888,6972,6973],{"xmlns":890},[892,6974,6975,7012],{},[895,6976,6977,6979,6981,6983,6985,6987,6989,6991,6993,6995,6997,6999,7001,7003,7005,7007,7009],{},[898,6978,4708],{"mathvariant":2334},[898,6980,5877],{},[898,6982,1658],{},[1701,6984,1792],{},[898,6986,5877],{},[898,6988,1658],{},[1701,6990,1799],{"stretchy":1798},[1850,6992,4181],{},[1701,6994,1805],{"stretchy":1798},[1701,6996,2317],{},[898,6998,5877],{},[898,7000,1658],{},[1701,7002,1799],{"stretchy":1798},[1850,7004,3703],{},[1701,7006,1805],{"stretchy":1798},[1701,7008,1792],{},[1850,7010,7011],{},"4,2",[902,7013,7014],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,7017,7018],{},"Přibližný (lineární):",[883,7020,7022],{"className":7021},[886],[888,7023,7024],{"xmlns":890},[892,7025,7026,7030],{},[895,7027,7028],{},[1850,7029,6460],{},[902,7031,6460],{"encoding":904},[724,7033,7034,7035,7039],{},"(Viz aplikace v ",[207,7036,7038],{"className":7037,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",".)",[115,7041,7043],{"id":7042},"diferenciál","Diferenciál",[724,7045,7046],{},[883,7047,7049],{"className":7048},[886],[888,7050,7051],{"xmlns":890},[892,7052,7053,7079],{},[895,7054,7055,7057,7059,7061,7067,7069,7071,7073,7075,7077],{},[898,7056,2312],{},[898,7058,6132],{},[1701,7060,1792],{},[3243,7062,7063,7065],{},[898,7064,6132],{},[1701,7066,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,7068,1799],{"stretchy":1798},[898,7070,6137],{},[1701,7072,1805],{"stretchy":1798},[1939,7074,1941],{},[898,7076,2312],{},[898,7078,6137],{},[902,7080,7081],{"encoding":904},"df = f'(x)\\, dx",[724,7083,7084,7085,7101,7102,7150,7151,1715],{},"Pro malá ",[883,7086,7088],{"className":7087},[886],[888,7089,7090],{"xmlns":890},[892,7091,7092,7098],{},[895,7093,7094,7096],{},[898,7095,2312],{},[898,7097,6137],{},[902,7099,7100],{"encoding":904},"dx"," platí: ",[883,7103,7105],{"className":7104},[886],[888,7106,7107],{"xmlns":890},[892,7108,7109,7147],{},[895,7110,7111,7113,7115,7117,7119,7121,7123,7125,7127,7129,7131,7133,7135,7137,7139,7141,7143,7145],{},[898,7112,4708],{"mathvariant":2334},[898,7114,6132],{},[1701,7116,1792],{},[898,7118,6132],{},[1701,7120,1799],{"stretchy":1798},[898,7122,6137],{},[1701,7124,1703],{},[898,7126,2312],{},[898,7128,6137],{},[1701,7130,1805],{"stretchy":1798},[1701,7132,2317],{},[898,7134,6132],{},[1701,7136,1799],{"stretchy":1798},[898,7138,6137],{},[1701,7140,1805],{"stretchy":1798},[1701,7142,4067],{},[898,7144,2312],{},[898,7146,6132],{},[902,7148,7149],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,7152,7153],{},"lineární odhad přírůstku",[198,7155,7157],{"id":7156},"příklad","Příklad",[724,7159,7160,7190,7191,7215,7216,4539],{},[883,7161,7163],{"className":7162},[886],[888,7164,7165],{"xmlns":890},[892,7166,7167,7187],{},[895,7168,7169,7171,7173,7175,7177,7179,7181],{},[898,7170,5877],{},[898,7172,1658],{},[1701,7174,1792],{},[1850,7176,5158],{},[1701,7178,1703],{},[1850,7180,4033],{},[3243,7182,7183,7185],{},[898,7184,1802],{},[1850,7186,3938],{},[902,7188,7189],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,7192,7194],{"className":7193},[886],[888,7195,7196],{"xmlns":890},[892,7197,7198,7212],{},[895,7199,7200,7202,7204,7207,7209],{},[898,7201,1802],{},[1701,7203,2246],{},[1850,7205,7206],{},"50",[1701,7208,4108],{},[1850,7210,7211],{},"60",[902,7213,7214],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,7217,7219],{"className":7218},[886],[888,7220,7221],{"xmlns":890},[892,7222,7223,7233],{},[895,7224,7225,7227,7229,7231],{},[898,7226,2312],{},[898,7228,1802],{},[1701,7230,1792],{},[1850,7232,3703],{},[902,7234,7235],{"encoding":904},"dQ = 10",[724,7237,7238],{},[883,7239,7241],{"className":7240},[886],[888,7242,7243],{"xmlns":890},[892,7244,7245,7281],{},[895,7246,7247,7249,7251,7253,7255,7257,7259,7261,7263,7265,7267,7269,7271,7273,7275,7277,7279],{},[898,7248,2312],{},[898,7250,5877],{},[898,7252,1658],{},[1701,7254,1792],{},[1850,7256,6930],{},[898,7258,1802],{},[1701,7260,3408],{},[898,7262,2312],{},[898,7264,1802],{},[1701,7266,1792],{},[1850,7268,6930],{},[1701,7270,3408],{},[1850,7272,7206],{},[1701,7274,3408],{},[1850,7276,3703],{},[1701,7278,1792],{},[1850,7280,5158],{},[902,7282,7283],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,7285,7286,7287,7310,7311,7327],{},"Přesná změna: ",[883,7288,7290],{"className":7289},[886],[888,7291,7292],{"xmlns":890},[892,7293,7294,7307],{},[895,7295,7296,7298,7300,7302,7304],{},[898,7297,4708],{"mathvariant":2334},[898,7299,5877],{},[898,7301,1658],{},[1701,7303,1792],{},[1850,7305,7306],{},"110",[902,7308,7309],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,7312,7314],{"className":7313},[886],[888,7315,7316],{"xmlns":890},[892,7317,7318,7324],{},[895,7319,7320,7322],{},[898,7321,5877],{},[898,7323,1658],{},[902,7325,7326],{"encoding":904},"TC"," je konvexní.",[115,7329,7331],{"id":7330},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,7333,7335],{"id":7334},"nutná-podmínka","Nutná podmínka",[724,7337,7338,7339,6723,7359,7372,7373,7401,7402,7405],{},"Má-li ",[883,7340,7342],{"className":7341},[886],[888,7343,7344],{"xmlns":890},[892,7345,7346,7356],{},[895,7347,7348,7350,7352,7354],{},[898,7349,6132],{},[1701,7351,1799],{"stretchy":1798},[898,7353,6137],{},[1701,7355,1805],{"stretchy":1798},[902,7357,7358],{"encoding":904},"f(x)",[883,7360,7362],{"className":7361},[886],[888,7363,7364],{"xmlns":890},[892,7365,7366,7370],{},[895,7367,7368],{},[898,7369,207],{},[902,7371,207],{"encoding":904}," extrém, pak ",[883,7374,7376],{"className":7375},[886],[888,7377,7378],{"xmlns":890},[892,7379,7380,7398],{},[895,7381,7382,7388,7390,7392,7394,7396],{},[3243,7383,7384,7386],{},[898,7385,6132],{},[1701,7387,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,7389,1799],{"stretchy":1798},[898,7391,207],{},[1701,7393,1805],{"stretchy":1798},[1701,7395,1792],{},[1850,7397,1852],{},[902,7399,7400],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,7403,7404],{},"stacionární"," (podezřelé) body.",[198,7407,7409],{"id":7408},"postačující-podmínka","Postačující podmínka",[724,7411,7412,7413,7426,7427,2246],{},"Pro stacionární bod ",[883,7414,7416],{"className":7415},[886],[888,7417,7418],{"xmlns":890},[892,7419,7420,7424],{},[895,7421,7422],{},[898,7423,207],{},[902,7425,207],{"encoding":904},", je-li ",[883,7428,7430],{"className":7429},[886],[888,7431,7432],{"xmlns":890},[892,7433,7434,7457],{},[895,7435,7436,7446,7448,7450,7452,7455],{},[3243,7437,7438,7440],{},[898,7439,6132],{},[895,7441,7442,7444],{},[1701,7443,4783],{"mathvariant":2334},[1701,7445,4783],{"mathvariant":2334},[1701,7447,1799],{"stretchy":1798},[898,7449,207],{},[1701,7451,1805],{"stretchy":1798},[1701,7453,7454],{"mathvariant":2334},"≠",[1850,7456,1852],{},[902,7458,7459],{"encoding":904},"f''(a) \\neq 0",[120,7461,7462,7501],{},[123,7463,7464,7497,7498],{},[883,7465,7467],{"className":7466},[886],[888,7468,7469],{"xmlns":890},[892,7470,7471,7494],{},[895,7472,7473,7483,7485,7487,7489,7492],{},[3243,7474,7475,7477],{},[898,7476,6132],{},[895,7478,7479,7481],{},[1701,7480,4783],{"mathvariant":2334},[1701,7482,4783],{"mathvariant":2334},[1701,7484,1799],{"stretchy":1798},[898,7486,207],{},[1701,7488,1805],{"stretchy":1798},[1701,7490,7491],{},">",[1850,7493,1852],{},[902,7495,7496],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,7499,7500],{},"lokální minimum",[123,7502,7503,7497,7536],{},[883,7504,7506],{"className":7505},[886],[888,7507,7508],{"xmlns":890},[892,7509,7510,7533],{},[895,7511,7512,7522,7524,7526,7528,7531],{},[3243,7513,7514,7516],{},[898,7515,6132],{},[895,7517,7518,7520],{},[1701,7519,4783],{"mathvariant":2334},[1701,7521,4783],{"mathvariant":2334},[1701,7523,1799],{"stretchy":1798},[898,7525,207],{},[1701,7527,1805],{"stretchy":1798},[1701,7529,7530],{},"\u003C",[1850,7532,1852],{},[902,7534,7535],{"encoding":904},"f''(a) \u003C 0",[38,7537,7538],{},"lokální maximum",[724,7540,7541],{},[2139,7542],{"alt":7543,"className":7544,"src":7545},"imek-extremy-1d",[210,2143],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,7547,7157],{"id":7548},"příklad-1",[724,7550,7551],{},[883,7552,7554],{"className":7553},[886],[888,7555,7556],{"xmlns":890},[892,7557,7558,7599],{},[895,7559,7560,7562,7564,7566,7568,7570,7572,7578,7580,7582,7588,7590,7593,7595,7597],{},[898,7561,6132],{},[1701,7563,1799],{"stretchy":1798},[898,7565,6137],{},[1701,7567,1805],{"stretchy":1798},[1701,7569,1792],{},[1850,7571,3938],{},[3243,7573,7574,7576],{},[898,7575,6137],{},[1850,7577,3646],{},[1701,7579,2317],{},[1850,7581,3646],{},[3243,7583,7584,7586],{},[898,7585,6137],{},[1850,7587,3938],{},[1701,7589,2317],{},[1850,7591,7592],{},"12",[898,7594,6137],{},[1701,7596,1703],{},[1850,7598,3646],{},[902,7600,7601],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,7603,7604,7715,7755,7818],{},[123,7605,7606,7678,7679],{},[883,7607,7609],{"className":7608},[886],[888,7610,7611],{"xmlns":890},[892,7612,7613,7675],{},[895,7614,7615,7621,7623,7625,7627,7629,7631,7637,7639,7641,7643,7645,7647,7649,7651,7653,7655,7657,7659,7661,7663,7665,7667,7669,7671,7673],{},[3243,7616,7617,7619],{},[898,7618,6132],{},[1701,7620,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,7622,1799],{"stretchy":1798},[898,7624,6137],{},[1701,7626,1805],{"stretchy":1798},[1701,7628,1792],{},[1850,7630,6352],{},[3243,7632,7633,7635],{},[898,7634,6137],{},[1850,7636,3938],{},[1701,7638,2317],{},[1850,7640,6352],{},[898,7642,6137],{},[1701,7644,2317],{},[1850,7646,7592],{},[1701,7648,1792],{},[1850,7650,6352],{},[1701,7652,1799],{"stretchy":1798},[898,7654,6137],{},[1701,7656,1703],{},[1850,7658,4062],{},[1701,7660,1805],{"stretchy":1798},[1701,7662,1799],{"stretchy":1798},[898,7664,6137],{},[1701,7666,2317],{},[1850,7668,3938],{},[1701,7670,1805],{"stretchy":1798},[1701,7672,1792],{},[1850,7674,1852],{},[902,7676,7677],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,7680,7682],{"className":7681},[886],[888,7683,7684],{"xmlns":890},[892,7685,7686,7712],{},[895,7687,7688,7694,7696,7698,7700,7702,7708,7710],{},[1845,7689,7690,7692],{},[898,7691,6137],{},[1850,7693,4062],{},[1701,7695,1792],{},[1701,7697,2317],{},[1850,7699,4062],{},[1701,7701,2012],{"separator":2011},[1845,7703,7704,7706],{},[898,7705,6137],{},[1850,7707,3938],{},[1701,7709,1792],{},[1850,7711,3938],{},[902,7713,7714],{"encoding":904},"x_1 = -1, x_2 = 2",[123,7716,7717],{},[883,7718,7720],{"className":7719},[886],[888,7721,7722],{"xmlns":890},[892,7723,7724,7752],{},[895,7725,7726,7736,7738,7740,7742,7744,7746,7748,7750],{},[3243,7727,7728,7730],{},[898,7729,6132],{},[895,7731,7732,7734],{},[1701,7733,4783],{"mathvariant":2334},[1701,7735,4783],{"mathvariant":2334},[1701,7737,1799],{"stretchy":1798},[898,7739,6137],{},[1701,7741,1805],{"stretchy":1798},[1701,7743,1792],{},[1850,7745,7592],{},[898,7747,6137],{},[1701,7749,2317],{},[1850,7751,6352],{},[902,7753,7754],{"encoding":904},"f''(x) = 12x - 6",[123,7756,7757,7497,7798,7801,7802],{},[883,7758,7760],{"className":7759},[886],[888,7761,7762],{"xmlns":890},[892,7763,7764,7795],{},[895,7765,7766,7776,7778,7780,7782,7784,7786,7788,7791,7793],{},[3243,7767,7768,7770],{},[898,7769,6132],{},[895,7771,7772,7774],{},[1701,7773,4783],{"mathvariant":2334},[1701,7775,4783],{"mathvariant":2334},[1701,7777,1799],{"stretchy":1798},[1701,7779,2317],{},[1850,7781,4062],{},[1701,7783,1805],{"stretchy":1798},[1701,7785,1792],{},[1701,7787,2317],{},[1850,7789,7790],{},"18",[1701,7792,7530],{},[1850,7794,1852],{},[902,7796,7797],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,7799,7800],{},"maximum"," v ",[883,7803,7805],{"className":7804},[886],[888,7806,7807],{"xmlns":890},[892,7808,7809,7815],{},[895,7810,7811,7813],{},[1701,7812,2317],{},[1850,7814,4062],{},[902,7816,7817],{"encoding":904},"-1",[123,7819,7820,7497,7856,7801,7859],{},[883,7821,7823],{"className":7822},[886],[888,7824,7825],{"xmlns":890},[892,7826,7827,7853],{},[895,7828,7829,7839,7841,7843,7845,7847,7849,7851],{},[3243,7830,7831,7833],{},[898,7832,6132],{},[895,7834,7835,7837],{},[1701,7836,4783],{"mathvariant":2334},[1701,7838,4783],{"mathvariant":2334},[1701,7840,1799],{"stretchy":1798},[1850,7842,3938],{},[1701,7844,1805],{"stretchy":1798},[1701,7846,1792],{},[1850,7848,7790],{},[1701,7850,7491],{},[1850,7852,1852],{},[902,7854,7855],{"encoding":904},"f''(2) = 18 > 0",[38,7857,7858],{},"minimum",[883,7860,7862],{"className":7861},[886],[888,7863,7864],{"xmlns":890},[892,7865,7866,7870],{},[895,7867,7868],{},[1850,7869,3938],{},[902,7871,3938],{"encoding":904},[115,7873,5984],{"id":5983},[120,7875,7876,7884,7892],{},[123,7877,7878,4088,7881],{},[38,7879,7880],{},"Předchozí:",[207,7882,757],{"className":7883,"dataFsResolvedFilePath":755,"href":756},[210],[123,7885,7886,4088,7889],{},[38,7887,7888],{},"Navazující:",[207,7890,775],{"className":7891,"dataFsResolvedFilePath":773,"href":774},[210],[123,7893,7894,4088,7897,7900,7901,7904,7905,7909],{},[38,7895,7896],{},"Souvislosti:",[207,7898,784],{"className":7899,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,7902,6017],{"className":7903,"dataFsResolvedFilePath":827,"href":828},[210]," (aplikace mezních veličin), ",[207,7906,7908],{"className":7907,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":7911},[7912,7913,7918,7921,7926],{"id":6111,"depth":642,"text":6112},{"id":1145,"depth":642,"text":6007,"children":7914},[7915,7916,7917],{"id":2347,"depth":649,"text":2348},{"id":6666,"depth":649,"text":6667},{"id":6853,"depth":649,"text":6854},{"id":7042,"depth":642,"text":7043,"children":7919},[7920],{"id":7156,"depth":649,"text":7157},{"id":7330,"depth":642,"text":7331,"children":7922},[7923,7924,7925],{"id":7334,"depth":649,"text":7335},{"id":7408,"depth":649,"text":7409},{"id":7548,"depth":649,"text":7157},{"id":5983,"depth":642,"text":5984},"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":6084,"description":7927},[1135],"topics\u002Fderivace",[1128,1145,7934,7935,7936],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":7939,"title":7940,"body":7941,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":13615,"navigation":664,"path":13616,"seo":13617,"sources":13618,"stem":13619,"tags":13620,"type":6074,"updated":677,"__hash__":13625},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":7942,"toc":13588},[7943,7946,7965,7969,7994,7998,8039,8130,8174,8178,8202,8209,8213,8223,8234,8238,8266,8275,8330,8336,8339,8345,8372,8378,8476,8635,8924,8928,9008,9014,9018,9115,9181,9348,9352,9430,9461,9488,9494,9526,9604,9690,9694,9757,9763,9766,9772,9886,9970,10014,10018,10064,10071,10388,10393,10417,10446,10513,10610,10614,10621,10628,10699,10819,10903,10906,10912,11238,11242,11405,11413,11549,11557,11795,11803,11806,11811,12067,12071,12245,12379,12416,12460,12463,12593,12683,12701,12705,12712,12718,12778,12781,12805,12808,12814,12817,12823,12826,12830,12868,12926,13115,13119,13192,13198,13205,13209,13215,13355,13359,13365,13401,13406,13583],[12,7944,7940],{"id":7945},"elasticita-poptávky-a-nabídky",[1635,7947,7948],{},[724,7949,7950,1642,7952,7954,7955,7958,7959,2633,7962,1715],{},[883,7951,1641],{},[38,7953,7908],{}," 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: ",[38,7956,7957],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,7960,7961],{},"křížově-cenovou elasticitu",[38,7963,7964],{},"důchodovou elasticitu",[115,7966,7968],{"id":7967},"úvod-motivace","Úvod — motivace",[724,7970,7971,7972,7975,7976,7979,7980,7983,7984,1889,7987,7990,7991,2506],{},"Termín ",[614,7973,7974],{},"elasticita"," (alternativně ",[614,7977,7978],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,7981,7982],{},"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 ",[614,7985,7986],{},"cenové elasticity poptávky",[614,7988,7989],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,7992,6007],{"className":7993,"dataFsResolvedFilePath":764,"href":765},[210],[198,7995,7997],{"id":7996},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,7999,8000,8001,8019,8020,8038],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,8002,8004],{"className":8003},[886],[888,8005,8006],{"xmlns":890},[892,8007,8008,8016],{},[895,8009,8010,8012,8014],{},[898,8011,1680],{},[1701,8013,1792],{},[1850,8015,3703],{},[902,8017,8018],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,8021,8023],{"className":8022},[886],[888,8024,8025],{"xmlns":890},[892,8026,8027,8035],{},[895,8028,8029,8031,8033],{},[898,8030,1802],{},[1701,8032,1792],{},[1850,8034,5158],{},[902,8036,8037],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,8040,8041,8087],{},[123,8042,8043,8046,8047,8086],{},[38,8044,8045],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,8048,8050],{"className":8049},[886],[888,8051,8052],{"xmlns":890},[892,8053,8054,8083],{},[895,8055,8056,8059,8062,8064,8066,8069,8071,8074,8076,8078,8080],{},[1939,8057,8058],{},"  ",[1701,8060,8061],{},"⇒",[1939,8063,8058],{},[898,8065,5877],{},[898,8067,8068],{},"R",[1701,8070,1792],{},[1850,8072,8073],{},"9",[1701,8075,3408],{},[1850,8077,7306],{},[1701,8079,1792],{},[1850,8081,8082],{},"990",[902,8084,8085],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,8088,8089,8092,8093,8129],{},[38,8090,8091],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,8094,8096],{"className":8095},[886],[888,8097,8098],{"xmlns":890},[892,8099,8100,8126],{},[895,8101,8102,8104,8106,8108,8110,8112,8114,8116,8118,8121,8123],{},[1939,8103,8058],{},[1701,8105,8061],{},[1939,8107,8058],{},[898,8109,5877],{},[898,8111,8068],{},[1701,8113,1792],{},[1850,8115,8073],{},[1701,8117,3408],{},[1850,8119,8120],{},"120",[1701,8122,1792],{},[1850,8124,8125],{},"1080",[902,8127,8128],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,8131,8132,8133,8136,8137,8140,8141,8144,8145,8148,8149,8152,8153,8169,8170,8173],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,8134,8135],{},"nerozumné",", na Trhu 2 ",[38,8138,8139],{},"rozumné",". Trh 2 je ",[38,8142,8143],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,8146,8147],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,8150,8151],{},"neelastická"," a vyššího ",[883,8154,8156],{"className":8155},[886],[888,8157,8158],{"xmlns":890},[892,8159,8160,8166],{},[895,8161,8162,8164],{},[898,8163,5877],{},[898,8165,8068],{},[902,8167,8168],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,8171,8172],{},"zvýšením"," ceny.",[198,8175,8177],{"id":8176},"hypotéza-41","Hypotéza 4.1",[1635,8179,8180],{},[724,8181,8182,8183],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,8184,8186],{"className":8185},[886],[888,8187,8188],{"xmlns":890},[892,8189,8190,8199],{},[895,8191,8192,8194,8197],{},[1701,8193,1799],{"stretchy":1798},[1850,8195,8196],{},"4.1",[1701,8198,1805],{"stretchy":1798},[902,8200,8201],{"encoding":904},"(4.1)",[724,8203,8204,8205,8208],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,8206,8207],{},"procentní změny"," obou faktorů.",[115,8210,8212],{"id":8211},"pojem-elasticity","Pojem elasticity",[724,8214,8215,8216,8218,8219,8222],{},"Obecně ",[38,8217,7974],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,8220,8221],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1635,8224,8225],{},[724,8226,8227,8229,8230,8233],{},[883,8228,2063],{}," Intuice\nElasticitu lze číst jako ",[38,8231,8232],{},"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.",[115,8235,8237],{"id":8236},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,8239,8240,8241,8265],{},"Nechť ",[883,8242,8244],{"className":8243},[886],[888,8245,8246],{"xmlns":890},[892,8247,8248,8262],{},[895,8249,8250,8252,8254,8256,8258,8260],{},[898,8251,1802],{},[1701,8253,1792],{},[898,8255,1795],{},[1701,8257,1799],{"stretchy":1798},[898,8259,1680],{},[1701,8261,1805],{"stretchy":1798},[902,8263,8264],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,8267,8268],{},[883,8269,8274],{"className":8270,"title":8272,"style":8273},[8271],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,8276,8277,8278,2633,8294,8310,8311,8329],{},"Znaménko minus je korekce: změny ",[883,8279,8281],{"className":8280},[886],[888,8282,8283],{"xmlns":890},[892,8284,8285,8291],{},[895,8286,8287,8289],{},[898,8288,4708],{"mathvariant":2334},[898,8290,1802],{},[902,8292,8293],{"encoding":904},"\\Delta Q",[883,8295,8297],{"className":8296},[886],[888,8298,8299],{"xmlns":890},[892,8300,8301,8307],{},[895,8302,8303,8305],{},[898,8304,4708],{"mathvariant":2334},[898,8306,1680],{},[902,8308,8309],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,8312,8314],{"className":8313},[886],[888,8315,8316],{"xmlns":890},[892,8317,8318,8326],{},[895,8319,8320],{},[3243,8321,8322,8324],{},[898,8323,3249],{},[898,8325,1983],{},[902,8327,8328],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,8331,8332],{},[883,8333,8335],{"className":8334,"title":8272,"style":8273},[8271],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,8337,8338],{},"Po dosazení:",[724,8340,8341],{},[883,8342,8344],{"className":8343,"title":8272,"style":8273},[8271],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,8346,8347,8348,8368,8369,8371],{},"Limitním přechodem ",[883,8349,8351],{"className":8350},[886],[888,8352,8353],{"xmlns":890},[892,8354,8355,8365],{},[895,8356,8357,8359,8361,8363],{},[898,8358,4708],{"mathvariant":2334},[898,8360,1680],{},[1701,8362,4108],{},[1850,8364,1852],{},[902,8366,8367],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,8370,7986],{}," (price elasticity of demand):",[724,8373,8374],{},[883,8375,8377],{"className":8376,"title":8272,"style":8273},[8271],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,8379,8380,8381,8404,8405,8428,8429,8453,8454,8475],{},"kde ",[883,8382,8384],{"className":8383},[886],[888,8385,8386],{"xmlns":890},[892,8387,8388,8402],{},[895,8389,8390,8392,8394,8396,8398,8400],{},[898,8391,1802],{},[1701,8393,1792],{},[898,8395,1795],{},[1701,8397,1799],{"stretchy":1798},[898,8399,1680],{},[1701,8401,1805],{"stretchy":1798},[902,8403,8264],{"encoding":904},". Pro pevnou cenu ",[883,8406,8408],{"className":8407},[886],[888,8409,8410],{"xmlns":890},[892,8411,8412,8425],{},[895,8413,8414,8416,8418],{},[898,8415,1680],{},[1701,8417,1792],{},[3243,8419,8420,8422],{},[898,8421,1680],{},[1701,8423,8424],{},"∗",[902,8426,8427],{"encoding":904},"P = P^*"," se ",[883,8430,8432],{"className":8431},[886],[888,8433,8434],{"xmlns":890},[892,8435,8436,8450],{},[895,8437,8438,8440,8442,8448],{},[898,8439,3249],{},[1701,8441,1799],{"stretchy":1798},[3243,8443,8444,8446],{},[898,8445,1680],{},[1701,8447,8424],{},[1701,8449,1805],{"stretchy":1798},[902,8451,8452],{"encoding":904},"E(P^*)"," nazývá ",[614,8455,8456,8457],{},"elasticita poptávky při ceně ",[883,8458,8460],{"className":8459},[886],[888,8461,8462],{"xmlns":890},[892,8463,8464,8472],{},[895,8465,8466],{},[3243,8467,8468,8470],{},[898,8469,1680],{},[1701,8471,8424],{},[902,8473,8474],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1635,8477,8478],{},[724,8479,8480,8482,8483,8501,8502,8530,8531,8560,8561,1343,8579,1343,8597,8615,8616,8631,8632,1715],{},[883,8481,4695],{}," Pozor na znaménko\nV (4.5) je ",[38,8484,8485,8486],{},"explicitní ",[883,8487,8489],{"className":8488},[886],[888,8490,8491],{"xmlns":890},[892,8492,8493,8499],{},[895,8494,8495,8497],{},[1701,8496,2317],{},[1850,8498,4062],{},[902,8500,7817],{"encoding":904}," právě proto, že ",[883,8503,8505],{"className":8504},[886],[888,8506,8507],{"xmlns":890},[892,8508,8509,8527],{},[895,8510,8511,8517,8519,8521,8523,8525],{},[3243,8512,8513,8515],{},[898,8514,1802],{},[1701,8516,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,8518,1799],{"stretchy":1798},[898,8520,1680],{},[1701,8522,1805],{"stretchy":1798},[1701,8524,7530],{},[1850,8526,1852],{},[902,8528,8529],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,8532,8534],{"className":8533},[886],[888,8535,8536],{"xmlns":890},[892,8537,8538,8557],{},[895,8539,8540,8542,8544,8550,8552,8555],{},[898,8541,3249],{},[1701,8543,1799],{"stretchy":1798},[3243,8545,8546,8548],{},[898,8547,1680],{},[1701,8549,8424],{},[1701,8551,1805],{"stretchy":1798},[1701,8553,8554],{},"≥",[1850,8556,1852],{},[902,8558,8559],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,8562,8564],{"className":8563},[886],[888,8565,8566],{"xmlns":890},[892,8567,8568,8576],{},[895,8569,8570,8572,8574],{},[898,8571,3249],{},[1701,8573,7491],{},[1850,8575,4062],{},[902,8577,8578],{"encoding":904},"E > 1",[883,8580,8582],{"className":8581},[886],[888,8583,8584],{"xmlns":890},[892,8585,8586,8594],{},[895,8587,8588,8590,8592],{},[898,8589,3249],{},[1701,8591,7530],{},[1850,8593,4062],{},[902,8595,8596],{"encoding":904},"E \u003C 1",[883,8598,8600],{"className":8599},[886],[888,8601,8602],{"xmlns":890},[892,8603,8604,8612],{},[895,8605,8606,8608,8610],{},[898,8607,3249],{},[1701,8609,1792],{},[1850,8611,4062],{},[902,8613,8614],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,8617,8619],{"className":8618},[886],[888,8620,8621],{"xmlns":890},[892,8622,8623,8629],{},[895,8624,8625,8627],{},[1701,8626,2317],{},[1850,8628,4062],{},[902,8630,7817],{"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 ",[38,8633,8634],{},"absolutní hodnotou",[1635,8636,8637,8656],{},[724,8638,8639,8641,8642,8655],{},[883,8640,3140],{}," Postup: jak spočítat ",[883,8643,8645],{"className":8644},[886],[888,8646,8647],{"xmlns":890},[892,8648,8649,8653],{},[895,8650,8651],{},[898,8652,3249],{},[902,8654,3249],{"encoding":904}," v bodě",[152,8657,8658,8709,8749,8802,8867],{},[123,8659,8660,8661,8684,8685,8708],{},"Zapište ",[883,8662,8664],{"className":8663},[886],[888,8665,8666],{"xmlns":890},[892,8667,8668,8682],{},[895,8669,8670,8672,8674,8676,8678,8680],{},[898,8671,1802],{},[1701,8673,1792],{},[898,8675,1795],{},[1701,8677,1799],{"stretchy":1798},[898,8679,1680],{},[1701,8681,1805],{"stretchy":1798},[902,8683,8264],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,8686,8688],{"className":8687},[886],[888,8689,8690],{"xmlns":890},[892,8691,8692,8706],{},[895,8693,8694,8696,8698,8700,8702,8704],{},[898,8695,1680],{},[1701,8697,1792],{},[898,8699,1795],{},[1701,8701,1799],{"stretchy":1798},[898,8703,1802],{},[1701,8705,1805],{"stretchy":1798},[902,8707,1808],{"encoding":904},", použijte vztah (4.9).",[123,8710,8711,8712,1715],{},"Spočítejte derivaci ",[883,8713,8715],{"className":8714},[886],[888,8716,8717],{"xmlns":890},[892,8718,8719,8746],{},[895,8720,8721,8727,8729,8731,8733,8735,8737,8739,8742,8744],{},[3243,8722,8723,8725],{},[898,8724,1802],{},[1701,8726,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,8728,1799],{"stretchy":1798},[898,8730,1680],{},[1701,8732,1805],{"stretchy":1798},[1701,8734,1792],{},[898,8736,2312],{"mathvariant":2334},[898,8738,1802],{},[898,8740,8741],{"mathvariant":2334},"\u002F",[898,8743,2312],{"mathvariant":2334},[898,8745,1680],{},[902,8747,8748],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,8750,8751,8752,8769,8770,1715],{},"Dosaďte zadanou cenu ",[883,8753,8755],{"className":8754},[886],[888,8756,8757],{"xmlns":890},[892,8758,8759,8767],{},[895,8760,8761],{},[3243,8762,8763,8765],{},[898,8764,1680],{},[1701,8766,8424],{},[902,8768,8474],{"encoding":904}," a dopočítejte odpovídající ",[883,8771,8773],{"className":8772},[886],[888,8774,8775],{"xmlns":890},[892,8776,8777,8799],{},[895,8778,8779,8785,8787,8789,8791,8797],{},[3243,8780,8781,8783],{},[898,8782,1802],{},[1701,8784,8424],{},[1701,8786,1792],{},[898,8788,1795],{},[1701,8790,1799],{"stretchy":1798},[3243,8792,8793,8795],{},[898,8794,1680],{},[1701,8796,8424],{},[1701,8798,1805],{"stretchy":1798},[902,8800,8801],{"encoding":904},"Q^* = D(P^*)",[123,8803,8804,8805,1715],{},"Dosaďte do (4.5): ",[883,8806,8808],{"className":8807},[886],[888,8809,8810],{"xmlns":890},[892,8811,8812,8864],{},[895,8813,8814,8816,8818,8824,8826,8828,8830,8846,8848,8854,8856,8862],{},[898,8815,3249],{},[1701,8817,1799],{"stretchy":1798},[3243,8819,8820,8822],{},[898,8821,1680],{},[1701,8823,8424],{},[1701,8825,1805],{"stretchy":1798},[1701,8827,1792],{},[1701,8829,2317],{},[2363,8831,8832],{"scriptlevel":1852,"displaystyle":2011},[3726,8833,8834,8840],{},[3243,8835,8836,8838],{},[898,8837,1680],{},[1701,8839,8424],{},[3243,8841,8842,8844],{},[898,8843,1802],{},[1701,8845,8424],{},[1939,8847,1941],{},[3243,8849,8850,8852],{},[898,8851,1802],{},[1701,8853,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,8855,1799],{"stretchy":1798},[3243,8857,8858,8860],{},[898,8859,1680],{},[1701,8861,8424],{},[1701,8863,1805],{"stretchy":1798},[902,8865,8866],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,8868,8869,8870,8887,8888,8905,8906,8923],{},"Klasifikujte: ",[883,8871,8873],{"className":8872},[886],[888,8874,8875],{"xmlns":890},[892,8876,8877,8885],{},[895,8878,8879,8881,8883],{},[898,8880,3249],{},[1701,8882,7491],{},[1850,8884,4062],{},[902,8886,8578],{"encoding":904}," elastická, ",[883,8889,8891],{"className":8890},[886],[888,8892,8893],{"xmlns":890},[892,8894,8895,8903],{},[895,8896,8897,8899,8901],{},[898,8898,3249],{},[1701,8900,1792],{},[1850,8902,4062],{},[902,8904,8614],{"encoding":904}," jednotková, ",[883,8907,8909],{"className":8908},[886],[888,8910,8911],{"xmlns":890},[892,8912,8913,8921],{},[895,8914,8915,8917,8919],{},[898,8916,3249],{},[1701,8918,7530],{},[1850,8920,4062],{},[902,8922,8596],{"encoding":904}," neelastická.",[198,8925,8927],{"id":8926},"interpretace-46","Interpretace (4.6)",[1635,8929,8930],{},[724,8931,8932,8933,8956,8957,8970,8971,8988,8989],{},"Číslo ",[883,8934,8936],{"className":8935},[886],[888,8937,8938],{"xmlns":890},[892,8939,8940,8954],{},[895,8941,8942,8944,8946,8952],{},[898,8943,3249],{},[1701,8945,1799],{"stretchy":1798},[3243,8947,8948,8950],{},[898,8949,1680],{},[1701,8951,8424],{},[1701,8953,1805],{"stretchy":1798},[902,8955,8452],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,8958,8960],{"className":8959},[886],[888,8961,8962],{"xmlns":890},[892,8963,8964,8968],{},[895,8965,8966],{},[898,8967,1802],{},[902,8969,1802],{"encoding":904},", jestliže se cena ",[883,8972,8974],{"className":8973},[886],[888,8975,8976],{"xmlns":890},[892,8977,8978,8986],{},[895,8979,8980],{},[3243,8981,8982,8984],{},[898,8983,1680],{},[1701,8985,8424],{},[902,8987,8474],{"encoding":904}," změní o 1 %. ",[883,8990,8992],{"className":8991},[886],[888,8993,8994],{"xmlns":890},[892,8995,8996,9005],{},[895,8997,8998,9000,9003],{},[1701,8999,1799],{"stretchy":1798},[1850,9001,9002],{},"4.6",[1701,9004,1805],{"stretchy":1798},[902,9006,9007],{"encoding":904},"(4.6)",[724,9009,9010,9013],{},[38,9011,9012],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,9015,9017],{"id":9016},"příklad-41","Příklad 4.1",[724,9019,9020,9021,9055,9056,1343,9081,2246],{},"Poptávka ",[883,9022,9024],{"className":9023},[886],[888,9025,9026],{"xmlns":890},[892,9027,9028,9052],{},[895,9029,9030,9032,9034,9036,9038,9040,9042,9044,9046,9048,9050],{},[898,9031,1680],{},[1701,9033,1792],{},[898,9035,1795],{},[1701,9037,1799],{"stretchy":1798},[898,9039,1802],{},[1701,9041,1805],{"stretchy":1798},[1701,9043,1792],{},[1850,9045,7206],{},[1701,9047,2317],{},[1850,9049,3938],{},[898,9051,1802],{},[902,9053,9054],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,9057,9059],{"className":9058},[886],[888,9060,9061],{"xmlns":890},[892,9062,9063,9078],{},[895,9064,9065,9067,9069,9072,9074,9076],{},[898,9066,1802],{},[1701,9068,1792],{},[1850,9070,9071],{},"25",[1701,9073,2317],{},[1850,9075,3684],{},[898,9077,1680],{},[902,9079,9080],{"encoding":904},"Q = 25 - 0{,}5P",[883,9082,9084],{"className":9083},[886],[888,9085,9086],{"xmlns":890},[892,9087,9088,9112],{},[895,9089,9090,9106,9108,9110],{},[2363,9091,9092],{"scriptlevel":1852,"displaystyle":2011},[3726,9093,9094,9100],{},[895,9095,9096,9098],{},[898,9097,2312],{"mathvariant":2334},[898,9099,1802],{},[895,9101,9102,9104],{},[898,9103,2312],{"mathvariant":2334},[898,9105,1680],{},[1701,9107,1792],{},[1701,9109,2317],{},[1850,9111,3684],{},[902,9113,9114],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,9116,9117],{},[883,9118,9120],{"className":9119},[886],[888,9121,9122],{"xmlns":890},[892,9123,9124,9178],{},[895,9125,9126,9128,9130,9132,9146,9148,9150,9152,9154,9156,9158,9176],{},[898,9127,3249],{},[1701,9129,1792],{},[1701,9131,2317],{},[3726,9133,9134,9136],{},[898,9135,1680],{},[895,9137,9138,9140,9142,9144],{},[1850,9139,9071],{},[1701,9141,2317],{},[1850,9143,3684],{},[898,9145,1680],{},[1701,9147,3408],{},[1701,9149,1799],{"stretchy":1798},[1701,9151,2317],{},[1850,9153,3684],{},[1701,9155,1805],{"stretchy":1798},[1701,9157,1792],{},[3726,9159,9160,9166],{},[895,9161,9162,9164],{},[1850,9163,3684],{},[898,9165,1680],{},[895,9167,9168,9170,9172,9174],{},[1850,9169,9071],{},[1701,9171,2317],{},[1850,9173,3684],{},[898,9175,1680],{},[898,9177,1715],{"mathvariant":2334},[902,9179,9180],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,9182,9183,9184,1343,9208,1343,9238,1343,9262,9286,9287,9310,9311,3856,9329,2506],{},"Potom ",[883,9185,9187],{"className":9186},[886],[888,9188,9189],{"xmlns":890},[892,9190,9191,9205],{},[895,9192,9193,9195,9197,9199,9201,9203],{},[898,9194,3249],{},[1701,9196,1799],{"stretchy":1798},[1850,9198,1852],{},[1701,9200,1805],{"stretchy":1798},[1701,9202,1792],{},[1850,9204,1852],{},[902,9206,9207],{"encoding":904},"E(0)=0",[883,9209,9211],{"className":9210},[886],[888,9212,9213],{"xmlns":890},[892,9214,9215,9235],{},[895,9216,9217,9219,9221,9223,9225,9227],{},[898,9218,3249],{},[1701,9220,1799],{"stretchy":1798},[1850,9222,3703],{},[1701,9224,1805],{"stretchy":1798},[1701,9226,1792],{},[2363,9228,9229],{"scriptlevel":1852,"displaystyle":1798},[3726,9230,9231,9233],{},[1850,9232,4062],{},[1850,9234,6460],{},[902,9236,9237],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,9239,9241],{"className":9240},[886],[888,9242,9243],{"xmlns":890},[892,9244,9245,9259],{},[895,9246,9247,9249,9251,9253,9255,9257],{},[898,9248,3249],{},[1701,9250,1799],{"stretchy":1798},[1850,9252,9071],{},[1701,9254,1805],{"stretchy":1798},[1701,9256,1792],{},[1850,9258,4062],{},[902,9260,9261],{"encoding":904},"E(25)=1",[883,9263,9265],{"className":9264},[886],[888,9266,9267],{"xmlns":890},[892,9268,9269,9283],{},[895,9270,9271,9273,9275,9277,9279,9281],{},[898,9272,3249],{},[1701,9274,1799],{"stretchy":1798},[1850,9276,3665],{},[1701,9278,1805],{"stretchy":1798},[1701,9280,1792],{},[1850,9282,6460],{},[902,9284,9285],{"encoding":904},"E(40)=4",". Např. ",[883,9288,9290],{"className":9289},[886],[888,9291,9292],{"xmlns":890},[892,9293,9294,9308],{},[895,9295,9296,9298,9300,9302,9304,9306],{},[898,9297,3249],{},[1701,9299,1799],{"stretchy":1798},[1850,9301,3665],{},[1701,9303,1805],{"stretchy":1798},[1701,9305,1792],{},[1850,9307,6460],{},[902,9309,9285],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,9312,9314],{"className":9313},[886],[888,9315,9316],{"xmlns":890},[892,9317,9318,9326],{},[895,9319,9320,9322,9324],{},[898,9321,1802],{},[1701,9323,1792],{},[1850,9325,4225],{},[902,9327,9328],{"encoding":904},"Q=5",[883,9330,9332],{"className":9331},[886],[888,9333,9334],{"xmlns":890},[892,9335,9336,9345],{},[895,9337,9338,9340,9342],{},[898,9339,1802],{},[1701,9341,1792],{},[1850,9343,9344],{},"4,8",[902,9346,9347],{"encoding":904},"Q=4{,}8",[198,9349,9351],{"id":9350},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,9353,9354,9410],{},[123,9355,9356,9359,9360,9377,9378,1715],{},[38,9357,9358],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,9361,9363],{"className":9362},[886],[888,9364,9365],{"xmlns":890},[892,9366,9367,9375],{},[895,9368,9369],{},[3243,9370,9371,9373],{},[898,9372,3249],{},[898,9374,1983],{},[902,9376,8328],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,9379,9381],{"className":9380},[886],[888,9382,9383],{"xmlns":890},[892,9384,9385,9407],{},[895,9386,9387,9390,9392,9394,9396,9398,9400,9402,9404],{},[1701,9388,9389],{"stretchy":1798},"⟨",[898,9391,1680],{},[1701,9393,2012],{"separator":2011},[1939,9395,1941],{},[898,9397,1680],{},[1701,9399,1703],{},[898,9401,4708],{"mathvariant":2334},[898,9403,1680],{},[1701,9405,9406],{"stretchy":1798},"⟩",[902,9408,9409],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,9411,9412,9415,9416,9429],{},[38,9413,9414],{},"Bodová"," (okamžitá) elasticita: ",[883,9417,9419],{"className":9418},[886],[888,9420,9421],{"xmlns":890},[892,9422,9423,9427],{},[895,9424,9425],{},[898,9426,3249],{},[902,9428,3249],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,9431,9433,9434,9447,9448],{"id":9432},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,9435,9437],{"className":9436},[886],[888,9438,9439],{"xmlns":890},[892,9440,9441,9445],{},[895,9442,9443],{},[898,9444,1680],{},[902,9446,1680],{"encoding":904}," jako funkce ",[883,9449,9451],{"className":9450},[886],[888,9452,9453],{"xmlns":890},[892,9454,9455,9459],{},[895,9456,9457],{},[898,9458,1802],{},[902,9460,1802],{"encoding":904},[724,9462,9463,9464,9487],{},"Pokud je poptávka zadaná ve tvaru ",[883,9465,9467],{"className":9466},[886],[888,9468,9469],{"xmlns":890},[892,9470,9471,9485],{},[895,9472,9473,9475,9477,9479,9481,9483],{},[898,9474,1680],{},[1701,9476,1792],{},[898,9478,1795],{},[1701,9480,1799],{"stretchy":1798},[898,9482,1802],{},[1701,9484,1805],{"stretchy":1798},[902,9486,1808],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,9489,9490],{},[883,9491,9493],{"className":9492,"title":8272,"style":8273},[8271],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,9495,9496,4088,9499,9525],{},[38,9497,9498],{},"Příklad 4.3.",[883,9500,9502],{"className":9501},[886],[888,9503,9504],{"xmlns":890},[892,9505,9506,9522],{},[895,9507,9508,9510,9512,9514,9516],{},[898,9509,1680],{},[1701,9511,1792],{},[1850,9513,5158],{},[1701,9515,2317],{},[3243,9517,9518,9520],{},[898,9519,1802],{},[1850,9521,3938],{},[902,9523,9524],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,9527,9528],{},[883,9529,9531],{"className":9530},[886],[888,9532,9533],{"xmlns":890},[892,9534,9535,9601],{},[895,9536,9537,9539,9541,9543,9559,9561,9573,9575,9599],{},[898,9538,3249],{},[1701,9540,1792],{},[1701,9542,2317],{},[3726,9544,9545,9557],{},[895,9546,9547,9549,9551],{},[1850,9548,5158],{},[1701,9550,2317],{},[3243,9552,9553,9555],{},[898,9554,1802],{},[1850,9556,3938],{},[898,9558,1802],{},[1701,9560,3408],{},[3726,9562,9563,9565],{},[1850,9564,4062],{},[895,9566,9567,9569,9571],{},[1701,9568,2317],{},[1850,9570,3938],{},[898,9572,1802],{},[1701,9574,1792],{},[3726,9576,9577,9589],{},[895,9578,9579,9581,9583],{},[1850,9580,5158],{},[1701,9582,2317],{},[3243,9584,9585,9587],{},[898,9586,1802],{},[1850,9588,3938],{},[895,9590,9591,9593],{},[1850,9592,3938],{},[3243,9594,9595,9597],{},[898,9596,1802],{},[1850,9598,3938],{},[898,9600,1715],{"mathvariant":2334},[902,9602,9603],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,9605,9606,9607,9634,9635,4185,9654,1715],{},"Z rovnice ",[883,9608,9610],{"className":9609},[886],[888,9611,9612],{"xmlns":890},[892,9613,9614,9631],{},[895,9615,9616,9618,9620,9626,9628],{},[1850,9617,5158],{},[1701,9619,2317],{},[3243,9621,9622,9624],{},[898,9623,1802],{},[1850,9625,3938],{},[1701,9627,1792],{},[1850,9629,9630],{},"36",[902,9632,9633],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,9636,9638],{"className":9637},[886],[888,9639,9640],{"xmlns":890},[892,9641,9642,9651],{},[895,9643,9644,9646,9648],{},[898,9645,1802],{},[1701,9647,1792],{},[1850,9649,9650],{},"8",[902,9652,9653],{"encoding":904},"Q = 8",[883,9655,9657],{"className":9656},[886],[888,9658,9659],{"xmlns":890},[892,9660,9661,9687],{},[895,9662,9663,9665,9667,9669,9671,9673,9682,9684],{},[898,9664,3249],{},[1701,9666,1799],{"stretchy":1798},[1850,9668,9650],{},[1701,9670,1805],{"stretchy":1798},[1701,9672,1792],{},[2363,9674,9675],{"scriptlevel":1852,"displaystyle":1798},[3726,9676,9677,9679],{},[1850,9678,9630],{},[1850,9680,9681],{},"128",[1701,9683,1792],{},[1850,9685,9686],{},"0,281",[902,9688,9689],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,9691,9693],{"id":9692},"přibližné-změny","Přibližné změny",[724,9695,9696,9697,9733,9734,9756],{},"Diferenciál ",[883,9698,9700],{"className":9699},[886],[888,9701,9702],{"xmlns":890},[892,9703,9704,9730],{},[895,9705,9706,9708,9710,9712,9718,9720,9722,9724,9726,9728],{},[898,9707,2312],{"mathvariant":2334},[898,9709,1802],{},[1701,9711,1792],{},[3243,9713,9714,9716],{},[898,9715,1802],{},[1701,9717,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,9719,1799],{"stretchy":1798},[898,9721,1680],{},[1701,9723,1805],{"stretchy":1798},[1939,9725,1941],{},[898,9727,2312],{"mathvariant":2334},[898,9729,1680],{},[902,9731,9732],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[883,9735,9737],{"className":9736},[886],[888,9738,9739],{"xmlns":890},[892,9740,9741,9753],{},[895,9742,9743,9745,9747,9749,9751],{},[898,9744,2312],{"mathvariant":2334},[898,9746,1680],{},[1701,9748,1792],{},[898,9750,4708],{"mathvariant":2334},[898,9752,1680],{},[902,9754,9755],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,9758,9759],{},[883,9760,9762],{"className":9761,"title":8272,"style":8273},[8271],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,9764,9765],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,9767,9768],{},[883,9769,9771],{"className":9770,"title":8272,"style":8273},[8271],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,9773,9774,4088,9777,9812,9813,9832,9833,9867,9868,9885],{},[38,9775,9776],{},"Příklad 4.5.",[883,9778,9780],{"className":9779},[886],[888,9781,9782],{"xmlns":890},[892,9783,9784,9809],{},[895,9785,9786,9788,9790,9792,9798,9800,9802,9804,9806],{},[898,9787,1680],{},[1701,9789,1792],{},[1701,9791,2317],{},[3243,9793,9794,9796],{},[898,9795,1802],{},[1850,9797,3938],{},[1701,9799,2317],{},[1850,9801,6460],{},[898,9803,1802],{},[1701,9805,1703],{},[1850,9807,9808],{},"96",[902,9810,9811],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,9814,9816],{"className":9815},[886],[888,9817,9818],{"xmlns":890},[892,9819,9820,9829],{},[895,9821,9822,9824,9826],{},[898,9823,1680],{},[1701,9825,1792],{},[1850,9827,9828],{},"51",[902,9830,9831],{"encoding":904},"P=51",". Z rovnice ",[883,9834,9836],{"className":9835},[886],[888,9837,9838],{"xmlns":890},[892,9839,9840,9864],{},[895,9841,9842,9844,9846,9848,9854,9856,9858,9860,9862],{},[1850,9843,9828],{},[1701,9845,1792],{},[1701,9847,2317],{},[3243,9849,9850,9852],{},[898,9851,1802],{},[1850,9853,3938],{},[1701,9855,2317],{},[1850,9857,6460],{},[898,9859,1802],{},[1701,9861,1703],{},[1850,9863,9808],{},[902,9865,9866],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,9869,9871],{"className":9870},[886],[888,9872,9873],{"xmlns":890},[892,9874,9875,9883],{},[895,9876,9877,9879,9881],{},[898,9878,1802],{},[1701,9880,1792],{},[1850,9882,4225],{},[902,9884,9328],{"encoding":904},". Elasticita:",[724,9887,9888],{},[883,9889,9891],{"className":9890},[886],[888,9892,9893],{"xmlns":890},[892,9894,9895,9967],{},[895,9896,9897,9899,9901,9939,9941,9945,9947,9949,9951,9953,9955,9962,9964],{},[898,9898,3249],{},[1701,9900,1792],{},[3726,9902,9903,9923],{},[895,9904,9905,9907,9913,9915,9917,9919,9921],{},[1701,9906,2317],{},[3243,9908,9909,9911],{},[898,9910,1802],{},[1850,9912,3938],{},[1701,9914,2317],{},[1850,9916,6460],{},[898,9918,1802],{},[1701,9920,1703],{},[1850,9922,9808],{},[895,9924,9925,9927,9929,9931,9933,9935,9937],{},[898,9926,1802],{},[1701,9928,1799],{"stretchy":1798},[1850,9930,3938],{},[898,9932,1802],{},[1701,9934,1703],{},[1850,9936,6460],{},[1701,9938,1805],{"stretchy":1798},[1701,9940,2012],{"separator":2011},[9942,9943],"mspace",{"width":9944},"2em",[898,9946,3249],{},[1701,9948,1799],{"stretchy":1798},[1850,9950,4225],{},[1701,9952,1805],{"stretchy":1798},[1701,9954,1792],{},[3726,9956,9957,9959],{},[1850,9958,9828],{},[1850,9960,9961],{},"70",[1701,9963,3782],{},[1850,9965,9966],{},"0,728.",[902,9968,9969],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,9971,9972,9973,1715],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,9974,9976],{"className":9975},[886],[888,9977,9978],{"xmlns":890},[892,9979,9980,10011],{},[895,9981,9982,9984,9986,9989,9991,9993,9996,9998,10000,10002,10004,10007,10009],{},[898,9983,4708],{"mathvariant":2334},[898,9985,1802],{},[898,9987,9988],{"mathvariant":2334},"%",[1701,9990,4067],{},[1701,9992,2317],{},[1850,9994,9995],{},"0,728",[1701,9997,3408],{},[1850,9999,3938],{},[1701,10001,1792],{},[1701,10003,2317],{},[1850,10005,10006],{},"1,456",[1939,10008,1941],{},[898,10010,9988],{"mathvariant":2334},[902,10012,10013],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,10015,10017],{"id":10016},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,10019,10020,10021,10044,10045,2246],{},"V závislosti na hodnotě ",[883,10022,10024],{"className":10023},[886],[888,10025,10026],{"xmlns":890},[892,10027,10028,10042],{},[895,10029,10030,10032,10034,10040],{},[898,10031,3249],{},[1701,10033,1799],{"stretchy":1798},[3243,10035,10036,10038],{},[898,10037,1680],{},[1701,10039,8424],{},[1701,10041,1805],{"stretchy":1798},[902,10043,8452],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,10046,10048],{"className":10047},[886],[888,10049,10050],{"xmlns":890},[892,10051,10052,10061],{},[895,10053,10054,10056,10059],{},[1701,10055,1799],{"stretchy":1798},[1850,10057,10058],{},"4.7",[1701,10060,1805],{"stretchy":1798},[902,10062,10063],{"encoding":904},"(4.7)",[724,10065,10066],{},[2139,10067],{"alt":10068,"className":10069,"src":10070},"imek-typy-elasticity-5panelu",[210,2143],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,10072,10073,10112],{},[19,10074,10075],{},[22,10076,10077,10103,10106,10109],{},[25,10078,10079,10080],{},"Hodnota ",[883,10081,10083],{"className":10082},[886],[888,10084,10085],{"xmlns":890},[892,10086,10087,10101],{},[895,10088,10089,10091,10093,10099],{},[898,10090,3249],{},[1701,10092,1799],{"stretchy":1798},[3243,10094,10095,10097],{},[898,10096,1680],{},[1701,10098,8424],{},[1701,10100,1805],{"stretchy":1798},[902,10102,8452],{"encoding":904},[25,10104,10105],{},"Typ poptávky",[25,10107,10108],{},"Termín",[25,10110,10111],{},"Význam",[30,10113,10114,10147,10209,10284,10341],{},[22,10115,10116,10136,10141,10144],{},[35,10117,10118],{},[883,10119,10121],{"className":10120},[886],[888,10122,10123],{"xmlns":890},[892,10124,10125,10133],{},[895,10126,10127,10129,10131],{},[898,10128,3249],{},[1701,10130,1792],{},[1850,10132,1852],{},[902,10134,10135],{"encoding":904},"E = 0",[35,10137,10138],{},[38,10139,10140],{},"dokonale neelastická",[35,10142,10143],{},"perfectly inelastic",[35,10145,10146],{},"množství se nemění bez ohledu na cenu",[22,10148,10149,10173,10177,10180],{},[35,10150,10151],{},[883,10152,10154],{"className":10153},[886],[888,10155,10156],{"xmlns":890},[892,10157,10158,10170],{},[895,10159,10160,10162,10164,10166,10168],{},[1850,10161,1852],{},[1701,10163,7530],{},[898,10165,3249],{},[1701,10167,7530],{},[1850,10169,4062],{},[902,10171,10172],{"encoding":904},"0 \u003C E \u003C 1",[35,10174,10175],{},[38,10176,8151],{},[35,10178,10179],{},"inelastic",[35,10181,10182,10195,10196],{},[883,10183,10185],{"className":10184},[886],[888,10186,10187],{"xmlns":890},[892,10188,10189,10193],{},[895,10190,10191],{},[898,10192,1802],{},[902,10194,1802],{"encoding":904}," se mění pomaleji než ",[883,10197,10199],{"className":10198},[886],[888,10200,10201],{"xmlns":890},[892,10202,10203,10207],{},[895,10204,10205],{},[898,10206,1680],{},[902,10208,1680],{"encoding":904},[22,10210,10211,10230,10235,10238],{},[35,10212,10213],{},[883,10214,10216],{"className":10215},[886],[888,10217,10218],{"xmlns":890},[892,10219,10220,10228],{},[895,10221,10222,10224,10226],{},[898,10223,3249],{},[1701,10225,1792],{},[1850,10227,4062],{},[902,10229,8614],{"encoding":904},[35,10231,10232],{},[38,10233,10234],{},"jednotkově elastická",[35,10236,10237],{},"unit elastic",[35,10239,10240,10253,10254,10267,10268,10283],{},[883,10241,10243],{"className":10242},[886],[888,10244,10245],{"xmlns":890},[892,10246,10247,10251],{},[895,10248,10249],{},[898,10250,1802],{},[902,10252,1802],{"encoding":904}," i ",[883,10255,10257],{"className":10256},[886],[888,10258,10259],{"xmlns":890},[892,10260,10261,10265],{},[895,10262,10263],{},[898,10264,1680],{},[902,10266,1680],{"encoding":904}," se mění stejně rychle; ",[883,10269,10271],{"className":10270},[886],[888,10272,10273],{"xmlns":890},[892,10274,10275,10281],{},[895,10276,10277,10279],{},[898,10278,5877],{},[898,10280,8068],{},[902,10282,8168],{"encoding":904}," má maximum",[22,10285,10286,10305,10309,10312],{},[35,10287,10288],{},[883,10289,10291],{"className":10290},[886],[888,10292,10293],{"xmlns":890},[892,10294,10295,10303],{},[895,10296,10297,10299,10301],{},[898,10298,3249],{},[1701,10300,7491],{},[1850,10302,4062],{},[902,10304,8578],{"encoding":904},[35,10306,10307],{},[38,10308,8147],{},[35,10310,10311],{},"elastic",[35,10313,10314,10327,10328],{},[883,10315,10317],{"className":10316},[886],[888,10318,10319],{"xmlns":890},[892,10320,10321,10325],{},[895,10322,10323],{},[898,10324,1802],{},[902,10326,1802],{"encoding":904}," se mění rychleji než ",[883,10329,10331],{"className":10330},[886],[888,10332,10333],{"xmlns":890},[892,10334,10335,10339],{},[895,10336,10337],{},[898,10338,1680],{},[902,10340,1680],{"encoding":904},[22,10342,10343,10364,10369,10372],{},[35,10344,10345],{},[883,10346,10348],{"className":10347},[886],[888,10349,10350],{"xmlns":890},[892,10351,10352,10361],{},[895,10353,10354,10356,10358],{},[898,10355,3249],{},[1701,10357,4108],{},[898,10359,10360],{"mathvariant":2334},"∞",[902,10362,10363],{"encoding":904},"E \\to \\infty",[35,10365,10366],{},[38,10367,10368],{},"dokonale elastická",[35,10370,10371],{},"perfectly elastic",[35,10373,10374,10375],{},"sebemenší změna ceny úplně mění ",[883,10376,10378],{"className":10377},[886],[888,10379,10380],{"xmlns":890},[892,10381,10382,10386],{},[895,10383,10384],{},[898,10385,1802],{},[902,10387,1802],{"encoding":904},[724,10389,10390],{},[38,10391,10392],{},"Pravidlo růstu elasticity s cenou:",[1635,10394,10395],{},[724,10396,10397,10398],{},"S rostoucí cenou elasticita poptávky roste. ",[883,10399,10401],{"className":10400},[886],[888,10402,10403],{"xmlns":890},[892,10404,10405,10414],{},[895,10406,10407,10409,10412],{},[1701,10408,1799],{"stretchy":1798},[1850,10410,10411],{},"4.8",[1701,10413,1805],{"stretchy":1798},[902,10415,10416],{"encoding":904},"(4.8)",[724,10418,10419,10420,10423,10424,10427,10428,10445],{},"Z toho plyne, že při ",[614,10421,10422],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,10425,10426],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,10429,10431],{"className":10430},[886],[888,10432,10433],{"xmlns":890},[892,10434,10435,10443],{},[895,10436,10437],{},[3243,10438,10439,10441],{},[898,10440,1680],{},[1701,10442,8424],{},[902,10444,8474],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1635,10447,10448,10453],{},[724,10449,10450,10452],{},[883,10451,3140],{}," Postup: jak klasifikovat poptávku",[152,10454,10455,10482,10485],{},[123,10456,10457,10458,10481],{},"Spočítejte ",[883,10459,10461],{"className":10460},[886],[888,10462,10463],{"xmlns":890},[892,10464,10465,10479],{},[895,10466,10467,10469,10471,10477],{},[898,10468,3249],{},[1701,10470,1799],{"stretchy":1798},[3243,10472,10473,10475],{},[898,10474,1680],{},[1701,10476,8424],{},[1701,10478,1805],{"stretchy":1798},[902,10480,8452],{"encoding":904}," dle (4.5).",[123,10483,10484],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,10486,10487,10488,10512],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,10489,10491],{"className":10490},[886],[888,10492,10493],{"xmlns":890},[892,10494,10495,10509],{},[895,10496,10497,10499,10501,10503,10505,10507],{},[898,10498,3249],{},[1701,10500,1799],{"stretchy":1798},[898,10502,1680],{},[1701,10504,1805],{"stretchy":1798},[1701,10506,1792],{},[1850,10508,4062],{},[902,10510,10511],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,10514,10515,10518,10519,10536,10537,10555,10556,10583,10584,1715],{},[38,10516,10517],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,10520,10522],{"className":10521},[886],[888,10523,10524],{"xmlns":890},[892,10525,10526,10534],{},[895,10527,10528,10530,10532],{},[898,10529,3249],{},[1701,10531,1792],{},[1850,10533,4062],{},[902,10535,8614],{"encoding":904}," pro ",[883,10538,10540],{"className":10539},[886],[888,10541,10542],{"xmlns":890},[892,10543,10544,10552],{},[895,10545,10546,10548,10550],{},[898,10547,1680],{},[1701,10549,1792],{},[1850,10551,9071],{},[902,10553,10554],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,10557,10559],{"className":10558},[886],[888,10560,10561],{"xmlns":890},[892,10562,10563,10580],{},[895,10564,10565,10567,10570,10572,10574,10576,10578],{},[898,10566,1680],{},[1701,10568,10569],{},"∈",[1701,10571,9389],{"stretchy":1798},[1850,10573,1852],{},[1701,10575,2012],{"separator":2011},[1850,10577,9071],{},[1701,10579,1805],{"stretchy":1798},[902,10581,10582],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,10585,10587],{"className":10586},[886],[888,10588,10589],{"xmlns":890},[892,10590,10591,10607],{},[895,10592,10593,10595,10597,10599,10601,10603,10605],{},[898,10594,1680],{},[1701,10596,10569],{},[1701,10598,1799],{"stretchy":1798},[1850,10600,9071],{},[1701,10602,2012],{"separator":2011},[1850,10604,7206],{},[1701,10606,9406],{"stretchy":1798},[902,10608,10609],{"encoding":904},"P \\in (25, 50\\rangle",[115,10611,10613],{"id":10612},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,10615,10616],{},[2139,10617],{"alt":10618,"className":10619,"src":10620},"imek-elasticita-tr",[210,2143],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,10622,10623],{},[2139,10624],{"alt":10625,"className":10626,"src":10627},"imek-elasticita-podel-linearni-poptavky",[210,2143],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,10629,10630,10631,10681,10682,10698],{},"Pro celkový příjem platí ",[883,10632,10634],{"className":10633},[886],[888,10635,10636],{"xmlns":890},[892,10637,10638,10678],{},[895,10639,10640,10642,10644,10646,10648,10650,10652,10654,10656,10658,10660,10662,10664,10666,10668,10670,10672,10674,10676],{},[898,10641,5877],{},[898,10643,8068],{},[1701,10645,1792],{},[898,10647,5877],{},[898,10649,8068],{},[1701,10651,1799],{"stretchy":1798},[898,10653,1802],{},[1701,10655,1805],{"stretchy":1798},[1701,10657,1792],{},[898,10659,1680],{},[1701,10661,3408],{},[898,10663,1802],{},[1701,10665,1792],{},[898,10667,1802],{},[1701,10669,3408],{},[898,10671,1795],{},[1701,10673,1799],{"stretchy":1798},[898,10675,1802],{},[1701,10677,1805],{"stretchy":1798},[902,10679,10680],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,10683,10685],{"className":10684},[886],[888,10686,10687],{"xmlns":890},[892,10688,10689,10695],{},[895,10690,10691,10693],{},[898,10692,6909],{},[898,10694,8068],{},[902,10696,10697],{"encoding":904},"MR"," odvodíme:",[724,10700,10701],{},[883,10702,10704],{"className":10703},[886],[888,10705,10706],{"xmlns":890},[892,10707,10708,10816],{},[895,10709,10710,10712,10714,10716,10718,10724,10726,10728,10730,10732,10734,10736,10738,10740,10742,10744,10746,10752,10754,10756,10758,10760,10762,10764,10766,10780,10782,10784],{},[898,10711,6909],{},[898,10713,8068],{},[1701,10715,1792],{},[898,10717,5877],{},[3243,10719,10720,10722],{},[898,10721,8068],{},[1701,10723,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,10725,1799],{"stretchy":1798},[898,10727,1802],{},[1701,10729,1805],{"stretchy":1798},[1701,10731,1792],{},[898,10733,1795],{},[1701,10735,1799],{"stretchy":1798},[898,10737,1802],{},[1701,10739,1805],{"stretchy":1798},[1701,10741,1703],{},[898,10743,1802],{},[1939,10745,1941],{},[3243,10747,10748,10750],{},[898,10749,1795],{},[1701,10751,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,10753,1799],{"stretchy":1798},[898,10755,1802],{},[1701,10757,1805],{"stretchy":1798},[1701,10759,1792],{},[898,10761,1680],{},[1701,10763,1703],{},[898,10765,1802],{},[3726,10767,10768,10774],{},[895,10769,10770,10772],{},[898,10771,2312],{"mathvariant":2334},[898,10773,1680],{},[895,10775,10776,10778],{},[898,10777,2312],{"mathvariant":2334},[898,10779,1802],{},[1701,10781,1792],{},[898,10783,1680],{},[895,10785,10786,10788,10790,10792,10798,10800,10814],{},[1701,10787,1799],{"fence":2011},[1850,10789,4062],{},[1701,10791,1703],{},[3726,10793,10794,10796],{},[898,10795,1802],{},[898,10797,1680],{},[1701,10799,3408],{},[3726,10801,10802,10808],{},[895,10803,10804,10806],{},[898,10805,2312],{"mathvariant":2334},[898,10807,1680],{},[895,10809,10810,10812],{},[898,10811,2312],{"mathvariant":2334},[898,10813,1802],{},[1701,10815,1805],{"fence":2011},[902,10817,10818],{"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)",[724,10820,10821],{},[883,10822,10824],{"className":10823},[886],[888,10825,10826],{"xmlns":890},[892,10827,10828,10900],{},[895,10829,10830,10832,10834,10876,10878,10880],{},[1701,10831,1792],{},[898,10833,1680],{},[895,10835,10836,10838,10840,10842,10874],{},[1701,10837,1799],{"fence":2011},[1850,10839,4062],{},[1701,10841,1703],{},[3726,10843,10844,10846],{},[1850,10845,4062],{},[895,10847,10848,10856,10858],{},[2363,10849,10850],{"scriptlevel":1852,"displaystyle":1798},[3726,10851,10852,10854],{},[898,10853,1680],{},[898,10855,1802],{},[1701,10857,3408],{},[2363,10859,10860],{"scriptlevel":1852,"displaystyle":1798},[3726,10861,10862,10868],{},[895,10863,10864,10866],{},[898,10865,2312],{"mathvariant":2334},[898,10867,1802],{},[895,10869,10870,10872],{},[898,10871,2312],{"mathvariant":2334},[898,10873,1680],{},[1701,10875,1805],{"fence":2011},[1701,10877,1792],{},[898,10879,1680],{},[895,10881,10882,10884,10886,10888,10898],{},[1701,10883,1799],{"fence":2011},[1850,10885,4062],{},[1701,10887,1703],{},[3726,10889,10890,10892],{},[1850,10891,4062],{},[895,10893,10894,10896],{},[1701,10895,2317],{},[898,10897,3249],{},[1701,10899,1805],{"fence":2011},[902,10901,10902],{"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)",[724,10904,10905],{},"a tedy",[724,10907,10908],{},[883,10909,10911],{"className":10910,"title":8272,"style":8273},[8271],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1635,10913,10914,10983,11232],{},[724,10915,10916,10918,10919,10953,10954,10969,10970,2246],{},[883,10917,2063],{}," Intuice: vztah ",[883,10920,10922],{"className":10921},[886],[888,10923,10924],{"xmlns":890},[892,10925,10926,10950],{},[895,10927,10928,10930,10932,10934,10936,10938,10940,10942,10944,10946,10948],{},[898,10929,6909],{},[898,10931,8068],{},[1701,10933,1792],{},[898,10935,1680],{},[1701,10937,1799],{"stretchy":1798},[1850,10939,4062],{},[1701,10941,2317],{},[1850,10943,4062],{},[898,10945,8741],{"mathvariant":2334},[898,10947,3249],{},[1701,10949,1805],{"stretchy":1798},[902,10951,10952],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,10955,10957],{"className":10956},[886],[888,10958,10959],{"xmlns":890},[892,10960,10961,10967],{},[895,10962,10963,10965],{},[898,10964,6909],{},[898,10966,8068],{},[902,10968,10697],{"encoding":904}," jednoznačně určuje hodnota ",[883,10971,10973],{"className":10972},[886],[888,10974,10975],{"xmlns":890},[892,10976,10977,10981],{},[895,10978,10979],{},[898,10980,3249],{},[902,10982,3249],{"encoding":904},[120,10984,10985,11094,11163],{},[123,10986,10987,11004,11005,4088,11019,4088,11045,4088,11058,2979,11078,11093],{},[883,10988,10990],{"className":10989},[886],[888,10991,10992],{"xmlns":890},[892,10993,10994,11002],{},[895,10995,10996,10998,11000],{},[898,10997,3249],{},[1701,10999,7491],{},[1850,11001,4062],{},[902,11003,8578],{"encoding":904}," (elastická) ",[883,11006,11008],{"className":11007},[886],[888,11009,11010],{"xmlns":890},[892,11011,11012,11016],{},[895,11013,11014],{},[1701,11015,8061],{},[902,11017,11018],{"encoding":904},"\\Rightarrow",[883,11020,11022],{"className":11021},[886],[888,11023,11024],{"xmlns":890},[892,11025,11026,11042],{},[895,11027,11028,11030,11032,11034,11036,11038,11040],{},[1850,11029,4062],{},[1701,11031,2317],{},[1850,11033,4062],{},[898,11035,8741],{"mathvariant":2334},[898,11037,3249],{},[1701,11039,7491],{},[1850,11041,1852],{},[902,11043,11044],{"encoding":904},"1 - 1\u002FE > 0",[883,11046,11048],{"className":11047},[886],[888,11049,11050],{"xmlns":890},[892,11051,11052,11056],{},[895,11053,11054],{},[1701,11055,8061],{},[902,11057,11018],{"encoding":904},[883,11059,11061],{"className":11060},[886],[888,11062,11063],{"xmlns":890},[892,11064,11065,11075],{},[895,11066,11067,11069,11071,11073],{},[898,11068,6909],{},[898,11070,8068],{},[1701,11072,7491],{},[1850,11074,1852],{},[902,11076,11077],{"encoding":904},"MR > 0",[883,11079,11081],{"className":11080},[886],[888,11082,11083],{"xmlns":890},[892,11084,11085,11091],{},[895,11086,11087,11089],{},[898,11088,5877],{},[898,11090,8068],{},[902,11092,8168],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,11095,11096,11113,11114,4088,11127,2979,11147,11162],{},[883,11097,11099],{"className":11098},[886],[888,11100,11101],{"xmlns":890},[892,11102,11103,11111],{},[895,11104,11105,11107,11109],{},[898,11106,3249],{},[1701,11108,1792],{},[1850,11110,4062],{},[902,11112,8614],{"encoding":904}," (jednotková) ",[883,11115,11117],{"className":11116},[886],[888,11118,11119],{"xmlns":890},[892,11120,11121,11125],{},[895,11122,11123],{},[1701,11124,8061],{},[902,11126,11018],{"encoding":904},[883,11128,11130],{"className":11129},[886],[888,11131,11132],{"xmlns":890},[892,11133,11134,11144],{},[895,11135,11136,11138,11140,11142],{},[898,11137,6909],{},[898,11139,8068],{},[1701,11141,1792],{},[1850,11143,1852],{},[902,11145,11146],{"encoding":904},"MR = 0",[883,11148,11150],{"className":11149},[886],[888,11151,11152],{"xmlns":890},[892,11153,11154,11160],{},[895,11155,11156,11158],{},[898,11157,5877],{},[898,11159,8068],{},[902,11161,8168],{"encoding":904}," je extrém (maximum).",[123,11164,11165,11182,11183,4088,11196,2979,11216,11231],{},[883,11166,11168],{"className":11167},[886],[888,11169,11170],{"xmlns":890},[892,11171,11172,11180],{},[895,11173,11174,11176,11178],{},[898,11175,3249],{},[1701,11177,7530],{},[1850,11179,4062],{},[902,11181,8596],{"encoding":904}," (neelastická) ",[883,11184,11186],{"className":11185},[886],[888,11187,11188],{"xmlns":890},[892,11189,11190,11194],{},[895,11191,11192],{},[1701,11193,8061],{},[902,11195,11018],{"encoding":904},[883,11197,11199],{"className":11198},[886],[888,11200,11201],{"xmlns":890},[892,11202,11203,11213],{},[895,11204,11205,11207,11209,11211],{},[898,11206,6909],{},[898,11208,8068],{},[1701,11210,7530],{},[1850,11212,1852],{},[902,11214,11215],{"encoding":904},"MR \u003C 0",[883,11217,11219],{"className":11218},[886],[888,11220,11221],{"xmlns":890},[892,11222,11223,11229],{},[895,11224,11225,11227],{},[898,11226,5877],{},[898,11228,8068],{},[902,11230,8168],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,11233,11234,11235,1715],{},"Viz také ",[207,11236,6017],{"className":11237,"dataFsResolvedFilePath":827,"href":828},[210],[198,11239,11241],{"id":11240},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,11243,11244,11264,11265,11291,11292,11307,11308,11321,11322,11335,11336,11349,11350,11366,11367,4088,11382,11385,11386,11366,11402,1715],{},[38,11245,11246,11247,2506],{},"(a) Poptávka elastická (",[883,11248,11250],{"className":11249},[886],[888,11251,11252],{"xmlns":890},[892,11253,11254,11262],{},[895,11255,11256,11258,11260],{},[898,11257,3249],{},[1701,11259,7491],{},[1850,11261,4062],{},[902,11263,8578],{"encoding":904}," Z (4.12) plyne ",[883,11266,11268],{"className":11267},[886],[888,11269,11270],{"xmlns":890},[892,11271,11272,11288],{},[895,11273,11274,11276,11278,11280,11282,11284,11286],{},[898,11275,6909],{},[898,11277,8068],{},[1701,11279,1799],{"stretchy":1798},[898,11281,1802],{},[1701,11283,1805],{"stretchy":1798},[1701,11285,7491],{},[1850,11287,1852],{},[902,11289,11290],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,11293,11295],{"className":11294},[886],[888,11296,11297],{"xmlns":890},[892,11298,11299,11305],{},[895,11300,11301,11303],{},[898,11302,5877],{},[898,11304,8068],{},[902,11306,8168],{"encoding":904}," je rostoucí funkcí ",[883,11309,11311],{"className":11310},[886],[888,11312,11313],{"xmlns":890},[892,11314,11315,11319],{},[895,11316,11317],{},[898,11318,1802],{},[902,11320,1802],{"encoding":904},". Avšak růst ",[883,11323,11325],{"className":11324},[886],[888,11326,11327],{"xmlns":890},[892,11328,11329,11333],{},[895,11330,11331],{},[898,11332,1802],{},[902,11334,1802],{"encoding":904}," je odezvou na pokles ceny ",[883,11337,11339],{"className":11338},[886],[888,11340,11341],{"xmlns":890},[892,11342,11343,11347],{},[895,11344,11345],{},[898,11346,1680],{},[902,11348,1680],{"encoding":904},". Tudíž s ",[614,11351,11352,11353],{},"poklesem ceny ",[883,11354,11356],{"className":11355},[886],[888,11357,11358],{"xmlns":890},[892,11359,11360,11364],{},[895,11361,11362],{},[898,11363,1680],{},[902,11365,1680],{"encoding":904}," celkový příjem ",[883,11368,11370],{"className":11369},[886],[888,11371,11372],{"xmlns":890},[892,11373,11374,11380],{},[895,11375,11376,11378],{},[898,11377,5877],{},[898,11379,8068],{},[902,11381,8168],{"encoding":904},[614,11383,11384],{},"roste"," a s ",[614,11387,11388,11389],{},"růstem ceny ",[883,11390,11392],{"className":11391},[886],[888,11393,11394],{"xmlns":890},[892,11395,11396,11400],{},[895,11397,11398],{},[898,11399,1680],{},[902,11401,1680],{"encoding":904},[614,11403,11404],{},"klesá",[1635,11406,11407],{},[724,11408,11409,11412],{},[38,11410,11411],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,11414,11415,11264,11435,1343,11461,11476,11477,11490,11491,11504,11505,11518,11519,11366,11532,4088,11547,1715],{},[38,11416,11417,11418,2506],{},"(b) Poptávka neelastická (",[883,11419,11421],{"className":11420},[886],[888,11422,11423],{"xmlns":890},[892,11424,11425,11433],{},[895,11426,11427,11429,11431],{},[898,11428,3249],{},[1701,11430,7530],{},[1850,11432,4062],{},[902,11434,8596],{"encoding":904},[883,11436,11438],{"className":11437},[886],[888,11439,11440],{"xmlns":890},[892,11441,11442,11458],{},[895,11443,11444,11446,11448,11450,11452,11454,11456],{},[898,11445,6909],{},[898,11447,8068],{},[1701,11449,1799],{"stretchy":1798},[898,11451,1802],{},[1701,11453,1805],{"stretchy":1798},[1701,11455,7530],{},[1850,11457,1852],{},[902,11459,11460],{"encoding":904},"MR(Q) \u003C 0",[883,11462,11464],{"className":11463},[886],[888,11465,11466],{"xmlns":890},[892,11467,11468,11474],{},[895,11469,11470,11472],{},[898,11471,5877],{},[898,11473,8068],{},[902,11475,8168],{"encoding":904}," je klesající funkce ",[883,11478,11480],{"className":11479},[886],[888,11481,11482],{"xmlns":890},[892,11483,11484,11488],{},[895,11485,11486],{},[898,11487,1802],{},[902,11489,1802],{"encoding":904},", tj. s růstem ",[883,11492,11494],{"className":11493},[886],[888,11495,11496],{"xmlns":890},[892,11497,11498,11502],{},[895,11499,11500],{},[898,11501,1802],{},[902,11503,1802],{"encoding":904}," (s poklesem ceny ",[883,11506,11508],{"className":11507},[886],[888,11509,11510],{"xmlns":890},[892,11511,11512,11516],{},[895,11513,11514],{},[898,11515,1680],{},[902,11517,1680],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,11520,11522],{"className":11521},[886],[888,11523,11524],{"xmlns":890},[892,11525,11526,11530],{},[895,11527,11528],{},[898,11529,1680],{},[902,11531,1680],{"encoding":904},[883,11533,11535],{"className":11534},[886],[888,11536,11537],{"xmlns":890},[892,11538,11539,11545],{},[895,11540,11541,11543],{},[898,11542,5877],{},[898,11544,8068],{},[902,11546,8168],{"encoding":904},[614,11548,11384],{},[1635,11550,11551],{},[724,11552,11553,11556],{},[38,11554,11555],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,11558,11559,11264,11579,11598,11599,11614,11615,11685,11686,2633,11714,11747,11748,4185,11776,11791,11792,1715],{},[38,11560,11561,11562,2506],{},"(c) Jednotková elasticita (",[883,11563,11565],{"className":11564},[886],[888,11566,11567],{"xmlns":890},[892,11568,11569,11577],{},[895,11570,11571,11573,11575],{},[898,11572,3249],{},[1701,11574,1792],{},[1850,11576,4062],{},[902,11578,8614],{"encoding":904},[883,11580,11582],{"className":11581},[886],[888,11583,11584],{"xmlns":890},[892,11585,11586,11596],{},[895,11587,11588,11590,11592,11594],{},[898,11589,6909],{},[898,11591,8068],{},[1701,11593,1792],{},[1850,11595,1852],{},[902,11597,11146],{"encoding":904}," — nutná podmínka extrému ",[883,11600,11602],{"className":11601},[886],[888,11603,11604],{"xmlns":890},[892,11605,11606,11612],{},[895,11607,11608,11610],{},[898,11609,5877],{},[898,11611,8068],{},[902,11613,8168],{"encoding":904},". Dále ",[883,11616,11618],{"className":11617},[886],[888,11619,11620],{"xmlns":890},[892,11621,11622,11682],{},[895,11623,11624,11626,11636,11638,11640,11646,11648,11654,11656,11658,11660,11662,11664,11666,11676,11678,11680],{},[898,11625,5877],{},[3243,11627,11628,11630],{},[898,11629,8068],{},[895,11631,11632,11634],{},[1701,11633,4783],{"mathvariant":2334},[1701,11635,4783],{"mathvariant":2334},[1701,11637,1792],{},[898,11639,6909],{},[3243,11641,11642,11644],{},[898,11643,8068],{},[1701,11645,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,11647,1792],{},[3243,11649,11650,11652],{},[898,11651,1795],{},[1701,11653,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,11655,1799],{"stretchy":1798},[898,11657,1802],{},[1701,11659,1805],{"stretchy":1798},[1701,11661,1703],{},[898,11663,1802],{},[1939,11665,1941],{},[3243,11667,11668,11670],{},[898,11669,1795],{},[895,11671,11672,11674],{},[1701,11673,4783],{"mathvariant":2334},[1701,11675,4783],{"mathvariant":2334},[1701,11677,1799],{"stretchy":1798},[898,11679,1802],{},[1701,11681,1805],{"stretchy":1798},[902,11683,11684],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,11687,11689],{"className":11688},[886],[888,11690,11691],{"xmlns":890},[892,11692,11693,11711],{},[895,11694,11695,11701,11703,11705,11707,11709],{},[3243,11696,11697,11699],{},[898,11698,1795],{},[1701,11700,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,11702,1799],{"stretchy":1798},[898,11704,1802],{},[1701,11706,1805],{"stretchy":1798},[1701,11708,7530],{},[1850,11710,1852],{},[902,11712,11713],{"encoding":904},"D'(Q) \u003C 0",[883,11715,11717],{"className":11716},[886],[888,11718,11719],{"xmlns":890},[892,11720,11721,11744],{},[895,11722,11723,11733,11735,11737,11739,11742],{},[3243,11724,11725,11727],{},[898,11726,1795],{},[895,11728,11729,11731],{},[1701,11730,4783],{"mathvariant":2334},[1701,11732,4783],{"mathvariant":2334},[1701,11734,1799],{"stretchy":1798},[898,11736,1802],{},[1701,11738,1805],{"stretchy":1798},[1701,11740,11741],{},"≤",[1850,11743,1852],{},[902,11745,11746],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,11749,11751],{"className":11750},[886],[888,11752,11753],{"xmlns":890},[892,11754,11755,11773],{},[895,11756,11757,11759,11769,11771],{},[898,11758,5877],{},[3243,11760,11761,11763],{},[898,11762,8068],{},[895,11764,11765,11767],{},[1701,11766,4783],{"mathvariant":2334},[1701,11768,4783],{"mathvariant":2334},[1701,11770,7530],{},[1850,11772,1852],{},[902,11774,11775],{"encoding":904},"TR'' \u003C 0",[883,11777,11779],{"className":11778},[886],[888,11780,11781],{"xmlns":890},[892,11782,11783,11789],{},[895,11784,11785,11787],{},[898,11786,5877],{},[898,11788,8068],{},[902,11790,8168],{"encoding":904}," nabývá ",[38,11793,11794],{},"maxima",[1635,11796,11797],{},[724,11798,11799,11802],{},[38,11800,11801],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,11804,11805],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,11807,11808],{},[38,11809,11810],{},"Souhrnná tabulka Pravidel 1–3:",[16,11812,11813,11917],{},[19,11814,11815],{},[22,11816,11817,11820,11835,11852,11883,11914],{},[25,11818,11819],{},"Charakter poptávky",[25,11821,11822],{},[883,11823,11825],{"className":11824},[886],[888,11826,11827],{"xmlns":890},[892,11828,11829,11833],{},[895,11830,11831],{},[898,11832,3249],{},[902,11834,3249],{"encoding":904},[25,11836,11837],{},[883,11838,11840],{"className":11839},[886],[888,11841,11842],{"xmlns":890},[892,11843,11844,11850],{},[895,11845,11846,11848],{},[898,11847,6909],{},[898,11849,8068],{},[902,11851,10697],{"encoding":904},[25,11853,11854,11855,4088,11868],{},"Pokles ceny ",[883,11856,11858],{"className":11857},[886],[888,11859,11860],{"xmlns":890},[892,11861,11862,11866],{},[895,11863,11864],{},[1701,11865,8061],{},[902,11867,11018],{"encoding":904},[883,11869,11871],{"className":11870},[886],[888,11872,11873],{"xmlns":890},[892,11874,11875,11881],{},[895,11876,11877,11879],{},[898,11878,5877],{},[898,11880,8068],{},[902,11882,8168],{"encoding":904},[25,11884,11885,11886,4088,11899],{},"Růst ceny ",[883,11887,11889],{"className":11888},[886],[888,11890,11891],{"xmlns":890},[892,11892,11893,11897],{},[895,11894,11895],{},[1701,11896,8061],{},[902,11898,11018],{"encoding":904},[883,11900,11902],{"className":11901},[886],[888,11903,11904],{"xmlns":890},[892,11905,11906,11912],{},[895,11907,11908,11910],{},[898,11909,5877],{},[898,11911,8068],{},[902,11913,8168],{"encoding":904},[25,11915,11916],{},"Doporučení",[30,11918,11919,11968,12018],{},[22,11920,11921,11923,11941,11959,11961,11963],{},[35,11922,8147],{},[35,11924,11925],{},[883,11926,11928],{"className":11927},[886],[888,11929,11930],{"xmlns":890},[892,11931,11932,11938],{},[895,11933,11934,11936],{},[1701,11935,7491],{},[1850,11937,4062],{},[902,11939,11940],{"encoding":904},"> 1",[35,11942,11943],{},[883,11944,11946],{"className":11945},[886],[888,11947,11948],{"xmlns":890},[892,11949,11950,11956],{},[895,11951,11952,11954],{},[1701,11953,7491],{},[1850,11955,1852],{},[902,11957,11958],{"encoding":904},"> 0",[35,11960,11384],{},[35,11962,11404],{},[35,11964,11965],{},[38,11966,11967],{},"snížit cenu",[22,11969,11970,11973,11991,12009,12011,12013],{},[35,11971,11972],{},"jednotková",[35,11974,11975],{},[883,11976,11978],{"className":11977},[886],[888,11979,11980],{"xmlns":890},[892,11981,11982,11988],{},[895,11983,11984,11986],{},[1701,11985,1792],{},[1850,11987,4062],{},[902,11989,11990],{"encoding":904},"= 1",[35,11992,11993],{},[883,11994,11996],{"className":11995},[886],[888,11997,11998],{"xmlns":890},[892,11999,12000,12006],{},[895,12001,12002,12004],{},[1701,12003,1792],{},[1850,12005,1852],{},[902,12007,12008],{"encoding":904},"= 0",[35,12010,7800],{},[35,12012,7800],{},[35,12014,12015],{},[38,12016,12017],{},"držet cenu",[22,12019,12020,12022,12040,12058,12060,12062],{},[35,12021,8151],{},[35,12023,12024],{},[883,12025,12027],{"className":12026},[886],[888,12028,12029],{"xmlns":890},[892,12030,12031,12037],{},[895,12032,12033,12035],{},[1701,12034,7530],{},[1850,12036,4062],{},[902,12038,12039],{"encoding":904},"\u003C 1",[35,12041,12042],{},[883,12043,12045],{"className":12044},[886],[888,12046,12047],{"xmlns":890},[892,12048,12049,12055],{},[895,12050,12051,12053],{},[1701,12052,7530],{},[1850,12054,1852],{},[902,12056,12057],{"encoding":904},"\u003C 0",[35,12059,11404],{},[35,12061,11384],{},[35,12063,12064],{},[38,12065,12066],{},"zvýšit cenu",[198,12068,12070],{"id":12069},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,12072,12073,12074,12099,12100,12122,12123,12136,12137,12150,12151,12164,12165,4185,12192,12244],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,12075,12077],{"className":12076},[886],[888,12078,12079],{"xmlns":890},[892,12080,12081,12097],{},[895,12082,12083,12085,12087,12089,12091],{},[898,12084,1680],{},[1701,12086,1792],{},[1850,12088,5158],{},[1701,12090,2317],{},[3243,12092,12093,12095],{},[898,12094,1802],{},[1850,12096,3938],{},[902,12098,9524],{"encoding":904},". Reálné cenové rozpětí je ",[883,12101,12103],{"className":12102},[886],[888,12104,12105],{"xmlns":890},[892,12106,12107,12119],{},[895,12108,12109,12111,12113,12115,12117],{},[1701,12110,9389],{"stretchy":1798},[1850,12112,4062],{},[1701,12114,2012],{"separator":2011},[1850,12116,5158],{},[1701,12118,9406],{"stretchy":1798},[902,12120,12121],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,12124,12126],{"className":12125},[886],[888,12127,12128],{"xmlns":890},[892,12129,12130,12134],{},[895,12131,12132],{},[898,12133,1802],{},[902,12135,1802],{"encoding":904}," jako funkci ",[883,12138,12140],{"className":12139},[886],[888,12141,12142],{"xmlns":890},[892,12143,12144,12148],{},[895,12145,12146],{},[898,12147,1680],{},[902,12149,1680],{"encoding":904},"; pro nezáporné ",[883,12152,12154],{"className":12153},[886],[888,12155,12156],{"xmlns":890},[892,12157,12158,12162],{},[895,12159,12160],{},[898,12161,1802],{},[902,12163,1802],{"encoding":904}," je ",[883,12166,12168],{"className":12167},[886],[888,12169,12170],{"xmlns":890},[892,12171,12172,12189],{},[895,12173,12174,12176,12178],{},[898,12175,1802],{},[1701,12177,1792],{},[12179,12180,12181],"msqrt",{},[895,12182,12183,12185,12187],{},[1850,12184,5158],{},[1701,12186,2317],{},[898,12188,1680],{},[902,12190,12191],{"encoding":904},"Q = \\sqrt{100 - P}",[883,12193,12195],{"className":12194},[886],[888,12196,12197],{"xmlns":890},[892,12198,12199,12241],{},[895,12200,12201,12217,12219,12221],{},[2363,12202,12203],{"scriptlevel":1852,"displaystyle":2011},[3726,12204,12205,12211],{},[895,12206,12207,12209],{},[898,12208,2312],{"mathvariant":2334},[898,12210,1802],{},[895,12212,12213,12215],{},[898,12214,2312],{"mathvariant":2334},[898,12216,1680],{},[1701,12218,1792],{},[1701,12220,2317],{},[2363,12222,12223],{"scriptlevel":1852,"displaystyle":2011},[3726,12224,12225,12227],{},[1850,12226,4062],{},[895,12228,12229,12231],{},[1850,12230,3938],{},[12179,12232,12233],{},[895,12234,12235,12237,12239],{},[1850,12236,5158],{},[1701,12238,2317],{},[898,12240,1680],{},[902,12242,12243],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,12246,12247],{},[883,12248,12250],{"className":12249},[886],[888,12251,12252],{"xmlns":890},[892,12253,12254,12376],{},[895,12255,12256,12258,12260,12262,12264,12266,12268,12274,12276,12290,12292,12294,12308,12310,12336,12338,12356,12358,12374],{},[898,12257,3249],{},[1701,12259,1799],{"stretchy":1798},[898,12261,1680],{},[1701,12263,1805],{"stretchy":1798},[1701,12265,1792],{},[1701,12267,2317],{},[3726,12269,12270,12272],{},[898,12271,1680],{},[898,12273,1802],{},[1701,12275,3408],{},[3726,12277,12278,12284],{},[895,12279,12280,12282],{},[898,12281,2312],{"mathvariant":2334},[898,12283,1802],{},[895,12285,12286,12288],{},[898,12287,2312],{"mathvariant":2334},[898,12289,1680],{},[1701,12291,1792],{},[1701,12293,2317],{},[3726,12295,12296,12298],{},[898,12297,1680],{},[12179,12299,12300],{},[895,12301,12302,12304,12306],{},[1850,12303,5158],{},[1701,12305,2317],{},[898,12307,1680],{},[1701,12309,3408],{},[895,12311,12312,12314,12316,12334],{},[1701,12313,1799],{"fence":2011},[1701,12315,2317],{},[3726,12317,12318,12320],{},[1850,12319,4062],{},[895,12321,12322,12324],{},[1850,12323,3938],{},[12179,12325,12326],{},[895,12327,12328,12330,12332],{},[1850,12329,5158],{},[1701,12331,2317],{},[898,12333,1680],{},[1701,12335,1805],{"fence":2011},[1701,12337,1792],{},[3726,12339,12340,12342],{},[898,12341,1680],{},[895,12343,12344,12346,12348,12350,12352,12354],{},[1850,12345,3938],{},[1701,12347,1799],{"stretchy":1798},[1850,12349,5158],{},[1701,12351,2317],{},[898,12353,1680],{},[1701,12355,1805],{"stretchy":1798},[1701,12357,1792],{},[3726,12359,12360,12366],{},[895,12361,12362,12364],{},[1850,12363,3684],{},[898,12365,1680],{},[895,12367,12368,12370,12372],{},[1850,12369,5158],{},[1701,12371,2317],{},[898,12373,1680],{},[898,12375,1715],{"mathvariant":2334},[902,12377,12378],{"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}.",[724,12380,12381,12382,2246],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,12383,12385],{"className":12384},[886],[888,12386,12387],{"xmlns":890},[892,12388,12389,12413],{},[895,12390,12391,12409,12411],{},[2363,12392,12393],{"scriptlevel":1852,"displaystyle":2011},[3726,12394,12395,12401],{},[895,12396,12397,12399],{},[1850,12398,3684],{},[898,12400,1680],{},[895,12402,12403,12405,12407],{},[1850,12404,5158],{},[1701,12406,2317],{},[898,12408,1680],{},[1701,12410,1792],{},[1850,12412,4062],{},[902,12414,12415],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,12417,12418],{},[883,12419,12421],{"className":12420},[886],[888,12422,12423],{"xmlns":890},[892,12424,12425,12457],{},[895,12426,12427,12433,12435,12442,12444,12447,12455],{},[3243,12428,12429,12431],{},[898,12430,1680],{},[1701,12432,8424],{},[1701,12434,1792],{},[3726,12436,12437,12440],{},[1850,12438,12439],{},"200",[1850,12441,3646],{},[1701,12443,3782],{},[1850,12445,12446],{},"66,",[12448,12449,12450,12452],"mover",{"accent":2011},[1850,12451,6352],{},[1701,12453,12454],{"stretchy":2011},"‾",[898,12456,1715],{"mathvariant":2334},[902,12458,12459],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,12461,12462],{},"S využitím vlastnosti (4.8):",[120,12464,12465,12511,12553],{},[123,12466,12467,12468,12503,12504,12506,12507,12510],{},"Při cenách ",[883,12469,12471],{"className":12470},[886],[888,12472,12473],{"xmlns":890},[892,12474,12475,12500],{},[895,12476,12477,12479,12481,12483,12485,12488,12490,12492,12498],{},[898,12478,1680],{},[1701,12480,10569],{},[1701,12482,9389],{"stretchy":1798},[1850,12484,4062],{},[1701,12486,12487],{"separator":2011},";",[1939,12489,1941],{},[1850,12491,12446],{},[12448,12493,12494,12496],{"accent":2011},[1850,12495,6352],{},[1701,12497,12454],{"stretchy":2011},[1701,12499,1805],{"stretchy":1798},[902,12501,12502],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,12505,8151],{}," — dle ",[614,12508,12509],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,12512,12467,12513,12503,12547,12506,12549,12552],{},[883,12514,12516],{"className":12515},[886],[888,12517,12518],{"xmlns":890},[892,12519,12520,12544],{},[895,12521,12522,12524,12526,12528,12530,12536,12538,12540,12542],{},[898,12523,1680],{},[1701,12525,10569],{},[1701,12527,1799],{"stretchy":1798},[1850,12529,12446],{},[12448,12531,12532,12534],{"accent":2011},[1850,12533,6352],{},[1701,12535,12454],{"stretchy":2011},[1701,12537,12487],{"separator":2011},[1939,12539,1941],{},[1850,12541,5158],{},[1701,12543,9406],{"stretchy":1798},[902,12545,12546],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,12548,8147],{},[614,12550,12551],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,12554,12555,12556,12559,12560,12588,12589,12592],{},"Dle ",[614,12557,12558],{},"Pravidla 3"," je při ceně ",[883,12561,12563],{"className":12562},[886],[888,12564,12565],{"xmlns":890},[892,12566,12567,12585],{},[895,12568,12569,12575,12577,12579],{},[3243,12570,12571,12573],{},[898,12572,1680],{},[1701,12574,8424],{},[1701,12576,1792],{},[1850,12578,12446],{},[12448,12580,12581,12583],{"accent":2011},[1850,12582,6352],{},[1701,12584,12454],{"stretchy":2011},[902,12586,12587],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,12590,12591],{},"maxima celkového příjmu"," ve výši",[724,12594,12595],{},[883,12596,12598],{"className":12597},[886],[888,12599,12600],{"xmlns":890},[892,12601,12602,12680],{},[895,12603,12604,12606,12608,12610,12616,12618,12620,12626,12628,12642,12644,12650,12652,12660,12662,12675,12677],{},[898,12605,5877],{},[898,12607,8068],{},[1701,12609,1799],{"stretchy":1798},[3243,12611,12612,12614],{},[898,12613,1680],{},[1701,12615,8424],{},[1701,12617,1805],{"stretchy":1798},[1701,12619,1792],{},[3243,12621,12622,12624],{},[898,12623,1680],{},[1701,12625,8424],{},[1701,12627,3408],{},[12179,12629,12630],{},[895,12631,12632,12634,12636],{},[1850,12633,5158],{},[1701,12635,2317],{},[3243,12637,12638,12640],{},[898,12639,1680],{},[1701,12641,8424],{},[1701,12643,1792],{},[3726,12645,12646,12648],{},[1850,12647,12439],{},[1850,12649,3646],{},[1701,12651,3408],{},[12179,12653,12654],{},[3726,12655,12656,12658],{},[1850,12657,5158],{},[1850,12659,3646],{},[1701,12661,1792],{},[3726,12663,12664,12667],{},[1850,12665,12666],{},"2000",[895,12668,12669,12671],{},[1850,12670,3646],{},[12179,12672,12673],{},[1850,12674,3646],{},[1701,12676,3782],{},[1850,12678,12679],{},"384,9.",[902,12681,12682],{"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.",[724,12684,12685,12686,1715],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,12687,12689],{"className":12688},[886],[888,12690,12691],{"xmlns":890},[892,12692,12693,12699],{},[895,12694,12695,12697],{},[898,12696,5877],{},[898,12698,8068],{},[902,12700,8168],{"encoding":904},[115,12702,12704],{"id":12703},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,12706,12707,12708,12711],{},"Analogicky se definuje ",[38,12709,12710],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,12713,12714],{},[883,12715,12717],{"className":12716,"title":8272,"style":8273},[8271],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,12719,8380,12720,12744,12745,12777],{},[883,12721,12723],{"className":12722},[886],[888,12724,12725],{"xmlns":890},[892,12726,12727,12741],{},[895,12728,12729,12731,12733,12735,12737,12739],{},[898,12730,1802],{},[1701,12732,1792],{},[898,12734,1661],{},[1701,12736,1799],{"stretchy":1798},[898,12738,1680],{},[1701,12740,1805],{"stretchy":1798},[902,12742,12743],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,12746,12748],{"className":12747},[886],[888,12749,12750],{"xmlns":890},[892,12751,12752,12774],{},[895,12753,12754,12770,12772],{},[2363,12755,12756],{"scriptlevel":1852,"displaystyle":2011},[3726,12757,12758,12764],{},[895,12759,12760,12762],{},[898,12761,2312],{"mathvariant":2334},[898,12763,1802],{},[895,12765,12766,12768],{},[898,12767,2312],{"mathvariant":2334},[898,12769,1680],{},[1701,12771,7491],{},[1850,12773,1852],{},[902,12775,12776],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,12779,12780],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1635,12782,12783],{},[724,12784,12785,12786],{},"S rostoucí cenou elasticita nabídky roste. ",[883,12787,12789],{"className":12788},[886],[888,12790,12791],{"xmlns":890},[892,12792,12793,12802],{},[895,12794,12795,12797,12800],{},[1701,12796,1799],{"stretchy":1798},[1850,12798,12799],{},"4.14",[1701,12801,1805],{"stretchy":1798},[902,12803,12804],{"encoding":904},"(4.14)",[724,12806,12807],{},"Pro nominální změny platí",[724,12809,12810],{},[883,12811,12813],{"className":12812,"title":8272,"style":8273},[8271],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,12815,12816],{},"a pro procentní změny",[724,12818,12819],{},[883,12820,12822],{"className":12821,"title":8272,"style":8273},[8271],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,12824,12825],{},"(bez znaménka minus).",[198,12827,12829],{"id":12828},"příklad-47","Příklad 4.7",[724,12831,12832,12833,2246],{},"Nabídka ",[883,12834,12836],{"className":12835},[886],[888,12837,12838],{"xmlns":890},[892,12839,12840,12865],{},[895,12841,12842,12844,12846,12848,12854,12856,12858,12860,12862],{},[898,12843,1802],{},[1701,12845,1792],{},[1850,12847,4033],{},[3243,12849,12850,12852],{},[898,12851,1680],{},[1850,12853,3938],{},[1701,12855,1703],{},[1850,12857,4225],{},[898,12859,1680],{},[1701,12861,1703],{},[1850,12863,12864],{},"150",[902,12866,12867],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,12869,12870],{},[883,12871,12873],{"className":12872},[886],[888,12874,12875],{"xmlns":890},[892,12876,12877,12923],{},[895,12878,12879,12881,12883,12907,12909,12911,12913,12915,12917,12919,12921],{},[898,12880,3249],{},[1701,12882,1792],{},[3726,12884,12885,12887],{},[898,12886,1680],{},[895,12888,12889,12891,12897,12899,12901,12903,12905],{},[1850,12890,4033],{},[3243,12892,12893,12895],{},[898,12894,1680],{},[1850,12896,3938],{},[1701,12898,1703],{},[1850,12900,4225],{},[898,12902,1680],{},[1701,12904,1703],{},[1850,12906,12864],{},[1939,12908,1941],{},[1701,12910,1799],{"stretchy":1798},[1850,12912,6930],{},[898,12914,1680],{},[1701,12916,1703],{},[1850,12918,4225],{},[1701,12920,1805],{"stretchy":1798},[898,12922,1715],{"mathvariant":2334},[902,12924,12925],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,12927,9183,12928,1343,12958,1343,12985,13021,13022,13047,13048,13066,13067,1715],{},[883,12929,12931],{"className":12930},[886],[888,12932,12933],{"xmlns":890},[892,12934,12935,12955],{},[895,12936,12937,12939,12941,12943,12945,12947],{},[898,12938,3249],{},[1701,12940,1799],{"stretchy":1798},[1850,12942,3703],{},[1701,12944,1805],{"stretchy":1798},[1701,12946,1792],{},[2363,12948,12949],{"scriptlevel":1852,"displaystyle":1798},[3726,12950,12951,12953],{},[1850,12952,4062],{},[1850,12954,3646],{},[902,12956,12957],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,12959,12961],{"className":12960},[886],[888,12962,12963],{"xmlns":890},[892,12964,12965,12982],{},[895,12966,12967,12969,12971,12976,12978,12980],{},[898,12968,3249],{},[1701,12970,1799],{"stretchy":1798},[12179,12972,12973],{},[1850,12974,12975],{},"1500",[1701,12977,1805],{"stretchy":1798},[1701,12979,1792],{},[1850,12981,4062],{},[902,12983,12984],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,12986,12988],{"className":12987},[886],[888,12989,12990],{"xmlns":890},[892,12991,12992,13018],{},[895,12993,12994,12996,12998,13000,13002,13004,13013,13015],{},[898,12995,3249],{},[1701,12997,1799],{"stretchy":1798},[1850,12999,5158],{},[1701,13001,1805],{"stretchy":1798},[1701,13003,1792],{},[2363,13005,13006],{"scriptlevel":1852,"displaystyle":1798},[3726,13007,13008,13010],{},[1850,13009,7206],{},[1850,13011,13012],{},"33",[1701,13014,3782],{},[1850,13016,13017],{},"1,515",[902,13019,13020],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,13023,13025],{"className":13024},[886],[888,13026,13027],{"xmlns":890},[892,13028,13029,13044],{},[895,13030,13031,13033,13035,13039,13041],{},[898,13032,1680],{},[1701,13034,7491],{},[12179,13036,13037],{},[1850,13038,12975],{},[1701,13040,4067],{},[1850,13042,13043],{},"38,7",[902,13045,13046],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,13049,13051],{"className":13050},[886],[888,13052,13053],{"xmlns":890},[892,13054,13055,13063],{},[895,13056,13057,13059,13061],{},[898,13058,1680],{},[1701,13060,7530],{},[1850,13062,13043],{},[902,13064,13065],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,13068,13070],{"className":13069},[886],[888,13071,13072],{"xmlns":890},[892,13073,13074,13112],{},[895,13075,13076,13078,13080,13082,13084,13092,13094,13097,13099,13102,13108,13110],{},[898,13077,4708],{"mathvariant":2334},[898,13079,1802],{},[898,13081,9988],{"mathvariant":2334},[1701,13083,4067],{},[2363,13085,13086],{"scriptlevel":1852,"displaystyle":1798},[3726,13087,13088,13090],{},[1850,13089,4062],{},[1850,13091,3646],{},[1701,13093,3408],{},[1850,13095,13096],{},"20",[1701,13098,1792],{},[1850,13100,13101],{},"6,",[12448,13103,13104,13106],{"accent":2011},[1850,13105,6352],{},[1701,13107,12454],{"stretchy":2011},[1939,13109,1941],{},[898,13111,9988],{"mathvariant":2334},[902,13113,13114],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,13116,13118],{"id":13117},"vícefaktorový-model","Vícefaktorový model",[724,13120,13121,13122,13135,13136,4088,13139,13152,13153,4088,13156,13174,13175,4088,13178,2246],{},"Předpokládejme, že poptávané množství ",[883,13123,13125],{"className":13124},[886],[888,13126,13127],{"xmlns":890},[892,13128,13129,13133],{},[895,13130,13131],{},[898,13132,1802],{},[902,13134,1802],{"encoding":904}," závisí na ",[38,13137,13138],{},"ceně základního zboží",[883,13140,13142],{"className":13141},[886],[888,13143,13144],{"xmlns":890},[892,13145,13146,13150],{},[895,13147,13148],{},[898,13149,1680],{},[902,13151,1680],{"encoding":904},", na ",[38,13154,13155],{},"ceně alternativního zboží",[883,13157,13159],{"className":13158},[886],[888,13160,13161],{"xmlns":890},[892,13162,13163,13171],{},[895,13164,13165],{},[1845,13166,13167,13169],{},[898,13168,1680],{},[898,13170,1983],{},[902,13172,13173],{"encoding":904},"P_A"," a na ",[38,13176,13177],{},"důchodu",[883,13179,13181],{"className":13180},[886],[888,13182,13183],{"xmlns":890},[892,13184,13185,13190],{},[895,13186,13187],{},[898,13188,13189],{},"Y",[902,13191,13189],{"encoding":904},[724,13193,13194],{},[883,13195,13197],{"className":13196,"title":8272,"style":8273},[8271],"Q = D(P, P_A, Y). \\tag{4.17}",[724,13199,13200,13201,13204],{},"V analogii jednofaktorového modelu pracujeme s ",[38,13202,13203],{},"parciálními derivacemi"," funkce poptávky.",[198,13206,13208],{"id":13207},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,13210,13211],{},[883,13212,13214],{"className":13213,"title":8272,"style":8273},[8271],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,13216,8380,13217,13237,13238,13251,13252,7015,13274,4088,13277,13323,13324,13337,13338,3872],{},[883,13218,13220],{"className":13219},[886],[888,13221,13222],{"xmlns":890},[892,13223,13224,13234],{},[895,13225,13226],{},[2287,13227,13228,13230,13232],{},[898,13229,1802],{},[898,13231,1680],{},[1701,13233,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,13235,13236],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,13239,13241],{"className":13240},[886],[888,13242,13243],{"xmlns":890},[892,13244,13245,13249],{},[895,13246,13247],{},[898,13248,1680],{},[902,13250,1680],{"encoding":904},". Vždy ",[883,13253,13255],{"className":13254},[886],[888,13256,13257],{"xmlns":890},[892,13258,13259,13271],{},[895,13260,13261,13267,13269],{},[1845,13262,13263,13265],{},[898,13264,3249],{},[898,13266,1680],{},[1701,13268,8554],{},[1850,13270,1852],{},[902,13272,13273],{"encoding":904},"E_P \\ge 0",[614,13275,13276],{},"Interpretace:",[883,13278,13280],{"className":13279},[886],[888,13281,13282],{"xmlns":890},[892,13283,13284,13320],{},[895,13285,13286,13292,13294,13300,13302,13310,13312,13318],{},[1845,13287,13288,13290],{},[898,13289,3249],{},[898,13291,1680],{},[1701,13293,1799],{"stretchy":1798},[3243,13295,13296,13298],{},[898,13297,1680],{},[1701,13299,8424],{},[1701,13301,2012],{"separator":2011},[2287,13303,13304,13306,13308],{},[898,13305,1680],{},[898,13307,1983],{},[1701,13309,8424],{},[1701,13311,2012],{"separator":2011},[3243,13313,13314,13316],{},[898,13315,13189],{},[1701,13317,8424],{},[1701,13319,1805],{"stretchy":1798},[902,13321,13322],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,13325,13327],{"className":13326},[886],[888,13328,13329],{"xmlns":890},[892,13330,13331,13335],{},[895,13332,13333],{},[898,13334,1802],{},[902,13336,1802],{"encoding":904}," při 1% změně ",[883,13339,13341],{"className":13340},[886],[888,13342,13343],{"xmlns":890},[892,13344,13345,13353],{},[895,13346,13347],{},[3243,13348,13349,13351],{},[898,13350,1680],{},[1701,13352,8424],{},[902,13354,8474],{"encoding":904},[198,13356,13358],{"id":13357},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,13360,13361],{},[883,13362,13364],{"className":13363,"title":8272,"style":8273},[8271],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,13366,13367,13323,13369,13382,13383,13400],{},[614,13368,13276],{},[883,13370,13372],{"className":13371},[886],[888,13373,13374],{"xmlns":890},[892,13375,13376,13380],{},[895,13377,13378],{},[898,13379,1802],{},[902,13381,1802],{"encoding":904}," základního zboží při 1% změně ceny ",[883,13384,13386],{"className":13385},[886],[888,13387,13388],{"xmlns":890},[892,13389,13390,13398],{},[895,13391,13392],{},[1845,13393,13394,13396],{},[898,13395,1680],{},[898,13397,1983],{},[902,13399,13173],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,13402,13403],{},[38,13404,13405],{},"Znaménko závisí na povaze alternativního zboží:",[120,13407,13408,13496],{},[123,13409,13410,13411,13414,13415,13432,13433,4088,13446,1715],{},"Je-li alternativní zboží ",[38,13412,13413],{},"komplement",", růst ",[883,13416,13418],{"className":13417},[886],[888,13419,13420],{"xmlns":890},[892,13421,13422,13430],{},[895,13423,13424],{},[1845,13425,13426,13428],{},[898,13427,1680],{},[898,13429,1983],{},[902,13431,13173],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,13434,13436],{"className":13435},[886],[888,13437,13438],{"xmlns":890},[892,13439,13440,13444],{},[895,13441,13442],{},[898,13443,1802],{},[902,13445,1802],{"encoding":904},[883,13447,13449],{"className":13448},[886],[888,13450,13451],{"xmlns":890},[892,13452,13453,13493],{},[895,13454,13455,13457,13459,13471,13473,13475,13477,13479,13489,13491],{},[1701,13456,8061],{},[1939,13458,8058],{},[2287,13460,13461,13463,13469],{},[898,13462,1802],{},[1845,13464,13465,13467],{},[898,13466,1680],{},[898,13468,1983],{},[1701,13470,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,13472,7530],{},[1850,13474,1852],{},[1701,13476,2012],{"separator":2011},[1939,13478,8058],{},[1845,13480,13481,13483],{},[898,13482,3249],{},[1845,13484,13485,13487],{},[898,13486,1680],{},[898,13488,1983],{},[1701,13490,7530],{},[1850,13492,1852],{},[902,13494,13495],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,13497,13410,13498,13414,13501,13518,13519,13532,13533,1715],{},[38,13499,13500],{},"substitut",[883,13502,13504],{"className":13503},[886],[888,13505,13506],{"xmlns":890},[892,13507,13508,13516],{},[895,13509,13510],{},[1845,13511,13512,13514],{},[898,13513,1680],{},[898,13515,1983],{},[902,13517,13173],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,13520,13522],{"className":13521},[886],[888,13523,13524],{"xmlns":890},[892,13525,13526,13530],{},[895,13527,13528],{},[898,13529,1802],{},[902,13531,1802],{"encoding":904}," roste ",[883,13534,13536],{"className":13535},[886],[888,13537,13538],{"xmlns":890},[892,13539,13540,13580],{},[895,13541,13542,13544,13546,13558,13560,13562,13564,13566,13576,13578],{},[1701,13543,8061],{},[1939,13545,8058],{},[2287,13547,13548,13550,13556],{},[898,13549,1802],{},[1845,13551,13552,13554],{},[898,13553,1680],{},[898,13555,1983],{},[1701,13557,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,13559,7491],{},[1850,13561,1852],{},[1701,13563,2012],{"separator":2011},[1939,13565,8058],{},[1845,13567,13568,13570],{},[898,13569,3249],{},[1845,13571,13572,13574],{},[898,13573,1680],{},[898,13575,1983],{},[1701,13577,7491],{},[1850,13579,1852],{},[902,13581,13582],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,13584,13587],{"className":13585,"title":13586,"style":8273},[8271],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":13589},[13590,13594,13595,13603,13604,13608,13611],{"id":7967,"depth":642,"text":7968,"children":13591},[13592,13593],{"id":7996,"depth":649,"text":7997},{"id":8176,"depth":649,"text":8177},{"id":8211,"depth":642,"text":8212},{"id":8236,"depth":642,"text":8237,"children":13596},[13597,13598,13599,13600,13602],{"id":8926,"depth":649,"text":8927},{"id":9016,"depth":649,"text":9017},{"id":9350,"depth":649,"text":9351},{"id":9432,"depth":649,"text":13601},"Výpočet, je-li dáno PP jako funkce QQ",{"id":9692,"depth":649,"text":9693},{"id":10016,"depth":642,"text":10017},{"id":10612,"depth":642,"text":10613,"children":13605},[13606,13607],{"id":11240,"depth":649,"text":11241},{"id":12069,"depth":649,"text":12070},{"id":12703,"depth":642,"text":12704,"children":13609},[13610],{"id":12828,"depth":649,"text":12829},{"id":13117,"depth":642,"text":13118,"children":13612},[13613,13614],{"id":13207,"depth":649,"text":13208},{"id":13357,"depth":649,"text":13358},{},"\u002Ftopics\u002Felasticita",{"title":7940,"description":641},[1138,1136],"topics\u002Felasticita",[1128,7974,13621,13622,13623,13624],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":13627,"title":13628,"body":13629,"course":1128,"courses":659,"created":1129,"description":15169,"extension":661,"meta":15170,"navigation":664,"path":15171,"seo":15172,"sources":15173,"stem":15174,"tags":15175,"type":6074,"updated":677,"__hash__":15180},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":13630,"toc":15154},[13631,13634,13708,13715,13719,13783,13872,13876,13903,13969,14024,14028,14055,14147,14149,14181,14352,14356,14426,14474,14478,14539,14645,14660,14664,14666,14694,14759,14761,14768,14856,14881,15079,15083,15119,15121],[12,13632,13628],{"id":13633},"kalkul-funkcí-více-proměnných",[724,13635,13636,13637,13640,13641,1343,13670,1715],{},"Většina ekonomických veličin závisí na ",[38,13638,13639],{},"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 ",[883,13642,13644],{"className":13643},[886],[888,13645,13646],{"xmlns":890},[892,13647,13648,13667],{},[895,13649,13650,13653,13655,13657,13659,13661,13663,13665],{},[898,13651,13652],{},"z",[1701,13654,1792],{},[898,13656,6132],{},[1701,13658,1799],{"stretchy":1798},[898,13660,6137],{},[1701,13662,2012],{"separator":2011},[898,13664,6127],{},[1701,13666,1805],{"stretchy":1798},[902,13668,13669],{"encoding":904},"z = f(x, y)",[883,13671,13673],{"className":13672},[886],[888,13674,13675],{"xmlns":890},[892,13676,13677,13705],{},[895,13678,13679,13682,13684,13686,13688,13690,13692,13694,13696,13698,13700,13702],{},[898,13680,13681],{},"w",[1701,13683,1792],{},[898,13685,6132],{},[1701,13687,1799],{"stretchy":1798},[898,13689,6137],{},[1701,13691,2012],{"separator":2011},[898,13693,6127],{},[1701,13695,2012],{"separator":2011},[898,13697,13652],{},[1701,13699,1805],{"stretchy":1798},[1701,13701,2012],{"separator":2011},[1701,13703,13704],{},"…",[902,13706,13707],{"encoding":904},"w = f(x, y, z), \\ldots",[724,13709,13710],{},[2139,13711],{"alt":13712,"className":13713,"src":13714},"imek-funkce-2d-vrstevnice",[210,2143],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,13716,13718],{"id":13717},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,13720,13721,13722,13749,13750,13778,13779,13782],{},"Pro ",[883,13723,13725],{"className":13724},[886],[888,13726,13727],{"xmlns":890},[892,13728,13729,13747],{},[895,13730,13731,13733,13735,13737,13739,13741,13743,13745],{},[898,13732,13652],{},[1701,13734,1792],{},[898,13736,6132],{},[1701,13738,1799],{"stretchy":1798},[898,13740,6137],{},[1701,13742,2012],{"separator":2011},[898,13744,6127],{},[1701,13746,1805],{"stretchy":1798},[902,13748,13669],{"encoding":904}," se křivkou s předpisem ",[883,13751,13753],{"className":13752},[886],[888,13754,13755],{"xmlns":890},[892,13756,13757,13775],{},[895,13758,13759,13761,13763,13765,13767,13769,13771,13773],{},[898,13760,6132],{},[1701,13762,1799],{"stretchy":1798},[898,13764,6137],{},[1701,13766,2012],{"separator":2011},[898,13768,6127],{},[1701,13770,1805],{"stretchy":1798},[1701,13772,1792],{},[898,13774,3618],{},[902,13776,13777],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,13780,13781],{},"vrstevnice"," funkce. V ekonomii:",[120,13784,13785,13832],{},[123,13786,13787,13790,13791,13827,13828,1715],{},[38,13788,13789],{},"Indiferenční křivky"," užitečnosti ",[883,13792,13794],{"className":13793},[886],[888,13795,13796],{"xmlns":890},[892,13797,13798,13824],{},[895,13799,13800,13802,13804,13810,13812,13818,13820,13822],{},[898,13801,900],{},[1701,13803,1799],{"stretchy":1798},[1845,13805,13806,13808],{},[898,13807,1802],{},[1850,13809,4062],{},[1701,13811,2012],{"separator":2011},[1845,13813,13814,13816],{},[898,13815,1802],{},[1850,13817,3938],{},[1701,13819,1805],{"stretchy":1798},[1701,13821,1792],{},[898,13823,3618],{},[902,13825,13826],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,13829,13831],{"className":13830,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,13833,13834,13837,13838,13827,13868,1715],{},[38,13835,13836],{},"Izokvanty"," produkce ",[883,13839,13841],{"className":13840},[886],[888,13842,13843],{"xmlns":890},[892,13844,13845,13865],{},[895,13846,13847,13849,13851,13854,13856,13859,13861,13863],{},[898,13848,1802],{},[1701,13850,1799],{"stretchy":1798},[898,13852,13853],{},"L",[1701,13855,2012],{"separator":2011},[898,13857,13858],{},"K",[1701,13860,1805],{"stretchy":1798},[1701,13862,1792],{},[898,13864,3618],{},[902,13866,13867],{"encoding":904},"Q(L, K) = c",[207,13869,13871],{"className":13870,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,13873,13875],{"id":13874},"parciální-derivace","Parciální derivace",[724,13877,13721,13878,13902],{},[883,13879,13881],{"className":13880},[886],[888,13882,13883],{"xmlns":890},[892,13884,13885,13899],{},[895,13886,13887,13889,13891,13893,13895,13897],{},[898,13888,6132],{},[1701,13890,1799],{"stretchy":1798},[898,13892,6137],{},[1701,13894,2012],{"separator":2011},[898,13896,6127],{},[1701,13898,1805],{"stretchy":1798},[902,13900,13901],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,13904,13905],{},[883,13906,13908],{"className":13907},[886],[888,13909,13910],{"xmlns":890},[892,13911,13912,13966],{},[895,13913,13914,13922,13924,13938,13940,13942,13950,13952],{},[2287,13915,13916,13918,13920],{},[898,13917,6132],{},[898,13919,6137],{},[1701,13921,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,13923,1792],{},[3726,13925,13926,13932],{},[895,13927,13928,13930],{},[898,13929,3893],{"mathvariant":2334},[898,13931,6132],{},[895,13933,13934,13936],{},[898,13935,3893],{"mathvariant":2334},[898,13937,6137],{},[1701,13939,2012],{"separator":2011},[9942,13941],{"width":9944},[2287,13943,13944,13946,13948],{},[898,13945,6132],{},[898,13947,6127],{},[1701,13949,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,13951,1792],{},[3726,13953,13954,13960],{},[895,13955,13956,13958],{},[898,13957,3893],{"mathvariant":2334},[898,13959,6132],{},[895,13961,13962,13964],{},[898,13963,3893],{"mathvariant":2334},[898,13965,6127],{},[902,13967,13968],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,13970,13971,13972,1715],{},"Hodnoty v bodě: ",[883,13973,13975],{"className":13974},[886],[888,13976,13977],{"xmlns":890},[892,13978,13979,14021],{},[895,13980,13981,13989,13991,13993,13995,13997,13999,14001,14003,14011,14013,14015,14017,14019],{},[2287,13982,13983,13985,13987],{},[898,13984,6132],{},[898,13986,6137],{},[1701,13988,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,13990,1799],{"stretchy":1798},[898,13992,207],{},[1701,13994,2012],{"separator":2011},[898,13996,3598],{},[1701,13998,1805],{"stretchy":1798},[1701,14000,2012],{"separator":2011},[1939,14002,6402],{},[2287,14004,14005,14007,14009],{},[898,14006,6132],{},[898,14008,6127],{},[1701,14010,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14012,1799],{"stretchy":1798},[898,14014,207],{},[1701,14016,2012],{"separator":2011},[898,14018,3598],{},[1701,14020,1805],{"stretchy":1798},[902,14022,14023],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,14025,14027],{"id":14026},"ekonomické-značení","Ekonomické značení",[724,14029,14030,14031,2246],{},"Pro produkční funkci ",[883,14032,14034],{"className":14033},[886],[888,14035,14036],{"xmlns":890},[892,14037,14038,14052],{},[895,14039,14040,14042,14044,14046,14048,14050],{},[898,14041,1802],{},[1701,14043,1799],{"stretchy":1798},[898,14045,13853],{},[1701,14047,2012],{"separator":2011},[898,14049,13858],{},[1701,14051,1805],{"stretchy":1798},[902,14053,14054],{"encoding":904},"Q(L, K)",[120,14056,14057,14102],{},[123,14058,14059,6573,14079,1646,14082,1805],{},[883,14060,14062],{"className":14061},[886],[888,14063,14064],{"xmlns":890},[892,14065,14066,14076],{},[895,14067,14068],{},[2287,14069,14070,14072,14074],{},[898,14071,1802],{},[898,14073,13853],{},[1701,14075,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,14077,14078],{"encoding":904},"Q'_L",[38,14080,14081],{},"mezní produkt práce",[883,14083,14085],{"className":14084},[886],[888,14086,14087],{"xmlns":890},[892,14088,14089,14099],{},[895,14090,14091,14093],{},[898,14092,6909],{},[1845,14094,14095,14097],{},[898,14096,1680],{},[898,14098,13853],{},[902,14100,14101],{"encoding":904},"MP_L",[123,14103,14104,6573,14124,1646,14127,1805],{},[883,14105,14107],{"className":14106},[886],[888,14108,14109],{"xmlns":890},[892,14110,14111,14121],{},[895,14112,14113],{},[2287,14114,14115,14117,14119],{},[898,14116,1802],{},[898,14118,13858],{},[1701,14120,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,14122,14123],{"encoding":904},"Q'_K",[38,14125,14126],{},"mezní produkt kapitálu",[883,14128,14130],{"className":14129},[886],[888,14131,14132],{"xmlns":890},[892,14133,14134,14144],{},[895,14135,14136,14138],{},[898,14137,6909],{},[1845,14139,14140,14142],{},[898,14141,1680],{},[898,14143,13858],{},[902,14145,14146],{"encoding":904},"MP_K",[198,14148,6667],{"id":6666},[724,14150,14151,2246],{},[883,14152,14154],{"className":14153},[886],[888,14155,14156],{"xmlns":890},[892,14157,14158,14178],{},[895,14159,14160,14168,14170,14172,14174,14176],{},[2287,14161,14162,14164,14166],{},[898,14163,6132],{},[898,14165,6137],{},[1701,14167,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14169,1799],{"stretchy":1798},[898,14171,207],{},[1701,14173,2012],{"separator":2011},[898,14175,3598],{},[1701,14177,1805],{"stretchy":1798},[902,14179,14180],{"encoding":904},"f'_x(a, b)",[120,14182,14183,14241],{},[123,14184,14185,14186,14199,14200,14213,14214,14240],{},"rychlost změny ",[883,14187,14189],{"className":14188},[886],[888,14190,14191],{"xmlns":890},[892,14192,14193,14197],{},[895,14194,14195],{},[898,14196,6132],{},[902,14198,6132],{"encoding":904}," vůči ",[883,14201,14203],{"className":14202},[886],[888,14204,14205],{"xmlns":890},[892,14206,14207,14211],{},[895,14208,14209],{},[898,14210,6137],{},[902,14212,6137],{"encoding":904}," při ",[883,14215,14217],{"className":14216},[886],[888,14218,14219],{"xmlns":890},[892,14220,14221,14237],{},[895,14222,14223,14225,14227,14229,14231,14233,14235],{},[898,14224,6137],{},[1701,14226,1792],{},[898,14228,207],{},[1701,14230,2012],{"separator":2011},[898,14232,6127],{},[1701,14234,1792],{},[898,14236,3598],{},[902,14238,14239],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,14242,14243,14244,6756,14257,14270,14271,14289,14290,1715],{},"přibližná změna ",[883,14245,14247],{"className":14246},[886],[888,14248,14249],{"xmlns":890},[892,14250,14251,14255],{},[895,14252,14253],{},[898,14254,6132],{},[902,14256,6132],{"encoding":904},[883,14258,14260],{"className":14259},[886],[888,14261,14262],{"xmlns":890},[892,14263,14264,14268],{},[895,14265,14266],{},[898,14267,6137],{},[902,14269,6137],{"encoding":904}," o 1 (a pevném ",[883,14272,14274],{"className":14273},[886],[888,14275,14276],{"xmlns":890},[892,14277,14278,14286],{},[895,14279,14280,14282,14284],{},[898,14281,6127],{},[1701,14283,1792],{},[898,14285,3598],{},[902,14287,14288],{"encoding":904},"y = b","): ",[883,14291,14293],{"className":14292},[886],[888,14294,14295],{"xmlns":890},[892,14296,14297,14349],{},[895,14298,14299,14301,14303,14305,14307,14309,14311,14313,14315,14317,14319,14321,14323,14325,14327,14329,14331,14339,14341,14343,14345,14347],{},[898,14300,6132],{},[1701,14302,1799],{"stretchy":1798},[898,14304,207],{},[1701,14306,1703],{},[1850,14308,4062],{},[1701,14310,2012],{"separator":2011},[898,14312,3598],{},[1701,14314,1805],{"stretchy":1798},[1701,14316,4067],{},[898,14318,6132],{},[1701,14320,1799],{"stretchy":1798},[898,14322,207],{},[1701,14324,2012],{"separator":2011},[898,14326,3598],{},[1701,14328,1805],{"stretchy":1798},[1701,14330,1703],{},[2287,14332,14333,14335,14337],{},[898,14334,6132],{},[898,14336,6137],{},[1701,14338,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14340,1799],{"stretchy":1798},[898,14342,207],{},[1701,14344,2012],{"separator":2011},[898,14346,3598],{},[1701,14348,1805],{"stretchy":1798},[902,14350,14351],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,14353,14355],{"id":14354},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,14357,14358],{},[883,14359,14361],{"className":14360},[886],[888,14362,14363],{"xmlns":890},[892,14364,14365,14423],{},[895,14366,14367,14369,14371,14373,14381,14383,14385,14387,14389,14391,14393,14395,14397,14399,14407,14409,14411,14413,14415,14417,14419,14421],{},[898,14368,2312],{},[898,14370,6132],{},[1701,14372,1792],{},[2287,14374,14375,14377,14379],{},[898,14376,6132],{},[898,14378,6137],{},[1701,14380,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14382,1799],{"stretchy":1798},[898,14384,6137],{},[1701,14386,2012],{"separator":2011},[898,14388,6127],{},[1701,14390,1805],{"stretchy":1798},[1939,14392,1941],{},[898,14394,2312],{},[898,14396,6137],{},[1701,14398,1703],{},[2287,14400,14401,14403,14405],{},[898,14402,6132],{},[898,14404,6127],{},[1701,14406,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14408,1799],{"stretchy":1798},[898,14410,6137],{},[1701,14412,2012],{"separator":2011},[898,14414,6127],{},[1701,14416,1805],{"stretchy":1798},[1939,14418,1941],{},[898,14420,2312],{},[898,14422,6127],{},[902,14424,14425],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,14427,7084,14428,14450,14451,14473],{},[883,14429,14431],{"className":14430},[886],[888,14432,14433],{"xmlns":890},[892,14434,14435,14447],{},[895,14436,14437,14439,14441,14443,14445],{},[898,14438,2312],{},[898,14440,6137],{},[1701,14442,2012],{"separator":2011},[898,14444,2312],{},[898,14446,6127],{},[902,14448,14449],{"encoding":904},"dx, dy"," platí ",[883,14452,14454],{"className":14453},[886],[888,14455,14456],{"xmlns":890},[892,14457,14458,14470],{},[895,14459,14460,14462,14464,14466,14468],{},[898,14461,4708],{"mathvariant":2334},[898,14463,6132],{},[1701,14465,4067],{},[898,14467,2312],{},[898,14469,6132],{},[902,14471,14472],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,14475,14477],{"id":14476},"implicitní-funkce","Implicitní funkce",[724,14479,14480,14481,14510,14511,14524,14525,14538],{},"Je-li vztah dán rovnicí ",[883,14482,14484],{"className":14483},[886],[888,14485,14486],{"xmlns":890},[892,14487,14488,14507],{},[895,14489,14490,14493,14495,14497,14499,14501,14503,14505],{},[898,14491,14492],{},"F",[1701,14494,1799],{"stretchy":1798},[898,14496,6137],{},[1701,14498,2012],{"separator":2011},[898,14500,6127],{},[1701,14502,1805],{"stretchy":1798},[1701,14504,1792],{},[1850,14506,1852],{},[902,14508,14509],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,14512,14514],{"className":14513},[886],[888,14515,14516],{"xmlns":890},[892,14517,14518,14522],{},[895,14519,14520],{},[898,14521,6127],{},[902,14523,6127],{"encoding":904}," podle ",[883,14526,14528],{"className":14527},[886],[888,14529,14530],{"xmlns":890},[892,14531,14532,14536],{},[895,14533,14534],{},[898,14535,6137],{},[902,14537,6137],{"encoding":904}," (nebo naopak):",[724,14540,14541],{},[883,14542,14544],{"className":14543},[886],[888,14545,14546],{"xmlns":890},[892,14547,14548,14642],{},[895,14549,14550,14556,14558,14572,14574,14576,14594,14596,14598,14604,14606,14620,14622,14624],{},[3243,14551,14552,14554],{},[898,14553,6127],{},[1701,14555,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14557,1792],{},[3726,14559,14560,14566],{},[895,14561,14562,14564],{},[898,14563,2312],{},[898,14565,6127],{},[895,14567,14568,14570],{},[898,14569,2312],{},[898,14571,6137],{},[1701,14573,1792],{},[1701,14575,2317],{},[3726,14577,14578,14586],{},[2287,14579,14580,14582,14584],{},[898,14581,14492],{},[898,14583,6137],{},[1701,14585,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,14587,14588,14590,14592],{},[898,14589,14492],{},[898,14591,6127],{},[1701,14593,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14595,2012],{"separator":2011},[9942,14597],{"width":9944},[3243,14599,14600,14602],{},[898,14601,6137],{},[1701,14603,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14605,1792],{},[3726,14607,14608,14614],{},[895,14609,14610,14612],{},[898,14611,2312],{},[898,14613,6137],{},[895,14615,14616,14618],{},[898,14617,2312],{},[898,14619,6127],{},[1701,14621,1792],{},[1701,14623,2317],{},[3726,14625,14626,14634],{},[2287,14627,14628,14630,14632],{},[898,14629,14492],{},[898,14631,6127],{},[1701,14633,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,14635,14636,14638,14640],{},[898,14637,14492],{},[898,14639,6137],{},[1701,14641,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,14643,14644],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,14646,14647,14648,14651,14652,2633,14656,1715],{},"Tato vzorec dává ",[38,14649,14650],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,14653,14655],{"className":14654,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,14657,14659],{"className":14658,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,14661,14663],{"id":14662},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,14665,7335],{"id":7334},[724,14667,14668,14669,14693],{},"V bodě extrému ",[883,14670,14672],{"className":14671},[886],[888,14673,14674],{"xmlns":890},[892,14675,14676,14690],{},[895,14677,14678,14680,14682,14684,14686,14688],{},[898,14679,1983],{},[1701,14681,2036],{"stretchy":1798},[898,14683,207],{},[1701,14685,2012],{"separator":2011},[898,14687,3598],{},[1701,14689,2053],{"stretchy":1798},[902,14691,14692],{"encoding":904},"A[a, b]"," musí platit současně:",[724,14695,14696],{},[883,14697,14699],{"className":14698},[886],[888,14700,14701],{"xmlns":890},[892,14702,14703,14756],{},[895,14704,14705,14713,14715,14717,14719,14721,14723,14725,14727,14729,14732,14734,14742,14744,14746,14748,14750,14752,14754],{},[2287,14706,14707,14709,14711],{},[898,14708,6132],{},[898,14710,6137],{},[1701,14712,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14714,1799],{"stretchy":1798},[898,14716,207],{},[1701,14718,2012],{"separator":2011},[898,14720,3598],{},[1701,14722,1805],{"stretchy":1798},[1701,14724,1792],{},[1850,14726,1852],{},[1939,14728,8058],{},[1701,14730,14731],{},"∧",[1939,14733,8058],{},[2287,14735,14736,14738,14740],{},[898,14737,6132],{},[898,14739,6127],{},[1701,14741,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,14743,1799],{"stretchy":1798},[898,14745,207],{},[1701,14747,2012],{"separator":2011},[898,14749,3598],{},[1701,14751,1805],{"stretchy":1798},[1701,14753,1792],{},[1850,14755,1852],{},[902,14757,14758],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,14760,7409],{"id":7408},[724,14762,14763,14764,14767],{},"Definujeme ",[38,14765,14766],{},"diskriminant"," (Hessián zjednodušeně):",[724,14769,14770],{},[883,14771,14773],{"className":14772},[886],[888,14774,14775],{"xmlns":890},[892,14776,14777,14853],{},[895,14778,14779,14781,14783,14785,14787,14789,14791,14793,14809,14811,14827,14829,14831,14847],{},[898,14780,1795],{},[1701,14782,1799],{"stretchy":1798},[898,14784,6137],{},[1701,14786,2012],{"separator":2011},[898,14788,6127],{},[1701,14790,1805],{"stretchy":1798},[1701,14792,1792],{},[2287,14794,14795,14797,14803],{},[898,14796,6132],{},[895,14798,14799,14801],{},[898,14800,6137],{},[898,14802,6137],{},[895,14804,14805,14807],{},[1701,14806,4783],{"mathvariant":2334},[1701,14808,4783],{"mathvariant":2334},[1701,14810,3408],{},[2287,14812,14813,14815,14821],{},[898,14814,6132],{},[895,14816,14817,14819],{},[898,14818,6127],{},[898,14820,6127],{},[895,14822,14823,14825],{},[1701,14824,4783],{"mathvariant":2334},[1701,14826,4783],{"mathvariant":2334},[1701,14828,2317],{},[1701,14830,1799],{"stretchy":1798},[2287,14832,14833,14835,14841],{},[898,14834,6132],{},[895,14836,14837,14839],{},[898,14838,6137],{},[898,14840,6127],{},[895,14842,14843,14845],{},[1701,14844,4783],{"mathvariant":2334},[1701,14846,4783],{"mathvariant":2334},[3243,14848,14849,14851],{},[1701,14850,1805],{"stretchy":1798},[1850,14852,3938],{},[902,14854,14855],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,14857,14858,14859,2246],{},"V podezřelém bodě ",[883,14860,14862],{"className":14861},[886],[888,14863,14864],{"xmlns":890},[892,14865,14866,14878],{},[895,14867,14868,14870,14872,14874,14876],{},[1701,14869,2036],{"stretchy":1798},[898,14871,207],{},[1701,14873,2012],{"separator":2011},[898,14875,3598],{},[1701,14877,2053],{"stretchy":1798},[902,14879,14880],{"encoding":904},"[a, b]",[152,14882,14883,15010,15046],{},[123,14884,14885,14915,14916],{},[38,14886,14887,2246],{},[883,14888,14890],{"className":14889},[886],[888,14891,14892],{"xmlns":890},[892,14893,14894,14912],{},[895,14895,14896,14898,14900,14902,14904,14906,14908,14910],{},[898,14897,1795],{},[1701,14899,1799],{"stretchy":1798},[898,14901,207],{},[1701,14903,2012],{"separator":2011},[898,14905,3598],{},[1701,14907,1805],{"stretchy":1798},[1701,14909,7491],{},[1850,14911,1852],{},[902,14913,14914],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,14917,14918,14964],{},[123,14919,14920,7497,14962],{},[883,14921,14923],{"className":14922},[886],[888,14924,14925],{"xmlns":890},[892,14926,14927,14959],{},[895,14928,14929,14945,14947,14949,14951,14953,14955,14957],{},[2287,14930,14931,14933,14939],{},[898,14932,6132],{},[895,14934,14935,14937],{},[898,14936,6137],{},[898,14938,6137],{},[895,14940,14941,14943],{},[1701,14942,4783],{"mathvariant":2334},[1701,14944,4783],{"mathvariant":2334},[1701,14946,1799],{"stretchy":1798},[898,14948,207],{},[1701,14950,2012],{"separator":2011},[898,14952,3598],{},[1701,14954,1805],{"stretchy":1798},[1701,14956,7491],{},[1850,14958,1852],{},[902,14960,14961],{"encoding":904},"f''_{xx}(a, b) > 0",[38,14963,7858],{},[123,14965,14966,7497,15008],{},[883,14967,14969],{"className":14968},[886],[888,14970,14971],{"xmlns":890},[892,14972,14973,15005],{},[895,14974,14975,14991,14993,14995,14997,14999,15001,15003],{},[2287,14976,14977,14979,14985],{},[898,14978,6132],{},[895,14980,14981,14983],{},[898,14982,6137],{},[898,14984,6137],{},[895,14986,14987,14989],{},[1701,14988,4783],{"mathvariant":2334},[1701,14990,4783],{"mathvariant":2334},[1701,14992,1799],{"stretchy":1798},[898,14994,207],{},[1701,14996,2012],{"separator":2011},[898,14998,3598],{},[1701,15000,1805],{"stretchy":1798},[1701,15002,7530],{},[1850,15004,1852],{},[902,15006,15007],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,15009,7800],{},[123,15011,15012,4088,15042,15045],{},[38,15013,15014,2246],{},[883,15015,15017],{"className":15016},[886],[888,15018,15019],{"xmlns":890},[892,15020,15021,15039],{},[895,15022,15023,15025,15027,15029,15031,15033,15035,15037],{},[898,15024,1795],{},[1701,15026,1799],{"stretchy":1798},[898,15028,207],{},[1701,15030,2012],{"separator":2011},[898,15032,3598],{},[1701,15034,1805],{"stretchy":1798},[1701,15036,7530],{},[1850,15038,1852],{},[902,15040,15041],{"encoding":904},"D(a, b) \u003C 0",[38,15043,15044],{},"sedlo"," (v daném bodě extrém není).",[123,15047,15048,15078],{},[38,15049,15050,2246],{},[883,15051,15053],{"className":15052},[886],[888,15054,15055],{"xmlns":890},[892,15056,15057,15075],{},[895,15058,15059,15061,15063,15065,15067,15069,15071,15073],{},[898,15060,1795],{},[1701,15062,1799],{"stretchy":1798},[898,15064,207],{},[1701,15066,2012],{"separator":2011},[898,15068,3598],{},[1701,15070,1805],{"stretchy":1798},[1701,15072,1792],{},[1850,15074,1852],{},[902,15076,15077],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,15080,15082],{"id":15081},"vázané-extrémy","Vázané extrémy",[724,15084,15085,15086,15115,15116,1715],{},"Pro extrémy s omezující podmínkou ",[883,15087,15089],{"className":15088},[886],[888,15090,15091],{"xmlns":890},[892,15092,15093,15112],{},[895,15094,15095,15098,15100,15102,15104,15106,15108,15110],{},[898,15096,15097],{},"g",[1701,15099,1799],{"stretchy":1798},[898,15101,6137],{},[1701,15103,2012],{"separator":2011},[898,15105,6127],{},[1701,15107,1805],{"stretchy":1798},[1701,15109,1792],{},[1850,15111,1852],{},[902,15113,15114],{"encoding":904},"g(x, y) = 0"," se používá ",[207,15117,793],{"className":15118,"dataFsResolvedFilePath":791,"href":792},[210],[115,15120,5984],{"id":5983},[120,15122,15123,15130,15137],{},[123,15124,15125,4088,15127],{},[38,15126,7880],{},[207,15128,775],{"className":15129,"dataFsResolvedFilePath":773,"href":774},[210],[123,15131,15132,4088,15134],{},[38,15133,7888],{},[207,15135,793],{"className":15136,"dataFsResolvedFilePath":791,"href":792},[210],[123,15138,15139,4088,15141,15145,15146,15149,15150,15153],{},[38,15140,7896],{},[207,15142,15144],{"className":15143,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,15147,880],{"className":15148,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,15151,7908],{"className":15152,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":15155},[15156,15157,15161,15162,15163,15167,15168],{"id":13717,"depth":642,"text":13718},{"id":13874,"depth":642,"text":13875,"children":15158},[15159,15160],{"id":14026,"depth":649,"text":14027},{"id":6666,"depth":649,"text":6667},{"id":14354,"depth":642,"text":14355},{"id":14476,"depth":642,"text":14477},{"id":14662,"depth":642,"text":14663,"children":15164},[15165,15166],{"id":7334,"depth":649,"text":7335},{"id":7408,"depth":649,"text":7409},{"id":15081,"depth":642,"text":15082},{"id":5983,"depth":642,"text":5984},"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":13628,"description":15169},[1135],"topics\u002Ffunkce-vice-promennych",[1128,15176,7934,15177,15178,15179],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":15182,"title":775,"body":15183,"course":1128,"courses":659,"created":1129,"description":16037,"extension":661,"meta":16038,"navigation":664,"path":16039,"seo":16040,"sources":16041,"stem":16042,"tags":16043,"type":6074,"updated":677,"__hash__":16049},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":15184,"toc":16027},[15185,15188,15199,15203,15247,15327,15331,15407,15449,15456,15460,15464,15493,15551,15598,15636,15640,15690,15742,15794,15838,15840,15843,15915,15918,15990,15997,15999],[12,15186,775],{"id":15187},"integrál",[724,15189,15190,15191,15194,15195,15198],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,15192,15193],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,15196,15197],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,15200,15202],{"id":15201},"neurčitý-integrál","Neurčitý integrál",[724,15204,15205],{},[883,15206,15208],{"className":15207},[886],[888,15209,15210],{"xmlns":890},[892,15211,15212,15244],{},[895,15213,15214,15216,15218,15220,15222,15224,15226,15228,15230,15232,15234,15236,15238,15240,15242],{},[898,15215,14492],{},[1701,15217,1799],{"stretchy":1798},[898,15219,6137],{},[1701,15221,1805],{"stretchy":1798},[1701,15223,1792],{},[1701,15225,2291],{},[898,15227,6132],{},[1701,15229,1799],{"stretchy":1798},[898,15231,6137],{},[1701,15233,1805],{"stretchy":1798},[1939,15235,1941],{},[898,15237,2312],{},[898,15239,6137],{},[1701,15241,1703],{},[898,15243,1658],{},[902,15245,15246],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,15248,8380,15249,7015,15283,12164,15296,15299,15300,1343,15313,15326],{},[883,15250,15252],{"className":15251},[886],[888,15253,15254],{"xmlns":890},[892,15255,15256,15280],{},[895,15257,15258,15264,15266,15268,15270,15272,15274,15276,15278],{},[3243,15259,15260,15262],{},[898,15261,14492],{},[1701,15263,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,15265,1799],{"stretchy":1798},[898,15267,6137],{},[1701,15269,1805],{"stretchy":1798},[1701,15271,1792],{},[898,15273,6132],{},[1701,15275,1799],{"stretchy":1798},[898,15277,6137],{},[1701,15279,1805],{"stretchy":1798},[902,15281,15282],{"encoding":904},"F'(x) = f(x)",[883,15284,15286],{"className":15285},[886],[888,15287,15288],{"xmlns":890},[892,15289,15290,15294],{},[895,15291,15292],{},[898,15293,14492],{},[902,15295,14492],{"encoding":904},[38,15297,15298],{},"primitivní funkce"," k ",[883,15301,15303],{"className":15302},[886],[888,15304,15305],{"xmlns":890},[892,15306,15307,15311],{},[895,15308,15309],{},[898,15310,6132],{},[902,15312,6132],{"encoding":904},[883,15314,15316],{"className":15315},[886],[888,15317,15318],{"xmlns":890},[892,15319,15320,15324],{},[895,15321,15322],{},[898,15323,1658],{},[902,15325,1658],{"encoding":904}," konstanta.",[115,15328,15330],{"id":15329},"určitý-integrál","Určitý integrál",[724,15332,15333],{},[883,15334,15336],{"className":15335},[886],[888,15337,15338],{"xmlns":890},[892,15339,15340,15404],{},[895,15341,15342,15350,15352,15354,15356,15358,15360,15362,15364,15366,15368,15370,15372,15374,15376,15384,15386,15388,15390,15392,15394,15396,15398,15400,15402],{},[2287,15343,15344,15346,15348],{},[1701,15345,2291],{},[898,15347,207],{},[898,15349,3598],{},[898,15351,6132],{},[1701,15353,1799],{"stretchy":1798},[898,15355,6137],{},[1701,15357,1805],{"stretchy":1798},[1939,15359,1941],{},[898,15361,2312],{},[898,15363,6137],{},[1701,15365,1792],{},[1701,15367,2036],{"stretchy":1798},[898,15369,14492],{},[1701,15371,1799],{"stretchy":1798},[898,15373,6137],{},[1701,15375,1805],{"stretchy":1798},[2287,15377,15378,15380,15382],{},[1701,15379,2053],{"stretchy":1798},[898,15381,207],{},[898,15383,3598],{},[1701,15385,1792],{},[898,15387,14492],{},[1701,15389,1799],{"stretchy":1798},[898,15391,3598],{},[1701,15393,1805],{"stretchy":1798},[1701,15395,2317],{},[898,15397,14492],{},[1701,15399,1799],{"stretchy":1798},[898,15401,207],{},[1701,15403,1805],{"stretchy":1798},[902,15405,15406],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,15408,15409,15410,4088,15413,15426,15427,15448],{},"Geometricky ",[38,15411,15412],{},"plocha pod grafem",[883,15414,15416],{"className":15415},[886],[888,15417,15418],{"xmlns":890},[892,15419,15420,15424],{},[895,15421,15422],{},[898,15423,6132],{},[902,15425,6132],{"encoding":904}," na intervalu ",[883,15428,15430],{"className":15429},[886],[888,15431,15432],{"xmlns":890},[892,15433,15434,15446],{},[895,15435,15436,15438,15440,15442,15444],{},[1701,15437,2036],{"stretchy":1798},[898,15439,207],{},[1701,15441,2012],{"separator":2011},[898,15443,3598],{},[1701,15445,2053],{"stretchy":1798},[902,15447,14880],{"encoding":904}," (orientovaná).",[724,15450,15451],{},[2139,15452],{"alt":15453,"className":15454,"src":15455},"imek-integral-plocha",[210,2143],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,15457,15459],{"id":15458},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,15461,15463],{"id":15462},"příklad-tr-z-mr","Příklad — TR z MR",[724,15465,15466,15467,1715],{},"Mezní příjem ",[883,15468,15470],{"className":15469},[886],[888,15471,15472],{"xmlns":890},[892,15473,15474,15490],{},[895,15475,15476,15478,15480,15482,15484,15486,15488],{},[898,15477,6909],{},[898,15479,8068],{},[1701,15481,1792],{},[1850,15483,5158],{},[1701,15485,2317],{},[1850,15487,3938],{},[898,15489,1802],{},[902,15491,15492],{"encoding":904},"MR = 100 - 2Q",[724,15494,15495],{},[883,15496,15498],{"className":15497},[886],[888,15499,15500],{"xmlns":890},[892,15501,15502,15548],{},[895,15503,15504,15506,15508,15510,15512,15514,15516,15518,15520,15522,15524,15526,15528,15530,15532,15534,15536,15538,15544,15546],{},[898,15505,5877],{},[898,15507,8068],{},[1701,15509,1792],{},[1701,15511,2291],{},[1701,15513,1799],{"stretchy":1798},[1850,15515,5158],{},[1701,15517,2317],{},[1850,15519,3938],{},[898,15521,1802],{},[1701,15523,1805],{"stretchy":1798},[1939,15525,1941],{},[898,15527,2312],{},[898,15529,1802],{},[1701,15531,1792],{},[1850,15533,5158],{},[898,15535,1802],{},[1701,15537,2317],{},[3243,15539,15540,15542],{},[898,15541,1802],{},[1850,15543,3938],{},[1701,15545,1703],{},[898,15547,3618],{},[902,15549,15550],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,15552,15553,15554,7497,15580,2246],{},"Okrajová podmínka ",[883,15555,15557],{"className":15556},[886],[888,15558,15559],{"xmlns":890},[892,15560,15561,15577],{},[895,15562,15563,15565,15567,15569,15571,15573,15575],{},[898,15564,5877],{},[898,15566,8068],{},[1701,15568,1799],{"stretchy":1798},[1850,15570,1852],{},[1701,15572,1805],{"stretchy":1798},[1701,15574,1792],{},[1850,15576,1852],{},[902,15578,15579],{"encoding":904},"TR(0) = 0",[883,15581,15583],{"className":15582},[886],[888,15584,15585],{"xmlns":890},[892,15586,15587,15595],{},[895,15588,15589,15591,15593],{},[898,15590,3618],{},[1701,15592,1792],{},[1850,15594,1852],{},[902,15596,15597],{"encoding":904},"c = 0",[724,15599,15600],{},[883,15601,15603],{"className":15602},[886],[888,15604,15605],{"xmlns":890},[892,15606,15607,15633],{},[895,15608,15609,15611,15613,15615,15617,15619,15621,15623,15625,15627],{},[898,15610,5877],{},[898,15612,8068],{},[1701,15614,1799],{"stretchy":1798},[898,15616,1802],{},[1701,15618,1805],{"stretchy":1798},[1701,15620,1792],{},[1850,15622,5158],{},[898,15624,1802],{},[1701,15626,2317],{},[3243,15628,15629,15631],{},[898,15630,1802],{},[1850,15632,3938],{},[902,15634,15635],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,15637,15639],{"id":15638},"příklad-tc-z-mc","Příklad — TC z MC",[724,15641,15642,15643,15669,15670,1715],{},"Mezní náklady ",[883,15644,15646],{"className":15645},[886],[888,15647,15648],{"xmlns":890},[892,15649,15650,15666],{},[895,15651,15652,15654,15656,15658,15660,15662,15664],{},[898,15653,6909],{},[898,15655,1658],{},[1701,15657,1792],{},[1850,15659,3938],{},[1701,15661,1703],{},[1850,15663,6930],{},[898,15665,1802],{},[902,15667,15668],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,15671,15673],{"className":15672},[886],[888,15674,15675],{"xmlns":890},[892,15676,15677,15687],{},[895,15678,15679,15681,15683,15685],{},[898,15680,14492],{},[898,15682,1658],{},[1701,15684,1792],{},[1850,15686,5158],{},[902,15688,15689],{"encoding":904},"FC = 100",[724,15691,15692],{},[883,15693,15695],{"className":15694},[886],[888,15696,15697],{"xmlns":890},[892,15698,15699,15739],{},[895,15700,15701,15703,15705,15707,15709,15711,15713,15715,15717,15719,15721,15723,15725,15727,15729,15735,15737],{},[898,15702,5877],{},[898,15704,1658],{},[1701,15706,1792],{},[1701,15708,2291],{},[898,15710,6909],{},[898,15712,1658],{},[1939,15714,1941],{},[898,15716,2312],{},[898,15718,1802],{},[1701,15720,1792],{},[1850,15722,3938],{},[898,15724,1802],{},[1701,15726,1703],{},[1850,15728,4033],{},[3243,15730,15731,15733],{},[898,15732,1802],{},[1850,15734,3938],{},[1701,15736,1703],{},[898,15738,3618],{},[902,15740,15741],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,15743,15553,15744,7497,15776,2246],{},[883,15745,15747],{"className":15746},[886],[888,15748,15749],{"xmlns":890},[892,15750,15751,15773],{},[895,15752,15753,15755,15757,15759,15761,15763,15765,15767,15769,15771],{},[898,15754,5877],{},[898,15756,1658],{},[1701,15758,1799],{"stretchy":1798},[1850,15760,1852],{},[1701,15762,1805],{"stretchy":1798},[1701,15764,1792],{},[898,15766,14492],{},[898,15768,1658],{},[1701,15770,1792],{},[1850,15772,5158],{},[902,15774,15775],{"encoding":904},"TC(0) = FC = 100",[883,15777,15779],{"className":15778},[886],[888,15780,15781],{"xmlns":890},[892,15782,15783,15791],{},[895,15784,15785,15787,15789],{},[898,15786,3618],{},[1701,15788,1792],{},[1850,15790,5158],{},[902,15792,15793],{"encoding":904},"c = 100",[724,15795,15796],{},[883,15797,15799],{"className":15798},[886],[888,15800,15801],{"xmlns":890},[892,15802,15803,15835],{},[895,15804,15805,15807,15809,15811,15813,15815,15817,15819,15821,15823,15825,15827,15829],{},[898,15806,5877],{},[898,15808,1658],{},[1701,15810,1799],{"stretchy":1798},[898,15812,1802],{},[1701,15814,1805],{"stretchy":1798},[1701,15816,1792],{},[1850,15818,5158],{},[1701,15820,1703],{},[1850,15822,3938],{},[898,15824,1802],{},[1701,15826,1703],{},[1850,15828,4033],{},[3243,15830,15831,15833],{},[898,15832,1802],{},[1850,15834,3938],{},[902,15836,15837],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,15839,820],{"id":1633},[724,15841,15842],{},"Přebytek spotřebitele:",[724,15844,15845],{},[883,15846,15848],{"className":15847},[886],[888,15849,15850],{"xmlns":890},[892,15851,15852,15912],{},[895,15853,15854,15856,15858,15860,15866,15868,15870,15882,15884,15886,15888,15890,15892,15894,15896,15898,15904,15906],{},[898,15855,1658],{},[898,15857,1661],{},[1701,15859,1799],{"stretchy":1798},[1845,15861,15862,15864],{},[898,15863,1802],{},[1850,15865,1852],{},[1701,15867,1805],{"stretchy":1798},[1701,15869,1792],{},[2287,15871,15872,15874,15876],{},[1701,15873,2291],{},[1850,15875,1852],{},[1845,15877,15878,15880],{},[898,15879,1802],{},[1850,15881,1852],{},[898,15883,1795],{},[1701,15885,1799],{"stretchy":1798},[898,15887,1802],{},[1701,15889,1805],{"stretchy":1798},[1939,15891,1941],{},[898,15893,2312],{},[898,15895,1802],{},[1701,15897,2317],{},[1845,15899,15900,15902],{},[898,15901,1680],{},[1850,15903,1852],{},[1939,15905,1941],{},[1845,15907,15908,15910],{},[898,15909,1802],{},[1850,15911,1852],{},[902,15913,15914],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,15916,15917],{},"Přebytek výrobce:",[724,15919,15920],{},[883,15921,15923],{"className":15922},[886],[888,15924,15925],{"xmlns":890},[892,15926,15927,15987],{},[895,15928,15929,15931,15933,15935,15941,15943,15945,15951,15953,15959,15961,15973,15975,15977,15979,15981,15983,15985],{},[898,15930,1680],{},[898,15932,1661],{},[1701,15934,1799],{"stretchy":1798},[1845,15936,15937,15939],{},[898,15938,1802],{},[1850,15940,1852],{},[1701,15942,1805],{"stretchy":1798},[1701,15944,1792],{},[1845,15946,15947,15949],{},[898,15948,1680],{},[1850,15950,1852],{},[1939,15952,1941],{},[1845,15954,15955,15957],{},[898,15956,1802],{},[1850,15958,1852],{},[1701,15960,2317],{},[2287,15962,15963,15965,15967],{},[1701,15964,2291],{},[1850,15966,1852],{},[1845,15968,15969,15971],{},[898,15970,1802],{},[1850,15972,1852],{},[898,15974,1661],{},[1701,15976,1799],{"stretchy":1798},[898,15978,1802],{},[1701,15980,1805],{"stretchy":1798},[1939,15982,1941],{},[898,15984,2312],{},[898,15986,1802],{},[902,15988,15989],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,15991,15992,15993,1715],{},"Detailně viz ",[207,15994,15996],{"className":15995,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,15998,5984],{"id":5983},[120,16000,16001,16008,16015],{},[123,16002,16003,4088,16005],{},[38,16004,7880],{},[207,16006,766],{"className":16007,"dataFsResolvedFilePath":764,"href":765},[210],[123,16009,16010,4088,16012],{},[38,16011,7888],{},[207,16013,784],{"className":16014,"dataFsResolvedFilePath":782,"href":783},[210],[123,16016,16017,4088,16019,16022,16023,16026],{},[38,16018,7896],{},[207,16020,6017],{"className":16021,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,16024,15996],{"className":16025,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":16028},[16029,16030,16031,16036],{"id":15201,"depth":642,"text":15202},{"id":15329,"depth":642,"text":15330},{"id":15458,"depth":642,"text":15459,"children":16032},[16033,16034,16035],{"id":15462,"depth":649,"text":15463},{"id":15638,"depth":649,"text":15639},{"id":1633,"depth":649,"text":820},{"id":5983,"depth":642,"text":5984},"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":16037},[1135],"topics\u002Fintegral",[1128,6070,16044,16045,16046,16047,16048],"neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":16051,"title":16052,"body":16053,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":20312,"navigation":664,"path":20313,"seo":20314,"sources":20315,"stem":20316,"tags":20317,"type":6074,"updated":677,"__hash__":20323},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":16054,"toc":20300},[16055,16058,16062,16205,16212,16216,16286,16324,16427,16431,16461,16527,16574,16577,16646,16649,16684,16720,16724,16772,16779,16825,16871,16874,16953,17050,17133,17137,17181,17211,17217,17246,17268,17318,17371,17437,17440,17506,17535,17594,17610,17697,17795,17926,17930,18086,18235,18615,18619,18622,18681,18684,18770,18798,18836,18839,18876,18916,18950,18952,18989,19021,19118,19123,19247,19299,19381,19520,19524,19644,19651,19762,19769,19771,20246,20248],[12,16056,16052],{"id":16057},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,16059,16061],{"id":16060},"tldr","TL;DR",[724,16063,16064,16067,16068,1646,16071,16084,16085,16099,16100,16103,16104,1343,16107,16110,16111,1343,16114,16117,16118,4088,16121,16151,16152,16155,16156,1343,16170,1738,16183,16186,16187,2506],{},[38,16065,16066],{},"IS-LM"," je makroekonomický model se ",[38,16069,16070],{},"dvěma neznámými",[883,16072,16074],{"className":16073},[886],[888,16075,16076],{"xmlns":890},[892,16077,16078,16082],{},[895,16079,16080],{},[898,16081,13189],{},[902,16083,13189],{"encoding":904}," — národní důchod a ",[883,16086,16088],{"className":16087},[886],[888,16089,16090],{"xmlns":890},[892,16091,16092,16097],{},[895,16093,16094],{},[898,16095,16096],{},"r",[902,16098,16096],{"encoding":904}," — úroková míra) a ",[38,16101,16102],{},"dvěma trhy",": trhem zboží (křivka ",[38,16105,16106],{},"IS",[614,16108,16109],{},"Investment = Savings",") a trhem peněz (křivka ",[38,16112,16113],{},"LM",[614,16115,16116],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,16119,16120],{},"simultánní rovnováhu",[883,16122,16124],{"className":16123},[886],[888,16125,16126],{"xmlns":890},[892,16127,16128,16148],{},[895,16129,16130,16132,16138,16140,16146],{},[1701,16131,1799],{"stretchy":1798},[3243,16133,16134,16136],{},[898,16135,13189],{},[898,16137,3249],{},[1701,16139,2012],{"separator":2011},[3243,16141,16142,16144],{},[898,16143,16096],{},[898,16145,3249],{},[1701,16147,1805],{"stretchy":1798},[902,16149,16150],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,16153,16154],{},"fiskální politiky"," (posun IS změnou ",[883,16157,16159],{"className":16158},[886],[888,16160,16161],{"xmlns":890},[892,16162,16163,16168],{},[895,16164,16165],{},[898,16166,16167],{},"G",[902,16169,16167],{"encoding":904},[883,16171,16173],{"className":16172},[886],[888,16174,16175],{"xmlns":890},[892,16176,16177,16181],{},[895,16178,16179],{},[898,16180,5877],{},[902,16182,5877],{"encoding":904},[38,16184,16185],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,16188,16190],{"className":16189},[886],[888,16191,16192],{"xmlns":890},[892,16193,16194,16202],{},[895,16195,16196],{},[3243,16197,16198,16200],{},[898,16199,6909],{},[1701,16201,8424],{},[902,16203,16204],{"encoding":904},"M^*",[724,16206,16207],{},[2139,16208],{"alt":16209,"className":16210,"src":16211},"imek-is-lm-model",[210,2143],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,16213,16215],{"id":16214},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,16217,16218,16219,16223,16224,1646,16227,16250,16251,16254,16255,16271,16272,16285],{},"V modelech ",[207,16220,16222],{"className":16221,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,16225,16226],{},"investice pokládány za konstantní",[883,16228,16230],{"className":16229},[886],[888,16231,16232],{"xmlns":890},[892,16233,16234,16247],{},[895,16235,16236,16239,16241],{},[898,16237,16238],{},"I",[1701,16240,1792],{},[3243,16242,16243,16245],{},[898,16244,16238],{},[1701,16246,8424],{},[902,16248,16249],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,16252,16253],{},"ceně peněz",", tedy na ",[38,16256,16257,16258],{},"úrokové míře ",[883,16259,16261],{"className":16260},[886],[888,16262,16263],{"xmlns":890},[892,16264,16265,16269],{},[895,16266,16267],{},[898,16268,16096],{},[902,16270,16096],{"encoding":904},": čím vyšší ",[883,16273,16275],{"className":16274},[886],[888,16276,16277],{"xmlns":890},[892,16278,16279,16283],{},[895,16280,16281],{},[898,16282,16096],{},[902,16284,16096],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,16287,16288,16318],{},[123,16289,16290,4088,16293,16317],{},[38,16291,16292],{},"funkci investic",[883,16294,16296],{"className":16295},[886],[888,16297,16298],{"xmlns":890},[892,16299,16300,16314],{},[895,16301,16302,16304,16306,16308,16310,16312],{},[898,16303,16238],{},[1701,16305,1792],{},[898,16307,16238],{},[1701,16309,1799],{"stretchy":1798},[898,16311,16096],{},[1701,16313,1805],{"stretchy":1798},[902,16315,16316],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,16319,16320,16323],{},[38,16321,16322],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1635,16325,16326],{},[724,16327,16328,16330,16331,16350,16351,16378,16379,16392,16393,16422,16423,16426],{},[883,16329,4695],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,16332,16334],{"className":16333},[886],[888,16335,16336],{"xmlns":890},[892,16337,16338,16347],{},[895,16339,16340,16342,16345],{},[898,16341,1658],{},[1939,16343,16344],{},"-",[898,16346,16238],{},[902,16348,16349],{"encoding":904},"C\\text{-}I"," až ",[883,16352,16354],{"className":16353},[886],[888,16355,16356],{"xmlns":890},[892,16357,16358,16375],{},[895,16359,16360,16362,16364,16366,16368,16370,16372],{},[898,16361,1658],{},[1939,16363,16344],{},[898,16365,16238],{},[1939,16367,16344],{},[898,16369,16167],{},[1939,16371,16344],{},[898,16373,16374],{},"X",[902,16376,16377],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,16380,16382],{"className":16381},[886],[888,16383,16384],{"xmlns":890},[892,16385,16386,16390],{},[895,16387,16388],{},[898,16389,13189],{},[902,16391,13189],{"encoding":904},". V IS-LM jsou ",[38,16394,16395,16396,2633,16409],{},"dvě neznámé ",[883,16397,16399],{"className":16398},[886],[888,16400,16401],{"xmlns":890},[892,16402,16403,16407],{},[895,16404,16405],{},[898,16406,13189],{},[902,16408,13189],{"encoding":904},[883,16410,16412],{"className":16411},[886],[888,16413,16414],{"xmlns":890},[892,16415,16416,16420],{},[895,16417,16418],{},[898,16419,16096],{},[902,16421,16096],{"encoding":904},", a proto potřebujeme ",[38,16424,16425],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,16428,16430],{"id":16429},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,16432,16433,16434,16447,16448,2246],{},"Lineární závislost investic ",[883,16435,16437],{"className":16436},[886],[888,16438,16439],{"xmlns":890},[892,16440,16441,16445],{},[895,16442,16443],{},[898,16444,16238],{},[902,16446,16238],{"encoding":904}," na úrokové míře ",[883,16449,16451],{"className":16450},[886],[888,16452,16453],{"xmlns":890},[892,16454,16455,16459],{},[895,16456,16457],{},[898,16458,16096],{},[902,16460,16096],{"encoding":904},[724,16462,16463],{},[883,16464,16466],{"className":16465},[886],[888,16467,16468],{"xmlns":890},[892,16469,16470,16524],{},[895,16471,16472,16474,16476,16478,16480,16482,16484,16486,16488,16490,16492,16494,16496,16498,16500,16502,16504,16506,16508,16510,16512,16515,16517,16519,16522],{},[898,16473,16238],{},[1701,16475,1792],{},[898,16477,16238],{},[1701,16479,1799],{"stretchy":1798},[898,16481,16096],{},[1701,16483,1805],{"stretchy":1798},[1701,16485,1792],{},[898,16487,3618],{},[898,16489,16096],{},[1701,16491,1703],{},[898,16493,2312],{},[1701,16495,2012],{"separator":2011},[9942,16497],{"width":9944},[898,16499,3618],{},[1701,16501,7530],{},[1850,16503,1852],{},[1701,16505,2012],{"separator":2011},[1939,16507,6402],{},[898,16509,2312],{},[1701,16511,7491],{},[1850,16513,16514],{},"0.",[9942,16516],{"width":9944},[1701,16518,1799],{"stretchy":1798},[1850,16520,16521],{},"7.11",[1701,16523,1805],{"stretchy":1798},[902,16525,16526],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,16528,16529,16550],{},[123,16530,16531,16549],{},[883,16532,16534],{"className":16533},[886],[888,16535,16536],{"xmlns":890},[892,16537,16538,16546],{},[895,16539,16540,16542,16544],{},[898,16541,2312],{},[1701,16543,7491],{},[1850,16545,1852],{},[902,16547,16548],{"encoding":904},"d > 0"," zřejmé,",[123,16551,16552,16570,16571,1715],{},[883,16553,16555],{"className":16554},[886],[888,16556,16557],{"xmlns":890},[892,16558,16559,16567],{},[895,16560,16561,16563,16565],{},[898,16562,3618],{},[1701,16564,7530],{},[1850,16566,1852],{},[902,16568,16569],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,16572,16573],{},"klesající",[724,16575,16576],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,16578,16579],{},[883,16580,16582],{"className":16581},[886],[888,16583,16584],{"xmlns":890},[892,16585,16586,16643],{},[895,16587,16588,16590,16592,16594,16596,16598,16600,16602,16604,16606,16608,16610,16612,16614,16616,16618,16620,16622,16624,16626,16628,16630,16632,16634,16636,16638,16641],{},[898,16589,1658],{},[1701,16591,1792],{},[898,16593,1658],{},[1701,16595,1799],{"stretchy":1798},[898,16597,13189],{},[1701,16599,1805],{"stretchy":1798},[1701,16601,1792],{},[898,16603,207],{},[898,16605,13189],{},[1701,16607,1703],{},[898,16609,3598],{},[1701,16611,2012],{"separator":2011},[9942,16613],{"width":9944},[1850,16615,1852],{},[1701,16617,7530],{},[898,16619,207],{},[1701,16621,7530],{},[1850,16623,4062],{},[1701,16625,2012],{"separator":2011},[1939,16627,6402],{},[898,16629,3598],{},[1701,16631,7491],{},[1850,16633,16514],{},[9942,16635],{"width":9944},[1701,16637,1799],{"stretchy":1798},[1850,16639,16640],{},"7.12",[1701,16642,1805],{"stretchy":1798},[902,16644,16645],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,16647,16648],{},"Podmínka rovnováhy na trhu zboží:",[724,16650,16651],{},[883,16652,16654],{"className":16653},[886],[888,16655,16656],{"xmlns":890},[892,16657,16658,16681],{},[895,16659,16660,16662,16664,16666,16668,16670,16672,16674,16676,16679],{},[898,16661,13189],{},[1701,16663,1792],{},[898,16665,1658],{},[1701,16667,1703],{},[898,16669,16238],{},[898,16671,1715],{"mathvariant":2334},[9942,16673],{"width":9944},[1701,16675,1799],{"stretchy":1798},[1850,16677,16678],{},"7.13",[1701,16680,1805],{"stretchy":1798},[902,16682,16683],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,16685,16686,16687,4088,16690,16716,16717,1715],{},"To dává ",[38,16688,16689],{},"tři rovnice o čtyřech neznámých",[883,16691,16693],{"className":16692},[886],[888,16694,16695],{"xmlns":890},[892,16696,16697,16713],{},[895,16698,16699,16701,16703,16705,16707,16709,16711],{},[898,16700,13189],{},[1701,16702,2012],{"separator":2011},[898,16704,1658],{},[1701,16706,2012],{"separator":2011},[898,16708,16238],{},[1701,16710,2012],{"separator":2011},[898,16712,16096],{},[902,16714,16715],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,16718,16719],{},"rovnováhy na trhu peněz",[115,16721,16723],{"id":16722},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,16725,16726,16727,9634,16749,16767,16768,16771],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,16728,16730],{"className":16729},[886],[888,16731,16732],{"xmlns":890},[892,16733,16734,16746],{},[895,16735,16736,16738,16740,16742,16744],{},[898,16737,13189],{},[1701,16739,1792],{},[898,16741,1658],{},[1701,16743,1703],{},[898,16745,1661],{},[902,16747,16748],{"encoding":904},"Y = C + S",[883,16750,16752],{"className":16751},[886],[888,16753,16754],{"xmlns":890},[892,16755,16756,16764],{},[895,16757,16758,16760,16762],{},[898,16759,16238],{},[1701,16761,1792],{},[898,16763,1661],{},[902,16765,16766],{"encoding":904},"I = S"," (plánované ",[38,16769,16770],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,16773,16774],{},[2139,16775],{"alt":16776,"className":16777,"src":16778},"imek-odvozeni-is-4panelu",[210,2143],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,16780,16781],{},[883,16782,16784],{"className":16783},[886],[888,16785,16786],{"xmlns":890},[892,16787,16788,16822],{},[895,16789,16790,16792,16794,16796,16798,16800,16802,16804,16806,16808,16810,16812,16814,16816,16818,16820],{},[898,16791,13189],{},[1701,16793,1792],{},[1701,16795,1799],{"stretchy":1798},[898,16797,207],{},[898,16799,13189],{},[1701,16801,1703],{},[898,16803,3598],{},[1701,16805,1805],{"stretchy":1798},[1701,16807,1703],{},[1701,16809,1799],{"stretchy":1798},[898,16811,3618],{},[898,16813,16096],{},[1701,16815,1703],{},[898,16817,2312],{},[1701,16819,1805],{"stretchy":1798},[1701,16821,2012],{"separator":2011},[902,16823,16824],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,16826,16827],{},[883,16828,16830],{"className":16829},[886],[888,16831,16832],{"xmlns":890},[892,16833,16834,16868],{},[895,16835,16836,16838,16840,16842,16844,16846,16848,16850,16852,16854,16856,16858,16860,16862,16864,16866],{},[1701,16837,1799],{"stretchy":1798},[1850,16839,4062],{},[1701,16841,2317],{},[898,16843,207],{},[1701,16845,1805],{"stretchy":1798},[898,16847,13189],{},[1701,16849,2317],{},[898,16851,3618],{},[898,16853,16096],{},[1701,16855,2317],{},[898,16857,3598],{},[1701,16859,2317],{},[898,16861,2312],{},[1701,16863,1792],{},[1850,16865,1852],{},[1701,16867,2012],{"separator":2011},[902,16869,16870],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,16872,16873],{},"odkud",[724,16875,16876],{},[883,16877,16879],{"className":16878},[886],[888,16880,16881],{"xmlns":890},[892,16882,16883,16950],{},[895,16884,16885,16941,16943,16945,16948],{},[16886,16887,16889],"menclose",{"notation":16888},"box",[2363,16890,16891],{"scriptlevel":1852,"displaystyle":1798},[2363,16892,16893],{"scriptlevel":1852,"displaystyle":1798},[2363,16894,16895],{"scriptlevel":1852,"displaystyle":2011},[895,16896,16897,16899,16901,16903,16915,16917,16919,16921,16939],{},[1939,16898,1941],{},[898,16900,13189],{},[1701,16902,1792],{},[3726,16904,16905,16907],{},[898,16906,3618],{},[895,16908,16909,16911,16913],{},[1850,16910,4062],{},[1701,16912,2317],{},[898,16914,207],{},[1939,16916,1941],{},[898,16918,16096],{},[1701,16920,1703],{},[3726,16922,16923,16931],{},[895,16924,16925,16927,16929],{},[898,16926,3598],{},[1701,16928,1703],{},[898,16930,2312],{},[895,16932,16933,16935,16937],{},[1850,16934,4062],{},[1701,16936,2317],{},[898,16938,207],{},[1939,16940,1941],{},[9942,16942],{"width":9944},[1701,16944,1799],{"stretchy":1798},[1850,16946,16947],{},"7.14",[1701,16949,1805],{"stretchy":1798},[902,16951,16952],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,16954,16955,16956,1646,16959,16962,16963,16966,16967,16969,16970,16992,16993,17021,17022,17043,17044,17046,17047,17049],{},"Tento vztah se nazývá ",[38,16957,16958],{},"funkce IS",[614,16960,16961],{},"IS schedule",") a její graf ",[38,16964,16965],{},"křivka IS",". Křivka je ",[38,16968,16573],{}," přímka v rovině ",[883,16971,16973],{"className":16972},[886],[888,16974,16975],{"xmlns":890},[892,16976,16977,16989],{},[895,16978,16979,16981,16983,16985,16987],{},[1701,16980,1799],{"stretchy":1798},[898,16982,16096],{},[1701,16984,2012],{"separator":2011},[898,16986,13189],{},[1701,16988,1805],{"stretchy":1798},[902,16990,16991],{"encoding":904},"(r, Y)",", neboť ",[883,16994,16996],{"className":16995},[886],[888,16997,16998],{"xmlns":890},[892,16999,17000,17018],{},[895,17001,17002,17014,17016],{},[3726,17003,17004,17006],{},[898,17005,3618],{},[895,17007,17008,17010,17012],{},[1850,17009,4062],{},[1701,17011,2317],{},[898,17013,207],{},[1701,17015,7530],{},[1850,17017,1852],{},[902,17019,17020],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,17023,17025],{"className":17024},[886],[888,17026,17027],{"xmlns":890},[892,17028,17029,17041],{},[895,17030,17031,17033,17035,17037,17039],{},[1701,17032,1799],{"stretchy":1798},[898,17034,16096],{},[1701,17036,2012],{"separator":2011},[898,17038,13189],{},[1701,17040,1805],{"stretchy":1798},[902,17042,16991],{"encoding":904},", pro které plánované ",[38,17045,16238],{},"nvestment = ",[38,17048,1661],{},"avings.",[1635,17051,17052],{},[724,17053,17054,17056,17057,17070,17071,4088,17074,17087,17088,17101,17102,2633,17115,17128,17129,17132],{},[883,17055,2063],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,17058,17060],{"className":17059},[886],[888,17061,17062],{"xmlns":890},[892,17063,17064,17068],{},[895,17065,17066],{},[898,17067,16096],{},[902,17069,16096],{"encoding":904}," → levnější úvěr → ",[38,17072,17073],{},"více investic",[883,17075,17077],{"className":17076},[886],[888,17078,17079],{"xmlns":890},[892,17080,17081,17085],{},[895,17082,17083],{},[898,17084,16238],{},[902,17086,16238],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,17089,17091],{"className":17090},[886],[888,17092,17093],{"xmlns":890},[892,17094,17095,17099],{},[895,17096,17097],{},[898,17098,13189],{},[902,17100,13189],{"encoding":904},". Vztah mezi ",[883,17103,17105],{"className":17104},[886],[888,17106,17107],{"xmlns":890},[892,17108,17109,17113],{},[895,17110,17111],{},[898,17112,16096],{},[902,17114,16096],{"encoding":904},[883,17116,17118],{"className":17117},[886],[888,17119,17120],{"xmlns":890},[892,17121,17122,17126],{},[895,17123,17124],{},[898,17125,13189],{},[902,17127,13189],{"encoding":904}," na trhu zboží je proto ",[38,17130,17131],{},"nepřímý"," (klesající křivka).",[115,17134,17136],{"id":17135},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,17138,17139,17140,17158,17159,7015,17177,17180],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,17141,17143],{"className":17142},[886],[888,17144,17145],{"xmlns":890},[892,17146,17147,17155],{},[895,17148,17149],{},[3243,17150,17151,17153],{},[898,17152,6909],{},[898,17154,1795],{},[902,17156,17157],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,17160,17162],{"className":17161},[886],[888,17163,17164],{"xmlns":890},[892,17165,17166,17174],{},[895,17167,17168],{},[3243,17169,17170,17172],{},[898,17171,6909],{},[898,17173,1661],{},[902,17175,17176],{"encoding":904},"M^S",[38,17178,17179],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,17182,17183],{},[883,17184,17186],{"className":17185},[886],[888,17187,17188],{"xmlns":890},[892,17189,17190,17208],{},[895,17191,17192,17198,17200,17206],{},[3243,17193,17194,17196],{},[898,17195,6909],{},[898,17197,1661],{},[1701,17199,1792],{},[3243,17201,17202,17204],{},[898,17203,6909],{},[1701,17205,8424],{},[898,17207,1715],{"mathvariant":2334},[902,17209,17210],{"encoding":904},"M^S = M^*.",[724,17212,17213,17216],{},[38,17214,17215],{},"Poptávka"," po penězích má tři zdroje:",[120,17218,17219,17228,17237],{},[123,17220,17221,1646,17224,17227],{},[38,17222,17223],{},"transakční poptávka",[614,17225,17226],{},"transactions demand",") — peníze pro nákup zboží,",[123,17229,17230,1646,17233,17236],{},[38,17231,17232],{},"opatrnostní poptávka",[614,17234,17235],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,17238,17239,1646,17242,17245],{},[38,17240,17241],{},"spekulační poptávka",[614,17243,17244],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,17247,17248,17249,17267],{},"Součet transakční a opatrnostní poptávky ",[883,17250,17252],{"className":17251},[886],[888,17253,17254],{"xmlns":890},[892,17255,17256,17264],{},[895,17257,17258],{},[1845,17259,17260,17262],{},[898,17261,13853],{},[1850,17263,4062],{},[902,17265,17266],{"encoding":904},"L_1"," je úměrný důchodu:",[724,17269,17270],{},[883,17271,17273],{"className":17272},[886],[888,17274,17275],{"xmlns":890},[892,17276,17277,17315],{},[895,17278,17279,17285,17287,17294,17296,17298,17300,17302,17304,17310,17312],{},[1845,17280,17281,17283],{},[898,17282,13853],{},[1850,17284,4062],{},[1701,17286,1792],{},[1845,17288,17289,17292],{},[898,17290,17291],{},"k",[1850,17293,4062],{},[898,17295,13189],{},[1701,17297,2012],{"separator":2011},[9942,17299],{"width":9944},[1850,17301,1852],{},[1701,17303,7530],{},[1845,17305,17306,17308],{},[898,17307,17291],{},[1850,17309,4062],{},[1701,17311,7530],{},[1850,17313,17314],{},"1.",[902,17316,17317],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,17319,17320,17321,17339,17340,1343,17353,17370],{},"Spekulační poptávka ",[883,17322,17324],{"className":17323},[886],[888,17325,17326],{"xmlns":890},[892,17327,17328,17336],{},[895,17329,17330],{},[1845,17331,17332,17334],{},[898,17333,13853],{},[1850,17335,3938],{},[902,17337,17338],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,17341,17343],{"className":17342},[886],[888,17344,17345],{"xmlns":890},[892,17346,17347,17351],{},[895,17348,17349],{},[898,17350,16096],{},[902,17352,16096],{"encoding":904},[883,17354,17356],{"className":17355},[886],[888,17357,17358],{"xmlns":890},[892,17359,17360,17368],{},[895,17361,17362],{},[1845,17363,17364,17366],{},[898,17365,13853],{},[1850,17367,3938],{},[902,17369,17338],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,17372,17373],{},[883,17374,17376],{"className":17375},[886],[888,17377,17378],{"xmlns":890},[892,17379,17380,17434],{},[895,17381,17382,17388,17390,17396,17398,17400,17406,17408,17410,17416,17418,17420,17422,17424,17430,17432],{},[1845,17383,17384,17386],{},[898,17385,13853],{},[1850,17387,3938],{},[1701,17389,1792],{},[1845,17391,17392,17394],{},[898,17393,17291],{},[1850,17395,3938],{},[898,17397,16096],{},[1701,17399,1703],{},[1845,17401,17402,17404],{},[898,17403,17291],{},[1850,17405,3646],{},[1701,17407,2012],{"separator":2011},[9942,17409],{"width":9944},[1845,17411,17412,17414],{},[898,17413,17291],{},[1850,17415,3938],{},[1701,17417,7530],{},[1850,17419,1852],{},[1701,17421,2012],{"separator":2011},[1939,17423,6402],{},[1845,17425,17426,17428],{},[898,17427,17291],{},[1850,17429,3646],{},[1701,17431,7491],{},[1850,17433,16514],{},[902,17435,17436],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,17438,17439],{},"Celková poptávka po penězích:",[724,17441,17442],{},[883,17443,17445],{"className":17444},[886],[888,17446,17447],{"xmlns":890},[892,17448,17449,17503],{},[895,17450,17451,17457,17459,17465,17467,17473,17475,17481,17483,17485,17491,17493,17495,17501],{},[3243,17452,17453,17455],{},[898,17454,6909],{},[898,17456,1795],{},[1701,17458,1792],{},[1845,17460,17461,17463],{},[898,17462,13853],{},[1850,17464,4062],{},[1701,17466,1703],{},[1845,17468,17469,17471],{},[898,17470,13853],{},[1850,17472,3938],{},[1701,17474,1792],{},[1845,17476,17477,17479],{},[898,17478,17291],{},[1850,17480,4062],{},[898,17482,13189],{},[1701,17484,1703],{},[1845,17486,17487,17489],{},[898,17488,17291],{},[1850,17490,3938],{},[898,17492,16096],{},[1701,17494,1703],{},[1845,17496,17497,17499],{},[898,17498,17291],{},[1850,17500,3646],{},[898,17502,1715],{"mathvariant":2334},[902,17504,17505],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,17507,17508,17509,2246],{},"Podmínka rovnováhy na trhu peněz ",[883,17510,17512],{"className":17511},[886],[888,17513,17514],{"xmlns":890},[892,17515,17516,17532],{},[895,17517,17518,17524,17526],{},[3243,17519,17520,17522],{},[898,17521,6909],{},[898,17523,1795],{},[1701,17525,1792],{},[3243,17527,17528,17530],{},[898,17529,6909],{},[1701,17531,8424],{},[902,17533,17534],{"encoding":904},"M^D = M^*",[724,17536,17537],{},[883,17538,17540],{"className":17539},[886],[888,17541,17542],{"xmlns":890},[892,17543,17544,17591],{},[895,17545,17546,17552,17554,17560,17562,17564,17570,17572,17574,17580,17582,17584,17586,17589],{},[3243,17547,17548,17550],{},[898,17549,6909],{},[1701,17551,8424],{},[1701,17553,1792],{},[1845,17555,17556,17558],{},[898,17557,17291],{},[1850,17559,4062],{},[898,17561,13189],{},[1701,17563,1703],{},[1845,17565,17566,17568],{},[898,17567,17291],{},[1850,17569,3938],{},[898,17571,16096],{},[1701,17573,1703],{},[1845,17575,17576,17578],{},[898,17577,17291],{},[1850,17579,3646],{},[1701,17581,2012],{"separator":2011},[9942,17583],{"width":9944},[1701,17585,1799],{"stretchy":1798},[1850,17587,17588],{},"7.15",[1701,17590,1805],{"stretchy":1798},[902,17592,17593],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,17595,17596,17597,4539],{},"po úpravě (vyjádření ",[883,17598,17600],{"className":17599},[886],[888,17601,17602],{"xmlns":890},[892,17603,17604,17608],{},[895,17605,17606],{},[898,17607,13189],{},[902,17609,13189],{"encoding":904},[724,17611,17612],{},[883,17613,17615],{"className":17614},[886],[888,17616,17617],{"xmlns":890},[892,17618,17619,17694],{},[895,17620,17621,17685,17687,17689,17692],{},[16886,17622,17623],{"notation":16888},[2363,17624,17625],{"scriptlevel":1852,"displaystyle":1798},[2363,17626,17627],{"scriptlevel":1852,"displaystyle":1798},[2363,17628,17629],{"scriptlevel":1852,"displaystyle":2011},[895,17630,17631,17633,17635,17637,17639,17653,17655,17657,17659,17683],{},[1939,17632,1941],{},[898,17634,13189],{},[1701,17636,1792],{},[1701,17638,2317],{},[3726,17640,17641,17647],{},[1845,17642,17643,17645],{},[898,17644,17291],{},[1850,17646,3938],{},[1845,17648,17649,17651],{},[898,17650,17291],{},[1850,17652,4062],{},[1939,17654,1941],{},[898,17656,16096],{},[1701,17658,1703],{},[3726,17660,17661,17677],{},[895,17662,17663,17669,17671],{},[3243,17664,17665,17667],{},[898,17666,6909],{},[1701,17668,8424],{},[1701,17670,2317],{},[1845,17672,17673,17675],{},[898,17674,17291],{},[1850,17676,3646],{},[1845,17678,17679,17681],{},[898,17680,17291],{},[1850,17682,4062],{},[1939,17684,1941],{},[9942,17686],{"width":9944},[1701,17688,1799],{"stretchy":1798},[1850,17690,17691],{},"7.16",[1701,17693,1805],{"stretchy":1798},[902,17695,17696],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,17698,16955,17699,1646,17702,17705,17706,16966,17709,16969,17712,16992,17733,17765,17766,17788,17789,17791,17792,17794],{},[38,17700,17701],{},"funkce LM",[614,17703,17704],{},"LM schedule","), její graf ",[38,17707,17708],{},"křivka LM",[38,17710,17711],{},"rostoucí",[883,17713,17715],{"className":17714},[886],[888,17716,17717],{"xmlns":890},[892,17718,17719,17731],{},[895,17720,17721,17723,17725,17727,17729],{},[1701,17722,1799],{"stretchy":1798},[898,17724,16096],{},[1701,17726,2012],{"separator":2011},[898,17728,13189],{},[1701,17730,1805],{"stretchy":1798},[902,17732,16991],{"encoding":904},[883,17734,17736],{"className":17735},[886],[888,17737,17738],{"xmlns":890},[892,17739,17740,17762],{},[895,17741,17742,17744,17758,17760],{},[1701,17743,2317],{},[3726,17745,17746,17752],{},[1845,17747,17748,17750],{},[898,17749,17291],{},[1850,17751,3938],{},[1845,17753,17754,17756],{},[898,17755,17291],{},[1850,17757,4062],{},[1701,17759,7491],{},[1850,17761,1852],{},[902,17763,17764],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,17767,17769],{"className":17768},[886],[888,17770,17771],{"xmlns":890},[892,17772,17773,17785],{},[895,17774,17775,17781,17783],{},[1845,17776,17777,17779],{},[898,17778,17291],{},[1850,17780,3938],{},[1701,17782,7530],{},[1850,17784,1852],{},[902,17786,17787],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,17790,13853],{},"iquidity of ",[38,17793,6909],{},"oney.",[1635,17796,17797],{},[724,17798,17799,17801,17802,17815,17816,17844,17845,17862,17863,17876,17877,17894,17895,2633,17908,17921,17922,17925],{},[883,17800,2063],{}," Intuice — proč LM roste\nVyšší důchod ",[883,17803,17805],{"className":17804},[886],[888,17806,17807],{"xmlns":890},[892,17808,17809,17813],{},[895,17810,17811],{},[898,17812,13189],{},[902,17814,13189],{"encoding":904}," → větší transakční poptávka po penězích ",[883,17817,17819],{"className":17818},[886],[888,17820,17821],{"xmlns":890},[892,17822,17823,17841],{},[895,17824,17825,17831,17833,17839],{},[1845,17826,17827,17829],{},[898,17828,13853],{},[1850,17830,4062],{},[1701,17832,1792],{},[1845,17834,17835,17837],{},[898,17836,17291],{},[1850,17838,4062],{},[898,17840,13189],{},[902,17842,17843],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,17846,17848],{"className":17847},[886],[888,17849,17850],{"xmlns":890},[892,17851,17852,17860],{},[895,17853,17854],{},[3243,17855,17856,17858],{},[898,17857,6909],{},[1701,17859,8424],{},[902,17861,16204],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,17864,17866],{"className":17865},[886],[888,17867,17868],{"xmlns":890},[892,17869,17870,17874],{},[895,17871,17872],{},[898,17873,16096],{},[902,17875,16096],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,17878,17880],{"className":17879},[886],[888,17881,17882],{"xmlns":890},[892,17883,17884,17892],{},[895,17885,17886],{},[1845,17887,17888,17890],{},[898,17889,13853],{},[1850,17891,3938],{},[902,17893,17338],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,17896,17898],{"className":17897},[886],[888,17899,17900],{"xmlns":890},[892,17901,17902,17906],{},[895,17903,17904],{},[898,17905,13189],{},[902,17907,13189],{"encoding":904},[883,17909,17911],{"className":17910},[886],[888,17912,17913],{"xmlns":890},[892,17914,17915,17919],{},[895,17916,17917],{},[898,17918,16096],{},[902,17920,16096],{"encoding":904}," na trhu peněz je proto ",[38,17923,17924],{},"přímý"," (rostoucí křivka).",[115,17927,17929],{"id":17928},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,17931,17932,17933,17936,17937,4088,17940,2633,17958,4088,17961,17979,17980,17998,17999,18017,18018,18034,18035,2633,18050,1995,18065,1715],{},"Řešením ",[38,17934,17935],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,17938,17939],{},"rovnovážný důchod",[883,17941,17943],{"className":17942},[886],[888,17944,17945],{"xmlns":890},[892,17946,17947,17955],{},[895,17948,17949],{},[3243,17950,17951,17953],{},[898,17952,13189],{},[898,17954,3249],{},[902,17956,17957],{"encoding":904},"Y^E",[38,17959,17960],{},"rovnovážnou úrokovou míru",[883,17962,17964],{"className":17963},[886],[888,17965,17966],{"xmlns":890},[892,17967,17968,17976],{},[895,17969,17970],{},[3243,17971,17972,17974],{},[898,17973,16096],{},[898,17975,3249],{},[902,17977,17978],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,17981,17983],{"className":17982},[886],[888,17984,17985],{"xmlns":890},[892,17986,17987,17995],{},[895,17988,17989],{},[3243,17990,17991,17993],{},[898,17992,16238],{},[898,17994,3249],{},[902,17996,17997],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,18000,18002],{"className":18001},[886],[888,18003,18004],{"xmlns":890},[892,18005,18006,18014],{},[895,18007,18008],{},[3243,18009,18010,18012],{},[898,18011,1658],{},[898,18013,3249],{},[902,18015,18016],{"encoding":904},"C^E",". Graficky jde o ",[38,18019,18020,18021],{},"průsečík ",[883,18022,18024],{"className":18023},[886],[888,18025,18026],{"xmlns":890},[892,18027,18028,18032],{},[895,18029,18030],{},[898,18031,3249],{},[902,18033,3249],{"encoding":904}," křivek ",[883,18036,18038],{"className":18037},[886],[888,18039,18040],{"xmlns":890},[892,18041,18042,18048],{},[895,18043,18044,18046],{},[898,18045,16238],{},[898,18047,1661],{},[902,18049,16106],{"encoding":904},[883,18051,18053],{"className":18052},[886],[888,18054,18055],{"xmlns":890},[892,18056,18057,18063],{},[895,18058,18059,18061],{},[898,18060,13853],{},[898,18062,6909],{},[902,18064,16113],{"encoding":904},[883,18066,18068],{"className":18067},[886],[888,18069,18070],{"xmlns":890},[892,18071,18072,18084],{},[895,18073,18074,18076,18078,18080,18082],{},[1701,18075,1799],{"stretchy":1798},[898,18077,16096],{},[1701,18079,2012],{"separator":2011},[898,18081,13189],{},[1701,18083,1805],{"stretchy":1798},[902,18085,16991],{"encoding":904},[724,18087,18088],{},[614,18089,18090,18091,18112,18113,18128,18129,18144,18145,18158,18159,18176,18177,1738,18190,18176,18207,18220,18221,18234],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,18092,18094],{"className":18093},[886],[888,18095,18096],{"xmlns":890},[892,18097,18098,18110],{},[895,18099,18100,18102,18104,18106,18108],{},[1701,18101,1799],{"stretchy":1798},[898,18103,16096],{},[1701,18105,2012],{"separator":2011},[898,18107,13189],{},[1701,18109,1805],{"stretchy":1798},[902,18111,16991],{"encoding":904},". Rostoucí přímka ",[883,18114,18116],{"className":18115},[886],[888,18117,18118],{"xmlns":890},[892,18119,18120,18126],{},[895,18121,18122,18124],{},[898,18123,13853],{},[898,18125,6909],{},[902,18127,16113],{"encoding":904}," a klesající přímka ",[883,18130,18132],{"className":18131},[886],[888,18133,18134],{"xmlns":890},[892,18135,18136,18142],{},[895,18137,18138,18140],{},[898,18139,16238],{},[898,18141,1661],{},[902,18143,16106],{"encoding":904}," se protínají v bodě ",[883,18146,18148],{"className":18147},[886],[888,18149,18150],{"xmlns":890},[892,18151,18152,18156],{},[895,18153,18154],{},[898,18155,3249],{},[902,18157,3249],{"encoding":904}," se souřadnicemi ",[883,18160,18162],{"className":18161},[886],[888,18163,18164],{"xmlns":890},[892,18165,18166,18174],{},[895,18167,18168],{},[3243,18169,18170,18172],{},[898,18171,16096],{},[898,18173,3249],{},[902,18175,17978],{"encoding":904}," (na ose ",[883,18178,18180],{"className":18179},[886],[888,18181,18182],{"xmlns":890},[892,18183,18184,18188],{},[895,18185,18186],{},[898,18187,16096],{},[902,18189,16096],{"encoding":904},[883,18191,18193],{"className":18192},[886],[888,18194,18195],{"xmlns":890},[892,18196,18197,18205],{},[895,18198,18199],{},[3243,18200,18201,18203],{},[898,18202,13189],{},[898,18204,3249],{},[902,18206,17957],{"encoding":904},[883,18208,18210],{"className":18209},[886],[888,18211,18212],{"xmlns":890},[892,18213,18214,18218],{},[895,18215,18216],{},[898,18217,13189],{},[902,18219,13189],{"encoding":904},"); tečkované čáry z ",[883,18222,18224],{"className":18223},[886],[888,18225,18226],{"xmlns":890},[892,18227,18228,18232],{},[895,18229,18230],{},[898,18231,3249],{},[902,18233,3249],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1635,18236,18237,18242],{},[724,18238,18239,18241],{},[883,18240,3140],{}," Postup — jak najít IS-LM rovnováhu",[152,18243,18244,18320,18388,18446,18519],{},[123,18245,18246,18249,18250,2633,18270,18290,18291,2633,18304,18317,18318,1715],{},[38,18247,18248],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,18251,18253],{"className":18252},[886],[888,18254,18255],{"xmlns":890},[892,18256,18257,18267],{},[895,18258,18259,18261,18263,18265],{},[898,18260,1658],{},[1701,18262,1799],{"stretchy":1798},[898,18264,13189],{},[1701,18266,1805],{"stretchy":1798},[902,18268,18269],{"encoding":904},"C(Y)",[883,18271,18273],{"className":18272},[886],[888,18274,18275],{"xmlns":890},[892,18276,18277,18287],{},[895,18278,18279,18281,18283,18285],{},[898,18280,16238],{},[1701,18282,1799],{"stretchy":1798},[898,18284,16096],{},[1701,18286,1805],{"stretchy":1798},[902,18288,18289],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,18292,18294],{"className":18293},[886],[888,18295,18296],{"xmlns":890},[892,18297,18298,18302],{},[895,18299,18300],{},[898,18301,13189],{},[902,18303,13189],{"encoding":904},[883,18305,18307],{"className":18306},[886],[888,18308,18309],{"xmlns":890},[892,18310,18311,18315],{},[895,18312,18313],{},[898,18314,16096],{},[902,18316,16096],{"encoding":904}," — dostaneš rovnici ",[38,18319,16106],{},[123,18321,18322,18325,18326,2633,18343,18360,18361,18317,18386,1715],{},[38,18323,18324],{},"Z trhu peněz (7.15)"," dosaď ",[883,18327,18329],{"className":18328},[886],[888,18330,18331],{"xmlns":890},[892,18332,18333,18341],{},[895,18334,18335],{},[1845,18336,18337,18339],{},[898,18338,13853],{},[1850,18340,4062],{},[902,18342,17266],{"encoding":904},[883,18344,18346],{"className":18345},[886],[888,18347,18348],{"xmlns":890},[892,18349,18350,18358],{},[895,18351,18352],{},[1845,18353,18354,18356],{},[898,18355,13853],{},[1850,18357,3938],{},[902,18359,17338],{"encoding":904}," a vztah ",[883,18362,18364],{"className":18363},[886],[888,18365,18366],{"xmlns":890},[892,18367,18368,18384],{},[895,18369,18370,18376,18378],{},[3243,18371,18372,18374],{},[898,18373,6909],{},[898,18375,1795],{},[1701,18377,1792],{},[3243,18379,18380,18382],{},[898,18381,6909],{},[1701,18383,8424],{},[902,18385,17534],{"encoding":904},[38,18387,16113],{},[123,18389,18390,18393,18394,2633,18407,18420,18421,18445],{},[38,18391,18392],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,18395,18397],{"className":18396},[886],[888,18398,18399],{"xmlns":890},[892,18400,18401,18405],{},[895,18402,18403],{},[898,18404,13189],{},[902,18406,13189],{"encoding":904},[883,18408,18410],{"className":18409},[886],[888,18411,18412],{"xmlns":890},[892,18413,18414,18418],{},[895,18415,18416],{},[898,18417,16096],{},[902,18419,16096],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,18422,18424],{"className":18423},[886],[888,18425,18426],{"xmlns":890},[892,18427,18428,18442],{},[895,18429,18430,18432,18434,18436,18438,18440],{},[898,18431,13189],{},[1701,18433,1792],{},[898,18435,6132],{},[1701,18437,1799],{"stretchy":1798},[898,18439,16096],{},[1701,18441,1805],{"stretchy":1798},[902,18443,18444],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,18447,18448,4088,18451,2633,18485,1715],{},[38,18449,18450],{},"Zpětně dopočítej",[883,18452,18454],{"className":18453},[886],[888,18455,18456],{"xmlns":890},[892,18457,18458,18482],{},[895,18459,18460,18466,18468,18470,18472,18478,18480],{},[3243,18461,18462,18464],{},[898,18463,1658],{},[898,18465,3249],{},[1701,18467,1792],{},[898,18469,207],{},[1939,18471,1941],{},[3243,18473,18474,18476],{},[898,18475,13189],{},[898,18477,3249],{},[1701,18479,1703],{},[898,18481,3598],{},[902,18483,18484],{"encoding":904},"C^E = a\\,Y^E + b",[883,18486,18488],{"className":18487},[886],[888,18489,18490],{"xmlns":890},[892,18491,18492,18516],{},[895,18493,18494,18500,18502,18504,18506,18512,18514],{},[3243,18495,18496,18498],{},[898,18497,16238],{},[898,18499,3249],{},[1701,18501,1792],{},[898,18503,3618],{},[1939,18505,1941],{},[3243,18507,18508,18510],{},[898,18509,16096],{},[898,18511,3249],{},[1701,18513,1703],{},[898,18515,2312],{},[902,18517,18518],{"encoding":904},"I^E = c\\,r^E + d",[123,18520,18521,18524,18525,18559,18560,18614],{},[38,18522,18523],{},"Ověř:"," musí platit ",[883,18526,18528],{"className":18527},[886],[888,18529,18530],{"xmlns":890},[892,18531,18532,18556],{},[895,18533,18534,18540,18542,18548,18550],{},[3243,18535,18536,18538],{},[898,18537,13189],{},[898,18539,3249],{},[1701,18541,1792],{},[3243,18543,18544,18546],{},[898,18545,1658],{},[898,18547,3249],{},[1701,18549,1703],{},[3243,18551,18552,18554],{},[898,18553,16238],{},[898,18555,3249],{},[902,18557,18558],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,18561,18563],{"className":18562},[886],[888,18564,18565],{"xmlns":890},[892,18566,18567,18611],{},[895,18568,18569,18575,18577,18583,18589,18591,18597,18603,18605],{},[3243,18570,18571,18573],{},[898,18572,6909],{},[1701,18574,8424],{},[1701,18576,1792],{},[1845,18578,18579,18581],{},[898,18580,17291],{},[1850,18582,4062],{},[3243,18584,18585,18587],{},[898,18586,13189],{},[898,18588,3249],{},[1701,18590,1703],{},[1845,18592,18593,18595],{},[898,18594,17291],{},[1850,18596,3938],{},[3243,18598,18599,18601],{},[898,18600,16096],{},[898,18602,3249],{},[1701,18604,1703],{},[1845,18606,18607,18609],{},[898,18608,17291],{},[1850,18610,3646],{},[902,18612,18613],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,18616,18618],{"id":18617},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,18620,18621],{},"Pro trh zboží jsou dány:",[120,18623,18624,18652],{},[123,18625,18626,18627,2012],{},"spotřeba ",[883,18628,18630],{"className":18629},[886],[888,18631,18632],{"xmlns":890},[892,18633,18634,18649],{},[895,18635,18636,18638,18640,18643,18645,18647],{},[898,18637,1658],{},[1701,18639,1792],{},[1850,18641,18642],{},"0,8",[898,18644,13189],{},[1701,18646,1703],{},[1850,18648,5158],{},[902,18650,18651],{"encoding":904},"C = 0{,}8Y + 100",[123,18653,18654,18655,1715],{},"investice ",[883,18656,18658],{"className":18657},[886],[888,18659,18660],{"xmlns":890},[892,18661,18662,18678],{},[895,18663,18664,18666,18668,18670,18672,18674,18676],{},[898,18665,16238],{},[1701,18667,1792],{},[1701,18669,2317],{},[1850,18671,13096],{},[898,18673,16096],{},[1701,18675,1703],{},[1850,18677,6875],{},[902,18679,18680],{"encoding":904},"I = -20r + 1000",[724,18682,18683],{},"Pro trh peněz:",[120,18685,18686,18712,18744],{},[123,18687,18688,2012],{},[883,18689,18691],{"className":18690},[886],[888,18692,18693],{"xmlns":890},[892,18694,18695,18709],{},[895,18696,18697,18703,18705,18707],{},[1845,18698,18699,18701],{},[898,18700,13853],{},[1850,18702,4062],{},[1701,18704,1792],{},[1850,18706,4033],{},[898,18708,13189],{},[902,18710,18711],{"encoding":904},"L_1 = 0{,}1Y",[123,18713,18714,2012],{},[883,18715,18717],{"className":18716},[886],[888,18718,18719],{"xmlns":890},[892,18720,18721,18741],{},[895,18722,18723,18729,18731,18733,18735,18737,18739],{},[1845,18724,18725,18727],{},[898,18726,13853],{},[1850,18728,3938],{},[1701,18730,1792],{},[1701,18732,2317],{},[1850,18734,9071],{},[898,18736,16096],{},[1701,18738,1703],{},[1850,18740,12666],{},[902,18742,18743],{"encoding":904},"L_2 = -25r + 2000",[123,18745,18746,18747,1715],{},"nabídka peněz ",[883,18748,18750],{"className":18749},[886],[888,18751,18752],{"xmlns":890},[892,18753,18754,18767],{},[895,18755,18756,18762,18764],{},[3243,18757,18758,18760],{},[898,18759,6909],{},[1701,18761,8424],{},[1701,18763,1792],{},[1850,18765,18766],{},"2375",[902,18768,18769],{"encoding":904},"M^* = 2375",[724,18771,18772,18775,18776,2246],{},[38,18773,18774],{},"Funkce IS"," — dosazením do (7.13) ",[883,18777,18779],{"className":18778},[886],[888,18780,18781],{"xmlns":890},[892,18782,18783,18795],{},[895,18784,18785,18787,18789,18791,18793],{},[898,18786,13189],{},[1701,18788,1792],{},[898,18790,1658],{},[1701,18792,1703],{},[898,18794,16238],{},[902,18796,18797],{"encoding":904},"Y = C + I",[724,18799,18800],{},[883,18801,18803],{"className":18802},[886],[888,18804,18805],{"xmlns":890},[892,18806,18807,18833],{},[895,18808,18809,18811,18813,18815,18817,18819,18821,18823,18825,18827,18829,18831],{},[898,18810,13189],{},[1701,18812,1792],{},[1850,18814,18642],{},[898,18816,13189],{},[1701,18818,1703],{},[1850,18820,5158],{},[1701,18822,2317],{},[1850,18824,13096],{},[898,18826,16096],{},[1701,18828,1703],{},[1850,18830,6875],{},[1701,18832,2012],{"separator":2011},[902,18834,18835],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,18837,18838],{},"tj.",[724,18840,18841],{},[883,18842,18844],{"className":18843},[886],[888,18845,18846],{"xmlns":890},[892,18847,18848,18873],{},[895,18849,18850,18852,18854,18856,18858,18860,18862,18865,18867,18869,18871],{},[1850,18851,6930],{},[898,18853,13189],{},[1701,18855,1703],{},[1850,18857,13096],{},[898,18859,16096],{},[1701,18861,1792],{},[1850,18863,18864],{},"1100.",[9942,18866],{"width":9944},[1701,18868,1799],{"stretchy":1798},[1939,18870,16106],{},[1701,18872,1805],{"stretchy":1798},[902,18874,18875],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,18877,18878,18881,18882,2246],{},[38,18879,18880],{},"Funkce LM"," — dosazením do (7.15) ",[883,18883,18885],{"className":18884},[886],[888,18886,18887],{"xmlns":890},[892,18888,18889,18913],{},[895,18890,18891,18897,18899,18905,18907],{},[3243,18892,18893,18895],{},[898,18894,6909],{},[1701,18896,8424],{},[1701,18898,1792],{},[1845,18900,18901,18903],{},[898,18902,13853],{},[1850,18904,4062],{},[1701,18906,1703],{},[1845,18908,18909,18911],{},[898,18910,13853],{},[1850,18912,3938],{},[902,18914,18915],{"encoding":904},"M^* = L_1 + L_2",[724,18917,18918],{},[883,18919,18921],{"className":18920},[886],[888,18922,18923],{"xmlns":890},[892,18924,18925,18947],{},[895,18926,18927,18929,18931,18933,18935,18937,18939,18941,18943,18945],{},[1850,18928,18766],{},[1701,18930,1792],{},[1850,18932,4033],{},[898,18934,13189],{},[1701,18936,2317],{},[1850,18938,9071],{},[898,18940,16096],{},[1701,18942,1703],{},[1850,18944,12666],{},[1701,18946,2012],{"separator":2011},[902,18948,18949],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,18951,18838],{},[724,18953,18954],{},[883,18955,18957],{"className":18956},[886],[888,18958,18959],{"xmlns":890},[892,18960,18961,18986],{},[895,18962,18963,18965,18967,18969,18971,18973,18975,18978,18980,18982,18984],{},[1850,18964,4033],{},[898,18966,13189],{},[1701,18968,2317],{},[1850,18970,9071],{},[898,18972,16096],{},[1701,18974,1792],{},[1850,18976,18977],{},"375.",[9942,18979],{"width":9944},[1701,18981,1799],{"stretchy":1798},[1939,18983,16113],{},[1701,18985,1805],{"stretchy":1798},[902,18987,18988],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,18990,18991,18994,18995,19020],{},[38,18992,18993],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,18996,18998],{"className":18997},[886],[888,18999,19000],{"xmlns":890},[892,19001,19002,19017],{},[895,19003,19004,19006,19008,19011,19013,19015],{},[898,19005,13189],{},[1701,19007,1792],{},[1850,19009,19010],{},"5500",[1701,19012,2317],{},[1850,19014,5158],{},[898,19016,16096],{},[902,19018,19019],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,19022,19023],{},[883,19024,19026],{"className":19025},[886],[888,19027,19028],{"xmlns":890},[892,19029,19030,19115],{},[895,19031,19032,19034,19036,19038,19040,19042,19044,19046,19048,19050,19052,19054,19057,19059,19062,19064,19067,19069,19071,19073,19075,19077,19079,19081,19083,19085,19087,19089,19091,19093,19095,19098,19100,19102,19104,19110,19112],{},[1850,19033,4033],{},[1701,19035,1799],{"stretchy":1798},[1850,19037,19010],{},[1701,19039,2317],{},[1850,19041,5158],{},[898,19043,16096],{},[1701,19045,1805],{"stretchy":1798},[1701,19047,2317],{},[1850,19049,9071],{},[898,19051,16096],{},[1701,19053,1792],{},[1850,19055,19056],{},"375",[1939,19058,8058],{},[1701,19060,19061],{},"⟹",[1939,19063,8058],{},[1850,19065,19066],{},"550",[1701,19068,2317],{},[1850,19070,3703],{},[898,19072,16096],{},[1701,19074,2317],{},[1850,19076,9071],{},[898,19078,16096],{},[1701,19080,1792],{},[1850,19082,19056],{},[1939,19084,8058],{},[1701,19086,19061],{},[1939,19088,8058],{},[1850,19090,4136],{},[898,19092,16096],{},[1701,19094,1792],{},[1850,19096,19097],{},"175",[1939,19099,8058],{},[1701,19101,19061],{},[1939,19103,8058],{},[3243,19105,19106,19108],{},[898,19107,16096],{},[898,19109,3249],{},[1701,19111,1792],{},[1850,19113,19114],{},"5.",[902,19116,19117],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,19119,19120],{},[38,19121,19122],{},"Zpětné dosazení:",[120,19124,19125,19171,19208],{},[123,19126,19127,2012],{},[883,19128,19130],{"className":19129},[886],[888,19131,19132],{"xmlns":890},[892,19133,19134,19168],{},[895,19135,19136,19142,19144,19146,19148,19150,19152,19154,19156,19158,19160,19163,19165],{},[3243,19137,19138,19140],{},[898,19139,13189],{},[898,19141,3249],{},[1701,19143,1792],{},[1850,19145,19010],{},[1701,19147,2317],{},[1850,19149,5158],{},[1701,19151,3408],{},[1850,19153,4225],{},[1701,19155,1792],{},[1850,19157,19010],{},[1701,19159,2317],{},[1850,19161,19162],{},"500",[1701,19164,1792],{},[1850,19166,19167],{},"5000",[902,19169,19170],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,19172,19173,2012],{},[883,19174,19176],{"className":19175},[886],[888,19177,19178],{"xmlns":890},[892,19179,19180,19205],{},[895,19181,19182,19188,19190,19192,19194,19196,19198,19200,19202],{},[3243,19183,19184,19186],{},[898,19185,1658],{},[898,19187,3249],{},[1701,19189,1792],{},[1850,19191,18642],{},[1701,19193,3408],{},[1850,19195,19167],{},[1701,19197,1703],{},[1850,19199,5158],{},[1701,19201,1792],{},[1850,19203,19204],{},"4100",[902,19206,19207],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,19209,19210,1715],{},[883,19211,19213],{"className":19212},[886],[888,19214,19215],{"xmlns":890},[892,19216,19217,19244],{},[895,19218,19219,19225,19227,19229,19231,19233,19235,19237,19239,19241],{},[3243,19220,19221,19223],{},[898,19222,16238],{},[898,19224,3249],{},[1701,19226,1792],{},[1701,19228,2317],{},[1850,19230,13096],{},[1701,19232,3408],{},[1850,19234,4225],{},[1701,19236,1703],{},[1850,19238,6875],{},[1701,19240,1792],{},[1850,19242,19243],{},"900",[902,19245,19246],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,19248,19249,4088,19252,19298],{},[38,19250,19251],{},"Ověření:",[883,19253,19255],{"className":19254},[886],[888,19256,19257],{"xmlns":890},[892,19258,19259,19295],{},[895,19260,19261,19267,19269,19275,19277,19279,19281,19283,19285,19287,19289],{},[3243,19262,19263,19265],{},[898,19264,1658],{},[898,19266,3249],{},[1701,19268,1703],{},[3243,19270,19271,19273],{},[898,19272,16238],{},[898,19274,3249],{},[1701,19276,1792],{},[1850,19278,19204],{},[1701,19280,1703],{},[1850,19282,19243],{},[1701,19284,1792],{},[1850,19286,19167],{},[1701,19288,1792],{},[3243,19290,19291,19293],{},[898,19292,13189],{},[898,19294,3249],{},[902,19296,19297],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,19300,19301],{},[883,19302,19304],{"className":19303},[886],[888,19305,19306],{"xmlns":890},[892,19307,19308,19378],{},[895,19309,19310],{},[16886,19311,19312],{"notation":16888},[2363,19313,19314],{"scriptlevel":1852,"displaystyle":1798},[2363,19315,19316],{"scriptlevel":1852,"displaystyle":1798},[2363,19317,19318],{"scriptlevel":1852,"displaystyle":2011},[895,19319,19320,19322,19328,19330,19332,19334,19337,19343,19345,19347,19349,19351,19357,19359,19361,19363,19365,19371,19373,19376],{},[1939,19321,1941],{},[3243,19323,19324,19326],{},[898,19325,13189],{},[898,19327,3249],{},[1701,19329,1792],{},[1850,19331,19167],{},[1701,19333,2012],{"separator":2011},[9942,19335],{"width":19336},"1em",[3243,19338,19339,19341],{},[898,19340,16096],{},[898,19342,3249],{},[1701,19344,1792],{},[1850,19346,4225],{},[1701,19348,2012],{"separator":2011},[9942,19350],{"width":19336},[3243,19352,19353,19355],{},[898,19354,1658],{},[898,19356,3249],{},[1701,19358,1792],{},[1850,19360,19204],{},[1701,19362,2012],{"separator":2011},[9942,19364],{"width":19336},[3243,19366,19367,19369],{},[898,19368,16238],{},[898,19370,3249],{},[1701,19372,1792],{},[1850,19374,19375],{},"900.",[1939,19377,1941],{},[902,19379,19380],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,19382,19383],{},[614,19384,19385,19386,19399,19400,19413,19414,19429,19430,19443,19444,19459,19460,19473,19474,19487,19488,1715],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,19387,19389],{"className":19388},[886],[888,19390,19391],{"xmlns":890},[892,19392,19393,19397],{},[895,19394,19395],{},[898,19396,13189],{},[902,19398,13189],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,19401,19403],{"className":19402},[886],[888,19404,19405],{"xmlns":890},[892,19406,19407,19411],{},[895,19408,19409],{},[898,19410,16096],{},[902,19412,16096],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,19415,19417],{"className":19416},[886],[888,19418,19419],{"xmlns":890},[892,19420,19421,19427],{},[895,19422,19423,19425],{},[898,19424,13853],{},[898,19426,6909],{},[902,19428,16113],{"encoding":904}," stoupá z oblasti nízkých ",[883,19431,19433],{"className":19432},[886],[888,19434,19435],{"xmlns":890},[892,19436,19437,19441],{},[895,19438,19439],{},[898,19440,16096],{},[902,19442,16096],{"encoding":904},", přímka ",[883,19445,19447],{"className":19446},[886],[888,19448,19449],{"xmlns":890},[892,19450,19451,19457],{},[895,19452,19453,19455],{},[898,19454,16238],{},[898,19456,1661],{},[902,19458,16106],{"encoding":904}," klesá a protíná osu ",[883,19461,19463],{"className":19462},[886],[888,19464,19465],{"xmlns":890},[892,19466,19467,19471],{},[895,19468,19469],{},[898,19470,16096],{},[902,19472,16096],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,19475,19477],{"className":19476},[886],[888,19478,19479],{"xmlns":890},[892,19480,19481,19485],{},[895,19482,19483],{},[898,19484,3249],{},[902,19486,3249],{"encoding":904}," leží v bodě ",[883,19489,19491],{"className":19490},[886],[888,19492,19493],{"xmlns":890},[892,19494,19495,19517],{},[895,19496,19497,19499,19501,19503,19505,19507,19509,19511,19513,19515],{},[1701,19498,2036],{"stretchy":1798},[898,19500,16096],{},[1701,19502,1792],{},[1850,19504,4225],{},[1701,19506,2012],{"separator":2011},[1939,19508,6402],{},[898,19510,13189],{},[1701,19512,1792],{},[1850,19514,19167],{},[1701,19516,2053],{"stretchy":1798},[902,19518,19519],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,19521,19523],{"id":19522},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,19525,19526,19529,19530,19543,19544,2979,19557,19560,19561,19579,19580,19597,19598,19615,19616,19629,19630,19643],{},[38,19527,19528],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,19531,19533],{"className":19532},[886],[888,19534,19535],{"xmlns":890},[892,19536,19537,19541],{},[895,19538,19539],{},[898,19540,16167],{},[902,19542,16167],{"encoding":904}," nebo snížení daní ",[883,19545,19547],{"className":19546},[886],[888,19548,19549],{"xmlns":890},[892,19550,19551,19555],{},[895,19552,19553],{},[898,19554,5877],{},[902,19556,5877],{"encoding":904},[38,19558,19559],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,19562,19564],{"className":19563},[886],[888,19565,19566],{"xmlns":890},[892,19567,19568,19576],{},[895,19569,19570],{},[3243,19571,19572,19574],{},[898,19573,3249],{},[1701,19575,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,19577,19578],{"encoding":904},"E'"," má vyšší ",[883,19581,19583],{"className":19582},[886],[888,19584,19585],{"xmlns":890},[892,19586,19587,19595],{},[895,19588,19589],{},[3243,19590,19591,19593],{},[898,19592,13189],{},[898,19594,3249],{},[902,19596,17957],{"encoding":904}," i vyšší ",[883,19599,19601],{"className":19600},[886],[888,19602,19603],{"xmlns":890},[892,19604,19605,19613],{},[895,19606,19607],{},[3243,19608,19609,19611],{},[898,19610,16096],{},[898,19612,3249],{},[902,19614,17978],{"encoding":904}," (vyšší ",[883,19617,19619],{"className":19618},[886],[888,19620,19621],{"xmlns":890},[892,19622,19623,19627],{},[895,19624,19625],{},[898,19626,13189],{},[902,19628,13189],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,19631,19633],{"className":19632},[886],[888,19634,19635],{"xmlns":890},[892,19636,19637,19641],{},[895,19638,19639],{},[898,19640,16096],{},[902,19642,16096],{"encoding":904}," nahoru).",[724,19645,19646],{},[2139,19647],{"alt":19648,"className":19649,"src":19650},"imek-posun-is-lm-politiky",[210,2143],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,19652,19653,19656,19657,19674,19675,19678,19679,19696,19697,19714,19715,19728,19729,19748,19749,2506],{},[38,19654,19655],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,19658,19660],{"className":19659},[886],[888,19661,19662],{"xmlns":890},[892,19663,19664,19672],{},[895,19665,19666],{},[3243,19667,19668,19670],{},[898,19669,6909],{},[1701,19671,8424],{},[902,19673,16204],{"encoding":904}," národní bankou — ",[38,19676,19677],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,19680,19682],{"className":19681},[886],[888,19683,19684],{"xmlns":890},[892,19685,19686,19694],{},[895,19687,19688],{},[3243,19689,19690,19692],{},[898,19691,16096],{},[898,19693,3249],{},[902,19695,17978],{"encoding":904}," a vyšší ",[883,19698,19700],{"className":19699},[886],[888,19701,19702],{"xmlns":890},[892,19703,19704,19712],{},[895,19705,19706],{},[3243,19707,19708,19710],{},[898,19709,13189],{},[898,19711,3249],{},[902,19713,17957],{"encoding":904}," (nižší ",[883,19716,19718],{"className":19717},[886],[888,19719,19720],{"xmlns":890},[892,19721,19722,19726],{},[895,19723,19724],{},[898,19725,16096],{},[902,19727,16096],{"encoding":904}," povzbuzuje investice ",[883,19730,19732],{"className":19731},[886],[888,19733,19734],{"xmlns":890},[892,19735,19736,19746],{},[895,19737,19738,19740,19742,19744],{},[898,19739,16238],{},[1701,19741,1799],{"stretchy":1798},[898,19743,16096],{},[1701,19745,1805],{"stretchy":1798},[902,19747,18289],{"encoding":904},", ty zvedají ",[883,19750,19752],{"className":19751},[886],[888,19753,19754],{"xmlns":890},[892,19755,19756,19760],{},[895,19757,19758],{},[898,19759,13189],{},[902,19761,13189],{"encoding":904},[724,19763,19764,19765,19768],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,19766,19767],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,19770,5578],{"id":5577},[120,19772,19773,19846,19892,19974,20024,20091,20148,20189,20222],{},[123,19774,19775,2979,19808,1343,19825,19842,19843,19845],{},[38,19776,19777,19778],{},"Funkce investic ",[883,19779,19781],{"className":19780},[886],[888,19782,19783],{"xmlns":890},[892,19784,19785,19805],{},[895,19786,19787,19789,19791,19793,19795,19797,19799,19801,19803],{},[898,19788,16238],{},[1701,19790,1799],{"stretchy":1798},[898,19792,16096],{},[1701,19794,1805],{"stretchy":1798},[1701,19796,1792],{},[898,19798,3618],{},[898,19800,16096],{},[1701,19802,1703],{},[898,19804,2312],{},[902,19806,19807],{"encoding":904},"I(r) = cr + d",[883,19809,19811],{"className":19810},[886],[888,19812,19813],{"xmlns":890},[892,19814,19815,19823],{},[895,19816,19817,19819,19821],{},[898,19818,3618],{},[1701,19820,7530],{},[1850,19822,1852],{},[902,19824,16569],{"encoding":904},[883,19826,19828],{"className":19827},[886],[888,19829,19830],{"xmlns":890},[892,19831,19832,19840],{},[895,19833,19834,19836,19838],{},[898,19835,2312],{},[1701,19837,7491],{},[1850,19839,1852],{},[902,19841,16548],{"encoding":904},"; ",[38,19844,16573],{}," funkce úrokové míry.",[123,19847,19848,19851,19852,19873,19874,19891],{},[38,19849,19850],{},"Trh zboží"," — rovnováha ",[883,19853,19855],{"className":19854},[886],[888,19856,19857],{"xmlns":890},[892,19858,19859,19871],{},[895,19860,19861,19863,19865,19867,19869],{},[898,19862,13189],{},[1701,19864,1792],{},[898,19866,1658],{},[1701,19868,1703],{},[898,19870,16238],{},[902,19872,18797],{"encoding":904},", ekvivalentně ",[883,19875,19877],{"className":19876},[886],[888,19878,19879],{"xmlns":890},[892,19880,19881,19889],{},[895,19882,19883,19885,19887],{},[898,19884,16238],{},[1701,19886,1792],{},[898,19888,1661],{},[902,19890,16766],{"encoding":904}," (investice = úspory).",[123,19893,19894,1646,19897,19899,19900,19950,19951,16969,19953,1715],{},[38,19895,19896],{},"Křivka IS",[614,19898,16109],{},") — ",[883,19901,19903],{"className":19902},[886],[888,19904,19905],{"xmlns":890},[892,19906,19907,19947],{},[895,19908,19909,19911,19913,19925,19927,19929],{},[898,19910,13189],{},[1701,19912,1792],{},[3726,19914,19915,19917],{},[898,19916,3618],{},[895,19918,19919,19921,19923],{},[1850,19920,4062],{},[1701,19922,2317],{},[898,19924,207],{},[898,19926,16096],{},[1701,19928,1703],{},[3726,19930,19931,19939],{},[895,19932,19933,19935,19937],{},[898,19934,3598],{},[1701,19936,1703],{},[898,19938,2312],{},[895,19940,19941,19943,19945],{},[1850,19942,4062],{},[1701,19944,2317],{},[898,19946,207],{},[902,19948,19949],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,19952,16573],{},[883,19954,19956],{"className":19955},[886],[888,19957,19958],{"xmlns":890},[892,19959,19960,19972],{},[895,19961,19962,19964,19966,19968,19970],{},[1701,19963,1799],{"stretchy":1798},[898,19965,16096],{},[1701,19967,2012],{"separator":2011},[898,19969,13189],{},[1701,19971,1805],{"stretchy":1798},[902,19973,16991],{"encoding":904},[123,19975,19976,19851,19979,20005,20006,1715],{},[38,19977,19978],{},"Trh peněz",[883,19980,19982],{"className":19981},[886],[888,19983,19984],{"xmlns":890},[892,19985,19986,20002],{},[895,19987,19988,19994,19996],{},[3243,19989,19990,19992],{},[898,19991,6909],{},[898,19993,1795],{},[1701,19995,1792],{},[3243,19997,19998,20000],{},[898,19999,6909],{},[898,20001,1661],{},[902,20003,20004],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,20007,20009],{"className":20008},[886],[888,20010,20011],{"xmlns":890},[892,20012,20013,20021],{},[895,20014,20015],{},[3243,20016,20017,20019],{},[898,20018,6909],{},[1701,20020,8424],{},[902,20022,20023],{"encoding":904},"M^* ",[123,20025,20026,2979,20029,1715],{},[38,20027,20028],{},"Transakční, opatrnostní, spekulační poptávka",[883,20030,20032],{"className":20031},[886],[888,20033,20034],{"xmlns":890},[892,20035,20036,20088],{},[895,20037,20038,20044,20046,20052,20054,20060,20062,20068,20070,20072,20078,20080,20082],{},[3243,20039,20040,20042],{},[898,20041,6909],{},[898,20043,1795],{},[1701,20045,1792],{},[1845,20047,20048,20050],{},[898,20049,13853],{},[1850,20051,4062],{},[1701,20053,1703],{},[1845,20055,20056,20058],{},[898,20057,13853],{},[1850,20059,3938],{},[1701,20061,1792],{},[1845,20063,20064,20066],{},[898,20065,17291],{},[1850,20067,4062],{},[898,20069,13189],{},[1701,20071,1703],{},[1845,20073,20074,20076],{},[898,20075,17291],{},[1850,20077,3938],{},[898,20079,16096],{},[1701,20081,1703],{},[1845,20083,20084,20086],{},[898,20085,17291],{},[1850,20087,3646],{},[902,20089,20090],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,20092,20093,1646,20096,19899,20098,20144,20145,20147],{},[38,20094,20095],{},"Křivka LM",[614,20097,16116],{},[883,20099,20101],{"className":20100},[886],[888,20102,20103],{"xmlns":890},[892,20104,20105,20141],{},[895,20106,20107,20113,20115,20121,20123,20125,20131,20133,20135],{},[3243,20108,20109,20111],{},[898,20110,6909],{},[1701,20112,8424],{},[1701,20114,1792],{},[1845,20116,20117,20119],{},[898,20118,17291],{},[1850,20120,4062],{},[898,20122,13189],{},[1701,20124,1703],{},[1845,20126,20127,20129],{},[898,20128,17291],{},[1850,20130,3938],{},[898,20132,16096],{},[1701,20134,1703],{},[1845,20136,20137,20139],{},[898,20138,17291],{},[1850,20140,3646],{},[902,20142,20143],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,20146,17711],{}," přímka.",[123,20149,20150,20153,20154,20188],{},[38,20151,20152],{},"Simultánní rovnováha"," — průsečík ",[883,20155,20157],{"className":20156},[886],[888,20158,20159],{"xmlns":890},[892,20160,20161,20185],{},[895,20162,20163,20165,20167,20169,20175,20177,20183],{},[898,20164,3249],{},[1701,20166,1792],{},[1701,20168,1799],{"stretchy":1798},[3243,20170,20171,20173],{},[898,20172,16096],{},[898,20174,3249],{},[1701,20176,2012],{"separator":2011},[3243,20178,20179,20181],{},[898,20180,13189],{},[898,20182,3249],{},[1701,20184,1805],{"stretchy":1798},[902,20186,20187],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,20190,20191,20194,20195,1343,20208,20221],{},[38,20192,20193],{},"Fiskální politika"," — nástroje ",[883,20196,20198],{"className":20197},[886],[888,20199,20200],{"xmlns":890},[892,20201,20202,20206],{},[895,20203,20204],{},[898,20205,16167],{},[902,20207,16167],{"encoding":904},[883,20209,20211],{"className":20210},[886],[888,20212,20213],{"xmlns":890},[892,20214,20215,20219],{},[895,20216,20217],{},[898,20218,5877],{},[902,20220,5877],{"encoding":904}," posouvající křivku IS.",[123,20223,20224,20227,20228,20245],{},[38,20225,20226],{},"Monetární politika"," — nástroj ",[883,20229,20231],{"className":20230},[886],[888,20232,20233],{"xmlns":890},[892,20234,20235,20243],{},[895,20236,20237],{},[3243,20238,20239,20241],{},[898,20240,6909],{},[1701,20242,8424],{},[902,20244,16204],{"encoding":904}," posouvající křivku LM.",[115,20247,5984],{"id":5983},[120,20249,20250,20257,20266,20275],{},[123,20251,20252,4088,20254],{},[38,20253,6031],{},[207,20255,6037],{"className":20256,"dataFsResolvedFilePath":6035,"href":6036},[210],[123,20258,20259,4088,20262],{},[38,20260,20261],{},"Přednáška:",[207,20263,20265],{"className":20264,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,20267,20268,4088,20270,20274],{},[38,20269,5991],{},[207,20271,20273],{"className":20272,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,20276,20277,20279],{},[38,20278,6013],{},[120,20280,20281,20287,20293],{},[123,20282,20283,20286],{},[207,20284,6071],{"className":20285,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,20288,20289,20292],{},[207,20290,1145],{"className":20291,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,20294,20295,20299],{},[207,20296,20298],{"className":20297,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":20301},[20302,20303,20304,20305,20306,20307,20308,20309,20310,20311],{"id":16060,"depth":642,"text":16061},{"id":16214,"depth":642,"text":16215},{"id":16429,"depth":642,"text":16430},{"id":16722,"depth":642,"text":16723},{"id":17135,"depth":642,"text":17136},{"id":17928,"depth":642,"text":17929},{"id":18617,"depth":642,"text":18618},{"id":19522,"depth":642,"text":19523},{"id":5577,"depth":642,"text":5578},{"id":5983,"depth":642,"text":5984},{},"\u002Ftopics\u002Fis-lm",{"title":16052,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,20318,1143,20319,20320,20321,20322,20273],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":20325,"title":20326,"body":20327,"course":659,"courses":21920,"created":1129,"description":21921,"extension":661,"meta":21922,"navigation":664,"path":21923,"seo":21924,"sources":21925,"stem":21926,"tags":21927,"type":6074,"updated":677,"__hash__":21930},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":20328,"toc":21908},[20329,20332,20428,20435,20455,20459,20464,20527,20546,20548,20551,20687,20689,20899,20933,21070,21074,21138,21154,21182,21186,21284,21288,21292,21345,21451,21665,21669,21712,21818,21870,21872],[12,20330,20326],{"id":20331},"lagrangeova-metoda-vázané-extrémy",[724,20333,20334,20335,1889,20358,20390,20391,20394,20395,20422,20423,20427],{},"Hledáme extrém funkce ",[883,20336,20338],{"className":20337},[886],[888,20339,20340],{"xmlns":890},[892,20341,20342,20356],{},[895,20343,20344,20346,20348,20350,20352,20354],{},[898,20345,6132],{},[1701,20347,1799],{"stretchy":1798},[898,20349,6137],{},[1701,20351,2012],{"separator":2011},[898,20353,6127],{},[1701,20355,1805],{"stretchy":1798},[902,20357,13901],{"encoding":904},[883,20359,20361],{"className":20360},[886],[888,20362,20363],{"xmlns":890},[892,20364,20365,20387],{},[895,20366,20367,20369,20371,20377,20379,20385],{},[898,20368,900],{},[1701,20370,1799],{"stretchy":1798},[1845,20372,20373,20375],{},[898,20374,1802],{},[1850,20376,4062],{},[1701,20378,2012],{"separator":2011},[1845,20380,20381,20383],{},[898,20382,1802],{},[1850,20384,3938],{},[1701,20386,1805],{"stretchy":1798},[902,20388,20389],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,20392,20393],{},"podmíněný"," rovnicí ",[883,20396,20398],{"className":20397},[886],[888,20399,20400],{"xmlns":890},[892,20401,20402,20420],{},[895,20403,20404,20406,20408,20410,20412,20414,20416,20418],{},[898,20405,15097],{},[1701,20407,1799],{"stretchy":1798},[898,20409,6137],{},[1701,20411,2012],{"separator":2011},[898,20413,6127],{},[1701,20415,1805],{"stretchy":1798},[1701,20417,1792],{},[1850,20419,1852],{},[902,20421,15114],{"encoding":904},". V ",[207,20424,20426],{"className":20425,"dataFsResolvedFilePath":6035,"href":6036},[210],"matematické ekonomii"," se používá pro:",[724,20429,20430],{},[2139,20431],{"alt":20432,"className":20433,"src":20434},"imek-lagrange-tecnost",[210,2143],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,20436,20437,20446,20452],{},[123,20438,20439,20442,20443,1805],{},[38,20440,20441],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,20444,13831],{"className":20445,"dataFsResolvedFilePath":878,"href":879},[210],[123,20447,20448,20451],{},[38,20449,20450],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,20453,20454],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,20456,20458],{"id":20457},"princip","Princip",[724,20460,14763,20461,2246],{},[38,20462,20463],{},"Lagrangeovu funkci",[724,20465,20466],{},[883,20467,20469],{"className":20468},[886],[888,20470,20471],{"xmlns":890},[892,20472,20473,20524],{},[895,20474,20475,20477,20479,20481,20483,20485,20487,20490,20492,20494,20496,20498,20500,20502,20504,20506,20508,20510,20512,20514,20516,20518,20520,20522],{},[898,20476,13853],{},[1701,20478,1799],{"stretchy":1798},[898,20480,6137],{},[1701,20482,2012],{"separator":2011},[898,20484,6127],{},[1701,20486,2012],{"separator":2011},[898,20488,20489],{},"λ",[1701,20491,1805],{"stretchy":1798},[1701,20493,1792],{},[898,20495,6132],{},[1701,20497,1799],{"stretchy":1798},[898,20499,6137],{},[1701,20501,2012],{"separator":2011},[898,20503,6127],{},[1701,20505,1805],{"stretchy":1798},[1701,20507,1703],{},[898,20509,20489],{},[1939,20511,1941],{},[898,20513,15097],{},[1701,20515,1799],{"stretchy":1798},[898,20517,6137],{},[1701,20519,2012],{"separator":2011},[898,20521,6127],{},[1701,20523,1805],{"stretchy":1798},[902,20525,20526],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,20528,8380,20529,12164,20543,1715],{},[883,20530,20532],{"className":20531},[886],[888,20533,20534],{"xmlns":890},[892,20535,20536,20540],{},[895,20537,20538],{},[898,20539,20489],{},[902,20541,20542],{"encoding":904},"\\lambda",[38,20544,20545],{},"Lagrangeův multiplikátor",[115,20547,7335],{"id":7334},[724,20549,20550],{},"Řešíme soustavu:",[724,20552,20553,20601,20649],{},[883,20554,20556],{"className":20555},[886],[888,20557,20558],{"xmlns":890},[892,20559,20560,20598],{},[895,20561,20562,20570,20572,20580,20582,20584,20586,20594,20596],{},[2287,20563,20564,20566,20568],{},[898,20565,13853],{},[898,20567,6137],{},[1701,20569,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,20571,1792],{},[2287,20573,20574,20576,20578],{},[898,20575,6132],{},[898,20577,6137],{},[1701,20579,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,20581,1703],{},[898,20583,20489],{},[1939,20585,1941],{},[2287,20587,20588,20590,20592],{},[898,20589,15097],{},[898,20591,6137],{},[1701,20593,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,20595,1792],{},[1850,20597,1852],{},[902,20599,20600],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,20602,20604],{"className":20603},[886],[888,20605,20606],{"xmlns":890},[892,20607,20608,20646],{},[895,20609,20610,20618,20620,20628,20630,20632,20634,20642,20644],{},[2287,20611,20612,20614,20616],{},[898,20613,13853],{},[898,20615,6127],{},[1701,20617,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,20619,1792],{},[2287,20621,20622,20624,20626],{},[898,20623,6132],{},[898,20625,6127],{},[1701,20627,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,20629,1703],{},[898,20631,20489],{},[1939,20633,1941],{},[2287,20635,20636,20638,20640],{},[898,20637,15097],{},[898,20639,6127],{},[1701,20641,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,20643,1792],{},[1850,20645,1852],{},[902,20647,20648],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,20650,20652],{"className":20651},[886],[888,20653,20654],{"xmlns":890},[892,20655,20656,20684],{},[895,20657,20658,20666,20668,20670,20672,20674,20676,20678,20680,20682],{},[2287,20659,20660,20662,20664],{},[898,20661,13853],{},[898,20663,20489],{},[1701,20665,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,20667,1792],{},[898,20669,15097],{},[1701,20671,1799],{"stretchy":1798},[898,20673,6137],{},[1701,20675,2012],{"separator":2011},[898,20677,6127],{},[1701,20679,1805],{"stretchy":1798},[1701,20681,1792],{},[1850,20683,1852],{},[902,20685,20686],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,20688,7409],{"id":7408},[724,20690,20691],{},[883,20692,20694],{"className":20693},[886],[888,20695,20696],{"xmlns":890},[892,20697,20698,20896],{},[895,20699,20700,20702,20704,20706,20708,20710,20712,20714,20716,20718,20720,20736,20738,20740,20756,20758,20760,20768,20774,20776,20778,20794,20796,20798,20814,20816,20818,20826,20832,20834,20836,20838,20854,20856,20858,20874,20876,20878,20886,20888],{},[898,20701,1795],{},[1701,20703,1799],{"stretchy":1798},[898,20705,6137],{},[1701,20707,2012],{"separator":2011},[898,20709,6127],{},[1701,20711,2012],{"separator":2011},[898,20713,20489],{},[1701,20715,1805],{"stretchy":1798},[1701,20717,1792],{},[1701,20719,1799],{"stretchy":1798},[2287,20721,20722,20724,20730],{},[898,20723,6132],{},[895,20725,20726,20728],{},[898,20727,6137],{},[898,20729,6137],{},[895,20731,20732,20734],{},[1701,20733,4783],{"mathvariant":2334},[1701,20735,4783],{"mathvariant":2334},[1701,20737,1703],{},[898,20739,20489],{},[2287,20741,20742,20744,20750],{},[898,20743,15097],{},[895,20745,20746,20748],{},[898,20747,6137],{},[898,20749,6137],{},[895,20751,20752,20754],{},[1701,20753,4783],{"mathvariant":2334},[1701,20755,4783],{"mathvariant":2334},[1701,20757,1805],{"stretchy":1798},[1701,20759,1799],{"stretchy":1798},[2287,20761,20762,20764,20766],{},[898,20763,15097],{},[898,20765,6127],{},[1701,20767,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[3243,20769,20770,20772],{},[1701,20771,1805],{"stretchy":1798},[1850,20773,3938],{},[1701,20775,1703],{},[1701,20777,1799],{"stretchy":1798},[2287,20779,20780,20782,20788],{},[898,20781,6132],{},[895,20783,20784,20786],{},[898,20785,6127],{},[898,20787,6127],{},[895,20789,20790,20792],{},[1701,20791,4783],{"mathvariant":2334},[1701,20793,4783],{"mathvariant":2334},[1701,20795,1703],{},[898,20797,20489],{},[2287,20799,20800,20802,20808],{},[898,20801,15097],{},[895,20803,20804,20806],{},[898,20805,6127],{},[898,20807,6127],{},[895,20809,20810,20812],{},[1701,20811,4783],{"mathvariant":2334},[1701,20813,4783],{"mathvariant":2334},[1701,20815,1805],{"stretchy":1798},[1701,20817,1799],{"stretchy":1798},[2287,20819,20820,20822,20824],{},[898,20821,15097],{},[898,20823,6137],{},[1701,20825,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[3243,20827,20828,20830],{},[1701,20829,1805],{"stretchy":1798},[1850,20831,3938],{},[1701,20833,2317],{},[1850,20835,3938],{},[1701,20837,1799],{"stretchy":1798},[2287,20839,20840,20842,20848],{},[898,20841,6132],{},[895,20843,20844,20846],{},[898,20845,6137],{},[898,20847,6127],{},[895,20849,20850,20852],{},[1701,20851,4783],{"mathvariant":2334},[1701,20853,4783],{"mathvariant":2334},[1701,20855,1703],{},[898,20857,20489],{},[2287,20859,20860,20862,20868],{},[898,20861,15097],{},[895,20863,20864,20866],{},[898,20865,6137],{},[898,20867,6127],{},[895,20869,20870,20872],{},[1701,20871,4783],{"mathvariant":2334},[1701,20873,4783],{"mathvariant":2334},[1701,20875,1805],{"stretchy":1798},[1939,20877,1941],{},[2287,20879,20880,20882,20884],{},[898,20881,15097],{},[898,20883,6137],{},[1701,20885,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,20887,1941],{},[2287,20889,20890,20892,20894],{},[898,20891,15097],{},[898,20893,6127],{},[1701,20895,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,20897,20898],{"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",[724,20900,20901,20902,20932],{},"Je-li ",[883,20903,20905],{"className":20904},[886],[888,20906,20907],{"xmlns":890},[892,20908,20909,20929],{},[895,20910,20911,20913,20915,20917,20919,20921,20927],{},[1701,20912,2036],{"stretchy":1798},[898,20914,207],{},[1701,20916,2012],{"separator":2011},[898,20918,3598],{},[1701,20920,2012],{"separator":2011},[1845,20922,20923,20925],{},[898,20924,20489],{},[1850,20926,1852],{},[1701,20928,2053],{"stretchy":1798},[902,20930,20931],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,20934,20935,21003],{},[123,20936,20937,7497,20973,20975,20976],{},[883,20938,20940],{"className":20939},[886],[888,20941,20942],{"xmlns":890},[892,20943,20944,20970],{},[895,20945,20946,20948,20950,20952,20954,20956,20958,20964,20966,20968],{},[898,20947,1795],{},[1701,20949,1799],{"stretchy":1798},[898,20951,207],{},[1701,20953,2012],{"separator":2011},[898,20955,3598],{},[1701,20957,2012],{"separator":2011},[1845,20959,20960,20962],{},[898,20961,20489],{},[1850,20963,1852],{},[1701,20965,1805],{"stretchy":1798},[1701,20967,7530],{},[1850,20969,1852],{},[902,20971,20972],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,20974,7800],{}," vázané podmínkou ",[883,20977,20979],{"className":20978},[886],[888,20980,20981],{"xmlns":890},[892,20982,20983,21001],{},[895,20984,20985,20987,20989,20991,20993,20995,20997,20999],{},[898,20986,15097],{},[1701,20988,1799],{"stretchy":1798},[898,20990,6137],{},[1701,20992,2012],{"separator":2011},[898,20994,6127],{},[1701,20996,1805],{"stretchy":1798},[1701,20998,1792],{},[1850,21000,1852],{},[902,21002,15114],{"encoding":904},[123,21004,21005,7497,21041,20975,21043],{},[883,21006,21008],{"className":21007},[886],[888,21009,21010],{"xmlns":890},[892,21011,21012,21038],{},[895,21013,21014,21016,21018,21020,21022,21024,21026,21032,21034,21036],{},[898,21015,1795],{},[1701,21017,1799],{"stretchy":1798},[898,21019,207],{},[1701,21021,2012],{"separator":2011},[898,21023,3598],{},[1701,21025,2012],{"separator":2011},[1845,21027,21028,21030],{},[898,21029,20489],{},[1850,21031,1852],{},[1701,21033,1805],{"stretchy":1798},[1701,21035,7491],{},[1850,21037,1852],{},[902,21039,21040],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,21042,7858],{},[883,21044,21046],{"className":21045},[886],[888,21047,21048],{"xmlns":890},[892,21049,21050,21068],{},[895,21051,21052,21054,21056,21058,21060,21062,21064,21066],{},[898,21053,15097],{},[1701,21055,1799],{"stretchy":1798},[898,21057,6137],{},[1701,21059,2012],{"separator":2011},[898,21061,6127],{},[1701,21063,1805],{"stretchy":1798},[1701,21065,1792],{},[1850,21067,1852],{},[902,21069,15114],{"encoding":904},[115,21071,21073],{"id":21072},"význam-multiplikátoru","Význam multiplikátoru",[724,21075,21076],{},[883,21077,21079],{"className":21078},[886],[888,21080,21081],{"xmlns":890},[892,21082,21083,21135],{},[895,21084,21085,21087,21089,21111,21113],{},[898,21086,20489],{},[1701,21088,1792],{},[3726,21090,21091,21099],{},[2287,21092,21093,21095,21097],{},[898,21094,6132],{},[898,21096,6137],{},[1701,21098,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[895,21100,21101,21103],{},[1701,21102,2317],{},[2287,21104,21105,21107,21109],{},[898,21106,15097],{},[898,21108,6137],{},[1701,21110,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,21112,1792],{},[3726,21114,21115,21123],{},[2287,21116,21117,21119,21121],{},[898,21118,6132],{},[898,21120,6127],{},[1701,21122,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[895,21124,21125,21127],{},[1701,21126,2317],{},[2287,21128,21129,21131,21133],{},[898,21130,15097],{},[898,21132,6127],{},[1701,21134,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,21136,21137],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,21139,21140,21153],{},[883,21141,21143],{"className":21142},[886],[888,21144,21145],{"xmlns":890},[892,21146,21147,21151],{},[895,21148,21149],{},[898,21150,20489],{},[902,21152,20542],{"encoding":904}," udává:",[120,21155,21156,21162],{},[123,21157,21158,21159],{},"konstantní ",[38,21160,21161],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,21163,21164,21167,21168,21181],{},[38,21165,21166],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,21169,21171],{"className":21170},[886],[888,21172,21173],{"xmlns":890},[892,21174,21175,21179],{},[895,21176,21177],{},[898,21178,6132],{},[902,21180,6132],{"encoding":904},", uvolní-li se omezení o jednotku",[115,21183,21185],{"id":21184},"alternativní-postup","Alternativní postup",[724,21187,21188,21189,21216,21217,21241,21242,21266,21267,21280,21281,1715],{},"Lze-li z ",[883,21190,21192],{"className":21191},[886],[888,21193,21194],{"xmlns":890},[892,21195,21196,21214],{},[895,21197,21198,21200,21202,21204,21206,21208,21210,21212],{},[898,21199,15097],{},[1701,21201,1799],{"stretchy":1798},[898,21203,6137],{},[1701,21205,2012],{"separator":2011},[898,21207,6127],{},[1701,21209,1805],{"stretchy":1798},[1701,21211,1792],{},[1850,21213,1852],{},[902,21215,15114],{"encoding":904}," vyjádřit ",[883,21218,21220],{"className":21219},[886],[888,21221,21222],{"xmlns":890},[892,21223,21224,21238],{},[895,21225,21226,21228,21230,21232,21234,21236],{},[898,21227,6127],{},[1701,21229,1792],{},[898,21231,6127],{},[1701,21233,1799],{"stretchy":1798},[898,21235,6137],{},[1701,21237,1805],{"stretchy":1798},[902,21239,21240],{"encoding":904},"y = y(x)"," (nebo ",[883,21243,21245],{"className":21244},[886],[888,21246,21247],{"xmlns":890},[892,21248,21249,21263],{},[895,21250,21251,21253,21255,21257,21259,21261],{},[898,21252,6137],{},[1701,21254,1792],{},[898,21256,6137],{},[1701,21258,1799],{"stretchy":1798},[898,21260,6127],{},[1701,21262,1805],{"stretchy":1798},[902,21264,21265],{"encoding":904},"x = x(y)","), dosadíme do ",[883,21268,21270],{"className":21269},[886],[888,21271,21272],{"xmlns":890},[892,21273,21274,21278],{},[895,21275,21276],{},[898,21277,6132],{},[902,21279,6132],{"encoding":904}," a převedeme na ",[38,21282,21283],{},"extrém funkce jedné proměnné",[115,21285,21287],{"id":21286},"použití-v-imek","Použití v ImeK",[198,21289,21291],{"id":21290},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,21293,21294,21295,1715],{},"Rozpočtové omezení: ",[883,21296,21298],{"className":21297},[886],[888,21299,21300],{"xmlns":890},[892,21301,21302,21342],{},[895,21303,21304,21310,21312,21320,21326,21328,21336],{},[3243,21305,21306,21308],{},[898,21307,13189],{},[1701,21309,8424],{},[1701,21311,1792],{},[2287,21313,21314,21316,21318],{},[898,21315,1680],{},[1850,21317,4062],{},[1701,21319,8424],{},[1845,21321,21322,21324],{},[898,21323,1802],{},[1850,21325,4062],{},[1701,21327,1703],{},[2287,21329,21330,21332,21334],{},[898,21331,1680],{},[1850,21333,3938],{},[1701,21335,8424],{},[1845,21337,21338,21340],{},[898,21339,1802],{},[1850,21341,3938],{},[902,21343,21344],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,21346,21347],{},[883,21348,21350],{"className":21349},[886],[888,21351,21352],{"xmlns":890},[892,21353,21354,21448],{},[895,21355,21356,21358,21360,21366,21368,21374,21376,21378,21380,21382,21384,21386,21392,21394,21400,21402,21404,21406,21408,21414,21416,21424,21430,21432,21440,21446],{},[898,21357,13853],{},[1701,21359,1799],{"stretchy":1798},[1845,21361,21362,21364],{},[898,21363,1802],{},[1850,21365,4062],{},[1701,21367,2012],{"separator":2011},[1845,21369,21370,21372],{},[898,21371,1802],{},[1850,21373,3938],{},[1701,21375,2012],{"separator":2011},[898,21377,20489],{},[1701,21379,1805],{"stretchy":1798},[1701,21381,1792],{},[898,21383,900],{},[1701,21385,1799],{"stretchy":1798},[1845,21387,21388,21390],{},[898,21389,1802],{},[1850,21391,4062],{},[1701,21393,2012],{"separator":2011},[1845,21395,21396,21398],{},[898,21397,1802],{},[1850,21399,3938],{},[1701,21401,1805],{"stretchy":1798},[1701,21403,1703],{},[898,21405,20489],{},[1701,21407,1799],{"stretchy":1798},[3243,21409,21410,21412],{},[898,21411,13189],{},[1701,21413,8424],{},[1701,21415,2317],{},[2287,21417,21418,21420,21422],{},[898,21419,1680],{},[1850,21421,4062],{},[1701,21423,8424],{},[1845,21425,21426,21428],{},[898,21427,1802],{},[1850,21429,4062],{},[1701,21431,2317],{},[2287,21433,21434,21436,21438],{},[898,21435,1680],{},[1850,21437,3938],{},[1701,21439,8424],{},[1845,21441,21442,21444],{},[898,21443,1802],{},[1850,21445,3938],{},[1701,21447,1805],{"stretchy":1798},[902,21449,21450],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,21452,21453,21454,1343,21486,1343,21518,21567,21568,21622,21623,1715],{},"Soustava: ",[883,21455,21457],{"className":21456},[886],[888,21458,21459],{"xmlns":890},[892,21460,21461,21483],{},[895,21462,21463,21471,21473,21475],{},[2287,21464,21465,21467,21469],{},[898,21466,900],{},[1850,21468,4062],{},[1701,21470,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,21472,1792],{},[898,21474,20489],{},[2287,21476,21477,21479,21481],{},[898,21478,1680],{},[1850,21480,4062],{},[1701,21482,8424],{},[902,21484,21485],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,21487,21489],{"className":21488},[886],[888,21490,21491],{"xmlns":890},[892,21492,21493,21515],{},[895,21494,21495,21503,21505,21507],{},[2287,21496,21497,21499,21501],{},[898,21498,900],{},[1850,21500,3938],{},[1701,21502,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,21504,1792],{},[898,21506,20489],{},[2287,21508,21509,21511,21513],{},[898,21510,1680],{},[1850,21512,3938],{},[1701,21514,8424],{},[902,21516,21517],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,21519,21521],{"className":21520},[886],[888,21522,21523],{"xmlns":890},[892,21524,21525,21565],{},[895,21526,21527,21533,21535,21543,21549,21551,21559],{},[3243,21528,21529,21531],{},[898,21530,13189],{},[1701,21532,8424],{},[1701,21534,1792],{},[2287,21536,21537,21539,21541],{},[898,21538,1680],{},[1850,21540,4062],{},[1701,21542,8424],{},[1845,21544,21545,21547],{},[898,21546,1802],{},[1850,21548,4062],{},[1701,21550,1703],{},[2287,21552,21553,21555,21557],{},[898,21554,1680],{},[1850,21556,3938],{},[1701,21558,8424],{},[1845,21560,21561,21563],{},[898,21562,1802],{},[1850,21564,3938],{},[902,21566,21344],{"encoding":904},". Z prvních dvou: ",[883,21569,21571],{"className":21570},[886],[888,21572,21573],{"xmlns":890},[892,21574,21575,21619],{},[895,21576,21577,21597,21599],{},[2363,21578,21579],{"scriptlevel":1852,"displaystyle":1798},[3726,21580,21581,21589],{},[2287,21582,21583,21585,21587],{},[898,21584,900],{},[1850,21586,4062],{},[1701,21588,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,21590,21591,21593,21595],{},[898,21592,900],{},[1850,21594,3938],{},[1701,21596,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,21598,1792],{},[2363,21600,21601],{"scriptlevel":1852,"displaystyle":1798},[3726,21602,21603,21611],{},[2287,21604,21605,21607,21609],{},[898,21606,1680],{},[1850,21608,4062],{},[1701,21610,8424],{},[2287,21612,21613,21615,21617],{},[898,21614,1680],{},[1850,21616,3938],{},[1701,21618,8424],{},[902,21620,21621],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,21624,21626],{"className":21625},[886],[888,21627,21628],{"xmlns":890},[892,21629,21630,21662],{},[895,21631,21632,21634,21636,21638,21640,21642],{},[898,21633,6909],{},[898,21635,8068],{},[898,21637,1658],{},[898,21639,1661],{},[1701,21641,1792],{},[2363,21643,21644],{"scriptlevel":1852,"displaystyle":1798},[3726,21645,21646,21654],{},[2287,21647,21648,21650,21652],{},[898,21649,1680],{},[1850,21651,4062],{},[1701,21653,8424],{},[2287,21655,21656,21658,21660],{},[898,21657,1680],{},[1850,21659,3938],{},[1701,21661,8424],{},[902,21663,21664],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,21666,21668],{"id":21667},"minimalizace-výdajů","Minimalizace výdajů",[724,21670,21671,21672,1715],{},"Podmínka dané užitečnosti ",[883,21673,21675],{"className":21674},[886],[888,21676,21677],{"xmlns":890},[892,21678,21679,21709],{},[895,21680,21681,21687,21689,21691,21693,21699,21701,21707],{},[3243,21682,21683,21685],{},[898,21684,900],{},[1701,21686,8424],{},[1701,21688,1792],{},[898,21690,900],{},[1701,21692,1799],{"stretchy":1798},[1845,21694,21695,21697],{},[898,21696,1802],{},[1850,21698,4062],{},[1701,21700,2012],{"separator":2011},[1845,21702,21703,21705],{},[898,21704,1802],{},[1850,21706,3938],{},[1701,21708,1805],{"stretchy":1798},[902,21710,21711],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,21713,21714],{},[883,21715,21717],{"className":21716},[886],[888,21718,21719],{"xmlns":890},[892,21720,21721,21815],{},[895,21722,21723,21725,21727,21733,21735,21741,21743,21745,21747,21749,21757,21763,21765,21773,21779,21781,21783,21785,21791,21793,21795,21797,21803,21805,21811,21813],{},[898,21724,13853],{},[1701,21726,1799],{"stretchy":1798},[1845,21728,21729,21731],{},[898,21730,1802],{},[1850,21732,4062],{},[1701,21734,2012],{"separator":2011},[1845,21736,21737,21739],{},[898,21738,1802],{},[1850,21740,3938],{},[1701,21742,2012],{"separator":2011},[898,21744,20489],{},[1701,21746,1805],{"stretchy":1798},[1701,21748,1792],{},[2287,21750,21751,21753,21755],{},[898,21752,1680],{},[1850,21754,4062],{},[1701,21756,8424],{},[1845,21758,21759,21761],{},[898,21760,1802],{},[1850,21762,4062],{},[1701,21764,1703],{},[2287,21766,21767,21769,21771],{},[898,21768,1680],{},[1850,21770,3938],{},[1701,21772,8424],{},[1845,21774,21775,21777],{},[898,21776,1802],{},[1850,21778,3938],{},[1701,21780,1703],{},[898,21782,20489],{},[1701,21784,1799],{"stretchy":1798},[3243,21786,21787,21789],{},[898,21788,900],{},[1701,21790,8424],{},[1701,21792,2317],{},[898,21794,900],{},[1701,21796,1799],{"stretchy":1798},[1845,21798,21799,21801],{},[898,21800,1802],{},[1850,21802,4062],{},[1701,21804,2012],{"separator":2011},[1845,21806,21807,21809],{},[898,21808,1802],{},[1850,21810,3938],{},[1701,21812,1805],{"stretchy":1798},[1701,21814,1805],{"stretchy":1798},[902,21816,21817],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,21819,21820,21821,1715],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,21822,21824],{"className":21823},[886],[888,21825,21826],{"xmlns":890},[892,21827,21828,21867],{},[895,21829,21830,21837,21839,21845,21847,21853,21855,21861,21863,21865],{},[1845,21831,21832,21834],{},[898,21833,1802],{},[898,21835,21836],{},"i",[1701,21838,1792],{},[1845,21840,21841,21843],{},[898,21842,1795],{},[898,21844,21836],{},[1701,21846,1799],{"stretchy":1798},[1845,21848,21849,21851],{},[898,21850,1680],{},[1850,21852,4062],{},[1701,21854,2012],{"separator":2011},[1845,21856,21857,21859],{},[898,21858,1680],{},[1850,21860,3938],{},[1701,21862,2012],{"separator":2011},[898,21864,900],{},[1701,21866,1805],{"stretchy":1798},[902,21868,21869],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,21871,5984],{"id":5983},[120,21873,21874,21881,21888,21897],{},[123,21875,21876,4088,21878],{},[38,21877,7880],{},[207,21879,784],{"className":21880,"dataFsResolvedFilePath":782,"href":783},[210],[123,21882,21883,4088,21885],{},[38,21884,7888],{},[207,21886,15996],{"className":21887,"dataFsResolvedFilePath":800,"href":801},[210],[123,21889,21890,4088,21893,21896],{},[38,21891,21892],{},"Aplikace v kurzu:",[207,21894,880],{"className":21895,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,21898,21899,4088,21901,1343,21904,21907],{},[38,21900,7896],{},[207,21902,936],{"className":21903,"dataFsResolvedFilePath":934,"href":935},[210],[207,21905,1400],{"className":21906,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":21909},[21910,21911,21912,21913,21914,21915,21919],{"id":20457,"depth":642,"text":20458},{"id":7334,"depth":642,"text":7335},{"id":7408,"depth":642,"text":7409},{"id":21072,"depth":642,"text":21073},{"id":21184,"depth":642,"text":21185},{"id":21286,"depth":642,"text":21287,"children":21916},[21917,21918],{"id":21290,"depth":649,"text":21291},{"id":21667,"depth":649,"text":21668},{"id":5983,"depth":642,"text":5984},[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":20326,"description":21921},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,21928,21929],"vazane-extremy","multiplikator","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":21932,"title":936,"body":21933,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":31792,"navigation":664,"path":31793,"seo":31794,"sources":31795,"stem":31796,"tags":31797,"type":6074,"updated":677,"__hash__":31801},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":21934,"toc":31754},[21935,21938,21940,22063,22198,22202,22205,22318,22322,22350,22397,22400,22466,22511,22514,22540,22571,22575,22579,22623,22667,22729,22784,22787,22791,22794,22841,22938,23044,23050,23127,23156,23295,23299,23328,23377,23524,23614,23618,23644,23682,23709,23747,23809,23884,23962,24020,24086,24130,24134,24191,24240,24285,24498,24618,24624,24628,24651,24655,24662,24666,24697,24732,24736,24786,24871,24913,24934,24996,25056,25060,25131,25199,25271,25386,25434,25438,25441,25482,25521,25544,25657,25821,25829,25856,25886,25889,25966,26119,26203,26542,26546,26670,26806,26941,26994,26997,27247,27327,27331,27334,27392,27424,27427,27476,27479,27550,27746,27750,27901,28131,28169,28222,28268,28271,28327,28376,28580,28670,28674,28690,28697,28866,28870,28941,29022,29103,29182,29327,29415,29419,29602,29733,29778,29875,29879,30618,30620,31671,31673],[12,21936,936],{"id":21937},"národní-důchod",[115,21939,16061],{"id":16060},[724,21941,21942,21943,4088,21947,21950,21951,4088,21954,21967,21968,21971,21972,21975,21976,21979,21980,21982,21983,4088,21985,22002,22003,22020,22021,22024,22025,2506],{},"Kapitola 7 ",[207,21944,21946],{"className":21945,"dataFsResolvedFilePath":6035,"href":6036},[210],"Matematické ekonomie",[38,21948,21949],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,21952,21953],{},"národním důchodem",[883,21955,21957],{"className":21956},[886],[888,21958,21959],{"xmlns":890},[892,21960,21961,21965],{},[895,21962,21963],{},[898,21964,13189],{},[902,21966,13189],{"encoding":904},". Budují se postupně bohatší modely — ",[38,21969,21970],{},"C-I"," (jen spotřeba a investice) → ",[38,21973,21974],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,21977,21978],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,21981,16066],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,21984,17939],{},[883,21986,21988],{"className":21987},[886],[888,21989,21990],{"xmlns":890},[892,21991,21992,22000],{},[895,21993,21994],{},[3243,21995,21996,21998],{},[898,21997,13189],{},[898,21999,3249],{},[902,22001,17957],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,22004,22006],{"className":22005},[886],[888,22007,22008],{"xmlns":890},[892,22009,22010,22018],{},[895,22011,22012],{},[3243,22013,22014,22016],{},[898,22015,13189],{},[898,22017,3249],{},[902,22019,17957],{"encoding":904}," na exogenní veličiny popisují ",[38,22022,22023],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,22026,22028],{"className":22027},[886],[888,22029,22030],{"xmlns":890},[892,22031,22032,22060],{},[895,22033,22034,22036,22038,22040,22042,22044,22046,22048,22050,22052,22054,22056,22058],{},[1850,22035,4062],{},[898,22037,8741],{"mathvariant":2334},[1701,22039,1799],{"stretchy":1798},[1850,22041,4062],{},[1701,22043,2317],{},[898,22045,207],{},[1701,22047,1805],{"stretchy":1798},[1701,22049,1792],{},[1850,22051,4062],{},[898,22053,8741],{"mathvariant":2334},[898,22055,6909],{},[898,22057,1680],{},[898,22059,1661],{},[902,22061,22062],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1635,22064,22065],{},[724,22066,22067,22069,22070,22073,22074,22092,22093,22123,22124,22171,22172,22174,22175,22197],{},[883,22068,2063],{}," Intuice\n",[38,22071,22072],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,22075,22077],{"className":22076},[886],[888,22078,22079],{"xmlns":890},[892,22080,22081,22089],{},[895,22082,22083,22085,22087],{},[898,22084,6909],{},[898,22086,1680],{},[898,22088,1658],{},[902,22090,22091],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,22094,22096],{"className":22095},[886],[888,22097,22098],{"xmlns":890},[892,22099,22100,22120],{},[895,22101,22102,22104,22106,22108,22110,22112,22114,22116,22118],{},[898,22103,6909],{},[898,22105,1680],{},[898,22107,1661],{},[1701,22109,1792],{},[1850,22111,4062],{},[1701,22113,2317],{},[898,22115,6909],{},[898,22117,1680],{},[898,22119,1658],{},[902,22121,22122],{"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 ",[883,22125,22127],{"className":22126},[886],[888,22128,22129],{"xmlns":890},[892,22130,22131,22168],{},[895,22132,22133,22135,22137,22139,22141,22147,22149,22152,22154,22156,22158,22160,22162,22164,22166],{},[1850,22134,4062],{},[1701,22136,1703],{},[898,22138,207],{},[1701,22140,1703],{},[3243,22142,22143,22145],{},[898,22144,207],{},[1850,22146,3938],{},[1701,22148,1703],{},[1701,22150,22151],{},"⋯",[1701,22153,1792],{},[1850,22155,4062],{},[898,22157,8741],{"mathvariant":2334},[1701,22159,1799],{"stretchy":1798},[1850,22161,4062],{},[1701,22163,2317],{},[898,22165,207],{},[1701,22167,1805],{"stretchy":1798},[902,22169,22170],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,22173,16066],{}," 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 ",[883,22176,22178],{"className":22177},[886],[888,22179,22180],{"xmlns":890},[892,22181,22182,22194],{},[895,22183,22184,22186,22188,22190,22192],{},[1701,22185,1799],{"stretchy":1798},[898,22187,13189],{},[1701,22189,2012],{"separator":2011},[898,22191,16096],{},[1701,22193,1805],{"stretchy":1798},[902,22195,22196],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,22199,22201],{"id":22200},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,22203,22204],{},"Po prostudování kapitoly by čtenář měl umět:",[120,22206,22207,22210,22213,22216,22219,22222,22225,22315],{},[123,22208,22209],{},"popsat zjednodušený model národní ekonomiky,",[123,22211,22212],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,22214,22215],{},"popsat lineární model spotřeby a úspor,",[123,22217,22218],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,22220,22221],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,22223,22224],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,22226,22227,22228,1343,22245,1343,22267,2633,22292,22314],{},"popsat modely ",[883,22229,22231],{"className":22230},[886],[888,22232,22233],{"xmlns":890},[892,22234,22235,22243],{},[895,22236,22237,22239,22241],{},[898,22238,1658],{},[1939,22240,16344],{},[898,22242,16238],{},[902,22244,16349],{"encoding":904},[883,22246,22248],{"className":22247},[886],[888,22249,22250],{"xmlns":890},[892,22251,22252,22264],{},[895,22253,22254,22256,22258,22260,22262],{},[898,22255,1658],{},[1939,22257,16344],{},[898,22259,16238],{},[1939,22261,16344],{},[898,22263,16167],{},[902,22265,22266],{"encoding":904},"C\\text{-}I\\text{-}G",[883,22268,22270],{"className":22269},[886],[888,22271,22272],{"xmlns":890},[892,22273,22274,22290],{},[895,22275,22276,22278,22280,22282,22284,22286,22288],{},[898,22277,1658],{},[1939,22279,16344],{},[898,22281,16238],{},[1939,22283,16344],{},[898,22285,16167],{},[1939,22287,16344],{},[898,22289,16374],{},[902,22291,16377],{"encoding":904},[883,22293,22295],{"className":22294},[886],[888,22296,22297],{"xmlns":890},[892,22298,22299,22311],{},[895,22300,22301,22303,22305,22307,22309],{},[898,22302,16238],{},[898,22304,1661],{},[1939,22306,16344],{},[898,22308,13853],{},[898,22310,6909],{},[902,22312,22313],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,22316,22317],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,22319,22321],{"id":22320},"gnp-a-národní-důchod","GNP a národní důchod",[724,22323,22324,4088,22327,1646,22346,22349],{},[38,22325,22326],{},"Hrubý národní produkt",[883,22328,22330],{"className":22329},[886],[888,22331,22332],{"xmlns":890},[892,22333,22334,22343],{},[895,22335,22336,22338,22341],{},[898,22337,16167],{},[898,22339,22340],{},"N",[898,22342,1680],{},[902,22344,22345],{"encoding":904},"GNP",[614,22347,22348],{},"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:",[724,22351,22352],{},[883,22353,22355],{"className":22354},[886],[888,22356,22357],{"xmlns":890},[892,22358,22359,22394],{},[895,22360,22361,22363,22365,22367,22369,22371,22373,22375,22377,22379,22381,22383,22385,22387,22389,22392],{},[898,22362,16167],{},[898,22364,22340],{},[898,22366,1680],{},[1701,22368,1792],{},[898,22370,1658],{},[1701,22372,1703],{},[898,22374,16238],{},[1701,22376,1703],{},[898,22378,16167],{},[1701,22380,1703],{},[898,22382,16374],{},[1701,22384,2012],{"separator":2011},[9942,22386],{"width":9944},[1701,22388,1799],{"stretchy":1798},[1850,22390,22391],{},"7.1",[1701,22393,1805],{"stretchy":1798},[902,22395,22396],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,22398,22399],{},"kde",[120,22401,22402,22418,22434,22450],{},[123,22403,22404,22417],{},[883,22405,22407],{"className":22406},[886],[888,22408,22409],{"xmlns":890},[892,22410,22411,22415],{},[895,22412,22413],{},[898,22414,1658],{},[902,22416,1658],{"encoding":904}," — výdaje domácností na spotřebu,",[123,22419,22420,22433],{},[883,22421,22423],{"className":22422},[886],[888,22424,22425],{"xmlns":890},[892,22426,22427,22431],{},[895,22428,22429],{},[898,22430,16238],{},[902,22432,16238],{"encoding":904}," — hrubé domácí investice,",[123,22435,22436,22449],{},[883,22437,22439],{"className":22438},[886],[888,22440,22441],{"xmlns":890},[892,22442,22443,22447],{},[895,22444,22445],{},[898,22446,16167],{},[902,22448,16167],{"encoding":904}," — vládní výdaje,",[123,22451,22452,22465],{},[883,22453,22455],{"className":22454},[886],[888,22456,22457],{"xmlns":890},[892,22458,22459,22463],{},[895,22460,22461],{},[898,22462,16374],{},[902,22464,16374],{"encoding":904}," — čistý export.",[724,22467,22468,22469,22486,22487,22490,22491,4088,22494,1646,22507,22510],{},"K měření ",[883,22470,22472],{"className":22471},[886],[888,22473,22474],{"xmlns":890},[892,22475,22476,22484],{},[895,22477,22478,22480,22482],{},[898,22479,16167],{},[898,22481,22340],{},[898,22483,1680],{},[902,22485,22345],{"encoding":904}," se užívá ",[38,22488,22489],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,22492,22493],{},"národní důchod",[883,22495,22497],{"className":22496},[886],[888,22498,22499],{"xmlns":890},[892,22500,22501,22505],{},[895,22502,22503],{},[898,22504,13189],{},[902,22506,13189],{"encoding":904},[614,22508,22509],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,22512,22513],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,22515,22516],{},[883,22517,22519],{"className":22518},[886],[888,22520,22521],{"xmlns":890},[892,22522,22523,22537],{},[895,22524,22525,22527,22529,22531,22533,22535],{},[898,22526,16167],{},[898,22528,22340],{},[898,22530,1680],{},[1701,22532,4067],{},[898,22534,13189],{},[1701,22536,2012],{"separator":2011},[902,22538,22539],{"encoding":904},"GNP \\approx Y,",[724,22541,22542,22543,1646,22546,22549,22550,22563,22564,22567,22568,1715],{},"a užívá se společného názvu ",[38,22544,22545],{},"důchod",[614,22547,22548],{},"income",") s označením ",[883,22551,22553],{"className":22552},[886],[888,22554,22555],{"xmlns":890},[892,22556,22557,22561],{},[895,22558,22559],{},[898,22560,13189],{},[902,22562,13189],{"encoding":904},". Domácnosti důchod použijí ke ",[38,22565,22566],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,22569,22570],{},"úspor",[115,22572,22574],{"id":22573},"spotřeba-a-úspory","Spotřeba a úspory",[198,22576,22578],{"id":22577},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,22580,22581,22582,22595,22596,22609,22610,2246],{},"Jak spotřeba ",[883,22583,22585],{"className":22584},[886],[888,22586,22587],{"xmlns":890},[892,22588,22589,22593],{},[895,22590,22591],{},[898,22592,1658],{},[902,22594,1658],{"encoding":904},", tak úspory ",[883,22597,22599],{"className":22598},[886],[888,22600,22601],{"xmlns":890},[892,22602,22603,22607],{},[895,22604,22605],{},[898,22606,1661],{},[902,22608,1661],{"encoding":904}," závisejí na důchodu ",[883,22611,22613],{"className":22612},[886],[888,22614,22615],{"xmlns":890},[892,22616,22617,22621],{},[895,22618,22619],{},[898,22620,13189],{},[902,22622,13189],{"encoding":904},[724,22624,22625],{},[883,22626,22628],{"className":22627},[886],[888,22629,22630],{"xmlns":890},[892,22631,22632,22664],{},[895,22633,22634,22636,22638,22640,22642,22644,22646,22648,22650,22652,22654,22656,22658,22660,22662],{},[898,22635,1658],{},[1701,22637,1792],{},[898,22639,1658],{},[1701,22641,1799],{"stretchy":1798},[898,22643,13189],{},[1701,22645,1805],{"stretchy":1798},[1701,22647,2012],{"separator":2011},[9942,22649],{"width":9944},[898,22651,1661],{},[1701,22653,1792],{},[898,22655,1661],{},[1701,22657,1799],{"stretchy":1798},[898,22659,13189],{},[1701,22661,1805],{"stretchy":1798},[898,22663,1715],{"mathvariant":2334},[902,22665,22666],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,22668,22669,12164,22688,1646,22691,22694,22695,12164,22715,1646,22718,22721,22722,2633,22725,22728],{},[883,22670,22672],{"className":22671},[886],[888,22673,22674],{"xmlns":890},[892,22675,22676,22686],{},[895,22677,22678,22680,22682,22684],{},[898,22679,1658],{},[1701,22681,1799],{"stretchy":1798},[898,22683,13189],{},[1701,22685,1805],{"stretchy":1798},[902,22687,18269],{"encoding":904},[38,22689,22690],{},"funkce spotřeby",[614,22692,22693],{},"consumption function","), ",[883,22696,22698],{"className":22697},[886],[888,22699,22700],{"xmlns":890},[892,22701,22702,22712],{},[895,22703,22704,22706,22708,22710],{},[898,22705,1661],{},[1701,22707,1799],{"stretchy":1798},[898,22709,13189],{},[1701,22711,1805],{"stretchy":1798},[902,22713,22714],{"encoding":904},"S(Y)",[38,22716,22717],{},"funkce úspor",[614,22719,22720],{},"savings function","); jejich grafy se nazývají ",[38,22723,22724],{},"křivka spotřeby",[38,22726,22727],{},"křivka úspor",". Platí základní identita",[724,22730,22731],{},[883,22732,22734],{"className":22733},[886],[888,22735,22736],{"xmlns":890},[892,22737,22738,22781],{},[895,22739,22740,22742,22744,22746,22748,22750,22752,22754,22756,22758,22760,22762,22764,22766,22768,22770,22772,22774,22776,22779],{},[898,22741,13189],{},[1701,22743,1792],{},[898,22745,1658],{},[1701,22747,1703],{},[898,22749,1661],{},[1701,22751,1792],{},[898,22753,1658],{},[1701,22755,1799],{"stretchy":1798},[898,22757,13189],{},[1701,22759,1805],{"stretchy":1798},[1701,22761,1703],{},[898,22763,1661],{},[1701,22765,1799],{"stretchy":1798},[898,22767,13189],{},[1701,22769,1805],{"stretchy":1798},[898,22771,1715],{"mathvariant":2334},[9942,22773],{"width":9944},[1701,22775,1799],{"stretchy":1798},[1850,22777,22778],{},"7.2",[1701,22780,1805],{"stretchy":1798},[902,22782,22783],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,22785,22786],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,22788,22790],{"id":22789},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,22792,22793],{},"Nejjednodušší model předpokládá lineární tvar",[724,22795,22796],{},[883,22797,22799],{"className":22798},[886],[888,22800,22801],{"xmlns":890},[892,22802,22803,22838],{},[895,22804,22805,22807,22809,22811,22813,22815,22817,22819,22821,22823,22825,22827,22829,22831,22833,22836],{},[898,22806,1658],{},[1701,22808,1792],{},[898,22810,1658],{},[1701,22812,1799],{"stretchy":1798},[898,22814,13189],{},[1701,22816,1805],{"stretchy":1798},[1701,22818,1792],{},[898,22820,207],{},[898,22822,13189],{},[1701,22824,1703],{},[898,22826,3598],{},[1701,22828,2012],{"separator":2011},[9942,22830],{"width":9944},[1701,22832,1799],{"stretchy":1798},[1850,22834,22835],{},"7.3",[1701,22837,1805],{"stretchy":1798},[902,22839,22840],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,22842,8380,22843,2633,22861,22883,22884,22924,22925,1715],{},[883,22844,22846],{"className":22845},[886],[888,22847,22848],{"xmlns":890},[892,22849,22850,22858],{},[895,22851,22852,22854,22856],{},[898,22853,3598],{},[1701,22855,7491],{},[1850,22857,1852],{},[902,22859,22860],{"encoding":904},"b > 0",[883,22862,22864],{"className":22863},[886],[888,22865,22866],{"xmlns":890},[892,22867,22868,22880],{},[895,22869,22870,22872,22874,22876,22878],{},[1850,22871,1852],{},[1701,22873,7530],{},[898,22875,207],{},[1701,22877,7530],{},[1850,22879,4062],{},[902,22881,22882],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,22885,22887],{"className":22886},[886],[888,22888,22889],{"xmlns":890},[892,22890,22891,22921],{},[895,22892,22893,22895,22897,22904,22906,22909,22911,22913,22915,22917,22919],{},[898,22894,207],{},[1701,22896,1792],{},[895,22898,22899,22902],{},[898,22900,22901],{"mathvariant":2334},"t",[898,22903,15097],{"mathvariant":2334},[1939,22905,1941],{},[898,22907,22908],{},"α",[1701,22910,1792],{},[898,22912,4708],{"mathvariant":2334},[898,22914,1658],{},[898,22916,8741],{"mathvariant":2334},[898,22918,4708],{"mathvariant":2334},[898,22920,13189],{},[902,22922,22923],{"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 ",[883,22926,22928],{"className":22927},[886],[888,22929,22930],{"xmlns":890},[892,22931,22932,22936],{},[895,22933,22934],{},[898,22935,13189],{},[902,22937,13189],{"encoding":904},[724,22939,22940],{},[614,22941,22942,22943,22967,22968,23006,23007,23023,23024,1715],{},"Obrázek 7.1 — Přímka spotřeby ",[883,22944,22946],{"className":22945},[886],[888,22947,22948],{"xmlns":890},[892,22949,22950,22964],{},[895,22951,22952,22954,22956,22958,22960,22962],{},[898,22953,1658],{},[1701,22955,1792],{},[898,22957,207],{},[898,22959,13189],{},[1701,22961,1703],{},[898,22963,3598],{},[902,22965,22966],{"encoding":904},"C = aY + b"," se směrnicí ",[883,22969,22971],{"className":22970},[886],[888,22972,22973],{"xmlns":890},[892,22974,22975,23003],{},[895,22976,22977,22979,22981,22987,22989,22991,22993,22995,22997,22999,23001],{},[898,22978,207],{},[1701,22980,1792],{},[895,22982,22983,22985],{},[898,22984,22901],{"mathvariant":2334},[898,22986,15097],{"mathvariant":2334},[1939,22988,1941],{},[898,22990,22908],{},[1701,22992,1792],{},[898,22994,4708],{"mathvariant":2334},[898,22996,1658],{},[898,22998,8741],{"mathvariant":2334},[898,23000,4708],{"mathvariant":2334},[898,23002,13189],{},[902,23004,23005],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,23008,23010],{"className":23009},[886],[888,23011,23012],{"xmlns":890},[892,23013,23014,23020],{},[895,23015,23016,23018],{},[898,23017,4708],{"mathvariant":2334},[898,23019,1658],{},[902,23021,23022],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,23025,23027],{"className":23026},[886],[888,23028,23029],{"xmlns":890},[892,23030,23031,23041],{},[895,23032,23033,23035,23037,23039],{},[898,23034,4708],{"mathvariant":2334},[898,23036,13189],{},[1701,23038,1792],{},[1850,23040,4062],{},[902,23042,23043],{"encoding":904},"\\Delta Y = 1",[724,23045,23046,23047,2246],{},"Dosazením do (7.2) plyne ",[38,23048,23049],{},"lineární model úspor",[724,23051,23052],{},[883,23053,23055],{"className":23054},[886],[888,23056,23057],{"xmlns":890},[892,23058,23059,23124],{},[895,23060,23061,23063,23065,23067,23069,23071,23073,23075,23077,23079,23081,23083,23085,23087,23089,23091,23093,23095,23097,23099,23101,23103,23105,23107,23109,23111,23113,23115,23117,23119,23122],{},[898,23062,1661],{},[1701,23064,1792],{},[898,23066,13189],{},[1701,23068,2317],{},[898,23070,1658],{},[1701,23072,1799],{"stretchy":1798},[898,23074,13189],{},[1701,23076,1805],{"stretchy":1798},[1701,23078,1792],{},[898,23080,13189],{},[1701,23082,2317],{},[1701,23084,1799],{"stretchy":1798},[898,23086,207],{},[898,23088,13189],{},[1701,23090,1703],{},[898,23092,3598],{},[1701,23094,1805],{"stretchy":1798},[1701,23096,1792],{},[1701,23098,1799],{"stretchy":1798},[1850,23100,4062],{},[1701,23102,2317],{},[898,23104,207],{},[1701,23106,1805],{"stretchy":1798},[898,23108,13189],{},[1701,23110,2317],{},[898,23112,3598],{},[898,23114,1715],{"mathvariant":2334},[9942,23116],{"width":9944},[1701,23118,1799],{"stretchy":1798},[1850,23120,23121],{},"7.4",[1701,23123,1805],{"stretchy":1798},[902,23125,23126],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,23128,23129,23130,2506],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,23131,23133],{"className":23132},[886],[888,23134,23135],{"xmlns":890},[892,23136,23137,23153],{},[895,23138,23139,23141,23143,23145,23147,23149,23151],{},[1850,23140,1852],{},[1701,23142,7530],{},[1850,23144,4062],{},[1701,23146,2317],{},[898,23148,207],{},[1701,23150,7530],{},[1850,23152,4062],{},[902,23154,23155],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,23157,23158],{},[614,23159,23160,23161,2633,23184,23216,23217,6723,23230,23260,23261,6723,23279,1715],{},"Obrázek 7.2 — Přímky ",[883,23162,23164],{"className":23163},[886],[888,23165,23166],{"xmlns":890},[892,23167,23168,23182],{},[895,23169,23170,23172,23174,23176,23178,23180],{},[898,23171,1658],{},[1701,23173,1792],{},[898,23175,207],{},[898,23177,13189],{},[1701,23179,1703],{},[898,23181,3598],{},[902,23183,22966],{"encoding":904},[883,23185,23187],{"className":23186},[886],[888,23188,23189],{"xmlns":890},[892,23190,23191,23213],{},[895,23192,23193,23195,23197,23199,23201,23203,23205,23207,23209,23211],{},[898,23194,1661],{},[1701,23196,1792],{},[1701,23198,1799],{"stretchy":1798},[1850,23200,4062],{},[1701,23202,2317],{},[898,23204,207],{},[1701,23206,1805],{"stretchy":1798},[898,23208,13189],{},[1701,23210,2317],{},[898,23212,3598],{},[902,23214,23215],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,23218,23220],{"className":23219},[886],[888,23221,23222],{"xmlns":890},[892,23223,23224,23228],{},[895,23225,23226],{},[898,23227,13189],{},[902,23229,13189],{"encoding":904},[883,23231,23233],{"className":23232},[886],[888,23234,23235],{"xmlns":890},[892,23236,23237,23257],{},[895,23238,23239,23241,23243,23245,23247,23249,23251,23253,23255],{},[898,23240,13189],{},[1701,23242,1792],{},[898,23244,3598],{},[898,23246,8741],{"mathvariant":2334},[1701,23248,1799],{"stretchy":1798},[1850,23250,4062],{},[1701,23252,2317],{},[898,23254,207],{},[1701,23256,1805],{"stretchy":1798},[902,23258,23259],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,23262,23264],{"className":23263},[886],[888,23265,23266],{"xmlns":890},[892,23267,23268,23276],{},[895,23269,23270,23272,23274],{},[898,23271,1658],{},[1701,23273,2012],{"separator":2011},[898,23275,1661],{},[902,23277,23278],{"encoding":904},"C, S",[883,23280,23282],{"className":23281},[886],[888,23283,23284],{"xmlns":890},[892,23285,23286,23292],{},[895,23287,23288,23290],{},[1701,23289,2317],{},[898,23291,3598],{},[902,23293,23294],{"encoding":904},"-b",[198,23296,23298],{"id":23297},"příklad-71","Příklad 7.1",[724,23300,23301,23302,23327],{},"Pro spotřebu ",[883,23303,23305],{"className":23304},[886],[888,23306,23307],{"xmlns":890},[892,23308,23309,23324],{},[895,23310,23311,23313,23315,23318,23320,23322],{},[898,23312,1658],{},[1701,23314,1792],{},[1850,23316,23317],{},"0,4",[898,23319,13189],{},[1701,23321,1703],{},[1850,23323,3703],{},[902,23325,23326],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,23329,23330],{},[883,23331,23333],{"className":23332},[886],[888,23334,23335],{"xmlns":890},[892,23336,23337,23374],{},[895,23338,23339,23341,23343,23345,23347,23349,23351,23353,23355,23357,23359,23361,23363,23365,23367,23369,23371],{},[898,23340,1661],{},[1701,23342,1792],{},[898,23344,13189],{},[1701,23346,2317],{},[898,23348,1658],{},[1701,23350,1792],{},[898,23352,13189],{},[1701,23354,2317],{},[1850,23356,23317],{},[898,23358,13189],{},[1701,23360,2317],{},[1850,23362,3703],{},[1701,23364,1792],{},[1850,23366,3868],{},[898,23368,13189],{},[1701,23370,2317],{},[1850,23372,23373],{},"10.",[902,23375,23376],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,23378,23379],{},[614,23380,23381,23382,2633,23405,23429,23430,12164,23443,23467,23468,12164,23485,23501,23502,1715],{},"Obrázek 7.3 — Přímky ",[883,23383,23385],{"className":23384},[886],[888,23386,23387],{"xmlns":890},[892,23388,23389,23403],{},[895,23390,23391,23393,23395,23397,23399,23401],{},[898,23392,1658],{},[1701,23394,1792],{},[1850,23396,23317],{},[898,23398,13189],{},[1701,23400,1703],{},[1850,23402,3703],{},[902,23404,23326],{"encoding":904},[883,23406,23408],{"className":23407},[886],[888,23409,23410],{"xmlns":890},[892,23411,23412,23426],{},[895,23413,23414,23416,23418,23420,23422,23424],{},[898,23415,1661],{},[1701,23417,1792],{},[1850,23419,3868],{},[898,23421,13189],{},[1701,23423,2317],{},[1850,23425,3703],{},[902,23427,23428],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,23431,23433],{"className":23432},[886],[888,23434,23435],{"xmlns":890},[892,23436,23437,23441],{},[895,23438,23439],{},[898,23440,13189],{},[902,23442,13189],{"encoding":904},[883,23444,23446],{"className":23445},[886],[888,23447,23448],{"xmlns":890},[892,23449,23450,23464],{},[895,23451,23452,23454,23457],{},[1701,23453,4067],{},[1850,23455,23456],{},"16,",[12448,23458,23459,23461],{"accent":2011},[1850,23460,6352],{},[1701,23462,23463],{},"ˉ",[902,23465,23466],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,23469,23471],{"className":23470},[886],[888,23472,23473],{"xmlns":890},[892,23474,23475,23483],{},[895,23476,23477,23479,23481],{},[898,23478,1658],{},[1701,23480,2012],{"separator":2011},[898,23482,1661],{},[902,23484,23278],{"encoding":904},[883,23486,23488],{"className":23487},[886],[888,23489,23490],{"xmlns":890},[892,23491,23492,23498],{},[895,23493,23494,23496],{},[1701,23495,2317],{},[1850,23497,3703],{},[902,23499,23500],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,23503,23505],{"className":23504},[886],[888,23506,23507],{"xmlns":890},[892,23508,23509,23521],{},[895,23510,23511,23513,23515,23517,23519],{},[1701,23512,1799],{"stretchy":1798},[1850,23514,1852],{},[1701,23516,2012],{"separator":2011},[1850,23518,3703],{},[1701,23520,1805],{"stretchy":1798},[902,23522,23523],{"encoding":904},"(0, 10)",[724,23525,23526,23527,12164,23545,23575,23576,1646,23579,23582,23583,12164,23607,1646,23610,23613],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,23528,23530],{"className":23529},[886],[888,23531,23532],{"xmlns":890},[892,23533,23534,23542],{},[895,23535,23536,23538,23540],{},[898,23537,13189],{},[1701,23539,1792],{},[1850,23541,1852],{},[902,23543,23544],{"encoding":904},"Y = 0",[883,23546,23548],{"className":23547},[886],[888,23549,23550],{"xmlns":890},[892,23551,23552,23572],{},[895,23553,23554,23556,23558,23560,23562,23564,23566,23568,23570],{},[898,23555,1661],{},[1701,23557,1799],{"stretchy":1798},[1850,23559,1852],{},[1701,23561,1805],{"stretchy":1798},[1701,23563,1792],{},[1701,23565,2317],{},[898,23567,3598],{},[1701,23569,7530],{},[1850,23571,1852],{},[902,23573,23574],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,23577,23578],{},"autonomních úsporách",[614,23580,23581],{},"autonomous savings","). Analogicky ",[883,23584,23586],{"className":23585},[886],[888,23587,23588],{"xmlns":890},[892,23589,23590,23604],{},[895,23591,23592,23594,23596,23598,23600,23602],{},[898,23593,1658],{},[1701,23595,1799],{"stretchy":1798},[1850,23597,1852],{},[1701,23599,1805],{"stretchy":1798},[1701,23601,1792],{},[898,23603,3598],{},[902,23605,23606],{"encoding":904},"C(0) = b",[38,23608,23609],{},"autonomní spotřeba",[614,23611,23612],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,23615,23617],{"id":23616},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,23619,23620,4088,23623,1646,23640,23643],{},[38,23621,23622],{},"Mezní sklon ke spotřebě",[883,23624,23626],{"className":23625},[886],[888,23627,23628],{"xmlns":890},[892,23629,23630,23638],{},[895,23631,23632,23634,23636],{},[898,23633,6909],{},[898,23635,1680],{},[898,23637,1658],{},[902,23639,22091],{"encoding":904},[614,23641,23642],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,23645,23646],{},[883,23647,23649],{"className":23648},[886],[888,23650,23651],{"xmlns":890},[892,23652,23653,23679],{},[895,23654,23655,23657,23659,23661,23663,23677],{},[898,23656,6909],{},[898,23658,1680],{},[898,23660,1658],{},[1701,23662,1792],{},[3726,23664,23665,23671],{},[895,23666,23667,23669],{},[898,23668,2312],{"mathvariant":2334},[898,23670,1658],{},[895,23672,23673,23675],{},[898,23674,2312],{"mathvariant":2334},[898,23676,13189],{},[898,23678,1715],{"mathvariant":2334},[902,23680,23681],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,23683,23684,4088,23687,1646,23705,23708],{},[38,23685,23686],{},"Mezní sklon k úsporám",[883,23688,23690],{"className":23689},[886],[888,23691,23692],{"xmlns":890},[892,23693,23694,23702],{},[895,23695,23696,23698,23700],{},[898,23697,6909],{},[898,23699,1680],{},[898,23701,1661],{},[902,23703,23704],{"encoding":904},"MPS",[614,23706,23707],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,23710,23711],{},[883,23712,23714],{"className":23713},[886],[888,23715,23716],{"xmlns":890},[892,23717,23718,23744],{},[895,23719,23720,23722,23724,23726,23728,23742],{},[898,23721,6909],{},[898,23723,1680],{},[898,23725,1661],{},[1701,23727,1792],{},[3726,23729,23730,23736],{},[895,23731,23732,23734],{},[898,23733,2312],{"mathvariant":2334},[898,23735,1661],{},[895,23737,23738,23740],{},[898,23739,2312],{"mathvariant":2334},[898,23741,13189],{},[898,23743,1715],{"mathvariant":2334},[902,23745,23746],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,23748,23749,23750,23808],{},"Z (7.2) plyne ",[883,23751,23753],{"className":23752},[886],[888,23754,23755],{"xmlns":890},[892,23756,23757,23805],{},[895,23758,23759,23773,23775,23789,23791],{},[3726,23760,23761,23767],{},[895,23762,23763,23765],{},[898,23764,2312],{"mathvariant":2334},[898,23766,13189],{},[895,23768,23769,23771],{},[898,23770,2312],{"mathvariant":2334},[898,23772,13189],{},[1701,23774,1792],{},[3726,23776,23777,23783],{},[895,23778,23779,23781],{},[898,23780,2312],{"mathvariant":2334},[898,23782,1658],{},[895,23784,23785,23787],{},[898,23786,2312],{"mathvariant":2334},[898,23788,13189],{},[1701,23790,1703],{},[3726,23792,23793,23799],{},[895,23794,23795,23797],{},[898,23796,2312],{"mathvariant":2334},[898,23798,1661],{},[895,23800,23801,23803],{},[898,23802,2312],{"mathvariant":2334},[898,23804,13189],{},[902,23806,23807],{"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",[724,23810,23811],{},[883,23812,23814],{"className":23813},[886],[888,23815,23816],{"xmlns":890},[892,23817,23818,23881],{},[895,23819,23820,23872,23874,23876,23879],{},[16886,23821,23822],{"notation":16888},[2363,23823,23824],{"scriptlevel":1852,"displaystyle":1798},[2363,23825,23826],{"scriptlevel":1852,"displaystyle":1798},[2363,23827,23828],{"scriptlevel":1852,"displaystyle":2011},[895,23829,23830,23832,23834,23836,23838,23840,23842,23844,23846,23848,23850,23852,23854,23856,23858,23860,23862,23864,23866,23868,23870],{},[898,23831,6909],{},[898,23833,1680],{},[898,23835,1658],{},[1701,23837,1703],{},[898,23839,6909],{},[898,23841,1680],{},[898,23843,1661],{},[1701,23845,1792],{},[1850,23847,4062],{},[1701,23849,2012],{"separator":2011},[9942,23851],{"width":9944},[898,23853,6909],{},[898,23855,1680],{},[898,23857,1661],{},[1701,23859,1792],{},[1850,23861,4062],{},[1701,23863,2317],{},[898,23865,6909],{},[898,23867,1680],{},[898,23869,1658],{},[898,23871,1715],{"mathvariant":2334},[9942,23873],{"width":9944},[1701,23875,1799],{"stretchy":1798},[1850,23877,23878],{},"7.5",[1701,23880,1805],{"stretchy":1798},[902,23882,23883],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,23885,23886,4088,23889,23912,23913,2633,23935,23961],{},[38,23887,23888],{},"Pro lineární model",[883,23890,23892],{"className":23891},[886],[888,23893,23894],{"xmlns":890},[892,23895,23896,23910],{},[895,23897,23898,23900,23902,23904,23906,23908],{},[898,23899,1658],{},[1701,23901,1792],{},[898,23903,207],{},[898,23905,13189],{},[1701,23907,1703],{},[898,23909,3598],{},[902,23911,22966],{"encoding":904}," vychází ",[883,23914,23916],{"className":23915},[886],[888,23917,23918],{"xmlns":890},[892,23919,23920,23932],{},[895,23921,23922,23924,23926,23928,23930],{},[898,23923,6909],{},[898,23925,1680],{},[898,23927,1658],{},[1701,23929,1792],{},[898,23931,207],{},[902,23933,23934],{"encoding":904},"MPC = a",[883,23936,23938],{"className":23937},[886],[888,23939,23940],{"xmlns":890},[892,23941,23942,23958],{},[895,23943,23944,23946,23948,23950,23952,23954,23956],{},[898,23945,6909],{},[898,23947,1680],{},[898,23949,1661],{},[1701,23951,1792],{},[1850,23953,4062],{},[1701,23955,2317],{},[898,23957,207],{},[902,23959,23960],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,23963,23964,23967,23968,23990,23991,24019],{},[38,23965,23966],{},"Interpretace diferenciálem."," Pro pevné ",[883,23969,23971],{"className":23970},[886],[888,23972,23973],{"xmlns":890},[892,23974,23975,23987],{},[895,23976,23977,23979,23981],{},[898,23978,13189],{},[1701,23980,1792],{},[3243,23982,23983,23985],{},[898,23984,13189],{},[1701,23986,8424],{},[902,23988,23989],{"encoding":904},"Y = Y^*"," udává ",[883,23992,23994],{"className":23993},[886],[888,23995,23996],{"xmlns":890},[892,23997,23998,24016],{},[895,23999,24000,24002,24004,24006,24008,24014],{},[898,24001,6909],{},[898,24003,1680],{},[898,24005,1658],{},[1701,24007,1799],{"stretchy":1798},[3243,24009,24010,24012],{},[898,24011,13189],{},[1701,24013,8424],{},[1701,24015,1805],{"stretchy":1798},[902,24017,24018],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,24021,24022],{},[883,24023,24025],{"className":24024},[886],[888,24026,24027],{"xmlns":890},[892,24028,24029,24083],{},[895,24030,24031,24033,24035,24037,24039,24041,24043,24049,24051,24053,24055,24057,24059,24061,24063,24065,24067,24069,24071,24073,24075,24077,24079,24081],{},[898,24032,4708],{"mathvariant":2334},[898,24034,1658],{},[1701,24036,4067],{},[898,24038,2312],{"mathvariant":2334},[898,24040,1658],{},[1701,24042,1792],{},[3243,24044,24045,24047],{},[898,24046,1658],{},[1701,24048,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,24050,1799],{"stretchy":1798},[898,24052,13189],{},[1701,24054,1805],{"stretchy":1798},[1939,24056,1941],{},[898,24058,2312],{"mathvariant":2334},[898,24060,13189],{},[1701,24062,1792],{},[898,24064,6909],{},[898,24066,1680],{},[898,24068,1658],{},[1701,24070,1799],{"stretchy":1798},[898,24072,13189],{},[1701,24074,1805],{"stretchy":1798},[1939,24076,1941],{},[898,24078,2312],{"mathvariant":2334},[898,24080,13189],{},[898,24082,1715],{"mathvariant":2334},[902,24084,24085],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,24087,24088,24089,24125,24126,24129],{},"Analogicky ",[883,24090,24092],{"className":24091},[886],[888,24093,24094],{"xmlns":890},[892,24095,24096,24122],{},[895,24097,24098,24100,24102,24104,24106,24108,24110,24112,24114,24116,24118,24120],{},[898,24099,4708],{"mathvariant":2334},[898,24101,1661],{},[1701,24103,4067],{},[898,24105,6909],{},[898,24107,1680],{},[898,24109,1661],{},[1701,24111,1799],{"stretchy":1798},[898,24113,13189],{},[1701,24115,1805],{"stretchy":1798},[1939,24117,1941],{},[898,24119,2312],{"mathvariant":2334},[898,24121,13189],{},[902,24123,24124],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,24127,1145],{"className":24128,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,24131,24133],{"id":24132},"příklad-72","Příklad 7.2",[724,24135,23301,24136,3318,24171,24190],{},[883,24137,24139],{"className":24138},[886],[888,24140,24141],{"xmlns":890},[892,24142,24143,24168],{},[895,24144,24145,24147,24149,24152,24158,24160,24162,24164,24166],{},[898,24146,1658],{},[1701,24148,1792],{},[1850,24150,24151],{},"0,001",[3243,24153,24154,24156],{},[898,24155,13189],{},[1850,24157,3938],{},[1701,24159,1703],{},[1850,24161,6930],{},[898,24163,13189],{},[1701,24165,1703],{},[1850,24167,7206],{},[902,24169,24170],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50",[883,24172,24174],{"className":24173},[886],[888,24175,24176],{"xmlns":890},[892,24177,24178,24187],{},[895,24179,24180,24182,24184],{},[898,24181,13189],{},[1701,24183,7530],{},[1850,24185,24186],{},"400",[902,24188,24189],{"encoding":904},"Y \u003C 400",") platí",[724,24192,24193],{},[883,24194,24196],{"className":24195},[886],[888,24197,24198],{"xmlns":890},[892,24199,24200,24237],{},[895,24201,24202,24204,24206,24208,24210,24224,24226,24229,24231,24233,24235],{},[898,24203,6909],{},[898,24205,1680],{},[898,24207,1658],{},[1701,24209,1792],{},[3726,24211,24212,24218],{},[895,24213,24214,24216],{},[898,24215,2312],{"mathvariant":2334},[898,24217,1658],{},[895,24219,24220,24222],{},[898,24221,2312],{"mathvariant":2334},[898,24223,13189],{},[1701,24225,1792],{},[1850,24227,24228],{},"0,002",[898,24230,13189],{},[1701,24232,1703],{},[1850,24234,6930],{},[1701,24236,2012],{"separator":2011},[902,24238,24239],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,24241,24242],{},[883,24243,24245],{"className":24244},[886],[888,24246,24247],{"xmlns":890},[892,24248,24249,24282],{},[895,24250,24251,24253,24255,24257,24259,24261,24263,24265,24267,24269,24271,24273,24275,24277,24279],{},[898,24252,6909],{},[898,24254,1680],{},[898,24256,1661],{},[1701,24258,1792],{},[1850,24260,4062],{},[1701,24262,2317],{},[898,24264,6909],{},[898,24266,1680],{},[898,24268,1658],{},[1701,24270,1792],{},[1701,24272,2317],{},[1850,24274,24228],{},[898,24276,13189],{},[1701,24278,1703],{},[1850,24280,24281],{},"0,8.",[902,24283,24284],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,24286,24287,24367,24446],{},[123,24288,24289,1343,24317,24345,24346,12164,24364,1715],{},[883,24290,24292],{"className":24291},[886],[888,24293,24294],{"xmlns":890},[892,24295,24296,24314],{},[895,24297,24298,24300,24302,24304,24306,24308,24310,24312],{},[898,24299,6909],{},[898,24301,1680],{},[898,24303,1658],{},[1701,24305,1799],{"stretchy":1798},[1850,24307,5158],{},[1701,24309,1805],{"stretchy":1798},[1701,24311,1792],{},[1850,24313,23317],{},[902,24315,24316],{"encoding":904},"MPC(100) = 0{,}4",[883,24318,24320],{"className":24319},[886],[888,24321,24322],{"xmlns":890},[892,24323,24324,24342],{},[895,24325,24326,24328,24330,24332,24334,24336,24338,24340],{},[898,24327,6909],{},[898,24329,1680],{},[898,24331,1661],{},[1701,24333,1799],{"stretchy":1798},[1850,24335,5158],{},[1701,24337,1805],{"stretchy":1798},[1701,24339,1792],{},[1850,24341,3868],{},[902,24343,24344],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,24347,24349],{"className":24348},[886],[888,24350,24351],{"xmlns":890},[892,24352,24353,24361],{},[895,24354,24355,24357,24359],{},[898,24356,13189],{},[1701,24358,1792],{},[1850,24360,5158],{},[902,24362,24363],{"encoding":904},"Y = 100",[38,24365,24366],{},"větší sklon k úsporám",[123,24368,24369,1343,24397,24345,24425,12164,24443,1715],{},[883,24370,24372],{"className":24371},[886],[888,24373,24374],{"xmlns":890},[892,24375,24376,24394],{},[895,24377,24378,24380,24382,24384,24386,24388,24390,24392],{},[898,24379,6909],{},[898,24381,1680],{},[898,24383,1658],{},[1701,24385,1799],{"stretchy":1798},[1850,24387,12439],{},[1701,24389,1805],{"stretchy":1798},[1701,24391,1792],{},[1850,24393,3868],{},[902,24395,24396],{"encoding":904},"MPC(200) = 0{,}6",[883,24398,24400],{"className":24399},[886],[888,24401,24402],{"xmlns":890},[892,24403,24404,24422],{},[895,24405,24406,24408,24410,24412,24414,24416,24418,24420],{},[898,24407,6909],{},[898,24409,1680],{},[898,24411,1661],{},[1701,24413,1799],{"stretchy":1798},[1850,24415,12439],{},[1701,24417,1805],{"stretchy":1798},[1701,24419,1792],{},[1850,24421,23317],{},[902,24423,24424],{"encoding":904},"MPS(200) = 0{,}4",[883,24426,24428],{"className":24427},[886],[888,24429,24430],{"xmlns":890},[892,24431,24432,24440],{},[895,24433,24434,24436,24438],{},[898,24435,13189],{},[1701,24437,1792],{},[1850,24439,12439],{},[902,24441,24442],{"encoding":904},"Y = 200",[38,24444,24445],{},"větší sklon ke spotřebě",[123,24447,24448,24449,24467,24468,2506],{},"Přesně při ",[883,24450,24452],{"className":24451},[886],[888,24453,24454],{"xmlns":890},[892,24455,24456,24464],{},[895,24457,24458,24460,24462],{},[898,24459,13189],{},[1701,24461,1792],{},[1850,24463,12864],{},[902,24465,24466],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,24469,24471],{"className":24470},[886],[888,24472,24473],{"xmlns":890},[892,24474,24475,24495],{},[895,24476,24477,24479,24481,24483,24485,24487,24489,24491,24493],{},[898,24478,6909],{},[898,24480,1680],{},[898,24482,1658],{},[1701,24484,1792],{},[898,24486,6909],{},[898,24488,1680],{},[898,24490,1661],{},[1701,24492,1792],{},[1850,24494,3684],{},[902,24496,24497],{"encoding":904},"MPC = MPS = 0{,}5",[724,24499,24500,24501,24518,24519,24533,24534,3856,24547,24561,24562,24575,24576,24617],{},"Interpretace: při ",[883,24502,24504],{"className":24503},[886],[888,24505,24506],{"xmlns":890},[892,24507,24508,24516],{},[895,24509,24510,24512,24514],{},[898,24511,13189],{},[1701,24513,1792],{},[1850,24515,5158],{},[902,24517,24363],{"encoding":904}," se spotřeba mění ",[883,24520,24522],{"className":24521},[886],[888,24523,24524],{"xmlns":890},[892,24525,24526,24530],{},[895,24527,24528],{},[1850,24529,23317],{},[902,24531,24532],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,24535,24537],{"className":24536},[886],[888,24538,24539],{"xmlns":890},[892,24540,24541,24545],{},[895,24542,24543],{},[1850,24544,5158],{},[902,24546,5158],{"encoding":904},[883,24548,24550],{"className":24549},[886],[888,24551,24552],{"xmlns":890},[892,24553,24554,24559],{},[895,24555,24556],{},[1850,24557,24558],{},"101",[902,24560,24558],{"encoding":904},", změní se spotřeba přibližně o ",[883,24563,24565],{"className":24564},[886],[888,24566,24567],{"xmlns":890},[892,24568,24569,24573],{},[895,24570,24571],{},[1850,24572,23317],{},[902,24574,24532],{"encoding":904},". Skutečná změna ",[883,24577,24579],{"className":24578},[886],[888,24580,24581],{"xmlns":890},[892,24582,24583,24614],{},[895,24584,24585,24587,24589,24591,24593,24595,24597,24599,24601,24603,24605,24607,24609,24611],{},[898,24586,4708],{"mathvariant":2334},[898,24588,1658],{},[1701,24590,1792],{},[898,24592,1658],{},[1701,24594,1799],{"stretchy":1798},[1850,24596,24558],{},[1701,24598,1805],{"stretchy":1798},[1701,24600,2317],{},[898,24602,1658],{},[1701,24604,1799],{"stretchy":1798},[1850,24606,5158],{},[1701,24608,1805],{"stretchy":1798},[1701,24610,1792],{},[1850,24612,24613],{},"0,401",[902,24615,24616],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,24619,24620,24621],{},"Obecný trend: ",[38,24622,24623],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,24625,24627],{"id":24626},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,24629,24630,24631,1646,24634,24637,24638,1646,24641,1738,24644,1646,24647,24650],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,24632,24633],{},"makroekonomická rovnováha",[614,24635,24636],{},"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 ",[38,24639,24640],{},"agregátní poptávky",[614,24642,24643],{},"aggregate demand",[38,24645,24646],{},"agregátní nabídky",[614,24648,24649],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,24652,24654],{"id":24653},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,24656,24657],{},[2139,24658],{"alt":24659,"className":24660,"src":24661},"imek-keynesian-kriz",[210,2143],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,24663,24665],{"id":24664},"zadání-modelu","Zadání modelu",[724,24667,24668,24669,24682,24683,24696],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,24670,24672],{"className":24671},[886],[888,24673,24674],{"xmlns":890},[892,24675,24676,24680],{},[895,24677,24678],{},[898,24679,1658],{},[902,24681,1658],{"encoding":904}," a investice ",[883,24684,24686],{"className":24685},[886],[888,24687,24688],{"xmlns":890},[892,24689,24690,24694],{},[895,24691,24692],{},[898,24693,16238],{},[902,24695,16238],{"encoding":904},". Podmínka rovnováhy:",[724,24698,24699],{},[883,24700,24702],{"className":24701},[886],[888,24703,24704],{"xmlns":890},[892,24705,24706,24729],{},[895,24707,24708,24710,24712,24714,24716,24718,24720,24722,24724,24727],{},[898,24709,13189],{},[1701,24711,1792],{},[898,24713,1658],{},[1701,24715,1703],{},[898,24717,16238],{},[898,24719,1715],{"mathvariant":2334},[9942,24721],{"width":9944},[1701,24723,1799],{"stretchy":1798},[1850,24725,24726],{},"7.6",[1701,24728,1805],{"stretchy":1798},[902,24730,24731],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,24733,24735],{"id":24734},"soustava-rovnic","Soustava rovnic",[724,24737,24738,24739,24760,24761,24785],{},"Pro pevně zadané (plánované) investice ",[883,24740,24742],{"className":24741},[886],[888,24743,24744],{"xmlns":890},[892,24745,24746,24758],{},[895,24747,24748,24750,24752],{},[898,24749,16238],{},[1701,24751,1792],{},[3243,24753,24754,24756],{},[898,24755,16238],{},[1701,24757,8424],{},[902,24759,16249],{"encoding":904}," a funkci spotřeby ",[883,24762,24764],{"className":24763},[886],[888,24765,24766],{"xmlns":890},[892,24767,24768,24782],{},[895,24769,24770,24772,24774,24776,24778,24780],{},[898,24771,1658],{},[1701,24773,1792],{},[898,24775,1658],{},[1701,24777,1799],{"stretchy":1798},[898,24779,13189],{},[1701,24781,1805],{"stretchy":1798},[902,24783,24784],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,24787,24788],{},[883,24789,24791],{"className":24790},[886],[888,24792,24793],{"xmlns":890},[892,24794,24795,24868],{},[895,24796,24797,24859,24861,24863,24866],{},[2256,24798,24801,24831],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},"0.25em","right left",[2260,24802,24803,24809],{},[2263,24804,24805],{},[2363,24806,24807],{"scriptlevel":1852,"displaystyle":2011},[898,24808,13189],{},[2263,24810,24811],{},[2363,24812,24813],{"scriptlevel":1852,"displaystyle":2011},[895,24814,24815,24817,24819,24821,24823,24829],{},[895,24816],{},[1701,24818,1792],{},[898,24820,1658],{},[1701,24822,1703],{},[3243,24824,24825,24827],{},[898,24826,16238],{},[1701,24828,8424],{},[1701,24830,2012],{"separator":2011},[2260,24832,24833,24839],{},[2263,24834,24835],{},[2363,24836,24837],{"scriptlevel":1852,"displaystyle":2011},[898,24838,1658],{},[2263,24840,24841],{},[2363,24842,24843],{"scriptlevel":1852,"displaystyle":2011},[895,24844,24845,24847,24849,24851,24853,24855,24857],{},[895,24846],{},[1701,24848,1792],{},[898,24850,1658],{},[1701,24852,1799],{"stretchy":1798},[898,24854,13189],{},[1701,24856,1805],{"stretchy":1798},[1701,24858,2012],{"separator":2011},[9942,24860],{"width":9944},[1701,24862,1799],{"stretchy":1798},[1850,24864,24865],{},"7.7",[1701,24867,1805],{"stretchy":1798},[902,24869,24870],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,24872,24873,24874,4088,24876,2633,24893,4088,24896,1715],{},"jejímž řešením jsou ",[38,24875,17939],{},[883,24877,24879],{"className":24878},[886],[888,24880,24881],{"xmlns":890},[892,24882,24883,24891],{},[895,24884,24885],{},[3243,24886,24887,24889],{},[898,24888,13189],{},[898,24890,3249],{},[902,24892,17957],{"encoding":904},[38,24894,24895],{},"rovnovážná spotřeba",[883,24897,24899],{"className":24898},[886],[888,24900,24901],{"xmlns":890},[892,24902,24903,24911],{},[895,24904,24905],{},[3243,24906,24907,24909],{},[898,24908,1658],{},[898,24910,3249],{},[902,24912,18016],{"encoding":904},[198,24914,24916,24917],{"id":24915},"výpočet-yeye","Výpočet ",[883,24918,24920],{"className":24919},[886],[888,24921,24922],{"xmlns":890},[892,24923,24924,24932],{},[895,24925,24926],{},[3243,24927,24928,24930],{},[898,24929,13189],{},[898,24931,3249],{},[902,24933,17957],{"encoding":904},[724,24935,24936,24937,24960,24961,11747,24993],{},"Pro lineární spotřebu ",[883,24938,24940],{"className":24939},[886],[888,24941,24942],{"xmlns":890},[892,24943,24944,24958],{},[895,24945,24946,24948,24950,24952,24954,24956],{},[898,24947,1658],{},[1701,24949,1792],{},[898,24951,207],{},[898,24953,13189],{},[1701,24955,1703],{},[898,24957,3598],{},[902,24959,22966],{"encoding":904}," plyne z (7.7) rovnice ",[883,24962,24964],{"className":24963},[886],[888,24965,24966],{"xmlns":890},[892,24967,24968,24990],{},[895,24969,24970,24972,24974,24976,24978,24980,24982,24984],{},[898,24971,13189],{},[1701,24973,1792],{},[898,24975,207],{},[898,24977,13189],{},[1701,24979,1703],{},[898,24981,3598],{},[1701,24983,1703],{},[3243,24985,24986,24988],{},[898,24987,16238],{},[1701,24989,8424],{},[902,24991,24992],{"encoding":904},"Y = aY + b + I^*",[38,24994,24995],{},"redukovaný tvar",[724,24997,24998],{},[883,24999,25001],{"className":25000},[886],[888,25002,25003],{"xmlns":890},[892,25004,25005,25053],{},[895,25006,25007],{},[16886,25008,25009],{"notation":16888},[2363,25010,25011],{"scriptlevel":1852,"displaystyle":1798},[2363,25012,25013],{"scriptlevel":1852,"displaystyle":1798},[2363,25014,25015],{"scriptlevel":1852,"displaystyle":2011},[895,25016,25017,25019,25025,25027,25049,25051],{},[1939,25018,1941],{},[3243,25020,25021,25023],{},[898,25022,13189],{},[898,25024,3249],{},[1701,25026,1792],{},[3726,25028,25029,25041],{},[895,25030,25031,25033,25035],{},[898,25032,3598],{},[1701,25034,1703],{},[3243,25036,25037,25039],{},[898,25038,16238],{},[1701,25040,8424],{},[895,25042,25043,25045,25047],{},[1850,25044,4062],{},[1701,25046,2317],{},[898,25048,207],{},[898,25050,1715],{"mathvariant":2334},[1939,25052,1941],{},[902,25054,25055],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,25057,25059],{"id":25058},"příklad-73","Příklad 7.3",[724,25061,25062,25063,12164,25080,2633,25104,25130],{},"V modelu ",[883,25064,25066],{"className":25065},[886],[888,25067,25068],{"xmlns":890},[892,25069,25070,25078],{},[895,25071,25072,25074,25076],{},[898,25073,1658],{},[1939,25075,16344],{},[898,25077,16238],{},[902,25079,16349],{"encoding":904},[883,25081,25083],{"className":25082},[886],[888,25084,25085],{"xmlns":890},[892,25086,25087,25101],{},[895,25088,25089,25091,25093,25095,25097,25099],{},[898,25090,1658],{},[1701,25092,1792],{},[1850,25094,3868],{},[898,25096,13189],{},[1701,25098,1703],{},[1850,25100,3703],{},[902,25102,25103],{"encoding":904},"C = 0{,}6Y + 10",[883,25105,25107],{"className":25106},[886],[888,25108,25109],{"xmlns":890},[892,25110,25111,25127],{},[895,25112,25113,25115,25117,25119,25121],{},[898,25114,16238],{},[1701,25116,1792],{},[1850,25118,7592],{},[1701,25120,1792],{},[3243,25122,25123,25125],{},[898,25124,16238],{},[1701,25126,8424],{},[902,25128,25129],{"encoding":904},"I = 12 = I^*",". Soustava",[724,25132,25133],{},[883,25134,25136],{"className":25135},[886],[888,25137,25138],{"xmlns":890},[892,25139,25140,25196],{},[2256,25141,25142,25168],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,25143,25144,25150],{},[2263,25145,25146],{},[2363,25147,25148],{"scriptlevel":1852,"displaystyle":2011},[898,25149,13189],{},[2263,25151,25152],{},[2363,25153,25154],{"scriptlevel":1852,"displaystyle":2011},[895,25155,25156,25158,25160,25162,25164,25166],{},[895,25157],{},[1701,25159,1792],{},[898,25161,1658],{},[1701,25163,1703],{},[1850,25165,7592],{},[1701,25167,2012],{"separator":2011},[2260,25169,25170,25176],{},[2263,25171,25172],{},[2363,25173,25174],{"scriptlevel":1852,"displaystyle":2011},[898,25175,1658],{},[2263,25177,25178],{},[2363,25179,25180],{"scriptlevel":1852,"displaystyle":2011},[895,25181,25182,25184,25186,25188,25190,25192,25194],{},[895,25183],{},[1701,25185,1792],{},[1850,25187,3868],{},[898,25189,13189],{},[1701,25191,1703],{},[1850,25193,3703],{},[1701,25195,2012],{"separator":2011},[902,25197,25198],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,25200,25201,25202,1343,25225,25248,25249,2506],{},"má řešení ",[883,25203,25205],{"className":25204},[886],[888,25206,25207],{"xmlns":890},[892,25208,25209,25222],{},[895,25210,25211,25217,25219],{},[3243,25212,25213,25215],{},[898,25214,13189],{},[898,25216,3249],{},[1701,25218,1792],{},[1850,25220,25221],{},"55",[902,25223,25224],{"encoding":904},"Y^E = 55",[883,25226,25228],{"className":25227},[886],[888,25229,25230],{"xmlns":890},[892,25231,25232,25245],{},[895,25233,25234,25240,25242],{},[3243,25235,25236,25238],{},[898,25237,1658],{},[898,25239,3249],{},[1701,25241,1792],{},[1850,25243,25244],{},"43",[902,25246,25247],{"encoding":904},"C^E = 43"," (a ",[883,25250,25252],{"className":25251},[886],[888,25253,25254],{"xmlns":890},[892,25255,25256,25268],{},[895,25257,25258,25264,25266],{},[3243,25259,25260,25262],{},[898,25261,1661],{},[898,25263,3249],{},[1701,25265,1792],{},[1850,25267,7592],{},[902,25269,25270],{"encoding":904},"S^E = 12",[724,25272,25273],{},[614,25274,25275,25276,25298,25299,1738,25320,25343,25344,1715],{},"Obrázek 7.5 — Přímky ",[883,25277,25279],{"className":25278},[886],[888,25280,25281],{"xmlns":890},[892,25282,25283,25295],{},[895,25284,25285,25287,25289,25291,25293],{},[898,25286,1658],{},[1701,25288,1792],{},[898,25290,13189],{},[1701,25292,2317],{},[1850,25294,7592],{},[902,25296,25297],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,25300,25302],{"className":25301},[886],[888,25303,25304],{"xmlns":890},[892,25305,25306,25318],{},[895,25307,25308,25310,25312,25314,25316],{},[898,25309,13189],{},[1701,25311,1792],{},[898,25313,1658],{},[1701,25315,1703],{},[898,25317,16238],{},[902,25319,18797],{"encoding":904},[883,25321,25323],{"className":25322},[886],[888,25324,25325],{"xmlns":890},[892,25326,25327,25341],{},[895,25328,25329,25331,25333,25335,25337,25339],{},[898,25330,1658],{},[1701,25332,1792],{},[1850,25334,3868],{},[898,25336,13189],{},[1701,25338,1703],{},[1850,25340,3703],{},[902,25342,25103],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,25345,25347],{"className":25346},[886],[888,25348,25349],{"xmlns":890},[892,25350,25351,25383],{},[895,25352,25353,25355,25361,25363,25369,25371,25373,25375,25377,25379,25381],{},[1701,25354,2036],{"stretchy":1798},[3243,25356,25357,25359],{},[898,25358,13189],{},[898,25360,3249],{},[1701,25362,2012],{"separator":2011},[3243,25364,25365,25367],{},[898,25366,1658],{},[898,25368,3249],{},[1701,25370,2053],{"stretchy":1798},[1701,25372,1792],{},[1701,25374,2036],{"stretchy":1798},[1850,25376,25221],{},[1701,25378,2012],{"separator":2011},[1850,25380,25244],{},[1701,25382,2053],{"stretchy":1798},[902,25384,25385],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,25387,25388,25391,25392,25409,25410,1715],{},[38,25389,25390],{},"Komentář k přechodu."," Model ",[883,25393,25395],{"className":25394},[886],[888,25396,25397],{"xmlns":890},[892,25398,25399,25407],{},[895,25400,25401,25403,25405],{},[898,25402,1658],{},[1939,25404,16344],{},[898,25406,16238],{},[902,25408,16349],{"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 ",[38,25411,25412,25413],{},"model ",[883,25414,25416],{"className":25415},[886],[888,25417,25418],{"xmlns":890},[892,25419,25420,25432],{},[895,25421,25422,25424,25426,25428,25430],{},[898,25423,1658],{},[1939,25425,16344],{},[898,25427,16238],{},[1939,25429,16344],{},[898,25431,16167],{},[902,25433,22266],{"encoding":904},[115,25435,25437],{"id":25436},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,25439,24665],{"id":25440},"zadání-modelu-1",[724,25442,25443,25444,25461,25462,4088,25465,1646,25478,25481],{},"Rozšíření modelu ",[883,25445,25447],{"className":25446},[886],[888,25448,25449],{"xmlns":890},[892,25450,25451,25459],{},[895,25452,25453,25455,25457],{},[898,25454,1658],{},[1939,25456,16344],{},[898,25458,16238],{},[902,25460,16349],{"encoding":904}," o ",[38,25463,25464],{},"vládní výdaje",[883,25466,25468],{"className":25467},[886],[888,25469,25470],{"xmlns":890},[892,25471,25472,25476],{},[895,25473,25474],{},[898,25475,16167],{},[902,25477,16167],{"encoding":904},[614,25479,25480],{},"government expenditure","). Podmínka rovnováhy:",[724,25483,25484],{},[883,25485,25487],{"className":25486},[886],[888,25488,25489],{"xmlns":890},[892,25490,25491,25518],{},[895,25492,25493,25495,25497,25499,25501,25503,25505,25507,25509,25511,25513,25516],{},[898,25494,13189],{},[1701,25496,1792],{},[898,25498,1658],{},[1701,25500,1703],{},[898,25502,16238],{},[1701,25504,1703],{},[898,25506,16167],{},[898,25508,1715],{"mathvariant":2334},[9942,25510],{"width":9944},[1701,25512,1799],{"stretchy":1798},[1850,25514,25515],{},"7.8",[1701,25517,1805],{"stretchy":1798},[902,25519,25520],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,25522,25523,25524,4088,25527,1646,25540,25543],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,25525,25526],{},"zdaněním domácností",[883,25528,25530],{"className":25529},[886],[888,25531,25532],{"xmlns":890},[892,25533,25534,25538],{},[895,25535,25536],{},[898,25537,5877],{},[902,25539,5877],{"encoding":904},[614,25541,25542],{},"taxation","). Zdanění bývá:",[120,25545,25546,25579,25604],{},[123,25547,25548,25549,2012],{},"úměrné důchodu: ",[883,25550,25552],{"className":25551},[886],[888,25553,25554],{"xmlns":890},[892,25555,25556,25576],{},[895,25557,25558,25560,25562,25564,25566,25568,25570,25572,25574],{},[898,25559,5877],{},[1701,25561,1792],{},[898,25563,5877],{},[1701,25565,1799],{"stretchy":1798},[898,25567,13189],{},[1701,25569,1805],{"stretchy":1798},[1701,25571,1792],{},[898,25573,22901],{},[898,25575,13189],{},[902,25577,25578],{"encoding":904},"T = T(Y) = tY",[123,25580,25581,25582,2012],{},"fixní: ",[883,25583,25585],{"className":25584},[886],[888,25586,25587],{"xmlns":890},[892,25588,25589,25601],{},[895,25590,25591,25593,25595],{},[898,25592,5877],{},[1701,25594,1792],{},[3243,25596,25597,25599],{},[898,25598,5877],{},[1701,25600,8424],{},[902,25602,25603],{"encoding":904},"T = T^*",[123,25605,25606,25607,2020,25635,1715],{},"kombinované: ",[883,25608,25610],{"className":25609},[886],[888,25611,25612],{"xmlns":890},[892,25613,25614,25632],{},[895,25615,25616,25618,25620,25626,25628,25630],{},[898,25617,5877],{},[1701,25619,1792],{},[3243,25621,25622,25624],{},[898,25623,5877],{},[1701,25625,8424],{},[1701,25627,1703],{},[898,25629,22901],{},[898,25631,13189],{},[902,25633,25634],{"encoding":904},"T = T^* + tY",[883,25636,25638],{"className":25637},[886],[888,25639,25640],{"xmlns":890},[892,25641,25642,25654],{},[895,25643,25644,25646,25648,25650,25652],{},[1850,25645,1852],{},[1701,25647,11741],{},[898,25649,22901],{},[1701,25651,7530],{},[1850,25653,4062],{},[902,25655,25656],{"encoding":904},"0 \\le t \u003C 1",[1635,25658,25659],{},[724,25660,25661,25663,25664,25685,25686,25689,25690,25703,25704,1738,25730,4088,25733,25759,25760,25788,25789,2633,25802,25820],{},[883,25662,4695],{}," Pozor na disponibilní důchod\nV modelu ",[883,25665,25667],{"className":25666},[886],[888,25668,25669],{"xmlns":890},[892,25670,25671,25683],{},[895,25672,25673,25675,25677,25679,25681],{},[898,25674,1658],{},[1939,25676,16344],{},[898,25678,16238],{},[1939,25680,16344],{},[898,25682,16167],{},[902,25684,22266],{"encoding":904}," je nutné ",[38,25687,25688],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,25691,25693],{"className":25692},[886],[888,25694,25695],{"xmlns":890},[892,25696,25697,25701],{},[895,25698,25699],{},[898,25700,13189],{},[902,25702,13189],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,25705,25707],{"className":25706},[886],[888,25708,25709],{"xmlns":890},[892,25710,25711,25727],{},[895,25712,25713,25715,25717,25719,25721,25723,25725],{},[898,25714,13189],{},[1701,25716,1792],{},[898,25718,1658],{},[1701,25720,1703],{},[898,25722,16238],{},[1701,25724,1703],{},[898,25726,16167],{},[902,25728,25729],{"encoding":904},"Y = C + I + G",[38,25731,25732],{},"disponibilní důchod",[883,25734,25736],{"className":25735},[886],[888,25737,25738],{"xmlns":890},[892,25739,25740,25756],{},[895,25741,25742,25748,25750,25752,25754],{},[1845,25743,25744,25746],{},[898,25745,13189],{},[898,25747,1795],{},[1701,25749,1792],{},[898,25751,13189],{},[1701,25753,2317],{},[898,25755,5877],{},[902,25757,25758],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,25761,25763],{"className":25762},[886],[888,25764,25765],{"xmlns":890},[892,25766,25767,25785],{},[895,25768,25769,25771,25773,25775,25777,25783],{},[898,25770,1658],{},[1701,25772,1792],{},[898,25774,1658],{},[1701,25776,1799],{"stretchy":1798},[1845,25778,25779,25781],{},[898,25780,13189],{},[898,25782,1795],{},[1701,25784,1805],{"stretchy":1798},[902,25786,25787],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,25790,25792],{"className":25791},[886],[888,25793,25794],{"xmlns":890},[892,25795,25796,25800],{},[895,25797,25798],{},[898,25799,13189],{},[902,25801,13189],{"encoding":904},[883,25803,25805],{"className":25804},[886],[888,25806,25807],{"xmlns":890},[892,25808,25809,25817],{},[895,25810,25811],{},[1845,25812,25813,25815],{},[898,25814,13189],{},[898,25816,1795],{},[902,25818,25819],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,25822,25823,1646,25826,1805],{},[38,25824,25825],{},"Disponibilní důchod",[614,25827,25828],{},"disposable income",[724,25830,25831],{},[883,25832,25834],{"className":25833},[886],[888,25835,25836],{"xmlns":890},[892,25837,25838,25854],{},[895,25839,25840,25846,25848,25850,25852],{},[1845,25841,25842,25844],{},[898,25843,13189],{},[898,25845,1795],{},[1701,25847,1792],{},[898,25849,13189],{},[1701,25851,2317],{},[898,25853,5877],{},[902,25855,25758],{"encoding":904},[724,25857,25858,25859,1715],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,25860,25862],{"className":25861},[886],[888,25863,25864],{"xmlns":890},[892,25865,25866,25884],{},[895,25867,25868,25870,25872,25874,25876,25882],{},[898,25869,1658],{},[1701,25871,1792],{},[898,25873,1658],{},[1701,25875,1799],{"stretchy":1798},[1845,25877,25878,25880],{},[898,25879,13189],{},[898,25881,1795],{},[1701,25883,1805],{"stretchy":1798},[902,25885,25787],{"encoding":904},[198,25887,24735],{"id":25888},"soustava-rovnic-1",[724,25890,25891,25892,1343,25913,25935,25936,2246],{},"Pro pevně zadané ",[883,25893,25895],{"className":25894},[886],[888,25896,25897],{"xmlns":890},[892,25898,25899,25911],{},[895,25900,25901,25903,25905],{},[898,25902,16238],{},[1701,25904,1792],{},[3243,25906,25907,25909],{},[898,25908,16238],{},[1701,25910,8424],{},[902,25912,16249],{"encoding":904},[883,25914,25916],{"className":25915},[886],[888,25917,25918],{"xmlns":890},[892,25919,25920,25932],{},[895,25921,25922,25924,25926],{},[898,25923,16167],{},[1701,25925,1792],{},[3243,25927,25928,25930],{},[898,25929,16167],{},[1701,25931,8424],{},[902,25933,25934],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,25937,25939],{"className":25938},[886],[888,25940,25941],{"xmlns":890},[892,25942,25943,25963],{},[895,25944,25945,25947,25949,25951,25953,25959,25961],{},[898,25946,13189],{},[1701,25948,2012],{"separator":2011},[898,25950,1658],{},[1701,25952,2012],{"separator":2011},[1845,25954,25955,25957],{},[898,25956,13189],{},[898,25958,1795],{},[1701,25960,2012],{"separator":2011},[898,25962,5877],{},[902,25964,25965],{"encoding":904},"Y, C, Y_D, T",[724,25967,25968],{},[883,25969,25971],{"className":25970},[886],[888,25972,25973],{"xmlns":890},[892,25974,25975,26116],{},[895,25976,25977,26107,26109,26111,26114],{},[2256,25978,25979,26017,26045,26077],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,25980,25981,25987],{},[2263,25982,25983],{},[2363,25984,25985],{"scriptlevel":1852,"displaystyle":2011},[898,25986,13189],{},[2263,25988,25989],{},[2363,25990,25991],{"scriptlevel":1852,"displaystyle":2011},[895,25992,25993,25995,25997,25999,26001,26007,26009,26015],{},[895,25994],{},[1701,25996,1792],{},[898,25998,1658],{},[1701,26000,1703],{},[3243,26002,26003,26005],{},[898,26004,16238],{},[1701,26006,8424],{},[1701,26008,1703],{},[3243,26010,26011,26013],{},[898,26012,16167],{},[1701,26014,8424],{},[1701,26016,2012],{"separator":2011},[2260,26018,26019,26025],{},[2263,26020,26021],{},[2363,26022,26023],{"scriptlevel":1852,"displaystyle":2011},[898,26024,5877],{},[2263,26026,26027],{},[2363,26028,26029],{"scriptlevel":1852,"displaystyle":2011},[895,26030,26031,26033,26035,26037,26039,26041,26043],{},[895,26032],{},[1701,26034,1792],{},[898,26036,5877],{},[1701,26038,1799],{"stretchy":1798},[898,26040,13189],{},[1701,26042,1805],{"stretchy":1798},[1701,26044,2012],{"separator":2011},[2260,26046,26047,26053],{},[2263,26048,26049],{},[2363,26050,26051],{"scriptlevel":1852,"displaystyle":2011},[898,26052,1658],{},[2263,26054,26055],{},[2363,26056,26057],{"scriptlevel":1852,"displaystyle":2011},[895,26058,26059,26061,26063,26065,26067,26073,26075],{},[895,26060],{},[1701,26062,1792],{},[898,26064,1658],{},[1701,26066,1799],{"stretchy":1798},[1845,26068,26069,26071],{},[898,26070,13189],{},[898,26072,1795],{},[1701,26074,1805],{"stretchy":1798},[1701,26076,2012],{"separator":2011},[2260,26078,26079,26089],{},[2263,26080,26081],{},[2363,26082,26083],{"scriptlevel":1852,"displaystyle":2011},[1845,26084,26085,26087],{},[898,26086,13189],{},[898,26088,1795],{},[2263,26090,26091],{},[2363,26092,26093],{"scriptlevel":1852,"displaystyle":2011},[895,26094,26095,26097,26099,26101,26103,26105],{},[895,26096],{},[1701,26098,1792],{},[898,26100,13189],{},[1701,26102,2317],{},[898,26104,5877],{},[1701,26106,2012],{"separator":2011},[9942,26108],{"width":9944},[1701,26110,1799],{"stretchy":1798},[1850,26112,26113],{},"7.9",[1701,26115,1805],{"stretchy":1798},[902,26117,26118],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,26120,26121,26122,26166,26167,1715],{},"s řešeními ",[883,26123,26125],{"className":26124},[886],[888,26126,26127],{"xmlns":890},[892,26128,26129,26163],{},[895,26130,26131,26137,26139,26145,26147,26153,26155],{},[3243,26132,26133,26135],{},[898,26134,13189],{},[898,26136,3249],{},[1701,26138,2012],{"separator":2011},[3243,26140,26141,26143],{},[898,26142,1658],{},[898,26144,3249],{},[1701,26146,2012],{"separator":2011},[3243,26148,26149,26151],{},[898,26150,5877],{},[898,26152,3249],{},[1701,26154,2012],{"separator":2011},[2287,26156,26157,26159,26161],{},[898,26158,13189],{},[898,26160,1795],{},[898,26162,3249],{},[902,26164,26165],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,26168,26170],{"className":26169},[886],[888,26171,26172],{"xmlns":890},[892,26173,26174,26200],{},[895,26175,26176,26182,26184,26192,26194],{},[3243,26177,26178,26180],{},[898,26179,1661],{},[898,26181,3249],{},[1701,26183,1792],{},[2287,26185,26186,26188,26190],{},[898,26187,13189],{},[898,26189,1795],{},[898,26191,3249],{},[1701,26193,2317],{},[3243,26195,26196,26198],{},[898,26197,1658],{},[898,26199,3249],{},[902,26201,26202],{"encoding":904},"S^E = Y_D^E - C^E",[1635,26204,26205,26210],{},[724,26206,26207,26209],{},[883,26208,3140],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,26211,26212,26235,26318,26373,26463],{},[123,26213,26214,26217,26218,1715],{},[38,26215,26216],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,26219,26221],{"className":26220},[886],[888,26222,26223],{"xmlns":890},[892,26224,26225,26233],{},[895,26226,26227],{},[1845,26228,26229,26231],{},[898,26230,13189],{},[898,26232,1795],{},[902,26234,25819],{"encoding":904},[123,26236,26237,26286,26287,26304,26305,1715],{},[38,26238,26239,26240,26260,26261],{},"Dosaď ",[883,26241,26243],{"className":26242},[886],[888,26244,26245],{"xmlns":890},[892,26246,26247,26257],{},[895,26248,26249,26251,26253,26255],{},[898,26250,5877],{},[1701,26252,1799],{"stretchy":1798},[898,26254,13189],{},[1701,26256,1805],{"stretchy":1798},[902,26258,26259],{"encoding":904},"T(Y)"," do ",[883,26262,26264],{"className":26263},[886],[888,26265,26266],{"xmlns":890},[892,26267,26268,26284],{},[895,26269,26270,26276,26278,26280,26282],{},[1845,26271,26272,26274],{},[898,26273,13189],{},[898,26275,1795],{},[1701,26277,1792],{},[898,26279,13189],{},[1701,26281,2317],{},[898,26283,5877],{},[902,26285,25758],{"encoding":904}," — dostaneš ",[883,26288,26290],{"className":26289},[886],[888,26291,26292],{"xmlns":890},[892,26293,26294,26302],{},[895,26295,26296],{},[1845,26297,26298,26300],{},[898,26299,13189],{},[898,26301,1795],{},[902,26303,25819],{"encoding":904}," jako lineární funkci ",[883,26306,26308],{"className":26307},[886],[888,26309,26310],{"xmlns":890},[892,26311,26312,26316],{},[895,26313,26314],{},[898,26315,13189],{},[902,26317,13189],{"encoding":904},[123,26319,26320,26286,26347,26304,26360,1715],{},[38,26321,26239,26322,26346],{},[883,26323,26325],{"className":26324},[886],[888,26326,26327],{"xmlns":890},[892,26328,26329,26343],{},[895,26330,26331,26337,26339,26341],{},[1845,26332,26333,26335],{},[898,26334,13189],{},[898,26336,1795],{},[1701,26338,1799],{"stretchy":1798},[898,26340,13189],{},[1701,26342,1805],{"stretchy":1798},[902,26344,26345],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,26348,26350],{"className":26349},[886],[888,26351,26352],{"xmlns":890},[892,26353,26354,26358],{},[895,26355,26356],{},[898,26357,1658],{},[902,26359,1658],{"encoding":904},[883,26361,26363],{"className":26362},[886],[888,26364,26365],{"xmlns":890},[892,26366,26367,26371],{},[895,26368,26369],{},[898,26370,13189],{},[902,26372,13189],{"encoding":904},[123,26374,26375,4088,26397,26431,26432,26445,26446,1715],{},[38,26376,26239,26377,26396],{},[883,26378,26380],{"className":26379},[886],[888,26381,26382],{"xmlns":890},[892,26383,26384,26394],{},[895,26385,26386,26388,26390,26392],{},[898,26387,1658],{},[1701,26389,1799],{"stretchy":1798},[898,26391,13189],{},[1701,26393,1805],{"stretchy":1798},[902,26395,18269],{"encoding":904}," do podmínky rovnováhy",[883,26398,26400],{"className":26399},[886],[888,26401,26402],{"xmlns":890},[892,26403,26404,26428],{},[895,26405,26406,26408,26410,26412,26414,26420,26422],{},[898,26407,13189],{},[1701,26409,1792],{},[898,26411,1658],{},[1701,26413,1703],{},[3243,26415,26416,26418],{},[898,26417,16238],{},[1701,26419,8424],{},[1701,26421,1703],{},[3243,26423,26424,26426],{},[898,26425,16167],{},[1701,26427,8424],{},[902,26429,26430],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,26433,26435],{"className":26434},[886],[888,26436,26437],{"xmlns":890},[892,26438,26439,26443],{},[895,26440,26441],{},[898,26442,13189],{},[902,26444,13189],{"encoding":904},", odtud ",[883,26447,26449],{"className":26448},[886],[888,26450,26451],{"xmlns":890},[892,26452,26453,26461],{},[895,26454,26455],{},[3243,26456,26457,26459],{},[898,26458,13189],{},[898,26460,3249],{},[902,26462,17957],{"encoding":904},[123,26464,26465,26468,26469,1343,26487,1343,26507,1343,26524,1715],{},[38,26466,26467],{},"Zpětným dosazením"," dopočítej ",[883,26470,26472],{"className":26471},[886],[888,26473,26474],{"xmlns":890},[892,26475,26476,26484],{},[895,26477,26478],{},[3243,26479,26480,26482],{},[898,26481,5877],{},[898,26483,3249],{},[902,26485,26486],{"encoding":904},"T^E",[883,26488,26490],{"className":26489},[886],[888,26491,26492],{"xmlns":890},[892,26493,26494,26504],{},[895,26495,26496],{},[2287,26497,26498,26500,26502],{},[898,26499,13189],{},[898,26501,1795],{},[898,26503,3249],{},[902,26505,26506],{"encoding":904},"Y_D^E",[883,26508,26510],{"className":26509},[886],[888,26511,26512],{"xmlns":890},[892,26513,26514,26522],{},[895,26515,26516],{},[3243,26517,26518,26520],{},[898,26519,1658],{},[898,26521,3249],{},[902,26523,18016],{"encoding":904},[883,26525,26527],{"className":26526},[886],[888,26528,26529],{"xmlns":890},[892,26530,26531,26539],{},[895,26532,26533],{},[3243,26534,26535,26537],{},[898,26536,1661],{},[898,26538,3249],{},[902,26540,26541],{"encoding":904},"S^E",[198,26543,26545],{"id":26544},"příklad-74","Příklad 7.4",[724,26547,25062,26548,26569,26570,1343,26601,1343,26625,1343,26647,26669],{},[883,26549,26551],{"className":26550},[886],[888,26552,26553],{"xmlns":890},[892,26554,26555,26567],{},[895,26556,26557,26559,26561,26563,26565],{},[898,26558,1658],{},[1939,26560,16344],{},[898,26562,16238],{},[1939,26564,16344],{},[898,26566,16167],{},[902,26568,22266],{"encoding":904}," jsou dány ",[883,26571,26573],{"className":26572},[886],[888,26574,26575],{"xmlns":890},[892,26576,26577,26598],{},[895,26578,26579,26581,26583,26586,26588,26594,26596],{},[898,26580,1658],{},[1701,26582,1792],{},[1850,26584,26585],{},"0,9",[1939,26587,1941],{},[1845,26589,26590,26592],{},[898,26591,13189],{},[898,26593,1795],{},[1701,26595,1703],{},[1850,26597,9961],{},[902,26599,26600],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,26602,26604],{"className":26603},[886],[888,26605,26606],{"xmlns":890},[892,26607,26608,26622],{},[895,26609,26610,26612,26614,26616,26618,26620],{},[898,26611,5877],{},[1701,26613,1792],{},[1850,26615,6930],{},[898,26617,13189],{},[1701,26619,1703],{},[1850,26621,9071],{},[902,26623,26624],{"encoding":904},"T = 0{,}2Y + 25",[883,26626,26628],{"className":26627},[886],[888,26629,26630],{"xmlns":890},[892,26631,26632,26644],{},[895,26633,26634,26640,26642],{},[3243,26635,26636,26638],{},[898,26637,16238],{},[1701,26639,8424],{},[1701,26641,1792],{},[1850,26643,4136],{},[902,26645,26646],{"encoding":904},"I^* = 35",[883,26648,26650],{"className":26649},[886],[888,26651,26652],{"xmlns":890},[892,26653,26654,26666],{},[895,26655,26656,26662,26664],{},[3243,26657,26658,26660],{},[898,26659,16167],{},[1701,26661,8424],{},[1701,26663,1792],{},[1850,26665,13096],{},[902,26667,26668],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,26671,26672],{},[883,26673,26675],{"className":26674},[886],[888,26676,26677],{"xmlns":890},[892,26678,26679,26803],{},[2256,26680,26681,26711,26739,26773],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,26682,26683,26689],{},[2263,26684,26685],{},[2363,26686,26687],{"scriptlevel":1852,"displaystyle":2011},[898,26688,13189],{},[2263,26690,26691],{},[2363,26692,26693],{"scriptlevel":1852,"displaystyle":2011},[895,26694,26695,26697,26699,26701,26703,26705,26707,26709],{},[895,26696],{},[1701,26698,1792],{},[898,26700,1658],{},[1701,26702,1703],{},[1850,26704,4136],{},[1701,26706,1703],{},[1850,26708,13096],{},[1701,26710,2012],{"separator":2011},[2260,26712,26713,26719],{},[2263,26714,26715],{},[2363,26716,26717],{"scriptlevel":1852,"displaystyle":2011},[898,26718,5877],{},[2263,26720,26721],{},[2363,26722,26723],{"scriptlevel":1852,"displaystyle":2011},[895,26724,26725,26727,26729,26731,26733,26735,26737],{},[895,26726],{},[1701,26728,1792],{},[1850,26730,6930],{},[898,26732,13189],{},[1701,26734,1703],{},[1850,26736,9071],{},[1701,26738,2012],{"separator":2011},[2260,26740,26741,26747],{},[2263,26742,26743],{},[2363,26744,26745],{"scriptlevel":1852,"displaystyle":2011},[898,26746,1658],{},[2263,26748,26749],{},[2363,26750,26751],{"scriptlevel":1852,"displaystyle":2011},[895,26752,26753,26755,26757,26759,26761,26767,26769,26771],{},[895,26754],{},[1701,26756,1792],{},[1850,26758,26585],{},[1939,26760,1941],{},[1845,26762,26763,26765],{},[898,26764,13189],{},[898,26766,1795],{},[1701,26768,1703],{},[1850,26770,9961],{},[1701,26772,2012],{"separator":2011},[2260,26774,26775,26785],{},[2263,26776,26777],{},[2363,26778,26779],{"scriptlevel":1852,"displaystyle":2011},[1845,26780,26781,26783],{},[898,26782,13189],{},[898,26784,1795],{},[2263,26786,26787],{},[2363,26788,26789],{"scriptlevel":1852,"displaystyle":2011},[895,26790,26791,26793,26795,26797,26799,26801],{},[895,26792],{},[1701,26794,1792],{},[898,26796,13189],{},[1701,26798,2317],{},[898,26800,5877],{},[898,26802,1715],{"mathvariant":2334},[902,26804,26805],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,26807,26808,26810,26811,26865,26866,26912,26913,2246],{},[38,26809,5001],{}," Z definice ",[883,26812,26814],{"className":26813},[886],[888,26815,26816],{"xmlns":890},[892,26817,26818,26862],{},[895,26819,26820,26826,26828,26830,26832,26834,26836,26838,26840,26842,26844,26846,26848,26850,26852,26854,26856,26858,26860],{},[1845,26821,26822,26824],{},[898,26823,13189],{},[898,26825,1795],{},[1701,26827,1792],{},[898,26829,13189],{},[1701,26831,2317],{},[898,26833,5877],{},[1701,26835,1792],{},[898,26837,13189],{},[1701,26839,2317],{},[1701,26841,1799],{"stretchy":1798},[1850,26843,6930],{},[898,26845,13189],{},[1701,26847,1703],{},[1850,26849,9071],{},[1701,26851,1805],{"stretchy":1798},[1701,26853,1792],{},[1850,26855,18642],{},[898,26857,13189],{},[1701,26859,2317],{},[1850,26861,9071],{},[902,26863,26864],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,26867,26869],{"className":26868},[886],[888,26870,26871],{"xmlns":890},[892,26872,26873,26909],{},[895,26874,26875,26877,26879,26881,26883,26885,26887,26889,26891,26893,26895,26897,26899,26902,26904,26906],{},[898,26876,1658],{},[1701,26878,1792],{},[1850,26880,26585],{},[1701,26882,1799],{"stretchy":1798},[1850,26884,18642],{},[898,26886,13189],{},[1701,26888,2317],{},[1850,26890,9071],{},[1701,26892,1805],{"stretchy":1798},[1701,26894,1703],{},[1850,26896,9961],{},[1701,26898,1792],{},[1850,26900,26901],{},"0,72",[898,26903,13189],{},[1701,26905,1703],{},[1850,26907,26908],{},"47,5",[902,26910,26911],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,26914,26916],{"className":26915},[886],[888,26917,26918],{"xmlns":890},[892,26919,26920,26938],{},[895,26921,26922,26924,26926,26928,26930,26932,26934,26936],{},[898,26923,13189],{},[1701,26925,1792],{},[1850,26927,26901],{},[898,26929,13189],{},[1701,26931,1703],{},[1850,26933,26908],{},[1701,26935,1703],{},[1850,26937,25221],{},[902,26939,26940],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,26942,26943],{},[883,26944,26946],{"className":26945},[886],[888,26947,26948],{"xmlns":890},[892,26949,26950,26991],{},[895,26951,26952,26955,26957,26959,26962,26964,26966,26968,26974,26976,26986,26988],{},[1850,26953,26954],{},"0,28",[898,26956,13189],{},[1701,26958,1792],{},[1850,26960,26961],{},"102,5",[1939,26963,8058],{},[1701,26965,19061],{},[1939,26967,8058],{},[3243,26969,26970,26972],{},[898,26971,13189],{},[898,26973,3249],{},[1701,26975,1792],{},[2363,26977,26978],{"scriptlevel":1852,"displaystyle":1798},[3726,26979,26980,26983],{},[1850,26981,26982],{},"5125",[1850,26984,26985],{},"14",[1701,26987,3782],{},[1850,26989,26990],{},"366,071.",[902,26992,26993],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,26995,26996],{},"Rovnovážné veličiny:",[120,26998,26999,27034,27086,27140,27188],{},[123,27000,27001,2012],{},[883,27002,27004],{"className":27003},[886],[888,27005,27006],{"xmlns":890},[892,27007,27008,27031],{},[895,27009,27010,27016,27018,27026,27028],{},[3243,27011,27012,27014],{},[898,27013,13189],{},[898,27015,3249],{},[1701,27017,1792],{},[2363,27019,27020],{"scriptlevel":1852,"displaystyle":1798},[3726,27021,27022,27024],{},[1850,27023,26982],{},[1850,27025,26985],{},[1701,27027,3782],{},[1850,27029,27030],{},"366,071",[902,27032,27033],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,27035,27036,2012],{},[883,27037,27039],{"className":27038},[886],[888,27040,27041],{"xmlns":890},[892,27042,27043,27083],{},[895,27044,27045,27051,27053,27055,27057,27063,27065,27067,27069,27078,27080],{},[3243,27046,27047,27049],{},[898,27048,5877],{},[898,27050,3249],{},[1701,27052,1792],{},[1850,27054,6930],{},[1939,27056,1941],{},[3243,27058,27059,27061],{},[898,27060,13189],{},[898,27062,3249],{},[1701,27064,1703],{},[1850,27066,9071],{},[1701,27068,1792],{},[2363,27070,27071],{"scriptlevel":1852,"displaystyle":1798},[3726,27072,27073,27076],{},[1850,27074,27075],{},"1375",[1850,27077,26985],{},[1701,27079,3782],{},[1850,27081,27082],{},"98,214",[902,27084,27085],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,27087,27088,2012],{},[883,27089,27091],{"className":27090},[886],[888,27092,27093],{"xmlns":890},[892,27094,27095,27137],{},[895,27096,27097,27105,27107,27113,27115,27121,27123,27132,27134],{},[2287,27098,27099,27101,27103],{},[898,27100,13189],{},[898,27102,1795],{},[898,27104,3249],{},[1701,27106,1792],{},[3243,27108,27109,27111],{},[898,27110,13189],{},[898,27112,3249],{},[1701,27114,2317],{},[3243,27116,27117,27119],{},[898,27118,5877],{},[898,27120,3249],{},[1701,27122,1792],{},[2363,27124,27125],{"scriptlevel":1852,"displaystyle":1798},[3726,27126,27127,27130],{},[1850,27128,27129],{},"3750",[1850,27131,26985],{},[1701,27133,3782],{},[1850,27135,27136],{},"267,857",[902,27138,27139],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,27141,27142,2012],{},[883,27143,27145],{"className":27144},[886],[888,27146,27147],{"xmlns":890},[892,27148,27149,27185],{},[895,27150,27151,27157,27159,27165,27167,27169,27171,27180,27182],{},[3243,27152,27153,27155],{},[898,27154,1658],{},[898,27156,3249],{},[1701,27158,1792],{},[3243,27160,27161,27163],{},[898,27162,13189],{},[898,27164,3249],{},[1701,27166,2317],{},[1850,27168,25221],{},[1701,27170,1792],{},[2363,27172,27173],{"scriptlevel":1852,"displaystyle":1798},[3726,27174,27175,27178],{},[1850,27176,27177],{},"4355",[1850,27179,26985],{},[1701,27181,3782],{},[1850,27183,27184],{},"311,071",[902,27186,27187],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,27189,27190,27246],{},[883,27191,27193],{"className":27192},[886],[888,27194,27195],{"xmlns":890},[892,27196,27197,27243],{},[895,27198,27199,27205,27207,27215,27217,27223,27225,27227,27236,27238,27240],{},[3243,27200,27201,27203],{},[898,27202,1661],{},[898,27204,3249],{},[1701,27206,1792],{},[2287,27208,27209,27211,27213],{},[898,27210,13189],{},[898,27212,1795],{},[898,27214,3249],{},[1701,27216,2317],{},[3243,27218,27219,27221],{},[898,27220,1658],{},[898,27222,3249],{},[1701,27224,1792],{},[1701,27226,2317],{},[2363,27228,27229],{"scriptlevel":1852,"displaystyle":1798},[3726,27230,27231,27234],{},[1850,27232,27233],{},"605",[1850,27235,26985],{},[1701,27237,3782],{},[1701,27239,2317],{},[1850,27241,27242],{},"43,214",[902,27244,27245],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,27248,27249,25391,27251,27272,27273,27276,27277,27299,27300,1715],{},[38,27250,25390],{},[883,27252,27254],{"className":27253},[886],[888,27255,27256],{"xmlns":890},[892,27257,27258,27270],{},[895,27259,27260,27262,27264,27266,27268],{},[898,27261,1658],{},[1939,27263,16344],{},[898,27265,16238],{},[1939,27267,16344],{},[898,27269,16167],{},[902,27271,22266],{"encoding":904}," stále uvažuje ",[38,27274,27275],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,27278,27280],{"className":27279},[886],[888,27281,27282],{"xmlns":890},[892,27283,27284,27296],{},[895,27285,27286,27288,27290,27292,27294],{},[898,27287,16374],{},[1701,27289,1792],{},[898,27291,2593],{},[1701,27293,2317],{},[898,27295,6909],{},[902,27297,27298],{"encoding":904},"X = B - M"," dává ",[38,27301,25412,27302],{},[883,27303,27305],{"className":27304},[886],[888,27306,27307],{"xmlns":890},[892,27308,27309,27325],{},[895,27310,27311,27313,27315,27317,27319,27321,27323],{},[898,27312,1658],{},[1939,27314,16344],{},[898,27316,16238],{},[1939,27318,16344],{},[898,27320,16167],{},[1939,27322,16344],{},[898,27324,16374],{},[902,27326,16377],{"encoding":904},[115,27328,27330],{"id":27329},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,27332,24665],{"id":27333},"zadání-modelu-2",[724,27335,27336,27337,4088,27340,2020,27361,27374,27375,1738,27378,27391],{},"Rozšíření o ",[38,27338,27339],{},"čistý export",[883,27341,27343],{"className":27342},[886],[888,27344,27345],{"xmlns":890},[892,27346,27347,27359],{},[895,27348,27349,27351,27353,27355,27357],{},[898,27350,16374],{},[1701,27352,1792],{},[898,27354,2593],{},[1701,27356,2317],{},[898,27358,6909],{},[902,27360,27298],{"encoding":904},[883,27362,27364],{"className":27363},[886],[888,27365,27366],{"xmlns":890},[892,27367,27368,27372],{},[895,27369,27370],{},[898,27371,2593],{},[902,27373,2593],{"encoding":904}," je hrubý export (",[614,27376,27377],{},"brutto export",[883,27379,27381],{"className":27380},[886],[888,27382,27383],{"xmlns":890},[892,27384,27385,27389],{},[895,27386,27387],{},[898,27388,6909],{},[902,27390,6909],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,27393,27394],{},[883,27395,27397],{"className":27396},[886],[888,27398,27399],{"xmlns":890},[892,27400,27401,27421],{},[895,27402,27403,27405,27407,27409,27411,27417,27419],{},[898,27404,6909],{},[1701,27406,1792],{},[898,27408,6909],{},[1701,27410,1799],{"stretchy":1798},[1845,27412,27413,27415],{},[898,27414,13189],{},[898,27416,1795],{},[1701,27418,1805],{"stretchy":1798},[898,27420,1715],{"mathvariant":2334},[902,27422,27423],{"encoding":904},"M = M(Y_D).",[724,27425,27426],{},"Podmínka rovnováhy:",[724,27428,27429],{},[883,27430,27432],{"className":27431},[886],[888,27433,27434],{"xmlns":890},[892,27435,27436,27473],{},[895,27437,27438,27440,27442,27444,27446,27448,27450,27452,27454,27456,27458,27460,27462,27464,27466,27469,27471],{},[898,27439,13189],{},[1701,27441,1792],{},[898,27443,1658],{},[1701,27445,1703],{},[898,27447,16238],{},[1701,27449,1703],{},[898,27451,16167],{},[1701,27453,1703],{},[898,27455,2593],{},[1701,27457,2317],{},[898,27459,6909],{},[898,27461,1715],{"mathvariant":2334},[9942,27463],{"width":9944},[1701,27465,1799],{"stretchy":1798},[1850,27467,27468],{},"7.10",[1939,27470,207],{},[1701,27472,1805],{"stretchy":1798},[902,27474,27475],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,27477,24735],{"id":27478},"soustava-rovnic-2",[724,27480,25891,27481,27515,27516,2246],{},[883,27482,27484],{"className":27483},[886],[888,27485,27486],{"xmlns":890},[892,27487,27488,27512],{},[895,27489,27490,27496,27498,27504,27506],{},[3243,27491,27492,27494],{},[898,27493,16238],{},[1701,27495,8424],{},[1701,27497,2012],{"separator":2011},[3243,27499,27500,27502],{},[898,27501,16167],{},[1701,27503,8424],{},[1701,27505,2012],{"separator":2011},[3243,27507,27508,27510],{},[898,27509,2593],{},[1701,27511,8424],{},[902,27513,27514],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,27517,27519],{"className":27518},[886],[888,27520,27521],{"xmlns":890},[892,27522,27523,27547],{},[895,27524,27525,27527,27529,27531,27533,27535,27537,27543,27545],{},[898,27526,13189],{},[1701,27528,2012],{"separator":2011},[898,27530,1658],{},[1701,27532,2012],{"separator":2011},[898,27534,5877],{},[1701,27536,2012],{"separator":2011},[1845,27538,27539,27541],{},[898,27540,13189],{},[898,27542,1795],{},[1701,27544,2012],{"separator":2011},[898,27546,6909],{},[902,27548,27549],{"encoding":904},"Y, C, T, Y_D, M",[724,27551,27552],{},[883,27553,27555],{"className":27554},[886],[888,27556,27557],{"xmlns":890},[892,27558,27559,27743],{},[895,27560,27561,27735,27737,27739,27741],{},[2256,27562,27563,27595,27625,27653,27685],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,27564,27565,27571],{},[2263,27566,27567],{},[2363,27568,27569],{"scriptlevel":1852,"displaystyle":2011},[898,27570,1658],{},[2263,27572,27573],{},[2363,27574,27575],{"scriptlevel":1852,"displaystyle":2011},[895,27576,27577,27579,27581,27583,27585,27591,27593],{},[895,27578],{},[1701,27580,1792],{},[898,27582,1658],{},[1701,27584,1799],{"stretchy":1798},[1845,27586,27587,27589],{},[898,27588,13189],{},[898,27590,1795],{},[1701,27592,1805],{"stretchy":1798},[1701,27594,2012],{"separator":2011},[2260,27596,27597,27607],{},[2263,27598,27599],{},[2363,27600,27601],{"scriptlevel":1852,"displaystyle":2011},[1845,27602,27603,27605],{},[898,27604,13189],{},[898,27606,1795],{},[2263,27608,27609],{},[2363,27610,27611],{"scriptlevel":1852,"displaystyle":2011},[895,27612,27613,27615,27617,27619,27621,27623],{},[895,27614],{},[1701,27616,1792],{},[898,27618,13189],{},[1701,27620,2317],{},[898,27622,5877],{},[1701,27624,2012],{"separator":2011},[2260,27626,27627,27633],{},[2263,27628,27629],{},[2363,27630,27631],{"scriptlevel":1852,"displaystyle":2011},[898,27632,5877],{},[2263,27634,27635],{},[2363,27636,27637],{"scriptlevel":1852,"displaystyle":2011},[895,27638,27639,27641,27643,27645,27647,27649,27651],{},[895,27640],{},[1701,27642,1792],{},[898,27644,5877],{},[1701,27646,1799],{"stretchy":1798},[898,27648,13189],{},[1701,27650,1805],{"stretchy":1798},[1701,27652,2012],{"separator":2011},[2260,27654,27655,27661],{},[2263,27656,27657],{},[2363,27658,27659],{"scriptlevel":1852,"displaystyle":2011},[898,27660,6909],{},[2263,27662,27663],{},[2363,27664,27665],{"scriptlevel":1852,"displaystyle":2011},[895,27666,27667,27669,27671,27673,27675,27681,27683],{},[895,27668],{},[1701,27670,1792],{},[898,27672,6909],{},[1701,27674,1799],{"stretchy":1798},[1845,27676,27677,27679],{},[898,27678,13189],{},[898,27680,1795],{},[1701,27682,1805],{"stretchy":1798},[1701,27684,2012],{"separator":2011},[2260,27686,27687,27693],{},[2263,27688,27689],{},[2363,27690,27691],{"scriptlevel":1852,"displaystyle":2011},[898,27692,13189],{},[2263,27694,27695],{},[2363,27696,27697],{"scriptlevel":1852,"displaystyle":2011},[895,27698,27699,27701,27703,27705,27707,27713,27715,27721,27723,27729,27731,27733],{},[895,27700],{},[1701,27702,1792],{},[898,27704,1658],{},[1701,27706,1703],{},[3243,27708,27709,27711],{},[898,27710,16238],{},[1701,27712,8424],{},[1701,27714,1703],{},[3243,27716,27717,27719],{},[898,27718,16167],{},[1701,27720,8424],{},[1701,27722,1703],{},[3243,27724,27725,27727],{},[898,27726,2593],{},[1701,27728,8424],{},[1701,27730,2317],{},[898,27732,6909],{},[898,27734,1715],{"mathvariant":2334},[9942,27736],{"width":9944},[1701,27738,1799],{"stretchy":1798},[1850,27740,27468],{},[1701,27742,1805],{"stretchy":1798},[902,27744,27745],{"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)",[198,27747,27749],{"id":27748},"příklad-75","Příklad 7.5",[724,27751,27752,27753,1343,27785,1343,27812,1343,27833,1343,27855,1343,27877,27900],{},"Dáno: ",[883,27754,27756],{"className":27755},[886],[888,27757,27758],{"xmlns":890},[892,27759,27760,27782],{},[895,27761,27762,27764,27766,27769,27771,27777,27779],{},[898,27763,1658],{},[1701,27765,1792],{},[1850,27767,27768],{},"0,75",[1939,27770,1941],{},[1845,27772,27773,27775],{},[898,27774,13189],{},[898,27776,1795],{},[1701,27778,1703],{},[1850,27780,27781],{},"750",[902,27783,27784],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,27786,27788],{"className":27787},[886],[888,27789,27790],{"xmlns":890},[892,27791,27792,27809],{},[895,27793,27794,27796,27798,27801,27803],{},[898,27795,6909],{},[1701,27797,1792],{},[1850,27799,27800],{},"0,15",[1939,27802,1941],{},[1845,27804,27805,27807],{},[898,27806,13189],{},[898,27808,1795],{},[902,27810,27811],{"encoding":904},"M = 0{,}15\\,Y_D",[883,27813,27815],{"className":27814},[886],[888,27816,27817],{"xmlns":890},[892,27818,27819,27830],{},[895,27820,27821,27823,27825,27828],{},[898,27822,5877],{},[1701,27824,1792],{},[1850,27826,27827],{},"0,25",[898,27829,13189],{},[902,27831,27832],{"encoding":904},"T = 0{,}25Y",[883,27834,27836],{"className":27835},[886],[888,27837,27838],{"xmlns":890},[892,27839,27840,27852],{},[895,27841,27842,27848,27850],{},[3243,27843,27844,27846],{},[898,27845,16238],{},[1701,27847,8424],{},[1701,27849,1792],{},[1850,27851,19162],{},[902,27853,27854],{"encoding":904},"I^* = 500",[883,27856,27858],{"className":27857},[886],[888,27859,27860],{"xmlns":890},[892,27861,27862,27874],{},[895,27863,27864,27870,27872],{},[3243,27865,27866,27868],{},[898,27867,16167],{},[1701,27869,8424],{},[1701,27871,1792],{},[1850,27873,12864],{},[902,27875,27876],{"encoding":904},"G^* = 150",[883,27878,27880],{"className":27879},[886],[888,27881,27882],{"xmlns":890},[892,27883,27884,27897],{},[895,27885,27886,27892,27894],{},[3243,27887,27888,27890],{},[898,27889,2593],{},[1701,27891,8424],{},[1701,27893,1792],{},[1850,27895,27896],{},"800",[902,27898,27899],{"encoding":904},"B^* = 800",". Soustava:",[724,27902,27903],{},[883,27904,27906],{"className":27905},[886],[888,27907,27908],{"xmlns":890},[892,27909,27910,28128],{},[2256,27911,27912,27958,28000,28036,28078],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,27913,27914,27930],{},[2263,27915,27916],{},[2363,27917,27918],{"scriptlevel":1852,"displaystyle":2011},[895,27919,27920,27922,27924,27926,27928],{},[1701,27921,1799],{"stretchy":1798},[898,27923,16096],{},[1850,27925,4062],{},[1701,27927,1805],{"stretchy":1798},[1939,27929,6402],{},[2263,27931,27932],{},[2363,27933,27934],{"scriptlevel":1852,"displaystyle":2011},[895,27935,27936,27938,27940,27942,27944,27946,27952,27954,27956],{},[895,27937],{},[898,27939,1658],{},[1701,27941,1792],{},[1850,27943,27768],{},[1939,27945,1941],{},[1845,27947,27948,27950],{},[898,27949,13189],{},[898,27951,1795],{},[1701,27953,1703],{},[1850,27955,27781],{},[1701,27957,2012],{"separator":2011},[2260,27959,27960,27976],{},[2263,27961,27962],{},[2363,27963,27964],{"scriptlevel":1852,"displaystyle":2011},[895,27965,27966,27968,27970,27972,27974],{},[1701,27967,1799],{"stretchy":1798},[898,27969,16096],{},[1850,27971,3938],{},[1701,27973,1805],{"stretchy":1798},[1939,27975,6402],{},[2263,27977,27978],{},[2363,27979,27980],{"scriptlevel":1852,"displaystyle":2011},[895,27981,27982,27984,27990,27992,27994,27996,27998],{},[895,27983],{},[1845,27985,27986,27988],{},[898,27987,13189],{},[898,27989,1795],{},[1701,27991,1792],{},[898,27993,13189],{},[1701,27995,2317],{},[898,27997,5877],{},[1701,27999,2012],{"separator":2011},[2260,28001,28002,28018],{},[2263,28003,28004],{},[2363,28005,28006],{"scriptlevel":1852,"displaystyle":2011},[895,28007,28008,28010,28012,28014,28016],{},[1701,28009,1799],{"stretchy":1798},[898,28011,16096],{},[1850,28013,3646],{},[1701,28015,1805],{"stretchy":1798},[1939,28017,6402],{},[2263,28019,28020],{},[2363,28021,28022],{"scriptlevel":1852,"displaystyle":2011},[895,28023,28024,28026,28028,28030,28032,28034],{},[895,28025],{},[898,28027,5877],{},[1701,28029,1792],{},[1850,28031,27827],{},[898,28033,13189],{},[1701,28035,2012],{"separator":2011},[2260,28037,28038,28054],{},[2263,28039,28040],{},[2363,28041,28042],{"scriptlevel":1852,"displaystyle":2011},[895,28043,28044,28046,28048,28050,28052],{},[1701,28045,1799],{"stretchy":1798},[898,28047,16096],{},[1850,28049,6460],{},[1701,28051,1805],{"stretchy":1798},[1939,28053,6402],{},[2263,28055,28056],{},[2363,28057,28058],{"scriptlevel":1852,"displaystyle":2011},[895,28059,28060,28062,28064,28066,28068,28070,28076],{},[895,28061],{},[898,28063,6909],{},[1701,28065,1792],{},[1850,28067,27800],{},[1939,28069,1941],{},[1845,28071,28072,28074],{},[898,28073,13189],{},[898,28075,1795],{},[1701,28077,2012],{"separator":2011},[2260,28079,28080,28096],{},[2263,28081,28082],{},[2363,28083,28084],{"scriptlevel":1852,"displaystyle":2011},[895,28085,28086,28088,28090,28092,28094],{},[1701,28087,1799],{"stretchy":1798},[898,28089,16096],{},[1850,28091,4225],{},[1701,28093,1805],{"stretchy":1798},[1939,28095,6402],{},[2263,28097,28098],{},[2363,28099,28100],{"scriptlevel":1852,"displaystyle":2011},[895,28101,28102,28104,28106,28108,28110,28112,28114,28116,28118,28120,28122,28124,28126],{},[895,28103],{},[898,28105,13189],{},[1701,28107,1792],{},[898,28109,1658],{},[1701,28111,1703],{},[1850,28113,19162],{},[1701,28115,1703],{},[1850,28117,12864],{},[1701,28119,1703],{},[1850,28121,27896],{},[1701,28123,2317],{},[898,28125,6909],{},[898,28127,1715],{"mathvariant":2334},[902,28129,28130],{"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}",[724,28132,28133,28134,28168],{},"Postupná substituce — z (r3) do (r2): ",[883,28135,28137],{"className":28136},[886],[888,28138,28139],{"xmlns":890},[892,28140,28141,28165],{},[895,28142,28143,28149,28151,28153,28155,28157,28159,28161,28163],{},[1845,28144,28145,28147],{},[898,28146,13189],{},[898,28148,1795],{},[1701,28150,1792],{},[898,28152,13189],{},[1701,28154,2317],{},[1850,28156,27827],{},[898,28158,13189],{},[1701,28160,1792],{},[1850,28162,27768],{},[898,28164,13189],{},[902,28166,28167],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,28170,28171],{},[883,28172,28174],{"className":28173},[886],[888,28175,28176],{"xmlns":890},[892,28177,28178,28219],{},[895,28179,28180,28182,28184,28186,28188,28190,28192,28194,28196,28198,28200,28202,28204,28206,28208,28211,28213,28215,28217],{},[1701,28181,1799],{"stretchy":1798},[898,28183,16096],{},[1850,28185,6352],{},[1701,28187,1805],{"stretchy":1798},[1939,28189,6402],{},[898,28191,1658],{},[1701,28193,1792],{},[1850,28195,27768],{},[1701,28197,3408],{},[1850,28199,27768],{},[898,28201,13189],{},[1701,28203,1703],{},[1850,28205,27781],{},[1701,28207,1792],{},[1850,28209,28210],{},"0,5625",[898,28212,13189],{},[1701,28214,1703],{},[1850,28216,27781],{},[1701,28218,2012],{"separator":2011},[902,28220,28221],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,28223,28224],{},[883,28225,28227],{"className":28226},[886],[888,28228,28229],{"xmlns":890},[892,28230,28231,28265],{},[895,28232,28233,28235,28237,28240,28242,28244,28246,28248,28250,28252,28254,28256,28258,28261,28263],{},[1701,28234,1799],{"stretchy":1798},[898,28236,16096],{},[1850,28238,28239],{},"7",[1701,28241,1805],{"stretchy":1798},[1939,28243,6402],{},[898,28245,6909],{},[1701,28247,1792],{},[1850,28249,27800],{},[1701,28251,3408],{},[1850,28253,27768],{},[898,28255,13189],{},[1701,28257,1792],{},[1850,28259,28260],{},"0,1125",[898,28262,13189],{},[898,28264,1715],{"mathvariant":2334},[902,28266,28267],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,28269,28270],{},"Dosazením do (r5):",[724,28272,28273],{},[883,28274,28276],{"className":28275},[886],[888,28277,28278],{"xmlns":890},[892,28279,28280,28324],{},[895,28281,28282,28284,28286,28288,28290,28292,28294,28296,28298,28300,28302,28304,28306,28308,28310,28312,28314,28317,28319,28321],{},[898,28283,13189],{},[1701,28285,1792],{},[1850,28287,28210],{},[898,28289,13189],{},[1701,28291,1703],{},[1850,28293,27781],{},[1701,28295,1703],{},[1850,28297,19162],{},[1701,28299,1703],{},[1850,28301,12864],{},[1701,28303,1703],{},[1850,28305,27896],{},[1701,28307,2317],{},[1850,28309,28260],{},[898,28311,13189],{},[1701,28313,1792],{},[1850,28315,28316],{},"0,45",[898,28318,13189],{},[1701,28320,1703],{},[1850,28322,28323],{},"2200.",[902,28325,28326],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,28328,28329,28330,4185,28352,28375],{},"Odtud ",[883,28331,28333],{"className":28332},[886],[888,28334,28335],{"xmlns":890},[892,28336,28337,28349],{},[895,28338,28339,28342,28344,28346],{},[1850,28340,28341],{},"0,55",[898,28343,13189],{},[1701,28345,1792],{},[1850,28347,28348],{},"2200",[902,28350,28351],{"encoding":904},"0{,}55Y = 2200",[883,28353,28355],{"className":28354},[886],[888,28356,28357],{"xmlns":890},[892,28358,28359,28372],{},[895,28360,28361,28367,28369],{},[3243,28362,28363,28365],{},[898,28364,13189],{},[898,28366,3249],{},[1701,28368,1792],{},[1850,28370,28371],{},"4000",[902,28373,28374],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,28377,28378,28401,28433,28468,28501,28537],{},[123,28379,28380,2012],{},[883,28381,28383],{"className":28382},[886],[888,28384,28385],{"xmlns":890},[892,28386,28387,28399],{},[895,28388,28389,28395,28397],{},[3243,28390,28391,28393],{},[898,28392,13189],{},[898,28394,3249],{},[1701,28396,1792],{},[1850,28398,28371],{},[902,28400,28374],{"encoding":904},[123,28402,28403,2012],{},[883,28404,28406],{"className":28405},[886],[888,28407,28408],{"xmlns":890},[892,28409,28410,28430],{},[895,28411,28412,28418,28420,28422,28424,28426,28428],{},[3243,28413,28414,28416],{},[898,28415,5877],{},[898,28417,3249],{},[1701,28419,1792],{},[1850,28421,27827],{},[1701,28423,3408],{},[1850,28425,28371],{},[1701,28427,1792],{},[1850,28429,6875],{},[902,28431,28432],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,28434,28435,2012],{},[883,28436,28438],{"className":28437},[886],[888,28439,28440],{"xmlns":890},[892,28441,28442,28465],{},[895,28443,28444,28452,28454,28456,28458,28460,28462],{},[2287,28445,28446,28448,28450],{},[898,28447,13189],{},[898,28449,1795],{},[898,28451,3249],{},[1701,28453,1792],{},[1850,28455,27768],{},[1701,28457,3408],{},[1850,28459,28371],{},[1701,28461,1792],{},[1850,28463,28464],{},"3000",[902,28466,28467],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,28469,28470,2012],{},[883,28471,28473],{"className":28472},[886],[888,28474,28475],{"xmlns":890},[892,28476,28477,28498],{},[895,28478,28479,28485,28487,28489,28491,28493,28495],{},[3243,28480,28481,28483],{},[898,28482,6909],{},[898,28484,3249],{},[1701,28486,1792],{},[1850,28488,27800],{},[1701,28490,3408],{},[1850,28492,28464],{},[1701,28494,1792],{},[1850,28496,28497],{},"450",[902,28499,28500],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,28502,28503,2012],{},[883,28504,28506],{"className":28505},[886],[888,28507,28508],{"xmlns":890},[892,28509,28510,28534],{},[895,28511,28512,28518,28520,28522,28524,28526,28528,28530,28532],{},[3243,28513,28514,28516],{},[898,28515,1658],{},[898,28517,3249],{},[1701,28519,1792],{},[1850,28521,27768],{},[1701,28523,3408],{},[1850,28525,28464],{},[1701,28527,1703],{},[1850,28529,27781],{},[1701,28531,1792],{},[1850,28533,28464],{},[902,28535,28536],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,28538,28539,28579],{},[883,28540,28542],{"className":28541},[886],[888,28543,28544],{"xmlns":890},[892,28545,28546,28576],{},[895,28547,28548,28554,28556,28564,28566,28572,28574],{},[3243,28549,28550,28552],{},[898,28551,1661],{},[898,28553,3249],{},[1701,28555,1792],{},[2287,28557,28558,28560,28562],{},[898,28559,13189],{},[898,28561,1795],{},[898,28563,3249],{},[1701,28565,2317],{},[3243,28567,28568,28570],{},[898,28569,1658],{},[898,28571,3249],{},[1701,28573,1792],{},[1850,28575,1852],{},[902,28577,28578],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,28581,28582,28584,28585,1343,28602,2633,28623,28648,28649,28652,28653,28666,28667,1715],{},[38,28583,25390],{}," Modely ",[883,28586,28588],{"className":28587},[886],[888,28589,28590],{"xmlns":890},[892,28591,28592,28600],{},[895,28593,28594,28596,28598],{},[898,28595,1658],{},[1939,28597,16344],{},[898,28599,16238],{},[902,28601,16349],{"encoding":904},[883,28603,28605],{"className":28604},[886],[888,28606,28607],{"xmlns":890},[892,28608,28609,28621],{},[895,28610,28611,28613,28615,28617,28619],{},[898,28612,1658],{},[1939,28614,16344],{},[898,28616,16238],{},[1939,28618,16344],{},[898,28620,16167],{},[902,28622,22266],{"encoding":904},[883,28624,28626],{"className":28625},[886],[888,28627,28628],{"xmlns":890},[892,28629,28630,28646],{},[895,28631,28632,28634,28636,28638,28640,28642,28644],{},[898,28633,1658],{},[1939,28635,16344],{},[898,28637,16238],{},[1939,28639,16344],{},[898,28641,16167],{},[1939,28643,16344],{},[898,28645,16374],{},[902,28647,16377],{"encoding":904}," pokládají investice za ",[38,28650,28651],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,28654,28656],{"className":28655},[886],[888,28657,28658],{"xmlns":890},[892,28659,28660,28664],{},[895,28661,28662],{},[898,28663,16096],{},[902,28665,16096],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,28668,28669],{},"model IS-LM",[115,28671,28673],{"id":28672},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,28675,28676,28677,28681,28682,28685,28686,28689],{},"V článku ",[207,28678,28680],{"className":28679,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,28683,28684],{},"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 ",[38,28687,28688],{},"výraznější"," než v mikroekonomických modelech.",[724,28691,28692],{},[2139,28693],{"alt":28694,"className":28695,"src":28696},"imek-multiplikatorovy-efekt-chain",[210,2143],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,28698,16218,28699,1343,28716,1343,28737,28762,28763,28766,28767,28785,28786,28804,28805,28823,28824,28827,28828,1343,28845,28862,28863,28865],{},[883,28700,28702],{"className":28701},[886],[888,28703,28704],{"xmlns":890},[892,28705,28706,28714],{},[895,28707,28708,28710,28712],{},[898,28709,1658],{},[1939,28711,16344],{},[898,28713,16238],{},[902,28715,16349],{"encoding":904},[883,28717,28719],{"className":28718},[886],[888,28720,28721],{"xmlns":890},[892,28722,28723,28735],{},[895,28724,28725,28727,28729,28731,28733],{},[898,28726,1658],{},[1939,28728,16344],{},[898,28730,16238],{},[1939,28732,16344],{},[898,28734,16167],{},[902,28736,22266],{"encoding":904},[883,28738,28740],{"className":28739},[886],[888,28741,28742],{"xmlns":890},[892,28743,28744,28760],{},[895,28745,28746,28748,28750,28752,28754,28756,28758],{},[898,28747,1658],{},[1939,28749,16344],{},[898,28751,16238],{},[1939,28753,16344],{},[898,28755,16167],{},[1939,28757,16344],{},[898,28759,16374],{},[902,28761,16377],{"encoding":904}," se vyšetřuje vliv změn ",[38,28764,28765],{},"exogenních"," veličin (plánovaných investic ",[883,28768,28770],{"className":28769},[886],[888,28771,28772],{"xmlns":890},[892,28773,28774,28782],{},[895,28775,28776],{},[3243,28777,28778,28780],{},[898,28779,16238],{},[1701,28781,8424],{},[902,28783,28784],{"encoding":904},"I^*",", vládních výdajů ",[883,28787,28789],{"className":28788},[886],[888,28790,28791],{"xmlns":890},[892,28792,28793,28801],{},[895,28794,28795],{},[3243,28796,28797,28799],{},[898,28798,16167],{},[1701,28800,8424],{},[902,28802,28803],{"encoding":904},"G^*",", exportu ",[883,28806,28808],{"className":28807},[886],[888,28809,28810],{"xmlns":890},[892,28811,28812,28820],{},[895,28813,28814],{},[3243,28815,28816,28818],{},[898,28817,2593],{},[1701,28819,8424],{},[902,28821,28822],{"encoding":904},"B^*",") na změny ",[38,28825,28826],{},"endogenních"," rovnovážných veličin (",[883,28829,28831],{"className":28830},[886],[888,28832,28833],{"xmlns":890},[892,28834,28835,28843],{},[895,28836,28837],{},[3243,28838,28839,28841],{},[898,28840,13189],{},[898,28842,3249],{},[902,28844,17957],{"encoding":904},[883,28846,28848],{"className":28847},[886],[888,28849,28850],{"xmlns":890},[892,28851,28852,28860],{},[895,28853,28854],{},[3243,28855,28856,28858],{},[898,28857,1658],{},[898,28859,3249],{},[902,28861,18016],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,28864,22023],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,28867,28869],{"id":28868},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,28871,24936,28872,28895,28896,28940],{},[883,28873,28875],{"className":28874},[886],[888,28876,28877],{"xmlns":890},[892,28878,28879,28893],{},[895,28880,28881,28883,28885,28887,28889,28891],{},[898,28882,1658],{},[1701,28884,1792],{},[898,28886,207],{},[898,28888,13189],{},[1701,28890,1703],{},[898,28892,3598],{},[902,28894,22966],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,28897,28899],{"className":28898},[886],[888,28900,28901],{"xmlns":890},[892,28902,28903,28937],{},[895,28904,28905,28911,28913],{},[3243,28906,28907,28909],{},[898,28908,13189],{},[898,28910,3249],{},[1701,28912,1792],{},[2363,28914,28915],{"scriptlevel":1852,"displaystyle":2011},[3726,28916,28917,28929],{},[895,28918,28919,28921,28923],{},[898,28920,3598],{},[1701,28922,1703],{},[3243,28924,28925,28927],{},[898,28926,16238],{},[1701,28928,8424],{},[895,28930,28931,28933,28935],{},[1850,28932,4062],{},[1701,28934,2317],{},[898,28936,207],{},[902,28938,28939],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,28942,28943],{},[883,28944,28946],{"className":28945},[886],[888,28947,28948],{"xmlns":890},[892,28949,28950,29019],{},[895,28951,28952,28970,28972,29002,29004],{},[3726,28953,28954,28964],{},[895,28955,28956,28958],{},[898,28957,3893],{"mathvariant":2334},[3243,28959,28960,28962],{},[898,28961,13189],{},[898,28963,3249],{},[895,28965,28966,28968],{},[898,28967,3893],{"mathvariant":2334},[898,28969,207],{},[1701,28971,1792],{},[3726,28973,28974,28986],{},[895,28975,28976,28978,28980],{},[898,28977,3598],{},[1701,28979,1703],{},[3243,28981,28982,28984],{},[898,28983,16238],{},[1701,28985,8424],{},[895,28987,28988,28990,28992,28994,28996],{},[1701,28989,1799],{"stretchy":1798},[1850,28991,4062],{},[1701,28993,2317],{},[898,28995,207],{},[3243,28997,28998,29000],{},[1701,28999,1805],{"stretchy":1798},[1850,29001,3938],{},[9942,29003],{"width":9944},[895,29005,29006,29009,29016],{},[1939,29007,29008],{},"(multiplik",[12448,29010,29011,29013],{"accent":2011},[1939,29012,207],{},[1701,29014,29015],{},"ˊ",[1939,29017,29018],{},"tor MPC)",[902,29020,29021],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,29023,29024],{},[883,29025,29027],{"className":29026},[886],[888,29028,29029],{"xmlns":890},[892,29030,29031,29100],{},[895,29032,29033,29051,29053,29065,29067],{},[3726,29034,29035,29045],{},[895,29036,29037,29039],{},[898,29038,3893],{"mathvariant":2334},[3243,29040,29041,29043],{},[898,29042,13189],{},[898,29044,3249],{},[895,29046,29047,29049],{},[898,29048,3893],{"mathvariant":2334},[898,29050,3598],{},[1701,29052,1792],{},[3726,29054,29055,29057],{},[1850,29056,4062],{},[895,29058,29059,29061,29063],{},[1850,29060,4062],{},[1701,29062,2317],{},[898,29064,207],{},[9942,29066],{"width":9944},[895,29068,29069,29071,29077,29080,29087,29090,29097],{},[1939,29070,29008],{},[12448,29072,29073,29075],{"accent":2011},[1939,29074,207],{},[1701,29076,29015],{},[1939,29078,29079],{},"tor autonomn",[12448,29081,29082,29085],{"accent":2011},[1939,29083,29084],{},"ı",[1701,29086,29015],{},[1939,29088,29089],{}," spot",[12448,29091,29092,29094],{"accent":2011},[1939,29093,16096],{},[1701,29095,29096],{},"ˇ",[1939,29098,29099],{},"eby)",[902,29101,29102],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,29104,29105],{},[883,29106,29108],{"className":29107},[886],[888,29109,29110],{"xmlns":890},[892,29111,29112,29179],{},[895,29113,29114,29136,29138,29150,29152,29164,29166],{},[3726,29115,29116,29126],{},[895,29117,29118,29120],{},[898,29119,3893],{"mathvariant":2334},[3243,29121,29122,29124],{},[898,29123,13189],{},[898,29125,3249],{},[895,29127,29128,29130],{},[898,29129,3893],{"mathvariant":2334},[3243,29131,29132,29134],{},[898,29133,16238],{},[1701,29135,8424],{},[1701,29137,1792],{},[3726,29139,29140,29142],{},[1850,29141,4062],{},[895,29143,29144,29146,29148],{},[1850,29145,4062],{},[1701,29147,2317],{},[898,29149,207],{},[1701,29151,1792],{},[3726,29153,29154,29156],{},[1850,29155,4062],{},[895,29157,29158,29160,29162],{},[898,29159,6909],{},[898,29161,1680],{},[898,29163,1661],{},[9942,29165],{"width":9944},[895,29167,29168,29170,29176],{},[1939,29169,29008],{},[12448,29171,29172,29174],{"accent":2011},[1939,29173,207],{},[1701,29175,29015],{},[1939,29177,29178],{},"tor investic)",[902,29180,29181],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1635,29183,29184],{},[724,29185,29186,29188,29189,29192,29193,29206,29207,29224,29225,29243,29244,29288,29289,25461,29306,29308,29309,29326],{},[883,29187,2063],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,29190,29191],{},"důchodem","; z něj se utratí ",[883,29194,29196],{"className":29195},[886],[888,29197,29198],{"xmlns":890},[892,29199,29200,29204],{},[895,29201,29202],{},[898,29203,207],{},[902,29205,207],{"encoding":904}," Kč (= ",[883,29208,29210],{"className":29209},[886],[888,29211,29212],{"xmlns":890},[892,29213,29214,29222],{},[895,29215,29216,29218,29220],{},[898,29217,6909],{},[898,29219,1680],{},[898,29221,1658],{},[902,29223,22091],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,29226,29228],{"className":29227},[886],[888,29229,29230],{"xmlns":890},[892,29231,29232,29240],{},[895,29233,29234],{},[3243,29235,29236,29238],{},[898,29237,207],{},[1850,29239,3938],{},[902,29241,29242],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,29245,29247],{"className":29246},[886],[888,29248,29249],{"xmlns":890},[892,29250,29251,29285],{},[895,29252,29253,29255,29257,29259,29261,29267,29269,29271,29273],{},[1850,29254,4062],{},[1701,29256,1703],{},[898,29258,207],{},[1701,29260,1703],{},[3243,29262,29263,29265],{},[898,29264,207],{},[1850,29266,3938],{},[1701,29268,1703],{},[1701,29270,22151],{},[1701,29272,1792],{},[3726,29274,29275,29277],{},[1850,29276,4062],{},[895,29278,29279,29281,29283],{},[1850,29280,4062],{},[1701,29282,2317],{},[898,29284,207],{},[902,29286,29287],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,29290,29292],{"className":29291},[886],[888,29293,29294],{"xmlns":890},[892,29295,29296,29304],{},[895,29297,29298],{},[3243,29299,29300,29302],{},[898,29301,13189],{},[898,29303,3249],{},[902,29305,17957],{"encoding":904},[38,29307,2076],{}," než korunu — čím vyšší ",[883,29310,29312],{"className":29311},[886],[888,29313,29314],{"xmlns":890},[892,29315,29316,29324],{},[895,29317,29318,29320,29322],{},[898,29319,6909],{},[898,29321,1680],{},[898,29323,1658],{},[902,29325,22091],{"encoding":904},", tím silnější multiplikační efekt.",[724,29328,29329,29332,29333,29359,29360,29363,29364,2633,29385,29410,29411,1715],{},[38,29330,29331],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,29334,29336],{"className":29335},[886],[888,29337,29338],{"xmlns":890},[892,29339,29340,29356],{},[895,29341,29342],{},[2363,29343,29344],{"scriptlevel":1852,"displaystyle":1798},[3726,29345,29346,29348],{},[1850,29347,4062],{},[895,29349,29350,29352,29354],{},[1850,29351,4062],{},[1701,29353,2317],{},[898,29355,207],{},[902,29357,29358],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,29361,29362],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,29365,29367],{"className":29366},[886],[888,29368,29369],{"xmlns":890},[892,29370,29371,29383],{},[895,29372,29373,29375,29377,29379,29381],{},[898,29374,1658],{},[1939,29376,16344],{},[898,29378,16238],{},[1939,29380,16344],{},[898,29382,16167],{},[902,29384,22266],{"encoding":904},[883,29386,29388],{"className":29387},[886],[888,29389,29390],{"xmlns":890},[892,29391,29392,29408],{},[895,29393,29394,29396,29398,29400,29402,29404,29406],{},[898,29395,1658],{},[1939,29397,16344],{},[898,29399,16238],{},[1939,29401,16344],{},[898,29403,16167],{},[1939,29405,16344],{},[898,29407,16374],{},[902,29409,16377],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,29412,29414],{"className":29413,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,29416,29418],{"id":29417},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,29420,16218,29421,1343,29438,2633,29459,16223,29484,1646,29487,29508,29509,4088,29512,29525,29526,9733,29555,29572,29573,29576,29577,29579,29580,29601],{},[883,29422,29424],{"className":29423},[886],[888,29425,29426],{"xmlns":890},[892,29427,29428,29436],{},[895,29429,29430,29432,29434],{},[898,29431,1658],{},[1939,29433,16344],{},[898,29435,16238],{},[902,29437,16349],{"encoding":904},[883,29439,29441],{"className":29440},[886],[888,29442,29443],{"xmlns":890},[892,29444,29445,29457],{},[895,29446,29447,29449,29451,29453,29455],{},[898,29448,1658],{},[1939,29450,16344],{},[898,29452,16238],{},[1939,29454,16344],{},[898,29456,16167],{},[902,29458,22266],{"encoding":904},[883,29460,29462],{"className":29461},[886],[888,29463,29464],{"xmlns":890},[892,29465,29466,29482],{},[895,29467,29468,29470,29472,29474,29476,29478,29480],{},[898,29469,1658],{},[1939,29471,16344],{},[898,29473,16238],{},[1939,29475,16344],{},[898,29477,16167],{},[1939,29479,16344],{},[898,29481,16374],{},[902,29483,16377],{"encoding":904},[38,29485,29486],{},"investice konstantní",[883,29488,29490],{"className":29489},[886],[888,29491,29492],{"xmlns":890},[892,29493,29494,29506],{},[895,29495,29496,29498,29500],{},[898,29497,16238],{},[1701,29499,1792],{},[3243,29501,29502,29504],{},[898,29503,16238],{},[1701,29505,8424],{},[902,29507,16249],{"encoding":904},"). Reálnější je předpoklad, že ",[38,29510,29511],{},"investice závisejí na úrokové míře",[883,29513,29515],{"className":29514},[886],[888,29516,29517],{"xmlns":890},[892,29518,29519,29523],{},[895,29520,29521],{},[898,29522,16096],{},[902,29524,16096],{"encoding":904}," — klesající funkce ",[883,29527,29529],{"className":29528},[886],[888,29530,29531],{"xmlns":890},[892,29532,29533,29553],{},[895,29534,29535,29537,29539,29541,29543,29545,29547,29549,29551],{},[898,29536,16238],{},[1701,29538,1799],{"stretchy":1798},[898,29540,16096],{},[1701,29542,1805],{"stretchy":1798},[1701,29544,1792],{},[898,29546,3618],{},[898,29548,16096],{},[1701,29550,1703],{},[898,29552,2312],{},[902,29554,19807],{"encoding":904},[883,29556,29558],{"className":29557},[886],[888,29559,29560],{"xmlns":890},[892,29561,29562,29570],{},[895,29563,29564,29566,29568],{},[898,29565,3618],{},[1701,29567,7530],{},[1850,29569,1852],{},[902,29571,16569],{"encoding":904},". Přidáním ",[38,29574,29575],{},"trhu peněz"," k trhu zboží vzniká model ",[38,29578,16066],{}," se dvěma neznámými ",[883,29581,29583],{"className":29582},[886],[888,29584,29585],{"xmlns":890},[892,29586,29587,29599],{},[895,29588,29589,29591,29593,29595,29597],{},[1701,29590,1799],{"stretchy":1798},[898,29592,13189],{},[1701,29594,2012],{"separator":2011},[898,29596,16096],{},[1701,29598,1805],{"stretchy":1798},[902,29600,22196],{"encoding":904}," a dvěma rovnicemi:",[120,29603,29604,29654],{},[123,29605,29606,1646,29608,29610,29611,29632,29633,1715],{},[38,29607,19896],{},[614,29609,16109],{},") — klesající přímka v rovině ",[883,29612,29614],{"className":29613},[886],[888,29615,29616],{"xmlns":890},[892,29617,29618,29630],{},[895,29619,29620,29622,29624,29626,29628],{},[1701,29621,1799],{"stretchy":1798},[898,29623,16096],{},[1701,29625,2012],{"separator":2011},[898,29627,13189],{},[1701,29629,1805],{"stretchy":1798},[902,29631,16991],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,29634,29636],{"className":29635},[886],[888,29637,29638],{"xmlns":890},[892,29639,29640,29652],{},[895,29641,29642,29644,29646,29648,29650],{},[898,29643,13189],{},[1701,29645,1792],{},[898,29647,1658],{},[1701,29649,1703],{},[898,29651,16238],{},[902,29653,18797],{"encoding":904},[123,29655,29656,1646,29658,29660,29661,2020,29686,29732],{},[38,29657,20095],{},[614,29659,16116],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,29662,29664],{"className":29663},[886],[888,29665,29666],{"xmlns":890},[892,29667,29668,29684],{},[895,29669,29670,29676,29678],{},[3243,29671,29672,29674],{},[898,29673,6909],{},[898,29675,1795],{},[1701,29677,1792],{},[3243,29679,29680,29682],{},[898,29681,6909],{},[1701,29683,8424],{},[902,29685,17534],{"encoding":904},[883,29687,29689],{"className":29688},[886],[888,29690,29691],{"xmlns":890},[892,29692,29693,29729],{},[895,29694,29695,29701,29703,29709,29711,29713,29719,29721,29723],{},[3243,29696,29697,29699],{},[898,29698,6909],{},[898,29700,1795],{},[1701,29702,1792],{},[1845,29704,29705,29707],{},[898,29706,17291],{},[1850,29708,4062],{},[898,29710,13189],{},[1701,29712,1703],{},[1845,29714,29715,29717],{},[898,29716,17291],{},[1850,29718,3938],{},[898,29720,16096],{},[1701,29722,1703],{},[1845,29724,29725,29727],{},[898,29726,17291],{},[1850,29728,3646],{},[902,29730,29731],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,29734,29735,4088,29738,29771,29772,29774,29775,29777],{},[38,29736,29737],{},"Simultánní rovnovážný bod",[883,29739,29741],{"className":29740},[886],[888,29742,29743],{"xmlns":890},[892,29744,29745,29769],{},[895,29746,29747,29749,29751,29753,29759,29761,29767],{},[898,29748,3249],{},[1701,29750,1792],{},[1701,29752,1799],{"stretchy":1798},[3243,29754,29755,29757],{},[898,29756,16096],{},[898,29758,3249],{},[1701,29760,2012],{"separator":2011},[3243,29762,29763,29765],{},[898,29764,13189],{},[898,29766,3249],{},[1701,29768,1805],{"stretchy":1798},[902,29770,20187],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,29773,16154],{}," (posun IS) a ",[38,29776,16185],{}," (posun LM).",[724,29779,29780],{},[38,29781,29782,29783,1343,29805,1343,29827,1343,29849,29871,29872,1715],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,29784,29786],{"className":29785},[886],[888,29787,29788],{"xmlns":890},[892,29789,29790,29802],{},[895,29791,29792,29798,29800],{},[3243,29793,29794,29796],{},[898,29795,13189],{},[898,29797,3249],{},[1701,29799,1792],{},[1850,29801,19167],{},[902,29803,29804],{"encoding":904},"Y^E = 5000",[883,29806,29808],{"className":29807},[886],[888,29809,29810],{"xmlns":890},[892,29811,29812,29824],{},[895,29813,29814,29820,29822],{},[3243,29815,29816,29818],{},[898,29817,16096],{},[898,29819,3249],{},[1701,29821,1792],{},[1850,29823,4225],{},[902,29825,29826],{"encoding":904},"r^E = 5",[883,29828,29830],{"className":29829},[886],[888,29831,29832],{"xmlns":890},[892,29833,29834,29846],{},[895,29835,29836,29842,29844],{},[3243,29837,29838,29840],{},[898,29839,1658],{},[898,29841,3249],{},[1701,29843,1792],{},[1850,29845,19204],{},[902,29847,29848],{"encoding":904},"C^E = 4100",[883,29850,29852],{"className":29851},[886],[888,29853,29854],{"xmlns":890},[892,29855,29856,29868],{},[895,29857,29858,29864,29866],{},[3243,29859,29860,29862],{},[898,29861,16238],{},[898,29863,3249],{},[1701,29865,1792],{},[1850,29867,19243],{},[902,29869,29870],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,29873,945],{"className":29874,"dataFsResolvedFilePath":943,"href":944},[210],[115,29876,29878],{"id":29877},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,29880,29881,29945,30056,30199,30441,30509],{},[123,29882,29883,29886,29887,29909,29910,29944],{},[38,29884,29885],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,29888,29890],{"className":29889},[886],[888,29891,29892],{"xmlns":890},[892,29893,29894,29906],{},[895,29895,29896,29898,29900,29902,29904],{},[898,29897,16167],{},[898,29899,22340],{},[898,29901,1680],{},[1701,29903,4067],{},[898,29905,13189],{},[902,29907,29908],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,29911,29913],{"className":29912},[886],[888,29914,29915],{"xmlns":890},[892,29916,29917,29941],{},[895,29918,29919,29921,29923,29925,29927,29929,29931,29933,29935,29937,29939],{},[898,29920,16167],{},[898,29922,22340],{},[898,29924,1680],{},[1701,29926,1792],{},[898,29928,1658],{},[1701,29930,1703],{},[898,29932,16238],{},[1701,29934,1703],{},[898,29936,16167],{},[1701,29938,1703],{},[898,29940,16374],{},[902,29942,29943],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,29946,29947,29949,29950,29971,29972,1343,29995,30026,30027,30040,30041,1715],{},[38,29948,22574],{}," splňují ",[883,29951,29953],{"className":29952},[886],[888,29954,29955],{"xmlns":890},[892,29956,29957,29969],{},[895,29958,29959,29961,29963,29965,29967],{},[898,29960,13189],{},[1701,29962,1792],{},[898,29964,1658],{},[1701,29966,1703],{},[898,29968,1661],{},[902,29970,16748],{"encoding":904}," (7.2); lineární model ",[883,29973,29975],{"className":29974},[886],[888,29976,29977],{"xmlns":890},[892,29978,29979,29993],{},[895,29980,29981,29983,29985,29987,29989,29991],{},[898,29982,1658],{},[1701,29984,1792],{},[898,29986,207],{},[898,29988,13189],{},[1701,29990,1703],{},[898,29992,3598],{},[902,29994,22966],{"encoding":904},[883,29996,29998],{"className":29997},[886],[888,29999,30000],{"xmlns":890},[892,30001,30002,30024],{},[895,30003,30004,30006,30008,30010,30012,30014,30016,30018,30020,30022],{},[898,30005,1661],{},[1701,30007,1792],{},[1701,30009,1799],{"stretchy":1798},[1850,30011,4062],{},[1701,30013,2317],{},[898,30015,207],{},[1701,30017,1805],{"stretchy":1798},[898,30019,13189],{},[1701,30021,2317],{},[898,30023,3598],{},[902,30025,23215],{"encoding":904}," s autonomní spotřebou ",[883,30028,30030],{"className":30029},[886],[888,30031,30032],{"xmlns":890},[892,30033,30034,30038],{},[895,30035,30036],{},[898,30037,3598],{},[902,30039,3598],{"encoding":904}," a autonomními úsporami ",[883,30042,30044],{"className":30043},[886],[888,30045,30046],{"xmlns":890},[892,30047,30048,30054],{},[895,30049,30050,30052],{},[1701,30051,2317],{},[898,30053,3598],{},[902,30055,23294],{"encoding":904},[123,30057,30058,4088,30061,1343,30091,30121,30122,30152,30153,1343,30174,1715],{},[38,30059,30060],{},"Mezní sklony",[883,30062,30064],{"className":30063},[886],[888,30065,30066],{"xmlns":890},[892,30067,30068,30088],{},[895,30069,30070,30072,30074,30076,30078,30080,30082,30084,30086],{},[898,30071,6909],{},[898,30073,1680],{},[898,30075,1658],{},[1701,30077,1792],{},[898,30079,2312],{"mathvariant":2334},[898,30081,1658],{},[898,30083,8741],{"mathvariant":2334},[898,30085,2312],{"mathvariant":2334},[898,30087,13189],{},[902,30089,30090],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,30092,30094],{"className":30093},[886],[888,30095,30096],{"xmlns":890},[892,30097,30098,30118],{},[895,30099,30100,30102,30104,30106,30108,30110,30112,30114,30116],{},[898,30101,6909],{},[898,30103,1680],{},[898,30105,1661],{},[1701,30107,1792],{},[898,30109,2312],{"mathvariant":2334},[898,30111,1661],{},[898,30113,8741],{"mathvariant":2334},[898,30115,2312],{"mathvariant":2334},[898,30117,13189],{},[902,30119,30120],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,30123,30125],{"className":30124},[886],[888,30126,30127],{"xmlns":890},[892,30128,30129,30149],{},[895,30130,30131,30133,30135,30137,30139,30141,30143,30145,30147],{},[898,30132,6909],{},[898,30134,1680],{},[898,30136,1658],{},[1701,30138,1703],{},[898,30140,6909],{},[898,30142,1680],{},[898,30144,1661],{},[1701,30146,1792],{},[1850,30148,4062],{},[902,30150,30151],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,30154,30156],{"className":30155},[886],[888,30157,30158],{"xmlns":890},[892,30159,30160,30172],{},[895,30161,30162,30164,30166,30168,30170],{},[898,30163,6909],{},[898,30165,1680],{},[898,30167,1658],{},[1701,30169,1792],{},[898,30171,207],{},[902,30173,23934],{"encoding":904},[883,30175,30177],{"className":30176},[886],[888,30178,30179],{"xmlns":890},[892,30180,30181,30197],{},[895,30182,30183,30185,30187,30189,30191,30193,30195],{},[898,30184,6909],{},[898,30186,1680],{},[898,30188,1661],{},[1701,30190,1792],{},[1850,30192,4062],{},[1701,30194,2317],{},[898,30196,207],{},[902,30198,23960],{"encoding":904},[123,30200,30201,30204,30205],{},[38,30202,30203],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,30206,30207,30295,30364],{},[123,30208,30209,30226,30227,30248,30249,2012],{},[883,30210,30212],{"className":30211},[886],[888,30213,30214],{"xmlns":890},[892,30215,30216,30224],{},[895,30217,30218,30220,30222],{},[898,30219,1658],{},[1939,30221,16344],{},[898,30223,16238],{},[902,30225,16349],{"encoding":904},": ",[883,30228,30230],{"className":30229},[886],[888,30231,30232],{"xmlns":890},[892,30233,30234,30246],{},[895,30235,30236,30238,30240,30242,30244],{},[898,30237,13189],{},[1701,30239,1792],{},[898,30241,1658],{},[1701,30243,1703],{},[898,30245,16238],{},[902,30247,18797],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,30250,30252],{"className":30251},[886],[888,30253,30254],{"xmlns":890},[892,30255,30256,30292],{},[895,30257,30258,30264,30266,30268,30270,30272,30278,30280,30282,30284,30286,30288,30290],{},[3243,30259,30260,30262],{},[898,30261,13189],{},[898,30263,3249],{},[1701,30265,1792],{},[1701,30267,1799],{"stretchy":1798},[898,30269,3598],{},[1701,30271,1703],{},[3243,30273,30274,30276],{},[898,30275,16238],{},[1701,30277,8424],{},[1701,30279,1805],{"stretchy":1798},[898,30281,8741],{"mathvariant":2334},[1701,30283,1799],{"stretchy":1798},[1850,30285,4062],{},[1701,30287,2317],{},[898,30289,207],{},[1701,30291,1805],{"stretchy":1798},[902,30293,30294],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,30296,30297,30318,30319,30338,30339,2012],{},[883,30298,30300],{"className":30299},[886],[888,30301,30302],{"xmlns":890},[892,30303,30304,30316],{},[895,30305,30306,30308,30310,30312,30314],{},[898,30307,1658],{},[1939,30309,16344],{},[898,30311,16238],{},[1939,30313,16344],{},[898,30315,16167],{},[902,30317,22266],{"encoding":904},": přidává vládu, zdanění ",[883,30320,30322],{"className":30321},[886],[888,30323,30324],{"xmlns":890},[892,30325,30326,30336],{},[895,30327,30328,30330,30332,30334],{},[898,30329,5877],{},[1701,30331,1799],{"stretchy":1798},[898,30333,13189],{},[1701,30335,1805],{"stretchy":1798},[902,30337,26259],{"encoding":904}," a disponibilní důchod ",[883,30340,30342],{"className":30341},[886],[888,30343,30344],{"xmlns":890},[892,30345,30346,30362],{},[895,30347,30348,30354,30356,30358,30360],{},[1845,30349,30350,30352],{},[898,30351,13189],{},[898,30353,1795],{},[1701,30355,1792],{},[898,30357,13189],{},[1701,30359,2317],{},[898,30361,5877],{},[902,30363,25758],{"encoding":904},[123,30365,30366,30391,30392,2020,30413,1715],{},[883,30367,30369],{"className":30368},[886],[888,30370,30371],{"xmlns":890},[892,30372,30373,30389],{},[895,30374,30375,30377,30379,30381,30383,30385,30387],{},[898,30376,1658],{},[1939,30378,16344],{},[898,30380,16238],{},[1939,30382,16344],{},[898,30384,16167],{},[1939,30386,16344],{},[898,30388,16374],{},[902,30390,16377],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,30393,30395],{"className":30394},[886],[888,30396,30397],{"xmlns":890},[892,30398,30399,30411],{},[895,30400,30401,30403,30405,30407,30409],{},[898,30402,16374],{},[1701,30404,1792],{},[898,30406,2593],{},[1701,30408,2317],{},[898,30410,6909],{},[902,30412,27298],{"encoding":904},[883,30414,30416],{"className":30415},[886],[888,30417,30418],{"xmlns":890},[892,30419,30420,30438],{},[895,30421,30422,30424,30426,30428,30430,30436],{},[898,30423,6909],{},[1701,30425,1792],{},[898,30427,6909],{},[1701,30429,1799],{"stretchy":1798},[1845,30431,30432,30434],{},[898,30433,13189],{},[898,30435,1795],{},[1701,30437,1805],{"stretchy":1798},[902,30439,30440],{"encoding":904},"M = M(Y_D)",[123,30442,30443,30446,30447,4088,30450,30508],{},[38,30444,30445],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,30448,30449],{},"multiplikátor investic",[883,30451,30453],{"className":30452},[886],[888,30454,30455],{"xmlns":890},[892,30456,30457,30505],{},[895,30458,30459,30461,30467,30469,30471,30477,30479,30481,30483,30485,30487,30489,30491,30493,30495,30497,30499,30501,30503],{},[898,30460,3893],{"mathvariant":2334},[3243,30462,30463,30465],{},[898,30464,13189],{},[898,30466,3249],{},[898,30468,8741],{"mathvariant":2334},[898,30470,3893],{"mathvariant":2334},[3243,30472,30473,30475],{},[898,30474,16238],{},[1701,30476,8424],{},[1701,30478,1792],{},[1850,30480,4062],{},[898,30482,8741],{"mathvariant":2334},[1701,30484,1799],{"stretchy":1798},[1850,30486,4062],{},[1701,30488,2317],{},[898,30490,207],{},[1701,30492,1805],{"stretchy":1798},[1701,30494,1792],{},[1850,30496,4062],{},[898,30498,8741],{"mathvariant":2334},[898,30500,6909],{},[898,30502,1680],{},[898,30504,1661],{},[902,30506,30507],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,30510,30511,30513,30514,30529,30530,22694,30547,30562,30563,30588,30589,1715],{},[38,30512,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,30515,30517],{"className":30516},[886],[888,30518,30519],{"xmlns":890},[892,30520,30521,30527],{},[895,30522,30523,30525],{},[898,30524,16238],{},[898,30526,1661],{},[902,30528,16106],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,30531,30533],{"className":30532},[886],[888,30534,30535],{"xmlns":890},[892,30536,30537,30545],{},[895,30538,30539,30541,30543],{},[898,30540,16238],{},[1701,30542,1792],{},[898,30544,1661],{},[902,30546,16766],{"encoding":904},[883,30548,30550],{"className":30549},[886],[888,30551,30552],{"xmlns":890},[892,30553,30554,30560],{},[895,30555,30556,30558],{},[898,30557,13853],{},[898,30559,6909],{},[902,30561,16113],{"encoding":904}," rovnováhu trhu peněz (",[883,30564,30566],{"className":30565},[886],[888,30567,30568],{"xmlns":890},[892,30569,30570,30586],{},[895,30571,30572,30578,30580],{},[3243,30573,30574,30576],{},[898,30575,6909],{},[898,30577,1795],{},[1701,30579,1792],{},[3243,30581,30582,30584],{},[898,30583,6909],{},[1701,30585,8424],{},[902,30587,17534],{"encoding":904},"); průsečík dává ",[883,30590,30592],{"className":30591},[886],[888,30593,30594],{"xmlns":890},[892,30595,30596,30616],{},[895,30597,30598,30600,30606,30608,30614],{},[1701,30599,1799],{"stretchy":1798},[3243,30601,30602,30604],{},[898,30603,13189],{},[898,30605,3249],{},[1701,30607,2012],{"separator":2011},[3243,30609,30610,30612],{},[898,30611,16096],{},[898,30613,3249],{},[1701,30615,1805],{"stretchy":1798},[902,30617,16150],{"encoding":904},[115,30619,5578],{"id":5577},[120,30621,30622,30660,30700,30790,30872,30926,30982,31041,31076,31081,31153,31228,31314,31376,31444,31502,31555,31594],{},[123,30623,30624,2979,30627,29944],{},[38,30625,30626],{},"Hrubý národní produkt (GNP)",[883,30628,30630],{"className":30629},[886],[888,30631,30632],{"xmlns":890},[892,30633,30634,30658],{},[895,30635,30636,30638,30640,30642,30644,30646,30648,30650,30652,30654,30656],{},[898,30637,16167],{},[898,30639,22340],{},[898,30641,1680],{},[1701,30643,1792],{},[898,30645,1658],{},[1701,30647,1703],{},[898,30649,16238],{},[1701,30651,1703],{},[898,30653,16167],{},[1701,30655,1703],{},[898,30657,16374],{},[902,30659,29943],{"encoding":904},[123,30661,30662,30678,30679,1715],{},[38,30663,30664,30665],{},"Národní důchod ",[883,30666,30668],{"className":30667},[886],[888,30669,30670],{"xmlns":890},[892,30671,30672,30676],{},[895,30673,30674],{},[898,30675,13189],{},[902,30677,13189],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,30680,30682],{"className":30681},[886],[888,30683,30684],{"xmlns":890},[892,30685,30686,30698],{},[895,30687,30688,30690,30692,30694,30696],{},[898,30689,16167],{},[898,30691,22340],{},[898,30693,1680],{},[1701,30695,4067],{},[898,30697,13189],{},[902,30699,29908],{"encoding":904},[123,30701,30702,30728,30729,1343,30752,1343,30773,1715],{},[38,30703,30704,30705],{},"Funkce spotřeby ",[883,30706,30708],{"className":30707},[886],[888,30709,30710],{"xmlns":890},[892,30711,30712,30726],{},[895,30713,30714,30716,30718,30720,30722,30724],{},[898,30715,1658],{},[1701,30717,1792],{},[898,30719,1658],{},[1701,30721,1799],{"stretchy":1798},[898,30723,13189],{},[1701,30725,1805],{"stretchy":1798},[902,30727,24784],{"encoding":904}," — lineární model ",[883,30730,30732],{"className":30731},[886],[888,30733,30734],{"xmlns":890},[892,30735,30736,30750],{},[895,30737,30738,30740,30742,30744,30746,30748],{},[898,30739,1658],{},[1701,30741,1792],{},[898,30743,207],{},[898,30745,13189],{},[1701,30747,1703],{},[898,30749,3598],{},[902,30751,22966],{"encoding":904},[883,30753,30755],{"className":30754},[886],[888,30756,30757],{"xmlns":890},[892,30758,30759,30771],{},[895,30760,30761,30763,30765,30767,30769],{},[1850,30762,1852],{},[1701,30764,7530],{},[898,30766,207],{},[1701,30768,7530],{},[1850,30770,4062],{},[902,30772,22882],{"encoding":904},[883,30774,30776],{"className":30775},[886],[888,30777,30778],{"xmlns":890},[892,30779,30780,30788],{},[895,30781,30782,30784,30786],{},[898,30783,3598],{},[1701,30785,7491],{},[1850,30787,1852],{},[902,30789,22860],{"encoding":904},[123,30791,30792,2979,30819,30840,30841,1715],{},[38,30793,30794,30795],{},"Funkce úspor ",[883,30796,30798],{"className":30797},[886],[888,30799,30800],{"xmlns":890},[892,30801,30802,30816],{},[895,30803,30804,30806,30808,30810,30812,30814],{},[898,30805,1661],{},[1701,30807,1792],{},[898,30809,1661],{},[1701,30811,1799],{"stretchy":1798},[898,30813,13189],{},[1701,30815,1805],{"stretchy":1798},[902,30817,30818],{"encoding":904},"S = S(Y)",[883,30820,30822],{"className":30821},[886],[888,30823,30824],{"xmlns":890},[892,30825,30826,30838],{},[895,30827,30828,30830,30832,30834,30836],{},[898,30829,13189],{},[1701,30831,1792],{},[898,30833,1658],{},[1701,30835,1703],{},[898,30837,1661],{},[902,30839,16748],{"encoding":904},"; lineární ",[883,30842,30844],{"className":30843},[886],[888,30845,30846],{"xmlns":890},[892,30847,30848,30870],{},[895,30849,30850,30852,30854,30856,30858,30860,30862,30864,30866,30868],{},[898,30851,1661],{},[1701,30853,1792],{},[1701,30855,1799],{"stretchy":1798},[1850,30857,4062],{},[1701,30859,2317],{},[898,30861,207],{},[1701,30863,1805],{"stretchy":1798},[898,30865,13189],{},[1701,30867,2317],{},[898,30869,3598],{},[902,30871,23215],{"encoding":904},[123,30873,30874,2979,30877,1343,30900,1715],{},[38,30875,30876],{},"Autonomní spotřeba\u002Fúspory",[883,30878,30880],{"className":30879},[886],[888,30881,30882],{"xmlns":890},[892,30883,30884,30898],{},[895,30885,30886,30888,30890,30892,30894,30896],{},[898,30887,1658],{},[1701,30889,1799],{"stretchy":1798},[1850,30891,1852],{},[1701,30893,1805],{"stretchy":1798},[1701,30895,1792],{},[898,30897,3598],{},[902,30899,23606],{"encoding":904},[883,30901,30903],{"className":30902},[886],[888,30904,30905],{"xmlns":890},[892,30906,30907,30923],{},[895,30908,30909,30911,30913,30915,30917,30919,30921],{},[898,30910,1661],{},[1701,30912,1799],{"stretchy":1798},[1850,30914,1852],{},[1701,30916,1805],{"stretchy":1798},[1701,30918,1792],{},[1701,30920,2317],{},[898,30922,3598],{},[902,30924,30925],{"encoding":904},"S(0) = -b",[123,30927,30928,30960,30961,2506],{},[38,30929,30930,30931],{},"Mezní sklon ke spotřebě ",[883,30932,30934],{"className":30933},[886],[888,30935,30936],{"xmlns":890},[892,30937,30938,30958],{},[895,30939,30940,30942,30944,30946,30948,30950,30952,30954,30956],{},[898,30941,6909],{},[898,30943,1680],{},[898,30945,1658],{},[1701,30947,1792],{},[898,30949,2312],{"mathvariant":2334},[898,30951,1658],{},[898,30953,8741],{"mathvariant":2334},[898,30955,2312],{"mathvariant":2334},[898,30957,13189],{},[902,30959,30090],{"encoding":904}," (v lineárním modelu ",[883,30962,30964],{"className":30963},[886],[888,30965,30966],{"xmlns":890},[892,30967,30968,30980],{},[895,30969,30970,30972,30974,30976,30978],{},[898,30971,6909],{},[898,30973,1680],{},[898,30975,1658],{},[1701,30977,1792],{},[898,30979,207],{},[902,30981,23934],{"encoding":904},[123,30983,30984,30960,31016,2506],{},[38,30985,30986,30987],{},"Mezní sklon k úsporám ",[883,30988,30990],{"className":30989},[886],[888,30991,30992],{"xmlns":890},[892,30993,30994,31014],{},[895,30995,30996,30998,31000,31002,31004,31006,31008,31010,31012],{},[898,30997,6909],{},[898,30999,1680],{},[898,31001,1661],{},[1701,31003,1792],{},[898,31005,2312],{"mathvariant":2334},[898,31007,1661],{},[898,31009,8741],{"mathvariant":2334},[898,31011,2312],{"mathvariant":2334},[898,31013,13189],{},[902,31015,30120],{"encoding":904},[883,31017,31019],{"className":31018},[886],[888,31020,31021],{"xmlns":890},[892,31022,31023,31039],{},[895,31024,31025,31027,31029,31031,31033,31035,31037],{},[898,31026,6909],{},[898,31028,1680],{},[898,31030,1661],{},[1701,31032,1792],{},[1850,31034,4062],{},[1701,31036,2317],{},[898,31038,207],{},[902,31040,23960],{"encoding":904},[123,31042,31043,4088,31046,31075],{},[38,31044,31045],{},"Vztah",[883,31047,31049],{"className":31048},[886],[888,31050,31051],{"xmlns":890},[892,31052,31053,31073],{},[895,31054,31055,31057,31059,31061,31063,31065,31067,31069,31071],{},[898,31056,6909],{},[898,31058,1680],{},[898,31060,1658],{},[1701,31062,1703],{},[898,31064,6909],{},[898,31066,1680],{},[898,31068,1661],{},[1701,31070,1792],{},[1850,31072,4062],{},[902,31074,30151],{"encoding":904}," (7.5).",[123,31077,31078,31080],{},[38,31079,24627],{}," — rovnováha agregátní poptávky a nabídky.",[123,31082,31083,31086,31087,19842,31108,1715],{},[38,31084,31085],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,31088,31090],{"className":31089},[886],[888,31091,31092],{"xmlns":890},[892,31093,31094,31106],{},[895,31095,31096,31098,31100,31102,31104],{},[898,31097,13189],{},[1701,31099,1792],{},[898,31101,1658],{},[1701,31103,1703],{},[898,31105,16238],{},[902,31107,18797],{"encoding":904},[883,31109,31111],{"className":31110},[886],[888,31112,31113],{"xmlns":890},[892,31114,31115,31151],{},[895,31116,31117,31123,31125,31127,31129,31131,31137,31139,31141,31143,31145,31147,31149],{},[3243,31118,31119,31121],{},[898,31120,13189],{},[898,31122,3249],{},[1701,31124,1792],{},[1701,31126,1799],{"stretchy":1798},[898,31128,3598],{},[1701,31130,1703],{},[3243,31132,31133,31135],{},[898,31134,16238],{},[1701,31136,8424],{},[1701,31138,1805],{"stretchy":1798},[898,31140,8741],{"mathvariant":2334},[1701,31142,1799],{"stretchy":1798},[1850,31144,4062],{},[1701,31146,2317],{},[898,31148,207],{},[1701,31150,1805],{"stretchy":1798},[902,31152,30294],{"encoding":904},[123,31154,31155,31158,31159,1343,31178,19842,31203,1715],{},[38,31156,31157],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,31160,31162],{"className":31161},[886],[888,31163,31164],{"xmlns":890},[892,31165,31166,31176],{},[895,31167,31168,31170,31172,31174],{},[898,31169,5877],{},[1701,31171,1799],{"stretchy":1798},[898,31173,13189],{},[1701,31175,1805],{"stretchy":1798},[902,31177,26259],{"encoding":904},[883,31179,31181],{"className":31180},[886],[888,31182,31183],{"xmlns":890},[892,31184,31185,31201],{},[895,31186,31187,31193,31195,31197,31199],{},[1845,31188,31189,31191],{},[898,31190,13189],{},[898,31192,1795],{},[1701,31194,1792],{},[898,31196,13189],{},[1701,31198,2317],{},[898,31200,5877],{},[902,31202,25758],{"encoding":904},[883,31204,31206],{"className":31205},[886],[888,31207,31208],{"xmlns":890},[892,31209,31210,31226],{},[895,31211,31212,31214,31216,31218,31220,31222,31224],{},[898,31213,13189],{},[1701,31215,1792],{},[898,31217,1658],{},[1701,31219,1703],{},[898,31221,16238],{},[1701,31223,1703],{},[898,31225,16167],{},[902,31227,25729],{"encoding":904},[123,31229,31230,31233,31234,31255,31256,19842,31280,1715],{},[38,31231,31232],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,31235,31237],{"className":31236},[886],[888,31238,31239],{"xmlns":890},[892,31240,31241,31253],{},[895,31242,31243,31245,31247,31249,31251],{},[898,31244,16374],{},[1701,31246,1792],{},[898,31248,2593],{},[1701,31250,2317],{},[898,31252,6909],{},[902,31254,27298],{"encoding":904},", importem ",[883,31257,31259],{"className":31258},[886],[888,31260,31261],{"xmlns":890},[892,31262,31263,31277],{},[895,31264,31265,31267,31269,31275],{},[898,31266,6909],{},[1701,31268,1799],{"stretchy":1798},[1845,31270,31271,31273],{},[898,31272,13189],{},[898,31274,1795],{},[1701,31276,1805],{"stretchy":1798},[902,31278,31279],{"encoding":904},"M(Y_D)",[883,31281,31283],{"className":31282},[886],[888,31284,31285],{"xmlns":890},[892,31286,31287,31311],{},[895,31288,31289,31291,31293,31295,31297,31299,31301,31303,31305,31307,31309],{},[898,31290,13189],{},[1701,31292,1792],{},[898,31294,1658],{},[1701,31296,1703],{},[898,31298,16238],{},[1701,31300,1703],{},[898,31302,16167],{},[1701,31304,1703],{},[898,31306,2593],{},[1701,31308,2317],{},[898,31310,6909],{},[902,31312,31313],{"encoding":904},"Y = C + I + G + B - M",[123,31315,31316,2979,31319,30508],{},[38,31317,31318],{},"Multiplikátor investic",[883,31320,31322],{"className":31321},[886],[888,31323,31324],{"xmlns":890},[892,31325,31326,31374],{},[895,31327,31328,31330,31336,31338,31340,31346,31348,31350,31352,31354,31356,31358,31360,31362,31364,31366,31368,31370,31372],{},[898,31329,3893],{"mathvariant":2334},[3243,31331,31332,31334],{},[898,31333,13189],{},[898,31335,3249],{},[898,31337,8741],{"mathvariant":2334},[898,31339,3893],{"mathvariant":2334},[3243,31341,31342,31344],{},[898,31343,16238],{},[1701,31345,8424],{},[1701,31347,1792],{},[1850,31349,4062],{},[898,31351,8741],{"mathvariant":2334},[1701,31353,1799],{"stretchy":1798},[1850,31355,4062],{},[1701,31357,2317],{},[898,31359,207],{},[1701,31361,1805],{"stretchy":1798},[1701,31363,1792],{},[1850,31365,4062],{},[898,31367,8741],{"mathvariant":2334},[898,31369,6909],{},[898,31371,1680],{},[898,31373,1661],{},[902,31375,30507],{"encoding":904},[123,31377,31378,2979,31409,1343,31426,31443],{},[38,31379,19777,31380],{},[883,31381,31383],{"className":31382},[886],[888,31384,31385],{"xmlns":890},[892,31386,31387,31407],{},[895,31388,31389,31391,31393,31395,31397,31399,31401,31403,31405],{},[898,31390,16238],{},[1701,31392,1799],{"stretchy":1798},[898,31394,16096],{},[1701,31396,1805],{"stretchy":1798},[1701,31398,1792],{},[898,31400,3618],{},[898,31402,16096],{},[1701,31404,1703],{},[898,31406,2312],{},[902,31408,19807],{"encoding":904},[883,31410,31412],{"className":31411},[886],[888,31413,31414],{"xmlns":890},[892,31415,31416,31424],{},[895,31417,31418,31420,31422],{},[898,31419,3618],{},[1701,31421,7530],{},[1850,31423,1852],{},[902,31425,16569],{"encoding":904},[883,31427,31429],{"className":31428},[886],[888,31430,31431],{"xmlns":890},[892,31432,31433,31441],{},[895,31434,31435,31437,31439],{},[898,31436,2312],{},[1701,31438,7491],{},[1850,31440,1852],{},[902,31442,16548],{"encoding":904},"; klesající.",[123,31445,31446,31448,31449,31451,31452,31501],{},[38,31447,19896],{}," — rovnováha na trhu zboží (",[614,31450,16109],{},"); ",[883,31453,31455],{"className":31454},[886],[888,31456,31457],{"xmlns":890},[892,31458,31459,31499],{},[895,31460,31461,31463,31465,31477,31479,31481],{},[898,31462,13189],{},[1701,31464,1792],{},[3726,31466,31467,31469],{},[898,31468,3618],{},[895,31470,31471,31473,31475],{},[1850,31472,4062],{},[1701,31474,2317],{},[898,31476,207],{},[898,31478,16096],{},[1701,31480,1703],{},[3726,31482,31483,31491],{},[895,31484,31485,31487,31489],{},[898,31486,3598],{},[1701,31488,1703],{},[898,31490,2312],{},[895,31492,31493,31495,31497],{},[1850,31494,4062],{},[1701,31496,2317],{},[898,31498,207],{},[902,31500,19949],{"encoding":904}," (7.14); klesající.",[123,31503,31504,31506,31507,31451,31509,31554],{},[38,31505,20095],{}," — rovnováha na trhu peněz (",[614,31508,16116],{},[883,31510,31512],{"className":31511},[886],[888,31513,31514],{"xmlns":890},[892,31515,31516,31552],{},[895,31517,31518,31524,31526,31532,31534,31536,31542,31544,31546],{},[3243,31519,31520,31522],{},[898,31521,6909],{},[1701,31523,8424],{},[1701,31525,1792],{},[1845,31527,31528,31530],{},[898,31529,17291],{},[1850,31531,4062],{},[898,31533,13189],{},[1701,31535,1703],{},[1845,31537,31538,31540],{},[898,31539,17291],{},[1850,31541,3938],{},[898,31543,16096],{},[1701,31545,1703],{},[1845,31547,31548,31550],{},[898,31549,17291],{},[1850,31551,3646],{},[902,31553,20143],{"encoding":904}," (7.15); rostoucí.",[123,31556,31557,2979,31560,1715],{},[38,31558,31559],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,31561,31563],{"className":31562},[886],[888,31564,31565],{"xmlns":890},[892,31566,31567,31591],{},[895,31568,31569,31575,31577,31583,31585],{},[3243,31570,31571,31573],{},[898,31572,6909],{},[898,31574,1795],{},[1701,31576,1792],{},[1845,31578,31579,31581],{},[898,31580,13853],{},[1850,31582,4062],{},[1701,31584,1703],{},[1845,31586,31587,31589],{},[898,31588,13853],{},[1850,31590,3938],{},[902,31592,31593],{"encoding":904},"M^D = L_1 + L_2",[123,31595,31596,20153,31598,18034,31611,2633,31626,31641,31642,1715],{},[38,31597,945],{},[883,31599,31601],{"className":31600},[886],[888,31602,31603],{"xmlns":890},[892,31604,31605,31609],{},[895,31606,31607],{},[898,31608,3249],{},[902,31610,3249],{"encoding":904},[883,31612,31614],{"className":31613},[886],[888,31615,31616],{"xmlns":890},[892,31617,31618,31624],{},[895,31619,31620,31622],{},[898,31621,16238],{},[898,31623,1661],{},[902,31625,16106],{"encoding":904},[883,31627,31629],{"className":31628},[886],[888,31630,31631],{"xmlns":890},[892,31632,31633,31639],{},[895,31634,31635,31637],{},[898,31636,13853],{},[898,31638,6909],{},[902,31640,16113],{"encoding":904}," určuje ",[883,31643,31645],{"className":31644},[886],[888,31646,31647],{"xmlns":890},[892,31648,31649,31669],{},[895,31650,31651,31653,31659,31661,31667],{},[1701,31652,1799],{"stretchy":1798},[3243,31654,31655,31657],{},[898,31656,13189],{},[898,31658,3249],{},[1701,31660,2012],{"separator":2011},[3243,31662,31663,31665],{},[898,31664,16096],{},[898,31666,3249],{},[1701,31668,1805],{"stretchy":1798},[902,31670,16150],{"encoding":904},[115,31672,5984],{"id":5983},[120,31674,31675,31682,31689],{},[123,31676,31677,4088,31679],{},[38,31678,6031],{},[207,31680,6037],{"className":31681,"dataFsResolvedFilePath":6035,"href":6036},[210],[123,31683,31684,4088,31686],{},[38,31685,20261],{},[207,31687,20265],{"className":31688,"dataFsResolvedFilePath":868,"href":869},[210],[123,31690,31691,31693],{},[38,31692,6013],{},[120,31694,31695,31701,31707,31713],{},[123,31696,31697,31700],{},[207,31698,20318],{"className":31699,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,31702,31703,31706],{},[207,31704,6071],{"className":31705,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,31708,31709,31712],{},[207,31710,7038],{"className":31711,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,31714,31715,31718,31719,1343,31736,31753],{},[207,31716,1145],{"className":31717,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,31720,31722],{"className":31721},[886],[888,31723,31724],{"xmlns":890},[892,31725,31726,31734],{},[895,31727,31728,31730,31732],{},[898,31729,6909],{},[898,31731,1680],{},[898,31733,1658],{},[902,31735,22091],{"encoding":904},[883,31737,31739],{"className":31738},[886],[888,31740,31741],{"xmlns":890},[892,31742,31743,31751],{},[895,31744,31745,31747,31749],{},[898,31746,6909],{},[898,31748,1680],{},[898,31750,1661],{},[902,31752,23704],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":31755},[31756,31757,31758,31759,31764,31767,31768,31775,31780,31785,31788,31789,31790,31791],{"id":16060,"depth":642,"text":16061},{"id":22200,"depth":642,"text":22201},{"id":22320,"depth":642,"text":22321},{"id":22573,"depth":642,"text":22574,"children":31760},[31761,31762,31763],{"id":22577,"depth":649,"text":22578},{"id":22789,"depth":649,"text":22790},{"id":23297,"depth":649,"text":23298},{"id":23616,"depth":642,"text":23617,"children":31765},[31766],{"id":24132,"depth":649,"text":24133},{"id":24626,"depth":642,"text":24627},{"id":24653,"depth":642,"text":24654,"children":31769},[31770,31771,31772,31774],{"id":24664,"depth":649,"text":24665},{"id":24734,"depth":649,"text":24735},{"id":24915,"depth":649,"text":31773},"Výpočet YEY^E",{"id":25058,"depth":649,"text":25059},{"id":25436,"depth":642,"text":25437,"children":31776},[31777,31778,31779],{"id":25440,"depth":649,"text":24665},{"id":25888,"depth":649,"text":24735},{"id":26544,"depth":649,"text":26545},{"id":27329,"depth":642,"text":27330,"children":31781},[31782,31783,31784],{"id":27333,"depth":649,"text":24665},{"id":27478,"depth":649,"text":24735},{"id":27748,"depth":649,"text":27749},{"id":28672,"depth":642,"text":28673,"children":31786},[31787],{"id":28868,"depth":649,"text":28869},{"id":29417,"depth":642,"text":29418},{"id":29877,"depth":642,"text":29878},{"id":5577,"depth":642,"text":5578},{"id":5983,"depth":642,"text":5984},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,20273,1143,31798,31799,31800,20318,21929],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":31803,"title":31804,"body":31805,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":40778,"navigation":664,"path":40779,"seo":40780,"sources":40781,"stem":40782,"tags":40783,"type":6074,"updated":677,"__hash__":40788},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":31806,"toc":40747},[31807,31810,31812,32041,32045,32098,32165,32277,32436,32440,32556,32560,32563,32685,32688,32881,32905,32973,33137,33155,33220,33598,33602,33609,33853,33909,33913,33978,34096,34226,34258,34378,34460,34463,34585,34778,34999,35003,35043,35148,35205,35305,35482,35612,35665,35668,35755,35759,35935,35939,35942,36027,36030,36087,36192,36196,36317,36320,36503,36506,36614,36823,37143,37191,37264,37338,37340,37564,37799,38067,38071,38074,38179,38236,38270,38317,38350,38434,38436,38668,38801,38878,39000,39155,39159,39300,39307,39531,39542,39546,39550,39655,39797,39907,40006,40010,40169,40279,40281,40674,40676],[12,31808,31804],{"id":31809},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,31811,16061],{"id":16060},[724,31813,31814,31816,31817,31851,31852,31855,31856,31887,31888,31934,31935,31938,31939,31981,31982,32000,32001,32005,32006,32036,32037,32040],{},[38,31815,913],{}," řeší, jaký svazek zboží ",[883,31818,31820],{"className":31819},[886],[888,31821,31822],{"xmlns":890},[892,31823,31824,31848],{},[895,31825,31826,31828,31836,31838,31846],{},[1701,31827,2036],{"stretchy":1798},[2287,31829,31830,31832,31834],{},[898,31831,1802],{},[1850,31833,4062],{},[1701,31835,8424],{},[1701,31837,2012],{"separator":2011},[2287,31839,31840,31842,31844],{},[898,31841,1802],{},[1850,31843,3938],{},[1701,31845,8424],{},[1701,31847,2053],{"stretchy":1798},[902,31849,31850],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,31853,31854],{},"primární úloha"," — maximalizace užitečnosti ",[883,31857,31859],{"className":31858},[886],[888,31860,31861],{"xmlns":890},[892,31862,31863,31885],{},[895,31864,31865,31867,31869,31875,31877,31883],{},[898,31866,900],{},[1701,31868,1799],{"stretchy":1798},[1845,31870,31871,31873],{},[898,31872,1802],{},[1850,31874,4062],{},[1701,31876,2012],{"separator":2011},[1845,31878,31879,31881],{},[898,31880,1802],{},[1850,31882,3938],{},[1701,31884,1805],{"stretchy":1798},[902,31886,20389],{"encoding":904}," při rozpočtovém omezení ",[883,31889,31891],{"className":31890},[886],[888,31892,31893],{"xmlns":890},[892,31894,31895,31931],{},[895,31896,31897,31903,31905,31911,31917,31919,31925],{},[3243,31898,31899,31901],{},[898,31900,13189],{},[1701,31902,8424],{},[1701,31904,1792],{},[1845,31906,31907,31909],{},[898,31908,1680],{},[1850,31910,4062],{},[1845,31912,31913,31915],{},[898,31914,1802],{},[1850,31916,4062],{},[1701,31918,1703],{},[1845,31920,31921,31923],{},[898,31922,1680],{},[1850,31924,3938],{},[1845,31926,31927,31929],{},[898,31928,1802],{},[1850,31930,3938],{},[902,31932,31933],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,31936,31937],{},"duální úloha"," — minimalizace výdajů ",[883,31940,31942],{"className":31941},[886],[888,31943,31944],{"xmlns":890},[892,31945,31946,31978],{},[895,31947,31948,31950,31952,31958,31964,31966,31972],{},[898,31949,3249],{},[1701,31951,1792],{},[1845,31953,31954,31956],{},[898,31955,1680],{},[1850,31957,4062],{},[1845,31959,31960,31962],{},[898,31961,1802],{},[1850,31963,4062],{},[1701,31965,1703],{},[1845,31967,31968,31970],{},[898,31969,1680],{},[1850,31971,3938],{},[1845,31973,31974,31976],{},[898,31975,1802],{},[1850,31977,3938],{},[902,31979,31980],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,31983,31985],{"className":31984},[886],[888,31986,31987],{"xmlns":890},[892,31988,31989,31997],{},[895,31990,31991],{},[3243,31992,31993,31995],{},[898,31994,900],{},[1701,31996,8424],{},[902,31998,31999],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,32002,32004],{"className":32003,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,32007,32009],{"className":32008},[886],[888,32010,32011],{"xmlns":890},[892,32012,32013,32033],{},[895,32014,32015,32017,32019,32025,32027],{},[1939,32016,14659],{},[1701,32018,1792],{},[1845,32020,32021,32023],{},[898,32022,1680],{},[1850,32024,4062],{},[898,32026,8741],{"mathvariant":2334},[1845,32028,32029,32031],{},[898,32030,1680],{},[1850,32032,3938],{},[902,32034,32035],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,32038,32039],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,32042,32044],{"id":32043},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,32046,32047,32048,32066,32067,32097],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,32049,32051],{"className":32050},[886],[888,32052,32053],{"xmlns":890},[892,32054,32055,32063],{},[895,32056,32057],{},[3243,32058,32059,32061],{},[898,32060,13189],{},[1701,32062,8424],{},[902,32064,32065],{"encoding":904},"Y^*"," a ceny ",[883,32068,32070],{"className":32069},[886],[888,32071,32072],{"xmlns":890},[892,32073,32074,32094],{},[895,32075,32076,32084,32086],{},[2287,32077,32078,32080,32082],{},[898,32079,1680],{},[1850,32081,4062],{},[1701,32083,8424],{},[1701,32085,2012],{"separator":2011},[2287,32087,32088,32090,32092],{},[898,32089,1680],{},[1850,32091,3938],{},[1701,32093,8424],{},[902,32095,32096],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,32099,32101],{"className":32100},[886],[888,32102,32103],{"xmlns":890,"display":2252},[892,32104,32105,32162],{},[2256,32106,32107],{"width":2258},[2260,32108,32109,32111,32155,32157],{},[2263,32110],{"width":2265},[2263,32112,32113],{},[895,32114,32115,32121,32123,32131,32137,32139,32147,32153],{},[3243,32116,32117,32119],{},[898,32118,13189],{},[1701,32120,8424],{},[1701,32122,1792],{},[2287,32124,32125,32127,32129],{},[898,32126,1680],{},[1850,32128,4062],{},[1701,32130,8424],{},[1845,32132,32133,32135],{},[898,32134,1802],{},[1850,32136,4062],{},[1701,32138,1703],{},[2287,32140,32141,32143,32145],{},[898,32142,1680],{},[1850,32144,3938],{},[1701,32146,8424],{},[1845,32148,32149,32151],{},[898,32150,1802],{},[1850,32152,3938],{},[1701,32154,2012],{"separator":2011},[2263,32156],{"width":2265},[2263,32158,32159],{},[1939,32160,32161],{},"(6.12)",[902,32163,32164],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,32166,32167,32168,32171,32172,2633,32208,32244,32245,32258,32259,32273,32274,1715],{},"geometricky ",[38,32169,32170],{},"rozpočtová přímka (budget line)"," procházející body ",[883,32173,32175],{"className":32174},[886],[888,32176,32177],{"xmlns":890},[892,32178,32179,32205],{},[895,32180,32181,32183,32189,32191,32199,32201,32203],{},[1701,32182,2036],{"stretchy":1798},[3243,32184,32185,32187],{},[898,32186,13189],{},[1701,32188,8424],{},[898,32190,8741],{"mathvariant":2334},[2287,32192,32193,32195,32197],{},[898,32194,1680],{},[1850,32196,4062],{},[1701,32198,8424],{},[1701,32200,2012],{"separator":2011},[1850,32202,1852],{},[1701,32204,2053],{"stretchy":1798},[902,32206,32207],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,32209,32211],{"className":32210},[886],[888,32212,32213],{"xmlns":890},[892,32214,32215,32241],{},[895,32216,32217,32219,32221,32223,32229,32231,32239],{},[1701,32218,2036],{"stretchy":1798},[1850,32220,1852],{},[1701,32222,2012],{"separator":2011},[3243,32224,32225,32227],{},[898,32226,13189],{},[1701,32228,8424],{},[898,32230,8741],{"mathvariant":2334},[2287,32232,32233,32235,32237],{},[898,32234,1680],{},[1850,32236,3938],{},[1701,32238,8424],{},[1701,32240,2053],{"stretchy":1798},[902,32242,32243],{"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 ",[883,32246,32248],{"className":32247},[886],[888,32249,32250],{"xmlns":890},[892,32251,32252,32256],{},[895,32253,32254],{},[898,32255,900],{},[902,32257,900],{"encoding":904},", indiferenční křivky a ",[883,32260,32262],{"className":32261},[886],[888,32263,32264],{"xmlns":890},[892,32265,32266,32270],{},[895,32267,32268],{},[1939,32269,14659],{},[902,32271,32272],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,32275,880],{"className":32276,"dataFsResolvedFilePath":878,"href":879},[210],[1635,32278,32279],{},[724,32280,32281,32283,32284,32287,32288,32301,32302,32304,32305,32318,32319,4088,32322,32362,32363,32380,32381,32398,32399,32416,32417,32435],{},[883,32282,4695],{}," Pozor — dvě úlohy, totéž řešení\n",[38,32285,32286],{},"Primární úloha"," (max ",[883,32289,32291],{"className":32290},[886],[888,32292,32293],{"xmlns":890},[892,32294,32295,32299],{},[895,32296,32297],{},[898,32298,900],{},[902,32300,900],{"encoding":904}," při pevném rozpočtu) a ",[38,32303,31937],{}," (min ",[883,32306,32308],{"className":32307},[886],[888,32309,32310],{"xmlns":890},[892,32311,32312,32316],{},[895,32313,32314],{},[898,32315,3249],{},[902,32317,3249],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,32320,32321],{},"tentýž bod",[883,32323,32325],{"className":32324},[886],[888,32326,32327],{"xmlns":890},[892,32328,32329,32359],{},[895,32330,32331,32337,32339,32347,32349,32357],{},[3243,32332,32333,32335],{},[898,32334,1802],{},[1701,32336,8424],{},[1701,32338,2036],{"stretchy":1798},[2287,32340,32341,32343,32345],{},[898,32342,1802],{},[1850,32344,4062],{},[1701,32346,8424],{},[1701,32348,2012],{"separator":2011},[2287,32350,32351,32353,32355],{},[898,32352,1802],{},[1850,32354,3938],{},[1701,32356,8424],{},[1701,32358,2053],{"stretchy":1798},[902,32360,32361],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,32364,32366],{"className":32365},[886],[888,32367,32368],{"xmlns":890},[892,32369,32370,32378],{},[895,32371,32372],{},[3243,32373,32374,32376],{},[898,32375,13189],{},[1701,32377,8424],{},[902,32379,32065],{"encoding":904}," a hledáme maximální ",[883,32382,32384],{"className":32383},[886],[888,32385,32386],{"xmlns":890},[892,32387,32388,32396],{},[895,32389,32390],{},[3243,32391,32392,32394],{},[898,32393,900],{},[1701,32395,8424],{},[902,32397,31999],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,32400,32402],{"className":32401},[886],[888,32403,32404],{"xmlns":890},[892,32405,32406,32414],{},[895,32407,32408],{},[3243,32409,32410,32412],{},[898,32411,900],{},[1701,32413,8424],{},[902,32415,31999],{"encoding":904}," a hledáme minimální ",[883,32418,32420],{"className":32419},[886],[888,32421,32422],{"xmlns":890},[892,32423,32424,32432],{},[895,32425,32426],{},[3243,32427,32428,32430],{},[898,32429,3249],{},[1701,32431,8424],{},[902,32433,32434],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,32437,32439],{"id":32438},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,32441,32442,32443,32474,32475,32551,32552,1715],{},"Úlohou je najít maximum ",[883,32444,32446],{"className":32445},[886],[888,32447,32448],{"xmlns":890},[892,32449,32450,32472],{},[895,32451,32452,32454,32456,32462,32464,32470],{},[898,32453,900],{},[1701,32455,1799],{"stretchy":1798},[1845,32457,32458,32460],{},[898,32459,1802],{},[1850,32461,4062],{},[1701,32463,2012],{"separator":2011},[1845,32465,32466,32468],{},[898,32467,1802],{},[1850,32469,3938],{},[1701,32471,1805],{"stretchy":1798},[902,32473,20389],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,32476,32478],{"className":32477},[886],[888,32479,32480],{"xmlns":890},[892,32481,32482,32548],{},[895,32483,32484,32486,32488,32494,32496,32502,32504,32506,32512,32514,32522,32528,32530,32538,32544,32546],{},[898,32485,15097],{},[1701,32487,1799],{"stretchy":1798},[1845,32489,32490,32492],{},[898,32491,1802],{},[1850,32493,4062],{},[1701,32495,2012],{"separator":2011},[1845,32497,32498,32500],{},[898,32499,1802],{},[1850,32501,3938],{},[1701,32503,1805],{"stretchy":1798},[1701,32505,1792],{},[3243,32507,32508,32510],{},[898,32509,13189],{},[1701,32511,8424],{},[1701,32513,2317],{},[2287,32515,32516,32518,32520],{},[898,32517,1680],{},[1850,32519,4062],{},[1701,32521,8424],{},[1845,32523,32524,32526],{},[898,32525,1802],{},[1850,32527,4062],{},[1701,32529,2317],{},[2287,32531,32532,32534,32536],{},[898,32533,1680],{},[1850,32535,3938],{},[1701,32537,8424],{},[1845,32539,32540,32542],{},[898,32541,1802],{},[1850,32543,3938],{},[1701,32545,1792],{},[1850,32547,1852],{},[902,32549,32550],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,32553,32555],{"className":32554,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,32557,32559],{"id":32558},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,32561,32562],{},"Sestavíme",[883,32564,32566],{"className":32565},[886],[888,32567,32568],{"xmlns":890,"display":2252},[892,32569,32570,32682],{},[2256,32571,32572],{"width":2258},[2260,32573,32574,32576,32675,32677],{},[2263,32575],{"width":2265},[2263,32577,32578],{},[895,32579,32580,32583,32585,32591,32593,32599,32601,32603,32605,32607,32609,32611,32617,32619,32625,32627,32629,32631,32633,32639,32641,32649,32655,32657,32665,32671,32673],{},[898,32581,13853],{"mathvariant":32582},"script",[1701,32584,1799],{"stretchy":1798},[1845,32586,32587,32589],{},[898,32588,1802],{},[1850,32590,4062],{},[1701,32592,2012],{"separator":2011},[1845,32594,32595,32597],{},[898,32596,1802],{},[1850,32598,3938],{},[1701,32600,2012],{"separator":2011},[898,32602,20489],{},[1701,32604,1805],{"stretchy":1798},[1701,32606,1792],{},[898,32608,900],{},[1701,32610,1799],{"stretchy":1798},[1845,32612,32613,32615],{},[898,32614,1802],{},[1850,32616,4062],{},[1701,32618,2012],{"separator":2011},[1845,32620,32621,32623],{},[898,32622,1802],{},[1850,32624,3938],{},[1701,32626,1805],{"stretchy":1798},[1701,32628,1703],{},[898,32630,20489],{},[1701,32632,1799],{"stretchy":1798},[3243,32634,32635,32637],{},[898,32636,13189],{},[1701,32638,8424],{},[1701,32640,2317],{},[2287,32642,32643,32645,32647],{},[898,32644,1680],{},[1850,32646,4062],{},[1701,32648,8424],{},[1845,32650,32651,32653],{},[898,32652,1802],{},[1850,32654,4062],{},[1701,32656,2317],{},[2287,32658,32659,32661,32663],{},[898,32660,1680],{},[1850,32662,3938],{},[1701,32664,8424],{},[1845,32666,32667,32669],{},[898,32668,1802],{},[1850,32670,3938],{},[1701,32672,1805],{"stretchy":1798},[898,32674,1715],{"mathvariant":2334},[2263,32676],{"width":2265},[2263,32678,32679],{},[1939,32680,32681],{},"(6.13)",[902,32683,32684],{"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}",[724,32686,32687],{},"Soustava prvního řádu:",[883,32689,32691],{"className":32690},[886],[888,32692,32693],{"xmlns":890,"display":2252},[892,32694,32695,32878],{},[2256,32696,32697],{"width":2258},[2260,32698,32699,32701,32871,32873],{},[2263,32700],{"width":2265},[2263,32702,32703],{},[2256,32704,32705,32755,32805],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,32706,32707,32719],{},[2263,32708,32709],{},[2363,32710,32711],{"scriptlevel":1852,"displaystyle":2011},[2287,32712,32713,32715,32717],{},[898,32714,13853],{"mathvariant":32582},[1850,32716,4062],{},[1701,32718,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,32720,32721],{},[2363,32722,32723],{"scriptlevel":1852,"displaystyle":2011},[895,32724,32725,32727,32729,32737,32739,32741,32749,32751,32753],{},[895,32726],{},[1701,32728,1792],{},[2287,32730,32731,32733,32735],{},[898,32732,900],{},[1850,32734,4062],{},[1701,32736,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,32738,2317],{},[898,32740,20489],{},[2287,32742,32743,32745,32747],{},[898,32744,1680],{},[1850,32746,4062],{},[1701,32748,8424],{},[1701,32750,1792],{},[1850,32752,1852],{},[1701,32754,2012],{"separator":2011},[2260,32756,32757,32769],{},[2263,32758,32759],{},[2363,32760,32761],{"scriptlevel":1852,"displaystyle":2011},[2287,32762,32763,32765,32767],{},[898,32764,13853],{"mathvariant":32582},[1850,32766,3938],{},[1701,32768,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,32770,32771],{},[2363,32772,32773],{"scriptlevel":1852,"displaystyle":2011},[895,32774,32775,32777,32779,32787,32789,32791,32799,32801,32803],{},[895,32776],{},[1701,32778,1792],{},[2287,32780,32781,32783,32785],{},[898,32782,900],{},[1850,32784,3938],{},[1701,32786,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,32788,2317],{},[898,32790,20489],{},[2287,32792,32793,32795,32797],{},[898,32794,1680],{},[1850,32796,3938],{},[1701,32798,8424],{},[1701,32800,1792],{},[1850,32802,1852],{},[1701,32804,2012],{"separator":2011},[2260,32806,32807,32819],{},[2263,32808,32809],{},[2363,32810,32811],{"scriptlevel":1852,"displaystyle":2011},[2287,32812,32813,32815,32817],{},[898,32814,13853],{"mathvariant":32582},[898,32816,20489],{},[1701,32818,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,32820,32821],{},[2363,32822,32823],{"scriptlevel":1852,"displaystyle":2011},[895,32824,32825,32827,32829,32835,32837,32845,32851,32853,32861,32867,32869],{},[895,32826],{},[1701,32828,1792],{},[3243,32830,32831,32833],{},[898,32832,13189],{},[1701,32834,8424],{},[1701,32836,2317],{},[2287,32838,32839,32841,32843],{},[898,32840,1680],{},[1850,32842,4062],{},[1701,32844,8424],{},[1845,32846,32847,32849],{},[898,32848,1802],{},[1850,32850,4062],{},[1701,32852,2317],{},[2287,32854,32855,32857,32859],{},[898,32856,1680],{},[1850,32858,3938],{},[1701,32860,8424],{},[1845,32862,32863,32865],{},[898,32864,1802],{},[1850,32866,3938],{},[1701,32868,1792],{},[1850,32870,16514],{},[2263,32872],{"width":2265},[2263,32874,32875],{},[1939,32876,32877],{},"(6.14)",[902,32879,32880],{"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}",[724,32882,32883,32884,32887,32888,32901,32902,2246],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,32885,32886],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,32889,32891],{"className":32890},[886],[888,32892,32893],{"xmlns":890},[892,32894,32895,32899],{},[895,32896,32897],{},[898,32898,20489],{},[902,32900,20542],{"encoding":904}," dostáváme ",[38,32903,32904],{},"podmínku optimality",[883,32906,32908],{"className":32907},[886],[888,32909,32910],{"xmlns":890,"display":2252},[892,32911,32912,32970],{},[895,32913,32914],{},[16886,32915,32916],{"notation":16888},[2363,32917,32918],{"scriptlevel":1852,"displaystyle":1798},[2363,32919,32920],{"scriptlevel":1852,"displaystyle":1798},[2363,32921,32922],{"scriptlevel":1852,"displaystyle":2011},[895,32923,32924,32926,32928,32930,32948,32950,32968],{},[1939,32925,8058],{},[1939,32927,14659],{},[1701,32929,1792],{},[3726,32931,32932,32940],{},[2287,32933,32934,32936,32938],{},[898,32935,900],{},[1850,32937,4062],{},[1701,32939,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,32941,32942,32944,32946],{},[898,32943,900],{},[1850,32945,3938],{},[1701,32947,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,32949,1792],{},[3726,32951,32952,32960],{},[2287,32953,32954,32956,32958],{},[898,32955,1680],{},[1850,32957,4062],{},[1701,32959,8424],{},[2287,32961,32962,32964,32966],{},[898,32963,1680],{},[1850,32965,3938],{},[1701,32967,8424],{},[1939,32969,8058],{},[902,32971,32972],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1635,32974,32975],{},[724,32976,32977,32979,32980,33014,33015,33018,33019,33037,33038,33056,33057,33087,33088,33105,33106,33136],{},[883,32978,2063],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,32981,32983],{"className":32982},[886],[888,32984,32985],{"xmlns":890},[892,32986,32987,33011],{},[895,32988,32989,32991,32993,33001,33003],{},[1939,32990,14659],{},[1701,32992,1792],{},[2287,32994,32995,32997,32999],{},[898,32996,1680],{},[1850,32998,4062],{},[1701,33000,8424],{},[898,33002,8741],{"mathvariant":2334},[2287,33004,33005,33007,33009],{},[898,33006,1680],{},[1850,33008,3938],{},[1701,33010,8424],{},[902,33012,33013],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,33016,33017],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,33020,33022],{"className":33021},[886],[888,33023,33024],{"xmlns":890},[892,33025,33026,33034],{},[895,33027,33028],{},[1845,33029,33030,33032],{},[898,33031,1802],{},[1850,33033,4062],{},[902,33035,33036],{"encoding":904},"Q_1"," za ",[883,33039,33041],{"className":33040},[886],[888,33042,33043],{"xmlns":890},[892,33044,33045,33053],{},[895,33046,33047],{},[1845,33048,33049,33051],{},[898,33050,1802],{},[1850,33052,3938],{},[902,33054,33055],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,33058,33060],{"className":33059},[886],[888,33061,33062],{"xmlns":890},[892,33063,33064,33084],{},[895,33065,33066,33068,33070,33076,33078],{},[1939,33067,14659],{},[1701,33069,7491],{},[1845,33071,33072,33074],{},[898,33073,1680],{},[1850,33075,4062],{},[898,33077,8741],{"mathvariant":2334},[1845,33079,33080,33082],{},[898,33081,1680],{},[1850,33083,3938],{},[902,33085,33086],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,33089,33091],{"className":33090},[886],[888,33092,33093],{"xmlns":890},[892,33094,33095,33103],{},[895,33096,33097],{},[1845,33098,33099,33101],{},[898,33100,1802],{},[1850,33102,4062],{},[902,33104,33036],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,33107,33109],{"className":33108},[886],[888,33110,33111],{"xmlns":890},[892,33112,33113,33133],{},[895,33114,33115,33117,33119,33125,33127],{},[1939,33116,14659],{},[1701,33118,7530],{},[1845,33120,33121,33123],{},[898,33122,1680],{},[1850,33124,4062],{},[898,33126,8741],{"mathvariant":2334},[1845,33128,33129,33131],{},[898,33130,1680],{},[1850,33132,3938],{},[902,33134,33135],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,33138,33140,33141,33154],{"id":33139},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,33142,33144],{"className":33143},[886],[888,33145,33146],{"xmlns":890},[892,33147,33148,33152],{},[895,33149,33150],{},[898,33151,20489],{},[902,33153,20542],{"encoding":904}," — mezní užitečnost důchodu",[724,33156,33157,33158,2745,33176,33179,33180,33197,33198,33215,33216,33219],{},"Lagrangeův multiplikátor ",[883,33159,33161],{"className":33160},[886],[888,33162,33163],{"xmlns":890},[892,33164,33165,33173],{},[895,33166,33167],{},[3243,33168,33169,33171],{},[898,33170,20489],{},[1701,33172,8424],{},[902,33174,33175],{"encoding":904},"\\lambda^*",[38,33177,33178],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,33181,33183],{"className":33182},[886],[888,33184,33185],{"xmlns":890},[892,33186,33187,33195],{},[895,33188,33189],{},[3243,33190,33191,33193],{},[898,33192,900],{},[1701,33194,8424],{},[902,33196,31999],{"encoding":904}," při jednotkové změně důchodu ",[883,33199,33201],{"className":33200},[886],[888,33202,33203],{"xmlns":890},[892,33204,33205,33213],{},[895,33206,33207],{},[3243,33208,33209,33211],{},[898,33210,13189],{},[1701,33212,8424],{},[902,33214,32065],{"encoding":904},". Je to ",[38,33217,33218],{},"stínová cena"," rozpočtového omezení.",[1635,33221,33222,33227],{},[724,33223,33224,33226],{},[883,33225,3140],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,33228,33229,33289,33376,33412,33499],{},[123,33230,33231,33234,33235,1715],{},[38,33232,33233],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,33236,33238],{"className":33237},[886],[888,33239,33240],{"xmlns":890},[892,33241,33242,33286],{},[895,33243,33244,33250,33252,33260,33266,33268,33276,33282,33284],{},[3243,33245,33246,33248],{},[898,33247,13189],{},[1701,33249,8424],{},[1701,33251,2317],{},[2287,33253,33254,33256,33258],{},[898,33255,1680],{},[1850,33257,4062],{},[1701,33259,8424],{},[1845,33261,33262,33264],{},[898,33263,1802],{},[1850,33265,4062],{},[1701,33267,2317],{},[2287,33269,33270,33272,33274],{},[898,33271,1680],{},[1850,33273,3938],{},[1701,33275,8424],{},[1845,33277,33278,33280],{},[898,33279,1802],{},[1850,33281,3938],{},[1701,33283,1792],{},[1850,33285,1852],{},[902,33287,33288],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,33290,33291,4088,33294,1715],{},[38,33292,33293],{},"Sestav Lagrangeovu funkci",[883,33295,33297],{"className":33296},[886],[888,33298,33299],{"xmlns":890},[892,33300,33301,33373],{},[895,33302,33303,33305,33307,33309,33311,33317,33319,33325,33327,33329,33331,33333,33339,33341,33349,33355,33357,33365,33371],{},[898,33304,13853],{"mathvariant":32582},[1701,33306,1792],{},[898,33308,900],{},[1701,33310,1799],{"stretchy":1798},[1845,33312,33313,33315],{},[898,33314,1802],{},[1850,33316,4062],{},[1701,33318,2012],{"separator":2011},[1845,33320,33321,33323],{},[898,33322,1802],{},[1850,33324,3938],{},[1701,33326,1805],{"stretchy":1798},[1701,33328,1703],{},[898,33330,20489],{},[1701,33332,1799],{"stretchy":1798},[3243,33334,33335,33337],{},[898,33336,13189],{},[1701,33338,8424],{},[1701,33340,2317],{},[2287,33342,33343,33345,33347],{},[898,33344,1680],{},[1850,33346,4062],{},[1701,33348,8424],{},[1845,33350,33351,33353],{},[898,33352,1802],{},[1850,33354,4062],{},[1701,33356,2317],{},[2287,33358,33359,33361,33363],{},[898,33360,1680],{},[1850,33362,3938],{},[1701,33364,8424],{},[1845,33366,33367,33369],{},[898,33368,1802],{},[1850,33370,3938],{},[1701,33372,1805],{"stretchy":1798},[902,33374,33375],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,33377,33378,14524,33381,33411],{},[38,33379,33380],{},"Spočítej parciální derivace",[883,33382,33384],{"className":33383},[886],[888,33385,33386],{"xmlns":890},[892,33387,33388,33408],{},[895,33389,33390,33396,33398,33404,33406],{},[1845,33391,33392,33394],{},[898,33393,1802],{},[1850,33395,4062],{},[1701,33397,2012],{"separator":2011},[1845,33399,33400,33402],{},[898,33401,1802],{},[1850,33403,3938],{},[1701,33405,2012],{"separator":2011},[898,33407,20489],{},[902,33409,33410],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,33413,33414,33430,33431,33464,33465,2633,33482,1715],{},[38,33415,33416,33417],{},"Vyluč ",[883,33418,33420],{"className":33419},[886],[888,33421,33422],{"xmlns":890},[892,33423,33424,33428],{},[895,33425,33426],{},[898,33427,20489],{},[902,33429,20542],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,33432,33434],{"className":33433},[886],[888,33435,33436],{"xmlns":890},[892,33437,33438,33462],{},[895,33439,33440,33442,33444,33452,33454],{},[1939,33441,14659],{},[1701,33443,1792],{},[2287,33445,33446,33448,33450],{},[898,33447,1680],{},[1850,33449,4062],{},[1701,33451,8424],{},[898,33453,8741],{"mathvariant":2334},[2287,33455,33456,33458,33460],{},[898,33457,1680],{},[1850,33459,3938],{},[1701,33461,8424],{},[902,33463,33013],{"encoding":904},", která dá vztah mezi ",[883,33466,33468],{"className":33467},[886],[888,33469,33470],{"xmlns":890},[892,33471,33472,33480],{},[895,33473,33474],{},[1845,33475,33476,33478],{},[898,33477,1802],{},[1850,33479,4062],{},[902,33481,33036],{"encoding":904},[883,33483,33485],{"className":33484},[886],[888,33486,33487],{"xmlns":890},[892,33488,33489,33497],{},[895,33490,33491],{},[1845,33492,33493,33495],{},[898,33494,1802],{},[1850,33496,3938],{},[902,33498,33055],{"encoding":904},[123,33500,33501,33504,33505,33535,33536,33553,33554,1715],{},[38,33502,33503],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,33506,33508],{"className":33507},[886],[888,33509,33510],{"xmlns":890},[892,33511,33512,33532],{},[895,33513,33514,33522,33524],{},[2287,33515,33516,33518,33520],{},[898,33517,1802],{},[1850,33519,4062],{},[1701,33521,8424],{},[1701,33523,2012],{"separator":2011},[2287,33525,33526,33528,33530],{},[898,33527,1802],{},[1850,33529,3938],{},[1701,33531,8424],{},[902,33533,33534],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,33537,33539],{"className":33538},[886],[888,33540,33541],{"xmlns":890},[892,33542,33543,33551],{},[895,33544,33545],{},[3243,33546,33547,33549],{},[898,33548,20489],{},[1701,33550,8424],{},[902,33552,33175],{"encoding":904}," a maximální užitečnost ",[883,33555,33557],{"className":33556},[886],[888,33558,33559],{"xmlns":890},[892,33560,33561,33595],{},[895,33562,33563,33569,33571,33573,33575,33583,33585,33593],{},[3243,33564,33565,33567],{},[898,33566,900],{},[1701,33568,8424],{},[1701,33570,1792],{},[898,33572,900],{},[1701,33574,1799],{"stretchy":1798},[2287,33576,33577,33579,33581],{},[898,33578,1802],{},[1850,33580,4062],{},[1701,33582,8424],{},[1701,33584,2012],{"separator":2011},[2287,33586,33587,33589,33591],{},[898,33588,1802],{},[1850,33590,3938],{},[1701,33592,8424],{},[1701,33594,1805],{"stretchy":1798},[902,33596,33597],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,33599,33601],{"id":33600},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,33603,33604],{},[2139,33605],{"alt":33606,"className":33607,"src":33608},"imek-uzitecnost-optimum",[210,2143],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,33610,33611],{},[614,33612,33613,33614,33663,33664,2633,33692,33720,33721,33755,33756,33795,33796,33814,33815,33833,33834,33852],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,33615,33617],{"className":33616},[886],[888,33618,33619],{"xmlns":890},[892,33620,33621,33661],{},[895,33622,33623,33629,33631,33639,33645,33647,33655],{},[3243,33624,33625,33627],{},[898,33626,13189],{},[1701,33628,8424],{},[1701,33630,1792],{},[2287,33632,33633,33635,33637],{},[898,33634,1680],{},[1850,33636,4062],{},[1701,33638,8424],{},[1845,33640,33641,33643],{},[898,33642,1802],{},[1850,33644,4062],{},[1701,33646,1703],{},[2287,33648,33649,33651,33653],{},[898,33650,1680],{},[1850,33652,3938],{},[1701,33654,8424],{},[1845,33656,33657,33659],{},[898,33658,1802],{},[1850,33660,3938],{},[902,33662,21344],{"encoding":904}," protíná osy v ",[883,33665,33667],{"className":33666},[886],[888,33668,33669],{"xmlns":890},[892,33670,33671,33689],{},[895,33672,33673,33679,33681],{},[3243,33674,33675,33677],{},[898,33676,13189],{},[1701,33678,8424],{},[898,33680,8741],{"mathvariant":2334},[2287,33682,33683,33685,33687],{},[898,33684,1680],{},[1850,33686,4062],{},[1701,33688,8424],{},[902,33690,33691],{"encoding":904},"Y^*\u002FP_1^*",[883,33693,33695],{"className":33694},[886],[888,33696,33697],{"xmlns":890},[892,33698,33699,33717],{},[895,33700,33701,33707,33709],{},[3243,33702,33703,33705],{},[898,33704,13189],{},[1701,33706,8424],{},[898,33708,8741],{"mathvariant":2334},[2287,33710,33711,33713,33715],{},[898,33712,1680],{},[1850,33714,3938],{},[1701,33716,8424],{},[902,33718,33719],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,33722,33724],{"className":33723},[886],[888,33725,33726],{"xmlns":890},[892,33727,33728,33752],{},[895,33729,33730,33736,33738,33744,33746],{},[1845,33731,33732,33734],{},[898,33733,3618],{},[1850,33735,4062],{},[1701,33737,7530],{},[3243,33739,33740,33742],{},[898,33741,3618],{},[1701,33743,8424],{},[1701,33745,7530],{},[1845,33747,33748,33750],{},[898,33749,3618],{},[1850,33751,3938],{},[902,33753,33754],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,33757,33759],{"className":33758},[886],[888,33760,33761],{"xmlns":890},[892,33762,33763,33793],{},[895,33764,33765,33771,33773,33781,33783,33791],{},[3243,33766,33767,33769],{},[898,33768,1802],{},[1701,33770,8424],{},[1701,33772,2036],{"stretchy":1798},[2287,33774,33775,33777,33779],{},[898,33776,1802],{},[1850,33778,4062],{},[1701,33780,8424],{},[1701,33782,2012],{"separator":2011},[2287,33784,33785,33787,33789],{},[898,33786,1802],{},[1850,33788,3938],{},[1701,33790,8424],{},[1701,33792,2053],{"stretchy":1798},[902,33794,32361],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,33797,33799],{"className":33798},[886],[888,33800,33801],{"xmlns":890},[892,33802,33803,33811],{},[895,33804,33805],{},[3243,33806,33807,33809],{},[898,33808,3618],{},[1701,33810,8424],{},[902,33812,33813],{"encoding":904},"c^*",". Křivka ",[883,33816,33818],{"className":33817},[886],[888,33819,33820],{"xmlns":890},[892,33821,33822,33830],{},[895,33823,33824],{},[1845,33825,33826,33828],{},[898,33827,3618],{},[1850,33829,4062],{},[902,33831,33832],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,33835,33837],{"className":33836},[886],[888,33838,33839],{"xmlns":890},[892,33840,33841,33849],{},[895,33842,33843],{},[1845,33844,33845,33847],{},[898,33846,3618],{},[1850,33848,3938],{},[902,33850,33851],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,33854,33855,33856,33859,33860,33878,33879,33908],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,33857,33858],{},"dotýkají",", tj. mají v bodě ",[883,33861,33863],{"className":33862},[886],[888,33864,33865],{"xmlns":890},[892,33866,33867,33875],{},[895,33868,33869],{},[3243,33870,33871,33873],{},[898,33872,1802],{},[1701,33874,8424],{},[902,33876,33877],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,33880,33882],{"className":33881},[886],[888,33883,33884],{"xmlns":890},[892,33885,33886,33906],{},[895,33887,33888,33890,33892,33898,33900],{},[1939,33889,14659],{},[1701,33891,1792],{},[1845,33893,33894,33896],{},[898,33895,1680],{},[1850,33897,4062],{},[898,33899,8741],{"mathvariant":2334},[1845,33901,33902,33904],{},[898,33903,1680],{},[1850,33905,3938],{},[902,33907,32035],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,33910,33912],{"id":33911},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,33914,13721,33915,33977],{},[883,33916,33918],{"className":33917},[886],[888,33919,33920],{"xmlns":890},[892,33921,33922,33974],{},[895,33923,33924,33926,33928,33934,33936,33942,33944,33946,33960],{},[898,33925,900],{},[1701,33927,1799],{"stretchy":1798},[1845,33929,33930,33932],{},[898,33931,1802],{},[1850,33933,4062],{},[1701,33935,2012],{"separator":2011},[1845,33937,33938,33940],{},[898,33939,1802],{},[1850,33941,3938],{},[1701,33943,1805],{"stretchy":1798},[1701,33945,1792],{},[2287,33947,33948,33950,33952],{},[898,33949,1802],{},[1850,33951,4062],{},[895,33953,33954,33956,33958],{},[1850,33955,4062],{},[898,33957,8741],{"mathvariant":2334},[1850,33959,3938],{},[2287,33961,33962,33964,33966],{},[898,33963,1802],{},[1850,33965,3938],{},[895,33967,33968,33970,33972],{},[1850,33969,4062],{},[898,33971,8741],{"mathvariant":2334},[1850,33973,3938],{},[902,33975,33976],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,33979,33980],{},[883,33981,33983],{"className":33982},[886],[888,33984,33985],{"xmlns":890},[892,33986,33987,34093],{},[895,33988,33989,33991,33993,34075,34077,34091],{},[1939,33990,14659],{},[1701,33992,1792],{},[3726,33994,33995,34035],{},[895,33996,33997,34005,34021],{},[2363,33998,33999],{"scriptlevel":1852,"displaystyle":1798},[3726,34000,34001,34003],{},[1850,34002,4062],{},[1850,34004,3938],{},[2287,34006,34007,34009,34011],{},[898,34008,1802],{},[1850,34010,4062],{},[895,34012,34013,34015,34017,34019],{},[1701,34014,2317],{},[1850,34016,4062],{},[898,34018,8741],{"mathvariant":2334},[1850,34020,3938],{},[2287,34022,34023,34025,34027],{},[898,34024,1802],{},[1850,34026,3938],{},[895,34028,34029,34031,34033],{},[1850,34030,4062],{},[898,34032,8741],{"mathvariant":2334},[1850,34034,3938],{},[895,34036,34037,34045,34059],{},[2363,34038,34039],{"scriptlevel":1852,"displaystyle":1798},[3726,34040,34041,34043],{},[1850,34042,4062],{},[1850,34044,3938],{},[2287,34046,34047,34049,34051],{},[898,34048,1802],{},[1850,34050,4062],{},[895,34052,34053,34055,34057],{},[1850,34054,4062],{},[898,34056,8741],{"mathvariant":2334},[1850,34058,3938],{},[2287,34060,34061,34063,34065],{},[898,34062,1802],{},[1850,34064,3938],{},[895,34066,34067,34069,34071,34073],{},[1701,34068,2317],{},[1850,34070,4062],{},[898,34072,8741],{"mathvariant":2334},[1850,34074,3938],{},[1701,34076,1792],{},[3726,34078,34079,34085],{},[1845,34080,34081,34083],{},[898,34082,1802],{},[1850,34084,3938],{},[1845,34086,34087,34089],{},[898,34088,1802],{},[1850,34090,4062],{},[898,34092,1715],{"mathvariant":2334},[902,34094,34095],{"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}.",[724,34097,4654,34098,7015,34142,34144,34145,34165,34166,34196,34197,1715],{},[883,34099,34101],{"className":34100},[886],[888,34102,34103],{"xmlns":890},[892,34104,34105,34139],{},[895,34106,34107,34109,34111,34113,34115,34117,34119,34121,34129,34131],{},[1939,34108,14659],{},[1701,34110,1799],{"stretchy":1798},[1850,34112,5151],{},[1701,34114,2012],{"separator":2011},[1850,34116,19162],{},[1701,34118,1805],{"stretchy":1798},[1701,34120,1792],{},[2363,34122,34123],{"scriptlevel":1852,"displaystyle":1798},[3726,34124,34125,34127],{},[1850,34126,19162],{},[1850,34128,5151],{},[1701,34130,1792],{},[2363,34132,34133],{"scriptlevel":1852,"displaystyle":1798},[3726,34134,34135,34137],{},[1850,34136,4225],{},[1850,34138,3646],{},[902,34140,34141],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,34143,13276],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,34146,34148],{"className":34147},[886],[888,34149,34150],{"xmlns":890},[892,34151,34152,34162],{},[895,34153,34154],{},[2363,34155,34156],{"scriptlevel":1852,"displaystyle":1798},[3726,34157,34158,34160],{},[1850,34159,4225],{},[1850,34161,3646],{},[902,34163,34164],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,34167,34169],{"className":34168},[886],[888,34170,34171],{"xmlns":890},[892,34172,34173,34193],{},[895,34174,34175,34177,34179,34185,34187],{},[1939,34176,14659],{},[1701,34178,1792],{},[1845,34180,34181,34183],{},[898,34182,1802],{},[1850,34184,3938],{},[898,34186,8741],{"mathvariant":2334},[1845,34188,34189,34191],{},[898,34190,1802],{},[1850,34192,4062],{},[902,34194,34195],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,34198,34200],{"className":34199},[886],[888,34201,34202],{"xmlns":890},[892,34203,34204,34224],{},[895,34205,34206,34208,34210,34216,34218],{},[1939,34207,14659],{},[1701,34209,1792],{},[1845,34211,34212,34214],{},[898,34213,1680],{},[1850,34215,4062],{},[898,34217,8741],{"mathvariant":2334},[1845,34219,34220,34222],{},[898,34221,1680],{},[1850,34223,3938],{},[902,34225,32035],{"encoding":904},[115,34227,34229,34230],{"id":34228},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,34231,34233],{"className":34232},[886],[888,34234,34235],{"xmlns":890},[892,34236,34237,34255],{},[895,34238,34239,34241,34243,34249],{},[898,34240,900],{},[1701,34242,1792],{},[1845,34244,34245,34247],{},[898,34246,1802],{},[1850,34248,4062],{},[1845,34250,34251,34253],{},[898,34252,1802],{},[1850,34254,3938],{},[902,34256,34257],{"encoding":904},"U = Q_1 Q_2",[724,34259,34260,34261,1343,34307,1343,34331,1343,34355,34377],{},"Je dána ",[883,34262,34264],{"className":34263},[886],[888,34265,34266],{"xmlns":890},[892,34267,34268,34304],{},[895,34269,34270,34272,34274,34280,34282,34288,34290,34292,34298],{},[898,34271,900],{},[1701,34273,1799],{"stretchy":1798},[1845,34275,34276,34278],{},[898,34277,1802],{},[1850,34279,4062],{},[1701,34281,2012],{"separator":2011},[1845,34283,34284,34286],{},[898,34285,1802],{},[1850,34287,3938],{},[1701,34289,1805],{"stretchy":1798},[1701,34291,1792],{},[1845,34293,34294,34296],{},[898,34295,1802],{},[1850,34297,4062],{},[1845,34299,34300,34302],{},[898,34301,1802],{},[1850,34303,3938],{},[902,34305,34306],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,34308,34310],{"className":34309},[886],[888,34311,34312],{"xmlns":890},[892,34313,34314,34328],{},[895,34315,34316,34324,34326],{},[2287,34317,34318,34320,34322],{},[898,34319,1680],{},[1850,34321,4062],{},[1701,34323,8424],{},[1701,34325,1792],{},[1850,34327,3938],{},[902,34329,34330],{"encoding":904},"P_1^* = 2",[883,34332,34334],{"className":34333},[886],[888,34335,34336],{"xmlns":890},[892,34337,34338,34352],{},[895,34339,34340,34348,34350],{},[2287,34341,34342,34344,34346],{},[898,34343,1680],{},[1850,34345,3938],{},[1701,34347,8424],{},[1701,34349,1792],{},[1850,34351,4225],{},[902,34353,34354],{"encoding":904},"P_2^* = 5",[883,34356,34358],{"className":34357},[886],[888,34359,34360],{"xmlns":890},[892,34361,34362,34374],{},[895,34363,34364,34370,34372],{},[3243,34365,34366,34368],{},[898,34367,13189],{},[1701,34369,8424],{},[1701,34371,1792],{},[1850,34373,5158],{},[902,34375,34376],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,34379,34381],{"className":34380},[886],[888,34382,34383],{"xmlns":890,"display":2252},[892,34384,34385,34457],{},[895,34386,34387,34389,34391,34397,34399,34405,34407,34409,34411,34413,34419,34425,34427,34429,34431,34433,34435,34437,34443,34445,34447,34453,34455],{},[898,34388,13853],{"mathvariant":32582},[1701,34390,1799],{"stretchy":1798},[1845,34392,34393,34395],{},[898,34394,1802],{},[1850,34396,4062],{},[1701,34398,2012],{"separator":2011},[1845,34400,34401,34403],{},[898,34402,1802],{},[1850,34404,3938],{},[1701,34406,2012],{"separator":2011},[898,34408,20489],{},[1701,34410,1805],{"stretchy":1798},[1701,34412,1792],{},[1845,34414,34415,34417],{},[898,34416,1802],{},[1850,34418,4062],{},[1845,34420,34421,34423],{},[898,34422,1802],{},[1850,34424,3938],{},[1701,34426,1703],{},[898,34428,20489],{},[1701,34430,1799],{"stretchy":1798},[1850,34432,5158],{},[1701,34434,2317],{},[1850,34436,3938],{},[1845,34438,34439,34441],{},[898,34440,1802],{},[1850,34442,4062],{},[1701,34444,2317],{},[1850,34446,4225],{},[1845,34448,34449,34451],{},[898,34450,1802],{},[1850,34452,3938],{},[1701,34454,1805],{"stretchy":1798},[898,34456,1715],{"mathvariant":2334},[902,34458,34459],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,34461,34462],{},"Soustava:",[883,34464,34466],{"className":34465},[886],[888,34467,34468],{"xmlns":890,"display":2252},[892,34469,34470,34582],{},[2256,34471,34472,34506,34540],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,34473,34474,34492],{},[2263,34475,34476],{},[2363,34477,34478],{"scriptlevel":1852,"displaystyle":2011},[895,34479,34480,34486,34488,34490],{},[1845,34481,34482,34484],{},[898,34483,1802],{},[1850,34485,3938],{},[1701,34487,2317],{},[1850,34489,3938],{},[898,34491,20489],{},[2263,34493,34494],{},[2363,34495,34496],{"scriptlevel":1852,"displaystyle":2011},[895,34497,34498,34500,34502,34504],{},[895,34499],{},[1701,34501,1792],{},[1850,34503,1852],{},[1701,34505,2012],{"separator":2011},[2260,34507,34508,34526],{},[2263,34509,34510],{},[2363,34511,34512],{"scriptlevel":1852,"displaystyle":2011},[895,34513,34514,34520,34522,34524],{},[1845,34515,34516,34518],{},[898,34517,1802],{},[1850,34519,4062],{},[1701,34521,2317],{},[1850,34523,4225],{},[898,34525,20489],{},[2263,34527,34528],{},[2363,34529,34530],{"scriptlevel":1852,"displaystyle":2011},[895,34531,34532,34534,34536,34538],{},[895,34533],{},[1701,34535,1792],{},[1850,34537,1852],{},[1701,34539,2012],{"separator":2011},[2260,34541,34542,34570],{},[2263,34543,34544],{},[2363,34545,34546],{"scriptlevel":1852,"displaystyle":2011},[895,34547,34548,34550,34552,34554,34560,34562,34564],{},[1850,34549,5158],{},[1701,34551,2317],{},[1850,34553,3938],{},[1845,34555,34556,34558],{},[898,34557,1802],{},[1850,34559,4062],{},[1701,34561,2317],{},[1850,34563,4225],{},[1845,34565,34566,34568],{},[898,34567,1802],{},[1850,34569,3938],{},[2263,34571,34572],{},[2363,34573,34574],{"scriptlevel":1852,"displaystyle":2011},[895,34575,34576,34578,34580],{},[895,34577],{},[1701,34579,1792],{},[1850,34581,16514],{},[902,34583,34584],{"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}",[724,34586,34587,34588,1343,34612,34636,34637,4185,34677,34695,34696,34746,34747,1715],{},"Z prvních dvou rovnic ",[883,34589,34591],{"className":34590},[886],[888,34592,34593],{"xmlns":890},[892,34594,34595,34609],{},[895,34596,34597,34603,34605,34607],{},[1845,34598,34599,34601],{},[898,34600,1802],{},[1850,34602,3938],{},[1701,34604,1792],{},[1850,34606,3938],{},[898,34608,20489],{},[902,34610,34611],{"encoding":904},"Q_2 = 2\\lambda",[883,34613,34615],{"className":34614},[886],[888,34616,34617],{"xmlns":890},[892,34618,34619,34633],{},[895,34620,34621,34627,34629,34631],{},[1845,34622,34623,34625],{},[898,34624,1802],{},[1850,34626,4062],{},[1701,34628,1792],{},[1850,34630,4225],{},[898,34632,20489],{},[902,34634,34635],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,34638,34640],{"className":34639},[886],[888,34641,34642],{"xmlns":890},[892,34643,34644,34674],{},[895,34645,34646,34648,34650,34652,34654,34656,34658,34660,34662,34664,34666,34668,34670,34672],{},[1850,34647,5158],{},[1701,34649,1792],{},[1850,34651,3938],{},[1701,34653,3408],{},[1850,34655,4225],{},[898,34657,20489],{},[1701,34659,1703],{},[1850,34661,4225],{},[1701,34663,3408],{},[1850,34665,3938],{},[898,34667,20489],{},[1701,34669,1792],{},[1850,34671,13096],{},[898,34673,20489],{},[902,34675,34676],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,34678,34680],{"className":34679},[886],[888,34681,34682],{"xmlns":890},[892,34683,34684,34692],{},[895,34685,34686,34688,34690],{},[898,34687,20489],{},[1701,34689,1792],{},[1850,34691,4225],{},[902,34693,34694],{"encoding":904},"\\lambda = 5",". Odtud ",[38,34697,34698,1343,34722],{},[883,34699,34701],{"className":34700},[886],[888,34702,34703],{"xmlns":890},[892,34704,34705,34719],{},[895,34706,34707,34715,34717],{},[2287,34708,34709,34711,34713],{},[898,34710,1802],{},[1850,34712,4062],{},[1701,34714,8424],{},[1701,34716,1792],{},[1850,34718,9071],{},[902,34720,34721],{"encoding":904},"Q_1^* = 25",[883,34723,34725],{"className":34724},[886],[888,34726,34727],{"xmlns":890},[892,34728,34729,34743],{},[895,34730,34731,34739,34741],{},[2287,34732,34733,34735,34737],{},[898,34734,1802],{},[1850,34736,3938],{},[1701,34738,8424],{},[1701,34740,1792],{},[1850,34742,3703],{},[902,34744,34745],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,34748,34750],{"className":34749},[886],[888,34751,34752],{"xmlns":890},[892,34753,34754,34775],{},[895,34755,34756,34762,34764,34766,34768,34770,34772],{},[3243,34757,34758,34760],{},[898,34759,900],{},[1701,34761,8424],{},[1701,34763,1792],{},[1850,34765,9071],{},[1701,34767,3408],{},[1850,34769,3703],{},[1701,34771,1792],{},[1850,34773,34774],{},"250",[902,34776,34777],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,34779,34780],{},[614,34781,34782,34783,32171,34821,2633,34845,34869,34870,34900,34901,34925,34926,34948,34949,1715],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,34784,34786],{"className":34785},[886],[888,34787,34788],{"xmlns":890},[892,34789,34790,34818],{},[895,34791,34792,34794,34796,34798,34804,34806,34808,34814,34816],{},[1850,34793,5158],{},[1701,34795,2317],{},[1850,34797,3938],{},[1845,34799,34800,34802],{},[898,34801,1802],{},[1850,34803,4062],{},[1701,34805,2317],{},[1850,34807,4225],{},[1845,34809,34810,34812],{},[898,34811,1802],{},[1850,34813,3938],{},[1701,34815,1792],{},[1850,34817,1852],{},[902,34819,34820],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,34822,34824],{"className":34823},[886],[888,34825,34826],{"xmlns":890},[892,34827,34828,34842],{},[895,34829,34830,34832,34834,34836,34838,34840],{},[898,34831,1983],{},[1701,34833,2036],{"stretchy":1798},[1850,34835,1852],{},[1701,34837,2012],{"separator":2011},[1850,34839,13096],{},[1701,34841,2053],{"stretchy":1798},[902,34843,34844],{"encoding":904},"A[0, 20]",[883,34846,34848],{"className":34847},[886],[888,34849,34850],{"xmlns":890},[892,34851,34852,34866],{},[895,34853,34854,34856,34858,34860,34862,34864],{},[898,34855,2593],{},[1701,34857,2036],{"stretchy":1798},[1850,34859,7206],{},[1701,34861,2012],{"separator":2011},[1850,34863,1852],{},[1701,34865,2053],{"stretchy":1798},[902,34867,34868],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,34871,34873],{"className":34872},[886],[888,34874,34875],{"xmlns":890},[892,34876,34877,34897],{},[895,34878,34879,34885,34887,34889,34891],{},[1845,34880,34881,34883],{},[898,34882,1802],{},[1850,34884,3938],{},[1701,34886,1792],{},[1850,34888,34774],{},[898,34890,8741],{"mathvariant":2334},[1845,34892,34893,34895],{},[898,34894,1802],{},[1850,34896,4062],{},[902,34898,34899],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,34902,34904],{"className":34903},[886],[888,34905,34906],{"xmlns":890},[892,34907,34908,34922],{},[895,34909,34910,34912,34914,34916,34918,34920],{},[898,34911,3249],{},[1701,34913,2036],{"stretchy":1798},[1850,34915,9071],{},[1701,34917,2012],{"separator":2011},[1850,34919,3703],{},[1701,34921,2053],{"stretchy":1798},[902,34923,34924],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,34927,34929],{"className":34928},[886],[888,34930,34931],{"xmlns":890},[892,34932,34933,34945],{},[895,34934,34935,34937],{},[1701,34936,2317],{},[2363,34938,34939],{"scriptlevel":1852,"displaystyle":1798},[3726,34940,34941,34943],{},[1850,34942,3938],{},[1850,34944,4225],{},[902,34946,34947],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,34950,34952],{"className":34951},[886],[888,34953,34954],{"xmlns":890},[892,34955,34956,34996],{},[895,34957,34958,34960,34962,34964,34966,34968,34970,34972,34974,34976,34984,34986,34988],{},[1701,34959,2317],{},[1939,34961,14659],{},[1701,34963,1799],{"stretchy":1798},[1850,34965,9071],{},[1701,34967,2012],{"separator":2011},[1850,34969,3703],{},[1701,34971,1805],{"stretchy":1798},[1701,34973,1792],{},[1701,34975,2317],{},[2363,34977,34978],{"scriptlevel":1852,"displaystyle":1798},[3726,34979,34980,34982],{},[1850,34981,3703],{},[1850,34983,9071],{},[1701,34985,1792],{},[1701,34987,2317],{},[2363,34989,34990],{"scriptlevel":1852,"displaystyle":1798},[3726,34991,34992,34994],{},[1850,34993,3938],{},[1850,34995,4225],{},[902,34997,34998],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,35000,35002],{"id":35001},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,35004,35005,35006,33037,35036,35039,35040,2246],{},"Považujeme-li v úloze ",[883,35007,35009],{"className":35008},[886],[888,35010,35011],{"xmlns":890},[892,35012,35013,35033],{},[895,35014,35015,35021,35023,35029,35031],{},[1845,35016,35017,35019],{},[898,35018,1680],{},[1850,35020,4062],{},[1701,35022,2012],{"separator":2011},[1845,35024,35025,35027],{},[898,35026,1680],{},[1850,35028,3938],{},[1701,35030,2012],{"separator":2011},[898,35032,13189],{},[902,35034,35035],{"encoding":904},"P_1, P_2, Y",[38,35037,35038],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,35041,35042],{},"Marshallovy poptávkové funkce",[883,35044,35046],{"className":35045},[886],[888,35047,35048],{"xmlns":890,"display":2252},[892,35049,35050,35145],{},[2256,35051,35052],{"width":2258},[2260,35053,35054,35056,35138,35140],{},[2263,35055],{"width":2265},[2263,35057,35058],{},[895,35059,35060,35066,35068,35074,35076,35082,35084,35090,35092,35094,35096,35098,35100,35106,35108,35114,35116,35122,35124,35130,35132,35134,35136],{},[1845,35061,35062,35064],{},[898,35063,1802],{},[1850,35065,4062],{},[1701,35067,1792],{},[1845,35069,35070,35072],{},[898,35071,1795],{},[1850,35073,4062],{},[1701,35075,1799],{"stretchy":1798},[1845,35077,35078,35080],{},[898,35079,1680],{},[1850,35081,4062],{},[1701,35083,2012],{"separator":2011},[1845,35085,35086,35088],{},[898,35087,1680],{},[1850,35089,3938],{},[1701,35091,2012],{"separator":2011},[898,35093,13189],{},[1701,35095,1805],{"stretchy":1798},[1701,35097,2012],{"separator":2011},[9942,35099],{"width":19336},[1845,35101,35102,35104],{},[898,35103,1802],{},[1850,35105,3938],{},[1701,35107,1792],{},[1845,35109,35110,35112],{},[898,35111,1795],{},[1850,35113,3938],{},[1701,35115,1799],{"stretchy":1798},[1845,35117,35118,35120],{},[898,35119,1680],{},[1850,35121,4062],{},[1701,35123,2012],{"separator":2011},[1845,35125,35126,35128],{},[898,35127,1680],{},[1850,35129,3938],{},[1701,35131,2012],{"separator":2011},[898,35133,13189],{},[1701,35135,1805],{"stretchy":1798},[1701,35137,2012],{"separator":2011},[2263,35139],{"width":2265},[2263,35141,35142],{},[1939,35143,35144],{},"(6.15)",[902,35146,35147],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,35149,35151],{"className":35150},[886],[888,35152,35153],{"xmlns":890,"display":2252},[892,35154,35155,35202],{},[2256,35156,35157],{"width":2258},[2260,35158,35159,35161,35195,35197],{},[2263,35160],{"width":2265},[2263,35162,35163],{},[895,35164,35165,35167,35169,35171,35173,35179,35181,35187,35189,35191,35193],{},[898,35166,20489],{},[1701,35168,1792],{},[898,35170,20489],{},[1701,35172,1799],{"stretchy":1798},[1845,35174,35175,35177],{},[898,35176,1680],{},[1850,35178,4062],{},[1701,35180,2012],{"separator":2011},[1845,35182,35183,35185],{},[898,35184,1680],{},[1850,35186,3938],{},[1701,35188,2012],{"separator":2011},[898,35190,13189],{},[1701,35192,1805],{"stretchy":1798},[898,35194,1715],{"mathvariant":2334},[2263,35196],{"width":2265},[2263,35198,35199],{},[1939,35200,35201],{},"(6.16)",[902,35203,35204],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,35206,35207,35237,35238,35304],{},[38,35208,35209,35210,1715],{},"Odvození pro ",[883,35211,35213],{"className":35212},[886],[888,35214,35215],{"xmlns":890},[892,35216,35217,35235],{},[895,35218,35219,35221,35223,35229],{},[898,35220,900],{},[1701,35222,1792],{},[1845,35224,35225,35227],{},[898,35226,1802],{},[1850,35228,4062],{},[1845,35230,35231,35233],{},[898,35232,1802],{},[1850,35234,3938],{},[902,35236,34257],{"encoding":904}," Lagrangeova funkce ",[883,35239,35241],{"className":35240},[886],[888,35242,35243],{"xmlns":890},[892,35244,35245,35301],{},[895,35246,35247,35249,35251,35257,35263,35265,35267,35269,35271,35273,35279,35285,35287,35293,35299],{},[898,35248,13853],{"mathvariant":32582},[1701,35250,1792],{},[1845,35252,35253,35255],{},[898,35254,1802],{},[1850,35256,4062],{},[1845,35258,35259,35261],{},[898,35260,1802],{},[1850,35262,3938],{},[1701,35264,1703],{},[898,35266,20489],{},[1701,35268,1799],{"stretchy":1798},[898,35270,13189],{},[1701,35272,2317],{},[1845,35274,35275,35277],{},[898,35276,1680],{},[1850,35278,4062],{},[1845,35280,35281,35283],{},[898,35282,1802],{},[1850,35284,4062],{},[1701,35286,2317],{},[1845,35288,35289,35291],{},[898,35290,1680],{},[1850,35292,3938],{},[1845,35294,35295,35297],{},[898,35296,1802],{},[1850,35298,3938],{},[1701,35300,1805],{"stretchy":1798},[902,35302,35303],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,35306,35308],{"className":35307},[886],[888,35309,35310],{"xmlns":890,"display":2252},[892,35311,35312,35479],{},[2256,35313,35314],{"width":2258},[2260,35315,35316,35318,35472,35474],{},[2263,35317],{"width":2265},[2263,35319,35320],{},[2256,35321,35322,35368,35414],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,35323,35324,35336],{},[2263,35325,35326],{},[2363,35327,35328],{"scriptlevel":1852,"displaystyle":2011},[2287,35329,35330,35332,35334],{},[898,35331,13853],{"mathvariant":32582},[1850,35333,4062],{},[1701,35335,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,35337,35338],{},[2363,35339,35340],{"scriptlevel":1852,"displaystyle":2011},[895,35341,35342,35344,35346,35352,35354,35356,35362,35364,35366],{},[895,35343],{},[1701,35345,1792],{},[1845,35347,35348,35350],{},[898,35349,1802],{},[1850,35351,3938],{},[1701,35353,2317],{},[898,35355,20489],{},[1845,35357,35358,35360],{},[898,35359,1680],{},[1850,35361,4062],{},[1701,35363,1792],{},[1850,35365,1852],{},[1701,35367,2012],{"separator":2011},[2260,35369,35370,35382],{},[2263,35371,35372],{},[2363,35373,35374],{"scriptlevel":1852,"displaystyle":2011},[2287,35375,35376,35378,35380],{},[898,35377,13853],{"mathvariant":32582},[1850,35379,3938],{},[1701,35381,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,35383,35384],{},[2363,35385,35386],{"scriptlevel":1852,"displaystyle":2011},[895,35387,35388,35390,35392,35398,35400,35402,35408,35410,35412],{},[895,35389],{},[1701,35391,1792],{},[1845,35393,35394,35396],{},[898,35395,1802],{},[1850,35397,4062],{},[1701,35399,2317],{},[898,35401,20489],{},[1845,35403,35404,35406],{},[898,35405,1680],{},[1850,35407,3938],{},[1701,35409,1792],{},[1850,35411,1852],{},[1701,35413,2012],{"separator":2011},[2260,35415,35416,35428],{},[2263,35417,35418],{},[2363,35419,35420],{"scriptlevel":1852,"displaystyle":2011},[2287,35421,35422,35424,35426],{},[898,35423,13853],{"mathvariant":32582},[898,35425,20489],{},[1701,35427,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,35429,35430],{},[2363,35431,35432],{"scriptlevel":1852,"displaystyle":2011},[895,35433,35434,35436,35438,35440,35442,35448,35454,35456,35462,35468,35470],{},[895,35435],{},[1701,35437,1792],{},[898,35439,13189],{},[1701,35441,2317],{},[1845,35443,35444,35446],{},[898,35445,1680],{},[1850,35447,4062],{},[1845,35449,35450,35452],{},[898,35451,1802],{},[1850,35453,4062],{},[1701,35455,2317],{},[1845,35457,35458,35460],{},[898,35459,1680],{},[1850,35461,3938],{},[1845,35463,35464,35466],{},[898,35465,1802],{},[1850,35467,3938],{},[1701,35469,1792],{},[1850,35471,16514],{},[2263,35473],{"width":2265},[2263,35475,35476],{},[1939,35477,35478],{},"(6.17)",[902,35480,35481],{"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}",[724,35483,35484,35485,35513,35514,35542,35543,35611],{},"Z prvních dvou: ",[883,35486,35488],{"className":35487},[886],[888,35489,35490],{"xmlns":890},[892,35491,35492,35510],{},[895,35493,35494,35500,35502,35508],{},[1845,35495,35496,35498],{},[898,35497,1802],{},[1850,35499,3938],{},[1701,35501,1792],{},[1845,35503,35504,35506],{},[898,35505,1680],{},[1850,35507,4062],{},[898,35509,20489],{},[902,35511,35512],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,35515,35517],{"className":35516},[886],[888,35518,35519],{"xmlns":890},[892,35520,35521,35539],{},[895,35522,35523,35529,35531,35537],{},[1845,35524,35525,35527],{},[898,35526,1802],{},[1850,35528,4062],{},[1701,35530,1792],{},[1845,35532,35533,35535],{},[898,35534,1680],{},[1850,35536,3938],{},[898,35538,20489],{},[902,35540,35541],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,35544,35546],{"className":35545},[886],[888,35547,35548],{"xmlns":890},[892,35549,35550,35608],{},[895,35551,35552,35554,35556,35562,35564,35570,35572,35574,35580,35582,35588,35590,35592,35594,35600,35606],{},[898,35553,13189],{},[1701,35555,1792],{},[1845,35557,35558,35560],{},[898,35559,1680],{},[1850,35561,4062],{},[1701,35563,3408],{},[1845,35565,35566,35568],{},[898,35567,1680],{},[1850,35569,3938],{},[898,35571,20489],{},[1701,35573,1703],{},[1845,35575,35576,35578],{},[898,35577,1680],{},[1850,35579,3938],{},[1701,35581,3408],{},[1845,35583,35584,35586],{},[898,35585,1680],{},[1850,35587,4062],{},[898,35589,20489],{},[1701,35591,1792],{},[1850,35593,3938],{},[1845,35595,35596,35598],{},[898,35597,1680],{},[1850,35599,4062],{},[1845,35601,35602,35604],{},[898,35603,1680],{},[1850,35605,3938],{},[898,35607,20489],{},[902,35609,35610],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,35613,35615],{"className":35614},[886],[888,35616,35617],{"xmlns":890,"display":2252},[892,35618,35619,35662],{},[2256,35620,35621],{"width":2258},[2260,35622,35623,35625,35655,35657],{},[2263,35624],{"width":2265},[2263,35626,35627],{},[895,35628,35629,35631,35633,35653],{},[898,35630,20489],{},[1701,35632,1792],{},[3726,35634,35635,35637],{},[898,35636,13189],{},[895,35638,35639,35641,35647],{},[1850,35640,3938],{},[1845,35642,35643,35645],{},[898,35644,1680],{},[1850,35646,4062],{},[1845,35648,35649,35651],{},[898,35650,1680],{},[1850,35652,3938],{},[898,35654,1715],{"mathvariant":2334},[2263,35656],{"width":2265},[2263,35658,35659],{},[1939,35660,35661],{},"(6.20)",[902,35663,35664],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,35666,35667],{},"Zpětně:",[883,35669,35671],{"className":35670},[886],[888,35672,35673],{"xmlns":890,"display":2252},[892,35674,35675,35752],{},[2256,35676,35677],{"width":2258},[2260,35678,35679,35681,35745,35747],{},[2263,35680],{"width":2265},[2263,35682,35683],{},[16886,35684,35685],{"notation":16888},[2363,35686,35687],{"scriptlevel":1852,"displaystyle":1798},[2363,35688,35689],{"scriptlevel":1852,"displaystyle":1798},[2363,35690,35691],{"scriptlevel":1852,"displaystyle":2011},[895,35692,35693,35695,35701,35703,35717,35719,35721,35727,35729,35743],{},[1939,35694,8058],{},[1845,35696,35697,35699],{},[898,35698,1802],{},[1850,35700,4062],{},[1701,35702,1792],{},[3726,35704,35705,35707],{},[898,35706,13189],{},[895,35708,35709,35711],{},[1850,35710,3938],{},[1845,35712,35713,35715],{},[898,35714,1680],{},[1850,35716,4062],{},[1701,35718,2012],{"separator":2011},[9942,35720],{"width":19336},[1845,35722,35723,35725],{},[898,35724,1802],{},[1850,35726,3938],{},[1701,35728,1792],{},[3726,35730,35731,35733],{},[898,35732,13189],{},[895,35734,35735,35737],{},[1850,35736,3938],{},[1845,35738,35739,35741],{},[898,35740,1680],{},[1850,35742,3938],{},[1939,35744,8058],{},[2263,35746],{"width":2265},[2263,35748,35749],{},[1939,35750,35751],{},"(6.21)",[902,35753,35754],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,35756,35758],{"id":35757},"engelova-funkce","Engelova funkce",[724,35760,13721,35761,35764,35765,35768,35769,23912,35786,1343,35816,35846,35847,35881,35882,1343,35908,35934],{},[38,35762,35763],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,35766,35767],{},"Engelovou funkcí",": pro ",[883,35770,35772],{"className":35771},[886],[888,35773,35774],{"xmlns":890},[892,35775,35776,35784],{},[895,35777,35778,35780,35782],{},[898,35779,13189],{},[1701,35781,1792],{},[1850,35783,5158],{},[902,35785,24363],{"encoding":904},[883,35787,35789],{"className":35788},[886],[888,35790,35791],{"xmlns":890},[892,35792,35793,35813],{},[895,35794,35795,35801,35803,35805,35807],{},[1845,35796,35797,35799],{},[898,35798,1802],{},[1850,35800,4062],{},[1701,35802,1792],{},[1850,35804,7206],{},[898,35806,8741],{"mathvariant":2334},[1845,35808,35809,35811],{},[898,35810,1680],{},[1850,35812,4062],{},[902,35814,35815],{"encoding":904},"Q_1 = 50\u002FP_1",[883,35817,35819],{"className":35818},[886],[888,35820,35821],{"xmlns":890},[892,35822,35823,35843],{},[895,35824,35825,35831,35833,35835,35837],{},[1845,35826,35827,35829],{},[898,35828,1802],{},[1850,35830,3938],{},[1701,35832,1792],{},[1850,35834,7206],{},[898,35836,8741],{"mathvariant":2334},[1845,35838,35839,35841],{},[898,35840,1680],{},[1850,35842,3938],{},[902,35844,35845],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,35848,35850],{"className":35849},[886],[888,35851,35852],{"xmlns":890},[892,35853,35854,35878],{},[895,35855,35856,35862,35864,35866,35868,35874,35876],{},[1845,35857,35858,35860],{},[898,35859,1680],{},[1850,35861,4062],{},[1701,35863,1792],{},[1850,35865,3703],{},[1701,35867,2012],{"separator":2011},[1845,35869,35870,35872],{},[898,35871,1680],{},[1850,35873,3938],{},[1701,35875,1792],{},[1850,35877,13096],{},[902,35879,35880],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,35883,35885],{"className":35884},[886],[888,35886,35887],{"xmlns":890},[892,35888,35889,35905],{},[895,35890,35891,35897,35899,35901,35903],{},[1845,35892,35893,35895],{},[898,35894,1802],{},[1850,35896,4062],{},[1701,35898,1792],{},[898,35900,13189],{},[898,35902,8741],{"mathvariant":2334},[1850,35904,13096],{},[902,35906,35907],{"encoding":904},"Q_1 = Y\u002F20",[883,35909,35911],{"className":35910},[886],[888,35912,35913],{"xmlns":890},[892,35914,35915,35931],{},[895,35916,35917,35923,35925,35927,35929],{},[1845,35918,35919,35921],{},[898,35920,1802],{},[1850,35922,3938],{},[1701,35924,1792],{},[898,35926,13189],{},[898,35928,8741],{"mathvariant":2334},[1850,35930,3665],{},[902,35932,35933],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,35936,35938],{"id":35937},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,35940,35941],{},"Výdaje spotřebitele jsou",[883,35943,35945],{"className":35944},[886],[888,35946,35947],{"xmlns":890,"display":2252},[892,35948,35949,36024],{},[2256,35950,35951],{"width":2258},[2260,35952,35953,35955,36017,36019],{},[2263,35954],{"width":2265},[2263,35956,35957],{},[895,35958,35959,35961,35963,35965,35967,35973,35975,35981,35983,35985,35993,35999,36001,36009,36015],{},[898,35960,3249],{},[1701,35962,1792],{},[898,35964,3249],{},[1701,35966,1799],{"stretchy":1798},[1845,35968,35969,35971],{},[898,35970,1802],{},[1850,35972,4062],{},[1701,35974,2012],{"separator":2011},[1845,35976,35977,35979],{},[898,35978,1802],{},[1850,35980,3938],{},[1701,35982,1805],{"stretchy":1798},[1701,35984,1792],{},[2287,35986,35987,35989,35991],{},[898,35988,1680],{},[1850,35990,4062],{},[1701,35992,8424],{},[1845,35994,35995,35997],{},[898,35996,1802],{},[1850,35998,4062],{},[1701,36000,1703],{},[2287,36002,36003,36005,36007],{},[898,36004,1680],{},[1850,36006,3938],{},[1701,36008,8424],{},[1845,36010,36011,36013],{},[898,36012,1802],{},[1850,36014,3938],{},[1701,36016,2012],{"separator":2011},[2263,36018],{"width":2265},[2263,36020,36021],{},[1939,36022,36023],{},"(6.22)",[902,36025,36026],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,36028,36029],{},"a je pevně zadána hladina užitečnosti",[883,36031,36033],{"className":36032},[886],[888,36034,36035],{"xmlns":890,"display":2252},[892,36036,36037,36084],{},[2256,36038,36039],{"width":2258},[2260,36040,36041,36043,36077,36079],{},[2263,36042],{"width":2265},[2263,36044,36045],{},[895,36046,36047,36053,36055,36057,36059,36065,36067,36073,36075],{},[3243,36048,36049,36051],{},[898,36050,900],{},[1701,36052,8424],{},[1701,36054,1792],{},[898,36056,900],{},[1701,36058,1799],{"stretchy":1798},[1845,36060,36061,36063],{},[898,36062,1802],{},[1850,36064,4062],{},[1701,36066,2012],{"separator":2011},[1845,36068,36069,36071],{},[898,36070,1802],{},[1850,36072,3938],{},[1701,36074,1805],{"stretchy":1798},[898,36076,1715],{"mathvariant":2334},[2263,36078],{"width":2265},[2263,36080,36081],{},[1939,36082,36083],{},"(6.23)",[902,36085,36086],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,36088,36089,36092,36093,36125,36126,1715],{},[38,36090,36091],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,36094,36096],{"className":36095},[886],[888,36097,36098],{"xmlns":890},[892,36099,36100,36122],{},[895,36101,36102,36104,36106,36112,36114,36120],{},[898,36103,3249],{},[1701,36105,1799],{"stretchy":1798},[1845,36107,36108,36110],{},[898,36109,1802],{},[1850,36111,4062],{},[1701,36113,2012],{"separator":2011},[1845,36115,36116,36118],{},[898,36117,1802],{},[1850,36119,3938],{},[1701,36121,1805],{"stretchy":1798},[902,36123,36124],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,36127,36129],{"className":36128},[886],[888,36130,36131],{"xmlns":890},[892,36132,36133,36189],{},[895,36134,36135,36137,36139,36145,36147,36153,36155,36157,36163,36165,36167,36169,36175,36177,36183,36185,36187],{},[898,36136,15097],{},[1701,36138,1799],{"stretchy":1798},[1845,36140,36141,36143],{},[898,36142,1802],{},[1850,36144,4062],{},[1701,36146,2012],{"separator":2011},[1845,36148,36149,36151],{},[898,36150,1802],{},[1850,36152,3938],{},[1701,36154,1805],{"stretchy":1798},[1701,36156,1792],{},[3243,36158,36159,36161],{},[898,36160,900],{},[1701,36162,8424],{},[1701,36164,2317],{},[898,36166,900],{},[1701,36168,1799],{"stretchy":1798},[1845,36170,36171,36173],{},[898,36172,1802],{},[1850,36174,4062],{},[1701,36176,2012],{"separator":2011},[1845,36178,36179,36181],{},[898,36180,1802],{},[1850,36182,3938],{},[1701,36184,1805],{"stretchy":1798},[1701,36186,1792],{},[1850,36188,1852],{},[902,36190,36191],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,36193,36195],{"id":36194},"lagrangeova-funkce","Lagrangeova funkce",[883,36197,36199],{"className":36198},[886],[888,36200,36201],{"xmlns":890,"display":2252},[892,36202,36203,36314],{},[2256,36204,36205],{"width":2258},[2260,36206,36207,36209,36307,36309],{},[2263,36208],{"width":2265},[2263,36210,36211],{},[895,36212,36213,36215,36217,36223,36225,36231,36233,36235,36237,36239,36247,36253,36255,36263,36269,36271,36273,36275,36281,36283,36285,36287,36293,36295,36301,36303,36305],{},[898,36214,13853],{"mathvariant":32582},[1701,36216,1799],{"stretchy":1798},[1845,36218,36219,36221],{},[898,36220,1802],{},[1850,36222,4062],{},[1701,36224,2012],{"separator":2011},[1845,36226,36227,36229],{},[898,36228,1802],{},[1850,36230,3938],{},[1701,36232,2012],{"separator":2011},[898,36234,20489],{},[1701,36236,1805],{"stretchy":1798},[1701,36238,1792],{},[2287,36240,36241,36243,36245],{},[898,36242,1680],{},[1850,36244,4062],{},[1701,36246,8424],{},[1845,36248,36249,36251],{},[898,36250,1802],{},[1850,36252,4062],{},[1701,36254,1703],{},[2287,36256,36257,36259,36261],{},[898,36258,1680],{},[1850,36260,3938],{},[1701,36262,8424],{},[1845,36264,36265,36267],{},[898,36266,1802],{},[1850,36268,3938],{},[1701,36270,1703],{},[898,36272,20489],{},[1701,36274,1799],{"stretchy":1798},[3243,36276,36277,36279],{},[898,36278,900],{},[1701,36280,8424],{},[1701,36282,2317],{},[898,36284,900],{},[1701,36286,1799],{"stretchy":1798},[1845,36288,36289,36291],{},[898,36290,1802],{},[1850,36292,4062],{},[1701,36294,2012],{"separator":2011},[1845,36296,36297,36299],{},[898,36298,1802],{},[1850,36300,3938],{},[1701,36302,1805],{"stretchy":1798},[1701,36304,1805],{"stretchy":1798},[898,36306,1715],{"mathvariant":2334},[2263,36308],{"width":2265},[2263,36310,36311],{},[1939,36312,36313],{},"(6.24)",[902,36315,36316],{"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}",[724,36318,36319],{},"Soustava podmínek prvního řádu:",[883,36321,36323],{"className":36322},[886],[888,36324,36325],{"xmlns":890,"display":2252},[892,36326,36327,36500],{},[2256,36328,36329],{"width":2258},[2260,36330,36331,36333,36493,36495],{},[2263,36332],{"width":2265},[2263,36334,36335],{},[2256,36336,36337,36387,36437],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,36338,36339,36351],{},[2263,36340,36341],{},[2363,36342,36343],{"scriptlevel":1852,"displaystyle":2011},[2287,36344,36345,36347,36349],{},[898,36346,13853],{"mathvariant":32582},[1850,36348,4062],{},[1701,36350,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,36352,36353],{},[2363,36354,36355],{"scriptlevel":1852,"displaystyle":2011},[895,36356,36357,36359,36361,36369,36371,36373,36381,36383,36385],{},[895,36358],{},[1701,36360,1792],{},[2287,36362,36363,36365,36367],{},[898,36364,1680],{},[1850,36366,4062],{},[1701,36368,8424],{},[1701,36370,2317],{},[898,36372,20489],{},[2287,36374,36375,36377,36379],{},[898,36376,900],{},[1850,36378,4062],{},[1701,36380,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,36382,1792],{},[1850,36384,1852],{},[1701,36386,2012],{"separator":2011},[2260,36388,36389,36401],{},[2263,36390,36391],{},[2363,36392,36393],{"scriptlevel":1852,"displaystyle":2011},[2287,36394,36395,36397,36399],{},[898,36396,13853],{"mathvariant":32582},[1850,36398,3938],{},[1701,36400,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,36402,36403],{},[2363,36404,36405],{"scriptlevel":1852,"displaystyle":2011},[895,36406,36407,36409,36411,36419,36421,36423,36431,36433,36435],{},[895,36408],{},[1701,36410,1792],{},[2287,36412,36413,36415,36417],{},[898,36414,1680],{},[1850,36416,3938],{},[1701,36418,8424],{},[1701,36420,2317],{},[898,36422,20489],{},[2287,36424,36425,36427,36429],{},[898,36426,900],{},[1850,36428,3938],{},[1701,36430,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,36432,1792],{},[1850,36434,1852],{},[1701,36436,2012],{"separator":2011},[2260,36438,36439,36451],{},[2263,36440,36441],{},[2363,36442,36443],{"scriptlevel":1852,"displaystyle":2011},[2287,36444,36445,36447,36449],{},[898,36446,13853],{"mathvariant":32582},[898,36448,20489],{},[1701,36450,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,36452,36453],{},[2363,36454,36455],{"scriptlevel":1852,"displaystyle":2011},[895,36456,36457,36459,36461,36467,36469,36471,36473,36479,36481,36487,36489,36491],{},[895,36458],{},[1701,36460,1792],{},[3243,36462,36463,36465],{},[898,36464,900],{},[1701,36466,8424],{},[1701,36468,2317],{},[898,36470,900],{},[1701,36472,1799],{"stretchy":1798},[1845,36474,36475,36477],{},[898,36476,1802],{},[1850,36478,4062],{},[1701,36480,2012],{"separator":2011},[1845,36482,36483,36485],{},[898,36484,1802],{},[1850,36486,3938],{},[1701,36488,1805],{"stretchy":1798},[1701,36490,1792],{},[1850,36492,16514],{},[2263,36494],{"width":2265},[2263,36496,36497],{},[1939,36498,36499],{},"(6.25)",[902,36501,36502],{"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}",[724,36504,36505],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,36507,36509],{"className":36508},[886],[888,36510,36511],{"xmlns":890,"display":2252},[892,36512,36513,36611],{},[2256,36514,36515],{"width":2258},[2260,36516,36517,36519,36604,36606],{},[2263,36518],{"width":2265},[2263,36520,36521],{},[895,36522,36523,36525,36527,36533,36535,36541,36543,36545,36547,36549,36551,36553,36602],{},[898,36524,1795],{},[1701,36526,1799],{"stretchy":1798},[1845,36528,36529,36531],{},[898,36530,1802],{},[1850,36532,4062],{},[1701,36534,2012],{"separator":2011},[1845,36536,36537,36539],{},[898,36538,1802],{},[1850,36540,3938],{},[1701,36542,2012],{"separator":2011},[898,36544,20489],{},[1701,36546,1805],{"stretchy":1798},[1701,36548,1792],{},[1701,36550,2317],{},[898,36552,20489],{},[895,36554,36555,36557,36569,36571,36584,36586,36588,36600],{},[1701,36556,1799],{"fence":2011},[2287,36558,36559,36561,36563],{},[898,36560,900],{},[1850,36562,4181],{},[895,36564,36565,36567],{},[1701,36566,4783],{"mathvariant":2334},[1701,36568,4783],{"mathvariant":2334},[1701,36570,1703],{},[2287,36572,36573,36575,36578],{},[898,36574,900],{},[1850,36576,36577],{},"22",[895,36579,36580,36582],{},[1701,36581,4783],{"mathvariant":2334},[1701,36583,4783],{"mathvariant":2334},[1701,36585,1703],{},[1850,36587,3938],{},[2287,36589,36590,36592,36594],{},[898,36591,900],{},[1850,36593,7592],{},[895,36595,36596,36598],{},[1701,36597,4783],{"mathvariant":2334},[1701,36599,4783],{"mathvariant":2334},[1701,36601,1805],{"fence":2011},[898,36603,1715],{"mathvariant":2334},[2263,36605],{"width":2265},[2263,36607,36608],{},[1939,36609,36610],{},"(6.26)",[902,36612,36613],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,36615,36616,36619,36620,36659,36660,36699,36700,36750,36751,36777,36778,36795,36796,36822],{},[38,36617,36618],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,36621,36623],{"className":36622},[886],[888,36624,36625],{"xmlns":890},[892,36626,36627,36657],{},[895,36628,36629,36635,36637,36645,36647,36655],{},[3243,36630,36631,36633],{},[898,36632,1802],{},[1701,36634,8424],{},[1701,36636,2036],{"stretchy":1798},[2287,36638,36639,36641,36643],{},[898,36640,1802],{},[1850,36642,4062],{},[1701,36644,8424],{},[1701,36646,2012],{"separator":2011},[2287,36648,36649,36651,36653],{},[898,36650,1802],{},[1850,36652,3938],{},[1701,36654,8424],{},[1701,36656,2053],{"stretchy":1798},[902,36658,32361],{"encoding":904}," dotyku křivky užitečnosti ",[883,36661,36663],{"className":36662},[886],[888,36664,36665],{"xmlns":890},[892,36666,36667,36697],{},[895,36668,36669,36675,36677,36679,36681,36687,36689,36695],{},[3243,36670,36671,36673],{},[898,36672,900],{},[1701,36674,8424],{},[1701,36676,1792],{},[898,36678,900],{},[1701,36680,1799],{"stretchy":1798},[1845,36682,36683,36685],{},[898,36684,1802],{},[1850,36686,4062],{},[1701,36688,2012],{"separator":2011},[1845,36690,36691,36693],{},[898,36692,1802],{},[1850,36694,3938],{},[1701,36696,1805],{"stretchy":1798},[902,36698,21711],{"encoding":904}," s přímkou výdajů ",[883,36701,36703],{"className":36702},[886],[888,36704,36705],{"xmlns":890},[892,36706,36707,36747],{},[895,36708,36709,36715,36717,36725,36731,36733,36741],{},[3243,36710,36711,36713],{},[898,36712,3249],{},[1701,36714,8424],{},[1701,36716,1792],{},[2287,36718,36719,36721,36723],{},[898,36720,1680],{},[1850,36722,4062],{},[1701,36724,8424],{},[1845,36726,36727,36729],{},[898,36728,1802],{},[1850,36730,4062],{},[1701,36732,1703],{},[2287,36734,36735,36737,36739],{},[898,36736,1680],{},[1850,36738,3938],{},[1701,36740,8424],{},[1845,36742,36743,36745],{},[898,36744,1802],{},[1850,36746,3938],{},[902,36748,36749],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,36752,36754],{"className":36753},[886],[888,36755,36756],{"xmlns":890},[892,36757,36758,36774],{},[895,36759,36760,36766,36768],{},[1845,36761,36762,36764],{},[898,36763,3249],{},[1850,36765,1852],{},[1701,36767,7530],{},[3243,36769,36770,36772],{},[898,36771,3249],{},[1701,36773,8424],{},[902,36775,36776],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,36779,36781],{"className":36780},[886],[888,36782,36783],{"xmlns":890},[892,36784,36785,36793],{},[895,36786,36787],{},[3243,36788,36789,36791],{},[898,36790,900],{},[1701,36792,8424],{},[902,36794,31999],{"encoding":904},", hladina ",[883,36797,36799],{"className":36798},[886],[888,36800,36801],{"xmlns":890},[892,36802,36803,36819],{},[895,36804,36805,36811,36813],{},[1845,36806,36807,36809],{},[898,36808,3249],{},[1850,36810,4062],{},[1701,36812,7491],{},[3243,36814,36815,36817],{},[898,36816,3249],{},[1701,36818,8424],{},[902,36820,36821],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1635,36824,36825,36830],{},[724,36826,36827,36829],{},[883,36828,3140],{}," Postup — duální úloha (minimalizace výdajů)",[152,36831,36832,36882,36968,37008,37083],{},[123,36833,36834,4088,36837,36881],{},[38,36835,36836],{},"Zapiš vazbu",[883,36838,36840],{"className":36839},[886],[888,36841,36842],{"xmlns":890},[892,36843,36844,36878],{},[895,36845,36846,36852,36854,36856,36858,36864,36866,36872,36874,36876],{},[3243,36847,36848,36850],{},[898,36849,900],{},[1701,36851,8424],{},[1701,36853,2317],{},[898,36855,900],{},[1701,36857,1799],{"stretchy":1798},[1845,36859,36860,36862],{},[898,36861,1802],{},[1850,36863,4062],{},[1701,36865,2012],{"separator":2011},[1845,36867,36868,36870],{},[898,36869,1802],{},[1850,36871,3938],{},[1701,36873,1805],{"stretchy":1798},[1701,36875,1792],{},[1850,36877,1852],{},[902,36879,36880],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,36883,36884,4088,36886,1715],{},[38,36885,33293],{},[883,36887,36889],{"className":36888},[886],[888,36890,36891],{"xmlns":890},[892,36892,36893,36965],{},[895,36894,36895,36897,36899,36907,36913,36915,36923,36929,36931,36933,36935,36941,36943,36945,36947,36953,36955,36961,36963],{},[898,36896,13853],{"mathvariant":32582},[1701,36898,1792],{},[2287,36900,36901,36903,36905],{},[898,36902,1680],{},[1850,36904,4062],{},[1701,36906,8424],{},[1845,36908,36909,36911],{},[898,36910,1802],{},[1850,36912,4062],{},[1701,36914,1703],{},[2287,36916,36917,36919,36921],{},[898,36918,1680],{},[1850,36920,3938],{},[1701,36922,8424],{},[1845,36924,36925,36927],{},[898,36926,1802],{},[1850,36928,3938],{},[1701,36930,1703],{},[898,36932,20489],{},[1701,36934,1799],{"stretchy":1798},[3243,36936,36937,36939],{},[898,36938,900],{},[1701,36940,8424],{},[1701,36942,2317],{},[898,36944,900],{},[1701,36946,1799],{"stretchy":1798},[1845,36948,36949,36951],{},[898,36950,1802],{},[1850,36952,4062],{},[1701,36954,2012],{"separator":2011},[1845,36956,36957,36959],{},[898,36958,1802],{},[1850,36960,3938],{},[1701,36962,1805],{"stretchy":1798},[1701,36964,1805],{"stretchy":1798},[902,36966,36967],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,36969,36970,36973,36974,37007],{},[38,36971,36972],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,36975,36977],{"className":36976},[886],[888,36978,36979],{"xmlns":890},[892,36980,36981,37005],{},[895,36982,36983,36985,36987,36995,36997],{},[1939,36984,14659],{},[1701,36986,1792],{},[2287,36988,36989,36991,36993],{},[898,36990,1680],{},[1850,36992,4062],{},[1701,36994,8424],{},[898,36996,8741],{"mathvariant":2334},[2287,36998,36999,37001,37003],{},[898,37000,1680],{},[1850,37002,3938],{},[1701,37004,8424],{},[902,37006,33013],{"encoding":904}," (stejná jako u maximalizace!).",[123,37009,37010,4088,37013,37053,37054,1715],{},[38,37011,37012],{},"Dosaď do vazby",[883,37014,37016],{"className":37015},[886],[888,37017,37018],{"xmlns":890},[892,37019,37020,37050],{},[895,37021,37022,37024,37026,37032,37034,37040,37042,37044],{},[898,37023,900],{},[1701,37025,1799],{"stretchy":1798},[1845,37027,37028,37030],{},[898,37029,1802],{},[1850,37031,4062],{},[1701,37033,2012],{"separator":2011},[1845,37035,37036,37038],{},[898,37037,1802],{},[1850,37039,3938],{},[1701,37041,1805],{"stretchy":1798},[1701,37043,1792],{},[3243,37045,37046,37048],{},[898,37047,900],{},[1701,37049,8424],{},[902,37051,37052],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,37055,37057],{"className":37056},[886],[888,37058,37059],{"xmlns":890},[892,37060,37061,37081],{},[895,37062,37063,37071,37073],{},[2287,37064,37065,37067,37069],{},[898,37066,1802],{},[1850,37068,4062],{},[1701,37070,8424],{},[1701,37072,2012],{"separator":2011},[2287,37074,37075,37077,37079],{},[898,37076,1802],{},[1850,37078,3938],{},[1701,37080,8424],{},[902,37082,33534],{"encoding":904},[123,37084,37085,4088,37088,37142],{},[38,37086,37087],{},"Vypočítej minimální výdaje",[883,37089,37091],{"className":37090},[886],[888,37092,37093],{"xmlns":890},[892,37094,37095,37139],{},[895,37096,37097,37103,37105,37113,37121,37123,37131],{},[3243,37098,37099,37101],{},[898,37100,3249],{},[1701,37102,8424],{},[1701,37104,1792],{},[2287,37106,37107,37109,37111],{},[898,37108,1680],{},[1850,37110,4062],{},[1701,37112,8424],{},[2287,37114,37115,37117,37119],{},[898,37116,1802],{},[1850,37118,4062],{},[1701,37120,8424],{},[1701,37122,1703],{},[2287,37124,37125,37127,37129],{},[898,37126,1680],{},[1850,37128,3938],{},[1701,37130,8424],{},[2287,37132,37133,37135,37137],{},[898,37134,1802],{},[1850,37136,3938],{},[1701,37138,8424],{},[902,37140,37141],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,37144,37146,37147],{"id":37145},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,37148,37150],{"className":37149},[886],[888,37151,37152],{"xmlns":890},[892,37153,37154,37188],{},[895,37155,37156,37158,37160,37174],{},[898,37157,900],{},[1701,37159,1792],{},[2287,37161,37162,37164,37166],{},[898,37163,1802],{},[1850,37165,4062],{},[895,37167,37168,37170,37172],{},[1850,37169,4062],{},[898,37171,8741],{"mathvariant":2334},[1850,37173,3938],{},[2287,37175,37176,37178,37180],{},[898,37177,1802],{},[1850,37179,3938],{},[895,37181,37182,37184,37186],{},[1850,37183,4062],{},[898,37185,8741],{"mathvariant":2334},[1850,37187,3938],{},[902,37189,37190],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,37192,37193,37194,1343,37216,1343,37240,34377],{},"Dáno ",[883,37195,37197],{"className":37196},[886],[888,37198,37199],{"xmlns":890},[892,37200,37201,37213],{},[895,37202,37203,37209,37211],{},[3243,37204,37205,37207],{},[898,37206,900],{},[1701,37208,8424],{},[1701,37210,1792],{},[1850,37212,3938],{},[902,37214,37215],{"encoding":904},"U^* = 2",[883,37217,37219],{"className":37218},[886],[888,37220,37221],{"xmlns":890},[892,37222,37223,37237],{},[895,37224,37225,37233,37235],{},[2287,37226,37227,37229,37231],{},[898,37228,1680],{},[1850,37230,4062],{},[1701,37232,8424],{},[1701,37234,1792],{},[1850,37236,27827],{},[902,37238,37239],{"encoding":904},"P_1^* = 0{,}25",[883,37241,37243],{"className":37242},[886],[888,37244,37245],{"xmlns":890},[892,37246,37247,37261],{},[895,37248,37249,37257,37259],{},[2287,37250,37251,37253,37255],{},[898,37252,1680],{},[1850,37254,3938],{},[1701,37256,8424],{},[1701,37258,1792],{},[1850,37260,4062],{},[902,37262,37263],{"encoding":904},"P_2^* = 1",[883,37265,37267],{"className":37266},[886],[888,37268,37269],{"xmlns":890,"display":2252},[892,37270,37271,37335],{},[895,37272,37273,37275,37277,37279,37285,37287,37293,37295,37297,37299,37301,37303,37317,37331,37333],{},[898,37274,13853],{"mathvariant":32582},[1701,37276,1792],{},[1850,37278,27827],{},[1845,37280,37281,37283],{},[898,37282,1802],{},[1850,37284,4062],{},[1701,37286,1703],{},[1845,37288,37289,37291],{},[898,37290,1802],{},[1850,37292,3938],{},[1701,37294,1703],{},[898,37296,20489],{},[1701,37298,1799],{"stretchy":1798},[1850,37300,3938],{},[1701,37302,2317],{},[2287,37304,37305,37307,37309],{},[898,37306,1802],{},[1850,37308,4062],{},[895,37310,37311,37313,37315],{},[1850,37312,4062],{},[898,37314,8741],{"mathvariant":2334},[1850,37316,3938],{},[2287,37318,37319,37321,37323],{},[898,37320,1802],{},[1850,37322,3938],{},[895,37324,37325,37327,37329],{},[1850,37326,4062],{},[898,37328,8741],{"mathvariant":2334},[1850,37330,3938],{},[1701,37332,1805],{"stretchy":1798},[898,37334,1715],{"mathvariant":2334},[902,37336,37337],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,37339,34462],{},[883,37341,37343],{"className":37342},[886],[888,37344,37345],{"xmlns":890,"display":2252},[892,37346,37347,37561],{},[2256,37348,37349,37425,37501],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,37350,37351,37363],{},[2263,37352,37353],{},[2363,37354,37355],{"scriptlevel":1852,"displaystyle":2011},[2287,37356,37357,37359,37361],{},[898,37358,13853],{"mathvariant":32582},[1850,37360,4062],{},[1701,37362,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,37364,37365],{},[2363,37366,37367],{"scriptlevel":1852,"displaystyle":2011},[895,37368,37369,37371,37373,37375,37377,37379,37381,37389,37405,37419,37421,37423],{},[895,37370],{},[1701,37372,1792],{},[1850,37374,27827],{},[1701,37376,2317],{},[898,37378,20489],{},[1701,37380,3408],{},[2363,37382,37383],{"scriptlevel":1852,"displaystyle":1798},[3726,37384,37385,37387],{},[1850,37386,4062],{},[1850,37388,3938],{},[2287,37390,37391,37393,37395],{},[898,37392,1802],{},[1850,37394,4062],{},[895,37396,37397,37399,37401,37403],{},[1701,37398,2317],{},[1850,37400,4062],{},[898,37402,8741],{"mathvariant":2334},[1850,37404,3938],{},[2287,37406,37407,37409,37411],{},[898,37408,1802],{},[1850,37410,3938],{},[895,37412,37413,37415,37417],{},[1850,37414,4062],{},[898,37416,8741],{"mathvariant":2334},[1850,37418,3938],{},[1701,37420,1792],{},[1850,37422,1852],{},[1701,37424,2012],{"separator":2011},[2260,37426,37427,37439],{},[2263,37428,37429],{},[2363,37430,37431],{"scriptlevel":1852,"displaystyle":2011},[2287,37432,37433,37435,37437],{},[898,37434,13853],{"mathvariant":32582},[1850,37436,3938],{},[1701,37438,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,37440,37441],{},[2363,37442,37443],{"scriptlevel":1852,"displaystyle":2011},[895,37444,37445,37447,37449,37451,37453,37455,37457,37465,37479,37495,37497,37499],{},[895,37446],{},[1701,37448,1792],{},[1850,37450,4062],{},[1701,37452,2317],{},[898,37454,20489],{},[1701,37456,3408],{},[2363,37458,37459],{"scriptlevel":1852,"displaystyle":1798},[3726,37460,37461,37463],{},[1850,37462,4062],{},[1850,37464,3938],{},[2287,37466,37467,37469,37471],{},[898,37468,1802],{},[1850,37470,4062],{},[895,37472,37473,37475,37477],{},[1850,37474,4062],{},[898,37476,8741],{"mathvariant":2334},[1850,37478,3938],{},[2287,37480,37481,37483,37485],{},[898,37482,1802],{},[1850,37484,3938],{},[895,37486,37487,37489,37491,37493],{},[1701,37488,2317],{},[1850,37490,4062],{},[898,37492,8741],{"mathvariant":2334},[1850,37494,3938],{},[1701,37496,1792],{},[1850,37498,1852],{},[1701,37500,2012],{"separator":2011},[2260,37502,37503,37515],{},[2263,37504,37505],{},[2363,37506,37507],{"scriptlevel":1852,"displaystyle":2011},[2287,37508,37509,37511,37513],{},[898,37510,13853],{"mathvariant":32582},[898,37512,20489],{},[1701,37514,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,37516,37517],{},[2363,37518,37519],{"scriptlevel":1852,"displaystyle":2011},[895,37520,37521,37523,37525,37527,37529,37543,37557,37559],{},[895,37522],{},[1701,37524,1792],{},[1850,37526,3938],{},[1701,37528,2317],{},[2287,37530,37531,37533,37535],{},[898,37532,1802],{},[1850,37534,4062],{},[895,37536,37537,37539,37541],{},[1850,37538,4062],{},[898,37540,8741],{"mathvariant":2334},[1850,37542,3938],{},[2287,37544,37545,37547,37549],{},[898,37546,1802],{},[1850,37548,3938],{},[895,37550,37551,37553,37555],{},[1850,37552,4062],{},[898,37554,8741],{"mathvariant":2334},[1850,37556,3938],{},[1701,37558,1792],{},[1850,37560,16514],{},[902,37562,37563],{"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}",[724,37565,37566,37567,21622,37597,37625,37626,4185,37688,1343,37738,37760,37761,1715],{},"Podílem prvních dvou rovnic: ",[883,37568,37570],{"className":37569},[886],[888,37571,37572],{"xmlns":890},[892,37573,37574,37594],{},[895,37575,37576,37578,37580,37586,37588],{},[1850,37577,27827],{},[1701,37579,1792],{},[1845,37581,37582,37584],{},[898,37583,1802],{},[1850,37585,3938],{},[898,37587,8741],{"mathvariant":2334},[1845,37589,37590,37592],{},[898,37591,1802],{},[1850,37593,4062],{},[902,37595,37596],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,37598,37600],{"className":37599},[886],[888,37601,37602],{"xmlns":890},[892,37603,37604,37622],{},[895,37605,37606,37612,37614,37616],{},[1845,37607,37608,37610],{},[898,37609,1802],{},[1850,37611,3938],{},[1701,37613,1792],{},[1850,37615,27827],{},[1845,37617,37618,37620],{},[898,37619,1802],{},[1850,37621,4062],{},[902,37623,37624],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,37627,37629],{"className":37628},[886],[888,37630,37631],{"xmlns":890},[892,37632,37633,37685],{},[895,37634,37635,37649,37651,37653,37659,37671,37673,37675,37681,37683],{},[2287,37636,37637,37639,37641],{},[898,37638,1802],{},[1850,37640,4062],{},[895,37642,37643,37645,37647],{},[1850,37644,4062],{},[898,37646,8741],{"mathvariant":2334},[1850,37648,3938],{},[1701,37650,1799],{"stretchy":1798},[1850,37652,27827],{},[1845,37654,37655,37657],{},[898,37656,1802],{},[1850,37658,4062],{},[3243,37660,37661,37663],{},[1701,37662,1805],{"stretchy":1798},[895,37664,37665,37667,37669],{},[1850,37666,4062],{},[898,37668,8741],{"mathvariant":2334},[1850,37670,3938],{},[1701,37672,1792],{},[1850,37674,3684],{},[1845,37676,37677,37679],{},[898,37678,1802],{},[1850,37680,4062],{},[1701,37682,1792],{},[1850,37684,3938],{},[902,37686,37687],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,37689,37690,1343,37714],{},[883,37691,37693],{"className":37692},[886],[888,37694,37695],{"xmlns":890},[892,37696,37697,37711],{},[895,37698,37699,37707,37709],{},[2287,37700,37701,37703,37705],{},[898,37702,1802],{},[1850,37704,4062],{},[1701,37706,8424],{},[1701,37708,1792],{},[1850,37710,6460],{},[902,37712,37713],{"encoding":904},"Q_1^* = 4",[883,37715,37717],{"className":37716},[886],[888,37718,37719],{"xmlns":890},[892,37720,37721,37735],{},[895,37722,37723,37731,37733],{},[2287,37724,37725,37727,37729],{},[898,37726,1802],{},[1850,37728,3938],{},[1701,37730,8424],{},[1701,37732,1792],{},[1850,37734,4062],{},[902,37736,37737],{"encoding":904},"Q_2^* = 1",[883,37739,37741],{"className":37740},[886],[888,37742,37743],{"xmlns":890},[892,37744,37745,37757],{},[895,37746,37747,37753,37755],{},[3243,37748,37749,37751],{},[898,37750,20489],{},[1701,37752,8424],{},[1701,37754,1792],{},[1850,37756,4062],{},[902,37758,37759],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,37762,37764],{"className":37763},[886],[888,37765,37766],{"xmlns":890},[892,37767,37768,37796],{},[895,37769,37770,37776,37778,37780,37782,37784,37786,37788,37790,37792,37794],{},[3243,37771,37772,37774],{},[898,37773,3249],{},[1701,37775,8424],{},[1701,37777,1792],{},[1850,37779,27827],{},[1701,37781,3408],{},[1850,37783,6460],{},[1701,37785,1703],{},[1850,37787,4062],{},[1701,37789,3408],{},[1850,37791,4062],{},[1701,37793,1792],{},[1850,37795,3938],{},[902,37797,37798],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,37800,37801,37804,37805,1343,37871,1343,37937,38003,38004,38041,38042,38064,38065,1715],{},[614,37802,37803],{},"Ověření postačující podmínky"," (6.26): ",[883,37806,37808],{"className":37807},[886],[888,37809,37810],{"xmlns":890},[892,37811,37812,37868],{},[895,37813,37814,37826,37828,37830,37838,37854],{},[2287,37815,37816,37818,37820],{},[898,37817,900],{},[1850,37819,4181],{},[895,37821,37822,37824],{},[1701,37823,4783],{"mathvariant":2334},[1701,37825,4783],{"mathvariant":2334},[1701,37827,1792],{},[1701,37829,2317],{},[2363,37831,37832],{"scriptlevel":1852,"displaystyle":1798},[3726,37833,37834,37836],{},[1850,37835,4062],{},[1850,37837,6460],{},[2287,37839,37840,37842,37844],{},[898,37841,1802],{},[1850,37843,4062],{},[895,37845,37846,37848,37850,37852],{},[1701,37847,2317],{},[1850,37849,3646],{},[898,37851,8741],{"mathvariant":2334},[1850,37853,3938],{},[2287,37855,37856,37858,37860],{},[898,37857,1802],{},[1850,37859,3938],{},[895,37861,37862,37864,37866],{},[1850,37863,4062],{},[898,37865,8741],{"mathvariant":2334},[1850,37867,3938],{},[902,37869,37870],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,37872,37874],{"className":37873},[886],[888,37875,37876],{"xmlns":890},[892,37877,37878,37934],{},[895,37879,37880,37892,37894,37896,37904,37918],{},[2287,37881,37882,37884,37886],{},[898,37883,900],{},[1850,37885,36577],{},[895,37887,37888,37890],{},[1701,37889,4783],{"mathvariant":2334},[1701,37891,4783],{"mathvariant":2334},[1701,37893,1792],{},[1701,37895,2317],{},[2363,37897,37898],{"scriptlevel":1852,"displaystyle":1798},[3726,37899,37900,37902],{},[1850,37901,4062],{},[1850,37903,6460],{},[2287,37905,37906,37908,37910],{},[898,37907,1802],{},[1850,37909,4062],{},[895,37911,37912,37914,37916],{},[1850,37913,4062],{},[898,37915,8741],{"mathvariant":2334},[1850,37917,3938],{},[2287,37919,37920,37922,37924],{},[898,37921,1802],{},[1850,37923,3938],{},[895,37925,37926,37928,37930,37932],{},[1701,37927,2317],{},[1850,37929,3646],{},[898,37931,8741],{"mathvariant":2334},[1850,37933,3938],{},[902,37935,37936],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,37938,37940],{"className":37939},[886],[888,37941,37942],{"xmlns":890},[892,37943,37944,38000],{},[895,37945,37946,37958,37960,37968,37984],{},[2287,37947,37948,37950,37952],{},[898,37949,900],{},[1850,37951,7592],{},[895,37953,37954,37956],{},[1701,37955,4783],{"mathvariant":2334},[1701,37957,4783],{"mathvariant":2334},[1701,37959,1792],{},[2363,37961,37962],{"scriptlevel":1852,"displaystyle":1798},[3726,37963,37964,37966],{},[1850,37965,4062],{},[1850,37967,6460],{},[2287,37969,37970,37972,37974],{},[898,37971,1802],{},[1850,37973,4062],{},[895,37975,37976,37978,37980,37982],{},[1701,37977,2317],{},[1850,37979,4062],{},[898,37981,8741],{"mathvariant":2334},[1850,37983,3938],{},[2287,37985,37986,37988,37990],{},[898,37987,1802],{},[1850,37989,3938],{},[895,37991,37992,37994,37996,37998],{},[1701,37993,2317],{},[1850,37995,4062],{},[898,37997,8741],{"mathvariant":2334},[1850,37999,3938],{},[902,38001,38002],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,38005,38007],{"className":38006},[886],[888,38008,38009],{"xmlns":890},[892,38010,38011,38038],{},[895,38012,38013,38015,38017,38019,38021,38023,38025,38027,38029,38031,38034,38036],{},[898,38014,1795],{},[1701,38016,1799],{"stretchy":1798},[1850,38018,6460],{},[1701,38020,2012],{"separator":2011},[1850,38022,4062],{},[1701,38024,2012],{"separator":2011},[1850,38026,4062],{},[1701,38028,1805],{"stretchy":1798},[1701,38030,1792],{},[1850,38032,38033],{},"0,28125",[1701,38035,7491],{},[1850,38037,1852],{},[902,38039,38040],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,38043,38045],{"className":38044},[886],[888,38046,38047],{"xmlns":890},[892,38048,38049,38061],{},[895,38050,38051,38053,38055,38057,38059],{},[1701,38052,2036],{"stretchy":1798},[1850,38054,6460],{},[1701,38056,2012],{"separator":2011},[1850,38058,4062],{},[1701,38060,2053],{"stretchy":1798},[902,38062,38063],{"encoding":904},"[4, 1]"," je vázané ",[38,38066,7858],{},[115,38068,38070],{"id":38069},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,38072,38073],{},"Obecně:",[883,38075,38077],{"className":38076},[886],[888,38078,38079],{"xmlns":890,"display":2252},[892,38080,38081,38176],{},[2256,38082,38083],{"width":2258},[2260,38084,38085,38087,38169,38171],{},[2263,38086],{"width":2265},[2263,38088,38089],{},[895,38090,38091,38097,38099,38105,38107,38113,38115,38121,38123,38125,38127,38129,38131,38137,38139,38145,38147,38153,38155,38161,38163,38165,38167],{},[1845,38092,38093,38095],{},[898,38094,1802],{},[1850,38096,4062],{},[1701,38098,1792],{},[1845,38100,38101,38103],{},[898,38102,1795],{},[1850,38104,4062],{},[1701,38106,1799],{"stretchy":1798},[1845,38108,38109,38111],{},[898,38110,1680],{},[1850,38112,4062],{},[1701,38114,2012],{"separator":2011},[1845,38116,38117,38119],{},[898,38118,1680],{},[1850,38120,3938],{},[1701,38122,2012],{"separator":2011},[898,38124,900],{},[1701,38126,1805],{"stretchy":1798},[1701,38128,2012],{"separator":2011},[9942,38130],{"width":19336},[1845,38132,38133,38135],{},[898,38134,1802],{},[1850,38136,3938],{},[1701,38138,1792],{},[1845,38140,38141,38143],{},[898,38142,1795],{},[1850,38144,3938],{},[1701,38146,1799],{"stretchy":1798},[1845,38148,38149,38151],{},[898,38150,1680],{},[1850,38152,4062],{},[1701,38154,2012],{"separator":2011},[1845,38156,38157,38159],{},[898,38158,1680],{},[1850,38160,3938],{},[1701,38162,2012],{"separator":2011},[898,38164,900],{},[1701,38166,1805],{"stretchy":1798},[1701,38168,2012],{"separator":2011},[2263,38170],{"width":2265},[2263,38172,38173],{},[1939,38174,38175],{},"(6.27)",[902,38177,38178],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,38180,38182],{"className":38181},[886],[888,38183,38184],{"xmlns":890,"display":2252},[892,38185,38186,38233],{},[2256,38187,38188],{"width":2258},[2260,38189,38190,38192,38226,38228],{},[2263,38191],{"width":2265},[2263,38193,38194],{},[895,38195,38196,38198,38200,38202,38204,38210,38212,38218,38220,38222,38224],{},[898,38197,20489],{},[1701,38199,1792],{},[898,38201,20489],{},[1701,38203,1799],{"stretchy":1798},[1845,38205,38206,38208],{},[898,38207,1680],{},[1850,38209,4062],{},[1701,38211,2012],{"separator":2011},[1845,38213,38214,38216],{},[898,38215,1680],{},[1850,38217,3938],{},[1701,38219,2012],{"separator":2011},[898,38221,900],{},[1701,38223,1805],{"stretchy":1798},[898,38225,1715],{"mathvariant":2334},[2263,38227],{"width":2265},[2263,38229,38230],{},[1939,38231,38232],{},"(6.28)",[902,38234,38235],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,38237,38238,38239,4088,38242,38255,38256,38269],{},"Hicksova poptávka závisí na ",[38,38240,38241],{},"hladině užitečnosti",[883,38243,38245],{"className":38244},[886],[888,38246,38247],{"xmlns":890},[892,38248,38249,38253],{},[895,38250,38251],{},[898,38252,900],{},[902,38254,900],{"encoding":904}," (nikoli na důchodu ",[883,38257,38259],{"className":38258},[886],[888,38260,38261],{"xmlns":890},[892,38262,38263,38267],{},[895,38264,38265],{},[898,38266,13189],{},[902,38268,13189],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,38271,38273,38274],{"id":38272},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,38275,38277],{"className":38276},[886],[888,38278,38279],{"xmlns":890},[892,38280,38281,38315],{},[895,38282,38283,38285,38287,38301],{},[898,38284,900],{},[1701,38286,1792],{},[2287,38288,38289,38291,38293],{},[898,38290,1802],{},[1850,38292,4062],{},[895,38294,38295,38297,38299],{},[1850,38296,4062],{},[898,38298,8741],{"mathvariant":2334},[1850,38300,3938],{},[2287,38302,38303,38305,38307],{},[898,38304,1802],{},[1850,38306,3938],{},[895,38308,38309,38311,38313],{},[1850,38310,4062],{},[898,38312,8741],{"mathvariant":2334},[1850,38314,3938],{},[902,38316,37190],{"encoding":904},[724,38318,38319,38349],{},[883,38320,38322],{"className":38321},[886],[888,38323,38324],{"xmlns":890},[892,38325,38326,38346],{},[895,38327,38328,38334,38336,38342,38344],{},[1845,38329,38330,38332],{},[898,38331,1680],{},[1850,38333,4062],{},[1701,38335,2012],{"separator":2011},[1845,38337,38338,38340],{},[898,38339,1680],{},[1850,38341,3938],{},[1701,38343,2012],{"separator":2011},[898,38345,900],{},[902,38347,38348],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,38351,38353],{"className":38352},[886],[888,38354,38355],{"xmlns":890,"display":2252},[892,38356,38357,38431],{},[895,38358,38359,38361,38363,38369,38375,38377,38383,38389,38391,38393,38395,38397,38399,38413,38427,38429],{},[898,38360,13853],{"mathvariant":32582},[1701,38362,1792],{},[1845,38364,38365,38367],{},[898,38366,1680],{},[1850,38368,4062],{},[1845,38370,38371,38373],{},[898,38372,1802],{},[1850,38374,4062],{},[1701,38376,1703],{},[1845,38378,38379,38381],{},[898,38380,1680],{},[1850,38382,3938],{},[1845,38384,38385,38387],{},[898,38386,1802],{},[1850,38388,3938],{},[1701,38390,1703],{},[898,38392,20489],{},[1701,38394,1799],{"stretchy":1798},[898,38396,900],{},[1701,38398,2317],{},[2287,38400,38401,38403,38405],{},[898,38402,1802],{},[1850,38404,4062],{},[895,38406,38407,38409,38411],{},[1850,38408,4062],{},[898,38410,8741],{"mathvariant":2334},[1850,38412,3938],{},[2287,38414,38415,38417,38419],{},[898,38416,1802],{},[1850,38418,3938],{},[895,38420,38421,38423,38425],{},[1850,38422,4062],{},[898,38424,8741],{"mathvariant":2334},[1850,38426,3938],{},[1701,38428,1805],{"stretchy":1798},[898,38430,1715],{"mathvariant":2334},[902,38432,38433],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,38435,34462],{},[883,38437,38439],{"className":38438},[886],[888,38440,38441],{"xmlns":890,"display":2252},[892,38442,38443,38665],{},[2256,38444,38445,38525,38605],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,38446,38447,38459],{},[2263,38448,38449],{},[2363,38450,38451],{"scriptlevel":1852,"displaystyle":2011},[2287,38452,38453,38455,38457],{},[898,38454,13853],{"mathvariant":32582},[1850,38456,4062],{},[1701,38458,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,38460,38461],{},[2363,38462,38463],{"scriptlevel":1852,"displaystyle":2011},[895,38464,38465,38467,38469,38475,38477,38479,38481,38489,38505,38519,38521,38523],{},[895,38466],{},[1701,38468,1792],{},[1845,38470,38471,38473],{},[898,38472,1680],{},[1850,38474,4062],{},[1701,38476,2317],{},[898,38478,20489],{},[1701,38480,3408],{},[2363,38482,38483],{"scriptlevel":1852,"displaystyle":1798},[3726,38484,38485,38487],{},[1850,38486,4062],{},[1850,38488,3938],{},[2287,38490,38491,38493,38495],{},[898,38492,1802],{},[1850,38494,4062],{},[895,38496,38497,38499,38501,38503],{},[1701,38498,2317],{},[1850,38500,4062],{},[898,38502,8741],{"mathvariant":2334},[1850,38504,3938],{},[2287,38506,38507,38509,38511],{},[898,38508,1802],{},[1850,38510,3938],{},[895,38512,38513,38515,38517],{},[1850,38514,4062],{},[898,38516,8741],{"mathvariant":2334},[1850,38518,3938],{},[1701,38520,1792],{},[1850,38522,1852],{},[1701,38524,2012],{"separator":2011},[2260,38526,38527,38539],{},[2263,38528,38529],{},[2363,38530,38531],{"scriptlevel":1852,"displaystyle":2011},[2287,38532,38533,38535,38537],{},[898,38534,13853],{"mathvariant":32582},[1850,38536,3938],{},[1701,38538,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,38540,38541],{},[2363,38542,38543],{"scriptlevel":1852,"displaystyle":2011},[895,38544,38545,38547,38549,38555,38557,38559,38561,38569,38583,38599,38601,38603],{},[895,38546],{},[1701,38548,1792],{},[1845,38550,38551,38553],{},[898,38552,1680],{},[1850,38554,3938],{},[1701,38556,2317],{},[898,38558,20489],{},[1701,38560,3408],{},[2363,38562,38563],{"scriptlevel":1852,"displaystyle":1798},[3726,38564,38565,38567],{},[1850,38566,4062],{},[1850,38568,3938],{},[2287,38570,38571,38573,38575],{},[898,38572,1802],{},[1850,38574,4062],{},[895,38576,38577,38579,38581],{},[1850,38578,4062],{},[898,38580,8741],{"mathvariant":2334},[1850,38582,3938],{},[2287,38584,38585,38587,38589],{},[898,38586,1802],{},[1850,38588,3938],{},[895,38590,38591,38593,38595,38597],{},[1701,38592,2317],{},[1850,38594,4062],{},[898,38596,8741],{"mathvariant":2334},[1850,38598,3938],{},[1701,38600,1792],{},[1850,38602,1852],{},[1701,38604,2012],{"separator":2011},[2260,38606,38607,38619],{},[2263,38608,38609],{},[2363,38610,38611],{"scriptlevel":1852,"displaystyle":2011},[2287,38612,38613,38615,38617],{},[898,38614,13853],{"mathvariant":32582},[898,38616,20489],{},[1701,38618,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2263,38620,38621],{},[2363,38622,38623],{"scriptlevel":1852,"displaystyle":2011},[895,38624,38625,38627,38629,38631,38633,38647,38661,38663],{},[895,38626],{},[1701,38628,1792],{},[898,38630,900],{},[1701,38632,2317],{},[2287,38634,38635,38637,38639],{},[898,38636,1802],{},[1850,38638,4062],{},[895,38640,38641,38643,38645],{},[1850,38642,4062],{},[898,38644,8741],{"mathvariant":2334},[1850,38646,3938],{},[2287,38648,38649,38651,38653],{},[898,38650,1802],{},[1850,38652,3938],{},[895,38654,38655,38657,38659],{},[1850,38656,4062],{},[898,38658,8741],{"mathvariant":2334},[1850,38660,3938],{},[1701,38662,1792],{},[1850,38664,16514],{},[902,38666,38667],{"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}",[724,38669,38670,38671,38741,38742,38800],{},"Podílem rovnic: ",[883,38672,38674],{"className":38673},[886],[888,38675,38676],{"xmlns":890},[892,38677,38678,38738],{},[895,38679,38680,38686,38688,38694,38696,38702,38704,38710,38712,38718,38724,38726,38732],{},[1845,38681,38682,38684],{},[898,38683,1680],{},[1850,38685,4062],{},[898,38687,8741],{"mathvariant":2334},[1845,38689,38690,38692],{},[898,38691,1680],{},[1850,38693,3938],{},[1701,38695,1792],{},[1845,38697,38698,38700],{},[898,38699,1802],{},[1850,38701,3938],{},[898,38703,8741],{"mathvariant":2334},[1845,38705,38706,38708],{},[898,38707,1802],{},[1850,38709,4062],{},[1701,38711,8061],{},[1845,38713,38714,38716],{},[898,38715,1680],{},[1850,38717,4062],{},[1845,38719,38720,38722],{},[898,38721,1802],{},[1850,38723,4062],{},[1701,38725,1792],{},[1845,38727,38728,38730],{},[898,38729,1680],{},[1850,38731,3938],{},[1845,38733,38734,38736],{},[898,38735,1802],{},[1850,38737,3938],{},[902,38739,38740],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,38743,38745],{"className":38744},[886],[888,38746,38747],{"xmlns":890},[892,38748,38749,38797],{},[895,38750,38751,38753,38755,38761,38767,38769,38775,38781,38783,38785,38791],{},[898,38752,3249],{},[1701,38754,1792],{},[1845,38756,38757,38759],{},[898,38758,1680],{},[1850,38760,4062],{},[1845,38762,38763,38765],{},[898,38764,1802],{},[1850,38766,4062],{},[1701,38768,1703],{},[1845,38770,38771,38773],{},[898,38772,1680],{},[1850,38774,3938],{},[1845,38776,38777,38779],{},[898,38778,1802],{},[1850,38780,3938],{},[1701,38782,1792],{},[1850,38784,3938],{},[1845,38786,38787,38789],{},[898,38788,1680],{},[1850,38790,4062],{},[1845,38792,38793,38795],{},[898,38794,1802],{},[1850,38796,4062],{},[902,38798,38799],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,38802,38804],{"className":38803},[886],[888,38805,38806],{"xmlns":890,"display":2252},[892,38807,38808,38875],{},[2256,38809,38810],{"width":2258},[2260,38811,38812,38814,38868,38870],{},[2263,38813],{"width":2265},[2263,38815,38816],{},[895,38817,38818,38824,38826,38840,38842,38844,38850,38852,38866],{},[1845,38819,38820,38822],{},[898,38821,1802],{},[1850,38823,4062],{},[1701,38825,1792],{},[3726,38827,38828,38830],{},[898,38829,3249],{},[895,38831,38832,38834],{},[1850,38833,3938],{},[1845,38835,38836,38838],{},[898,38837,1680],{},[1850,38839,4062],{},[1701,38841,2012],{"separator":2011},[9942,38843],{"width":19336},[1845,38845,38846,38848],{},[898,38847,1802],{},[1850,38849,3938],{},[1701,38851,1792],{},[3726,38853,38854,38856],{},[898,38855,3249],{},[895,38857,38858,38860],{},[1850,38859,3938],{},[1845,38861,38862,38864],{},[898,38863,1680],{},[1850,38865,3938],{},[898,38867,1715],{"mathvariant":2334},[2263,38869],{"width":2265},[2263,38871,38872],{},[1939,38873,38874],{},"(6.29)",[902,38876,38877],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,38879,38880,38881,21622,38963,38999],{},"Ze třetí rovnice ",[883,38882,38884],{"className":38883},[886],[888,38885,38886],{"xmlns":890},[892,38887,38888,38960],{},[895,38889,38890,38892,38894,38932,38934],{},[898,38891,900],{},[1701,38893,1792],{},[12179,38895,38896],{},[895,38897,38898,38914,38916],{},[2363,38899,38900],{"scriptlevel":1852,"displaystyle":1798},[3726,38901,38902,38904],{},[898,38903,3249],{},[895,38905,38906,38908],{},[1850,38907,3938],{},[1845,38909,38910,38912],{},[898,38911,1680],{},[1850,38913,4062],{},[1701,38915,3408],{},[2363,38917,38918],{"scriptlevel":1852,"displaystyle":1798},[3726,38919,38920,38922],{},[898,38921,3249],{},[895,38923,38924,38926],{},[1850,38925,3938],{},[1845,38927,38928,38930],{},[898,38929,1680],{},[1850,38931,3938],{},[1701,38933,1792],{},[2363,38935,38936],{"scriptlevel":1852,"displaystyle":1798},[3726,38937,38938,38940],{},[898,38939,3249],{},[895,38941,38942,38944],{},[1850,38943,3938],{},[12179,38945,38946],{},[895,38947,38948,38954],{},[1845,38949,38950,38952],{},[898,38951,1680],{},[1850,38953,4062],{},[1845,38955,38956,38958],{},[898,38957,1680],{},[1850,38959,3938],{},[902,38961,38962],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,38964,38966],{"className":38965},[886],[888,38967,38968],{"xmlns":890},[892,38969,38970,38996],{},[895,38971,38972,38974,38976,38978,38980],{},[898,38973,3249],{},[1701,38975,1792],{},[1850,38977,3938],{},[898,38979,900],{},[12179,38981,38982],{},[895,38983,38984,38990],{},[1845,38985,38986,38988],{},[898,38987,1680],{},[1850,38989,4062],{},[1845,38991,38992,38994],{},[898,38993,1680],{},[1850,38995,3938],{},[902,38997,38998],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,39001,39003],{"className":39002},[886],[888,39004,39005],{"xmlns":890,"display":2252},[892,39006,39007,39152],{},[2256,39008,39009],{"width":2258},[2260,39010,39011,39013,39145,39147],{},[2263,39012],{"width":2265},[2263,39014,39015],{},[16886,39016,39017],{"notation":16888},[2363,39018,39019],{"scriptlevel":1852,"displaystyle":1798},[2363,39020,39021],{"scriptlevel":1852,"displaystyle":1798},[2363,39022,39023],{"scriptlevel":1852,"displaystyle":2011},[895,39024,39025,39027,39033,39035,39037,39053,39055,39061,39063,39069,39071,39077,39079,39081,39083,39085,39087,39093,39095,39097,39113,39115,39121,39123,39129,39131,39137,39139,39141,39143],{},[1939,39026,8058],{},[1845,39028,39029,39031],{},[898,39030,1802],{},[1850,39032,4062],{},[1701,39034,1792],{},[898,39036,900],{},[12179,39038,39039],{},[3726,39040,39041,39047],{},[1845,39042,39043,39045],{},[898,39044,1680],{},[1850,39046,3938],{},[1845,39048,39049,39051],{},[898,39050,1680],{},[1850,39052,4062],{},[1701,39054,1792],{},[1845,39056,39057,39059],{},[898,39058,1795],{},[1850,39060,4062],{},[1701,39062,1799],{"stretchy":1798},[1845,39064,39065,39067],{},[898,39066,1680],{},[1850,39068,4062],{},[1701,39070,2012],{"separator":2011},[1845,39072,39073,39075],{},[898,39074,1680],{},[1850,39076,3938],{},[1701,39078,2012],{"separator":2011},[898,39080,900],{},[1701,39082,1805],{"stretchy":1798},[1701,39084,2012],{"separator":2011},[9942,39086],{"width":19336},[1845,39088,39089,39091],{},[898,39090,1802],{},[1850,39092,3938],{},[1701,39094,1792],{},[898,39096,900],{},[12179,39098,39099],{},[3726,39100,39101,39107],{},[1845,39102,39103,39105],{},[898,39104,1680],{},[1850,39106,4062],{},[1845,39108,39109,39111],{},[898,39110,1680],{},[1850,39112,3938],{},[1701,39114,1792],{},[1845,39116,39117,39119],{},[898,39118,1795],{},[1850,39120,3938],{},[1701,39122,1799],{"stretchy":1798},[1845,39124,39125,39127],{},[898,39126,1680],{},[1850,39128,4062],{},[1701,39130,2012],{"separator":2011},[1845,39132,39133,39135],{},[898,39134,1680],{},[1850,39136,3938],{},[1701,39138,2012],{"separator":2011},[898,39140,900],{},[1701,39142,1805],{"stretchy":1798},[1939,39144,8058],{},[2263,39146],{"width":2265},[2263,39148,39149],{},[1939,39150,39151],{},"(6.30)",[902,39153,39154],{"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}",[115,39156,39158],{"id":39157},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,39160,39161,39162,39175,39176,39193,39194,39207,39208,39225,39226,39229,39230,39269,39270,39299],{},"Primární (max ",[883,39163,39165],{"className":39164},[886],[888,39166,39167],{"xmlns":890},[892,39168,39169,39173],{},[895,39170,39171],{},[898,39172,900],{},[902,39174,900],{"encoding":904}," při rozpočtu ",[883,39177,39179],{"className":39178},[886],[888,39180,39181],{"xmlns":890},[892,39182,39183,39191],{},[895,39184,39185],{},[3243,39186,39187,39189],{},[898,39188,13189],{},[1701,39190,8424],{},[902,39192,32065],{"encoding":904},") a duální (min ",[883,39195,39197],{"className":39196},[886],[888,39198,39199],{"xmlns":890},[892,39200,39201,39205],{},[895,39202,39203],{},[898,39204,3249],{},[902,39206,3249],{"encoding":904}," při užitečnosti ",[883,39209,39211],{"className":39210},[886],[888,39212,39213],{"xmlns":890},[892,39214,39215,39223],{},[895,39216,39217],{},[3243,39218,39219,39221],{},[898,39220,900],{},[1701,39222,8424],{},[902,39224,31999],{"encoding":904},") úloha jsou ",[38,39227,39228],{},"ekvivalentní",": mají tentýž bod optima ",[883,39231,39233],{"className":39232},[886],[888,39234,39235],{"xmlns":890},[892,39236,39237,39267],{},[895,39238,39239,39245,39247,39255,39257,39265],{},[3243,39240,39241,39243],{},[898,39242,1802],{},[1701,39244,8424],{},[1701,39246,2036],{"stretchy":1798},[2287,39248,39249,39251,39253],{},[898,39250,1802],{},[1850,39252,4062],{},[1701,39254,8424],{},[1701,39256,2012],{"separator":2011},[2287,39258,39259,39261,39263],{},[898,39260,1802],{},[1850,39262,3938],{},[1701,39264,8424],{},[1701,39266,2053],{"stretchy":1798},[902,39268,32361],{"encoding":904}," a v obou platí ",[883,39271,39273],{"className":39272},[886],[888,39274,39275],{"xmlns":890},[892,39276,39277,39297],{},[895,39278,39279,39281,39283,39289,39291],{},[1939,39280,14659],{},[1701,39282,1792],{},[1845,39284,39285,39287],{},[898,39286,1680],{},[1850,39288,4062],{},[898,39290,8741],{"mathvariant":2334},[1845,39292,39293,39295],{},[898,39294,1680],{},[1850,39296,3938],{},[902,39298,32035],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,39301,39302],{},[2139,39303],{"alt":39304,"className":39305,"src":39306},"imek-primarni-vs-dualni",[210,2143],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,39308,39309,39420],{},[123,39310,39311,39314,39315,39328,39329,39369,39370,1715],{},[38,39312,39313],{},"Primární"," (Marshall): zadáno ",[883,39316,39318],{"className":39317},[886],[888,39319,39320],{"xmlns":890},[892,39321,39322,39326],{},[895,39323,39324],{},[898,39325,13189],{},[902,39327,13189],{"encoding":904},", hledáme maximální ",[883,39330,39332],{"className":39331},[886],[888,39333,39334],{"xmlns":890},[892,39335,39336,39366],{},[895,39337,39338,39344,39346,39352,39354,39360,39362,39364],{},[3243,39339,39340,39342],{},[898,39341,900],{},[1701,39343,8424],{},[1701,39345,1799],{"stretchy":1798},[1845,39347,39348,39350],{},[898,39349,1680],{},[1850,39351,4062],{},[1701,39353,2012],{"separator":2011},[1845,39355,39356,39358],{},[898,39357,1680],{},[1850,39359,3938],{},[1701,39361,2012],{"separator":2011},[898,39363,13189],{},[1701,39365,1805],{"stretchy":1798},[902,39367,39368],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,39371,39373],{"className":39372},[886],[888,39374,39375],{"xmlns":890},[892,39376,39377,39417],{},[895,39378,39379,39385,39387,39395,39397,39403,39405,39411,39413,39415],{},[1845,39380,39381,39383],{},[898,39382,1802],{},[898,39384,21836],{},[1701,39386,1792],{},[2287,39388,39389,39391,39393],{},[898,39390,1795],{},[898,39392,21836],{},[898,39394,6909],{},[1701,39396,1799],{"stretchy":1798},[1845,39398,39399,39401],{},[898,39400,1680],{},[1850,39402,4062],{},[1701,39404,2012],{"separator":2011},[1845,39406,39407,39409],{},[898,39408,1680],{},[1850,39410,3938],{},[1701,39412,2012],{"separator":2011},[898,39414,13189],{},[1701,39416,1805],{"stretchy":1798},[902,39418,39419],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,39421,39422,39425,39426,39439,39440,39369,39480,1715],{},[38,39423,39424],{},"Duální"," (Hicks): zadáno ",[883,39427,39429],{"className":39428},[886],[888,39430,39431],{"xmlns":890},[892,39432,39433,39437],{},[895,39434,39435],{},[898,39436,900],{},[902,39438,900],{"encoding":904},", hledáme minimální ",[883,39441,39443],{"className":39442},[886],[888,39444,39445],{"xmlns":890},[892,39446,39447,39477],{},[895,39448,39449,39455,39457,39463,39465,39471,39473,39475],{},[3243,39450,39451,39453],{},[898,39452,3249],{},[1701,39454,8424],{},[1701,39456,1799],{"stretchy":1798},[1845,39458,39459,39461],{},[898,39460,1680],{},[1850,39462,4062],{},[1701,39464,2012],{"separator":2011},[1845,39466,39467,39469],{},[898,39468,1680],{},[1850,39470,3938],{},[1701,39472,2012],{"separator":2011},[898,39474,900],{},[1701,39476,1805],{"stretchy":1798},[902,39478,39479],{"encoding":904},"E^*(P_1, P_2, U)",[883,39481,39483],{"className":39482},[886],[888,39484,39485],{"xmlns":890},[892,39486,39487,39528],{},[895,39488,39489,39495,39497,39506,39508,39514,39516,39522,39524,39526],{},[1845,39490,39491,39493],{},[898,39492,1802],{},[898,39494,21836],{},[1701,39496,1792],{},[2287,39498,39499,39501,39503],{},[898,39500,1795],{},[898,39502,21836],{},[898,39504,39505],{},"H",[1701,39507,1799],{"stretchy":1798},[1845,39509,39510,39512],{},[898,39511,1680],{},[1850,39513,4062],{},[1701,39515,2012],{"separator":2011},[1845,39517,39518,39520],{},[898,39519,1680],{},[1850,39521,3938],{},[1701,39523,2012],{"separator":2011},[898,39525,900],{},[1701,39527,1805],{"stretchy":1798},[902,39529,39530],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,39532,39533,39534,39537,39538,39541],{},"Proč se studují obě? Marshallova poptávka je ",[38,39535,39536],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,39539,39540],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,39543,39545],{"id":39544},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,39547,39549],{"id":39548},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,39551,39552,39555,39556,39588,39589,39627,39628,39654],{},[38,39553,39554],{},"6.8"," Jsou dány užitečnost ",[883,39557,39559],{"className":39558},[886],[888,39560,39561],{"xmlns":890},[892,39562,39563,39585],{},[895,39564,39565,39567,39569,39577],{},[898,39566,900],{},[1701,39568,1792],{},[2287,39570,39571,39573,39575],{},[898,39572,1802],{},[1850,39574,4062],{},[1850,39576,3684],{},[2287,39578,39579,39581,39583],{},[898,39580,1802],{},[1850,39582,3938],{},[1850,39584,3684],{},[902,39586,39587],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,39590,39592],{"className":39591},[886],[888,39593,39594],{"xmlns":890},[892,39595,39596,39624],{},[895,39597,39598,39606,39608,39610,39612,39620,39622],{},[2287,39599,39600,39602,39604],{},[898,39601,1680],{},[1850,39603,4062],{},[1701,39605,8424],{},[1701,39607,1792],{},[1850,39609,6460],{},[1701,39611,2012],{"separator":2011},[2287,39613,39614,39616,39618],{},[898,39615,1680],{},[1850,39617,3938],{},[1701,39619,8424],{},[1701,39621,1792],{},[1850,39623,3703],{},[902,39625,39626],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,39629,39631],{"className":39630},[886],[888,39632,39633],{"xmlns":890},[892,39634,39635,39651],{},[895,39636,39637,39643,39645],{},[1845,39638,39639,39641],{},[898,39640,1802],{},[1850,39642,4062],{},[1701,39644,2012],{"separator":2011},[1845,39646,39647,39649],{},[898,39648,1802],{},[1850,39650,3938],{},[902,39652,39653],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,39656,39657,39660,39661,39703,39704,39735,39736,39758,39759,1715],{},[38,39658,39659],{},"6.9"," Jsou dány rozpočtové omezení ",[883,39662,39664],{"className":39663},[886],[888,39665,39666],{"xmlns":890},[892,39667,39668,39700],{},[895,39669,39670,39672,39674,39680,39686,39688,39694],{},[898,39671,13189],{},[1701,39673,1792],{},[1845,39675,39676,39678],{},[898,39677,1680],{},[1850,39679,4062],{},[1845,39681,39682,39684],{},[898,39683,1802],{},[1850,39685,4062],{},[1701,39687,1703],{},[1845,39689,39690,39692],{},[898,39691,1680],{},[1850,39693,3938],{},[1845,39695,39696,39698],{},[898,39697,1802],{},[1850,39699,3938],{},[902,39701,39702],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,39705,39707],{"className":39706},[886],[888,39708,39709],{"xmlns":890},[892,39710,39711,39733],{},[895,39712,39713,39715,39717,39725],{},[898,39714,900],{},[1701,39716,1792],{},[2287,39718,39719,39721,39723],{},[898,39720,1802],{},[1850,39722,4062],{},[1850,39724,3684],{},[2287,39726,39727,39729,39731],{},[898,39728,1802],{},[1850,39730,3938],{},[1850,39732,3684],{},[902,39734,39587],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,39737,39739],{"className":39738},[886],[888,39740,39741],{"xmlns":890},[892,39742,39743,39755],{},[895,39744,39745,39751,39753],{},[3243,39746,39747,39749],{},[898,39748,13189],{},[1701,39750,8424],{},[1701,39752,1792],{},[1850,39754,19162],{},[902,39756,39757],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,39760,39762],{"className":39761},[886],[888,39763,39764],{"xmlns":890},[892,39765,39766,39794],{},[895,39767,39768,39776,39778,39780,39782,39790,39792],{},[2287,39769,39770,39772,39774],{},[898,39771,1680],{},[1850,39773,4062],{},[1701,39775,8424],{},[1701,39777,1792],{},[1850,39779,4225],{},[1701,39781,2012],{"separator":2011},[2287,39783,39784,39786,39788],{},[898,39785,1680],{},[1850,39787,3938],{},[1701,39789,8424],{},[1701,39791,1792],{},[1850,39793,3703],{},[902,39795,39796],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,39798,39799,39802,39803,2020,39835,39865,39866,1715],{},[38,39800,39801],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,39804,39806],{"className":39805},[886],[888,39807,39808],{"xmlns":890},[892,39809,39810,39832],{},[895,39811,39812,39814,39816,39824],{},[898,39813,900],{},[1701,39815,1792],{},[2287,39817,39818,39820,39822],{},[898,39819,1802],{},[1850,39821,4062],{},[898,39823,207],{},[2287,39825,39826,39828,39830],{},[898,39827,1802],{},[1850,39829,3938],{},[898,39831,3598],{},[902,39833,39834],{"encoding":904},"U = Q_1^a Q_2^b",[883,39836,39838],{"className":39837},[886],[888,39839,39840],{"xmlns":890},[892,39841,39842,39862],{},[895,39843,39844,39846,39848,39850,39852,39854,39856,39858,39860],{},[898,39845,207],{},[1701,39847,2012],{"separator":2011},[898,39849,3598],{},[1701,39851,10569],{},[1701,39853,9389],{"stretchy":1798},[1850,39855,1852],{},[1701,39857,2012],{"separator":2011},[1850,39859,4062],{},[1701,39861,9406],{"stretchy":1798},[902,39863,39864],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,39867,39869],{"className":39868},[886],[888,39870,39871],{"xmlns":890},[892,39872,39873,39905],{},[895,39874,39875,39877,39879,39885,39891,39893,39899],{},[898,39876,13189],{},[1701,39878,1792],{},[1845,39880,39881,39883],{},[898,39882,1680],{},[1850,39884,4062],{},[1845,39886,39887,39889],{},[898,39888,1802],{},[1850,39890,4062],{},[1701,39892,1703],{},[1845,39894,39895,39897],{},[898,39896,1680],{},[1850,39898,3938],{},[1845,39900,39901,39903],{},[898,39902,1802],{},[1850,39904,3938],{},[902,39906,39702],{"encoding":904},[724,39908,39909,39912,39913,2020,39947,39865,39965,1715],{},[38,39910,39911],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,39914,39916],{"className":39915},[886],[888,39917,39918],{"xmlns":890},[892,39919,39920,39944],{},[895,39921,39922,39924,39926,39934,39936],{},[898,39923,900],{},[1701,39925,1792],{},[2287,39927,39928,39930,39932],{},[898,39929,1802],{},[1850,39931,4062],{},[898,39933,207],{},[1701,39935,1703],{},[2287,39937,39938,39940,39942],{},[898,39939,1802],{},[1850,39941,3938],{},[898,39943,207],{},[902,39945,39946],{"encoding":904},"U = Q_1^a + Q_2^a",[883,39948,39950],{"className":39949},[886],[888,39951,39952],{"xmlns":890},[892,39953,39954,39962],{},[895,39955,39956,39958,39960],{},[898,39957,207],{},[1701,39959,7454],{"mathvariant":2334},[1850,39961,1852],{},[902,39963,39964],{"encoding":904},"a \\neq 0",[883,39966,39968],{"className":39967},[886],[888,39969,39970],{"xmlns":890},[892,39971,39972,40004],{},[895,39973,39974,39976,39978,39984,39990,39992,39998],{},[898,39975,13189],{},[1701,39977,1792],{},[1845,39979,39980,39982],{},[898,39981,1680],{},[1850,39983,4062],{},[1845,39985,39986,39988],{},[898,39987,1802],{},[1850,39989,4062],{},[1701,39991,1703],{},[1845,39993,39994,39996],{},[898,39995,1680],{},[1850,39997,3938],{},[1845,39999,40000,40002],{},[898,40001,1802],{},[1850,40003,3938],{},[902,40005,39702],{"encoding":904},[198,40007,40009],{"id":40008},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,40011,40012,39555,40015,1343,40042,40064,40065,1343,40088,40112,40113,40138,40139,1715],{},[38,40013,40014],{},"6.12",[883,40016,40018],{"className":40017},[886],[888,40019,40020],{"xmlns":890},[892,40021,40022,40040],{},[895,40023,40024,40026,40028,40034],{},[898,40025,900],{},[1701,40027,1792],{},[1845,40029,40030,40032],{},[898,40031,1802],{},[1850,40033,4062],{},[1845,40035,40036,40038],{},[898,40037,1802],{},[1850,40039,3938],{},[902,40041,34257],{"encoding":904},[883,40043,40045],{"className":40044},[886],[888,40046,40047],{"xmlns":890},[892,40048,40049,40061],{},[895,40050,40051,40057,40059],{},[3243,40052,40053,40055],{},[898,40054,900],{},[1701,40056,8424],{},[1701,40058,1792],{},[1850,40060,3703],{},[902,40062,40063],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,40066,40068],{"className":40067},[886],[888,40069,40070],{"xmlns":890},[892,40071,40072,40086],{},[895,40073,40074,40082,40084],{},[2287,40075,40076,40078,40080],{},[898,40077,1680],{},[1850,40079,4062],{},[1701,40081,8424],{},[1701,40083,1792],{},[1850,40085,3938],{},[902,40087,34330],{"encoding":904},[883,40089,40091],{"className":40090},[886],[888,40092,40093],{"xmlns":890},[892,40094,40095,40109],{},[895,40096,40097,40105,40107],{},[2287,40098,40099,40101,40103],{},[898,40100,1680],{},[1850,40102,3938],{},[1701,40104,8424],{},[1701,40106,1792],{},[1850,40108,6460],{},[902,40110,40111],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,40114,40116],{"className":40115},[886],[888,40117,40118],{"xmlns":890},[892,40119,40120,40136],{},[895,40121,40122,40128,40130],{},[1845,40123,40124,40126],{},[898,40125,1802],{},[1850,40127,4062],{},[1701,40129,2012],{"separator":2011},[1845,40131,40132,40134],{},[898,40133,1802],{},[1850,40135,3938],{},[902,40137,39653],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,40140,40142],{"className":40141},[886],[888,40143,40144],{"xmlns":890},[892,40145,40146,40166],{},[895,40147,40148,40150,40152,40158,40160],{},[898,40149,900],{},[1701,40151,1792],{},[1845,40153,40154,40156],{},[898,40155,1802],{},[1850,40157,4062],{},[1701,40159,3408],{},[1845,40161,40162,40164],{},[898,40163,1802],{},[1850,40165,3938],{},[902,40167,40168],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,40170,40171,40174,40175,40216,40217,40239,40240,1715],{},[38,40172,40173],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,40176,40178],{"className":40177},[886],[888,40179,40180],{"xmlns":890},[892,40181,40182,40214],{},[895,40183,40184,40186,40188,40194,40200,40202,40208],{},[898,40185,3249],{},[1701,40187,1792],{},[1845,40189,40190,40192],{},[898,40191,1680],{},[1850,40193,4062],{},[1845,40195,40196,40198],{},[898,40197,1802],{},[1850,40199,4062],{},[1701,40201,1703],{},[1845,40203,40204,40206],{},[898,40205,1680],{},[1850,40207,3938],{},[1845,40209,40210,40212],{},[898,40211,1802],{},[1850,40213,3938],{},[902,40215,31980],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,40218,40220],{"className":40219},[886],[888,40221,40222],{"xmlns":890},[892,40223,40224,40236],{},[895,40225,40226,40232,40234],{},[3243,40227,40228,40230],{},[898,40229,900],{},[1701,40231,8424],{},[1701,40233,1792],{},[1850,40235,9071],{},[902,40237,40238],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,40241,40243],{"className":40242},[886],[888,40244,40245],{"xmlns":890},[892,40246,40247,40276],{},[895,40248,40249,40257,40259,40261,40263,40271,40273],{},[2287,40250,40251,40253,40255],{},[898,40252,1680],{},[1850,40254,4062],{},[1701,40256,8424],{},[1701,40258,1792],{},[1850,40260,13096],{},[1701,40262,2012],{"separator":2011},[2287,40264,40265,40267,40269],{},[898,40266,1680],{},[1850,40268,3938],{},[1701,40270,8424],{},[1701,40272,1792],{},[1850,40274,40275],{},"15",[902,40277,40278],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,40280,5578],{"id":5577},[120,40282,40283,40340,40379,40399,40434,40488,40493,40499,40595,40640],{},[123,40284,40285,4088,40288,40337,40338,1715],{},[38,40286,40287],{},"Rozpočtové omezení (budget constraint)",[883,40289,40291],{"className":40290},[886],[888,40292,40293],{"xmlns":890},[892,40294,40295,40335],{},[895,40296,40297,40303,40305,40313,40319,40321,40329],{},[3243,40298,40299,40301],{},[898,40300,13189],{},[1701,40302,8424],{},[1701,40304,1792],{},[2287,40306,40307,40309,40311],{},[898,40308,1680],{},[1850,40310,4062],{},[1701,40312,8424],{},[1845,40314,40315,40317],{},[898,40316,1802],{},[1850,40318,4062],{},[1701,40320,1703],{},[2287,40322,40323,40325,40327],{},[898,40324,1680],{},[1850,40326,3938],{},[1701,40328,8424],{},[1845,40330,40331,40333],{},[898,40332,1802],{},[1850,40334,3938],{},[902,40336,21344],{"encoding":904}," — (6.12); ",[38,40339,32170],{},[123,40341,40342,40345,40346,1715],{},[38,40343,40344],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,40347,40349],{"className":40348},[886],[888,40350,40351],{"xmlns":890},[892,40352,40353,40377],{},[895,40354,40355,40357,40359,40367,40369],{},[1939,40356,14659],{},[1701,40358,1792],{},[2287,40360,40361,40363,40365],{},[898,40362,1680],{},[1850,40364,4062],{},[1701,40366,8424],{},[898,40368,8741],{"mathvariant":2334},[2287,40370,40371,40373,40375],{},[898,40372,1680],{},[1850,40374,3938],{},[1701,40376,8424],{},[902,40378,33013],{"encoding":904},[123,40380,40381,40396,40397,1715],{},[38,40382,33157,40383],{},[883,40384,40386],{"className":40385},[886],[888,40387,40388],{"xmlns":890},[892,40389,40390,40394],{},[895,40391,40392],{},[898,40393,20489],{},[902,40395,20542],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,40398,33178],{},[123,40400,40401,40404,40405,1715],{},[38,40402,40403],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,40406,40408],{"className":40407},[886],[888,40409,40410],{"xmlns":890},[892,40411,40412,40432],{},[895,40413,40414,40416,40418,40424,40426],{},[1939,40415,14659],{},[1701,40417,1792],{},[1845,40419,40420,40422],{},[898,40421,1680],{},[1850,40423,4062],{},[898,40425,8741],{"mathvariant":2334},[1845,40427,40428,40430],{},[898,40429,1680],{},[1850,40431,3938],{},[902,40433,32035],{"encoding":904},[123,40435,40436,2979,40439,40487],{},[38,40437,40438],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,40440,40442],{"className":40441},[886],[888,40443,40444],{"xmlns":890},[892,40445,40446,40484],{},[895,40447,40448,40454,40456,40462,40464,40470,40472,40478,40480,40482],{},[1845,40449,40450,40452],{},[898,40451,1802],{},[898,40453,21836],{},[1701,40455,1792],{},[1845,40457,40458,40460],{},[898,40459,1795],{},[898,40461,21836],{},[1701,40463,1799],{"stretchy":1798},[1845,40465,40466,40468],{},[898,40467,1680],{},[1850,40469,4062],{},[1701,40471,2012],{"separator":2011},[1845,40473,40474,40476],{},[898,40475,1680],{},[1850,40477,3938],{},[1701,40479,2012],{"separator":2011},[898,40481,13189],{},[1701,40483,1805],{"stretchy":1798},[902,40485,40486],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,40489,40490,40492],{},[38,40491,35758],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,40494,40495,40498],{},[38,40496,40497],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,40500,40501,2979,40503,40550,40551,40594],{},[38,40502,38070],{},[883,40504,40506],{"className":40505},[886],[888,40507,40508],{"xmlns":890},[892,40509,40510,40548],{},[895,40511,40512,40518,40520,40526,40528,40534,40536,40542,40544,40546],{},[1845,40513,40514,40516],{},[898,40515,1802],{},[898,40517,21836],{},[1701,40519,1792],{},[1845,40521,40522,40524],{},[898,40523,1795],{},[898,40525,21836],{},[1701,40527,1799],{"stretchy":1798},[1845,40529,40530,40532],{},[898,40531,1680],{},[1850,40533,4062],{},[1701,40535,2012],{"separator":2011},[1845,40537,40538,40540],{},[898,40539,1680],{},[1850,40541,3938],{},[1701,40543,2012],{"separator":2011},[898,40545,900],{},[1701,40547,1805],{"stretchy":1798},[902,40549,21869],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,40552,40554],{"className":40553},[886],[888,40555,40556],{"xmlns":890},[892,40557,40558,40592],{},[895,40559,40560,40562,40564,40578],{},[898,40561,900],{},[1701,40563,1792],{},[2287,40565,40566,40568,40570],{},[898,40567,1802],{},[1850,40569,4062],{},[895,40571,40572,40574,40576],{},[1850,40573,4062],{},[898,40575,8741],{"mathvariant":2334},[1850,40577,3938],{},[2287,40579,40580,40582,40584],{},[898,40581,1802],{},[1850,40583,3938],{},[895,40585,40586,40588,40590],{},[1850,40587,4062],{},[898,40589,8741],{"mathvariant":2334},[1850,40591,3938],{},[902,40593,37190],{"encoding":904},": (6.30).",[123,40596,40597,40639],{},[38,40598,40599,40600],{},"Bod dotyku ",[883,40601,40603],{"className":40602},[886],[888,40604,40605],{"xmlns":890},[892,40606,40607,40637],{},[895,40608,40609,40615,40617,40625,40627,40635],{},[3243,40610,40611,40613],{},[898,40612,1802],{},[1701,40614,8424],{},[1701,40616,2036],{"stretchy":1798},[2287,40618,40619,40621,40623],{},[898,40620,1802],{},[1850,40622,4062],{},[1701,40624,8424],{},[1701,40626,2012],{"separator":2011},[2287,40628,40629,40631,40633],{},[898,40630,1802],{},[1850,40632,3938],{},[1701,40634,8424],{},[1701,40636,2053],{"stretchy":1798},[902,40638,32361],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,40641,40642,40645,40646,40659,40660,40673],{},[38,40643,40644],{},"Dualita"," — ekvivalence max ",[883,40647,40649],{"className":40648},[886],[888,40650,40651],{"xmlns":890},[892,40652,40653,40657],{},[895,40654,40655],{},[898,40656,900],{},[902,40658,900],{"encoding":904}," a min ",[883,40661,40663],{"className":40662},[886],[888,40664,40665],{"xmlns":890},[892,40666,40667,40671],{},[895,40668,40669],{},[898,40670,3249],{},[902,40672,3249],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,40675,5984],{"id":5983},[120,40677,40678,40701,40716,40729,40740],{},[123,40679,40680,4088,40683,40686,40687,40700],{},[38,40681,40682],{},"Teorie před optimalizací:",[207,40684,880],{"className":40685,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,40688,40690],{"className":40689},[886],[888,40691,40692],{"xmlns":890},[892,40693,40694,40698],{},[895,40695,40696],{},[898,40697,900],{},[902,40699,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,40702,40703,4088,40705,40708,40709,40712,40713,1715],{},[38,40704,5999],{},[207,40706,793],{"className":40707,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,40710,784],{"className":40711,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,40714,6007],{"className":40715,"dataFsResolvedFilePath":764,"href":765},[210],[123,40717,40718,4088,40721,40724,40725,40728],{},[38,40719,40720],{},"Paralely:",[207,40722,15144],{"className":40723,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,40726,15996],{"className":40727,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,40730,40731,4088,40734,1343,40737],{},[38,40732,40733],{},"Přednášky:",[207,40735,1094],{"className":40736,"dataFsResolvedFilePath":838,"href":839},[210],[207,40738,1101],{"className":40739,"dataFsResolvedFilePath":868,"href":869},[210],[123,40741,40742,4088,40744],{},[38,40743,6031],{},[207,40745,6037],{"className":40746,"dataFsResolvedFilePath":6035,"href":6036},[210],{"title":641,"searchDepth":642,"depth":642,"links":40748},[40749,40750,40751,40756,40757,40758,40760,40763,40766,40768,40769,40771,40772,40776,40777],{"id":16060,"depth":642,"text":16061},{"id":32043,"depth":642,"text":32044},{"id":32438,"depth":642,"text":32439,"children":40752},[40753,40754],{"id":32558,"depth":649,"text":32559},{"id":33139,"depth":649,"text":40755},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":33600,"depth":642,"text":33601},{"id":33911,"depth":642,"text":33912},{"id":34228,"depth":642,"text":40759},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":35001,"depth":642,"text":35002,"children":40761},[40762],{"id":35757,"depth":649,"text":35758},{"id":35937,"depth":642,"text":35938,"children":40764},[40765],{"id":36194,"depth":649,"text":36195},{"id":37145,"depth":642,"text":40767},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":38069,"depth":642,"text":38070},{"id":38272,"depth":642,"text":40770},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":39157,"depth":642,"text":39158},{"id":39544,"depth":642,"text":39545,"children":40773},[40774,40775],{"id":39548,"depth":649,"text":39549},{"id":40008,"depth":649,"text":40009},{"id":5577,"depth":642,"text":5578},{"id":5983,"depth":642,"text":5984},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":31804,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,40784,1144,13831,40785,40786,40787],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":40790,"title":802,"body":40791,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":54799,"navigation":664,"path":54800,"seo":54801,"sources":54802,"stem":54803,"tags":54804,"type":6074,"updated":677,"__hash__":54809},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":40792,"toc":54755},[40793,40796,40822,40826,40833,40985,40999,41001,41003,41089,41093,41129,41202,41223,41348,41358,41371,41375,41380,41410,41472,41481,41485,41547,41554,41575,41693,41770,41774,41777,41836,41951,41956,41988,42049,42097,42152,42156,42177,42201,42249,42253,42265,42269,42378,42382,42398,42439,42450,42609,42619,42624,42628,42750,42760,42767,42771,42849,42860,42940,42946,42953,43091,43098,43101,43158,43162,43240,43286,43330,43336,43449,43453,43456,43651,43655,43892,43895,44049,44202,44204,44206,44285,44288,44393,44462,44471,44475,44478,44539,44548,44552,44585,44663,44702,44706,44755,44809,44813,44842,44871,44923,44930,44984,45062,45066,45108,45175,45219,45323,45342,45344,45348,45456,45460,45528,45577,45584,45669,45673,45745,45750,45798,45986,45990,45995,46171,46176,46235,46340,46344,46371,46375,46382,46545,46632,46637,46639,46642,46742,46892,46964,47038,47040,47044,47058,47062,47195,47250,47362,47439,47443,47500,47603,47662,47823,47827,47902,47974,48072,48130,48224,48277,48298,48352,48357,48433,48479,48565,48601,48685,48837,48871,48923,48926,48928,48930,48975,48980,48987,49072,49079,49164,49171,49173,49177,49402,49404,49408,49412,49481,49532,49735,49741,49752,49820,49826,50248,50252,50316,50340,50536,50542,50556,50624,50627,50667,50891,50959,51261,51670,51746,51912,51918,51921,51996,52449,52500,52903,53008,53671,53674,53751,53759,53833,53864,53866,53870,53914,53916,53918,53922,54152,54156,54247,54252,54346,54351,54524,54528,54646,54651,54700,54702,54704],[12,40794,802],{"id":40795},"poptávka-nabídka-a-tržní-rovnováha",[1635,40797,40798],{},[724,40799,40800,40802,40803,40806,40807,40810,40811,40814,40815,40817,40818,40821],{},[883,40801,2063],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,40804,40805],{},"poptávka",") a výrobce (",[38,40808,40809],{},"nabídka","), jejich interakci v ",[38,40812,40813],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,40816,22023],{},"). Uzavírá ji pojem ",[38,40819,40820],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,40823,40825],{"id":40824},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,40827,40828,40829,40832],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,40830,40831],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,40834,40835,40852,40894,40910],{},[123,40836,40837,40838,40851],{},"cena ",[883,40839,40841],{"className":40840},[886],[888,40842,40843],{"xmlns":890},[892,40844,40845,40849],{},[895,40846,40847],{},[898,40848,1680],{},[902,40850,1680],{"encoding":904}," zkoumaného zboží,",[123,40853,40854,40855,2012],{},"ceny alternativních zboží ",[883,40856,40858],{"className":40857},[886],[888,40859,40860],{"xmlns":890},[892,40861,40862,40891],{},[895,40863,40864,40870,40872,40878,40880,40882,40884],{},[1845,40865,40866,40868],{},[898,40867,1680],{},[1850,40869,4062],{},[1701,40871,2012],{"separator":2011},[1845,40873,40874,40876],{},[898,40875,1680],{},[1850,40877,3938],{},[1701,40879,2012],{"separator":2011},[1701,40881,13704],{},[1701,40883,2012],{"separator":2011},[1845,40885,40886,40888],{},[898,40887,1680],{},[898,40889,40890],{},"n",[902,40892,40893],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,40895,40896,40897,2012],{},"důchod ",[883,40898,40900],{"className":40899},[886],[888,40901,40902],{"xmlns":890},[892,40903,40904,40908],{},[895,40905,40906],{},[898,40907,13189],{},[902,40909,13189],{"encoding":904},[123,40911,40912,40913,40926,40927,40940,40941,40954,40955,40969,40970,40984],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,40914,40916],{"className":40915},[886],[888,40917,40918],{"xmlns":890},[892,40919,40920,40924],{},[895,40921,40922],{},[898,40923,13853],{},[902,40925,13853],{"encoding":904},", kapitál ",[883,40928,40930],{"className":40929},[886],[888,40931,40932],{"xmlns":890},[892,40933,40934,40938],{},[895,40935,40936],{},[898,40937,13858],{},[902,40939,13858],{"encoding":904},", půda ",[883,40942,40944],{"className":40943},[886],[888,40945,40946],{"xmlns":890},[892,40947,40948,40952],{},[895,40949,40950],{},[898,40951,3249],{},[902,40953,3249],{"encoding":904},"), technologie, počet výrobců ",[883,40956,40958],{"className":40957},[886],[888,40959,40960],{"xmlns":890},[892,40961,40962,40967],{},[895,40963,40964],{},[898,40965,40966],{},"O",[902,40968,40966],{"encoding":904},", počasí ",[883,40971,40973],{"className":40972},[886],[888,40974,40975],{"xmlns":890},[892,40976,40977,40982],{},[895,40978,40979],{},[898,40980,40981],{},"W",[902,40983,40981],{"encoding":904}," atd.",[724,40986,40987,40988,40991,40992,40995,40996,1715],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,40989,40990],{},"ceteris paribus","), hovoříme o ",[38,40993,40994],{},"jednofaktorovém modelu","; jinak jde o model ",[38,40997,40998],{},"vícefaktorový",[1771,41000],{},[115,41002,17215],{"id":40805},[1635,41004,41005],{},[724,41006,41007,41009,41010,41023,41024,41037,41038,41041,41042,41065,41066,1715],{},[883,41008,2063],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,41011,41013],{"className":41012},[886],[888,41014,41015],{"xmlns":890},[892,41016,41017,41021],{},[895,41018,41019],{},[898,41020,1802],{},[902,41022,1802],{"encoding":904}," na ceně ",[883,41025,41027],{"className":41026},[886],[888,41028,41029],{"xmlns":890},[892,41030,41031,41035],{},[895,41032,41033],{},[898,41034,1680],{},[902,41036,1680],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,41039,41040],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,41043,41045],{"className":41044},[886],[888,41046,41047],{"xmlns":890},[892,41048,41049,41063],{},[895,41050,41051,41053,41055,41057,41059,41061],{},[898,41052,1802],{},[1701,41054,1792],{},[898,41056,1795],{},[1701,41058,1799],{"stretchy":1798},[898,41060,1680],{},[1701,41062,1805],{"stretchy":1798},[902,41064,8264],{"encoding":904}," a jeho lineární verzí ",[883,41067,41069],{"className":41068},[886],[888,41070,41071],{"xmlns":890},[892,41072,41073,41087],{},[895,41074,41075,41077,41079,41081,41083,41085],{},[898,41076,1680],{},[1701,41078,1792],{},[898,41080,207],{},[898,41082,1802],{},[1701,41084,1703],{},[898,41086,3598],{},[902,41088,3601],{"encoding":904},[198,41090,41092],{"id":41091},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,41094,41095,41096,41109,41110,41123,41124,1646,41126,4539],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,41097,41099],{"className":41098},[886],[888,41100,41101],{"xmlns":890},[892,41102,41103,41107],{},[895,41104,41105],{},[898,41106,1802],{},[902,41108,1802],{"encoding":904}," závisí na ceně ",[883,41111,41113],{"className":41112},[886],[888,41114,41115],{"xmlns":890},[892,41116,41117,41121],{},[895,41118,41119],{},[898,41120,1680],{},[902,41122,1680],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,41125,32039],{},[614,41127,41128],{},"demand function",[883,41130,41132],{"className":41131},[886],[888,41133,41134],{"xmlns":890,"display":2252},[892,41135,41136,41199],{},[2256,41137,41138],{"width":2258},[2260,41139,41140,41142,41192,41194],{},[2263,41141],{"width":2265},[2263,41143,41144],{},[895,41145,41146,41148,41150,41152,41154,41156,41158,41164,41166,41172,41174,41176,41178,41184,41186,41188,41190],{},[898,41147,1802],{},[1701,41149,1792],{},[898,41151,1795],{},[1701,41153,1799],{"stretchy":1798},[898,41155,1680],{},[1701,41157,2012],{"separator":2011},[1845,41159,41160,41162],{},[898,41161,1680],{},[1850,41163,4062],{},[1701,41165,2012],{"separator":2011},[1845,41167,41168,41170],{},[898,41169,1680],{},[1850,41171,3938],{},[1701,41173,2012],{"separator":2011},[1701,41175,13704],{},[1701,41177,2012],{"separator":2011},[1845,41179,41180,41182],{},[898,41181,1680],{},[898,41183,40890],{},[1701,41185,2012],{"separator":2011},[898,41187,13189],{},[1701,41189,1805],{"stretchy":1798},[898,41191,1715],{"mathvariant":2334},[2263,41193],{"width":2265},[2263,41195,41196],{},[1939,41197,41198],{},"(2.1)",[902,41200,41201],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,41203,41204,41205,41208,41209,41222],{},"Důležitou vlastností je ",[38,41206,41207],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,41210,41212],{"className":41211},[886],[888,41213,41214],{"xmlns":890},[892,41215,41216,41220],{},[895,41217,41218],{},[898,41219,16096],{},[902,41221,16096],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,41224,41226],{"className":41225},[886],[888,41227,41228],{"xmlns":890,"display":2252},[892,41229,41230,41345],{},[2256,41231,41232],{"width":2258},[2260,41233,41234,41236,41338,41340],{},[2263,41235],{"width":2265},[2263,41237,41238],{},[895,41239,41240,41242,41244,41246,41248,41250,41252,41254,41256,41262,41264,41266,41272,41274,41276,41278,41280,41286,41288,41290,41292,41294,41296,41298,41300,41302,41304,41310,41312,41318,41320,41322,41324,41330,41332,41334,41336],{},[898,41241,1802],{},[1701,41243,1792],{},[898,41245,1795],{},[1701,41247,1799],{"stretchy":1798},[898,41249,16096],{},[898,41251,1680],{},[1701,41253,2012],{"separator":2011},[898,41255,16096],{},[1845,41257,41258,41260],{},[898,41259,1680],{},[1850,41261,4062],{},[1701,41263,2012],{"separator":2011},[898,41265,16096],{},[1845,41267,41268,41270],{},[898,41269,1680],{},[1850,41271,3938],{},[1701,41273,2012],{"separator":2011},[1701,41275,13704],{},[1701,41277,2012],{"separator":2011},[898,41279,16096],{},[1845,41281,41282,41284],{},[898,41283,1680],{},[898,41285,40890],{},[1701,41287,2012],{"separator":2011},[898,41289,16096],{},[898,41291,13189],{},[1701,41293,1805],{"stretchy":1798},[1701,41295,1792],{},[898,41297,1795],{},[1701,41299,1799],{"stretchy":1798},[898,41301,1680],{},[1701,41303,2012],{"separator":2011},[1845,41305,41306,41308],{},[898,41307,1680],{},[1850,41309,4062],{},[1701,41311,2012],{"separator":2011},[1845,41313,41314,41316],{},[898,41315,1680],{},[1850,41317,3938],{},[1701,41319,2012],{"separator":2011},[1701,41321,13704],{},[1701,41323,2012],{"separator":2011},[1845,41325,41326,41328],{},[898,41327,1680],{},[898,41329,40890],{},[1701,41331,2012],{"separator":2011},[898,41333,13189],{},[1701,41335,1805],{"stretchy":1798},[898,41337,1715],{"mathvariant":2334},[2263,41339],{"width":2265},[2263,41341,41342],{},[1939,41343,41344],{},"(2.2)",[902,41346,41347],{"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}",[1635,41349,41350],{},[724,41351,41352,41354,41355,1715],{},[883,41353,4695],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,41356,41357],{},"v jednofaktorových modelech neplatí",[724,41359,41360,41361,1343,41364,2633,41367,41370],{},"Rozlišuje se poptávka ",[38,41362,41363],{},"individuální",[38,41365,41366],{},"tržní",[38,41368,41369],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,41372,41374],{"id":41373},"jednofaktorové-modely","Jednofaktorové modely",[41376,41377,41379],"h4",{"id":41378},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,41381,41382,41383,41396,41397,2246],{},"Poptávané množství ",[883,41384,41386],{"className":41385},[886],[888,41387,41388],{"xmlns":890},[892,41389,41390,41394],{},[895,41391,41392],{},[898,41393,1802],{},[902,41395,1802],{"encoding":904}," závisí pouze na ceně ",[883,41398,41400],{"className":41399},[886],[888,41401,41402],{"xmlns":890},[892,41403,41404,41408],{},[895,41405,41406],{},[898,41407,1680],{},[902,41409,1680],{"encoding":904},[883,41411,41413],{"className":41412},[886],[888,41414,41415],{"xmlns":890,"display":2252},[892,41416,41417,41469],{},[2256,41418,41419],{"width":2258},[2260,41420,41421,41423,41462,41464],{},[2263,41422],{"width":2265},[2263,41424,41425],{},[895,41426,41427,41429,41431,41433,41435,41437,41439,41441,41443,41446,41448,41450,41452,41454,41456,41458,41460],{},[898,41428,1802],{},[1701,41430,1792],{},[898,41432,1795],{},[1701,41434,1799],{"stretchy":1798},[898,41436,1680],{},[1701,41438,1805],{"stretchy":1798},[1701,41440,2012],{"separator":2011},[9942,41442],{"width":9944},[1939,41444,41445],{},"resp.",[9942,41447],{"width":9944},[898,41449,1680],{},[1701,41451,1792],{},[898,41453,1795],{},[1701,41455,1799],{"stretchy":1798},[898,41457,1802],{},[1701,41459,1805],{"stretchy":1798},[898,41461,1715],{"mathvariant":2334},[2263,41463],{"width":2265},[2263,41465,41466],{},[1939,41467,41468],{},"(2.3)",[902,41470,41471],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,41473,41474,41475,1646,41478,2506],{},"Graf této funkce se nazývá ",[38,41476,41477],{},"křivka poptávky",[614,41479,41480],{},"demand curve",[41376,41482,41484],{"id":41483},"zákon-klesající-poptávky","Zákon klesající poptávky",[1635,41486,41487],{},[724,41488,41489],{},[38,41490,41491,41492,41505,41506,41519,41520,41505,41533,41546],{},"Roste-li cena ",[883,41493,41495],{"className":41494},[886],[888,41496,41497],{"xmlns":890},[892,41498,41499,41503],{},[895,41500,41501],{},[898,41502,1680],{},[902,41504,1680],{"encoding":904},", pak množství ",[883,41507,41509],{"className":41508},[886],[888,41510,41511],{"xmlns":890},[892,41512,41513,41517],{},[895,41514,41515],{},[898,41516,1802],{},[902,41518,1802],{"encoding":904}," klesá; klesá-li cena ",[883,41521,41523],{"className":41522},[886],[888,41524,41525],{"xmlns":890},[892,41526,41527,41531],{},[895,41528,41529],{},[898,41530,1680],{},[902,41532,1680],{"encoding":904},[883,41534,41536],{"className":41535},[886],[888,41537,41538],{"xmlns":890},[892,41539,41540,41544],{},[895,41541,41542],{},[898,41543,1802],{},[902,41545,1802],{"encoding":904}," roste.",[724,41548,41549,41550,41553],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,41551,41552],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1635,41555,41556,41561],{},[724,41557,41558,41560],{},[883,41559,2063],{}," Intuice — proč zákon platí",[120,41562,41563,41569],{},[123,41564,41565,41568],{},[38,41566,41567],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,41570,41571,41574],{},[38,41572,41573],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,41576,41577,41578,41591,41592,41605,41606,41632,41633,41659,41660,12164,41686,41689,41690,1715],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,41579,41581],{"className":41580},[886],[888,41582,41583],{"xmlns":890},[892,41584,41585,41589],{},[895,41586,41587],{},[898,41588,1680],{},[902,41590,1680],{"encoding":904}," se vynáší na svislou osu, množství ",[883,41593,41595],{"className":41594},[886],[888,41596,41597],{"xmlns":890},[892,41598,41599,41603],{},[895,41600,41601],{},[898,41602,1802],{},[902,41604,1802],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,41607,41609],{"className":41608},[886],[888,41610,41611],{"xmlns":890},[892,41612,41613,41629],{},[895,41614,41615,41617,41619,41621,41627],{},[1701,41616,2036],{"stretchy":1798},[1850,41618,1852],{},[1701,41620,2012],{"separator":2011},[1845,41622,41623,41625],{},[898,41624,1680],{},[1850,41626,1852],{},[1701,41628,2053],{"stretchy":1798},[902,41630,41631],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,41634,41636],{"className":41635},[886],[888,41637,41638],{"xmlns":890},[892,41639,41640,41656],{},[895,41641,41642,41644,41650,41652,41654],{},[1701,41643,2036],{"stretchy":1798},[1845,41645,41646,41648],{},[898,41647,1802],{},[1850,41649,1852],{},[1701,41651,2012],{"separator":2011},[1850,41653,1852],{},[1701,41655,2053],{"stretchy":1798},[902,41657,41658],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,41661,41663],{"className":41662},[886],[888,41664,41665],{"xmlns":890},[892,41666,41667,41683],{},[895,41668,41669,41671,41673,41675,41681],{},[1701,41670,1799],{"stretchy":1798},[1850,41672,1852],{},[1701,41674,2012],{"separator":2011},[1845,41676,41677,41679],{},[898,41678,1680],{},[1850,41680,1852],{},[1701,41682,1805],{"stretchy":1798},[902,41684,41685],{"encoding":904},"(0, P_0)",[38,41687,41688],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,41691,41692],{},"konvexní",[724,41694,41695],{},[614,41696,41697,41698,41719,41720,2633,41745,1715],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,41699,41701],{"className":41700},[886],[888,41702,41703],{"xmlns":890},[892,41704,41705,41717],{},[895,41706,41707,41709,41711,41713,41715],{},[1701,41708,1799],{"stretchy":1798},[898,41710,1802],{},[1701,41712,2012],{"separator":2011},[898,41714,1680],{},[1701,41716,1805],{"stretchy":1798},[902,41718,2019],{"encoding":904}," — klesající, konvexní, procházející body ",[883,41721,41723],{"className":41722},[886],[888,41724,41725],{"xmlns":890},[892,41726,41727,41743],{},[895,41728,41729,41731,41733,41735,41741],{},[1701,41730,2036],{"stretchy":1798},[1850,41732,1852],{},[1701,41734,2012],{"separator":2011},[1845,41736,41737,41739],{},[898,41738,1680],{},[1850,41740,1852],{},[1701,41742,2053],{"stretchy":1798},[902,41744,41631],{"encoding":904},[883,41746,41748],{"className":41747},[886],[888,41749,41750],{"xmlns":890},[892,41751,41752,41768],{},[895,41753,41754,41756,41762,41764,41766],{},[1701,41755,2036],{"stretchy":1798},[1845,41757,41758,41760],{},[898,41759,1802],{},[1850,41761,1852],{},[1701,41763,2012],{"separator":2011},[1850,41765,1852],{},[1701,41767,2053],{"stretchy":1798},[902,41769,41658],{"encoding":904},[41376,41771,41773],{"id":41772},"lineární-model-poptávky","Lineární model poptávky",[724,41775,41776],{},"Nejjednodušší závislostí je",[883,41778,41780],{"className":41779},[886],[888,41781,41782],{"xmlns":890,"display":2252},[892,41783,41784,41833],{},[2256,41785,41786],{"width":2258},[2260,41787,41788,41790,41826,41828],{},[2263,41789],{"width":2265},[2263,41791,41792],{},[895,41793,41794,41796,41798,41800,41802,41804,41806,41808,41810,41812,41814,41816,41818,41820,41822,41824],{},[898,41795,1680],{},[1701,41797,1792],{},[898,41799,207],{},[898,41801,1802],{},[1701,41803,1703],{},[898,41805,3598],{},[1701,41807,2012],{"separator":2011},[9942,41809],{"width":9944},[898,41811,207],{},[1701,41813,7530],{},[1850,41815,1852],{},[1701,41817,2012],{"separator":2011},[1939,41819,6402],{},[898,41821,3598],{},[1701,41823,7491],{},[1850,41825,16514],{},[2263,41827],{"width":2265},[2263,41829,41830],{},[1939,41831,41832],{},"(2.4)",[902,41834,41835],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,41837,41838,41839,2020,41875,2633,41899,12099,41925,41947,41948,1715],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,41840,41842],{"className":41841},[886],[888,41843,41844],{"xmlns":890},[892,41845,41846,41872],{},[895,41847,41848,41850,41852,41860,41862,41864],{},[898,41849,1802],{},[1701,41851,1792],{},[2363,41853,41854],{"scriptlevel":1852,"displaystyle":1798},[3726,41855,41856,41858],{},[1850,41857,4062],{},[898,41859,207],{},[898,41861,1680],{},[1701,41863,2317],{},[2363,41865,41866],{"scriptlevel":1852,"displaystyle":1798},[3726,41867,41868,41870],{},[898,41869,3598],{},[898,41871,207],{},[902,41873,41874],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,41876,41878],{"className":41877},[886],[888,41879,41880],{"xmlns":890},[892,41881,41882,41896],{},[895,41883,41884,41892,41894],{},[2363,41885,41886],{"scriptlevel":1852,"displaystyle":1798},[3726,41887,41888,41890],{},[1850,41889,4062],{},[898,41891,207],{},[1701,41893,7530],{},[1850,41895,1852],{},[902,41897,41898],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,41900,41902],{"className":41901},[886],[888,41903,41904],{"xmlns":890},[892,41905,41906,41922],{},[895,41907,41908,41910,41918,41920],{},[1701,41909,2317],{},[2363,41911,41912],{"scriptlevel":1852,"displaystyle":1798},[3726,41913,41914,41916],{},[898,41915,3598],{},[898,41917,207],{},[1701,41919,7491],{},[1850,41921,1852],{},[902,41923,41924],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,41926,41928],{"className":41927},[886],[888,41929,41930],{"xmlns":890},[892,41931,41932,41944],{},[895,41933,41934,41936,41938,41940,41942],{},[1701,41935,1799],{"stretchy":1798},[1850,41937,1852],{},[1701,41939,2012],{"separator":2011},[898,41941,3598],{},[1701,41943,1805],{"stretchy":1798},[902,41945,41946],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,41949,41950],{},"nedokonalé konkurenci",[41952,41953,41955],"h5",{"id":41954},"příklad-21","Příklad 2.1",[724,41957,41958,41961,41962,1715],{},[38,41959,41960],{},"Zadání:"," Lineární poptávka ",[883,41963,41965],{"className":41964},[886],[888,41966,41967],{"xmlns":890},[892,41968,41969,41985],{},[895,41970,41971,41973,41975,41977,41979,41981,41983],{},[898,41972,1680],{},[1701,41974,1792],{},[1701,41976,2317],{},[1850,41978,3938],{},[898,41980,1802],{},[1701,41982,1703],{},[1850,41984,7211],{},[902,41986,41987],{"encoding":904},"P = -2Q + 60",[724,41989,41990,41993,41994,42016,42017,1715],{},[38,41991,41992],{},"Řešení:"," Reálné cenové rozpětí je ",[883,41995,41997],{"className":41996},[886],[888,41998,41999],{"xmlns":890},[892,42000,42001,42013],{},[895,42002,42003,42005,42007,42009,42011],{},[1701,42004,1799],{"stretchy":1798},[1850,42006,1852],{},[1701,42008,2012],{"separator":2011},[1850,42010,7211],{},[1701,42012,1805],{"stretchy":1798},[902,42014,42015],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,42018,42020],{"className":42019},[886],[888,42021,42022],{"xmlns":890},[892,42023,42024,42046],{},[895,42025,42026,42028,42030,42032,42040,42042,42044],{},[898,42027,1802],{},[1701,42029,1792],{},[1701,42031,2317],{},[2363,42033,42034],{"scriptlevel":1852,"displaystyle":1798},[3726,42035,42036,42038],{},[1850,42037,4062],{},[1850,42039,3938],{},[898,42041,1680],{},[1701,42043,1703],{},[1850,42045,3776],{},[902,42047,42048],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,42050,42051,42074],{},[19,42052,42053],{},[22,42054,42055,42070,42072],{},[25,42056,42057],{},[883,42058,42060],{"className":42059},[886],[888,42061,42062],{"xmlns":890},[892,42063,42064,42068],{},[895,42065,42066],{},[898,42067,1680],{},[902,42069,1680],{"encoding":904},[25,42071,3665],{},[25,42073,13096],{},[30,42075,42076],{},[22,42077,42078,42093,42095],{},[35,42079,42080],{},[883,42081,42083],{"className":42082},[886],[888,42084,42085],{"xmlns":890},[892,42086,42087,42091],{},[895,42088,42089],{},[898,42090,1802],{},[902,42092,1802],{"encoding":904},[35,42094,3703],{},[35,42096,13096],{},[724,42098,42099],{},[614,42100,42101,42102,2633,42124,1715],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,42103,42105],{"className":42104},[886],[888,42106,42107],{"xmlns":890},[892,42108,42109,42121],{},[895,42110,42111,42113,42115,42117,42119],{},[1701,42112,2036],{"stretchy":1798},[1850,42114,1852],{},[1701,42116,2012],{"separator":2011},[898,42118,3598],{},[1701,42120,2053],{"stretchy":1798},[902,42122,42123],{"encoding":904},"[0, b]",[883,42125,42127],{"className":42126},[886],[888,42128,42129],{"xmlns":890},[892,42130,42131,42149],{},[895,42132,42133,42135,42137,42139,42141,42143,42145,42147],{},[1701,42134,2036],{"stretchy":1798},[1701,42136,2317],{},[898,42138,3598],{},[898,42140,8741],{"mathvariant":2334},[898,42142,207],{},[1701,42144,2012],{"separator":2011},[1850,42146,1852],{},[1701,42148,2053],{"stretchy":1798},[902,42150,42151],{"encoding":904},"[-b\u002Fa, 0]",[41376,42153,42155],{"id":42154},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,42157,42158,42159,42176],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,42160,42162],{"className":42161},[886],[888,42163,42164],{"xmlns":890},[892,42165,42166,42174],{},[895,42167,42168],{},[3243,42169,42170,42172],{},[898,42171,1680],{},[1701,42173,8424],{},[902,42175,8474],{"encoding":904},", je funkce poptávky konstantní:",[883,42178,42180],{"className":42179},[886],[888,42181,42182],{"xmlns":890,"display":2252},[892,42183,42184,42198],{},[895,42185,42186,42188,42190,42196],{},[898,42187,1680],{},[1701,42189,1792],{},[3243,42191,42192,42194],{},[898,42193,1680],{},[1701,42195,8424],{},[898,42197,1715],{"mathvariant":2334},[902,42199,42200],{"encoding":904},"P = P^*.",[724,42202,42203],{},[614,42204,42205,42206,42227,42228,1715],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,42207,42209],{"className":42208},[886],[888,42210,42211],{"xmlns":890},[892,42212,42213,42225],{},[895,42214,42215,42217,42219,42221,42223],{},[1701,42216,1799],{"stretchy":1798},[898,42218,1802],{},[1701,42220,2012],{"separator":2011},[898,42222,1680],{},[1701,42224,1805],{"stretchy":1798},[902,42226,2019],{"encoding":904}," na úrovni ",[883,42229,42231],{"className":42230},[886],[888,42232,42233],{"xmlns":890},[892,42234,42235,42247],{},[895,42236,42237,42239,42241],{},[898,42238,1680],{},[1701,42240,1792],{},[3243,42242,42243,42245],{},[898,42244,1680],{},[1701,42246,8424],{},[902,42248,8427],{"encoding":904},[41376,42250,42252],{"id":42251},"giffenův-statek","Giffenův statek",[724,42254,42255,42256,42258,42259,42261,42262,1715],{},"Existují zboží, u nichž je křivka poptávky ",[38,42257,17711],{}," — tzv. ",[38,42260,42252],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,42263,42264],{},"podřadnému zboží",[41952,42266,42268],{"id":42267},"příklad-22","Příklad 2.2",[724,42270,42271,42274,42275,42293,42294,42316,42317,42334,42335,42353,42354,42377],{},[38,42272,42273],{},"Zadání a popis:"," Křivka ",[883,42276,42278],{"className":42277},[886],[888,42279,42280],{"xmlns":890},[892,42281,42282,42290],{},[895,42283,42284],{},[1845,42285,42286,42288],{},[898,42287,1795],{},[1850,42289,4062],{},[902,42291,42292],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,42295,42297],{"className":42296},[886],[888,42298,42299],{"xmlns":890},[892,42300,42301,42313],{},[895,42302,42303,42305,42307,42309,42311],{},[1701,42304,1799],{"stretchy":1798},[1850,42306,1852],{},[1701,42308,2012],{"separator":2011},[1850,42310,40275],{},[1701,42312,1805],{"stretchy":1798},[902,42314,42315],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,42318,42320],{"className":42319},[886],[888,42321,42322],{"xmlns":890},[892,42323,42324,42332],{},[895,42325,42326],{},[1845,42327,42328,42330],{},[898,42329,1802],{},[1850,42331,1852],{},[902,42333,1855],{"encoding":904}," konkávní, se saturací kolem 17 liber. Křivka ",[883,42336,42338],{"className":42337},[886],[888,42339,42340],{"xmlns":890},[892,42341,42342,42350],{},[895,42343,42344],{},[1845,42345,42346,42348],{},[898,42347,1795],{},[1850,42349,3938],{},[902,42351,42352],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,42355,42357],{"className":42356},[886],[888,42358,42359],{"xmlns":890},[892,42360,42361,42374],{},[895,42362,42363,42365,42367,42369,42372],{},[1701,42364,2036],{"stretchy":1798},[1850,42366,1852],{},[1701,42368,2012],{"separator":2011},[1850,42370,42371],{},"21",[1701,42373,2053],{"stretchy":1798},[902,42375,42376],{"encoding":904},"[0, 21]"," centů.",[198,42379,42381],{"id":42380},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,42383,42384,42385,2246],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,42386,42388],{"className":42387},[886],[888,42389,42390],{"xmlns":890},[892,42391,42392,42396],{},[895,42393,42394],{},[898,42395,13189],{},[902,42397,13189],{"encoding":904},[883,42399,42401],{"className":42400},[886],[888,42402,42403],{"xmlns":890,"display":2252},[892,42404,42405,42436],{},[2256,42406,42407],{"width":2258},[2260,42408,42409,42411,42429,42431],{},[2263,42410],{"width":2265},[2263,42412,42413],{},[895,42414,42415,42417,42419,42421,42423,42425,42427],{},[898,42416,1802],{},[1701,42418,1792],{},[898,42420,3249],{},[1701,42422,1799],{"stretchy":1798},[898,42424,13189],{},[1701,42426,1805],{"stretchy":1798},[898,42428,1715],{"mathvariant":2334},[2263,42430],{"width":2265},[2263,42432,42433],{},[1939,42434,42435],{},"(2.5)",[902,42437,42438],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,42440,42441,42442,42445,42446,42449],{},"Funkce se nazývá ",[38,42443,42444],{},"Engelova",", její graf ",[38,42447,42448],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,42451,42452,42584],{},[123,42453,42454,2979,42457,42470,42471,42484,42485,42502,42503],{},[38,42455,42456],{},"Normální (superior) zboží",[883,42458,42460],{"className":42459},[886],[888,42461,42462],{"xmlns":890},[892,42463,42464,42468],{},[895,42465,42466],{},[898,42467,1802],{},[902,42469,1802],{"encoding":904}," roste s ",[883,42472,42474],{"className":42473},[886],[888,42475,42476],{"xmlns":890},[892,42477,42478,42482],{},[895,42479,42480],{},[898,42481,13189],{},[902,42483,13189],{"encoding":904},", nepřesáhne hodnotu ",[883,42486,42488],{"className":42487},[886],[888,42489,42490],{"xmlns":890},[892,42491,42492,42500],{},[895,42493,42494],{},[1845,42495,42496,42498],{},[898,42497,1802],{},[1850,42499,1852],{},[902,42501,1855],{"encoding":904},":\n",[120,42504,42505,42537],{},[123,42506,42507,42510,42511,42514,42515,1715],{},[38,42508,42509],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,42512,42513],{},"konkávní"," křivka, autonomní spotřeba ",[883,42516,42518],{"className":42517},[886],[888,42519,42520],{"xmlns":890},[892,42521,42522,42534],{},[895,42523,42524,42530,42532],{},[1845,42525,42526,42528],{},[898,42527,1802],{},[1850,42529,4062],{},[1701,42531,7491],{},[1850,42533,1852],{},[902,42535,42536],{"encoding":904},"Q_1 > 0",[123,42538,42539,42542,42543,42561,42562,42564,42565,4088,42582,1715],{},[38,42540,42541],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,42544,42546],{"className":42545},[886],[888,42547,42548],{"xmlns":890},[892,42549,42550,42558],{},[895,42551,42552],{},[1845,42553,42554,42556],{},[898,42555,13189],{},[1850,42557,4062],{},[902,42559,42560],{"encoding":904},"Y_1",", křivka je nejprve ",[38,42563,41692],{}," a od ",[883,42566,42568],{"className":42567},[886],[888,42569,42570],{"xmlns":890},[892,42571,42572,42580],{},[895,42573,42574],{},[1845,42575,42576,42578],{},[898,42577,13189],{},[1850,42579,4062],{},[902,42581,42560],{"encoding":904},[38,42583,42513],{},[123,42585,42586,42589,42590,42608],{},[38,42587,42588],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,42591,42593],{"className":42592},[886],[888,42594,42595],{"xmlns":890},[892,42596,42597,42605],{},[895,42598,42599],{},[1845,42600,42601,42603],{},[898,42602,13189],{},[1850,42604,1852],{},[902,42606,42607],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,42610,42611,42612,42615,42616,2506],{},"Mírou citlivosti je ",[614,42613,42614],{},"důchodová elasticita"," (viz ",[207,42617,7974],{"className":42618,"dataFsResolvedFilePath":848,"href":849},[210],[724,42620,42621],{},[614,42622,42623],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[41376,42625,42627],{"id":42626},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1635,42629,42630,42701,42744],{},[724,42631,42632,42634,42635,4088,42638,4088,42651,9733,42653,42666,42667,42670,42671,1715],{},[883,42633,4695],{}," Pozor — nezbytné ≠ podřadné\n",[38,42636,42637],{},"Nezbytné zboží:",[883,42639,42641],{"className":42640},[886],[888,42642,42643],{"xmlns":890},[892,42644,42645,42649],{},[895,42646,42647],{},[898,42648,1802],{},[902,42650,1802],{"encoding":904},[38,42652,11384],{},[883,42654,42656],{"className":42655},[886],[888,42657,42658],{"xmlns":890},[892,42659,42660,42664],{},[895,42661,42662],{},[898,42663,13189],{},[902,42665,13189],{"encoding":904},", ale ",[38,42668,42669],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,42672,42674],{"className":42673},[886],[888,42675,42676],{"xmlns":890},[892,42677,42678,42698],{},[895,42679,42680,42686,42688,42690,42692,42694,42696],{},[1845,42681,42682,42684],{},[898,42683,3249],{},[898,42685,13189],{},[1701,42687,10569],{},[1701,42689,1799],{"stretchy":1798},[1850,42691,1852],{},[1701,42693,2012],{"separator":2011},[1850,42695,4062],{},[1701,42697,1805],{"stretchy":1798},[902,42699,42700],{"encoding":904},"E_Y \\in (0, 1)",[724,42702,42703,4088,42706,4088,42719,42721,42722,1715],{},[38,42704,42705],{},"Podřadné zboží:",[883,42707,42709],{"className":42708},[886],[888,42710,42711],{"xmlns":890},[892,42712,42713,42717],{},[895,42714,42715],{},[898,42716,1802],{},[902,42718,1802],{"encoding":904},[38,42720,11404],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,42723,42725],{"className":42724},[886],[888,42726,42727],{"xmlns":890},[892,42728,42729,42741],{},[895,42730,42731,42737,42739],{},[1845,42732,42733,42735],{},[898,42734,3249],{},[898,42736,13189],{},[1701,42738,7530],{},[1850,42740,1852],{},[902,42742,42743],{"encoding":904},"E_Y \u003C 0",[724,42745,42746,42747,1715],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,42748,42749],{},"méně kusů, ne jen proporčně méně",[724,42751,42752,42755,42756,42759],{},[38,42753,42754],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,42757,42758],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,42761,42762],{},[2139,42763],{"alt":42764,"className":42765,"src":42766},"imek-engelovy-krivky-3typy",[210,2143],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[41952,42768,42770],{"id":42769},"české-příklady","České příklady",[16,42772,42773,42783],{},[19,42774,42775],{},[22,42776,42777,42780],{},[25,42778,42779],{},"Podřadné",[25,42781,42782],{},"Nahradí se za",[30,42784,42785,42793,42801,42809,42817,42825,42833,42841],{},[22,42786,42787,42790],{},[35,42788,42789],{},"Instantní polévky, ramen",[35,42791,42792],{},"Čerstvé jídlo, restaurace",[22,42794,42795,42798],{},[35,42796,42797],{},"MHD (autobus, tramvaj)",[35,42799,42800],{},"Vlastní auto, Uber, taxi",[22,42802,42803,42806],{},[35,42804,42805],{},"Mražené polotovary, pizza z mrazáku",[35,42807,42808],{},"Čerstvé suroviny, hotovky",[22,42810,42811,42814],{},[35,42812,42813],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,42815,42816],{},"Značkové produkty",[22,42818,42819,42822],{},[35,42820,42821],{},"Paštika Májka, obyčejný měkký salám",[35,42823,42824],{},"Kvalitní uzeniny, šunka od kosti",[22,42826,42827,42830],{},[35,42828,42829],{},"Second hand oblečení",[35,42831,42832],{},"Nové oblečení, značky",[22,42834,42835,42838],{},[35,42836,42837],{},"Krabicové víno, nejlevnější pivo",[35,42839,42840],{},"Lahvové víno, řemeslná piva",[22,42842,42843,42846],{},[35,42844,42845],{},"Ojetá auta nižších tříd",[35,42847,42848],{},"Nová auta, prémiové značky",[1635,42850,42851],{},[724,42852,42853,42855,42856,42859],{},[883,42854,3140],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,42857,42858],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,42861,42862,42865,42866,1646,42869,42891,42892,1646,42895,42916,42917,42935,42936,42939],{},[38,42863,42864],{},"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 ",[38,42867,42868],{},"luxus",[883,42870,42872],{"className":42871},[886],[888,42873,42874],{"xmlns":890},[892,42875,42876,42888],{},[895,42877,42878,42884,42886],{},[1845,42879,42880,42882],{},[898,42881,3249],{},[898,42883,13189],{},[1701,42885,7491],{},[1850,42887,4062],{},[902,42889,42890],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,42893,42894],{},"podřadné",[883,42896,42898],{"className":42897},[886],[888,42899,42900],{"xmlns":890},[892,42901,42902,42914],{},[895,42903,42904,42910,42912],{},[1845,42905,42906,42908],{},[898,42907,3249],{},[898,42909,13189],{},[1701,42911,7530],{},[1850,42913,1852],{},[902,42915,42743],{"encoding":904},"). Proto je ",[883,42918,42920],{"className":42919},[886],[888,42921,42922],{"xmlns":890},[892,42923,42924,42932],{},[895,42925,42926],{},[1845,42927,42928,42930],{},[898,42929,3249],{},[898,42931,13189],{},[902,42933,42934],{"encoding":904},"E_Y"," vždy ",[38,42937,42938],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,42941,42942,42943,42945],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,42944,42252],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,42947,42949,42950,1805],{"id":42948},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,42951,42952],{},"shift of demand",[724,42954,42955,42956,42973,42974,42991,42992,43005,43006,3856,43019,43041,43042,43059,43060,43086,43087,43090],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,42957,42959],{"className":42958},[886],[888,42960,42961],{"xmlns":890},[892,42962,42963,42971],{},[895,42964,42965],{},[1845,42966,42967,42969],{},[898,42968,1680],{},[1850,42970,1852],{},[902,42972,2095],{"encoding":904}," odpovídá množství ",[883,42975,42977],{"className":42976},[886],[888,42978,42979],{"xmlns":890},[892,42980,42981,42989],{},[895,42982,42983],{},[1845,42984,42985,42987],{},[898,42986,1802],{},[1850,42988,1852],{},[902,42990,1855],{"encoding":904}," na křivce ",[883,42993,42995],{"className":42994},[886],[888,42996,42997],{"xmlns":890},[892,42998,42999,43003],{},[895,43000,43001],{},[898,43002,1795],{},[902,43004,1795],{"encoding":904},"; vzroste-li důchod z ",[883,43007,43009],{"className":43008},[886],[888,43010,43011],{"xmlns":890},[892,43012,43013,43017],{},[895,43014,43015],{},[898,43016,13189],{},[902,43018,13189],{"encoding":904},[883,43020,43022],{"className":43021},[886],[888,43023,43024],{"xmlns":890},[892,43025,43026,43038],{},[895,43027,43028,43034,43036],{},[1845,43029,43030,43032],{},[898,43031,13189],{},[1850,43033,4062],{},[1701,43035,7491],{},[898,43037,13189],{},[902,43039,43040],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,43043,43045],{"className":43044},[886],[888,43046,43047],{"xmlns":890},[892,43048,43049,43057],{},[895,43050,43051],{},[1845,43052,43053,43055],{},[898,43054,1680],{},[1850,43056,1852],{},[902,43058,2095],{"encoding":904}," odpovídá vyšší ",[883,43061,43063],{"className":43062},[886],[888,43064,43065],{"xmlns":890},[892,43066,43067,43083],{},[895,43068,43069,43075,43077],{},[1845,43070,43071,43073],{},[898,43072,1802],{},[1850,43074,4062],{},[1701,43076,7491],{},[1845,43078,43079,43081],{},[898,43080,1802],{},[1850,43082,1852],{},[902,43084,43085],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,43088,43089],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,43092,43093],{},[2139,43094],{"alt":43095,"className":43096,"src":43097},"imek-posun-vs-pohyb-po-krivce",[210,2143],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,43099,43100],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,43102,43103],{},[614,43104,43105,43106,1995,43136,43157],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,43107,43109],{"className":43108},[886],[888,43110,43111],{"xmlns":890},[892,43112,43113,43133],{},[895,43114,43115,43121,43123,43125,43127],{},[1845,43116,43117,43119],{},[898,43118,1795],{},[1850,43120,3938],{},[1701,43122,2012],{"separator":2011},[898,43124,1795],{},[1701,43126,2012],{"separator":2011},[1845,43128,43129,43131],{},[898,43130,1795],{},[1850,43132,4062],{},[902,43134,43135],{"encoding":904},"D_2, D, D_1",[883,43137,43139],{"className":43138},[886],[888,43140,43141],{"xmlns":890},[892,43142,43143,43155],{},[895,43144,43145,43147,43149,43151,43153],{},[1701,43146,1799],{"stretchy":1798},[898,43148,1802],{},[1701,43150,2012],{"separator":2011},[898,43152,1680],{},[1701,43154,1805],{"stretchy":1798},[902,43156,2019],{"encoding":904},", šipky naznačují posuny.",[41952,43159,43161],{"id":43160},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,43163,43164,43166,43167,43190,43191,43208,43209,43226,43227,1715],{},[38,43165,41960],{}," Poptávce ",[883,43168,43170],{"className":43169},[886],[888,43171,43172],{"xmlns":890},[892,43173,43174,43188],{},[895,43175,43176,43178,43180,43182,43184,43186],{},[898,43177,1680],{},[1701,43179,1792],{},[898,43181,1795],{},[1701,43183,1799],{"stretchy":1798},[898,43185,1802],{},[1701,43187,1805],{"stretchy":1798},[902,43189,1808],{"encoding":904}," odpovídá ceně ",[883,43192,43194],{"className":43193},[886],[888,43195,43196],{"xmlns":890},[892,43197,43198,43206],{},[895,43199,43200],{},[1845,43201,43202,43204],{},[898,43203,1680],{},[1850,43205,1852],{},[902,43207,2095],{"encoding":904}," množství ",[883,43210,43212],{"className":43211},[886],[888,43213,43214],{"xmlns":890},[892,43215,43216,43224],{},[895,43217,43218],{},[1845,43219,43220,43222],{},[898,43221,1802],{},[1850,43223,1852],{},[902,43225,1855],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,43228,43230],{"className":43229},[886],[888,43231,43232],{"xmlns":890},[892,43233,43234,43238],{},[895,43235,43236],{},[898,43237,5877],{},[902,43239,5877],{"encoding":904},[724,43241,43242,43244,43245,43262,43263,43285],{},[38,43243,41992],{}," Kupující nakupuje množství ",[883,43246,43248],{"className":43247},[886],[888,43249,43250],{"xmlns":890},[892,43251,43252,43260],{},[895,43253,43254],{},[1845,43255,43256,43258],{},[898,43257,1802],{},[1850,43259,4062],{},[902,43261,33036],{"encoding":904},", které odpovídá ceně ",[883,43264,43266],{"className":43265},[886],[888,43267,43268],{"xmlns":890},[892,43269,43270,43282],{},[895,43271,43272,43278,43280],{},[1845,43273,43274,43276],{},[898,43275,1680],{},[1850,43277,1852],{},[1701,43279,1703],{},[898,43281,5877],{},[902,43283,43284],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,43287,43289],{"className":43288},[886],[888,43290,43291],{"xmlns":890,"display":2252},[892,43292,43293,43327],{},[895,43294,43295,43297,43299,43305,43307,43309,43311,43313,43315,43317,43319,43321,43323,43325],{},[898,43296,1680],{},[1701,43298,1792],{},[1845,43300,43301,43303],{},[898,43302,1795],{},[1850,43304,4062],{},[1701,43306,1799],{"stretchy":1798},[898,43308,1802],{},[1701,43310,1805],{"stretchy":1798},[1701,43312,1792],{},[898,43314,1795],{},[1701,43316,1799],{"stretchy":1798},[898,43318,1802],{},[1701,43320,1805],{"stretchy":1798},[1701,43322,2317],{},[898,43324,5877],{},[1701,43326,2012],{"separator":2011},[902,43328,43329],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,43331,43332,43333,1715],{},"tj. dojde k ",[38,43334,43335],{},"posunu poptávky doleva",[724,43337,43338],{},[614,43339,43340,43341,43362,43363,1343,43380,1343,43393,43414,43415,2633,43432,1715],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,43342,43344],{"className":43343},[886],[888,43345,43346],{"xmlns":890},[892,43347,43348,43360],{},[895,43349,43350,43352,43354,43356,43358],{},[1701,43351,1799],{"stretchy":1798},[898,43353,1802],{},[1701,43355,2012],{"separator":2011},[898,43357,1680],{},[1701,43359,1805],{"stretchy":1798},[902,43361,2019],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,43364,43366],{"className":43365},[886],[888,43367,43368],{"xmlns":890},[892,43369,43370,43378],{},[895,43371,43372],{},[1845,43373,43374,43376],{},[898,43375,1680],{},[1850,43377,1852],{},[902,43379,2095],{"encoding":904},[883,43381,43383],{"className":43382},[886],[888,43384,43385],{"xmlns":890},[892,43386,43387,43391],{},[895,43388,43389],{},[898,43390,5877],{},[902,43392,5877],{"encoding":904},[883,43394,43396],{"className":43395},[886],[888,43397,43398],{"xmlns":890},[892,43399,43400,43412],{},[895,43401,43402,43408,43410],{},[1845,43403,43404,43406],{},[898,43405,1680],{},[1850,43407,1852],{},[1701,43409,1703],{},[898,43411,5877],{},[902,43413,43284],{"encoding":904},"; na vodorovné ",[883,43416,43418],{"className":43417},[886],[888,43419,43420],{"xmlns":890},[892,43421,43422,43430],{},[895,43423,43424],{},[1845,43425,43426,43428],{},[898,43427,1802],{},[1850,43429,4062],{},[902,43431,33036],{"encoding":904},[883,43433,43435],{"className":43434},[886],[888,43436,43437],{"xmlns":890},[892,43438,43439,43447],{},[895,43440,43441],{},[1845,43442,43443,43445],{},[898,43444,1802],{},[1850,43446,1852],{},[902,43448,1855],{"encoding":904},[198,43450,43452],{"id":43451},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,43454,43455],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,43457,43459],{"className":43458},[886],[888,43460,43461],{"xmlns":890,"display":2252},[892,43462,43463,43648],{},[2256,43464,43465],{"width":2258},[2260,43466,43467,43469,43641,43643],{},[2263,43468],{"width":2265},[2263,43470,43471],{},[2256,43472,43473,43557],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,43474,43475,43485],{},[2263,43476,43477],{},[2363,43478,43479],{"scriptlevel":1852,"displaystyle":2011},[1845,43480,43481,43483],{},[898,43482,1802],{},[1850,43484,4062],{},[2263,43486,43487],{},[2363,43488,43489],{"scriptlevel":1852,"displaystyle":2011},[895,43490,43491,43493,43495,43501,43503,43509,43511,43517,43519,43521,43527,43529,43535,43541,43543,43549,43555],{},[895,43492],{},[1701,43494,1792],{},[1845,43496,43497,43499],{},[898,43498,1795],{},[1850,43500,4062],{},[1701,43502,1799],{"stretchy":1798},[1845,43504,43505,43507],{},[898,43506,1680],{},[1850,43508,4062],{},[1701,43510,2012],{"separator":2011},[1845,43512,43513,43515],{},[898,43514,1680],{},[1850,43516,3938],{},[1701,43518,1805],{"stretchy":1798},[1701,43520,1792],{},[1845,43522,43523,43525],{},[898,43524,207],{},[1850,43526,4062],{},[1701,43528,1703],{},[1845,43530,43531,43533],{},[898,43532,3598],{},[1850,43534,4062],{},[1845,43536,43537,43539],{},[898,43538,1680],{},[1850,43540,4062],{},[1701,43542,1703],{},[1845,43544,43545,43547],{},[898,43546,3618],{},[1850,43548,4062],{},[1845,43550,43551,43553],{},[898,43552,1680],{},[1850,43554,3938],{},[1701,43556,2012],{"separator":2011},[2260,43558,43559,43569],{},[2263,43560,43561],{},[2363,43562,43563],{"scriptlevel":1852,"displaystyle":2011},[1845,43564,43565,43567],{},[898,43566,1802],{},[1850,43568,3938],{},[2263,43570,43571],{},[2363,43572,43573],{"scriptlevel":1852,"displaystyle":2011},[895,43574,43575,43577,43579,43585,43587,43593,43595,43601,43603,43605,43611,43613,43619,43625,43627,43633,43639],{},[895,43576],{},[1701,43578,1792],{},[1845,43580,43581,43583],{},[898,43582,1795],{},[1850,43584,3938],{},[1701,43586,1799],{"stretchy":1798},[1845,43588,43589,43591],{},[898,43590,1680],{},[1850,43592,4062],{},[1701,43594,2012],{"separator":2011},[1845,43596,43597,43599],{},[898,43598,1680],{},[1850,43600,3938],{},[1701,43602,1805],{"stretchy":1798},[1701,43604,1792],{},[1845,43606,43607,43609],{},[898,43608,207],{},[1850,43610,3938],{},[1701,43612,1703],{},[1845,43614,43615,43617],{},[898,43616,3598],{},[1850,43618,3938],{},[1845,43620,43621,43623],{},[898,43622,1680],{},[1850,43624,4062],{},[1701,43626,1703],{},[1845,43628,43629,43631],{},[898,43630,3618],{},[1850,43632,3938],{},[1845,43634,43635,43637],{},[898,43636,1680],{},[1850,43638,3938],{},[898,43640,1715],{"mathvariant":2334},[2263,43642],{"width":2265},[2263,43644,43645],{},[1939,43646,43647],{},"(2.6)",[902,43649,43650],{"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}",[41376,43652,43654],{"id":43653},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,43656,43657,43704,43751],{},[123,43658,43659,1343,43681,43703],{},[883,43660,43662],{"className":43661},[886],[888,43663,43664],{"xmlns":890},[892,43665,43666,43678],{},[895,43667,43668,43674,43676],{},[1845,43669,43670,43672],{},[898,43671,207],{},[1850,43673,4062],{},[1701,43675,7491],{},[1850,43677,1852],{},[902,43679,43680],{"encoding":904},"a_1 > 0",[883,43682,43684],{"className":43683},[886],[888,43685,43686],{"xmlns":890},[892,43687,43688,43700],{},[895,43689,43690,43696,43698],{},[1845,43691,43692,43694],{},[898,43693,207],{},[1850,43695,3938],{},[1701,43697,7491],{},[1850,43699,1852],{},[902,43701,43702],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,43705,43706,1343,43728,43750],{},[883,43707,43709],{"className":43708},[886],[888,43710,43711],{"xmlns":890},[892,43712,43713,43725],{},[895,43714,43715,43721,43723],{},[1845,43716,43717,43719],{},[898,43718,3598],{},[1850,43720,4062],{},[1701,43722,7530],{},[1850,43724,1852],{},[902,43726,43727],{"encoding":904},"b_1 \u003C 0",[883,43729,43731],{"className":43730},[886],[888,43732,43733],{"xmlns":890},[892,43734,43735,43747],{},[895,43736,43737,43743,43745],{},[1845,43738,43739,43741],{},[898,43740,3618],{},[1850,43742,3938],{},[1701,43744,7530],{},[1850,43746,1852],{},[902,43748,43749],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,43752,43753,43754,1343,43771,43789,43790],{},"zkřížené koeficienty ",[883,43755,43757],{"className":43756},[886],[888,43758,43759],{"xmlns":890},[892,43760,43761,43769],{},[895,43762,43763],{},[1845,43764,43765,43767],{},[898,43766,3618],{},[1850,43768,4062],{},[902,43770,33832],{"encoding":904},[883,43772,43774],{"className":43773},[886],[888,43775,43776],{"xmlns":890},[892,43777,43778,43786],{},[895,43779,43780],{},[1845,43781,43782,43784],{},[898,43783,3598],{},[1850,43785,3938],{},[902,43787,43788],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,43791,43792,43842],{},[123,43793,43794,43797,43798,1343,43820,2012],{},[38,43795,43796],{},"substituty"," (máslo vs. margarín): ",[883,43799,43801],{"className":43800},[886],[888,43802,43803],{"xmlns":890},[892,43804,43805,43817],{},[895,43806,43807,43813,43815],{},[1845,43808,43809,43811],{},[898,43810,3618],{},[1850,43812,4062],{},[1701,43814,7491],{},[1850,43816,1852],{},[902,43818,43819],{"encoding":904},"c_1 > 0",[883,43821,43823],{"className":43822},[886],[888,43824,43825],{"xmlns":890},[892,43826,43827,43839],{},[895,43828,43829,43835,43837],{},[1845,43830,43831,43833],{},[898,43832,3598],{},[1850,43834,3938],{},[1701,43836,7491],{},[1850,43838,1852],{},[902,43840,43841],{"encoding":904},"b_2 > 0",[123,43843,43844,43847,43848,1343,43870,1715],{},[38,43845,43846],{},"komplementy"," (auto vs. benzín): ",[883,43849,43851],{"className":43850},[886],[888,43852,43853],{"xmlns":890},[892,43854,43855,43867],{},[895,43856,43857,43863,43865],{},[1845,43858,43859,43861],{},[898,43860,3618],{},[1850,43862,4062],{},[1701,43864,7530],{},[1850,43866,1852],{},[902,43868,43869],{"encoding":904},"c_1 \u003C 0",[883,43871,43873],{"className":43872},[886],[888,43874,43875],{"xmlns":890},[892,43876,43877,43889],{},[895,43878,43879,43885,43887],{},[1845,43880,43881,43883],{},[898,43882,3598],{},[1850,43884,3938],{},[1701,43886,7530],{},[1850,43888,1852],{},[902,43890,43891],{"encoding":904},"b_2 \u003C 0",[724,43893,43894],{},"Schematicky:",[724,43896,43897,43900],{},[38,43898,43899],{},"Substituty",[883,43901,43903],{"className":43902},[886],[888,43904,43905],{"xmlns":890},[892,43906,43907,44046],{},[895,43908,43909,43915,43917,43932,43934,43954,43956,43976,43978,43980,43986,43988,44002,44004,44024,44026],{},[1845,43910,43911,43913],{},[898,43912,1802],{},[1850,43914,4062],{},[1701,43916,1792],{},[898,43918,43919],{},[43920,43921,43922,43930],"munder",{},[1701,43923,43924],{},[1845,43925,43926,43928],{},[898,43927,207],{},[1850,43929,4062],{},[1701,43931,1703],{"lspace":4782,"rspace":4782},[1701,43933,1703],{},[898,43935,43936],{},[43920,43937,43938,43952],{},[1701,43939,43940,43946],{},[1845,43941,43942,43944],{},[898,43943,3598],{},[1850,43945,4062],{},[1845,43947,43948,43950],{},[898,43949,1680],{},[1850,43951,4062],{},[1701,43953,2317],{"lspace":4782,"rspace":4782},[1701,43955,1703],{},[898,43957,43958],{},[43920,43959,43960,43974],{},[1701,43961,43962,43968],{},[1845,43963,43964,43966],{},[898,43965,3618],{},[1850,43967,4062],{},[1845,43969,43970,43972],{},[898,43971,1680],{},[1850,43973,3938],{},[1701,43975,1703],{"lspace":4782,"rspace":4782},[1701,43977,2012],{"separator":2011},[9942,43979],{"width":9944},[1845,43981,43982,43984],{},[898,43983,1802],{},[1850,43985,3938],{},[1701,43987,1792],{},[898,43989,43990],{},[43920,43991,43992,44000],{},[1701,43993,43994],{},[1845,43995,43996,43998],{},[898,43997,207],{},[1850,43999,3938],{},[1701,44001,1703],{"lspace":4782,"rspace":4782},[1701,44003,1703],{},[898,44005,44006],{},[43920,44007,44008,44022],{},[1701,44009,44010,44016],{},[1845,44011,44012,44014],{},[898,44013,3598],{},[1850,44015,3938],{},[1845,44017,44018,44020],{},[898,44019,1680],{},[1850,44021,4062],{},[1701,44023,1703],{"lspace":4782,"rspace":4782},[1701,44025,1703],{},[898,44027,44028],{},[43920,44029,44030,44044],{},[1701,44031,44032,44038],{},[1845,44033,44034,44036],{},[898,44035,3618],{},[1850,44037,3938],{},[1845,44039,44040,44042],{},[898,44041,1680],{},[1850,44043,3938],{},[1701,44045,2317],{"lspace":4782,"rspace":4782},[902,44047,44048],{"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}",[724,44050,44051,44054],{},[38,44052,44053],{},"Komplementy",[883,44055,44057],{"className":44056},[886],[888,44058,44059],{"xmlns":890},[892,44060,44061,44199],{},[895,44062,44063,44069,44071,44085,44087,44107,44109,44129,44131,44133,44139,44141,44155,44157,44177,44179],{},[1845,44064,44065,44067],{},[898,44066,1802],{},[1850,44068,4062],{},[1701,44070,1792],{},[898,44072,44073],{},[43920,44074,44075,44083],{},[1701,44076,44077],{},[1845,44078,44079,44081],{},[898,44080,207],{},[1850,44082,4062],{},[1701,44084,1703],{"lspace":4782,"rspace":4782},[1701,44086,1703],{},[898,44088,44089],{},[43920,44090,44091,44105],{},[1701,44092,44093,44099],{},[1845,44094,44095,44097],{},[898,44096,3598],{},[1850,44098,4062],{},[1845,44100,44101,44103],{},[898,44102,1680],{},[1850,44104,4062],{},[1701,44106,2317],{"lspace":4782,"rspace":4782},[1701,44108,1703],{},[898,44110,44111],{},[43920,44112,44113,44127],{},[1701,44114,44115,44121],{},[1845,44116,44117,44119],{},[898,44118,3618],{},[1850,44120,4062],{},[1845,44122,44123,44125],{},[898,44124,1680],{},[1850,44126,3938],{},[1701,44128,2317],{"lspace":4782,"rspace":4782},[1701,44130,2012],{"separator":2011},[9942,44132],{"width":9944},[1845,44134,44135,44137],{},[898,44136,1802],{},[1850,44138,3938],{},[1701,44140,1792],{},[898,44142,44143],{},[43920,44144,44145,44153],{},[1701,44146,44147],{},[1845,44148,44149,44151],{},[898,44150,207],{},[1850,44152,3938],{},[1701,44154,1703],{"lspace":4782,"rspace":4782},[1701,44156,1703],{},[898,44158,44159],{},[43920,44160,44161,44175],{},[1701,44162,44163,44169],{},[1845,44164,44165,44167],{},[898,44166,3598],{},[1850,44168,3938],{},[1845,44170,44171,44173],{},[898,44172,1680],{},[1850,44174,4062],{},[1701,44176,2317],{"lspace":4782,"rspace":4782},[1701,44178,1703],{},[898,44180,44181],{},[43920,44182,44183,44197],{},[1701,44184,44185,44191],{},[1845,44186,44187,44189],{},[898,44188,3618],{},[1850,44190,3938],{},[1845,44192,44193,44195],{},[898,44194,1680],{},[1850,44196,3938],{},[1701,44198,2317],{"lspace":4782,"rspace":4782},[902,44200,44201],{"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}",[1771,44203],{},[115,44205,17179],{"id":40809},[1635,44207,44208],{},[724,44209,44210,44212,44213,41023,44226,41037,44239,44242,44243,9733,44266,44284],{},[883,44211,2063],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,44214,44216],{"className":44215},[886],[888,44217,44218],{"xmlns":890},[892,44219,44220,44224],{},[895,44221,44222],{},[898,44223,1802],{},[902,44225,1802],{"encoding":904},[883,44227,44229],{"className":44228},[886],[888,44230,44231],{"xmlns":890},[892,44232,44233,44237],{},[895,44234,44235],{},[898,44236,1680],{},[902,44238,1680],{"encoding":904},[38,44240,44241],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,44244,44246],{"className":44245},[886],[888,44247,44248],{"xmlns":890},[892,44249,44250,44264],{},[895,44251,44252,44254,44256,44258,44260,44262],{},[898,44253,1680],{},[1701,44255,1792],{},[898,44257,3618],{},[898,44259,1802],{},[1701,44261,1703],{},[898,44263,2312],{},[902,44265,3627],{"encoding":904},[883,44267,44269],{"className":44268},[886],[888,44270,44271],{"xmlns":890},[892,44272,44273,44281],{},[895,44274,44275,44277,44279],{},[898,44276,3618],{},[1701,44278,7491],{},[1850,44280,1852],{},[902,44282,44283],{"encoding":904},"c > 0"," je standardní aproximací.",[198,44286,41092],{"id":44287},"obecný-vícefaktorový-model-1",[724,44289,44290,1646,44293,44296,44297,44310,44311,40926,44324,40940,44337,44350,44351,44365,44366,40969,44379,44392],{},[38,44291,44292],{},"Nabízené množství",[614,44294,44295],{},"quantity supplied",") závisí na ceně ",[883,44298,44300],{"className":44299},[886],[888,44301,44302],{"xmlns":890},[892,44303,44304,44308],{},[895,44305,44306],{},[898,44307,1680],{},[902,44309,1680],{"encoding":904},", cenách výrobních faktorů (práce ",[883,44312,44314],{"className":44313},[886],[888,44315,44316],{"xmlns":890},[892,44317,44318,44322],{},[895,44319,44320],{},[898,44321,13853],{},[902,44323,13853],{"encoding":904},[883,44325,44327],{"className":44326},[886],[888,44328,44329],{"xmlns":890},[892,44330,44331,44335],{},[895,44332,44333],{},[898,44334,13858],{},[902,44336,13858],{"encoding":904},[883,44338,44340],{"className":44339},[886],[888,44341,44342],{"xmlns":890},[892,44343,44344,44348],{},[895,44345,44346],{},[898,44347,3249],{},[902,44349,3249],{"encoding":904},"), očekávání ",[883,44352,44354],{"className":44353},[886],[888,44355,44356],{"xmlns":890},[892,44357,44358,44363],{},[895,44359,44360],{},[898,44361,44362],{},"V",[902,44364,44362],{"encoding":904},", počtu výrobců ",[883,44367,44369],{"className":44368},[886],[888,44370,44371],{"xmlns":890},[892,44372,44373,44377],{},[895,44374,44375],{},[898,44376,40966],{},[902,44378,40966],{"encoding":904},[883,44380,44382],{"className":44381},[886],[888,44383,44384],{"xmlns":890},[892,44385,44386,44390],{},[895,44387,44388],{},[898,44389,40981],{},[902,44391,40981],{"encoding":904}," a dalších:",[883,44394,44396],{"className":44395},[886],[888,44397,44398],{"xmlns":890,"display":2252},[892,44399,44400,44459],{},[2256,44401,44402],{"width":2258},[2260,44403,44404,44406,44452,44454],{},[2263,44405],{"width":2265},[2263,44407,44408],{},[895,44409,44410,44412,44414,44416,44418,44420,44422,44424,44426,44428,44430,44432,44434,44436,44438,44440,44442,44444,44446,44448,44450],{},[898,44411,1802],{},[1701,44413,1792],{},[898,44415,1661],{},[1701,44417,1799],{"stretchy":1798},[898,44419,1680],{},[1701,44421,2012],{"separator":2011},[898,44423,13853],{},[1701,44425,2012],{"separator":2011},[898,44427,13858],{},[1701,44429,2012],{"separator":2011},[898,44431,3249],{},[1701,44433,2012],{"separator":2011},[898,44435,44362],{},[1701,44437,2012],{"separator":2011},[898,44439,40966],{},[1701,44441,2012],{"separator":2011},[898,44443,40981],{},[1701,44445,2012],{"separator":2011},[1701,44447,13704],{},[1701,44449,1805],{"stretchy":1798},[898,44451,1715],{"mathvariant":2334},[2263,44453],{"width":2265},[2263,44455,44456],{},[1939,44457,44458],{},"(2.7)",[902,44460,44461],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,44463,42441,44464,1646,44467,44470],{},[38,44465,44466],{},"funkce nabídky",[614,44468,44469],{},"supply function",") v širším slova smyslu.",[198,44472,44474],{"id":44473},"jednofaktorový-model","Jednofaktorový model",[724,44476,44477],{},"V nejpřirozenějším jednofaktorovém modelu",[883,44479,44481],{"className":44480},[886],[888,44482,44483],{"xmlns":890,"display":2252},[892,44484,44485,44536],{},[2256,44486,44487],{"width":2258},[2260,44488,44489,44491,44529,44531],{},[2263,44490],{"width":2265},[2263,44492,44493],{},[895,44494,44495,44497,44499,44501,44503,44505,44507,44509,44511,44513,44515,44517,44519,44521,44523,44525,44527],{},[898,44496,1802],{},[1701,44498,1792],{},[898,44500,1661],{},[1701,44502,1799],{"stretchy":1798},[898,44504,1680],{},[1701,44506,1805],{"stretchy":1798},[1701,44508,2012],{"separator":2011},[9942,44510],{"width":9944},[1939,44512,41445],{},[9942,44514],{"width":9944},[898,44516,1680],{},[1701,44518,1792],{},[898,44520,1661],{},[1701,44522,1799],{"stretchy":1798},[898,44524,1802],{},[1701,44526,1805],{"stretchy":1798},[898,44528,1715],{"mathvariant":2334},[2263,44530],{"width":2265},[2263,44532,44533],{},[1939,44534,44535],{},"(2.8)",[902,44537,44538],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,44540,44541,44542,1646,44545,2506],{},"Graf je ",[38,44543,44544],{},"křivka nabídky",[614,44546,44547],{},"supply curve",[41376,44549,44551],{"id":44550},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1635,44553,44554],{},[724,44555,44556],{},[38,44557,41491,44558,44571,44572,41546],{},[883,44559,44561],{"className":44560},[886],[888,44562,44563],{"xmlns":890},[892,44564,44565,44569],{},[895,44566,44567],{},[898,44568,1680],{},[902,44570,1680],{"encoding":904},", pak nabízené množství ",[883,44573,44575],{"className":44574},[886],[888,44576,44577],{"xmlns":890},[892,44578,44579,44583],{},[895,44580,44581],{},[898,44582,1802],{},[902,44584,1802],{"encoding":904},[724,44586,44587,44588,44613,44614,44644,44645,44662],{},"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 ",[883,44589,44591],{"className":44590},[886],[888,44592,44593],{"xmlns":890},[892,44594,44595,44611],{},[895,44596,44597,44599,44601,44603,44609],{},[1701,44598,2036],{"stretchy":1798},[1850,44600,1852],{},[1701,44602,2012],{"separator":2011},[1845,44604,44605,44607],{},[898,44606,1680],{},[1850,44608,1852],{},[1701,44610,2053],{"stretchy":1798},[902,44612,41631],{"encoding":904}," na svislé ose (případně z ",[883,44615,44617],{"className":44616},[886],[888,44618,44619],{"xmlns":890},[892,44620,44621,44641],{},[895,44622,44623,44625,44631,44633,44639],{},[1701,44624,2036],{"stretchy":1798},[1845,44626,44627,44629],{},[898,44628,1802],{},[1850,44630,4062],{},[1701,44632,2012],{"separator":2011},[1845,44634,44635,44637],{},[898,44636,1680],{},[1850,44638,4062],{},[1701,44640,2053],{"stretchy":1798},[902,44642,44643],{"encoding":904},"[Q_1, P_1]","), kde ",[883,44646,44648],{"className":44647},[886],[888,44649,44650],{"xmlns":890},[892,44651,44652,44660],{},[895,44653,44654],{},[1845,44655,44656,44658],{},[898,44657,1680],{},[1850,44659,1852],{},[902,44661,2095],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,44664,44665],{},[614,44666,44667,44668,7801,44681,1715],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,44669,44671],{"className":44670},[886],[888,44672,44673],{"xmlns":890},[892,44674,44675,44679],{},[895,44676,44677],{},[898,44678,1661],{},[902,44680,1661],{"encoding":904},[883,44682,44684],{"className":44683},[886],[888,44685,44686],{"xmlns":890},[892,44687,44688,44700],{},[895,44689,44690,44692,44694,44696,44698],{},[1701,44691,1799],{"stretchy":1798},[898,44693,1802],{},[1701,44695,2012],{"separator":2011},[898,44697,1680],{},[1701,44699,1805],{"stretchy":1798},[902,44701,2019],{"encoding":904},[41376,44703,44705],{"id":44704},"lineární-model-nabídky","Lineární model nabídky",[883,44707,44709],{"className":44708},[886],[888,44710,44711],{"xmlns":890,"display":2252},[892,44712,44713,44752],{},[2256,44714,44715],{"width":2258},[2260,44716,44717,44719,44745,44747],{},[2263,44718],{"width":2265},[2263,44720,44721],{},[895,44722,44723,44725,44727,44729,44731,44733,44735,44737,44739,44741,44743],{},[898,44724,1680],{},[1701,44726,1792],{},[898,44728,3618],{},[898,44730,1802],{},[1701,44732,1703],{},[898,44734,2312],{},[1701,44736,2012],{"separator":2011},[9942,44738],{"width":9944},[898,44740,3618],{},[1701,44742,7491],{},[1850,44744,16514],{},[2263,44746],{"width":2265},[2263,44748,44749],{},[1939,44750,44751],{},"(2.9)",[902,44753,44754],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,44756,44757,44758,44794,44795,44808],{},"Alternativně ",[883,44759,44761],{"className":44760},[886],[888,44762,44763],{"xmlns":890},[892,44764,44765,44791],{},[895,44766,44767,44769,44771,44779,44781,44783],{},[898,44768,1802],{},[1701,44770,1792],{},[2363,44772,44773],{"scriptlevel":1852,"displaystyle":1798},[3726,44774,44775,44777],{},[1850,44776,4062],{},[898,44778,3618],{},[898,44780,1680],{},[1701,44782,2317],{},[2363,44784,44785],{"scriptlevel":1852,"displaystyle":1798},[3726,44786,44787,44789],{},[898,44788,2312],{},[898,44790,3618],{},[902,44792,44793],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,44796,44798],{"className":44797},[886],[888,44799,44800],{"xmlns":890},[892,44801,44802,44806],{},[895,44803,44804],{},[898,44805,1680],{},[902,44807,1680],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[41952,44810,44812],{"id":44811},"příklad-25","Příklad 2.5",[724,44814,44815,44817,44818,1715],{},[38,44816,41960],{}," Lineární nabídka ",[883,44819,44821],{"className":44820},[886],[888,44822,44823],{"xmlns":890},[892,44824,44825,44839],{},[895,44826,44827,44829,44831,44833,44835,44837],{},[898,44828,1680],{},[1701,44830,1792],{},[1850,44832,3684],{},[898,44834,1802],{},[1701,44836,1703],{},[1850,44838,9071],{},[902,44840,44841],{"encoding":904},"P = 0{,}5Q + 25",[724,44843,44844,44846,44847,1715],{},[38,44845,41992],{}," Alternativní tvar ",[883,44848,44850],{"className":44849},[886],[888,44851,44852],{"xmlns":890},[892,44853,44854,44868],{},[895,44855,44856,44858,44860,44862,44864,44866],{},[898,44857,1802],{},[1701,44859,1792],{},[1850,44861,3938],{},[898,44863,1680],{},[1701,44865,2317],{},[1850,44867,7206],{},[902,44869,44870],{"encoding":904},"Q = 2P - 50",[16,44872,44873,44898],{},[19,44874,44875],{},[22,44876,44877,44892,44894,44896],{},[25,44878,44879],{},[883,44880,44882],{"className":44881},[886],[888,44883,44884],{"xmlns":890},[892,44885,44886,44890],{},[895,44887,44888],{},[898,44889,1680],{},[902,44891,1680],{"encoding":904},[25,44893,3776],{},[25,44895,4136],{},[25,44897,3665],{},[30,44899,44900],{},[22,44901,44902,44917,44919,44921],{},[35,44903,44904],{},[883,44905,44907],{"className":44906},[886],[888,44908,44909],{"xmlns":890},[892,44910,44911,44915],{},[895,44912,44913],{},[898,44914,1802],{},[902,44916,1802],{"encoding":904},[35,44918,3703],{},[35,44920,13096],{},[35,44922,3776],{},[198,44924,44926,44927,1805],{"id":44925},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,44928,44929],{},"shift of supply",[724,44931,44932,44933,44936,44937,44954,44955,44980,44981,1715],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,44934,44935],{},"doprava",": při stejné ceně ",[883,44938,44940],{"className":44939},[886],[888,44941,44942],{"xmlns":890},[892,44943,44944,44952],{},[895,44945,44946],{},[1845,44947,44948,44950],{},[898,44949,1680],{},[1850,44951,1852],{},[902,44953,2095],{"encoding":904}," vyrobí výrobce větší ",[883,44956,44958],{"className":44957},[886],[888,44959,44960],{"xmlns":890},[892,44961,44962,44978],{},[895,44963,44964,44970,44972],{},[1845,44965,44966,44968],{},[898,44967,1802],{},[1850,44969,4062],{},[1701,44971,7491],{},[1845,44973,44974,44976],{},[898,44975,1802],{},[1850,44977,1852],{},[902,44979,43085],{"encoding":904},"); zdražení vstupů posune křivku ",[38,44982,44983],{},"doleva",[724,44985,44986],{},[614,44987,44988,44989,45002,45003,45021,45022,45040,45041,1715],{},"Obrázek 2.11: Původní ",[883,44990,44992],{"className":44991},[886],[888,44993,44994],{"xmlns":890},[892,44995,44996,45000],{},[895,44997,44998],{},[898,44999,1661],{},[902,45001,1661],{"encoding":904},", posunuté ",[883,45004,45006],{"className":45005},[886],[888,45007,45008],{"xmlns":890},[892,45009,45010,45018],{},[895,45011,45012],{},[1845,45013,45014,45016],{},[898,45015,1661],{},[1850,45017,4062],{},[902,45019,45020],{"encoding":904},"S_1"," (doprava) a ",[883,45023,45025],{"className":45024},[886],[888,45026,45027],{"xmlns":890},[892,45028,45029,45037],{},[895,45030,45031],{},[1845,45032,45033,45035],{},[898,45034,1661],{},[1850,45036,3938],{},[902,45038,45039],{"encoding":904},"S_2"," (doleva) v ",[883,45042,45044],{"className":45043},[886],[888,45045,45046],{"xmlns":890},[892,45047,45048,45060],{},[895,45049,45050,45052,45054,45056,45058],{},[1701,45051,1799],{"stretchy":1798},[898,45053,1802],{},[1701,45055,2012],{"separator":2011},[898,45057,1680],{},[1701,45059,1805],{"stretchy":1798},[902,45061,2019],{"encoding":904},[41952,45063,45065],{"id":45064},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,45067,45068,45070,45071,45094,45095,1715],{},[38,45069,41960],{}," Nabídka ",[883,45072,45074],{"className":45073},[886],[888,45075,45076],{"xmlns":890},[892,45077,45078,45092],{},[895,45079,45080,45082,45084,45086,45088,45090],{},[898,45081,1680],{},[1701,45083,1792],{},[898,45085,1661],{},[1701,45087,1799],{"stretchy":1798},[898,45089,1802],{},[1701,45091,1805],{"stretchy":1798},[902,45093,1833],{"encoding":904},"; na výrobce je uložena jednotková daň ",[883,45096,45098],{"className":45097},[886],[888,45099,45100],{"xmlns":890},[892,45101,45102,45106],{},[895,45103,45104],{},[898,45105,5877],{},[902,45107,5877],{"encoding":904},[724,45109,45110,45112,45113,45126,45127,45145,45146,45174],{},[38,45111,41992],{}," Spotřebitel zaplatí ",[883,45114,45116],{"className":45115},[886],[888,45117,45118],{"xmlns":890},[892,45119,45120,45124],{},[895,45121,45122],{},[898,45123,1680],{},[902,45125,1680],{"encoding":904},", výrobce obdrží ",[883,45128,45130],{"className":45129},[886],[888,45131,45132],{"xmlns":890},[892,45133,45134,45142],{},[895,45135,45136,45138,45140],{},[898,45137,1680],{},[1701,45139,2317],{},[898,45141,5877],{},[902,45143,45144],{"encoding":904},"P - T",". Z podmínky ",[883,45147,45149],{"className":45148},[886],[888,45150,45151],{"xmlns":890},[892,45152,45153,45171],{},[895,45154,45155,45157,45159,45161,45163,45165,45167,45169],{},[898,45156,1680],{},[1701,45158,2317],{},[898,45160,5877],{},[1701,45162,1792],{},[898,45164,1661],{},[1701,45166,1799],{"stretchy":1798},[898,45168,1802],{},[1701,45170,1805],{"stretchy":1798},[902,45172,45173],{"encoding":904},"P - T = S(Q)"," plyne",[883,45176,45178],{"className":45177},[886],[888,45179,45180],{"xmlns":890,"display":2252},[892,45181,45182,45216],{},[895,45183,45184,45186,45188,45194,45196,45198,45200,45202,45204,45206,45208,45210,45212,45214],{},[898,45185,1680],{},[1701,45187,1792],{},[1845,45189,45190,45192],{},[898,45191,1661],{},[1850,45193,4062],{},[1701,45195,1799],{"stretchy":1798},[898,45197,1802],{},[1701,45199,1805],{"stretchy":1798},[1701,45201,1792],{},[898,45203,1661],{},[1701,45205,1799],{"stretchy":1798},[898,45207,1802],{},[1701,45209,1805],{"stretchy":1798},[1701,45211,1703],{},[898,45213,5877],{},[898,45215,1715],{"mathvariant":2334},[902,45217,45218],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,45220,45221,45222,45235,45236,4088,45249,45252,45253,2633,45273,12164,45291,1715],{},"Křivka ",[883,45223,45225],{"className":45224},[886],[888,45226,45227],{"xmlns":890},[892,45228,45229,45233],{},[895,45230,45231],{},[898,45232,1661],{},[902,45234,1661],{"encoding":904}," se tedy posune o ",[883,45237,45239],{"className":45238},[886],[888,45240,45241],{"xmlns":890},[892,45242,45243,45247],{},[895,45244,45245],{},[898,45246,5877],{},[902,45248,5877],{"encoding":904},[38,45250,45251],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,45254,45256],{"className":45255},[886],[888,45257,45258],{"xmlns":890},[892,45259,45260,45270],{},[895,45261,45262,45264,45266,45268],{},[898,45263,1680],{},[1701,45265,1792],{},[1850,45267,3938],{},[898,45269,1802],{},[902,45271,45272],{"encoding":904},"P = 2Q",[883,45274,45276],{"className":45275},[886],[888,45277,45278],{"xmlns":890},[892,45279,45280,45288],{},[895,45281,45282,45284,45286],{},[898,45283,5877],{},[1701,45285,1792],{},[1850,45287,6352],{},[902,45289,45290],{"encoding":904},"T = 6",[883,45292,45294],{"className":45293},[886],[888,45295,45296],{"xmlns":890},[892,45297,45298,45320],{},[895,45299,45300,45306,45308,45310,45312,45314,45316,45318],{},[1845,45301,45302,45304],{},[898,45303,1661],{},[1850,45305,4062],{},[1701,45307,2246],{},[898,45309,1680],{},[1701,45311,1792],{},[1850,45313,3938],{},[898,45315,1802],{},[1701,45317,1703],{},[1850,45319,6352],{},[902,45321,45322],{"encoding":904},"S_1: P = 2Q + 6",[724,45324,45325],{},[614,45326,45327,45328,45341],{},"Obrázek 2.12: Posun nabídky o ",[883,45329,45331],{"className":45330},[886],[888,45332,45333],{"xmlns":890},[892,45334,45335,45339],{},[895,45336,45337],{},[898,45338,5877],{},[902,45340,5877],{"encoding":904}," svisle nahoru.",[1771,45343],{},[115,45345,45347],{"id":45346},"tržní-rovnováha","Tržní rovnováha",[1635,45349,45350],{},[724,45351,45352,45354,45355,4088,45358,45390,45391,1343,45414,45437,45438,45441,45442,45455],{},[883,45353,2063],{}," TL;DR\nV ",[38,45356,45357],{},"rovnovážném bodě",[883,45359,45361],{"className":45360},[886],[888,45362,45363],{"xmlns":890},[892,45364,45365,45387],{},[895,45366,45367,45369,45371,45377,45379,45385],{},[898,45368,3249],{},[1701,45370,2036],{"stretchy":1798},[3243,45372,45373,45375],{},[898,45374,1802],{},[898,45376,3249],{},[1701,45378,2012],{"separator":2011},[3243,45380,45381,45383],{},[898,45382,1680],{},[898,45384,3249],{},[1701,45386,2053],{"stretchy":1798},[902,45388,45389],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,45392,45394],{"className":45393},[886],[888,45395,45396],{"xmlns":890},[892,45397,45398,45412],{},[895,45399,45400,45402,45404,45406,45408,45410],{},[898,45401,1680],{},[1701,45403,1792],{},[898,45405,1795],{},[1701,45407,1799],{"stretchy":1798},[898,45409,1802],{},[1701,45411,1805],{"stretchy":1798},[902,45413,1808],{"encoding":904},[883,45415,45417],{"className":45416},[886],[888,45418,45419],{"xmlns":890},[892,45420,45421,45435],{},[895,45422,45423,45425,45427,45429,45431,45433],{},[898,45424,1680],{},[1701,45426,1792],{},[898,45428,1661],{},[1701,45430,1799],{"stretchy":1798},[898,45432,1802],{},[1701,45434,1805],{"stretchy":1798},[902,45436,1833],{"encoding":904},". Čtyři ",[38,45439,45440],{},"pravidla komparativní statiky"," popisují, jak se ",[883,45443,45445],{"className":45444},[886],[888,45446,45447],{"xmlns":890},[892,45448,45449,45453],{},[895,45450,45451],{},[898,45452,3249],{},[902,45454,3249],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,45457,45459],{"id":45458},"definice","Definice",[724,45461,45462,1646,45464,45467,45468,4088,45471,45489,45490,45521,45522,1646,45525,2506],{},[38,45463,45347],{},[614,45465,45466],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,45469,45470],{},"rovnovážné ceně",[883,45472,45474],{"className":45473},[886],[888,45475,45476],{"xmlns":890},[892,45477,45478,45486],{},[895,45479,45480],{},[3243,45481,45482,45484],{},[898,45483,1680],{},[898,45485,3249],{},[902,45487,45488],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,45491,45493],{"className":45492},[886],[888,45494,45495],{"xmlns":890},[892,45496,45497,45519],{},[895,45498,45499,45501,45503,45509,45511,45517],{},[898,45500,3249],{},[1701,45502,2036],{"stretchy":1798},[3243,45504,45505,45507],{},[898,45506,1802],{},[898,45508,3249],{},[1701,45510,2012],{"separator":2011},[3243,45512,45513,45515],{},[898,45514,1680],{},[898,45516,3249],{},[1701,45518,2053],{"stretchy":1798},[902,45520,45389],{"encoding":904}," se nazývá ",[38,45523,45524],{},"rovnovážný bod",[614,45526,45527],{},"equilibrium point",[724,45529,45530,45531,1343,45554,1715],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,45532,45534],{"className":45533},[886],[888,45535,45536],{"xmlns":890},[892,45537,45538,45552],{},[895,45539,45540,45542,45544,45546,45548,45550],{},[898,45541,1680],{},[1701,45543,1792],{},[898,45545,1795],{},[1701,45547,1799],{"stretchy":1798},[898,45549,1802],{},[1701,45551,1805],{"stretchy":1798},[902,45553,1808],{"encoding":904},[883,45555,45557],{"className":45556},[886],[888,45558,45559],{"xmlns":890},[892,45560,45561,45575],{},[895,45562,45563,45565,45567,45569,45571,45573],{},[898,45564,1680],{},[1701,45566,1792],{},[898,45568,1661],{},[1701,45570,1799],{"stretchy":1798},[898,45572,1802],{},[1701,45574,1805],{"stretchy":1798},[902,45576,1833],{"encoding":904},[724,45578,45579],{},[2139,45580],{"alt":45581,"className":45582,"src":45583},"imek-poptavka-nabidka-rovnovaha",[210,2143],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,45585,45586],{},[614,45587,45588,45589,45602,45603,1995,45616,45637,45638,1715],{},"Obrázek 2.13: Klesající ",[883,45590,45592],{"className":45591},[886],[888,45593,45594],{"xmlns":890},[892,45595,45596,45600],{},[895,45597,45598],{},[898,45599,1795],{},[902,45601,1795],{"encoding":904}," a rostoucí ",[883,45604,45606],{"className":45605},[886],[888,45607,45608],{"xmlns":890},[892,45609,45610,45614],{},[895,45611,45612],{},[898,45613,1661],{},[902,45615,1661],{"encoding":904},[883,45617,45619],{"className":45618},[886],[888,45620,45621],{"xmlns":890},[892,45622,45623,45635],{},[895,45624,45625,45627,45629,45631,45633],{},[1701,45626,1799],{"stretchy":1798},[898,45628,1802],{},[1701,45630,2012],{"separator":2011},[898,45632,1680],{},[1701,45634,1805],{"stretchy":1798},[902,45636,2019],{"encoding":904}," protínající se v ",[883,45639,45641],{"className":45640},[886],[888,45642,45643],{"xmlns":890},[892,45644,45645,45667],{},[895,45646,45647,45649,45651,45657,45659,45665],{},[898,45648,3249],{},[1701,45650,2036],{"stretchy":1798},[3243,45652,45653,45655],{},[898,45654,1802],{},[898,45656,3249],{},[1701,45658,2012],{"separator":2011},[3243,45660,45661,45663],{},[898,45662,1680],{},[898,45664,3249],{},[1701,45666,2053],{"stretchy":1798},[902,45668,45389],{"encoding":904},[198,45670,45672],{"id":45671},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,45674,45675,45677,45678,45712,45713,1715],{},[38,45676,41960],{}," Poptávka ",[883,45679,45681],{"className":45680},[886],[888,45682,45683],{"xmlns":890},[892,45684,45685,45709],{},[895,45686,45687,45689,45691,45693,45699,45701,45703,45705,45707],{},[898,45688,1680],{},[1701,45690,1792],{},[1701,45692,2317],{},[3243,45694,45695,45697],{},[898,45696,1802],{},[1850,45698,3938],{},[1701,45700,2317],{},[1850,45702,3703],{},[898,45704,1802],{},[1701,45706,1703],{},[1850,45708,12864],{},[902,45710,45711],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,45714,45716],{"className":45715},[886],[888,45717,45718],{"xmlns":890},[892,45719,45720,45742],{},[895,45721,45722,45724,45726,45732,45734,45736,45738,45740],{},[898,45723,1680],{},[1701,45725,1792],{},[3243,45727,45728,45730],{},[898,45729,1802],{},[1850,45731,3938],{},[1701,45733,1703],{},[1850,45735,26985],{},[898,45737,1802],{},[1701,45739,1703],{},[1850,45741,36577],{},[902,45743,45744],{"encoding":904},"P = Q^2 + 14Q + 22",[724,45746,45747,45749],{},[38,45748,41992],{}," Z rovnosti",[883,45751,45753],{"className":45752},[886],[888,45754,45755],{"xmlns":890,"display":2252},[892,45756,45757,45795],{},[895,45758,45759,45761,45767,45769,45771,45773,45775,45777,45779,45785,45787,45789,45791,45793],{},[1701,45760,2317],{},[3243,45762,45763,45765],{},[898,45764,1802],{},[1850,45766,3938],{},[1701,45768,2317],{},[1850,45770,3703],{},[898,45772,1802],{},[1701,45774,1703],{},[1850,45776,12864],{},[1701,45778,1792],{},[3243,45780,45781,45783],{},[898,45782,1802],{},[1850,45784,3938],{},[1701,45786,1703],{},[1850,45788,26985],{},[898,45790,1802],{},[1701,45792,1703],{},[1850,45794,36577],{},[902,45796,45797],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,45799,45800,45801,45835,45836,45869,45870,45887,45888,45901,45902,1343,45924,45961,45962,1715],{},"dostaneme ",[883,45802,45804],{"className":45803},[886],[888,45805,45806],{"xmlns":890},[892,45807,45808,45832],{},[895,45809,45810,45812,45818,45820,45822,45824,45826,45828,45830],{},[1850,45811,3938],{},[3243,45813,45814,45816],{},[898,45815,1802],{},[1850,45817,3938],{},[1701,45819,1703],{},[1850,45821,4840],{},[898,45823,1802],{},[1701,45825,2317],{},[1850,45827,9681],{},[1701,45829,1792],{},[1850,45831,1852],{},[902,45833,45834],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,45837,45839],{"className":45838},[886],[888,45840,45841],{"xmlns":890},[892,45842,45843,45866],{},[895,45844,45845,45851,45853,45855,45857,45859,45862,45864],{},[3243,45846,45847,45849],{},[898,45848,1802],{},[1850,45850,3938],{},[1701,45852,1703],{},[1850,45854,7592],{},[898,45856,1802],{},[1701,45858,2317],{},[1850,45860,45861],{},"64",[1701,45863,1792],{},[1850,45865,1852],{},[902,45867,45868],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,45871,45873],{"className":45872},[886],[888,45874,45875],{"xmlns":890},[892,45876,45877,45884],{},[895,45878,45879,45881],{},[1701,45880,2317],{},[1850,45882,45883],{},"16",[902,45885,45886],{"encoding":904},"-16"," (nevyhovuje) a ",[883,45889,45891],{"className":45890},[886],[888,45892,45893],{"xmlns":890},[892,45894,45895,45899],{},[895,45896,45897],{},[1850,45898,6460],{},[902,45900,6460],{"encoding":904},". Tedy ",[883,45903,45905],{"className":45904},[886],[888,45906,45907],{"xmlns":890},[892,45908,45909,45921],{},[895,45910,45911,45917,45919],{},[3243,45912,45913,45915],{},[898,45914,1802],{},[898,45916,3249],{},[1701,45918,1792],{},[1850,45920,6460],{},[902,45922,45923],{"encoding":904},"Q^E = 4",[883,45925,45927],{"className":45926},[886],[888,45928,45929],{"xmlns":890},[892,45930,45931,45958],{},[895,45932,45933,45939,45941,45943,45945,45947,45949,45951,45953,45955],{},[3243,45934,45935,45937],{},[898,45936,1680],{},[898,45938,3249],{},[1701,45940,1792],{},[1701,45942,2317],{},[1850,45944,45883],{},[1701,45946,2317],{},[1850,45948,3665],{},[1701,45950,1703],{},[1850,45952,12864],{},[1701,45954,1792],{},[1850,45956,45957],{},"94",[902,45959,45960],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,45963,45965],{"className":45964},[886],[888,45966,45967],{"xmlns":890},[892,45968,45969,45983],{},[895,45970,45971,45973,45975,45977,45979,45981],{},[898,45972,3249],{},[1701,45974,2036],{"stretchy":1798},[1850,45976,6460],{},[1701,45978,2012],{"separator":2011},[1850,45980,45957],{},[1701,45982,2053],{"stretchy":1798},[902,45984,45985],{"encoding":904},"E[4, 94]",[198,45987,45989],{"id":45988},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,45991,45992,45994],{},[38,45993,41960],{}," Poptávky a nabídky dvou zboží",[883,45996,45998],{"className":45997},[886],[888,45999,46000],{"xmlns":890,"display":2252},[892,46001,46002,46168],{},[2256,46003,46006,46094],{"rowspacing":24799,"columnalign":46004,"columnspacing":46005},"right left right left","0em 1em 0em",[2260,46007,46008,46018,46050,46060],{},[2263,46009,46010],{},[2363,46011,46012],{"scriptlevel":1852,"displaystyle":2011},[1845,46013,46014,46016],{},[898,46015,1802],{},[1850,46017,4062],{},[2263,46019,46020],{},[2363,46021,46022],{"scriptlevel":1852,"displaystyle":2011},[895,46023,46024,46026,46028,46030,46032,46034,46040,46042,46048],{},[895,46025],{},[1701,46027,1792],{},[1850,46029,3665],{},[1701,46031,2317],{},[1850,46033,4225],{},[1845,46035,46036,46038],{},[898,46037,1680],{},[1850,46039,4062],{},[1701,46041,2317],{},[1845,46043,46044,46046],{},[898,46045,1680],{},[1850,46047,3938],{},[1701,46049,2012],{"separator":2011},[2263,46051,46052],{},[2363,46053,46054],{"scriptlevel":1852,"displaystyle":2011},[1845,46055,46056,46058],{},[898,46057,1802],{},[1850,46059,3938],{},[2263,46061,46062],{},[2363,46063,46064],{"scriptlevel":1852,"displaystyle":2011},[895,46065,46066,46068,46070,46072,46074,46076,46082,46084,46086,46092],{},[895,46067],{},[1701,46069,1792],{},[1850,46071,7206],{},[1701,46073,2317],{},[1850,46075,3938],{},[1845,46077,46078,46080],{},[898,46079,1680],{},[1850,46081,4062],{},[1701,46083,2317],{},[1850,46085,6460],{},[1845,46087,46088,46090],{},[898,46089,1680],{},[1850,46091,3938],{},[1701,46093,2012],{"separator":2011},[2260,46095,46096,46106,46132,46142],{},[2263,46097,46098],{},[2363,46099,46100],{"scriptlevel":1852,"displaystyle":2011},[1845,46101,46102,46104],{},[898,46103,1802],{},[1850,46105,4062],{},[2263,46107,46108],{},[2363,46109,46110],{"scriptlevel":1852,"displaystyle":2011},[895,46111,46112,46114,46116,46118,46120,46122,46124,46130],{},[895,46113],{},[1701,46115,1792],{},[1701,46117,2317],{},[1850,46119,3646],{},[1701,46121,1703],{},[1850,46123,6460],{},[1845,46125,46126,46128],{},[898,46127,1680],{},[1850,46129,4062],{},[1701,46131,2012],{"separator":2011},[2263,46133,46134],{},[2363,46135,46136],{"scriptlevel":1852,"displaystyle":2011},[1845,46137,46138,46140],{},[898,46139,1802],{},[1850,46141,3938],{},[2263,46143,46144],{},[2363,46145,46146],{"scriptlevel":1852,"displaystyle":2011},[895,46147,46148,46150,46152,46154,46156,46158,46160,46166],{},[895,46149],{},[1701,46151,1792],{},[1701,46153,2317],{},[1850,46155,28239],{},[1701,46157,1703],{},[1850,46159,3646],{},[1845,46161,46162,46164],{},[898,46163,1680],{},[1850,46165,3938],{},[898,46167,1715],{"mathvariant":2334},[902,46169,46170],{"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}",[724,46172,46173,46175],{},[38,46174,41992],{}," Z rovností poptávek a nabídek dostaneme",[883,46177,46179],{"className":46178},[886],[888,46180,46181],{"xmlns":890,"display":2252},[892,46182,46183,46232],{},[895,46184,46185,46187,46193,46195,46201,46203,46205,46207,46209,46211,46217,46219,46221,46227,46229],{},[1850,46186,8073],{},[1845,46188,46189,46191],{},[898,46190,1680],{},[1850,46192,4062],{},[1701,46194,1703],{},[1845,46196,46197,46199],{},[898,46198,1680],{},[1850,46200,3938],{},[1701,46202,1792],{},[1850,46204,25244],{},[1701,46206,2012],{"separator":2011},[9942,46208],{"width":9944},[1850,46210,3938],{},[1845,46212,46213,46215],{},[898,46214,1680],{},[1850,46216,4062],{},[1701,46218,1703],{},[1850,46220,28239],{},[1845,46222,46223,46225],{},[898,46224,1680],{},[1850,46226,3938],{},[1701,46228,1792],{},[1850,46230,46231],{},"57.",[902,46233,46234],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,46236,46237,46238,1343,46262,46286,46287,1343,46312,46336,46337,46339],{},"Řešením je ",[883,46239,46241],{"className":46240},[886],[888,46242,46243],{"xmlns":890},[892,46244,46245,46259],{},[895,46246,46247,46255,46257],{},[2287,46248,46249,46251,46253],{},[898,46250,1680],{},[1850,46252,4062],{},[898,46254,3249],{},[1701,46256,1792],{},[1850,46258,6460],{},[902,46260,46261],{"encoding":904},"P_1^E = 4",[883,46263,46265],{"className":46264},[886],[888,46266,46267],{"xmlns":890},[892,46268,46269,46283],{},[895,46270,46271,46279,46281],{},[2287,46272,46273,46275,46277],{},[898,46274,1680],{},[1850,46276,3938],{},[898,46278,3249],{},[1701,46280,1792],{},[1850,46282,28239],{},[902,46284,46285],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,46288,46290],{"className":46289},[886],[888,46291,46292],{"xmlns":890},[892,46293,46294,46309],{},[895,46295,46296,46304,46306],{},[2287,46297,46298,46300,46302],{},[898,46299,1802],{},[1850,46301,4062],{},[898,46303,3249],{},[1701,46305,1792],{},[1850,46307,46308],{},"13",[902,46310,46311],{"encoding":904},"Q_1^E = 13",[883,46313,46315],{"className":46314},[886],[888,46316,46317],{"xmlns":890},[892,46318,46319,46333],{},[895,46320,46321,46329,46331],{},[2287,46322,46323,46325,46327],{},[898,46324,1802],{},[1850,46326,3938],{},[898,46328,3249],{},[1701,46330,1792],{},[1850,46332,26985],{},[902,46334,46335],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,46338,43846],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,46341,46343],{"id":46342},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,46345,46346,46347,46364,46365,1646,46368,2506],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,46348,46350],{"className":46349},[886],[888,46351,46352],{"xmlns":890},[892,46353,46354,46362],{},[895,46355,46356],{},[3243,46357,46358,46360],{},[898,46359,1680],{},[898,46361,3249],{},[902,46363,45488],{"encoding":904},"; mechanismus popisuje ",[38,46366,46367],{},"teorém pavučiny",[614,46369,46370],{},"cobweb model",[198,46372,46374],{"id":46373},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,46376,46377],{},[2139,46378],{"alt":46379,"className":46380,"src":46381},"imek-komparativni-statika-4pripady",[210,2143],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1635,46383,46384,46424,46464,46504],{},[724,46385,46386,46389,46390,10253,46407,1715],{},[38,46387,46388],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,46391,46393],{"className":46392},[886],[888,46394,46395],{"xmlns":890},[892,46396,46397,46405],{},[895,46398,46399],{},[3243,46400,46401,46403],{},[898,46402,1680],{},[898,46404,3249],{},[902,46406,45488],{"encoding":904},[883,46408,46410],{"className":46409},[886],[888,46411,46412],{"xmlns":890},[892,46413,46414,46422],{},[895,46415,46416],{},[3243,46417,46418,46420],{},[898,46419,1802],{},[898,46421,3249],{},[902,46423,3807],{"encoding":904},[724,46425,46426,46429,46430,10253,46447,1715],{},[38,46427,46428],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,46431,46433],{"className":46432},[886],[888,46434,46435],{"xmlns":890},[892,46436,46437,46445],{},[895,46438,46439],{},[3243,46440,46441,46443],{},[898,46442,1680],{},[898,46444,3249],{},[902,46446,45488],{"encoding":904},[883,46448,46450],{"className":46449},[886],[888,46451,46452],{"xmlns":890},[892,46453,46454,46462],{},[895,46455,46456],{},[3243,46457,46458,46460],{},[898,46459,1802],{},[898,46461,3249],{},[902,46463,3807],{"encoding":904},[724,46465,46466,46469,46470,13414,46487,1715],{},[38,46467,46468],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,46471,46473],{"className":46472},[886],[888,46474,46475],{"xmlns":890},[892,46476,46477,46485],{},[895,46478,46479],{},[3243,46480,46481,46483],{},[898,46482,1680],{},[898,46484,3249],{},[902,46486,45488],{"encoding":904},[883,46488,46490],{"className":46489},[886],[888,46491,46492],{"xmlns":890},[892,46493,46494,46502],{},[895,46495,46496],{},[3243,46497,46498,46500],{},[898,46499,1802],{},[898,46501,3249],{},[902,46503,3807],{"encoding":904},[724,46505,46506,46509,46510,46527,46528,1715],{},[38,46507,46508],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,46511,46513],{"className":46512},[886],[888,46514,46515],{"xmlns":890},[892,46516,46517,46525],{},[895,46518,46519],{},[3243,46520,46521,46523],{},[898,46522,1680],{},[898,46524,3249],{},[902,46526,45488],{"encoding":904},", pokles ",[883,46529,46531],{"className":46530},[886],[888,46532,46533],{"xmlns":890},[892,46534,46535,46543],{},[895,46536,46537],{},[3243,46538,46539,46541],{},[898,46540,1802],{},[898,46542,3249],{},[902,46544,3807],{"encoding":904},[16,46546,46547,46592],{},[19,46548,46549],{},[22,46550,46551,46554,46573],{},[25,46552,46553],{},"Změna",[25,46555,46556],{},[883,46557,46559],{"className":46558},[886],[888,46560,46561],{"xmlns":890},[892,46562,46563,46571],{},[895,46564,46565],{},[3243,46566,46567,46569],{},[898,46568,1680],{},[898,46570,3249],{},[902,46572,45488],{"encoding":904},[25,46574,46575],{},[883,46576,46578],{"className":46577},[886],[888,46579,46580],{"xmlns":890},[892,46581,46582,46590],{},[895,46583,46584],{},[3243,46585,46586,46588],{},[898,46587,1802],{},[898,46589,3249],{},[902,46591,3807],{"encoding":904},[30,46593,46594,46604,46614,46623],{},[22,46595,46596,46599,46602],{},[35,46597,46598],{},"Růst poptávky",[35,46600,46601],{},"↑",[35,46603,46601],{},[22,46605,46606,46609,46612],{},[35,46607,46608],{},"Pokles poptávky",[35,46610,46611],{},"↓",[35,46613,46611],{},[22,46615,46616,46619,46621],{},[35,46617,46618],{},"Růst nabídky",[35,46620,46611],{},[35,46622,46601],{},[22,46624,46625,46628,46630],{},[35,46626,46627],{},"Pokles nabídky",[35,46629,46601],{},[35,46631,46611],{},[724,46633,46634],{},[614,46635,46636],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[1771,46638],{},[115,46640,811],{"id":46641},"zdanění-trhu",[1635,46643,46644,46733],{},[724,46645,46646,46648,46649,46662,46663,7015,46676,46679,46680,40806,46703,46728,46729,46732],{},[883,46647,2063],{}," TL;DR\nJednotková daň ",[883,46650,46652],{"className":46651},[886],[888,46653,46654],{"xmlns":890},[892,46655,46656,46660],{},[895,46657,46658],{},[898,46659,5877],{},[902,46661,5877],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,46664,46666],{"className":46665},[886],[888,46667,46668],{"xmlns":890},[892,46669,46670,46674],{},[895,46671,46672],{},[898,46673,5877],{},[902,46675,5877],{"encoding":904},[38,46677,46678],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,46681,46683],{"className":46682},[886],[888,46684,46685],{"xmlns":890},[892,46686,46687,46700],{},[895,46688,46689],{},[1845,46690,46691,46693],{},[898,46692,5877],{},[895,46694,46695,46698],{},[898,46696,46697],{},"s",[898,46699,724],{},[902,46701,46702],{"encoding":904},"T_{sp}",[883,46704,46706],{"className":46705},[886],[888,46707,46708],{"xmlns":890},[892,46709,46710,46725],{},[895,46711,46712],{},[1845,46713,46714,46716],{},[898,46715,5877],{},[895,46717,46718,46721,46723],{},[898,46719,46720],{},"v",[898,46722,6127],{},[898,46724,16096],{},[902,46726,46727],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,46730,46731],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,46734,46735],{},[614,46736,46737,46738,1715],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,46739,46741],{"className":46740,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,46743,46744,46745,46748,46749,46775,46776,46779,46780,46806,46807,46824,46825,46865,46866,2633,46879,1715],{},"Existují dvě formy zdanění — daň uložená ",[38,46746,46747],{},"výrobci"," (posun nabídky ",[883,46750,46752],{"className":46751},[886],[888,46753,46754],{"xmlns":890},[892,46755,46756,46772],{},[895,46757,46758,46764,46766,46768,46770],{},[1845,46759,46760,46762],{},[898,46761,1661],{},[1850,46763,4062],{},[1701,46765,1792],{},[898,46767,1661],{},[1701,46769,1703],{},[898,46771,5877],{},[902,46773,46774],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,46777,46778],{},"spotřebiteli"," (posun poptávky ",[883,46781,46783],{"className":46782},[886],[888,46784,46785],{"xmlns":890},[892,46786,46787,46803],{},[895,46788,46789,46795,46797,46799,46801],{},[1845,46790,46791,46793],{},[898,46792,1795],{},[1850,46794,3938],{},[1701,46796,1792],{},[898,46798,1795],{},[1701,46800,2317],{},[898,46802,5877],{},[902,46804,46805],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,46808,46810],{"className":46809},[886],[888,46811,46812],{"xmlns":890},[892,46813,46814,46822],{},[895,46815,46816],{},[3243,46817,46818,46820],{},[898,46819,1802],{},[898,46821,3249],{},[902,46823,3807],{"encoding":904}," klesá a vzniká rozklad daně ",[883,46826,46828],{"className":46827},[886],[888,46829,46830],{"xmlns":890},[892,46831,46832,46862],{},[895,46833,46834,46836,46838,46848,46850],{},[898,46835,5877],{},[1701,46837,1792],{},[1845,46839,46840,46842],{},[898,46841,5877],{},[895,46843,46844,46846],{},[898,46845,46697],{},[898,46847,724],{},[1701,46849,1703],{},[1845,46851,46852,46854],{},[898,46853,5877],{},[895,46855,46856,46858,46860],{},[898,46857,46720],{},[898,46859,6127],{},[898,46861,16096],{},[902,46863,46864],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,46867,46869],{"className":46868},[886],[888,46870,46871],{"xmlns":890},[892,46872,46873,46877],{},[895,46874,46875],{},[898,46876,1795],{},[902,46878,1795],{"encoding":904},[883,46880,46882],{"className":46881},[886],[888,46883,46884],{"xmlns":890},[892,46885,46886,46890],{},[895,46887,46888],{},[898,46889,1661],{},[902,46891,1661],{"encoding":904},[724,46893,46894,46895,46898,46899,2633,46929,46963],{},"Zásadním výsledkem kapitoly je ",[38,46896,46897],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,46900,46902],{"className":46901},[886],[888,46903,46904],{"xmlns":890},[892,46905,46906,46926],{},[895,46907,46908,46916,46918],{},[2287,46909,46910,46912,46914],{},[898,46911,1802],{},[1850,46913,4062],{},[898,46915,3249],{},[1701,46917,1792],{},[2287,46919,46920,46922,46924],{},[898,46921,1802],{},[1850,46923,3938],{},[898,46925,3249],{},[902,46927,46928],{"encoding":904},"Q_1^E = Q_2^E",[883,46930,46932],{"className":46931},[886],[888,46933,46934],{"xmlns":890},[892,46935,46936,46960],{},[895,46937,46938,46946,46948,46950,46952],{},[2287,46939,46940,46942,46944],{},[898,46941,1680],{},[1850,46943,4062],{},[898,46945,3249],{},[1701,46947,2317],{},[898,46949,5877],{},[1701,46951,1792],{},[2287,46953,46954,46956,46958],{},[898,46955,1680],{},[1850,46957,3938],{},[898,46959,3249],{},[902,46961,46962],{"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.",[724,46965,46966,46967,46970,46971,46997,46998,47026,47027,47030,47031,47034,47035,1715],{},"Podrobný výklad, Příklady ",[38,46968,46969],{},"2.9"," (daň výrobci, ",[883,46972,46974],{"className":46973},[886],[888,46975,46976],{"xmlns":890},[892,46977,46978,46994],{},[895,46979,46980,46990,46992],{},[1845,46981,46982,46984],{},[898,46983,5877],{},[895,46985,46986,46988],{},[898,46987,46697],{},[898,46989,724],{},[1701,46991,1792],{},[1850,46993,3938],{},[902,46995,46996],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,46999,47001],{"className":47000},[886],[888,47002,47003],{"xmlns":890},[892,47004,47005,47023],{},[895,47006,47007,47019,47021],{},[1845,47008,47009,47011],{},[898,47010,5877],{},[895,47012,47013,47015,47017],{},[898,47014,46720],{},[898,47016,6127],{},[898,47018,16096],{},[1701,47020,1792],{},[1850,47022,6460],{},[902,47024,47025],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,47028,47029],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,47032,47033],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,47036,46741],{"className":47037,"dataFsResolvedFilePath":809,"href":810},[210],[1771,47039],{},[115,47041,47043],{"id":47042},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1635,47045,47046],{},[724,47047,47048,47050,47051,47054,47055,47057],{},[883,47049,2063],{}," TL;DR\nMultiplikátory jsou ",[38,47052,47053],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,47056,40990],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,47059,47061],{"id":47060},"redukovaný-tvar","Redukovaný tvar",[724,47063,47064,47065,1646,47088,1343,47106,1738,47123,1646,47146,47163,47164,47194],{},"Pro lineární model ",[883,47066,47068],{"className":47067},[886],[888,47069,47070],{"xmlns":890},[892,47071,47072,47086],{},[895,47073,47074,47076,47078,47080,47082,47084],{},[898,47075,1680],{},[1701,47077,1792],{},[898,47079,207],{},[898,47081,1802],{},[1701,47083,1703],{},[898,47085,3598],{},[902,47087,3601],{"encoding":904},[883,47089,47091],{"className":47090},[886],[888,47092,47093],{"xmlns":890},[892,47094,47095,47103],{},[895,47096,47097,47099,47101],{},[898,47098,207],{},[1701,47100,7530],{},[1850,47102,1852],{},[902,47104,47105],{"encoding":904},"a \u003C 0",[883,47107,47109],{"className":47108},[886],[888,47110,47111],{"xmlns":890},[892,47112,47113,47121],{},[895,47114,47115,47117,47119],{},[898,47116,3598],{},[1701,47118,7491],{},[1850,47120,1852],{},[902,47122,22860],{"encoding":904},[883,47124,47126],{"className":47125},[886],[888,47127,47128],{"xmlns":890},[892,47129,47130,47144],{},[895,47131,47132,47134,47136,47138,47140,47142],{},[898,47133,1680],{},[1701,47135,1792],{},[898,47137,3618],{},[898,47139,1802],{},[1701,47141,1703],{},[898,47143,2312],{},[902,47145,3627],{"encoding":904},[883,47147,47149],{"className":47148},[886],[888,47150,47151],{"xmlns":890},[892,47152,47153,47161],{},[895,47154,47155,47157,47159],{},[898,47156,3618],{},[1701,47158,7491],{},[1850,47160,1852],{},[902,47162,44283],{"encoding":904},") dává podmínka rovnováhy ",[883,47165,47167],{"className":47166},[886],[888,47168,47169],{"xmlns":890},[892,47170,47171,47191],{},[895,47172,47173,47175,47177,47179,47181,47183,47185,47187,47189],{},[898,47174,207],{},[898,47176,1802],{},[1701,47178,1703],{},[898,47180,3598],{},[1701,47182,1792],{},[898,47184,3618],{},[898,47186,1802],{},[1701,47188,1703],{},[898,47190,2312],{},[902,47192,47193],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,47196,47198],{"className":47197},[886],[888,47199,47200],{"xmlns":890,"display":2252},[892,47201,47202,47247],{},[2256,47203,47204],{"width":2258},[2260,47205,47206,47208,47240,47242],{},[2263,47207],{"width":2265},[2263,47209,47210],{},[895,47211,47212,47218,47220,47238],{},[3243,47213,47214,47216],{},[898,47215,1802],{},[898,47217,3249],{},[1701,47219,1792],{},[3726,47221,47222,47230],{},[895,47223,47224,47226,47228],{},[898,47225,3598],{},[1701,47227,2317],{},[898,47229,2312],{},[895,47231,47232,47234,47236],{},[898,47233,3618],{},[1701,47235,2317],{},[898,47237,207],{},[898,47239,1715],{"mathvariant":2334},[2263,47241],{"width":2265},[2263,47243,47244],{},[1939,47245,47246],{},"(2.10)",[902,47248,47249],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,47251,47252,47253,1646,47255,47258,47259,47276,47277,4088,47280,47306,47307,47320,47321,47339,47340,2506],{},"Vztah (2.10) je ",[38,47254,24995],{},[614,47256,47257],{},"reduced form",") pro ",[883,47260,47262],{"className":47261},[886],[888,47263,47264],{"xmlns":890},[892,47265,47266,47274],{},[895,47267,47268],{},[3243,47269,47270,47272],{},[898,47271,1802],{},[898,47273,3249],{},[902,47275,3807],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,47278,47279],{},"parametrů",[883,47281,47283],{"className":47282},[886],[888,47284,47285],{"xmlns":890},[892,47286,47287,47303],{},[895,47288,47289,47291,47293,47295,47297,47299,47301],{},[898,47290,207],{},[1701,47292,2012],{"separator":2011},[898,47294,3598],{},[1701,47296,2012],{"separator":2011},[898,47298,3618],{},[1701,47300,2012],{"separator":2011},[898,47302,2312],{},[902,47304,47305],{"encoding":904},"a, b, c, d",". Aby ",[883,47308,47310],{"className":47309},[886],[888,47311,47312],{"xmlns":890},[892,47313,47314,47318],{},[895,47315,47316],{},[898,47317,3249],{},[902,47319,3249],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,47322,47324],{"className":47323},[886],[888,47325,47326],{"xmlns":890},[892,47327,47328,47336],{},[895,47329,47330,47332,47334],{},[898,47331,3598],{},[1701,47333,7491],{},[898,47335,2312],{},[902,47337,47338],{"encoding":904},"b > d"," (neboť ",[883,47341,47343],{"className":47342},[886],[888,47344,47345],{"xmlns":890},[892,47346,47347,47359],{},[895,47348,47349,47351,47353,47355,47357],{},[898,47350,3618],{},[1701,47352,2317],{},[898,47354,207],{},[1701,47356,7491],{},[1850,47358,1852],{},[902,47360,47361],{"encoding":904},"c - a > 0",[724,47363,47364],{},[614,47365,47366,47367,47380,47381,47394,47395,22694,47408,45961,47425,47438],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,47368,47370],{"className":47369},[886],[888,47371,47372],{"xmlns":890},[892,47373,47374,47378],{},[895,47375,47376],{},[898,47377,3598],{},[902,47379,3598],{"encoding":904}," na ose ",[883,47382,47384],{"className":47383},[886],[888,47385,47386],{"xmlns":890},[892,47387,47388,47392],{},[895,47389,47390],{},[898,47391,1680],{},[902,47393,1680],{"encoding":904},") a nabídka (úsek ",[883,47396,47398],{"className":47397},[886],[888,47399,47400],{"xmlns":890},[892,47401,47402,47406],{},[895,47403,47404],{},[898,47405,2312],{},[902,47407,2312],{"encoding":904},[883,47409,47411],{"className":47410},[886],[888,47412,47413],{"xmlns":890},[892,47414,47415,47423],{},[895,47416,47417,47419,47421],{},[898,47418,3598],{},[1701,47420,7491],{},[898,47422,2312],{},[902,47424,47338],{"encoding":904},[883,47426,47428],{"className":47427},[886],[888,47429,47430],{"xmlns":890},[892,47431,47432,47436],{},[895,47433,47434],{},[898,47435,3249],{},[902,47437,3249],{"encoding":904}," v 1. kvadrantu.",[198,47440,47442],{"id":47441},"definice-multiplikátorů","Definice multiplikátorů",[724,47444,47445,47446,47471,47472,47485,47486,47499],{},"V komparativní statice jsou ",[883,47447,47449],{"className":47448},[886],[888,47450,47451],{"xmlns":890},[892,47452,47453,47469],{},[895,47454,47455,47457,47459,47461,47463,47465,47467],{},[898,47456,207],{},[1701,47458,2012],{"separator":2011},[898,47460,3598],{},[1701,47462,2012],{"separator":2011},[898,47464,3618],{},[1701,47466,2012],{"separator":2011},[898,47468,2312],{},[902,47470,47305],{"encoding":904}," exogenní proměnné a ",[883,47473,47475],{"className":47474},[886],[888,47476,47477],{"xmlns":890},[892,47478,47479,47483],{},[895,47480,47481],{},[898,47482,1802],{},[902,47484,1802],{"encoding":904}," endogenní. Přibližná změna ",[883,47487,47489],{"className":47488},[886],[888,47490,47491],{"xmlns":890},[892,47492,47493,47497],{},[895,47494,47495],{},[898,47496,1802],{},[902,47498,1802],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,47501,47503],{"className":47502},[886],[888,47504,47505],{"xmlns":890,"display":2252},[892,47506,47507,47600],{},[2256,47508,47509],{"width":2258},[2260,47510,47511,47513,47593,47595],{},[2263,47512],{"width":2265},[2263,47514,47515],{},[895,47516,47517,47519,47521,47523,47525,47527,47529,47537,47539,47541,47543,47545,47553,47555,47557,47559,47561,47569,47571,47573,47575,47577,47585,47587,47589,47591],{},[898,47518,4708],{"mathvariant":2334},[898,47520,1802],{},[1701,47522,4067],{},[898,47524,2312],{},[898,47526,1802],{},[1701,47528,1792],{},[2287,47530,47531,47533,47535],{},[898,47532,1802],{},[898,47534,207],{},[1701,47536,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,47538,1941],{},[898,47540,2312],{},[898,47542,207],{},[1701,47544,1703],{},[2287,47546,47547,47549,47551],{},[898,47548,1802],{},[898,47550,3598],{},[1701,47552,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,47554,1941],{},[898,47556,2312],{},[898,47558,3598],{},[1701,47560,1703],{},[2287,47562,47563,47565,47567],{},[898,47564,1802],{},[898,47566,3618],{},[1701,47568,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,47570,1941],{},[898,47572,2312],{},[898,47574,3618],{},[1701,47576,1703],{},[2287,47578,47579,47581,47583],{},[898,47580,1802],{},[898,47582,2312],{},[1701,47584,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,47586,1941],{},[898,47588,2312],{},[898,47590,2312],{},[898,47592,1715],{"mathvariant":2334},[2263,47594],{"width":2265},[2263,47596,47597],{},[1939,47598,47599],{},"(2.11)",[902,47601,47602],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,47604,47605,47606,47656,47657,1646,47659,4539],{},"Parciální derivace ",[883,47607,47609],{"className":47608},[886],[888,47610,47611],{"xmlns":890},[892,47612,47613,47653],{},[895,47614,47615,47623,47625,47633,47635,47643,47645],{},[2287,47616,47617,47619,47621],{},[898,47618,1802],{},[898,47620,207],{},[1701,47622,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47624,2012],{"separator":2011},[2287,47626,47627,47629,47631],{},[898,47628,1802],{},[898,47630,3598],{},[1701,47632,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47634,2012],{"separator":2011},[2287,47636,47637,47639,47641],{},[898,47638,1802],{},[898,47640,3618],{},[1701,47642,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47644,2012],{"separator":2011},[2287,47646,47647,47649,47651],{},[898,47648,1802],{},[898,47650,2312],{},[1701,47652,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,47654,47655],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,47658,22023],{},[614,47660,47661],{},"multipliers",[883,47663,47665],{"className":47664},[886],[888,47666,47667],{"xmlns":890,"display":2252},[892,47668,47669,47820],{},[2256,47670,47671],{"width":2258},[2260,47672,47673,47675,47813,47815],{},[2263,47674],{"width":2265},[2263,47676,47677],{},[895,47678,47679,47687,47689,47715,47717,47719,47727,47729,47741,47743,47745,47753,47755,47757,47783,47785,47787,47795,47797,47799,47811],{},[2287,47680,47681,47683,47685],{},[898,47682,1802],{},[898,47684,207],{},[1701,47686,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47688,1792],{},[3726,47690,47691,47699],{},[895,47692,47693,47695,47697],{},[898,47694,3598],{},[1701,47696,2317],{},[898,47698,2312],{},[895,47700,47701,47703,47705,47707,47709],{},[1701,47702,1799],{"stretchy":1798},[898,47704,3618],{},[1701,47706,2317],{},[898,47708,207],{},[3243,47710,47711,47713],{},[1701,47712,1805],{"stretchy":1798},[1850,47714,3938],{},[1701,47716,2012],{"separator":2011},[9942,47718],{"width":19336},[2287,47720,47721,47723,47725],{},[898,47722,1802],{},[898,47724,3598],{},[1701,47726,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47728,1792],{},[3726,47730,47731,47733],{},[1850,47732,4062],{},[895,47734,47735,47737,47739],{},[898,47736,3618],{},[1701,47738,2317],{},[898,47740,207],{},[1701,47742,2012],{"separator":2011},[9942,47744],{"width":19336},[2287,47746,47747,47749,47751],{},[898,47748,1802],{},[898,47750,3618],{},[1701,47752,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47754,1792],{},[1701,47756,2317],{},[3726,47758,47759,47767],{},[895,47760,47761,47763,47765],{},[898,47762,3598],{},[1701,47764,2317],{},[898,47766,2312],{},[895,47768,47769,47771,47773,47775,47777],{},[1701,47770,1799],{"stretchy":1798},[898,47772,3618],{},[1701,47774,2317],{},[898,47776,207],{},[3243,47778,47779,47781],{},[1701,47780,1805],{"stretchy":1798},[1850,47782,3938],{},[1701,47784,2012],{"separator":2011},[9942,47786],{"width":19336},[2287,47788,47789,47791,47793],{},[898,47790,1802],{},[898,47792,2312],{},[1701,47794,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47796,1792],{},[1701,47798,2317],{},[3726,47800,47801,47803],{},[1850,47802,4062],{},[895,47804,47805,47807,47809],{},[898,47806,3618],{},[1701,47808,2317],{},[898,47810,207],{},[898,47812,1715],{"mathvariant":2334},[2263,47814],{"width":2265},[2263,47816,47817],{},[1939,47818,47819],{},"(2.12)",[902,47821,47822],{"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}",[198,47824,47826],{"id":47825},"znaménka-a-interpretace","Znaménka a interpretace",[724,47828,47829,47830,1343,47847,1343,47864,1343,47881,47898,47899,4539],{},"Za podmínek ",[883,47831,47833],{"className":47832},[886],[888,47834,47835],{"xmlns":890},[892,47836,47837,47845],{},[895,47838,47839,47841,47843],{},[898,47840,207],{},[1701,47842,7530],{},[1850,47844,1852],{},[902,47846,47105],{"encoding":904},[883,47848,47850],{"className":47849},[886],[888,47851,47852],{"xmlns":890},[892,47853,47854,47862],{},[895,47855,47856,47858,47860],{},[898,47857,3598],{},[1701,47859,7491],{},[1850,47861,1852],{},[902,47863,22860],{"encoding":904},[883,47865,47867],{"className":47866},[886],[888,47868,47869],{"xmlns":890},[892,47870,47871,47879],{},[895,47872,47873,47875,47877],{},[898,47874,3618],{},[1701,47876,7491],{},[1850,47878,1852],{},[902,47880,44283],{"encoding":904},[883,47882,47884],{"className":47883},[886],[888,47885,47886],{"xmlns":890},[892,47887,47888,47896],{},[895,47889,47890,47892,47894],{},[898,47891,3598],{},[1701,47893,7491],{},[898,47895,2312],{},[902,47897,47338],{"encoding":904}," platí (znaménka se ",[38,47900,47901],{},"nemění",[883,47903,47905],{"className":47904},[886],[888,47906,47907],{"xmlns":890,"display":2252},[892,47908,47909,47971],{},[895,47910,47911,47919,47921,47923,47925,47927,47935,47937,47939,47941,47943,47951,47953,47955,47957,47959,47967,47969],{},[2287,47912,47913,47915,47917],{},[898,47914,1802],{},[898,47916,207],{},[1701,47918,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47920,7491],{},[1850,47922,1852],{},[1701,47924,2012],{"separator":2011},[9942,47926],{"width":9944},[2287,47928,47929,47931,47933],{},[898,47930,1802],{},[898,47932,3598],{},[1701,47934,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47936,7491],{},[1850,47938,1852],{},[1701,47940,2012],{"separator":2011},[9942,47942],{"width":9944},[2287,47944,47945,47947,47949],{},[898,47946,1802],{},[898,47948,3618],{},[1701,47950,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47952,7530],{},[1850,47954,1852],{},[1701,47956,2012],{"separator":2011},[9942,47958],{"width":9944},[2287,47960,47961,47963,47965],{},[898,47962,1802],{},[898,47964,2312],{},[1701,47966,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,47968,7530],{},[1850,47970,16514],{},[902,47972,47973],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,47975,47976,48035],{},[123,47977,47978,4088,47981,48001,48002,48019,48020,1343,48033,1715],{},[38,47979,47980],{},"Kvantitativní smysl:",[883,47982,47984],{"className":47983},[886],[888,47985,47986],{"xmlns":890},[892,47987,47988,47998],{},[895,47989,47990],{},[2287,47991,47992,47994,47996],{},[898,47993,1802],{},[898,47995,6137],{},[1701,47997,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,47999,48000],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,48003,48005],{"className":48004},[886],[888,48006,48007],{"xmlns":890},[892,48008,48009,48017],{},[895,48010,48011],{},[3243,48012,48013,48015],{},[898,48014,1802],{},[898,48016,3249],{},[902,48018,3807],{"encoding":904}," při jednotkové změně parametru ",[883,48021,48023],{"className":48022},[886],[888,48024,48025],{"xmlns":890},[892,48026,48027,48031],{},[895,48028,48029],{},[898,48030,6137],{},[902,48032,6137],{"encoding":904},[614,48034,40990],{},[123,48036,48037,48040,48041,48058,48059,1715],{},[38,48038,48039],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,48042,48044],{"className":48043},[886],[888,48045,48046],{"xmlns":890},[892,48047,48048,48056],{},[895,48049,48050],{},[3243,48051,48052,48054],{},[898,48053,1802],{},[898,48055,3249],{},[902,48057,3807],{"encoding":904}," na růst ",[883,48060,48062],{"className":48061},[886],[888,48063,48064],{"xmlns":890},[892,48065,48066,48070],{},[895,48067,48068],{},[898,48069,6137],{},[902,48071,6137],{"encoding":904},[724,48073,48074,48075,48088,48089,47339,48106,2506],{},"Např. růst ",[883,48076,48078],{"className":48077},[886],[888,48079,48080],{"xmlns":890},[892,48081,48082,48086],{},[895,48083,48084],{},[898,48085,3618],{},[902,48087,3618],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,48090,48092],{"className":48091},[886],[888,48093,48094],{"xmlns":890},[892,48095,48096,48104],{},[895,48097,48098],{},[3243,48099,48100,48102],{},[898,48101,1802],{},[898,48103,3249],{},[902,48105,3807],{"encoding":904},[883,48107,48109],{"className":48108},[886],[888,48110,48111],{"xmlns":890},[892,48112,48113,48127],{},[895,48114,48115,48123,48125],{},[2287,48116,48117,48119,48121],{},[898,48118,1802],{},[898,48120,3618],{},[1701,48122,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,48124,7530],{},[1850,48126,1852],{},[902,48128,48129],{"encoding":904},"Q'_c \u003C 0",[724,48131,48132],{},[614,48133,48134,48135,48155,48156,48180,48181,48203,48204,1715],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,48136,48138],{"className":48137},[886],[888,48139,48140],{"xmlns":890},[892,48141,48142,48152],{},[895,48143,48144,48146,48148,48150],{},[898,48145,3618],{},[898,48147,1802],{},[1701,48149,1703],{},[898,48151,2312],{},[902,48153,48154],{"encoding":904},"cQ + d"," na strmější ",[883,48157,48159],{"className":48158},[886],[888,48160,48161],{"xmlns":890},[892,48162,48163,48177],{},[895,48164,48165,48171,48173,48175],{},[1845,48166,48167,48169],{},[898,48168,3618],{},[1850,48170,4062],{},[898,48172,1802],{},[1701,48174,1703],{},[898,48176,2312],{},[902,48178,48179],{"encoding":904},"c_1 Q + d"," (při ",[883,48182,48184],{"className":48183},[886],[888,48185,48186],{"xmlns":890},[892,48187,48188,48200],{},[895,48189,48190,48196,48198],{},[1845,48191,48192,48194],{},[898,48193,3618],{},[1850,48195,4062],{},[1701,48197,7491],{},[898,48199,3618],{},[902,48201,48202],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,48205,48207],{"className":48206},[886],[888,48208,48209],{"xmlns":890},[892,48210,48211,48221],{},[895,48212,48213,48219],{},[3243,48214,48215,48217],{},[898,48216,1802],{},[898,48218,3249],{},[1701,48220,46611],{},[902,48222,48223],{"encoding":904},"Q^E \\downarrow",[724,48225,48226,48227,48259,48260,1715],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,48228,48230],{"className":48229},[886],[888,48231,48232],{"xmlns":890},[892,48233,48234,48256],{},[895,48235,48236,48238,48240,48242,48250,48252,48254],{},[898,48237,4708],{"mathvariant":2334},[898,48239,1802],{},[1701,48241,4067],{},[2287,48243,48244,48246,48248],{},[898,48245,1802],{},[898,48247,3598],{},[1701,48249,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,48251,1941],{},[898,48253,2312],{},[898,48255,3598],{},[902,48257,48258],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,48261,48263],{"className":48262},[886],[888,48264,48265],{"xmlns":890},[892,48266,48267,48275],{},[895,48268,48269],{},[3243,48270,48271,48273],{},[898,48272,1680],{},[898,48274,3249],{},[902,48276,45488],{"encoding":904},[198,48278,48280,48281],{"id":48279},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,48282,48284],{"className":48283},[886],[888,48285,48286],{"xmlns":890},[892,48287,48288,48296],{},[895,48289,48290],{},[3243,48291,48292,48294],{},[898,48293,1802],{},[898,48295,3249],{},[902,48297,3807],{"encoding":904},[724,48299,48300,45677,48302,45712,48328,1715],{},[38,48301,41960],{},[883,48303,48305],{"className":48304},[886],[888,48306,48307],{"xmlns":890},[892,48308,48309,48325],{},[895,48310,48311,48313,48315,48317,48319,48321,48323],{},[898,48312,1680],{},[1701,48314,1792],{},[1701,48316,2317],{},[1850,48318,3646],{},[898,48320,1802],{},[1701,48322,1703],{},[1850,48324,3665],{},[902,48326,48327],{"encoding":904},"P = -3Q + 40",[883,48329,48331],{"className":48330},[886],[888,48332,48333],{"xmlns":890},[892,48334,48335,48349],{},[895,48336,48337,48339,48341,48343,48345,48347],{},[898,48338,1680],{},[1701,48340,1792],{},[1850,48342,3684],{},[898,48344,1802],{},[1701,48346,1703],{},[1850,48348,3703],{},[902,48350,48351],{"encoding":904},"P = 0{,}5Q + 10",[724,48353,48354,48356],{},[38,48355,41992],{}," Rovnovážné množství",[883,48358,48360],{"className":48359},[886],[888,48361,48362],{"xmlns":890,"display":2252},[892,48363,48364,48430],{},[895,48365,48366,48372,48374,48392,48394,48418,48420,48426,48428],{},[3243,48367,48368,48370],{},[898,48369,1802],{},[898,48371,3249],{},[1701,48373,1792],{},[3726,48375,48376,48384],{},[895,48377,48378,48380,48382],{},[898,48379,3598],{},[1701,48381,2317],{},[898,48383,2312],{},[895,48385,48386,48388,48390],{},[898,48387,3618],{},[1701,48389,2317],{},[898,48391,207],{},[1701,48393,1792],{},[3726,48395,48396,48404],{},[895,48397,48398,48400,48402],{},[1850,48399,3665],{},[1701,48401,2317],{},[1850,48403,3703],{},[895,48405,48406,48408,48410,48412,48414,48416],{},[1850,48407,3684],{},[1701,48409,2317],{},[1701,48411,1799],{"stretchy":1798},[1701,48413,2317],{},[1850,48415,3646],{},[1701,48417,1805],{"stretchy":1798},[1701,48419,1792],{},[3726,48421,48422,48424],{},[1850,48423,3776],{},[1850,48425,3779],{},[1701,48427,4067],{},[1850,48429,3785],{},[902,48431,48432],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,48434,48435,48478],{},[38,48436,48437,48438,3841,48451,3856,48464,48477],{},"(a) Změna ",[883,48439,48441],{"className":48440},[886],[888,48442,48443],{"xmlns":890},[892,48444,48445,48449],{},[895,48446,48447],{},[898,48448,3618],{},[902,48450,3618],{"encoding":904},[883,48452,48454],{"className":48453},[886],[888,48455,48456],{"xmlns":890},[892,48457,48458,48462],{},[895,48459,48460],{},[1850,48461,3684],{},[902,48463,3855],{"encoding":904},[883,48465,48467],{"className":48466},[886],[888,48468,48469],{"xmlns":890},[892,48470,48471,48475],{},[895,48472,48473],{},[1850,48474,3868],{},[902,48476,3871],{"encoding":904}," (ceteris paribus)."," Dle (2.12):",[883,48480,48482],{"className":48481},[886],[888,48483,48484],{"xmlns":890,"display":2252},[892,48485,48486,48562],{},[895,48487,48488,48496,48498,48500,48502,48504,48506,48532,48534,48536,48538,48540,48542,48552,48554,48556,48558,48560],{},[2287,48489,48490,48492,48494],{},[898,48491,1802],{},[898,48493,3618],{},[1701,48495,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,48497,1941],{},[898,48499,2312],{},[898,48501,3618],{},[1701,48503,1792],{},[1701,48505,2317],{},[3726,48507,48508,48516],{},[895,48509,48510,48512,48514],{},[898,48511,3598],{},[1701,48513,2317],{},[898,48515,2312],{},[895,48517,48518,48520,48522,48524,48526],{},[1701,48519,1799],{"stretchy":1798},[898,48521,3618],{},[1701,48523,2317],{},[898,48525,207],{},[3243,48527,48528,48530],{},[1701,48529,1805],{"stretchy":1798},[1850,48531,3938],{},[1939,48533,1941],{},[898,48535,2312],{},[898,48537,3618],{},[1701,48539,1792],{},[1701,48541,2317],{},[3726,48543,48544,48546],{},[1850,48545,3776],{},[3243,48547,48548,48550],{},[1850,48549,3779],{},[1850,48551,3938],{},[1701,48553,3408],{},[1850,48555,4033],{},[1701,48557,4067],{},[1701,48559,2317],{},[1850,48561,4040],{},[902,48563,48564],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,48566,48567,48568,1715],{},"Nové rovnovážné množství ",[883,48569,48571],{"className":48570},[886],[888,48572,48573],{"xmlns":890},[892,48574,48575,48598],{},[895,48576,48577,48585,48587,48589,48591,48593,48595],{},[2287,48578,48579,48581,48583],{},[898,48580,1802],{},[1850,48582,4062],{},[898,48584,3249],{},[1701,48586,4067],{},[1850,48588,4026],{},[1701,48590,2317],{},[1850,48592,4074],{},[1701,48594,1792],{},[1850,48596,48597],{},"8,326",[902,48599,48600],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,48602,48603,48684],{},[38,48604,48605,48606,1343,48625,1343,48646,1343,48665,1715],{},"(b) Současné změny ",[883,48607,48609],{"className":48608},[886],[888,48610,48611],{"xmlns":890},[892,48612,48613,48623],{},[895,48614,48615,48617,48619,48621],{},[898,48616,2312],{},[898,48618,207],{},[1701,48620,1792],{},[1850,48622,3684],{},[902,48624,4205],{"encoding":904},[883,48626,48628],{"className":48627},[886],[888,48629,48630],{"xmlns":890},[892,48631,48632,48644],{},[895,48633,48634,48636,48638,48640,48642],{},[898,48635,2312],{},[898,48637,3598],{},[1701,48639,1792],{},[1701,48641,2317],{},[1850,48643,4225],{},[902,48645,4228],{"encoding":904},[883,48647,48649],{"className":48648},[886],[888,48650,48651],{"xmlns":890},[892,48652,48653,48663],{},[895,48654,48655,48657,48659,48661],{},[898,48656,2312],{},[898,48658,3618],{},[1701,48660,1792],{},[1850,48662,4033],{},[902,48664,4248],{"encoding":904},[883,48666,48668],{"className":48667},[886],[888,48669,48670],{"xmlns":890},[892,48671,48672,48682],{},[895,48673,48674,48676,48678,48680],{},[898,48675,2312],{},[898,48677,2312],{},[1701,48679,1792],{},[1850,48681,4062],{},[902,48683,4268],{"encoding":904}," Dosazením do (2.11):",[883,48686,48688],{"className":48687},[886],[888,48689,48690],{"xmlns":890,"display":2252},[892,48691,48692,48834],{},[2256,48693,48694,48776,48812],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,48695,48696,48706],{},[2263,48697,48698],{},[2363,48699,48700],{"scriptlevel":1852,"displaystyle":2011},[895,48701,48702,48704],{},[898,48703,4708],{"mathvariant":2334},[898,48705,1802],{},[2263,48707,48708],{},[2363,48709,48710],{"scriptlevel":1852,"displaystyle":2011},[895,48711,48712,48714,48716,48726,48728,48730,48732,48738,48740,48742,48744,48746,48748,48750,48760,48762,48764,48766,48772,48774],{},[895,48713],{},[1701,48715,4067],{},[3726,48717,48718,48720],{},[1850,48719,3776],{},[3243,48721,48722,48724],{},[1850,48723,3779],{},[1850,48725,3938],{},[1701,48727,3408],{},[1850,48729,3684],{},[1701,48731,1703],{},[3726,48733,48734,48736],{},[1850,48735,4062],{},[1850,48737,3779],{},[1701,48739,3408],{},[1701,48741,1799],{"stretchy":1798},[1701,48743,2317],{},[1850,48745,4225],{},[1701,48747,1805],{"stretchy":1798},[1701,48749,2317],{},[3726,48751,48752,48754],{},[1850,48753,3776],{},[3243,48755,48756,48758],{},[1850,48757,3779],{},[1850,48759,3938],{},[1701,48761,3408],{},[1850,48763,4033],{},[1701,48765,2317],{},[3726,48767,48768,48770],{},[1850,48769,4062],{},[1850,48771,3779],{},[1701,48773,3408],{},[1850,48775,4062],{},[2260,48777,48778,48784],{},[2263,48779,48780],{},[2363,48781,48782],{"scriptlevel":1852,"displaystyle":2011},[895,48783],{},[2263,48785,48786],{},[2363,48787,48788],{"scriptlevel":1852,"displaystyle":2011},[895,48789,48790,48792,48794,48797,48799,48802,48804,48807,48809],{},[895,48791],{},[1701,48793,1792],{},[1850,48795,48796],{},"1,2245",[1701,48798,2317],{},[1850,48800,48801],{},"1,4286",[1701,48803,2317],{},[1850,48805,48806],{},"0,2449",[1701,48808,2317],{},[1850,48810,48811],{},"0,2857",[2260,48813,48814,48820],{},[2263,48815,48816],{},[2363,48817,48818],{"scriptlevel":1852,"displaystyle":2011},[895,48819],{},[2263,48821,48822],{},[2363,48823,48824],{"scriptlevel":1852,"displaystyle":2011},[895,48825,48826,48828,48830,48832],{},[895,48827],{},[1701,48829,4067],{},[1701,48831,2317],{},[1850,48833,4648],{},[902,48835,48836],{"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}",[724,48838,4654,48839,1715],{},[883,48840,48842],{"className":48841},[886],[888,48843,48844],{"xmlns":890},[892,48845,48846,48868],{},[895,48847,48848,48856,48858,48860,48862,48864,48866],{},[2287,48849,48850,48852,48854],{},[898,48851,1802],{},[1850,48853,4062],{},[898,48855,3249],{},[1701,48857,4067],{},[1850,48859,4026],{},[1701,48861,2317],{},[1850,48863,4680],{},[1701,48865,1792],{},[1850,48867,4685],{},[902,48869,48870],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1635,48872,48873],{},[724,48874,48875,48877,48878,48899,48900,48922],{},[883,48876,4695],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,48879,48881],{"className":48880},[886],[888,48882,48883],{"xmlns":890},[892,48884,48885,48897],{},[895,48886,48887,48889,48891,48893,48895],{},[898,48888,4708],{"mathvariant":2334},[898,48890,1802],{},[1701,48892,4067],{},[1701,48894,2317],{},[1850,48896,4717],{},[902,48898,4720],{"encoding":904},", ta však neodpovídá přepočtu parciálních derivací podle (2.11) a (2.12). Správná hodnota při uvedených změnách je ",[883,48901,48903],{"className":48902},[886],[888,48904,48905],{"xmlns":890},[892,48906,48907,48919],{},[895,48908,48909,48911,48913,48915,48917],{},[898,48910,4708],{"mathvariant":2334},[898,48912,1802],{},[1701,48914,4067],{},[1701,48916,2317],{},[1850,48918,4680],{},[902,48920,48921],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,48924,48925],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[1771,48927],{},[115,48929,820],{"id":1633},[1635,48931,48932],{},[724,48933,48934,1642,48936,1646,48938,1738,48953,1646,48955,48970,48971,1715],{},[883,48935,2063],{},[38,48937,1645],{},[883,48939,48941],{"className":48940},[886],[888,48942,48943],{"xmlns":890},[892,48944,48945,48951],{},[895,48946,48947,48949],{},[898,48948,1658],{},[898,48950,1661],{},[902,48952,1664],{"encoding":904},[38,48954,1741],{},[883,48956,48958],{"className":48957},[886],[888,48959,48960],{"xmlns":890},[892,48961,48962,48968],{},[895,48963,48964,48966],{},[898,48965,1680],{},[898,48967,1661],{},[902,48969,1685],{"encoding":904},") 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 ",[207,48972,48974],{"className":48973,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,48976,48977],{},[2139,48978],{"alt":2141,"className":48979,"src":2144},[210,2143],[724,48981,48982,1646,48984,48986],{},[38,48983,1645],{},[614,48985,1722],{},") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,48988,48990],{"className":48989},[886],[888,48991,48992],{"xmlns":890,"display":2252},[892,48993,48994,49070],{},[2256,48995,48996],{"width":2258},[2260,48997,48998,49000,49064,49066],{},[2263,48999],{"width":2265},[2263,49001,49002],{},[895,49003,49004,49006,49008,49010,49016,49018,49020,49032,49034,49036,49038,49040,49042,49044,49046,49048,49054,49056,49062],{},[898,49005,1658],{},[898,49007,1661],{},[1701,49009,1799],{"stretchy":1798},[1845,49011,49012,49014],{},[898,49013,1802],{},[1850,49015,1852],{},[1701,49017,1805],{"stretchy":1798},[1701,49019,1792],{},[2287,49021,49022,49024,49026],{},[1701,49023,2291],{},[1850,49025,1852],{},[1845,49027,49028,49030],{},[898,49029,1802],{},[1850,49031,1852],{},[898,49033,1795],{},[1701,49035,1799],{"stretchy":1798},[898,49037,1802],{},[1701,49039,1805],{"stretchy":1798},[1939,49041,1941],{},[898,49043,2312],{},[898,49045,1802],{},[1701,49047,2317],{},[1845,49049,49050,49052],{},[898,49051,1680],{},[1850,49053,1852],{},[1939,49055,1941],{},[1845,49057,49058,49060],{},[898,49059,1802],{},[1850,49061,1852],{},[898,49063,1715],{"mathvariant":2334},[2263,49065],{"width":2265},[2263,49067,49068],{},[1939,49069,2341],{},[902,49071,2344],{"encoding":904},[724,49073,49074,1646,49076,49078],{},[38,49075,1668],{},[614,49077,1744],{},") — rozdíl mezi tržbou a minimální cenou:",[883,49080,49082],{"className":49081},[886],[888,49083,49084],{"xmlns":890,"display":2252},[892,49085,49086,49162],{},[2256,49087,49088],{"width":2258},[2260,49089,49090,49092,49156,49158],{},[2263,49091],{"width":2265},[2263,49093,49094],{},[895,49095,49096,49098,49100,49102,49108,49110,49112,49118,49120,49126,49128,49140,49142,49144,49146,49148,49150,49152,49154],{},[898,49097,1680],{},[898,49099,1661],{},[1701,49101,1799],{"stretchy":1798},[1845,49103,49104,49106],{},[898,49105,1802],{},[1850,49107,1852],{},[1701,49109,1805],{"stretchy":1798},[1701,49111,1792],{},[1845,49113,49114,49116],{},[898,49115,1680],{},[1850,49117,1852],{},[1939,49119,1941],{},[1845,49121,49122,49124],{},[898,49123,1802],{},[1850,49125,1852],{},[1701,49127,2317],{},[2287,49129,49130,49132,49134],{},[1701,49131,2291],{},[1850,49133,1852],{},[1845,49135,49136,49138],{},[898,49137,1802],{},[1850,49139,1852],{},[898,49141,1661],{},[1701,49143,1799],{"stretchy":1798},[898,49145,1802],{},[1701,49147,1805],{"stretchy":1798},[1939,49149,1941],{},[898,49151,2312],{},[898,49153,1802],{},[898,49155,1715],{"mathvariant":2334},[2263,49157],{"width":2265},[2263,49159,49160],{},[1939,49161,2943],{},[902,49163,2946],{"encoding":904},[724,49165,49166,49167,1715],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,49168,49170],{"className":49169,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[1771,49172],{},[115,49174,49176],{"id":49175},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,49178,49179,49210,49215,49221,49249,49255,49284,49290,49370,49396],{},[123,49180,49181,49183,49184,49209],{},[38,49182,41955],{}," — lineární poptávka ",[883,49185,49187],{"className":49186},[886],[888,49188,49189],{"xmlns":890},[892,49190,49191,49207],{},[895,49192,49193,49195,49197,49199,49201,49203,49205],{},[898,49194,1680],{},[1701,49196,1792],{},[1701,49198,2317],{},[1850,49200,3938],{},[898,49202,1802],{},[1701,49204,1703],{},[1850,49206,7211],{},[902,49208,41987],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,49211,49212,49214],{},[38,49213,42268],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,49216,49217,49220],{},[38,49218,49219],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,49222,49223,49225,49226,1715],{},[38,49224,44812],{}," — lineární nabídka ",[883,49227,49229],{"className":49228},[886],[888,49230,49231],{"xmlns":890},[892,49232,49233,49247],{},[895,49234,49235,49237,49239,49241,49243,49245],{},[898,49236,1680],{},[1701,49238,1792],{},[1850,49240,3684],{},[898,49242,1802],{},[1701,49244,1703],{},[1850,49246,9071],{},[902,49248,44841],{"encoding":904},[123,49250,49251,49254],{},[38,49252,49253],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,49256,49257,49260,49261,1715],{},[38,49258,49259],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,49262,49264],{"className":49263},[886],[888,49265,49266],{"xmlns":890},[892,49267,49268,49282],{},[895,49269,49270,49272,49274,49276,49278,49280],{},[898,49271,3249],{},[1701,49273,2036],{"stretchy":1798},[1850,49275,6460],{},[1701,49277,2012],{"separator":2011},[1850,49279,45957],{},[1701,49281,2053],{"stretchy":1798},[902,49283,45985],{"encoding":904},[123,49285,49286,49289],{},[38,49287,49288],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,49291,49292,49295,49296,49313,49314,1343,49339,49366,49367,7039],{},[38,49293,49294],{},"Příklad 2.9"," — daň ",[883,49297,49299],{"className":49298},[886],[888,49300,49301],{"xmlns":890},[892,49302,49303,49311],{},[895,49304,49305,49307,49309],{},[898,49306,5877],{},[1701,49308,1792],{},[1850,49310,6352],{},[902,49312,45290],{"encoding":904}," na výrobce; rozklad ",[883,49315,49317],{"className":49316},[886],[888,49318,49319],{"xmlns":890},[892,49320,49321,49337],{},[895,49322,49323,49333,49335],{},[1845,49324,49325,49327],{},[898,49326,5877],{},[895,49328,49329,49331],{},[898,49330,46697],{},[898,49332,724],{},[1701,49334,1792],{},[1850,49336,3938],{},[902,49338,46996],{"encoding":904},[883,49340,49342],{"className":49341},[886],[888,49343,49344],{"xmlns":890},[892,49345,49346,49364],{},[895,49347,49348,49360,49362],{},[1845,49349,49350,49352],{},[898,49351,5877],{},[895,49353,49354,49356,49358],{},[898,49355,46720],{},[898,49357,6127],{},[898,49359,16096],{},[1701,49361,1792],{},[1850,49363,6460],{},[902,49365,47025],{"encoding":904},". (Viz ",[207,49368,46741],{"className":49369,"dataFsResolvedFilePath":809,"href":810},[210],[123,49371,49372,49295,49375,49392,49393,7039],{},[38,49373,49374],{},"Příklad 2.10",[883,49376,49378],{"className":49377},[886],[888,49379,49380],{"xmlns":890},[892,49381,49382,49390],{},[895,49383,49384,49386,49388],{},[898,49385,5877],{},[1701,49387,1792],{},[1850,49389,6352],{},[902,49391,45290],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,49394,46741],{"className":49395,"dataFsResolvedFilePath":809,"href":810},[210],[123,49397,49398,49401],{},[38,49399,49400],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[1771,49403],{},[115,49405,49407],{"id":49406},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,49409,49411],{"id":49410},"základní-analýza-poptávky","Základní analýza poptávky",[724,49413,49414,49417,49418,49453,49454,49480],{},[38,49415,49416],{},"2.1"," Je dána poptávka ",[883,49419,49421],{"className":49420},[886],[888,49422,49423],{"xmlns":890},[892,49424,49425,49450],{},[895,49426,49427,49429,49431,49433,49435,49437,49439,49441,49444,49446,49448],{},[898,49428,1802],{},[1701,49430,1792],{},[898,49432,1795],{},[1701,49434,1799],{"stretchy":1798},[898,49436,1680],{},[1701,49438,1805],{"stretchy":1798},[1701,49440,1792],{},[1850,49442,49443],{},"75",[1701,49445,2317],{},[1850,49447,4225],{},[898,49449,1680],{},[902,49451,49452],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,49455,49457],{"className":49456},[886],[888,49458,49459],{"xmlns":890},[892,49460,49461,49477],{},[895,49462,49463,49465,49467,49469,49471,49473,49475],{},[1850,49464,1852],{},[1701,49466,2012],{"separator":2011},[1850,49468,4225],{},[1701,49470,2012],{"separator":2011},[1850,49472,3703],{},[1701,49474,2012],{"separator":2011},[1850,49476,40275],{},[902,49478,49479],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,49482,49483,49486,49487,49505,49506,4539],{},[38,49484,49485],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,49488,49490],{"className":49489},[886],[888,49491,49492],{"xmlns":890},[892,49493,49494,49502],{},[895,49495,49496,49498,49500],{},[898,49497,1680],{},[1701,49499,2012],{"separator":2011},[898,49501,1802],{},[902,49503,49504],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,49507,49509],{"className":49508},[886],[888,49510,49511],{"xmlns":890},[892,49512,49513,49529],{},[895,49514,49515,49517,49519,49521,49523,49525,49527],{},[898,49516,207],{},[1701,49518,2012],{"separator":2011},[898,49520,3598],{},[1701,49522,2012],{"separator":2011},[898,49524,3618],{},[1701,49526,7491],{},[1850,49528,1852],{},[902,49530,49531],{"encoding":904},"a, b, c > 0",[120,49533,49534,49567,49598,49633,49664,49699],{},[123,49535,49536,49537],{},"(a) ",[883,49538,49540],{"className":49539},[886],[888,49541,49542],{"xmlns":890},[892,49543,49544,49564],{},[895,49545,49546,49548,49550],{},[898,49547,1802],{},[1701,49549,1792],{},[2363,49551,49552],{"scriptlevel":1852,"displaystyle":2011},[3726,49553,49554,49556],{},[898,49555,207],{},[895,49557,49558,49560,49562],{},[898,49559,1680],{},[1701,49561,1703],{},[898,49563,3618],{},[902,49565,49566],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,49568,49569,49570],{},"(b) ",[883,49571,49573],{"className":49572},[886],[888,49574,49575],{"xmlns":890},[892,49576,49577,49595],{},[895,49578,49579,49581,49583],{},[898,49580,1802],{},[1701,49582,1792],{},[12179,49584,49585],{},[895,49586,49587,49589,49591,49593],{},[898,49588,207],{},[1701,49590,2317],{},[898,49592,3598],{},[898,49594,1802],{},[902,49596,49597],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,49599,49600,49601],{},"(c) ",[883,49602,49604],{"className":49603},[886],[888,49605,49606],{"xmlns":890},[892,49607,49608,49630],{},[895,49609,49610,49612,49614],{},[898,49611,1802],{},[1701,49613,1792],{},[2363,49615,49616],{"scriptlevel":1852,"displaystyle":2011},[3726,49617,49618,49628],{},[895,49619,49620,49622,49624],{},[898,49621,207],{},[1701,49623,2317],{},[12179,49625,49626],{},[898,49627,1680],{},[898,49629,3598],{},[902,49631,49632],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,49634,49635,49636],{},"(d) ",[883,49637,49639],{"className":49638},[886],[888,49640,49641],{"xmlns":890},[892,49642,49643,49661],{},[895,49644,49645,49647,49649,49651,49653,49655],{},[898,49646,1680],{},[1701,49648,1792],{},[898,49650,207],{},[1701,49652,2317],{},[898,49654,3598],{},[3243,49656,49657,49659],{},[898,49658,1802],{},[1850,49660,3938],{},[902,49662,49663],{"encoding":904},"P = a - bQ^2",[123,49665,49666,49667],{},"(e) ",[883,49668,49670],{"className":49669},[886],[888,49671,49672],{"xmlns":890},[892,49673,49674,49696],{},[895,49675,49676,49678,49680,49682,49692,49694],{},[898,49677,1802],{},[1701,49679,1792],{},[898,49681,3598],{},[3243,49683,49684,49686],{},[898,49685,1680],{},[895,49687,49688,49690],{},[1701,49689,2317],{},[898,49691,207],{},[1701,49693,1703],{},[898,49695,3618],{},[902,49697,49698],{"encoding":904},"Q = bP^{-a} + c",[123,49700,49701,49702],{},"(f) ",[883,49703,49705],{"className":49704},[886],[888,49706,49707],{"xmlns":890},[892,49708,49709,49732],{},[895,49710,49711,49713,49715,49717,49719],{},[898,49712,1802],{},[1701,49714,1792],{},[898,49716,207],{},[1701,49718,3408],{},[3243,49720,49721,49724],{},[898,49722,49723],{},"e",[895,49725,49726,49728,49730],{},[1701,49727,2317],{},[898,49729,3598],{},[898,49731,1680],{},[902,49733,49734],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,49736,49737,49740],{},[38,49738,49739],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,49742,49743,49746,49749],{},[123,49744,49745],{},"(a) Cena substitutu.",[123,49747,49748],{},"(b) Cena komplementu.",[123,49750,49751],{},"(c) Výdaje na reklamu.",[724,49753,49754,49417,49756,49790,49791,49819],{},[38,49755,28680],{},[883,49757,49759],{"className":49758},[886],[888,49760,49761],{"xmlns":890},[892,49762,49763,49787],{},[895,49764,49765,49767,49769,49771,49773,49775,49777,49779,49781,49783,49785],{},[898,49766,1680],{},[1701,49768,1792],{},[898,49770,1795],{},[1701,49772,1799],{"stretchy":1798},[898,49774,1802],{},[1701,49776,1805],{"stretchy":1798},[1701,49778,1792],{},[1850,49780,7592],{},[1701,49782,2317],{},[1850,49784,3938],{},[898,49786,1802],{},[902,49788,49789],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,49792,49794],{"className":49793},[886],[888,49795,49796],{"xmlns":890},[892,49797,49798,49816],{},[895,49799,49800,49802,49804,49810,49812,49814],{},[898,49801,1680],{},[1701,49803,1792],{},[3243,49805,49806,49808],{},[898,49807,1795],{},[1701,49809,8424],{},[1701,49811,1799],{"stretchy":1798},[898,49813,1802],{},[1701,49815,1805],{"stretchy":1798},[902,49817,49818],{"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.",[724,49821,49822,49825],{},[38,49823,49824],{},"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:",[120,49827,49828,49912,49988,50074,50162],{},[123,49829,49536,49830,1343,49870,1715],{},[883,49831,49833],{"className":49832},[886],[888,49834,49835],{"xmlns":890},[892,49836,49837,49867],{},[895,49838,49839,49845,49847,49849,49851,49853,49859,49861],{},[1845,49840,49841,49843],{},[898,49842,2593],{},[1850,49844,4062],{},[1701,49846,1792],{},[1850,49848,13096],{},[1701,49850,2317],{},[1850,49852,6460],{},[1845,49854,49855,49857],{},[898,49856,1983],{},[1850,49858,4062],{},[1701,49860,1703],{},[1845,49862,49863,49865],{},[898,49864,1983],{},[1850,49866,3938],{},[902,49868,49869],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,49871,49873],{"className":49872},[886],[888,49874,49875],{"xmlns":890},[892,49876,49877,49909],{},[895,49878,49879,49885,49887,49889,49891,49893,49899,49901,49903],{},[1845,49880,49881,49883],{},[898,49882,2593],{},[1850,49884,3938],{},[1701,49886,1792],{},[1850,49888,3703],{},[1701,49890,1703],{},[1850,49892,3938],{},[1845,49894,49895,49897],{},[898,49896,1983],{},[1850,49898,4062],{},[1701,49900,2317],{},[1850,49902,6460],{},[1845,49904,49905,49907],{},[898,49906,1983],{},[1850,49908,3938],{},[902,49910,49911],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,49913,49569,49914,1343,49956,1715],{},[883,49915,49917],{"className":49916},[886],[888,49918,49919],{"xmlns":890},[892,49920,49921,49953],{},[895,49922,49923,49929,49931,49933,49935,49937,49943,49945,49947],{},[1845,49924,49925,49927],{},[898,49926,2593],{},[1850,49928,4062],{},[1701,49930,1792],{},[1850,49932,7206],{},[1701,49934,2317],{},[1850,49936,3703],{},[1845,49938,49939,49941],{},[898,49940,1983],{},[1850,49942,4062],{},[1701,49944,2317],{},[1850,49946,6352],{},[1845,49948,49949,49951],{},[898,49950,1983],{},[1850,49952,3938],{},[902,49954,49955],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,49957,49959],{"className":49958},[886],[888,49960,49961],{"xmlns":890},[892,49962,49963,49985],{},[895,49964,49965,49971,49973,49975,49977,49979],{},[1845,49966,49967,49969],{},[898,49968,2593],{},[1850,49970,3938],{},[1701,49972,1792],{},[1850,49974,40275],{},[1701,49976,2317],{},[1850,49978,3703],{},[1845,49980,49981,49983],{},[898,49982,1983],{},[1850,49984,3938],{},[902,49986,49987],{"encoding":904},"B_2 = 15 - 10A_2",[123,49989,49600,49990,1343,50032,1715],{},[883,49991,49993],{"className":49992},[886],[888,49994,49995],{"xmlns":890},[892,49996,49997,50029],{},[895,49998,49999,50005,50007,50009,50011,50013,50019,50021,50023],{},[1845,50000,50001,50003],{},[898,50002,2593],{},[1850,50004,4062],{},[1701,50006,1792],{},[1850,50008,3776],{},[1701,50010,2317],{},[1850,50012,3938],{},[1845,50014,50015,50017],{},[898,50016,1983],{},[1850,50018,4062],{},[1701,50020,2317],{},[1850,50022,6460],{},[1845,50024,50025,50027],{},[898,50026,1983],{},[1850,50028,3938],{},[902,50030,50031],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,50033,50035],{"className":50034},[886],[888,50036,50037],{"xmlns":890},[892,50038,50039,50071],{},[895,50040,50041,50047,50049,50051,50053,50055,50061,50063,50065],{},[1845,50042,50043,50045],{},[898,50044,2593],{},[1850,50046,3938],{},[1701,50048,1792],{},[1850,50050,40275],{},[1701,50052,1703],{},[1850,50054,3938],{},[1845,50056,50057,50059],{},[898,50058,1983],{},[1850,50060,4062],{},[1701,50062,2317],{},[1850,50064,3938],{},[1845,50066,50067,50069],{},[898,50068,1983],{},[1850,50070,3938],{},[902,50072,50073],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,50075,49635,50076,1343,50120,1715],{},[883,50077,50079],{"className":50078},[886],[888,50080,50081],{"xmlns":890},[892,50082,50083,50117],{},[895,50084,50085,50091,50093,50095,50097,50099,50101,50107,50109,50111],{},[1845,50086,50087,50089],{},[898,50088,2593],{},[1850,50090,4062],{},[1701,50092,1792],{},[1701,50094,2317],{},[1850,50096,13096],{},[1701,50098,2317],{},[1850,50100,3938],{},[1845,50102,50103,50105],{},[898,50104,1983],{},[1850,50106,4062],{},[1701,50108,1703],{},[1850,50110,3646],{},[1845,50112,50113,50115],{},[898,50114,1983],{},[1850,50116,3938],{},[902,50118,50119],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,50121,50123],{"className":50122},[886],[888,50124,50125],{"xmlns":890},[892,50126,50127,50159],{},[895,50128,50129,50135,50137,50139,50141,50143,50149,50151,50153],{},[1845,50130,50131,50133],{},[898,50132,2593],{},[1850,50134,3938],{},[1701,50136,1792],{},[1850,50138,3703],{},[1701,50140,1703],{},[1850,50142,3938],{},[1845,50144,50145,50147],{},[898,50146,1983],{},[1850,50148,4062],{},[1701,50150,2317],{},[1850,50152,3938],{},[1845,50154,50155,50157],{},[898,50156,1983],{},[1850,50158,3938],{},[902,50160,50161],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,50163,49666,50164,1343,50206,1715],{},[883,50165,50167],{"className":50166},[886],[888,50168,50169],{"xmlns":890},[892,50170,50171,50203],{},[895,50172,50173,50179,50181,50183,50185,50187,50193,50195,50197],{},[1845,50174,50175,50177],{},[898,50176,2593],{},[1850,50178,4062],{},[1701,50180,1792],{},[1850,50182,13096],{},[1701,50184,1703],{},[1850,50186,3938],{},[1845,50188,50189,50191],{},[898,50190,1983],{},[1850,50192,4062],{},[1701,50194,1703],{},[1850,50196,6460],{},[1845,50198,50199,50201],{},[898,50200,1983],{},[1850,50202,3938],{},[902,50204,50205],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,50207,50209],{"className":50208},[886],[888,50210,50211],{"xmlns":890},[892,50212,50213,50245],{},[895,50214,50215,50221,50223,50225,50227,50229,50235,50237,50239],{},[1845,50216,50217,50219],{},[898,50218,2593],{},[1850,50220,3938],{},[1701,50222,1792],{},[1850,50224,3665],{},[1701,50226,2317],{},[1850,50228,3646],{},[1845,50230,50231,50233],{},[898,50232,1983],{},[1850,50234,4062],{},[1701,50236,1703],{},[1850,50238,4225],{},[1845,50240,50241,50243],{},[898,50242,1983],{},[1850,50244,3938],{},[902,50246,50247],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,50249,50251],{"id":50250},"základní-analýza-nabídky","Základní analýza nabídky",[724,50253,50254,50257,50258,50292,50293,50315],{},[38,50255,50256],{},"2.6"," Je dána nabídka ",[883,50259,50261],{"className":50260},[886],[888,50262,50263],{"xmlns":890},[892,50264,50265,50289],{},[895,50266,50267,50269,50271,50273,50275,50277,50279,50281,50283,50285,50287],{},[898,50268,1680],{},[1701,50270,1792],{},[898,50272,1661],{},[1701,50274,1799],{"stretchy":1798},[898,50276,1802],{},[1701,50278,1805],{"stretchy":1798},[1701,50280,1792],{},[1850,50282,13096],{},[1701,50284,1703],{},[1850,50286,6930],{},[898,50288,1802],{},[902,50290,50291],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,50294,50296],{"className":50295},[886],[888,50297,50298],{"xmlns":890},[892,50299,50300,50312],{},[895,50301,50302,50304,50306,50308,50310],{},[1850,50303,9071],{},[1701,50305,2012],{"separator":2011},[1850,50307,3776],{},[1701,50309,2012],{"separator":2011},[1850,50311,4136],{},[902,50313,50314],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,50317,50318,50321,50322,50339],{},[38,50319,50320],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,50323,50325],{"className":50324},[886],[888,50326,50327],{"xmlns":890},[892,50328,50329,50337],{},[895,50330,50331,50333,50335],{},[898,50332,1680],{},[1701,50334,2012],{"separator":2011},[898,50336,1802],{},[902,50338,49504],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,50341,50342,50368,50396,50429,50463,50499],{},[123,50343,49536,50344],{},[883,50345,50347],{"className":50346},[886],[888,50348,50349],{"xmlns":890},[892,50350,50351,50365],{},[895,50352,50353,50355,50357,50359,50361,50363],{},[898,50354,1680],{},[1701,50356,1792],{},[1850,50358,3776],{},[1701,50360,1703],{},[1850,50362,3938],{},[898,50364,1802],{},[902,50366,50367],{"encoding":904},"P = 30 + 2Q",[123,50369,49569,50370],{},[883,50371,50373],{"className":50372},[886],[888,50374,50375],{"xmlns":890},[892,50376,50377,50393],{},[895,50378,50379,50381,50383,50385,50387,50389,50391],{},[898,50380,1802],{},[1701,50382,1792],{},[1701,50384,2317],{},[1850,50386,3646],{},[1701,50388,1703],{},[1850,50390,7592],{},[898,50392,1680],{},[902,50394,50395],{"encoding":904},"Q = -3 + 12P",[123,50397,49600,50398],{},[883,50399,50401],{"className":50400},[886],[888,50402,50403],{"xmlns":890},[892,50404,50405,50427],{},[895,50406,50407,50409,50411,50417,50419,50421,50423,50425],{},[898,50408,1680],{},[1701,50410,1792],{},[3243,50412,50413,50415],{},[898,50414,1802],{},[1850,50416,3938],{},[1701,50418,1703],{},[1850,50420,26985],{},[898,50422,1802],{},[1701,50424,1703],{},[1850,50426,36577],{},[902,50428,45744],{"encoding":904},[123,50430,49635,50431],{},[883,50432,50434],{"className":50433},[886],[888,50435,50436],{"xmlns":890},[892,50437,50438,50460],{},[895,50439,50440,50442,50444,50450,50452,50454,50456,50458],{},[898,50441,1680],{},[1701,50443,1792],{},[3243,50445,50446,50448],{},[898,50447,1802],{},[1850,50449,3938],{},[1701,50451,1703],{},[1850,50453,3938],{},[898,50455,1802],{},[1701,50457,1703],{},[1850,50459,7592],{},[902,50461,50462],{"encoding":904},"P = Q^2 + 2Q + 12",[123,50464,49666,50465],{},[883,50466,50468],{"className":50467},[886],[888,50469,50470],{"xmlns":890},[892,50471,50472,50496],{},[895,50473,50474,50476,50478,50480,50482,50484,50486,50488,50490],{},[898,50475,1802],{},[1701,50477,1792],{},[1850,50479,12864],{},[1701,50481,1703],{},[1850,50483,4225],{},[898,50485,1680],{},[1701,50487,1703],{},[1850,50489,4033],{},[3243,50491,50492,50494],{},[898,50493,1680],{},[1850,50495,3938],{},[902,50497,50498],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,50500,49701,50501],{},[883,50502,50504],{"className":50503},[886],[888,50505,50506],{"xmlns":890},[892,50507,50508,50533],{},[895,50509,50510,50512,50514,50516,50518,50520,50522,50524,50527],{},[898,50511,1802],{},[1701,50513,1792],{},[1850,50515,28239],{},[1701,50517,1703],{},[1850,50519,4033],{},[898,50521,1680],{},[1701,50523,1703],{},[1850,50525,50526],{},"0,004",[3243,50528,50529,50531],{},[898,50530,1680],{},[1850,50532,3938],{},[902,50534,50535],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,50537,50538,50541],{},[38,50539,50540],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,50543,50544,50547,50550,50553],{},[123,50545,50546],{},"(a) Sníží ceny surovin — vstupů.",[123,50548,50549],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,50551,50552],{},"(c) Zvýší ceny všech energií.",[123,50554,50555],{},"(d) Sníží daňové odvody státu.",[724,50557,50558,50257,50560,50594,50595,50623],{},[38,50559,46969],{},[883,50561,50563],{"className":50562},[886],[888,50564,50565],{"xmlns":890},[892,50566,50567,50591],{},[895,50568,50569,50571,50573,50575,50577,50579,50581,50583,50585,50587,50589],{},[898,50570,1680],{},[1701,50572,1792],{},[898,50574,1661],{},[1701,50576,1799],{"stretchy":1798},[898,50578,1802],{},[1701,50580,1805],{"stretchy":1798},[1701,50582,1792],{},[1850,50584,3684],{},[898,50586,1802],{},[1701,50588,1703],{},[1850,50590,40275],{},[902,50592,50593],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,50596,50598],{"className":50597},[886],[888,50599,50600],{"xmlns":890},[892,50601,50602,50620],{},[895,50603,50604,50606,50608,50614,50616,50618],{},[898,50605,1680],{},[1701,50607,1792],{},[3243,50609,50610,50612],{},[898,50611,1661],{},[1701,50613,8424],{},[1701,50615,1799],{"stretchy":1798},[898,50617,1802],{},[1701,50619,1805],{"stretchy":1798},[902,50621,50622],{"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.",[198,50625,45347],{"id":50626},"tržní-rovnováha-1",[724,50628,50629,50631,50632,50649,50650,2246],{},[38,50630,47029],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,50633,50635],{"className":50634},[886],[888,50636,50637],{"xmlns":890},[892,50638,50639,50647],{},[895,50640,50641],{},[3243,50642,50643,50645],{},[898,50644,1802],{},[898,50646,3249],{},[902,50648,3807],{"encoding":904}," a rovnovážnou cenu ",[883,50651,50653],{"className":50652},[886],[888,50654,50655],{"xmlns":890},[892,50656,50657,50665],{},[895,50658,50659],{},[3243,50660,50661,50663],{},[898,50662,1680],{},[898,50664,3249],{},[902,50666,45488],{"encoding":904},[120,50668,50669,50722,50773,50832],{},[123,50670,49536,50671,1343,50698,1715],{},[883,50672,50674],{"className":50673},[886],[888,50675,50676],{"xmlns":890},[892,50677,50678,50695],{},[895,50679,50680,50682,50684,50686,50688,50690,50692],{},[898,50681,1680],{},[1701,50683,1792],{},[1701,50685,2317],{},[1850,50687,4225],{},[898,50689,1802],{},[1701,50691,1703],{},[1850,50693,50694],{},"80",[902,50696,50697],{"encoding":904},"P = -5Q + 80",[883,50699,50701],{"className":50700},[886],[888,50702,50703],{"xmlns":890},[892,50704,50705,50719],{},[895,50706,50707,50709,50711,50713,50715,50717],{},[898,50708,1680],{},[1701,50710,1792],{},[1850,50712,3938],{},[898,50714,1802],{},[1701,50716,1703],{},[1850,50718,3703],{},[902,50720,50721],{"encoding":904},"P = 2Q + 10",[123,50723,49569,50724,1343,50750,1715],{},[883,50725,50727],{"className":50726},[886],[888,50728,50729],{"xmlns":890},[892,50730,50731,50747],{},[895,50732,50733,50735,50737,50739,50741,50743,50745],{},[898,50734,1802],{},[1701,50736,1792],{},[1701,50738,2317],{},[1850,50740,3684],{},[898,50742,1680],{},[1701,50744,1703],{},[1850,50746,9071],{},[902,50748,50749],{"encoding":904},"Q = -0{,}5P + 25",[883,50751,50753],{"className":50752},[886],[888,50754,50755],{"xmlns":890},[892,50756,50757,50771],{},[895,50758,50759,50761,50763,50765,50767,50769],{},[898,50760,1802],{},[1701,50762,1792],{},[1850,50764,3938],{},[898,50766,1680],{},[1701,50768,2317],{},[1850,50770,7206],{},[902,50772,44870],{"encoding":904},[123,50774,49600,50775,1343,50801,1715],{},[883,50776,50778],{"className":50777},[886],[888,50779,50780],{"xmlns":890},[892,50781,50782,50798],{},[895,50783,50784,50786,50788,50790,50792,50794,50796],{},[898,50785,1680],{},[1701,50787,1792],{},[1701,50789,2317],{},[1850,50791,6460],{},[898,50793,1802],{},[1701,50795,1703],{},[1850,50797,8120],{},[902,50799,50800],{"encoding":904},"P = -4Q + 120",[883,50802,50804],{"className":50803},[886],[888,50805,50806],{"xmlns":890},[892,50807,50808,50829],{},[895,50809,50810,50812,50814,50822,50824,50826],{},[898,50811,1680],{},[1701,50813,1792],{},[2363,50815,50816],{"scriptlevel":1852,"displaystyle":1798},[3726,50817,50818,50820],{},[1850,50819,4062],{},[1850,50821,3646],{},[898,50823,1802],{},[1701,50825,1703],{},[1850,50827,50828],{},"29",[902,50830,50831],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,50833,49635,50834,1343,50863,1715],{},[883,50835,50837],{"className":50836},[886],[888,50838,50839],{"xmlns":890},[892,50840,50841,50860],{},[895,50842,50843,50845,50847,50849,50855,50857],{},[898,50844,1680],{},[1701,50846,1792],{},[1701,50848,2317],{},[3243,50850,50851,50853],{},[898,50852,1802],{},[1850,50854,3938],{},[1701,50856,1703],{},[1850,50858,50859],{},"52",[902,50861,50862],{"encoding":904},"P = -Q^2 + 52",[883,50864,50866],{"className":50865},[886],[888,50867,50868],{"xmlns":890},[892,50869,50870,50888],{},[895,50871,50872,50874,50876,50878,50884,50886],{},[898,50873,1680],{},[1701,50875,1792],{},[1850,50877,3938],{},[3243,50879,50880,50882],{},[898,50881,1802],{},[1850,50883,3938],{},[1701,50885,1703],{},[1850,50887,3703],{},[902,50889,50890],{"encoding":904},"P = 2Q^2 + 10",[724,50892,50893,50896,50897,50927,50928,50958],{},[38,50894,50895],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,50898,50900],{"className":50899},[886],[888,50901,50902],{"xmlns":890},[892,50903,50904,50924],{},[895,50905,50906,50914,50916],{},[2287,50907,50908,50910,50912],{},[898,50909,1802],{},[1850,50911,4062],{},[898,50913,3249],{},[1701,50915,2012],{"separator":2011},[2287,50917,50918,50920,50922],{},[898,50919,1802],{},[1850,50921,3938],{},[898,50923,3249],{},[902,50925,50926],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,50929,50931],{"className":50930},[886],[888,50932,50933],{"xmlns":890},[892,50934,50935,50955],{},[895,50936,50937,50945,50947],{},[2287,50938,50939,50941,50943],{},[898,50940,1680],{},[1850,50942,4062],{},[898,50944,3249],{},[1701,50946,2012],{"separator":2011},[2287,50948,50949,50951,50953],{},[898,50950,1680],{},[1850,50952,3938],{},[898,50954,3249],{},[902,50956,50957],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,50960,50961,51113],{},[123,50962,49536,50963,1343,51003,1343,51045,1343,51079,1715],{},[883,50964,50966],{"className":50965},[886],[888,50967,50968],{"xmlns":890},[892,50969,50970,51000],{},[895,50971,50972,50978,50980,50982,50984,50986,50992,50994],{},[1845,50973,50974,50976],{},[898,50975,1802],{},[1850,50977,4062],{},[1701,50979,1792],{},[1850,50981,3703],{},[1701,50983,2317],{},[1850,50985,3938],{},[1845,50987,50988,50990],{},[898,50989,1680],{},[1850,50991,4062],{},[1701,50993,1703],{},[1845,50995,50996,50998],{},[898,50997,1680],{},[1850,50999,3938],{},[902,51001,51002],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,51004,51006],{"className":51005},[886],[888,51007,51008],{"xmlns":890},[892,51009,51010,51042],{},[895,51011,51012,51018,51020,51022,51024,51026,51032,51034,51036],{},[1845,51013,51014,51016],{},[898,51015,1802],{},[1850,51017,3938],{},[1701,51019,1792],{},[1850,51021,4225],{},[1701,51023,1703],{},[1850,51025,3938],{},[1845,51027,51028,51030],{},[898,51029,1680],{},[1850,51031,4062],{},[1701,51033,2317],{},[1850,51035,3938],{},[1845,51037,51038,51040],{},[898,51039,1680],{},[1850,51041,3938],{},[902,51043,51044],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,51046,51048],{"className":51047},[886],[888,51049,51050],{"xmlns":890},[892,51051,51052,51076],{},[895,51053,51054,51060,51062,51064,51066,51068,51070],{},[1845,51055,51056,51058],{},[898,51057,1802],{},[1850,51059,4062],{},[1701,51061,1792],{},[1701,51063,2317],{},[1850,51065,3646],{},[1701,51067,1703],{},[1850,51069,3938],{},[1845,51071,51072,51074],{},[898,51073,1680],{},[1850,51075,4062],{},[902,51077,51078],{"encoding":904},"Q_1 = -3 + 2P_1",[883,51080,51082],{"className":51081},[886],[888,51083,51084],{"xmlns":890},[892,51085,51086,51110],{},[895,51087,51088,51094,51096,51098,51100,51102,51104],{},[1845,51089,51090,51092],{},[898,51091,1802],{},[1850,51093,3938],{},[1701,51095,1792],{},[1701,51097,2317],{},[1850,51099,3938],{},[1701,51101,1703],{},[1850,51103,3646],{},[1845,51105,51106,51108],{},[898,51107,1680],{},[1850,51109,3938],{},[902,51111,51112],{"encoding":904},"Q_2 = -2 + 3P_2",[123,51114,49569,51115,1343,51155,1343,51197,1343,51229,1715],{},[883,51116,51118],{"className":51117},[886],[888,51119,51120],{"xmlns":890},[892,51121,51122,51152],{},[895,51123,51124,51130,51132,51134,51136,51138,51144,51146],{},[1845,51125,51126,51128],{},[898,51127,1802],{},[1850,51129,4062],{},[1701,51131,1792],{},[1850,51133,5158],{},[1701,51135,2317],{},[1850,51137,3938],{},[1845,51139,51140,51142],{},[898,51141,1680],{},[1850,51143,4062],{},[1701,51145,1703],{},[1845,51147,51148,51150],{},[898,51149,1680],{},[1850,51151,3938],{},[902,51153,51154],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,51156,51158],{"className":51157},[886],[888,51159,51160],{"xmlns":890},[892,51161,51162,51194],{},[895,51163,51164,51170,51172,51174,51176,51178,51184,51186,51188],{},[1845,51165,51166,51168],{},[898,51167,1802],{},[1850,51169,3938],{},[1701,51171,1792],{},[1850,51173,4225],{},[1701,51175,1703],{},[1850,51177,3938],{},[1845,51179,51180,51182],{},[898,51181,1680],{},[1850,51183,4062],{},[1701,51185,2317],{},[1850,51187,3646],{},[1845,51189,51190,51192],{},[898,51191,1680],{},[1850,51193,3938],{},[902,51195,51196],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,51198,51200],{"className":51199},[886],[888,51201,51202],{"xmlns":890},[892,51203,51204,51226],{},[895,51205,51206,51212,51214,51216,51218,51220],{},[1845,51207,51208,51210],{},[898,51209,1802],{},[1850,51211,4062],{},[1701,51213,1792],{},[1701,51215,2317],{},[1850,51217,3703],{},[1701,51219,1703],{},[1845,51221,51222,51224],{},[898,51223,1680],{},[1850,51225,4062],{},[902,51227,51228],{"encoding":904},"Q_1 = -10 + P_1",[883,51230,51232],{"className":51231},[886],[888,51233,51234],{"xmlns":890},[892,51235,51236,51258],{},[895,51237,51238,51244,51246,51248,51250,51252],{},[1845,51239,51240,51242],{},[898,51241,1802],{},[1850,51243,3938],{},[1701,51245,1792],{},[1850,51247,4225],{},[1701,51249,1703],{},[1850,51251,6352],{},[1845,51253,51254,51256],{},[898,51255,1680],{},[1850,51257,3938],{},[902,51259,51260],{"encoding":904},"Q_2 = 5 + 6P_2",[724,51262,51263,51266,51267,1343,51315,1343,51361,51411,51412,1343,51444,1343,51478,2020,51512,2633,51530,51548,51549,51562,51563,51589,51590,50927,51630,1715],{},[38,51264,51265],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,51268,51270],{"className":51269},[886],[888,51271,51272],{"xmlns":890},[892,51273,51274,51312],{},[895,51275,51276,51282,51284,51286,51288,51294,51296,51298,51304,51306],{},[1845,51277,51278,51280],{},[898,51279,1802],{},[1850,51281,4062],{},[1701,51283,1792],{},[1850,51285,40275],{},[1701,51287,2317],{},[1845,51289,51290,51292],{},[898,51291,1680],{},[1850,51293,4062],{},[1701,51295,1703],{},[1850,51297,3938],{},[1845,51299,51300,51302],{},[898,51301,1680],{},[1850,51303,3938],{},[1701,51305,1703],{},[1845,51307,51308,51310],{},[898,51309,1680],{},[1850,51311,3646],{},[902,51313,51314],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,51316,51318],{"className":51317},[886],[888,51319,51320],{"xmlns":890},[892,51321,51322,51358],{},[895,51323,51324,51330,51332,51334,51336,51342,51344,51350,51352],{},[1845,51325,51326,51328],{},[898,51327,1802],{},[1850,51329,3938],{},[1701,51331,1792],{},[1850,51333,8073],{},[1701,51335,1703],{},[1845,51337,51338,51340],{},[898,51339,1680],{},[1850,51341,4062],{},[1701,51343,2317],{},[1845,51345,51346,51348],{},[898,51347,1680],{},[1850,51349,3938],{},[1701,51351,2317],{},[1845,51353,51354,51356],{},[898,51355,1680],{},[1850,51357,3646],{},[902,51359,51360],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,51362,51364],{"className":51363},[886],[888,51365,51366],{"xmlns":890},[892,51367,51368,51408],{},[895,51369,51370,51376,51378,51380,51382,51384,51390,51392,51398,51400,51402],{},[1845,51371,51372,51374],{},[898,51373,1802],{},[1850,51375,3646],{},[1701,51377,1792],{},[1850,51379,9650],{},[1701,51381,1703],{},[1850,51383,3938],{},[1845,51385,51386,51388],{},[898,51387,1680],{},[1850,51389,4062],{},[1701,51391,2317],{},[1845,51393,51394,51396],{},[898,51395,1680],{},[1850,51397,3938],{},[1701,51399,2317],{},[1850,51401,6460],{},[1845,51403,51404,51406],{},[898,51405,1680],{},[1850,51407,3646],{},[902,51409,51410],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,51413,51415],{"className":51414},[886],[888,51416,51417],{"xmlns":890},[892,51418,51419,51441],{},[895,51420,51421,51427,51429,51431,51433,51435],{},[1845,51422,51423,51425],{},[898,51424,1802],{},[1850,51426,4062],{},[1701,51428,1792],{},[1701,51430,2317],{},[1850,51432,28239],{},[1701,51434,1703],{},[1845,51436,51437,51439],{},[898,51438,1680],{},[1850,51440,4062],{},[902,51442,51443],{"encoding":904},"Q_1 = -7 + P_1",[883,51445,51447],{"className":51446},[886],[888,51448,51449],{"xmlns":890},[892,51450,51451,51475],{},[895,51452,51453,51459,51461,51463,51465,51467,51469],{},[1845,51454,51455,51457],{},[898,51456,1802],{},[1850,51458,3938],{},[1701,51460,1792],{},[1701,51462,2317],{},[1850,51464,6460],{},[1701,51466,1703],{},[1850,51468,6460],{},[1845,51470,51471,51473],{},[898,51472,1680],{},[1850,51474,3938],{},[902,51476,51477],{"encoding":904},"Q_2 = -4 + 4P_2",[883,51479,51481],{"className":51480},[886],[888,51482,51483],{"xmlns":890},[892,51484,51485,51509],{},[895,51486,51487,51493,51495,51497,51499,51501,51503],{},[1845,51488,51489,51491],{},[898,51490,1802],{},[1850,51492,3646],{},[1701,51494,1792],{},[1701,51496,2317],{},[1850,51498,4225],{},[1701,51500,1703],{},[1850,51502,3938],{},[1845,51504,51505,51507],{},[898,51506,1680],{},[1850,51508,3646],{},[902,51510,51511],{"encoding":904},"Q_3 = -5 + 2P_3",[883,51513,51515],{"className":51514},[886],[888,51516,51517],{"xmlns":890},[892,51518,51519,51527],{},[895,51520,51521],{},[1845,51522,51523,51525],{},[898,51524,1802],{},[898,51526,21836],{},[902,51528,51529],{"encoding":904},"Q_i",[883,51531,51533],{"className":51532},[886],[888,51534,51535],{"xmlns":890},[892,51536,51537,51545],{},[895,51538,51539],{},[1845,51540,51541,51543],{},[898,51542,1680],{},[898,51544,21836],{},[902,51546,51547],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,51550,51552],{"className":51551},[886],[888,51553,51554],{"xmlns":890},[892,51555,51556,51560],{},[895,51557,51558],{},[898,51559,21836],{},[902,51561,21836],{"encoding":904},"-tého zboží, ",[883,51564,51566],{"className":51565},[886],[888,51567,51568],{"xmlns":890},[892,51569,51570,51586],{},[895,51571,51572,51574,51576,51578,51580,51582,51584],{},[898,51573,21836],{},[1701,51575,1792],{},[1850,51577,4062],{},[1701,51579,2012],{"separator":2011},[1850,51581,3938],{},[1701,51583,2012],{"separator":2011},[1850,51585,3646],{},[902,51587,51588],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,51591,51593],{"className":51592},[886],[888,51594,51595],{"xmlns":890},[892,51596,51597,51627],{},[895,51598,51599,51607,51609,51617,51619],{},[2287,51600,51601,51603,51605],{},[898,51602,1802],{},[1850,51604,4062],{},[898,51606,3249],{},[1701,51608,2012],{"separator":2011},[2287,51610,51611,51613,51615],{},[898,51612,1802],{},[1850,51614,3938],{},[898,51616,3249],{},[1701,51618,2012],{"separator":2011},[2287,51620,51621,51623,51625],{},[898,51622,1802],{},[1850,51624,3646],{},[898,51626,3249],{},[902,51628,51629],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,51631,51633],{"className":51632},[886],[888,51634,51635],{"xmlns":890},[892,51636,51637,51667],{},[895,51638,51639,51647,51649,51657,51659],{},[2287,51640,51641,51643,51645],{},[898,51642,1680],{},[1850,51644,4062],{},[898,51646,3249],{},[1701,51648,2012],{"separator":2011},[2287,51650,51651,51653,51655],{},[898,51652,1680],{},[1850,51654,3938],{},[898,51656,3249],{},[1701,51658,2012],{"separator":2011},[2287,51660,51661,51663,51665],{},[898,51662,1680],{},[1850,51664,3646],{},[898,51666,3249],{},[902,51668,51669],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,51671,51672,51675,51676,3602,51712,1715],{},[38,51673,51674],{},"2.13"," Jsou dány poptávka ",[883,51677,51679],{"className":51678},[886],[888,51680,51681],{"xmlns":890},[892,51682,51683,51709],{},[895,51684,51685,51687,51689,51691,51693,51695,51697,51699,51701,51703,51705,51707],{},[898,51686,1680],{},[1701,51688,1792],{},[898,51690,1795],{},[1701,51692,1799],{"stretchy":1798},[898,51694,1802],{},[1701,51696,1805],{"stretchy":1798},[1701,51698,1792],{},[1701,51700,2317],{},[1850,51702,6460],{},[898,51704,1802],{},[1701,51706,1703],{},[1850,51708,50694],{},[902,51710,51711],{"encoding":904},"P = D(Q) = -4Q + 80",[883,51713,51715],{"className":51714},[886],[888,51716,51717],{"xmlns":890},[892,51718,51719,51743],{},[895,51720,51721,51723,51725,51727,51729,51731,51733,51735,51737,51739,51741],{},[898,51722,1680],{},[1701,51724,1792],{},[898,51726,1661],{},[1701,51728,1799],{"stretchy":1798},[898,51730,1802],{},[1701,51732,1805],{"stretchy":1798},[1701,51734,1792],{},[1850,51736,3646],{},[898,51738,1802],{},[1701,51740,1703],{},[1850,51742,3703],{},[902,51744,51745],{"encoding":904},"P = S(Q) = 3Q + 10",[120,51747,51748,51785,51849,51909],{},[123,51749,51750,51751,50649,51768,1715],{},"(a) Určete rovnovážné množství ",[883,51752,51754],{"className":51753},[886],[888,51755,51756],{"xmlns":890},[892,51757,51758,51766],{},[895,51759,51760],{},[3243,51761,51762,51764],{},[898,51763,1802],{},[898,51765,3249],{},[902,51767,3807],{"encoding":904},[883,51769,51771],{"className":51770},[886],[888,51772,51773],{"xmlns":890},[892,51774,51775,51783],{},[895,51776,51777],{},[3243,51778,51779,51781],{},[898,51780,1680],{},[898,51782,3249],{},[902,51784,45488],{"encoding":904},[123,51786,51787,51788,51806,51807,51827,51828,51848],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,51789,51791],{"className":51790},[886],[888,51792,51793],{"xmlns":890},[892,51794,51795,51803],{},[895,51796,51797,51799,51801],{},[898,51798,5877],{},[1701,51800,1792],{},[1850,51802,28239],{},[902,51804,51805],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,51808,51810],{"className":51809},[886],[888,51811,51812],{"xmlns":890},[892,51813,51814,51824],{},[895,51815,51816],{},[2287,51817,51818,51820,51822],{},[898,51819,1802],{},[1850,51821,4062],{},[898,51823,3249],{},[902,51825,51826],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,51829,51831],{"className":51830},[886],[888,51832,51833],{"xmlns":890},[892,51834,51835,51845],{},[895,51836,51837],{},[2287,51838,51839,51841,51843],{},[898,51840,1680],{},[1850,51842,4062],{},[898,51844,3249],{},[902,51846,51847],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,51850,51851,51852,51806,51869,51827,51889,51848],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,51853,51855],{"className":51854},[886],[888,51856,51857],{"xmlns":890},[892,51858,51859,51867],{},[895,51860,51861,51863,51865],{},[898,51862,5877],{},[1701,51864,1792],{},[1850,51866,28239],{},[902,51868,51805],{"encoding":904},[883,51870,51872],{"className":51871},[886],[888,51873,51874],{"xmlns":890},[892,51875,51876,51886],{},[895,51877,51878],{},[2287,51879,51880,51882,51884],{},[898,51881,1802],{},[1850,51883,3938],{},[898,51885,3249],{},[902,51887,51888],{"encoding":904},"Q_2^E",[883,51890,51892],{"className":51891},[886],[888,51893,51894],{"xmlns":890},[892,51895,51896,51906],{},[895,51897,51898],{},[2287,51899,51900,51902,51904],{},[898,51901,1680],{},[1850,51903,3938],{},[898,51905,3249],{},[902,51907,51908],{"encoding":904},"P_2^E",[123,51910,51911],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,51913,51914,51915,1715],{},"Viz též ",[207,51916,46741],{"className":51917,"dataFsResolvedFilePath":809,"href":810},[210],[198,51919,47043],{"id":51920},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,51922,51923,51675,51926,3602,51962,1715],{},[38,51924,51925],{},"2.14",[883,51927,51929],{"className":51928},[886],[888,51930,51931],{"xmlns":890},[892,51932,51933,51959],{},[895,51934,51935,51937,51939,51941,51943,51945,51947,51949,51951,51953,51955,51957],{},[898,51936,1680],{},[1701,51938,1792],{},[898,51940,207],{},[898,51942,1802],{},[1701,51944,1703],{},[898,51946,3598],{},[1701,51948,1792],{},[1701,51950,2317],{},[1850,51952,3938],{},[898,51954,1802],{},[1701,51956,1703],{},[1850,51958,7206],{},[902,51960,51961],{"encoding":904},"P = aQ + b = -2Q + 50",[883,51963,51965],{"className":51964},[886],[888,51966,51967],{"xmlns":890},[892,51968,51969,51993],{},[895,51970,51971,51973,51975,51977,51979,51981,51983,51985,51987,51989,51991],{},[898,51972,1680],{},[1701,51974,1792],{},[898,51976,3618],{},[898,51978,1802],{},[1701,51980,1703],{},[898,51982,2312],{},[1701,51984,1792],{},[1850,51986,3868],{},[898,51988,1802],{},[1701,51990,1703],{},[1850,51992,13096],{},[902,51994,51995],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,51997,51998,52034,52037,52123,52176,52256,52310],{},[123,51999,51750,52000,50649,52017,1715],{},[883,52001,52003],{"className":52002},[886],[888,52004,52005],{"xmlns":890},[892,52006,52007,52015],{},[895,52008,52009],{},[3243,52010,52011,52013],{},[898,52012,1802],{},[898,52014,3249],{},[902,52016,3807],{"encoding":904},[883,52018,52020],{"className":52019},[886],[888,52021,52022],{"xmlns":890},[892,52023,52024,52032],{},[895,52025,52026],{},[3243,52027,52028,52030],{},[898,52029,1680],{},[898,52031,3249],{},[902,52033,45488],{"encoding":904},[123,52035,52036],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,52038,52039,52040,52057,52058,3841,52071,3856,52087,52103,52104,1715],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,52041,52043],{"className":52042},[886],[888,52044,52045],{"xmlns":890},[892,52046,52047,52055],{},[895,52048,52049],{},[3243,52050,52051,52053],{},[898,52052,1802],{},[898,52054,3249],{},[902,52056,3807],{"encoding":904}," odpovídající změně ",[883,52059,52061],{"className":52060},[886],[888,52062,52063],{"xmlns":890},[892,52064,52065,52069],{},[895,52066,52067],{},[898,52068,207],{},[902,52070,207],{"encoding":904},[883,52072,52074],{"className":52073},[886],[888,52075,52076],{"xmlns":890},[892,52077,52078,52084],{},[895,52079,52080,52082],{},[1701,52081,2317],{},[1850,52083,3938],{},[902,52085,52086],{"encoding":904},"-2",[883,52088,52090],{"className":52089},[886],[888,52091,52092],{"xmlns":890},[892,52093,52094,52100],{},[895,52095,52096,52098],{},[1701,52097,2317],{},[1850,52099,3646],{},[902,52101,52102],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52105,52107],{"className":52106},[886],[888,52108,52109],{"xmlns":890},[892,52110,52111,52121],{},[895,52112,52113],{},[2287,52114,52115,52117,52119],{},[898,52116,1802],{},[1850,52118,4062],{},[898,52120,3249],{},[902,52122,51826],{"encoding":904},[123,52124,52125,52126,52057,52143,52156,52157,1715],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,52127,52129],{"className":52128},[886],[888,52130,52131],{"xmlns":890},[892,52132,52133,52141],{},[895,52134,52135],{},[3243,52136,52137,52139],{},[898,52138,1802],{},[898,52140,3249],{},[902,52142,3807],{"encoding":904},[883,52144,52146],{"className":52145},[886],[888,52147,52148],{"xmlns":890},[892,52149,52150,52154],{},[895,52151,52152],{},[898,52153,3598],{},[902,52155,3598],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52158,52160],{"className":52159},[886],[888,52161,52162],{"xmlns":890},[892,52163,52164,52174],{},[895,52165,52166],{},[2287,52167,52168,52170,52172],{},[898,52169,1802],{},[1850,52171,3938],{},[898,52173,3249],{},[902,52175,51888],{"encoding":904},[123,52177,52178,52179,52057,52196,3841,52209,3856,52222,52103,52236,1715],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,52180,52182],{"className":52181},[886],[888,52183,52184],{"xmlns":890},[892,52185,52186,52194],{},[895,52187,52188],{},[3243,52189,52190,52192],{},[898,52191,1802],{},[898,52193,3249],{},[902,52195,3807],{"encoding":904},[883,52197,52199],{"className":52198},[886],[888,52200,52201],{"xmlns":890},[892,52202,52203,52207],{},[895,52204,52205],{},[898,52206,3618],{},[902,52208,3618],{"encoding":904},[883,52210,52212],{"className":52211},[886],[888,52213,52214],{"xmlns":890},[892,52215,52216,52220],{},[895,52217,52218],{},[1850,52219,3868],{},[902,52221,3871],{"encoding":904},[883,52223,52225],{"className":52224},[886],[888,52226,52227],{"xmlns":890},[892,52228,52229,52233],{},[895,52230,52231],{},[1850,52232,18642],{},[902,52234,52235],{"encoding":904},"0{,}8",[883,52237,52239],{"className":52238},[886],[888,52240,52241],{"xmlns":890},[892,52242,52243,52253],{},[895,52244,52245],{},[2287,52246,52247,52249,52251],{},[898,52248,1802],{},[1850,52250,3646],{},[898,52252,3249],{},[902,52254,52255],{"encoding":904},"Q_3^E",[123,52257,52258,52259,52057,52276,52289,52290,1715],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,52260,52262],{"className":52261},[886],[888,52263,52264],{"xmlns":890},[892,52265,52266,52274],{},[895,52267,52268],{},[3243,52269,52270,52272],{},[898,52271,1802],{},[898,52273,3249],{},[902,52275,3807],{"encoding":904},[883,52277,52279],{"className":52278},[886],[888,52280,52281],{"xmlns":890},[892,52282,52283,52287],{},[895,52284,52285],{},[898,52286,2312],{},[902,52288,2312],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,52291,52293],{"className":52292},[886],[888,52294,52295],{"xmlns":890},[892,52296,52297,52307],{},[895,52298,52299],{},[2287,52300,52301,52303,52305],{},[898,52302,1802],{},[1850,52304,6460],{},[898,52306,3249],{},[902,52308,52309],{"encoding":904},"Q_4^E",[123,52311,52312,52313,52330,52331,52344,52345,25461,52358,1343,52373,25461,52386,2633,52400,25461,52413,52428,52429,1715],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,52314,52316],{"className":52315},[886],[888,52317,52318],{"xmlns":890},[892,52319,52320,52328],{},[895,52321,52322],{},[3243,52323,52324,52326],{},[898,52325,1802],{},[898,52327,3249],{},[902,52329,3807],{"encoding":904}," odpovídající změnám ",[883,52332,52334],{"className":52333},[886],[888,52335,52336],{"xmlns":890},[892,52337,52338,52342],{},[895,52339,52340],{},[898,52341,207],{},[902,52343,207],{"encoding":904}," o 1, ",[883,52346,52348],{"className":52347},[886],[888,52349,52350],{"xmlns":890},[892,52351,52352,52356],{},[895,52353,52354],{},[898,52355,3598],{},[902,52357,3598],{"encoding":904},[883,52359,52361],{"className":52360},[886],[888,52362,52363],{"xmlns":890},[892,52364,52365,52371],{},[895,52366,52367,52369],{},[1701,52368,2317],{},[1850,52370,3703],{},[902,52372,23500],{"encoding":904},[883,52374,52376],{"className":52375},[886],[888,52377,52378],{"xmlns":890},[892,52379,52380,52384],{},[895,52381,52382],{},[898,52383,3618],{},[902,52385,3618],{"encoding":904},[883,52387,52389],{"className":52388},[886],[888,52390,52391],{"xmlns":890},[892,52392,52393,52397],{},[895,52394,52395],{},[1850,52396,4033],{},[902,52398,52399],{"encoding":904},"0{,}1",[883,52401,52403],{"className":52402},[886],[888,52404,52405],{"xmlns":890},[892,52406,52407,52411],{},[895,52408,52409],{},[898,52410,2312],{},[902,52412,2312],{"encoding":904},[883,52414,52416],{"className":52415},[886],[888,52417,52418],{"xmlns":890},[892,52419,52420,52426],{},[895,52421,52422,52424],{},[1701,52423,2317],{},[1850,52425,3703],{},[902,52427,23500],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,52430,52432],{"className":52431},[886],[888,52433,52434],{"xmlns":890},[892,52435,52436,52446],{},[895,52437,52438],{},[2287,52439,52440,52442,52444],{},[898,52441,1802],{},[1850,52443,4225],{},[898,52445,3249],{},[902,52447,52448],{"encoding":904},"Q_5^E",[724,52450,52451,51675,52454,3602,52477,1715],{},[38,52452,52453],{},"2.15",[883,52455,52457],{"className":52456},[886],[888,52458,52459],{"xmlns":890},[892,52460,52461,52475],{},[895,52462,52463,52465,52467,52469,52471,52473],{},[898,52464,1680],{},[1701,52466,1792],{},[898,52468,207],{},[898,52470,1802],{},[1701,52472,1703],{},[898,52474,3598],{},[902,52476,3601],{"encoding":904},[883,52478,52480],{"className":52479},[886],[888,52481,52482],{"xmlns":890},[892,52483,52484,52498],{},[895,52485,52486,52488,52490,52492,52494,52496],{},[898,52487,1680],{},[1701,52489,1792],{},[898,52491,3618],{},[898,52493,1802],{},[1701,52495,1703],{},[898,52497,2312],{},[902,52499,3627],{"encoding":904},[120,52501,52502,52577,52594,52700,52753,52807],{},[123,52503,52504,52505,52518,52519,52544,52545,52576],{},"(a) Odvoďte redukovaný tvar pro ",[883,52506,52508],{"className":52507},[886],[888,52509,52510],{"xmlns":890},[892,52511,52512,52516],{},[895,52513,52514],{},[898,52515,1680],{},[902,52517,1680],{"encoding":904},". Stanovte podmínky pro ",[883,52520,52522],{"className":52521},[886],[888,52523,52524],{"xmlns":890},[892,52525,52526,52542],{},[895,52527,52528,52530,52532,52534,52536,52538,52540],{},[898,52529,207],{},[1701,52531,2012],{"separator":2011},[898,52533,3598],{},[1701,52535,2012],{"separator":2011},[898,52537,3618],{},[1701,52539,2012],{"separator":2011},[898,52541,2312],{},[902,52543,47305],{"encoding":904}," tak, aby rovnovážný bod ",[883,52546,52548],{"className":52547},[886],[888,52549,52550],{"xmlns":890},[892,52551,52552,52574],{},[895,52553,52554,52556,52558,52564,52566,52572],{},[898,52555,3249],{},[1701,52557,2036],{"stretchy":1798},[3243,52559,52560,52562],{},[898,52561,1802],{},[898,52563,3249],{},[1701,52565,2012],{"separator":2011},[3243,52567,52568,52570],{},[898,52569,1680],{},[898,52571,3249],{},[1701,52573,2053],{"stretchy":1798},[902,52575,45389],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,52578,52579,52580,52593],{},"(b) Vypočtěte multiplikátory pro ",[883,52581,52583],{"className":52582},[886],[888,52584,52585],{"xmlns":890},[892,52586,52587,52591],{},[895,52588,52589],{},[898,52590,1680],{},[902,52592,1680],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,52595,52596,52597,1343,52617,1343,52634,1343,52651,52668,52669,52686,52687,1715],{},"(c) Pro hodnoty parametrů ",[883,52598,52600],{"className":52599},[886],[888,52601,52602],{"xmlns":890},[892,52603,52604,52614],{},[895,52605,52606,52608,52610,52612],{},[898,52607,207],{},[1701,52609,1792],{},[1701,52611,2317],{},[1850,52613,3938],{},[902,52615,52616],{"encoding":904},"a = -2",[883,52618,52620],{"className":52619},[886],[888,52621,52622],{"xmlns":890},[892,52623,52624,52632],{},[895,52625,52626,52628,52630],{},[898,52627,3598],{},[1701,52629,1792],{},[1850,52631,3665],{},[902,52633,3668],{"encoding":904},[883,52635,52637],{"className":52636},[886],[888,52638,52639],{"xmlns":890},[892,52640,52641,52649],{},[895,52642,52643,52645,52647],{},[898,52644,3618],{},[1701,52646,1792],{},[1850,52648,3684],{},[902,52650,3687],{"encoding":904},[883,52652,52654],{"className":52653},[886],[888,52655,52656],{"xmlns":890},[892,52657,52658,52666],{},[895,52659,52660,52662,52664],{},[898,52661,2312],{},[1701,52663,1792],{},[1850,52665,3703],{},[902,52667,3706],{"encoding":904}," určete rovnovážnou cenu ",[883,52670,52672],{"className":52671},[886],[888,52673,52674],{"xmlns":890},[892,52675,52676,52684],{},[895,52677,52678],{},[3243,52679,52680,52682],{},[898,52681,1680],{},[898,52683,3249],{},[902,52685,45488],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,52688,52690],{"className":52689},[886],[888,52691,52692],{"xmlns":890},[892,52693,52694,52698],{},[895,52695,52696],{},[898,52697,1680],{},[902,52699,1680],{"encoding":904},[123,52701,52702,52703,52057,52720,52733,52734,1715],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,52704,52706],{"className":52705},[886],[888,52707,52708],{"xmlns":890},[892,52709,52710,52718],{},[895,52711,52712],{},[3243,52713,52714,52716],{},[898,52715,1680],{},[898,52717,3249],{},[902,52719,45488],{"encoding":904},[883,52721,52723],{"className":52722},[886],[888,52724,52725],{"xmlns":890},[892,52726,52727,52731],{},[895,52728,52729],{},[898,52730,207],{},[902,52732,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,52735,52737],{"className":52736},[886],[888,52738,52739],{"xmlns":890},[892,52740,52741,52751],{},[895,52742,52743],{},[2287,52744,52745,52747,52749],{},[898,52746,1680],{},[1850,52748,4062],{},[898,52750,3249],{},[902,52752,51847],{"encoding":904},[123,52754,52755,52756,52773,52774,52787,52788,1715],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,52757,52759],{"className":52758},[886],[888,52760,52761],{"xmlns":890},[892,52762,52763,52771],{},[895,52764,52765],{},[3243,52766,52767,52769],{},[898,52768,1680],{},[898,52770,3249],{},[902,52772,45488],{"encoding":904}," odpovídající poklesu ",[883,52775,52777],{"className":52776},[886],[888,52778,52779],{"xmlns":890},[892,52780,52781,52785],{},[895,52782,52783],{},[898,52784,207],{},[902,52786,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,52789,52791],{"className":52790},[886],[888,52792,52793],{"xmlns":890},[892,52794,52795,52805],{},[895,52796,52797],{},[2287,52798,52799,52801,52803],{},[898,52800,1680],{},[1850,52802,3938],{},[898,52804,3249],{},[902,52806,51908],{"encoding":904},[123,52808,52809,52810,52330,52827,52840,52841,3856,52854,2633,52869,52882,52883,1715],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,52811,52813],{"className":52812},[886],[888,52814,52815],{"xmlns":890},[892,52816,52817,52825],{},[895,52818,52819],{},[3243,52820,52821,52823],{},[898,52822,1680],{},[898,52824,3249],{},[902,52826,45488],{"encoding":904},[883,52828,52830],{"className":52829},[886],[888,52831,52832],{"xmlns":890},[892,52833,52834,52838],{},[895,52835,52836],{},[898,52837,207],{},[902,52839,207],{"encoding":904}," na 35, ",[883,52842,52844],{"className":52843},[886],[888,52845,52846],{"xmlns":890},[892,52847,52848,52852],{},[895,52849,52850],{},[898,52851,3618],{},[902,52853,3618],{"encoding":904},[883,52855,52857],{"className":52856},[886],[888,52858,52859],{"xmlns":890},[892,52860,52861,52866],{},[895,52862,52863],{},[1850,52864,52865],{},"0,7",[902,52867,52868],{"encoding":904},"0{,}7",[883,52870,52872],{"className":52871},[886],[888,52873,52874],{"xmlns":890},[892,52875,52876,52880],{},[895,52877,52878],{},[898,52879,2312],{},[902,52881,2312],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,52884,52886],{"className":52885},[886],[888,52887,52888],{"xmlns":890},[892,52889,52890,52900],{},[895,52891,52892],{},[2287,52893,52894,52896,52898],{},[898,52895,1680],{},[1850,52897,3646],{},[898,52899,3249],{},[902,52901,52902],{"encoding":904},"P_3^E",[724,52904,52905,51675,52908,3602,52936,2020,52964,2633,52990,1715],{},[38,52906,52907],{},"2.16",[883,52909,52911],{"className":52910},[886],[888,52912,52913],{"xmlns":890},[892,52914,52915,52933],{},[895,52916,52917,52919,52921,52923,52925,52927],{},[898,52918,1680],{},[1701,52920,1792],{},[898,52922,207],{},[1701,52924,1703],{},[898,52926,3598],{},[3243,52928,52929,52931],{},[898,52930,1802],{},[1850,52932,3938],{},[902,52934,52935],{"encoding":904},"P = a + bQ^2",[883,52937,52939],{"className":52938},[886],[888,52940,52941],{"xmlns":890},[892,52942,52943,52961],{},[895,52944,52945,52947,52949,52951,52953,52955],{},[898,52946,1680],{},[1701,52948,1792],{},[898,52950,3618],{},[1701,52952,1703],{},[898,52954,2312],{},[3243,52956,52957,52959],{},[898,52958,1802],{},[1850,52960,3938],{},[902,52962,52963],{"encoding":904},"P = c + dQ^2",[883,52965,52967],{"className":52966},[886],[888,52968,52969],{"xmlns":890},[892,52970,52971,52987],{},[895,52972,52973,52975,52977,52979,52981,52983,52985],{},[898,52974,207],{},[1701,52976,2012],{"separator":2011},[898,52978,3618],{},[1701,52980,2012],{"separator":2011},[898,52982,2312],{},[1701,52984,7491],{},[1850,52986,1852],{},[902,52988,52989],{"encoding":904},"a, c, d > 0",[883,52991,52993],{"className":52992},[886],[888,52994,52995],{"xmlns":890},[892,52996,52997,53005],{},[895,52998,52999,53001,53003],{},[898,53000,3598],{},[1701,53002,7530],{},[1850,53004,1852],{},[902,53006,53007],{"encoding":904},"b \u003C 0",[120,53009,53010,53058,53074,53181,53233,53285,53394,53410,53509,53562],{},[123,53011,52504,53012,53025,53026,53057],{},[883,53013,53015],{"className":53014},[886],[888,53016,53017],{"xmlns":890},[892,53018,53019,53023],{},[895,53020,53021],{},[898,53022,1802],{},[902,53024,1802],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,53027,53029],{"className":53028},[886],[888,53030,53031],{"xmlns":890},[892,53032,53033,53055],{},[895,53034,53035,53037,53039,53045,53047,53053],{},[898,53036,3249],{},[1701,53038,2036],{"stretchy":1798},[3243,53040,53041,53043],{},[898,53042,1802],{},[898,53044,3249],{},[1701,53046,2012],{"separator":2011},[3243,53048,53049,53051],{},[898,53050,1680],{},[898,53052,3249],{},[1701,53054,2053],{"stretchy":1798},[902,53056,45389],{"encoding":904}," patřil do 1. kvadrantu.",[123,53059,52579,53060,53073],{},[883,53061,53063],{"className":53062},[886],[888,53064,53065],{"xmlns":890},[892,53066,53067,53071],{},[895,53068,53069],{},[898,53070,1802],{},[902,53072,1802],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,53075,52596,53076,1343,53094,1343,53114,1343,53132,53150,53151,52686,53168,1715],{},[883,53077,53079],{"className":53078},[886],[888,53080,53081],{"xmlns":890},[892,53082,53083,53091],{},[895,53084,53085,53087,53089],{},[898,53086,207],{},[1701,53088,1792],{},[1850,53090,5158],{},[902,53092,53093],{"encoding":904},"a = 100",[883,53095,53097],{"className":53096},[886],[888,53098,53099],{"xmlns":890},[892,53100,53101,53111],{},[895,53102,53103,53105,53107,53109],{},[898,53104,3598],{},[1701,53106,1792],{},[1701,53108,2317],{},[1850,53110,4062],{},[902,53112,53113],{"encoding":904},"b = -1",[883,53115,53117],{"className":53116},[886],[888,53118,53119],{"xmlns":890},[892,53120,53121,53129],{},[895,53122,53123,53125,53127],{},[898,53124,3618],{},[1701,53126,1792],{},[1850,53128,13096],{},[902,53130,53131],{"encoding":904},"c = 20",[883,53133,53135],{"className":53134},[886],[888,53136,53137],{"xmlns":890},[892,53138,53139,53147],{},[895,53140,53141,53143,53145],{},[898,53142,2312],{},[1701,53144,1792],{},[1850,53146,4062],{},[902,53148,53149],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,53152,53154],{"className":53153},[886],[888,53155,53156],{"xmlns":890},[892,53157,53158,53166],{},[895,53159,53160],{},[3243,53161,53162,53164],{},[898,53163,1802],{},[898,53165,3249],{},[902,53167,3807],{"encoding":904},[883,53169,53171],{"className":53170},[886],[888,53172,53173],{"xmlns":890},[892,53174,53175,53179],{},[895,53176,53177],{},[898,53178,1802],{},[902,53180,1802],{"encoding":904},[123,53182,52125,53183,52057,53200,53213,53214,1715],{},[883,53184,53186],{"className":53185},[886],[888,53187,53188],{"xmlns":890},[892,53189,53190,53198],{},[895,53191,53192],{},[3243,53193,53194,53196],{},[898,53195,1802],{},[898,53197,3249],{},[902,53199,3807],{"encoding":904},[883,53201,53203],{"className":53202},[886],[888,53204,53205],{"xmlns":890},[892,53206,53207,53211],{},[895,53208,53209],{},[898,53210,207],{},[902,53212,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,53215,53217],{"className":53216},[886],[888,53218,53219],{"xmlns":890},[892,53220,53221,53231],{},[895,53222,53223],{},[2287,53224,53225,53227,53229],{},[898,53226,1802],{},[1850,53228,4062],{},[898,53230,3249],{},[902,53232,51826],{"encoding":904},[123,53234,52178,53235,52057,53252,53265,53266,1715],{},[883,53236,53238],{"className":53237},[886],[888,53239,53240],{"xmlns":890},[892,53241,53242,53250],{},[895,53243,53244],{},[3243,53245,53246,53248],{},[898,53247,1802],{},[898,53249,3249],{},[902,53251,3807],{"encoding":904},[883,53253,53255],{"className":53254},[886],[888,53256,53257],{"xmlns":890},[892,53258,53259,53263],{},[895,53260,53261],{},[898,53262,3618],{},[902,53264,3618],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,53267,53269],{"className":53268},[886],[888,53270,53271],{"xmlns":890},[892,53272,53273,53283],{},[895,53274,53275],{},[2287,53276,53277,53279,53281],{},[898,53278,1802],{},[1850,53280,3938],{},[898,53282,3249],{},[902,53284,51888],{"encoding":904},[123,53286,52258,53287,52330,53304,53317,53318,3856,53331,53346,53347,53360,53361,53374,53375,1715],{},[883,53288,53290],{"className":53289},[886],[888,53291,53292],{"xmlns":890},[892,53293,53294,53302],{},[895,53295,53296],{},[3243,53297,53298,53300],{},[898,53299,1802],{},[898,53301,3249],{},[902,53303,3807],{"encoding":904},[883,53305,53307],{"className":53306},[886],[888,53308,53309],{"xmlns":890},[892,53310,53311,53315],{},[895,53312,53313],{},[898,53314,207],{},[902,53316,207],{"encoding":904}," na 110, poklesu ",[883,53319,53321],{"className":53320},[886],[888,53322,53323],{"xmlns":890},[892,53324,53325,53329],{},[895,53326,53327],{},[898,53328,3598],{},[902,53330,3598],{"encoding":904},[883,53332,53334],{"className":53333},[886],[888,53335,53336],{"xmlns":890},[892,53337,53338,53344],{},[895,53339,53340,53342],{},[1701,53341,2317],{},[1850,53343,3938],{},[902,53345,52086],{"encoding":904},", růstu ",[883,53348,53350],{"className":53349},[886],[888,53351,53352],{"xmlns":890},[892,53353,53354,53358],{},[895,53355,53356],{},[898,53357,3618],{},[902,53359,3618],{"encoding":904}," na 25 a růstu ",[883,53362,53364],{"className":53363},[886],[888,53365,53366],{"xmlns":890},[892,53367,53368,53372],{},[895,53369,53370],{},[898,53371,2312],{},[902,53373,2312],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,53376,53378],{"className":53377},[886],[888,53379,53380],{"xmlns":890},[892,53381,53382,53392],{},[895,53383,53384],{},[2287,53385,53386,53388,53390],{},[898,53387,1802],{},[1850,53389,3646],{},[898,53391,3249],{},[902,53393,52255],{"encoding":904},[123,53395,53396,53397,53073],{},"(i) Vypočtěte multiplikátory pro ",[883,53398,53400],{"className":53399},[886],[888,53401,53402],{"xmlns":890},[892,53403,53404,53408],{},[895,53405,53406],{},[898,53407,1680],{},[902,53409,1680],{"encoding":904},[123,53411,53412,53413,52686,53430,53443,53444,52057,53461,3856,53474,53489,53490,1715],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,53414,53416],{"className":53415},[886],[888,53417,53418],{"xmlns":890},[892,53419,53420,53428],{},[895,53421,53422],{},[3243,53423,53424,53426],{},[898,53425,1680],{},[898,53427,3249],{},[902,53429,45488],{"encoding":904},[883,53431,53433],{"className":53432},[886],[888,53434,53435],{"xmlns":890},[892,53436,53437,53441],{},[895,53438,53439],{},[898,53440,1680],{},[902,53442,1680],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,53445,53447],{"className":53446},[886],[888,53448,53449],{"xmlns":890},[892,53450,53451,53459],{},[895,53452,53453],{},[3243,53454,53455,53457],{},[898,53456,1680],{},[898,53458,3249],{},[902,53460,45488],{"encoding":904},[883,53462,53464],{"className":53463},[886],[888,53465,53466],{"xmlns":890},[892,53467,53468,53472],{},[895,53469,53470],{},[898,53471,207],{},[902,53473,207],{"encoding":904},[883,53475,53477],{"className":53476},[886],[888,53478,53479],{"xmlns":890},[892,53480,53481,53487],{},[895,53482,53483,53485],{},[1701,53484,2317],{},[1850,53486,3646],{},[902,53488,52102],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53491,53493],{"className":53492},[886],[888,53494,53495],{"xmlns":890},[892,53496,53497,53507],{},[895,53498,53499],{},[2287,53500,53501,53503,53505],{},[898,53502,1680],{},[1850,53504,4062],{},[898,53506,3249],{},[902,53508,51847],{"encoding":904},[123,53510,53511,53512,52057,53529,53542,53543,1715],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,53513,53515],{"className":53514},[886],[888,53516,53517],{"xmlns":890},[892,53518,53519,53527],{},[895,53520,53521],{},[3243,53522,53523,53525],{},[898,53524,1680],{},[898,53526,3249],{},[902,53528,45488],{"encoding":904},[883,53530,53532],{"className":53531},[886],[888,53533,53534],{"xmlns":890},[892,53535,53536,53540],{},[895,53537,53538],{},[898,53539,207],{},[902,53541,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53544,53546],{"className":53545},[886],[888,53547,53548],{"xmlns":890},[892,53549,53550,53560],{},[895,53551,53552],{},[2287,53553,53554,53556,53558],{},[898,53555,1680],{},[1850,53557,3938],{},[898,53559,3249],{},[902,53561,51908],{"encoding":904},[123,53563,53564,53565,52773,53582,53595,53596,3856,53609,53346,53624,53637,53638,53651,53652,1715],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,53566,53568],{"className":53567},[886],[888,53569,53570],{"xmlns":890},[892,53571,53572,53580],{},[895,53573,53574],{},[3243,53575,53576,53578],{},[898,53577,1680],{},[898,53579,3249],{},[902,53581,45488],{"encoding":904},[883,53583,53585],{"className":53584},[886],[888,53586,53587],{"xmlns":890},[892,53588,53589,53593],{},[895,53590,53591],{},[898,53592,207],{},[902,53594,207],{"encoding":904}," na 90, poklesu ",[883,53597,53599],{"className":53598},[886],[888,53600,53601],{"xmlns":890},[892,53602,53603,53607],{},[895,53604,53605],{},[898,53606,3598],{},[902,53608,3598],{"encoding":904},[883,53610,53612],{"className":53611},[886],[888,53613,53614],{"xmlns":890},[892,53615,53616,53622],{},[895,53617,53618,53620],{},[1701,53619,2317],{},[1850,53621,3646],{},[902,53623,52102],{"encoding":904},[883,53625,53627],{"className":53626},[886],[888,53628,53629],{"xmlns":890},[892,53630,53631,53635],{},[895,53632,53633],{},[898,53634,3618],{},[902,53636,3618],{"encoding":904}," na 30 a růstu ",[883,53639,53641],{"className":53640},[886],[888,53642,53643],{"xmlns":890},[892,53644,53645,53649],{},[895,53646,53647],{},[898,53648,2312],{},[902,53650,2312],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,53653,53655],{"className":53654},[886],[888,53656,53657],{"xmlns":890},[892,53658,53659,53669],{},[895,53660,53661],{},[2287,53662,53663,53665,53667],{},[898,53664,1680],{},[1850,53666,3646],{},[898,53668,3249],{},[902,53670,52902],{"encoding":904},[198,53672,820],{"id":53673},"přebytek-spotřebitele-a-výrobce-1",[724,53675,53676,51675,53679,3602,53715,1715],{},[38,53677,53678],{},"2.17",[883,53680,53682],{"className":53681},[886],[888,53683,53684],{"xmlns":890},[892,53685,53686,53712],{},[895,53687,53688,53690,53692,53694,53696,53698,53700,53702,53704,53706],{},[898,53689,1680],{},[1701,53691,1792],{},[898,53693,1795],{},[1701,53695,1799],{"stretchy":1798},[898,53697,1802],{},[1701,53699,1805],{"stretchy":1798},[1701,53701,1792],{},[1850,53703,4136],{},[1701,53705,2317],{},[3243,53707,53708,53710],{},[898,53709,1802],{},[1850,53711,3938],{},[902,53713,53714],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,53716,53718],{"className":53717},[886],[888,53719,53720],{"xmlns":890},[892,53721,53722,53748],{},[895,53723,53724,53726,53728,53730,53732,53734,53736,53738,53740,53742],{},[898,53725,1680],{},[1701,53727,1792],{},[898,53729,1661],{},[1701,53731,1799],{"stretchy":1798},[898,53733,1802],{},[1701,53735,1805],{"stretchy":1798},[1701,53737,1792],{},[1850,53739,3646],{},[1701,53741,1703],{},[3243,53743,53744,53746],{},[898,53745,1802],{},[1850,53747,3938],{},[902,53749,53750],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,53752,53753,53756],{},[123,53754,53755],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,53757,53758],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,53760,53761,51675,53764,3602,53798,1715],{},[38,53762,53763],{},"2.18",[883,53765,53767],{"className":53766},[886],[888,53768,53769],{"xmlns":890},[892,53770,53771,53795],{},[895,53772,53773,53775,53777,53779,53781,53783,53785,53787,53789,53791,53793],{},[898,53774,1680],{},[1701,53776,1792],{},[898,53778,1795],{},[1701,53780,1799],{"stretchy":1798},[898,53782,1802],{},[1701,53784,1805],{"stretchy":1798},[1701,53786,1792],{},[1850,53788,7790],{},[1701,53790,2317],{},[1850,53792,3938],{},[898,53794,1802],{},[902,53796,53797],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,53799,53801],{"className":53800},[886],[888,53802,53803],{"xmlns":890},[892,53804,53805,53831],{},[895,53806,53807,53809,53811,53813,53815,53817,53819,53821,53823,53825],{},[898,53808,1680],{},[1701,53810,1792],{},[898,53812,1661],{},[1701,53814,1799],{"stretchy":1798},[898,53816,1802],{},[1701,53818,1805],{"stretchy":1798},[1701,53820,1792],{},[1850,53822,3646],{},[1701,53824,1703],{},[3243,53826,53827,53829],{},[898,53828,1802],{},[1850,53830,3938],{},[902,53832,53750],{"encoding":904},[120,53834,53835,53855,53858,53861],{},[123,53836,53837,53838,1715],{},"(a) Vypočtěte rovnovážné množství ",[883,53839,53841],{"className":53840},[886],[888,53842,53843],{"xmlns":890},[892,53844,53845,53853],{},[895,53846,53847],{},[3243,53848,53849,53851],{},[898,53850,1802],{},[898,53852,3249],{},[902,53854,3807],{"encoding":904},[123,53856,53857],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,53859,53860],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,53862,53863],{},"(c) Graficky interpretujte.",[1771,53865],{},[115,53867,53869],{"id":53868},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,53871,53872,53875,53878,53881,53884,53887,53890,53893,53896,53899,53902,53905,53908,53911],{},[123,53873,53874],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,53876,53877],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,53879,53880],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,53882,53883],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,53885,53886],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,53888,53889],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,53891,53892],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,53894,53895],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,53897,53898],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,53900,53901],{},"K čemu slouží multiplikátory?",[123,53903,53904],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,53906,53907],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,53909,53910],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,53912,53913],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[1771,53915],{},[115,53917,5578],{"id":5577},[724,53919,53920],{},[38,53921,17215],{},[120,53923,53924,53959,53964,53994,53999,54062,54088,54093,54123,54132,54139,54145],{},[123,53925,53926,1646,53929,22694,53932,4088,53934,1343,53957],{},[38,53927,53928],{},"Poptávané množství",[614,53930,53931],{},"quantity demanded",[38,53933,32039],{},[883,53935,53937],{"className":53936},[886],[888,53938,53939],{"xmlns":890},[892,53940,53941,53955],{},[895,53942,53943,53945,53947,53949,53951,53953],{},[898,53944,1802],{},[1701,53946,1792],{},[898,53948,1795],{},[1701,53950,1799],{"stretchy":1798},[898,53952,1680],{},[1701,53954,1805],{"stretchy":1798},[902,53956,8264],{"encoding":904},[38,53958,41477],{},[123,53960,53961,53963],{},[38,53962,41484],{}," — substituční + důchodový efekt",[123,53965,53966,4088,53969],{},[38,53967,53968],{},"Reálné cenové rozpětí",[883,53970,53972],{"className":53971},[886],[888,53973,53974],{"xmlns":890},[892,53975,53976,53992],{},[895,53977,53978,53980,53982,53984,53990],{},[1701,53979,1799],{"stretchy":1798},[1850,53981,1852],{},[1701,53983,2012],{"separator":2011},[1845,53985,53986,53988],{},[898,53987,1680],{},[1850,53989,1852],{},[1701,53991,1805],{"stretchy":1798},[902,53993,41685],{"encoding":904},[123,53995,53996,15153],{},[38,53997,53998],{},"Homogenita poptávky",[123,54000,54001,4088,54004,1343,54027,1343,54044,54061],{},[38,54002,54003],{},"Lineární poptávka",[883,54005,54007],{"className":54006},[886],[888,54008,54009],{"xmlns":890},[892,54010,54011,54025],{},[895,54012,54013,54015,54017,54019,54021,54023],{},[898,54014,1680],{},[1701,54016,1792],{},[898,54018,207],{},[898,54020,1802],{},[1701,54022,1703],{},[898,54024,3598],{},[902,54026,3601],{"encoding":904},[883,54028,54030],{"className":54029},[886],[888,54031,54032],{"xmlns":890},[892,54033,54034,54042],{},[895,54035,54036,54038,54040],{},[898,54037,207],{},[1701,54039,7530],{},[1850,54041,1852],{},[902,54043,47105],{"encoding":904},[883,54045,54047],{"className":54046},[886],[888,54048,54049],{"xmlns":890},[892,54050,54051,54059],{},[895,54052,54053,54055,54057],{},[898,54054,3598],{},[1701,54056,7491],{},[1850,54058,1852],{},[902,54060,22860],{"encoding":904}," — nedokonalá konkurence",[123,54063,54064,2979,54067],{},[38,54065,54066],{},"Dokonalá konkurence",[883,54068,54070],{"className":54069},[886],[888,54071,54072],{"xmlns":890},[892,54073,54074,54086],{},[895,54075,54076,54078,54080],{},[898,54077,1680],{},[1701,54079,1792],{},[3243,54081,54082,54084],{},[898,54083,1680],{},[1701,54085,8424],{},[902,54087,8427],{"encoding":904},[123,54089,54090,54092],{},[38,54091,42252],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,54094,54095,4088,54097,1343,54121],{},[38,54096,35758],{},[883,54098,54100],{"className":54099},[886],[888,54101,54102],{"xmlns":890},[892,54103,54104,54118],{},[895,54105,54106,54108,54110,54112,54114,54116],{},[898,54107,1802],{},[1701,54109,1792],{},[898,54111,3249],{},[1701,54113,1799],{"stretchy":1798},[898,54115,13189],{},[1701,54117,1805],{"stretchy":1798},[902,54119,54120],{"encoding":904},"Q = E(Y)",[38,54122,42448],{},[123,54124,54125,54128,54129,54131],{},[38,54126,54127],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,54130,42894],{}," zboží",[123,54133,54134,2633,54136,54138],{},[38,54135,43899],{},[38,54137,43846],{}," — znaménka zkřížených koeficientů",[123,54140,54141,54144],{},[38,54142,54143],{},"Dvoukomoditní trh"," (2.6)",[123,54146,54147,1646,54150,1805],{},[38,54148,54149],{},"Posun poptávky",[614,54151,42952],{},[724,54153,54154],{},[38,54155,17179],{},[120,54157,54158,54191,54195,54240],{},[123,54159,54160,1646,54162,22694,54164,4088,54166,1343,54189],{},[38,54161,44292],{},[614,54163,44295],{},[38,54165,44466],{},[883,54167,54169],{"className":54168},[886],[888,54170,54171],{"xmlns":890},[892,54172,54173,54187],{},[895,54174,54175,54177,54179,54181,54183,54185],{},[898,54176,1802],{},[1701,54178,1792],{},[898,54180,1661],{},[1701,54182,1799],{"stretchy":1798},[898,54184,1680],{},[1701,54186,1805],{"stretchy":1798},[902,54188,12743],{"encoding":904},[38,54190,44544],{},[123,54192,54193],{},[38,54194,44551],{},[123,54196,54197,4088,54200,1343,54223],{},[38,54198,54199],{},"Lineární nabídka",[883,54201,54203],{"className":54202},[886],[888,54204,54205],{"xmlns":890},[892,54206,54207,54221],{},[895,54208,54209,54211,54213,54215,54217,54219],{},[898,54210,1680],{},[1701,54212,1792],{},[898,54214,3618],{},[898,54216,1802],{},[1701,54218,1703],{},[898,54220,2312],{},[902,54222,3627],{"encoding":904},[883,54224,54226],{"className":54225},[886],[888,54227,54228],{"xmlns":890},[892,54229,54230,54238],{},[895,54231,54232,54234,54236],{},[898,54233,3618],{},[1701,54235,7491],{},[1850,54237,1852],{},[902,54239,44283],{"encoding":904},[123,54241,54242,1646,54245,1805],{},[38,54243,54244],{},"Posun nabídky",[614,54246,44929],{},[724,54248,54249],{},[38,54250,54251],{},"Rovnováha a komparativní statika",[120,54253,54254,54333,54339],{},[123,54255,54256,1646,54258,22694,54260,4088,54263,1343,54280,4088,54283,1343,54300,4088,54302],{},[38,54257,45347],{},[614,54259,45466],{},[38,54261,54262],{},"rovnovážná cena",[883,54264,54266],{"className":54265},[886],[888,54267,54268],{"xmlns":890},[892,54269,54270,54278],{},[895,54271,54272],{},[3243,54273,54274,54276],{},[898,54275,1680],{},[898,54277,3249],{},[902,54279,45488],{"encoding":904},[38,54281,54282],{},"rovnovážné množství",[883,54284,54286],{"className":54285},[886],[888,54287,54288],{"xmlns":890},[892,54289,54290,54298],{},[895,54291,54292],{},[3243,54293,54294,54296],{},[898,54295,1802],{},[898,54297,3249],{},[902,54299,3807],{"encoding":904},[38,54301,45524],{},[883,54303,54305],{"className":54304},[886],[888,54306,54307],{"xmlns":890},[892,54308,54309,54331],{},[895,54310,54311,54313,54315,54321,54323,54329],{},[898,54312,3249],{},[1701,54314,2036],{"stretchy":1798},[3243,54316,54317,54319],{},[898,54318,1802],{},[898,54320,3249],{},[1701,54322,2012],{"separator":2011},[3243,54324,54325,54327],{},[898,54326,1680],{},[898,54328,3249],{},[1701,54330,2053],{"stretchy":1798},[902,54332,45389],{"encoding":904},[123,54334,54335,54338],{},[38,54336,54337],{},"Pravidla 1–4"," komparativní statiky",[123,54340,54341,1646,54344,1805],{},[38,54342,54343],{},"Teorém pavučiny",[614,54345,46370],{},[724,54347,54348],{},[38,54349,54350],{},"Zdanění",[120,54352,54353,54409,54457],{},[123,54354,54355,54357,54358,54383,54384,1805],{},[38,54356,54350],{}," — daň výrobci (",[883,54359,54361],{"className":54360},[886],[888,54362,54363],{"xmlns":890},[892,54364,54365,54381],{},[895,54366,54367,54373,54375,54377,54379],{},[1845,54368,54369,54371],{},[898,54370,1661],{},[1850,54372,4062],{},[1701,54374,1792],{},[898,54376,1661],{},[1701,54378,1703],{},[898,54380,5877],{},[902,54382,46774],{"encoding":904},") vs. daň spotřebiteli (",[883,54385,54387],{"className":54386},[886],[888,54388,54389],{"xmlns":890},[892,54390,54391,54407],{},[895,54392,54393,54399,54401,54403,54405],{},[1845,54394,54395,54397],{},[898,54396,1795],{},[1850,54398,3938],{},[1701,54400,1792],{},[898,54402,1795],{},[1701,54404,2317],{},[898,54406,5877],{},[902,54408,46805],{"encoding":904},[123,54410,54411,4088,54413,1343,54434],{},[38,54412,46678],{},[883,54414,54416],{"className":54415},[886],[888,54417,54418],{"xmlns":890},[892,54419,54420,54432],{},[895,54421,54422],{},[1845,54423,54424,54426],{},[898,54425,5877],{},[895,54427,54428,54430],{},[898,54429,46697],{},[898,54431,724],{},[902,54433,46702],{"encoding":904},[883,54435,54437],{"className":54436},[886],[888,54438,54439],{"xmlns":890},[892,54440,54441,54455],{},[895,54442,54443],{},[1845,54444,54445,54447],{},[898,54446,5877],{},[895,54448,54449,54451,54453],{},[898,54450,46720],{},[898,54452,6127],{},[898,54454,16096],{},[902,54456,46727],{"encoding":904},[123,54458,54459,4088,54462,1343,54491],{},[38,54460,54461],{},"Ekvivalence zdanění",[883,54463,54465],{"className":54464},[886],[888,54466,54467],{"xmlns":890},[892,54468,54469,54489],{},[895,54470,54471,54479,54481],{},[2287,54472,54473,54475,54477],{},[898,54474,1802],{},[1850,54476,4062],{},[898,54478,3249],{},[1701,54480,1792],{},[2287,54482,54483,54485,54487],{},[898,54484,1802],{},[1850,54486,3938],{},[898,54488,3249],{},[902,54490,46928],{"encoding":904},[883,54492,54494],{"className":54493},[886],[888,54495,54496],{"xmlns":890},[892,54497,54498,54522],{},[895,54499,54500,54508,54510,54512,54514],{},[2287,54501,54502,54504,54506],{},[898,54503,1680],{},[1850,54505,4062],{},[898,54507,3249],{},[1701,54509,2317],{},[898,54511,5877],{},[1701,54513,1792],{},[2287,54515,54516,54518,54520],{},[898,54517,1680],{},[1850,54519,3938],{},[898,54521,3249],{},[902,54523,46962],{"encoding":904},[724,54525,54526],{},[38,54527,30445],{},[120,54529,54530,54576,54607,54612,54618,54625],{},[123,54531,54532,4088,54534],{},[38,54533,47061],{},[883,54535,54537],{"className":54536},[886],[888,54538,54539],{"xmlns":890},[892,54540,54541,54573],{},[895,54542,54543,54549,54551,54553,54555,54557,54559,54561,54563,54565,54567,54569,54571],{},[3243,54544,54545,54547],{},[898,54546,1802],{},[898,54548,3249],{},[1701,54550,1792],{},[1701,54552,1799],{"stretchy":1798},[898,54554,3598],{},[1701,54556,2317],{},[898,54558,2312],{},[1701,54560,1805],{"stretchy":1798},[898,54562,8741],{"mathvariant":2334},[1701,54564,1799],{"stretchy":1798},[898,54566,3618],{},[1701,54568,2317],{},[898,54570,207],{},[1701,54572,1805],{"stretchy":1798},[902,54574,54575],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,54577,54578,4088,54581,54606],{},[38,54579,54580],{},"Parametry",[883,54582,54584],{"className":54583},[886],[888,54585,54586],{"xmlns":890},[892,54587,54588,54604],{},[895,54589,54590,54592,54594,54596,54598,54600,54602],{},[898,54591,207],{},[1701,54593,2012],{"separator":2011},[898,54595,3598],{},[1701,54597,2012],{"separator":2011},[898,54599,3618],{},[1701,54601,2012],{"separator":2011},[898,54603,2312],{},[902,54605,47305],{"encoding":904}," — exogenní proměnné",[123,54608,54609],{},[38,54610,54611],{},"Endogenní \u002F exogenní proměnná",[123,54613,54614,54617],{},[38,54615,54616],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,54619,54620,1343,54623],{},[38,54621,54622],{},"Komparativní statika",[38,54624,40990],{},[123,54626,54627,4088,54629,54645],{},[38,54628,7043],{},[883,54630,54632],{"className":54631},[886],[888,54633,54634],{"xmlns":890},[892,54635,54636,54642],{},[895,54637,54638,54640],{},[898,54639,2312],{},[898,54641,1802],{},[902,54643,54644],{"encoding":904},"dQ"," (2.11)",[724,54647,54648],{},[38,54649,54650],{},"Přebytky a ostatní",[120,54652,54653,54691],{},[123,54654,54655,4088,54657,54672,54673,4088,54675,54690],{},[38,54656,1645],{},[883,54658,54660],{"className":54659},[886],[888,54661,54662],{"xmlns":890},[892,54663,54664,54670],{},[895,54665,54666,54668],{},[898,54667,1658],{},[898,54669,1661],{},[902,54671,1664],{"encoding":904}," (2.14), ",[38,54674,1741],{},[883,54676,54678],{"className":54677},[886],[888,54679,54680],{"xmlns":890},[892,54681,54682,54688],{},[895,54683,54684,54686],{},[898,54685,1680],{},[898,54687,1661],{},[902,54689,1685],{"encoding":904}," (2.15)",[123,54692,54693,1343,54696,54699],{},[38,54694,54695],{},"Homo economicus",[38,54697,54698],{},"Marshallova formulace"," (1890)",[1771,54701],{},[115,54703,5984],{"id":5983},[120,54705,54706,54741,54748],{},[123,54707,54708,4088,54711,54714,54715,1343,54718,54721,54722,54725,54726,54729,54730,54733,54734,54737,54738],{},[38,54709,54710],{},"Související témata:",[207,54712,811],{"className":54713,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,54716,820],{"className":54717,"dataFsResolvedFilePath":818,"href":819},[210],[207,54719,6007],{"className":54720,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,54723,775],{"className":54724,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,54727,784],{"className":54728,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,54731,793],{"className":54732,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,54735,7908],{"className":54736,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,54739,6017],{"className":54740,"dataFsResolvedFilePath":827,"href":828},[210],[123,54742,54743,4088,54745],{},[38,54744,6022],{},[207,54746,6026],{"className":54747,"dataFsResolvedFilePath":745,"href":746},[210],[123,54749,54750,4088,54752],{},[38,54751,6031],{},[207,54753,6037],{"className":54754,"dataFsResolvedFilePath":6035,"href":6036},[210],{"title":641,"searchDepth":642,"depth":642,"links":54756},[54757,54758,54766,54772,54779,54780,54787,54788,54789,54796,54797,54798],{"id":40824,"depth":642,"text":40825},{"id":40805,"depth":642,"text":17215,"children":54759},[54760,54761,54762,54763,54765],{"id":41091,"depth":649,"text":41092},{"id":41373,"depth":649,"text":41374},{"id":42380,"depth":649,"text":42381},{"id":42948,"depth":649,"text":54764},"Posun poptávky (shift of demand)",{"id":43451,"depth":649,"text":43452},{"id":40809,"depth":642,"text":17179,"children":54767},[54768,54769,54770],{"id":44287,"depth":649,"text":41092},{"id":44473,"depth":649,"text":44474},{"id":44925,"depth":649,"text":54771},"Posun nabídky (shift of supply)",{"id":45346,"depth":642,"text":45347,"children":54773},[54774,54775,54776,54777,54778],{"id":45458,"depth":649,"text":45459},{"id":45671,"depth":649,"text":45672},{"id":45988,"depth":649,"text":45989},{"id":46342,"depth":649,"text":46343},{"id":46373,"depth":649,"text":46374},{"id":46641,"depth":642,"text":811},{"id":47042,"depth":642,"text":47043,"children":54781},[54782,54783,54784,54785],{"id":47060,"depth":649,"text":47061},{"id":47441,"depth":649,"text":47442},{"id":47825,"depth":649,"text":47826},{"id":48279,"depth":649,"text":54786},"Příklad 2.11 — komparativní statika pro 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sh__":78207},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":58868,"toc":78160},[58869,58872,59058,59060,59151,59156,59482,59486,59493,59497,59542,59609,59640,59690,59725,59729,59788,59793,59859,59977,60079,60083,60106,60184,60227,60231,60260,60327,60333,60447,60451,60531,60568,60620,60818,60882,60969,60973,60976,61055,61058,61176,61195,61260,61264,61356,61424,61465,61519,61587,61624,61628,61686,61716,61927,61999,62051,62217,62310,62345,62349,62353,62390,62455,62510,62514,62537,62626,62730,62799,62803,62900,63013,63069,63123,63181,63242,63245,63281,63346,63376,63605,63663,63697,63701,63728,63807,63921,63942,64021,64023,64131,64135,64273,64595,64599,64602,64606,64655,64659,64913,65065,65072,65145,65329,65334,65677,65681,65704,65706,65727,65786,65796,65845,65987,66061,66156,66271,66369,66487,66491,66560,66565,66677,66822,66873,66985,67027,67031,67051,67112,67139,67201,67205,67227,67296,67576,67583,67613,67620,67813,67817,67895,67900,67976,67979,68067,68143,68210,68259,68362,68435,68556,68907,69020,69122,69126,69129,69136,69139,69175,69234,69243,69392,69616,69620,69683,69862,69954,70009,70013,70069,70139,70191,70212,70293,70296,70371,70415,70419,70460,70503,70529,70533,70604,70700,70762,70814,70917,70995,71018,71047,71051,71217,71334,71406,71721,71881,71885,71936,71998,72033,72063,72163,72205,72374,72379,72475,72513,72517,72636,72937,72939,72974,72978,72982,73110,73242,73564,73752,73830,73834,74139,74252,74398,74583,74689,74921,75036,75118,75237,75335,75376,75380,75435,75579,75733,75893,75986,76180,76492,76623,76752,76756,76828,76870,76921,76923,78118,78120],[12,58870,58866],{"id":58871},"příjem-náklady-zisk-a-nabídka-firmy",[1635,58873,58874],{},[724,58875,58876,1642,58878,4088,58881,58896,58897,4088,58900,58915,58916,4088,58919,58947,58948,58970,58971,58995,58996,59018,59019,59022,59023,59039,59040,1715],{},[883,58877,1641],{},[38,58879,58880],{},"Příjem",[883,58882,58884],{"className":58883},[886],[888,58885,58886],{"xmlns":890},[892,58887,58888,58894],{},[895,58889,58890,58892],{},[898,58891,5877],{},[898,58893,8068],{},[902,58895,8168],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,58898,58899],{},"náklady",[883,58901,58903],{"className":58902},[886],[888,58904,58905],{"xmlns":890},[892,58906,58907,58913],{},[895,58908,58909,58911],{},[898,58910,5877],{},[898,58912,1658],{},[902,58914,7326],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,58917,58918],{},"zisk",[883,58920,58922],{"className":58921},[886],[888,58923,58924],{"xmlns":890},[892,58925,58926,58944],{},[895,58927,58928,58930,58932,58934,58936,58938,58940,58942],{},[898,58929,1680],{},[898,58931,8068],{},[1701,58933,1792],{},[898,58935,5877],{},[898,58937,8068],{},[1701,58939,2317],{},[898,58941,5877],{},[898,58943,1658],{},[902,58945,58946],{"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: ",[883,58949,58951],{"className":58950},[886],[888,58952,58953],{"xmlns":890},[892,58954,58955,58967],{},[895,58956,58957,58959,58961,58963,58965],{},[898,58958,1983],{},[898,58960,1658],{},[1701,58962,1792],{},[898,58964,6909],{},[898,58966,1658],{},[902,58968,58969],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,58972,58974],{"className":58973},[886],[888,58975,58976],{"xmlns":890},[892,58977,58978,58992],{},[895,58979,58980,58982,58984,58986,58988,58990],{},[898,58981,1983],{},[898,58983,44362],{},[898,58985,1658],{},[1701,58987,1792],{},[898,58989,6909],{},[898,58991,1658],{},[902,58993,58994],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,58997,58999],{"className":58998},[886],[888,59000,59001],{"xmlns":890},[892,59002,59003,59015],{},[895,59004,59005,59007,59009,59011,59013],{},[898,59006,6909],{},[898,59008,8068],{},[1701,59010,1792],{},[898,59012,6909],{},[898,59014,1658],{},[902,59016,59017],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,59020,59021],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,59024,59026],{"className":59025},[886],[888,59027,59028],{"xmlns":890},[892,59029,59030,59036],{},[895,59031,59032,59034],{},[898,59033,6909],{},[898,59035,1658],{},[902,59037,59038],{"encoding":904},"MC"," nad bodem minima ",[883,59041,59043],{"className":59042},[886],[888,59044,59045],{"xmlns":890},[892,59046,59047,59055],{},[895,59048,59049,59051,59053],{},[898,59050,1983],{},[898,59052,44362],{},[898,59054,1658],{},[902,59056,59057],{"encoding":904},"AVC",[115,59059,1241],{"id":1775},[724,59061,59062,59063,59066,59067,59069,59070,1343,59073,1343,59076,59078,59079,59082,59083,59086,59087,59090,59091,3841,59106,1348,59121,3841,59136,2506],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,59064,59065],{},"příjmem"," (revenue) a ",[38,59068,58899],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,59071,59072],{},"zisku",[38,59074,59075],{},"bodů zvratu",[38,59077,6104],{}," a konstrukcí ",[38,59080,59081],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,59084,1145],{"className":59085,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,59088,15187],{"className":59089,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,59092,59094],{"className":59093},[886],[888,59095,59096],{"xmlns":890},[892,59097,59098,59104],{},[895,59099,59100,59102],{},[898,59101,5877],{},[898,59103,8068],{},[902,59105,8168],{"encoding":904},[883,59107,59109],{"className":59108},[886],[888,59110,59111],{"xmlns":890},[892,59112,59113,59119],{},[895,59114,59115,59117],{},[898,59116,6909],{},[898,59118,8068],{},[902,59120,10697],{"encoding":904},[883,59122,59124],{"className":59123},[886],[888,59125,59126],{"xmlns":890},[892,59127,59128,59134],{},[895,59129,59130,59132],{},[898,59131,5877],{},[898,59133,1658],{},[902,59135,7326],{"encoding":904},[883,59137,59139],{"className":59138},[886],[888,59140,59141],{"xmlns":890},[892,59142,59143,59149],{},[895,59144,59145,59147],{},[898,59146,6909],{},[898,59148,1658],{},[902,59150,59038],{"encoding":904},[724,59152,59153],{},[38,59154,59155],{},"Cílové znalosti:",[120,59157,59158,59322,59325,59328,59421,59468,59475],{},[123,59159,59160,59161,1343,59176,1343,59192,2633,59207,1343,59222,1343,59238,1343,59256,1343,59274,1343,59291,1343,59307,12487],{},"odvodit a interpretovat funkce ",[883,59162,59164],{"className":59163},[886],[888,59165,59166],{"xmlns":890},[892,59167,59168,59174],{},[895,59169,59170,59172],{},[898,59171,5877],{},[898,59173,8068],{},[902,59175,8168],{"encoding":904},[883,59177,59179],{"className":59178},[886],[888,59180,59181],{"xmlns":890},[892,59182,59183,59189],{},[895,59184,59185,59187],{},[898,59186,1983],{},[898,59188,8068],{},[902,59190,59191],{"encoding":904},"AR",[883,59193,59195],{"className":59194},[886],[888,59196,59197],{"xmlns":890},[892,59198,59199,59205],{},[895,59200,59201,59203],{},[898,59202,6909],{},[898,59204,8068],{},[902,59206,10697],{"encoding":904},[883,59208,59210],{"className":59209},[886],[888,59211,59212],{"xmlns":890},[892,59213,59214,59220],{},[895,59215,59216,59218],{},[898,59217,5877],{},[898,59219,1658],{},[902,59221,7326],{"encoding":904},[883,59223,59225],{"className":59224},[886],[888,59226,59227],{"xmlns":890},[892,59228,59229,59235],{},[895,59230,59231,59233],{},[898,59232,14492],{},[898,59234,1658],{},[902,59236,59237],{"encoding":904},"FC",[883,59239,59241],{"className":59240},[886],[888,59242,59243],{"xmlns":890},[892,59244,59245,59253],{},[895,59246,59247,59249,59251],{},[898,59248,5877],{},[898,59250,44362],{},[898,59252,1658],{},[902,59254,59255],{"encoding":904},"TVC",[883,59257,59259],{"className":59258},[886],[888,59260,59261],{"xmlns":890},[892,59262,59263,59271],{},[895,59264,59265,59267,59269],{},[898,59266,1983],{},[898,59268,14492],{},[898,59270,1658],{},[902,59272,59273],{"encoding":904},"AFC",[883,59275,59277],{"className":59276},[886],[888,59278,59279],{"xmlns":890},[892,59280,59281,59289],{},[895,59282,59283,59285,59287],{},[898,59284,1983],{},[898,59286,44362],{},[898,59288,1658],{},[902,59290,59057],{"encoding":904},[883,59292,59294],{"className":59293},[886],[888,59295,59296],{"xmlns":890},[892,59297,59298,59304],{},[895,59299,59300,59302],{},[898,59301,1983],{},[898,59303,1658],{},[902,59305,59306],{"encoding":904},"AC",[883,59308,59310],{"className":59309},[886],[888,59311,59312],{"xmlns":890},[892,59313,59314,59320],{},[895,59315,59316,59318],{},[898,59317,6909],{},[898,59319,1658],{},[902,59321,59038],{"encoding":904},[123,59323,59324],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,59326,59327],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,59329,59330,59331,59334,59335,45835,59377,12487],{},"osvojit si ",[38,59332,59333],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,59336,59338],{"className":59337},[886],[888,59339,59340],{"xmlns":890},[892,59341,59342,59374],{},[895,59343,59344,59346,59348,59350,59356,59358,59360,59362,59364,59366,59372],{},[898,59345,1983],{},[898,59347,1658],{},[1701,59349,1799],{"stretchy":1798},[1845,59351,59352,59354],{},[898,59353,1802],{},[1850,59355,1852],{},[1701,59357,1805],{"stretchy":1798},[1701,59359,1792],{},[898,59361,6909],{},[898,59363,1658],{},[1701,59365,1799],{"stretchy":1798},[1845,59367,59368,59370],{},[898,59369,1802],{},[1850,59371,1852],{},[1701,59373,1805],{"stretchy":1798},[902,59375,59376],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,59378,59380],{"className":59379},[886],[888,59381,59382],{"xmlns":890},[892,59383,59384,59418],{},[895,59385,59386,59388,59390,59392,59394,59400,59402,59404,59406,59408,59410,59416],{},[898,59387,1983],{},[898,59389,44362],{},[898,59391,1658],{},[1701,59393,1799],{"stretchy":1798},[1845,59395,59396,59398],{},[898,59397,1802],{},[1850,59399,1852],{},[1701,59401,1805],{"stretchy":1798},[1701,59403,1792],{},[898,59405,6909],{},[898,59407,1658],{},[1701,59409,1799],{"stretchy":1798},[1845,59411,59412,59414],{},[898,59413,1802],{},[1850,59415,1852],{},[1701,59417,1805],{"stretchy":1798},[902,59419,59420],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,59422,59330,59423,59334,59426,12487],{},[38,59424,59425],{},"princip maximalizace zisku",[883,59427,59429],{"className":59428},[886],[888,59430,59431],{"xmlns":890},[892,59432,59433,59465],{},[895,59434,59435,59437,59439,59441,59447,59449,59451,59453,59455,59457,59463],{},[898,59436,6909],{},[898,59438,8068],{},[1701,59440,1799],{"stretchy":1798},[1845,59442,59443,59445],{},[898,59444,1802],{},[1850,59446,1852],{},[1701,59448,1805],{"stretchy":1798},[1701,59450,1792],{},[898,59452,6909],{},[898,59454,1658],{},[1701,59456,1799],{"stretchy":1798},[1845,59458,59459,59461],{},[898,59460,1802],{},[1850,59462,1852],{},[1701,59464,1805],{"stretchy":1798},[902,59466,59467],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,59469,59470,59471,59474],{},"stanovit ",[38,59472,59473],{},"body zvratu"," a interval zisku;",[123,59476,59477,59478,59481],{},"zkonstruovat ",[38,59479,59480],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,59483,59485],{"id":59484},"příjem-firmy","Příjem firmy",[724,59487,59488],{},[2139,59489],{"alt":59490,"className":59491,"src":59492},"imek-ar-mr-dvojnasobny-sklon",[210,2143],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,59494,59496],{"id":59495},"celkový-příjem","Celkový příjem",[724,59498,59499,59500,1646,59515,59518,59519,33977],{},"Celkový příjem ",[883,59501,59503],{"className":59502},[886],[888,59504,59505],{"xmlns":890},[892,59506,59507,59513],{},[895,59508,59509,59511],{},[898,59510,5877],{},[898,59512,8068],{},[902,59514,8168],{"encoding":904},[38,59516,59517],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,59520,59522],{"className":59521},[886],[888,59523,59524],{"xmlns":890},[892,59525,59526,59540],{},[895,59527,59528,59530,59532,59534,59536,59538],{},[898,59529,1680],{},[1701,59531,1792],{},[898,59533,1795],{},[1701,59535,1799],{"stretchy":1798},[898,59537,1802],{},[1701,59539,1805],{"stretchy":1798},[902,59541,1808],{"encoding":904},[883,59543,59545],{"className":59544},[886],[888,59546,59547],{"xmlns":890,"display":2252},[892,59548,59549,59606],{},[2256,59550,59551],{"width":2258},[2260,59552,59553,59555,59599,59601],{},[2263,59554],{"width":2265},[2263,59556,59557],{},[895,59558,59559,59561,59563,59565,59567,59569,59571,59573,59575,59577,59579,59581,59583,59585,59587,59589,59591,59593,59595,59597],{},[898,59560,5877],{},[898,59562,8068],{},[1701,59564,1792],{},[898,59566,5877],{},[898,59568,8068],{},[1701,59570,1799],{"stretchy":1798},[898,59572,1802],{},[1701,59574,1805],{"stretchy":1798},[1701,59576,1792],{},[898,59578,1680],{},[1701,59580,3408],{},[898,59582,1802],{},[1701,59584,1792],{},[898,59586,1795],{},[1701,59588,1799],{"stretchy":1798},[898,59590,1802],{},[1701,59592,1805],{"stretchy":1798},[1701,59594,3408],{},[898,59596,1802],{},[898,59598,1715],{"mathvariant":2334},[2263,59600],{"width":2265},[2263,59602,59603],{},[1939,59604,59605],{},"(3.1)",[902,59607,59608],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,59610,59611,59612,59615,59616,59639],{},"Graf funkce se nazývá ",[38,59613,59614],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,59617,59619],{"className":59618},[886],[888,59620,59621],{"xmlns":890},[892,59622,59623,59637],{},[895,59624,59625,59627,59629,59631,59633,59635],{},[898,59626,1680],{},[1701,59628,1792],{},[898,59630,207],{},[898,59632,1802],{},[1701,59634,1703],{},[898,59636,3598],{},[902,59638,3601],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,59641,59643],{"className":59642},[886],[888,59644,59645],{"xmlns":890,"display":2252},[892,59646,59647,59687],{},[895,59648,59649,59651,59653,59655,59657,59659,59661,59663,59665,59667,59669,59671,59673,59679,59681,59683,59685],{},[898,59650,5877],{},[898,59652,8068],{},[1701,59654,1792],{},[898,59656,1802],{},[1701,59658,1799],{"stretchy":1798},[898,59660,207],{},[898,59662,1802],{},[1701,59664,1703],{},[898,59666,3598],{},[1701,59668,1805],{"stretchy":1798},[1701,59670,1792],{},[898,59672,207],{},[3243,59674,59675,59677],{},[898,59676,1802],{},[1850,59678,3938],{},[1701,59680,1703],{},[898,59682,3598],{},[898,59684,1802],{},[1701,59686,2012],{"separator":2011},[902,59688,59689],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,59691,59692,59693,59706,59707,59724],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,59694,59696],{"className":59695},[886],[888,59697,59698],{"xmlns":890},[892,59699,59700,59704],{},[895,59701,59702],{},[898,59703,900],{},[902,59705,900],{"encoding":904}," (jelikož ",[883,59708,59710],{"className":59709},[886],[888,59711,59712],{"xmlns":890},[892,59713,59714,59722],{},[895,59715,59716,59718,59720],{},[898,59717,207],{},[1701,59719,7530],{},[1850,59721,1852],{},[902,59723,47105],{"encoding":904},") procházející počátkem.",[41376,59726,59728],{"id":59727},"příklad-31","Příklad 3.1",[724,59730,59731,59734,59735,59771,59772,59787],{},[38,59732,59733],{},"Zadání."," Pro poptávku ",[883,59736,59738],{"className":59737},[886],[888,59739,59740],{"xmlns":890},[892,59741,59742,59768],{},[895,59743,59744,59746,59748,59750,59752,59754,59756,59758,59760,59762,59764,59766],{},[898,59745,1680],{},[1701,59747,1792],{},[898,59749,1795],{},[1701,59751,1799],{"stretchy":1798},[898,59753,1802],{},[1701,59755,1805],{"stretchy":1798},[1701,59757,1792],{},[1701,59759,2317],{},[1850,59761,3938],{},[898,59763,1802],{},[1701,59765,1703],{},[1850,59767,5158],{},[902,59769,59770],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,59773,59775],{"className":59774},[886],[888,59776,59777],{"xmlns":890},[892,59778,59779,59785],{},[895,59780,59781,59783],{},[898,59782,5877],{},[898,59784,8068],{},[902,59786,8168],{"encoding":904}," a charakterizujte jeho křivku.",[724,59789,59790,59792],{},[38,59791,5001],{}," Celkový příjem je",[883,59794,59796],{"className":59795},[886],[888,59797,59798],{"xmlns":890,"display":2252},[892,59799,59800,59856],{},[895,59801,59802,59804,59806,59808,59810,59812,59814,59816,59818,59820,59822,59824,59826,59828,59830,59832,59834,59836,59838,59840,59842,59848,59850,59852,59854],{},[898,59803,5877],{},[898,59805,8068],{},[1701,59807,1792],{},[898,59809,5877],{},[898,59811,8068],{},[1701,59813,1799],{"stretchy":1798},[898,59815,1802],{},[1701,59817,1805],{"stretchy":1798},[1701,59819,1792],{},[898,59821,1802],{},[1701,59823,1799],{"stretchy":1798},[1701,59825,2317],{},[1850,59827,3938],{},[898,59829,1802],{},[1701,59831,1703],{},[1850,59833,5158],{},[1701,59835,1805],{"stretchy":1798},[1701,59837,1792],{},[1701,59839,2317],{},[1850,59841,3938],{},[3243,59843,59844,59846],{},[898,59845,1802],{},[1850,59847,3938],{},[1701,59849,1703],{},[1850,59851,5158],{},[898,59853,1802],{},[898,59855,1715],{"mathvariant":2334},[902,59857,59858],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,59860,59861,59862,2633,59884,59906,59907,59925,59926,1715],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,59863,59865],{"className":59864},[886],[888,59866,59867],{"xmlns":890},[892,59868,59869,59881],{},[895,59870,59871,59877,59879],{},[1845,59872,59873,59875],{},[898,59874,1802],{},[1850,59876,4062],{},[1701,59878,1792],{},[1850,59880,1852],{},[902,59882,59883],{"encoding":904},"Q_1 = 0",[883,59885,59887],{"className":59886},[886],[888,59888,59889],{"xmlns":890},[892,59890,59891,59903],{},[895,59892,59893,59899,59901],{},[1845,59894,59895,59897],{},[898,59896,1802],{},[1850,59898,3938],{},[1701,59900,1792],{},[1850,59902,7206],{},[902,59904,59905],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,59908,59910],{"className":59909},[886],[888,59911,59912],{"xmlns":890},[892,59913,59914,59922],{},[895,59915,59916,59918,59920],{},[898,59917,1802],{},[1701,59919,1792],{},[1850,59921,9071],{},[902,59923,59924],{"encoding":904},"Q = 25"," ve výši ",[883,59927,59929],{"className":59928},[886],[888,59930,59931],{"xmlns":890},[892,59932,59933,59974],{},[895,59934,59935,59937,59947,59949,59951,59953,59955,59958,59960,59962,59964,59966,59968,59970,59972],{},[898,59936,5877],{},[1845,59938,59939,59941,59944],{},[898,59940,8068],{},[898,59942,59943],{},"max",[1701,59945,59946],{},"⁡",[1701,59948,1792],{},[1701,59950,2317],{},[1850,59952,3938],{},[1701,59954,3408],{},[1850,59956,59957],{},"625",[1701,59959,1703],{},[1850,59961,5158],{},[1701,59963,3408],{},[1850,59965,9071],{},[1701,59967,1792],{},[1850,59969,4062],{},[1939,59971,1941],{},[1850,59973,34774],{},[902,59975,59976],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,59978,59979],{},[614,59980,59981,59982,60016,60017,2633,60030,60043,60044,6723,60062,1715],{},"Obrázek 3.1: Parabola ",[883,59983,59985],{"className":59984},[886],[888,59986,59987],{"xmlns":890},[892,59988,59989,60013],{},[895,59990,59991,59993,59995,59997,59999,60001,60007,60009,60011],{},[898,59992,5877],{},[898,59994,8068],{},[1701,59996,1792],{},[1701,59998,2317],{},[1850,60000,3938],{},[3243,60002,60003,60005],{},[898,60004,1802],{},[1850,60006,3938],{},[1701,60008,1703],{},[1850,60010,5158],{},[898,60012,1802],{},[902,60014,60015],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,60018,60020],{"className":60019},[886],[888,60021,60022],{"xmlns":890},[892,60023,60024,60028],{},[895,60025,60026],{},[1850,60027,1852],{},[902,60029,1852],{"encoding":904},[883,60031,60033],{"className":60032},[886],[888,60034,60035],{"xmlns":890},[892,60036,60037,60041],{},[895,60038,60039],{},[1850,60040,7206],{},[902,60042,7206],{"encoding":904}," a maximem ",[883,60045,60047],{"className":60046},[886],[888,60048,60049],{"xmlns":890},[892,60050,60051,60059],{},[895,60052,60053,60055,60057],{},[1850,60054,4062],{},[1939,60056,1941],{},[1850,60058,34774],{},[902,60060,60061],{"encoding":904},"1\\,250",[883,60063,60065],{"className":60064},[886],[888,60066,60067],{"xmlns":890},[892,60068,60069,60077],{},[895,60070,60071,60073,60075],{},[898,60072,1802],{},[1701,60074,1792],{},[1850,60076,9071],{},[902,60078,59924],{"encoding":904},[198,60080,60082],{"id":60081},"průměrný-příjem","Průměrný příjem",[724,60084,60085,4088,60087,1646,60102,60105],{},[38,60086,60082],{},[883,60088,60090],{"className":60089},[886],[888,60091,60092],{"xmlns":890},[892,60093,60094,60100],{},[895,60095,60096,60098],{},[898,60097,1983],{},[898,60099,8068],{},[902,60101,59191],{"encoding":904},[38,60103,60104],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,60107,60109],{"className":60108},[886],[888,60110,60111],{"xmlns":890,"display":2252},[892,60112,60113,60181],{},[895,60114,60115,60117,60119,60121,60123,60125,60127,60129,60131,60133,60149,60151,60169,60171,60173,60175,60177,60179],{},[898,60116,1983],{},[898,60118,8068],{},[1701,60120,1792],{},[898,60122,1983],{},[898,60124,8068],{},[1701,60126,1799],{"stretchy":1798},[898,60128,1802],{},[1701,60130,1805],{"stretchy":1798},[1701,60132,1792],{},[3726,60134,60135,60147],{},[895,60136,60137,60139,60141,60143,60145],{},[898,60138,5877],{},[898,60140,8068],{},[1701,60142,1799],{"stretchy":1798},[898,60144,1802],{},[1701,60146,1805],{"stretchy":1798},[898,60148,1802],{},[1701,60150,1792],{},[3726,60152,60153,60167],{},[895,60154,60155,60157,60159,60161,60163,60165],{},[898,60156,1802],{},[1939,60158,1941],{},[898,60160,1795],{},[1701,60162,1799],{"stretchy":1798},[898,60164,1802],{},[1701,60166,1805],{"stretchy":1798},[898,60168,1802],{},[1701,60170,1792],{},[898,60172,1795],{},[1701,60174,1799],{"stretchy":1798},[898,60176,1802],{},[1701,60178,1805],{"stretchy":1798},[898,60180,1715],{"mathvariant":2334},[902,60182,60183],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1635,60185,60186],{},[724,60187,60188,60191,60192,1343,60195,1715],{},[883,60189,60190],{},"!note"," Klíčové pozorování\n",[38,60193,60194],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,60196,60198],{"className":60197},[886],[888,60199,60200],{"xmlns":890},[892,60201,60202,60224],{},[895,60203,60204,60206,60208,60210,60212,60214,60216,60218,60220,60222],{},[898,60205,1983],{},[898,60207,8068],{},[1701,60209,1799],{"stretchy":1798},[898,60211,1802],{},[1701,60213,1805],{"stretchy":1798},[1701,60215,1792],{},[898,60217,1795],{},[1701,60219,1799],{"stretchy":1798},[898,60221,1802],{},[1701,60223,1805],{"stretchy":1798},[902,60225,60226],{"encoding":904},"AR(Q) = D(Q)",[198,60228,60230],{"id":60229},"mezní-příjem","Mezní příjem",[724,60232,60233,60234,4088,60237,1646,60252,60255,60256,60259],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,60235,60236],{},"mezní příjem",[883,60238,60240],{"className":60239},[886],[888,60241,60242],{"xmlns":890},[892,60243,60244,60250],{},[895,60245,60246,60248],{},[898,60247,6909],{},[898,60249,8068],{},[902,60251,10697],{"encoding":904},[38,60253,60254],{},"marginal revenue","), definovaný jako ",[207,60257,1145],{"className":60258,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,60261,60263],{"className":60262},[886],[888,60264,60265],{"xmlns":890,"display":2252},[892,60266,60267,60324],{},[2256,60268,60269],{"width":2258},[2260,60270,60271,60273,60317,60319],{},[2263,60272],{"width":2265},[2263,60274,60275],{},[895,60276,60277,60279,60281,60283,60299,60301,60303,60309,60311,60313,60315],{},[898,60278,6909],{},[898,60280,8068],{},[1701,60282,1792],{},[3726,60284,60285,60293],{},[895,60286,60287,60289,60291],{},[898,60288,2312],{"mathvariant":2334},[898,60290,5877],{},[898,60292,8068],{},[895,60294,60295,60297],{},[898,60296,2312],{"mathvariant":2334},[898,60298,1802],{},[1701,60300,1792],{},[898,60302,5877],{},[3243,60304,60305,60307],{},[898,60306,8068],{},[1701,60308,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,60310,1799],{"stretchy":1798},[898,60312,1802],{},[1701,60314,1805],{"stretchy":1798},[898,60316,1715],{"mathvariant":2334},[2263,60318],{"width":2265},[2263,60320,60321],{},[1939,60322,60323],{},"(3.2)",[902,60325,60326],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,60328,60329,60330,60332],{},"Mezní příjem udává ",[38,60331,6695],{}," celkového příjmu vzhledem k množství.",[1635,60334,60335],{},[724,60336,60337,60339,60340,60366,60367,60384,60385,1715],{},[883,60338,2063],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,60341,60343],{"className":60342},[886],[888,60344,60345],{"xmlns":890},[892,60346,60347,60363],{},[895,60348,60349,60351,60353,60355,60361],{},[898,60350,6909],{},[898,60352,8068],{},[1701,60354,1799],{"stretchy":1798},[3243,60356,60357,60359],{},[898,60358,1802],{},[1701,60360,8424],{},[1701,60362,1805],{"stretchy":1798},[902,60364,60365],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,60368,60370],{"className":60369},[886],[888,60371,60372],{"xmlns":890},[892,60373,60374,60382],{},[895,60375,60376],{},[3243,60377,60378,60380],{},[898,60379,1802],{},[1701,60381,8424],{},[902,60383,33877],{"encoding":904},". Jinak řečeno: ",[883,60386,60388],{"className":60387},[886],[888,60389,60390],{"xmlns":890},[892,60391,60392,60444],{},[895,60393,60394,60396,60398,60400,60406,60408,60410,60412,60414,60416,60422,60424,60426,60428,60430,60432,60434,60436,60442],{},[898,60395,6909],{},[898,60397,8068],{},[1701,60399,1799],{"stretchy":1798},[3243,60401,60402,60404],{},[898,60403,1802],{},[1701,60405,8424],{},[1701,60407,1805],{"stretchy":1798},[1701,60409,4067],{},[898,60411,5877],{},[898,60413,8068],{},[1701,60415,1799],{"stretchy":1798},[3243,60417,60418,60420],{},[898,60419,1802],{},[1701,60421,8424],{},[1701,60423,1703],{},[1850,60425,4062],{},[1701,60427,1805],{"stretchy":1798},[1701,60429,2317],{},[898,60431,5877],{},[898,60433,8068],{},[1701,60435,1799],{"stretchy":1798},[3243,60437,60438,60440],{},[898,60439,1802],{},[1701,60441,8424],{},[1701,60443,1805],{"stretchy":1798},[902,60445,60446],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[41376,60448,60450],{"id":60449},"příklad-32","Příklad 3.2",[724,60452,60453,59734,60455,59771,60489,60504,60505,1715],{},[38,60454,59733],{},[883,60456,60458],{"className":60457},[886],[888,60459,60460],{"xmlns":890},[892,60461,60462,60486],{},[895,60463,60464,60466,60468,60470,60472,60474,60476,60478,60480,60482,60484],{},[898,60465,1680],{},[1701,60467,1792],{},[898,60469,1795],{},[1701,60471,1799],{"stretchy":1798},[898,60473,1802],{},[1701,60475,1805],{"stretchy":1798},[1701,60477,1792],{},[1850,60479,5158],{},[1701,60481,2317],{},[1850,60483,3938],{},[898,60485,1802],{},[902,60487,60488],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,60490,60492],{"className":60491},[886],[888,60493,60494],{"xmlns":890},[892,60495,60496,60502],{},[895,60497,60498,60500],{},[898,60499,6909],{},[898,60501,8068],{},[902,60503,10697],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,60506,60508],{"className":60507},[886],[888,60509,60510],{"xmlns":890},[892,60511,60512,60528],{},[895,60513,60514,60516,60518,60520,60522,60524,60526],{},[898,60515,1802],{},[1701,60517,1792],{},[1850,60519,40275],{},[1701,60521,2012],{"separator":2011},[1850,60523,45883],{},[1701,60525,2012],{"separator":2011},[1850,60527,13096],{},[902,60529,60530],{"encoding":904},"Q = 15, 16, 20",[724,60532,60533,4088,60535,60567],{},[38,60534,5001],{},[883,60536,60538],{"className":60537},[886],[888,60539,60540],{"xmlns":890},[892,60541,60542,60564],{},[895,60543,60544,60546,60548,60550,60552,60554,60556,60558],{},[898,60545,5877],{},[898,60547,8068],{},[1701,60549,1792],{},[1850,60551,5158],{},[898,60553,1802],{},[1701,60555,2317],{},[1850,60557,3938],{},[3243,60559,60560,60562],{},[898,60561,1802],{},[1850,60563,3938],{},[902,60565,60566],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,60569,60571],{"className":60570},[886],[888,60572,60573],{"xmlns":890,"display":2252},[892,60574,60575,60617],{},[895,60576,60577,60579,60581,60583,60585,60587,60589,60591,60593,60599,60605,60607,60609,60611,60613,60615],{},[898,60578,6909],{},[898,60580,8068],{},[1701,60582,1792],{},[1701,60584,1799],{"stretchy":1798},[1850,60586,5158],{},[898,60588,1802],{},[1701,60590,2317],{},[1850,60592,3938],{},[3243,60594,60595,60597],{},[898,60596,1802],{},[1850,60598,3938],{},[3243,60600,60601,60603],{},[1701,60602,1805],{"stretchy":1798},[1701,60604,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,60606,1792],{},[1850,60608,5158],{},[1701,60610,2317],{},[1850,60612,6460],{},[898,60614,1802],{},[898,60616,1715],{"mathvariant":2334},[902,60618,60619],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,60621,13721,60622,12164,60640,60666,60667,8428,60680,60695,60696,60709,60710,25461,60723,8428,60736,60751,60752,60765,60766,60797,60798,60817],{},[883,60623,60625],{"className":60624},[886],[888,60626,60627],{"xmlns":890},[892,60628,60629,60637],{},[895,60630,60631,60633,60635],{},[898,60632,1802],{},[1701,60634,1792],{},[1850,60636,40275],{},[902,60638,60639],{"encoding":904},"Q = 15",[883,60641,60643],{"className":60642},[886],[888,60644,60645],{"xmlns":890},[892,60646,60647,60663],{},[895,60648,60649,60651,60653,60655,60657,60659,60661],{},[898,60650,6909],{},[898,60652,8068],{},[1701,60654,1799],{"stretchy":1798},[1850,60656,40275],{},[1701,60658,1805],{"stretchy":1798},[1701,60660,1792],{},[1850,60662,3665],{},[902,60664,60665],{"encoding":904},"MR(15) = 40",": při množství ",[883,60668,60670],{"className":60669},[886],[888,60671,60672],{"xmlns":890},[892,60673,60674,60678],{},[895,60675,60676],{},[1850,60677,40275],{},[902,60679,40275],{"encoding":904},[883,60681,60683],{"className":60682},[886],[888,60684,60685],{"xmlns":890},[892,60686,60687,60693],{},[895,60688,60689,60691],{},[898,60690,5877],{},[898,60692,8068],{},[902,60694,8168],{"encoding":904}," mění asi ",[883,60697,60699],{"className":60698},[886],[888,60700,60701],{"xmlns":890},[892,60702,60703,60707],{},[895,60704,60705],{},[1850,60706,3665],{},[902,60708,3665],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,60711,60713],{"className":60712},[886],[888,60714,60715],{"xmlns":890},[892,60716,60717,60721],{},[895,60718,60719],{},[898,60720,1802],{},[902,60722,1802],{"encoding":904},[883,60724,60726],{"className":60725},[886],[888,60727,60728],{"xmlns":890},[892,60729,60730,60734],{},[895,60731,60732],{},[1850,60733,4062],{},[902,60735,4062],{"encoding":904},[883,60737,60739],{"className":60738},[886],[888,60740,60741],{"xmlns":890},[892,60742,60743,60749],{},[895,60744,60745,60747],{},[898,60746,5877],{},[898,60748,8068],{},[902,60750,8168],{"encoding":904}," zvýší přibližně o ",[883,60753,60755],{"className":60754},[886],[888,60756,60757],{"xmlns":890},[892,60758,60759,60763],{},[895,60760,60761],{},[1850,60762,3665],{},[902,60764,3665],{"encoding":904},", tj. ze skutečné hodnoty ",[883,60767,60769],{"className":60768},[886],[888,60770,60771],{"xmlns":890},[892,60772,60773,60794],{},[895,60774,60775,60777,60779,60781,60783,60785,60787,60789,60791],{},[898,60776,5877],{},[898,60778,8068],{},[1701,60780,1799],{"stretchy":1798},[1850,60782,40275],{},[1701,60784,1805],{"stretchy":1798},[1701,60786,1792],{},[1850,60788,4062],{},[1939,60790,1941],{},[1850,60792,60793],{},"050",[902,60795,60796],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,60799,60801],{"className":60800},[886],[888,60802,60803],{"xmlns":890},[892,60804,60805,60814],{},[895,60806,60807,60809,60811],{},[1850,60808,4062],{},[1939,60810,1941],{},[1850,60812,60813],{},"090",[902,60815,60816],{"encoding":904},"1\\,090",". Skutečná změna je",[883,60819,60821],{"className":60820},[886],[888,60822,60823],{"xmlns":890,"display":2252},[892,60824,60825,60879],{},[895,60826,60827,60829,60831,60833,60835,60837,60839,60841,60843,60845,60847,60849,60851,60853,60855,60857,60859,60861,60863,60866,60868,60870,60872,60874,60876],{},[898,60828,4708],{"mathvariant":2334},[898,60830,5877],{},[898,60832,8068],{},[1701,60834,1792],{},[898,60836,5877],{},[898,60838,8068],{},[1701,60840,1799],{"stretchy":1798},[1850,60842,45883],{},[1701,60844,1805],{"stretchy":1798},[1701,60846,2317],{},[898,60848,5877],{},[898,60850,8068],{},[1701,60852,1799],{"stretchy":1798},[1850,60854,40275],{},[1701,60856,1805],{"stretchy":1798},[1701,60858,1792],{},[1850,60860,4062],{},[1939,60862,1941],{},[1850,60864,60865],{},"088",[1701,60867,2317],{},[1850,60869,4062],{},[1939,60871,1941],{},[1850,60873,60793],{},[1701,60875,1792],{},[1850,60877,60878],{},"38.",[902,60880,60881],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,60883,60884,60885,1343,60911,7015,60937,60952,60953,60968],{},"Podobně ",[883,60886,60888],{"className":60887},[886],[888,60889,60890],{"xmlns":890},[892,60891,60892,60908],{},[895,60893,60894,60896,60898,60900,60902,60904,60906],{},[898,60895,6909],{},[898,60897,8068],{},[1701,60899,1799],{"stretchy":1798},[1850,60901,45883],{},[1701,60903,1805],{"stretchy":1798},[1701,60905,1792],{},[1850,60907,9630],{},[902,60909,60910],{"encoding":904},"MR(16) = 36",[883,60912,60914],{"className":60913},[886],[888,60915,60916],{"xmlns":890},[892,60917,60918,60934],{},[895,60919,60920,60922,60924,60926,60928,60930,60932],{},[898,60921,6909],{},[898,60923,8068],{},[1701,60925,1799],{"stretchy":1798},[1850,60927,13096],{},[1701,60929,1805],{"stretchy":1798},[1701,60931,1792],{},[1850,60933,13096],{},[902,60935,60936],{"encoding":904},"MR(20) = 20",[883,60938,60940],{"className":60939},[886],[888,60941,60942],{"xmlns":890},[892,60943,60944,60950],{},[895,60945,60946,60948],{},[898,60947,6909],{},[898,60949,8068],{},[902,60951,10697],{"encoding":904}," je klesající funkce — rychlost změny ",[883,60954,60956],{"className":60955},[886],[888,60957,60958],{"xmlns":890},[892,60959,60960,60966],{},[895,60961,60962,60964],{},[898,60963,5877],{},[898,60965,8068],{},[902,60967,8168],{"encoding":904}," s růstem množství klesá.",[198,60970,60972],{"id":60971},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,60974,60975],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,60977,60979],{"className":60978},[886],[888,60980,60981],{"xmlns":890,"display":2252},[892,60982,60983,61052],{},[2256,60984,60985],{"width":2258},[2260,60986,60987,60989,61045,61047],{},[2263,60988],{"width":2265},[2263,60990,60991],{},[895,60992,60993,60995,60997,60999,61001,61003,61005,61007,61009,61011,61013,61015,61017,61019,61025,61027,61029,61031,61033,61035,61037,61039,61041,61043],{},[898,60994,4708],{"mathvariant":2334},[898,60996,5877],{},[898,60998,8068],{},[1939,61000,8058],{},[1701,61002,4067],{},[1939,61004,8058],{},[898,61006,2312],{"mathvariant":2334},[898,61008,5877],{},[898,61010,8068],{},[1701,61012,1792],{},[1701,61014,1799],{"stretchy":1798},[898,61016,5877],{},[898,61018,8068],{},[3243,61020,61021,61023],{},[1701,61022,1805],{"stretchy":1798},[1701,61024,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,61026,1941],{},[898,61028,2312],{"mathvariant":2334},[898,61030,1802],{},[1701,61032,1792],{},[898,61034,6909],{},[898,61036,8068],{},[1939,61038,1941],{},[898,61040,2312],{"mathvariant":2334},[898,61042,1802],{},[1701,61044,2012],{"separator":2011},[2263,61046],{"width":2265},[2263,61048,61049],{},[1939,61050,61051],{},"(3.3)",[902,61053,61054],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,61056,61057],{},"schematicky:",[883,61059,61061],{"className":61060},[886],[888,61062,61063],{"xmlns":890,"display":2252},[892,61064,61065,61173],{},[895,61066,61067,61105,61107,61109,61111,61140,61143,61171],{},[895,61068,61069,61072,61078,61081,61087,61090,61096,61102],{},[1939,61070,61071],{},"zm",[12448,61073,61074,61076],{"accent":2011},[1939,61075,49723],{},[1701,61077,29096],{},[1939,61079,61080],{},"na celkov",[12448,61082,61083,61085],{"accent":2011},[1939,61084,49723],{},[1701,61086,29015],{},[1939,61088,61089],{},"ho p",[12448,61091,61092,61094],{"accent":2011},[1939,61093,16096],{},[1701,61095,29096],{},[12448,61097,61098,61100],{"accent":2011},[1939,61099,29084],{},[1701,61101,29015],{},[1939,61103,61104],{},"jmu",[1939,61106,8058],{},[1701,61108,4067],{},[1939,61110,8058],{},[895,61112,61113,61116,61122,61125,61131,61137],{},[1939,61114,61115],{},"mezn",[12448,61117,61118,61120],{"accent":2011},[1939,61119,29084],{},[1701,61121,29015],{},[1939,61123,61124],{}," p",[12448,61126,61127,61129],{"accent":2011},[1939,61128,16096],{},[1701,61130,29096],{},[12448,61132,61133,61135],{"accent":2011},[1939,61134,29084],{},[1701,61136,29015],{},[1939,61138,61139],{},"jem",[1701,61141,61142],{},"×",[895,61144,61145,61147,61153,61156,61162,61165],{},[1939,61146,61071],{},[12448,61148,61149,61151],{"accent":2011},[1939,61150,49723],{},[1701,61152,29096],{},[1939,61154,61155],{},"na mno",[12448,61157,61158,61160],{"accent":2011},[1939,61159,13652],{},[1701,61161,29096],{},[1939,61163,61164],{},"stv",[12448,61166,61167,61169],{"accent":2011},[1939,61168,29084],{},[1701,61170,29015],{},[898,61172,1715],{"mathvariant":2334},[902,61174,61175],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,61177,61178,61179,61194],{},"Pro porovnání skutečná změna ",[883,61180,61182],{"className":61181},[886],[888,61183,61184],{"xmlns":890},[892,61185,61186,61192],{},[895,61187,61188,61190],{},[898,61189,5877],{},[898,61191,8068],{},[902,61193,8168],{"encoding":904}," je",[883,61196,61198],{"className":61197},[886],[888,61199,61200],{"xmlns":890,"display":2252},[892,61201,61202,61257],{},[2256,61203,61204],{"width":2258},[2260,61205,61206,61208,61250,61252],{},[2263,61207],{"width":2265},[2263,61209,61210],{},[895,61211,61212,61214,61216,61218,61220,61222,61224,61226,61228,61230,61232,61234,61236,61238,61240,61242,61244,61246,61248],{},[898,61213,4708],{"mathvariant":2334},[898,61215,5877],{},[898,61217,8068],{},[1701,61219,1792],{},[898,61221,5877],{},[898,61223,8068],{},[1701,61225,1799],{"stretchy":1798},[898,61227,1802],{},[1701,61229,1703],{},[898,61231,2312],{"mathvariant":2334},[898,61233,1802],{},[1701,61235,1805],{"stretchy":1798},[1701,61237,2317],{},[898,61239,5877],{},[898,61241,8068],{},[1701,61243,1799],{"stretchy":1798},[898,61245,1802],{},[1701,61247,1805],{"stretchy":1798},[898,61249,1715],{"mathvariant":2334},[2263,61251],{"width":2265},[2263,61253,61254],{},[1939,61255,61256],{},"(3.4)",[902,61258,61259],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[41376,61261,61263],{"id":61262},"příklad-33","Příklad 3.3",[724,61265,61266,61268,61269,61299,61300,6756,61315,3841,61328,3856,61341,61355],{},[38,61267,59733],{}," Pro ",[883,61270,61272],{"className":61271},[886],[888,61273,61274],{"xmlns":890},[892,61275,61276,61296],{},[895,61277,61278,61280,61282,61284,61286,61288,61290],{},[898,61279,5877],{},[898,61281,8068],{},[1701,61283,1792],{},[1850,61285,5158],{},[898,61287,1802],{},[1701,61289,2317],{},[3243,61291,61292,61294],{},[898,61293,1802],{},[1850,61295,3938],{},[902,61297,61298],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,61301,61303],{"className":61302},[886],[888,61304,61305],{"xmlns":890},[892,61306,61307,61313],{},[895,61308,61309,61311],{},[898,61310,5877],{},[898,61312,8068],{},[902,61314,8168],{"encoding":904},[883,61316,61318],{"className":61317},[886],[888,61319,61320],{"xmlns":890},[892,61321,61322,61326],{},[895,61323,61324],{},[898,61325,1802],{},[902,61327,1802],{"encoding":904},[883,61329,61331],{"className":61330},[886],[888,61332,61333],{"xmlns":890},[892,61334,61335,61339],{},[895,61336,61337],{},[1850,61338,7211],{},[902,61340,7211],{"encoding":904},[883,61342,61344],{"className":61343},[886],[888,61345,61346],{"xmlns":890},[892,61347,61348,61353],{},[895,61349,61350],{},[1850,61351,61352],{},"63",[902,61354,61352],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,61357,61358,4088,61360,61385,61386,1343,61404,2246],{},[38,61359,5001],{},[883,61361,61363],{"className":61362},[886],[888,61364,61365],{"xmlns":890},[892,61366,61367,61383],{},[895,61368,61369,61371,61373,61375,61377,61379,61381],{},[898,61370,6909],{},[898,61372,8068],{},[1701,61374,1792],{},[1850,61376,5158],{},[1701,61378,2317],{},[1850,61380,3938],{},[898,61382,1802],{},[902,61384,15492],{"encoding":904},", tedy při ",[883,61387,61389],{"className":61388},[886],[888,61390,61391],{"xmlns":890},[892,61392,61393,61401],{},[895,61394,61395,61397,61399],{},[898,61396,1802],{},[1701,61398,1792],{},[1850,61400,7211],{},[902,61402,61403],{"encoding":904},"Q = 60",[883,61405,61407],{"className":61406},[886],[888,61408,61409],{"xmlns":890},[892,61410,61411,61421],{},[895,61412,61413,61415,61417,61419],{},[898,61414,2312],{"mathvariant":2334},[898,61416,1802],{},[1701,61418,1792],{},[1850,61420,3646],{},[902,61422,61423],{"encoding":904},"\\mathrm{d}Q = 3",[883,61425,61427],{"className":61426},[886],[888,61428,61429],{"xmlns":890,"display":2252},[892,61430,61431,61462],{},[895,61432,61433,61435,61437,61439,61441,61443,61445,61447,61449,61451,61453,61455,61457,61459],{},[898,61434,2312],{"mathvariant":2334},[898,61436,5877],{},[898,61438,8068],{},[1701,61440,1792],{},[1701,61442,1799],{"stretchy":1798},[1850,61444,5158],{},[1701,61446,2317],{},[1850,61448,8120],{},[1701,61450,1805],{"stretchy":1798},[1701,61452,3408],{},[1850,61454,3646],{},[1701,61456,1792],{},[1701,61458,2317],{},[1850,61460,61461],{},"60.",[902,61463,61464],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,61466,61467,61468,61498,61499,61518],{},"Celkový příjem klesne z ",[883,61469,61471],{"className":61470},[886],[888,61472,61473],{"xmlns":890},[892,61474,61475,61495],{},[895,61476,61477,61479,61481,61483,61485,61487,61489,61491,61493],{},[898,61478,5877],{},[898,61480,8068],{},[1701,61482,1799],{"stretchy":1798},[1850,61484,7211],{},[1701,61486,1805],{"stretchy":1798},[1701,61488,1792],{},[1850,61490,3938],{},[1939,61492,1941],{},[1850,61494,24186],{},[902,61496,61497],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,61500,61502],{"className":61501},[886],[888,61503,61504],{"xmlns":890},[892,61505,61506,61515],{},[895,61507,61508,61510,61512],{},[1850,61509,3938],{},[1939,61511,1941],{},[1850,61513,61514],{},"340",[902,61516,61517],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,61520,61522],{"className":61521},[886],[888,61523,61524],{"xmlns":890,"display":2252},[892,61525,61526,61584],{},[895,61527,61528,61530,61532,61534,61536,61538,61540,61542,61544,61546,61548,61550,61552,61554,61556,61558,61560,61562,61564,61567,61569,61571,61573,61575,61577,61579,61582],{},[898,61529,4708],{"mathvariant":2334},[898,61531,5877],{},[898,61533,8068],{},[1701,61535,1792],{},[898,61537,5877],{},[898,61539,8068],{},[1701,61541,1799],{"stretchy":1798},[1850,61543,61352],{},[1701,61545,1805],{"stretchy":1798},[1701,61547,2317],{},[898,61549,5877],{},[898,61551,8068],{},[1701,61553,1799],{"stretchy":1798},[1850,61555,7211],{},[1701,61557,1805],{"stretchy":1798},[1701,61559,1792],{},[1850,61561,3938],{},[1939,61563,1941],{},[1850,61565,61566],{},"331",[1701,61568,2317],{},[1850,61570,3938],{},[1939,61572,1941],{},[1850,61574,24186],{},[1701,61576,1792],{},[1701,61578,2317],{},[1850,61580,61581],{},"69",[1701,61583,2012],{"separator":2011},[902,61585,61586],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,61588,61589,61590,61605,61606,1715],{},"tj. ",[883,61591,61593],{"className":61592},[886],[888,61594,61595],{"xmlns":890},[892,61596,61597,61603],{},[895,61598,61599,61601],{},[898,61600,5877],{},[898,61602,8068],{},[902,61604,8168],{"encoding":904}," klesne na ",[883,61607,61609],{"className":61608},[886],[888,61610,61611],{"xmlns":890},[892,61612,61613,61621],{},[895,61614,61615,61617,61619],{},[1850,61616,3938],{},[1939,61618,1941],{},[1850,61620,61566],{},[902,61622,61623],{"encoding":904},"2\\,331",[198,61625,61627],{"id":61626},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,61629,61630,61631,14450,61654,35611],{},"Obecně pro lineární poptávku ",[883,61632,61634],{"className":61633},[886],[888,61635,61636],{"xmlns":890},[892,61637,61638,61652],{},[895,61639,61640,61642,61644,61646,61648,61650],{},[898,61641,1680],{},[1701,61643,1792],{},[898,61645,207],{},[898,61647,1802],{},[1701,61649,1703],{},[898,61651,3598],{},[902,61653,3601],{"encoding":904},[883,61655,61657],{"className":61656},[886],[888,61658,61659],{"xmlns":890},[892,61660,61661,61683],{},[895,61662,61663,61665,61667,61669,61671,61677,61679,61681],{},[898,61664,5877],{},[898,61666,8068],{},[1701,61668,1792],{},[898,61670,207],{},[3243,61672,61673,61675],{},[898,61674,1802],{},[1850,61676,3938],{},[1701,61678,1703],{},[898,61680,3598],{},[898,61682,1802],{},[902,61684,61685],{"encoding":904},"TR = aQ^2 + bQ",[883,61687,61689],{"className":61688},[886],[888,61690,61691],{"xmlns":890,"display":2252},[892,61692,61693,61713],{},[895,61694,61695,61697,61699,61701,61703,61705,61707,61709,61711],{},[898,61696,6909],{},[898,61698,8068],{},[1701,61700,1792],{},[1850,61702,3938],{},[898,61704,207],{},[898,61706,1802],{},[1701,61708,1703],{},[898,61710,3598],{},[898,61712,1715],{"mathvariant":2334},[902,61714,61715],{"encoding":904},"MR = 2aQ + b.",[724,61717,61718,61719,61734,61735,61750,61751,61764,61765,1646,61768,61784,61785,61798,61799,61814,61815,61830,61831,61846,61847,6723,61860,61890,61891,61910,61911,61926],{},"Křivky ",[883,61720,61722],{"className":61721},[886],[888,61723,61724],{"xmlns":890},[892,61725,61726,61732],{},[895,61727,61728,61730],{},[898,61729,6909],{},[898,61731,8068],{},[902,61733,10697],{"encoding":904}," a poptávky (resp. ",[883,61736,61738],{"className":61737},[886],[888,61739,61740],{"xmlns":890},[892,61741,61742,61748],{},[895,61743,61744,61746],{},[898,61745,1983],{},[898,61747,8068],{},[902,61749,59191],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,61752,61754],{"className":61753},[886],[888,61755,61756],{"xmlns":890},[892,61757,61758,61762],{},[895,61759,61760],{},[898,61761,3598],{},[902,61763,3598],{"encoding":904},", přičemž ",[38,61766,61767],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,61769,61771],{"className":61770},[886],[888,61772,61773],{"xmlns":890},[892,61774,61775,61781],{},[895,61776,61777,61779],{},[1850,61778,3938],{},[898,61780,207],{},[902,61782,61783],{"encoding":904},"2a"," vs. ",[883,61786,61788],{"className":61787},[886],[888,61789,61790],{"xmlns":890},[892,61791,61792,61796],{},[895,61793,61794],{},[898,61795,207],{},[902,61797,207],{"encoding":904},", obrázek 3.2). ",[883,61800,61802],{"className":61801},[886],[888,61803,61804],{"xmlns":890},[892,61805,61806,61812],{},[895,61807,61808,61810],{},[898,61809,6909],{},[898,61811,8068],{},[902,61813,10697],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,61816,61818],{"className":61817},[886],[888,61819,61820],{"xmlns":890},[892,61821,61822,61828],{},[895,61823,61824,61826],{},[898,61825,5877],{},[898,61827,8068],{},[902,61829,8168],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,61832,61834],{"className":61833},[886],[888,61835,61836],{"xmlns":890},[892,61837,61838,61844],{},[895,61839,61840,61842],{},[898,61841,6909],{},[898,61843,8068],{},[902,61845,10697],{"encoding":904}," osu ",[883,61848,61850],{"className":61849},[886],[888,61851,61852],{"xmlns":890},[892,61853,61854,61858],{},[895,61855,61856],{},[898,61857,1802],{},[902,61859,1802],{"encoding":904},[883,61861,61863],{"className":61862},[886],[888,61864,61865],{"xmlns":890},[892,61866,61867,61887],{},[895,61868,61869,61871,61873,61875],{},[898,61870,1802],{},[1701,61872,1792],{},[1701,61874,2317],{},[2363,61876,61877],{"scriptlevel":1852,"displaystyle":1798},[3726,61878,61879,61881],{},[898,61880,3598],{},[895,61882,61883,61885],{},[1850,61884,3938],{},[898,61886,207],{},[902,61888,61889],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,61892,61894],{"className":61893},[886],[888,61895,61896],{"xmlns":890},[892,61897,61898,61908],{},[895,61899,61900,61902,61904,61906],{},[898,61901,6909],{},[898,61903,8068],{},[1701,61905,1792],{},[1850,61907,1852],{},[902,61909,11146],{"encoding":904},", a dále ",[883,61912,61914],{"className":61913},[886],[888,61915,61916],{"xmlns":890},[892,61917,61918,61924],{},[895,61919,61920,61922],{},[898,61921,5877],{},[898,61923,8068],{},[902,61925,8168],{"encoding":904}," klesá.",[724,61928,61929,61930,61936,61937,61969,61970,61998],{},"V případě ",[38,61931,61932],{},[207,61933,61935],{"className":61934,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,61938,61940],{"className":61939},[886],[888,61941,61942],{"xmlns":890},[892,61943,61944,61966],{},[895,61945,61946,61948,61950,61952,61954,61956,61958,61960],{},[898,61947,1680],{},[1701,61949,1792],{},[898,61951,1795],{},[1701,61953,1799],{"stretchy":1798},[898,61955,1802],{},[1701,61957,1805],{"stretchy":1798},[1701,61959,1792],{},[3243,61961,61962,61964],{},[898,61963,1680],{},[1701,61965,8424],{},[902,61967,61968],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,61971,61973],{"className":61972},[886],[888,61974,61975],{"xmlns":890},[892,61976,61977,61995],{},[895,61978,61979,61981,61983,61985,61987,61989],{},[898,61980,5877],{},[898,61982,8068],{},[1701,61984,1792],{},[898,61986,1802],{},[1701,61988,3408],{},[3243,61990,61991,61993],{},[898,61992,1680],{},[1701,61994,8424],{},[902,61996,61997],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,62000,62002],{"className":62001},[886],[888,62003,62004],{"xmlns":890,"display":2252},[892,62005,62006,62048],{},[895,62007,62008,62010,62012,62014,62016,62018,62020,62026,62028,62030,62044,62046],{},[898,62009,6909],{},[898,62011,8068],{},[1701,62013,1792],{},[898,62015,1983],{},[898,62017,8068],{},[1701,62019,1792],{},[3243,62021,62022,62024],{},[898,62023,1680],{},[1701,62025,8424],{},[9942,62027],{"width":19336},[1701,62029,1799],{"stretchy":1798},[895,62031,62032,62035,62041],{},[1939,62033,62034],{},"obr",[12448,62036,62037,62039],{"accent":2011},[1939,62038,207],{},[1701,62040,29015],{},[1939,62042,62043],{},"zek 3.4",[1701,62045,1805],{"stretchy":1798},[898,62047,1715],{"mathvariant":2334},[902,62049,62050],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,62052,62053],{},[614,62054,62055,62056,2633,62082,62110,62111,62124,62125,62140,62141,7801,62154,1343,62180,7801,62195,1715],{},"Obrázek 3.2: Přímky ",[883,62057,62059],{"className":62058},[886],[888,62060,62061],{"xmlns":890},[892,62062,62063,62079],{},[895,62064,62065,62067,62069,62071,62073,62075,62077],{},[898,62066,1983],{},[898,62068,8068],{},[1701,62070,1792],{},[898,62072,207],{},[898,62074,1802],{},[1701,62076,1703],{},[898,62078,3598],{},[902,62080,62081],{"encoding":904},"AR = aQ + b",[883,62083,62085],{"className":62084},[886],[888,62086,62087],{"xmlns":890},[892,62088,62089,62107],{},[895,62090,62091,62093,62095,62097,62099,62101,62103,62105],{},[898,62092,6909],{},[898,62094,8068],{},[1701,62096,1792],{},[1850,62098,3938],{},[898,62100,207],{},[898,62102,1802],{},[1701,62104,1703],{},[898,62106,3598],{},[902,62108,62109],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,62112,62114],{"className":62113},[886],[888,62115,62116],{"xmlns":890},[892,62117,62118,62122],{},[895,62119,62120],{},[898,62121,3598],{},[902,62123,3598],{"encoding":904}," se svislou osou, ",[883,62126,62128],{"className":62127},[886],[888,62129,62130],{"xmlns":890},[892,62131,62132,62138],{},[895,62133,62134,62136],{},[898,62135,6909],{},[898,62137,8068],{},[902,62139,10697],{"encoding":904}," protíná osu ",[883,62142,62144],{"className":62143},[886],[888,62145,62146],{"xmlns":890},[892,62147,62148,62152],{},[895,62149,62150],{},[898,62151,1802],{},[902,62153,1802],{"encoding":904},[883,62155,62157],{"className":62156},[886],[888,62158,62159],{"xmlns":890},[892,62160,62161,62177],{},[895,62162,62163,62165],{},[1701,62164,2317],{},[2363,62166,62167],{"scriptlevel":1852,"displaystyle":1798},[3726,62168,62169,62171],{},[898,62170,3598],{},[895,62172,62173,62175],{},[1850,62174,3938],{},[898,62176,207],{},[902,62178,62179],{"encoding":904},"-\\tfrac{b}{2a}",[883,62181,62183],{"className":62182},[886],[888,62184,62185],{"xmlns":890},[892,62186,62187,62193],{},[895,62188,62189,62191],{},[898,62190,1983],{},[898,62192,8068],{},[902,62194,59191],{"encoding":904},[883,62196,62198],{"className":62197},[886],[888,62199,62200],{"xmlns":890},[892,62201,62202,62214],{},[895,62203,62204,62206],{},[1701,62205,2317],{},[2363,62207,62208],{"scriptlevel":1852,"displaystyle":1798},[3726,62209,62210,62212],{},[898,62211,3598],{},[898,62213,207],{},[902,62215,62216],{"encoding":904},"-\\tfrac{b}{a}",[724,62218,62219],{},[614,62220,62221,62222,62253,62254,62283,62284,1715],{},"Obrázek 3.3: Parabola ",[883,62223,62225],{"className":62224},[886],[888,62226,62227],{"xmlns":890},[892,62228,62229,62251],{},[895,62230,62231,62233,62235,62237,62239,62245,62247,62249],{},[898,62232,5877],{},[898,62234,8068],{},[1701,62236,1792],{},[898,62238,207],{},[3243,62240,62241,62243],{},[898,62242,1802],{},[1850,62244,3938],{},[1701,62246,1703],{},[898,62248,3598],{},[898,62250,1802],{},[902,62252,61685],{"encoding":904}," s maximem v ",[883,62255,62257],{"className":62256},[886],[888,62258,62259],{"xmlns":890},[892,62260,62261,62281],{},[895,62262,62263,62265,62267,62269],{},[898,62264,1802],{},[1701,62266,1792],{},[1701,62268,2317],{},[2363,62270,62271],{"scriptlevel":1852,"displaystyle":1798},[3726,62272,62273,62275],{},[898,62274,3598],{},[895,62276,62277,62279],{},[1850,62278,3938],{},[898,62280,207],{},[902,62282,61889],{"encoding":904}," a nulou v ",[883,62285,62287],{"className":62286},[886],[888,62288,62289],{"xmlns":890},[892,62290,62291,62307],{},[895,62292,62293,62295,62297,62299],{},[898,62294,1802],{},[1701,62296,1792],{},[1701,62298,2317],{},[2363,62300,62301],{"scriptlevel":1852,"displaystyle":1798},[3726,62302,62303,62305],{},[898,62304,3598],{},[898,62306,207],{},[902,62308,62309],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,62311,62312],{},[614,62313,62314,62315,1715],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,62316,62318],{"className":62317},[886],[888,62319,62320],{"xmlns":890},[892,62321,62322,62342],{},[895,62323,62324,62326,62328,62330,62332,62334,62336],{},[898,62325,1983],{},[898,62327,8068],{},[1701,62329,1792],{},[898,62331,6909],{},[898,62333,8068],{},[1701,62335,1792],{},[3243,62337,62338,62340],{},[898,62339,1680],{},[1701,62341,8424],{},[902,62343,62344],{"encoding":904},"AR = MR = P^*",[115,62346,62348],{"id":62347},"náklady-firmy","Náklady firmy",[198,62350,62352],{"id":62351},"celkové-náklady","Celkové náklady",[724,62354,62355,4088,62357,1646,62372,62375,62376,62389],{},[38,62356,62352],{},[883,62358,62360],{"className":62359},[886],[888,62361,62362],{"xmlns":890},[892,62363,62364,62370],{},[895,62365,62366,62368],{},[898,62367,5877],{},[898,62369,1658],{},[902,62371,7326],{"encoding":904},[38,62373,62374],{},"total cost",") jsou veškeré náklady na realizaci ",[883,62377,62379],{"className":62378},[886],[888,62380,62381],{"xmlns":890},[892,62382,62383,62387],{},[895,62384,62385],{},[898,62386,1802],{},[902,62388,1802],{"encoding":904}," jednotek produkce:",[883,62391,62393],{"className":62392},[886],[888,62394,62395],{"xmlns":890,"display":2252},[892,62396,62397,62452],{},[2256,62398,62399],{"width":2258},[2260,62400,62401,62403,62445,62447],{},[2263,62402],{"width":2265},[2263,62404,62405],{},[895,62406,62407,62409,62411,62413,62415,62417,62419,62421,62423,62425,62427,62429,62431,62433,62435,62437,62439,62441,62443],{},[898,62408,5877],{},[898,62410,1658],{},[1701,62412,1792],{},[898,62414,5877],{},[898,62416,1658],{},[1701,62418,1799],{"stretchy":1798},[898,62420,1802],{},[1701,62422,1805],{"stretchy":1798},[1701,62424,1792],{},[898,62426,14492],{},[898,62428,1658],{},[1701,62430,1703],{},[898,62432,5877],{},[898,62434,44362],{},[898,62436,1658],{},[1701,62438,1799],{"stretchy":1798},[898,62440,1802],{},[1701,62442,1805],{"stretchy":1798},[1701,62444,2012],{"separator":2011},[2263,62446],{"width":2265},[2263,62448,62449],{},[1939,62450,62451],{},"(3.5)",[902,62453,62454],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,62456,8380,62457,62472,62473,1646,62476,1738,62479,62472,62503,1646,62506,62509],{},[883,62458,62460],{"className":62459},[886],[888,62461,62462],{"xmlns":890},[892,62463,62464,62470],{},[895,62465,62466,62468],{},[898,62467,14492],{},[898,62469,1658],{},[902,62471,59237],{"encoding":904}," jsou ",[38,62474,62475],{},"fixní náklady",[38,62477,62478],{},"fixed cost",[883,62480,62482],{"className":62481},[886],[888,62483,62484],{"xmlns":890},[892,62485,62486,62500],{},[895,62487,62488,62490,62492,62494,62496,62498],{},[898,62489,5877],{},[898,62491,44362],{},[898,62493,1658],{},[1701,62495,1799],{"stretchy":1798},[898,62497,1802],{},[1701,62499,1805],{"stretchy":1798},[902,62501,62502],{"encoding":904},"TVC(Q)",[38,62504,62505],{},"celkové variabilní náklady",[38,62507,62508],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,62511,62513],{"id":62512},"průměrné-náklady","Průměrné náklady",[724,62515,62516,4088,62518,1646,62533,62536],{},[38,62517,62513],{},[883,62519,62521],{"className":62520},[886],[888,62522,62523],{"xmlns":890},[892,62524,62525,62531],{},[895,62526,62527,62529],{},[898,62528,1983],{},[898,62530,1658],{},[902,62532,59306],{"encoding":904},[38,62534,62535],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,62538,62540],{"className":62539},[886],[888,62541,62542],{"xmlns":890,"display":2252},[892,62543,62544,62623],{},[2256,62545,62546],{"width":2258},[2260,62547,62548,62550,62616,62618],{},[2263,62549],{"width":2265},[2263,62551,62552],{},[895,62553,62554,62556,62558,62560,62562,62564,62566,62568,62570,62572,62582,62584,62594,62596,62614],{},[898,62555,1983],{},[898,62557,1658],{},[1701,62559,1792],{},[898,62561,1983],{},[898,62563,1658],{},[1701,62565,1799],{"stretchy":1798},[898,62567,1802],{},[1701,62569,1805],{"stretchy":1798},[1701,62571,1792],{},[3726,62573,62574,62580],{},[895,62575,62576,62578],{},[898,62577,5877],{},[898,62579,1658],{},[898,62581,1802],{},[1701,62583,1792],{},[3726,62585,62586,62592],{},[895,62587,62588,62590],{},[898,62589,14492],{},[898,62591,1658],{},[898,62593,1802],{},[1701,62595,1703],{},[3726,62597,62598,62612],{},[895,62599,62600,62602,62604,62606,62608,62610],{},[898,62601,5877],{},[898,62603,44362],{},[898,62605,1658],{},[1701,62607,1799],{"stretchy":1798},[898,62609,1802],{},[1701,62611,1805],{"stretchy":1798},[898,62613,1802],{},[1701,62615,2012],{"separator":2011},[2263,62617],{"width":2265},[2263,62619,62620],{},[1939,62621,62622],{},"(3.6)",[902,62624,62625],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,62627,8380,62628,62472,62652,4088,62655,1646,62672,1738,62675,62472,62707,4088,62710,1646,62727,4539],{},[883,62629,62631],{"className":62630},[886],[888,62632,62633],{"xmlns":890},[892,62634,62635,62649],{},[895,62636,62637],{},[2363,62638,62639],{"scriptlevel":1852,"displaystyle":1798},[3726,62640,62641,62647],{},[895,62642,62643,62645],{},[898,62644,14492],{},[898,62646,1658],{},[898,62648,1802],{},[902,62650,62651],{"encoding":904},"\\tfrac{FC}{Q}",[38,62653,62654],{},"průměrné fixní náklady",[883,62656,62658],{"className":62657},[886],[888,62659,62660],{"xmlns":890},[892,62661,62662,62670],{},[895,62663,62664,62666,62668],{},[898,62665,1983],{},[898,62667,14492],{},[898,62669,1658],{},[902,62671,59273],{"encoding":904},[38,62673,62674],{},"average fixed cost",[883,62676,62678],{"className":62677},[886],[888,62679,62680],{"xmlns":890},[892,62681,62682,62704],{},[895,62683,62684],{},[2363,62685,62686],{"scriptlevel":1852,"displaystyle":1798},[3726,62687,62688,62702],{},[895,62689,62690,62692,62694,62696,62698,62700],{},[898,62691,5877],{},[898,62693,44362],{},[898,62695,1658],{},[1701,62697,1799],{"stretchy":1798},[898,62699,1802],{},[1701,62701,1805],{"stretchy":1798},[898,62703,1802],{},[902,62705,62706],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,62708,62709],{},"průměrné variabilní náklady",[883,62711,62713],{"className":62712},[886],[888,62714,62715],{"xmlns":890},[892,62716,62717,62725],{},[895,62718,62719,62721,62723],{},[898,62720,1983],{},[898,62722,44362],{},[898,62724,1658],{},[902,62726,59057],{"encoding":904},[38,62728,62729],{},"average variable cost",[883,62731,62733],{"className":62732},[886],[888,62734,62735],{"xmlns":890,"display":2252},[892,62736,62737,62796],{},[2256,62738,62739],{"width":2258},[2260,62740,62741,62743,62789,62791],{},[2263,62742],{"width":2265},[2263,62744,62745],{},[895,62746,62747,62749,62751,62753,62755,62757,62759,62761,62763,62765,62767,62769,62787],{},[898,62748,1983],{},[898,62750,44362],{},[898,62752,1658],{},[1701,62754,1792],{},[898,62756,1983],{},[898,62758,44362],{},[898,62760,1658],{},[1701,62762,1799],{"stretchy":1798},[898,62764,1802],{},[1701,62766,1805],{"stretchy":1798},[1701,62768,1792],{},[3726,62770,62771,62785],{},[895,62772,62773,62775,62777,62779,62781,62783],{},[898,62774,5877],{},[898,62776,44362],{},[898,62778,1658],{},[1701,62780,1799],{"stretchy":1798},[898,62782,1802],{},[1701,62784,1805],{"stretchy":1798},[898,62786,1802],{},[898,62788,1715],{"mathvariant":2334},[2263,62790],{"width":2265},[2263,62792,62793],{},[1939,62794,62795],{},"(3.7)",[902,62797,62798],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[41376,62800,62802],{"id":62801},"příklad-34","Příklad 3.4",[724,62804,62805,61268,62807,2633,62832,59771,62856,2633,62871,62886,62887,1715],{},[38,62806,59733],{},[883,62808,62810],{"className":62809},[886],[888,62811,62812],{"xmlns":890},[892,62813,62814,62829],{},[895,62815,62816,62818,62820,62822,62824,62826],{},[898,62817,14492],{},[898,62819,1658],{},[1701,62821,1792],{},[1850,62823,4062],{},[1939,62825,1941],{},[1850,62827,62828],{},"000",[902,62830,62831],{"encoding":904},"FC = 1\\,000",[883,62833,62835],{"className":62834},[886],[888,62836,62837],{"xmlns":890},[892,62838,62839,62853],{},[895,62840,62841,62843,62845,62847,62849,62851],{},[898,62842,5877],{},[898,62844,44362],{},[898,62846,1658],{},[1701,62848,1792],{},[1850,62850,6460],{},[898,62852,1802],{},[902,62854,62855],{"encoding":904},"TVC = 4Q",[883,62857,62859],{"className":62858},[886],[888,62860,62861],{"xmlns":890},[892,62862,62863,62869],{},[895,62864,62865,62867],{},[898,62866,5877],{},[898,62868,1658],{},[902,62870,7326],{"encoding":904},[883,62872,62874],{"className":62873},[886],[888,62875,62876],{"xmlns":890},[892,62877,62878,62884],{},[895,62879,62880,62882],{},[898,62881,1983],{},[898,62883,1658],{},[902,62885,59306],{"encoding":904}," a jejich chování s rostoucím ",[883,62888,62890],{"className":62889},[886],[888,62891,62892],{"xmlns":890},[892,62893,62894,62898],{},[895,62895,62896],{},[898,62897,1802],{},[902,62899,1802],{"encoding":904},[724,62901,62902,4088,62904,2633,62934,62970,62971,8428,62984,62999,63000,2246],{},[38,62903,5001],{},[883,62905,62907],{"className":62906},[886],[888,62908,62909],{"xmlns":890},[892,62910,62911,62931],{},[895,62912,62913,62915,62917,62919,62921,62923,62925,62927,62929],{},[898,62914,5877],{},[898,62916,1658],{},[1701,62918,1792],{},[1850,62920,4062],{},[1939,62922,1941],{},[1850,62924,62828],{},[1701,62926,1703],{},[1850,62928,6460],{},[898,62930,1802],{},[902,62932,62933],{"encoding":904},"TC = 1\\,000 + 4Q",[883,62935,62937],{"className":62936},[886],[888,62938,62939],{"xmlns":890},[892,62940,62941,62967],{},[895,62942,62943,62945,62947,62949,62963,62965],{},[898,62944,1983],{},[898,62946,1658],{},[1701,62948,1792],{},[2363,62950,62951],{"scriptlevel":1852,"displaystyle":1798},[3726,62952,62953,62961],{},[895,62954,62955,62957,62959],{},[1850,62956,4062],{},[1939,62958,1941],{},[1850,62960,62828],{},[898,62962,1802],{},[1701,62964,1703],{},[1850,62966,6460],{},[902,62968,62969],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,62972,62974],{"className":62973},[886],[888,62975,62976],{"xmlns":890},[892,62977,62978,62982],{},[895,62979,62980],{},[898,62981,1802],{},[902,62983,1802],{"encoding":904},[883,62985,62987],{"className":62986},[886],[888,62988,62989],{"xmlns":890},[892,62990,62991,62997],{},[895,62992,62993,62995],{},[898,62994,1983],{},[898,62996,1658],{},[902,62998,59306],{"encoding":904}," blíží ",[883,63001,63003],{"className":63002},[886],[888,63004,63005],{"xmlns":890},[892,63006,63007,63011],{},[895,63008,63009],{},[1850,63010,6460],{},[902,63012,6460],{"encoding":904},[883,63014,63016],{"className":63015},[886],[888,63017,63018],{"xmlns":890,"display":2252},[892,63019,63020,63066],{},[895,63021,63022,63039,63061,63063],{},[43920,63023,63024,63031],{},[895,63025,63026,63029],{},[898,63027,63028],{},"lim",[1701,63030,59946],{},[895,63032,63033,63035,63037],{},[898,63034,1802],{},[1701,63036,4108],{},[898,63038,10360],{"mathvariant":2334},[895,63040,63041,63043,63055,63057,63059],{},[1701,63042,1799],{"fence":2011},[3726,63044,63045,63053],{},[895,63046,63047,63049,63051],{},[1850,63048,4062],{},[1939,63050,1941],{},[1850,63052,62828],{},[898,63054,1802],{},[1701,63056,1703],{},[1850,63058,6460],{},[1701,63060,1805],{"fence":2011},[1701,63062,1792],{},[1850,63064,63065],{},"4.",[902,63067,63068],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,63070,63071,63109,63110,1715],{},[883,63072,63074],{"className":63073},[886],[888,63075,63076],{"xmlns":890},[892,63077,63078,63106],{},[895,63079,63080,63082,63084,63086,63088,63102,63104],{},[898,63081,1983],{},[898,63083,14492],{},[898,63085,1658],{},[1701,63087,1792],{},[2363,63089,63090],{"scriptlevel":1852,"displaystyle":1798},[3726,63091,63092,63100],{},[895,63093,63094,63096,63098],{},[1850,63095,4062],{},[1939,63097,1941],{},[1850,63099,62828],{},[898,63101,1802],{},[1701,63103,4108],{},[1850,63105,1852],{},[902,63107,63108],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,63111,63113],{"className":63112},[886],[888,63114,63115],{"xmlns":890},[892,63116,63117,63121],{},[895,63118,63119],{},[898,63120,1802],{},[902,63122,1802],{"encoding":904},[724,63124,63125],{},[614,63126,63127,63128,63157,63158,1715],{},"Obrázek 3.5: Přímka ",[883,63129,63131],{"className":63130},[886],[888,63132,63133],{"xmlns":890},[892,63134,63135,63155],{},[895,63136,63137,63139,63141,63143,63145,63147,63149,63151,63153],{},[898,63138,5877],{},[898,63140,1658],{},[1701,63142,1792],{},[1850,63144,4062],{},[1939,63146,1941],{},[1850,63148,62828],{},[1701,63150,1703],{},[1850,63152,6460],{},[898,63154,1802],{},[902,63156,62933],{"encoding":904}," protínající svislou osu ve výši ",[883,63159,63161],{"className":63160},[886],[888,63162,63163],{"xmlns":890},[892,63164,63165,63179],{},[895,63166,63167,63169,63171,63173,63175,63177],{},[898,63168,14492],{},[898,63170,1658],{},[1701,63172,1792],{},[1850,63174,4062],{},[1939,63176,1941],{},[1850,63178,62828],{},[902,63180,62831],{"encoding":904},[724,63182,63183],{},[614,63184,63185,63186,63221,63222,1715],{},"Obrázek 3.6: Hyperbola ",[883,63187,63189],{"className":63188},[886],[888,63190,63191],{"xmlns":890},[892,63192,63193,63219],{},[895,63194,63195,63197,63199,63201,63215,63217],{},[898,63196,1983],{},[898,63198,1658],{},[1701,63200,1792],{},[2363,63202,63203],{"scriptlevel":1852,"displaystyle":1798},[3726,63204,63205,63213],{},[895,63206,63207,63209,63211],{},[1850,63208,4062],{},[1939,63210,1941],{},[1850,63212,62828],{},[898,63214,1802],{},[1701,63216,1703],{},[1850,63218,6460],{},[902,63220,62969],{"encoding":904}," s vodorovnou asymptotou ",[883,63223,63225],{"className":63224},[886],[888,63226,63227],{"xmlns":890},[892,63228,63229,63239],{},[895,63230,63231,63233,63235,63237],{},[898,63232,1983],{},[898,63234,1658],{},[1701,63236,1792],{},[1850,63238,6460],{},[902,63240,63241],{"encoding":904},"AC = 4",[724,63243,63244],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,63246,63248],{"className":63247},[886],[888,63249,63250],{"xmlns":890,"display":2252},[892,63251,63252,63278],{},[895,63253,63254,63256,63258,63260,63262,63264,63266,63268,63270,63272,63274,63276],{},[898,63255,5877],{},[898,63257,44362],{},[898,63259,1658],{},[1701,63261,1792],{},[898,63263,1802],{},[1701,63265,3408],{},[898,63267,44362],{},[898,63269,1658],{},[1701,63271,1799],{"stretchy":1798},[898,63273,1802],{},[1701,63275,1805],{"stretchy":1798},[1701,63277,2012],{"separator":2011},[902,63279,63280],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,63282,8380,63283,62472,63311,63314,63315,63345],{},[883,63284,63286],{"className":63285},[886],[888,63287,63288],{"xmlns":890},[892,63289,63290,63308],{},[895,63291,63292,63294,63296,63298,63300,63302,63304,63306],{},[898,63293,44362],{},[898,63295,1658],{},[1701,63297,1792],{},[898,63299,44362],{},[898,63301,1658],{},[1701,63303,1799],{"stretchy":1798},[898,63305,1802],{},[1701,63307,1805],{"stretchy":1798},[902,63309,63310],{"encoding":904},"VC = VC(Q)",[38,63312,63313],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,63316,63318],{"className":63317},[886],[888,63319,63320],{"xmlns":890},[892,63321,63322,63342],{},[895,63323,63324,63326,63328,63330,63332,63334,63336,63338,63340],{},[898,63325,5877],{},[898,63327,44362],{},[898,63329,1658],{},[1701,63331,1799],{"stretchy":1798},[898,63333,1802],{},[1701,63335,1805],{"stretchy":1798},[1701,63337,1792],{},[898,63339,207],{},[898,63341,1802],{},[902,63343,63344],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,63347,63349],{"className":63348},[886],[888,63350,63351],{"xmlns":890,"display":2252},[892,63352,63353,63373],{},[895,63354,63355,63357,63359,63361,63363,63365,63367,63369,63371],{},[898,63356,5877],{},[898,63358,1658],{},[1701,63360,1792],{},[898,63362,14492],{},[898,63364,1658],{},[1701,63366,1703],{},[898,63368,207],{},[898,63370,1802],{},[898,63372,1715],{"mathvariant":2334},[902,63374,63375],{"encoding":904},"TC = FC + aQ.",[724,63377,63378,63379,63394,63395,63410,63411,63434,63435,63469,63470,63221,63483,63496,63497,2633,63545,63589,63590,1715],{},"Křivkou ",[883,63380,63382],{"className":63381},[886],[888,63383,63384],{"xmlns":890},[892,63385,63386,63392],{},[895,63387,63388,63390],{},[898,63389,5877],{},[898,63391,1658],{},[902,63393,7326],{"encoding":904}," je přímka se svislým průsečíkem ",[883,63396,63398],{"className":63397},[886],[888,63399,63400],{"xmlns":890},[892,63401,63402,63408],{},[895,63403,63404,63406],{},[898,63405,14492],{},[898,63407,1658],{},[902,63409,59237],{"encoding":904}," a sklonem ",[883,63412,63414],{"className":63413},[886],[888,63415,63416],{"xmlns":890},[892,63417,63418,63431],{},[895,63419,63420,63423,63425,63427,63429],{},[898,63421,63422],{},"tan",[1701,63424,59946],{},[898,63426,22908],{},[1701,63428,1792],{},[898,63430,207],{},[902,63432,63433],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,63436,63438],{"className":63437},[886],[888,63439,63440],{"xmlns":890},[892,63441,63442,63466],{},[895,63443,63444,63446,63448,63450,63462,63464],{},[898,63445,1983],{},[898,63447,1658],{},[1701,63449,1792],{},[2363,63451,63452],{"scriptlevel":1852,"displaystyle":1798},[3726,63453,63454,63460],{},[895,63455,63456,63458],{},[898,63457,14492],{},[898,63459,1658],{},[898,63461,1802],{},[1701,63463,1703],{},[898,63465,207],{},[902,63467,63468],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,63471,63473],{"className":63472},[886],[888,63474,63475],{"xmlns":890},[892,63476,63477,63481],{},[895,63478,63479],{},[898,63480,13853],{},[902,63482,13853],{"encoding":904},[883,63484,63486],{"className":63485},[886],[888,63487,63488],{"xmlns":890},[892,63489,63490,63494],{},[895,63491,63492],{},[898,63493,207],{},[902,63495,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,63498,63500],{"className":63499},[886],[888,63501,63502],{"xmlns":890},[892,63503,63504,63542],{},[895,63505,63506,63526,63538,63540],{},[1845,63507,63508,63514],{},[895,63509,63510,63512],{},[898,63511,63028],{},[1701,63513,59946],{},[895,63515,63516,63518,63520],{},[898,63517,1802],{},[1701,63519,4108],{},[3243,63521,63522,63524],{},[1850,63523,1852],{},[1701,63525,1703],{},[2363,63527,63528],{"scriptlevel":1852,"displaystyle":1798},[3726,63529,63530,63536],{},[895,63531,63532,63534],{},[898,63533,14492],{},[898,63535,1658],{},[898,63537,1802],{},[1701,63539,1792],{},[898,63541,10360],{"mathvariant":2334},[902,63543,63544],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,63546,63548],{"className":63547},[886],[888,63549,63550],{"xmlns":890},[892,63551,63552,63586],{},[895,63553,63554,63570,63582,63584],{},[1845,63555,63556,63562],{},[895,63557,63558,63560],{},[898,63559,63028],{},[1701,63561,59946],{},[895,63563,63564,63566,63568],{},[898,63565,1802],{},[1701,63567,4108],{},[898,63569,10360],{"mathvariant":2334},[2363,63571,63572],{"scriptlevel":1852,"displaystyle":1798},[3726,63573,63574,63580],{},[895,63575,63576,63578],{},[898,63577,14492],{},[898,63579,1658],{},[898,63581,1802],{},[1701,63583,1792],{},[1850,63585,1852],{},[902,63587,63588],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,63591,63593],{"className":63592},[886],[888,63594,63595],{"xmlns":890},[892,63596,63597,63603],{},[895,63598,63599,63601],{},[898,63600,1983],{},[898,63602,1658],{},[902,63604,59306],{"encoding":904},[724,63606,63607],{},[614,63608,63609,63610,63625,63626,63641,63642,1715],{},"Obrázek 3.7: Přímka ",[883,63611,63613],{"className":63612},[886],[888,63614,63615],{"xmlns":890},[892,63616,63617,63623],{},[895,63618,63619,63621],{},[898,63620,5877],{},[898,63622,1658],{},[902,63624,7326],{"encoding":904}," s osovým průsečíkem ve výši ",[883,63627,63629],{"className":63628},[886],[888,63630,63631],{"xmlns":890},[892,63632,63633,63639],{},[895,63634,63635,63637],{},[898,63636,14492],{},[898,63638,1658],{},[902,63640,59237],{"encoding":904}," a se sklonem ",[883,63643,63645],{"className":63644},[886],[888,63646,63647],{"xmlns":890},[892,63648,63649,63661],{},[895,63650,63651,63653,63655,63657,63659],{},[898,63652,63422],{},[1701,63654,59946],{},[898,63656,22908],{},[1701,63658,1792],{},[898,63660,207],{},[902,63662,63433],{"encoding":904},[724,63664,63665],{},[614,63666,63667,63668,63683,63684,1715],{},"Obrázek 3.8: Klesající hyperbola ",[883,63669,63671],{"className":63670},[886],[888,63672,63673],{"xmlns":890},[892,63674,63675,63681],{},[895,63676,63677,63679],{},[898,63678,1983],{},[898,63680,1658],{},[902,63682,59306],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,63685,63687],{"className":63686},[886],[888,63688,63689],{"xmlns":890},[892,63690,63691,63695],{},[895,63692,63693],{},[898,63694,207],{},[902,63696,207],{"encoding":904},[198,63698,63700],{"id":63699},"mezní-náklady","Mezní náklady",[724,63702,63703,4088,63705,1646,63720,63723,63724,63727],{},[38,63704,63700],{},[883,63706,63708],{"className":63707},[886],[888,63709,63710],{"xmlns":890},[892,63711,63712,63718],{},[895,63713,63714,63716],{},[898,63715,6909],{},[898,63717,1658],{},[902,63719,59038],{"encoding":904},[38,63721,63722],{},"marginal cost",") jsou ",[207,63725,1145],{"className":63726,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,63729,63731],{"className":63730},[886],[888,63732,63733],{"xmlns":890,"display":2252},[892,63734,63735,63804],{},[2256,63736,63737],{"width":2258},[2260,63738,63739,63741,63797,63799],{},[2263,63740],{"width":2265},[2263,63742,63743],{},[895,63744,63745,63747,63749,63751,63753,63755,63757,63759,63761,63763,63779,63781,63783,63789,63791,63793,63795],{},[898,63746,6909],{},[898,63748,1658],{},[1701,63750,1792],{},[898,63752,6909],{},[898,63754,1658],{},[1701,63756,1799],{"stretchy":1798},[898,63758,1802],{},[1701,63760,1805],{"stretchy":1798},[1701,63762,1792],{},[3726,63764,63765,63773],{},[895,63766,63767,63769,63771],{},[898,63768,2312],{"mathvariant":2334},[898,63770,5877],{},[898,63772,1658],{},[895,63774,63775,63777],{},[898,63776,2312],{"mathvariant":2334},[898,63778,1802],{},[1701,63780,1792],{},[898,63782,5877],{},[3243,63784,63785,63787],{},[898,63786,1658],{},[1701,63788,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,63790,1799],{"stretchy":1798},[898,63792,1802],{},[1701,63794,1805],{"stretchy":1798},[898,63796,1715],{"mathvariant":2334},[2263,63798],{"width":2265},[2263,63800,63801],{},[1939,63802,63803],{},"(3.8)",[902,63805,63806],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1635,63808,63809],{},[724,63810,63811,63813,63814,63840,63841,63858,63859,1715],{},[883,63812,2063],{}," Intuice — „kolik stojí další kus\"\n",[883,63815,63817],{"className":63816},[886],[888,63818,63819],{"xmlns":890},[892,63820,63821,63837],{},[895,63822,63823,63825,63827,63829,63835],{},[898,63824,6909],{},[898,63826,1658],{},[1701,63828,1799],{"stretchy":1798},[3243,63830,63831,63833],{},[898,63832,1802],{},[1701,63834,8424],{},[1701,63836,1805],{"stretchy":1798},[902,63838,63839],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,63842,63844],{"className":63843},[886],[888,63845,63846],{"xmlns":890},[892,63847,63848,63856],{},[895,63849,63850],{},[3243,63851,63852,63854],{},[898,63853,1802],{},[1701,63855,8424],{},[902,63857,33877],{"encoding":904},". Formálně ",[883,63860,63862],{"className":63861},[886],[888,63863,63864],{"xmlns":890},[892,63865,63866,63918],{},[895,63867,63868,63870,63872,63874,63880,63882,63884,63886,63888,63890,63896,63898,63900,63902,63904,63906,63908,63910,63916],{},[898,63869,6909],{},[898,63871,1658],{},[1701,63873,1799],{"stretchy":1798},[3243,63875,63876,63878],{},[898,63877,1802],{},[1701,63879,8424],{},[1701,63881,1805],{"stretchy":1798},[1701,63883,4067],{},[898,63885,5877],{},[898,63887,1658],{},[1701,63889,1799],{"stretchy":1798},[3243,63891,63892,63894],{},[898,63893,1802],{},[1701,63895,8424],{},[1701,63897,1703],{},[1850,63899,4062],{},[1701,63901,1805],{"stretchy":1798},[1701,63903,2317],{},[898,63905,5877],{},[898,63907,1658],{},[1701,63909,1799],{"stretchy":1798},[3243,63911,63912,63914],{},[898,63913,1802],{},[1701,63915,8424],{},[1701,63917,1805],{"stretchy":1798},[902,63919,63920],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,63922,63923,63924,2246],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,63925,63927],{"className":63926},[886],[888,63928,63929],{"xmlns":890},[892,63930,63931,63939],{},[895,63932,63933,63935,63937],{},[898,63934,4708],{"mathvariant":2334},[898,63936,5877],{},[898,63938,1658],{},[902,63940,63941],{"encoding":904},"\\Delta TC",[883,63943,63945],{"className":63944},[886],[888,63946,63947],{"xmlns":890,"display":2252},[892,63948,63949,64018],{},[2256,63950,63951],{"width":2258},[2260,63952,63953,63955,64011,64013],{},[2263,63954],{"width":2265},[2263,63956,63957],{},[895,63958,63959,63961,63963,63965,63967,63969,63971,63973,63975,63977,63979,63981,63983,63985,63991,63993,63995,63997,63999,64001,64003,64005,64007,64009],{},[898,63960,4708],{"mathvariant":2334},[898,63962,5877],{},[898,63964,1658],{},[1939,63966,8058],{},[1701,63968,4067],{},[1939,63970,8058],{},[898,63972,2312],{"mathvariant":2334},[898,63974,5877],{},[898,63976,1658],{},[1701,63978,1792],{},[1701,63980,1799],{"stretchy":1798},[898,63982,5877],{},[898,63984,1658],{},[3243,63986,63987,63989],{},[1701,63988,1805],{"stretchy":1798},[1701,63990,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,63992,1941],{},[898,63994,2312],{"mathvariant":2334},[898,63996,1802],{},[1701,63998,1792],{},[898,64000,6909],{},[898,64002,1658],{},[1939,64004,1941],{},[898,64006,2312],{"mathvariant":2334},[898,64008,1802],{},[1701,64010,2012],{"separator":2011},[2263,64012],{"width":2265},[2263,64014,64015],{},[1939,64016,64017],{},"(3.9)",[902,64019,64020],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,64022,61057],{},[883,64024,64026],{"className":64025},[886],[888,64027,64028],{"xmlns":890,"display":2252},[892,64029,64030,64128],{},[895,64031,64032,64070,64072,64074,64076,64098,64100,64126],{},[895,64033,64034,64036,64042,64044,64050,64053,64059,64062],{},[1939,64035,61071],{},[12448,64037,64038,64040],{"accent":2011},[1939,64039,49723],{},[1701,64041,29096],{},[1939,64043,61080],{},[12448,64045,64046,64048],{"accent":2011},[1939,64047,6127],{},[1701,64049,29015],{},[1939,64051,64052],{},"ch n",[12448,64054,64055,64057],{"accent":2011},[1939,64056,207],{},[1701,64058,29015],{},[1939,64060,64061],{},"klad",[12448,64063,64064,64067],{"accent":2011},[1939,64065,64066],{},"u",[1701,64068,64069],{},"˚",[1939,64071,8058],{},[1701,64073,4067],{},[1939,64075,8058],{},[895,64077,64078,64080,64086,64089,64095],{},[1939,64079,61115],{},[12448,64081,64082,64084],{"accent":2011},[1939,64083,29084],{},[1701,64085,29015],{},[1939,64087,64088],{}," n",[12448,64090,64091,64093],{"accent":2011},[1939,64092,207],{},[1701,64094,29015],{},[1939,64096,64097],{},"klady",[1701,64099,61142],{},[895,64101,64102,64104,64110,64112,64118,64120],{},[1939,64103,61071],{},[12448,64105,64106,64108],{"accent":2011},[1939,64107,49723],{},[1701,64109,29096],{},[1939,64111,61155],{},[12448,64113,64114,64116],{"accent":2011},[1939,64115,13652],{},[1701,64117,29096],{},[1939,64119,61164],{},[12448,64121,64122,64124],{"accent":2011},[1939,64123,29084],{},[1701,64125,29015],{},[898,64127,1715],{"mathvariant":2334},[902,64129,64130],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[41376,64132,64134],{"id":64133},"příklad-35","Příklad 3.5",[724,64136,64137,61268,64139,59771,64175,64190,64191,64206,64207,3841,64220,3856,64233,64246,64247,3856,64260,1715],{},[38,64138,59733],{},[883,64140,64142],{"className":64141},[886],[888,64143,64144],{"xmlns":890},[892,64145,64146,64172],{},[895,64147,64148,64150,64152,64154,64156,64158,64160,64162,64164,64166],{},[898,64149,5877],{},[898,64151,1658],{},[1701,64153,1792],{},[1850,64155,12439],{},[1701,64157,1703],{},[1850,64159,6352],{},[898,64161,1802],{},[1701,64163,1703],{},[1850,64165,3938],{},[3243,64167,64168,64170],{},[898,64169,1802],{},[1850,64171,3938],{},[902,64173,64174],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,64176,64178],{"className":64177},[886],[888,64179,64180],{"xmlns":890},[892,64181,64182,64188],{},[895,64183,64184,64186],{},[898,64185,6909],{},[898,64187,1658],{},[902,64189,59038],{"encoding":904}," a odhadněte změny ",[883,64192,64194],{"className":64193},[886],[888,64195,64196],{"xmlns":890},[892,64197,64198,64204],{},[895,64199,64200,64202],{},[898,64201,5877],{},[898,64203,1658],{},[902,64205,7326],{"encoding":904}," při změnách ",[883,64208,64210],{"className":64209},[886],[888,64211,64212],{"xmlns":890},[892,64213,64214,64218],{},[895,64215,64216],{},[898,64217,1802],{},[902,64219,1802],{"encoding":904},[883,64221,64223],{"className":64222},[886],[888,64224,64225],{"xmlns":890},[892,64226,64227,64231],{},[895,64228,64229],{},[1850,64230,40275],{},[902,64232,40275],{"encoding":904},[883,64234,64236],{"className":64235},[886],[888,64237,64238],{"xmlns":890},[892,64239,64240,64244],{},[895,64241,64242],{},[1850,64243,45883],{},[902,64245,45883],{"encoding":904}," a z ",[883,64248,64250],{"className":64249},[886],[888,64251,64252],{"xmlns":890},[892,64253,64254,64258],{},[895,64255,64256],{},[1850,64257,40275],{},[902,64259,40275],{"encoding":904},[883,64261,64263],{"className":64262},[886],[888,64264,64265],{"xmlns":890},[892,64266,64267,64271],{},[895,64268,64269],{},[1850,64270,7592],{},[902,64272,7592],{"encoding":904},[724,64274,64275,4088,64277,7015,64303,1343,64330,64357,64358,64373,64374,64389,64390,64417,64418,64438,64439,24575,64460,64516,64517,3841,64530,3856,64543,12164,64556,1715],{},[38,64276,5001],{},[883,64278,64280],{"className":64279},[886],[888,64281,64282],{"xmlns":890},[892,64283,64284,64300],{},[895,64285,64286,64288,64290,64292,64294,64296,64298],{},[898,64287,6909],{},[898,64289,1658],{},[1701,64291,1792],{},[1850,64293,6352],{},[1701,64295,1703],{},[1850,64297,6460],{},[898,64299,1802],{},[902,64301,64302],{"encoding":904},"MC = 6 + 4Q",[883,64304,64306],{"className":64305},[886],[888,64307,64308],{"xmlns":890},[892,64309,64310,64327],{},[895,64311,64312,64314,64316,64318,64320,64322,64324],{},[898,64313,6909],{},[898,64315,1658],{},[1701,64317,1799],{"stretchy":1798},[1850,64319,40275],{},[1701,64321,1805],{"stretchy":1798},[1701,64323,1792],{},[1850,64325,64326],{},"66",[902,64328,64329],{"encoding":904},"MC(15) = 66",[883,64331,64333],{"className":64332},[886],[888,64334,64335],{"xmlns":890},[892,64336,64337,64354],{},[895,64338,64339,64341,64343,64345,64347,64349,64351],{},[898,64340,6909],{},[898,64342,1658],{},[1701,64344,1799],{"stretchy":1798},[1850,64346,13096],{},[1701,64348,1805],{"stretchy":1798},[1701,64350,1792],{},[1850,64352,64353],{},"86",[902,64355,64356],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,64359,64361],{"className":64360},[886],[888,64362,64363],{"xmlns":890},[892,64364,64365,64371],{},[895,64366,64367,64369],{},[898,64368,5877],{},[898,64370,1658],{},[902,64372,7326],{"encoding":904}," zvyšuje (",[883,64375,64377],{"className":64376},[886],[888,64378,64379],{"xmlns":890},[892,64380,64381,64387],{},[895,64382,64383,64385],{},[898,64384,6909],{},[898,64386,1658],{},[902,64388,59038],{"encoding":904}," je rostoucí). Z ",[883,64391,64393],{"className":64392},[886],[888,64394,64395],{"xmlns":890},[892,64396,64397,64414],{},[895,64398,64399,64401,64403,64405,64407,64409,64411],{},[898,64400,5877],{},[898,64402,1658],{},[1701,64404,1799],{"stretchy":1798},[1850,64406,40275],{},[1701,64408,1805],{"stretchy":1798},[1701,64410,1792],{},[1850,64412,64413],{},"740",[902,64415,64416],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,64419,64421],{"className":64420},[886],[888,64422,64423],{"xmlns":890},[892,64424,64425,64435],{},[895,64426,64427,64429,64431,64433],{},[898,64428,2312],{"mathvariant":2334},[898,64430,1802],{},[1701,64432,1792],{},[1850,64434,4062],{},[902,64436,64437],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,64440,64442],{"className":64441},[886],[888,64443,64444],{"xmlns":890},[892,64445,64446,64457],{},[895,64447,64448,64450,64452,64454],{},[898,64449,5877],{},[898,64451,1658],{},[1701,64453,4067],{},[1850,64455,64456],{},"806",[902,64458,64459],{"encoding":904},"TC \\approx 806",[883,64461,64463],{"className":64462},[886],[888,64464,64465],{"xmlns":890},[892,64466,64467,64513],{},[895,64468,64469,64471,64473,64475,64477,64479,64481,64483,64485,64487,64489,64491,64493,64495,64497,64499,64501,64504,64506,64508,64510],{},[898,64470,4708],{"mathvariant":2334},[898,64472,5877],{},[898,64474,1658],{},[1701,64476,1792],{},[898,64478,5877],{},[898,64480,1658],{},[1701,64482,1799],{"stretchy":1798},[1850,64484,45883],{},[1701,64486,1805],{"stretchy":1798},[1701,64488,2317],{},[898,64490,5877],{},[898,64492,1658],{},[1701,64494,1799],{"stretchy":1798},[1850,64496,40275],{},[1701,64498,1805],{"stretchy":1798},[1701,64500,1792],{},[1850,64502,64503],{},"808",[1701,64505,2317],{},[1850,64507,64413],{},[1701,64509,1792],{},[1850,64511,64512],{},"68",[902,64514,64515],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,64518,64520],{"className":64519},[886],[888,64521,64522],{"xmlns":890},[892,64523,64524,64528],{},[895,64525,64526],{},[898,64527,1802],{},[902,64529,1802],{"encoding":904},[883,64531,64533],{"className":64532},[886],[888,64534,64535],{"xmlns":890},[892,64536,64537,64541],{},[895,64538,64539],{},[1850,64540,40275],{},[902,64542,40275],{"encoding":904},[883,64544,64546],{"className":64545},[886],[888,64547,64548],{"xmlns":890},[892,64549,64550,64554],{},[895,64551,64552],{},[1850,64553,7592],{},[902,64555,7592],{"encoding":904},[883,64557,64559],{"className":64558},[886],[888,64560,64561],{"xmlns":890},[892,64562,64563,64592],{},[895,64564,64565,64567,64569,64571,64573,64575,64577,64579,64581,64583,64585,64587,64589],{},[898,64566,4708],{"mathvariant":2334},[898,64568,5877],{},[898,64570,1658],{},[1701,64572,4067],{},[1850,64574,64326],{},[1701,64576,3408],{},[1701,64578,1799],{"stretchy":1798},[1701,64580,2317],{},[1850,64582,3646],{},[1701,64584,1805],{"stretchy":1798},[1701,64586,1792],{},[1701,64588,2317],{},[1850,64590,64591],{},"198",[902,64593,64594],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,64596,64598],{"id":64597},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,64600,64601],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[41376,64603,64605],{"id":64604},"příklad-36","Příklad 3.6",[724,64607,64608,61268,64610,64654],{},[38,64609,59733],{},[883,64611,64613],{"className":64612},[886],[888,64614,64615],{"xmlns":890},[892,64616,64617,64651],{},[895,64618,64619,64621,64623,64625,64627,64629,64631,64633,64635,64637,64643,64645],{},[898,64620,5877],{},[898,64622,1658],{},[1701,64624,1792],{},[1850,64626,5158],{},[1701,64628,1703],{},[1850,64630,9071],{},[898,64632,1802],{},[1701,64634,2317],{},[1850,64636,4225],{},[3243,64638,64639,64641],{},[898,64640,1802],{},[1850,64642,3938],{},[1701,64644,1703],{},[3243,64646,64647,64649],{},[898,64648,1802],{},[1850,64650,3646],{},[902,64652,64653],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,64656,64657],{},[38,64658,5001],{},[883,64660,64662],{"className":64661},[886],[888,64663,64664],{"xmlns":890,"display":2252},[892,64665,64666,64910],{},[2256,64667,64668,64694,64742,64776,64818,64868],{"rowspacing":24799,"columnalign":24800,"columnspacing":4782},[2260,64669,64670,64680],{},[2263,64671,64672],{},[2363,64673,64674],{"scriptlevel":1852,"displaystyle":2011},[895,64675,64676,64678],{},[898,64677,14492],{},[898,64679,1658],{},[2263,64681,64682],{},[2363,64683,64684],{"scriptlevel":1852,"displaystyle":2011},[895,64685,64686,64688,64690,64692],{},[895,64687],{},[1701,64689,1792],{},[1850,64691,5158],{},[1701,64693,2012],{"separator":2011},[2260,64695,64696,64708],{},[2263,64697,64698],{},[2363,64699,64700],{"scriptlevel":1852,"displaystyle":2011},[895,64701,64702,64704,64706],{},[898,64703,5877],{},[898,64705,44362],{},[898,64707,1658],{},[2263,64709,64710],{},[2363,64711,64712],{"scriptlevel":1852,"displaystyle":2011},[895,64713,64714,64716,64718,64720,64722,64724,64726,64732,64734,64740],{},[895,64715],{},[1701,64717,1792],{},[1850,64719,9071],{},[898,64721,1802],{},[1701,64723,2317],{},[1850,64725,4225],{},[3243,64727,64728,64730],{},[898,64729,1802],{},[1850,64731,3938],{},[1701,64733,1703],{},[3243,64735,64736,64738],{},[898,64737,1802],{},[1850,64739,3646],{},[1701,64741,2012],{"separator":2011},[2260,64743,64744,64756],{},[2263,64745,64746],{},[2363,64747,64748],{"scriptlevel":1852,"displaystyle":2011},[895,64749,64750,64752,64754],{},[898,64751,1983],{},[898,64753,14492],{},[898,64755,1658],{},[2263,64757,64758],{},[2363,64759,64760],{"scriptlevel":1852,"displaystyle":2011},[895,64761,64762,64764,64766,64774],{},[895,64763],{},[1701,64765,1792],{},[2363,64767,64768],{"scriptlevel":1852,"displaystyle":1798},[3726,64769,64770,64772],{},[1850,64771,5158],{},[898,64773,1802],{},[1701,64775,2012],{"separator":2011},[2260,64777,64778,64790],{},[2263,64779,64780],{},[2363,64781,64782],{"scriptlevel":1852,"displaystyle":2011},[895,64783,64784,64786,64788],{},[898,64785,1983],{},[898,64787,44362],{},[898,64789,1658],{},[2263,64791,64792],{},[2363,64793,64794],{"scriptlevel":1852,"displaystyle":2011},[895,64795,64796,64798,64800,64802,64804,64806,64808,64810,64816],{},[895,64797],{},[1701,64799,1792],{},[1850,64801,9071],{},[1701,64803,2317],{},[1850,64805,4225],{},[898,64807,1802],{},[1701,64809,1703],{},[3243,64811,64812,64814],{},[898,64813,1802],{},[1850,64815,3938],{},[1701,64817,2012],{"separator":2011},[2260,64819,64820,64830],{},[2263,64821,64822],{},[2363,64823,64824],{"scriptlevel":1852,"displaystyle":2011},[895,64825,64826,64828],{},[898,64827,1983],{},[898,64829,1658],{},[2263,64831,64832],{},[2363,64833,64834],{"scriptlevel":1852,"displaystyle":2011},[895,64835,64836,64838,64840,64848,64850,64852,64854,64856,64858,64860,64866],{},[895,64837],{},[1701,64839,1792],{},[2363,64841,64842],{"scriptlevel":1852,"displaystyle":1798},[3726,64843,64844,64846],{},[1850,64845,5158],{},[898,64847,1802],{},[1701,64849,1703],{},[1850,64851,9071],{},[1701,64853,2317],{},[1850,64855,4225],{},[898,64857,1802],{},[1701,64859,1703],{},[3243,64861,64862,64864],{},[898,64863,1802],{},[1850,64865,3938],{},[1701,64867,2012],{"separator":2011},[2260,64869,64870,64880],{},[2263,64871,64872],{},[2363,64873,64874],{"scriptlevel":1852,"displaystyle":2011},[895,64875,64876,64878],{},[898,64877,6909],{},[898,64879,1658],{},[2263,64881,64882],{},[2363,64883,64884],{"scriptlevel":1852,"displaystyle":2011},[895,64885,64886,64888,64890,64892,64894,64896,64898,64900,64902,64908],{},[895,64887],{},[1701,64889,1792],{},[1850,64891,9071],{},[1701,64893,2317],{},[1850,64895,3703],{},[898,64897,1802],{},[1701,64899,1703],{},[1850,64901,3646],{},[3243,64903,64904,64906],{},[898,64905,1802],{},[1850,64907,3938],{},[898,64909,1715],{"mathvariant":2334},[902,64911,64912],{"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}",[724,64914,64915,64916,19842,64931,19842,64946,64961,64962,64977,64978,1343,64996,64977,65013,1343,65031,64977,65046,65064],{},"Význačné body ",[883,64917,64919],{"className":64918},[886],[888,64920,64921],{"xmlns":890},[892,64922,64923,64928],{},[895,64924,64925],{},[1850,64926,64927],{},"1,67",[902,64929,64930],{"encoding":904},"1{,}67",[883,64932,64934],{"className":64933},[886],[888,64935,64936],{"xmlns":890},[892,64937,64938,64943],{},[895,64939,64940],{},[1850,64941,64942],{},"2,50",[902,64944,64945],{"encoding":904},"2{,}50",[883,64947,64949],{"className":64948},[886],[888,64950,64951],{"xmlns":890},[892,64952,64953,64958],{},[895,64954,64955],{},[1850,64956,64957],{},"4,73",[902,64959,64960],{"encoding":904},"4{,}73"," odpovídají: ",[883,64963,64965],{"className":64964},[886],[888,64966,64967],{"xmlns":890},[892,64968,64969,64975],{},[895,64970,64971,64973],{},[898,64972,6909],{},[898,64974,1658],{},[902,64976,59038],{"encoding":904}," minimum v ",[883,64979,64981],{"className":64980},[886],[888,64982,64983],{"xmlns":890},[892,64984,64985,64993],{},[895,64986,64987,64989,64991],{},[898,64988,1802],{},[1701,64990,3782],{},[1850,64992,64927],{},[902,64994,64995],{"encoding":904},"Q \\doteq 1{,}67",[883,64997,64999],{"className":64998},[886],[888,65000,65001],{"xmlns":890},[892,65002,65003,65011],{},[895,65004,65005,65007,65009],{},[898,65006,1983],{},[898,65008,44362],{},[898,65010,1658],{},[902,65012,59057],{"encoding":904},[883,65014,65016],{"className":65015},[886],[888,65017,65018],{"xmlns":890},[892,65019,65020,65028],{},[895,65021,65022,65024,65026],{},[898,65023,1802],{},[1701,65025,1792],{},[1850,65027,64942],{},[902,65029,65030],{"encoding":904},"Q = 2{,}50",[883,65032,65034],{"className":65033},[886],[888,65035,65036],{"xmlns":890},[892,65037,65038,65044],{},[895,65039,65040,65042],{},[898,65041,1983],{},[898,65043,1658],{},[902,65045,59306],{"encoding":904},[883,65047,65049],{"className":65048},[886],[888,65050,65051],{"xmlns":890},[892,65052,65053,65061],{},[895,65054,65055,65057,65059],{},[898,65056,1802],{},[1701,65058,3782],{},[1850,65060,64957],{},[902,65062,65063],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,65066,65067],{},[2139,65068],{"alt":65069,"className":65070,"src":65071},"imek-ac-avc-mc",[210,2143],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,65073,65074],{},[614,65075,65076,65077,2633,65092,65109,65110,19842,65129,65144],{},"Obrázek 3.9: Kubické křivky ",[883,65078,65080],{"className":65079},[886],[888,65081,65082],{"xmlns":890},[892,65083,65084,65090],{},[895,65085,65086,65088],{},[898,65087,5877],{},[898,65089,1658],{},[902,65091,7326],{"encoding":904},[883,65093,65095],{"className":65094},[886],[888,65096,65097],{"xmlns":890},[892,65098,65099,65107],{},[895,65100,65101,65103,65105],{},[898,65102,5877],{},[898,65104,44362],{},[898,65106,1658],{},[902,65108,59255],{"encoding":904}," rostoucí od bodu ",[883,65111,65113],{"className":65112},[886],[888,65114,65115],{"xmlns":890},[892,65116,65117,65127],{},[895,65118,65119,65121,65123,65125],{},[898,65120,14492],{},[898,65122,1658],{},[1701,65124,1792],{},[1850,65126,5158],{},[902,65128,15689],{"encoding":904},[883,65130,65132],{"className":65131},[886],[888,65133,65134],{"xmlns":890},[892,65135,65136,65142],{},[895,65137,65138,65140],{},[898,65139,14492],{},[898,65141,1658],{},[902,65143,59237],{"encoding":904}," je vodorovná přímka.",[724,65146,65147],{},[614,65148,65149,65150,1343,65165,1343,65182,33234,65197,65210,65211,7015,65228,65243,65244,10253,65261,65276,65277,30226,65290,1343,65303,1343,65316,1715],{},"Obrázek 3.10: Křivky ",[883,65151,65153],{"className":65152},[886],[888,65154,65155],{"xmlns":890},[892,65156,65157,65163],{},[895,65158,65159,65161],{},[898,65160,1983],{},[898,65162,1658],{},[902,65164,59306],{"encoding":904},[883,65166,65168],{"className":65167},[886],[888,65169,65170],{"xmlns":890},[892,65171,65172,65180],{},[895,65173,65174,65176,65178],{},[898,65175,1983],{},[898,65177,44362],{},[898,65179,1658],{},[902,65181,59057],{"encoding":904},[883,65183,65185],{"className":65184},[886],[888,65186,65187],{"xmlns":890},[892,65188,65189,65195],{},[895,65190,65191,65193],{},[898,65192,6909],{},[898,65194,1658],{},[902,65196,59038],{"encoding":904},[883,65198,65200],{"className":65199},[886],[888,65201,65202],{"xmlns":890},[892,65203,65204,65208],{},[895,65205,65206],{},[898,65207,900],{},[902,65209,900],{"encoding":904}," a klesající hyperbola ",[883,65212,65214],{"className":65213},[886],[888,65215,65216],{"xmlns":890},[892,65217,65218,65226],{},[895,65219,65220,65222,65224],{},[898,65221,1983],{},[898,65223,14492],{},[898,65225,1658],{},[902,65227,59273],{"encoding":904},[883,65229,65231],{"className":65230},[886],[888,65232,65233],{"xmlns":890},[892,65234,65235,65241],{},[895,65236,65237,65239],{},[898,65238,6909],{},[898,65240,1658],{},[902,65242,59038],{"encoding":904}," protíná ",[883,65245,65247],{"className":65246},[886],[888,65248,65249],{"xmlns":890},[892,65250,65251,65259],{},[895,65252,65253,65255,65257],{},[898,65254,1983],{},[898,65256,44362],{},[898,65258,1658],{},[902,65260,59057],{"encoding":904},[883,65262,65264],{"className":65263},[886],[888,65265,65266],{"xmlns":890},[892,65267,65268,65274],{},[895,65269,65270,65272],{},[898,65271,1983],{},[898,65273,1658],{},[902,65275,59306],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,65278,65280],{"className":65279},[886],[888,65281,65282],{"xmlns":890},[892,65283,65284,65288],{},[895,65285,65286],{},[898,65287,1802],{},[902,65289,1802],{"encoding":904},[883,65291,65293],{"className":65292},[886],[888,65294,65295],{"xmlns":890},[892,65296,65297,65301],{},[895,65298,65299],{},[1850,65300,64927],{},[902,65302,64930],{"encoding":904},[883,65304,65306],{"className":65305},[886],[888,65307,65308],{"xmlns":890},[892,65309,65310,65314],{},[895,65311,65312],{},[1850,65313,64942],{},[902,65315,64945],{"encoding":904},[883,65317,65319],{"className":65318},[886],[888,65320,65321],{"xmlns":890},[892,65322,65323,65327],{},[895,65324,65325],{},[1850,65326,64957],{},[902,65328,64960],{"encoding":904},[724,65330,65331],{},[38,65332,65333],{},"Standardní vlastnosti:",[120,65335,65336,65371,65435,65503,65553,65573],{},[123,65337,65338,2633,65353,65370],{},[883,65339,65341],{"className":65340},[886],[888,65342,65343],{"xmlns":890},[892,65344,65345,65351],{},[895,65346,65347,65349],{},[898,65348,5877],{},[898,65350,1658],{},[902,65352,7326],{"encoding":904},[883,65354,65356],{"className":65355},[886],[888,65357,65358],{"xmlns":890},[892,65359,65360,65368],{},[895,65361,65362,65364,65366],{},[898,65363,5877],{},[898,65365,44362],{},[898,65367,1658],{},[902,65369,59255],{"encoding":904}," jsou kubické funkce;",[123,65372,65373,1343,65388,1343,65405,65420,65421,65434],{},[883,65374,65376],{"className":65375},[886],[888,65377,65378],{"xmlns":890},[892,65379,65380,65386],{},[895,65381,65382,65384],{},[898,65383,1983],{},[898,65385,1658],{},[902,65387,59306],{"encoding":904},[883,65389,65391],{"className":65390},[886],[888,65392,65393],{"xmlns":890},[892,65394,65395,65403],{},[895,65396,65397,65399,65401],{},[898,65398,1983],{},[898,65400,44362],{},[898,65402,1658],{},[902,65404,59057],{"encoding":904},[883,65406,65408],{"className":65407},[886],[888,65409,65410],{"xmlns":890},[892,65411,65412,65418],{},[895,65413,65414,65416],{},[898,65415,6909],{},[898,65417,1658],{},[902,65419,59038],{"encoding":904}," jsou křivky tvaru ",[883,65422,65424],{"className":65423},[886],[888,65425,65426],{"xmlns":890},[892,65427,65428,65432],{},[895,65429,65430],{},[898,65431,900],{},[902,65433,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,65436,65437,65452,65453,1343,65470,65487,65488,12487],{},[883,65438,65440],{"className":65439},[886],[888,65441,65442],{"xmlns":890},[892,65443,65444,65450],{},[895,65445,65446,65448],{},[898,65447,6909],{},[898,65449,1658],{},[902,65451,59038],{"encoding":904}," nabývá minima před ",[883,65454,65456],{"className":65455},[886],[888,65457,65458],{"xmlns":890},[892,65459,65460,65468],{},[895,65461,65462,65464,65466],{},[898,65463,1983],{},[898,65465,44362],{},[898,65467,1658],{},[902,65469,59057],{"encoding":904},[883,65471,65473],{"className":65472},[886],[888,65474,65475],{"xmlns":890},[892,65476,65477,65485],{},[895,65478,65479,65481,65483],{},[898,65480,1983],{},[898,65482,44362],{},[898,65484,1658],{},[902,65486,59057],{"encoding":904}," před ",[883,65489,65491],{"className":65490},[886],[888,65492,65493],{"xmlns":890},[892,65494,65495,65501],{},[895,65496,65497,65499],{},[898,65498,1983],{},[898,65500,1658],{},[902,65502,59306],{"encoding":904},[123,65504,65505,65243,65520,2633,65535,65552],{},[883,65506,65508],{"className":65507},[886],[888,65509,65510],{"xmlns":890},[892,65511,65512,65518],{},[895,65513,65514,65516],{},[898,65515,6909],{},[898,65517,1658],{},[902,65519,59038],{"encoding":904},[883,65521,65523],{"className":65522},[886],[888,65524,65525],{"xmlns":890},[892,65526,65527,65533],{},[895,65528,65529,65531],{},[898,65530,1983],{},[898,65532,1658],{},[902,65534,59306],{"encoding":904},[883,65536,65538],{"className":65537},[886],[888,65539,65540],{"xmlns":890},[892,65541,65542,65550],{},[895,65543,65544,65546,65548],{},[898,65545,1983],{},[898,65547,44362],{},[898,65549,1658],{},[902,65551,59057],{"encoding":904}," zdola právě v jejich minimech;",[123,65554,65555,65572],{},[883,65556,65558],{"className":65557},[886],[888,65559,65560],{"xmlns":890},[892,65561,65562,65570],{},[895,65563,65564,65566,65568],{},[898,65565,1983],{},[898,65567,14492],{},[898,65569,1658],{},[902,65571,59273],{"encoding":904}," je hyperbola, stále klesající;",[123,65574,65575,65607,65608,2633,65623,65640,65641,65654,65655,2506],{},[883,65576,65578],{"className":65577},[886],[888,65579,65580],{"xmlns":890},[892,65581,65582,65604],{},[895,65583,65584,65586,65588,65590,65592,65594,65596,65598,65600,65602],{},[898,65585,1983],{},[898,65587,1658],{},[1701,65589,1792],{},[898,65591,1983],{},[898,65593,14492],{},[898,65595,1658],{},[1701,65597,1703],{},[898,65599,1983],{},[898,65601,44362],{},[898,65603,1658],{},[902,65605,65606],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,65609,65611],{"className":65610},[886],[888,65612,65613],{"xmlns":890},[892,65614,65615,65621],{},[895,65616,65617,65619],{},[898,65618,1983],{},[898,65620,1658],{},[902,65622,59306],{"encoding":904},[883,65624,65626],{"className":65625},[886],[888,65627,65628],{"xmlns":890},[892,65629,65630,65638],{},[895,65631,65632,65634,65636],{},[898,65633,1983],{},[898,65635,44362],{},[898,65637,1658],{},[902,65639,59057],{"encoding":904}," klesá s rostoucím ",[883,65642,65644],{"className":65643},[886],[888,65645,65646],{"xmlns":890},[892,65647,65648,65652],{},[895,65649,65650],{},[898,65651,1802],{},[902,65653,1802],{"encoding":904}," (protože ",[883,65656,65658],{"className":65657},[886],[888,65659,65660],{"xmlns":890},[892,65661,65662,65674],{},[895,65663,65664,65666,65668,65670,65672],{},[898,65665,1983],{},[898,65667,14492],{},[898,65669,1658],{},[1701,65671,4108],{},[1850,65673,1852],{},[902,65675,65676],{"encoding":904},"AFC \\to 0",[115,65678,65680],{"id":65679},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,65682,65683,65684,65687,65688,65703],{},"Častou optimalizační úlohou je ",[38,65685,65686],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,65689,65691],{"className":65690},[886],[888,65692,65693],{"xmlns":890},[892,65694,65695,65701],{},[895,65696,65697,65699],{},[898,65698,1983],{},[898,65700,1658],{},[902,65702,59306],{"encoding":904}," minimální.",[198,65705,20458],{"id":20457},[724,65707,65708,65709,65726],{},"Mají-li průměrné náklady minimum v bodě ",[883,65710,65712],{"className":65711},[886],[888,65713,65714],{"xmlns":890},[892,65715,65716,65724],{},[895,65717,65718],{},[1845,65719,65720,65722],{},[898,65721,1802],{},[1850,65723,1852],{},[902,65725,1855],{"encoding":904},", pak platí",[883,65728,65730],{"className":65729},[886],[888,65731,65732],{"xmlns":890,"display":2252},[892,65733,65734,65783],{},[2256,65735,65736],{"width":2258},[2260,65737,65738,65740,65776,65778],{},[2263,65739],{"width":2265},[2263,65741,65742],{},[895,65743,65744,65746,65748,65750,65756,65758,65760,65762,65764,65766,65772,65774],{},[898,65745,1983],{},[898,65747,1658],{},[1701,65749,1799],{"stretchy":1798},[1845,65751,65752,65754],{},[898,65753,1802],{},[1850,65755,1852],{},[1701,65757,1805],{"stretchy":1798},[1701,65759,1792],{},[898,65761,6909],{},[898,65763,1658],{},[1701,65765,1799],{"stretchy":1798},[1845,65767,65768,65770],{},[898,65769,1802],{},[1850,65771,1852],{},[1701,65773,1805],{"stretchy":1798},[898,65775,1715],{"mathvariant":2334},[2263,65777],{"width":2265},[2263,65779,65780],{},[1939,65781,65782],{},"(3.10)",[902,65784,65785],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1635,65787,65788],{},[724,65789,65790,65792,65793],{},[883,65791,60190],{}," Princip\n",[38,65794,65795],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,65797,65798,65801,65802,65844],{},[38,65799,65800],{},"Odvození."," Z ",[883,65803,65805],{"className":65804},[886],[888,65806,65807],{"xmlns":890},[892,65808,65809,65841],{},[895,65810,65811,65813,65815,65817,65819,65821,65823],{},[898,65812,1983],{},[898,65814,1658],{},[1701,65816,1799],{"stretchy":1798},[898,65818,1802],{},[1701,65820,1805],{"stretchy":1798},[1701,65822,1792],{},[2363,65824,65825],{"scriptlevel":1852,"displaystyle":1798},[3726,65826,65827,65839],{},[895,65828,65829,65831,65833,65835,65837],{},[898,65830,5877],{},[898,65832,1658],{},[1701,65834,1799],{"stretchy":1798},[898,65836,1802],{},[1701,65838,1805],{"stretchy":1798},[898,65840,1802],{},[902,65842,65843],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,65846,65848],{"className":65847},[886],[888,65849,65850],{"xmlns":890,"display":2252},[892,65851,65852,65984],{},[895,65853,65854,65856,65862,65864,65866,65868,65870,65910,65912,65952,65954,65982],{},[898,65855,1983],{},[3243,65857,65858,65860],{},[898,65859,1658],{},[1701,65861,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,65863,1799],{"stretchy":1798},[898,65865,1802],{},[1701,65867,1805],{"stretchy":1798},[1701,65869,1792],{},[3726,65871,65872,65904],{},[895,65873,65874,65876,65882,65884,65886,65888,65890,65892,65894,65896,65898,65900,65902],{},[898,65875,5877],{},[3243,65877,65878,65880],{},[898,65879,1658],{},[1701,65881,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,65883,1799],{"stretchy":1798},[898,65885,1802],{},[1701,65887,1805],{"stretchy":1798},[1701,65889,3408],{},[898,65891,1802],{},[1701,65893,2317],{},[898,65895,5877],{},[898,65897,1658],{},[1701,65899,1799],{"stretchy":1798},[898,65901,1802],{},[1701,65903,1805],{"stretchy":1798},[3243,65905,65906,65908],{},[898,65907,1802],{},[1850,65909,3938],{},[1701,65911,1792],{},[3726,65913,65914,65946],{},[895,65915,65916,65918,65920,65922,65924,65926,65928,65930,65932,65934,65936,65938,65940,65942,65944],{},[898,65917,6909],{},[898,65919,1658],{},[1701,65921,1799],{"stretchy":1798},[898,65923,1802],{},[1701,65925,1805],{"stretchy":1798},[1701,65927,3408],{},[898,65929,1802],{},[1701,65931,2317],{},[898,65933,1983],{},[898,65935,1658],{},[1701,65937,1799],{"stretchy":1798},[898,65939,1802],{},[1701,65941,1805],{"stretchy":1798},[1701,65943,3408],{},[898,65945,1802],{},[3243,65947,65948,65950],{},[898,65949,1802],{},[1850,65951,3938],{},[1701,65953,1792],{},[3726,65955,65956,65980],{},[895,65957,65958,65960,65962,65964,65966,65968,65970,65972,65974,65976,65978],{},[898,65959,6909],{},[898,65961,1658],{},[1701,65963,1799],{"stretchy":1798},[898,65965,1802],{},[1701,65967,1805],{"stretchy":1798},[1701,65969,2317],{},[898,65971,1983],{},[898,65973,1658],{},[1701,65975,1799],{"stretchy":1798},[898,65977,1802],{},[1701,65979,1805],{"stretchy":1798},[898,65981,1802],{},[898,65983,1715],{"mathvariant":2334},[902,65985,65986],{"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}.",[724,65988,65989,65990,6723,66005,12164,66027,60567],{},"Nutnou podmínkou minima ",[883,65991,65993],{"className":65992},[886],[888,65994,65995],{"xmlns":890},[892,65996,65997,66003],{},[895,65998,65999,66001],{},[898,66000,1983],{},[898,66002,1658],{},[902,66004,59306],{"encoding":904},[883,66006,66008],{"className":66007},[886],[888,66009,66010],{"xmlns":890},[892,66011,66012,66024],{},[895,66013,66014,66020,66022],{},[1845,66015,66016,66018],{},[898,66017,1802],{},[1850,66019,1852],{},[1701,66021,7491],{},[1850,66023,1852],{},[902,66025,66026],{"encoding":904},"Q_0 > 0",[883,66028,66030],{"className":66029},[886],[888,66031,66032],{"xmlns":890},[892,66033,66034,66058],{},[895,66035,66036,66038,66044,66046,66052,66054,66056],{},[898,66037,1983],{},[3243,66039,66040,66042],{},[898,66041,1658],{},[1701,66043,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,66045,1799],{"stretchy":1798},[1845,66047,66048,66050],{},[898,66049,1802],{},[1850,66051,1852],{},[1701,66053,1805],{"stretchy":1798},[1701,66055,1792],{},[1850,66057,1852],{},[902,66059,66060],{"encoding":904},"AC'(Q_0) = 0",[883,66062,66064],{"className":66063},[886],[888,66065,66066],{"xmlns":890,"display":2252},[892,66067,66068,66153],{},[895,66069,66070,66110,66112,66114,66116,66119,66121,66123,66125,66127,66133,66135,66137,66139,66141,66143,66149,66151],{},[3726,66071,66072,66104],{},[895,66073,66074,66076,66078,66080,66086,66088,66090,66092,66094,66096,66102],{},[898,66075,6909],{},[898,66077,1658],{},[1701,66079,1799],{"stretchy":1798},[1845,66081,66082,66084],{},[898,66083,1802],{},[1850,66085,1852],{},[1701,66087,1805],{"stretchy":1798},[1701,66089,2317],{},[898,66091,1983],{},[898,66093,1658],{},[1701,66095,1799],{"stretchy":1798},[1845,66097,66098,66100],{},[898,66099,1802],{},[1850,66101,1852],{},[1701,66103,1805],{"stretchy":1798},[1845,66105,66106,66108],{},[898,66107,1802],{},[1850,66109,1852],{},[1701,66111,1792],{},[1850,66113,1852],{},[9942,66115],{"width":19336},[1701,66117,66118],{},"⟺",[9942,66120],{"width":19336},[898,66122,6909],{},[898,66124,1658],{},[1701,66126,1799],{"stretchy":1798},[1845,66128,66129,66131],{},[898,66130,1802],{},[1850,66132,1852],{},[1701,66134,1805],{"stretchy":1798},[1701,66136,1792],{},[898,66138,1983],{},[898,66140,1658],{},[1701,66142,1799],{"stretchy":1798},[1845,66144,66145,66147],{},[898,66146,1802],{},[1850,66148,1852],{},[1701,66150,1805],{"stretchy":1798},[898,66152,1715],{"mathvariant":2334},[902,66154,66155],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,66157,66158,4088,66161,65243,66176,66191,66192,66207,66208,12164,66225,66247,66248,66270],{},[38,66159,66160],{},"Geometrická interpretace.",[883,66162,66164],{"className":66163},[886],[888,66165,66166],{"xmlns":890},[892,66167,66168,66174],{},[895,66169,66170,66172],{},[898,66171,6909],{},[898,66173,1658],{},[902,66175,59038],{"encoding":904},[883,66177,66179],{"className":66178},[886],[888,66180,66181],{"xmlns":890},[892,66182,66183,66189],{},[895,66184,66185,66187],{},[898,66186,1983],{},[898,66188,1658],{},[902,66190,59306],{"encoding":904}," právě v bodě minima ",[883,66193,66195],{"className":66194},[886],[888,66196,66197],{"xmlns":890},[892,66198,66199,66205],{},[895,66200,66201,66203],{},[898,66202,1983],{},[898,66204,1658],{},[902,66206,59306],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,66209,66211],{"className":66210},[886],[888,66212,66213],{"xmlns":890},[892,66214,66215,66223],{},[895,66216,66217],{},[1845,66218,66219,66221],{},[898,66220,1802],{},[1850,66222,1852],{},[902,66224,1855],{"encoding":904},[883,66226,66228],{"className":66227},[886],[888,66229,66230],{"xmlns":890},[892,66231,66232,66244],{},[895,66233,66234,66236,66238,66240,66242],{},[898,66235,6909],{},[898,66237,1658],{},[1701,66239,7530],{},[898,66241,1983],{},[898,66243,1658],{},[902,66245,66246],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,66249,66251],{"className":66250},[886],[888,66252,66253],{"xmlns":890},[892,66254,66255,66267],{},[895,66256,66257,66259,66261,66263,66265],{},[898,66258,6909],{},[898,66260,1658],{},[1701,66262,7491],{},[898,66264,1983],{},[898,66266,1658],{},[902,66268,66269],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,66272,66273,66274,66316,66317,66334,66335,1715],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,66275,66277],{"className":66276},[886],[888,66278,66279],{"xmlns":890},[892,66280,66281,66313],{},[895,66282,66283,66285,66287,66289,66295,66297,66299,66301,66303,66305,66311],{},[898,66284,1983],{},[898,66286,1658],{},[1701,66288,1799],{"stretchy":1798},[1845,66290,66291,66293],{},[898,66292,1802],{},[1850,66294,1852],{},[1701,66296,1805],{"stretchy":1798},[1701,66298,1792],{},[898,66300,6909],{},[898,66302,1658],{},[1701,66304,1799],{"stretchy":1798},[1845,66306,66307,66309],{},[898,66308,1802],{},[1850,66310,1852],{},[1701,66312,1805],{"stretchy":1798},[902,66314,66315],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,66318,66320],{"className":66319},[886],[888,66321,66322],{"xmlns":890},[892,66323,66324,66332],{},[895,66325,66326],{},[1845,66327,66328,66330],{},[898,66329,1802],{},[1850,66331,1852],{},[902,66333,1855],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,66336,66338],{"className":66337},[886],[888,66339,66340],{"xmlns":890},[892,66341,66342,66366],{},[895,66343,66344,66346,66348,66350,66352,66354,66356,66358,66360,66362,66364],{},[898,66345,1983],{},[898,66347,1658],{},[1701,66349,1799],{"stretchy":1798},[898,66351,1802],{},[1701,66353,1805],{"stretchy":1798},[1701,66355,1792],{},[898,66357,6909],{},[898,66359,1658],{},[1701,66361,1799],{"stretchy":1798},[898,66363,1802],{},[1701,66365,1805],{"stretchy":1798},[902,66367,66368],{"encoding":904},"AC(Q) = MC(Q)",[1635,66370,66371],{},[724,66372,66373,66375,66376,14450,66394,66415,66416,14450,66419,66440,66441,66456,66457,61784,66472,2506],{},[883,66374,4695],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,66377,66378,66379],{},"minimum ",[883,66380,66382],{"className":66381},[886],[888,66383,66384],{"xmlns":890},[892,66385,66386,66392],{},[895,66387,66388,66390],{},[898,66389,1983],{},[898,66391,1658],{},[902,66393,59306],{"encoding":904},[883,66395,66397],{"className":66396},[886],[888,66398,66399],{"xmlns":890},[892,66400,66401,66413],{},[895,66402,66403,66405,66407,66409,66411],{},[898,66404,1983],{},[898,66406,1658],{},[1701,66408,1792],{},[898,66410,6909],{},[898,66412,1658],{},[902,66414,58969],{"encoding":904},", pro ",[38,66417,66418],{},"maximum zisku",[883,66420,66422],{"className":66421},[886],[888,66423,66424],{"xmlns":890},[892,66425,66426,66438],{},[895,66427,66428,66430,66432,66434,66436],{},[898,66429,6909],{},[898,66431,8068],{},[1701,66433,1792],{},[898,66435,6909],{},[898,66437,1658],{},[902,66439,59017],{"encoding":904},". Obě podmínky využívají ",[883,66442,66444],{"className":66443},[886],[888,66445,66446],{"xmlns":890},[892,66447,66448,66454],{},[895,66449,66450,66452],{},[898,66451,6909],{},[898,66453,1658],{},[902,66455,59038],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,66458,66460],{"className":66459},[886],[888,66461,66462],{"xmlns":890},[892,66463,66464,66470],{},[895,66465,66466,66468],{},[898,66467,1983],{},[898,66469,1658],{},[902,66471,59306],{"encoding":904},[883,66473,66475],{"className":66474},[886],[888,66476,66477],{"xmlns":890},[892,66478,66479,66485],{},[895,66480,66481,66483],{},[898,66482,6909],{},[898,66484,8068],{},[902,66486,10697],{"encoding":904},[41376,66488,66490],{"id":66489},"příklad-37","Příklad 3.7",[724,66492,66493,61268,66495,66529,66530,66543,66544,66559],{},[38,66494,59733],{},[883,66496,66498],{"className":66497},[886],[888,66499,66500],{"xmlns":890},[892,66501,66502,66526],{},[895,66503,66504,66506,66508,66510,66516,66518,66520,66522,66524],{},[898,66505,5877],{},[898,66507,1658],{},[1701,66509,1792],{},[3243,66511,66512,66514],{},[898,66513,1802],{},[1850,66515,3938],{},[1701,66517,1703],{},[1850,66519,3646],{},[898,66521,1802],{},[1701,66523,1703],{},[1850,66525,9630],{},[902,66527,66528],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,66531,66533],{"className":66532},[886],[888,66534,66535],{"xmlns":890},[892,66536,66537,66541],{},[895,66538,66539],{},[898,66540,1802],{},[902,66542,1802],{"encoding":904}," minimalizující ",[883,66545,66547],{"className":66546},[886],[888,66548,66549],{"xmlns":890},[892,66550,66551,66557],{},[895,66552,66553,66555],{},[898,66554,1983],{},[898,66556,1658],{},[902,66558,59306],{"encoding":904}," a ověřte princip (3.10).",[724,66561,66562,66564],{},[38,66563,5001],{}," Přímý výpočet:",[883,66566,66568],{"className":66567},[886],[888,66569,66570],{"xmlns":890,"display":2252},[892,66571,66572,66674],{},[895,66573,66574,66576,66578,66580,66602,66604,66606,66608,66610,66612,66618,66620,66622,66624,66626,66628,66634,66636,66638,66640,66650,66652,66672],{},[898,66575,1983],{},[898,66577,1658],{},[1701,66579,1792],{},[3726,66581,66582,66600],{},[895,66583,66584,66590,66592,66594,66596,66598],{},[3243,66585,66586,66588],{},[898,66587,1802],{},[1850,66589,3938],{},[1701,66591,1703],{},[1850,66593,3646],{},[898,66595,1802],{},[1701,66597,1703],{},[1850,66599,9630],{},[898,66601,1802],{},[1701,66603,1792],{},[898,66605,1802],{},[1701,66607,1703],{},[1850,66609,3646],{},[1701,66611,1703],{},[3726,66613,66614,66616],{},[1850,66615,9630],{},[898,66617,1802],{},[1701,66619,2012],{"separator":2011},[9942,66621],{"width":9944},[1701,66623,1799],{"stretchy":1798},[898,66625,1983],{},[898,66627,1658],{},[3243,66629,66630,66632],{},[1701,66631,1805],{"stretchy":1798},[1701,66633,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,66635,1792],{},[1850,66637,4062],{},[1701,66639,2317],{},[3726,66641,66642,66644],{},[1850,66643,9630],{},[3243,66645,66646,66648],{},[898,66647,1802],{},[1850,66649,3938],{},[1701,66651,1792],{},[3726,66653,66654,66666],{},[895,66655,66656,66662,66664],{},[3243,66657,66658,66660],{},[898,66659,1802],{},[1850,66661,3938],{},[1701,66663,2317],{},[1850,66665,9630],{},[3243,66667,66668,66670],{},[898,66669,1802],{},[1850,66671,3938],{},[898,66673,1715],{"mathvariant":2334},[902,66675,66676],{"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}.",[724,66678,66679,66719,66720,66744,66745,66795,66796,1715],{},[883,66680,66682],{"className":66681},[886],[888,66683,66684],{"xmlns":890},[892,66685,66686,66716],{},[895,66687,66688,66690,66692,66694,66700,66702,66704,66706,66712,66714],{},[1701,66689,1799],{"stretchy":1798},[898,66691,1983],{},[898,66693,1658],{},[3243,66695,66696,66698],{},[1701,66697,1805],{"stretchy":1798},[1701,66699,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,66701,1792],{},[1850,66703,1852],{},[1701,66705,8061],{},[1845,66707,66708,66710],{},[898,66709,1802],{},[1850,66711,4062],{},[1701,66713,1792],{},[1850,66715,6352],{},[902,66717,66718],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,66721,66723],{"className":66722},[886],[888,66724,66725],{"xmlns":890},[892,66726,66727,66741],{},[895,66728,66729,66735,66737,66739],{},[1845,66730,66731,66733],{},[898,66732,1802],{},[1850,66734,3938],{},[1701,66736,1792],{},[1701,66738,2317],{},[1850,66740,6352],{},[902,66742,66743],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,66746,66748],{"className":66747},[886],[888,66749,66750],{"xmlns":890},[892,66751,66752,66792],{},[895,66753,66754,66756,66758,66760,66770,66772,66774,66776,66778,66786,66788,66790],{},[1701,66755,1799],{"stretchy":1798},[898,66757,1983],{},[898,66759,1658],{},[3243,66761,66762,66764],{},[1701,66763,1805],{"stretchy":1798},[895,66765,66766,66768],{},[1701,66767,4783],{"mathvariant":2334},[1701,66769,4783],{"mathvariant":2334},[1701,66771,1799],{"stretchy":1798},[1850,66773,6352],{},[1701,66775,1805],{"stretchy":1798},[1701,66777,1792],{},[2363,66779,66780],{"scriptlevel":1852,"displaystyle":1798},[3726,66781,66782,66784],{},[1850,66783,4062],{},[1850,66785,3646],{},[1701,66787,7491],{},[1850,66789,1852],{},[1701,66791,8061],{},[902,66793,66794],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,66797,66799],{"className":66798},[886],[888,66800,66801],{"xmlns":890},[892,66802,66803,66819],{},[895,66804,66805,66807,66809,66811,66813,66815,66817],{},[898,66806,1983],{},[898,66808,1658],{},[1701,66810,1799],{"stretchy":1798},[1850,66812,6352],{},[1701,66814,1805],{"stretchy":1798},[1701,66816,1792],{},[1850,66818,40275],{},[902,66820,66821],{"encoding":904},"AC(6) = 15",[724,66823,66824,66825,66851,66852,2246],{},"Pomocí principu: ",[883,66826,66828],{"className":66827},[886],[888,66829,66830],{"xmlns":890},[892,66831,66832,66848],{},[895,66833,66834,66836,66838,66840,66842,66844,66846],{},[898,66835,6909],{},[898,66837,1658],{},[1701,66839,1792],{},[1850,66841,3938],{},[898,66843,1802],{},[1701,66845,1703],{},[1850,66847,3646],{},[902,66849,66850],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,66853,66855],{"className":66854},[886],[888,66856,66857],{"xmlns":890},[892,66858,66859,66871],{},[895,66860,66861,66863,66865,66867,66869],{},[898,66862,1983],{},[898,66864,1658],{},[1701,66866,1792],{},[898,66868,6909],{},[898,66870,1658],{},[902,66872,58969],{"encoding":904},[883,66874,66876],{"className":66875},[886],[888,66877,66878],{"xmlns":890,"display":2252},[892,66879,66880,66982],{},[895,66881,66882,66904,66906,66908,66910,66912,66914,66916,66918,66920,66926,66928,66930,66932,66934,66936,66938,66940,66946,66948,66950,66952,66954,66956,66958,66964,66966,66968,66970,66972,66974,66976,66978,66980],{},[3726,66883,66884,66902],{},[895,66885,66886,66892,66894,66896,66898,66900],{},[3243,66887,66888,66890],{},[898,66889,1802],{},[1850,66891,3938],{},[1701,66893,1703],{},[1850,66895,3646],{},[898,66897,1802],{},[1701,66899,1703],{},[1850,66901,9630],{},[898,66903,1802],{},[1701,66905,1792],{},[1850,66907,3938],{},[898,66909,1802],{},[1701,66911,1703],{},[1850,66913,3646],{},[1939,66915,8058],{},[1701,66917,8061],{},[1939,66919,8058],{},[3243,66921,66922,66924],{},[898,66923,1802],{},[1850,66925,3938],{},[1701,66927,1703],{},[1850,66929,3646],{},[898,66931,1802],{},[1701,66933,1703],{},[1850,66935,9630],{},[1701,66937,1792],{},[1850,66939,3938],{},[3243,66941,66942,66944],{},[898,66943,1802],{},[1850,66945,3938],{},[1701,66947,1703],{},[1850,66949,3646],{},[898,66951,1802],{},[1939,66953,8058],{},[1701,66955,8061],{},[1939,66957,8058],{},[3243,66959,66960,66962],{},[898,66961,1802],{},[1850,66963,3938],{},[1701,66965,1792],{},[1850,66967,9630],{},[1939,66969,8058],{},[1701,66971,8061],{},[1939,66973,8058],{},[898,66975,1802],{},[1701,66977,1792],{},[1850,66979,6352],{},[1701,66981,2012],{"separator":2011},[902,66983,66984],{"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,",[724,66986,66987,66988,67026],{},"a ",[883,66989,66991],{"className":66990},[886],[888,66992,66993],{"xmlns":890},[892,66994,66995,67023],{},[895,66996,66997,66999,67001,67003,67005,67007,67009,67011,67013,67015,67017,67019,67021],{},[898,66998,1983],{},[898,67000,1658],{},[1701,67002,1799],{"stretchy":1798},[1850,67004,6352],{},[1701,67006,1805],{"stretchy":1798},[1701,67008,1792],{},[898,67010,6909],{},[898,67012,1658],{},[1701,67014,1799],{"stretchy":1798},[1850,67016,6352],{},[1701,67018,1805],{"stretchy":1798},[1701,67020,1792],{},[1850,67022,40275],{},[902,67024,67025],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,67028,67030],{"id":67029},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,67032,67033,67034,2246],{},"Analogicky pro ",[883,67035,67037],{"className":67036},[886],[888,67038,67039],{"xmlns":890},[892,67040,67041,67049],{},[895,67042,67043,67045,67047],{},[898,67044,1983],{},[898,67046,44362],{},[898,67048,1658],{},[902,67050,59057],{"encoding":904},[883,67052,67054],{"className":67053},[886],[888,67055,67056],{"xmlns":890,"display":2252},[892,67057,67058,67109],{},[2256,67059,67060],{"width":2258},[2260,67061,67062,67064,67102,67104],{},[2263,67063],{"width":2265},[2263,67065,67066],{},[895,67067,67068,67070,67072,67074,67076,67082,67084,67086,67088,67090,67092,67098,67100],{},[898,67069,1983],{},[898,67071,44362],{},[898,67073,1658],{},[1701,67075,1799],{"stretchy":1798},[1845,67077,67078,67080],{},[898,67079,1802],{},[1850,67081,1852],{},[1701,67083,1805],{"stretchy":1798},[1701,67085,1792],{},[898,67087,6909],{},[898,67089,1658],{},[1701,67091,1799],{"stretchy":1798},[1845,67093,67094,67096],{},[898,67095,1802],{},[1850,67097,1852],{},[1701,67099,1805],{"stretchy":1798},[898,67101,1715],{"mathvariant":2334},[2263,67103],{"width":2265},[2263,67105,67106],{},[1939,67107,67108],{},"(3.11)",[902,67110,67111],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1635,67113,67114],{},[724,67115,67116,65792,67118],{},[883,67117,60190],{},[38,67119,67120,67121,67138],{},"V bodě minima průměrných variabilních nákladů se ",[883,67122,67124],{"className":67123},[886],[888,67125,67126],{"xmlns":890},[892,67127,67128,67136],{},[895,67129,67130,67132,67134],{},[898,67131,1983],{},[898,67133,44362],{},[898,67135,1658],{},[902,67137,59057],{"encoding":904}," rovnají mezním nákladům.",[724,67140,67141,67142,67164,67165,1715],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,67143,67145],{"className":67144},[886],[888,67146,67147],{"xmlns":890},[892,67148,67149,67161],{},[895,67150,67151,67157,67159],{},[1845,67152,67153,67155],{},[898,67154,1802],{},[1850,67156,1852],{},[1701,67158,1792],{},[1850,67160,4113],{},[902,67162,67163],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,67166,67168],{"className":67167},[886],[888,67169,67170],{"xmlns":890},[892,67171,67172,67198],{},[895,67173,67174,67176,67178,67180,67182,67184,67186,67188,67190,67192,67194,67196],{},[898,67175,1983],{},[898,67177,44362],{},[898,67179,1658],{},[1701,67181,1799],{"stretchy":1798},[898,67183,1802],{},[1701,67185,1805],{"stretchy":1798},[1701,67187,1792],{},[898,67189,6909],{},[898,67191,1658],{},[1701,67193,1799],{"stretchy":1798},[898,67195,1802],{},[1701,67197,1805],{"stretchy":1798},[902,67199,67200],{"encoding":904},"AVC(Q) = MC(Q)",[115,67202,67204],{"id":67203},"zisk-a-body-zvratu","Zisk a body zvratu",[724,67206,67207,4088,67210,67226],{},[38,67208,67209],{},"Zisk",[883,67211,67213],{"className":67212},[886],[888,67214,67215],{"xmlns":890},[892,67216,67217,67223],{},[895,67218,67219,67221],{},[898,67220,1680],{},[898,67222,8068],{},[902,67224,67225],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,67228,67230],{"className":67229},[886],[888,67231,67232],{"xmlns":890,"display":2252},[892,67233,67234,67293],{},[2256,67235,67236],{"width":2258},[2260,67237,67238,67240,67286,67288],{},[2263,67239],{"width":2265},[2263,67241,67242],{},[895,67243,67244,67246,67248,67250,67252,67254,67256,67258,67260,67262,67264,67266,67268,67270,67272,67274,67276,67278,67280,67282,67284],{},[898,67245,1680],{},[898,67247,8068],{},[1701,67249,1792],{},[898,67251,1680],{},[898,67253,8068],{},[1701,67255,1799],{"stretchy":1798},[898,67257,1802],{},[1701,67259,1805],{"stretchy":1798},[1701,67261,1792],{},[898,67263,5877],{},[898,67265,8068],{},[1701,67267,1799],{"stretchy":1798},[898,67269,1802],{},[1701,67271,1805],{"stretchy":1798},[1701,67273,2317],{},[898,67275,5877],{},[898,67277,1658],{},[1701,67279,1799],{"stretchy":1798},[898,67281,1802],{},[1701,67283,1805],{"stretchy":1798},[898,67285,1715],{"mathvariant":2334},[2263,67287],{"width":2265},[2263,67289,67290],{},[1939,67291,67292],{},"(3.12)",[902,67294,67295],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,67297,67298,67299,2633,67314,47656,67329,67331,67332,67335,67336,67352,67353,67368,67369,67384,67385,1343,67398,67411,67412,1343,67430,67448,67449,1646,67452,67455,67456,1348,67478,12164,67500,67522,67523,12164,67553,67575],{},"Body rovnosti ",[883,67300,67302],{"className":67301},[886],[888,67303,67304],{"xmlns":890},[892,67305,67306,67312],{},[895,67307,67308,67310],{},[898,67309,5877],{},[898,67311,8068],{},[902,67313,8168],{"encoding":904},[883,67315,67317],{"className":67316},[886],[888,67318,67319],{"xmlns":890},[892,67320,67321,67327],{},[895,67322,67323,67325],{},[898,67324,5877],{},[898,67326,1658],{},[902,67328,7326],{"encoding":904},[38,67330,59473],{}," (též vyrovnání, ",[614,67333,67334],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,67337,67339],{"className":67338},[886],[888,67340,67341],{"xmlns":890},[892,67342,67343,67349],{},[895,67344,67345,67347],{},[898,67346,44362],{},[898,67348,1658],{},[902,67350,67351],{"encoding":904},"VC",") je ",[883,67354,67356],{"className":67355},[886],[888,67357,67358],{"xmlns":890},[892,67359,67360,67366],{},[895,67361,67362,67364],{},[898,67363,5877],{},[898,67365,8068],{},[902,67367,8168],{"encoding":904}," kvadratická a ",[883,67370,67372],{"className":67371},[886],[888,67373,67374],{"xmlns":890},[892,67375,67376,67382],{},[895,67377,67378,67380],{},[898,67379,5877],{},[898,67381,1658],{},[902,67383,7326],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,67386,67388],{"className":67387},[886],[888,67389,67390],{"xmlns":890},[892,67391,67392,67396],{},[895,67393,67394],{},[898,67395,1983],{},[902,67397,1983],{"encoding":904},[883,67399,67401],{"className":67400},[886],[888,67402,67403],{"xmlns":890},[892,67404,67405,67409],{},[895,67406,67407],{},[898,67408,2593],{},[902,67410,2593],{"encoding":904}," odpovídajících množstvím ",[883,67413,67415],{"className":67414},[886],[888,67416,67417],{"xmlns":890},[892,67418,67419,67427],{},[895,67420,67421],{},[1845,67422,67423,67425],{},[898,67424,1802],{},[898,67426,1983],{},[902,67428,67429],{"encoding":904},"Q_A",[883,67431,67433],{"className":67432},[886],[888,67434,67435],{"xmlns":890},[892,67436,67437,67445],{},[895,67438,67439],{},[1845,67440,67441,67443],{},[898,67442,1802],{},[898,67444,2593],{},[902,67446,67447],{"encoding":904},"Q_B"," — firma je na ",[38,67450,67451],{},"prahu rentability",[614,67453,67454],{},"break even","). Pro ",[883,67457,67459],{"className":67458},[886],[888,67460,67461],{"xmlns":890},[892,67462,67463,67475],{},[895,67464,67465,67467,67469],{},[898,67466,1802],{},[1701,67468,7530],{},[1845,67470,67471,67473],{},[898,67472,1802],{},[898,67474,1983],{},[902,67476,67477],{"encoding":904},"Q \u003C Q_A",[883,67479,67481],{"className":67480},[886],[888,67482,67483],{"xmlns":890},[892,67484,67485,67497],{},[895,67486,67487,67489,67491],{},[898,67488,1802],{},[1701,67490,7491],{},[1845,67492,67493,67495],{},[898,67494,1802],{},[898,67496,2593],{},[902,67498,67499],{"encoding":904},"Q > Q_B",[883,67501,67503],{"className":67502},[886],[888,67504,67505],{"xmlns":890},[892,67506,67507,67519],{},[895,67508,67509,67511,67513,67515,67517],{},[898,67510,5877],{},[898,67512,1658],{},[1701,67514,7491],{},[898,67516,5877],{},[898,67518,8068],{},[902,67520,67521],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,67524,67526],{"className":67525},[886],[888,67527,67528],{"xmlns":890},[892,67529,67530,67550],{},[895,67531,67532,67538,67540,67542,67544],{},[1845,67533,67534,67536],{},[898,67535,1802],{},[898,67537,1983],{},[1701,67539,7530],{},[898,67541,1802],{},[1701,67543,7530],{},[1845,67545,67546,67548],{},[898,67547,1802],{},[898,67549,2593],{},[902,67551,67552],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,67554,67556],{"className":67555},[886],[888,67557,67558],{"xmlns":890},[892,67559,67560,67572],{},[895,67561,67562,67564,67566,67568,67570],{},[898,67563,5877],{},[898,67565,8068],{},[1701,67567,7491],{},[898,67569,5877],{},[898,67571,1658],{},[902,67573,67574],{"encoding":904},"TR > TC"," (zisk).",[1635,67577,67578],{},[724,67579,67580,67582],{},[883,67581,2063],{}," 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.",[724,67584,67585,67586,67612],{},"Body zvratu jsou řešení rovnice ",[883,67587,67589],{"className":67588},[886],[888,67590,67591],{"xmlns":890},[892,67592,67593,67609],{},[895,67594,67595,67597,67599,67601,67603,67605,67607],{},[898,67596,1680],{},[898,67598,8068],{},[1701,67600,1799],{"stretchy":1798},[898,67602,1802],{},[1701,67604,1805],{"stretchy":1798},[1701,67606,1792],{},[1850,67608,1852],{},[902,67610,67611],{"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.",[724,67614,67615],{},[2139,67616],{"alt":67617,"className":67618,"src":67619},"imek-tr-tc-body-zvratu",[210,2143],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,67621,67622],{},[614,67623,67624,67625,67640,67641,67656,67657,2633,67670,47380,67683,67696,67697,2633,67714,67731,67732,67752,67753,2633,67768,10536,67783,67812],{},"Obrázek 3.11: Body zvratu — křivky ",[883,67626,67628],{"className":67627},[886],[888,67629,67630],{"xmlns":890},[892,67631,67632,67638],{},[895,67633,67634,67636],{},[898,67635,5877],{},[898,67637,8068],{},[902,67639,8168],{"encoding":904}," (obrácená parabola) a ",[883,67642,67644],{"className":67643},[886],[888,67645,67646],{"xmlns":890},[892,67647,67648,67654],{},[895,67649,67650,67652],{},[898,67651,5877],{},[898,67653,1658],{},[902,67655,7326],{"encoding":904}," (přímka) se protínají v bodech ",[883,67658,67660],{"className":67659},[886],[888,67661,67662],{"xmlns":890},[892,67663,67664,67668],{},[895,67665,67666],{},[898,67667,1983],{},[902,67669,1983],{"encoding":904},[883,67671,67673],{"className":67672},[886],[888,67674,67675],{"xmlns":890},[892,67676,67677,67681],{},[895,67678,67679],{},[898,67680,2593],{},[902,67682,2593],{"encoding":904},[883,67684,67686],{"className":67685},[886],[888,67687,67688],{"xmlns":890},[892,67689,67690,67694],{},[895,67691,67692],{},[898,67693,1802],{},[902,67695,1802],{"encoding":904}," v hodnotách ",[883,67698,67700],{"className":67699},[886],[888,67701,67702],{"xmlns":890},[892,67703,67704,67712],{},[895,67705,67706],{},[1845,67707,67708,67710],{},[898,67709,1802],{},[898,67711,1983],{},[902,67713,67429],{"encoding":904},[883,67715,67717],{"className":67716},[886],[888,67718,67719],{"xmlns":890},[892,67720,67721,67729],{},[895,67722,67723],{},[1845,67724,67725,67727],{},[898,67726,1802],{},[898,67728,2593],{},[902,67730,67447],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,67733,67735],{"className":67734},[886],[888,67736,67737],{"xmlns":890},[892,67738,67739,67749],{},[895,67740,67741],{},[1845,67742,67743,67745,67747],{},[898,67744,1802],{},[898,67746,59943],{},[1701,67748,59946],{},[902,67750,67751],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,67754,67756],{"className":67755},[886],[888,67757,67758],{"xmlns":890},[892,67759,67760,67766],{},[895,67761,67762,67764],{},[898,67763,5877],{},[898,67765,8068],{},[902,67767,8168],{"encoding":904},[883,67769,67771],{"className":67770},[886],[888,67772,67773],{"xmlns":890},[892,67774,67775,67781],{},[895,67776,67777,67779],{},[898,67778,5877],{},[898,67780,1658],{},[902,67782,7326],{"encoding":904},[883,67784,67786],{"className":67785},[886],[888,67787,67788],{"xmlns":890},[892,67789,67790,67810],{},[895,67791,67792,67798,67800,67802,67804],{},[1845,67793,67794,67796],{},[898,67795,1802],{},[898,67797,1983],{},[1701,67799,7530],{},[898,67801,1802],{},[1701,67803,7530],{},[1845,67805,67806,67808],{},[898,67807,1802],{},[898,67809,2593],{},[902,67811,67552],{"encoding":904}," vyznačuje zisk.",[41376,67814,67816],{"id":67815},"příklad-38","Příklad 3.8",[724,67818,67819,67821,67822,1343,67842,1343,67868,67894],{},[38,67820,59733],{}," Dáno ",[883,67823,67825],{"className":67824},[886],[888,67826,67827],{"xmlns":890},[892,67828,67829,67839],{},[895,67830,67831,67833,67835,67837],{},[898,67832,14492],{},[898,67834,1658],{},[1701,67836,1792],{},[1850,67838,6460],{},[902,67840,67841],{"encoding":904},"FC = 4",[883,67843,67845],{"className":67844},[886],[888,67846,67847],{"xmlns":890},[892,67848,67849,67865],{},[895,67850,67851,67853,67855,67857,67859],{},[898,67852,5877],{},[898,67854,44362],{},[898,67856,1658],{},[1701,67858,1792],{},[3243,67860,67861,67863],{},[898,67862,1802],{},[1850,67864,3938],{},[902,67866,67867],{"encoding":904},"TVC = Q^2",[883,67869,67871],{"className":67870},[886],[888,67872,67873],{"xmlns":890},[892,67874,67875,67891],{},[895,67876,67877,67879,67881,67883,67885,67887,67889],{},[898,67878,1680],{},[1701,67880,1792],{},[1701,67882,2317],{},[1850,67884,3938],{},[898,67886,1802],{},[1701,67888,1703],{},[1850,67890,8073],{},[902,67892,67893],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,67896,67897,67899],{},[38,67898,5001],{}," Celkové náklady a příjem:",[883,67901,67903],{"className":67902},[886],[888,67904,67905],{"xmlns":890,"display":2252},[892,67906,67907,67973],{},[895,67908,67909,67911,67913,67915,67917,67919,67925,67927,67929,67931,67933,67935,67937,67939,67941,67943,67945,67947,67949,67951,67953,67955,67957,67959,67965,67967,67969,67971],{},[898,67910,5877],{},[898,67912,1658],{},[1701,67914,1792],{},[1850,67916,6460],{},[1701,67918,1703],{},[3243,67920,67921,67923],{},[898,67922,1802],{},[1850,67924,3938],{},[1701,67926,2012],{"separator":2011},[9942,67928],{"width":9944},[898,67930,5877],{},[898,67932,8068],{},[1701,67934,1792],{},[898,67936,1802],{},[1701,67938,3408],{},[1701,67940,1799],{"stretchy":1798},[1701,67942,2317],{},[1850,67944,3938],{},[898,67946,1802],{},[1701,67948,1703],{},[1850,67950,8073],{},[1701,67952,1805],{"stretchy":1798},[1701,67954,1792],{},[1701,67956,2317],{},[1850,67958,3938],{},[3243,67960,67961,67963],{},[898,67962,1802],{},[1850,67964,3938],{},[1701,67966,1703],{},[1850,67968,8073],{},[898,67970,1802],{},[898,67972,1715],{"mathvariant":2334},[902,67974,67975],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,67977,67978],{},"Zisk dle (3.12):",[883,67980,67982],{"className":67981},[886],[888,67983,67984],{"xmlns":890,"display":2252},[892,67985,67986,68064],{},[895,67987,67988,67990,67992,67994,67996,67998,68000,68002,68004,68006,68008,68010,68012,68018,68020,68022,68024,68026,68028,68030,68032,68034,68040,68042,68044,68046,68048,68054,68056,68058,68060,68062],{},[898,67989,1680],{},[898,67991,8068],{},[1701,67993,1792],{},[898,67995,5877],{},[898,67997,8068],{},[1701,67999,2317],{},[898,68001,5877],{},[898,68003,1658],{},[1701,68005,1792],{},[1701,68007,1799],{"stretchy":1798},[1701,68009,2317],{},[1850,68011,3938],{},[3243,68013,68014,68016],{},[898,68015,1802],{},[1850,68017,3938],{},[1701,68019,1703],{},[1850,68021,8073],{},[898,68023,1802],{},[1701,68025,1805],{"stretchy":1798},[1701,68027,2317],{},[1701,68029,1799],{"stretchy":1798},[1850,68031,6460],{},[1701,68033,1703],{},[3243,68035,68036,68038],{},[898,68037,1802],{},[1850,68039,3938],{},[1701,68041,1805],{"stretchy":1798},[1701,68043,1792],{},[1701,68045,2317],{},[1850,68047,3646],{},[3243,68049,68050,68052],{},[898,68051,1802],{},[1850,68053,3938],{},[1701,68055,1703],{},[1850,68057,8073],{},[898,68059,1802],{},[1701,68061,2317],{},[1850,68063,63065],{},[902,68065,68066],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,68068,68069,68072,68073,21622,68109,2246],{},[38,68070,68071],{},"Body zvratu"," jsou kořeny rovnice ",[883,68074,68076],{"className":68075},[886],[888,68077,68078],{"xmlns":890},[892,68079,68080,68106],{},[895,68081,68082,68084,68086,68092,68094,68096,68098,68100,68102,68104],{},[1701,68083,2317],{},[1850,68085,3646],{},[3243,68087,68088,68090],{},[898,68089,1802],{},[1850,68091,3938],{},[1701,68093,1703],{},[1850,68095,8073],{},[898,68097,1802],{},[1701,68099,2317],{},[1850,68101,6460],{},[1701,68103,1792],{},[1850,68105,1852],{},[902,68107,68108],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,68110,68112],{"className":68111},[886],[888,68113,68114],{"xmlns":890},[892,68115,68116,68140],{},[895,68117,68118,68120,68126,68128,68130,68132,68134,68136,68138],{},[1850,68119,3646],{},[3243,68121,68122,68124],{},[898,68123,1802],{},[1850,68125,3938],{},[1701,68127,2317],{},[1850,68129,8073],{},[898,68131,1802],{},[1701,68133,1703],{},[1850,68135,6460],{},[1701,68137,1792],{},[1850,68139,1852],{},[902,68141,68142],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,68144,68146],{"className":68145},[886],[888,68147,68148],{"xmlns":890,"display":2252},[892,68149,68150,68207],{},[895,68151,68152,68164,68166,68189,68191,68205],{},[1845,68153,68154,68156],{},[898,68155,1802],{},[895,68157,68158,68160,68162],{},[1850,68159,4062],{},[1701,68161,2012],{"separator":2011},[1850,68163,3938],{},[1701,68165,1792],{},[3726,68167,68168,68187],{},[895,68169,68170,68172,68175],{},[1850,68171,8073],{},[1701,68173,68174],{},"±",[12179,68176,68177],{},[895,68178,68179,68182,68184],{},[1850,68180,68181],{},"81",[1701,68183,2317],{},[1850,68185,68186],{},"48",[1850,68188,6352],{},[1701,68190,1792],{},[3726,68192,68193,68203],{},[895,68194,68195,68197,68199],{},[1850,68196,8073],{},[1701,68198,68174],{},[12179,68200,68201],{},[1850,68202,13012],{},[1850,68204,6352],{},[1701,68206,2012],{"separator":2011},[902,68208,68209],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,68211,68212,68213,2633,68236,1715],{},"numericky ",[883,68214,68216],{"className":68215},[886],[888,68217,68218],{"xmlns":890},[892,68219,68220,68233],{},[895,68221,68222,68228,68230],{},[1845,68223,68224,68226],{},[898,68225,1802],{},[1850,68227,4062],{},[1701,68229,3782],{},[1850,68231,68232],{},"0,543",[902,68234,68235],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,68237,68239],{"className":68238},[886],[888,68240,68241],{"xmlns":890},[892,68242,68243,68256],{},[895,68244,68245,68251,68253],{},[1845,68246,68247,68249],{},[898,68248,1802],{},[1850,68250,3938],{},[1701,68252,3782],{},[1850,68254,68255],{},"2,457",[902,68257,68258],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,68260,68261,4088,68264,11614,68309,21622,68343,68361],{},[38,68262,68263],{},"Maximum zisku.",[883,68265,68267],{"className":68266},[886],[888,68268,68269],{"xmlns":890},[892,68270,68271,68306],{},[895,68272,68273,68275,68281,68283,68285,68287,68289,68291,68293,68295,68297,68299,68301,68303],{},[898,68274,1680],{},[3243,68276,68277,68279],{},[898,68278,8068],{},[1701,68280,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,68282,1792],{},[1701,68284,2317],{},[1850,68286,6352],{},[898,68288,1802],{},[1701,68290,1703],{},[1850,68292,8073],{},[1701,68294,1792],{},[1850,68296,1852],{},[1701,68298,8061],{},[898,68300,1802],{},[1701,68302,1792],{},[1850,68304,68305],{},"1,5",[902,68307,68308],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,68310,68312],{"className":68311},[886],[888,68313,68314],{"xmlns":890},[892,68315,68316,68340],{},[895,68317,68318,68320,68330,68332,68334,68336,68338],{},[898,68319,1680],{},[3243,68321,68322,68324],{},[898,68323,8068],{},[895,68325,68326,68328],{},[1701,68327,4783],{"mathvariant":2334},[1701,68329,4783],{"mathvariant":2334},[1701,68331,1792],{},[1701,68333,2317],{},[1850,68335,6352],{},[1701,68337,7530],{},[1850,68339,1852],{},[902,68341,68342],{"encoding":904},"PR'' = -6 \u003C 0",[883,68344,68346],{"className":68345},[886],[888,68347,68348],{"xmlns":890},[892,68349,68350,68358],{},[895,68351,68352,68354,68356],{},[898,68353,1802],{},[1701,68355,1792],{},[1850,68357,68305],{},[902,68359,68360],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,68363,68365],{"className":68364},[886],[888,68366,68367],{"xmlns":890,"display":2252},[892,68368,68369,68432],{},[895,68370,68371,68373,68375,68377,68379,68381,68383,68385,68387,68389,68391,68393,68399,68401,68403,68405,68407,68409,68411,68413,68415,68418,68420,68423,68425,68427,68429],{},[898,68372,1680],{},[898,68374,8068],{},[1701,68376,1799],{"stretchy":1798},[1850,68378,68305],{},[1701,68380,1805],{"stretchy":1798},[1701,68382,1792],{},[1701,68384,2317],{},[1850,68386,3646],{},[1701,68388,3408],{},[1701,68390,1799],{"stretchy":1798},[1850,68392,68305],{},[3243,68394,68395,68397],{},[1701,68396,1805],{"stretchy":1798},[1850,68398,3938],{},[1701,68400,1703],{},[1850,68402,8073],{},[1701,68404,3408],{},[1850,68406,68305],{},[1701,68408,2317],{},[1850,68410,6460],{},[1701,68412,1792],{},[1701,68414,2317],{},[1850,68416,68417],{},"6,75",[1701,68419,1703],{},[1850,68421,68422],{},"13,5",[1701,68424,2317],{},[1850,68426,6460],{},[1701,68428,1792],{},[1850,68430,68431],{},"2,75.",[902,68433,68434],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,68436,68437,68438,1343,68483,68536,68537,68555],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,68439,68441],{"className":68440},[886],[888,68442,68443],{"xmlns":890},[892,68444,68445,68480],{},[895,68446,68447,68449,68455,68457,68459,68461,68463,68465,68467,68469,68471,68473,68475,68477],{},[898,68448,5877],{},[3243,68450,68451,68453],{},[898,68452,8068],{},[1701,68454,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,68456,1792],{},[1701,68458,2317],{},[1850,68460,6460],{},[898,68462,1802],{},[1701,68464,1703],{},[1850,68466,8073],{},[1701,68468,1792],{},[1850,68470,1852],{},[1701,68472,8061],{},[898,68474,1802],{},[1701,68476,1792],{},[1850,68478,68479],{},"2,25",[902,68481,68482],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,68484,68486],{"className":68485},[886],[888,68487,68488],{"xmlns":890},[892,68489,68490,68533],{},[895,68491,68492,68494,68502,68504,68506,68508,68510,68512,68514,68520,68522,68524,68526,68528,68530],{},[898,68493,5877],{},[1845,68495,68496,68498,68500],{},[898,68497,8068],{},[898,68499,59943],{},[1701,68501,59946],{},[1701,68503,1792],{},[1701,68505,2317],{},[1850,68507,3938],{},[1701,68509,3408],{},[1701,68511,1799],{"stretchy":1798},[1850,68513,68479],{},[3243,68515,68516,68518],{},[1701,68517,1805],{"stretchy":1798},[1850,68519,3938],{},[1701,68521,1703],{},[1850,68523,8073],{},[1701,68525,3408],{},[1850,68527,68479],{},[1701,68529,1792],{},[1850,68531,68532],{},"10,125",[902,68534,68535],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,68538,68540],{"className":68539},[886],[888,68541,68542],{"xmlns":890},[892,68543,68544,68552],{},[895,68545,68546,68548,68550],{},[898,68547,1802],{},[1701,68549,1792],{},[1850,68551,68479],{},[902,68553,68554],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1635,68557,68558],{},[724,68559,68560,68562,68563,1343,68585,68607,68608,1343,68625,68646,68647,68679,68680,68718,68719,3841,68737,68754,68755,2633,68783,68817,68818,11747,68856,2633,68880,1715],{},[883,68561,4695],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,68564,68566],{"className":68565},[886],[888,68567,68568],{"xmlns":890},[892,68569,68570,68582],{},[895,68571,68572,68578,68580],{},[1845,68573,68574,68576],{},[898,68575,1802],{},[1850,68577,4062],{},[1701,68579,1792],{},[1850,68581,3684],{},[902,68583,68584],{"encoding":904},"Q_1 = 0{,}5",[883,68586,68588],{"className":68587},[886],[888,68589,68590],{"xmlns":890},[892,68591,68592,68604],{},[895,68593,68594,68600,68602],{},[1845,68595,68596,68598],{},[898,68597,1802],{},[1850,68599,3938],{},[1701,68601,1792],{},[1850,68603,6460],{},[902,68605,68606],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,68609,68611],{"className":68610},[886],[888,68612,68613],{"xmlns":890},[892,68614,68615,68623],{},[895,68616,68617,68619,68621],{},[898,68618,1802],{},[1701,68620,1792],{},[1850,68622,68479],{},[902,68624,68554],{"encoding":904},[883,68626,68628],{"className":68627},[886],[888,68629,68630],{"xmlns":890},[892,68631,68632,68643],{},[895,68633,68634,68636,68638,68640],{},[898,68635,1680],{},[898,68637,8068],{},[1701,68639,1792],{},[1850,68641,68642],{},"6,125",[902,68644,68645],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,68648,68650],{"className":68649},[886],[888,68651,68652],{"xmlns":890},[892,68653,68654,68676],{},[895,68655,68656,68658,68664,68666,68668,68670,68672,68674],{},[898,68657,1680],{},[3243,68659,68660,68662],{},[898,68661,8068],{},[1701,68663,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,68665,1792],{},[1701,68667,2317],{},[1850,68669,6460],{},[898,68671,1802],{},[1701,68673,1703],{},[1850,68675,8073],{},[902,68677,68678],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,68681,68683],{"className":68682},[886],[888,68684,68685],{"xmlns":890},[892,68686,68687,68715],{},[895,68688,68689,68691,68693,68695,68697,68699,68705,68707,68709,68711,68713],{},[898,68690,1680],{},[898,68692,8068],{},[1701,68694,1792],{},[1701,68696,2317],{},[1850,68698,3938],{},[3243,68700,68701,68703],{},[898,68702,1802],{},[1850,68704,3938],{},[1701,68706,1703],{},[1850,68708,8073],{},[898,68710,1802],{},[1701,68712,2317],{},[1850,68714,6460],{},[902,68716,68717],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,68720,68722],{"className":68721},[886],[888,68723,68724],{"xmlns":890},[892,68725,68726,68734],{},[895,68727,68728],{},[3243,68729,68730,68732],{},[898,68731,1802],{},[1850,68733,3938],{},[902,68735,68736],{"encoding":904},"Q^2",[883,68738,68740],{"className":68739},[886],[888,68741,68742],{"xmlns":890},[892,68743,68744,68752],{},[895,68745,68746,68748,68750],{},[898,68747,5877],{},[898,68749,44362],{},[898,68751,1658],{},[902,68753,59255],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,68756,68758],{"className":68757},[886],[888,68759,68760],{"xmlns":890},[892,68761,68762,68780],{},[895,68763,68764,68766,68768,68770,68772,68774],{},[898,68765,5877],{},[898,68767,1658],{},[1701,68769,1792],{},[1850,68771,6460],{},[1701,68773,1703],{},[3243,68775,68776,68778],{},[898,68777,1802],{},[1850,68779,3938],{},[902,68781,68782],{"encoding":904},"TC = 4 + Q^2",[883,68784,68786],{"className":68785},[886],[888,68787,68788],{"xmlns":890},[892,68789,68790,68814],{},[895,68791,68792,68794,68796,68798,68800,68802,68808,68810,68812],{},[898,68793,5877],{},[898,68795,8068],{},[1701,68797,1792],{},[1701,68799,2317],{},[1850,68801,3938],{},[3243,68803,68804,68806],{},[898,68805,1802],{},[1850,68807,3938],{},[1701,68809,1703],{},[1850,68811,8073],{},[898,68813,1802],{},[902,68815,68816],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,68819,68821],{"className":68820},[886],[888,68822,68823],{"xmlns":890},[892,68824,68825,68853],{},[895,68826,68827,68829,68831,68833,68835,68837,68843,68845,68847,68849,68851],{},[898,68828,1680],{},[898,68830,8068],{},[1701,68832,1792],{},[1701,68834,2317],{},[1850,68836,3646],{},[3243,68838,68839,68841],{},[898,68840,1802],{},[1850,68842,3938],{},[1701,68844,1703],{},[1850,68846,8073],{},[898,68848,1802],{},[1701,68850,2317],{},[1850,68852,6460],{},[902,68854,68855],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,68857,68859],{"className":68858},[886],[888,68860,68861],{"xmlns":890},[892,68862,68863,68877],{},[895,68864,68865,68873,68875],{},[1845,68866,68867,68869,68871],{},[898,68868,1802],{},[898,68870,59943],{},[1701,68872,59946],{},[1701,68874,1792],{},[1850,68876,68305],{},[902,68878,68879],{"encoding":904},"Q_{\\max} = 1{,}5",[883,68881,68883],{"className":68882},[886],[888,68884,68885],{"xmlns":890},[892,68886,68887,68904],{},[895,68888,68889,68891,68899,68901],{},[898,68890,1680],{},[1845,68892,68893,68895,68897],{},[898,68894,8068],{},[898,68896,59943],{},[1701,68898,59946],{},[1701,68900,1792],{},[1850,68902,68903],{},"2,75",[902,68905,68906],{"encoding":904},"PR_{\\max} = 2{,}75",[724,68908,68909],{},[614,68910,68911,68912,68939,68940,68973,68974,1343,68997,1715],{},"Obrázek 3.12: Graf ",[883,68913,68915],{"className":68914},[886],[888,68916,68917],{"xmlns":890},[892,68918,68919,68937],{},[895,68920,68921,68923,68925,68927,68929,68931],{},[898,68922,5877],{},[898,68924,1658],{},[1701,68926,1792],{},[1850,68928,6460],{},[1701,68930,1703],{},[3243,68932,68933,68935],{},[898,68934,1802],{},[1850,68936,3938],{},[902,68938,68782],{"encoding":904}," (parabola) a ",[883,68941,68943],{"className":68942},[886],[888,68944,68945],{"xmlns":890},[892,68946,68947,68971],{},[895,68948,68949,68951,68953,68955,68957,68959,68965,68967,68969],{},[898,68950,5877],{},[898,68952,8068],{},[1701,68954,1792],{},[1701,68956,2317],{},[1850,68958,3938],{},[3243,68960,68961,68963],{},[898,68962,1802],{},[1850,68964,3938],{},[1701,68966,1703],{},[1850,68968,8073],{},[898,68970,1802],{},[902,68972,68816],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,68975,68977],{"className":68976},[886],[888,68978,68979],{"xmlns":890},[892,68980,68981,68994],{},[895,68982,68983,68989,68991],{},[1845,68984,68985,68987],{},[898,68986,1802],{},[1850,68988,4062],{},[1701,68990,3782],{},[1850,68992,68993],{},"0,54",[902,68995,68996],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,68998,69000],{"className":68999},[886],[888,69001,69002],{"xmlns":890},[892,69003,69004,69017],{},[895,69005,69006,69012,69014],{},[1845,69007,69008,69010],{},[898,69009,1802],{},[1850,69011,3938],{},[1701,69013,3782],{},[1850,69015,69016],{},"2,46",[902,69018,69019],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,69021,69022],{},[614,69023,69024,69025,62253,69062,69079,69080,1343,69101,1715],{},"Obrázek 3.13: Graf zisku ",[883,69026,69028],{"className":69027},[886],[888,69029,69030],{"xmlns":890},[892,69031,69032,69060],{},[895,69033,69034,69036,69038,69040,69042,69044,69050,69052,69054,69056,69058],{},[898,69035,1680],{},[898,69037,8068],{},[1701,69039,1792],{},[1701,69041,2317],{},[1850,69043,3646],{},[3243,69045,69046,69048],{},[898,69047,1802],{},[1850,69049,3938],{},[1701,69051,1703],{},[1850,69053,8073],{},[898,69055,1802],{},[1701,69057,2317],{},[1850,69059,6460],{},[902,69061,68855],{"encoding":904},[883,69063,69065],{"className":69064},[886],[888,69066,69067],{"xmlns":890},[892,69068,69069,69077],{},[895,69070,69071,69073,69075],{},[898,69072,1802],{},[1701,69074,1792],{},[1850,69076,68305],{},[902,69078,68360],{"encoding":904}," a nulami ",[883,69081,69083],{"className":69082},[886],[888,69084,69085],{"xmlns":890},[892,69086,69087,69099],{},[895,69088,69089,69095,69097],{},[1845,69090,69091,69093],{},[898,69092,1802],{},[1850,69094,4062],{},[1701,69096,3782],{},[1850,69098,68993],{},[902,69100,68996],{"encoding":904},[883,69102,69104],{"className":69103},[886],[888,69105,69106],{"xmlns":890},[892,69107,69108,69120],{},[895,69109,69110,69116,69118],{},[1845,69111,69112,69114],{},[898,69113,1802],{},[1850,69115,3938],{},[1701,69117,3782],{},[1850,69119,69016],{},[902,69121,69019],{"encoding":904},[115,69123,69125],{"id":69124},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,69127,69128],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,69130,69131],{},[2139,69132],{"alt":69133,"className":69134,"src":69135},"imek-max-zisku-dva-pohledy",[210,2143],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,69137,20458],{"id":69138},"princip-1",[724,69140,69141,69142,6723,69157,69174],{},"Má-li zisk ",[883,69143,69145],{"className":69144},[886],[888,69146,69147],{"xmlns":890},[892,69148,69149,69155],{},[895,69150,69151,69153],{},[898,69152,1680],{},[898,69154,8068],{},[902,69156,67225],{"encoding":904},[883,69158,69160],{"className":69159},[886],[888,69161,69162],{"xmlns":890},[892,69163,69164,69172],{},[895,69165,69166],{},[1845,69167,69168,69170],{},[898,69169,1802],{},[1850,69171,1852],{},[902,69173,1855],{"encoding":904}," maximum, pak platí",[883,69176,69178],{"className":69177},[886],[888,69179,69180],{"xmlns":890,"display":2252},[892,69181,69182,69231],{},[2256,69183,69184],{"width":2258},[2260,69185,69186,69188,69224,69226],{},[2263,69187],{"width":2265},[2263,69189,69190],{},[895,69191,69192,69194,69196,69198,69204,69206,69208,69210,69212,69214,69220,69222],{},[898,69193,6909],{},[898,69195,8068],{},[1701,69197,1799],{"stretchy":1798},[1845,69199,69200,69202],{},[898,69201,1802],{},[1850,69203,1852],{},[1701,69205,1805],{"stretchy":1798},[1701,69207,1792],{},[898,69209,6909],{},[898,69211,1658],{},[1701,69213,1799],{"stretchy":1798},[1845,69215,69216,69218],{},[898,69217,1802],{},[1850,69219,1852],{},[1701,69221,1805],{"stretchy":1798},[898,69223,1715],{"mathvariant":2334},[2263,69225],{"width":2265},[2263,69227,69228],{},[1939,69229,69230],{},"(3.13)",[902,69232,69233],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1635,69235,69236],{},[724,69237,69238,65792,69240],{},[883,69239,60190],{},[38,69241,69242],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,69244,69245,69248,69249,12164,69276,21622,69350,1715],{},[38,69246,69247],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,69250,69252],{"className":69251},[886],[888,69253,69254],{"xmlns":890},[892,69255,69256,69274],{},[895,69257,69258,69260,69262,69264,69266,69268,69270,69272],{},[898,69259,1680],{},[898,69261,8068],{},[1701,69263,1792],{},[898,69265,5877],{},[898,69267,8068],{},[1701,69269,2317],{},[898,69271,5877],{},[898,69273,1658],{},[902,69275,58946],{"encoding":904},[883,69277,69279],{"className":69278},[886],[888,69280,69281],{"xmlns":890},[892,69282,69283,69347],{},[895,69284,69285,69287,69293,69295,69301,69303,69305,69307,69313,69315,69321,69323,69325,69327,69333,69335,69341,69343,69345],{},[898,69286,1680],{},[3243,69288,69289,69291],{},[898,69290,8068],{},[1701,69292,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,69294,1799],{"stretchy":1798},[1845,69296,69297,69299],{},[898,69298,1802],{},[1850,69300,1852],{},[1701,69302,1805],{"stretchy":1798},[1701,69304,1792],{},[898,69306,5877],{},[3243,69308,69309,69311],{},[898,69310,8068],{},[1701,69312,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,69314,1799],{"stretchy":1798},[1845,69316,69317,69319],{},[898,69318,1802],{},[1850,69320,1852],{},[1701,69322,1805],{"stretchy":1798},[1701,69324,2317],{},[898,69326,5877],{},[3243,69328,69329,69331],{},[898,69330,1658],{},[1701,69332,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,69334,1799],{"stretchy":1798},[1845,69336,69337,69339],{},[898,69338,1802],{},[1850,69340,1852],{},[1701,69342,1805],{"stretchy":1798},[1701,69344,1792],{},[1850,69346,1852],{},[902,69348,69349],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,69351,69353],{"className":69352},[886],[888,69354,69355],{"xmlns":890},[892,69356,69357,69389],{},[895,69358,69359,69361,69363,69365,69371,69373,69375,69377,69379,69381,69387],{},[898,69360,6909],{},[898,69362,8068],{},[1701,69364,1799],{"stretchy":1798},[1845,69366,69367,69369],{},[898,69368,1802],{},[1850,69370,1852],{},[1701,69372,1805],{"stretchy":1798},[1701,69374,1792],{},[898,69376,6909],{},[898,69378,1658],{},[1701,69380,1799],{"stretchy":1798},[1845,69382,69383,69385],{},[898,69384,1802],{},[1850,69386,1852],{},[1701,69388,1805],{"stretchy":1798},[902,69390,69391],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1635,69393,69394,69399],{},[724,69395,69396,69398],{},[883,69397,3140],{}," Postup — jak najít maximum zisku",[152,69400,69401,69465,69520,69557,69585],{},[123,69402,69403,69404,2633,69419,69434,69435,2506],{},"Sestavte ",[883,69405,69407],{"className":69406},[886],[888,69408,69409],{"xmlns":890},[892,69410,69411,69417],{},[895,69412,69413,69415],{},[898,69414,5877],{},[898,69416,8068],{},[902,69418,8168],{"encoding":904},[883,69420,69422],{"className":69421},[886],[888,69423,69424],{"xmlns":890},[892,69425,69426,69432],{},[895,69427,69428,69430],{},[898,69429,5877],{},[898,69431,1658],{},[902,69433,7326],{"encoding":904}," ze zadání (typicky ",[883,69436,69438],{"className":69437},[886],[888,69439,69440],{"xmlns":890},[892,69441,69442,69462],{},[895,69443,69444,69446,69448,69450,69452,69454,69456,69458,69460],{},[898,69445,5877],{},[898,69447,8068],{},[1701,69449,1792],{},[898,69451,1680],{},[1701,69453,1799],{"stretchy":1798},[898,69455,1802],{},[1701,69457,1805],{"stretchy":1798},[1701,69459,3408],{},[898,69461,1802],{},[902,69463,69464],{"encoding":904},"TR = P(Q) \\cdot Q",[123,69466,69467,69468,2633,69494,1715],{},"Vypočtěte ",[883,69469,69471],{"className":69470},[886],[888,69472,69473],{"xmlns":890},[892,69474,69475,69491],{},[895,69476,69477,69479,69481,69483,69485],{},[898,69478,6909],{},[898,69480,8068],{},[1701,69482,1792],{},[898,69484,5877],{},[3243,69486,69487,69489],{},[898,69488,8068],{},[1701,69490,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,69492,69493],{"encoding":904},"MR = TR'",[883,69495,69497],{"className":69496},[886],[888,69498,69499],{"xmlns":890},[892,69500,69501,69517],{},[895,69502,69503,69505,69507,69509,69511],{},[898,69504,6909],{},[898,69506,1658],{},[1701,69508,1792],{},[898,69510,5877],{},[3243,69512,69513,69515],{},[898,69514,1658],{},[1701,69516,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,69518,69519],{"encoding":904},"MC = TC'",[123,69521,69522,69523,1715],{},"Řešte rovnici ",[883,69524,69526],{"className":69525},[886],[888,69527,69528],{"xmlns":890},[892,69529,69530,69554],{},[895,69531,69532,69534,69536,69538,69540,69542,69544,69546,69548,69550,69552],{},[898,69533,6909],{},[898,69535,8068],{},[1701,69537,1799],{"stretchy":1798},[898,69539,1802],{},[1701,69541,1805],{"stretchy":1798},[1701,69543,1792],{},[898,69545,6909],{},[898,69547,1658],{},[1701,69549,1799],{"stretchy":1798},[898,69551,1802],{},[1701,69553,1805],{"stretchy":1798},[902,69555,69556],{"encoding":904},"MR(Q) = MC(Q)",[123,69558,69559,69560,69584],{},"Ověřte druhou derivaci ",[883,69561,69563],{"className":69562},[886],[888,69564,69565],{"xmlns":890},[892,69566,69567,69581],{},[895,69568,69569,69571],{},[898,69570,1680],{},[3243,69572,69573,69575],{},[898,69574,8068],{},[895,69576,69577,69579],{},[1701,69578,4783],{"mathvariant":2334},[1701,69580,4783],{"mathvariant":2334},[902,69582,69583],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,69586,69587,69588,69615],{},"Dosaďte do ",[883,69589,69591],{"className":69590},[886],[888,69592,69593],{"xmlns":890},[892,69594,69595,69613],{},[895,69596,69597,69599,69601,69603,69605,69607,69609,69611],{},[898,69598,1680],{},[898,69600,8068],{},[1701,69602,1792],{},[898,69604,5877],{},[898,69606,8068],{},[1701,69608,2317],{},[898,69610,5877],{},[898,69612,1658],{},[902,69614,58946],{"encoding":904}," pro hodnotu maxima.",[41376,69617,69619],{"id":69618},"příklad-39","Příklad 3.9",[724,69621,69622,59734,69624,2633,69646,69682],{},[38,69623,59733],{},[883,69625,69627],{"className":69626},[886],[888,69628,69629],{"xmlns":890},[892,69630,69631,69643],{},[895,69632,69633,69635,69637,69639,69641],{},[898,69634,1680],{},[1701,69636,1792],{},[1850,69638,3776],{},[1701,69640,2317],{},[898,69642,1802],{},[902,69644,69645],{"encoding":904},"P = 30 - Q",[883,69647,69649],{"className":69648},[886],[888,69650,69651],{"xmlns":890},[892,69652,69653,69679],{},[895,69654,69655,69657,69659,69661,69663,69669,69671,69673,69675,69677],{},[898,69656,5877],{},[898,69658,1658],{},[1701,69660,1792],{},[1850,69662,3684],{},[3243,69664,69665,69667],{},[898,69666,1802],{},[1850,69668,3938],{},[1701,69670,1703],{},[1850,69672,6352],{},[898,69674,1802],{},[1701,69676,1703],{},[1850,69678,28239],{},[902,69680,69681],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,69684,69685,4088,69687,1343,69717,69755,69756,19842,69800,69834,69835,1715],{},[38,69686,5001],{},[883,69688,69690],{"className":69689},[886],[888,69691,69692],{"xmlns":890},[892,69693,69694,69714],{},[895,69695,69696,69698,69700,69702,69704,69706,69708],{},[898,69697,5877],{},[898,69699,8068],{},[1701,69701,1792],{},[1850,69703,3776],{},[898,69705,1802],{},[1701,69707,2317],{},[3243,69709,69710,69712],{},[898,69711,1802],{},[1850,69713,3938],{},[902,69715,69716],{"encoding":904},"TR = 30Q - Q^2",[883,69718,69720],{"className":69719},[886],[888,69721,69722],{"xmlns":890},[892,69723,69724,69752],{},[895,69725,69726,69728,69730,69732,69734,69736,69742,69744,69746,69748,69750],{},[898,69727,1680],{},[898,69729,8068],{},[1701,69731,1792],{},[1701,69733,2317],{},[1850,69735,68305],{},[3243,69737,69738,69740],{},[898,69739,1802],{},[1850,69741,3938],{},[1701,69743,1703],{},[1850,69745,4840],{},[898,69747,1802],{},[1701,69749,2317],{},[1850,69751,28239],{},[902,69753,69754],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,69757,69759],{"className":69758},[886],[888,69760,69761],{"xmlns":890},[892,69762,69763,69797],{},[895,69764,69765,69767,69773,69775,69777,69779,69781,69783,69785,69787,69789,69791,69793,69795],{},[898,69766,1680],{},[3243,69768,69769,69771],{},[898,69770,8068],{},[1701,69772,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,69774,1792],{},[1701,69776,2317],{},[1850,69778,3646],{},[898,69780,1802],{},[1701,69782,1703],{},[1850,69784,4840],{},[1701,69786,1792],{},[1850,69788,1852],{},[1701,69790,8061],{},[898,69792,1802],{},[1701,69794,1792],{},[1850,69796,9650],{},[902,69798,69799],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,69801,69803],{"className":69802},[886],[888,69804,69805],{"xmlns":890},[892,69806,69807,69831],{},[895,69808,69809,69811,69821,69823,69825,69827,69829],{},[898,69810,1680],{},[3243,69812,69813,69815],{},[898,69814,8068],{},[895,69816,69817,69819],{},[1701,69818,4783],{"mathvariant":2334},[1701,69820,4783],{"mathvariant":2334},[1701,69822,1792],{},[1701,69824,2317],{},[1850,69826,3646],{},[1701,69828,7530],{},[1850,69830,1852],{},[902,69832,69833],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,69836,69838],{"className":69837},[886],[888,69839,69840],{"xmlns":890},[892,69841,69842,69859],{},[895,69843,69844,69846,69848,69850,69852,69854,69856],{},[898,69845,1680],{},[898,69847,8068],{},[1701,69849,1799],{"stretchy":1798},[1850,69851,9650],{},[1701,69853,1805],{"stretchy":1798},[1701,69855,1792],{},[1850,69857,69858],{},"89",[902,69860,69861],{"encoding":904},"PR(8) = 89",[724,69863,69864,69865,1343,69891,19842,69915,69953],{},"Ověření principu: ",[883,69866,69868],{"className":69867},[886],[888,69869,69870],{"xmlns":890},[892,69871,69872,69888],{},[895,69873,69874,69876,69878,69880,69882,69884,69886],{},[898,69875,6909],{},[898,69877,8068],{},[1701,69879,1792],{},[1850,69881,3776],{},[1701,69883,2317],{},[1850,69885,3938],{},[898,69887,1802],{},[902,69889,69890],{"encoding":904},"MR = 30 - 2Q",[883,69892,69894],{"className":69893},[886],[888,69895,69896],{"xmlns":890},[892,69897,69898,69912],{},[895,69899,69900,69902,69904,69906,69908,69910],{},[898,69901,6909],{},[898,69903,1658],{},[1701,69905,1792],{},[898,69907,1802],{},[1701,69909,1703],{},[1850,69911,6352],{},[902,69913,69914],{"encoding":904},"MC = Q + 6",[883,69916,69918],{"className":69917},[886],[888,69919,69920],{"xmlns":890},[892,69921,69922,69950],{},[895,69923,69924,69926,69928,69930,69932,69934,69936,69938,69940,69942,69944,69946,69948],{},[898,69925,6909],{},[898,69927,8068],{},[1701,69929,1799],{"stretchy":1798},[1850,69931,9650],{},[1701,69933,1805],{"stretchy":1798},[1701,69935,1792],{},[1850,69937,26985],{},[1701,69939,1792],{},[898,69941,6909],{},[898,69943,1658],{},[1701,69945,1799],{"stretchy":1798},[1850,69947,9650],{},[1701,69949,1805],{"stretchy":1798},[902,69951,69952],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,69955,69956,69957,69990,69991,70008],{},"V řadě případů — má-li rovnice ",[883,69958,69960],{"className":69959},[886],[888,69961,69962],{"xmlns":890},[892,69963,69964,69988],{},[895,69965,69966,69968,69970,69972,69974,69976,69978,69980,69982,69984,69986],{},[898,69967,6909],{},[898,69969,8068],{},[1701,69971,1799],{"stretchy":1798},[898,69973,1802],{},[1701,69975,1805],{"stretchy":1798},[1701,69977,1792],{},[898,69979,6909],{},[898,69981,1658],{},[1701,69983,1799],{"stretchy":1798},[898,69985,1802],{},[1701,69987,1805],{"stretchy":1798},[902,69989,69556],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,69992,69994],{"className":69993},[886],[888,69995,69996],{"xmlns":890},[892,69997,69998,70006],{},[895,69999,70000],{},[1845,70001,70002,70004],{},[898,70003,1802],{},[1850,70005,1852],{},[902,70007,1855],{"encoding":904}," — není třeba provádět test druhé derivace.",[41376,70010,70012],{"id":70011},"příklad-310","Příklad 3.10",[724,70014,70015,70017,70018,70022,70023,70036,70037,70068],{},[38,70016,59733],{}," Firma vyrábí minipočítače v ",[207,70019,70021],{"className":70020,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,70024,70026],{"className":70025},[886],[888,70027,70028],{"xmlns":890},[892,70029,70030,70034],{},[895,70031,70032],{},[1850,70033,19243],{},[902,70035,19243],{"encoding":904}," EUR\u002Fks. ",[883,70038,70040],{"className":70039},[886],[888,70041,70042],{"xmlns":890},[892,70043,70044,70065],{},[895,70045,70046,70048,70050,70052,70054,70056,70059],{},[898,70047,5877],{},[898,70049,1658],{},[1701,70051,1792],{},[1850,70053,7206],{},[1701,70055,1703],{},[1850,70057,70058],{},"28",[3243,70060,70061,70063],{},[898,70062,1802],{},[1850,70064,3938],{},[902,70066,70067],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,70070,70071,4088,70073,1343,70095,1343,70115,70138],{},[38,70072,5001],{},[883,70074,70076],{"className":70075},[886],[888,70077,70078],{"xmlns":890},[892,70079,70080,70092],{},[895,70081,70082,70084,70086,70088,70090],{},[898,70083,5877],{},[898,70085,8068],{},[1701,70087,1792],{},[1850,70089,19243],{},[898,70091,1802],{},[902,70093,70094],{"encoding":904},"TR = 900Q",[883,70096,70098],{"className":70097},[886],[888,70099,70100],{"xmlns":890},[892,70101,70102,70112],{},[895,70103,70104,70106,70108,70110],{},[898,70105,6909],{},[898,70107,8068],{},[1701,70109,1792],{},[1850,70111,19243],{},[902,70113,70114],{"encoding":904},"MR = 900",[883,70116,70118],{"className":70117},[886],[888,70119,70120],{"xmlns":890},[892,70121,70122,70135],{},[895,70123,70124,70126,70128,70130,70133],{},[898,70125,6909],{},[898,70127,1658],{},[1701,70129,1792],{},[1850,70131,70132],{},"56",[898,70134,1802],{},[902,70136,70137],{"encoding":904},"MC = 56Q",". Z principu:",[883,70140,70142],{"className":70141},[886],[888,70143,70144],{"xmlns":890,"display":2252},[892,70145,70146,70188],{},[895,70147,70148,70150,70152,70154,70156,70158,70160,70162,70164,70166,70174,70176,70179,70181,70183,70185],{},[1850,70149,19243],{},[1701,70151,1792],{},[1850,70153,70132],{},[898,70155,1802],{},[1939,70157,8058],{},[1701,70159,8061],{},[1939,70161,8058],{},[898,70163,1802],{},[1701,70165,1792],{},[2363,70167,70168],{"scriptlevel":1852,"displaystyle":1798},[3726,70169,70170,70172],{},[1850,70171,19243],{},[1850,70173,70132],{},[1701,70175,3782],{},[1850,70177,70178],{},"16,07",[1939,70180,8058],{},[1701,70182,4067],{},[1939,70184,8058],{},[1850,70186,70187],{},"16.",[902,70189,70190],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,70192,70193,70194,2246],{},"Zisk při ",[883,70195,70197],{"className":70196},[886],[888,70198,70199],{"xmlns":890},[892,70200,70201,70209],{},[895,70202,70203,70205,70207],{},[898,70204,1802],{},[1701,70206,1792],{},[1850,70208,45883],{},[902,70210,70211],{"encoding":904},"Q = 16",[883,70213,70215],{"className":70214},[886],[888,70216,70217],{"xmlns":890,"display":2252},[892,70218,70219,70290],{},[895,70220,70221,70223,70225,70227,70229,70231,70233,70235,70237,70239,70241,70243,70245,70247,70249,70251,70257,70259,70261,70263,70265,70267,70269,70271,70273,70276,70278,70280,70282,70285,70288],{},[898,70222,1680],{},[898,70224,8068],{},[1701,70226,1799],{"stretchy":1798},[1850,70228,45883],{},[1701,70230,1805],{"stretchy":1798},[1701,70232,1792],{},[1850,70234,19243],{},[1701,70236,3408],{},[1850,70238,45883],{},[1701,70240,2317],{},[1701,70242,1799],{"stretchy":1798},[1850,70244,7206],{},[1701,70246,1703],{},[1850,70248,70058],{},[1701,70250,3408],{},[3243,70252,70253,70255],{},[1850,70254,45883],{},[1850,70256,3938],{},[1701,70258,1805],{"stretchy":1798},[1701,70260,1792],{},[1850,70262,26985],{},[1939,70264,1941],{},[1850,70266,24186],{},[1701,70268,2317],{},[1850,70270,28239],{},[1939,70272,1941],{},[1850,70274,70275],{},"218",[1701,70277,1792],{},[1850,70279,28239],{},[1939,70281,1941],{},[1850,70283,70284],{},"182",[1939,70286,70287],{}," EUR",[898,70289,1715],{"mathvariant":2334},[902,70291,70292],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,70294,70295],{},"Pro srovnání při původních 30 ks:",[883,70297,70299],{"className":70298},[886],[888,70300,70301],{"xmlns":890,"display":2252},[892,70302,70303,70368],{},[895,70304,70305,70307,70309,70311,70313,70315,70317,70319,70321,70323,70325,70327,70329,70331,70333,70335,70337,70339,70341,70344,70346,70348,70350,70352,70354,70356,70358,70360,70362,70364,70366],{},[898,70306,1680],{},[898,70308,8068],{},[1701,70310,1799],{"stretchy":1798},[1850,70312,3776],{},[1701,70314,1805],{"stretchy":1798},[1701,70316,1792],{},[1850,70318,19243],{},[1701,70320,3408],{},[1850,70322,3776],{},[1701,70324,2317],{},[1701,70326,1799],{"stretchy":1798},[1850,70328,7206],{},[1701,70330,1703],{},[1850,70332,70058],{},[1701,70334,3408],{},[1850,70336,19243],{},[1701,70338,1805],{"stretchy":1798},[1701,70340,1792],{},[1850,70342,70343],{},"27",[1939,70345,1941],{},[1850,70347,62828],{},[1701,70349,2317],{},[1850,70351,9071],{},[1939,70353,1941],{},[1850,70355,34774],{},[1701,70357,1792],{},[1850,70359,4062],{},[1939,70361,1941],{},[1850,70363,27781],{},[1939,70365,70287],{},[898,70367,1715],{"mathvariant":2334},[902,70369,70370],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,70372,70373,70376,70377,70395,70396,70414],{},[38,70374,70375],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,70378,70380],{"className":70379},[886],[888,70381,70382],{"xmlns":890},[892,70383,70384,70392],{},[895,70385,70386,70388,70390],{},[1850,70387,28239],{},[1939,70389,1941],{},[1850,70391,70284],{},[902,70393,70394],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,70397,70399],{"className":70398},[886],[888,70400,70401],{"xmlns":890},[892,70402,70403,70411],{},[895,70404,70405,70407,70409],{},[1850,70406,4062],{},[1939,70408,1941],{},[1850,70410,27781],{},[902,70412,70413],{"encoding":904},"1\\,750"," EUR.",[198,70416,70418],{"id":70417},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,70420,70421,70422,66316,70435,70459],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,70423,70425],{"className":70424},[886],[888,70426,70427],{"xmlns":890},[892,70428,70429,70433],{},[895,70430,70431],{},[898,70432,1680],{},[902,70434,1680],{"encoding":904},[883,70436,70438],{"className":70437},[886],[888,70439,70440],{"xmlns":890},[892,70441,70442,70456],{},[895,70443,70444,70446,70448,70450,70452,70454],{},[898,70445,5877],{},[898,70447,8068],{},[1701,70449,1792],{},[898,70451,1680],{},[1701,70453,3408],{},[898,70455,1802],{},[902,70457,70458],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,70461,70463],{"className":70462},[886],[888,70464,70465],{"xmlns":890,"display":2252},[892,70466,70467,70500],{},[2256,70468,70469],{"width":2258},[2260,70470,70471,70473,70493,70495],{},[2263,70472],{"width":2265},[2263,70474,70475],{},[895,70476,70477,70479,70481,70483,70485,70487,70489,70491],{},[898,70478,1680],{},[1701,70480,1792],{},[898,70482,6909],{},[898,70484,1658],{},[1701,70486,1799],{"stretchy":1798},[898,70488,1802],{},[1701,70490,1805],{"stretchy":1798},[898,70492,1715],{"mathvariant":2334},[2263,70494],{"width":2265},[2263,70496,70497],{},[1939,70498,70499],{},"(3.14)",[902,70501,70502],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,70504,70505,70506,1715],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,70507,70509],{"className":70508},[886],[888,70510,70511],{"xmlns":890},[892,70512,70513,70527],{},[895,70514,70515,70517],{},[898,70516,1680],{},[3243,70518,70519,70521],{},[898,70520,8068],{},[895,70522,70523,70525],{},[1701,70524,4783],{"mathvariant":2334},[1701,70526,4783],{"mathvariant":2334},[902,70528,69583],{"encoding":904},[41376,70530,70532],{"id":70531},"příklad-311","Příklad 3.11",[724,70534,70535,61268,70537,70584,70585,70603],{},[38,70536,59733],{},[883,70538,70540],{"className":70539},[886],[888,70541,70542],{"xmlns":890},[892,70543,70544,70581],{},[895,70545,70546,70548,70550,70552,70555,70561,70563,70565,70571,70573,70575,70577,70579],{},[898,70547,5877],{},[898,70549,1658],{},[1701,70551,1792],{},[1850,70553,70554],{},"0,04",[3243,70556,70557,70559],{},[898,70558,1802],{},[1850,70560,3646],{},[1701,70562,2317],{},[1850,70564,26585],{},[3243,70566,70567,70569],{},[898,70568,1802],{},[1850,70570,3938],{},[1701,70572,1703],{},[1850,70574,3703],{},[898,70576,1802],{},[1701,70578,1703],{},[1850,70580,4225],{},[902,70582,70583],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,70586,70588],{"className":70587},[886],[888,70589,70590],{"xmlns":890},[892,70591,70592,70600],{},[895,70593,70594,70596,70598],{},[898,70595,1680],{},[1701,70597,1792],{},[1850,70599,6460],{},[902,70601,70602],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,70605,70606,70608,70609,21622,70651,70685,70686,2246],{},[38,70607,5001],{}," Z (3.14): ",[883,70610,70612],{"className":70611},[886],[888,70613,70614],{"xmlns":890},[892,70615,70616,70648],{},[895,70617,70618,70620,70622,70624,70627,70633,70635,70638,70640,70642,70644,70646],{},[898,70619,6909],{},[898,70621,1658],{},[1701,70623,1792],{},[1850,70625,70626],{},"0,12",[3243,70628,70629,70631],{},[898,70630,1802],{},[1850,70632,3938],{},[1701,70634,2317],{},[1850,70636,70637],{},"1,8",[898,70639,1802],{},[1701,70641,1703],{},[1850,70643,3703],{},[1701,70645,1792],{},[1850,70647,6460],{},[902,70649,70650],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,70652,70654],{"className":70653},[886],[888,70655,70656],{"xmlns":890},[892,70657,70658,70682],{},[895,70659,70660,70662,70668,70670,70672,70674,70676,70678,70680],{},[1850,70661,70626],{},[3243,70663,70664,70666],{},[898,70665,1802],{},[1850,70667,3938],{},[1701,70669,2317],{},[1850,70671,70637],{},[898,70673,1802],{},[1701,70675,1703],{},[1850,70677,6352],{},[1701,70679,1792],{},[1850,70681,1852],{},[902,70683,70684],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,70687,70689],{"className":70688},[886],[888,70690,70691],{"xmlns":890},[892,70692,70693,70697],{},[895,70694,70695],{},[1850,70696,70626],{},[902,70698,70699],{"encoding":904},"0{,}12",[883,70701,70703],{"className":70702},[886],[888,70704,70705],{"xmlns":890,"display":2252},[892,70706,70707,70759],{},[895,70708,70709,70715,70717,70719,70721,70723,70725,70727,70729,70731,70733,70735,70741,70743,70745,70747,70749,70755,70757],{},[3243,70710,70711,70713],{},[898,70712,1802],{},[1850,70714,3938],{},[1701,70716,2317],{},[1850,70718,40275],{},[898,70720,1802],{},[1701,70722,1703],{},[1850,70724,7206],{},[1701,70726,1792],{},[1850,70728,1852],{},[1939,70730,8058],{},[1701,70732,8061],{},[1939,70734,8058],{},[1845,70736,70737,70739],{},[898,70738,1802],{},[1850,70740,4062],{},[1701,70742,1792],{},[1850,70744,4225],{},[1701,70746,2012],{"separator":2011},[1939,70748,8058],{},[1845,70750,70751,70753],{},[898,70752,1802],{},[1850,70754,3938],{},[1701,70756,1792],{},[1850,70758,23373],{},[902,70760,70761],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,70763,70764,70765,2246],{},"Dále ",[883,70766,70768],{"className":70767},[886],[888,70769,70770],{"xmlns":890},[892,70771,70772,70811],{},[895,70773,70774,70776,70786,70788,70790,70792,70798,70800,70802,70805,70807,70809],{},[898,70775,1680],{},[3243,70777,70778,70780],{},[898,70779,8068],{},[895,70781,70782,70784],{},[1701,70783,4783],{"mathvariant":2334},[1701,70785,4783],{"mathvariant":2334},[1701,70787,1792],{},[1701,70789,2317],{},[898,70791,6909],{},[3243,70793,70794,70796],{},[898,70795,1658],{},[1701,70797,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,70799,1792],{},[1701,70801,2317],{},[1850,70803,70804],{},"0,24",[898,70806,1802],{},[1701,70808,1703],{},[1850,70810,70637],{},[902,70812,70813],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,70815,70816,70866],{},[123,70817,70818,70862,70863,70865],{},[883,70819,70821],{"className":70820},[886],[888,70822,70823],{"xmlns":890},[892,70824,70825,70859],{},[895,70826,70827,70829,70839,70841,70843,70845,70847,70849,70851,70853,70855,70857],{},[898,70828,1680],{},[3243,70830,70831,70833],{},[898,70832,8068],{},[895,70834,70835,70837],{},[1701,70836,4783],{"mathvariant":2334},[1701,70838,4783],{"mathvariant":2334},[1701,70840,1799],{"stretchy":1798},[1850,70842,4225],{},[1701,70844,1805],{"stretchy":1798},[1701,70846,1792],{},[1850,70848,3868],{},[1701,70850,7491],{},[1850,70852,1852],{},[1939,70854,8058],{},[1701,70856,8061],{},[1939,70858,8058],{},[902,70860,70861],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,70864,7858],{}," zisku (minimalizace ztráty);",[123,70867,70868,70862,70914,70916],{},[883,70869,70871],{"className":70870},[886],[888,70872,70873],{"xmlns":890},[892,70874,70875,70911],{},[895,70876,70877,70879,70889,70891,70893,70895,70897,70899,70901,70903,70905,70907,70909],{},[898,70878,1680],{},[3243,70880,70881,70883],{},[898,70882,8068],{},[895,70884,70885,70887],{},[1701,70886,4783],{"mathvariant":2334},[1701,70888,4783],{"mathvariant":2334},[1701,70890,1799],{"stretchy":1798},[1850,70892,3703],{},[1701,70894,1805],{"stretchy":1798},[1701,70896,1792],{},[1701,70898,2317],{},[1850,70900,3868],{},[1701,70902,7530],{},[1850,70904,1852],{},[1939,70906,8058],{},[1701,70908,8061],{},[1939,70910,8058],{},[902,70912,70913],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,70915,7800],{}," zisku, avšak",[883,70918,70920],{"className":70919},[886],[888,70921,70922],{"xmlns":890,"display":2252},[892,70923,70924,70992],{},[895,70925,70926,70928,70930,70932,70934,70936,70938,70940,70942,70944,70946,70948,70950,70952,70954,70956,70958,70960,70962,70964,70966,70968,70970,70972,70974,70976,70978,70980,70982,70984,70986,70988,70990],{},[898,70927,1680],{},[898,70929,8068],{},[1701,70931,1799],{"stretchy":1798},[1850,70933,3703],{},[1701,70935,1805],{"stretchy":1798},[1701,70937,1792],{},[1850,70939,6460],{},[1701,70941,3408],{},[1850,70943,3703],{},[1701,70945,2317],{},[1701,70947,1799],{"stretchy":1798},[1850,70949,70554],{},[1701,70951,3408],{},[1850,70953,4062],{},[1939,70955,1941],{},[1850,70957,62828],{},[1701,70959,2317],{},[1850,70961,26585],{},[1701,70963,3408],{},[1850,70965,5158],{},[1701,70967,1703],{},[1850,70969,5158],{},[1701,70971,1703],{},[1850,70973,4225],{},[1701,70975,1805],{"stretchy":1798},[1701,70977,1792],{},[1850,70979,3665],{},[1701,70981,2317],{},[1850,70983,25221],{},[1701,70985,1792],{},[1701,70987,2317],{},[1850,70989,40275],{},[1701,70991,2012],{"separator":2011},[902,70993,70994],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,70996,70997,70998,1715],{},"tj. ztráta větší než ",[883,70999,71001],{"className":71000},[886],[888,71002,71003],{"xmlns":890},[892,71004,71005,71015],{},[895,71006,71007,71009,71011,71013],{},[898,71008,14492],{},[898,71010,1658],{},[1701,71012,1792],{},[1850,71014,4225],{},[902,71016,71017],{"encoding":904},"FC = 5",[724,71019,71020,71023,71024,71027,71028,1715],{},[38,71021,71022],{},"Závěr:"," firma by měla ",[38,71025,71026],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,71029,71031],{"className":71030},[886],[888,71032,71033],{"xmlns":890},[892,71034,71035,71045],{},[895,71036,71037,71039,71041,71043],{},[898,71038,14492],{},[898,71040,1658],{},[1701,71042,1792],{},[1850,71044,4225],{},[902,71046,71017],{"encoding":904},[115,71048,71050],{"id":71049},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,71052,71053,71054,71056,71057,71072,71073,71086,71087,71113,71114,71127,71128,71145,71146,6723,71163,71166,71167,71187,71188,71203,71204,2246],{},"Důležitým završením analýzy je konstrukce ",[38,71055,59021],{},". S nabízeným množstvím rostou mezní náklady ",[883,71058,71060],{"className":71059},[886],[888,71061,71062],{"xmlns":890},[892,71063,71064,71070],{},[895,71065,71066,71068],{},[898,71067,6909],{},[898,71069,1658],{},[902,71071,59038],{"encoding":904}," a tyto určují cenu ",[883,71074,71076],{"className":71075},[886],[888,71077,71078],{"xmlns":890},[892,71079,71080,71084],{},[895,71081,71082],{},[898,71083,1680],{},[902,71085,1680],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,71088,71090],{"className":71089},[886],[888,71091,71092],{"xmlns":890},[892,71093,71094,71110],{},[895,71095,71096,71098,71100,71102,71104,71106,71108],{},[898,71097,1680],{},[1701,71099,1792],{},[898,71101,6909],{},[898,71103,1658],{},[1701,71105,1799],{"stretchy":1798},[898,71107,1802],{},[1701,71109,1805],{"stretchy":1798},[902,71111,71112],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,71115,71117],{"className":71116},[886],[888,71118,71119],{"xmlns":890},[892,71120,71121,71125],{},[895,71122,71123],{},[898,71124,1680],{},[902,71126,1680],{"encoding":904}," však nemůže být nižší než ",[883,71129,71131],{"className":71130},[886],[888,71132,71133],{"xmlns":890},[892,71134,71135,71143],{},[895,71136,71137],{},[3243,71138,71139,71141],{},[898,71140,1680],{},[1701,71142,8424],{},[902,71144,8474],{"encoding":904}," odpovídající množství ",[883,71147,71149],{"className":71148},[886],[888,71150,71151],{"xmlns":890},[892,71152,71153,71161],{},[895,71154,71155],{},[3243,71156,71157,71159],{},[898,71158,1802],{},[1701,71160,8424],{},[902,71162,33877],{"encoding":904},[38,71164,71165],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,71168,71170],{"className":71169},[886],[888,71171,71172],{"xmlns":890},[892,71173,71174,71184],{},[895,71175,71176,71178],{},[1850,71177,1852],{},[3243,71179,71180,71182],{},[898,71181,1802],{},[1701,71183,8424],{},[902,71185,71186],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,71189,71191],{"className":71190},[886],[888,71192,71193],{"xmlns":890},[892,71194,71195,71201],{},[895,71196,71197,71199],{},[898,71198,6909],{},[898,71200,1658],{},[902,71202,59038],{"encoding":904}," nad bodem ",[883,71205,71207],{"className":71206},[886],[888,71208,71209],{"xmlns":890},[892,71210,71211,71215],{},[895,71212,71213],{},[898,71214,1983],{},[902,71216,1983],{"encoding":904},[883,71218,71220],{"className":71219},[886],[888,71221,71222],{"xmlns":890,"display":2252},[892,71223,71224,71331],{},[2256,71225,71226],{"width":2258},[2260,71227,71228,71230,71324,71326],{},[2263,71229],{"width":2265},[2263,71231,71232],{},[895,71233,71234,71236,71238,71240,71242,71244,71246,71248],{},[898,71235,1680],{},[1701,71237,1792],{},[898,71239,1661],{},[1701,71241,1799],{"stretchy":1798},[898,71243,1802],{},[1701,71245,1805],{"stretchy":1798},[1701,71247,1792],{},[895,71249,71250,71253],{},[1701,71251,71252],{"fence":2011},"{",[2256,71254,71257,71296],{"rowspacing":71255,"columnalign":71256,"columnspacing":19336},"0.36em","left left",[2260,71258,71259,71275],{},[2263,71260,71261],{},[2363,71262,71263],{"scriptlevel":1852,"displaystyle":1798},[895,71264,71265,71267,71269,71271,71273],{},[898,71266,6909],{},[898,71268,1658],{},[1701,71270,1799],{"stretchy":1798},[898,71272,1802],{},[1701,71274,1805],{"stretchy":1798},[2263,71276,71277],{},[2363,71278,71279],{"scriptlevel":1852,"displaystyle":1798},[895,71280,71281,71284,71286,71288,71294],{},[1939,71282,71283],{},"pro ",[898,71285,1802],{},[1701,71287,8554],{},[3243,71289,71290,71292],{},[898,71291,1802],{},[1701,71293,8424],{},[1701,71295,2012],{"separator":2011},[2260,71297,71298,71304],{},[2263,71299,71300],{},[2363,71301,71302],{"scriptlevel":1852,"displaystyle":1798},[1850,71303,1852],{},[2263,71305,71306],{},[2363,71307,71308],{"scriptlevel":1852,"displaystyle":1798},[895,71309,71310,71312,71314,71316,71322],{},[1939,71311,71283],{},[898,71313,1802],{},[1701,71315,7530],{},[3243,71317,71318,71320],{},[898,71319,1802],{},[1701,71321,8424],{},[1701,71323,2012],{"separator":2011},[2263,71325],{"width":2265},[2263,71327,71328],{},[1939,71329,71330],{},"(3.15)",[902,71332,71333],{"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}",[724,71335,8380,71336,71353,71354,71371,71372,45521,71402,71405],{},[883,71337,71339],{"className":71338},[886],[888,71340,71341],{"xmlns":890},[892,71342,71343,71351],{},[895,71344,71345],{},[3243,71346,71347,71349],{},[898,71348,1802],{},[1701,71350,8424],{},[902,71352,33877],{"encoding":904}," je bod minima ",[883,71355,71357],{"className":71356},[886],[888,71358,71359],{"xmlns":890},[892,71360,71361,71369],{},[895,71362,71363,71365,71367],{},[898,71364,1983],{},[898,71366,44362],{},[898,71368,1658],{},[902,71370,59057],{"encoding":904},". Bod ",[883,71373,71375],{"className":71374},[886],[888,71376,71377],{"xmlns":890},[892,71378,71379,71399],{},[895,71380,71381,71383,71389,71391,71397],{},[1701,71382,1799],{"stretchy":1798},[3243,71384,71385,71387],{},[898,71386,1802],{},[1701,71388,8424],{},[1701,71390,2012],{"separator":2011},[3243,71392,71393,71395],{},[898,71394,1680],{},[1701,71396,8424],{},[1701,71398,1805],{"stretchy":1798},[902,71400,71401],{"encoding":904},"(Q^*, P^*)",[38,71403,71404],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1635,71407,71408,71413],{},[724,71409,71410,71412],{},[883,71411,3140],{}," Postup — jak odvodit nabídku firmy",[152,71414,71415,71464,71559,71614,71685],{},[123,71416,71417,71418,2633,71440,1715],{},"Ze zadaných nákladů určete ",[883,71419,71421],{"className":71420},[886],[888,71422,71423],{"xmlns":890},[892,71424,71425,71437],{},[895,71426,71427,71429,71431,71433,71435],{},[898,71428,6909],{},[898,71430,1658],{},[1701,71432,1799],{"stretchy":1798},[898,71434,1802],{},[1701,71436,1805],{"stretchy":1798},[902,71438,71439],{"encoding":904},"MC(Q)",[883,71441,71443],{"className":71442},[886],[888,71444,71445],{"xmlns":890},[892,71446,71447,71461],{},[895,71448,71449,71451,71453,71455,71457,71459],{},[898,71450,1983],{},[898,71452,44362],{},[898,71454,1658],{},[1701,71456,1799],{"stretchy":1798},[898,71458,1802],{},[1701,71460,1805],{"stretchy":1798},[902,71462,71463],{"encoding":904},"AVC(Q)",[123,71465,71466,71467,71484,71485,71502,71503,71535,71536,2506],{},"Najděte ",[883,71468,71470],{"className":71469},[886],[888,71471,71472],{"xmlns":890},[892,71473,71474,71482],{},[895,71475,71476],{},[3243,71477,71478,71480],{},[898,71479,1802],{},[1701,71481,8424],{},[902,71483,33877],{"encoding":904}," jako bod minima ",[883,71486,71488],{"className":71487},[886],[888,71489,71490],{"xmlns":890},[892,71491,71492,71500],{},[895,71493,71494,71496,71498],{},[898,71495,1983],{},[898,71497,44362],{},[898,71499,1658],{},[902,71501,59057],{"encoding":904}," (řešením ",[883,71504,71506],{"className":71505},[886],[888,71507,71508],{"xmlns":890},[892,71509,71510,71532],{},[895,71511,71512,71514,71516,71522,71524,71526,71528,71530],{},[898,71513,1983],{},[898,71515,44362],{},[3243,71517,71518,71520],{},[898,71519,1658],{},[1701,71521,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,71523,1799],{"stretchy":1798},[898,71525,1802],{},[1701,71527,1805],{"stretchy":1798},[1701,71529,1792],{},[1850,71531,1852],{},[902,71533,71534],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,71537,71539],{"className":71538},[886],[888,71540,71541],{"xmlns":890},[892,71542,71543,71557],{},[895,71544,71545,71547,71549,71551,71553,71555],{},[898,71546,1983],{},[898,71548,44362],{},[898,71550,1658],{},[1701,71552,1792],{},[898,71554,6909],{},[898,71556,1658],{},[902,71558,58994],{"encoding":904},[123,71560,69467,71561,71613],{},[883,71562,71564],{"className":71563},[886],[888,71565,71566],{"xmlns":890},[892,71567,71568,71610],{},[895,71569,71570,71576,71578,71580,71582,71584,71590,71592,71594,71596,71598,71600,71602,71608],{},[3243,71571,71572,71574],{},[898,71573,1680],{},[1701,71575,8424],{},[1701,71577,1792],{},[898,71579,6909],{},[898,71581,1658],{},[1701,71583,1799],{"stretchy":1798},[3243,71585,71586,71588],{},[898,71587,1802],{},[1701,71589,8424],{},[1701,71591,1805],{"stretchy":1798},[1701,71593,1792],{},[898,71595,1983],{},[898,71597,44362],{},[898,71599,1658],{},[1701,71601,1799],{"stretchy":1798},[3243,71603,71604,71606],{},[898,71605,1802],{},[1701,71607,8424],{},[1701,71609,1805],{"stretchy":1798},[902,71611,71612],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,71615,71616,71617,10536,71649,71671,71672,1715],{},"Zapište nabídku: ",[883,71618,71620],{"className":71619},[886],[888,71621,71622],{"xmlns":890},[892,71623,71624,71646],{},[895,71625,71626,71628,71630,71632,71634,71636,71638,71640,71642,71644],{},[898,71627,1661],{},[1701,71629,1799],{"stretchy":1798},[898,71631,1802],{},[1701,71633,1805],{"stretchy":1798},[1701,71635,1792],{},[898,71637,6909],{},[898,71639,1658],{},[1701,71641,1799],{"stretchy":1798},[898,71643,1802],{},[1701,71645,1805],{"stretchy":1798},[902,71647,71648],{"encoding":904},"S(Q) = MC(Q)",[883,71650,71652],{"className":71651},[886],[888,71653,71654],{"xmlns":890},[892,71655,71656,71668],{},[895,71657,71658,71660,71662],{},[898,71659,1802],{},[1701,71661,8554],{},[3243,71663,71664,71666],{},[898,71665,1802],{},[1701,71667,8424],{},[902,71669,71670],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,71673,71675],{"className":71674},[886],[888,71676,71677],{"xmlns":890},[892,71678,71679,71683],{},[895,71680,71681],{},[1850,71682,1852],{},[902,71684,1852],{"encoding":904},[123,71686,71687,71688,71720],{},"V případě potřeby vyjádřete inverzi ",[883,71689,71691],{"className":71690},[886],[888,71692,71693],{"xmlns":890},[892,71694,71695,71717],{},[895,71696,71697,71699,71701,71711,71713,71715],{},[898,71698,1802],{},[1701,71700,1792],{},[3243,71702,71703,71705],{},[898,71704,1661],{},[895,71706,71707,71709],{},[1701,71708,2317],{},[1850,71710,4062],{},[1701,71712,1799],{"stretchy":1798},[898,71714,1680],{},[1701,71716,1805],{"stretchy":1798},[902,71718,71719],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,71722,71723],{},[614,71724,71725,71726,1343,71741,2633,71758,33234,71773,71786,71787,71812,71813,71826,71827,71844,71845,71862,71863,71880],{},"Obrázek 3.14: Křivky ",[883,71727,71729],{"className":71728},[886],[888,71730,71731],{"xmlns":890},[892,71732,71733,71739],{},[895,71734,71735,71737],{},[898,71736,1983],{},[898,71738,1658],{},[902,71740,59306],{"encoding":904},[883,71742,71744],{"className":71743},[886],[888,71745,71746],{"xmlns":890},[892,71747,71748,71756],{},[895,71749,71750,71752,71754],{},[898,71751,1983],{},[898,71753,44362],{},[898,71755,1658],{},[902,71757,59057],{"encoding":904},[883,71759,71761],{"className":71760},[886],[888,71762,71763],{"xmlns":890},[892,71764,71765,71771],{},[895,71766,71767,71769],{},[898,71768,6909],{},[898,71770,1658],{},[902,71772,59038],{"encoding":904},[883,71774,71776],{"className":71775},[886],[888,71777,71778],{"xmlns":890},[892,71779,71780,71784],{},[895,71781,71782],{},[898,71783,900],{},[902,71785,900],{"encoding":904},"; křivka nabídky ",[883,71788,71790],{"className":71789},[886],[888,71791,71792],{"xmlns":890},[892,71793,71794,71810],{},[895,71795,71796,71798,71800,71802,71804,71806,71808],{},[898,71797,1680],{},[1701,71799,1792],{},[898,71801,6909],{},[898,71803,1658],{},[1701,71805,1799],{"stretchy":1798},[898,71807,1802],{},[1701,71809,1805],{"stretchy":1798},[902,71811,71112],{"encoding":904}," začíná v bodě ",[883,71814,71816],{"className":71815},[886],[888,71817,71818],{"xmlns":890},[892,71819,71820,71824],{},[895,71821,71822],{},[898,71823,1983],{},[902,71825,1983],{"encoding":904}," odpovídajícím minimu ",[883,71828,71830],{"className":71829},[886],[888,71831,71832],{"xmlns":890},[892,71833,71834,71842],{},[895,71835,71836,71838,71840],{},[898,71837,1983],{},[898,71839,44362],{},[898,71841,1658],{},[902,71843,59057],{"encoding":904}," při ceně ",[883,71846,71848],{"className":71847},[886],[888,71849,71850],{"xmlns":890},[892,71851,71852,71860],{},[895,71853,71854],{},[3243,71855,71856,71858],{},[898,71857,1680],{},[1701,71859,8424],{},[902,71861,8474],{"encoding":904}," (minimální cena nabídky); pod ",[883,71864,71866],{"className":71865},[886],[888,71867,71868],{"xmlns":890},[892,71869,71870,71878],{},[895,71871,71872],{},[3243,71873,71874,71876],{},[898,71875,1802],{},[1701,71877,8424],{},[902,71879,33877],{"encoding":904}," je nabídka nulová.",[41376,71882,71884],{"id":71883},"příklad-312","Příklad 3.12",[724,71886,71887,61268,71889,71935],{},[38,71888,59733],{},[883,71890,71892],{"className":71891},[886],[888,71893,71894],{"xmlns":890},[892,71895,71896,71932],{},[895,71897,71898,71900,71902,71904,71906,71912,71914,71916,71922,71924,71926,71928,71930],{},[898,71899,5877],{},[898,71901,1658],{},[1701,71903,1792],{},[1850,71905,4033],{},[3243,71907,71908,71910],{},[898,71909,1802],{},[1850,71911,3646],{},[1701,71913,2317],{},[1850,71915,3938],{},[3243,71917,71918,71920],{},[898,71919,1802],{},[1850,71921,3938],{},[1701,71923,1703],{},[1850,71925,40275],{},[898,71927,1802],{},[1701,71929,1703],{},[1850,71931,3703],{},[902,71933,71934],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,71937,71938,4088,71940,71977,71978,2246],{},[38,71939,5001],{},[883,71941,71943],{"className":71942},[886],[888,71944,71945],{"xmlns":890},[892,71946,71947,71974],{},[895,71948,71949,71951,71953,71955,71958,71964,71966,71968,71970,71972],{},[898,71950,6909],{},[898,71952,1658],{},[1701,71954,1792],{},[1850,71956,71957],{},"0,3",[3243,71959,71960,71962],{},[898,71961,1802],{},[1850,71963,3938],{},[1701,71965,2317],{},[1850,71967,6460],{},[898,71969,1802],{},[1701,71971,1703],{},[1850,71973,40275],{},[902,71975,71976],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,71979,71981],{"className":71980},[886],[888,71982,71983],{"xmlns":890},[892,71984,71985,71995],{},[895,71986,71987,71989,71991,71993],{},[898,71988,1680],{},[1701,71990,1792],{},[898,71992,6909],{},[898,71994,1658],{},[902,71996,71997],{"encoding":904},"P = MC",[883,71999,72001],{"className":72000},[886],[888,72002,72003],{"xmlns":890,"display":2252},[892,72004,72005,72030],{},[895,72006,72007,72009,72011,72013,72019,72021,72023,72025,72027],{},[898,72008,1680],{},[1701,72010,1792],{},[1850,72012,71957],{},[3243,72014,72015,72017],{},[898,72016,1802],{},[1850,72018,3938],{},[1701,72020,2317],{},[1850,72022,6460],{},[898,72024,1802],{},[1701,72026,1703],{},[1850,72028,72029],{},"15.",[902,72031,72032],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,72034,72035,72036,9447,72049,72062],{},"Vyjádření ",[883,72037,72039],{"className":72038},[886],[888,72040,72041],{"xmlns":890},[892,72042,72043,72047],{},[895,72044,72045],{},[898,72046,1802],{},[902,72048,1802],{"encoding":904},[883,72050,72052],{"className":72051},[886],[888,72053,72054],{"xmlns":890},[892,72055,72056,72060],{},[895,72057,72058],{},[898,72059,1680],{},[902,72061,1680],{"encoding":904}," doplněním na čtverec:",[883,72064,72066],{"className":72065},[886],[888,72067,72068],{"xmlns":890,"display":2252},[892,72069,72070,72160],{},[895,72071,72072,72074,72076,72078,72116,72118,72120,72142,72144,72158],{},[898,72073,1680],{},[1701,72075,1792],{},[1850,72077,71957],{},[895,72079,72080,72082,72104,72106,72114],{},[1701,72081,1799],{"fence":2011},[3243,72083,72084,72102],{},[895,72085,72086,72088,72090,72092,72100],{},[1701,72087,1799],{"fence":2011},[898,72089,1802],{},[1701,72091,2317],{},[2363,72093,72094],{"scriptlevel":1852,"displaystyle":1798},[3726,72095,72096,72098],{},[1850,72097,13096],{},[1850,72099,3646],{},[1701,72101,1805],{"fence":2011},[1850,72103,3938],{},[1701,72105,1703],{},[2363,72107,72108],{"scriptlevel":1852,"displaystyle":1798},[3726,72109,72110,72112],{},[1850,72111,7206],{},[1850,72113,8073],{},[1701,72115,1805],{"fence":2011},[1701,72117,2012],{"separator":2011},[9942,72119],{"width":9944},[3243,72121,72122,72140],{},[895,72123,72124,72126,72128,72130,72138],{},[1701,72125,1799],{"fence":2011},[898,72127,1802],{},[1701,72129,2317],{},[2363,72131,72132],{"scriptlevel":1852,"displaystyle":1798},[3726,72133,72134,72136],{},[1850,72135,13096],{},[1850,72137,3646],{},[1701,72139,1805],{"fence":2011},[1850,72141,3938],{},[1701,72143,1792],{},[3726,72145,72146,72156],{},[895,72147,72148,72150,72152,72154],{},[1850,72149,3776],{},[898,72151,1680],{},[1701,72153,2317],{},[1850,72155,7206],{},[1850,72157,8073],{},[1701,72159,2012],{"separator":2011},[902,72161,72162],{"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},",[883,72164,72166],{"className":72165},[886],[888,72167,72168],{"xmlns":890,"display":2252},[892,72169,72170,72202],{},[895,72171,72172,72174,72176,72182,72184,72200],{},[898,72173,1802],{},[1701,72175,1792],{},[3726,72177,72178,72180],{},[1850,72179,13096],{},[1850,72181,3646],{},[1701,72183,1703],{},[3726,72185,72186,72198],{},[12179,72187,72188],{},[895,72189,72190,72192,72194,72196],{},[1850,72191,3776],{},[898,72193,1680],{},[1701,72195,2317],{},[1850,72197,7206],{},[1850,72199,3646],{},[898,72201,1715],{"mathvariant":2334},[902,72203,72204],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,72206,70764,72207,1343,72245,1343,72293,72327,72328,1715],{},[883,72208,72210],{"className":72209},[886],[888,72211,72212],{"xmlns":890},[892,72213,72214,72242],{},[895,72215,72216,72218,72220,72222,72224,72226,72232,72234,72236,72238,72240],{},[898,72217,1983],{},[898,72219,44362],{},[898,72221,1658],{},[1701,72223,1792],{},[1850,72225,4033],{},[3243,72227,72228,72230],{},[898,72229,1802],{},[1850,72231,3938],{},[1701,72233,2317],{},[1850,72235,3938],{},[898,72237,1802],{},[1701,72239,1703],{},[1850,72241,40275],{},[902,72243,72244],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,72246,72248],{"className":72247},[886],[888,72249,72250],{"xmlns":890},[892,72251,72252,72290],{},[895,72253,72254,72256,72258,72264,72266,72268,72270,72272,72274,72276,72278,72280,72286,72288],{},[898,72255,1983],{},[898,72257,44362],{},[3243,72259,72260,72262],{},[898,72261,1658],{},[1701,72263,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,72265,1792],{},[1850,72267,6930],{},[898,72269,1802],{},[1701,72271,2317],{},[1850,72273,3938],{},[1701,72275,1792],{},[1850,72277,1852],{},[1701,72279,8061],{},[3243,72281,72282,72284],{},[898,72283,1802],{},[1701,72285,8424],{},[1701,72287,1792],{},[1850,72289,3703],{},[902,72291,72292],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,72294,72296],{"className":72295},[886],[888,72297,72298],{"xmlns":890},[892,72299,72300,72324],{},[895,72301,72302,72304,72306,72316,72318,72320,72322],{},[898,72303,1983],{},[898,72305,44362],{},[3243,72307,72308,72310],{},[898,72309,1658],{},[895,72311,72312,72314],{},[1701,72313,4783],{"mathvariant":2334},[1701,72315,4783],{"mathvariant":2334},[1701,72317,1792],{},[1850,72319,6930],{},[1701,72321,7491],{},[1850,72323,1852],{},[902,72325,72326],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,72329,72331],{"className":72330},[886],[888,72332,72333],{"xmlns":890},[892,72334,72335,72371],{},[895,72336,72337,72343,72345,72347,72349,72351,72353,72355,72357,72359,72361,72363,72365,72367,72369],{},[3243,72338,72339,72341],{},[898,72340,1680],{},[1701,72342,8424],{},[1701,72344,1792],{},[898,72346,6909],{},[898,72348,1658],{},[1701,72350,1799],{"stretchy":1798},[1850,72352,3703],{},[1701,72354,1805],{"stretchy":1798},[1701,72356,1792],{},[1850,72358,3776],{},[1701,72360,2317],{},[1850,72362,3665],{},[1701,72364,1703],{},[1850,72366,40275],{},[1701,72368,1792],{},[1850,72370,4225],{},[902,72372,72373],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,72375,72376],{},[38,72377,72378],{},"Závěr.",[883,72380,72382],{"className":72381},[886],[888,72383,72384],{"xmlns":890,"display":2252},[892,72385,72386,72472],{},[895,72387,72388,72390,72392,72394,72396,72398,72400,72402],{},[898,72389,1680],{},[1701,72391,1792],{},[898,72393,1661],{},[1701,72395,1799],{"stretchy":1798},[898,72397,1802],{},[1701,72399,1805],{"stretchy":1798},[1701,72401,1792],{},[895,72403,72404,72406],{},[1701,72405,71252],{"fence":2011},[2256,72407,72408,72450],{"rowspacing":71255,"columnalign":71256,"columnspacing":19336},[2260,72409,72410,72434],{},[2263,72411,72412],{},[2363,72413,72414],{"scriptlevel":1852,"displaystyle":1798},[895,72415,72416,72418,72424,72426,72428,72430,72432],{},[1850,72417,71957],{},[3243,72419,72420,72422],{},[898,72421,1802],{},[1850,72423,3938],{},[1701,72425,2317],{},[1850,72427,6460],{},[898,72429,1802],{},[1701,72431,1703],{},[1850,72433,40275],{},[2263,72435,72436],{},[2363,72437,72438],{"scriptlevel":1852,"displaystyle":1798},[895,72439,72440,72442,72444,72446,72448],{},[1939,72441,71283],{},[898,72443,1802],{},[1701,72445,8554],{},[1850,72447,3703],{},[1701,72449,2012],{"separator":2011},[2260,72451,72452,72458],{},[2263,72453,72454],{},[2363,72455,72456],{"scriptlevel":1852,"displaystyle":1798},[1850,72457,1852],{},[2263,72459,72460],{},[2363,72461,72462],{"scriptlevel":1852,"displaystyle":1798},[895,72463,72464,72466,72468,72470],{},[1939,72465,71283],{},[898,72467,1802],{},[1701,72469,7530],{},[1850,72471,23373],{},[902,72473,72474],{"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}",[724,72476,72477],{},[614,72478,72479,72480,72495,72496,1715],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,72481,72483],{"className":72482},[886],[888,72484,72485],{"xmlns":890},[892,72486,72487,72493],{},[895,72488,72489,72491],{},[898,72490,6909],{},[898,72492,1658],{},[902,72494,59038],{"encoding":904}," ležící nad minimem ",[883,72497,72499],{"className":72498},[886],[888,72500,72501],{"xmlns":890},[892,72502,72503,72511],{},[895,72504,72505,72507,72509],{},[898,72506,1983],{},[898,72508,44362],{},[898,72510,1658],{},[902,72512,59057],{"encoding":904},[115,72514,72516],{"id":72515},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,72518,72519,72520,72524,72525,72540,72541,72561,72562,2633,72565,72568,72569,72571,72572,23990,72594,72596,72597,2633,72599,62472,72602,4088,72605,45835,72620,72635],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,72521,72523],{"className":72522,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,72526,72528],{"className":72527},[886],[888,72529,72530],{"xmlns":890},[892,72531,72532,72538],{},[895,72533,72534,72536],{},[898,72535,5877],{},[898,72537,8068],{},[902,72539,8168],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,72542,72544],{"className":72543},[886],[888,72545,72546],{"xmlns":890},[892,72547,72548,72558],{},[895,72549,72550,72552,72554,72556],{},[898,72551,5877],{},[898,72553,8068],{},[898,72555,8741],{"mathvariant":2334},[898,72557,1802],{},[902,72559,72560],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,72563,72564],{},"fixních",[38,72566,72567],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,72570,68071],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,72573,72575],{"className":72574},[886],[888,72576,72577],{"xmlns":890},[892,72578,72579,72591],{},[895,72580,72581,72583,72585,72587,72589],{},[898,72582,5877],{},[898,72584,8068],{},[1701,72586,2317],{},[898,72588,5877],{},[898,72590,1658],{},[902,72592,72593],{"encoding":904},"TR - TC",[38,72595,58918],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,72598,60230],{},[38,72600,72601],{},"mezní náklady",[207,72603,1145],{"className":72604,"dataFsResolvedFilePath":764,"href":765},[210],[883,72606,72608],{"className":72607},[886],[888,72609,72610],{"xmlns":890},[892,72611,72612,72618],{},[895,72613,72614,72616],{},[898,72615,5877],{},[898,72617,8068],{},[902,72619,8168],{"encoding":904},[883,72621,72623],{"className":72622},[886],[888,72624,72625],{"xmlns":890},[892,72626,72627,72633],{},[895,72628,72629,72631],{},[898,72630,5877],{},[898,72632,1658],{},[902,72634,7326],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,72637,72638,72700,72766,72828],{},[123,72639,72640,72643,72644,14450,72659,1715],{},[38,72641,72642],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,72645,72647],{"className":72646},[886],[888,72648,72649],{"xmlns":890},[892,72650,72651,72657],{},[895,72652,72653,72655],{},[898,72654,1983],{},[898,72656,1658],{},[902,72658,59306],{"encoding":904},[883,72660,72662],{"className":72661},[886],[888,72663,72664],{"xmlns":890},[892,72665,72666,72698],{},[895,72667,72668,72670,72672,72674,72680,72682,72684,72686,72688,72690,72696],{},[898,72669,1983],{},[898,72671,1658],{},[1701,72673,1799],{"stretchy":1798},[1845,72675,72676,72678],{},[898,72677,1802],{},[1850,72679,1852],{},[1701,72681,1805],{"stretchy":1798},[1701,72683,1792],{},[898,72685,6909],{},[898,72687,1658],{},[1701,72689,1799],{"stretchy":1798},[1845,72691,72692,72694],{},[898,72693,1802],{},[1850,72695,1852],{},[1701,72697,1805],{"stretchy":1798},[902,72699,66315],{"encoding":904},[123,72701,72702,72643,72705,14450,72722,1715],{},[38,72703,72704],{},"Princip minimalizace průměrných variabilních nákladů:",[883,72706,72708],{"className":72707},[886],[888,72709,72710],{"xmlns":890},[892,72711,72712,72720],{},[895,72713,72714,72716,72718],{},[898,72715,1983],{},[898,72717,44362],{},[898,72719,1658],{},[902,72721,59057],{"encoding":904},[883,72723,72725],{"className":72724},[886],[888,72726,72727],{"xmlns":890},[892,72728,72729,72763],{},[895,72730,72731,72733,72735,72737,72739,72745,72747,72749,72751,72753,72755,72761],{},[898,72732,1983],{},[898,72734,44362],{},[898,72736,1658],{},[1701,72738,1799],{"stretchy":1798},[1845,72740,72741,72743],{},[898,72742,1802],{},[1850,72744,1852],{},[1701,72746,1805],{"stretchy":1798},[1701,72748,1792],{},[898,72750,6909],{},[898,72752,1658],{},[1701,72754,1799],{"stretchy":1798},[1845,72756,72757,72759],{},[898,72758,1802],{},[1850,72760,1852],{},[1701,72762,1805],{"stretchy":1798},[902,72764,72765],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,72767,72768,72771,72772,14450,72787,1715],{},[38,72769,72770],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,72773,72775],{"className":72774},[886],[888,72776,72777],{"xmlns":890},[892,72778,72779,72785],{},[895,72780,72781,72783],{},[898,72782,1680],{},[898,72784,8068],{},[902,72786,67225],{"encoding":904},[883,72788,72790],{"className":72789},[886],[888,72791,72792],{"xmlns":890},[892,72793,72794,72826],{},[895,72795,72796,72798,72800,72802,72808,72810,72812,72814,72816,72818,72824],{},[898,72797,6909],{},[898,72799,8068],{},[1701,72801,1799],{"stretchy":1798},[1845,72803,72804,72806],{},[898,72805,1802],{},[1850,72807,1852],{},[1701,72809,1805],{"stretchy":1798},[1701,72811,1792],{},[898,72813,6909],{},[898,72815,1658],{},[1701,72817,1799],{"stretchy":1798},[1845,72819,72820,72822],{},[898,72821,1802],{},[1850,72823,1852],{},[1701,72825,1805],{"stretchy":1798},[902,72827,69391],{"encoding":904},[123,72829,72830,4088,72833,10536,72869,71671,72890,2020,72903,71353,72920,1715],{},[38,72831,72832],{},"Funkce nabídky firmy:",[883,72834,72836],{"className":72835},[886],[888,72837,72838],{"xmlns":890},[892,72839,72840,72866],{},[895,72841,72842,72844,72846,72848,72850,72852,72854,72856,72858,72860,72862,72864],{},[898,72843,1680],{},[1701,72845,1792],{},[898,72847,1661],{},[1701,72849,1799],{"stretchy":1798},[898,72851,1802],{},[1701,72853,1805],{"stretchy":1798},[1701,72855,1792],{},[898,72857,6909],{},[898,72859,1658],{},[1701,72861,1799],{"stretchy":1798},[898,72863,1802],{},[1701,72865,1805],{"stretchy":1798},[902,72867,72868],{"encoding":904},"P = S(Q) = MC(Q)",[883,72870,72872],{"className":72871},[886],[888,72873,72874],{"xmlns":890},[892,72875,72876,72888],{},[895,72877,72878,72880,72882],{},[898,72879,1802],{},[1701,72881,8554],{},[3243,72883,72884,72886],{},[898,72885,1802],{},[1701,72887,8424],{},[902,72889,71670],{"encoding":904},[883,72891,72893],{"className":72892},[886],[888,72894,72895],{"xmlns":890},[892,72896,72897,72901],{},[895,72898,72899],{},[1850,72900,1852],{},[902,72902,1852],{"encoding":904},[883,72904,72906],{"className":72905},[886],[888,72907,72908],{"xmlns":890},[892,72909,72910,72918],{},[895,72911,72912],{},[3243,72913,72914,72916],{},[898,72915,1802],{},[1701,72917,8424],{},[902,72919,33877],{"encoding":904},[883,72921,72923],{"className":72922},[886],[888,72924,72925],{"xmlns":890},[892,72926,72927,72935],{},[895,72928,72929,72931,72933],{},[898,72930,1983],{},[898,72932,44362],{},[898,72934,1658],{},[902,72936,59057],{"encoding":904},[115,72938,53869],{"id":53868},[152,72940,72941,72944,72947,72950,72953,72956,72959,72962,72965,72968,72971],{},[123,72942,72943],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,72945,72946],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,72948,72949],{},"Jak se vypočte mezní příjem a co udává?",[123,72951,72952],{},"Z jakých složek se skládají celkové náklady?",[123,72954,72955],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,72957,72958],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,72960,72961],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,72963,72964],{},"Jak se vypočte zisk?",[123,72966,72967],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,72969,72970],{},"Co jsou body zvratu? Jak se najdou?",[123,72972,72973],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,72975,72977],{"id":72976},"úlohy-31328","Úlohy 3.1–3.28",[198,72979,72981],{"id":72980},"příjem-3135","Příjem (3.1–3.5)",[724,72983,72984,49417,72987,73015,73016,73031,73032,73047,73048,73063,73064,1343,73079,1343,73094,73109],{},[38,72985,72986],{},"3.1",[883,72988,72990],{"className":72989},[886],[888,72991,72992],{"xmlns":890},[892,72993,72994,73012],{},[895,72995,72996,72998,73000,73002,73004,73006,73008,73010],{},[898,72997,1680],{},[1701,72999,1792],{},[898,73001,1795],{},[1701,73003,1799],{"stretchy":1798},[898,73005,1802],{},[1701,73007,1805],{"stretchy":1798},[1701,73009,1792],{},[1850,73011,5158],{},[902,73013,73014],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,73017,73019],{"className":73018},[886],[888,73020,73021],{"xmlns":890},[892,73022,73023,73029],{},[895,73024,73025,73027],{},[898,73026,5877],{},[898,73028,8068],{},[902,73030,8168],{"encoding":904},", průměrný příjem ",[883,73033,73035],{"className":73034},[886],[888,73036,73037],{"xmlns":890},[892,73038,73039,73045],{},[895,73040,73041,73043],{},[898,73042,1983],{},[898,73044,8068],{},[902,73046,59191],{"encoding":904}," a mezní příjem ",[883,73049,73051],{"className":73050},[886],[888,73052,73053],{"xmlns":890},[892,73054,73055,73061],{},[895,73056,73057,73059],{},[898,73058,6909],{},[898,73060,8068],{},[902,73062,10697],{"encoding":904},". (c) Vypočtěte ",[883,73065,73067],{"className":73066},[886],[888,73068,73069],{"xmlns":890},[892,73070,73071,73077],{},[895,73072,73073,73075],{},[898,73074,5877],{},[898,73076,8068],{},[902,73078,8168],{"encoding":904},[883,73080,73082],{"className":73081},[886],[888,73083,73084],{"xmlns":890},[892,73085,73086,73092],{},[895,73087,73088,73090],{},[898,73089,1983],{},[898,73091,8068],{},[902,73093,59191],{"encoding":904},[883,73095,73097],{"className":73096},[886],[888,73098,73099],{"xmlns":890},[892,73100,73101,73107],{},[895,73102,73103,73105],{},[898,73104,6909],{},[898,73106,8068],{},[902,73108,10697],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,73111,73112,49417,73115,73015,73151,73031,73166,73047,73181,73063,73196,1343,73211,1343,73226,73241],{},[38,73113,73114],{},"3.2",[883,73116,73118],{"className":73117},[886],[888,73119,73120],{"xmlns":890},[892,73121,73122,73148],{},[895,73123,73124,73126,73128,73130,73132,73134,73136,73138,73140,73142,73144,73146],{},[898,73125,1680],{},[1701,73127,1792],{},[898,73129,1795],{},[1701,73131,1799],{"stretchy":1798},[898,73133,1802],{},[1701,73135,1805],{"stretchy":1798},[1701,73137,1792],{},[1701,73139,2317],{},[1850,73141,3684],{},[898,73143,1802],{},[1701,73145,1703],{},[1850,73147,13096],{},[902,73149,73150],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,73152,73154],{"className":73153},[886],[888,73155,73156],{"xmlns":890},[892,73157,73158,73164],{},[895,73159,73160,73162],{},[898,73161,5877],{},[898,73163,8068],{},[902,73165,8168],{"encoding":904},[883,73167,73169],{"className":73168},[886],[888,73170,73171],{"xmlns":890},[892,73172,73173,73179],{},[895,73174,73175,73177],{},[898,73176,1983],{},[898,73178,8068],{},[902,73180,59191],{"encoding":904},[883,73182,73184],{"className":73183},[886],[888,73185,73186],{"xmlns":890},[892,73187,73188,73194],{},[895,73189,73190,73192],{},[898,73191,6909],{},[898,73193,8068],{},[902,73195,10697],{"encoding":904},[883,73197,73199],{"className":73198},[886],[888,73200,73201],{"xmlns":890},[892,73202,73203,73209],{},[895,73204,73205,73207],{},[898,73206,5877],{},[898,73208,8068],{},[902,73210,8168],{"encoding":904},[883,73212,73214],{"className":73213},[886],[888,73215,73216],{"xmlns":890},[892,73217,73218,73224],{},[895,73219,73220,73222],{},[898,73221,1983],{},[898,73223,8068],{},[902,73225,59191],{"encoding":904},[883,73227,73229],{"className":73228},[886],[888,73230,73231],{"xmlns":890},[892,73232,73233,73239],{},[895,73234,73235,73237],{},[898,73236,6909],{},[898,73238,8068],{},[902,73240,10697],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,73243,73244,49417,73247,73284,73285,73031,73300,73047,73315,73330,73331,10536,73346,73372,73373,73388,73389,1343,73404,10536,73419,73372,73444,73459,73460,73473,73474,73489,73490,73505,73506,1343,73519,1343,73534,1343,73549,1715],{},[38,73245,73246],{},"3.3",[883,73248,73250],{"className":73249},[886],[888,73251,73252],{"xmlns":890},[892,73253,73254,73281],{},[895,73255,73256,73258,73260,73262,73264,73266,73268,73270,73273,73275],{},[898,73257,1680],{},[1701,73259,1792],{},[898,73261,1795],{},[1701,73263,1799],{"stretchy":1798},[898,73265,1802],{},[1701,73267,1805],{"stretchy":1798},[1701,73269,1792],{},[1850,73271,73272],{},"1200",[1701,73274,2317],{},[3243,73276,73277,73279],{},[898,73278,1802],{},[1850,73280,3938],{},[902,73282,73283],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,73286,73288],{"className":73287},[886],[888,73289,73290],{"xmlns":890},[892,73291,73292,73298],{},[895,73293,73294,73296],{},[898,73295,5877],{},[898,73297,8068],{},[902,73299,8168],{"encoding":904},[883,73301,73303],{"className":73302},[886],[888,73304,73305],{"xmlns":890},[892,73306,73307,73313],{},[895,73308,73309,73311],{},[898,73310,1983],{},[898,73312,8068],{},[902,73314,59191],{"encoding":904},[883,73316,73318],{"className":73317},[886],[888,73319,73320],{"xmlns":890},[892,73321,73322,73328],{},[895,73323,73324,73326],{},[898,73325,6909],{},[898,73327,8068],{},[902,73329,10697],{"encoding":904},". (b) Vypočtěte ",[883,73332,73334],{"className":73333},[886],[888,73335,73336],{"xmlns":890},[892,73337,73338,73344],{},[895,73339,73340,73342],{},[898,73341,5877],{},[898,73343,8068],{},[902,73345,8168],{"encoding":904},[883,73347,73349],{"className":73348},[886],[888,73350,73351],{"xmlns":890},[892,73352,73353,73369],{},[895,73354,73355,73357,73359,73361,73363,73365,73367],{},[898,73356,1802],{},[1701,73358,1792],{},[1850,73360,3703],{},[1701,73362,2012],{"separator":2011},[1850,73364,13096],{},[1701,73366,2012],{"separator":2011},[1850,73368,3776],{},[902,73370,73371],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,73374,73376],{"className":73375},[886],[888,73377,73378],{"xmlns":890},[892,73379,73380,73386],{},[895,73381,73382,73384],{},[898,73383,5877],{},[898,73385,8068],{},[902,73387,8168],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,73390,73392],{"className":73391},[886],[888,73393,73394],{"xmlns":890},[892,73395,73396,73402],{},[895,73397,73398,73400],{},[898,73399,1983],{},[898,73401,8068],{},[902,73403,59191],{"encoding":904},[883,73405,73407],{"className":73406},[886],[888,73408,73409],{"xmlns":890},[892,73410,73411,73417],{},[895,73412,73413,73415],{},[898,73414,6909],{},[898,73416,8068],{},[902,73418,10697],{"encoding":904},[883,73420,73422],{"className":73421},[886],[888,73423,73424],{"xmlns":890},[892,73425,73426,73442],{},[895,73427,73428,73430,73432,73434,73436,73438,73440],{},[898,73429,1802],{},[1701,73431,1792],{},[1850,73433,3703],{},[1701,73435,2012],{"separator":2011},[1850,73437,13096],{},[1701,73439,2012],{"separator":2011},[1850,73441,3776],{},[902,73443,73371],{"encoding":904},[883,73445,73447],{"className":73446},[886],[888,73448,73449],{"xmlns":890},[892,73450,73451,73457],{},[895,73452,73453,73455],{},[898,73454,6909],{},[898,73456,8068],{},[902,73458,10697],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,73461,73463],{"className":73462},[886],[888,73464,73465],{"xmlns":890},[892,73466,73467,73471],{},[895,73468,73469],{},[898,73470,1802],{},[902,73472,1802],{"encoding":904},", které maximalizuje ",[883,73475,73477],{"className":73476},[886],[888,73478,73479],{"xmlns":890},[892,73480,73481,73487],{},[895,73482,73483,73485],{},[898,73484,5877],{},[898,73486,8068],{},[902,73488,8168],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,73491,73493],{"className":73492},[886],[888,73494,73495],{"xmlns":890},[892,73496,73497,73503],{},[895,73498,73499,73501],{},[898,73500,5877],{},[898,73502,8068],{},[902,73504,8168],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,73507,73509],{"className":73508},[886],[888,73510,73511],{"xmlns":890},[892,73512,73513,73517],{},[895,73514,73515],{},[898,73516,1795],{},[902,73518,1795],{"encoding":904},[883,73520,73522],{"className":73521},[886],[888,73523,73524],{"xmlns":890},[892,73525,73526,73532],{},[895,73527,73528,73530],{},[898,73529,5877],{},[898,73531,8068],{},[902,73533,8168],{"encoding":904},[883,73535,73537],{"className":73536},[886],[888,73538,73539],{"xmlns":890},[892,73540,73541,73547],{},[895,73542,73543,73545],{},[898,73544,1983],{},[898,73546,8068],{},[902,73548,59191],{"encoding":904},[883,73550,73552],{"className":73551},[886],[888,73553,73554],{"xmlns":890},[892,73555,73556,73562],{},[895,73557,73558,73560],{},[898,73559,6909],{},[898,73561,8068],{},[902,73563,10697],{"encoding":904},[724,73565,73566,73569,73570,73600,73601,73616,73617,14213,73630,1343,73648,1343,73665,73683,73684,73706,73707,73722,73723,73736,73737,1715],{},[38,73567,73568],{},"3.4"," Je dán celkový příjem ",[883,73571,73573],{"className":73572},[886],[888,73574,73575],{"xmlns":890},[892,73576,73577,73597],{},[895,73578,73579,73581,73583,73585,73587,73589,73591],{},[898,73580,5877],{},[898,73582,8068],{},[1701,73584,1792],{},[1850,73586,73272],{},[898,73588,1802],{},[1701,73590,2317],{},[3243,73592,73593,73595],{},[898,73594,1802],{},[1850,73596,3646],{},[902,73598,73599],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,73602,73604],{"className":73603},[886],[888,73605,73606],{"xmlns":890},[892,73607,73608,73614],{},[895,73609,73610,73612],{},[898,73611,5877],{},[898,73613,8068],{},[902,73615,8168],{"encoding":904}," vzhledem ke ",[883,73618,73620],{"className":73619},[886],[888,73621,73622],{"xmlns":890},[892,73623,73624,73628],{},[895,73625,73626],{},[898,73627,1802],{},[902,73629,1802],{"encoding":904},[883,73631,73633],{"className":73632},[886],[888,73634,73635],{"xmlns":890},[892,73636,73637,73645],{},[895,73638,73639,73641,73643],{},[898,73640,1802],{},[1701,73642,1792],{},[1850,73644,4225],{},[902,73646,73647],{"encoding":904},"Q = 5",[883,73649,73651],{"className":73650},[886],[888,73652,73653],{"xmlns":890},[892,73654,73655,73663],{},[895,73656,73657,73659,73661],{},[898,73658,1802],{},[1701,73660,1792],{},[1850,73662,9650],{},[902,73664,9653],{"encoding":904},[883,73666,73668],{"className":73667},[886],[888,73669,73670],{"xmlns":890},[892,73671,73672,73680],{},[895,73673,73674,73676,73678],{},[898,73675,1802],{},[1701,73677,1792],{},[1850,73679,7592],{},[902,73681,73682],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,73685,73687],{"className":73686},[886],[888,73688,73689],{"xmlns":890},[892,73690,73691,73703],{},[895,73692,73693,73695,73697,73699,73701],{},[898,73694,6909],{},[898,73696,8068],{},[1701,73698,1799],{"stretchy":1798},[1850,73700,3703],{},[1701,73702,1805],{"stretchy":1798},[902,73704,73705],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,73708,73710],{"className":73709},[886],[888,73711,73712],{"xmlns":890},[892,73713,73714,73720],{},[895,73715,73716,73718],{},[898,73717,5877],{},[898,73719,8068],{},[902,73721,8168],{"encoding":904},", jestliže se ",[883,73724,73726],{"className":73725},[886],[888,73727,73728],{"xmlns":890},[892,73729,73730,73734],{},[895,73731,73732],{},[898,73733,1802],{},[902,73735,1802],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,73738,73740],{"className":73739},[886],[888,73741,73742],{"xmlns":890},[892,73743,73744,73750],{},[895,73745,73746,73748],{},[898,73747,5877],{},[898,73749,8068],{},[902,73751,8168],{"encoding":904},[724,73753,73754,73757,73758,73784,73785,73800,73801,73722,73816,73829],{},[38,73755,73756],{},"3.5"," Je dán mezní příjem ",[883,73759,73761],{"className":73760},[886],[888,73762,73763],{"xmlns":890},[892,73764,73765,73781],{},[895,73766,73767,73769,73771,73773,73775,73777,73779],{},[898,73768,6909],{},[898,73770,8068],{},[1701,73772,1792],{},[1701,73774,2317],{},[898,73776,1802],{},[1701,73778,1703],{},[1850,73780,13096],{},[902,73782,73783],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,73786,73788],{"className":73787},[886],[888,73789,73790],{"xmlns":890},[892,73791,73792,73798],{},[895,73793,73794,73796],{},[898,73795,5877],{},[898,73797,8068],{},[902,73799,8168],{"encoding":904},". (b) Vypočtěte změnu ",[883,73802,73804],{"className":73803},[886],[888,73805,73806],{"xmlns":890},[892,73807,73808,73814],{},[895,73809,73810,73812],{},[898,73811,5877],{},[898,73813,8068],{},[902,73815,8168],{"encoding":904},[883,73817,73819],{"className":73818},[886],[888,73820,73821],{"xmlns":890},[892,73822,73823,73827],{},[895,73824,73825],{},[898,73826,1802],{},[902,73828,1802],{"encoding":904}," změní z 8 na 12.",[198,73831,73833],{"id":73832},"náklady-36316","Náklady (3.6–3.16)",[724,73835,73836,73839,73840,73880,73881,73896,73897,73914,73915,73932,73933,73948,73949,73964,73965,73330,73980,1343,73995,1343,74012,1343,74029,1343,74044,1343,74059,10536,74074,74092,74093,1343,74108,1343,74123,74138],{},[38,73837,73838],{},"3.6"," Jsou dány celkové náklady ",[883,73841,73843],{"className":73842},[886],[888,73844,73845],{"xmlns":890},[892,73846,73847,73877],{},[895,73848,73849,73851,73853,73855,73857,73859,73861,73863,73865],{},[898,73850,5877],{},[898,73852,1658],{},[1701,73854,1792],{},[1850,73856,5158],{},[1701,73858,1703],{},[1850,73860,3938],{},[898,73862,1802],{},[1701,73864,1703],{},[2363,73866,73867],{"scriptlevel":1852,"displaystyle":1798},[3726,73868,73869,73875],{},[3243,73870,73871,73873],{},[898,73872,1802],{},[1850,73874,3938],{},[1850,73876,3703],{},[902,73878,73879],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,73882,73884],{"className":73883},[886],[888,73885,73886],{"xmlns":890},[892,73887,73888,73894],{},[895,73889,73890,73892],{},[898,73891,14492],{},[898,73893,1658],{},[902,73895,59237],{"encoding":904},", celkové variabilní náklady ",[883,73898,73900],{"className":73899},[886],[888,73901,73902],{"xmlns":890},[892,73903,73904,73912],{},[895,73905,73906,73908,73910],{},[898,73907,5877],{},[898,73909,44362],{},[898,73911,1658],{},[902,73913,59255],{"encoding":904},", průměrné variabilní náklady ",[883,73916,73918],{"className":73917},[886],[888,73919,73920],{"xmlns":890},[892,73921,73922,73930],{},[895,73923,73924,73926,73928],{},[898,73925,1983],{},[898,73927,44362],{},[898,73929,1658],{},[902,73931,59057],{"encoding":904},", variabilní náklady na jednotku ",[883,73934,73936],{"className":73935},[886],[888,73937,73938],{"xmlns":890},[892,73939,73940,73946],{},[895,73941,73942,73944],{},[898,73943,44362],{},[898,73945,1658],{},[902,73947,67351],{"encoding":904},", průměrné náklady ",[883,73950,73952],{"className":73951},[886],[888,73953,73954],{"xmlns":890},[892,73955,73956,73962],{},[895,73957,73958,73960],{},[898,73959,1983],{},[898,73961,1658],{},[902,73963,59306],{"encoding":904}," a mezní náklady ",[883,73966,73968],{"className":73967},[886],[888,73969,73970],{"xmlns":890},[892,73971,73972,73978],{},[895,73973,73974,73976],{},[898,73975,6909],{},[898,73977,1658],{},[902,73979,59038],{"encoding":904},[883,73981,73983],{"className":73982},[886],[888,73984,73985],{"xmlns":890},[892,73986,73987,73993],{},[895,73988,73989,73991],{},[898,73990,5877],{},[898,73992,1658],{},[902,73994,7326],{"encoding":904},[883,73996,73998],{"className":73997},[886],[888,73999,74000],{"xmlns":890},[892,74001,74002,74010],{},[895,74003,74004,74006,74008],{},[898,74005,5877],{},[898,74007,44362],{},[898,74009,1658],{},[902,74011,59255],{"encoding":904},[883,74013,74015],{"className":74014},[886],[888,74016,74017],{"xmlns":890},[892,74018,74019,74027],{},[895,74020,74021,74023,74025],{},[898,74022,1983],{},[898,74024,44362],{},[898,74026,1658],{},[902,74028,59057],{"encoding":904},[883,74030,74032],{"className":74031},[886],[888,74033,74034],{"xmlns":890},[892,74035,74036,74042],{},[895,74037,74038,74040],{},[898,74039,44362],{},[898,74041,1658],{},[902,74043,67351],{"encoding":904},[883,74045,74047],{"className":74046},[886],[888,74048,74049],{"xmlns":890},[892,74050,74051,74057],{},[895,74052,74053,74055],{},[898,74054,1983],{},[898,74056,1658],{},[902,74058,59306],{"encoding":904},[883,74060,74062],{"className":74061},[886],[888,74063,74064],{"xmlns":890},[892,74065,74066,74072],{},[895,74067,74068,74070],{},[898,74069,6909],{},[898,74071,1658],{},[902,74073,59038],{"encoding":904},[883,74075,74077],{"className":74076},[886],[888,74078,74079],{"xmlns":890},[892,74080,74081,74089],{},[895,74082,74083,74085,74087],{},[898,74084,1802],{},[1701,74086,1792],{},[1850,74088,7206],{},[902,74090,74091],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,74094,74096],{"className":74095},[886],[888,74097,74098],{"xmlns":890},[892,74099,74100,74106],{},[895,74101,74102,74104],{},[898,74103,5877],{},[898,74105,1658],{},[902,74107,7326],{"encoding":904},[883,74109,74111],{"className":74110},[886],[888,74112,74113],{"xmlns":890},[892,74114,74115,74121],{},[895,74116,74117,74119],{},[898,74118,1983],{},[898,74120,1658],{},[902,74122,59306],{"encoding":904},[883,74124,74126],{"className":74125},[886],[888,74127,74128],{"xmlns":890},[892,74129,74130,74136],{},[895,74131,74132,74134],{},[898,74133,6909],{},[898,74135,1658],{},[902,74137,59038],{"encoding":904}," rostou, resp. klesají.",[724,74140,74141,74144,74145,73964,74175,74190,74191,74206,74207,1343,74222,1343,74237,1715],{},[38,74142,74143],{},"3.7"," Jsou dány průměrné náklady ",[883,74146,74148],{"className":74147},[886],[888,74149,74150],{"xmlns":890},[892,74151,74152,74172],{},[895,74153,74154,74156,74158,74160,74168,74170],{},[898,74155,1983],{},[898,74157,1658],{},[1701,74159,1792],{},[2363,74161,74162],{"scriptlevel":1852,"displaystyle":1798},[3726,74163,74164,74166],{},[1850,74165,5158],{},[898,74167,1802],{},[1701,74169,1703],{},[1850,74171,13096],{},[902,74173,74174],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,74176,74178],{"className":74177},[886],[888,74179,74180],{"xmlns":890},[892,74181,74182,74188],{},[895,74183,74184,74186],{},[898,74185,6909],{},[898,74187,1658],{},[902,74189,59038],{"encoding":904},". (a) Určete celkové náklady ",[883,74192,74194],{"className":74193},[886],[888,74195,74196],{"xmlns":890},[892,74197,74198,74204],{},[895,74199,74200,74202],{},[898,74201,5877],{},[898,74203,1658],{},[902,74205,7326],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,74208,74210],{"className":74209},[886],[888,74211,74212],{"xmlns":890},[892,74213,74214,74220],{},[895,74215,74216,74218],{},[898,74217,1983],{},[898,74219,1658],{},[902,74221,59306],{"encoding":904},[883,74223,74225],{"className":74224},[886],[888,74226,74227],{"xmlns":890},[892,74228,74229,74235],{},[895,74230,74231,74233],{},[898,74232,5877],{},[898,74234,1658],{},[902,74236,7326],{"encoding":904},[883,74238,74240],{"className":74239},[886],[888,74241,74242],{"xmlns":890},[892,74243,74244,74250],{},[895,74245,74246,74248],{},[898,74247,6909],{},[898,74249,1658],{},[902,74251,59038],{"encoding":904},[724,74253,74254,73839,74257,74301,74302,1343,74319,1343,74334,1343,74351,1343,74366,1343,74383,1715],{},[38,74255,74256],{},"3.8",[883,74258,74260],{"className":74259},[886],[888,74261,74262],{"xmlns":890},[892,74263,74264,74298],{},[895,74265,74266,74268,74270,74272,74274,74276,74278,74280,74282,74284,74290,74292],{},[898,74267,5877],{},[898,74269,1658],{},[1701,74271,1792],{},[1850,74273,50694],{},[1701,74275,1703],{},[1850,74277,3776],{},[898,74279,1802],{},[1701,74281,2317],{},[1850,74283,6352],{},[3243,74285,74286,74288],{},[898,74287,1802],{},[1850,74289,3938],{},[1701,74291,1703],{},[3243,74293,74294,74296],{},[898,74295,1802],{},[1850,74297,3646],{},[902,74299,74300],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,74303,74305],{"className":74304},[886],[888,74306,74307],{"xmlns":890},[892,74308,74309,74317],{},[895,74310,74311,74313,74315],{},[898,74312,5877],{},[898,74314,44362],{},[898,74316,1658],{},[902,74318,59255],{"encoding":904},[883,74320,74322],{"className":74321},[886],[888,74323,74324],{"xmlns":890},[892,74325,74326,74332],{},[895,74327,74328,74330],{},[898,74329,14492],{},[898,74331,1658],{},[902,74333,59237],{"encoding":904},[883,74335,74337],{"className":74336},[886],[888,74338,74339],{"xmlns":890},[892,74340,74341,74349],{},[895,74342,74343,74345,74347],{},[898,74344,1983],{},[898,74346,44362],{},[898,74348,1658],{},[902,74350,59057],{"encoding":904},[883,74352,74354],{"className":74353},[886],[888,74355,74356],{"xmlns":890},[892,74357,74358,74364],{},[895,74359,74360,74362],{},[898,74361,1983],{},[898,74363,1658],{},[902,74365,59306],{"encoding":904},[883,74367,74369],{"className":74368},[886],[888,74370,74371],{"xmlns":890},[892,74372,74373,74381],{},[895,74374,74375,74377,74379],{},[898,74376,1983],{},[898,74378,14492],{},[898,74380,1658],{},[902,74382,59273],{"encoding":904},[883,74384,74386],{"className":74385},[886],[888,74387,74388],{"xmlns":890},[892,74389,74390,74396],{},[895,74391,74392,74394],{},[898,74393,6909],{},[898,74395,1658],{},[902,74397,59038],{"encoding":904},[724,74399,74400,73839,74403,74433,74434,73616,74449,10536,74462,1343,74480,1343,74498,73683,74516,73706,74538,74553,74554,74567,74568,1715],{},[38,74401,74402],{},"3.9",[883,74404,74406],{"className":74405},[886],[888,74407,74408],{"xmlns":890},[892,74409,74410,74430],{},[895,74411,74412,74414,74416,74418,74420,74422,74424],{},[898,74413,5877],{},[898,74415,1658],{},[1701,74417,1792],{},[1850,74419,19162],{},[1701,74421,1703],{},[1850,74423,3868],{},[3243,74425,74426,74428],{},[898,74427,1802],{},[1850,74429,3938],{},[902,74431,74432],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,74435,74437],{"className":74436},[886],[888,74438,74439],{"xmlns":890},[892,74440,74441,74447],{},[895,74442,74443,74445],{},[898,74444,5877],{},[898,74446,1658],{},[902,74448,7326],{"encoding":904},[883,74450,74452],{"className":74451},[886],[888,74453,74454],{"xmlns":890},[892,74455,74456,74460],{},[895,74457,74458],{},[898,74459,1802],{},[902,74461,1802],{"encoding":904},[883,74463,74465],{"className":74464},[886],[888,74466,74467],{"xmlns":890},[892,74468,74469,74477],{},[895,74470,74471,74473,74475],{},[898,74472,1802],{},[1701,74474,1792],{},[1850,74476,3703],{},[902,74478,74479],{"encoding":904},"Q = 10",[883,74481,74483],{"className":74482},[886],[888,74484,74485],{"xmlns":890},[892,74486,74487,74495],{},[895,74488,74489,74491,74493],{},[898,74490,1802],{},[1701,74492,1792],{},[1850,74494,13096],{},[902,74496,74497],{"encoding":904},"Q = 20",[883,74499,74501],{"className":74500},[886],[888,74502,74503],{"xmlns":890},[892,74504,74505,74513],{},[895,74506,74507,74509,74511],{},[898,74508,1802],{},[1701,74510,1792],{},[1850,74512,3776],{},[902,74514,74515],{"encoding":904},"Q = 30",[883,74517,74519],{"className":74518},[886],[888,74520,74521],{"xmlns":890},[892,74522,74523,74535],{},[895,74524,74525,74527,74529,74531,74533],{},[898,74526,6909],{},[898,74528,1658],{},[1701,74530,1799],{"stretchy":1798},[1850,74532,40275],{},[1701,74534,1805],{"stretchy":1798},[902,74536,74537],{"encoding":904},"MC(15)",[883,74539,74541],{"className":74540},[886],[888,74542,74543],{"xmlns":890},[892,74544,74545,74551],{},[895,74546,74547,74549],{},[898,74548,5877],{},[898,74550,1658],{},[902,74552,7326],{"encoding":904}," v důsledku změny ",[883,74555,74557],{"className":74556},[886],[888,74558,74559],{"xmlns":890},[892,74560,74561,74565],{},[895,74562,74563],{},[898,74564,1802],{},[902,74566,1802],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,74569,74571],{"className":74570},[886],[888,74572,74573],{"xmlns":890},[892,74574,74575,74581],{},[895,74576,74577,74579],{},[898,74578,5877],{},[898,74580,1658],{},[902,74582,7326],{"encoding":904},[724,74584,74585,74588,74589,74190,74625,74640,74641,73800,74660,74553,74675,74688],{},[38,74586,74587],{},"3.10"," Jsou dány mezní náklady ",[883,74590,74592],{"className":74591},[886],[888,74593,74594],{"xmlns":890},[892,74595,74596,74622],{},[895,74597,74598,74600,74602,74604,74606,74608,74610,74612,74614,74616],{},[898,74599,6909],{},[898,74601,1658],{},[1701,74603,1792],{},[1850,74605,7211],{},[1701,74607,2317],{},[1850,74609,45883],{},[898,74611,1802],{},[1701,74613,1703],{},[1850,74615,68305],{},[3243,74617,74618,74620],{},[898,74619,1802],{},[1850,74621,3938],{},[902,74623,74624],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,74626,74628],{"className":74627},[886],[888,74629,74630],{"xmlns":890},[892,74631,74632,74638],{},[895,74633,74634,74636],{},[898,74635,5877],{},[898,74637,1658],{},[902,74639,7326],{"encoding":904},", jestliže fixní náklady ",[883,74642,74644],{"className":74643},[886],[888,74645,74646],{"xmlns":890},[892,74647,74648,74658],{},[895,74649,74650,74652,74654,74656],{},[898,74651,14492],{},[898,74653,1658],{},[1701,74655,1792],{},[1850,74657,5158],{},[902,74659,15689],{"encoding":904},[883,74661,74663],{"className":74662},[886],[888,74664,74665],{"xmlns":890},[892,74666,74667,74673],{},[895,74668,74669,74671],{},[898,74670,5877],{},[898,74672,1658],{},[902,74674,7326],{"encoding":904},[883,74676,74678],{"className":74677},[886],[888,74679,74680],{"xmlns":890},[892,74681,74682,74686],{},[895,74683,74684],{},[898,74685,1802],{},[902,74687,1802],{"encoding":904}," z 15 na 20.",[724,74690,74691,73839,74694,74737,74738,74751,74752,74767,74768,74783,74784,74751,74797,74767,74814,74831,74832,74751,74845,74767,74860,74875,74876,74896,74897,74920],{},[38,74692,74693],{},"3.11",[883,74695,74697],{"className":74696},[886],[888,74698,74699],{"xmlns":890},[892,74700,74701,74735],{},[895,74702,74703,74705,74707,74709,74711,74713,74715,74717,74719,74721,74727,74729],{},[898,74704,5877],{},[898,74706,1658],{},[1701,74708,1792],{},[1850,74710,5158],{},[1701,74712,1703],{},[1850,74714,9071],{},[898,74716,1802],{},[1701,74718,2317],{},[1850,74720,4225],{},[3243,74722,74723,74725],{},[898,74724,1802],{},[1850,74726,3938],{},[1701,74728,1703],{},[3243,74730,74731,74733],{},[898,74732,1802],{},[1850,74734,3646],{},[902,74736,64653],{"encoding":904},". (a) Určete ",[883,74739,74741],{"className":74740},[886],[888,74742,74743],{"xmlns":890},[892,74744,74745,74749],{},[895,74746,74747],{},[898,74748,1802],{},[902,74750,1802],{"encoding":904},", které minimalizuje ",[883,74753,74755],{"className":74754},[886],[888,74756,74757],{"xmlns":890},[892,74758,74759,74765],{},[895,74760,74761,74763],{},[898,74762,6909],{},[898,74764,1658],{},[902,74766,59038],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,74769,74771],{"className":74770},[886],[888,74772,74773],{"xmlns":890},[892,74774,74775,74781],{},[895,74776,74777,74779],{},[898,74778,6909],{},[898,74780,1658],{},[902,74782,59038],{"encoding":904},". (b) Určete ",[883,74785,74787],{"className":74786},[886],[888,74788,74789],{"xmlns":890},[892,74790,74791,74795],{},[895,74792,74793],{},[898,74794,1802],{},[902,74796,1802],{"encoding":904},[883,74798,74800],{"className":74799},[886],[888,74801,74802],{"xmlns":890},[892,74803,74804,74812],{},[895,74805,74806,74808,74810],{},[898,74807,1983],{},[898,74809,44362],{},[898,74811,1658],{},[902,74813,59057],{"encoding":904},[883,74815,74817],{"className":74816},[886],[888,74818,74819],{"xmlns":890},[892,74820,74821,74829],{},[895,74822,74823,74825,74827],{},[898,74824,1983],{},[898,74826,44362],{},[898,74828,1658],{},[902,74830,59057],{"encoding":904},". (c) Určete ",[883,74833,74835],{"className":74834},[886],[888,74836,74837],{"xmlns":890},[892,74838,74839,74843],{},[895,74840,74841],{},[898,74842,1802],{},[902,74844,1802],{"encoding":904},[883,74846,74848],{"className":74847},[886],[888,74849,74850],{"xmlns":890},[892,74851,74852,74858],{},[895,74853,74854,74856],{},[898,74855,1983],{},[898,74857,1658],{},[902,74859,59306],{"encoding":904},[883,74861,74863],{"className":74862},[886],[888,74864,74865],{"xmlns":890},[892,74866,74867,74873],{},[895,74868,74869,74871],{},[898,74870,1983],{},[898,74872,1658],{},[902,74874,59306],{"encoding":904}," (rada: hledaný kořen ",[883,74877,74879],{"className":74878},[886],[888,74880,74881],{"xmlns":890},[892,74882,74883,74893],{},[895,74884,74885,74887],{},[898,74886,1983],{},[3243,74888,74889,74891],{},[898,74890,1658],{},[1701,74892,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,74894,74895],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,74898,74900],{"className":74899},[886],[888,74901,74902],{"xmlns":890},[892,74903,74904,74917],{},[895,74905,74906,74908,74911,74913,74915],{},[1701,74907,1799],{"stretchy":1798},[1850,74909,74910],{},"4,7",[1701,74912,12487],{"separator":2011},[1850,74914,9344],{},[1701,74916,1805],{"stretchy":1798},[902,74918,74919],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,74922,74923,74926,74927,6723,74955,74972,74973,2020,75014,75035],{},[38,74924,74925],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,74928,74930],{"className":74929},[886],[888,74931,74932],{"xmlns":890},[892,74933,74934,74952],{},[895,74935,74936,74938,74940,74942,74944,74946,74948,74950],{},[898,74937,1983],{},[898,74939,1658],{},[1701,74941,1792],{},[898,74943,1983],{},[898,74945,1658],{},[1701,74947,1799],{"stretchy":1798},[898,74949,1802],{},[1701,74951,1805],{"stretchy":1798},[902,74953,74954],{"encoding":904},"AC = AC(Q)",[883,74956,74958],{"className":74957},[886],[888,74959,74960],{"xmlns":890},[892,74961,74962,74970],{},[895,74963,74964],{},[1845,74965,74966,74968],{},[898,74967,1802],{},[1850,74969,1852],{},[902,74971,1855],{"encoding":904}," minimum, pak platí ",[883,74974,74976],{"className":74975},[886],[888,74977,74978],{"xmlns":890},[892,74979,74980,75012],{},[895,74981,74982,74984,74986,74988,74994,74996,74998,75000,75002,75004,75010],{},[898,74983,1983],{},[898,74985,1658],{},[1701,74987,1799],{"stretchy":1798},[1845,74989,74990,74992],{},[898,74991,1802],{},[1850,74993,1852],{},[1701,74995,1805],{"stretchy":1798},[1701,74997,1792],{},[898,74999,6909],{},[898,75001,1658],{},[1701,75003,1799],{"stretchy":1798},[1845,75005,75006,75008],{},[898,75007,1802],{},[1850,75009,1852],{},[1701,75011,1805],{"stretchy":1798},[902,75013,66315],{"encoding":904},[883,75015,75017],{"className":75016},[886],[888,75018,75019],{"xmlns":890},[892,75020,75021,75033],{},[895,75022,75023,75025,75027,75029,75031],{},[898,75024,6909],{},[898,75026,1658],{},[1701,75028,1799],{"stretchy":1798},[898,75030,1802],{},[1701,75032,1805],{"stretchy":1798},[902,75034,71439],{"encoding":904}," jsou mezní náklady.",[724,75037,75038,73839,75041,74301,75075,74751,75088,74767,75103,1715],{},[38,75039,75040],{},"3.13",[883,75042,75044],{"className":75043},[886],[888,75045,75046],{"xmlns":890},[892,75047,75048,75072],{},[895,75049,75050,75052,75054,75056,75062,75064,75066,75068,75070],{},[898,75051,5877],{},[898,75053,1658],{},[1701,75055,1792],{},[3243,75057,75058,75060],{},[898,75059,1802],{},[1850,75061,3938],{},[1701,75063,1703],{},[1850,75065,3938],{},[898,75067,1802],{},[1701,75069,1703],{},[1850,75071,9071],{},[902,75073,75074],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,75076,75078],{"className":75077},[886],[888,75079,75080],{"xmlns":890},[892,75081,75082,75086],{},[895,75083,75084],{},[898,75085,1802],{},[902,75087,1802],{"encoding":904},[883,75089,75091],{"className":75090},[886],[888,75092,75093],{"xmlns":890},[892,75094,75095,75101],{},[895,75096,75097,75099],{},[898,75098,1983],{},[898,75100,1658],{},[902,75102,59306],{"encoding":904},[883,75104,75106],{"className":75105},[886],[888,75107,75108],{"xmlns":890},[892,75109,75110,75116],{},[895,75111,75112,75114],{},[898,75113,1983],{},[898,75115,1658],{},[902,75117,59306],{"encoding":904},[724,75119,75120,75123,75124,6723,75156,74972,75173,2020,75216,75035],{},[38,75121,75122],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,75125,75127],{"className":75126},[886],[888,75128,75129],{"xmlns":890},[892,75130,75131,75153],{},[895,75132,75133,75135,75137,75139,75141,75143,75145,75147,75149,75151],{},[898,75134,1983],{},[898,75136,44362],{},[898,75138,1658],{},[1701,75140,1792],{},[898,75142,1983],{},[898,75144,44362],{},[898,75146,1658],{},[1701,75148,1799],{"stretchy":1798},[898,75150,1802],{},[1701,75152,1805],{"stretchy":1798},[902,75154,75155],{"encoding":904},"AVC = AVC(Q)",[883,75157,75159],{"className":75158},[886],[888,75160,75161],{"xmlns":890},[892,75162,75163,75171],{},[895,75164,75165],{},[1845,75166,75167,75169],{},[898,75168,1802],{},[1850,75170,1852],{},[902,75172,1855],{"encoding":904},[883,75174,75176],{"className":75175},[886],[888,75177,75178],{"xmlns":890},[892,75179,75180,75214],{},[895,75181,75182,75184,75186,75188,75190,75196,75198,75200,75202,75204,75206,75212],{},[898,75183,1983],{},[898,75185,44362],{},[898,75187,1658],{},[1701,75189,1799],{"stretchy":1798},[1845,75191,75192,75194],{},[898,75193,1802],{},[1850,75195,1852],{},[1701,75197,1805],{"stretchy":1798},[1701,75199,1792],{},[898,75201,6909],{},[898,75203,1658],{},[1701,75205,1799],{"stretchy":1798},[1845,75207,75208,75210],{},[898,75209,1802],{},[1850,75211,1852],{},[1701,75213,1805],{"stretchy":1798},[902,75215,72765],{"encoding":904},[883,75217,75219],{"className":75218},[886],[888,75220,75221],{"xmlns":890},[892,75222,75223,75235],{},[895,75224,75225,75227,75229,75231,75233],{},[898,75226,6909],{},[898,75228,1658],{},[1701,75230,1799],{"stretchy":1798},[898,75232,1802],{},[1701,75234,1805],{"stretchy":1798},[902,75236,71439],{"encoding":904},[724,75238,75239,73839,75242,74301,75288,74751,75301,74767,75318,1715],{},[38,75240,75241],{},"3.15",[883,75243,75245],{"className":75244},[886],[888,75246,75247],{"xmlns":890},[892,75248,75249,75285],{},[895,75250,75251,75253,75255,75257,75259,75261,75263,75265,75267,75269,75275,75277,75279],{},[898,75252,5877],{},[898,75254,1658],{},[1701,75256,1792],{},[1850,75258,7206],{},[1701,75260,1703],{},[1850,75262,40275],{},[898,75264,1802],{},[1701,75266,2317],{},[1850,75268,3938],{},[3243,75270,75271,75273],{},[898,75272,1802],{},[1850,75274,3938],{},[1701,75276,1703],{},[1850,75278,6930],{},[3243,75280,75281,75283],{},[898,75282,1802],{},[1850,75284,3646],{},[902,75286,75287],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,75289,75291],{"className":75290},[886],[888,75292,75293],{"xmlns":890},[892,75294,75295,75299],{},[895,75296,75297],{},[898,75298,1802],{},[902,75300,1802],{"encoding":904},[883,75302,75304],{"className":75303},[886],[888,75305,75306],{"xmlns":890},[892,75307,75308,75316],{},[895,75309,75310,75312,75314],{},[898,75311,1983],{},[898,75313,44362],{},[898,75315,1658],{},[902,75317,59057],{"encoding":904},[883,75319,75321],{"className":75320},[886],[888,75322,75323],{"xmlns":890},[892,75324,75325,75333],{},[895,75326,75327,75329,75331],{},[898,75328,1983],{},[898,75330,44362],{},[898,75332,1658],{},[902,75334,59057],{"encoding":904},[724,75336,75337,75340,75341,75354,75355,75375],{},[38,75338,75339],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,75342,75344],{"className":75343},[886],[888,75345,75346],{"xmlns":890},[892,75347,75348,75352],{},[895,75349,75350],{},[898,75351,6137],{},[902,75353,6137],{"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 ",[883,75356,75358],{"className":75357},[886],[888,75359,75360],{"xmlns":890},[892,75361,75362,75372],{},[895,75363,75364,75366,75368,75370],{},[1850,75365,3703],{},[1939,75367,1941],{},[1850,75369,62828],{},[898,75371,6137],{},[902,75373,75374],{"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.",[198,75377,75379],{"id":75378},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,75381,75382,75385,75386,2633,75408,75434],{},[38,75383,75384],{},"3.17"," Jsou dány ",[883,75387,75389],{"className":75388},[886],[888,75390,75391],{"xmlns":890},[892,75392,75393,75405],{},[895,75394,75395,75397,75399,75401,75403],{},[898,75396,5877],{},[898,75398,8068],{},[1701,75400,1792],{},[1850,75402,3703],{},[898,75404,1802],{},[902,75406,75407],{"encoding":904},"TR = 10Q",[883,75409,75411],{"className":75410},[886],[888,75412,75413],{"xmlns":890},[892,75414,75415,75431],{},[895,75416,75417,75419,75421,75423,75425,75427,75429],{},[898,75418,5877],{},[898,75420,1658],{},[1701,75422,1792],{},[1850,75424,5158],{},[1701,75426,1703],{},[1850,75428,4225],{},[898,75430,1802],{},[902,75432,75433],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,75436,75437,75440,75441,10253,75456,75471,75472,1343,75494,2020,75521,75543,75544,75578],{},[38,75438,75439],{},"3.18"," Odvoďte, že jestliže ",[883,75442,75444],{"className":75443},[886],[888,75445,75446],{"xmlns":890},[892,75447,75448,75454],{},[895,75449,75450,75452],{},[898,75451,5877],{},[898,75453,8068],{},[902,75455,8168],{"encoding":904},[883,75457,75459],{"className":75458},[886],[888,75460,75461],{"xmlns":890},[892,75462,75463,75469],{},[895,75464,75465,75467],{},[898,75466,5877],{},[898,75468,1658],{},[902,75470,7326],{"encoding":904}," jsou lineární tvaru ",[883,75473,75475],{"className":75474},[886],[888,75476,75477],{"xmlns":890},[892,75478,75479,75491],{},[895,75480,75481,75483,75485,75487,75489],{},[898,75482,5877],{},[898,75484,8068],{},[1701,75486,1792],{},[898,75488,724],{},[898,75490,1802],{},[902,75492,75493],{"encoding":904},"TR = pQ",[883,75495,75497],{"className":75496},[886],[888,75498,75499],{"xmlns":890},[892,75500,75501,75518],{},[895,75502,75503,75505,75507,75509,75512,75514,75516],{},[898,75504,5877],{},[898,75506,1658],{},[1701,75508,1792],{},[898,75510,75511],{},"m",[1701,75513,1703],{},[898,75515,40890],{},[898,75517,1802],{},[902,75519,75520],{"encoding":904},"TC = m + nQ",[883,75522,75524],{"className":75523},[886],[888,75525,75526],{"xmlns":890},[892,75527,75528,75540],{},[895,75529,75530,75532,75534,75536,75538],{},[898,75531,75511],{},[1701,75533,2012],{"separator":2011},[898,75535,40890],{},[1701,75537,2012],{"separator":2011},[898,75539,724],{},[902,75541,75542],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,75545,75547],{"className":75546},[886],[888,75548,75549],{"xmlns":890},[892,75550,75551,75575],{},[895,75552,75553,75559,75561],{},[3243,75554,75555,75557],{},[898,75556,1802],{},[1701,75558,8424],{},[1701,75560,1792],{},[2363,75562,75563],{"scriptlevel":1852,"displaystyle":1798},[3726,75564,75565,75567],{},[898,75566,75511],{},[895,75568,75569,75571,75573],{},[898,75570,724],{},[1701,75572,2317],{},[898,75574,40890],{},[902,75576,75577],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,75580,75581,75385,75584,2633,75618,74737,75644,75657,75658,73489,75673,75688,75689,73473,75702,73489,75717,75732],{},[38,75582,75583],{},"3.19",[883,75585,75587],{"className":75586},[886],[888,75588,75589],{"xmlns":890},[892,75590,75591,75615],{},[895,75592,75593,75595,75597,75599,75601,75603,75609,75611,75613],{},[898,75594,5877],{},[898,75596,8068],{},[1701,75598,1792],{},[1701,75600,2317],{},[1850,75602,3938],{},[3243,75604,75605,75607],{},[898,75606,1802],{},[1850,75608,3938],{},[1701,75610,1703],{},[1850,75612,26985],{},[898,75614,1802],{},[902,75616,75617],{"encoding":904},"TR = -2Q^2 + 14Q",[883,75619,75621],{"className":75620},[886],[888,75622,75623],{"xmlns":890},[892,75624,75625,75641],{},[895,75626,75627,75629,75631,75633,75635,75637,75639],{},[898,75628,5877],{},[898,75630,1658],{},[1701,75632,1792],{},[1850,75634,3938],{},[898,75636,1802],{},[1701,75638,1703],{},[1850,75640,3703],{},[902,75642,75643],{"encoding":904},"TC = 2Q + 10",[883,75645,75647],{"className":75646},[886],[888,75648,75649],{"xmlns":890},[892,75650,75651,75655],{},[895,75652,75653],{},[898,75654,1802],{},[902,75656,1802],{"encoding":904},", které maximalizuje zisk ",[883,75659,75661],{"className":75660},[886],[888,75662,75663],{"xmlns":890},[892,75664,75665,75671],{},[895,75666,75667,75669],{},[898,75668,1680],{},[898,75670,8068],{},[902,75672,67225],{"encoding":904},[883,75674,75676],{"className":75675},[886],[888,75677,75678],{"xmlns":890},[892,75679,75680,75686],{},[895,75681,75682,75684],{},[898,75683,1680],{},[898,75685,8068],{},[902,75687,67225],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,75690,75692],{"className":75691},[886],[888,75693,75694],{"xmlns":890},[892,75695,75696,75700],{},[895,75697,75698],{},[898,75699,1802],{},[902,75701,1802],{"encoding":904},[883,75703,75705],{"className":75704},[886],[888,75706,75707],{"xmlns":890},[892,75708,75709,75715],{},[895,75710,75711,75713],{},[898,75712,5877],{},[898,75714,8068],{},[902,75716,8168],{"encoding":904},[883,75718,75720],{"className":75719},[886],[888,75721,75722],{"xmlns":890},[892,75723,75724,75730],{},[895,75725,75726,75728],{},[898,75727,5877],{},[898,75729,8068],{},[902,75731,8168],{"encoding":904},". (d) Graficky interpretujte.",[724,75734,75735,51675,75738,1343,75764,1343,75783,74737,75803,75657,75816,73489,75831,75846,75847,75869,75870,74920],{},[38,75736,75737],{},"3.20",[883,75739,75741],{"className":75740},[886],[888,75742,75743],{"xmlns":890},[892,75744,75745,75761],{},[895,75746,75747,75749,75751,75753,75755],{},[898,75748,1680],{},[1701,75750,1792],{},[1850,75752,24186],{},[1701,75754,2317],{},[3243,75756,75757,75759],{},[898,75758,1802],{},[1850,75760,3938],{},[902,75762,75763],{"encoding":904},"P = 400 - Q^2",[883,75765,75767],{"className":75766},[886],[888,75768,75769],{"xmlns":890},[892,75770,75771,75781],{},[895,75772,75773,75775,75777,75779],{},[898,75774,14492],{},[898,75776,1658],{},[1701,75778,1792],{},[1850,75780,5158],{},[902,75782,15689],{"encoding":904},[883,75784,75786],{"className":75785},[886],[888,75787,75788],{"xmlns":890},[892,75789,75790,75800],{},[895,75791,75792,75794,75796,75798],{},[898,75793,6909],{},[898,75795,1658],{},[1701,75797,1792],{},[1850,75799,13096],{},[902,75801,75802],{"encoding":904},"MC = 20",[883,75804,75806],{"className":75805},[886],[888,75807,75808],{"xmlns":890},[892,75809,75810,75814],{},[895,75811,75812],{},[898,75813,1802],{},[902,75815,1802],{"encoding":904},[883,75817,75819],{"className":75818},[886],[888,75820,75821],{"xmlns":890},[892,75822,75823,75829],{},[895,75824,75825,75827],{},[898,75826,1680],{},[898,75828,8068],{},[902,75830,67225],{"encoding":904},[883,75832,75834],{"className":75833},[886],[888,75835,75836],{"xmlns":890},[892,75837,75838,75844],{},[895,75839,75840,75842],{},[898,75841,1680],{},[898,75843,8068],{},[902,75845,67225],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,75848,75850],{"className":75849},[886],[888,75851,75852],{"xmlns":890},[892,75853,75854,75866],{},[895,75855,75856,75858,75860,75862,75864],{},[1701,75857,1799],{"stretchy":1798},[1850,75859,1852],{},[1701,75861,2012],{"separator":2011},[1850,75863,4062],{},[1701,75865,1805],{"stretchy":1798},[902,75867,75868],{"encoding":904},"(0, 1)",", druhý do ",[883,75871,75873],{"className":75872},[886],[888,75874,75875],{"xmlns":890},[892,75876,75877,75890],{},[895,75878,75879,75881,75884,75886,75888],{},[1701,75880,1799],{"stretchy":1798},[1850,75882,75883],{},"19",[1701,75885,2012],{"separator":2011},[1850,75887,13096],{},[1701,75889,1805],{"stretchy":1798},[902,75891,75892],{"encoding":904},"(19, 20)",[724,75894,75895,75898,75899,6723,75927,75944,75945,1715],{},[38,75896,75897],{},"3.21"," Dokažte, že má-li zisk ",[883,75900,75902],{"className":75901},[886],[888,75903,75904],{"xmlns":890},[892,75905,75906,75924],{},[895,75907,75908,75910,75912,75914,75916,75918,75920,75922],{},[898,75909,1680],{},[898,75911,8068],{},[1701,75913,1792],{},[898,75915,1680],{},[898,75917,8068],{},[1701,75919,1799],{"stretchy":1798},[898,75921,1802],{},[1701,75923,1805],{"stretchy":1798},[902,75925,75926],{"encoding":904},"PR = PR(Q)",[883,75928,75930],{"className":75929},[886],[888,75931,75932],{"xmlns":890},[892,75933,75934,75942],{},[895,75935,75936],{},[1845,75937,75938,75940],{},[898,75939,1802],{},[1850,75941,1852],{},[902,75943,1855],{"encoding":904}," maximum, pak platí ",[883,75946,75948],{"className":75947},[886],[888,75949,75950],{"xmlns":890},[892,75951,75952,75984],{},[895,75953,75954,75956,75958,75960,75966,75968,75970,75972,75974,75976,75982],{},[898,75955,6909],{},[898,75957,8068],{},[1701,75959,1799],{"stretchy":1798},[1845,75961,75962,75964],{},[898,75963,1802],{},[1850,75965,1852],{},[1701,75967,1805],{"stretchy":1798},[1701,75969,1792],{},[898,75971,6909],{},[898,75973,1658],{},[1701,75975,1799],{"stretchy":1798},[1845,75977,75978,75980],{},[898,75979,1802],{},[1850,75981,1852],{},[1701,75983,1805],{"stretchy":1798},[902,75985,69391],{"encoding":904},[724,75987,75988,75991,75992,2633,76007,59771,76022,75657,76035,76050,76051,1343,76078,76115,76116,1343,76143,1715],{},[38,75989,75990],{},"3.22"," Pro zadané ",[883,75993,75995],{"className":75994},[886],[888,75996,75997],{"xmlns":890},[892,75998,75999,76005],{},[895,76000,76001,76003],{},[898,76002,6909],{},[898,76004,8068],{},[902,76006,10697],{"encoding":904},[883,76008,76010],{"className":76009},[886],[888,76011,76012],{"xmlns":890},[892,76013,76014,76020],{},[895,76015,76016,76018],{},[898,76017,6909],{},[898,76019,1658],{},[902,76021,59038],{"encoding":904},[883,76023,76025],{"className":76024},[886],[888,76026,76027],{"xmlns":890},[892,76028,76029,76033],{},[895,76030,76031],{},[898,76032,1802],{},[902,76034,1802],{"encoding":904},[883,76036,76038],{"className":76037},[886],[888,76039,76040],{"xmlns":890},[892,76041,76042,76048],{},[895,76043,76044,76046],{},[898,76045,1680],{},[898,76047,8068],{},[902,76049,67225],{"encoding":904},". (a) ",[883,76052,76054],{"className":76053},[886],[888,76055,76056],{"xmlns":890},[892,76057,76058,76075],{},[895,76059,76060,76062,76064,76066,76069,76071,76073],{},[898,76061,6909],{},[898,76063,8068],{},[1701,76065,1792],{},[1850,76067,76068],{},"236",[1701,76070,2317],{},[1850,76072,45883],{},[898,76074,1802],{},[902,76076,76077],{"encoding":904},"MR = 236 - 16Q",[883,76079,76081],{"className":76080},[886],[888,76082,76083],{"xmlns":890},[892,76084,76085,76112],{},[895,76086,76087,76089,76091,76093,76095,76101,76103,76106,76108,76110],{},[898,76088,6909],{},[898,76090,1658],{},[1701,76092,1792],{},[1850,76094,3646],{},[3243,76096,76097,76099],{},[898,76098,1802],{},[1850,76100,3938],{},[1701,76102,2317],{},[1850,76104,76105],{},"32",[898,76107,1802],{},[1701,76109,1703],{},[1850,76111,9808],{},[902,76113,76114],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,76117,76119],{"className":76118},[886],[888,76120,76121],{"xmlns":890},[892,76122,76123,76140],{},[895,76124,76125,76127,76129,76131,76134,76136,76138],{},[898,76126,6909],{},[898,76128,8068],{},[1701,76130,1792],{},[1850,76132,76133],{},"280",[1701,76135,2317],{},[1850,76137,13096],{},[898,76139,1802],{},[902,76141,76142],{"encoding":904},"MR = 280 - 20Q",[883,76144,76146],{"className":76145},[886],[888,76147,76148],{"xmlns":890},[892,76149,76150,76177],{},[895,76151,76152,76154,76156,76158,76161,76167,76169,76171,76173,76175],{},[898,76153,6909],{},[898,76155,1658],{},[1701,76157,1792],{},[1850,76159,76160],{},"1,6",[3243,76162,76163,76165],{},[898,76164,1802],{},[1850,76166,3938],{},[1701,76168,2317],{},[1850,76170,40275],{},[898,76172,1802],{},[1701,76174,1703],{},[1850,76176,7211],{},[902,76178,76179],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,76181,76182,75991,76185,2633,76200,59771,76215,73473,76228,73489,76243,76050,76258,1343,76289,76115,76325,1343,76357,76401,76402,1343,76434,1715],{},[38,76183,76184],{},"3.23",[883,76186,76188],{"className":76187},[886],[888,76189,76190],{"xmlns":890},[892,76191,76192,76198],{},[895,76193,76194,76196],{},[898,76195,5877],{},[898,76197,8068],{},[902,76199,8168],{"encoding":904},[883,76201,76203],{"className":76202},[886],[888,76204,76205],{"xmlns":890},[892,76206,76207,76213],{},[895,76208,76209,76211],{},[898,76210,5877],{},[898,76212,1658],{},[902,76214,7326],{"encoding":904},[883,76216,76218],{"className":76217},[886],[888,76219,76220],{"xmlns":890},[892,76221,76222,76226],{},[895,76223,76224],{},[898,76225,1802],{},[902,76227,1802],{"encoding":904},[883,76229,76231],{"className":76230},[886],[888,76232,76233],{"xmlns":890},[892,76234,76235,76241],{},[895,76236,76237,76239],{},[898,76238,1680],{},[898,76240,8068],{},[902,76242,67225],{"encoding":904},[883,76244,76246],{"className":76245},[886],[888,76247,76248],{"xmlns":890},[892,76249,76250,76256],{},[895,76251,76252,76254],{},[898,76253,1680],{},[898,76255,8068],{},[902,76257,67225],{"encoding":904},[883,76259,76261],{"className":76260},[886],[888,76262,76263],{"xmlns":890},[892,76264,76265,76286],{},[895,76266,76267,76269,76271,76273,76276,76278,76280],{},[898,76268,5877],{},[898,76270,8068],{},[1701,76272,1792],{},[1850,76274,76275],{},"125",[898,76277,1802],{},[1701,76279,2317],{},[3243,76281,76282,76284],{},[898,76283,1802],{},[1850,76285,3938],{},[902,76287,76288],{"encoding":904},"TR = 125Q - Q^2",[883,76290,76292],{"className":76291},[886],[888,76293,76294],{"xmlns":890},[892,76295,76296,76322],{},[895,76297,76298,76300,76302,76304,76306,76308,76310,76312,76314,76316],{},[898,76299,5877],{},[898,76301,1658],{},[1701,76303,1792],{},[1850,76305,19162],{},[1701,76307,1703],{},[1850,76309,4225],{},[898,76311,1802],{},[1701,76313,1703],{},[1850,76315,3684],{},[3243,76317,76318,76320],{},[898,76319,1802],{},[1850,76321,3938],{},[902,76323,76324],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,76326,76328],{"className":76327},[886],[888,76329,76330],{"xmlns":890},[892,76331,76332,76354],{},[895,76333,76334,76336,76338,76340,76342,76344,76346,76348],{},[898,76335,5877],{},[898,76337,8068],{},[1701,76339,1792],{},[1850,76341,13096],{},[898,76343,1802],{},[1701,76345,2317],{},[1850,76347,3938],{},[3243,76349,76350,76352],{},[898,76351,1802],{},[1850,76353,3938],{},[902,76355,76356],{"encoding":904},"TR = 20Q - 2Q^2",[883,76358,76360],{"className":76359},[886],[888,76361,76362],{"xmlns":890},[892,76363,76364,76398],{},[895,76365,76366,76368,76370,76372,76374,76376,76378,76380,76382,76384,76390,76392],{},[898,76367,5877],{},[898,76369,1658],{},[1701,76371,1792],{},[1850,76373,3938],{},[1701,76375,1703],{},[1850,76377,13096],{},[898,76379,1802],{},[1701,76381,2317],{},[1850,76383,9650],{},[3243,76385,76386,76388],{},[898,76387,1802],{},[1850,76389,3938],{},[1701,76391,1703],{},[3243,76393,76394,76396],{},[898,76395,1802],{},[1850,76397,3646],{},[902,76399,76400],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,76403,76405],{"className":76404},[886],[888,76406,76407],{"xmlns":890},[892,76408,76409,76431],{},[895,76410,76411,76413,76415,76417,76419,76421,76423,76425],{},[898,76412,5877],{},[898,76414,8068],{},[1701,76416,1792],{},[1850,76418,6460],{},[898,76420,1802],{},[1701,76422,2317],{},[1850,76424,27827],{},[3243,76426,76427,76429],{},[898,76428,1802],{},[1850,76430,3938],{},[902,76432,76433],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,76435,76437],{"className":76436},[886],[888,76438,76439],{"xmlns":890},[892,76440,76441,76489],{},[895,76442,76443,76445,76447,76449,76451,76453,76455,76457,76459,76475,76477],{},[898,76444,5877],{},[898,76446,1658],{},[1701,76448,1792],{},[1850,76450,6460],{},[1701,76452,1703],{},[1850,76454,3938],{},[898,76456,1802],{},[1701,76458,2317],{},[2363,76460,76461],{"scriptlevel":1852,"displaystyle":1798},[3726,76462,76463,76473],{},[895,76464,76465,76467],{},[1850,76466,3646],{},[3243,76468,76469,76471],{},[898,76470,1802],{},[1850,76472,3938],{},[1850,76474,3703],{},[1701,76476,1703],{},[2363,76478,76479],{"scriptlevel":1852,"displaystyle":1798},[3726,76480,76481,76487],{},[3243,76482,76483,76485],{},[898,76484,1802],{},[1850,76486,3646],{},[1850,76488,13096],{},[902,76490,76491],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,76493,76494,76497,76498,76528,76529,76561,76562,2020,76592,76622],{},[38,76495,76496],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,76499,76501],{"className":76500},[886],[888,76502,76503],{"xmlns":890},[892,76504,76505,76525],{},[895,76506,76507,76513,76515,76517,76519],{},[1845,76508,76509,76511],{},[898,76510,1680],{},[1850,76512,4062],{},[1701,76514,1792],{},[1850,76516,19162],{},[1701,76518,2317],{},[1845,76520,76521,76523],{},[898,76522,1802],{},[1850,76524,4062],{},[902,76526,76527],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,76530,76532],{"className":76531},[886],[888,76533,76534],{"xmlns":890},[892,76535,76536,76558],{},[895,76537,76538,76544,76546,76548,76550,76552],{},[1845,76539,76540,76542],{},[898,76541,1680],{},[1850,76543,3938],{},[1701,76545,1792],{},[1850,76547,5151],{},[1701,76549,2317],{},[1850,76551,68305],{},[1845,76553,76554,76556],{},[898,76555,1802],{},[1850,76557,3938],{},[902,76559,76560],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,76563,76565],{"className":76564},[886],[888,76566,76567],{"xmlns":890},[892,76568,76569,76589],{},[895,76570,76571,76573,76575,76577,76579,76581,76583,76585,76587],{},[898,76572,5877],{},[898,76574,1658],{},[1701,76576,1792],{},[1850,76578,7206],{},[1939,76580,1941],{},[1850,76582,62828],{},[1701,76584,1703],{},[1850,76586,13096],{},[898,76588,1802],{},[902,76590,76591],{"encoding":904},"TC = 50\\,000 + 20Q",[883,76593,76595],{"className":76594},[886],[888,76596,76597],{"xmlns":890},[892,76598,76599,76619],{},[895,76600,76601,76603,76605,76611,76613],{},[898,76602,1802],{},[1701,76604,1792],{},[1845,76606,76607,76609],{},[898,76608,1802],{},[1850,76610,4062],{},[1701,76612,1703],{},[1845,76614,76615,76617],{},[898,76616,1802],{},[1850,76618,3938],{},[902,76620,76621],{"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.",[724,76624,76625,76628,76629,76659,76660,76561,76692,2020,76722,76751],{},[38,76626,76627],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,76630,76632],{"className":76631},[886],[888,76633,76634],{"xmlns":890},[892,76635,76636,76656],{},[895,76637,76638,76644,76646,76648,76650],{},[1845,76639,76640,76642],{},[898,76641,1680],{},[1850,76643,4062],{},[1701,76645,1792],{},[1850,76647,5151],{},[1701,76649,2317],{},[1845,76651,76652,76654],{},[898,76653,1802],{},[1850,76655,4062],{},[902,76657,76658],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,76661,76663],{"className":76662},[886],[888,76664,76665],{"xmlns":890},[892,76666,76667,76689],{},[895,76668,76669,76675,76677,76679,76681,76683],{},[1845,76670,76671,76673],{},[898,76672,1680],{},[1850,76674,3938],{},[1701,76676,1792],{},[1850,76678,12439],{},[1701,76680,2317],{},[1850,76682,3684],{},[1845,76684,76685,76687],{},[898,76686,1802],{},[1850,76688,3938],{},[902,76690,76691],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,76693,76695],{"className":76694},[886],[888,76696,76697],{"xmlns":890},[892,76698,76699,76719],{},[895,76700,76701,76703,76705,76707,76709,76711,76713,76715,76717],{},[898,76702,5877],{},[898,76704,1658],{},[1701,76706,1792],{},[1850,76708,4225],{},[1939,76710,1941],{},[1850,76712,62828],{},[1701,76714,1703],{},[1850,76716,5158],{},[898,76718,1802],{},[902,76720,76721],{"encoding":904},"TC = 5\\,000 + 100Q",[883,76723,76725],{"className":76724},[886],[888,76726,76727],{"xmlns":890},[892,76728,76729,76749],{},[895,76730,76731,76733,76735,76741,76743],{},[898,76732,1802],{},[1701,76734,1792],{},[1845,76736,76737,76739],{},[898,76738,1802],{},[1850,76740,4062],{},[1701,76742,1703],{},[1845,76744,76745,76747],{},[898,76746,1802],{},[1850,76748,3938],{},[902,76750,76621],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,76753,76755],{"id":76754},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,76757,76758,76761,76762,76809,76810,76827],{},[38,76759,76760],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,76763,76765],{"className":76764},[886],[888,76766,76767],{"xmlns":890},[892,76768,76769,76806],{},[895,76770,76771,76773,76775,76777,76779,76782,76788,76790,76793,76799,76801,76804],{},[898,76772,5877],{},[898,76774,44362],{},[898,76776,1658],{},[1701,76778,1792],{},[1850,76780,76781],{},"0,85",[3243,76783,76784,76786],{},[898,76785,1802],{},[1850,76787,3646],{},[1701,76789,2317],{},[1850,76791,76792],{},"11,9",[3243,76794,76795,76797],{},[898,76796,1802],{},[1850,76798,3938],{},[1701,76800,1703],{},[1850,76802,76803],{},"102",[898,76805,1802],{},[902,76807,76808],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,76811,76813],{"className":76812},[886],[888,76814,76815],{"xmlns":890},[892,76816,76817,76825],{},[895,76818,76819],{},[3243,76820,76821,76823],{},[898,76822,1680],{},[1701,76824,8424],{},[902,76826,8474],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,76829,76830,74588,76833,76869],{},[38,76831,76832],{},"3.27",[883,76834,76836],{"className":76835},[886],[888,76837,76838],{"xmlns":890},[892,76839,76840,76866],{},[895,76841,76842,76844,76846,76848,76850,76856,76858,76860,76862,76864],{},[898,76843,6909],{},[898,76845,1658],{},[1701,76847,1792],{},[1850,76849,7011],{},[3243,76851,76852,76854],{},[898,76853,1802],{},[1850,76855,3938],{},[1701,76857,2317],{},[1850,76859,68186],{},[898,76861,1802],{},[1701,76863,1703],{},[1850,76865,34774],{},[902,76867,76868],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,76871,76872,73839,76875,76869],{},[38,76873,76874],{},"3.28",[883,76876,76878],{"className":76877},[886],[888,76879,76880],{"xmlns":890},[892,76881,76882,76918],{},[895,76883,76884,76886,76888,76890,76892,76898,76900,76902,76908,76910,76912,76914,76916],{},[898,76885,5877],{},[898,76887,1658],{},[1701,76889,1792],{},[1850,76891,3684],{},[3243,76893,76894,76896],{},[898,76895,1802],{},[1850,76897,3646],{},[1701,76899,2317],{},[1850,76901,28239],{},[3243,76903,76904,76906],{},[898,76905,1802],{},[1850,76907,3938],{},[1701,76909,1703],{},[1850,76911,7211],{},[898,76913,1802],{},[1701,76915,1703],{},[1850,76917,19162],{},[902,76919,76920],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,76922,5578],{"id":5577},[120,76924,76925,76953,76998,77070,77135,77175,77267,77373,77413,77527,77620,77684,77716,77776,77782,77846,77895,77949,78057,78112],{},[123,76926,76927,4088,76929,76952],{},[38,76928,59496],{},[883,76930,76932],{"className":76931},[886],[888,76933,76934],{"xmlns":890},[892,76935,76936,76950],{},[895,76937,76938,76940,76942,76944,76946,76948],{},[898,76939,5877],{},[898,76941,8068],{},[1701,76943,1792],{},[898,76945,1680],{},[1701,76947,3408],{},[898,76949,1802],{},[902,76951,70458],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,76954,76955,4088,76957,76997],{},[38,76956,60082],{},[883,76958,76960],{"className":76959},[886],[888,76961,76962],{"xmlns":890},[892,76963,76964,76994],{},[895,76965,76966,76968,76970,76972,76984,76986,76988,76990,76992],{},[898,76967,1983],{},[898,76969,8068],{},[1701,76971,1792],{},[2363,76973,76974],{"scriptlevel":1852,"displaystyle":1798},[3726,76975,76976,76982],{},[895,76977,76978,76980],{},[898,76979,5877],{},[898,76981,8068],{},[898,76983,1802],{},[1701,76985,1792],{},[898,76987,1795],{},[1701,76989,1799],{"stretchy":1798},[898,76991,1802],{},[1701,76993,1805],{"stretchy":1798},[902,76995,76996],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,76999,77000,4088,77002,77038,77039,77054,77055,1715],{},[38,77001,60230],{},[883,77003,77005],{"className":77004},[886],[888,77006,77007],{"xmlns":890},[892,77008,77009,77035],{},[895,77010,77011,77013,77015,77017],{},[898,77012,6909],{},[898,77014,8068],{},[1701,77016,1792],{},[2363,77018,77019],{"scriptlevel":1852,"displaystyle":1798},[3726,77020,77021,77029],{},[895,77022,77023,77025,77027],{},[898,77024,2312],{"mathvariant":2334},[898,77026,5877],{},[898,77028,8068],{},[895,77030,77031,77033],{},[898,77032,2312],{"mathvariant":2334},[898,77034,1802],{},[902,77036,77037],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,77040,77042],{"className":77041},[886],[888,77043,77044],{"xmlns":890},[892,77045,77046,77052],{},[895,77047,77048,77050],{},[898,77049,5877],{},[898,77051,8068],{},[902,77053,8168],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,77056,77058],{"className":77057},[886],[888,77059,77060],{"xmlns":890},[892,77061,77062,77068],{},[895,77063,77064,77066],{},[898,77065,1983],{},[898,77067,8068],{},[902,77069,59191],{"encoding":904},[123,77071,77072,4088,77075,1343,77105,1715],{},[38,77073,77074],{},"Diferenciál příjmu\u002Fnákladů",[883,77076,77078],{"className":77077},[886],[888,77079,77080],{"xmlns":890},[892,77081,77082,77102],{},[895,77083,77084,77086,77088,77090,77092,77094,77096,77098,77100],{},[898,77085,4708],{"mathvariant":2334},[898,77087,5877],{},[898,77089,8068],{},[1701,77091,4067],{},[898,77093,6909],{},[898,77095,8068],{},[1939,77097,1941],{},[898,77099,2312],{"mathvariant":2334},[898,77101,1802],{},[902,77103,77104],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,77106,77108],{"className":77107},[886],[888,77109,77110],{"xmlns":890},[892,77111,77112,77132],{},[895,77113,77114,77116,77118,77120,77122,77124,77126,77128,77130],{},[898,77115,4708],{"mathvariant":2334},[898,77117,5877],{},[898,77119,1658],{},[1701,77121,4067],{},[898,77123,6909],{},[898,77125,1658],{},[1939,77127,1941],{},[898,77129,2312],{"mathvariant":2334},[898,77131,1802],{},[902,77133,77134],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,77136,77137,4088,77139,1715],{},[38,77138,62352],{},[883,77140,77142],{"className":77141},[886],[888,77143,77144],{"xmlns":890},[892,77145,77146,77172],{},[895,77147,77148,77150,77152,77154,77156,77158,77160,77162,77164,77166,77168,77170],{},[898,77149,5877],{},[898,77151,1658],{},[1701,77153,1792],{},[898,77155,14492],{},[898,77157,1658],{},[1701,77159,1703],{},[898,77161,5877],{},[898,77163,44362],{},[898,77165,1658],{},[1701,77167,1799],{"stretchy":1798},[898,77169,1802],{},[1701,77171,1805],{"stretchy":1798},[902,77173,77174],{"encoding":904},"TC = FC + TVC(Q)",[123,77176,77177,4088,77180,1343,77195,4088,77197,1343,77220,4088,77223,1715],{},[38,77178,77179],{},"Fixní náklady",[883,77181,77183],{"className":77182},[886],[888,77184,77185],{"xmlns":890},[892,77186,77187,77193],{},[895,77188,77189,77191],{},[898,77190,14492],{},[898,77192,1658],{},[902,77194,59237],{"encoding":904},[38,77196,62505],{},[883,77198,77200],{"className":77199},[886],[888,77201,77202],{"xmlns":890},[892,77203,77204,77218],{},[895,77205,77206,77208,77210,77212,77214,77216],{},[898,77207,5877],{},[898,77209,44362],{},[898,77211,1658],{},[1701,77213,1799],{"stretchy":1798},[898,77215,1802],{},[1701,77217,1805],{"stretchy":1798},[902,77219,62502],{"encoding":904},[38,77221,77222],{},"variabilní náklady na jednotku",[883,77224,77226],{"className":77225},[886],[888,77227,77228],{"xmlns":890},[892,77229,77230,77264],{},[895,77231,77232,77234,77236,77238,77240,77242,77244],{},[898,77233,44362],{},[898,77235,1658],{},[1701,77237,1799],{"stretchy":1798},[898,77239,1802],{},[1701,77241,1805],{"stretchy":1798},[1701,77243,1792],{},[2363,77245,77246],{"scriptlevel":1852,"displaystyle":1798},[3726,77247,77248,77262],{},[895,77249,77250,77252,77254,77256,77258,77260],{},[898,77251,5877],{},[898,77253,44362],{},[898,77255,1658],{},[1701,77257,1799],{"stretchy":1798},[898,77259,1802],{},[1701,77261,1805],{"stretchy":1798},[898,77263,1802],{},[902,77265,77266],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,77268,77269,4088,77271,1343,77301,4088,77304,1343,77336,4088,77339,1715],{},[38,77270,62513],{},[883,77272,77274],{"className":77273},[886],[888,77275,77276],{"xmlns":890},[892,77277,77278,77298],{},[895,77279,77280,77282,77284,77286],{},[898,77281,1983],{},[898,77283,1658],{},[1701,77285,1792],{},[2363,77287,77288],{"scriptlevel":1852,"displaystyle":1798},[3726,77289,77290,77296],{},[895,77291,77292,77294],{},[898,77293,5877],{},[898,77295,1658],{},[898,77297,1802],{},[902,77299,77300],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,77302,77303],{},"průměrné fixní",[883,77305,77307],{"className":77306},[886],[888,77308,77309],{"xmlns":890},[892,77310,77311,77333],{},[895,77312,77313,77315,77317,77319,77321],{},[898,77314,1983],{},[898,77316,14492],{},[898,77318,1658],{},[1701,77320,1792],{},[2363,77322,77323],{"scriptlevel":1852,"displaystyle":1798},[3726,77324,77325,77331],{},[895,77326,77327,77329],{},[898,77328,14492],{},[898,77330,1658],{},[898,77332,1802],{},[902,77334,77335],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,77337,77338],{},"průměrné variabilní",[883,77340,77342],{"className":77341},[886],[888,77343,77344],{"xmlns":890},[892,77345,77346,77370],{},[895,77347,77348,77350,77352,77354,77356],{},[898,77349,1983],{},[898,77351,44362],{},[898,77353,1658],{},[1701,77355,1792],{},[2363,77357,77358],{"scriptlevel":1852,"displaystyle":1798},[3726,77359,77360,77368],{},[895,77361,77362,77364,77366],{},[898,77363,5877],{},[898,77365,44362],{},[898,77367,1658],{},[898,77369,1802],{},[902,77371,77372],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,77374,77375,4088,77377,1715],{},[38,77376,63700],{},[883,77378,77380],{"className":77379},[886],[888,77381,77382],{"xmlns":890},[892,77383,77384,77410],{},[895,77385,77386,77388,77390,77392],{},[898,77387,6909],{},[898,77389,1658],{},[1701,77391,1792],{},[2363,77393,77394],{"scriptlevel":1852,"displaystyle":1798},[3726,77395,77396,77404],{},[895,77397,77398,77400,77402],{},[898,77399,2312],{"mathvariant":2334},[898,77401,5877],{},[898,77403,1658],{},[895,77405,77406,77408],{},[898,77407,2312],{"mathvariant":2334},[898,77409,1802],{},[902,77411,77412],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,77414,77415,4088,77417,77465,77466,77479,77480,1343,77495,1343,77512,1715],{},[38,77416,64598],{},[883,77418,77420],{"className":77419},[886],[888,77421,77422],{"xmlns":890},[892,77423,77424,77462],{},[895,77425,77426,77428,77430,77432,77434,77436,77438,77440,77442,77444,77446,77452,77454,77456],{},[898,77427,5877],{},[898,77429,1658],{},[1701,77431,1792],{},[898,77433,14492],{},[898,77435,1658],{},[1701,77437,1703],{},[898,77439,207],{},[898,77441,1802],{},[1701,77443,1703],{},[898,77445,3598],{},[3243,77447,77448,77450],{},[898,77449,1802],{},[1850,77451,3938],{},[1701,77453,1703],{},[898,77455,3618],{},[3243,77457,77458,77460],{},[898,77459,1802],{},[1850,77461,3646],{},[902,77463,77464],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,77467,77469],{"className":77468},[886],[888,77470,77471],{"xmlns":890},[892,77472,77473,77477],{},[895,77474,77475],{},[898,77476,900],{},[902,77478,900],{"encoding":904},"-průběhem ",[883,77481,77483],{"className":77482},[886],[888,77484,77485],{"xmlns":890},[892,77486,77487,77493],{},[895,77488,77489,77491],{},[898,77490,1983],{},[898,77492,1658],{},[902,77494,59306],{"encoding":904},[883,77496,77498],{"className":77497},[886],[888,77499,77500],{"xmlns":890},[892,77501,77502,77510],{},[895,77503,77504,77506,77508],{},[898,77505,1983],{},[898,77507,44362],{},[898,77509,1658],{},[902,77511,59057],{"encoding":904},[883,77513,77515],{"className":77514},[886],[888,77516,77517],{"xmlns":890},[892,77518,77519,77525],{},[895,77520,77521,77523],{},[898,77522,6909],{},[898,77524,1658],{},[902,77526,59038],{"encoding":904},[123,77528,77529,77531,77532,14450,77547,77588,77589,65243,77604,77619],{},[38,77530,65680],{},": v bodě minima ",[883,77533,77535],{"className":77534},[886],[888,77536,77537],{"xmlns":890},[892,77538,77539,77545],{},[895,77540,77541,77543],{},[898,77542,1983],{},[898,77544,1658],{},[902,77546,59306],{"encoding":904},[883,77548,77550],{"className":77549},[886],[888,77551,77552],{"xmlns":890},[892,77553,77554,77586],{},[895,77555,77556,77558,77560,77562,77568,77570,77572,77574,77576,77578,77584],{},[898,77557,1983],{},[898,77559,1658],{},[1701,77561,1799],{"stretchy":1798},[1845,77563,77564,77566],{},[898,77565,1802],{},[1850,77567,1852],{},[1701,77569,1805],{"stretchy":1798},[1701,77571,1792],{},[898,77573,6909],{},[898,77575,1658],{},[1701,77577,1799],{"stretchy":1798},[1845,77579,77580,77582],{},[898,77581,1802],{},[1850,77583,1852],{},[1701,77585,1805],{"stretchy":1798},[902,77587,66315],{"encoding":904},"; geometricky ",[883,77590,77592],{"className":77591},[886],[888,77593,77594],{"xmlns":890},[892,77595,77596,77602],{},[895,77597,77598,77600],{},[898,77599,6909],{},[898,77601,1658],{},[902,77603,59038],{"encoding":904},[883,77605,77607],{"className":77606},[886],[888,77608,77609],{"xmlns":890},[892,77610,77611,77617],{},[895,77612,77613,77615],{},[898,77614,1983],{},[898,77616,1658],{},[902,77618,59306],{"encoding":904}," v jejím minimu.",[123,77621,77622,77531,77624,14450,77641,1715],{},[38,77623,67030],{},[883,77625,77627],{"className":77626},[886],[888,77628,77629],{"xmlns":890},[892,77630,77631,77639],{},[895,77632,77633,77635,77637],{},[898,77634,1983],{},[898,77636,44362],{},[898,77638,1658],{},[902,77640,59057],{"encoding":904},[883,77642,77644],{"className":77643},[886],[888,77645,77646],{"xmlns":890},[892,77647,77648,77682],{},[895,77649,77650,77652,77654,77656,77658,77664,77666,77668,77670,77672,77674,77680],{},[898,77651,1983],{},[898,77653,44362],{},[898,77655,1658],{},[1701,77657,1799],{"stretchy":1798},[1845,77659,77660,77662],{},[898,77661,1802],{},[1850,77663,1852],{},[1701,77665,1805],{"stretchy":1798},[1701,77667,1792],{},[898,77669,6909],{},[898,77671,1658],{},[1701,77673,1799],{"stretchy":1798},[1845,77675,77676,77678],{},[898,77677,1802],{},[1850,77679,1852],{},[1701,77681,1805],{"stretchy":1798},[902,77683,72765],{"encoding":904},[123,77685,77686,4088,77688,77715],{},[38,77687,67209],{},[883,77689,77691],{"className":77690},[886],[888,77692,77693],{"xmlns":890},[892,77694,77695,77713],{},[895,77696,77697,77699,77701,77703,77705,77707,77709,77711],{},[898,77698,1680],{},[898,77700,8068],{},[1701,77702,1792],{},[898,77704,5877],{},[898,77706,8068],{},[1701,77708,2317],{},[898,77710,5877],{},[898,77712,1658],{},[902,77714,58946],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,77717,77718,1646,77720,77722,77723,77749,77750,77775],{},[38,77719,68071],{},[614,77721,67334],{},") — hodnoty ",[883,77724,77726],{"className":77725},[886],[888,77727,77728],{"xmlns":890},[892,77729,77730,77746],{},[895,77731,77732,77738,77740],{},[1845,77733,77734,77736],{},[898,77735,1802],{},[898,77737,1983],{},[1701,77739,2012],{"separator":2011},[1845,77741,77742,77744],{},[898,77743,1802],{},[898,77745,2593],{},[902,77747,77748],{"encoding":904},"Q_A, Q_B"," splňující ",[883,77751,77753],{"className":77752},[886],[888,77754,77755],{"xmlns":890},[892,77756,77757,77773],{},[895,77758,77759,77761,77763,77765,77767,77769,77771],{},[898,77760,1680],{},[898,77762,8068],{},[1701,77764,1799],{"stretchy":1798},[898,77766,1802],{},[1701,77768,1805],{"stretchy":1798},[1701,77770,1792],{},[1850,77772,1852],{},[902,77774,67611],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,77777,77778,77781],{},[38,77779,77780],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,77783,77784,77786,77787,14450,77804,77845],{},[38,77785,69125],{}," — v bodě maxima zisku ",[883,77788,77790],{"className":77789},[886],[888,77791,77792],{"xmlns":890},[892,77793,77794,77802],{},[895,77795,77796],{},[1845,77797,77798,77800],{},[898,77799,1802],{},[1850,77801,1852],{},[902,77803,1855],{"encoding":904},[883,77805,77807],{"className":77806},[886],[888,77808,77809],{"xmlns":890},[892,77810,77811,77843],{},[895,77812,77813,77815,77817,77819,77825,77827,77829,77831,77833,77835,77841],{},[898,77814,6909],{},[898,77816,8068],{},[1701,77818,1799],{"stretchy":1798},[1845,77820,77821,77823],{},[898,77822,1802],{},[1850,77824,1852],{},[1701,77826,1805],{"stretchy":1798},[1701,77828,1792],{},[898,77830,6909],{},[898,77832,1658],{},[1701,77834,1799],{"stretchy":1798},[1845,77836,77837,77839],{},[898,77838,1802],{},[1850,77840,1852],{},[1701,77842,1805],{"stretchy":1798},[902,77844,69391],{"encoding":904}," (3.13).",[123,77847,77848,24345,77850,14450,77869,77894],{},[38,77849,70418],{},[883,77851,77853],{"className":77852},[886],[888,77854,77855],{"xmlns":890},[892,77856,77857,77866],{},[895,77858,77859,77861,77863],{},[898,77860,1680],{},[1701,77862,1792],{},[1939,77864,77865],{},"konst",[902,77867,77868],{"encoding":904},"P = \\text{konst}",[883,77870,77872],{"className":77871},[886],[888,77873,77874],{"xmlns":890},[892,77875,77876,77892],{},[895,77877,77878,77880,77882,77884,77886,77888,77890],{},[898,77879,1680],{},[1701,77881,1792],{},[898,77883,6909],{},[898,77885,1658],{},[1701,77887,1799],{"stretchy":1798},[898,77889,1802],{},[1701,77891,1805],{"stretchy":1798},[902,77893,71112],{"encoding":904}," (3.14).",[123,77896,77897,77900,77901,77930,77931,77948],{},[38,77898,77899],{},"Shutdown point"," — bod ",[883,77902,77904],{"className":77903},[886],[888,77905,77906],{"xmlns":890},[892,77907,77908,77928],{},[895,77909,77910,77912,77918,77920,77926],{},[1701,77911,1799],{"stretchy":1798},[3243,77913,77914,77916],{},[898,77915,1802],{},[1701,77917,8424],{},[1701,77919,2012],{"separator":2011},[3243,77921,77922,77924],{},[898,77923,1680],{},[1701,77925,8424],{},[1701,77927,1805],{"stretchy":1798},[902,77929,71401],{"encoding":904}," v minimu ",[883,77932,77934],{"className":77933},[886],[888,77935,77936],{"xmlns":890},[892,77937,77938,77946],{},[895,77939,77940,77942,77944],{},[898,77941,1983],{},[898,77943,44362],{},[898,77945,1658],{},[902,77947,59057],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,77950,77951,4088,77954,10536,77989,71671,78010,78023,78024,78039,78040,1715],{},[38,77952,77953],{},"Funkce nabídky firmy",[883,77955,77957],{"className":77956},[886],[888,77958,77959],{"xmlns":890},[892,77960,77961,77987],{},[895,77962,77963,77965,77967,77969,77971,77973,77975,77977,77979,77981,77983,77985],{},[898,77964,1680],{},[1701,77966,1792],{},[898,77968,1661],{},[1701,77970,1799],{"stretchy":1798},[898,77972,1802],{},[1701,77974,1805],{"stretchy":1798},[1701,77976,1792],{},[898,77978,6909],{},[898,77980,1658],{},[1701,77982,1799],{"stretchy":1798},[898,77984,1802],{},[1701,77986,1805],{"stretchy":1798},[902,77988,72868],{"encoding":904},[883,77990,77992],{"className":77991},[886],[888,77993,77994],{"xmlns":890},[892,77995,77996,78008],{},[895,77997,77998,78000,78002],{},[898,77999,1802],{},[1701,78001,8554],{},[3243,78003,78004,78006],{},[898,78005,1802],{},[1701,78007,8424],{},[902,78009,71670],{"encoding":904},[883,78011,78013],{"className":78012},[886],[888,78014,78015],{"xmlns":890},[892,78016,78017,78021],{},[895,78018,78019],{},[1850,78020,1852],{},[902,78022,1852],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,78025,78027],{"className":78026},[886],[888,78028,78029],{"xmlns":890},[892,78030,78031,78037],{},[895,78032,78033,78035],{},[898,78034,6909],{},[898,78036,1658],{},[902,78038,59038],{"encoding":904}," nad minimem ",[883,78041,78043],{"className":78042},[886],[888,78044,78045],{"xmlns":890},[892,78046,78047,78055],{},[895,78048,78049,78051,78053],{},[898,78050,1983],{},[898,78052,44362],{},[898,78054,1658],{},[902,78056,59057],{"encoding":904},[123,78058,78059,2979,78061,78082,78083,1715],{},[38,78060,54066],{},[883,78062,78064],{"className":78063},[886],[888,78065,78066],{"xmlns":890},[892,78067,78068,78080],{},[895,78069,78070,78072,78074],{},[898,78071,1680],{},[1701,78073,1792],{},[3243,78075,78076,78078],{},[898,78077,1680],{},[1701,78079,8424],{},[902,78081,8427],{"encoding":904}," konstantní ⇒ ",[883,78084,78086],{"className":78085},[886],[888,78087,78088],{"xmlns":890},[892,78089,78090,78110],{},[895,78091,78092,78094,78096,78098,78100,78102,78104],{},[898,78093,1983],{},[898,78095,8068],{},[1701,78097,1792],{},[898,78099,6909],{},[898,78101,8068],{},[1701,78103,1792],{},[3243,78105,78106,78108],{},[898,78107,1680],{},[1701,78109,8424],{},[902,78111,62344],{"encoding":904},[123,78113,78114,78117],{},[38,78115,78116],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,78119,5984],{"id":5983},[120,78121,78122,78141,78153],{},[123,78123,78124,4088,78126,1343,78129,1343,78132,1343,78135,1343,78138],{},[38,78125,54710],{},[207,78127,15996],{"className":78128,"dataFsResolvedFilePath":800,"href":801},[210],[207,78130,7908],{"className":78131,"dataFsResolvedFilePath":848,"href":849},[210],[207,78133,6007],{"className":78134,"dataFsResolvedFilePath":764,"href":765},[210],[207,78136,775],{"className":78137,"dataFsResolvedFilePath":773,"href":774},[210],[207,78139,859],{"className":78140,"dataFsResolvedFilePath":857,"href":858},[210],[123,78142,78143,4088,78145,1343,78149],{},[38,78144,40733],{},[207,78146,78148],{"className":78147,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,78150,78152],{"className":78151,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,78154,78155,4088,78157],{},[38,78156,6031],{},[207,78158,6037],{"className":78159,"dataFsResolvedFilePath":6035,"href":6036},[210],{"title":641,"searchDepth":642,"depth":642,"links":78161},[78162,78163,78170,78176,78180,78181,78185,78186,78187,78188,78194,78195],{"id":1775,"depth":642,"text":1241},{"id":59484,"depth":642,"text":59485,"children":78164},[78165,78166,78167,78168,78169],{"id":59495,"depth":649,"text":59496},{"id":60081,"depth":649,"text":60082},{"id":60229,"depth":649,"text":60230},{"id":60971,"depth":649,"text":60972},{"id":61626,"depth":649,"text":61627},{"id":62347,"depth":642,"text":62348,"children":78171},[78172,78173,78174,78175],{"id":62351,"depth":649,"text":62352},{"id":62512,"depth":649,"text":62513},{"id":63699,"depth":649,"text":63700},{"id":64597,"depth":649,"text":64598},{"id":65679,"depth":642,"text":65680,"children":78177},[78178,78179],{"id":20457,"depth":649,"text":20458},{"id":67029,"depth":649,"text":67030},{"id":67203,"depth":642,"text":67204},{"id":69124,"depth":642,"text":69125,"children":78182},[78183,78184],{"id":69138,"depth":649,"text":20458},{"id":70417,"depth":649,"text":70418},{"id":71049,"depth":642,"text":71050},{"id":72515,"depth":642,"text":72516},{"id":53868,"depth":642,"text":53869},{"id":72976,"depth":642,"text":72977,"children":78189},[78190,78191,78192,78193],{"id":72980,"depth":649,"text":72981},{"id":73832,"depth":649,"text":73833},{"id":75378,"depth":649,"text":75379},{"id":76754,"depth":649,"text":76755},{"id":5577,"depth":642,"text":5578},{"id":5983,"depth":642,"text":5984},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":58866,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,78202,78203,58918,78204,78205,78206],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":78209,"title":78210,"body":78211,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":90308,"navigation":664,"path":90309,"seo":90310,"sources":90311,"stem":90312,"tags":90313,"type":6074,"updated":677,"__hash__":90319},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":78212,"toc":90265},[78213,78216,78572,78576,78579,78647,78699,78709,78713,78747,78788,78812,78835,78864,78931,79038,79081,79138,79213,79258,79262,79270,79278,79281,79546,79597,79677,79747,79770,79798,79843,79865,79869,79876,79925,79951,80102,80105,80142,80305,80413,80417,80454,80529,80598,80717,80839,80920,80926,80967,81040,81133,81137,81173,81261,81375,81480,81565,81705,81709,81757,81802,81808,81812,81815,81866,81916,81923,81989,82122,82167,82171,82192,82571,82666,82683,82737,82741,82823,82907,83077,83080,83123,83190,83264,83268,83273,83342,83350,83359,83437,83503,83508,83603,83646,83651,83699,83704,83752,83870,83953,83991,84094,84153,84294,84298,84341,84414,84438,84492,84499,84501,84546,84591,84602,84607,84643,84705,84728,84737,84838,84905,84978,84985,85076,85138,85174,85231,85290,85475,85571,85575,85579,85658,85663,85787,85873,85879,85989,86026,86117,86215,86218,86222,86288,86325,86447,86499,86503,86531,86583,86657,86762,86786,86845,86849,86867,87010,87158,87160,87195,87199,87201,87291,87421,87547,87639,87714,87718,87834,87938,88128,88164,88258,88264,88377,88680,88686,88804,88903,88979,88981,90143,90145],[12,78214,78210],{"id":78215},"produkce-produkční-funkce-cobb-douglas-mrts",[1635,78217,78218],{},[724,78219,78220,1642,78222,78224,78225,40926,78238,78251,78252,20422,78265,1646,78267,78291,78292,4088,78294,2633,78328,4088,78331,78359,78360,14450,78380,78410,78411,1646,78414,78442,78443,78446,78447,78477,78478,78508,78509,4088,78512,78552,78553,78571],{},[883,78221,1641],{},[38,78223,859],{}," popisuje vztah mezi vstupy (práce ",[883,78226,78228],{"className":78227},[886],[888,78229,78230],{"xmlns":890},[892,78231,78232,78236],{},[895,78233,78234],{},[898,78235,13853],{},[902,78237,13853],{"encoding":904},[883,78239,78241],{"className":78240},[886],[888,78242,78243],{"xmlns":890},[892,78244,78245,78249],{},[895,78246,78247],{},[898,78248,13858],{},[902,78250,13858],{"encoding":904},") a výstupem ",[883,78253,78255],{"className":78254},[886],[888,78256,78257],{"xmlns":890},[892,78258,78259,78263],{},[895,78260,78261],{},[898,78262,1802],{},[902,78264,1802],{"encoding":904},[38,78266,40994],{},[883,78268,78270],{"className":78269},[886],[888,78271,78272],{"xmlns":890},[892,78273,78274,78288],{},[895,78275,78276,78278,78280,78282,78284,78286],{},[898,78277,1802],{},[1701,78279,1792],{},[898,78281,1802],{},[1701,78283,1799],{"stretchy":1798},[898,78285,13853],{},[1701,78287,1805],{"stretchy":1798},[902,78289,78290],{"encoding":904},"Q = Q(L)",") studujeme ",[614,78293,14081],{},[883,78295,78297],{"className":78296},[886],[888,78298,78299],{"xmlns":890},[892,78300,78301,78325],{},[895,78302,78303,78305,78311,78313,78319,78321,78323],{},[898,78304,6909],{},[1845,78306,78307,78309],{},[898,78308,1680],{},[898,78310,13853],{},[1701,78312,1792],{},[3243,78314,78315,78317],{},[898,78316,1802],{},[1701,78318,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,78320,1799],{"stretchy":1798},[898,78322,13853],{},[1701,78324,1805],{"stretchy":1798},[902,78326,78327],{"encoding":904},"MP_L = Q'(L)",[614,78329,78330],{},"průměrný produkt",[883,78332,78334],{"className":78333},[886],[888,78335,78336],{"xmlns":890},[892,78337,78338,78356],{},[895,78339,78340,78342,78348,78350,78352,78354],{},[898,78341,1983],{},[1845,78343,78344,78346],{},[898,78345,1680],{},[898,78347,13853],{},[1701,78349,1792],{},[898,78351,1802],{},[898,78353,8741],{"mathvariant":2334},[898,78355,13853],{},[902,78357,78358],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,78361,78363],{"className":78362},[886],[888,78364,78365],{"xmlns":890},[892,78366,78367,78377],{},[895,78368,78369,78371],{},[898,78370,1983],{},[1845,78372,78373,78375],{},[898,78374,1680],{},[898,78376,13853],{},[902,78378,78379],{"encoding":904},"AP_L",[883,78381,78383],{"className":78382},[886],[888,78384,78385],{"xmlns":890},[892,78386,78387,78407],{},[895,78388,78389,78391,78397,78399,78401],{},[898,78390,6909],{},[1845,78392,78393,78395],{},[898,78394,1680],{},[898,78396,13853],{},[1701,78398,1792],{},[898,78400,1983],{},[1845,78402,78403,78405],{},[898,78404,1680],{},[898,78406,13853],{},[902,78408,78409],{"encoding":904},"MP_L = AP_L",". Ve ",[38,78412,78413],{},"dvoufaktorovém modelu",[883,78415,78417],{"className":78416},[886],[888,78418,78419],{"xmlns":890},[892,78420,78421,78439],{},[895,78422,78423,78425,78427,78429,78431,78433,78435,78437],{},[898,78424,1802],{},[1701,78426,1792],{},[898,78428,1802],{},[1701,78430,1799],{"stretchy":1798},[898,78432,13853],{},[1701,78434,2012],{"separator":2011},[898,78436,13858],{},[1701,78438,1805],{"stretchy":1798},[902,78440,78441],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,78444,78445],{},"Cobb-Douglasovy"," funkce ",[883,78448,78450],{"className":78449},[886],[888,78451,78452],{"xmlns":890},[892,78453,78454,78474],{},[895,78455,78456,78458,78460,78462,78468],{},[898,78457,1802],{},[1701,78459,1792],{},[898,78461,1983],{},[3243,78463,78464,78466],{},[898,78465,13853],{},[898,78467,207],{},[3243,78469,78470,78472],{},[898,78471,13858],{},[898,78473,3598],{},[902,78475,78476],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,78479,78481],{"className":78480},[886],[888,78482,78483],{"xmlns":890},[892,78484,78485,78505],{},[895,78486,78487,78489,78495,78497,78499],{},[898,78488,6909],{},[1845,78490,78491,78493],{},[898,78492,1680],{},[898,78494,13853],{},[1701,78496,2012],{"separator":2011},[898,78498,6909],{},[1845,78500,78501,78503],{},[898,78502,1680],{},[898,78504,13858],{},[902,78506,78507],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,78510,78511],{},"mezní míru technické substituce",[883,78513,78515],{"className":78514},[886],[888,78516,78517],{"xmlns":890},[892,78518,78519,78549],{},[895,78520,78521,78523,78525,78527,78529,78531,78533,78539,78541,78543],{},[898,78522,6909],{},[898,78524,8068],{},[898,78526,5877],{},[898,78528,1661],{},[1701,78530,1792],{},[898,78532,6909],{},[1845,78534,78535,78537],{},[898,78536,1680],{},[898,78538,13853],{},[898,78540,8741],{"mathvariant":2334},[898,78542,6909],{},[1845,78544,78545,78547],{},[898,78546,1680],{},[898,78548,13858],{},[902,78550,78551],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,78554,78556],{"className":78555},[886],[888,78557,78558],{"xmlns":890},[892,78559,78560,78568],{},[895,78561,78562,78564,78566],{},[898,78563,207],{},[1701,78565,1703],{},[898,78567,3598],{},[902,78569,78570],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,78573,78575],{"id":78574},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,78577,78578],{},"Po prostudování kapitoly 5 student umí:",[120,78580,78581,78587,78597,78603,78609,78614,78620,78630,78635,78641],{},[123,78582,78583,78584,2012],{},"popsat ",[38,78585,78586],{},"jednofaktorový model produkce",[123,78588,78589,78590,2633,78593,78596],{},"vypočítat ",[38,78591,78592],{},"mezní",[38,78594,78595],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,78598,78599,78600,2012],{},"charakterizovat průběh ",[38,78601,78602],{},"křivky produkce",[123,78604,78605,78606,2012],{},"formulovat ",[38,78607,78608],{},"princip maximalizace průměrného produktu práce",[123,78610,78583,78611,2012],{},[38,78612,78613],{},"dvoufaktorový model produkce",[123,78615,78616,78617,2012],{},"uvést tvar ",[38,78618,78619],{},"Cobb–Douglasových produkčních funkcí",[123,78621,78622,78623,1343,78625,1343,78627,2012],{},"vyložit, co jsou ",[38,78624,28651],{},[38,78626,17711],{},[38,78628,78629],{},"klesající výnosy z rozsahu",[123,78631,78589,78632,78596],{},[38,78633,78634],{},"mezní produkty práce a kapitálu",[123,78636,78637,78638,2012],{},"najít ",[38,78639,78640],{},"izokvanty",[123,78642,78589,78643,78646],{},[38,78644,78645],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,78648,78649,78650,78653,78654,78657,78658,4088,78661,1343,78674,4088,78677,2633,78690,78693,78694,78696,78697,1715],{},"Každý proces produkce je určován ",[38,78651,78652],{},"faktory"," (též ",[38,78655,78656],{},"vstupy",") produkce. K hlavním patří ",[38,78659,78660],{},"práce",[883,78662,78664],{"className":78663},[886],[888,78665,78666],{"xmlns":890},[892,78667,78668,78672],{},[895,78669,78670],{},[898,78671,13853],{},[902,78673,13853],{"encoding":904},[38,78675,78676],{},"kapitál",[883,78678,78680],{"className":78679},[886],[888,78681,78682],{"xmlns":890},[892,78683,78684,78688],{},[895,78685,78686],{},[898,78687,13858],{},[902,78689,13858],{"encoding":904},[38,78691,78692],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,78695,40994],{}," (produkce závisí jen na práci); v opačném případě o ",[38,78698,78413],{},[724,78700,78701,78702,1343,78705,78708],{},"Související matematický aparát: ",[207,78703,6007],{"className":78704,"dataFsResolvedFilePath":764,"href":765},[210],[207,78706,784],{"className":78707,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,78710,78712],{"id":78711},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,78714,78715,78716,78729,78730,78743,78744],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,78717,78719],{"className":78718},[886],[888,78720,78721],{"xmlns":890},[892,78722,78723,78727],{},[895,78724,78725],{},[898,78726,1802],{},[902,78728,1802],{"encoding":904}," na práci ",[883,78731,78733],{"className":78732},[886],[888,78734,78735],{"xmlns":890},[892,78736,78737,78741],{},[895,78738,78739],{},[898,78740,13853],{},[902,78742,13853],{"encoding":904}," vyjadřuje ",[38,78745,78746],{},"produkční funkce",[883,78748,78750],{"className":78749},[886],[888,78751,78752],{"xmlns":890,"display":2252},[892,78753,78754,78785],{},[2256,78755,78756],{"width":2258},[2260,78757,78758,78760,78778,78780],{},[2263,78759],{"width":2265},[2263,78761,78762],{},[895,78763,78764,78766,78768,78770,78772,78774,78776],{},[898,78765,1802],{},[1701,78767,1792],{},[898,78769,1802],{},[1701,78771,1799],{"stretchy":1798},[898,78773,13853],{},[1701,78775,1805],{"stretchy":1798},[1701,78777,2012],{"separator":2011},[2263,78779],{"width":2265},[2263,78781,78782],{},[1939,78783,78784],{},"(5.1)",[902,78786,78787],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,78789,78790,78791,1646,78794,78797,78798,78811],{},"jejíž graf se nazývá ",[38,78792,78793],{},"křivka produkce",[614,78795,78796],{},"production curve","). Práce ",[883,78799,78801],{"className":78800},[886],[888,78802,78803],{"xmlns":890},[892,78804,78805,78809],{},[895,78806,78807],{},[898,78808,13853],{},[902,78810,13853],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,78813,78815,78816,1805],{"id":78814},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,78817,78819],{"className":78818},[886],[888,78820,78821],{"xmlns":890},[892,78822,78823,78833],{},[895,78824,78825,78827],{},[898,78826,6909],{},[1845,78828,78829,78831],{},[898,78830,1680],{},[898,78832,13853],{},[902,78834,14101],{"encoding":904},[724,78836,78837,1646,78840,78843,78844,78863],{},[38,78838,78839],{},"Mezní produkt práce",[614,78841,78842],{},"marginal product of labour",") ",[883,78845,78847],{"className":78846},[886],[888,78848,78849],{"xmlns":890},[892,78850,78851,78861],{},[895,78852,78853,78855],{},[898,78854,6909],{},[1845,78856,78857,78859],{},[898,78858,1680],{},[898,78860,13853],{},[902,78862,14101],{"encoding":904}," je derivace produkce podle práce:",[883,78865,78867],{"className":78866},[886],[888,78868,78869],{"xmlns":890,"display":2252},[892,78870,78871,78928],{},[2256,78872,78873],{"width":2258},[2260,78874,78875,78877,78921,78923],{},[2263,78876],{"width":2265},[2263,78878,78879],{},[895,78880,78881,78883,78889,78891,78905,78907,78913,78915,78917,78919],{},[898,78882,6909],{},[1845,78884,78885,78887],{},[898,78886,1680],{},[898,78888,13853],{},[1701,78890,1792],{},[3726,78892,78893,78899],{},[895,78894,78895,78897],{},[898,78896,2312],{},[898,78898,1802],{},[895,78900,78901,78903],{},[898,78902,2312],{},[898,78904,13853],{},[1701,78906,1792],{},[3243,78908,78909,78911],{},[898,78910,1802],{},[1701,78912,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,78914,1799],{"stretchy":1798},[898,78916,13853],{},[1701,78918,1805],{"stretchy":1798},[898,78920,1715],{"mathvariant":2334},[2263,78922],{"width":2265},[2263,78924,78925],{},[1939,78926,78927],{},"(5.2)",[902,78929,78930],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,78932,78933,78934,23990,78952,78980,78981,78998,78999,3856,79016,2506],{},"Pro pevnou hodnotu ",[883,78935,78937],{"className":78936},[886],[888,78938,78939],{"xmlns":890},[892,78940,78941,78949],{},[895,78942,78943],{},[3243,78944,78945,78947],{},[898,78946,13853],{},[1701,78948,8424],{},[902,78950,78951],{"encoding":904},"L^*",[883,78953,78955],{"className":78954},[886],[888,78956,78957],{"xmlns":890},[892,78958,78959,78977],{},[895,78960,78961,78967,78969,78975],{},[3243,78962,78963,78965],{},[898,78964,1802],{},[1701,78966,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,78968,1799],{"stretchy":1798},[3243,78970,78971,78973],{},[898,78972,13853],{},[1701,78974,8424],{},[1701,78976,1805],{"stretchy":1798},[902,78978,78979],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,78982,78984],{"className":78983},[886],[888,78985,78986],{"xmlns":890},[892,78987,78988,78996],{},[895,78989,78990],{},[3243,78991,78992,78994],{},[898,78993,13853],{},[1701,78995,8424],{},[902,78997,78951],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,79000,79002],{"className":79001},[886],[888,79003,79004],{"xmlns":890},[892,79005,79006,79014],{},[895,79007,79008],{},[3243,79009,79010,79012],{},[898,79011,13853],{},[1701,79013,8424],{},[902,79015,78951],{"encoding":904},[883,79017,79019],{"className":79018},[886],[888,79020,79021],{"xmlns":890},[892,79022,79023,79035],{},[895,79024,79025,79031,79033],{},[3243,79026,79027,79029],{},[898,79028,13853],{},[1701,79030,8424],{},[1701,79032,1703],{},[1850,79034,4062],{},[902,79036,79037],{"encoding":904},"L^*+1",[1635,79039,79040],{},[724,79041,79042,22069,79044,79063,79064,79067,79068,1715],{},[883,79043,2063],{},[883,79045,79047],{"className":79046},[886],[888,79048,79049],{"xmlns":890},[892,79050,79051,79061],{},[895,79052,79053,79055],{},[898,79054,6909],{},[1845,79056,79057,79059],{},[898,79058,1680],{},[898,79060,13853],{},[902,79062,14101],{"encoding":904}," odpovídá na otázku „",[38,79065,79066],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,79069,79071],{"className":79070},[886],[888,79072,79073],{"xmlns":890},[892,79074,79075,79079],{},[895,79076,79077],{},[898,79078,13853],{},[902,79080,13853],{"encoding":904},[724,79082,79083,79086,79087,79103,79104,3856,79117,79137],{},[38,79084,79085],{},"Přibližná změna produkce"," pro změnu práce o ",[883,79088,79090],{"className":79089},[886],[888,79091,79092],{"xmlns":890},[892,79093,79094,79100],{},[895,79095,79096,79098],{},[898,79097,2312],{},[898,79099,13853],{},[902,79101,79102],{"encoding":904},"dL"," (z ",[883,79105,79107],{"className":79106},[886],[888,79108,79109],{"xmlns":890},[892,79110,79111,79115],{},[895,79112,79113],{},[898,79114,13853],{},[902,79116,13853],{"encoding":904},[883,79118,79120],{"className":79119},[886],[888,79121,79122],{"xmlns":890},[892,79123,79124,79134],{},[895,79125,79126,79128,79130,79132],{},[898,79127,13853],{},[1701,79129,1703],{},[898,79131,2312],{},[898,79133,13853],{},[902,79135,79136],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,79139,79141],{"className":79140},[886],[888,79142,79143],{"xmlns":890,"display":2252},[892,79144,79145,79210],{},[2256,79146,79147],{"width":2258},[2260,79148,79149,79151,79203,79205],{},[2263,79150],{"width":2265},[2263,79152,79153],{},[895,79154,79155,79157,79159,79161,79163,79165,79167,79173,79175,79177,79179,79181,79183,79185,79187,79189,79195,79197,79199,79201],{},[898,79156,4708],{"mathvariant":2334},[898,79158,1802],{},[1701,79160,4067],{},[898,79162,2312],{},[898,79164,1802],{},[1701,79166,1792],{},[3243,79168,79169,79171],{},[898,79170,1802],{},[1701,79172,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,79174,1799],{"stretchy":1798},[898,79176,13853],{},[1701,79178,1805],{"stretchy":1798},[1939,79180,1941],{},[898,79182,2312],{},[898,79184,13853],{},[1701,79186,1792],{},[898,79188,6909],{},[1845,79190,79191,79193],{},[898,79192,1680],{},[898,79194,13853],{},[1939,79196,1941],{},[898,79198,2312],{},[898,79200,13853],{},[898,79202,1715],{"mathvariant":2334},[2263,79204],{"width":2265},[2263,79206,79207],{},[1939,79208,79209],{},"(5.3)",[902,79211,79212],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,79214,79215,79216,1715],{},"Skutečná změna je ",[883,79217,79219],{"className":79218},[886],[888,79220,79221],{"xmlns":890},[892,79222,79223,79255],{},[895,79224,79225,79227,79229,79231,79233,79235,79237,79239,79241,79243,79245,79247,79249,79251,79253],{},[898,79226,4708],{"mathvariant":2334},[898,79228,1802],{},[1701,79230,1792],{},[898,79232,1802],{},[1701,79234,1799],{"stretchy":1798},[898,79236,13853],{},[1701,79238,1703],{},[898,79240,2312],{},[898,79242,13853],{},[1701,79244,1805],{"stretchy":1798},[1701,79246,2317],{},[898,79248,1802],{},[1701,79250,1799],{"stretchy":1798},[898,79252,13853],{},[1701,79254,1805],{"stretchy":1798},[902,79256,79257],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,79259,79261],{"id":79260},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,79263,79264,1646,79267,4539],{},[38,79265,79266],{},"Zákon klesajících výnosů",[614,79268,79269],{},"law of diminishing marginal productivity",[1635,79271,79272],{},[724,79273,79274,79275,79277],{},"Roste-li postupně některý ze vstupů (",[614,79276,40990],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,79279,79280],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,79282,79283,79284,4088,79305,79324,79325,79375,79376,79378,79379,4088,79399,79418,79419,79375,79451,7015,79453,79472,79473,2020,79490,79524,79525,12164,79542,79545],{},"1° ",[38,79285,79286,79287,2246],{},"Do bodu ",[883,79288,79290],{"className":79289},[886],[888,79291,79292],{"xmlns":890},[892,79293,79294,79302],{},[895,79295,79296],{},[1845,79297,79298,79300],{},[898,79299,13853],{},[1850,79301,1852],{},[902,79303,79304],{"encoding":904},"L_0",[883,79306,79308],{"className":79307},[886],[888,79309,79310],{"xmlns":890},[892,79311,79312,79322],{},[895,79313,79314,79316],{},[898,79315,6909],{},[1845,79317,79318,79320],{},[898,79319,1680],{},[898,79321,13853],{},[902,79323,14101],{"encoding":904}," roste, tj. ",[883,79326,79328],{"className":79327},[886],[888,79329,79330],{"xmlns":890},[892,79331,79332,79372],{},[895,79333,79334,79336,79338,79344,79350,79352,79362,79364,79366,79368,79370],{},[1701,79335,1799],{"stretchy":1798},[898,79337,6909],{},[1845,79339,79340,79342],{},[898,79341,1680],{},[898,79343,13853],{},[3243,79345,79346,79348],{},[1701,79347,1805],{"stretchy":1798},[1701,79349,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,79351,1792],{},[3243,79353,79354,79356],{},[898,79355,1802],{},[895,79357,79358,79360],{},[1701,79359,4783],{"mathvariant":2334},[1701,79361,4783],{"mathvariant":2334},[1701,79363,1799],{"stretchy":1798},[898,79365,13853],{},[1701,79367,1805],{"stretchy":1798},[1701,79369,7491],{},[1850,79371,1852],{},[902,79373,79374],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,79377,41692],{},".\n2° ",[38,79380,79381,79382,2246],{},"Od bodu ",[883,79383,79385],{"className":79384},[886],[888,79386,79387],{"xmlns":890},[892,79388,79389,79397],{},[895,79390,79391],{},[1845,79392,79393,79395],{},[898,79394,13853],{},[1850,79396,1852],{},[902,79398,79304],{"encoding":904},[883,79400,79402],{"className":79401},[886],[888,79403,79404],{"xmlns":890},[892,79405,79406,79416],{},[895,79407,79408,79410],{},[898,79409,6909],{},[1845,79411,79412,79414],{},[898,79413,1680],{},[898,79415,13853],{},[902,79417,14101],{"encoding":904}," klesá, ",[883,79420,79422],{"className":79421},[886],[888,79423,79424],{"xmlns":890},[892,79425,79426,79448],{},[895,79427,79428,79438,79440,79442,79444,79446],{},[3243,79429,79430,79432],{},[898,79431,1802],{},[895,79433,79434,79436],{},[1701,79435,4783],{"mathvariant":2334},[1701,79437,4783],{"mathvariant":2334},[1701,79439,1799],{"stretchy":1798},[898,79441,13853],{},[1701,79443,1805],{"stretchy":1798},[1701,79445,7530],{},[1850,79447,1852],{},[902,79449,79450],{"encoding":904},"Q''(L) \u003C 0",[38,79452,42513],{},[883,79454,79456],{"className":79455},[886],[888,79457,79458],{"xmlns":890},[892,79459,79460,79470],{},[895,79461,79462,79464],{},[898,79463,6909],{},[1845,79465,79466,79468],{},[898,79467,1680],{},[898,79469,13853],{},[902,79471,14101],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,79474,79476],{"className":79475},[886],[888,79477,79478],{"xmlns":890},[892,79479,79480,79488],{},[895,79481,79482],{},[1845,79483,79484,79486],{},[898,79485,13853],{},[1850,79487,4062],{},[902,79489,17266],{"encoding":904},[883,79491,79493],{"className":79492},[886],[888,79494,79495],{"xmlns":890},[892,79496,79497,79521],{},[895,79498,79499,79501,79507,79509,79515,79517,79519],{},[898,79500,6909],{},[1845,79502,79503,79505],{},[898,79504,1680],{},[898,79506,13853],{},[1701,79508,1799],{"stretchy":1798},[1845,79510,79511,79513],{},[898,79512,13853],{},[1850,79514,4062],{},[1701,79516,1805],{"stretchy":1798},[1701,79518,1792],{},[1850,79520,1852],{},[902,79522,79523],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,79526,79528],{"className":79527},[886],[888,79529,79530],{"xmlns":890},[892,79531,79532,79540],{},[895,79533,79534],{},[1845,79535,79536,79538],{},[898,79537,13853],{},[1850,79539,1852],{},[902,79541,79304],{"encoding":904},[38,79543,79544],{},"inflexním bodem"," produkční funkce.",[724,79547,79548,79549,14450,79566,1715],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,79550,79552],{"className":79551},[886],[888,79553,79554],{"xmlns":890},[892,79555,79556,79564],{},[895,79557,79558],{},[1845,79559,79560,79562],{},[898,79561,13853],{},[1850,79563,1852],{},[902,79565,79304],{"encoding":904},[883,79567,79569],{"className":79568},[886],[888,79570,79571],{"xmlns":890},[892,79572,79573,79595],{},[895,79574,79575,79585,79587,79589,79591,79593],{},[3243,79576,79577,79579],{},[898,79578,1802],{},[895,79580,79581,79583],{},[1701,79582,4783],{"mathvariant":2334},[1701,79584,4783],{"mathvariant":2334},[1701,79586,1799],{"stretchy":1798},[898,79588,13853],{},[1701,79590,1805],{"stretchy":1798},[1701,79592,7530],{},[1850,79594,1852],{},[902,79596,79450],{"encoding":904},[724,79598,79599,4088,79602,9733,79642,1343,79659,79676],{},[38,79600,79601],{},"Typický polynom třetího stupně:",[883,79603,79605],{"className":79604},[886],[888,79606,79607],{"xmlns":890},[892,79608,79609,79639],{},[895,79610,79611,79613,79615,79617,79619,79621,79623,79629,79631,79633],{},[898,79612,1802],{},[1701,79614,1799],{"stretchy":1798},[898,79616,13853],{},[1701,79618,1805],{"stretchy":1798},[1701,79620,1792],{},[898,79622,207],{},[3243,79624,79625,79627],{},[898,79626,13853],{},[1850,79628,3646],{},[1701,79630,1703],{},[898,79632,3598],{},[3243,79634,79635,79637],{},[898,79636,13853],{},[1850,79638,3938],{},[902,79640,79641],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,79643,79645],{"className":79644},[886],[888,79646,79647],{"xmlns":890},[892,79648,79649,79657],{},[895,79650,79651,79653,79655],{},[898,79652,207],{},[1701,79654,7530],{},[1850,79656,1852],{},[902,79658,47105],{"encoding":904},[883,79660,79662],{"className":79661},[886],[888,79663,79664],{"xmlns":890},[892,79665,79666,79674],{},[895,79667,79668,79670,79672],{},[898,79669,3598],{},[1701,79671,7491],{},[1850,79673,1852],{},[902,79675,22860],{"encoding":904},". Pak",[883,79678,79680],{"className":79679},[886],[888,79681,79682],{"xmlns":890,"display":2252},[892,79683,79684,79744],{},[895,79685,79686,79692,79694,79696,79704,79712,79714,79716,79722,79724,79726,79734,79742],{},[1845,79687,79688,79690],{},[898,79689,13853],{},[1850,79691,1852],{},[1701,79693,1792],{},[1701,79695,2317],{},[2363,79697,79698],{"scriptlevel":1852,"displaystyle":1798},[3726,79699,79700,79702],{},[1850,79701,4062],{},[1850,79703,3646],{},[2363,79705,79706],{"scriptlevel":1852,"displaystyle":1798},[3726,79707,79708,79710],{},[898,79709,3598],{},[898,79711,207],{},[1701,79713,2012],{"separator":2011},[9942,79715],{"width":9944},[1845,79717,79718,79720],{},[898,79719,13853],{},[1850,79721,4062],{},[1701,79723,1792],{},[1701,79725,2317],{},[2363,79727,79728],{"scriptlevel":1852,"displaystyle":1798},[3726,79729,79730,79732],{},[1850,79731,3938],{},[1850,79733,3646],{},[2363,79735,79736],{"scriptlevel":1852,"displaystyle":1798},[3726,79737,79738,79740],{},[898,79739,3598],{},[898,79741,207],{},[898,79743,1715],{"mathvariant":2334},[902,79745,79746],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,79748,79750,79751,1805],{"id":79749},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,79752,79754],{"className":79753},[886],[888,79755,79756],{"xmlns":890},[892,79757,79758,79768],{},[895,79759,79760,79762],{},[898,79761,1983],{},[1845,79763,79764,79766],{},[898,79765,1680],{},[898,79767,13853],{},[902,79769,78379],{"encoding":904},[724,79771,79772,1646,79775,78843,79778,79797],{},[38,79773,79774],{},"Průměrný produkt práce",[614,79776,79777],{},"average product of labour",[883,79779,79781],{"className":79780},[886],[888,79782,79783],{"xmlns":890},[892,79784,79785,79795],{},[895,79786,79787,79789],{},[898,79788,1983],{},[1845,79790,79791,79793],{},[898,79792,1680],{},[898,79794,13853],{},[902,79796,78379],{"encoding":904}," je podíl produkce a práce:",[883,79799,79801],{"className":79800},[886],[888,79802,79803],{"xmlns":890,"display":2252},[892,79804,79805,79840],{},[2256,79806,79807],{"width":2258},[2260,79808,79809,79811,79833,79835],{},[2263,79810],{"width":2265},[2263,79812,79813],{},[895,79814,79815,79817,79823,79825,79831],{},[898,79816,1983],{},[1845,79818,79819,79821],{},[898,79820,1680],{},[898,79822,13853],{},[1701,79824,1792],{},[3726,79826,79827,79829],{},[898,79828,1802],{},[898,79830,13853],{},[898,79832,1715],{"mathvariant":2334},[2263,79834],{"width":2265},[2263,79836,79837],{},[1939,79838,79839],{},"(5.4)",[902,79841,79842],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,79844,79845,79846,1715],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,79847,79849],{"className":79848},[886],[888,79850,79851],{"xmlns":890},[892,79852,79853,79863],{},[895,79854,79855,79857],{},[898,79856,1983],{},[1845,79858,79859,79861],{},[898,79860,1680],{},[898,79862,13853],{},[902,79864,78379],{"encoding":904},[115,79866,79868],{"id":79867},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,79870,79871],{},[2139,79872],{"alt":79873,"className":79874,"src":79875},"imek-q-mpl-apl-tripanel",[210,2143],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1635,79877,79878],{},[724,79879,79880,79883,79884,6723,79903,79920,79921],{},[38,79881,79882],{},"Princip:"," Má-li ",[883,79885,79887],{"className":79886},[886],[888,79888,79889],{"xmlns":890},[892,79890,79891,79901],{},[895,79892,79893,79895],{},[898,79894,1983],{},[1845,79896,79897,79899],{},[898,79898,1680],{},[898,79900,13853],{},[902,79902,78379],{"encoding":904},[883,79904,79906],{"className":79905},[886],[888,79907,79908],{"xmlns":890},[892,79909,79910,79918],{},[895,79911,79912],{},[1845,79913,79914,79916],{},[898,79915,13853],{},[1850,79917,1852],{},[902,79919,79304],{"encoding":904}," maximum, pak platí\n",[883,79922,79924],{"className":79923,"title":8272,"style":8273},[8271],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,79926,79927,79928,79931,79932,4088,79936,1715],{},"Slovně: ",[38,79929,79930],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,79933,79935],{"className":79934,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,79937,79939],{"className":79938},[886],[888,79940,79941],{"xmlns":890},[892,79942,79943,79949],{},[895,79944,79945,79947],{},[898,79946,1983],{},[898,79948,1658],{},[902,79950,59306],{"encoding":904},[1635,79952,79953,79977],{},[724,79954,79955,79957,79958],{},[883,79956,3140],{}," Postup — jak najít max ",[883,79959,79961],{"className":79960},[886],[888,79962,79963],{"xmlns":890},[892,79964,79965,79975],{},[895,79966,79967,79969],{},[898,79968,1983],{},[1845,79970,79971,79973],{},[898,79972,1680],{},[898,79974,13853],{},[902,79976,78379],{"encoding":904},[152,79978,79979,80017,80099],{},[123,79980,79981,79982,80016],{},"Napište ",[883,79983,79985],{"className":79984},[886],[888,79986,79987],{"xmlns":890},[892,79988,79989,80013],{},[895,79990,79991,79993,79999,80001,80003,80005,80007,80009,80011],{},[898,79992,1983],{},[1845,79994,79995,79997],{},[898,79996,1680],{},[898,79998,13853],{},[1701,80000,1792],{},[898,80002,1802],{},[1701,80004,1799],{"stretchy":1798},[898,80006,13853],{},[1701,80008,1805],{"stretchy":1798},[898,80010,8741],{"mathvariant":2334},[898,80012,13853],{},[902,80014,80015],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,80018,80019,80020,80052,80053,80056,80057,1715],{},"Položte ",[883,80021,80023],{"className":80022},[886],[888,80024,80025],{"xmlns":890},[892,80026,80027,80049],{},[895,80028,80029,80031,80033,80039,80045,80047],{},[1701,80030,1799],{"stretchy":1798},[898,80032,1983],{},[1845,80034,80035,80037],{},[898,80036,1680],{},[898,80038,13853],{},[3243,80040,80041,80043],{},[1701,80042,1805],{"stretchy":1798},[1701,80044,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,80046,1792],{},[1850,80048,1852],{},[902,80050,80051],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,80054,80055],{},"Zkratka:"," můžete rovnou řešit ",[883,80058,80060],{"className":80059},[886],[888,80061,80062],{"xmlns":890},[892,80063,80064,80096],{},[895,80065,80066,80068,80074,80076,80078,80080,80082,80084,80090,80092,80094],{},[898,80067,6909],{},[1845,80069,80070,80072],{},[898,80071,1680],{},[898,80073,13853],{},[1701,80075,1799],{"stretchy":1798},[898,80077,13853],{},[1701,80079,1805],{"stretchy":1798},[1701,80081,1792],{},[898,80083,1983],{},[1845,80085,80086,80088],{},[898,80087,1680],{},[898,80089,13853],{},[1701,80091,1799],{"stretchy":1798},[898,80093,13853],{},[1701,80095,1805],{"stretchy":1798},[902,80097,80098],{"encoding":904},"MP_L(L) = AP_L(L)",[123,80100,80101],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,80103,69247],{"id":80104},"odvození",[724,80106,80107,80108,80141],{},"Z ",[883,80109,80111],{"className":80110},[886],[888,80112,80113],{"xmlns":890},[892,80114,80115,80139],{},[895,80116,80117,80119,80125,80127,80129,80131,80133,80135,80137],{},[898,80118,1983],{},[1845,80120,80121,80123],{},[898,80122,1680],{},[898,80124,13853],{},[1701,80126,1792],{},[898,80128,1802],{},[1701,80130,1799],{"stretchy":1798},[898,80132,13853],{},[1701,80134,1805],{"stretchy":1798},[898,80136,8741],{"mathvariant":2334},[898,80138,13853],{},[902,80140,80015],{"encoding":904}," a derivace podílu:",[883,80143,80145],{"className":80144},[886],[888,80146,80147],{"xmlns":890,"display":2252},[892,80148,80149,80302],{},[895,80150,80151,80153,80155,80161,80167,80169,80171,80173,80175,80215,80217,80223,80257,80259,80265,80268,80270,80276,80278,80280,80282,80284,80286,80292,80294,80296,80298,80300],{},[1701,80152,1799],{"stretchy":1798},[898,80154,1983],{},[1845,80156,80157,80159],{},[898,80158,1680],{},[898,80160,13853],{},[3243,80162,80163,80165],{},[1701,80164,1805],{"stretchy":1798},[1701,80166,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,80168,1799],{"stretchy":1798},[898,80170,13853],{},[1701,80172,1805],{"stretchy":1798},[1701,80174,1792],{},[3726,80176,80177,80209],{},[895,80178,80179,80185,80187,80189,80191,80193,80195,80197,80199,80201,80203,80205,80207],{},[3243,80180,80181,80183],{},[898,80182,1802],{},[1701,80184,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,80186,1799],{"stretchy":1798},[898,80188,13853],{},[1701,80190,1805],{"stretchy":1798},[1701,80192,3408],{},[898,80194,13853],{},[1701,80196,2317],{},[898,80198,1802],{},[1701,80200,1799],{"stretchy":1798},[898,80202,13853],{},[1701,80204,1805],{"stretchy":1798},[1701,80206,3408],{},[1850,80208,4062],{},[3243,80210,80211,80213],{},[898,80212,13853],{},[1850,80214,3938],{},[1701,80216,1792],{},[3726,80218,80219,80221],{},[1850,80220,4062],{},[898,80222,13853],{},[895,80224,80225,80227,80233,80235,80237,80239,80241,80255],{},[1701,80226,1799],{"fence":2011},[3243,80228,80229,80231],{},[898,80230,1802],{},[1701,80232,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,80234,1799],{"stretchy":1798},[898,80236,13853],{},[1701,80238,1805],{"stretchy":1798},[1701,80240,2317],{},[3726,80242,80243,80253],{},[895,80244,80245,80247,80249,80251],{},[898,80246,1802],{},[1701,80248,1799],{"stretchy":1798},[898,80250,13853],{},[1701,80252,1805],{"stretchy":1798},[898,80254,13853],{},[1701,80256,1805],{"fence":2011},[1701,80258,1792],{},[3726,80260,80261,80263],{},[1850,80262,4062],{},[898,80264,13853],{},[1701,80266,1799],{"fence":2011,"stretchy":2011,"minsize":80267,"maxsize":80267},"1.2em",[898,80269,6909],{},[1845,80271,80272,80274],{},[898,80273,1680],{},[898,80275,13853],{},[1701,80277,1799],{"stretchy":1798},[898,80279,13853],{},[1701,80281,1805],{"stretchy":1798},[1701,80283,2317],{},[898,80285,1983],{},[1845,80287,80288,80290],{},[898,80289,1680],{},[898,80291,13853],{},[1701,80293,1799],{"stretchy":1798},[898,80295,13853],{},[1701,80297,1805],{"stretchy":1798},[1701,80299,1805],{"fence":2011,"stretchy":2011,"minsize":80267,"maxsize":80267},[898,80301,1715],{"mathvariant":2334},[902,80303,80304],{"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).",[724,80306,13721,80307,12164,80329,80412],{},[883,80308,80310],{"className":80309},[886],[888,80311,80312],{"xmlns":890},[892,80313,80314,80326],{},[895,80315,80316,80322,80324],{},[1845,80317,80318,80320],{},[898,80319,13853],{},[1850,80321,1852],{},[1701,80323,7491],{},[1850,80325,1852],{},[902,80327,80328],{"encoding":904},"L_0 > 0",[883,80330,80332],{"className":80331},[886],[888,80333,80334],{"xmlns":890},[892,80335,80336,80409],{},[895,80337,80338,80340,80342,80348,80354,80356,80362,80364,80366,80368,80371,80373,80379,80381,80387,80389,80391,80393,80399,80401,80407],{},[1701,80339,1799],{"stretchy":1798},[898,80341,1983],{},[1845,80343,80344,80346],{},[898,80345,1680],{},[898,80347,13853],{},[3243,80349,80350,80352],{},[1701,80351,1805],{"stretchy":1798},[1701,80353,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,80355,1799],{"stretchy":1798},[1845,80357,80358,80360],{},[898,80359,13853],{},[1850,80361,1852],{},[1701,80363,1805],{"stretchy":1798},[1701,80365,1792],{},[1850,80367,1852],{},[1701,80369,80370],{},"⇔",[898,80372,6909],{},[1845,80374,80375,80377],{},[898,80376,1680],{},[898,80378,13853],{},[1701,80380,1799],{"stretchy":1798},[1845,80382,80383,80385],{},[898,80384,13853],{},[1850,80386,1852],{},[1701,80388,1805],{"stretchy":1798},[1701,80390,1792],{},[898,80392,1983],{},[1845,80394,80395,80397],{},[898,80396,1680],{},[898,80398,13853],{},[1701,80400,1799],{"stretchy":1798},[1845,80402,80403,80405],{},[898,80404,13853],{},[1850,80406,1852],{},[1701,80408,1805],{"stretchy":1798},[902,80410,80411],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,80414,80416],{"id":80415},"příklad-51","Příklad 5.1",[724,80418,80419,80420,1715],{},"Je dána produkce ",[883,80421,80423],{"className":80422},[886],[888,80424,80425],{"xmlns":890},[892,80426,80427,80451],{},[895,80428,80429,80431,80433,80435,80441,80443,80445],{},[898,80430,1802],{},[1701,80432,1792],{},[1850,80434,6352],{},[3243,80436,80437,80439],{},[898,80438,13853],{},[1850,80440,3938],{},[1701,80442,2317],{},[1850,80444,6930],{},[3243,80446,80447,80449],{},[898,80448,13853],{},[1850,80450,3646],{},[902,80452,80453],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,80455,80456,61268,80459,80509,80510,1715],{},[38,80457,80458],{},"(a)",[883,80460,80462],{"className":80461},[886],[888,80463,80464],{"xmlns":890},[892,80465,80466,80506],{},[895,80467,80468,80470,80472,80474,80476,80478,80480,80482,80484,80486,80488,80490,80492,80494,80496,80498,80500,80502,80504],{},[898,80469,13853],{},[1701,80471,1792],{},[1850,80473,3938],{},[1701,80475,2012],{"separator":2011},[1850,80477,4225],{},[1701,80479,2012],{"separator":2011},[1850,80481,9650],{},[1701,80483,2012],{"separator":2011},[1850,80485,3703],{},[1701,80487,2012],{"separator":2011},[1850,80489,26985],{},[1701,80491,2012],{"separator":2011},[1850,80493,7790],{},[1701,80495,2012],{"separator":2011},[1850,80497,13096],{},[1701,80499,2012],{"separator":2011},[1850,80501,42371],{},[1701,80503,2012],{"separator":2011},[1850,80505,9071],{},[902,80507,80508],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,80511,80513],{"className":80512},[886],[888,80514,80515],{"xmlns":890},[892,80516,80517,80527],{},[895,80518,80519,80521],{},[898,80520,6909],{},[1845,80522,80523,80525],{},[898,80524,1680],{},[898,80526,13853],{},[902,80528,14101],{"encoding":904},[724,80530,80531,80532,38999],{},"Podle (5.2): ",[883,80533,80535],{"className":80534},[886],[888,80536,80537],{"xmlns":890},[892,80538,80539,80595],{},[895,80540,80541,80543,80549,80551,80557,80559,80561,80563,80565,80567,80569,80571,80573,80579,80581,80583,80585,80587,80589,80591,80593],{},[898,80542,6909],{},[1845,80544,80545,80547],{},[898,80546,1680],{},[898,80548,13853],{},[1701,80550,1792],{},[3243,80552,80553,80555],{},[898,80554,1802],{},[1701,80556,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,80558,1799],{"stretchy":1798},[898,80560,13853],{},[1701,80562,1805],{"stretchy":1798},[1701,80564,1792],{},[1850,80566,7592],{},[898,80568,13853],{},[1701,80570,2317],{},[1850,80572,3868],{},[3243,80574,80575,80577],{},[898,80576,13853],{},[1850,80578,3938],{},[1701,80580,1792],{},[898,80582,13853],{},[1701,80584,1799],{"stretchy":1798},[1850,80586,7592],{},[1701,80588,2317],{},[1850,80590,3868],{},[898,80592,13853],{},[1701,80594,1805],{"stretchy":1798},[902,80596,80597],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,80599,80600,80637],{},[19,80601,80602],{},[22,80603,80604,80619,80621,80623,80625,80627,80629,80631,80633,80635],{},[25,80605,80606],{},[883,80607,80609],{"className":80608},[886],[888,80610,80611],{"xmlns":890},[892,80612,80613,80617],{},[895,80614,80615],{},[898,80616,13853],{},[902,80618,13853],{"encoding":904},[25,80620,3938],{},[25,80622,4225],{},[25,80624,9650],{},[25,80626,3703],{},[25,80628,26985],{},[25,80630,7790],{},[25,80632,13096],{},[25,80634,42371],{},[25,80636,9071],{},[30,80638,80639],{},[22,80640,80641,80662,80665,80668,80671,80673,80676,80678,80680,80699],{},[35,80642,80643],{},[883,80644,80646],{"className":80645},[886],[888,80647,80648],{"xmlns":890},[892,80649,80650,80660],{},[895,80651,80652,80654],{},[898,80653,6909],{},[1845,80655,80656,80658],{},[898,80657,1680],{},[898,80659,13853],{},[902,80661,14101],{"encoding":904},[35,80663,80664],{},"21,6",[35,80666,80667],{},"45",[35,80669,80670],{},"57,6",[35,80672,7211],{},[35,80674,80675],{},"50,4",[35,80677,80664],{},[35,80679,1852],{},[35,80681,80682],{},[883,80683,80685],{"className":80684},[886],[888,80686,80687],{"xmlns":890},[892,80688,80689,80696],{},[895,80690,80691,80693],{},[1701,80692,2317],{},[1850,80694,80695],{},"12,6",[902,80697,80698],{"encoding":904},"-12{,}6",[35,80700,80701],{},[883,80702,80704],{"className":80703},[886],[888,80705,80706],{"xmlns":890},[892,80707,80708,80714],{},[895,80709,80710,80712],{},[1701,80711,2317],{},[1850,80713,49443],{},[902,80715,80716],{"encoding":904},"-75",[724,80718,80719,80738,80739,80757,80758,80775,80776,80794,80795,80819,80820,80838],{},[883,80720,80722],{"className":80721},[886],[888,80723,80724],{"xmlns":890},[892,80725,80726,80736],{},[895,80727,80728,80730],{},[898,80729,6909],{},[1845,80731,80732,80734],{},[898,80733,1680],{},[898,80735,13853],{},[902,80737,14101],{"encoding":904}," nabývá maxima pro ",[883,80740,80742],{"className":80741},[886],[888,80743,80744],{"xmlns":890},[892,80745,80746,80754],{},[895,80747,80748,80750,80752],{},[898,80749,13853],{},[1701,80751,1792],{},[1850,80753,3703],{},[902,80755,80756],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,80759,80761],{"className":80760},[886],[888,80762,80763],{"xmlns":890},[892,80764,80765,80773],{},[895,80766,80767,80769,80771],{},[898,80768,13853],{},[1701,80770,1792],{},[1850,80772,3703],{},[902,80774,80756],{"encoding":904}," přírůstky klesají, v ",[883,80777,80779],{"className":80778},[886],[888,80780,80781],{"xmlns":890},[892,80782,80783,80791],{},[895,80784,80785,80787,80789],{},[898,80786,13853],{},[1701,80788,1792],{},[1850,80790,13096],{},[902,80792,80793],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,80796,80798],{"className":80797},[886],[888,80799,80800],{"xmlns":890},[892,80801,80802,80816],{},[895,80803,80804,80806,80808,80810,80812,80814],{},[898,80805,1802],{},[1701,80807,1799],{"stretchy":1798},[1850,80809,13096],{},[1701,80811,1805],{"stretchy":1798},[1701,80813,1792],{},[1850,80815,27896],{},[902,80817,80818],{"encoding":904},"Q(20) = 800","), od ",[883,80821,80823],{"className":80822},[886],[888,80824,80825],{"xmlns":890},[892,80826,80827,80835],{},[895,80828,80829,80831,80833],{},[898,80830,13853],{},[1701,80832,7491],{},[1850,80834,13096],{},[902,80836,80837],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,80840,80841],{},[614,80842,80843,80844,80884,80885,6723,80903,1715],{},"Obrázek 5.1 — graf produkce ",[883,80845,80847],{"className":80846},[886],[888,80848,80849],{"xmlns":890},[892,80850,80851,80881],{},[895,80852,80853,80855,80857,80859,80861,80863,80865,80871,80873,80875],{},[898,80854,1802],{},[1701,80856,1799],{"stretchy":1798},[898,80858,13853],{},[1701,80860,1805],{"stretchy":1798},[1701,80862,1792],{},[1850,80864,6352],{},[3243,80866,80867,80869],{},[898,80868,13853],{},[1850,80870,3938],{},[1701,80872,2317],{},[1850,80874,6930],{},[3243,80876,80877,80879],{},[898,80878,13853],{},[1850,80880,3646],{},[902,80882,80883],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,80886,80888],{"className":80887},[886],[888,80889,80890],{"xmlns":890},[892,80891,80892,80900],{},[895,80893,80894,80896,80898],{},[898,80895,1802],{},[1701,80897,1792],{},[1850,80899,27896],{},[902,80901,80902],{"encoding":904},"Q = 800",[883,80904,80906],{"className":80905},[886],[888,80907,80908],{"xmlns":890},[892,80909,80910,80918],{},[895,80911,80912,80914,80916],{},[898,80913,13853],{},[1701,80915,1792],{},[1850,80917,13096],{},[902,80919,80793],{"encoding":904},[724,80921,80922,80925],{},[38,80923,80924],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,80927,80928,80929,1343,80947,2246],{},"Podle (5.3) s ",[883,80930,80932],{"className":80931},[886],[888,80933,80934],{"xmlns":890},[892,80935,80936,80944],{},[895,80937,80938,80940,80942],{},[898,80939,13853],{},[1701,80941,1792],{},[1850,80943,6352],{},[902,80945,80946],{"encoding":904},"L = 6",[883,80948,80950],{"className":80949},[886],[888,80951,80952],{"xmlns":890},[892,80953,80954,80964],{},[895,80955,80956,80958,80960,80962],{},[898,80957,2312],{},[898,80959,13853],{},[1701,80961,1792],{},[1850,80963,3646],{},[902,80965,80966],{"encoding":904},"dL = 3",[883,80968,80970],{"className":80969},[886],[888,80971,80972],{"xmlns":890,"display":2252},[892,80973,80974,81037],{},[895,80975,80976,80978,80980,80982,80984,80990,80992,80994,80996,80998,81000,81002,81004,81006,81008,81010,81012,81014,81016,81018,81020,81022,81024,81026,81028,81030,81032,81034],{},[898,80977,2312],{},[898,80979,1802],{},[1701,80981,1792],{},[898,80983,6909],{},[1845,80985,80986,80988],{},[898,80987,1680],{},[898,80989,13853],{},[1701,80991,1799],{"stretchy":1798},[1850,80993,6352],{},[1701,80995,1805],{"stretchy":1798},[1701,80997,3408],{},[1850,80999,3646],{},[1701,81001,1792],{},[1701,81003,1799],{"stretchy":1798},[1850,81005,7592],{},[1701,81007,3408],{},[1850,81009,6352],{},[1701,81011,2317],{},[1850,81013,3868],{},[1701,81015,3408],{},[1850,81017,9630],{},[1701,81019,1805],{"stretchy":1798},[1701,81021,3408],{},[1850,81023,3646],{},[1701,81025,1792],{},[1850,81027,80675],{},[1701,81029,3408],{},[1850,81031,3646],{},[1701,81033,1792],{},[1850,81035,81036],{},"151,2.",[902,81038,81039],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,81041,81042,81043,61498,81068,81082,81083,1715],{},"Produkce vzroste z ",[883,81044,81046],{"className":81045},[886],[888,81047,81048],{"xmlns":890},[892,81049,81050,81065],{},[895,81051,81052,81054,81056,81058,81060,81062],{},[898,81053,1802],{},[1701,81055,1799],{"stretchy":1798},[1850,81057,6352],{},[1701,81059,1805],{"stretchy":1798},[1701,81061,1792],{},[1850,81063,81064],{},"172,8",[902,81066,81067],{"encoding":904},"Q(6) = 172{,}8",[883,81069,81071],{"className":81070},[886],[888,81072,81073],{"xmlns":890},[892,81074,81075,81080],{},[895,81076,81077],{},[1850,81078,81079],{},"324",[902,81081,81079],{"encoding":904},". Skutečná hodnota: ",[883,81084,81086],{"className":81085},[886],[888,81087,81088],{"xmlns":890},[892,81089,81090,81130],{},[895,81091,81092,81094,81096,81098,81100,81102,81104,81106,81108,81110,81112,81114,81116,81118,81121,81123,81125,81127],{},[898,81093,4708],{"mathvariant":2334},[898,81095,1802],{},[1701,81097,1792],{},[898,81099,1802],{},[1701,81101,1799],{"stretchy":1798},[1850,81103,8073],{},[1701,81105,1805],{"stretchy":1798},[1701,81107,2317],{},[898,81109,1802],{},[1701,81111,1799],{"stretchy":1798},[1850,81113,6352],{},[1701,81115,1805],{"stretchy":1798},[1701,81117,1792],{},[1850,81119,81120],{},"340,2",[1701,81122,2317],{},[1850,81124,81064],{},[1701,81126,1792],{},[1850,81128,81129],{},"167,4",[902,81131,81132],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,81134,81136],{"id":81135},"příklad-52","Příklad 5.2",[724,81138,81139,81140,1715],{},"Ověříme princip (5.5) pro ",[883,81141,81143],{"className":81142},[886],[888,81144,81145],{"xmlns":890},[892,81146,81147,81171],{},[895,81148,81149,81151,81153,81155,81161,81163,81165],{},[898,81150,1802],{},[1701,81152,1792],{},[1850,81154,6352],{},[3243,81156,81157,81159],{},[898,81158,13853],{},[1850,81160,3938],{},[1701,81162,2317],{},[1850,81164,6930],{},[3243,81166,81167,81169],{},[898,81168,13853],{},[1850,81170,3646],{},[902,81172,80453],{"encoding":904},[883,81174,81176],{"className":81175},[886],[888,81177,81178],{"xmlns":890,"display":2252},[892,81179,81180,81258],{},[895,81181,81182,81184,81190,81192,81198,81200,81202,81204,81206,81208,81214,81216,81218,81220,81228,81230,81232,81234,81236,81238,81240,81242,81244,81246,81248,81254,81256],{},[898,81183,1983],{},[1845,81185,81186,81188],{},[898,81187,1680],{},[898,81189,13853],{},[1701,81191,1792],{},[3726,81193,81194,81196],{},[898,81195,1802],{},[898,81197,13853],{},[1701,81199,1792],{},[1850,81201,6352],{},[898,81203,13853],{},[1701,81205,2317],{},[1850,81207,6930],{},[3243,81209,81210,81212],{},[898,81211,13853],{},[1850,81213,3938],{},[1701,81215,2012],{"separator":2011},[9942,81217],{"width":19336},[898,81219,1983],{},[2287,81221,81222,81224,81226],{},[898,81223,1680],{},[898,81225,13853],{},[1701,81227,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,81229,1792],{},[1850,81231,6352],{},[1701,81233,2317],{},[1850,81235,23317],{},[898,81237,13853],{},[1701,81239,1792],{},[1850,81241,1852],{},[1939,81243,8058],{},[1701,81245,8061],{},[1939,81247,8058],{},[1845,81249,81250,81252],{},[898,81251,13853],{},[1850,81253,1852],{},[1701,81255,1792],{},[1850,81257,72029],{},[902,81259,81260],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,81262,81263,81299,81300,81318,81319,1715],{},[883,81264,81266],{"className":81265},[886],[888,81267,81268],{"xmlns":890},[892,81269,81270,81296],{},[895,81271,81272,81274,81286,81288,81290,81292,81294],{},[898,81273,1983],{},[2287,81275,81276,81278,81280],{},[898,81277,1680],{},[898,81279,13853],{},[895,81281,81282,81284],{},[1701,81283,4783],{"mathvariant":2334},[1701,81285,4783],{"mathvariant":2334},[1701,81287,1792],{},[1701,81289,2317],{},[1850,81291,23317],{},[1701,81293,7530],{},[1850,81295,1852],{},[902,81297,81298],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,81301,81303],{"className":81302},[886],[888,81304,81305],{"xmlns":890},[892,81306,81307,81315],{},[895,81308,81309,81311,81313],{},[898,81310,13853],{},[1701,81312,1792],{},[1850,81314,40275],{},[902,81316,81317],{"encoding":904},"L = 15"," je maximum, ",[883,81320,81322],{"className":81321},[886],[888,81323,81324],{"xmlns":890},[892,81325,81326,81372],{},[895,81327,81328,81330,81336,81338,81340,81342,81344,81346,81348,81350,81352,81354,81356,81359,81361,81364,81366,81368,81370],{},[898,81329,1983],{},[1845,81331,81332,81334],{},[898,81333,1680],{},[898,81335,13853],{},[1701,81337,1799],{"stretchy":1798},[1850,81339,40275],{},[1701,81341,1805],{"stretchy":1798},[1701,81343,1792],{},[1850,81345,6352],{},[1701,81347,3408],{},[1850,81349,40275],{},[1701,81351,2317],{},[1850,81353,6930],{},[1701,81355,3408],{},[1850,81357,81358],{},"225",[1701,81360,1792],{},[1850,81362,81363],{},"90",[1701,81365,2317],{},[1850,81367,80667],{},[1701,81369,1792],{},[1850,81371,80667],{},[902,81373,81374],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,81376,81377,45901,81433,81479],{},[883,81378,81380],{"className":81379},[886],[888,81381,81382],{"xmlns":890},[892,81383,81384,81430],{},[895,81385,81386,81388,81394,81396,81398,81400,81402,81404,81406,81408,81410,81412,81414,81416,81418,81421,81423,81426,81428],{},[898,81387,6909],{},[1845,81389,81390,81392],{},[898,81391,1680],{},[898,81393,13853],{},[1701,81395,1799],{"stretchy":1798},[1850,81397,40275],{},[1701,81399,1805],{"stretchy":1798},[1701,81401,1792],{},[1850,81403,7592],{},[1701,81405,3408],{},[1850,81407,40275],{},[1701,81409,2317],{},[1850,81411,3868],{},[1701,81413,3408],{},[1850,81415,81358],{},[1701,81417,1792],{},[1850,81419,81420],{},"180",[1701,81422,2317],{},[1850,81424,81425],{},"135",[1701,81427,1792],{},[1850,81429,80667],{},[902,81431,81432],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,81434,81436],{"className":81435},[886],[888,81437,81438],{"xmlns":890},[892,81439,81440,81476],{},[895,81441,81442,81444,81450,81452,81454,81456,81458,81460,81466,81468,81470,81472,81474],{},[898,81443,6909],{},[1845,81445,81446,81448],{},[898,81447,1680],{},[898,81449,13853],{},[1701,81451,1799],{"stretchy":1798},[1850,81453,40275],{},[1701,81455,1805],{"stretchy":1798},[1701,81457,1792],{},[898,81459,1983],{},[1845,81461,81462,81464],{},[898,81463,1680],{},[898,81465,13853],{},[1701,81467,1799],{"stretchy":1798},[1850,81469,40275],{},[1701,81471,1805],{"stretchy":1798},[1701,81473,1792],{},[1850,81475,80667],{},[902,81477,81478],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,81481,81482,81485,81486,21622,81515,1715],{},[38,81483,81484],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,81487,81489],{"className":81488},[886],[888,81490,81491],{"xmlns":890},[892,81492,81493,81513],{},[895,81494,81495,81497,81503,81505,81507],{},[898,81496,6909],{},[1845,81498,81499,81501],{},[898,81500,1680],{},[898,81502,13853],{},[1701,81504,1792],{},[898,81506,1983],{},[1845,81508,81509,81511],{},[898,81510,1680],{},[898,81512,13853],{},[902,81514,78409],{"encoding":904},[883,81516,81518],{"className":81517},[886],[888,81519,81520],{"xmlns":890},[892,81521,81522,81562],{},[895,81523,81524,81526,81528,81530,81532,81538,81540,81542,81544,81546,81548,81554,81556,81558,81560],{},[1850,81525,7592],{},[898,81527,13853],{},[1701,81529,2317],{},[1850,81531,3868],{},[3243,81533,81534,81536],{},[898,81535,13853],{},[1850,81537,3938],{},[1701,81539,1792],{},[1850,81541,6352],{},[898,81543,13853],{},[1701,81545,2317],{},[1850,81547,6930],{},[3243,81549,81550,81552],{},[898,81551,13853],{},[1850,81553,3938],{},[1701,81555,8061],{},[898,81557,13853],{},[1701,81559,1792],{},[1850,81561,40275],{},[902,81563,81564],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,81566,81567],{},[614,81568,81569,81570,81589,81590,1738,81608,81627,81628,81646,81647,81664,81665,81684,81685,81704],{},"Obrázek 5.3 — křivky ",[883,81571,81573],{"className":81572},[886],[888,81574,81575],{"xmlns":890},[892,81576,81577,81587],{},[895,81578,81579,81581],{},[898,81580,6909],{},[1845,81582,81583,81585],{},[898,81584,1680],{},[898,81586,13853],{},[902,81588,14101],{"encoding":904}," (max 60 při ",[883,81591,81593],{"className":81592},[886],[888,81594,81595],{"xmlns":890},[892,81596,81597,81605],{},[895,81598,81599,81601,81603],{},[898,81600,13853],{},[1701,81602,1792],{},[1850,81604,3703],{},[902,81606,81607],{"encoding":904},"L=10",[883,81609,81611],{"className":81610},[886],[888,81612,81613],{"xmlns":890},[892,81614,81615,81625],{},[895,81616,81617,81619],{},[898,81618,1983],{},[1845,81620,81621,81623],{},[898,81622,1680],{},[898,81624,13853],{},[902,81626,78379],{"encoding":904}," (max 45 při ",[883,81629,81631],{"className":81630},[886],[888,81632,81633],{"xmlns":890},[892,81634,81635,81643],{},[895,81636,81637,81639,81641],{},[898,81638,13853],{},[1701,81640,1792],{},[1850,81642,40275],{},[902,81644,81645],{"encoding":904},"L=15","), průsečík v ",[883,81648,81650],{"className":81649},[886],[888,81651,81652],{"xmlns":890},[892,81653,81654,81662],{},[895,81655,81656,81658,81660],{},[898,81657,13853],{},[1701,81659,1792],{},[1850,81661,40275],{},[902,81663,81317],{"encoding":904},". Nalevo od 15 leží ",[883,81666,81668],{"className":81667},[886],[888,81669,81670],{"xmlns":890},[892,81671,81672,81682],{},[895,81673,81674,81676],{},[898,81675,6909],{},[1845,81677,81678,81680],{},[898,81679,1680],{},[898,81681,13853],{},[902,81683,14101],{"encoding":904}," nad ",[883,81686,81688],{"className":81687},[886],[888,81689,81690],{"xmlns":890},[892,81691,81692,81702],{},[895,81693,81694,81696],{},[898,81695,1983],{},[1845,81697,81698,81700],{},[898,81699,1680],{},[898,81701,13853],{},[902,81703,78379],{"encoding":904},", napravo pod ní.",[115,81706,81708],{"id":81707},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,81710,81711,81712,3856,81725,4088,81728,10253,81741,4088,81744,2246],{},"V dvoufaktorovém modelu závisí produkce ",[883,81713,81715],{"className":81714},[886],[888,81716,81717],{"xmlns":890},[892,81718,81719,81723],{},[895,81720,81721],{},[898,81722,1802],{},[902,81724,1802],{"encoding":904},[38,81726,81727],{},"práci",[883,81729,81731],{"className":81730},[886],[888,81732,81733],{"xmlns":890},[892,81734,81735,81739],{},[895,81736,81737],{},[898,81738,13853],{},[902,81740,13853],{"encoding":904},[38,81742,81743],{},"kapitálu",[883,81745,81747],{"className":81746},[886],[888,81748,81749],{"xmlns":890},[892,81750,81751,81755],{},[895,81752,81753],{},[898,81754,13858],{},[902,81756,13858],{"encoding":904},[883,81758,81760],{"className":81759},[886],[888,81761,81762],{"xmlns":890,"display":2252},[892,81763,81764,81799],{},[2256,81765,81766],{"width":2258},[2260,81767,81768,81770,81792,81794],{},[2263,81769],{"width":2265},[2263,81771,81772],{},[895,81773,81774,81776,81778,81780,81782,81784,81786,81788,81790],{},[898,81775,1802],{},[1701,81777,1792],{},[898,81779,1802],{},[1701,81781,1799],{"stretchy":1798},[898,81783,13853],{},[1701,81785,2012],{"separator":2011},[898,81787,13858],{},[1701,81789,1805],{"stretchy":1798},[898,81791,1715],{"mathvariant":2334},[2263,81793],{"width":2265},[2263,81795,81796],{},[1939,81797,81798],{},"(5.6)",[902,81800,81801],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,81803,81804,81805,81807],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,81806,78746],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,81809,81811],{"id":81810},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,81813,81814],{},"Široce používané produkční funkce mají tvar",[883,81816,81818],{"className":81817},[886],[888,81819,81820],{"xmlns":890,"display":2252},[892,81821,81822,81863],{},[2256,81823,81824],{"width":2258},[2260,81825,81826,81828,81856,81858],{},[2263,81827],{"width":2265},[2263,81829,81830],{},[895,81831,81832,81834,81836,81838,81840,81846,81848,81854],{},[898,81833,1802],{},[1701,81835,1792],{},[898,81837,1983],{},[1939,81839,1941],{},[3243,81841,81842,81844],{},[898,81843,13853],{},[898,81845,207],{},[1939,81847,1941],{},[3243,81849,81850,81852],{},[898,81851,13858],{},[898,81853,3598],{},[1701,81855,2012],{"separator":2011},[2263,81857],{"width":2265},[2263,81859,81860],{},[1939,81861,81862],{},"(5.7)",[902,81864,81865],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,81867,8380,81868,81890,81891,81893,81894,1715],{},[883,81869,81871],{"className":81870},[886],[888,81872,81873],{"xmlns":890},[892,81874,81875,81887],{},[895,81876,81877,81879,81881,81883,81885],{},[898,81878,1983],{},[1701,81880,2012],{"separator":2011},[898,81882,207],{},[1701,81884,2012],{"separator":2011},[898,81886,3598],{},[902,81888,81889],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,81892,78445],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,81895,81897],{"className":81896},[886],[888,81898,81899],{"xmlns":890},[892,81900,81901,81913],{},[895,81902,81903,81905,81907,81909,81911],{},[898,81904,207],{},[1701,81906,2012],{"separator":2011},[898,81908,3598],{},[1701,81910,7530],{},[1850,81912,4062],{},[902,81914,81915],{"encoding":904},"a, b \u003C 1",[724,81917,81918],{},[2139,81919],{"alt":81920,"className":81921,"src":81922},"imek-vynosy-z-rozsahu-3typy",[210,2143],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,81924,81925,81926,81929,81930,3856,81943,81959,81960,3856,81973,2246],{},"Reflektují ekonomickou zákonitost, že ",[38,81927,81928],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,81931,81933],{"className":81932},[886],[888,81934,81935],{"xmlns":890},[892,81936,81937,81941],{},[895,81938,81939],{},[898,81940,13853],{},[902,81942,13853],{"encoding":904},[883,81944,81946],{"className":81945},[886],[888,81947,81948],{"xmlns":890},[892,81949,81950,81956],{},[895,81951,81952,81954],{},[898,81953,16096],{},[898,81955,13853],{},[902,81957,81958],{"encoding":904},"rL"," a kapitál z ",[883,81961,81963],{"className":81962},[886],[888,81964,81965],{"xmlns":890},[892,81966,81967,81971],{},[895,81968,81969],{},[898,81970,13858],{},[902,81972,13858],{"encoding":904},[883,81974,81976],{"className":81975},[886],[888,81977,81978],{"xmlns":890},[892,81979,81980,81986],{},[895,81981,81982,81984],{},[898,81983,16096],{},[898,81985,13858],{},[902,81987,81988],{"encoding":904},"rK",[883,81990,81992],{"className":81991},[886],[888,81993,81994],{"xmlns":890,"display":2252},[892,81995,81996,82119],{},[2256,81997,81998],{"width":2258},[2260,81999,82000,82002,82112,82114],{},[2263,82001],{"width":2265},[2263,82003,82004],{},[895,82005,82006,82008,82010,82012,82014,82016,82018,82020,82022,82024,82026,82028,82030,82032,82038,82040,82042,82044,82050,82052,82054,82056,82068,82070,82076,82082,82084,82096,82098,82100,82102,82104,82106,82108,82110],{},[898,82007,1802],{},[1701,82009,1799],{"stretchy":1798},[898,82011,16096],{},[898,82013,13853],{},[1701,82015,2012],{"separator":2011},[898,82017,16096],{},[898,82019,13858],{},[1701,82021,1805],{"stretchy":1798},[1701,82023,1792],{},[898,82025,1983],{},[1701,82027,1799],{"stretchy":1798},[898,82029,16096],{},[898,82031,13853],{},[3243,82033,82034,82036],{},[1701,82035,1805],{"stretchy":1798},[898,82037,207],{},[1701,82039,1799],{"stretchy":1798},[898,82041,16096],{},[898,82043,13858],{},[3243,82045,82046,82048],{},[1701,82047,1805],{"stretchy":1798},[898,82049,3598],{},[1701,82051,1792],{},[898,82053,1983],{},[1939,82055,1941],{},[3243,82057,82058,82060],{},[898,82059,16096],{},[895,82061,82062,82064,82066],{},[898,82063,207],{},[1701,82065,1703],{},[898,82067,3598],{},[1939,82069,1941],{},[3243,82071,82072,82074],{},[898,82073,13853],{},[898,82075,207],{},[3243,82077,82078,82080],{},[898,82079,13858],{},[898,82081,3598],{},[1701,82083,1792],{},[3243,82085,82086,82088],{},[898,82087,16096],{},[895,82089,82090,82092,82094],{},[898,82091,207],{},[1701,82093,1703],{},[898,82095,3598],{},[1939,82097,1941],{},[898,82099,1802],{},[1701,82101,1799],{"stretchy":1798},[898,82103,13853],{},[1701,82105,2012],{"separator":2011},[898,82107,13858],{},[1701,82109,1805],{"stretchy":1798},[898,82111,1715],{"mathvariant":2334},[2263,82113],{"width":2265},[2263,82115,82116],{},[1939,82117,82118],{},"(5.8)",[902,82120,82121],{"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}",[724,82123,82124,82125],{},"Volně: ",[38,82126,82127,82128,82141,82142,82166],{},"změní-li se vstupy ",[883,82129,82131],{"className":82130},[886],[888,82132,82133],{"xmlns":890},[892,82134,82135,82139],{},[895,82136,82137],{},[898,82138,16096],{},[902,82140,16096],{"encoding":904},"-krát, změní se výstup ",[883,82143,82145],{"className":82144},[886],[888,82146,82147],{"xmlns":890},[892,82148,82149,82163],{},[895,82150,82151],{},[3243,82152,82153,82155],{},[898,82154,16096],{},[895,82156,82157,82159,82161],{},[898,82158,207],{},[1701,82160,1703],{},[898,82162,3598],{},[902,82164,82165],{"encoding":904},"r^{a+b}","-krát.",[198,82168,82170],{"id":82169},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,82172,82173,82174,82191],{},"Součet exponentů ",[883,82175,82177],{"className":82176},[886],[888,82178,82179],{"xmlns":890},[892,82180,82181,82189],{},[895,82182,82183,82185,82187],{},[898,82184,207],{},[1701,82186,1703],{},[898,82188,3598],{},[902,82190,78570],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,82193,82194,82223],{},[19,82195,82196],{},[22,82197,82198,82201,82204,82221],{},[25,82199,82200],{},"Typ",[25,82202,82203],{},"Podmínka",[25,82205,82206,82207,82220],{},"Chování produkce při ",[883,82208,82210],{"className":82209},[886],[888,82211,82212],{"xmlns":890},[892,82213,82214,82218],{},[895,82215,82216],{},[898,82217,16096],{},[902,82219,16096],{"encoding":904},"-násobném zvýšení vstupů",[25,82222,7157],{},[30,82224,82225,82336,82451],{},[22,82226,82227,82235,82259,82292],{},[35,82228,79283,82229,1646,82232,1805],{},[38,82230,82231],{},"Konstantní",[614,82233,82234],{},"constant returns",[35,82236,82237],{},[883,82238,82240],{"className":82239},[886],[888,82241,82242],{"xmlns":890},[892,82243,82244,82256],{},[895,82245,82246,82248,82250,82252,82254],{},[898,82247,207],{},[1701,82249,1703],{},[898,82251,3598],{},[1701,82253,1792],{},[1850,82255,4062],{},[902,82257,82258],{"encoding":904},"a+b = 1",[35,82260,82261,82274,82275,4088,82278,82291],{},[883,82262,82264],{"className":82263},[886],[888,82265,82266],{"xmlns":890},[892,82267,82268,82272],{},[895,82269,82270],{},[898,82271,1802],{},[902,82273,1802],{"encoding":904}," vzroste ",[38,82276,82277],{},"přesně",[883,82279,82281],{"className":82280},[886],[888,82282,82283],{"xmlns":890},[892,82284,82285,82289],{},[895,82286,82287],{},[898,82288,16096],{},[902,82290,16096],{"encoding":904},"-krát",[35,82293,82294],{},[883,82295,82297],{"className":82296},[886],[888,82298,82299],{"xmlns":890},[892,82300,82301,82333],{},[895,82302,82303,82305,82307,82309,82321],{},[898,82304,1802],{},[1701,82306,1792],{},[1850,82308,3938],{},[3243,82310,82311,82313],{},[898,82312,13853],{},[895,82314,82315,82317,82319],{},[1850,82316,4062],{},[898,82318,8741],{"mathvariant":2334},[1850,82320,6460],{},[3243,82322,82323,82325],{},[898,82324,13858],{},[895,82326,82327,82329,82331],{},[1850,82328,3646],{},[898,82330,8741],{"mathvariant":2334},[1850,82332,6460],{},[902,82334,82335],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,82337,82338,82347,82371,82401],{},[35,82339,82340,82341,1646,82344,1805],{},"2° ",[38,82342,82343],{},"Rostoucí",[614,82345,82346],{},"increasing returns",[35,82348,82349],{},[883,82350,82352],{"className":82351},[886],[888,82353,82354],{"xmlns":890},[892,82355,82356,82368],{},[895,82357,82358,82360,82362,82364,82366],{},[898,82359,207],{},[1701,82361,1703],{},[898,82363,3598],{},[1701,82365,7491],{},[1850,82367,4062],{},[902,82369,82370],{"encoding":904},"a+b > 1",[35,82372,82373,82274,82386,2077,82388,82291],{},[883,82374,82376],{"className":82375},[886],[888,82377,82378],{"xmlns":890},[892,82379,82380,82384],{},[895,82381,82382],{},[898,82383,1802],{},[902,82385,1802],{"encoding":904},[38,82387,2076],{},[883,82389,82391],{"className":82390},[886],[888,82392,82393],{"xmlns":890},[892,82394,82395,82399],{},[895,82396,82397],{},[898,82398,16096],{},[902,82400,16096],{"encoding":904},[35,82402,82403,1646,82429,1805],{},[883,82404,82406],{"className":82405},[886],[888,82407,82408],{"xmlns":890},[892,82409,82410,82426],{},[895,82411,82412,82414,82416,82418,82420],{},[898,82413,1802],{},[1701,82415,1792],{},[1850,82417,28239],{},[898,82419,13853],{},[3243,82421,82422,82424],{},[898,82423,13858],{},[1850,82425,3938],{},[902,82427,82428],{"encoding":904},"Q = 7LK^2",[883,82430,82432],{"className":82431},[886],[888,82433,82434],{"xmlns":890},[892,82435,82436,82448],{},[895,82437,82438,82440,82442,82444,82446],{},[898,82439,207],{},[1701,82441,1703],{},[898,82443,3598],{},[1701,82445,1792],{},[1850,82447,3646],{},[902,82449,82450],{"encoding":904},"a+b = 3",[22,82452,82453,82462,82486,82517],{},[35,82454,82455,82456,1646,82459,1805],{},"3° ",[38,82457,82458],{},"Klesající",[614,82460,82461],{},"decreasing returns",[35,82463,82464],{},[883,82465,82467],{"className":82466},[886],[888,82468,82469],{"xmlns":890},[892,82470,82471,82483],{},[895,82472,82473,82475,82477,82479,82481],{},[898,82474,207],{},[1701,82476,1703],{},[898,82478,3598],{},[1701,82480,7530],{},[1850,82482,4062],{},[902,82484,82485],{"encoding":904},"a+b \u003C 1",[35,82487,82488,82274,82501,2077,82504,82291],{},[883,82489,82491],{"className":82490},[886],[888,82492,82493],{"xmlns":890},[892,82494,82495,82499],{},[895,82496,82497],{},[898,82498,1802],{},[902,82500,1802],{"encoding":904},[38,82502,82503],{},"méně",[883,82505,82507],{"className":82506},[886],[888,82508,82509],{"xmlns":890},[892,82510,82511,82515],{},[895,82512,82513],{},[898,82514,16096],{},[902,82516,16096],{"encoding":904},[35,82518,82519,1646,82549,1805],{},[883,82520,82522],{"className":82521},[886],[888,82523,82524],{"xmlns":890},[892,82525,82526,82546],{},[895,82527,82528,82530,82532,82534,82540],{},[898,82529,1802],{},[1701,82531,1792],{},[1850,82533,3703],{},[3243,82535,82536,82538],{},[898,82537,13853],{},[1850,82539,71957],{},[3243,82541,82542,82544],{},[898,82543,13858],{},[1850,82545,3684],{},[902,82547,82548],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,82550,82552],{"className":82551},[886],[888,82553,82554],{"xmlns":890},[892,82555,82556,82568],{},[895,82557,82558,82560,82562,82564,82566],{},[898,82559,207],{},[1701,82561,1703],{},[898,82563,3598],{},[1701,82565,1792],{},[1850,82567,18642],{},[902,82569,82570],{"encoding":904},"a+b = 0{,}8",[1635,82572,82573],{},[724,82574,82575,82577,82578,82595,82596,82599,82600,4088,82603,82639,82640,82662,82663,1715],{},[883,82576,4695],{}," Pozor\nSoučet ",[883,82579,82581],{"className":82580},[886],[888,82582,82583],{"xmlns":890},[892,82584,82585,82593],{},[895,82586,82587,82589,82591],{},[898,82588,207],{},[1701,82590,1703],{},[898,82592,3598],{},[902,82594,78570],{"encoding":904}," neudává velikost produkce, ale ",[38,82597,82598],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,82601,82602],{},"ryzí Cobb-Douglas",[883,82604,82606],{"className":82605},[886],[888,82607,82608],{"xmlns":890},[892,82609,82610,82636],{},[895,82611,82612,82614,82616,82618,82624],{},[898,82613,1802],{},[1701,82615,1792],{},[898,82617,1983],{},[3243,82619,82620,82622],{},[898,82621,13853],{},[898,82623,207],{},[3243,82625,82626,82628],{},[898,82627,13858],{},[895,82629,82630,82632,82634],{},[1850,82631,4062],{},[1701,82633,2317],{},[898,82635,207],{},[902,82637,82638],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,82641,82643],{"className":82642},[886],[888,82644,82645],{"xmlns":890},[892,82646,82647,82659],{},[895,82648,82649,82651,82653,82655,82657],{},[898,82650,3598],{},[1701,82652,1792],{},[1850,82654,4062],{},[1701,82656,2317],{},[898,82658,207],{},[902,82660,82661],{"encoding":904},"b = 1-a",", tedy vždy ",[38,82664,82665],{},"konstantní výnosy z rozsahu",[198,82667,82669,82670],{"id":82668},"parametr-efektivity-aa","Parametr efektivity ",[883,82671,82673],{"className":82672},[886],[888,82674,82675],{"xmlns":890},[892,82676,82677,82681],{},[895,82678,82679],{},[898,82680,1983],{},[902,82682,1983],{"encoding":904},[724,82684,82685,82686,82699,82700,82713,82714,82732,82733,82736],{},"Konstanta ",[883,82687,82689],{"className":82688},[886],[888,82690,82691],{"xmlns":890},[892,82692,82693,82697],{},[895,82694,82695],{},[898,82696,1983],{},[902,82698,1983],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,82701,82703],{"className":82702},[886],[888,82704,82705],{"xmlns":890},[892,82706,82707,82711],{},[895,82708,82709],{},[898,82710,1802],{},[902,82712,1802],{"encoding":904}," při pevně zadaných ",[883,82715,82717],{"className":82716},[886],[888,82718,82719],{"xmlns":890},[892,82720,82721,82729],{},[895,82722,82723,82725,82727],{},[898,82724,13853],{},[1701,82726,2012],{"separator":2011},[898,82728,13858],{},[902,82730,82731],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,82734,82735],{},"parametr efektivity"," — indikátor stavu technologie.",[198,82738,82740],{"id":82739},"příklad-53","Příklad 5.3",[724,82742,82743,82744,82639,82786,82788,82789,1715],{},"Produkční funkce ",[883,82745,82747],{"className":82746},[886],[888,82748,82749],{"xmlns":890},[892,82750,82751,82783],{},[895,82752,82753,82755,82757,82759,82771],{},[898,82754,1802],{},[1701,82756,1792],{},[1850,82758,3938],{},[3243,82760,82761,82763],{},[898,82762,13853],{},[895,82764,82765,82767,82769],{},[1850,82766,4062],{},[898,82768,8741],{"mathvariant":2334},[1850,82770,6460],{},[3243,82772,82773,82775],{},[898,82774,13858],{},[895,82776,82777,82779,82781],{},[1850,82778,3646],{},[898,82780,8741],{"mathvariant":2334},[1850,82782,6460],{},[902,82784,82785],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,82787,28651],{}," výnosy z rozsahu, neboť ",[883,82790,82792],{"className":82791},[886],[888,82793,82794],{"xmlns":890},[892,82795,82796,82820],{},[895,82797,82798,82806,82808,82816,82818],{},[2363,82799,82800],{"scriptlevel":1852,"displaystyle":1798},[3726,82801,82802,82804],{},[1850,82803,4062],{},[1850,82805,6460],{},[1701,82807,1703],{},[2363,82809,82810],{"scriptlevel":1852,"displaystyle":1798},[3726,82811,82812,82814],{},[1850,82813,3646],{},[1850,82815,6460],{},[1701,82817,1792],{},[1850,82819,4062],{},[902,82821,82822],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,82824,82825,82826,10253,82839,82852,82853,4088,82866,82906],{},"Změní-li se ",[883,82827,82829],{"className":82828},[886],[888,82830,82831],{"xmlns":890},[892,82832,82833,82837],{},[895,82834,82835],{},[898,82836,13853],{},[902,82838,13853],{"encoding":904},[883,82840,82842],{"className":82841},[886],[888,82843,82844],{"xmlns":890},[892,82845,82846,82850],{},[895,82847,82848],{},[898,82849,13858],{},[902,82851,13858],{"encoding":904}," čtyřnásobně, změní se ",[883,82854,82856],{"className":82855},[886],[888,82857,82858],{"xmlns":890},[892,82859,82860,82864],{},[895,82861,82862],{},[898,82863,1802],{},[902,82865,1802],{"encoding":904},[883,82867,82869],{"className":82868},[886],[888,82870,82871],{"xmlns":890},[892,82872,82873,82903],{},[895,82874,82875,82895,82897],{},[3243,82876,82877,82879],{},[1850,82878,6460],{},[895,82880,82881,82883,82885,82887,82889,82891,82893],{},[1850,82882,4062],{},[898,82884,8741],{"mathvariant":2334},[1850,82886,6460],{},[1701,82888,1703],{},[1850,82890,3646],{},[898,82892,8741],{"mathvariant":2334},[1850,82894,6460],{},[1701,82896,1792],{},[3243,82898,82899,82901],{},[1850,82900,6460],{},[1850,82902,4062],{},[902,82904,82905],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,82908,82910],{"className":82909},[886],[888,82911,82912],{"xmlns":890,"display":2252},[892,82913,82914,83074],{},[895,82915,82916,82918,82920,82922,82924,82926,82928,82930,82932,82934,82936,82938,82940,82942,82954,82956,82958,82960,82972,82974,82976,82978,82998,83010,83022,83024,83026,83028,83030,83042,83054,83056,83058,83060,83062,83064,83066,83068,83070,83072],{},[898,82917,1802],{},[1701,82919,1799],{"stretchy":1798},[1850,82921,6460],{},[898,82923,13853],{},[1701,82925,2012],{"separator":2011},[1850,82927,6460],{},[898,82929,13858],{},[1701,82931,1805],{"stretchy":1798},[1701,82933,1792],{},[1850,82935,3938],{},[1701,82937,1799],{"stretchy":1798},[1850,82939,6460],{},[898,82941,13853],{},[3243,82943,82944,82946],{},[1701,82945,1805],{"stretchy":1798},[895,82947,82948,82950,82952],{},[1850,82949,4062],{},[898,82951,8741],{"mathvariant":2334},[1850,82953,6460],{},[1701,82955,1799],{"stretchy":1798},[1850,82957,6460],{},[898,82959,13858],{},[3243,82961,82962,82964],{},[1701,82963,1805],{"stretchy":1798},[895,82965,82966,82968,82970],{},[1850,82967,3646],{},[898,82969,8741],{"mathvariant":2334},[1850,82971,6460],{},[1701,82973,1792],{},[1850,82975,3938],{},[1701,82977,3408],{},[3243,82979,82980,82982],{},[1850,82981,6460],{},[895,82983,82984,82986,82988,82990,82992,82994,82996],{},[1850,82985,4062],{},[898,82987,8741],{"mathvariant":2334},[1850,82989,6460],{},[1701,82991,1703],{},[1850,82993,3646],{},[898,82995,8741],{"mathvariant":2334},[1850,82997,6460],{},[3243,82999,83000,83002],{},[898,83001,13853],{},[895,83003,83004,83006,83008],{},[1850,83005,4062],{},[898,83007,8741],{"mathvariant":2334},[1850,83009,6460],{},[3243,83011,83012,83014],{},[898,83013,13858],{},[895,83015,83016,83018,83020],{},[1850,83017,3646],{},[898,83019,8741],{"mathvariant":2334},[1850,83021,6460],{},[1701,83023,1792],{},[1850,83025,6460],{},[1701,83027,3408],{},[1850,83029,3938],{},[3243,83031,83032,83034],{},[898,83033,13853],{},[895,83035,83036,83038,83040],{},[1850,83037,4062],{},[898,83039,8741],{"mathvariant":2334},[1850,83041,6460],{},[3243,83043,83044,83046],{},[898,83045,13858],{},[895,83047,83048,83050,83052],{},[1850,83049,3646],{},[898,83051,8741],{"mathvariant":2334},[1850,83053,6460],{},[1701,83055,1792],{},[1850,83057,6460],{},[1939,83059,1941],{},[898,83061,1802],{},[1701,83063,1799],{"stretchy":1798},[898,83065,13853],{},[1701,83067,2012],{"separator":2011},[898,83069,13858],{},[1701,83071,1805],{"stretchy":1798},[898,83073,1715],{"mathvariant":2334},[902,83075,83076],{"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).",[198,83078,83079],{"id":41207},"Homogenita",[724,83081,83082,83083,12164,83106,83122],{},"Funkce ",[883,83084,83086],{"className":83085},[886],[888,83087,83088],{"xmlns":890},[892,83089,83090,83104],{},[895,83091,83092,83094,83096,83098,83100,83102],{},[898,83093,1802],{},[1701,83095,1799],{"stretchy":1798},[898,83097,13853],{},[1701,83099,2012],{"separator":2011},[898,83101,13858],{},[1701,83103,1805],{"stretchy":1798},[902,83105,14054],{"encoding":904},[38,83107,83108,83109],{},"homogenní stupně ",[883,83110,83112],{"className":83111},[886],[888,83113,83114],{"xmlns":890},[892,83115,83116,83120],{},[895,83117,83118],{},[898,83119,40890],{},[902,83121,40890],{"encoding":904},", jestliže",[883,83124,83126],{"className":83125},[886],[888,83127,83128],{"xmlns":890,"display":2252},[892,83129,83130,83187],{},[2256,83131,83132],{"width":2258},[2260,83133,83134,83136,83180,83182],{},[2263,83135],{"width":2265},[2263,83137,83138],{},[895,83139,83140,83142,83144,83146,83148,83150,83152,83154,83156,83158,83164,83166,83168,83170,83172,83174,83176,83178],{},[898,83141,1802],{},[1701,83143,1799],{"stretchy":1798},[898,83145,16096],{},[898,83147,13853],{},[1701,83149,2012],{"separator":2011},[898,83151,16096],{},[898,83153,13858],{},[1701,83155,1805],{"stretchy":1798},[1701,83157,1792],{},[3243,83159,83160,83162],{},[898,83161,16096],{},[898,83163,40890],{},[1939,83165,1941],{},[898,83167,1802],{},[1701,83169,1799],{"stretchy":1798},[898,83171,13853],{},[1701,83173,2012],{"separator":2011},[898,83175,13858],{},[1701,83177,1805],{"stretchy":1798},[1701,83179,2012],{"separator":2011},[2263,83181],{"width":2265},[2263,83183,83184],{},[1939,83185,83186],{},"(5.10)",[902,83188,83189],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,83191,8380,83192,83210,83211,83229,83230,47656,83243,83246,83247,1715],{},[883,83193,83195],{"className":83194},[886],[888,83196,83197],{"xmlns":890},[892,83198,83199,83207],{},[895,83200,83201,83203,83205],{},[898,83202,40890],{},[1701,83204,8554],{},[1850,83206,1852],{},[902,83208,83209],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,83212,83214],{"className":83213},[886],[888,83215,83216],{"xmlns":890},[892,83217,83218,83226],{},[895,83219,83220,83222,83224],{},[898,83221,16096],{},[1701,83223,7491],{},[1850,83225,1852],{},[902,83227,83228],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,83231,83233],{"className":83232},[886],[888,83234,83235],{"xmlns":890},[892,83236,83237,83241],{},[895,83238,83239],{},[1850,83240,4062],{},[902,83242,4062],{"encoding":904},[38,83244,83245],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,83248,83250],{"className":83249},[886],[888,83251,83252],{"xmlns":890},[892,83253,83254,83262],{},[895,83255,83256,83258,83260],{},[898,83257,207],{},[1701,83259,1703],{},[898,83261,3598],{},[902,83263,78570],{"encoding":904},[115,83265,83267],{"id":83266},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,83269,83270],{},[38,83271,83272],{},"Ryzí Cobb-Douglasovy funkce:",[883,83274,83276],{"className":83275},[886],[888,83277,83278],{"xmlns":890,"display":2252},[892,83279,83280,83339],{},[2256,83281,83282],{"width":2258},[2260,83283,83284,83286,83332,83334],{},[2263,83285],{"width":2265},[2263,83287,83288],{},[895,83289,83290,83292,83294,83296,83298,83304,83306,83318,83320,83322,83324,83326,83328,83330],{},[898,83291,1802],{},[1701,83293,1792],{},[898,83295,1983],{},[1939,83297,1941],{},[3243,83299,83300,83302],{},[898,83301,13853],{},[898,83303,207],{},[1939,83305,1941],{},[3243,83307,83308,83310],{},[898,83309,13858],{},[895,83311,83312,83314,83316],{},[1850,83313,4062],{},[1701,83315,2317],{},[898,83317,207],{},[1701,83319,2012],{"separator":2011},[9942,83321],{"width":19336},[1850,83323,1852],{},[1701,83325,7530],{},[898,83327,207],{},[1701,83329,7530],{},[1850,83331,17314],{},[2263,83333],{"width":2265},[2263,83335,83336],{},[1939,83337,83338],{},"(5.9)",[902,83340,83341],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,83343,83344,83345,83347,83348,1715],{},"Mají vždy ",[38,83346,82665],{}," a jsou ",[38,83349,83245],{},[724,83351,83352,1646,83355,83358],{},[38,83353,83354],{},"CES produkční funkce",[614,83356,83357],{},"Constant Elasticity of Substitution",", 1961):",[883,83360,83362],{"className":83361},[886],[888,83363,83364],{"xmlns":890,"display":2252},[892,83365,83366,83434],{},[895,83367,83368,83370,83372,83374,83432],{},[898,83369,1802],{},[1701,83371,1792],{},[898,83373,1983],{},[3243,83375,83376,83420],{},[895,83377,83378,83380,83382,83384,83386,83388,83390,83392,83402,83404,83406,83408,83418],{},[1701,83379,2036],{"fence":2011},[1701,83381,1799],{"stretchy":1798},[1850,83383,4062],{},[1701,83385,2317],{},[898,83387,207],{},[1701,83389,1805],{"stretchy":1798},[1939,83391,1941],{},[3243,83393,83394,83396],{},[898,83395,13853],{},[895,83397,83398,83400],{},[1701,83399,2317],{},[898,83401,3598],{},[1701,83403,1703],{},[898,83405,207],{},[1939,83407,1941],{},[3243,83409,83410,83412],{},[898,83411,13858],{},[895,83413,83414,83416],{},[1701,83415,2317],{},[898,83417,3598],{},[1701,83419,2053],{"fence":2011},[895,83421,83422,83424],{},[1701,83423,2317],{},[2363,83425,83426],{"scriptlevel":1852,"displaystyle":1798},[3726,83427,83428,83430],{},[1850,83429,4062],{},[898,83431,3598],{},[1701,83433,2012],{"separator":2011},[902,83435,83436],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,83438,8380,83439,1343,83457,1343,83478,83502],{},[883,83440,83442],{"className":83441},[886],[888,83443,83444],{"xmlns":890},[892,83445,83446,83454],{},[895,83447,83448,83450,83452],{},[898,83449,1983],{},[1701,83451,7491],{},[1850,83453,1852],{},[902,83455,83456],{"encoding":904},"A > 0",[883,83458,83460],{"className":83459},[886],[888,83461,83462],{"xmlns":890},[892,83463,83464,83476],{},[895,83465,83466,83468,83470,83472,83474],{},[1850,83467,1852],{},[1701,83469,7530],{},[898,83471,207],{},[1701,83473,7530],{},[1850,83475,4062],{},[902,83477,22882],{"encoding":904},[883,83479,83481],{"className":83480},[886],[888,83482,83483],{"xmlns":890},[892,83484,83485,83499],{},[895,83486,83487,83489,83491,83493,83495,83497],{},[1701,83488,2317],{},[1850,83490,4062],{},[1701,83492,7530],{},[898,83494,3598],{},[1701,83496,7454],{"mathvariant":2334},[1850,83498,1852],{},[902,83500,83501],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,83504,83505],{},[38,83506,83507],{},"Další typy:",[120,83509,83510,83552],{},[123,83511,83512,4088,83515,83551],{},[38,83513,83514],{},"Lineární:",[883,83516,83518],{"className":83517},[886],[888,83519,83520],{"xmlns":890},[892,83521,83522,83548],{},[895,83523,83524,83526,83528,83530,83532,83534,83536,83538,83540,83542,83544,83546],{},[898,83525,1802],{},[1701,83527,1799],{"stretchy":1798},[898,83529,13853],{},[1701,83531,2012],{"separator":2011},[898,83533,13858],{},[1701,83535,1805],{"stretchy":1798},[1701,83537,1792],{},[898,83539,207],{},[898,83541,13853],{},[1701,83543,1703],{},[898,83545,3598],{},[898,83547,13858],{},[902,83549,83550],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,83553,83554,4088,83557,83602],{},[38,83555,83556],{},"Leontiefova:",[883,83558,83560],{"className":83559},[886],[888,83561,83562],{"xmlns":890},[892,83563,83564,83599],{},[895,83565,83566,83568,83570,83572,83574,83576,83578,83580,83583,83585,83587,83589,83591,83593,83595,83597],{},[898,83567,1802],{},[1701,83569,1799],{"stretchy":1798},[898,83571,13853],{},[1701,83573,2012],{"separator":2011},[898,83575,13858],{},[1701,83577,1805],{"stretchy":1798},[1701,83579,1792],{},[898,83581,83582],{},"min",[1701,83584,59946],{},[1701,83586,1799],{"stretchy":1798},[898,83588,207],{},[898,83590,13853],{},[1701,83592,2012],{"separator":2011},[898,83594,3598],{},[898,83596,13858],{},[1701,83598,1805],{"stretchy":1798},[902,83600,83601],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,83604,83606,83607,1343,83626,83645],{"id":83605},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,83608,83610],{"className":83609},[886],[888,83611,83612],{"xmlns":890},[892,83613,83614,83624],{},[895,83615,83616,83618],{},[898,83617,6909],{},[1845,83619,83620,83622],{},[898,83621,1680],{},[898,83623,13853],{},[902,83625,14101],{"encoding":904},[883,83627,83629],{"className":83628},[886],[888,83630,83631],{"xmlns":890},[892,83632,83633,83643],{},[895,83634,83635,83637],{},[898,83636,6909],{},[1845,83638,83639,83641],{},[898,83640,1680],{},[898,83642,13858],{},[902,83644,14146],{"encoding":904}," a totální diferenciál",[724,83647,83648],{},[38,83649,83650],{},"Mezní produkt práce:",[883,83652,83654],{"className":83653},[886],[888,83655,83656],{"xmlns":890,"display":2252},[892,83657,83658,83696],{},[895,83659,83660,83662,83668,83670,83678,83680,83694],{},[898,83661,6909],{},[1845,83663,83664,83666],{},[898,83665,1680],{},[898,83667,13853],{},[1701,83669,1792],{},[2287,83671,83672,83674,83676],{},[898,83673,1802],{},[898,83675,13853],{},[1701,83677,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,83679,1792],{},[3726,83681,83682,83688],{},[895,83683,83684,83686],{},[898,83685,3893],{"mathvariant":2334},[898,83687,1802],{},[895,83689,83690,83692],{},[898,83691,3893],{"mathvariant":2334},[898,83693,13853],{},[898,83695,1715],{"mathvariant":2334},[902,83697,83698],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,83700,83701],{},[38,83702,83703],{},"Mezní produkt kapitálu:",[883,83705,83707],{"className":83706},[886],[888,83708,83709],{"xmlns":890,"display":2252},[892,83710,83711,83749],{},[895,83712,83713,83715,83721,83723,83731,83733,83747],{},[898,83714,6909],{},[1845,83716,83717,83719],{},[898,83718,1680],{},[898,83720,13858],{},[1701,83722,1792],{},[2287,83724,83725,83727,83729],{},[898,83726,1802],{},[898,83728,13858],{},[1701,83730,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,83732,1792],{},[3726,83734,83735,83741],{},[895,83736,83737,83739],{},[898,83738,3893],{"mathvariant":2334},[898,83740,1802],{},[895,83742,83743,83745],{},[898,83744,3893],{"mathvariant":2334},[898,83746,13858],{},[898,83748,1715],{"mathvariant":2334},[902,83750,83751],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,83753,83754,83784,83785,83806,83807,83825,83826,83839,83840,1715],{},[883,83755,83757],{"className":83756},[886],[888,83758,83759],{"xmlns":890},[892,83760,83761,83781],{},[895,83762,83763,83765,83771,83773,83775,83777,83779],{},[898,83764,6909],{},[1845,83766,83767,83769],{},[898,83768,1680],{},[898,83770,13853],{},[1701,83772,1799],{"stretchy":1798},[898,83774,207],{},[1701,83776,2012],{"separator":2011},[898,83778,3598],{},[1701,83780,1805],{"stretchy":1798},[902,83782,83783],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,83786,83788],{"className":83787},[886],[888,83789,83790],{"xmlns":890},[892,83791,83792,83804],{},[895,83793,83794,83796,83798,83800,83802],{},[1701,83795,2036],{"stretchy":1798},[898,83797,207],{},[1701,83799,2012],{"separator":2011},[898,83801,3598],{},[1701,83803,2053],{"stretchy":1798},[902,83805,14880],{"encoding":904}," (na hladině ",[883,83808,83810],{"className":83809},[886],[888,83811,83812],{"xmlns":890},[892,83813,83814,83822],{},[895,83815,83816,83818,83820],{},[898,83817,13858],{},[1701,83819,1792],{},[898,83821,3598],{},[902,83823,83824],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,83827,83829],{"className":83828},[886],[888,83830,83831],{"xmlns":890},[892,83832,83833,83837],{},[895,83834,83835],{},[898,83836,13853],{},[902,83838,13853],{"encoding":904},". Analogicky ",[883,83841,83843],{"className":83842},[886],[888,83844,83845],{"xmlns":890},[892,83846,83847,83867],{},[895,83848,83849,83851,83857,83859,83861,83863,83865],{},[898,83850,6909],{},[1845,83852,83853,83855],{},[898,83854,1680],{},[898,83856,13858],{},[1701,83858,1799],{"stretchy":1798},[898,83860,207],{},[1701,83862,2012],{"separator":2011},[898,83864,3598],{},[1701,83866,1805],{"stretchy":1798},[902,83868,83869],{"encoding":904},"MP_K(a, b)",[1635,83871,83872,83876],{},[724,83873,83874,2064],{},[883,83875,2063],{},[120,83877,83878,83916],{},[123,83879,83880,30226,83899],{},[883,83881,83883],{"className":83882},[886],[888,83884,83885],{"xmlns":890},[892,83886,83887,83897],{},[895,83888,83889,83891],{},[898,83890,6909],{},[1845,83892,83893,83895],{},[898,83894,1680],{},[898,83896,13853],{},[902,83898,14101],{"encoding":904},[614,83900,83901,83902,83915],{},"„o kolik vzroste ",[883,83903,83905],{"className":83904},[886],[888,83906,83907],{"xmlns":890},[892,83908,83909,83913],{},[895,83910,83911],{},[898,83912,1802],{},[902,83914,1802],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,83917,83918,30226,83937],{},[883,83919,83921],{"className":83920},[886],[888,83922,83923],{"xmlns":890},[892,83924,83925,83935],{},[895,83926,83927,83929],{},[898,83928,6909],{},[1845,83930,83931,83933],{},[898,83932,1680],{},[898,83934,13858],{},[902,83936,14146],{"encoding":904},[614,83938,83901,83939,83952],{},[883,83940,83942],{"className":83941},[886],[888,83943,83944],{"xmlns":890},[892,83945,83946,83950],{},[895,83947,83948],{},[898,83949,1802],{},[902,83951,1802],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,83954,83955,83958,83959,83974,83975,2246],{},[38,83956,83957],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,83960,83962],{"className":83961},[886],[888,83963,83964],{"xmlns":890},[892,83965,83966,83972],{},[895,83967,83968,83970],{},[898,83969,2312],{},[898,83971,13853],{},[902,83973,79102],{"encoding":904}," a kapitálu o ",[883,83976,83978],{"className":83977},[886],[888,83979,83980],{"xmlns":890},[892,83981,83982,83988],{},[895,83983,83984,83986],{},[898,83985,2312],{},[898,83987,13858],{},[902,83989,83990],{"encoding":904},"dK",[883,83992,83994],{"className":83993},[886],[888,83995,83996],{"xmlns":890,"display":2252},[892,83997,83998,84091],{},[2256,83999,84000],{"width":2258},[2260,84001,84002,84004,84084,84086],{},[2263,84003],{"width":2265},[2263,84005,84006],{},[895,84007,84008,84010,84012,84014,84016,84018,84020,84028,84030,84032,84034,84036,84044,84046,84048,84050,84052,84054,84060,84062,84064,84066,84068,84070,84076,84078,84080,84082],{},[898,84009,4708],{"mathvariant":2334},[898,84011,1802],{},[1701,84013,4067],{},[898,84015,2312],{},[898,84017,1802],{},[1701,84019,1792],{},[2287,84021,84022,84024,84026],{},[898,84023,1802],{},[898,84025,13853],{},[1701,84027,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,84029,1941],{},[898,84031,2312],{},[898,84033,13853],{},[1701,84035,1703],{},[2287,84037,84038,84040,84042],{},[898,84039,1802],{},[898,84041,13858],{},[1701,84043,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1939,84045,1941],{},[898,84047,2312],{},[898,84049,13858],{},[1701,84051,1792],{},[898,84053,6909],{},[1845,84055,84056,84058],{},[898,84057,1680],{},[898,84059,13853],{},[1939,84061,1941],{},[898,84063,2312],{},[898,84065,13853],{},[1701,84067,1703],{},[898,84069,6909],{},[1845,84071,84072,84074],{},[898,84073,1680],{},[898,84075,13858],{},[1939,84077,1941],{},[898,84079,2312],{},[898,84081,13858],{},[898,84083,1715],{"mathvariant":2334},[2263,84085],{"width":2265},[2263,84087,84088],{},[1939,84089,84090],{},"(5.11)",[902,84092,84093],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,84095,84096,84097,1715],{},"Skutečná změna: ",[883,84098,84100],{"className":84099},[886],[888,84101,84102],{"xmlns":890},[892,84103,84104,84150],{},[895,84105,84106,84108,84110,84112,84114,84116,84118,84120,84122,84124,84126,84128,84130,84132,84134,84136,84138,84140,84142,84144,84146,84148],{},[898,84107,4708],{"mathvariant":2334},[898,84109,1802],{},[1701,84111,1792],{},[898,84113,1802],{},[1701,84115,1799],{"stretchy":1798},[898,84117,13853],{},[1701,84119,1703],{},[898,84121,2312],{},[898,84123,13853],{},[1701,84125,2012],{"separator":2011},[898,84127,13858],{},[1701,84129,1703],{},[898,84131,2312],{},[898,84133,13858],{},[1701,84135,1805],{"stretchy":1798},[1701,84137,2317],{},[898,84139,1802],{},[1701,84141,1799],{"stretchy":1798},[898,84143,13853],{},[1701,84145,2012],{"separator":2011},[898,84147,13858],{},[1701,84149,1805],{"stretchy":1798},[902,84151,84152],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,84154,84155,84157,84158,84176,84177,84190,84191,84210,84211,84243,84244,84276,84277,1715],{},[38,84156,79266],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,84159,84161],{"className":84160},[886],[888,84162,84163],{"xmlns":890},[892,84164,84165,84173],{},[895,84166,84167],{},[1845,84168,84169,84171],{},[898,84170,13858],{},[1850,84172,1852],{},[902,84174,84175],{"encoding":904},"K_0"," se od jistého ",[883,84178,84180],{"className":84179},[886],[888,84181,84182],{"xmlns":890},[892,84183,84184,84188],{},[895,84185,84186],{},[898,84187,13853],{},[902,84189,13853],{"encoding":904}," stane ",[883,84192,84194],{"className":84193},[886],[888,84195,84196],{"xmlns":890},[892,84197,84198,84208],{},[895,84199,84200,84202],{},[898,84201,6909],{},[1845,84203,84204,84206],{},[898,84205,1680],{},[898,84207,13853],{},[902,84209,14101],{"encoding":904}," klesající (",[883,84212,84214],{"className":84213},[886],[888,84215,84216],{"xmlns":890},[892,84217,84218,84240],{},[895,84219,84220,84236,84238],{},[2287,84221,84222,84224,84230],{},[898,84223,1802],{},[895,84225,84226,84228],{},[898,84227,13853],{},[898,84229,13853],{},[895,84231,84232,84234],{},[1701,84233,4783],{"mathvariant":2334},[1701,84235,4783],{"mathvariant":2334},[1701,84237,7530],{},[1850,84239,1852],{},[902,84241,84242],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,84245,84247],{"className":84246},[886],[888,84248,84249],{"xmlns":890},[892,84250,84251,84273],{},[895,84252,84253,84269,84271],{},[2287,84254,84255,84257,84263],{},[898,84256,1802],{},[895,84258,84259,84261],{},[898,84260,13858],{},[898,84262,13858],{},[895,84264,84265,84267],{},[1701,84266,4783],{"mathvariant":2334},[1701,84268,4783],{"mathvariant":2334},[1701,84270,7530],{},[1850,84272,1852],{},[902,84274,84275],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,84278,84280],{"className":84279},[886],[888,84281,84282],{"xmlns":890},[892,84283,84284,84292],{},[895,84285,84286],{},[1845,84287,84288,84290],{},[898,84289,13853],{},[1850,84291,1852],{},[902,84293,79304],{"encoding":904},[115,84295,84297],{"id":84296},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,84299,84300,84303,84304,84327,84328,33977],{},[38,84301,84302],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,84305,84307],{"className":84306},[886],[888,84308,84309],{"xmlns":890},[892,84310,84311,84325],{},[895,84312,84313,84315,84317,84319,84321,84323],{},[898,84314,1802],{},[1701,84316,1799],{"stretchy":1798},[898,84318,13853],{},[1701,84320,2012],{"separator":2011},[898,84322,13858],{},[1701,84324,1805],{"stretchy":1798},[902,84326,14054],{"encoding":904}," stupně ",[883,84329,84331],{"className":84330},[886],[888,84332,84333],{"xmlns":890},[892,84334,84335,84339],{},[895,84336,84337],{},[898,84338,40890],{},[902,84340,40890],{"encoding":904},[883,84342,84344],{"className":84343},[886],[888,84345,84346],{"xmlns":890,"display":2252},[892,84347,84348,84411],{},[2256,84349,84350],{"width":2258},[2260,84351,84352,84354,84404,84406],{},[2263,84353],{"width":2265},[2263,84355,84356],{},[895,84357,84358,84360,84362,84370,84372,84374,84376,84384,84386,84388,84390,84392,84394,84396,84398,84400,84402],{},[898,84359,13853],{},[1939,84361,1941],{},[2287,84363,84364,84366,84368],{},[898,84365,1802],{},[898,84367,13853],{},[1701,84369,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,84371,1703],{},[898,84373,13858],{},[1939,84375,1941],{},[2287,84377,84378,84380,84382],{},[898,84379,1802],{},[898,84381,13858],{},[1701,84383,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,84385,1792],{},[898,84387,40890],{},[1939,84389,1941],{},[898,84391,1802],{},[1701,84393,1799],{"stretchy":1798},[898,84395,13853],{},[1701,84397,2012],{"separator":2011},[898,84399,13858],{},[1701,84401,1805],{"stretchy":1798},[898,84403,1715],{"mathvariant":2334},[2263,84405],{"width":2265},[2263,84407,84408],{},[1939,84409,84410],{},"(5.12)",[902,84412,84413],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,84415,84416,84437],{},[38,84417,84418,84419],{},"Speciální případ ",[883,84420,84422],{"className":84421},[886],[888,84423,84424],{"xmlns":890},[892,84425,84426,84434],{},[895,84427,84428,84430,84432],{},[898,84429,40890],{},[1701,84431,1792],{},[1850,84433,4062],{},[902,84435,84436],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,84439,84441],{"className":84440},[886],[888,84442,84443],{"xmlns":890,"display":2252},[892,84444,84445,84489],{},[895,84446,84447,84449,84451,84453,84459,84461,84463,84465,84467,84473,84475,84477,84479,84481,84483,84485,84487],{},[898,84448,13853],{},[1701,84450,3408],{},[898,84452,6909],{},[1845,84454,84455,84457],{},[898,84456,1680],{},[898,84458,13853],{},[1701,84460,1703],{},[898,84462,13858],{},[1701,84464,3408],{},[898,84466,6909],{},[1845,84468,84469,84471],{},[898,84470,1680],{},[898,84472,13858],{},[1701,84474,1792],{},[898,84476,1802],{},[1701,84478,1799],{"stretchy":1798},[898,84480,13853],{},[1701,84482,2012],{"separator":2011},[898,84484,13858],{},[1701,84486,1805],{"stretchy":1798},[898,84488,1715],{"mathvariant":2334},[902,84490,84491],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,84493,84494,84495,84498],{},"Slovně — ",[38,84496,84497],{},"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).",[115,84500,13836],{"id":78640},[724,84502,84503,1646,84505,84508,84509,84531,84532,2246],{},[38,84504,13836],{},[614,84506,84507],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,84510,84512],{"className":84511},[886],[888,84513,84514],{"xmlns":890},[892,84515,84516,84528],{},[895,84517,84518,84520,84522,84524,84526],{},[1701,84519,2036],{"stretchy":1798},[898,84521,13853],{},[1701,84523,2012],{"separator":2011},[898,84525,13858],{},[1701,84527,2053],{"stretchy":1798},[902,84529,84530],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,84533,84535],{"className":84534},[886],[888,84536,84537],{"xmlns":890},[892,84538,84539,84544],{},[895,84540,84541],{},[898,84542,84543],{},"q",[902,84545,84543],{"encoding":904},[883,84547,84549],{"className":84548},[886],[888,84550,84551],{"xmlns":890,"display":2252},[892,84552,84553,84588],{},[2256,84554,84555],{"width":2258},[2260,84556,84557,84559,84581,84583],{},[2263,84558],{"width":2265},[2263,84560,84561],{},[895,84562,84563,84565,84567,84569,84571,84573,84575,84577,84579],{},[898,84564,1802],{},[1701,84566,1799],{"stretchy":1798},[898,84568,13853],{},[1701,84570,2012],{"separator":2011},[898,84572,13858],{},[1701,84574,1805],{"stretchy":1798},[1701,84576,1792],{},[898,84578,84543],{},[898,84580,1715],{"mathvariant":2334},[2263,84582],{"width":2265},[2263,84584,84585],{},[1939,84586,84587],{},"(5.13)",[902,84589,84590],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,84592,84593,84594,84597,84598,2506],{},"Jsou to ",[38,84595,84596],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,84599,84601],{"className":84600,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,84603,84604],{},[38,84605,84606],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,84608,84609,84614,84619,84624],{},[123,84610,84611,84613],{},[38,84612,16573],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,84615,84616,84618],{},[38,84617,41692],{}," (úloha 5.14);",[123,84620,84621,12487],{},[38,84622,84623],{},"neprotínají se",[123,84625,84626,84627,8428,84640,1715],{},"s rostoucím ",[883,84628,84630],{"className":84629},[886],[888,84631,84632],{"xmlns":890},[892,84633,84634,84638],{},[895,84635,84636],{},[898,84637,84543],{},[902,84639,84543],{"encoding":904},[38,84641,84642],{},"vzdalují od počátku",[724,84644,84645],{},[614,84646,84647,84648,84670,84671,1715],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,84649,84651],{"className":84650},[886],[888,84652,84653],{"xmlns":890},[892,84654,84655,84667],{},[895,84656,84657,84659,84661,84663,84665],{},[1701,84658,1799],{"stretchy":1798},[898,84660,13853],{},[1701,84662,2012],{"separator":2011},[898,84664,13858],{},[1701,84666,1805],{"stretchy":1798},[902,84668,84669],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,84672,84674],{"className":84673},[886],[888,84675,84676],{"xmlns":890},[892,84677,84678,84702],{},[895,84679,84680,84686,84688,84694,84696],{},[1845,84681,84682,84684],{},[898,84683,84543],{},[1850,84685,4062],{},[1701,84687,7530],{},[1845,84689,84690,84692],{},[898,84691,84543],{},[1850,84693,1852],{},[1701,84695,7530],{},[1845,84697,84698,84700],{},[898,84699,84543],{},[1850,84701,3938],{},[902,84703,84704],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,84706,84708,84709,1805],{"id":84707},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,84710,84712],{"className":84711},[886],[888,84713,84714],{"xmlns":890},[892,84715,84716,84726],{},[895,84717,84718,84720,84722,84724],{},[898,84719,6909],{},[898,84721,8068],{},[898,84723,5877],{},[898,84725,1661],{},[902,84727,14655],{"encoding":904},[724,84729,84730,1646,84733,84736],{},[38,84731,84732],{},"Mezní míra technické substituce",[614,84734,84735],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,84738,84740],{"className":84739},[886],[888,84741,84742],{"xmlns":890,"display":2252},[892,84743,84744,84835],{},[2256,84745,84746],{"width":2258},[2260,84747,84748,84750,84828,84830],{},[2263,84749],{"width":2265},[2263,84751,84752],{},[895,84753,84754,84756,84758,84760,84762,84764,84766,84768,84770,84772,84774,84776,84778,84780,84782,84784,84806,84808,84826],{},[898,84755,6909],{},[898,84757,8068],{},[898,84759,5877],{},[898,84761,1661],{},[1701,84763,1792],{},[898,84765,6909],{},[898,84767,8068],{},[898,84769,5877],{},[898,84771,1661],{},[1701,84773,1799],{"stretchy":1798},[898,84775,13853],{},[1701,84777,2012],{"separator":2011},[898,84779,13858],{},[1701,84781,1805],{"stretchy":1798},[1701,84783,1792],{},[3726,84785,84786,84796],{},[895,84787,84788,84790],{},[898,84789,6909],{},[1845,84791,84792,84794],{},[898,84793,1680],{},[898,84795,13853],{},[895,84797,84798,84800],{},[898,84799,6909],{},[1845,84801,84802,84804],{},[898,84803,1680],{},[898,84805,13858],{},[1701,84807,1792],{},[3726,84809,84810,84818],{},[2287,84811,84812,84814,84816],{},[898,84813,1802],{},[898,84815,13853],{},[1701,84817,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,84819,84820,84822,84824],{},[898,84821,1802],{},[898,84823,13858],{},[1701,84825,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[898,84827,1715],{"mathvariant":2334},[2263,84829],{"width":2265},[2263,84831,84832],{},[1939,84833,84834],{},"(5.14)",[902,84836,84837],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,84839,84840,4088,84842,84872,84873,84904],{},[38,84841,13276],{},[883,84843,84845],{"className":84844},[886],[888,84846,84847],{"xmlns":890},[892,84848,84849,84869],{},[895,84850,84851,84853,84855,84857,84859,84861,84863,84865,84867],{},[898,84852,6909],{},[898,84854,8068],{},[898,84856,5877],{},[898,84858,1661],{},[1701,84860,1799],{"stretchy":1798},[898,84862,13853],{},[1701,84864,2012],{"separator":2011},[898,84866,13858],{},[1701,84868,1805],{"stretchy":1798},[902,84870,84871],{"encoding":904},"MRTS(L, K)"," udává, ",[38,84874,84875,84876,84889,84890,84903],{},"o kolik se musí přibližně změnit kapitál ",[883,84877,84879],{"className":84878},[886],[888,84880,84881],{"xmlns":890},[892,84882,84883,84887],{},[895,84884,84885],{},[898,84886,13858],{},[902,84888,13858],{"encoding":904},", jestliže se práce ",[883,84891,84893],{"className":84892},[886],[888,84894,84895],{"xmlns":890},[892,84896,84897,84901],{},[895,84898,84899],{},[898,84900,13853],{},[902,84902,13853],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1635,84906,84907],{},[724,84908,84909,22069,84911,84930,84931,84968,84969,84972,84973,84977],{},[883,84910,2063],{},[883,84912,84914],{"className":84913},[886],[888,84915,84916],{"xmlns":890},[892,84917,84918,84928],{},[895,84919,84920,84922,84924,84926],{},[898,84921,6909],{},[898,84923,8068],{},[898,84925,5877],{},[898,84927,1661],{},[902,84929,14655],{"encoding":904}," říká: ",[614,84932,84933,84934,84953,84954,84967],{},"„jednu jednotku práce musím nahradit přibližně ",[883,84935,84937],{"className":84936},[886],[888,84938,84939],{"xmlns":890},[892,84940,84941,84951],{},[895,84942,84943,84945,84947,84949],{},[898,84944,6909],{},[898,84946,8068],{},[898,84948,5877],{},[898,84950,1661],{},[902,84952,14655],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,84955,84957],{"className":84956},[886],[888,84958,84959],{"xmlns":890},[892,84960,84961,84965],{},[895,84962,84963],{},[898,84964,1802],{},[902,84966,1802],{"encoding":904}," zůstala stejná.\""," Je to ",[38,84970,84971],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,84974,84976],{"className":84975,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,84979,84980],{},[2139,84981],{"alt":84982,"className":84983,"src":84984},"imek-izokvanty-mrts",[210,2143],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,84986,84987,84990,84991,12164,85021,85043,85044,4539],{},[38,84988,84989],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,84992,84994],{"className":84993},[886],[888,84995,84996],{"xmlns":890},[892,84997,84998,85018],{},[895,84999,85000,85002,85008,85010,85016],{},[1701,85001,2036],{"stretchy":1798},[1845,85003,85004,85006],{},[898,85005,13853],{},[1850,85007,1852],{},[1701,85009,2012],{"separator":2011},[1845,85011,85012,85014],{},[898,85013,13858],{},[1850,85015,1852],{},[1701,85017,2053],{"stretchy":1798},[902,85019,85020],{"encoding":904},"[L_0, K_0]",[883,85022,85024],{"className":85023},[886],[888,85025,85026],{"xmlns":890},[892,85027,85028,85040],{},[895,85029,85030,85032,85034,85036,85038],{},[1701,85031,2317],{},[898,85033,6909],{},[898,85035,8068],{},[898,85037,5877],{},[898,85039,1661],{},[902,85041,85042],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,85045,85047],{"className":85046},[886],[888,85048,85049],{"xmlns":890},[892,85050,85051,85073],{},[895,85052,85053,85055,85057,85059,85061,85063,85065,85067],{},[898,85054,1802],{},[1701,85056,1799],{"stretchy":1798},[898,85058,13853],{},[1701,85060,2012],{"separator":2011},[898,85062,13858],{},[1701,85064,1805],{"stretchy":1798},[1701,85066,1792],{},[1845,85068,85069,85071],{},[898,85070,84543],{},[1850,85072,1852],{},[902,85074,85075],{"encoding":904},"Q(L,K) = q_0",[883,85077,85079],{"className":85078},[886],[888,85080,85081],{"xmlns":890,"display":2252},[892,85082,85083,85135],{},[895,85084,85085,85099,85101,85103,85121,85123,85125,85127,85129,85131,85133],{},[3726,85086,85087,85093],{},[895,85088,85089,85091],{},[898,85090,2312],{},[898,85092,13858],{},[895,85094,85095,85097],{},[898,85096,2312],{},[898,85098,13853],{},[1701,85100,1792],{},[1701,85102,2317],{},[3726,85104,85105,85113],{},[2287,85106,85107,85109,85111],{},[898,85108,1802],{},[898,85110,13853],{},[1701,85112,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,85114,85115,85117,85119],{},[898,85116,1802],{},[898,85118,13858],{},[1701,85120,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,85122,1792],{},[1701,85124,2317],{},[898,85126,6909],{},[898,85128,8068],{},[898,85130,5877],{},[898,85132,1661],{},[898,85134,1715],{"mathvariant":2334},[902,85136,85137],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,85139,85140,85141,85156,85157,85173],{},"Změní-li se práce o ",[883,85142,85144],{"className":85143},[886],[888,85145,85146],{"xmlns":890},[892,85147,85148,85154],{},[895,85149,85150,85152],{},[898,85151,2312],{},[898,85153,13853],{},[902,85155,79102],{"encoding":904},", lze pro odhad změny kapitálu ",[883,85158,85160],{"className":85159},[886],[888,85161,85162],{"xmlns":890},[892,85163,85164,85170],{},[895,85165,85166,85168],{},[898,85167,4708],{"mathvariant":2334},[898,85169,13858],{},[902,85171,85172],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,85175,85177],{"className":85176},[886],[888,85178,85179],{"xmlns":890,"display":2252},[892,85180,85181,85228],{},[2256,85182,85183],{"width":2258},[2260,85184,85185,85187,85221,85223],{},[2263,85186],{"width":2265},[2263,85188,85189],{},[895,85190,85191,85193,85195,85197,85199,85201,85203,85205,85207,85209,85211,85213,85215,85217,85219],{},[898,85192,4708],{"mathvariant":2334},[898,85194,13858],{},[1701,85196,4067],{},[898,85198,2312],{},[898,85200,13858],{},[1701,85202,1792],{},[1701,85204,2317],{},[898,85206,6909],{},[898,85208,8068],{},[898,85210,5877],{},[898,85212,1661],{},[1939,85214,1941],{},[898,85216,2312],{},[898,85218,13853],{},[1701,85220,2012],{"separator":2011},[2263,85222],{"width":2265},[2263,85224,85225],{},[1939,85226,85227],{},"(5.15)",[902,85229,85230],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,85232,85234],{"className":85233},[886],[888,85235,85236],{"xmlns":890,"display":2252},[892,85237,85238,85287],{},[2256,85239,85240],{"width":2258},[2260,85241,85242,85244,85280,85282],{},[2263,85243],{"width":2265},[2263,85245,85246],{},[895,85247,85248,85250,85252,85254,85272,85274,85276,85278],{},[898,85249,2312],{},[898,85251,13853],{},[1701,85253,1792],{},[3726,85255,85256,85262],{},[895,85257,85258,85260],{},[1701,85259,2317],{},[1850,85261,4062],{},[895,85263,85264,85266,85268,85270],{},[898,85265,6909],{},[898,85267,8068],{},[898,85269,5877],{},[898,85271,1661],{},[1939,85273,1941],{},[898,85275,2312],{},[898,85277,13858],{},[898,85279,1715],{"mathvariant":2334},[2263,85281],{"width":2265},[2263,85283,85284],{},[1939,85285,85286],{},"(5.16)",[902,85288,85289],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1635,85291,85292,85316],{},[724,85293,85294,85296,85297],{},[883,85295,3140],{}," Postup — jak spočítat ",[883,85298,85300],{"className":85299},[886],[888,85301,85302],{"xmlns":890},[892,85303,85304,85314],{},[895,85305,85306,85308,85310,85312],{},[898,85307,6909],{},[898,85309,8068],{},[898,85311,5877],{},[898,85313,1661],{},[902,85315,14655],{"encoding":904},[152,85317,85318,85359,85402,85434],{},[123,85319,85320,85321,2633,85340,1715],{},"Vypočtěte parciální derivace ",[883,85322,85324],{"className":85323},[886],[888,85325,85326],{"xmlns":890},[892,85327,85328,85338],{},[895,85329,85330],{},[2287,85331,85332,85334,85336],{},[898,85333,1802],{},[898,85335,13853],{},[1701,85337,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,85339,14078],{"encoding":904},[883,85341,85343],{"className":85342},[886],[888,85344,85345],{"xmlns":890},[892,85346,85347,85357],{},[895,85348,85349],{},[2287,85350,85351,85353,85355],{},[898,85352,1802],{},[898,85354,13858],{},[1701,85356,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,85358,14123],{"encoding":904},[123,85360,69587,85361,85401],{},[883,85362,85364],{"className":85363},[886],[888,85365,85366],{"xmlns":890},[892,85367,85368,85398],{},[895,85369,85370,85372,85374,85376,85378,85380,85388,85390],{},[898,85371,6909],{},[898,85373,8068],{},[898,85375,5877],{},[898,85377,1661],{},[1701,85379,1792],{},[2287,85381,85382,85384,85386],{},[898,85383,1802],{},[898,85385,13853],{},[1701,85387,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[898,85389,8741],{"mathvariant":2334},[2287,85391,85392,85394,85396],{},[898,85393,1802],{},[898,85395,13858],{},[1701,85397,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,85399,85400],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,85403,85404,85405,1715],{},"Případně dosaďte konkrétní ",[883,85406,85408],{"className":85407},[886],[888,85409,85410],{"xmlns":890},[892,85411,85412,85432],{},[895,85413,85414,85416,85422,85424,85430],{},[1701,85415,2036],{"stretchy":1798},[1845,85417,85418,85420],{},[898,85419,13853],{},[1850,85421,1852],{},[1701,85423,2012],{"separator":2011},[1845,85425,85426,85428],{},[898,85427,13858],{},[1850,85429,1852],{},[1701,85431,2053],{"stretchy":1798},[902,85433,85020],{"encoding":904},[123,85435,85436,85437,85471,85472,85474],{},"Pro odhad substituce použijte ",[883,85438,85440],{"className":85439},[886],[888,85441,85442],{"xmlns":890},[892,85443,85444,85468],{},[895,85445,85446,85448,85450,85452,85454,85456,85458,85460,85462,85464,85466],{},[898,85447,4708],{"mathvariant":2334},[898,85449,13858],{},[1701,85451,4067],{},[1701,85453,2317],{},[898,85455,6909],{},[898,85457,8068],{},[898,85459,5877],{},[898,85461,1661],{},[1701,85463,3408],{},[898,85465,4708],{"mathvariant":2334},[898,85467,13853],{},[902,85469,85470],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,85473,3486],{}," — substituce, ne doplnění).",[724,85476,85477],{},[614,85478,85479,85480,85512,85513,6723,85526,19842,85555,85570],{},"Obrázek 5.7 — izokvanta ",[883,85481,85483],{"className":85482},[886],[888,85484,85485],{"xmlns":890},[892,85486,85487,85509],{},[895,85488,85489,85495,85497,85499,85501,85503,85505,85507],{},[1845,85490,85491,85493],{},[898,85492,84543],{},[1850,85494,1852],{},[1701,85496,1792],{},[898,85498,1802],{},[1701,85500,1799],{"stretchy":1798},[898,85502,13853],{},[1701,85504,2012],{"separator":2011},[898,85506,13858],{},[1701,85508,1805],{"stretchy":1798},[902,85510,85511],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,85514,85516],{"className":85515},[886],[888,85517,85518],{"xmlns":890},[892,85519,85520,85524],{},[895,85521,85522],{},[898,85523,22901],{},[902,85525,22901],{"encoding":904},[883,85527,85529],{"className":85528},[886],[888,85530,85531],{"xmlns":890},[892,85532,85533,85553],{},[895,85534,85535,85537,85543,85545,85551],{},[1701,85536,2036],{"stretchy":1798},[1845,85538,85539,85541],{},[898,85540,13853],{},[1850,85542,1852],{},[1701,85544,2012],{"separator":2011},[1845,85546,85547,85549],{},[898,85548,13858],{},[1850,85550,1852],{},[1701,85552,2053],{"stretchy":1798},[902,85554,85020],{"encoding":904},[883,85556,85558],{"className":85557},[886],[888,85559,85560],{"xmlns":890},[892,85561,85562,85568],{},[895,85563,85564,85566],{},[898,85565,4708],{"mathvariant":2334},[898,85567,13858],{},[902,85569,85172],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,85572,85574],{"id":85573},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,85576,85578],{"id":85577},"příklad-54","Příklad 5.4",[724,85580,80419,85581,1343,85623,1343,85640,1715],{},[883,85582,85584],{"className":85583},[886],[888,85585,85586],{"xmlns":890},[892,85587,85588,85620],{},[895,85589,85590,85592,85594,85596,85608],{},[898,85591,1802],{},[1701,85593,1792],{},[1850,85595,40275],{},[3243,85597,85598,85600],{},[898,85599,13853],{},[895,85601,85602,85604,85606],{},[1850,85603,4062],{},[898,85605,8741],{"mathvariant":2334},[1850,85607,3938],{},[3243,85609,85610,85612],{},[898,85611,13858],{},[895,85613,85614,85616,85618],{},[1850,85615,4062],{},[898,85617,8741],{"mathvariant":2334},[1850,85619,3646],{},[902,85621,85622],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,85624,85626],{"className":85625},[886],[888,85627,85628],{"xmlns":890},[892,85629,85630,85638],{},[895,85631,85632,85634,85636],{},[898,85633,13853],{},[1701,85635,1792],{},[1850,85637,13096],{},[902,85639,80793],{"encoding":904},[883,85641,85643],{"className":85642},[886],[888,85644,85645],{"xmlns":890},[892,85646,85647,85655],{},[895,85648,85649,85651,85653],{},[898,85650,13858],{},[1701,85652,1792],{},[1850,85654,5158],{},[902,85656,85657],{"encoding":904},"K = 100",[724,85659,85660],{},[38,85661,85662],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,85664,85666],{"className":85665},[886],[888,85667,85668],{"xmlns":890,"display":2252},[892,85669,85670,85784],{},[895,85671,85672,85674,85680,85682,85690,85692,85700,85714,85726,85728,85730,85732,85738,85740,85742,85744,85746,85748,85750,85758,85760,85770,85772,85779,85781],{},[898,85673,6909],{},[1845,85675,85676,85678],{},[898,85677,1680],{},[898,85679,13853],{},[1701,85681,1792],{},[2287,85683,85684,85686,85688],{},[898,85685,1802],{},[898,85687,13853],{},[1701,85689,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,85691,1792],{},[2363,85693,85694],{"scriptlevel":1852,"displaystyle":1798},[3726,85695,85696,85698],{},[1850,85697,40275],{},[1850,85699,3938],{},[3243,85701,85702,85704],{},[898,85703,13853],{},[895,85705,85706,85708,85710,85712],{},[1701,85707,2317],{},[1850,85709,4062],{},[898,85711,8741],{"mathvariant":2334},[1850,85713,3938],{},[3243,85715,85716,85718],{},[898,85717,13858],{},[895,85719,85720,85722,85724],{},[1850,85721,4062],{},[898,85723,8741],{"mathvariant":2334},[1850,85725,3646],{},[1701,85727,2012],{"separator":2011},[9942,85729],{"width":19336},[898,85731,6909],{},[1845,85733,85734,85736],{},[898,85735,1680],{},[898,85737,13853],{},[1701,85739,1799],{"stretchy":1798},[1850,85741,13096],{},[1701,85743,2012],{"separator":2011},[1850,85745,5158],{},[1701,85747,1805],{"stretchy":1798},[1701,85749,1792],{},[2363,85751,85752],{"scriptlevel":1852,"displaystyle":1798},[3726,85753,85754,85756],{},[1850,85755,40275],{},[1850,85757,3938],{},[1701,85759,3408],{},[2363,85761,85762],{"scriptlevel":1852,"displaystyle":1798},[3726,85763,85764,85766],{},[1850,85765,4062],{},[12179,85767,85768],{},[1850,85769,13096],{},[1701,85771,3408],{},[85773,85774,85775,85777],"mroot",{},[1850,85776,5158],{},[1850,85778,3646],{},[1701,85780,4067],{},[1850,85782,85783],{},"7,153.",[902,85785,85786],{"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.",[724,85788,85789,85790,48180,85812,14289,85829,85850,85851,85872],{},"Přibližná změna při ",[883,85791,85793],{"className":85792},[886],[888,85794,85795],{"xmlns":890},[892,85796,85797,85809],{},[895,85798,85799,85801,85803,85805,85807],{},[898,85800,13853],{},[1701,85802,2246],{},[1850,85804,13096],{},[1701,85806,4108],{},[1850,85808,42371],{},[902,85810,85811],{"encoding":904},"L: 20 \\to 21",[883,85813,85815],{"className":85814},[886],[888,85816,85817],{"xmlns":890},[892,85818,85819,85827],{},[895,85820,85821,85823,85825],{},[898,85822,13858],{},[1701,85824,1792],{},[1850,85826,5158],{},[902,85828,85657],{"encoding":904},[883,85830,85832],{"className":85831},[886],[888,85833,85834],{"xmlns":890},[892,85835,85836,85847],{},[895,85837,85838,85840,85842,85844],{},[898,85839,4708],{"mathvariant":2334},[898,85841,1802],{},[1701,85843,4067],{},[1850,85845,85846],{},"7,153",[902,85848,85849],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,85852,85854],{"className":85853},[886],[888,85855,85856],{"xmlns":890},[892,85857,85858,85869],{},[895,85859,85860,85862,85864,85866],{},[898,85861,4708],{"mathvariant":2334},[898,85863,1802],{},[1701,85865,4067],{},[1850,85867,85868],{},"26,888",[902,85870,85871],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,85874,85875,85878],{},[38,85876,85877],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,85880,85882],{"className":85881},[886],[888,85883,85884],{"xmlns":890,"display":2252},[892,85885,85886,85986],{},[895,85887,85888,85890,85896,85898,85906,85908,85910,85922,85936,85938,85940,85942,85948,85950,85952,85954,85956,85958,85960,85962,85966,85968,85981,85983],{},[898,85889,6909],{},[1845,85891,85892,85894],{},[898,85893,1680],{},[898,85895,13858],{},[1701,85897,1792],{},[2287,85899,85900,85902,85904],{},[898,85901,1802],{},[898,85903,13858],{},[1701,85905,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,85907,1792],{},[1850,85909,4225],{},[3243,85911,85912,85914],{},[898,85913,13853],{},[895,85915,85916,85918,85920],{},[1850,85917,4062],{},[898,85919,8741],{"mathvariant":2334},[1850,85921,3938],{},[3243,85923,85924,85926],{},[898,85925,13858],{},[895,85927,85928,85930,85932,85934],{},[1701,85929,2317],{},[1850,85931,3938],{},[898,85933,8741],{"mathvariant":2334},[1850,85935,3646],{},[1701,85937,2012],{"separator":2011},[9942,85939],{"width":19336},[898,85941,6909],{},[1845,85943,85944,85946],{},[898,85945,1680],{},[898,85947,13858],{},[1701,85949,1799],{"stretchy":1798},[1850,85951,13096],{},[1701,85953,2012],{"separator":2011},[1850,85955,5158],{},[1701,85957,1805],{"stretchy":1798},[1701,85959,1792],{},[1850,85961,4225],{},[12179,85963,85964],{},[1850,85965,13096],{},[1701,85967,3408],{},[2363,85969,85970],{"scriptlevel":1852,"displaystyle":1798},[3726,85971,85972,85974],{},[1850,85973,4062],{},[85773,85975,85976,85979],{},[1850,85977,85978],{},"10000",[1850,85980,3646],{},[1701,85982,4067],{},[1850,85984,85985],{},"4,525.",[902,85987,85988],{"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.",[724,85990,85991,85992,3856,86009,2506],{},"Produkce poklesne přibližně o 4,525 (z ",[883,85993,85995],{"className":85994},[886],[888,85996,85997],{"xmlns":890},[892,85998,85999,86006],{},[895,86000,86001,86003],{},[1701,86002,4067],{},[1850,86004,86005],{},"905,126",[902,86007,86008],{"encoding":904},"\\approx 905{,}126",[883,86010,86012],{"className":86011},[886],[888,86013,86014],{"xmlns":890},[892,86015,86016,86023],{},[895,86017,86018,86020],{},[1701,86019,4067],{},[1850,86021,86022],{},"900,601",[902,86024,86025],{"encoding":904},"\\approx 900{,}601",[724,86027,86028,7215,86075,1343,86097,2506],{},[38,86029,86030,86031,2633,86053],{},"(c) Změna ",[883,86032,86034],{"className":86033},[886],[888,86035,86036],{"xmlns":890},[892,86037,86038,86050],{},[895,86039,86040,86042,86044,86046,86048],{},[898,86041,13853],{},[1701,86043,2246],{},[1850,86045,13096],{},[1701,86047,4108],{},[1850,86049,40275],{},[902,86051,86052],{"encoding":904},"L: 20 \\to 15",[883,86054,86056],{"className":86055},[886],[888,86057,86058],{"xmlns":890},[892,86059,86060,86072],{},[895,86061,86062,86064,86066,86068,86070],{},[898,86063,13858],{},[1701,86065,2246],{},[1850,86067,5158],{},[1701,86069,4108],{},[1850,86071,12864],{},[902,86073,86074],{"encoding":904},"K: 100 \\to 150",[883,86076,86078],{"className":86077},[886],[888,86079,86080],{"xmlns":890},[892,86081,86082,86094],{},[895,86083,86084,86086,86088,86090,86092],{},[898,86085,2312],{},[898,86087,13853],{},[1701,86089,1792],{},[1701,86091,2317],{},[1850,86093,4225],{},[902,86095,86096],{"encoding":904},"dL = -5",[883,86098,86100],{"className":86099},[886],[888,86101,86102],{"xmlns":890},[892,86103,86104,86114],{},[895,86105,86106,86108,86110,86112],{},[898,86107,2312],{},[898,86109,13858],{},[1701,86111,1792],{},[1850,86113,7206],{},[902,86115,86116],{"encoding":904},"dK = 50",[883,86118,86120],{"className":86119},[886],[888,86121,86122],{"xmlns":890,"display":2252},[892,86123,86124,86212],{},[895,86125,86126,86128,86130,86132,86134,86140,86142,86144,86146,86148,86150,86152,86154,86156,86158,86160,86162,86164,86170,86172,86174,86176,86178,86180,86182,86184,86186,86188,86190,86192,86194,86196,86198,86200,86203,86205,86207,86209],{},[898,86127,2312],{},[898,86129,1802],{},[1701,86131,1792],{},[898,86133,6909],{},[1845,86135,86136,86138],{},[898,86137,1680],{},[898,86139,13853],{},[1701,86141,1799],{"stretchy":1798},[1850,86143,13096],{},[1701,86145,2012],{"separator":2011},[1850,86147,5158],{},[1701,86149,1805],{"stretchy":1798},[1701,86151,3408],{},[1701,86153,1799],{"stretchy":1798},[1701,86155,2317],{},[1850,86157,4225],{},[1701,86159,1805],{"stretchy":1798},[1701,86161,1703],{},[898,86163,6909],{},[1845,86165,86166,86168],{},[898,86167,1680],{},[898,86169,13858],{},[1701,86171,1799],{"stretchy":1798},[1850,86173,13096],{},[1701,86175,2012],{"separator":2011},[1850,86177,5158],{},[1701,86179,1805],{"stretchy":1798},[1701,86181,3408],{},[1850,86183,7206],{},[1701,86185,1792],{},[1850,86187,85846],{},[1701,86189,3408],{},[1701,86191,1799],{"stretchy":1798},[1701,86193,2317],{},[1850,86195,4225],{},[1701,86197,1805],{"stretchy":1798},[1701,86199,1703],{},[1850,86201,86202],{},"4,525",[1701,86204,3408],{},[1850,86206,7206],{},[1701,86208,4067],{},[1850,86210,86211],{},"190,485.",[902,86213,86214],{"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.",[724,86216,86217],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,86219,86221],{"id":86220},"příklad-55","Příklad 5.5",[724,86223,86224,86225,86261,86262,1715],{},"Pro produkci ",[883,86226,86228],{"className":86227},[886],[888,86229,86230],{"xmlns":890},[892,86231,86232,86258],{},[895,86233,86234,86236,86238,86240,86242,86244,86246,86248,86254],{},[898,86235,1802],{},[1701,86237,1799],{"stretchy":1798},[898,86239,13853],{},[1701,86241,2012],{"separator":2011},[898,86243,13858],{},[1701,86245,1805],{"stretchy":1798},[1701,86247,1792],{},[85773,86249,86250,86252],{},[898,86251,13853],{},[1850,86253,3646],{},[12179,86255,86256],{},[898,86257,13858],{},[902,86259,86260],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,86263,86265],{"className":86264},[886],[888,86266,86267],{"xmlns":890},[892,86268,86269,86285],{},[895,86270,86271,86277,86281,86283],{},[85773,86272,86273,86275],{},[898,86274,13853],{},[1850,86276,3646],{},[12179,86278,86279],{},[898,86280,13858],{},[1701,86282,1792],{},[898,86284,84543],{},[902,86286,86287],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,86289,86290,86291,1715],{},"Umocněním na druhou: ",[883,86292,86294],{"className":86293},[886],[888,86295,86296],{"xmlns":890},[892,86297,86298,86322],{},[895,86299,86300,86302,86304,86310,86312],{},[898,86301,13858],{},[1701,86303,1792],{},[3243,86305,86306,86308],{},[898,86307,84543],{},[1850,86309,3938],{},[898,86311,8741],{"mathvariant":2334},[85773,86313,86314,86320],{},[3243,86315,86316,86318],{},[898,86317,13853],{},[1850,86319,3938],{},[1850,86321,3646],{},[902,86323,86324],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,86326,86327,86367,86407],{},[123,86328,86329],{},[883,86330,86332],{"className":86331},[886],[888,86333,86334],{"xmlns":890},[892,86335,86336,86364],{},[895,86337,86338,86340,86342,86344,86346,86348,86350,86352,86354],{},[898,86339,84543],{},[1701,86341,1792],{},[1850,86343,4062],{},[1701,86345,8061],{},[898,86347,13858],{},[1701,86349,1792],{},[1850,86351,4062],{},[898,86353,8741],{"mathvariant":2334},[85773,86355,86356,86362],{},[3243,86357,86358,86360],{},[898,86359,13853],{},[1850,86361,3938],{},[1850,86363,3646],{},[902,86365,86366],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,86368,86369],{},[883,86370,86372],{"className":86371},[886],[888,86373,86374],{"xmlns":890},[892,86375,86376,86404],{},[895,86377,86378,86380,86382,86384,86386,86388,86390,86392,86394],{},[898,86379,84543],{},[1701,86381,1792],{},[1850,86383,3938],{},[1701,86385,8061],{},[898,86387,13858],{},[1701,86389,1792],{},[1850,86391,6460],{},[898,86393,8741],{"mathvariant":2334},[85773,86395,86396,86402],{},[3243,86397,86398,86400],{},[898,86399,13853],{},[1850,86401,3938],{},[1850,86403,3646],{},[902,86405,86406],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,86408,86409],{},[883,86410,86412],{"className":86411},[886],[888,86413,86414],{"xmlns":890},[892,86415,86416,86444],{},[895,86417,86418,86420,86422,86424,86426,86428,86430,86432,86434],{},[898,86419,84543],{},[1701,86421,1792],{},[1850,86423,3646],{},[1701,86425,8061],{},[898,86427,13858],{},[1701,86429,1792],{},[1850,86431,8073],{},[898,86433,8741],{"mathvariant":2334},[85773,86435,86436,86442],{},[3243,86437,86438,86440],{},[898,86439,13853],{},[1850,86441,3938],{},[1850,86443,3646],{},[902,86445,86446],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,86448,86449],{},[614,86450,86451,86452,10536,86473,1715],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,86453,86455],{"className":86454},[886],[888,86456,86457],{"xmlns":890},[892,86458,86459,86471],{},[895,86460,86461,86463,86465,86467,86469],{},[1701,86462,1799],{"stretchy":1798},[898,86464,13853],{},[1701,86466,2012],{"separator":2011},[898,86468,13858],{},[1701,86470,1805],{"stretchy":1798},[902,86472,84669],{"encoding":904},[883,86474,86476],{"className":86475},[886],[888,86477,86478],{"xmlns":890},[892,86479,86480,86496],{},[895,86481,86482,86484,86486,86488,86490,86492,86494],{},[898,86483,84543],{},[1701,86485,1792],{},[1850,86487,4062],{},[1701,86489,2012],{"separator":2011},[1850,86491,3938],{},[1701,86493,2012],{"separator":2011},[1850,86495,3646],{},[902,86497,86498],{"encoding":904},"q = 1, 2, 3",[198,86500,86502],{"id":86501},"příklad-56","Příklad 5.6",[724,86504,80419,86505,1715],{},[883,86506,86508],{"className":86507},[886],[888,86509,86510],{"xmlns":890},[892,86511,86512,86528],{},[895,86513,86514,86516,86518,86520,86522,86524],{},[898,86515,1802],{},[1701,86517,1792],{},[1850,86519,3938],{},[898,86521,13853],{},[1701,86523,1703],{},[12179,86525,86526],{},[898,86527,13858],{},[902,86529,86530],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,86532,86534],{"className":86533},[886],[888,86535,86536],{"xmlns":890,"display":2252},[892,86537,86538,86580],{},[895,86539,86540,86542,86548,86550,86552,86554,86556,86558,86564,86566,86578],{},[898,86541,6909],{},[1845,86543,86544,86546],{},[898,86545,1680],{},[898,86547,13853],{},[1701,86549,1792],{},[1850,86551,3938],{},[1701,86553,2012],{"separator":2011},[9942,86555],{"width":9944},[898,86557,6909],{},[1845,86559,86560,86562],{},[898,86561,1680],{},[898,86563,13858],{},[1701,86565,1792],{},[3726,86567,86568,86570],{},[1850,86569,4062],{},[895,86571,86572,86574],{},[1850,86573,3938],{},[12179,86575,86576],{},[898,86577,13858],{},[898,86579,1715],{"mathvariant":2334},[902,86581,86582],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,86584,86586],{"className":86585},[886],[888,86587,86588],{"xmlns":890,"display":2252},[892,86589,86590,86654],{},[895,86591,86592,86594,86596,86598,86600,86602,86624,86626,86644,86646,86648,86652],{},[898,86593,6909],{},[898,86595,8068],{},[898,86597,5877],{},[898,86599,1661],{},[1701,86601,1792],{},[3726,86603,86604,86614],{},[895,86605,86606,86608],{},[898,86607,6909],{},[1845,86609,86610,86612],{},[898,86611,1680],{},[898,86613,13853],{},[895,86615,86616,86618],{},[898,86617,6909],{},[1845,86619,86620,86622],{},[898,86621,1680],{},[898,86623,13858],{},[1701,86625,1792],{},[3726,86627,86628,86630],{},[1850,86629,3938],{},[2363,86631,86632],{"scriptlevel":1852,"displaystyle":1798},[3726,86633,86634,86636],{},[1850,86635,4062],{},[895,86637,86638,86640],{},[1850,86639,3938],{},[12179,86641,86642],{},[898,86643,13858],{},[1701,86645,1792],{},[1850,86647,6460],{},[12179,86649,86650],{},[898,86651,13858],{},[898,86653,1715],{"mathvariant":2334},[902,86655,86656],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,86658,86659,86660,86703,86704,86743,86744,1715],{},"Například ",[883,86661,86663],{"className":86662},[886],[888,86664,86665],{"xmlns":890},[892,86666,86667,86700],{},[895,86668,86669,86671,86673,86675,86677,86679,86681,86683,86685,86687,86689,86691,86695,86697],{},[898,86670,6909],{},[898,86672,8068],{},[898,86674,5877],{},[898,86676,1661],{},[1701,86678,1799],{"stretchy":1798},[1850,86680,6460],{},[1701,86682,2012],{"separator":2011},[1850,86684,28239],{},[1701,86686,1805],{"stretchy":1798},[1701,86688,1792],{},[1850,86690,6460],{},[12179,86692,86693],{},[1850,86694,28239],{},[1701,86696,4067],{},[1850,86698,86699],{},"10,58",[902,86701,86702],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,86705,86707],{"className":86706},[886],[888,86708,86709],{"xmlns":890},[892,86710,86711,86740],{},[895,86712,86713,86715,86717,86719,86721,86723,86725,86727,86729,86731,86735,86737],{},[898,86714,1802],{},[1701,86716,1799],{"stretchy":1798},[1850,86718,6460],{},[1701,86720,2012],{"separator":2011},[1850,86722,28239],{},[1701,86724,1805],{"stretchy":1798},[1701,86726,1792],{},[1850,86728,9650],{},[1701,86730,1703],{},[12179,86732,86733],{},[1850,86734,28239],{},[1701,86736,4067],{},[1850,86738,86739],{},"10,646",[902,86741,86742],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,86745,86747],{"className":86746},[886],[888,86748,86749],{"xmlns":890},[892,86750,86751,86759],{},[895,86752,86753,86755],{},[1850,86754,6460],{},[12179,86756,86757],{},[1850,86758,28239],{},[902,86760,86761],{"encoding":904},"4\\sqrt{7}",[724,86763,86764,86765,86785],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,86766,86768],{"className":86767},[886],[888,86769,86770],{"xmlns":890},[892,86771,86772,86782],{},[895,86773,86774,86776,86778,86780],{},[898,86775,2312],{},[898,86777,13853],{},[1701,86779,1792],{},[1850,86781,3938],{},[902,86783,86784],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,86787,86789],{"className":86788},[886],[888,86790,86791],{"xmlns":890,"display":2252},[892,86792,86793,86842],{},[895,86794,86795,86797,86799,86801,86803,86805,86807,86809,86811,86813,86815,86817,86819,86821,86823,86825,86827,86829,86831,86835,86837,86839],{},[898,86796,2312],{},[898,86798,13858],{},[1701,86800,1792],{},[1701,86802,2317],{},[898,86804,6909],{},[898,86806,8068],{},[898,86808,5877],{},[898,86810,1661],{},[1701,86812,1799],{"stretchy":1798},[1850,86814,6460],{},[1701,86816,2012],{"separator":2011},[1850,86818,28239],{},[1701,86820,1805],{"stretchy":1798},[1701,86822,3408],{},[1850,86824,3938],{},[1701,86826,1792],{},[1701,86828,2317],{},[1850,86830,9650],{},[12179,86832,86833],{},[1850,86834,28239],{},[1701,86836,4067],{},[1701,86838,2317],{},[1850,86840,86841],{},"21,17.",[902,86843,86844],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,86846,86848],{"id":86847},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,86850,86851,86852,1343,86854,2633,86856,86858,86859,86862,86863,86866],{},"Hlavními faktory produkce jsou ",[38,86853,78660],{},[38,86855,78676],{},[38,86857,78692],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,86860,86861],{},"jednofaktorový"," (pouze práce) a ",[38,86864,86865],{},"dvoufaktorový"," (práce + kapitál) model.",[724,86868,86869,86870,86873,86874,86876,86877,86879,86880,30226,86883,86902,86903,86920,86921,86938,86939,86961,86962,8428,86981,1715],{},"V ",[38,86871,86872],{},"1F modelu"," se definuje ",[38,86875,14081],{}," (derivace produkce podle práce) a ",[38,86878,78595],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,86881,86882],{},"zákonu klesajících výnosů",[883,86884,86886],{"className":86885},[886],[888,86887,86888],{"xmlns":890},[892,86889,86890,86900],{},[895,86891,86892,86894],{},[898,86893,6909],{},[1845,86895,86896,86898],{},[898,86897,1680],{},[898,86899,13853],{},[902,86901,14101],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,86904,86906],{"className":86905},[886],[888,86907,86908],{"xmlns":890},[892,86909,86910,86918],{},[895,86911,86912],{},[1845,86913,86914,86916],{},[898,86915,13853],{},[1850,86917,1852],{},[902,86919,79304],{"encoding":904}," klesá a v bodě ",[883,86922,86924],{"className":86923},[886],[888,86925,86926],{"xmlns":890},[892,86927,86928,86936],{},[895,86929,86930],{},[1845,86931,86932,86934],{},[898,86933,13853],{},[1850,86935,4062],{},[902,86937,17266],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,86940,86941,86942],{},"princip maximalizace ",[883,86943,86945],{"className":86944},[886],[888,86946,86947],{"xmlns":890},[892,86948,86949,86959],{},[895,86950,86951,86953],{},[898,86952,1983],{},[1845,86954,86955,86957],{},[898,86956,1680],{},[898,86958,13853],{},[902,86960,78379],{"encoding":904},": v bodě maxima ",[883,86963,86965],{"className":86964},[886],[888,86966,86967],{"xmlns":890},[892,86968,86969,86979],{},[895,86970,86971,86973],{},[898,86972,1983],{},[1845,86974,86975,86977],{},[898,86976,1680],{},[898,86978,13853],{},[902,86980,78379],{"encoding":904},[883,86982,86984],{"className":86983},[886],[888,86985,86986],{"xmlns":890},[892,86987,86988,87008],{},[895,86989,86990,86992,86998,87000,87002],{},[898,86991,6909],{},[1845,86993,86994,86996],{},[898,86995,1680],{},[898,86997,13853],{},[1701,86999,1792],{},[898,87001,1983],{},[1845,87003,87004,87006],{},[898,87005,1680],{},[898,87007,13853],{},[902,87009,78409],{"encoding":904},[724,87011,87012,87013,87016,87017,4088,87020,87049,87050,87067,87068,87071,87072,87101,87102,87104,87105,12164,87135,87157],{},"Ve ",[38,87014,87015],{},"2F modelu"," se obvykle používají ",[38,87018,87019],{},"Cobb-Douglasovy funkce",[883,87021,87023],{"className":87022},[886],[888,87024,87025],{"xmlns":890},[892,87026,87027,87047],{},[895,87028,87029,87031,87033,87035,87041],{},[898,87030,1802],{},[1701,87032,1792],{},[898,87034,1983],{},[3243,87036,87037,87039],{},[898,87038,13853],{},[898,87040,207],{},[3243,87042,87043,87045],{},[898,87044,13858],{},[898,87046,3598],{},[902,87048,78476],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,87051,87053],{"className":87052},[886],[888,87054,87055],{"xmlns":890},[892,87056,87057,87065],{},[895,87058,87059,87061,87063],{},[898,87060,207],{},[1701,87062,1703],{},[898,87064,3598],{},[902,87066,78570],{"encoding":904}," rozlišujeme ",[38,87069,87070],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,87073,87075],{"className":87074},[886],[888,87076,87077],{"xmlns":890},[892,87078,87079,87099],{},[895,87080,87081,87083,87089,87091,87093],{},[898,87082,6909],{},[1845,87084,87085,87087],{},[898,87086,1680],{},[898,87088,13853],{},[1701,87090,2012],{"separator":2011},[898,87092,6909],{},[1845,87094,87095,87097],{},[898,87096,1680],{},[898,87098,13858],{},[902,87100,78507],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,87103,13836],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,87106,87108],{"className":87107},[886],[888,87109,87110],{"xmlns":890},[892,87111,87112,87132],{},[895,87113,87114,87116,87122,87124,87126],{},[898,87115,6909],{},[1845,87117,87118,87120],{},[898,87119,1680],{},[898,87121,13853],{},[898,87123,8741],{"mathvariant":2334},[898,87125,6909],{},[1845,87127,87128,87130],{},[898,87129,1680],{},[898,87131,13858],{},[902,87133,87134],{"encoding":904},"MP_L\u002FMP_K",[38,87136,87137,87138,1805],{},"mezní míra technické substituce (",[883,87139,87141],{"className":87140},[886],[888,87142,87143],{"xmlns":890},[892,87144,87145,87155],{},[895,87146,87147,87149,87151,87153],{},[898,87148,6909],{},[898,87150,8068],{},[898,87152,5877],{},[898,87154,1661],{},[902,87156,14655],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,87159,53869],{"id":53868},[152,87161,87162,87165,87168,87171,87174,87177,87180,87183,87186,87189,87192],{},[123,87163,87164],{},"Jaké jsou faktory produkce?",[123,87166,87167],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,87169,87170],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,87172,87173],{},"Co udává mezní produkt práce?",[123,87175,87176],{},"Co musí respektovat průběh křivky produkce?",[123,87178,87179],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,87181,87182],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,87184,87185],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,87187,87188],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,87190,87191],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,87193,87194],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,87196,87198],{"id":87197},"úlohy-51517","Úlohy 5.1–5.17",[198,87200,44474],{"id":44473},[724,87202,87203,87206,87207,87229,87230,1343,87250,1343,87270,87290],{},[38,87204,87205],{},"5.1"," Je dána produkce ",[883,87208,87210],{"className":87209},[886],[888,87211,87212],{"xmlns":890},[892,87213,87214,87226],{},[895,87215,87216,87218,87220,87222],{},[898,87217,1802],{},[1701,87219,1792],{},[1850,87221,3703],{},[12179,87223,87224],{},[898,87225,13853],{},[902,87227,87228],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,87231,87233],{"className":87232},[886],[888,87234,87235],{"xmlns":890},[892,87236,87237,87247],{},[895,87238,87239,87241,87243,87245],{},[898,87240,1802],{},[1701,87242,1799],{"stretchy":1798},[1850,87244,4062],{},[1701,87246,1805],{"stretchy":1798},[902,87248,87249],{"encoding":904},"Q(1)",[883,87251,87253],{"className":87252},[886],[888,87254,87255],{"xmlns":890},[892,87256,87257,87267],{},[895,87258,87259,87261,87263,87265],{},[898,87260,1802],{},[1701,87262,1799],{"stretchy":1798},[1850,87264,6460],{},[1701,87266,1805],{"stretchy":1798},[902,87268,87269],{"encoding":904},"Q(4)",[883,87271,87273],{"className":87272},[886],[888,87274,87275],{"xmlns":890},[892,87276,87277,87287],{},[895,87278,87279,87281,87283,87285],{},[898,87280,1802],{},[1701,87282,1799],{"stretchy":1798},[1850,87284,8073],{},[1701,87286,1805],{"stretchy":1798},[902,87288,87289],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,87292,87293,87206,87296,87332,87333,87346,87347,87366,87367,87393,87394,3856,87407,87420],{},[38,87294,87295],{},"5.2",[883,87297,87299],{"className":87298},[886],[888,87300,87301],{"xmlns":890},[892,87302,87303,87329],{},[895,87304,87305,87307,87309,87311,87313,87319,87321,87323],{},[898,87306,1802],{},[1701,87308,1792],{},[1701,87310,2317],{},[1850,87312,4033],{},[3243,87314,87315,87317],{},[898,87316,13853],{},[1850,87318,3646],{},[1701,87320,1703],{},[1850,87322,8073],{},[3243,87324,87325,87327],{},[898,87326,13853],{},[1850,87328,3938],{},[902,87330,87331],{"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 ",[883,87334,87336],{"className":87335},[886],[888,87337,87338],{"xmlns":890},[892,87339,87340,87344],{},[895,87341,87342],{},[898,87343,13853],{},[902,87345,13853],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,87348,87350],{"className":87349},[886],[888,87351,87352],{"xmlns":890},[892,87353,87354,87364],{},[895,87355,87356,87358],{},[898,87357,6909],{},[1845,87359,87360,87362],{},[898,87361,1680],{},[898,87363,13853],{},[902,87365,14101],{"encoding":904},". (f) Vypočtěte ",[883,87368,87370],{"className":87369},[886],[888,87371,87372],{"xmlns":890},[892,87373,87374,87390],{},[895,87375,87376,87378,87384,87386,87388],{},[898,87377,6909],{},[1845,87379,87380,87382],{},[898,87381,1680],{},[898,87383,13853],{},[1701,87385,1799],{"stretchy":1798},[1850,87387,3703],{},[1701,87389,1805],{"stretchy":1798},[902,87391,87392],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,87395,87397],{"className":87396},[886],[888,87398,87399],{"xmlns":890},[892,87400,87401,87405],{},[895,87402,87403],{},[1850,87404,3703],{},[902,87406,3703],{"encoding":904},[883,87408,87410],{"className":87409},[886],[888,87411,87412],{"xmlns":890},[892,87413,87414,87418],{},[895,87415,87416],{},[1850,87417,46308],{},[902,87419,46308],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,87422,87423,87426,87427,87449,87450,87478,87479,87510,87511,1715],{},[38,87424,87425],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,87428,87430],{"className":87429},[886],[888,87431,87432],{"xmlns":890},[892,87433,87434,87446],{},[895,87435,87436,87438,87440,87442],{},[898,87437,1802],{},[1701,87439,1792],{},[1850,87441,19162],{},[12179,87443,87444],{},[898,87445,13853],{},[902,87447,87448],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,87451,87453],{"className":87452},[886],[888,87454,87455],{"xmlns":890},[892,87456,87457,87475],{},[895,87458,87459,87461,87463,87465,87469,87471,87473],{},[898,87460,1802],{},[1701,87462,1792],{},[1850,87464,5151],{},[12179,87466,87467],{},[898,87468,13853],{},[1701,87470,2317],{},[1850,87472,6460],{},[898,87474,13853],{},[902,87476,87477],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,87480,87482],{"className":87481},[886],[888,87483,87484],{"xmlns":890},[892,87485,87486,87507],{},[895,87487,87488,87490,87492,87494,87496,87498,87501],{},[898,87489,1802],{},[1701,87491,1792],{},[1850,87493,7206],{},[898,87495,13853],{},[1701,87497,2317],{},[1850,87499,87500],{},"0,01",[3243,87502,87503,87505],{},[898,87504,13853],{},[1850,87506,3938],{},[902,87508,87509],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,87512,87514],{"className":87513},[886],[888,87515,87516],{"xmlns":890},[892,87517,87518,87544],{},[895,87519,87520,87522,87524,87526,87528,87534,87536,87538],{},[898,87521,1802],{},[1701,87523,1792],{},[1701,87525,2317],{},[1850,87527,71957],{},[3243,87529,87530,87532],{},[898,87531,13853],{},[1850,87533,3646],{},[1701,87535,1703],{},[1850,87537,8073],{},[3243,87539,87540,87542],{},[898,87541,13853],{},[1850,87543,3938],{},[902,87545,87546],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,87548,87549,87552,87553,6723,87572,75944,87589,1715],{},[38,87550,87551],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,87554,87556],{"className":87555},[886],[888,87557,87558],{"xmlns":890},[892,87559,87560,87570],{},[895,87561,87562,87564],{},[898,87563,1983],{},[1845,87565,87566,87568],{},[898,87567,1680],{},[898,87569,13853],{},[902,87571,78379],{"encoding":904},[883,87573,87575],{"className":87574},[886],[888,87576,87577],{"xmlns":890},[892,87578,87579,87587],{},[895,87580,87581],{},[1845,87582,87583,87585],{},[898,87584,13853],{},[1850,87586,1852],{},[902,87588,79304],{"encoding":904},[883,87590,87592],{"className":87591},[886],[888,87593,87594],{"xmlns":890},[892,87595,87596,87636],{},[895,87597,87598,87600,87606,87608,87614,87616,87618,87620,87626,87628,87634],{},[898,87599,1983],{},[1845,87601,87602,87604],{},[898,87603,1680],{},[898,87605,13853],{},[1701,87607,1799],{"stretchy":1798},[1845,87609,87610,87612],{},[898,87611,13853],{},[1850,87613,1852],{},[1701,87615,1805],{"stretchy":1798},[1701,87617,1792],{},[898,87619,6909],{},[1845,87621,87622,87624],{},[898,87623,1680],{},[898,87625,13853],{},[1701,87627,1799],{"stretchy":1798},[1845,87629,87630,87632],{},[898,87631,13853],{},[1850,87633,1852],{},[1701,87635,1805],{"stretchy":1798},[902,87637,87638],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,87640,87641,87206,87644,2020,87680,87693,87694,87713],{},[38,87642,87643],{},"5.5",[883,87645,87647],{"className":87646},[886],[888,87648,87649],{"xmlns":890},[892,87650,87651,87677],{},[895,87652,87653,87655,87657,87659,87661,87667,87669,87671],{},[898,87654,1802],{},[1701,87656,1792],{},[1701,87658,2317],{},[1850,87660,6930],{},[3243,87662,87663,87665],{},[898,87664,13853],{},[1850,87666,3646],{},[1701,87668,1703],{},[1850,87670,7592],{},[3243,87672,87673,87675],{},[898,87674,13853],{},[1850,87676,3938],{},[902,87678,87679],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,87681,87683],{"className":87682},[886],[888,87684,87685],{"xmlns":890},[892,87686,87687,87691],{},[895,87688,87689],{},[898,87690,13853],{},[902,87692,13853],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,87695,87697],{"className":87696},[886],[888,87698,87699],{"xmlns":890},[892,87700,87701,87711],{},[895,87702,87703,87705],{},[898,87704,1983],{},[1845,87706,87707,87709],{},[898,87708,1680],{},[898,87710,13853],{},[902,87712,78379],{"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.",[198,87715,87717],{"id":87716},"dvoufaktorový-model","Dvoufaktorový model",[724,87719,87720,87723,87724,87449,87750,87478,87792,1715],{},[38,87721,87722],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,87725,87727],{"className":87726},[886],[888,87728,87729],{"xmlns":890},[892,87730,87731,87747],{},[895,87732,87733,87735,87737,87739,87741],{},[898,87734,1802],{},[1701,87736,1792],{},[1850,87738,28239],{},[898,87740,13853],{},[3243,87742,87743,87745],{},[898,87744,13858],{},[1850,87746,3938],{},[902,87748,87749],{"encoding":904},"Q = 7 L K^{2}",[883,87751,87753],{"className":87752},[886],[888,87754,87755],{"xmlns":890},[892,87756,87757,87789],{},[895,87758,87759,87761,87763,87765,87777],{},[898,87760,1802],{},[1701,87762,1792],{},[1850,87764,7206],{},[3243,87766,87767,87769],{},[898,87768,13853],{},[895,87770,87771,87773,87775],{},[1850,87772,3938],{},[898,87774,8741],{"mathvariant":2334},[1850,87776,3646],{},[3243,87778,87779,87781],{},[898,87780,13858],{},[895,87782,87783,87785,87787],{},[1850,87784,4062],{},[898,87786,8741],{"mathvariant":2334},[1850,87788,3646],{},[902,87790,87791],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,87793,87795],{"className":87794},[886],[888,87796,87797],{"xmlns":890},[892,87798,87799,87831],{},[895,87800,87801,87803,87805,87807,87819],{},[898,87802,1802],{},[1701,87804,1792],{},[1850,87806,7790],{},[3243,87808,87809,87811],{},[898,87810,13853],{},[895,87812,87813,87815,87817],{},[1850,87814,3646],{},[898,87816,8741],{"mathvariant":2334},[1850,87818,4225],{},[3243,87820,87821,87823],{},[898,87822,13858],{},[895,87824,87825,87827,87829],{},[1850,87826,3938],{},[898,87828,8741],{"mathvariant":2334},[1850,87830,4225],{},[902,87832,87833],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,87835,87836,87206,87839,87881,87882,1343,87900,87919,87920,87937],{},[38,87837,87838],{},"5.7",[883,87840,87842],{"className":87841},[886],[888,87843,87844],{"xmlns":890},[892,87845,87846,87878],{},[895,87847,87848,87850,87852,87854,87866],{},[898,87849,1802],{},[1701,87851,1792],{},[1850,87853,3703],{},[3243,87855,87856,87858],{},[898,87857,13853],{},[895,87859,87860,87862,87864],{},[1850,87861,4062],{},[898,87863,8741],{"mathvariant":2334},[1850,87865,3938],{},[3243,87867,87868,87870],{},[898,87869,13858],{},[895,87871,87872,87874,87876],{},[1850,87873,4062],{},[898,87875,8741],{"mathvariant":2334},[1850,87877,3938],{},[902,87879,87880],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,87883,87885],{"className":87884},[886],[888,87886,87887],{"xmlns":890},[892,87888,87889,87897],{},[895,87890,87891,87893,87895],{},[898,87892,13853],{},[1701,87894,1792],{},[1850,87896,24186],{},[902,87898,87899],{"encoding":904},"L = 400",[883,87901,87903],{"className":87902},[886],[888,87904,87905],{"xmlns":890},[892,87906,87907,87916],{},[895,87908,87909,87911,87913],{},[898,87910,13858],{},[1701,87912,1792],{},[1850,87914,87915],{},"17576",[902,87917,87918],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,87921,87923],{"className":87922},[886],[888,87924,87925],{"xmlns":890},[892,87926,87927,87935],{},[895,87928,87929,87931,87933],{},[898,87930,13853],{},[1701,87932,2012],{"separator":2011},[898,87934,13858],{},[902,87936,82731],{"encoding":904}," zdvojnásobí.",[724,87939,87940,87943,87944,87881,87975,1343,87993,73330,88011,88041,88042,88072,88073,3856,88086,88100,88101,3856,88114,88127],{},[38,87941,87942],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,87945,87947],{"className":87946},[886],[888,87948,87949],{"xmlns":890},[892,87950,87951,87972],{},[895,87952,87953,87955,87957,87960,87966],{},[898,87954,1802],{},[1701,87956,1792],{},[1850,87958,87959],{},"1,01",[3243,87961,87962,87964],{},[898,87963,13853],{},[1850,87965,27768],{},[3243,87967,87968,87970],{},[898,87969,13858],{},[1850,87971,27827],{},[902,87973,87974],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,87976,87978],{"className":87977},[886],[888,87979,87980],{"xmlns":890},[892,87981,87982,87990],{},[895,87983,87984,87986,87988],{},[898,87985,13853],{},[1701,87987,1792],{},[1850,87989,34774],{},[902,87991,87992],{"encoding":904},"L = 250",[883,87994,87996],{"className":87995},[886],[888,87997,87998],{"xmlns":890},[892,87999,88000,88008],{},[895,88001,88002,88004,88006],{},[898,88003,13858],{},[1701,88005,1792],{},[1850,88007,6875],{},[902,88009,88010],{"encoding":904},"K = 1000",[883,88012,88014],{"className":88013},[886],[888,88015,88016],{"xmlns":890},[892,88017,88018,88038],{},[895,88019,88020,88022,88028,88030,88032,88034,88036],{},[898,88021,6909],{},[1845,88023,88024,88026],{},[898,88025,1680],{},[898,88027,13853],{},[1701,88029,1799],{"stretchy":1798},[1850,88031,34774],{},[1701,88033,2012],{"separator":2011},[1850,88035,6875],{},[1701,88037,1805],{"stretchy":1798},[902,88039,88040],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,88043,88045],{"className":88044},[886],[888,88046,88047],{"xmlns":890},[892,88048,88049,88069],{},[895,88050,88051,88053,88059,88061,88063,88065,88067],{},[898,88052,6909],{},[1845,88054,88055,88057],{},[898,88056,1680],{},[898,88058,13858],{},[1701,88060,1799],{"stretchy":1798},[1850,88062,34774],{},[1701,88064,2012],{"separator":2011},[1850,88066,6875],{},[1701,88068,1805],{"stretchy":1798},[902,88070,88071],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,88074,88076],{"className":88075},[886],[888,88077,88078],{"xmlns":890},[892,88079,88080,88084],{},[895,88081,88082],{},[898,88083,13853],{},[902,88085,13853],{"encoding":904},[883,88087,88089],{"className":88088},[886],[888,88090,88091],{"xmlns":890},[892,88092,88093,88098],{},[895,88094,88095],{},[1850,88096,88097],{},"260",[902,88099,88097],{"encoding":904}," a současném poklesu ",[883,88102,88104],{"className":88103},[886],[888,88105,88106],{"xmlns":890},[892,88107,88108,88112],{},[895,88109,88110],{},[898,88111,13858],{},[902,88113,13858],{"encoding":904},[883,88115,88117],{"className":88116},[886],[888,88118,88119],{"xmlns":890},[892,88120,88121,88125],{},[895,88122,88123],{},[1850,88124,19243],{},[902,88126,19243],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,88129,88130,88133,88134,1715],{},[38,88131,88132],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,88135,88137],{"className":88136},[886],[888,88138,88139],{"xmlns":890},[892,88140,88141,88161],{},[895,88142,88143,88145,88147,88149,88155],{},[898,88144,1802],{},[1701,88146,1792],{},[1850,88148,3703],{},[3243,88150,88151,88153],{},[898,88152,13853],{},[1850,88154,71957],{},[3243,88156,88157,88159],{},[898,88158,13858],{},[1850,88160,3684],{},[902,88162,88163],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,88165,88166,88169,88170,84327,88193,14450,88206,1646,88256,2506],{},[38,88167,88168],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,88171,88173],{"className":88172},[886],[888,88174,88175],{"xmlns":890},[892,88176,88177,88191],{},[895,88178,88179,88181,88183,88185,88187,88189],{},[898,88180,1802],{},[1701,88182,1799],{"stretchy":1798},[898,88184,13853],{},[1701,88186,2012],{"separator":2011},[898,88188,13858],{},[1701,88190,1805],{"stretchy":1798},[902,88192,14054],{"encoding":904},[883,88194,88196],{"className":88195},[886],[888,88197,88198],{"xmlns":890},[892,88199,88200,88204],{},[895,88201,88202],{},[898,88203,40890],{},[902,88205,40890],{"encoding":904},[883,88207,88209],{"className":88208},[886],[888,88210,88211],{"xmlns":890},[892,88212,88213,88253],{},[895,88214,88215,88217,88225,88227,88229,88237,88239,88241,88243,88245,88247,88249,88251],{},[898,88216,13853],{},[2287,88218,88219,88221,88223],{},[898,88220,1802],{},[898,88222,13853],{},[1701,88224,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,88226,1703],{},[898,88228,13858],{},[2287,88230,88231,88233,88235],{},[898,88232,1802],{},[898,88234,13858],{},[1701,88236,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,88238,1792],{},[898,88240,40890],{},[898,88242,1802],{},[1701,88244,1799],{"stretchy":1798},[898,88246,13853],{},[1701,88248,2012],{"separator":2011},[898,88250,13858],{},[1701,88252,1805],{"stretchy":1798},[902,88254,88255],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,88257,84302],{},[724,88259,88260,88263],{},[38,88261,88262],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,88265,88266,87206,88269,88309,88310,1343,88332,1343,88354,88376],{},[38,88267,88268],{},"5.12",[883,88270,88272],{"className":88271},[886],[888,88273,88274],{"xmlns":890},[892,88275,88276,88306],{},[895,88277,88278,88280,88282,88294],{},[898,88279,1802],{},[1701,88281,1792],{},[3243,88283,88284,88286],{},[898,88285,13853],{},[895,88287,88288,88290,88292],{},[1850,88289,4062],{},[898,88291,8741],{"mathvariant":2334},[1850,88293,3646],{},[3243,88295,88296,88298],{},[898,88297,13858],{},[895,88299,88300,88302,88304],{},[1850,88301,4062],{},[898,88303,8741],{"mathvariant":2334},[1850,88305,6460],{},[902,88307,88308],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,88311,88313],{"className":88312},[886],[888,88314,88315],{"xmlns":890},[892,88316,88317,88329],{},[895,88318,88319,88325,88327],{},[1845,88320,88321,88323],{},[898,88322,84543],{},[1850,88324,1852],{},[1701,88326,1792],{},[1850,88328,4062],{},[902,88330,88331],{"encoding":904},"q_0 = 1",[883,88333,88335],{"className":88334},[886],[888,88336,88337],{"xmlns":890},[892,88338,88339,88351],{},[895,88340,88341,88347,88349],{},[1845,88342,88343,88345],{},[898,88344,84543],{},[1850,88346,4062],{},[1701,88348,1792],{},[1850,88350,3938],{},[902,88352,88353],{"encoding":904},"q_1 = 2",[883,88355,88357],{"className":88356},[886],[888,88358,88359],{"xmlns":890},[892,88360,88361,88373],{},[895,88362,88363,88369,88371],{},[1845,88364,88365,88367],{},[898,88366,84543],{},[1850,88368,3938],{},[1701,88370,1792],{},[1850,88372,3646],{},[902,88374,88375],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,88378,88379,87206,88382,88422,88423,1343,88451,1343,88479,1343,88507,1343,88536,1343,88565,1343,88594,1343,88623,1343,88652,1715],{},[38,88380,88381],{},"5.13",[883,88383,88385],{"className":88384},[886],[888,88386,88387],{"xmlns":890},[892,88388,88389,88419],{},[895,88390,88391,88393,88395,88407],{},[898,88392,1802],{},[1701,88394,1792],{},[3243,88396,88397,88399],{},[898,88398,13853],{},[895,88400,88401,88403,88405],{},[1850,88402,4062],{},[898,88404,8741],{"mathvariant":2334},[1850,88406,3646],{},[3243,88408,88409,88411],{},[898,88410,13858],{},[895,88412,88413,88415,88417],{},[1850,88414,4062],{},[898,88416,8741],{"mathvariant":2334},[1850,88418,3938],{},[902,88420,88421],{"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): ",[883,88424,88426],{"className":88425},[886],[888,88427,88428],{"xmlns":890},[892,88429,88430,88448],{},[895,88431,88432,88438,88440,88442,88444,88446],{},[1845,88433,88434,88436],{},[898,88435,1983],{},[1850,88437,4062],{},[1701,88439,2036],{"stretchy":1798},[1850,88441,4062],{},[1701,88443,12487],{"separator":2011},[1850,88445,4062],{},[1701,88447,2053],{"stretchy":1798},[902,88449,88450],{"encoding":904},"A_1[1; 1]",[883,88452,88454],{"className":88453},[886],[888,88455,88456],{"xmlns":890},[892,88457,88458,88476],{},[895,88459,88460,88466,88468,88470,88472,88474],{},[1845,88461,88462,88464],{},[898,88463,1983],{},[1850,88465,3938],{},[1701,88467,2036],{"stretchy":1798},[1850,88469,4062],{},[1701,88471,12487],{"separator":2011},[1850,88473,9650],{},[1701,88475,2053],{"stretchy":1798},[902,88477,88478],{"encoding":904},"A_2[1; 8]",[883,88480,88482],{"className":88481},[886],[888,88483,88484],{"xmlns":890},[892,88485,88486,88504],{},[895,88487,88488,88494,88496,88498,88500,88502],{},[1845,88489,88490,88492],{},[898,88491,1983],{},[1850,88493,3646],{},[1701,88495,2036],{"stretchy":1798},[1850,88497,4062],{},[1701,88499,12487],{"separator":2011},[1850,88501,70343],{},[1701,88503,2053],{"stretchy":1798},[902,88505,88506],{"encoding":904},"A_3[1; 27]",[883,88508,88510],{"className":88509},[886],[888,88511,88512],{"xmlns":890},[892,88513,88514,88533],{},[895,88515,88516,88522,88524,88526,88528,88531],{},[1845,88517,88518,88520],{},[898,88519,1983],{},[1850,88521,6460],{},[1701,88523,2036],{"stretchy":1798},[1850,88525,3938],{},[1701,88527,12487],{"separator":2011},[1850,88529,88530],{},"0,353",[1701,88532,2053],{"stretchy":1798},[902,88534,88535],{"encoding":904},"A_4[2; 0{,}353]",[883,88537,88539],{"className":88538},[886],[888,88540,88541],{"xmlns":890},[892,88542,88543,88562],{},[895,88544,88545,88551,88553,88555,88557,88560],{},[1845,88546,88547,88549],{},[898,88548,1983],{},[1850,88550,4225],{},[1701,88552,2036],{"stretchy":1798},[1850,88554,3938],{},[1701,88556,12487],{"separator":2011},[1850,88558,88559],{},"2,828",[1701,88561,2053],{"stretchy":1798},[902,88563,88564],{"encoding":904},"A_5[2; 2{,}828]",[883,88566,88568],{"className":88567},[886],[888,88569,88570],{"xmlns":890},[892,88571,88572,88591],{},[895,88573,88574,88580,88582,88584,88586,88589],{},[1845,88575,88576,88578],{},[898,88577,1983],{},[1850,88579,6352],{},[1701,88581,2036],{"stretchy":1798},[1850,88583,3938],{},[1701,88585,12487],{"separator":2011},[1850,88587,88588],{},"9,545",[1701,88590,2053],{"stretchy":1798},[902,88592,88593],{"encoding":904},"A_6[2; 9{,}545]",[883,88595,88597],{"className":88596},[886],[888,88598,88599],{"xmlns":890},[892,88600,88601,88620],{},[895,88602,88603,88609,88611,88613,88615,88618],{},[1845,88604,88605,88607],{},[898,88606,1983],{},[1850,88608,28239],{},[1701,88610,2036],{"stretchy":1798},[1850,88612,68305],{},[1701,88614,12487],{"separator":2011},[1850,88616,88617],{},"0,544",[1701,88619,2053],{"stretchy":1798},[902,88621,88622],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,88624,88626],{"className":88625},[886],[888,88627,88628],{"xmlns":890},[892,88629,88630,88649],{},[895,88631,88632,88638,88640,88642,88644,88647],{},[1845,88633,88634,88636],{},[898,88635,1983],{},[1850,88637,9650],{},[1701,88639,2036],{"stretchy":1798},[1850,88641,68305],{},[1701,88643,12487],{"separator":2011},[1850,88645,88646],{},"14,696",[1701,88648,2053],{"stretchy":1798},[902,88650,88651],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,88653,88655],{"className":88654},[886],[888,88656,88657],{"xmlns":890},[892,88658,88659,88677],{},[895,88660,88661,88667,88669,88671,88673,88675],{},[1845,88662,88663,88665],{},[898,88664,1983],{},[1850,88666,8073],{},[1701,88668,2036],{"stretchy":1798},[1850,88670,3938],{},[1701,88672,12487],{"separator":2011},[1850,88674,4225],{},[1701,88676,2053],{"stretchy":1798},[902,88678,88679],{"encoding":904},"A_9[2; 5]",[724,88681,88682,88685],{},[38,88683,88684],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,88687,88688,88691,88692,88722,88723,88736,88737,88750,88751,73063,88770,88789,88790,1715],{},[38,88689,88690],{},"5.15"," Produkce firmy je dána vztahem ",[883,88693,88695],{"className":88694},[886],[888,88696,88697],{"xmlns":890},[892,88698,88699,88719],{},[895,88700,88701,88703,88705,88707,88713],{},[898,88702,1802],{},[1701,88704,1792],{},[1850,88706,3938],{},[3243,88708,88709,88711],{},[898,88710,13853],{},[1850,88712,3684],{},[3243,88714,88715,88717],{},[898,88716,13858],{},[1850,88718,27827],{},[902,88720,88721],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,88724,88726],{"className":88725},[886],[888,88727,88728],{"xmlns":890},[892,88729,88730,88734],{},[895,88731,88732],{},[1850,88733,5158],{},[902,88735,5158],{"encoding":904}," pracovníků a disponuje-li ",[883,88738,88740],{"className":88739},[886],[888,88741,88742],{"xmlns":890},[892,88743,88744,88748],{},[895,88745,88746],{},[1850,88747,68181],{},[902,88749,68181],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,88752,88754],{"className":88753},[886],[888,88755,88756],{"xmlns":890},[892,88757,88758,88768],{},[895,88759,88760,88762,88764,88766],{},[898,88761,6909],{},[898,88763,8068],{},[898,88765,5877],{},[898,88767,1661],{},[902,88769,14655],{"encoding":904},[883,88771,88773],{"className":88772},[886],[888,88774,88775],{"xmlns":890},[892,88776,88777,88787],{},[895,88778,88779,88781,88783,88785],{},[898,88780,6909],{},[898,88782,8068],{},[898,88784,5877],{},[898,88786,1661],{},[902,88788,14655],{"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 ",[883,88791,88793],{"className":88792},[886],[888,88794,88795],{"xmlns":890},[892,88796,88797,88802],{},[895,88798,88799],{},[1850,88800,88801],{},"95",[902,88803,88801],{"encoding":904},[724,88805,88806,87206,88809,74737,88841,88860,88861,88874,88875,88888,88889,88902],{},[38,88807,88808],{},"5.16",[883,88810,88812],{"className":88811},[886],[888,88813,88814],{"xmlns":890},[892,88815,88816,88838],{},[895,88817,88818,88820,88822,88828,88830,88832],{},[898,88819,1802],{},[1701,88821,1792],{},[3243,88823,88824,88826],{},[898,88825,13858],{},[1850,88827,3938],{},[1701,88829,1703],{},[1850,88831,3938],{},[3243,88833,88834,88836],{},[898,88835,13853],{},[1850,88837,3938],{},[902,88839,88840],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,88842,88844],{"className":88843},[886],[888,88845,88846],{"xmlns":890},[892,88847,88848,88858],{},[895,88849,88850,88852,88854,88856],{},[898,88851,6909],{},[898,88853,8068],{},[898,88855,5877],{},[898,88857,1661],{},[902,88859,14655],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,88862,88864],{"className":88863},[886],[888,88865,88866],{"xmlns":890},[892,88867,88868,88872],{},[895,88869,88870],{},[1850,88871,7206],{},[902,88873,7206],{"encoding":904}," pracovníky a ",[883,88876,88878],{"className":88877},[886],[888,88879,88880],{"xmlns":890},[892,88881,88882,88886],{},[895,88883,88884],{},[1850,88885,81363],{},[902,88887,81363],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,88890,88892],{"className":88891},[886],[888,88893,88894],{"xmlns":890},[892,88895,88896,88900],{},[895,88897,88898],{},[1850,88899,50694],{},[902,88901,50694],{"encoding":904}," jednotek.",[724,88904,88905,88908,88909,14450,88939,1715],{},[38,88906,88907],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,88910,88912],{"className":88911},[886],[888,88913,88914],{"xmlns":890},[892,88915,88916,88936],{},[895,88917,88918,88920,88922,88924,88930],{},[898,88919,1802],{},[1701,88921,1792],{},[898,88923,1983],{},[3243,88925,88926,88928],{},[898,88927,13853],{},[898,88929,207],{},[3243,88931,88932,88934],{},[898,88933,13858],{},[898,88935,3598],{},[902,88937,88938],{"encoding":904},"Q = A L^{a} K^{b}",[883,88940,88942],{"className":88941},[886],[888,88943,88944],{"xmlns":890},[892,88945,88946,88976],{},[895,88947,88948,88950,88952,88954,88956,88958,88966,88968],{},[898,88949,6909],{},[898,88951,8068],{},[898,88953,5877],{},[898,88955,1661],{},[1701,88957,1792],{},[2363,88959,88960],{"scriptlevel":1852,"displaystyle":1798},[3726,88961,88962,88964],{},[898,88963,207],{},[898,88965,3598],{},[1701,88967,3408],{},[2363,88969,88970],{"scriptlevel":1852,"displaystyle":1798},[3726,88971,88972,88974],{},[898,88973,13858],{},[898,88975,13853],{},[902,88977,88978],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,88980,5578],{"id":5577},[120,88982,88983,89016,89043,89052,89102,89133,89186,89209,89264,89337,89415,89458,89490,89523,89564,89636,89697,89763,89780,89853,89919,89971,90027,90061,90104],{},[123,88984,88985,88988,88989,40926,89002,89015],{},[38,88986,88987],{},"Faktory (vstupy) produkce:"," práce ",[883,88990,88992],{"className":88991},[886],[888,88993,88994],{"xmlns":890},[892,88995,88996,89000],{},[895,88997,88998],{},[898,88999,13853],{},[902,89001,13853],{"encoding":904},[883,89003,89005],{"className":89004},[886],[888,89006,89007],{"xmlns":890},[892,89008,89009,89013],{},[895,89010,89011],{},[898,89012,13858],{},[902,89014,13858],{"encoding":904},", půda.",[123,89017,89018,2979,89020,1715],{},[38,89019,44474],{},[883,89021,89023],{"className":89022},[886],[888,89024,89025],{"xmlns":890},[892,89026,89027,89041],{},[895,89028,89029,89031,89033,89035,89037,89039],{},[898,89030,1802],{},[1701,89032,1792],{},[898,89034,1802],{},[1701,89036,1799],{"stretchy":1798},[898,89038,13853],{},[1701,89040,1805],{"stretchy":1798},[902,89042,78290],{"encoding":904},[123,89044,89045,1646,89047,1738,89050,1715],{},[38,89046,859],{},[614,89048,89049],{},"production function",[38,89051,78793],{},[123,89053,89054,4088,89056,1715],{},[38,89055,78839],{},[883,89057,89059],{"className":89058},[886],[888,89060,89061],{"xmlns":890},[892,89062,89063,89099],{},[895,89064,89065,89067,89073,89075,89077,89079,89081,89083,89085,89087,89093,89095,89097],{},[898,89066,6909],{},[1845,89068,89069,89071],{},[898,89070,1680],{},[898,89072,13853],{},[1701,89074,1792],{},[898,89076,2312],{},[898,89078,1802],{},[898,89080,8741],{"mathvariant":2334},[898,89082,2312],{},[898,89084,13853],{},[1701,89086,1792],{},[3243,89088,89089,89091],{},[898,89090,1802],{},[1701,89092,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,89094,1799],{"stretchy":1798},[898,89096,13853],{},[1701,89098,1805],{"stretchy":1798},[902,89100,89101],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,89103,89104,4088,89106,1715],{},[38,89105,79774],{},[883,89107,89109],{"className":89108},[886],[888,89110,89111],{"xmlns":890},[892,89112,89113,89131],{},[895,89114,89115,89117,89123,89125,89127,89129],{},[898,89116,1983],{},[1845,89118,89119,89121],{},[898,89120,1680],{},[898,89122,13853],{},[1701,89124,1792],{},[898,89126,1802],{},[898,89128,8741],{"mathvariant":2334},[898,89130,13853],{},[902,89132,78358],{"encoding":904},[123,89134,89135,89137,89138,14450,89155,1715],{},[38,89136,79261],{}," — od určitého ",[883,89139,89141],{"className":89140},[886],[888,89142,89143],{"xmlns":890},[892,89144,89145,89153],{},[895,89146,89147],{},[1845,89148,89149,89151],{},[898,89150,13853],{},[1850,89152,1852],{},[902,89154,79304],{"encoding":904},[883,89156,89158],{"className":89157},[886],[888,89159,89160],{"xmlns":890},[892,89161,89162,89184],{},[895,89163,89164,89174,89176,89178,89180,89182],{},[3243,89165,89166,89168],{},[898,89167,1802],{},[895,89169,89170,89172],{},[1701,89171,4783],{"mathvariant":2334},[1701,89173,4783],{"mathvariant":2334},[1701,89175,1799],{"stretchy":1798},[898,89177,13853],{},[1701,89179,1805],{"stretchy":1798},[1701,89181,7530],{},[1850,89183,1852],{},[902,89185,79450],{"encoding":904},[123,89187,89188,4088,89191,89208],{},[38,89189,89190],{},"Inflexní bod",[883,89192,89194],{"className":89193},[886],[888,89195,89196],{"xmlns":890},[892,89197,89198,89206],{},[895,89199,89200],{},[1845,89201,89202,89204],{},[898,89203,13853],{},[1850,89205,1852],{},[902,89207,79304],{"encoding":904}," — přechod z konvexity do konkavity.",[123,89210,89211,4088,89214,2979,89231,1715],{},[38,89212,89213],{},"Bod maxima produkce",[883,89215,89217],{"className":89216},[886],[888,89218,89219],{"xmlns":890},[892,89220,89221,89229],{},[895,89222,89223],{},[1845,89224,89225,89227],{},[898,89226,13853],{},[1850,89228,4062],{},[902,89230,17266],{"encoding":904},[883,89232,89234],{"className":89233},[886],[888,89235,89236],{"xmlns":890},[892,89237,89238,89262],{},[895,89239,89240,89242,89248,89250,89256,89258,89260],{},[898,89241,6909],{},[1845,89243,89244,89246],{},[898,89245,1680],{},[898,89247,13853],{},[1701,89249,1799],{"stretchy":1798},[1845,89251,89252,89254],{},[898,89253,13853],{},[1850,89255,4062],{},[1701,89257,1805],{"stretchy":1798},[1701,89259,1792],{},[1850,89261,1852],{},[902,89263,79523],{"encoding":904},[123,89265,89266,89288,89289,14450,89308,1715],{},[38,89267,89268,89269],{},"Princip maximalizace ",[883,89270,89272],{"className":89271},[886],[888,89273,89274],{"xmlns":890},[892,89275,89276,89286],{},[895,89277,89278,89280],{},[898,89279,1983],{},[1845,89281,89282,89284],{},[898,89283,1680],{},[898,89285,13853],{},[902,89287,78379],{"encoding":904}," — v bodě maxima ",[883,89290,89292],{"className":89291},[886],[888,89293,89294],{"xmlns":890},[892,89295,89296,89306],{},[895,89297,89298,89300],{},[898,89299,1983],{},[1845,89301,89302,89304],{},[898,89303,1680],{},[898,89305,13853],{},[902,89307,78379],{"encoding":904},[883,89309,89311],{"className":89310},[886],[888,89312,89313],{"xmlns":890},[892,89314,89315,89335],{},[895,89316,89317,89319,89325,89327,89329],{},[898,89318,6909],{},[1845,89320,89321,89323],{},[898,89322,1680],{},[898,89324,13853],{},[1701,89326,1792],{},[898,89328,1983],{},[1845,89330,89331,89333],{},[898,89332,1680],{},[898,89334,13853],{},[902,89336,78409],{"encoding":904},[123,89338,89339,4088,89342,1343,89381,1343,89398,1715],{},[38,89340,89341],{},"Polynomiální produkční funkce",[883,89343,89345],{"className":89344},[886],[888,89346,89347],{"xmlns":890},[892,89348,89349,89379],{},[895,89350,89351,89353,89355,89357,89359,89361,89363,89369,89371,89373],{},[898,89352,1802],{},[1701,89354,1799],{"stretchy":1798},[898,89356,13853],{},[1701,89358,1805],{"stretchy":1798},[1701,89360,1792],{},[898,89362,207],{},[3243,89364,89365,89367],{},[898,89366,13853],{},[1850,89368,3646],{},[1701,89370,1703],{},[898,89372,3598],{},[3243,89374,89375,89377],{},[898,89376,13853],{},[1850,89378,3938],{},[902,89380,79641],{"encoding":904},[883,89382,89384],{"className":89383},[886],[888,89385,89386],{"xmlns":890},[892,89387,89388,89396],{},[895,89389,89390,89392,89394],{},[898,89391,207],{},[1701,89393,7530],{},[1850,89395,1852],{},[902,89397,47105],{"encoding":904},[883,89399,89401],{"className":89400},[886],[888,89402,89403],{"xmlns":890},[892,89404,89405,89413],{},[895,89406,89407,89409,89411],{},[898,89408,3598],{},[1701,89410,7491],{},[1850,89412,1852],{},[902,89414,22860],{"encoding":904},[123,89416,89417,4088,89420,1715],{},[38,89418,89419],{},"Diferenciál produkce",[883,89421,89423],{"className":89422},[886],[888,89424,89425],{"xmlns":890},[892,89426,89427,89455],{},[895,89428,89429,89431,89433,89435,89437,89439,89441,89443,89449,89451,89453],{},[898,89430,4708],{"mathvariant":2334},[898,89432,1802],{},[1701,89434,4067],{},[898,89436,2312],{},[898,89438,1802],{},[1701,89440,1792],{},[898,89442,6909],{},[1845,89444,89445,89447],{},[898,89446,1680],{},[898,89448,13853],{},[1939,89450,1941],{},[898,89452,2312],{},[898,89454,13853],{},[902,89456,89457],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,89459,89460,2979,89462,1715],{},[38,89461,87717],{},[883,89463,89465],{"className":89464},[886],[888,89466,89467],{"xmlns":890},[892,89468,89469,89487],{},[895,89470,89471,89473,89475,89477,89479,89481,89483,89485],{},[898,89472,1802],{},[1701,89474,1792],{},[898,89476,1802],{},[1701,89478,1799],{"stretchy":1798},[898,89480,13853],{},[1701,89482,2012],{"separator":2011},[898,89484,13858],{},[1701,89486,1805],{"stretchy":1798},[902,89488,89489],{"encoding":904},"Q = Q(L, K)",[123,89491,89492,2979,89494,1715],{},[38,89493,81811],{},[883,89495,89497],{"className":89496},[886],[888,89498,89499],{"xmlns":890},[892,89500,89501,89521],{},[895,89502,89503,89505,89507,89509,89515],{},[898,89504,1802],{},[1701,89506,1792],{},[898,89508,1983],{},[3243,89510,89511,89513],{},[898,89512,13853],{},[898,89514,207],{},[3243,89516,89517,89519],{},[898,89518,13858],{},[898,89520,3598],{},[902,89522,78476],{"encoding":904},[123,89524,89525,2979,89528,89563],{},[38,89526,89527],{},"Ryzí Cobb-Douglas",[883,89529,89531],{"className":89530},[886],[888,89532,89533],{"xmlns":890},[892,89534,89535,89561],{},[895,89536,89537,89539,89541,89543,89549],{},[898,89538,1802],{},[1701,89540,1792],{},[898,89542,1983],{},[3243,89544,89545,89547],{},[898,89546,13853],{},[898,89548,207],{},[3243,89550,89551,89553],{},[898,89552,13858],{},[895,89554,89555,89557,89559],{},[1850,89556,4062],{},[1701,89558,2317],{},[898,89560,207],{},[902,89562,82638],{"encoding":904}," (konstantní výnosy).",[123,89565,89566,2979,89568,1715],{},[38,89567,83354],{},[883,89569,89571],{"className":89570},[886],[888,89572,89573],{"xmlns":890},[892,89574,89575,89633],{},[895,89576,89577,89579,89581,89583,89585,89587,89589,89591,89593,89595,89605,89607,89609,89619],{},[898,89578,1802],{},[1701,89580,1792],{},[898,89582,1983],{},[1701,89584,2036],{"stretchy":1798},[1701,89586,1799],{"stretchy":1798},[1850,89588,4062],{},[1701,89590,2317],{},[898,89592,207],{},[1701,89594,1805],{"stretchy":1798},[3243,89596,89597,89599],{},[898,89598,13853],{},[895,89600,89601,89603],{},[1701,89602,2317],{},[898,89604,3598],{},[1701,89606,1703],{},[898,89608,207],{},[3243,89610,89611,89613],{},[898,89612,13858],{},[895,89614,89615,89617],{},[1701,89616,2317],{},[898,89618,3598],{},[3243,89620,89621,89623],{},[1701,89622,2053],{"stretchy":1798},[895,89624,89625,89627,89629,89631],{},[1701,89626,2317],{},[1850,89628,4062],{},[898,89630,8741],{"mathvariant":2334},[898,89632,3598],{},[902,89634,89635],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,89637,89638,1646,89641,1738,89663,1646,89666,89696],{},[38,89639,89640],{},"Lineární",[883,89642,89644],{"className":89643},[886],[888,89645,89646],{"xmlns":890},[892,89647,89648,89660],{},[895,89649,89650,89652,89654,89656,89658],{},[898,89651,207],{},[898,89653,13853],{},[1701,89655,1703],{},[898,89657,3598],{},[898,89659,13858],{},[902,89661,89662],{"encoding":904},"aL + bK",[38,89664,89665],{},"Leontiefova",[883,89667,89669],{"className":89668},[886],[888,89670,89671],{"xmlns":890},[892,89672,89673,89693],{},[895,89674,89675,89677,89679,89681,89683,89685,89687,89689,89691],{},[898,89676,83582],{},[1701,89678,59946],{},[1701,89680,1799],{"stretchy":1798},[898,89682,207],{},[898,89684,13853],{},[1701,89686,2012],{"separator":2011},[898,89688,3598],{},[898,89690,13858],{},[1701,89692,1805],{"stretchy":1798},[902,89694,89695],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,89698,89699,2979,89715,1715],{},[38,89700,89701,89702],{},"Homogenita stupně ",[883,89703,89705],{"className":89704},[886],[888,89706,89707],{"xmlns":890},[892,89708,89709,89713],{},[895,89710,89711],{},[898,89712,40890],{},[902,89714,40890],{"encoding":904},[883,89716,89718],{"className":89717},[886],[888,89719,89720],{"xmlns":890},[892,89721,89722,89760],{},[895,89723,89724,89726,89728,89730,89732,89734,89736,89738,89740,89742,89748,89750,89752,89754,89756,89758],{},[898,89725,1802],{},[1701,89727,1799],{"stretchy":1798},[898,89729,16096],{},[898,89731,13853],{},[1701,89733,2012],{"separator":2011},[898,89735,16096],{},[898,89737,13858],{},[1701,89739,1805],{"stretchy":1798},[1701,89741,1792],{},[3243,89743,89744,89746],{},[898,89745,16096],{},[898,89747,40890],{},[898,89749,1802],{},[1701,89751,1799],{"stretchy":1798},[898,89753,13853],{},[1701,89755,2012],{"separator":2011},[898,89757,13858],{},[1701,89759,1805],{"stretchy":1798},[902,89761,89762],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,89764,89765,82736],{},[38,89766,82669,89767],{},[883,89768,89770],{"className":89769},[886],[888,89771,89772],{"xmlns":890},[892,89773,89774,89778],{},[895,89775,89776],{},[898,89777,1983],{},[902,89779,1983],{"encoding":904},[123,89781,89782,89784,89785,89807,89808,89830,89831,2506],{},[38,89783,82170],{}," — konstantní (",[883,89786,89788],{"className":89787},[886],[888,89789,89790],{"xmlns":890},[892,89791,89792,89804],{},[895,89793,89794,89796,89798,89800,89802],{},[898,89795,207],{},[1701,89797,1703],{},[898,89799,3598],{},[1701,89801,1792],{},[1850,89803,4062],{},[902,89805,89806],{"encoding":904},"a+b=1","), rostoucí (",[883,89809,89811],{"className":89810},[886],[888,89812,89813],{"xmlns":890},[892,89814,89815,89827],{},[895,89816,89817,89819,89821,89823,89825],{},[898,89818,207],{},[1701,89820,1703],{},[898,89822,3598],{},[1701,89824,7491],{},[1850,89826,4062],{},[902,89828,89829],{"encoding":904},"a+b>1","), klesající (",[883,89832,89834],{"className":89833},[886],[888,89835,89836],{"xmlns":890},[892,89837,89838,89850],{},[895,89839,89840,89842,89844,89846,89848],{},[898,89841,207],{},[1701,89843,1703],{},[898,89845,3598],{},[1701,89847,7530],{},[1850,89849,4062],{},[902,89851,89852],{"encoding":904},"a+b\u003C1",[123,89854,89855,4088,89857,1343,89887,4088,89889,1715],{},[38,89856,78839],{},[883,89858,89860],{"className":89859},[886],[888,89861,89862],{"xmlns":890},[892,89863,89864,89884],{},[895,89865,89866,89868,89874,89876],{},[898,89867,6909],{},[1845,89869,89870,89872],{},[898,89871,1680],{},[898,89873,13853],{},[1701,89875,1792],{},[2287,89877,89878,89880,89882],{},[898,89879,1802],{},[898,89881,13853],{},[1701,89883,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,89885,89886],{"encoding":904},"MP_L = Q'_L",[38,89888,81743],{},[883,89890,89892],{"className":89891},[886],[888,89893,89894],{"xmlns":890},[892,89895,89896,89916],{},[895,89897,89898,89900,89906,89908],{},[898,89899,6909],{},[1845,89901,89902,89904],{},[898,89903,1680],{},[898,89905,13858],{},[1701,89907,1792],{},[2287,89909,89910,89912,89914],{},[898,89911,1802],{},[898,89913,13858],{},[1701,89915,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,89917,89918],{"encoding":904},"MP_K = Q'_K",[123,89920,89921,4088,89923,1715],{},[38,89922,83957],{},[883,89924,89926],{"className":89925},[886],[888,89927,89928],{"xmlns":890},[892,89929,89930,89968],{},[895,89931,89932,89934,89936,89938,89940,89946,89948,89950,89952,89954,89956,89962,89964,89966],{},[898,89933,2312],{},[898,89935,1802],{},[1701,89937,1792],{},[898,89939,6909],{},[1845,89941,89942,89944],{},[898,89943,1680],{},[898,89945,13853],{},[1939,89947,1941],{},[898,89949,2312],{},[898,89951,13853],{},[1701,89953,1703],{},[898,89955,6909],{},[1845,89957,89958,89960],{},[898,89959,1680],{},[898,89961,13858],{},[1939,89963,1941],{},[898,89965,2312],{},[898,89967,13858],{},[902,89969,89970],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,89972,89973,2979,89975,1715],{},[38,89974,84302],{},[883,89976,89978],{"className":89977},[886],[888,89979,89980],{"xmlns":890},[892,89981,89982,90024],{},[895,89983,89984,89986,89994,89996,89998,90006,90008,90010,90012,90014,90016,90018,90020,90022],{},[898,89985,13853],{},[2287,89987,89988,89990,89992],{},[898,89989,1802],{},[898,89991,13853],{},[1701,89993,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,89995,1703],{},[898,89997,13858],{},[2287,89999,90000,90002,90004],{},[898,90001,1802],{},[898,90003,13858],{},[1701,90005,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,90007,1792],{},[898,90009,40890],{},[1939,90011,1941],{},[898,90013,1802],{},[1701,90015,1799],{"stretchy":1798},[898,90017,13853],{},[1701,90019,2012],{"separator":2011},[898,90021,13858],{},[1701,90023,1805],{"stretchy":1798},[902,90025,90026],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,90028,90029,90032,90033,1715],{},[38,90030,90031],{},"Izokvanta"," — křivka ",[883,90034,90036],{"className":90035},[886],[888,90037,90038],{"xmlns":890},[892,90039,90040,90058],{},[895,90041,90042,90044,90046,90048,90050,90052,90054,90056],{},[898,90043,1802],{},[1701,90045,1799],{"stretchy":1798},[898,90047,13853],{},[1701,90049,2012],{"separator":2011},[898,90051,13858],{},[1701,90053,1805],{"stretchy":1798},[1701,90055,1792],{},[898,90057,84543],{},[902,90059,90060],{"encoding":904},"Q(L, K) = q",[123,90062,90063,4088,90065,1715],{},[38,90064,84732],{},[883,90066,90068],{"className":90067},[886],[888,90069,90070],{"xmlns":890},[892,90071,90072,90102],{},[895,90073,90074,90076,90078,90080,90082,90084,90086,90092,90094,90096],{},[898,90075,6909],{},[898,90077,8068],{},[898,90079,5877],{},[898,90081,1661],{},[1701,90083,1792],{},[898,90085,6909],{},[1845,90087,90088,90090],{},[898,90089,1680],{},[898,90091,13853],{},[898,90093,8741],{"mathvariant":2334},[898,90095,6909],{},[1845,90097,90098,90100],{},[898,90099,1680],{},[898,90101,13858],{},[902,90103,78551],{"encoding":904},[123,90105,90106,4088,90109,1715],{},[38,90107,90108],{},"Substituční vztah",[883,90110,90112],{"className":90111},[886],[888,90113,90114],{"xmlns":890},[892,90115,90116,90140],{},[895,90117,90118,90120,90122,90124,90126,90128,90130,90132,90134,90136,90138],{},[898,90119,4708],{"mathvariant":2334},[898,90121,13858],{},[1701,90123,4067],{},[1701,90125,2317],{},[898,90127,6909],{},[898,90129,8068],{},[898,90131,5877],{},[898,90133,1661],{},[1939,90135,1941],{},[898,90137,2312],{},[898,90139,13853],{},[902,90141,90142],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,90144,5984],{"id":5983},[120,90146,90147,90244,90251,90258],{},[123,90148,90149,4088,90151,90154,90155,1343,90158,90161,90162,90165,90166,90185,90186,22694,90205,90208,90209,90228,90229,2506],{},[38,90150,54710],{},[207,90152,784],{"className":90153,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,90156,6007],{"className":90157,"dataFsResolvedFilePath":764,"href":765},[210],[207,90159,793],{"className":90160,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,90163,880],{"className":90164,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,90167,90169],{"className":90168},[886],[888,90170,90171],{"xmlns":890},[892,90172,90173,90183],{},[895,90174,90175,90177,90179,90181],{},[898,90176,6909],{},[898,90178,8068],{},[898,90180,5877],{},[898,90182,1661],{},[902,90184,14655],{"encoding":904}," ↔ ",[883,90187,90189],{"className":90188},[886],[888,90190,90191],{"xmlns":890},[892,90192,90193,90203],{},[895,90194,90195,90197,90199,90201],{},[898,90196,6909],{},[898,90198,8068],{},[898,90200,1658],{},[898,90202,1661],{},[902,90204,14659],{"encoding":904},[207,90206,6017],{"className":90207,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,90210,90212],{"className":90211},[886],[888,90213,90214],{"xmlns":890},[892,90215,90216,90226],{},[895,90217,90218,90220],{},[898,90219,1983],{},[1845,90221,90222,90224],{},[898,90223,1680],{},[898,90225,13853],{},[902,90227,78379],{"encoding":904}," ↔ min ",[883,90230,90232],{"className":90231},[886],[888,90233,90234],{"xmlns":890},[892,90235,90236,90242],{},[895,90237,90238,90240],{},[898,90239,1983],{},[898,90241,1658],{},[902,90243,59306],{"encoding":904},[123,90245,90246,4088,90248,1715],{},[38,90247,7880],{},[207,90249,7908],{"className":90250,"dataFsResolvedFilePath":848,"href":849},[210],[123,90252,90253,4088,90255,1715],{},[38,90254,20261],{},[207,90256,1094],{"className":90257,"dataFsResolvedFilePath":838,"href":839},[210],[123,90259,90260,4088,90262,1715],{},[38,90261,6031],{},[207,90263,6037],{"className":90264,"dataFsResolvedFilePath":6035,"href":6036},[210],{"title":641,"searchDepth":642,"depth":642,"links":90266},[90267,90268,90269,90273,90275,90280,90281,90288,90289,90291,90292,90293,90295,90300,90301,90302,90306,90307],{"id":78574,"depth":642,"text":78575},{"id":78711,"depth":642,"text":78712},{"id":78814,"depth":642,"text":90270,"children":90271},"Mezní produkt práce (MPLMP_L)",[90272],{"id":79260,"depth":649,"text":79261},{"id":79749,"depth":642,"text":90274},"Průměrný produkt práce (APLAP_L)",{"id":79867,"depth":642,"text":79868,"children":90276},[90277,90278,90279],{"id":80104,"depth":649,"text":69247},{"id":80415,"depth":649,"text":80416},{"id":81135,"depth":649,"text":81136},{"id":81707,"depth":642,"text":81708},{"id":81810,"depth":642,"text":81811,"children":90282},[90283,90284,90286,90287],{"id":82169,"depth":649,"text":82170},{"id":82668,"depth":649,"text":90285},"Parametr efektivity AA",{"id":82739,"depth":649,"text":82740},{"id":41207,"depth":649,"text":83079},{"id":83266,"depth":642,"text":83267},{"id":83605,"depth":642,"text":90290},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":84296,"depth":642,"text":84297},{"id":78640,"depth":642,"text":13836},{"id":84707,"depth":642,"text":90294},"Mezní míra technické substituce (MRTSMRTS)",{"id":85573,"depth":642,"text":85574,"children":90296},[90297,90298,90299],{"id":85577,"depth":649,"text":85578},{"id":86220,"depth":649,"text":86221},{"id":86501,"depth":649,"text":86502},{"id":86847,"depth":642,"text":86848},{"id":53868,"depth":642,"text":53869},{"id":87197,"depth":642,"text":87198,"children":90303},[90304,90305],{"id":44473,"depth":649,"text":44474},{"id":87716,"depth":649,"text":87717},{"id":5577,"depth":642,"text":5578},{"id":5983,"depth":642,"text":5984},{},"\u002Ftopics\u002Fprodukce",{"title":78210,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,13871,90314,90315,90316,78640,90317,90318],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":90321,"title":90322,"body":90323,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":99270,"navigation":664,"path":99271,"seo":99272,"sources":99273,"stem":99274,"tags":99275,"type":6074,"updated":677,"__hash__":99278},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":90324,"toc":99244},[90325,90328,90330,90527,90536,90540,90543,90596,90600,90612,90616,90619,90636,90759,90765,90909,90919,90923,90958,90996,91044,91101,91161,91203,91779,91783,91866,91975,92068,92326,92329,92382,92493,92575,92579,92590,92823,92878,92884,92924,92987,92998,93189,93295,93448,93496,93501,93615,93653,93779,93825,93852,93929,94004,94084,94214,94275,94363,94367,94370,94439,94522,94529,94589,94899,94903,94909,94962,94978,95029,95167,95243,95356,95673,95677,95684,95844,95903,95907,95929,96026,96147,96261,96284,96347,96404,96656,96664,96668,96675,96929,96979,97035,97038,97202,97206,97304,97306,97338,97342,97475,97717,97901,98069,98376,98509,98696,98708,98710,99145,99147],[12,90326,90322],{"id":90327},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,90329,16061],{"id":16060},[724,90331,90332,4088,90334,90365,90366,90369,90370,90400,90401,90419,90420,90460,90461,90464,90465,90478,90479,32287,90482,90495,90496,90509,90510,90523,90524,1715],{},[38,90333,880],{},[883,90335,90337],{"className":90336},[886],[888,90338,90339],{"xmlns":890},[892,90340,90341,90363],{},[895,90342,90343,90345,90347,90353,90355,90361],{},[898,90344,900],{},[1701,90346,1799],{"stretchy":1798},[1845,90348,90349,90351],{},[898,90350,1802],{},[1850,90352,4062],{},[1701,90354,2012],{"separator":2011},[1845,90356,90357,90359],{},[898,90358,1802],{},[1850,90360,3938],{},[1701,90362,1805],{"stretchy":1798},[902,90364,20389],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,90367,90368],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,90371,90373],{"className":90372},[886],[888,90374,90375],{"xmlns":890},[892,90376,90377,90397],{},[895,90378,90379,90381,90387,90389],{},[898,90380,6909],{},[1845,90382,90383,90385],{},[898,90384,900],{},[898,90386,21836],{},[1701,90388,1792],{},[2287,90390,90391,90393,90395],{},[898,90392,900],{},[898,90394,21836],{},[1701,90396,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,90398,90399],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,90402,90404],{"className":90403},[886],[888,90405,90406],{"xmlns":890},[892,90407,90408,90416],{},[895,90409,90410,90412,90414],{},[898,90411,900],{},[1701,90413,1792],{},[898,90415,3618],{},[902,90417,90418],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,90421,90423],{"className":90422},[886],[888,90424,90425],{"xmlns":890},[892,90426,90427,90457],{},[895,90428,90429,90431,90433,90435,90437,90439,90441,90447,90449,90451],{},[898,90430,6909],{},[898,90432,8068],{},[898,90434,1658],{},[898,90436,1661],{},[1701,90438,1792],{},[898,90440,6909],{},[1845,90442,90443,90445],{},[898,90444,900],{},[1850,90446,4062],{},[898,90448,8741],{"mathvariant":2334},[898,90450,6909],{},[1845,90452,90453,90455],{},[898,90454,900],{},[1850,90456,3938],{},[902,90458,90459],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,90462,90463],{},"teorii užitečnosti"," — funkce ",[883,90466,90468],{"className":90467},[886],[888,90469,90470],{"xmlns":890},[892,90471,90472,90476],{},[895,90473,90474],{},[898,90475,900],{},[902,90477,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,90480,90481],{},"Optimalizaci spotřebitele",[883,90483,90485],{"className":90484},[886],[888,90486,90487],{"xmlns":890},[892,90488,90489,90493],{},[895,90490,90491],{},[898,90492,900],{},[902,90494,900],{"encoding":904}," při rozpočtu, min ",[883,90497,90499],{"className":90498},[886],[888,90500,90501],{"xmlns":890},[892,90502,90503,90507],{},[895,90504,90505],{},[898,90506,3249],{},[902,90508,3249],{"encoding":904}," při dané ",[883,90511,90513],{"className":90512},[886],[888,90514,90515],{"xmlns":890},[892,90516,90517,90521],{},[895,90518,90519],{},[898,90520,900],{},[902,90522,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,90525,913],{"className":90526,"dataFsResolvedFilePath":911,"href":912},[210],[724,90528,90529,90530,90532,90533,1715],{},"Kapitola 6 knihy ",[614,90531,6037],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,90534,40784],{"className":90535,"dataFsResolvedFilePath":911,"href":912},[210],[115,90537,90539],{"id":90538},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,90541,90542],{},"Po prostudování této kapitoly byste měli umět:",[120,90544,90545,90551,90560,90565,90568,90574,90580,90583,90589],{},[123,90546,90547,90548,2012],{},"vyložit, co se rozumí termínem ",[38,90549,90550],{},"užitečnost",[123,90552,90553,90554,2633,90557,2012],{},"definovat pojmy ",[38,90555,90556],{},"svazek zboží",[38,90558,90559],{},"funkce užitečnosti",[123,90561,78589,90562,78596],{},[38,90563,90564],{},"mezní užitečnosti",[123,90566,90567],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,90569,78616,90570,90573],{},[38,90571,90572],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,90575,78637,90576,90579],{},[38,90577,90578],{},"křivky užitečnosti"," (indiferenční křivky),",[123,90581,90582],{},"vyjmenovat jejich základní vlastnosti,",[123,90584,78589,90585,90588],{},[38,90586,90587],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,90590,90591,90592,90595],{},"řešit ",[38,90593,90594],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,90597,90599],{"id":90598},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,90601,90602,90603,90607,90608,90611],{},"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 ",[207,90604,90606],{"className":90605,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,90609,90610],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,90613,90615],{"id":90614},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,90617,90618],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,90620,90621,90627],{},[123,90622,90623,90626],{},[38,90624,90625],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,90628,90629,90632,90633,90635],{},[38,90630,90631],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,90634,90368],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1635,90637,90638],{},[724,90639,90640,90642,90643,90646,90647,4088,90660,90663,90664,2633,90677,90696,90697,1343,90723,90750,90751,90754,90755,90758],{},[883,90641,4695],{}," Pozor — ordinalisté užitečnost ",[38,90644,90645],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,90648,90650],{"className":90649},[886],[888,90651,90652],{"xmlns":890},[892,90653,90654,90658],{},[895,90655,90656],{},[898,90657,900],{},[902,90659,900],{"encoding":904},[38,90661,90662],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,90665,90667],{"className":90666},[886],[888,90668,90669],{"xmlns":890},[892,90670,90671,90675],{},[895,90672,90673],{},[898,90674,900],{},[902,90676,900],{"encoding":904},[883,90678,90680],{"className":90679},[886],[888,90681,90682],{"xmlns":890},[892,90683,90684,90693],{},[895,90685,90686],{},[12448,90687,90688,90690],{"accent":2011},[898,90689,900],{},[1701,90691,90692],{},"~",[902,90694,90695],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,90698,90700],{"className":90699},[886],[888,90701,90702],{"xmlns":890},[892,90703,90704,90720],{},[895,90705,90706,90712,90714],{},[12448,90707,90708,90710],{"accent":2011},[898,90709,900],{},[1701,90711,90692],{},[1701,90713,1792],{},[3243,90715,90716,90718],{},[898,90717,900],{},[1850,90719,3938],{},[902,90721,90722],{"encoding":904},"\\tilde U = U^2",[883,90724,90726],{"className":90725},[886],[888,90727,90728],{"xmlns":890},[892,90729,90730,90747],{},[895,90731,90732,90738,90740,90743,90745],{},[12448,90733,90734,90736],{"accent":2011},[898,90735,900],{},[1701,90737,90692],{},[1701,90739,1792],{},[898,90741,90742],{},"ln",[1701,90744,59946],{},[898,90746,900],{},[902,90748,90749],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,90752,90753],{},"porovnání"," mezi svazky a ",[38,90756,90757],{},"poměry"," mezních veličin.",[724,90760,90761,90762,2246],{},"Ordinalistický přístup vychází z ",[38,90763,90764],{},"pěti hlavních předpokladů",[152,90766,90767,90773,90779,90897,90903],{},[123,90768,90769,90772],{},[38,90770,90771],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,90774,90775,90778],{},[38,90776,90777],{},"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.",[123,90780,90781,90784,90785,65487,90798,90811,90812,65487,90825,7015,90838,90841,90842,2633,90861,66316,90879,1715],{},[38,90782,90783],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,90786,90788],{"className":90787},[886],[888,90789,90790],{"xmlns":890},[892,90791,90792,90796],{},[895,90793,90794],{},[898,90795,1983],{},[902,90797,1983],{"encoding":904},[883,90799,90801],{"className":90800},[886],[888,90802,90803],{"xmlns":890},[892,90804,90805,90809],{},[895,90806,90807],{},[898,90808,2593],{},[902,90810,2593],{"encoding":904},", nebude jindy preferovat ",[883,90813,90815],{"className":90814},[886],[888,90816,90817],{"xmlns":890},[892,90818,90819,90823],{},[895,90820,90821],{},[898,90822,2593],{},[902,90824,2593],{"encoding":904},[883,90826,90828],{"className":90827},[886],[888,90829,90830],{"xmlns":890},[892,90831,90832,90836],{},[895,90833,90834],{},[898,90835,1983],{},[902,90837,1983],{"encoding":904},[38,90839,90840],{},"Tranzitivita",": pokud ",[883,90843,90845],{"className":90844},[886],[888,90846,90847],{"xmlns":890},[892,90848,90849,90858],{},[895,90850,90851,90853,90856],{},[898,90852,1983],{},[1701,90854,90855],{},"≻",[898,90857,2593],{},[902,90859,90860],{"encoding":904},"A \\succ B",[883,90862,90864],{"className":90863},[886],[888,90865,90866],{"xmlns":890},[892,90867,90868,90876],{},[895,90869,90870,90872,90874],{},[898,90871,2593],{},[1701,90873,90855],{},[898,90875,1658],{},[902,90877,90878],{"encoding":904},"B \\succ C",[883,90880,90882],{"className":90881},[886],[888,90883,90884],{"xmlns":890},[892,90885,90886,90894],{},[895,90887,90888,90890,90892],{},[898,90889,1983],{},[1701,90891,90855],{},[898,90893,1658],{},[902,90895,90896],{"encoding":904},"A \\succ C",[123,90898,90899,90902],{},[38,90900,90901],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,90904,90905,90908],{},[38,90906,90907],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,90910,90911,90912,90915,90916,1715],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,90913,90914],{},"preference"," a na příbuzné ",[614,90917,90918],{},"funkci užitečnosti",[115,90920,90922],{"id":90921},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,90924,90925,90926,90939,90940,90943,90944,90957],{},"Uvažujme ",[883,90927,90929],{"className":90928},[886],[888,90930,90931],{"xmlns":890},[892,90932,90933,90937],{},[895,90934,90935],{},[898,90936,40890],{},[902,90938,40890],{"encoding":904}," různých zboží. ",[38,90941,90942],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,90945,90947],{"className":90946},[886],[888,90948,90949],{"xmlns":890},[892,90950,90951,90955],{},[895,90952,90953],{},[898,90954,40890],{},[902,90956,40890],{"encoding":904},"-tice",[724,90959,90960],{},[883,90961,90963],{"className":90962},[886],[888,90964,90965],{"xmlns":890},[892,90966,90967,90993],{},[895,90968,90969,90971,90977,90979,90981,90983,90989,90991],{},[1701,90970,1799],{"stretchy":1798},[1845,90972,90973,90975],{},[898,90974,1802],{},[1850,90976,4062],{},[1701,90978,2012],{"separator":2011},[1701,90980,13704],{},[1701,90982,2012],{"separator":2011},[1845,90984,90985,90987],{},[898,90986,1802],{},[898,90988,40890],{},[1701,90990,1805],{"stretchy":1798},[1701,90992,2012],{"separator":2011},[902,90994,90995],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,90997,8380,90998,91015,91016,91029,91030,91033,91034,91037,91038,91041,91042,2246],{},[883,90999,91001],{"className":91000},[886],[888,91002,91003],{"xmlns":890},[892,91004,91005,91013],{},[895,91006,91007],{},[1845,91008,91009,91011],{},[898,91010,1802],{},[898,91012,21836],{},[902,91014,51529],{"encoding":904}," značí množství ",[883,91017,91019],{"className":91018},[886],[888,91020,91021],{"xmlns":890},[892,91022,91023,91027],{},[895,91024,91025],{},[898,91026,21836],{},[902,91028,21836],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,91031,91032],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,91035,91036],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,91039,91040],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,91043,90918],{},[883,91045,91047],{"className":91046},[886],[888,91048,91049],{"xmlns":890,"display":2252},[892,91050,91051,91098],{},[2256,91052,91053],{"width":2258},[2260,91054,91055,91057,91091,91093],{},[2263,91056],{"width":2265},[2263,91058,91059],{},[895,91060,91061,91063,91065,91067,91069,91075,91077,91079,91081,91087,91089],{},[898,91062,900],{},[1701,91064,1792],{},[898,91066,900],{},[1701,91068,1799],{"stretchy":1798},[1845,91070,91071,91073],{},[898,91072,1802],{},[1850,91074,4062],{},[1701,91076,2012],{"separator":2011},[1701,91078,13704],{},[1701,91080,2012],{"separator":2011},[1845,91082,91083,91085],{},[898,91084,1802],{},[898,91086,40890],{},[1701,91088,1805],{"stretchy":1798},[1701,91090,2012],{"separator":2011},[2263,91092],{"width":2265},[2263,91094,91095],{},[1939,91096,91097],{},"(6.1)",[902,91099,91100],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,91102,8380,91103,91133,91134,91156,91157,91160],{},[883,91104,91106],{"className":91105},[886],[888,91107,91108],{"xmlns":890},[892,91109,91110,91130],{},[895,91111,91112,91118,91120,91122,91124],{},[1845,91113,91114,91116],{},[898,91115,1802],{},[1850,91117,4062],{},[1701,91119,2012],{"separator":2011},[1701,91121,13704],{},[1701,91123,2012],{"separator":2011},[1845,91125,91126,91128],{},[898,91127,1802],{},[898,91129,40890],{},[902,91131,91132],{"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 ",[883,91135,91137],{"className":91136},[886],[888,91138,91139],{"xmlns":890},[892,91140,91141,91153],{},[895,91142,91143,91145,91147],{},[898,91144,900],{},[1701,91146,2012],{"separator":2011},[12448,91148,91149,91151],{"accent":2011},[898,91150,900],{},[1701,91152,90692],{},[902,91154,91155],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,91158,91159],{},"monotónní transformace"," zachovávající pořadí.",[724,91162,91163,91164,2979,91167,1715],{},"Dále se omezíme na funkce pro ",[38,91165,91166],{},"dvě zboží",[883,91168,91170],{"className":91169},[886],[888,91171,91172],{"xmlns":890},[892,91173,91174,91200],{},[895,91175,91176,91178,91180,91182,91184,91190,91192,91198],{},[898,91177,900],{},[1701,91179,1792],{},[898,91181,900],{},[1701,91183,1799],{"stretchy":1798},[1845,91185,91186,91188],{},[898,91187,1802],{},[1850,91189,4062],{},[1701,91191,2012],{"separator":2011},[1845,91193,91194,91196],{},[898,91195,1802],{},[1850,91197,3938],{},[1701,91199,1805],{"stretchy":1798},[902,91201,91202],{"encoding":904},"U = U(Q_1, Q_2)",[1635,91204,91205,91280],{},[724,91206,91207,91209,91210,2246],{},[883,91208,3575],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,91211,91213],{"className":91212},[886],[888,91214,91215],{"xmlns":890},[892,91216,91217,91277],{},[895,91218,91219,91221,91223,91225,91227,91233,91235,91241,91243,91249,91251,91253,91255],{},[898,91220,900],{},[1701,91222,1792],{},[898,91224,900],{},[1701,91226,1799],{"stretchy":1798},[1845,91228,91229,91231],{},[898,91230,1802],{},[1850,91232,4062],{},[1701,91234,2012],{"separator":2011},[1845,91236,91237,91239],{},[898,91238,1802],{},[1850,91240,3938],{},[1701,91242,2012],{"separator":2011},[1845,91244,91245,91247],{},[898,91246,1802],{},[1850,91248,3646],{},[1701,91250,1805],{"stretchy":1798},[1701,91252,1792],{},[1850,91254,3938],{},[12179,91256,91257],{},[895,91258,91259,91265,91271],{},[1845,91260,91261,91263],{},[898,91262,1802],{},[1850,91264,4062],{},[1845,91266,91267,91269],{},[898,91268,1802],{},[1850,91270,3938],{},[1845,91272,91273,91275],{},[898,91274,1802],{},[1850,91276,3646],{},[902,91278,91279],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,91281,91282,91475],{},[123,91283,91284,91285,91311,91312,16992,91338,2633,91397,4185,91457,12487],{},"svazek ",[883,91286,91288],{"className":91287},[886],[888,91289,91290],{"xmlns":890},[892,91291,91292,91308],{},[895,91293,91294,91296,91298,91300,91302,91304,91306],{},[1701,91295,1799],{"stretchy":1798},[1850,91297,45883],{},[1701,91299,2012],{"separator":2011},[1850,91301,6460],{},[1701,91303,2012],{"separator":2011},[1850,91305,45861],{},[1701,91307,1805],{"stretchy":1798},[902,91309,91310],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,91313,91315],{"className":91314},[886],[888,91316,91317],{"xmlns":890},[892,91318,91319,91335],{},[895,91320,91321,91323,91325,91327,91329,91331,91333],{},[1701,91322,1799],{"stretchy":1798},[1850,91324,8073],{},[1701,91326,2012],{"separator":2011},[1850,91328,8073],{},[1701,91330,2012],{"separator":2011},[1850,91332,70343],{},[1701,91334,1805],{"stretchy":1798},[902,91336,91337],{"encoding":904},"(9, 9, 27)",[883,91339,91341],{"className":91340},[886],[888,91342,91343],{"xmlns":890},[892,91344,91345,91394],{},[895,91346,91347,91349,91351,91353,91355,91357,91359,91361,91363,91365,91367,91381,91383,91385,91390,91392],{},[898,91348,900],{},[1701,91350,1799],{"stretchy":1798},[1850,91352,45883],{},[1701,91354,2012],{"separator":2011},[1850,91356,6460],{},[1701,91358,2012],{"separator":2011},[1850,91360,45861],{},[1701,91362,1805],{"stretchy":1798},[1701,91364,1792],{},[1850,91366,3938],{},[12179,91368,91369],{},[895,91370,91371,91373,91375,91377,91379],{},[1850,91372,45883],{},[1701,91374,3408],{},[1850,91376,6460],{},[1701,91378,3408],{},[1850,91380,45861],{},[1701,91382,1792],{},[1850,91384,3938],{},[12179,91386,91387],{},[1850,91388,91389],{},"4096",[1701,91391,1792],{},[1850,91393,9681],{},[902,91395,91396],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,91398,91400],{"className":91399},[886],[888,91401,91402],{"xmlns":890},[892,91403,91404,91454],{},[895,91405,91406,91408,91410,91412,91414,91416,91418,91420,91422,91424,91426,91440,91442,91444,91449,91451],{},[898,91407,900],{},[1701,91409,1799],{"stretchy":1798},[1850,91411,8073],{},[1701,91413,2012],{"separator":2011},[1850,91415,8073],{},[1701,91417,2012],{"separator":2011},[1850,91419,70343],{},[1701,91421,1805],{"stretchy":1798},[1701,91423,1792],{},[1850,91425,3938],{},[12179,91427,91428],{},[895,91429,91430,91432,91434,91436,91438],{},[1850,91431,8073],{},[1701,91433,3408],{},[1850,91435,8073],{},[1701,91437,3408],{},[1850,91439,70343],{},[1701,91441,1792],{},[1850,91443,3938],{},[12179,91445,91446],{},[1850,91447,91448],{},"2187",[1701,91450,3782],{},[1850,91452,91453],{},"93,53",[902,91455,91456],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,91458,91460],{"className":91459},[886],[888,91461,91462],{"xmlns":890},[892,91463,91464,91472],{},[895,91465,91466,91468,91470],{},[1850,91467,9681],{},[1701,91469,7491],{},[1850,91471,91453],{},[902,91473,91474],{"encoding":904},"128 > 93{,}53",[123,91476,91477,91478,2633,91504,91530,91531,2633,91571,91612,91613,91659,91660,2633,91686,6936,91712,2633,91730,91748,91749,1715],{},"svazky ",[883,91479,91481],{"className":91480},[886],[888,91482,91483],{"xmlns":890},[892,91484,91485,91501],{},[895,91486,91487,91489,91491,91493,91495,91497,91499],{},[1701,91488,1799],{"stretchy":1798},[1850,91490,6460],{},[1701,91492,2012],{"separator":2011},[1850,91494,9650],{},[1701,91496,2012],{"separator":2011},[1850,91498,3938],{},[1701,91500,1805],{"stretchy":1798},[902,91502,91503],{"encoding":904},"(4, 8, 2)",[883,91505,91507],{"className":91506},[886],[888,91508,91509],{"xmlns":890},[892,91510,91511,91527],{},[895,91512,91513,91515,91517,91519,91521,91523,91525],{},[1701,91514,1799],{"stretchy":1798},[1850,91516,45861],{},[1701,91518,2012],{"separator":2011},[1850,91520,4062],{},[1701,91522,2012],{"separator":2011},[1850,91524,6460],{},[1701,91526,1805],{"stretchy":1798},[902,91528,91529],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,91532,91534],{"className":91533},[886],[888,91535,91536],{"xmlns":890},[892,91537,91538,91568],{},[895,91539,91540,91542,91544,91546,91548,91550,91552,91554,91556,91558,91560,91564,91566],{},[898,91541,900],{},[1701,91543,1799],{"stretchy":1798},[1850,91545,6460],{},[1701,91547,2012],{"separator":2011},[1850,91549,9650],{},[1701,91551,2012],{"separator":2011},[1850,91553,3938],{},[1701,91555,1805],{"stretchy":1798},[1701,91557,1792],{},[1850,91559,3938],{},[12179,91561,91562],{},[1850,91563,45861],{},[1701,91565,1792],{},[1850,91567,45883],{},[902,91569,91570],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,91572,91574],{"className":91573},[886],[888,91575,91576],{"xmlns":890},[892,91577,91578,91609],{},[895,91579,91580,91582,91584,91586,91588,91590,91592,91594,91596,91598,91600,91605,91607],{},[898,91581,900],{},[1701,91583,1799],{"stretchy":1798},[1850,91585,45861],{},[1701,91587,2012],{"separator":2011},[1850,91589,4062],{},[1701,91591,2012],{"separator":2011},[1850,91593,6460],{},[1701,91595,1805],{"stretchy":1798},[1701,91597,1792],{},[1850,91599,3938],{},[12179,91601,91602],{},[1850,91603,91604],{},"256",[1701,91606,1792],{},[1850,91608,76105],{},[902,91610,91611],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,91614,91616],{"className":91615},[886],[888,91617,91618],{"xmlns":890},[892,91619,91620,91656],{},[895,91621,91622,91624,91626,91628,91630,91632,91634,91636,91638,91640,91642,91644,91646,91648,91650,91652,91654],{},[898,91623,900],{},[1701,91625,1799],{"stretchy":1798},[1850,91627,6460],{},[1701,91629,2012],{"separator":2011},[1850,91631,9650],{},[1701,91633,2012],{"separator":2011},[1850,91635,3938],{},[1701,91637,1805],{"stretchy":1798},[1701,91639,1792],{},[898,91641,900],{},[1701,91643,1799],{"stretchy":1798},[1850,91645,45861],{},[1701,91647,2012],{"separator":2011},[1850,91649,4062],{},[1701,91651,2012],{"separator":2011},[1850,91653,6460],{},[1701,91655,1805],{"stretchy":1798},[902,91657,91658],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,91661,91663],{"className":91662},[886],[888,91664,91665],{"xmlns":890},[892,91666,91667,91683],{},[895,91668,91669,91671,91673,91675,91677,91679,91681],{},[1850,91670,6460],{},[1701,91672,3408],{},[1850,91674,9650],{},[1701,91676,3408],{},[1850,91678,3938],{},[1701,91680,1792],{},[1850,91682,45861],{},[902,91684,91685],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,91687,91689],{"className":91688},[886],[888,91690,91691],{"xmlns":890},[892,91692,91693,91709],{},[895,91694,91695,91697,91699,91701,91703,91705,91707],{},[1850,91696,45861],{},[1701,91698,3408],{},[1850,91700,4062],{},[1701,91702,3408],{},[1850,91704,6460],{},[1701,91706,1792],{},[1850,91708,91604],{},[902,91710,91711],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,91713,91715],{"className":91714},[886],[888,91716,91717],{"xmlns":890},[892,91718,91719,91727],{},[895,91720,91721,91723,91725],{},[898,91722,900],{},[1701,91724,1792],{},[1850,91726,45883],{},[902,91728,91729],{"encoding":904},"U = 16",[883,91731,91733],{"className":91732},[886],[888,91734,91735],{"xmlns":890},[892,91736,91737,91745],{},[895,91738,91739,91741,91743],{},[898,91740,900],{},[1701,91742,1792],{},[1850,91744,76105],{},[902,91746,91747],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,91750,91752],{"className":91751},[886],[888,91753,91754],{"xmlns":890},[892,91755,91756,91776],{},[895,91757,91758,91764,91770],{},[1845,91759,91760,91762],{},[898,91761,1802],{},[1850,91763,4062],{},[1845,91765,91766,91768],{},[898,91767,1802],{},[1850,91769,3938],{},[1845,91771,91772,91774],{},[898,91773,1802],{},[1850,91775,3646],{},[902,91777,91778],{"encoding":904},"Q_1 Q_2 Q_3",[115,91780,91782],{"id":91781},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,91784,91785,91786,12164,91821,4088,91824,45835,91841,1646,91858,91861,91862,91865],{},"Pro funkci užitečnosti ",[883,91787,91789],{"className":91788},[886],[888,91790,91791],{"xmlns":890},[892,91792,91793,91819],{},[895,91794,91795,91797,91799,91801,91803,91809,91811,91817],{},[898,91796,900],{},[1701,91798,1792],{},[898,91800,900],{},[1701,91802,1799],{"stretchy":1798},[1845,91804,91805,91807],{},[898,91806,1802],{},[1850,91808,4062],{},[1701,91810,2012],{"separator":2011},[1845,91812,91813,91815],{},[898,91814,1802],{},[1850,91816,3938],{},[1701,91818,1805],{"stretchy":1798},[902,91820,91202],{"encoding":904},[38,91822,91823],{},"mezní užitečnost",[883,91825,91827],{"className":91826},[886],[888,91828,91829],{"xmlns":890},[892,91830,91831,91839],{},[895,91832,91833],{},[1845,91834,91835,91837],{},[898,91836,1802],{},[1850,91838,4062],{},[902,91840,33036],{"encoding":904},[883,91842,91844],{"className":91843},[886],[888,91845,91846],{"xmlns":890},[892,91847,91848,91856],{},[895,91849,91850],{},[1845,91851,91852,91854],{},[898,91853,1802],{},[1850,91855,3938],{},[902,91857,33055],{"encoding":904},[38,91859,91860],{},"marginal utility",") parciální ",[207,91863,1145],{"className":91864,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,91867,91869],{"className":91868},[886],[888,91870,91871],{"xmlns":890,"display":2252},[892,91872,91873,91972],{},[2256,91874,91875],{"width":2258},[2260,91876,91877,91879,91965,91967],{},[2263,91878],{"width":2265},[2263,91880,91881],{},[895,91882,91883,91885,91891,91893,91901,91903,91921,91923,91925,91927,91933,91935,91943,91945,91963],{},[898,91884,6909],{},[1845,91886,91887,91889],{},[898,91888,900],{},[1850,91890,4062],{},[1701,91892,1792],{},[2287,91894,91895,91897,91899],{},[898,91896,900],{},[1850,91898,4062],{},[1701,91900,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,91902,1792],{},[3726,91904,91905,91911],{},[895,91906,91907,91909],{},[898,91908,3893],{"mathvariant":2334},[898,91910,900],{},[895,91912,91913,91915],{},[898,91914,3893],{"mathvariant":2334},[1845,91916,91917,91919],{},[898,91918,1802],{},[1850,91920,4062],{},[1701,91922,2012],{"separator":2011},[9942,91924],{"width":19336},[898,91926,6909],{},[1845,91928,91929,91931],{},[898,91930,900],{},[1850,91932,3938],{},[1701,91934,1792],{},[2287,91936,91937,91939,91941],{},[898,91938,900],{},[1850,91940,3938],{},[1701,91942,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,91944,1792],{},[3726,91946,91947,91953],{},[895,91948,91949,91951],{},[898,91950,3893],{"mathvariant":2334},[898,91952,900],{},[895,91954,91955,91957],{},[898,91956,3893],{"mathvariant":2334},[1845,91958,91959,91961],{},[898,91960,1802],{},[1850,91962,3938],{},[898,91964,1715],{"mathvariant":2334},[2263,91966],{"width":2265},[2263,91968,91969],{},[1939,91970,91971],{},"(6.2)",[902,91973,91974],{"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}",[724,91976,91977,91978,92012,92013,92043,92044,4088,92047,1715],{},"Pro pevné ",[883,91979,91981],{"className":91980},[886],[888,91982,91983],{"xmlns":890},[892,91984,91985,92009],{},[895,91986,91987,91993,91995,91997,91999,92005,92007],{},[1845,91988,91989,91991],{},[898,91990,1802],{},[1850,91992,4062],{},[1701,91994,1792],{},[898,91996,207],{},[1701,91998,2012],{"separator":2011},[1845,92000,92001,92003],{},[898,92002,1802],{},[1850,92004,3938],{},[1701,92006,1792],{},[898,92008,3598],{},[902,92010,92011],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,92014,92016],{"className":92015},[886],[888,92017,92018],{"xmlns":890},[892,92019,92020,92040],{},[895,92021,92022,92024,92030,92032,92034,92036,92038],{},[898,92023,6909],{},[1845,92025,92026,92028],{},[898,92027,900],{},[1850,92029,4062],{},[1701,92031,1799],{"stretchy":1798},[898,92033,207],{},[1701,92035,2012],{"separator":2011},[898,92037,3598],{},[1701,92039,1805],{"stretchy":1798},[902,92041,92042],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,92045,92046],{},"v bodě (na hladině)",[883,92048,92050],{"className":92049},[886],[888,92051,92052],{"xmlns":890},[892,92053,92054,92066],{},[895,92055,92056,92058,92060,92062,92064],{},[1701,92057,2036],{"stretchy":1798},[898,92059,207],{},[1701,92061,2012],{"separator":2011},[898,92063,3598],{},[1701,92065,2053],{"stretchy":1798},[902,92067,14880],{"encoding":904},[1635,92069,92070],{},[724,92071,92072,92074,92075,92105,92134,92135,6709,92148,6723,92165,92186,92187,3841,92204,3856,92217,92234,92235,92257,92258,92287,92288,10536,92308,92325],{},[883,92073,2063],{}," Intuice — co říká ",[883,92076,92078],{"className":92077},[886],[888,92079,92080],{"xmlns":890},[892,92081,92082,92102],{},[895,92083,92084,92086,92092,92094,92096,92098,92100],{},[898,92085,6909],{},[1845,92087,92088,92090],{},[898,92089,900],{},[1850,92091,4062],{},[1701,92093,1799],{"stretchy":1798},[898,92095,207],{},[1701,92097,2012],{"separator":2011},[898,92099,3598],{},[1701,92101,1805],{"stretchy":1798},[902,92103,92104],{"encoding":904},"MU_1(a,b)",[883,92106,92108],{"className":92107},[886],[888,92109,92110],{"xmlns":890},[892,92111,92112,92132],{},[895,92113,92114,92116,92122,92124,92126,92128,92130],{},[898,92115,6909],{},[1845,92117,92118,92120],{},[898,92119,900],{},[1850,92121,4062],{},[1701,92123,1799],{"stretchy":1798},[898,92125,207],{},[1701,92127,2012],{"separator":2011},[898,92129,3598],{},[1701,92131,1805],{"stretchy":1798},[902,92133,92042],{"encoding":904}," je rychlost změny ",[883,92136,92138],{"className":92137},[886],[888,92139,92140],{"xmlns":890},[892,92141,92142,92146],{},[895,92143,92144],{},[898,92145,900],{},[902,92147,900],{"encoding":904},[883,92149,92151],{"className":92150},[886],[888,92152,92153],{"xmlns":890},[892,92154,92155,92163],{},[895,92156,92157],{},[1845,92158,92159,92161],{},[898,92160,1802],{},[1850,92162,4062],{},[902,92164,33036],{"encoding":904},[883,92166,92168],{"className":92167},[886],[888,92169,92170],{"xmlns":890},[892,92171,92172,92184],{},[895,92173,92174,92176,92178,92180,92182],{},[1701,92175,2036],{"stretchy":1798},[898,92177,207],{},[1701,92179,2012],{"separator":2011},[898,92181,3598],{},[1701,92183,2053],{"stretchy":1798},[902,92185,14880],{"encoding":904},". Přibližně: změní-li se ",[883,92188,92190],{"className":92189},[886],[888,92191,92192],{"xmlns":890},[892,92193,92194,92202],{},[895,92195,92196],{},[1845,92197,92198,92200],{},[898,92199,1802],{},[1850,92201,4062],{},[902,92203,33036],{"encoding":904},[883,92205,92207],{"className":92206},[886],[888,92208,92209],{"xmlns":890},[892,92210,92211,92215],{},[895,92212,92213],{},[898,92214,207],{},[902,92216,207],{"encoding":904},[883,92218,92220],{"className":92219},[886],[888,92221,92222],{"xmlns":890},[892,92223,92224,92232],{},[895,92225,92226,92228,92230],{},[898,92227,207],{},[1701,92229,1703],{},[1850,92231,4062],{},[902,92233,6800],{"encoding":904}," při pevném ",[883,92236,92238],{"className":92237},[886],[888,92239,92240],{"xmlns":890},[892,92241,92242,92254],{},[895,92243,92244,92250,92252],{},[1845,92245,92246,92248],{},[898,92247,1802],{},[1850,92249,3938],{},[1701,92251,1792],{},[898,92253,3598],{},[902,92255,92256],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,92259,92261],{"className":92260},[886],[888,92262,92263],{"xmlns":890},[892,92264,92265,92285],{},[895,92266,92267,92269,92275,92277,92279,92281,92283],{},[898,92268,6909],{},[1845,92270,92271,92273],{},[898,92272,900],{},[1850,92274,4062],{},[1701,92276,1799],{"stretchy":1798},[898,92278,207],{},[1701,92280,2012],{"separator":2011},[898,92282,3598],{},[1701,92284,1805],{"stretchy":1798},[902,92286,92042],{"encoding":904},". Stejně tak ",[883,92289,92291],{"className":92290},[886],[888,92292,92293],{"xmlns":890},[892,92294,92295,92305],{},[895,92296,92297,92299],{},[898,92298,6909],{},[1845,92300,92301,92303],{},[898,92302,900],{},[1850,92304,3938],{},[902,92306,92307],{"encoding":904},"MU_2",[883,92309,92311],{"className":92310},[886],[888,92312,92313],{"xmlns":890},[892,92314,92315,92323],{},[895,92316,92317],{},[1845,92318,92319,92321],{},[898,92320,1802],{},[1850,92322,3938],{},[902,92324,33055],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,92327,83957],{"id":92328},"totální-diferenciál",[724,92330,92331,92332,52330,92348,92378,92379,2246],{},"Přibližnou změnu užitečnosti ",[883,92333,92335],{"className":92334},[886],[888,92336,92337],{"xmlns":890},[892,92338,92339,92345],{},[895,92340,92341,92343],{},[898,92342,4708],{"mathvariant":2334},[898,92344,900],{},[902,92346,92347],{"encoding":904},"\\Delta U",[883,92349,92351],{"className":92350},[886],[888,92352,92353],{"xmlns":890},[892,92354,92355,92375],{},[895,92356,92357,92359,92365,92367,92369],{},[898,92358,2312],{"mathvariant":2334},[1845,92360,92361,92363],{},[898,92362,1802],{},[1850,92364,4062],{},[1701,92366,2012],{"separator":2011},[898,92368,2312],{"mathvariant":2334},[1845,92370,92371,92373],{},[898,92372,1802],{},[1850,92374,3938],{},[902,92376,92377],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,92380,92381],{},"totálního diferenciálu",[883,92383,92385],{"className":92384},[886],[888,92386,92387],{"xmlns":890,"display":2252},[892,92388,92389,92490],{},[2256,92390,92391],{"width":2258},[2260,92392,92393,92395,92483,92485],{},[2263,92394],{"width":2265},[2263,92396,92397],{},[895,92398,92399,92401,92403,92405,92407,92409,92411,92419,92421,92427,92429,92437,92439,92445,92447,92449,92455,92457,92463,92465,92467,92473,92475,92481],{},[898,92400,4708],{"mathvariant":2334},[898,92402,900],{},[1701,92404,4067],{},[898,92406,2312],{"mathvariant":2334},[898,92408,900],{},[1701,92410,1792],{},[2287,92412,92413,92415,92417],{},[898,92414,900],{},[1850,92416,4062],{},[1701,92418,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[898,92420,2312],{"mathvariant":2334},[1845,92422,92423,92425],{},[898,92424,1802],{},[1850,92426,4062],{},[1701,92428,1703],{},[2287,92430,92431,92433,92435],{},[898,92432,900],{},[1850,92434,3938],{},[1701,92436,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[898,92438,2312],{"mathvariant":2334},[1845,92440,92441,92443],{},[898,92442,1802],{},[1850,92444,3938],{},[1701,92446,1792],{},[898,92448,6909],{},[1845,92450,92451,92453],{},[898,92452,900],{},[1850,92454,4062],{},[898,92456,2312],{"mathvariant":2334},[1845,92458,92459,92461],{},[898,92460,1802],{},[1850,92462,4062],{},[1701,92464,1703],{},[898,92466,6909],{},[1845,92468,92469,92471],{},[898,92470,900],{},[1850,92472,3938],{},[898,92474,2312],{"mathvariant":2334},[1845,92476,92477,92479],{},[898,92478,1802],{},[1850,92480,3938],{},[898,92482,1715],{"mathvariant":2334},[2263,92484],{"width":2265},[2263,92486,92487],{},[1939,92488,92489],{},"(6.3)",[902,92491,92492],{"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}",[724,92494,79215,92495,1715],{},[883,92496,92498],{"className":92497},[886],[888,92499,92500],{"xmlns":890},[892,92501,92502,92572],{},[895,92503,92504,92506,92508,92510,92512,92514,92520,92522,92524,92530,92532,92538,92540,92542,92548,92550,92552,92554,92556,92562,92564,92570],{},[898,92505,4708],{"mathvariant":2334},[898,92507,900],{},[1701,92509,1792],{},[898,92511,900],{},[1701,92513,1799],{"stretchy":1798},[1845,92515,92516,92518],{},[898,92517,1802],{},[1850,92519,4062],{},[1701,92521,1703],{},[898,92523,2312],{"mathvariant":2334},[1845,92525,92526,92528],{},[898,92527,1802],{},[1850,92529,4062],{},[1701,92531,2012],{"separator":2011},[1845,92533,92534,92536],{},[898,92535,1802],{},[1850,92537,3938],{},[1701,92539,1703],{},[898,92541,2312],{"mathvariant":2334},[1845,92543,92544,92546],{},[898,92545,1802],{},[1850,92547,3938],{},[1701,92549,1805],{"stretchy":1798},[1701,92551,2317],{},[898,92553,900],{},[1701,92555,1799],{"stretchy":1798},[1845,92557,92558,92560],{},[898,92559,1802],{},[1850,92561,4062],{},[1701,92563,2012],{"separator":2011},[1845,92565,92566,92568],{},[898,92567,1802],{},[1850,92569,3938],{},[1701,92571,1805],{"stretchy":1798},[902,92573,92574],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,92576,92578],{"id":92577},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,92580,92581,92582,92585,92586,92589],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,92583,92584],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,92587,92588],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,92591,92592,92595,92596,45835,92622,92648,92649,1343,92681,92713,92714,2633,92768,92822],{},[38,92593,92594],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,92597,92599],{"className":92598},[886],[888,92600,92601],{"xmlns":890},[892,92602,92603,92619],{},[895,92604,92605,92611,92613],{},[1845,92606,92607,92609],{},[898,92608,1802],{},[1850,92610,3938],{},[1701,92612,1792],{},[1845,92614,92615,92617],{},[898,92616,207],{},[1850,92618,1852],{},[902,92620,92621],{"encoding":904},"Q_2 = a_0",[883,92623,92625],{"className":92624},[886],[888,92626,92627],{"xmlns":890},[892,92628,92629,92645],{},[895,92630,92631,92637,92639],{},[1845,92632,92633,92635],{},[898,92634,1802],{},[1850,92636,4062],{},[1701,92638,1792],{},[1845,92640,92641,92643],{},[898,92642,3598],{},[1850,92644,1852],{},[902,92646,92647],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,92650,92652],{"className":92651},[886],[888,92653,92654],{"xmlns":890},[892,92655,92656,92678],{},[895,92657,92658,92660,92662,92668,92670,92676],{},[898,92659,900],{},[1701,92661,1799],{"stretchy":1798},[1845,92663,92664,92666],{},[898,92665,1802],{},[1850,92667,4062],{},[1701,92669,2012],{"separator":2011},[1845,92671,92672,92674],{},[898,92673,207],{},[1850,92675,1852],{},[1701,92677,1805],{"stretchy":1798},[902,92679,92680],{"encoding":904},"U(Q_1, a_0)",[883,92682,92684],{"className":92683},[886],[888,92685,92686],{"xmlns":890},[892,92687,92688,92710],{},[895,92689,92690,92692,92694,92700,92702,92708],{},[898,92691,900],{},[1701,92693,1799],{"stretchy":1798},[1845,92695,92696,92698],{},[898,92697,3598],{},[1850,92699,1852],{},[1701,92701,2012],{"separator":2011},[1845,92703,92704,92706],{},[898,92705,1802],{},[1850,92707,3938],{},[1701,92709,1805],{"stretchy":1798},[902,92711,92712],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,92715,92717],{"className":92716},[886],[888,92718,92719],{"xmlns":890},[892,92720,92721,92765],{},[895,92722,92723,92761,92763],{},[2363,92724,92725],{"scriptlevel":1852,"displaystyle":2011},[3726,92726,92727,92751],{},[895,92728,92729,92731,92733,92735,92741,92743,92749],{},[898,92730,2312],{"mathvariant":2334},[898,92732,900],{},[1701,92734,1799],{"stretchy":1798},[1845,92736,92737,92739],{},[898,92738,1802],{},[1850,92740,4062],{},[1701,92742,2012],{"separator":2011},[1845,92744,92745,92747],{},[898,92746,207],{},[1850,92748,1852],{},[1701,92750,1805],{"stretchy":1798},[895,92752,92753,92755],{},[898,92754,2312],{"mathvariant":2334},[1845,92756,92757,92759],{},[898,92758,1802],{},[1850,92760,4062],{},[1701,92762,7491],{},[1850,92764,1852],{},[902,92766,92767],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,92769,92771],{"className":92770},[886],[888,92772,92773],{"xmlns":890},[892,92774,92775,92819],{},[895,92776,92777,92815,92817],{},[2363,92778,92779],{"scriptlevel":1852,"displaystyle":2011},[3726,92780,92781,92805],{},[895,92782,92783,92785,92787,92789,92795,92797,92803],{},[898,92784,2312],{"mathvariant":2334},[898,92786,900],{},[1701,92788,1799],{"stretchy":1798},[1845,92790,92791,92793],{},[898,92792,3598],{},[1850,92794,1852],{},[1701,92796,2012],{"separator":2011},[1845,92798,92799,92801],{},[898,92800,1802],{},[1850,92802,3938],{},[1701,92804,1805],{"stretchy":1798},[895,92806,92807,92809],{},[898,92808,2312],{"mathvariant":2334},[1845,92810,92811,92813],{},[898,92812,1802],{},[1850,92814,3938],{},[1701,92816,7491],{},[1850,92818,1852],{},[902,92820,92821],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,92824,92826],{"className":92825},[886],[888,92827,92828],{"xmlns":890,"display":2252},[892,92829,92830,92875],{},[2256,92831,92832],{"width":2258},[2260,92833,92834,92836,92868,92870],{},[2263,92835],{"width":2265},[2263,92837,92838],{},[895,92839,92840,92848,92850,92852,92854,92856,92864,92866],{},[2287,92841,92842,92844,92846],{},[898,92843,900],{},[1850,92845,4062],{},[1701,92847,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,92849,7491],{},[1850,92851,1852],{},[1701,92853,2012],{"separator":2011},[9942,92855],{"width":19336},[2287,92857,92858,92860,92862],{},[898,92859,900],{},[1850,92861,3938],{},[1701,92863,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,92865,7491],{},[1850,92867,16514],{},[2263,92869],{"width":2265},[2263,92871,92872],{},[1939,92873,92874],{},"(6.4)",[902,92876,92877],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,92879,92880,92881,92883],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,92882,3557],{}," — užitečnost roste s množstvím každého zboží.",[724,92885,92886,92889,92890,92920,92921,2246],{},[38,92887,92888],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,92891,92893],{"className":92892},[886],[888,92894,92895],{"xmlns":890},[892,92896,92897,92917],{},[895,92898,92899,92907,92909],{},[2287,92900,92901,92903,92905],{},[898,92902,900],{},[1850,92904,4062],{},[1701,92906,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,92908,2012],{"separator":2011},[2287,92910,92911,92913,92915],{},[898,92912,900],{},[1850,92914,3938],{},[1701,92916,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,92918,92919],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,92922,92923],{},"záporné",[883,92925,92927],{"className":92926},[886],[888,92928,92929],{"xmlns":890,"display":2252},[892,92930,92931,92984],{},[2256,92932,92933],{"width":2258},[2260,92934,92935,92937,92977,92979],{},[2263,92936],{"width":2265},[2263,92938,92939],{},[895,92940,92941,92953,92955,92957,92959,92961,92973,92975],{},[2287,92942,92943,92945,92947],{},[898,92944,900],{},[1850,92946,4181],{},[895,92948,92949,92951],{},[1701,92950,4783],{"mathvariant":2334},[1701,92952,4783],{"mathvariant":2334},[1701,92954,7530],{},[1850,92956,1852],{},[1701,92958,2012],{"separator":2011},[9942,92960],{"width":19336},[2287,92962,92963,92965,92967],{},[898,92964,900],{},[1850,92966,36577],{},[895,92968,92969,92971],{},[1701,92970,4783],{"mathvariant":2334},[1701,92972,4783],{"mathvariant":2334},[1701,92974,7530],{},[1850,92976,16514],{},[2263,92978],{"width":2265},[2263,92980,92981],{},[1939,92982,92983],{},"(6.5)",[902,92985,92986],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,92988,92989,92990,92993,92994,1715],{},"Podmínka (6.5) je známa jako ",[38,92991,92992],{},"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 ",[207,92995,92997],{"className":92996,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,92999,93000,93001,2633,93033,93065,93066,2633,93092,93118,93119,93147,93148,2633,93150,93152,93153,93188],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,93002,93004],{"className":93003},[886],[888,93005,93006],{"xmlns":890},[892,93007,93008,93030],{},[895,93009,93010,93012,93014,93020,93022,93028],{},[898,93011,900],{},[1701,93013,1799],{"stretchy":1798},[1845,93015,93016,93018],{},[898,93017,1802],{},[1850,93019,4062],{},[1701,93021,2012],{"separator":2011},[1845,93023,93024,93026],{},[898,93025,3598],{},[1850,93027,1852],{},[1701,93029,1805],{"stretchy":1798},[902,93031,93032],{"encoding":904},"U(Q_1, b_0)",[883,93034,93036],{"className":93035},[886],[888,93037,93038],{"xmlns":890},[892,93039,93040,93062],{},[895,93041,93042,93044,93046,93052,93054,93060],{},[898,93043,900],{},[1701,93045,1799],{"stretchy":1798},[1845,93047,93048,93050],{},[898,93049,207],{},[1850,93051,1852],{},[1701,93053,2012],{"separator":2011},[1845,93055,93056,93058],{},[898,93057,1802],{},[1850,93059,3938],{},[1701,93061,1805],{"stretchy":1798},[902,93063,93064],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,93067,93069],{"className":93068},[886],[888,93070,93071],{"xmlns":890},[892,93072,93073,93089],{},[895,93074,93075,93077,93079,93081,93087],{},[1701,93076,1799],{"stretchy":1798},[898,93078,900],{},[1701,93080,2012],{"separator":2011},[1845,93082,93083,93085],{},[898,93084,1802],{},[1850,93086,4062],{},[1701,93088,1805],{"stretchy":1798},[902,93090,93091],{"encoding":904},"(U, Q_1)",[883,93093,93095],{"className":93094},[886],[888,93096,93097],{"xmlns":890},[892,93098,93099,93115],{},[895,93100,93101,93103,93105,93107,93113],{},[1701,93102,1799],{"stretchy":1798},[898,93104,900],{},[1701,93106,2012],{"separator":2011},[1845,93108,93109,93111],{},[898,93110,1802],{},[1850,93112,3938],{},[1701,93114,1805],{"stretchy":1798},[902,93116,93117],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,93120,93122],{"className":93121},[886],[888,93123,93124],{"xmlns":890},[892,93125,93126,93144],{},[895,93127,93128,93130,93132,93134,93136,93138,93140,93142],{},[898,93129,900],{},[1701,93131,1799],{"stretchy":1798},[1850,93133,1852],{},[1701,93135,2012],{"separator":2011},[1850,93137,1852],{},[1701,93139,1805],{"stretchy":1798},[1701,93141,1792],{},[1850,93143,1852],{},[902,93145,93146],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,93149,17711],{},[38,93151,42513],{},". Typický tvar grafu ",[883,93154,93156],{"className":93155},[886],[888,93157,93158],{"xmlns":890},[892,93159,93160,93186],{},[895,93161,93162,93164,93166,93168,93170,93176,93178,93184],{},[898,93163,900],{},[1701,93165,1792],{},[898,93167,900],{},[1701,93169,1799],{"stretchy":1798},[1845,93171,93172,93174],{},[898,93173,1802],{},[1850,93175,4062],{},[1701,93177,2012],{"separator":2011},[1845,93179,93180,93182],{},[898,93181,1802],{},[1850,93183,3938],{},[1701,93185,1805],{"stretchy":1798},[902,93187,91202],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,93190,93191],{},[614,93192,93193,93194,92234,93222,93243,93244,92234,93272,93294],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,93195,93197],{"className":93196},[886],[888,93198,93199],{"xmlns":890},[892,93200,93201,93219],{},[895,93202,93203,93205,93207,93213,93215,93217],{},[898,93204,900],{},[1701,93206,1799],{"stretchy":1798},[1845,93208,93209,93211],{},[898,93210,1802],{},[1850,93212,4062],{},[1701,93214,2012],{"separator":2011},[898,93216,3598],{},[1701,93218,1805],{"stretchy":1798},[902,93220,93221],{"encoding":904},"U(Q_1, b)",[883,93223,93225],{"className":93224},[886],[888,93226,93227],{"xmlns":890},[892,93228,93229,93241],{},[895,93230,93231,93237,93239],{},[1845,93232,93233,93235],{},[898,93234,1802],{},[1850,93236,3938],{},[1701,93238,1792],{},[898,93240,3598],{},[902,93242,92256],{"encoding":904}," (vlevo) a ",[883,93245,93247],{"className":93246},[886],[888,93248,93249],{"xmlns":890},[892,93250,93251,93269],{},[895,93252,93253,93255,93257,93259,93261,93267],{},[898,93254,900],{},[1701,93256,1799],{"stretchy":1798},[898,93258,207],{},[1701,93260,2012],{"separator":2011},[1845,93262,93263,93265],{},[898,93264,1802],{},[1850,93266,3938],{},[1701,93268,1805],{"stretchy":1798},[902,93270,93271],{"encoding":904},"U(a, Q_2)",[883,93273,93275],{"className":93274},[886],[888,93276,93277],{"xmlns":890},[892,93278,93279,93291],{},[895,93280,93281,93287,93289],{},[1845,93282,93283,93285],{},[898,93284,1802],{},[1850,93286,4062],{},[1701,93288,1792],{},[898,93290,207],{},[902,93292,93293],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,93296,93297],{},[614,93298,93299,93300,93335,93336,93366,93367,2633,93390,93412,93413,1715],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,93301,93303],{"className":93302},[886],[888,93304,93305],{"xmlns":890},[892,93306,93307,93333],{},[895,93308,93309,93311,93313,93315,93317,93323,93325,93331],{},[898,93310,900],{},[1701,93312,1792],{},[898,93314,900],{},[1701,93316,1799],{"stretchy":1798},[1845,93318,93319,93321],{},[898,93320,1802],{},[1850,93322,4062],{},[1701,93324,2012],{"separator":2011},[1845,93326,93327,93329],{},[898,93328,1802],{},[1850,93330,3938],{},[1701,93332,1805],{"stretchy":1798},[902,93334,91202],{"encoding":904}," nad rovinou ",[883,93337,93339],{"className":93338},[886],[888,93340,93341],{"xmlns":890},[892,93342,93343,93363],{},[895,93344,93345,93347,93353,93355,93361],{},[1701,93346,1799],{"stretchy":1798},[1845,93348,93349,93351],{},[898,93350,1802],{},[1850,93352,4062],{},[1701,93354,2012],{"separator":2011},[1845,93356,93357,93359],{},[898,93358,1802],{},[1850,93360,3938],{},[1701,93362,1805],{"stretchy":1798},[902,93364,93365],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,93368,93370],{"className":93369},[886],[888,93371,93372],{"xmlns":890},[892,93373,93374,93387],{},[895,93375,93376,93382,93384],{},[1845,93377,93378,93380],{},[898,93379,1802],{},[1850,93381,4062],{},[1701,93383,1792],{},[1939,93385,93386],{},"const",[902,93388,93389],{"encoding":904},"Q_1 = \\text{const}",[883,93391,93393],{"className":93392},[886],[888,93394,93395],{"xmlns":890},[892,93396,93397,93409],{},[895,93398,93399,93405,93407],{},[1845,93400,93401,93403],{},[898,93402,1802],{},[1850,93404,3938],{},[1701,93406,1792],{},[1939,93408,93386],{},[902,93410,93411],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,93414,93416],{"className":93415},[886],[888,93417,93418],{"xmlns":890},[892,93419,93420,93446],{},[895,93421,93422,93424,93426,93432,93434,93440,93442,93444],{},[898,93423,900],{},[1701,93425,1799],{"stretchy":1798},[1845,93427,93428,93430],{},[898,93429,1802],{},[1850,93431,4062],{},[1701,93433,2012],{"separator":2011},[1845,93435,93436,93438],{},[898,93437,1802],{},[1850,93439,3938],{},[1701,93441,1805],{"stretchy":1798},[1701,93443,1792],{},[898,93445,3618],{},[902,93447,13826],{"encoding":904},[198,93449,93451,93452],{"id":93450},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,93453,93455],{"className":93454},[886],[888,93456,93457],{"xmlns":890},[892,93458,93459,93493],{},[895,93460,93461,93463,93465,93479],{},[898,93462,900],{},[1701,93464,1792],{},[2287,93466,93467,93469,93471],{},[898,93468,1802],{},[1850,93470,4062],{},[895,93472,93473,93475,93477],{},[1850,93474,4062],{},[898,93476,8741],{"mathvariant":2334},[1850,93478,3938],{},[2287,93480,93481,93483,93485],{},[898,93482,1802],{},[1850,93484,3938],{},[895,93486,93487,93489,93491],{},[1850,93488,4062],{},[898,93490,8741],{"mathvariant":2334},[1850,93492,3646],{},[902,93494,93495],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,93497,93498],{},[38,93499,93500],{},"Ověření (6.4) a (6.5).",[883,93502,93504],{"className":93503},[886],[888,93505,93506],{"xmlns":890,"display":2252},[892,93507,93508,93612],{},[895,93509,93510,93518,93520,93528,93544,93558,93560,93562,93570,93572,93580,93594,93610],{},[2287,93511,93512,93514,93516],{},[898,93513,900],{},[1850,93515,4062],{},[1701,93517,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,93519,1792],{},[2363,93521,93522],{"scriptlevel":1852,"displaystyle":1798},[3726,93523,93524,93526],{},[1850,93525,4062],{},[1850,93527,3938],{},[2287,93529,93530,93532,93534],{},[898,93531,1802],{},[1850,93533,4062],{},[895,93535,93536,93538,93540,93542],{},[1701,93537,2317],{},[1850,93539,4062],{},[898,93541,8741],{"mathvariant":2334},[1850,93543,3938],{},[2287,93545,93546,93548,93550],{},[898,93547,1802],{},[1850,93549,3938],{},[895,93551,93552,93554,93556],{},[1850,93553,4062],{},[898,93555,8741],{"mathvariant":2334},[1850,93557,3646],{},[1701,93559,2012],{"separator":2011},[9942,93561],{"width":19336},[2287,93563,93564,93566,93568],{},[898,93565,900],{},[1850,93567,3938],{},[1701,93569,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,93571,1792],{},[2363,93573,93574],{"scriptlevel":1852,"displaystyle":1798},[3726,93575,93576,93578],{},[1850,93577,4062],{},[1850,93579,3646],{},[2287,93581,93582,93584,93586],{},[898,93583,1802],{},[1850,93585,4062],{},[895,93587,93588,93590,93592],{},[1850,93589,4062],{},[898,93591,8741],{"mathvariant":2334},[1850,93593,3938],{},[2287,93595,93596,93598,93600],{},[898,93597,1802],{},[1850,93599,3938],{},[895,93601,93602,93604,93606,93608],{},[1701,93603,2317],{},[1850,93605,3938],{},[898,93607,8741],{"mathvariant":2334},[1850,93609,3646],{},[1701,93611,2012],{"separator":2011},[902,93613,93614],{"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},",[724,93616,93617,93618,93652],{},"zřejmě ",[883,93619,93621],{"className":93620},[886],[888,93622,93623],{"xmlns":890},[892,93624,93625,93649],{},[895,93626,93627,93635,93637,93645,93647],{},[2287,93628,93629,93631,93633],{},[898,93630,900],{},[1850,93632,4062],{},[1701,93634,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,93636,2012],{"separator":2011},[2287,93638,93639,93641,93643],{},[898,93640,900],{},[1850,93642,3938],{},[1701,93644,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,93646,7491],{},[1850,93648,1852],{},[902,93650,93651],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,93654,93656],{"className":93655},[886],[888,93657,93658],{"xmlns":890,"display":2252},[892,93659,93660,93776],{},[895,93661,93662,93674,93676,93678,93686,93702,93716,93718,93720,93732,93734,93736,93744,93758,93774],{},[2287,93663,93664,93666,93668],{},[898,93665,900],{},[1850,93667,4181],{},[895,93669,93670,93672],{},[1701,93671,4783],{"mathvariant":2334},[1701,93673,4783],{"mathvariant":2334},[1701,93675,1792],{},[1701,93677,2317],{},[2363,93679,93680],{"scriptlevel":1852,"displaystyle":1798},[3726,93681,93682,93684],{},[1850,93683,4062],{},[1850,93685,6460],{},[2287,93687,93688,93690,93692],{},[898,93689,1802],{},[1850,93691,4062],{},[895,93693,93694,93696,93698,93700],{},[1701,93695,2317],{},[1850,93697,3646],{},[898,93699,8741],{"mathvariant":2334},[1850,93701,3938],{},[2287,93703,93704,93706,93708],{},[898,93705,1802],{},[1850,93707,3938],{},[895,93709,93710,93712,93714],{},[1850,93711,4062],{},[898,93713,8741],{"mathvariant":2334},[1850,93715,3646],{},[1701,93717,2012],{"separator":2011},[9942,93719],{"width":19336},[2287,93721,93722,93724,93726],{},[898,93723,900],{},[1850,93725,36577],{},[895,93727,93728,93730],{},[1701,93729,4783],{"mathvariant":2334},[1701,93731,4783],{"mathvariant":2334},[1701,93733,1792],{},[1701,93735,2317],{},[2363,93737,93738],{"scriptlevel":1852,"displaystyle":1798},[3726,93739,93740,93742],{},[1850,93741,3938],{},[1850,93743,8073],{},[2287,93745,93746,93748,93750],{},[898,93747,1802],{},[1850,93749,4062],{},[895,93751,93752,93754,93756],{},[1850,93753,4062],{},[898,93755,8741],{"mathvariant":2334},[1850,93757,3938],{},[2287,93759,93760,93762,93764],{},[898,93761,1802],{},[1850,93763,3938],{},[895,93765,93766,93768,93770,93772],{},[1701,93767,2317],{},[1850,93769,4225],{},[898,93771,8741],{"mathvariant":2334},[1850,93773,3646],{},[1701,93775,2012],{"separator":2011},[902,93777,93778],{"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},",[724,93780,93781,93782,93824],{},"opět ",[883,93783,93785],{"className":93784},[886],[888,93786,93787],{"xmlns":890},[892,93788,93789,93821],{},[895,93790,93791,93803,93805,93817,93819],{},[2287,93792,93793,93795,93797],{},[898,93794,900],{},[1850,93796,4181],{},[895,93798,93799,93801],{},[1701,93800,4783],{"mathvariant":2334},[1701,93802,4783],{"mathvariant":2334},[1701,93804,2012],{"separator":2011},[2287,93806,93807,93809,93811],{},[898,93808,900],{},[1850,93810,36577],{},[895,93812,93813,93815],{},[1701,93814,4783],{"mathvariant":2334},[1701,93816,4783],{"mathvariant":2334},[1701,93818,7530],{},[1850,93820,1852],{},[902,93822,93823],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,93826,93827],{},[38,93828,93829,93830,1715],{},"(a) Mezní užitečnosti v bodě ",[883,93831,93833],{"className":93832},[886],[888,93834,93835],{"xmlns":890},[892,93836,93837,93849],{},[895,93838,93839,93841,93843,93845,93847],{},[1701,93840,2036],{"stretchy":1798},[1850,93842,5158],{},[1701,93844,2012],{"separator":2011},[1850,93846,12439],{},[1701,93848,2053],{"stretchy":1798},[902,93850,93851],{"encoding":904},"[100, 200]",[883,93853,93855],{"className":93854},[886],[888,93856,93857],{"xmlns":890,"display":2252},[892,93858,93859,93926],{},[895,93860,93861,93863,93869,93871,93873,93875,93877,93879,93881,93889,93891,93905,93907,93919,93921,93924],{},[898,93862,6909],{},[1845,93864,93865,93867],{},[898,93866,900],{},[1850,93868,4062],{},[1701,93870,1799],{"stretchy":1798},[1850,93872,5158],{},[1701,93874,2012],{"separator":2011},[1850,93876,12439],{},[1701,93878,1805],{"stretchy":1798},[1701,93880,1792],{},[2363,93882,93883],{"scriptlevel":1852,"displaystyle":1798},[3726,93884,93885,93887],{},[1850,93886,4062],{},[1850,93888,3938],{},[1701,93890,3408],{},[3243,93892,93893,93895],{},[1850,93894,5158],{},[895,93896,93897,93899,93901,93903],{},[1701,93898,2317],{},[1850,93900,4062],{},[898,93902,8741],{"mathvariant":2334},[1850,93904,3938],{},[1701,93906,3408],{},[3243,93908,93909,93911],{},[1850,93910,12439],{},[895,93912,93913,93915,93917],{},[1850,93914,4062],{},[898,93916,8741],{"mathvariant":2334},[1850,93918,3646],{},[1701,93920,3782],{},[1850,93922,93923],{},"0,4204",[1701,93925,2012],{"separator":2011},[902,93927,93928],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,93930,93932],{"className":93931},[886],[888,93933,93934],{"xmlns":890,"display":2252},[892,93935,93936,94001],{},[895,93937,93938,93940,93946,93948,93950,93952,93954,93956,93958,93966,93968,93980,93982,93996,93998],{},[898,93939,6909],{},[1845,93941,93942,93944],{},[898,93943,900],{},[1850,93945,3938],{},[1701,93947,1799],{"stretchy":1798},[1850,93949,5158],{},[1701,93951,2012],{"separator":2011},[1850,93953,12439],{},[1701,93955,1805],{"stretchy":1798},[1701,93957,1792],{},[2363,93959,93960],{"scriptlevel":1852,"displaystyle":1798},[3726,93961,93962,93964],{},[1850,93963,4062],{},[1850,93965,3646],{},[1701,93967,3408],{},[3243,93969,93970,93972],{},[1850,93971,5158],{},[895,93973,93974,93976,93978],{},[1850,93975,4062],{},[898,93977,8741],{"mathvariant":2334},[1850,93979,3938],{},[1701,93981,3408],{},[3243,93983,93984,93986],{},[1850,93985,12439],{},[895,93987,93988,93990,93992,93994],{},[1701,93989,2317],{},[1850,93991,3938],{},[898,93993,8741],{"mathvariant":2334},[1850,93995,3646],{},[1701,93997,3782],{},[1850,93999,94000],{},"0,63067.",[902,94002,94003],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,94005,94006,4088,94008,94043,94044,94065,94066,94083],{},[614,94007,13276],{},[883,94009,94011],{"className":94010},[886],[888,94012,94013],{"xmlns":890},[892,94014,94015,94040],{},[895,94016,94017,94019,94025,94027,94029,94031,94033,94035,94037],{},[898,94018,6909],{},[1845,94020,94021,94023],{},[898,94022,900],{},[1850,94024,3938],{},[1701,94026,1799],{"stretchy":1798},[1850,94028,5158],{},[1701,94030,2012],{"separator":2011},[1850,94032,12439],{},[1701,94034,1805],{"stretchy":1798},[1701,94036,3782],{},[1850,94038,94039],{},"0,63067",[902,94041,94042],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,94045,94047],{"className":94046},[886],[888,94048,94049],{"xmlns":890},[892,94050,94051,94063],{},[895,94052,94053,94055,94057,94059,94061],{},[1701,94054,2036],{"stretchy":1798},[1850,94056,5158],{},[1701,94058,2012],{"separator":2011},[1850,94060,12439],{},[1701,94062,2053],{"stretchy":1798},[902,94064,93851],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,94067,94069],{"className":94068},[886],[888,94070,94071],{"xmlns":890},[892,94072,94073,94081],{},[895,94074,94075],{},[1845,94076,94077,94079],{},[898,94078,1802],{},[1850,94080,3938],{},[902,94082,33055],{"encoding":904}," přibližně o 0,63067.",[724,94085,94086,94105,94106,43208,94127,94144,94145,94171,94172,94189,94190,4539],{},[38,94087,94088,94089,94104],{},"(b) Odhad změny ",[883,94090,94092],{"className":94091},[886],[888,94093,94094],{"xmlns":890},[892,94095,94096,94102],{},[895,94097,94098,94100],{},[898,94099,4708],{"mathvariant":2334},[898,94101,900],{},[902,94103,92347],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,94107,94109],{"className":94108},[886],[888,94110,94111],{"xmlns":890},[892,94112,94113,94125],{},[895,94114,94115,94117,94119,94121,94123],{},[1701,94116,2036],{"stretchy":1798},[1850,94118,5158],{},[1701,94120,2012],{"separator":2011},[1850,94122,12439],{},[1701,94124,2053],{"stretchy":1798},[902,94126,93851],{"encoding":904},[883,94128,94130],{"className":94129},[886],[888,94131,94132],{"xmlns":890},[892,94133,94134,94142],{},[895,94135,94136],{},[1845,94137,94138,94140],{},[898,94139,1802],{},[1850,94141,4062],{},[902,94143,33036],{"encoding":904}," na 98 (tj. ",[883,94146,94148],{"className":94147},[886],[888,94149,94150],{"xmlns":890},[892,94151,94152,94168],{},[895,94153,94154,94156,94162,94164,94166],{},[898,94155,2312],{"mathvariant":2334},[1845,94157,94158,94160],{},[898,94159,1802],{},[1850,94161,4062],{},[1701,94163,1792],{},[1701,94165,2317],{},[1850,94167,3938],{},[902,94169,94170],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,94173,94175],{"className":94174},[886],[888,94176,94177],{"xmlns":890},[892,94178,94179,94187],{},[895,94180,94181],{},[1845,94182,94183,94185],{},[898,94184,1802],{},[1850,94186,3938],{},[902,94188,33055],{"encoding":904}," o 3 (tj. ",[883,94191,94193],{"className":94192},[886],[888,94194,94195],{"xmlns":890},[892,94196,94197,94211],{},[895,94198,94199,94201,94207,94209],{},[898,94200,2312],{"mathvariant":2334},[1845,94202,94203,94205],{},[898,94204,1802],{},[1850,94206,3938],{},[1701,94208,1792],{},[1850,94210,3646],{},[902,94212,94213],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,94215,94217],{"className":94216},[886],[888,94218,94219],{"xmlns":890,"display":2252},[892,94220,94221,94272],{},[895,94222,94223,94225,94227,94229,94231,94233,94235,94237,94239,94241,94243,94245,94247,94249,94251,94253,94255,94257,94259,94262,94264,94267,94269],{},[898,94224,4708],{"mathvariant":2334},[898,94226,900],{},[1701,94228,4067],{},[898,94230,2312],{"mathvariant":2334},[898,94232,900],{},[1701,94234,1792],{},[1850,94236,93923],{},[1701,94238,3408],{},[1701,94240,1799],{"stretchy":1798},[1701,94242,2317],{},[1850,94244,3938],{},[1701,94246,1805],{"stretchy":1798},[1701,94248,1703],{},[1850,94250,94039],{},[1701,94252,3408],{},[1850,94254,3646],{},[1701,94256,1792],{},[1701,94258,2317],{},[1850,94260,94261],{},"0,8408",[1701,94263,1703],{},[1850,94265,94266],{},"1,89201",[1701,94268,3782],{},[1850,94270,94271],{},"1,05.",[902,94273,94274],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,94276,94277,94278,94281,94282,94333,94334,1715],{},"Užitečnost se tedy zvýší přibližně o ",[38,94279,94280],{},"1,05",". Skutečná změna je ",[883,94283,94285],{"className":94284},[886],[888,94286,94287],{"xmlns":890},[892,94288,94289,94330],{},[895,94290,94291,94293,94295,94297,94299,94301,94304,94306,94309,94311,94313,94315,94317,94319,94321,94323,94325,94327],{},[898,94292,4708],{"mathvariant":2334},[898,94294,900],{},[1701,94296,1792],{},[898,94298,900],{},[1701,94300,1799],{"stretchy":1798},[1850,94302,94303],{},"98",[1701,94305,2012],{"separator":2011},[1850,94307,94308],{},"203",[1701,94310,1805],{"stretchy":1798},[1701,94312,2317],{},[898,94314,900],{},[1701,94316,1799],{"stretchy":1798},[1850,94318,5158],{},[1701,94320,2012],{"separator":2011},[1850,94322,12439],{},[1701,94324,1805],{"stretchy":1798},[1701,94326,3782],{},[1850,94328,94329],{},"1,031",[902,94331,94332],{"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 ",[883,94335,94337],{"className":94336},[886],[888,94338,94339],{"xmlns":890},[892,94340,94341,94361],{},[895,94342,94343,94345,94351,94353,94355],{},[898,94344,2312],{"mathvariant":2334},[1845,94346,94347,94349],{},[898,94348,1802],{},[1850,94350,4062],{},[1701,94352,2012],{"separator":2011},[898,94354,2312],{"mathvariant":2334},[1845,94356,94357,94359],{},[898,94358,1802],{},[1850,94360,3938],{},[902,94362,92377],{"encoding":904},[115,94364,94366],{"id":94365},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,94368,94369],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,94371,94373],{"className":94372},[886],[888,94374,94375],{"xmlns":890,"display":2252},[892,94376,94377,94436],{},[2256,94378,94379],{"width":2258},[2260,94380,94381,94383,94429,94431],{},[2263,94382],{"width":2265},[2263,94384,94385],{},[895,94386,94387,94389,94391,94397,94399,94405,94407,94409,94417,94419,94427],{},[898,94388,900],{},[1701,94390,1799],{"stretchy":1798},[1845,94392,94393,94395],{},[898,94394,1802],{},[1850,94396,4062],{},[1701,94398,2012],{"separator":2011},[1845,94400,94401,94403],{},[898,94402,1802],{},[1850,94404,3938],{},[1701,94406,1805],{"stretchy":1798},[1701,94408,1792],{},[2287,94410,94411,94413,94415],{},[898,94412,1802],{},[1850,94414,4062],{},[898,94416,207],{},[1701,94418,3408],{},[2287,94420,94421,94423,94425],{},[898,94422,1802],{},[1850,94424,3938],{},[898,94426,3598],{},[1701,94428,2012],{"separator":2011},[2263,94430],{"width":2265},[2263,94432,94433],{},[1939,94434,94435],{},"(6.6)",[902,94437,94438],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,94440,8380,94441,94459,94460,94462,94463,94467,94468,94498,94499,94521],{},[883,94442,94444],{"className":94443},[886],[888,94445,94446],{"xmlns":890},[892,94447,94448,94456],{},[895,94449,94450,94452,94454],{},[898,94451,207],{},[1701,94453,2012],{"separator":2011},[898,94455,3598],{},[902,94457,94458],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,94461,78445],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,94464,94466],{"className":94465,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,94469,94471],{"className":94470},[886],[888,94472,94473],{"xmlns":890},[892,94474,94475,94495],{},[895,94476,94477,94479,94481,94483,94485,94487,94489,94491,94493],{},[898,94478,207],{},[1701,94480,2012],{"separator":2011},[898,94482,3598],{},[1701,94484,10569],{},[1701,94486,1799],{"stretchy":1798},[1850,94488,1852],{},[1701,94490,2012],{"separator":2011},[1850,94492,4062],{},[1701,94494,1805],{"stretchy":1798},[902,94496,94497],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,94500,94502],{"className":94501},[886],[888,94503,94504],{"xmlns":890},[892,94505,94506,94518],{},[895,94507,94508,94510,94512,94514,94516],{},[898,94509,3598],{},[1701,94511,1792],{},[1850,94513,4062],{},[1701,94515,2317],{},[898,94517,207],{},[902,94519,94520],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,94523,94524],{},[2139,94525],{"alt":94526,"className":94527,"src":94528},"imek-cobb-douglas-3d-plus-ic",[210,2143],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,94530,94532],{"className":94531},[886],[888,94533,94534],{"xmlns":890,"display":2252},[892,94535,94536,94586],{},[895,94537,94538,94540,94542,94548,94550,94556,94558,94560,94568,94570,94584],{},[898,94539,900],{},[1701,94541,1799],{"stretchy":1798},[1845,94543,94544,94546],{},[898,94545,1802],{},[1850,94547,4062],{},[1701,94549,2012],{"separator":2011},[1845,94551,94552,94554],{},[898,94553,1802],{},[1850,94555,3938],{},[1701,94557,1805],{"stretchy":1798},[1701,94559,1792],{},[2287,94561,94562,94564,94566],{},[898,94563,1802],{},[1850,94565,4062],{},[898,94567,207],{},[1701,94569,3408],{},[2287,94571,94572,94574,94576],{},[898,94573,1802],{},[1850,94575,3938],{},[895,94577,94578,94580,94582],{},[1850,94579,4062],{},[1701,94581,2317],{},[898,94583,207],{},[898,94585,1715],{"mathvariant":2334},[902,94587,94588],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1635,94590,94591,94640,94762,94896],{},[724,94592,94593,94595,94596],{},[883,94594,3575],{}," Příklad 6.3 — ověření vlastností pro ",[883,94597,94599],{"className":94598},[886],[888,94600,94601],{"xmlns":890},[892,94602,94603,94637],{},[895,94604,94605,94607,94609,94623],{},[898,94606,900],{},[1701,94608,1792],{},[2287,94610,94611,94613,94615],{},[898,94612,1802],{},[1850,94614,4062],{},[895,94616,94617,94619,94621],{},[1850,94618,4062],{},[898,94620,8741],{"mathvariant":2334},[1850,94622,6460],{},[2287,94624,94625,94627,94629],{},[898,94626,1802],{},[1850,94628,3938],{},[895,94630,94631,94633,94635],{},[1850,94632,3646],{},[898,94634,8741],{"mathvariant":2334},[1850,94636,6460],{},[902,94638,94639],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,94641,94643],{"className":94642},[886],[888,94644,94645],{"xmlns":890,"display":2252},[892,94646,94647,94759],{},[895,94648,94649,94657,94659,94667,94683,94697,94699,94701,94703,94705,94713,94715,94723,94737,94753,94755,94757],{},[2287,94650,94651,94653,94655],{},[898,94652,900],{},[1850,94654,4062],{},[1701,94656,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,94658,1792],{},[2363,94660,94661],{"scriptlevel":1852,"displaystyle":1798},[3726,94662,94663,94665],{},[1850,94664,4062],{},[1850,94666,6460],{},[2287,94668,94669,94671,94673],{},[898,94670,1802],{},[1850,94672,4062],{},[895,94674,94675,94677,94679,94681],{},[1701,94676,2317],{},[1850,94678,3646],{},[898,94680,8741],{"mathvariant":2334},[1850,94682,6460],{},[2287,94684,94685,94687,94689],{},[898,94686,1802],{},[1850,94688,3938],{},[895,94690,94691,94693,94695],{},[1850,94692,3646],{},[898,94694,8741],{"mathvariant":2334},[1850,94696,6460],{},[1701,94698,7491],{},[1850,94700,1852],{},[1701,94702,2012],{"separator":2011},[9942,94704],{"width":19336},[2287,94706,94707,94709,94711],{},[898,94708,900],{},[1850,94710,3938],{},[1701,94712,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,94714,1792],{},[2363,94716,94717],{"scriptlevel":1852,"displaystyle":1798},[3726,94718,94719,94721],{},[1850,94720,3646],{},[1850,94722,6460],{},[2287,94724,94725,94727,94729],{},[898,94726,1802],{},[1850,94728,4062],{},[895,94730,94731,94733,94735],{},[1850,94732,4062],{},[898,94734,8741],{"mathvariant":2334},[1850,94736,6460],{},[2287,94738,94739,94741,94743],{},[898,94740,1802],{},[1850,94742,3938],{},[895,94744,94745,94747,94749,94751],{},[1701,94746,2317],{},[1850,94748,4062],{},[898,94750,8741],{"mathvariant":2334},[1850,94752,6460],{},[1701,94754,7491],{},[1850,94756,1852],{},[1701,94758,2012],{"separator":2011},[902,94760,94761],{"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,",[883,94763,94765],{"className":94764},[886],[888,94766,94767],{"xmlns":890,"display":2252},[892,94768,94769,94893],{},[895,94770,94771,94783,94785,94787,94795,94811,94825,94827,94829,94831,94833,94845,94847,94849,94857,94871,94887,94889,94891],{},[2287,94772,94773,94775,94777],{},[898,94774,900],{},[1850,94776,4181],{},[895,94778,94779,94781],{},[1701,94780,4783],{"mathvariant":2334},[1701,94782,4783],{"mathvariant":2334},[1701,94784,1792],{},[1701,94786,2317],{},[2363,94788,94789],{"scriptlevel":1852,"displaystyle":1798},[3726,94790,94791,94793],{},[1850,94792,3646],{},[1850,94794,45883],{},[2287,94796,94797,94799,94801],{},[898,94798,1802],{},[1850,94800,4062],{},[895,94802,94803,94805,94807,94809],{},[1701,94804,2317],{},[1850,94806,28239],{},[898,94808,8741],{"mathvariant":2334},[1850,94810,6460],{},[2287,94812,94813,94815,94817],{},[898,94814,1802],{},[1850,94816,3938],{},[895,94818,94819,94821,94823],{},[1850,94820,3646],{},[898,94822,8741],{"mathvariant":2334},[1850,94824,6460],{},[1701,94826,7530],{},[1850,94828,1852],{},[1701,94830,2012],{"separator":2011},[9942,94832],{"width":19336},[2287,94834,94835,94837,94839],{},[898,94836,900],{},[1850,94838,36577],{},[895,94840,94841,94843],{},[1701,94842,4783],{"mathvariant":2334},[1701,94844,4783],{"mathvariant":2334},[1701,94846,1792],{},[1701,94848,2317],{},[2363,94850,94851],{"scriptlevel":1852,"displaystyle":1798},[3726,94852,94853,94855],{},[1850,94854,3646],{},[1850,94856,45883],{},[2287,94858,94859,94861,94863],{},[898,94860,1802],{},[1850,94862,4062],{},[895,94864,94865,94867,94869],{},[1850,94866,4062],{},[898,94868,8741],{"mathvariant":2334},[1850,94870,6460],{},[2287,94872,94873,94875,94877],{},[898,94874,1802],{},[1850,94876,3938],{},[895,94878,94879,94881,94883,94885],{},[1701,94880,2317],{},[1850,94882,4225],{},[898,94884,8741],{"mathvariant":2334},[1850,94886,6460],{},[1701,94888,7530],{},[1850,94890,1852],{},[1701,94892,2012],{"separator":2011},[902,94894,94895],{"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,",[724,94897,94898],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,94900,94902],{"id":94901},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,94904,94905,94908],{},[38,94906,94907],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,94910,94912],{"className":94911},[886],[888,94913,94914],{"xmlns":890,"display":2252},[892,94915,94916,94959],{},[2256,94917,94918],{"width":2258},[2260,94919,94920,94922,94952,94954],{},[2263,94921],{"width":2265},[2263,94923,94924],{},[895,94925,94926,94928,94930,94936,94938,94944,94946,94948,94950],{},[898,94927,900],{},[1701,94929,1799],{"stretchy":1798},[1845,94931,94932,94934],{},[898,94933,1802],{},[1850,94935,4062],{},[1701,94937,2012],{"separator":2011},[1845,94939,94940,94942],{},[898,94941,1802],{},[1850,94943,3938],{},[1701,94945,1805],{"stretchy":1798},[1701,94947,1792],{},[898,94949,3618],{},[1701,94951,2012],{"separator":2011},[2263,94953],{"width":2265},[2263,94955,94956],{},[1939,94957,94958],{},"(6.7)",[902,94960,94961],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,94963,8380,94964,94977],{},[883,94965,94967],{"className":94966},[886],[888,94968,94969],{"xmlns":890},[892,94970,94971,94975],{},[895,94972,94973],{},[898,94974,3618],{},[902,94976,3618],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,94979,94981],{"className":94980},[886],[888,94982,94983],{"xmlns":890,"display":2252},[892,94984,94985,95026],{},[2256,94986,94987],{"width":2258},[2260,94988,94989,94991,95019,95021],{},[2263,94990],{"width":2265},[2263,94992,94993],{},[895,94994,94995,95003,95005,95013,95015,95017],{},[2287,94996,94997,94999,95001],{},[898,94998,1802],{},[1850,95000,4062],{},[898,95002,207],{},[1701,95004,3408],{},[2287,95006,95007,95009,95011],{},[898,95008,1802],{},[1850,95010,3938],{},[898,95012,3598],{},[1701,95014,1792],{},[898,95016,3618],{},[898,95018,1715],{"mathvariant":2334},[2263,95020],{"width":2265},[2263,95022,95023],{},[1939,95024,95025],{},"(6.8)",[902,95027,95028],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,95030,95031,95032,8428,95062,4088,95065,95078,95079,95114,95115,95132,95133,95162,95163,95166],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,95033,95035],{"className":95034},[886],[888,95036,95037],{"xmlns":890},[892,95038,95039,95059],{},[895,95040,95041,95043,95049,95051,95057],{},[1701,95042,2036],{"stretchy":1798},[1845,95044,95045,95047],{},[898,95046,1802],{},[1850,95048,4062],{},[1701,95050,2012],{"separator":2011},[1845,95052,95053,95055],{},[898,95054,1802],{},[1850,95056,3938],{},[1701,95058,2053],{"stretchy":1798},[902,95060,95061],{"encoding":904},"[Q_1, Q_2]",[38,95063,95064],{},"stejnou úrovní uspokojení",[883,95066,95068],{"className":95067},[886],[888,95069,95070],{"xmlns":890},[892,95071,95072,95076],{},[895,95073,95074],{},[898,95075,3618],{},[902,95077,3618],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,95080,95082],{"className":95081},[886],[888,95083,95084],{"xmlns":890},[892,95085,95086,95112],{},[895,95087,95088,95090,95092,95094,95096,95102,95104,95110],{},[898,95089,900],{},[1701,95091,1792],{},[898,95093,900],{},[1701,95095,1799],{"stretchy":1798},[1845,95097,95098,95100],{},[898,95099,1802],{},[1850,95101,4062],{},[1701,95103,2012],{"separator":2011},[1845,95105,95106,95108],{},[898,95107,1802],{},[1850,95109,3938],{},[1701,95111,1805],{"stretchy":1798},[902,95113,91202],{"encoding":904}," s rovinami ",[883,95116,95118],{"className":95117},[886],[888,95119,95120],{"xmlns":890},[892,95121,95122,95130],{},[895,95123,95124,95126,95128],{},[898,95125,900],{},[1701,95127,1792],{},[898,95129,3618],{},[902,95131,90418],{"encoding":904}," rovnoběžnými s rovinou ",[883,95134,95136],{"className":95135},[886],[888,95137,95138],{"xmlns":890},[892,95139,95140,95160],{},[895,95141,95142,95144,95150,95152,95158],{},[1701,95143,1799],{"stretchy":1798},[1845,95145,95146,95148],{},[898,95147,1802],{},[1850,95149,4062],{},[1701,95151,2012],{"separator":2011},[1845,95153,95154,95156],{},[898,95155,1802],{},[1850,95157,3938],{},[1701,95159,1805],{"stretchy":1798},[902,95161,93365],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,95164,95165],{},"izokvantami"," produkčních funkcí.",[724,95168,95169],{},[614,95170,95171,95172,93243,95190,95208,95209,1715],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,95173,95175],{"className":95174},[886],[888,95176,95177],{"xmlns":890},[892,95178,95179,95187],{},[895,95180,95181,95183,95185],{},[898,95182,207],{},[1701,95184,7530],{},[898,95186,3598],{},[902,95188,95189],{"encoding":904},"a \u003C b",[883,95191,95193],{"className":95192},[886],[888,95194,95195],{"xmlns":890},[892,95196,95197,95205],{},[895,95198,95199,95201,95203],{},[898,95200,207],{},[1701,95202,7491],{},[898,95204,3598],{},[902,95206,95207],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,95210,95212],{"className":95211},[886],[888,95213,95214],{"xmlns":890},[892,95215,95216,95240],{},[895,95217,95218,95224,95226,95232,95234],{},[1845,95219,95220,95222],{},[898,95221,3618],{},[1850,95223,1852],{},[1701,95225,7530],{},[1845,95227,95228,95230],{},[898,95229,3618],{},[1850,95231,4062],{},[1701,95233,7530],{},[1845,95235,95236,95238],{},[898,95237,3618],{},[1850,95239,3938],{},[902,95241,95242],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,95244,95245],{},[614,95246,95247,95248,95277,95278,95336,95337,95355],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,95249,95251],{"className":95250},[886],[888,95252,95253],{"xmlns":890},[892,95254,95255,95275],{},[895,95256,95257,95259,95265,95267,95273],{},[1701,95258,1799],{"stretchy":1798},[1845,95260,95261,95263],{},[898,95262,1802],{},[1850,95264,4062],{},[1701,95266,2012],{"separator":2011},[1845,95268,95269,95271],{},[898,95270,1802],{},[1850,95272,3938],{},[1701,95274,1805],{"stretchy":1798},[902,95276,93365],{"encoding":904},"; body ",[883,95279,95281],{"className":95280},[886],[888,95282,95283],{"xmlns":890},[892,95284,95285,95333],{},[895,95286,95287,95289,95291,95293,95299,95301,95307,95309,95311,95313,95315,95317,95323,95325,95331],{},[898,95288,1983],{},[1701,95290,1792],{},[1701,95292,2036],{"stretchy":1798},[1845,95294,95295,95297],{},[898,95296,207],{},[1850,95298,4062],{},[1701,95300,2012],{"separator":2011},[1845,95302,95303,95305],{},[898,95304,207],{},[1850,95306,3938],{},[1701,95308,2053],{"stretchy":1798},[1701,95310,2012],{"separator":2011},[898,95312,2593],{},[1701,95314,1792],{},[1701,95316,2036],{"stretchy":1798},[1845,95318,95319,95321],{},[898,95320,3598],{},[1850,95322,4062],{},[1701,95324,2012],{"separator":2011},[1845,95326,95327,95329],{},[898,95328,3598],{},[1850,95330,3938],{},[1701,95332,2053],{"stretchy":1798},[902,95334,95335],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,95338,95340],{"className":95339},[886],[888,95341,95342],{"xmlns":890},[892,95343,95344,95352],{},[895,95345,95346,95348,95350],{},[898,95347,1658],{},[1701,95349,2012],{"separator":2011},[898,95351,1795],{},[902,95353,95354],{"encoding":904},"C, D"," na vyšší hladině.",[1635,95357,95358],{},[724,95359,95360,95362,95363,95425,95426,95470,95471,95505,95506,30226,95524,95505,95578,30226,95596,95672],{},[883,95361,3575],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,95364,95366],{"className":95365},[886],[888,95367,95368],{"xmlns":890},[892,95369,95370,95422],{},[895,95371,95372,95374,95376,95382,95384,95390,95392,95394,95408],{},[898,95373,900],{},[1701,95375,1799],{"stretchy":1798},[1845,95377,95378,95380],{},[898,95379,1802],{},[1850,95381,4062],{},[1701,95383,2012],{"separator":2011},[1845,95385,95386,95388],{},[898,95387,1802],{},[1850,95389,3938],{},[1701,95391,1805],{"stretchy":1798},[1701,95393,1792],{},[2287,95395,95396,95398,95400],{},[898,95397,1802],{},[1850,95399,4062],{},[895,95401,95402,95404,95406],{},[1850,95403,4062],{},[898,95405,8741],{"mathvariant":2334},[1850,95407,6460],{},[2287,95409,95410,95412,95414],{},[898,95411,1802],{},[1850,95413,3938],{},[895,95415,95416,95418,95420],{},[1850,95417,3646],{},[898,95419,8741],{"mathvariant":2334},[1850,95421,6460],{},[902,95423,95424],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,95427,95429],{"className":95428},[886],[888,95430,95431],{"xmlns":890},[892,95432,95433,95467],{},[895,95434,95435,95449,95463,95465],{},[2287,95436,95437,95439,95441],{},[898,95438,1802],{},[1850,95440,4062],{},[895,95442,95443,95445,95447],{},[1850,95444,4062],{},[898,95446,8741],{"mathvariant":2334},[1850,95448,6460],{},[2287,95450,95451,95453,95455],{},[898,95452,1802],{},[1850,95454,3938],{},[895,95456,95457,95459,95461],{},[1850,95458,3646],{},[898,95460,8741],{"mathvariant":2334},[1850,95462,6460],{},[1701,95464,1792],{},[898,95466,3618],{},[902,95468,95469],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,95472,95474],{"className":95473},[886],[888,95475,95476],{"xmlns":890},[892,95477,95478,95502],{},[895,95479,95480,95486,95494,95496],{},[1845,95481,95482,95484],{},[898,95483,1802],{},[1850,95485,4062],{},[2287,95487,95488,95490,95492],{},[898,95489,1802],{},[1850,95491,3938],{},[1850,95493,3646],{},[1701,95495,1792],{},[3243,95497,95498,95500],{},[898,95499,3618],{},[1850,95501,6460],{},[902,95503,95504],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,95507,95509],{"className":95508},[886],[888,95510,95511],{"xmlns":890},[892,95512,95513,95521],{},[895,95514,95515,95517,95519],{},[898,95516,3618],{},[1701,95518,1792],{},[1850,95520,4062],{},[902,95522,95523],{"encoding":904},"c = 1",[883,95525,95527],{"className":95526},[886],[888,95528,95529],{"xmlns":890},[892,95530,95531,95575],{},[895,95532,95533,95539,95541,95557,95559],{},[1845,95534,95535,95537],{},[898,95536,1802],{},[1850,95538,3938],{},[1701,95540,1792],{},[2287,95542,95543,95545,95547],{},[898,95544,1802],{},[1850,95546,4062],{},[895,95548,95549,95551,95553,95555],{},[1701,95550,2317],{},[1850,95552,4062],{},[898,95554,8741],{"mathvariant":2334},[1850,95556,3646],{},[1701,95558,1792],{},[2363,95560,95561],{"scriptlevel":1852,"displaystyle":2011},[3726,95562,95563,95565],{},[1850,95564,4062],{},[85773,95566,95567,95573],{},[1845,95568,95569,95571],{},[898,95570,1802],{},[1850,95572,4062],{},[1850,95574,3646],{},[902,95576,95577],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,95579,95581],{"className":95580},[886],[888,95582,95583],{"xmlns":890},[892,95584,95585,95593],{},[895,95586,95587,95589,95591],{},[898,95588,3618],{},[1701,95590,1792],{},[1850,95592,3938],{},[902,95594,95595],{"encoding":904},"c = 2",[883,95597,95599],{"className":95598},[886],[888,95600,95601],{"xmlns":890},[892,95602,95603,95669],{},[895,95604,95605,95611,95613,95625,95627,95643,95645],{},[1845,95606,95607,95609],{},[898,95608,1802],{},[1850,95610,3938],{},[1701,95612,1792],{},[3243,95614,95615,95617],{},[1850,95616,3938],{},[895,95618,95619,95621,95623],{},[1850,95620,6460],{},[898,95622,8741],{"mathvariant":2334},[1850,95624,3646],{},[1701,95626,3408],{},[2287,95628,95629,95631,95633],{},[898,95630,1802],{},[1850,95632,4062],{},[895,95634,95635,95637,95639,95641],{},[1701,95636,2317],{},[1850,95638,4062],{},[898,95640,8741],{"mathvariant":2334},[1850,95642,3646],{},[1701,95644,1792],{},[2363,95646,95647],{"scriptlevel":1852,"displaystyle":2011},[3726,95648,95649,95659],{},[895,95650,95651,95653],{},[1850,95652,3938],{},[85773,95654,95655,95657],{},[1850,95656,3938],{},[1850,95658,3646],{},[85773,95660,95661,95667],{},[1845,95662,95663,95665],{},[898,95664,1802],{},[1850,95666,4062],{},[1850,95668,3646],{},[902,95670,95671],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,95674,95676],{"id":95675},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,95678,95679],{},[2139,95680],{"alt":95681,"className":95682,"src":95683},"imek-ic-4vlastnosti-anotovane",[210,2143],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1635,95685,95686,95695,95742,95786,95792,95798],{},[724,95687,95688,95690,95691,95694],{},[883,95689,4695],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,95692,95693],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,95696,95697],{},[883,95698,95700],{"className":95699},[886],[888,95701,95702],{"xmlns":890},[892,95703,95704,95739],{},[895,95705,95706,95709,95711,95713,95715,95717,95735,95737],{},[898,95707,95708],{"mathvariant":2334},"tg",[1701,95710,59946],{},[898,95712,22908],{},[1701,95714,1792],{},[1701,95716,2317],{},[3726,95718,95719,95727],{},[2287,95720,95721,95723,95725],{},[898,95722,900],{},[1850,95724,4062],{},[1701,95726,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,95728,95729,95731,95733],{},[898,95730,900],{},[1850,95732,3938],{},[1701,95734,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,95736,7530],{},[1850,95738,1852],{},[902,95740,95741],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,95743,95744,95745,95785],{},"(derivace implicitně zadané funkce ",[883,95746,95748],{"className":95747},[886],[888,95749,95750],{"xmlns":890},[892,95751,95752,95782],{},[895,95753,95754,95756,95758,95764,95766,95772,95774,95776,95778,95780],{},[898,95755,900],{},[1701,95757,1799],{"stretchy":1798},[1845,95759,95760,95762],{},[898,95761,1802],{},[1850,95763,4062],{},[1701,95765,2012],{"separator":2011},[1845,95767,95768,95770],{},[898,95769,1802],{},[1850,95771,3938],{},[1701,95773,1805],{"stretchy":1798},[1701,95775,2317],{},[898,95777,3618],{},[1701,95779,1792],{},[1850,95781,1852],{},[902,95783,95784],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,95787,95788,95791],{},[38,95789,95790],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,95793,95794,95797],{},[38,95795,95796],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,95799,95800,95803,95804,95822,95823,95839,95840,95843],{},[38,95801,95802],{},"4° Konvexní."," Pro každé dva body ",[883,95805,95807],{"className":95806},[886],[888,95808,95809],{"xmlns":890},[892,95810,95811,95819],{},[895,95812,95813,95815,95817],{},[898,95814,1983],{},[1701,95816,2012],{"separator":2011},[898,95818,2593],{},[902,95820,95821],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,95824,95826],{"className":95825},[886],[888,95827,95828],{"xmlns":890},[892,95829,95830,95836],{},[895,95831,95832,95834],{},[898,95833,1983],{},[898,95835,2593],{},[902,95837,95838],{"encoding":904},"AB"," ve ",[38,95841,95842],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,95845,95846],{},[614,95847,95848,95849,95884,95885,1715],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,95850,95852],{"className":95851},[886],[888,95853,95854],{"xmlns":890},[892,95855,95856,95882],{},[895,95857,95858,95860,95862,95868,95870,95876,95878,95880],{},[898,95859,900],{},[1701,95861,1799],{"stretchy":1798},[1845,95863,95864,95866],{},[898,95865,1802],{},[1850,95867,4062],{},[1701,95869,2012],{"separator":2011},[1845,95871,95872,95874],{},[898,95873,1802],{},[1850,95875,3938],{},[1701,95877,1805],{"stretchy":1798},[1701,95879,1792],{},[898,95881,3618],{},[902,95883,13826],{"encoding":904}," s tečnou se sklonem ",[883,95886,95888],{"className":95887},[886],[888,95889,95890],{"xmlns":890},[892,95891,95892,95900],{},[895,95893,95894,95896,95898],{},[898,95895,95708],{"mathvariant":2334},[1701,95897,59946],{},[898,95899,22908],{},[902,95901,95902],{"encoding":904},"\\operatorname{tg}\\alpha",[115,95904,95906],{"id":95905},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,95908,95909,4088,95912,1646,95925,95928],{},[38,95910,95911],{},"Mezní míra komoditní substituce",[883,95913,95915],{"className":95914},[886],[888,95916,95917],{"xmlns":890},[892,95918,95919,95923],{},[895,95920,95921],{},[1939,95922,14659],{},[902,95924,32272],{"encoding":904},[38,95926,95927],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,95930,95932],{"className":95931},[886],[888,95933,95934],{"xmlns":890,"display":2252},[892,95935,95936,96023],{},[2256,95937,95938],{"width":2258},[2260,95939,95940,95942,96016,96018],{},[2263,95941],{"width":2265},[2263,95943,95944],{},[895,95945,95946,95948,95950,95952,95954,95960,95962,95968,95970,95972,95994,95996,96014],{},[1939,95947,14659],{},[1701,95949,1792],{},[1939,95951,14659],{},[1701,95953,1799],{"stretchy":1798},[1845,95955,95956,95958],{},[898,95957,1802],{},[1850,95959,4062],{},[1701,95961,2012],{"separator":2011},[1845,95963,95964,95966],{},[898,95965,1802],{},[1850,95967,3938],{},[1701,95969,1805],{"stretchy":1798},[1701,95971,1792],{},[3726,95973,95974,95984],{},[895,95975,95976,95978],{},[898,95977,6909],{},[1845,95979,95980,95982],{},[898,95981,900],{},[1850,95983,4062],{},[895,95985,95986,95988],{},[898,95987,6909],{},[1845,95989,95990,95992],{},[898,95991,900],{},[1850,95993,3938],{},[1701,95995,1792],{},[3726,95997,95998,96006],{},[2287,95999,96000,96002,96004],{},[898,96001,900],{},[1850,96003,4062],{},[1701,96005,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,96007,96008,96010,96012],{},[898,96009,900],{},[1850,96011,3938],{},[1701,96013,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[898,96015,1715],{"mathvariant":2334},[2263,96017],{"width":2265},[2263,96019,96020],{},[1939,96021,96022],{},"(6.9)",[902,96024,96025],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,96027,96028,96029,96063,96064,96096,96097,96132,96133,96146],{},"Geometricky: ",[883,96030,96032],{"className":96031},[886],[888,96033,96034],{"xmlns":890},[892,96035,96036,96060],{},[895,96037,96038,96040],{},[1701,96039,2317],{},[2363,96041,96042],{"scriptlevel":1852,"displaystyle":1798},[3726,96043,96044,96052],{},[2287,96045,96046,96048,96050],{},[898,96047,900],{},[1850,96049,4062],{},[1701,96051,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,96053,96054,96056,96058],{},[898,96055,900],{},[1850,96057,3938],{},[1701,96059,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,96061,96062],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,96065,96067],{"className":96066},[886],[888,96068,96069],{"xmlns":890},[892,96070,96071,96093],{},[895,96072,96073,96079,96081,96083,96085,96091],{},[1845,96074,96075,96077],{},[898,96076,1802],{},[1850,96078,3938],{},[1701,96080,1792],{},[898,96082,6132],{},[1701,96084,1799],{"stretchy":1798},[1845,96086,96087,96089],{},[898,96088,1802],{},[1850,96090,4062],{},[1701,96092,1805],{"stretchy":1798},[902,96094,96095],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,96098,96100],{"className":96099},[886],[888,96101,96102],{"xmlns":890},[892,96103,96104,96130],{},[895,96105,96106,96108,96110,96116,96118,96124,96126,96128],{},[898,96107,900],{},[1701,96109,1799],{"stretchy":1798},[1845,96111,96112,96114],{},[898,96113,1802],{},[1850,96115,4062],{},[1701,96117,2012],{"separator":2011},[1845,96119,96120,96122],{},[898,96121,1802],{},[1850,96123,3938],{},[1701,96125,1805],{"stretchy":1798},[1701,96127,1792],{},[898,96129,3618],{},[902,96131,13826],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,96134,96136],{"className":96135},[886],[888,96137,96138],{"xmlns":890},[892,96139,96140,96144],{},[895,96141,96142],{},[1939,96143,14659],{},[902,96145,32272],{"encoding":904}," chápeme jako velikost kompenzace.",[1635,96148,96149],{},[724,96150,96151,96153,96154,12164,96186,96224,96225,96242,96243,96260],{},[883,96152,2063],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,96155,96157],{"className":96156},[886],[888,96158,96159],{"xmlns":890},[892,96160,96161,96183],{},[895,96162,96163,96165,96167,96173,96175,96181],{},[1939,96164,14659],{},[1701,96166,1799],{"stretchy":1798},[1845,96168,96169,96171],{},[898,96170,1802],{},[1850,96172,4062],{},[1701,96174,2012],{"separator":2011},[1845,96176,96177,96179],{},[898,96178,1802],{},[1850,96180,3938],{},[1701,96182,1805],{"stretchy":1798},[902,96184,96185],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,96187,96188,96189,33037,96206,96223],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,96190,96192],{"className":96191},[886],[888,96193,96194],{"xmlns":890},[892,96195,96196,96204],{},[895,96197,96198],{},[1845,96199,96200,96202],{},[898,96201,1802],{},[1850,96203,4062],{},[902,96205,33036],{"encoding":904},[883,96207,96209],{"className":96208},[886],[888,96210,96211],{"xmlns":890},[892,96212,96213,96221],{},[895,96214,96215],{},[1845,96216,96217,96219],{},[898,96218,1802],{},[1850,96220,3938],{},[902,96222,33055],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,96226,96228],{"className":96227},[886],[888,96229,96230],{"xmlns":890},[892,96231,96232,96240],{},[895,96233,96234],{},[1845,96235,96236,96238],{},[898,96237,1802],{},[1850,96239,3938],{},[902,96241,33055],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,96244,96246],{"className":96245},[886],[888,96247,96248],{"xmlns":890},[892,96249,96250,96258],{},[895,96251,96252],{},[1845,96253,96254,96256],{},[898,96255,1802],{},[1850,96257,4062],{},[902,96259,33036],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,96262,96263,96264,33977],{},"Pro obecnou změnu ",[883,96265,96267],{"className":96266},[886],[888,96268,96269],{"xmlns":890},[892,96270,96271,96281],{},[895,96272,96273,96275],{},[898,96274,2312],{"mathvariant":2334},[1845,96276,96277,96279],{},[898,96278,1802],{},[1850,96280,4062],{},[902,96282,96283],{"encoding":904},"\\mathrm{d} Q_1",[883,96285,96287],{"className":96286},[886],[888,96288,96289],{"xmlns":890,"display":2252},[892,96290,96291,96344],{},[2256,96292,96293],{"width":2258},[2260,96294,96295,96297,96337,96339],{},[2263,96296],{"width":2265},[2263,96298,96299],{},[895,96300,96301,96303,96309,96311,96313,96319,96321,96323,96325,96327,96329,96335],{},[898,96302,4708],{"mathvariant":2334},[1845,96304,96305,96307],{},[898,96306,1802],{},[1850,96308,3938],{},[1701,96310,4067],{},[898,96312,2312],{"mathvariant":2334},[1845,96314,96315,96317],{},[898,96316,1802],{},[1850,96318,3938],{},[1701,96320,1792],{},[1701,96322,2317],{},[1939,96324,14659],{},[1701,96326,3408],{},[898,96328,2312],{"mathvariant":2334},[1845,96330,96331,96333],{},[898,96332,1802],{},[1850,96334,4062],{},[1701,96336,2012],{"separator":2011},[2263,96338],{"width":2265},[2263,96340,96341],{},[1939,96342,96343],{},"(6.10)",[902,96345,96346],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,96348,96350],{"className":96349},[886],[888,96351,96352],{"xmlns":890,"display":2252},[892,96353,96354,96401],{},[2256,96355,96356],{"width":2258},[2260,96357,96358,96360,96394,96396],{},[2263,96359],{"width":2265},[2263,96361,96362],{},[895,96363,96364,96366,96372,96374,96376,96382,96384,96386,96392],{},[898,96365,2312],{"mathvariant":2334},[1845,96367,96368,96370],{},[898,96369,1802],{},[1850,96371,4062],{},[1701,96373,1792],{},[1701,96375,2317],{},[3726,96377,96378,96380],{},[1850,96379,4062],{},[1939,96381,14659],{},[1939,96383,1941],{},[898,96385,2312],{"mathvariant":2334},[1845,96387,96388,96390],{},[898,96389,1802],{},[1850,96391,3938],{},[898,96393,1715],{"mathvariant":2334},[2263,96395],{"width":2265},[2263,96397,96398],{},[1939,96399,96400],{},"(6.11)",[902,96402,96403],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1635,96405,96406,96472,96589],{},[724,96407,96408,96410,96411,33977],{},[883,96409,3575],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,96412,96414],{"className":96413},[886],[888,96415,96416],{"xmlns":890},[892,96417,96418,96470],{},[895,96419,96420,96422,96424,96430,96432,96438,96440,96442,96456],{},[898,96421,900],{},[1701,96423,1799],{"stretchy":1798},[1845,96425,96426,96428],{},[898,96427,1802],{},[1850,96429,4062],{},[1701,96431,2012],{"separator":2011},[1845,96433,96434,96436],{},[898,96435,1802],{},[1850,96437,3938],{},[1701,96439,1805],{"stretchy":1798},[1701,96441,1792],{},[2287,96443,96444,96446,96448],{},[898,96445,1802],{},[1850,96447,4062],{},[895,96449,96450,96452,96454],{},[1850,96451,4062],{},[898,96453,8741],{"mathvariant":2334},[1850,96455,3938],{},[2287,96457,96458,96460,96462],{},[898,96459,1802],{},[1850,96461,3938],{},[895,96463,96464,96466,96468],{},[1850,96465,4062],{},[898,96467,8741],{"mathvariant":2334},[1850,96469,3938],{},[902,96471,33976],{"encoding":904},[724,96473,96474],{},[883,96475,96477],{"className":96476},[886],[888,96478,96479],{"xmlns":890},[892,96480,96481,96587],{},[895,96482,96483,96485,96487,96569,96571,96585],{},[1939,96484,14659],{},[1701,96486,1792],{},[3726,96488,96489,96529],{},[895,96490,96491,96499,96515],{},[2363,96492,96493],{"scriptlevel":1852,"displaystyle":1798},[3726,96494,96495,96497],{},[1850,96496,4062],{},[1850,96498,3938],{},[2287,96500,96501,96503,96505],{},[898,96502,1802],{},[1850,96504,4062],{},[895,96506,96507,96509,96511,96513],{},[1701,96508,2317],{},[1850,96510,4062],{},[898,96512,8741],{"mathvariant":2334},[1850,96514,3938],{},[2287,96516,96517,96519,96521],{},[898,96518,1802],{},[1850,96520,3938],{},[895,96522,96523,96525,96527],{},[1850,96524,4062],{},[898,96526,8741],{"mathvariant":2334},[1850,96528,3938],{},[895,96530,96531,96539,96553],{},[2363,96532,96533],{"scriptlevel":1852,"displaystyle":1798},[3726,96534,96535,96537],{},[1850,96536,4062],{},[1850,96538,3938],{},[2287,96540,96541,96543,96545],{},[898,96542,1802],{},[1850,96544,4062],{},[895,96546,96547,96549,96551],{},[1850,96548,4062],{},[898,96550,8741],{"mathvariant":2334},[1850,96552,3938],{},[2287,96554,96555,96557,96559],{},[898,96556,1802],{},[1850,96558,3938],{},[895,96560,96561,96563,96565,96567],{},[1701,96562,2317],{},[1850,96564,4062],{},[898,96566,8741],{"mathvariant":2334},[1850,96568,3938],{},[1701,96570,1792],{},[3726,96572,96573,96579],{},[1845,96574,96575,96577],{},[898,96576,1802],{},[1850,96578,3938],{},[1845,96580,96581,96583],{},[898,96582,1802],{},[1850,96584,4062],{},[898,96586,1715],{"mathvariant":2334},[902,96588,34095],{"encoding":904},[724,96590,4654,96591,7015,96634,34144,96636,96655],{},[883,96592,96594],{"className":96593},[886],[888,96595,96596],{"xmlns":890},[892,96597,96598,96632],{},[895,96599,96600,96602,96604,96606,96608,96610,96612,96614,96622,96624],{},[1939,96601,14659],{},[1701,96603,1799],{"stretchy":1798},[1850,96605,5151],{},[1701,96607,2012],{"separator":2011},[1850,96609,19162],{},[1701,96611,1805],{"stretchy":1798},[1701,96613,1792],{},[2363,96615,96616],{"scriptlevel":1852,"displaystyle":1798},[3726,96617,96618,96620],{},[1850,96619,19162],{},[1850,96621,5151],{},[1701,96623,1792],{},[2363,96625,96626],{"scriptlevel":1852,"displaystyle":1798},[3726,96627,96628,96630],{},[1850,96629,4225],{},[1850,96631,3646],{},[902,96633,34141],{"encoding":904},[614,96635,13276],{},[883,96637,96639],{"className":96638},[886],[888,96640,96641],{"xmlns":890},[892,96642,96643,96653],{},[895,96644,96645],{},[2363,96646,96647],{"scriptlevel":1852,"displaystyle":1798},[3726,96648,96649,96651],{},[1850,96650,4225],{},[1850,96652,3646],{},[902,96654,34164],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,96657,96658,96659,96663],{},"(Paralelou je ",[207,96660,96662],{"className":96661,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,96665,96667],{"id":96666},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,96669,96670,96671,96674],{},"Rámcově se v kapitole 6 studují ",[38,96672,96673],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,96676,96677,96813],{},[123,96678,96679,96681,96682,14213,96713,4088,96716,96765,96766,1715],{},[38,96680,32286],{}," — maximalizace ",[883,96683,96685],{"className":96684},[886],[888,96686,96687],{"xmlns":890},[892,96688,96689,96711],{},[895,96690,96691,96693,96695,96701,96703,96709],{},[898,96692,900],{},[1701,96694,1799],{"stretchy":1798},[1845,96696,96697,96699],{},[898,96698,1802],{},[1850,96700,4062],{},[1701,96702,2012],{"separator":2011},[1845,96704,96705,96707],{},[898,96706,1802],{},[1850,96708,3938],{},[1701,96710,1805],{"stretchy":1798},[902,96712,20389],{"encoding":904},[38,96714,96715],{},"rozpočtovém omezení",[883,96717,96719],{"className":96718},[886],[888,96720,96721],{"xmlns":890},[892,96722,96723,96763],{},[895,96724,96725,96731,96733,96741,96747,96749,96757],{},[3243,96726,96727,96729],{},[898,96728,13189],{},[1701,96730,8424],{},[1701,96732,1792],{},[2287,96734,96735,96737,96739],{},[898,96736,1680],{},[1850,96738,4062],{},[1701,96740,8424],{},[1845,96742,96743,96745],{},[898,96744,1802],{},[1850,96746,4062],{},[1701,96748,1703],{},[2287,96750,96751,96753,96755],{},[898,96752,1680],{},[1850,96754,3938],{},[1701,96756,8424],{},[1845,96758,96759,96761],{},[898,96760,1802],{},[1850,96762,3938],{},[902,96764,21344],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,96767,96769],{"className":96768},[886],[888,96770,96771],{"xmlns":890},[892,96772,96773,96811],{},[895,96774,96775,96781,96783,96789,96791,96797,96799,96805,96807,96809],{},[1845,96776,96777,96779],{},[898,96778,1802],{},[898,96780,21836],{},[1701,96782,1792],{},[1845,96784,96785,96787],{},[898,96786,1795],{},[898,96788,21836],{},[1701,96790,1799],{"stretchy":1798},[1845,96792,96793,96795],{},[898,96794,1680],{},[1850,96796,4062],{},[1701,96798,2012],{"separator":2011},[1845,96800,96801,96803],{},[898,96802,1680],{},[1850,96804,3938],{},[1701,96806,2012],{"separator":2011},[898,96808,13189],{},[1701,96810,1805],{"stretchy":1798},[902,96812,40486],{"encoding":904},[123,96814,96815,31938,96818,31981,96864,96881,96882,1715],{},[38,96816,96817],{},"Duální úloha",[883,96819,96821],{"className":96820},[886],[888,96822,96823],{"xmlns":890},[892,96824,96825,96861],{},[895,96826,96827,96829,96831,96839,96845,96847,96855],{},[898,96828,3249],{},[1701,96830,1792],{},[2287,96832,96833,96835,96837],{},[898,96834,1680],{},[1850,96836,4062],{},[1701,96838,8424],{},[1845,96840,96841,96843],{},[898,96842,1802],{},[1850,96844,4062],{},[1701,96846,1703],{},[2287,96848,96849,96851,96853],{},[898,96850,1680],{},[1850,96852,3938],{},[1701,96854,8424],{},[1845,96856,96857,96859],{},[898,96858,1802],{},[1850,96860,3938],{},[902,96862,96863],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,96865,96867],{"className":96866},[886],[888,96868,96869],{"xmlns":890},[892,96870,96871,96879],{},[895,96872,96873],{},[3243,96874,96875,96877],{},[898,96876,900],{},[1701,96878,8424],{},[902,96880,31999],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,96883,96885],{"className":96884},[886],[888,96886,96887],{"xmlns":890},[892,96888,96889,96927],{},[895,96890,96891,96897,96899,96905,96907,96913,96915,96921,96923,96925],{},[1845,96892,96893,96895],{},[898,96894,1802],{},[898,96896,21836],{},[1701,96898,1792],{},[1845,96900,96901,96903],{},[898,96902,1795],{},[898,96904,21836],{},[1701,96906,1799],{"stretchy":1798},[1845,96908,96909,96911],{},[898,96910,1680],{},[1850,96912,4062],{},[1701,96914,2012],{"separator":2011},[1845,96916,96917,96919],{},[898,96918,1680],{},[1850,96920,3938],{},[1701,96922,2012],{"separator":2011},[898,96924,900],{},[1701,96926,1805],{"stretchy":1798},[902,96928,21869],{"encoding":904},[724,96930,96931,96932,96935,96936,4088,96939,96978],{},"Obě úlohy se řeší ",[207,96933,32004],{"className":96934,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,96937,96938],{},"tentýž bod dotyku",[883,96940,96942],{"className":96941},[886],[888,96943,96944],{"xmlns":890},[892,96945,96946,96976],{},[895,96947,96948,96954,96956,96964,96966,96974],{},[3243,96949,96950,96952],{},[898,96951,1802],{},[1701,96953,8424],{},[1701,96955,2036],{"stretchy":1798},[2287,96957,96958,96960,96962],{},[898,96959,1802],{},[1850,96961,4062],{},[1701,96963,8424],{},[1701,96965,2012],{"separator":2011},[2287,96967,96968,96970,96972],{},[898,96969,1802],{},[1850,96971,3938],{},[1701,96973,8424],{},[1701,96975,2053],{"stretchy":1798},[902,96977,32361],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,96980,96982],{"className":96981},[886],[888,96983,96984],{"xmlns":890,"display":2252},[892,96985,96986,97032],{},[895,96987,96988,96990,96992,97010,97012,97030],{},[1939,96989,14659],{},[1701,96991,1792],{},[3726,96993,96994,97002],{},[2287,96995,96996,96998,97000],{},[898,96997,900],{},[1850,96999,4062],{},[1701,97001,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[2287,97003,97004,97006,97008],{},[898,97005,900],{},[1850,97007,3938],{},[1701,97009,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,97011,1792],{},[3726,97013,97014,97022],{},[2287,97015,97016,97018,97020],{},[898,97017,1680],{},[1850,97019,4062],{},[1701,97021,8424],{},[2287,97023,97024,97026,97028],{},[898,97025,1680],{},[1850,97027,3938],{},[1701,97029,8424],{},[898,97031,1715],{"mathvariant":2334},[902,97033,97034],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,97036,97037],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1635,97039,97040],{},[724,97041,97042,97044,97045,97048,97049,97052,97053,97080,97081,97115,97116,97150,97151,97194,97195,97198,97199,1715],{},[883,97043,2063],{}," Pro detailní postup viz ",[207,97046,40784],{"className":97047,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,97050,97051],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,97054,97056],{"className":97055},[886],[888,97057,97058],{"xmlns":890},[892,97059,97060,97078],{},[895,97061,97062,97064,97066,97072],{},[898,97063,900],{},[1701,97065,1792],{},[1845,97067,97068,97070],{},[898,97069,1802],{},[1850,97071,4062],{},[1845,97073,97074,97076],{},[898,97075,1802],{},[1850,97077,3938],{},[902,97079,34257],{"encoding":904}," s výsledkem ",[883,97082,97084],{"className":97083},[886],[888,97085,97086],{"xmlns":890},[892,97087,97088,97112],{},[895,97089,97090,97096,97098,97100,97102,97108,97110],{},[1845,97091,97092,97094],{},[898,97093,1802],{},[1850,97095,4062],{},[1701,97097,1792],{},[1850,97099,9071],{},[1701,97101,2012],{"separator":2011},[1845,97103,97104,97106],{},[898,97105,1802],{},[1850,97107,3938],{},[1701,97109,1792],{},[1850,97111,3703],{},[902,97113,97114],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,97117,97119],{"className":97118},[886],[888,97120,97121],{"xmlns":890},[892,97122,97123,97147],{},[895,97124,97125,97131,97133,97135,97137,97143,97145],{},[1845,97126,97127,97129],{},[898,97128,1802],{},[1850,97130,4062],{},[1701,97132,1792],{},[1850,97134,6460],{},[1701,97136,2012],{"separator":2011},[1845,97138,97139,97141],{},[898,97140,1802],{},[1850,97142,3938],{},[1701,97144,1792],{},[1850,97146,4062],{},[902,97148,97149],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,97152,97154],{"className":97153},[886],[888,97155,97156],{"xmlns":890},[892,97157,97158,97192],{},[895,97159,97160,97162,97164,97178],{},[898,97161,900],{},[1701,97163,1792],{},[2287,97165,97166,97168,97170],{},[898,97167,1802],{},[1850,97169,4062],{},[895,97171,97172,97174,97176],{},[1850,97173,4062],{},[898,97175,8741],{"mathvariant":2334},[1850,97177,3938],{},[2287,97179,97180,97182,97184],{},[898,97181,1802],{},[1850,97183,3938],{},[895,97185,97186,97188,97190],{},[1850,97187,4062],{},[898,97189,8741],{"mathvariant":2334},[1850,97191,3938],{},[902,97193,37190],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,97196,97197],{},"6.8–6.13"," jsou na stránce ",[207,97200,31804],{"className":97201,"dataFsResolvedFilePath":911,"href":912},[210],[115,97203,97205],{"id":97204},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,97207,97208,97209,97222,97223,97225,97226,97228,97229,97231,97232,97234,97235,97237,97238,97240,97241,4088,97243,97278,97279,97292,97293,97296,97297,97300,97301,1715],{},"Každá ",[883,97210,97212],{"className":97211},[886],[888,97213,97214],{"xmlns":890},[892,97215,97216,97220],{},[895,97217,97218],{},[898,97219,40890],{},[902,97221,40890],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,97224,90556],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,97227,91040],{}," a současně ",[38,97230,90559],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,97233,90564],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,97236,3557],{}," (6.4) a druhé parciální derivace ",[38,97239,92923],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,97242,13789],{},[883,97244,97246],{"className":97245},[886],[888,97247,97248],{"xmlns":890},[892,97249,97250,97276],{},[895,97251,97252,97254,97256,97262,97264,97270,97272,97274],{},[898,97253,900],{},[1701,97255,1799],{"stretchy":1798},[1845,97257,97258,97260],{},[898,97259,1802],{},[1850,97261,4062],{},[1701,97263,2012],{"separator":2011},[1845,97265,97266,97268],{},[898,97267,1802],{},[1850,97269,3938],{},[1701,97271,1805],{"stretchy":1798},[1701,97273,1792],{},[898,97275,3618],{},[902,97277,13826],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,97280,97282],{"className":97281},[886],[888,97283,97284],{"xmlns":890},[892,97285,97286,97290],{},[895,97287,97288],{},[1939,97289,14659],{},[902,97291,32272],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,97294,97295],{},"maximalizace užitečnosti"," a duální ",[38,97298,97299],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,97302,40784],{"className":97303,"dataFsResolvedFilePath":911,"href":912},[210],[115,97305,53869],{"id":53868},[152,97307,97308,97311,97314,97317,97320,97323,97326,97329,97332,97335],{},[123,97309,97310],{},"Co se zahrnuje pod termín užitečnost?",[123,97312,97313],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,97315,97316],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,97318,97319],{},"Jak se vypočítá mezní užitečnost?",[123,97321,97322],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,97324,97325],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,97327,97328],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,97330,97331],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,97333,97334],{},"Proč mají křivky užitečnosti záporný sklon?",[123,97336,97337],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,97339,97341],{"id":97340},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,97343,97344,97347,97348,87229,97390,1343,97418,1343,97446,97474],{},[38,97345,97346],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,97349,97351],{"className":97350},[886],[888,97352,97353],{"xmlns":890},[892,97354,97355,97387],{},[895,97356,97357,97359,97361,97367,97369,97371,97377,97379,97381],{},[898,97358,900],{},[1701,97360,1792],{},[1845,97362,97363,97365],{},[898,97364,1802],{},[1850,97366,4062],{},[1701,97368,1703],{},[1850,97370,68305],{},[1845,97372,97373,97375],{},[898,97374,1802],{},[1850,97376,3938],{},[1701,97378,1703],{},[1850,97380,3938],{},[1845,97382,97383,97385],{},[898,97384,1802],{},[1850,97386,3646],{},[902,97388,97389],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,97391,97393],{"className":97392},[886],[888,97394,97395],{"xmlns":890},[892,97396,97397,97415],{},[895,97398,97399,97401,97403,97405,97407,97409,97411,97413],{},[898,97400,900],{},[1701,97402,1799],{"stretchy":1798},[1850,97404,6460],{},[1701,97406,2012],{"separator":2011},[1850,97408,3938],{},[1701,97410,2012],{"separator":2011},[1850,97412,3938],{},[1701,97414,1805],{"stretchy":1798},[902,97416,97417],{"encoding":904},"U(4, 2, 2)",[883,97419,97421],{"className":97420},[886],[888,97422,97423],{"xmlns":890},[892,97424,97425,97443],{},[895,97426,97427,97429,97431,97433,97435,97437,97439,97441],{},[898,97428,900],{},[1701,97430,1799],{"stretchy":1798},[1850,97432,4062],{},[1701,97434,2012],{"separator":2011},[1850,97436,6460],{},[1701,97438,2012],{"separator":2011},[1850,97440,3938],{},[1701,97442,1805],{"stretchy":1798},[902,97444,97445],{"encoding":904},"U(1, 4, 2)",[883,97447,97449],{"className":97448},[886],[888,97450,97451],{"xmlns":890},[892,97452,97453,97471],{},[895,97454,97455,97457,97459,97461,97463,97465,97467,97469],{},[898,97456,900],{},[1701,97458,1799],{"stretchy":1798},[1850,97460,3938],{},[1701,97462,2012],{"separator":2011},[1850,97464,3646],{},[1701,97466,2012],{"separator":2011},[1850,97468,4062],{},[1701,97470,1805],{"stretchy":1798},[902,97472,97473],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,97476,97477,97480,97481,97533,97534,1343,97560,1343,97586,1343,97612,1343,97638,1343,97664,1343,97690,97716],{},[38,97478,97479],{},"6.2"," Je dána užitečnost ",[883,97482,97484],{"className":97483},[886],[888,97485,97486],{"xmlns":890},[892,97487,97488,97530],{},[895,97489,97490,97492,97494,97496,97510,97524],{},[898,97491,900],{},[1701,97493,1792],{},[1850,97495,3938],{},[2287,97497,97498,97500,97502],{},[898,97499,1802],{},[1850,97501,4062],{},[895,97503,97504,97506,97508],{},[1850,97505,4062],{},[898,97507,8741],{"mathvariant":2334},[1850,97509,3646],{},[2287,97511,97512,97514,97516],{},[898,97513,1802],{},[1850,97515,3938],{},[895,97517,97518,97520,97522],{},[1850,97519,4062],{},[898,97521,8741],{"mathvariant":2334},[1850,97523,3938],{},[1845,97525,97526,97528],{},[898,97527,1802],{},[1850,97529,3646],{},[902,97531,97532],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,97535,97537],{"className":97536},[886],[888,97538,97539],{"xmlns":890},[892,97540,97541,97557],{},[895,97542,97543,97545,97547,97549,97551,97553,97555],{},[1701,97544,1799],{"stretchy":1798},[1850,97546,9630],{},[1701,97548,2012],{"separator":2011},[1850,97550,70343],{},[1701,97552,2012],{"separator":2011},[1850,97554,3703],{},[1701,97556,1805],{"stretchy":1798},[902,97558,97559],{"encoding":904},"(36, 27, 10)",[883,97561,97563],{"className":97562},[886],[888,97564,97565],{"xmlns":890},[892,97566,97567,97583],{},[895,97568,97569,97571,97573,97575,97577,97579,97581],{},[1701,97570,1799],{"stretchy":1798},[1850,97572,45861],{},[1701,97574,2012],{"separator":2011},[1850,97576,9650],{},[1701,97578,2012],{"separator":2011},[1850,97580,13096],{},[1701,97582,1805],{"stretchy":1798},[902,97584,97585],{"encoding":904},"(64, 8, 20)",[883,97587,97589],{"className":97588},[886],[888,97590,97591],{"xmlns":890},[892,97592,97593,97609],{},[895,97594,97595,97597,97599,97601,97603,97605,97607],{},[1701,97596,1799],{"stretchy":1798},[1850,97598,9071],{},[1701,97600,2012],{"separator":2011},[1850,97602,45861],{},[1701,97604,2012],{"separator":2011},[1850,97606,9650],{},[1701,97608,1805],{"stretchy":1798},[902,97610,97611],{"encoding":904},"(25, 64, 8)",[883,97613,97615],{"className":97614},[886],[888,97616,97617],{"xmlns":890},[892,97618,97619,97635],{},[895,97620,97621,97623,97625,97627,97629,97631,97633],{},[1701,97622,1799],{"stretchy":1798},[1850,97624,6460],{},[1701,97626,2012],{"separator":2011},[1850,97628,76275],{},[1701,97630,2012],{"separator":2011},[1850,97632,6352],{},[1701,97634,1805],{"stretchy":1798},[902,97636,97637],{"encoding":904},"(4, 125, 6)",[883,97639,97641],{"className":97640},[886],[888,97642,97643],{"xmlns":890},[892,97644,97645,97661],{},[895,97646,97647,97649,97651,97653,97655,97657,97659],{},[1701,97648,1799],{"stretchy":1798},[1850,97650,8073],{},[1701,97652,2012],{"separator":2011},[1850,97654,3665],{},[1701,97656,2012],{"separator":2011},[1850,97658,7592],{},[1701,97660,1805],{"stretchy":1798},[902,97662,97663],{"encoding":904},"(9, 40, 12)",[883,97665,97667],{"className":97666},[886],[888,97668,97669],{"xmlns":890},[892,97670,97671,97687],{},[895,97672,97673,97675,97677,97679,97681,97683,97685],{},[1701,97674,1799],{"stretchy":1798},[1850,97676,8073],{},[1701,97678,2012],{"separator":2011},[1850,97680,45861],{},[1701,97682,2012],{"separator":2011},[1850,97684,4225],{},[1701,97686,1805],{"stretchy":1798},[902,97688,97689],{"encoding":904},"(9, 64, 5)",[883,97691,97693],{"className":97692},[886],[888,97694,97695],{"xmlns":890},[892,97696,97697,97713],{},[895,97698,97699,97701,97703,97705,97707,97709,97711],{},[1701,97700,1799],{"stretchy":1798},[1850,97702,45861],{},[1701,97704,2012],{"separator":2011},[1850,97706,9650],{},[1701,97708,2012],{"separator":2011},[1850,97710,3703],{},[1701,97712,1805],{"stretchy":1798},[902,97714,97715],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,97718,97719,97480,97722,97765,97766,97800,97801,10536,97831,97864,97865,97882,97883,97900],{},[38,97720,97721],{},"6.3",[883,97723,97725],{"className":97724},[886],[888,97726,97727],{"xmlns":890},[892,97728,97729,97763],{},[895,97730,97731,97733,97735,97749],{},[898,97732,900],{},[1701,97734,1792],{},[2287,97736,97737,97739,97741],{},[898,97738,1802],{},[1850,97740,4062],{},[895,97742,97743,97745,97747],{},[1850,97744,4062],{},[898,97746,8741],{"mathvariant":2334},[1850,97748,3938],{},[2287,97750,97751,97753,97755],{},[898,97752,1802],{},[1850,97754,3938],{},[895,97756,97757,97759,97761],{},[1850,97758,4062],{},[898,97760,8741],{"mathvariant":2334},[1850,97762,3938],{},[902,97764,37190],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,97767,97769],{"className":97768},[886],[888,97770,97771],{"xmlns":890},[892,97772,97773,97797],{},[895,97774,97775,97781,97783,97785,97787,97793,97795],{},[1845,97776,97777,97779],{},[898,97778,1802],{},[1850,97780,4062],{},[1701,97782,1792],{},[1850,97784,7206],{},[1701,97786,2012],{"separator":2011},[1845,97788,97789,97791],{},[898,97790,1802],{},[1850,97792,3938],{},[1701,97794,1792],{},[1850,97796,50694],{},[902,97798,97799],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,97802,97804],{"className":97803},[886],[888,97805,97806],{"xmlns":890},[892,97807,97808,97828],{},[895,97809,97810,97812,97818,97820,97822],{},[898,97811,6909],{},[1845,97813,97814,97816],{},[898,97815,900],{},[1850,97817,4062],{},[1701,97819,2012],{"separator":2011},[898,97821,6909],{},[1845,97823,97824,97826],{},[898,97825,900],{},[1850,97827,3938],{},[902,97829,97830],{"encoding":904},"MU_1, MU_2",[883,97832,97834],{"className":97833},[886],[888,97835,97836],{"xmlns":890},[892,97837,97838,97862],{},[895,97839,97840,97846,97848,97850,97852,97858,97860],{},[1845,97841,97842,97844],{},[898,97843,1802],{},[1850,97845,4062],{},[1701,97847,1792],{},[1850,97849,7206],{},[1701,97851,2012],{"separator":2011},[1845,97853,97854,97856],{},[898,97855,1802],{},[1850,97857,3938],{},[1701,97859,1792],{},[1850,97861,50694],{},[902,97863,97799],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,97866,97868],{"className":97867},[886],[888,97869,97870],{"xmlns":890},[892,97871,97872,97880],{},[895,97873,97874],{},[1845,97875,97876,97878],{},[898,97877,1802],{},[1850,97879,4062],{},[902,97881,33036],{"encoding":904}," na 60 a poklesu ",[883,97884,97886],{"className":97885},[886],[888,97887,97888],{"xmlns":890},[892,97889,97890,97898],{},[895,97891,97892],{},[1845,97893,97894,97896],{},[898,97895,1802],{},[1850,97897,3938],{},[902,97899,33055],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,97902,97903,97906,97907,97968,97969,1715],{},[38,97904,97905],{},"6.4"," Je dána funkce ",[883,97908,97910],{"className":97909},[886],[888,97911,97912],{"xmlns":890},[892,97913,97914,97966],{},[895,97915,97916,97918,97920,97926,97928,97934,97936,97938,97952],{},[898,97917,900],{},[1701,97919,1799],{"stretchy":1798},[1845,97921,97922,97924],{},[898,97923,1802],{},[1850,97925,4062],{},[1701,97927,2012],{"separator":2011},[1845,97929,97930,97932],{},[898,97931,1802],{},[1850,97933,3938],{},[1701,97935,1805],{"stretchy":1798},[1701,97937,1792],{},[2287,97939,97940,97942,97944],{},[898,97941,1802],{},[1850,97943,4062],{},[895,97945,97946,97948,97950],{},[1850,97947,4062],{},[898,97949,8741],{"mathvariant":2334},[1850,97951,3938],{},[2287,97953,97954,97956,97958],{},[898,97955,1802],{},[1850,97957,3938],{},[895,97959,97960,97962,97964],{},[1850,97961,4062],{},[898,97963,8741],{"mathvariant":2334},[1850,97965,3938],{},[902,97967,33976],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,97970,97972],{"className":97971},[886],[888,97973,97974],{"xmlns":890},[892,97975,97976,98066],{},[895,97977,97978,97980,97982,97988,97990,97992,97994,97996,97998,98000,98006,98008,98010,98012,98014,98016,98018,98020,98022,98028,98030,98032,98034,98036,98038,98040,98046,98048,98050,98052,98054,98056,98058,98064],{},[898,97979,900],{},[1701,97981,1799],{"stretchy":1798},[1845,97983,97984,97986],{},[898,97985,1802],{},[1850,97987,4062],{},[1701,97989,2012],{"separator":2011},[1850,97991,4062],{},[1701,97993,1805],{"stretchy":1798},[1701,97995,2012],{"separator":2011},[898,97997,900],{},[1701,97999,1799],{"stretchy":1798},[1845,98001,98002,98004],{},[898,98003,1802],{},[1850,98005,4062],{},[1701,98007,2012],{"separator":2011},[1850,98009,3938],{},[1701,98011,1805],{"stretchy":1798},[1701,98013,2012],{"separator":2011},[898,98015,900],{},[1701,98017,1799],{"stretchy":1798},[1850,98019,4062],{},[1701,98021,2012],{"separator":2011},[1845,98023,98024,98026],{},[898,98025,1802],{},[1850,98027,3938],{},[1701,98029,1805],{"stretchy":1798},[1701,98031,2012],{"separator":2011},[898,98033,900],{},[1701,98035,1799],{"stretchy":1798},[1850,98037,3938],{},[1701,98039,2012],{"separator":2011},[1845,98041,98042,98044],{},[898,98043,1802],{},[1850,98045,3938],{},[1701,98047,1805],{"stretchy":1798},[1701,98049,2012],{"separator":2011},[898,98051,900],{},[1701,98053,1799],{"stretchy":1798},[1850,98055,3646],{},[1701,98057,2012],{"separator":2011},[1845,98059,98060,98062],{},[898,98061,1802],{},[1850,98063,3938],{},[1701,98065,1805],{"stretchy":1798},[902,98067,98068],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,98070,98071,97480,98074,98118,98119,98227,98228,1343,98253,1343,98278,98320,98321,1343,98350,98375],{},[38,98072,98073],{},"6.5",[883,98075,98077],{"className":98076},[886],[888,98078,98079],{"xmlns":890},[892,98080,98081,98115],{},[895,98082,98083,98085,98087,98101],{},[898,98084,900],{},[1701,98086,1792],{},[2287,98088,98089,98091,98093],{},[898,98090,1802],{},[1850,98092,4062],{},[895,98094,98095,98097,98099],{},[1850,98096,3938],{},[898,98098,8741],{"mathvariant":2334},[1850,98100,3646],{},[2287,98102,98103,98105,98107],{},[898,98104,1802],{},[1850,98106,3938],{},[895,98108,98109,98111,98113],{},[1850,98110,4062],{},[898,98112,8741],{"mathvariant":2334},[1850,98114,3646],{},[902,98116,98117],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,98120,98122],{"className":98121},[886],[888,98123,98124],{"xmlns":890},[892,98125,98126,98224],{},[895,98127,98128,98130,98132,98138,98140,98146,98148,98150,98152,98154,98156,98158,98164,98166,98168,98170,98172,98174,98176,98182,98184,98186,98188,98190,98192,98194,98196,98198,98204,98206,98208,98210,98212,98214,98216,98222],{},[898,98129,900],{},[1701,98131,1799],{"stretchy":1798},[1845,98133,98134,98136],{},[898,98135,1802],{},[1850,98137,4062],{},[1701,98139,2012],{"separator":2011},[1845,98141,98142,98144],{},[898,98143,1802],{},[1850,98145,3938],{},[1701,98147,1805],{"stretchy":1798},[1701,98149,1792],{},[1850,98151,3938],{},[1701,98153,2012],{"separator":2011},[898,98155,900],{},[1701,98157,1799],{"stretchy":1798},[1845,98159,98160,98162],{},[898,98161,1802],{},[1850,98163,4062],{},[1701,98165,2012],{"separator":2011},[1850,98167,3646],{},[1701,98169,1805],{"stretchy":1798},[1701,98171,2012],{"separator":2011},[898,98173,900],{},[1701,98175,1799],{"stretchy":1798},[1845,98177,98178,98180],{},[898,98179,1802],{},[1850,98181,4062],{},[1701,98183,2012],{"separator":2011},[1850,98185,3938],{},[1701,98187,1805],{"stretchy":1798},[1701,98189,2012],{"separator":2011},[898,98191,900],{},[1701,98193,1799],{"stretchy":1798},[1850,98195,3938],{},[1701,98197,2012],{"separator":2011},[1845,98199,98200,98202],{},[898,98201,1802],{},[1850,98203,3938],{},[1701,98205,1805],{"stretchy":1798},[1701,98207,2012],{"separator":2011},[898,98209,900],{},[1701,98211,1799],{"stretchy":1798},[1850,98213,3646],{},[1701,98215,2012],{"separator":2011},[1845,98217,98218,98220],{},[898,98219,1802],{},[1850,98221,3938],{},[1701,98223,1805],{"stretchy":1798},[902,98225,98226],{"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 ",[883,98229,98231],{"className":98230},[886],[888,98232,98233],{"xmlns":890},[892,98234,98235,98250],{},[895,98236,98237,98239,98241,98243,98245,98248],{},[898,98238,1983],{},[1701,98240,2036],{"stretchy":1798},[1850,98242,68305],{},[1701,98244,12487],{"separator":2011},[1850,98246,98247],{},"3,555",[1701,98249,2053],{"stretchy":1798},[902,98251,98252],{"encoding":904},"A[1{,}5; 3{,}555]",[883,98254,98256],{"className":98255},[886],[888,98257,98258],{"xmlns":890},[892,98259,98260,98275],{},[895,98261,98262,98264,98266,98268,98270,98273],{},[898,98263,2593],{},[1701,98265,2036],{"stretchy":1798},[1850,98267,4113],{},[1701,98269,12487],{"separator":2011},[1850,98271,98272],{},"1,28",[1701,98274,2053],{"stretchy":1798},[902,98276,98277],{"encoding":904},"B[2{,}5; 1{,}28]",[883,98279,98281],{"className":98280},[886],[888,98282,98283],{"xmlns":890},[892,98284,98285,98317],{},[895,98286,98287,98289,98291,98293,98295,98297,98299,98305,98307,98309,98311,98313,98315],{},[898,98288,1658],{},[1701,98290,2036],{"stretchy":1798},[1850,98292,3938],{},[1701,98294,12487],{"separator":2011},[898,98296,900],{},[1701,98298,1799],{"stretchy":1798},[1845,98300,98301,98303],{},[898,98302,1802],{},[1850,98304,4062],{},[1701,98306,2012],{"separator":2011},[1850,98308,3646],{},[1701,98310,1805],{"stretchy":1798},[1701,98312,1792],{},[1850,98314,3646],{},[1701,98316,2053],{"stretchy":1798},[902,98318,98319],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,98322,98324],{"className":98323},[886],[888,98325,98326],{"xmlns":890},[892,98327,98328,98347],{},[895,98329,98330,98332,98334,98336,98338,98340,98342,98345],{},[898,98331,1795],{},[1701,98333,2036],{"stretchy":1798},[1850,98335,3646],{},[1701,98337,12487],{"separator":2011},[1850,98339,4062],{},[1701,98341,12487],{"separator":2011},[1850,98343,98344],{},"0,832",[1701,98346,2053],{"stretchy":1798},[902,98348,98349],{"encoding":904},"D[3; 1; 0{,}832]",[883,98351,98353],{"className":98352},[886],[888,98354,98355],{"xmlns":890},[892,98356,98357,98372],{},[895,98358,98359,98361,98363,98365,98367,98370],{},[898,98360,3249],{},[1701,98362,2036],{"stretchy":1798},[1850,98364,4113],{},[1701,98366,12487],{"separator":2011},[1850,98368,98369],{},"4,32",[1701,98371,2053],{"stretchy":1798},[902,98373,98374],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,98377,98378,97480,98381,98424,98425,10536,98438,98472,98473,98490,98491,98508],{},[38,98379,98380],{},"6.6",[883,98382,98384],{"className":98383},[886],[888,98385,98386],{"xmlns":890},[892,98387,98388,98422],{},[895,98389,98390,98392,98394,98408],{},[898,98391,900],{},[1701,98393,1792],{},[2287,98395,98396,98398,98400],{},[898,98397,1802],{},[1850,98399,4062],{},[895,98401,98402,98404,98406],{},[1850,98403,3938],{},[898,98405,8741],{"mathvariant":2334},[1850,98407,3646],{},[2287,98409,98410,98412,98414],{},[898,98411,1802],{},[1850,98413,3938],{},[895,98415,98416,98418,98420],{},[1850,98417,4062],{},[898,98419,8741],{"mathvariant":2334},[1850,98421,3646],{},[902,98423,98117],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,98426,98428],{"className":98427},[886],[888,98429,98430],{"xmlns":890},[892,98431,98432,98436],{},[895,98433,98434],{},[1939,98435,14659],{},[902,98437,32272],{"encoding":904},[883,98439,98441],{"className":98440},[886],[888,98442,98443],{"xmlns":890},[892,98444,98445,98469],{},[895,98446,98447,98453,98455,98457,98459,98465,98467],{},[1845,98448,98449,98451],{},[898,98450,1802],{},[1850,98452,4062],{},[1701,98454,1792],{},[1850,98456,5158],{},[1701,98458,2012],{"separator":2011},[1845,98460,98461,98463],{},[898,98462,1802],{},[1850,98464,3938],{},[1701,98466,1792],{},[1850,98468,12439],{},[902,98470,98471],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,98474,98476],{"className":98475},[886],[888,98477,98478],{"xmlns":890},[892,98479,98480,98488],{},[895,98481,98482],{},[1845,98483,98484,98486],{},[898,98485,1802],{},[1850,98487,4062],{},[902,98489,33036],{"encoding":904},", poklesne-li ",[883,98492,98494],{"className":98493},[886],[888,98495,98496],{"xmlns":890},[892,98497,98498,98506],{},[895,98499,98500],{},[1845,98501,98502,98504],{},[898,98503,1802],{},[1850,98505,3938],{},[902,98507,33055],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,98510,98511,98514,98515,98532,98533,98550,98551,98583,98584,98609,98610,98623,98624,1343,98648,1343,98672,1715],{},[38,98512,98513],{},"6.7"," Míra uspokojení z nákupu množství ",[883,98516,98518],{"className":98517},[886],[888,98519,98520],{"xmlns":890},[892,98521,98522,98530],{},[895,98523,98524],{},[1845,98525,98526,98528],{},[898,98527,1802],{},[1850,98529,4062],{},[902,98531,33036],{"encoding":904}," nealko nápojů a množství ",[883,98534,98536],{"className":98535},[886],[888,98537,98538],{"xmlns":890},[892,98539,98540,98548],{},[895,98541,98542],{},[1845,98543,98544,98546],{},[898,98545,1802],{},[1850,98547,3938],{},[902,98549,33055],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,98552,98554],{"className":98553},[886],[888,98555,98556],{"xmlns":890},[892,98557,98558,98580],{},[895,98559,98560,98562,98564],{},[898,98561,900],{},[1701,98563,1792],{},[12179,98565,98566],{},[895,98567,98568,98574],{},[1845,98569,98570,98572],{},[898,98571,1802],{},[1850,98573,4062],{},[1845,98575,98576,98578],{},[898,98577,1802],{},[1850,98579,3938],{},[902,98581,98582],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,98585,98587],{"className":98586},[886],[888,98588,98589],{"xmlns":890},[892,98590,98591,98607],{},[895,98592,98593,98599,98601],{},[1845,98594,98595,98597],{},[898,98596,1802],{},[1850,98598,4062],{},[1701,98600,2012],{"separator":2011},[1845,98602,98603,98605],{},[898,98604,1802],{},[1850,98606,3938],{},[902,98608,39653],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,98611,98613],{"className":98612},[886],[888,98614,98615],{"xmlns":890},[892,98616,98617,98621],{},[895,98618,98619],{},[1939,98620,14659],{},[902,98622,32272],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,98625,98627],{"className":98626},[886],[888,98628,98629],{"xmlns":890},[892,98630,98631,98645],{},[895,98632,98633,98635,98637,98639,98641,98643],{},[1939,98634,14659],{},[1701,98636,1799],{"stretchy":1798},[1850,98638,4225],{},[1701,98640,2012],{"separator":2011},[1850,98642,13096],{},[1701,98644,1805],{"stretchy":1798},[902,98646,98647],{"encoding":904},"\\text{MRCS}(5, 20)",[883,98649,98651],{"className":98650},[886],[888,98652,98653],{"xmlns":890},[892,98654,98655,98669],{},[895,98656,98657,98659,98661,98663,98665,98667],{},[1939,98658,14659],{},[1701,98660,1799],{"stretchy":1798},[1850,98662,13096],{},[1701,98664,2012],{"separator":2011},[1850,98666,4225],{},[1701,98668,1805],{"stretchy":1798},[902,98670,98671],{"encoding":904},"\\text{MRCS}(20, 5)",[883,98673,98675],{"className":98674},[886],[888,98676,98677],{"xmlns":890},[892,98678,98679,98693],{},[895,98680,98681,98683,98685,98687,98689,98691],{},[1939,98682,14659],{},[1701,98684,1799],{"stretchy":1798},[1850,98686,3938],{},[1701,98688,2012],{"separator":2011},[1850,98690,7206],{},[1701,98692,1805],{"stretchy":1798},[902,98694,98695],{"encoding":904},"\\text{MRCS}(2, 50)",[1635,98697,98698],{},[724,98699,98700,98702,98703,1715],{},[883,98701,3140],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,98704,98707],{"className":98705,"dataFsResolvedFilePath":911,"href":98706},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,98709,5578],{"id":5577},[120,98711,98712,98718,98723,98729,98782,98792,98838,98893,98956,99013,99068,99107],{},[123,98713,98714,98717],{},[38,98715,98716],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,98719,98720,98722],{},[38,98721,90615],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,98724,98725,98728],{},[38,98726,98727],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,98730,98731,98733,98734,98747,98748,1715],{},[38,98732,90942],{}," — uspořádaná ",[883,98735,98737],{"className":98736},[886],[888,98738,98739],{"xmlns":890},[892,98740,98741,98745],{},[895,98742,98743],{},[898,98744,40890],{},[902,98746,40890],{"encoding":904},"-tice ",[883,98749,98751],{"className":98750},[886],[888,98752,98753],{"xmlns":890},[892,98754,98755,98779],{},[895,98756,98757,98759,98765,98767,98769,98771,98777],{},[1701,98758,1799],{"stretchy":1798},[1845,98760,98761,98763],{},[898,98762,1802],{},[1850,98764,4062],{},[1701,98766,2012],{"separator":2011},[1701,98768,13704],{},[1701,98770,2012],{"separator":2011},[1845,98772,98773,98775],{},[898,98774,1802],{},[898,98776,40890],{},[1701,98778,1805],{"stretchy":1798},[902,98780,98781],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,98783,98784,98787,98788,98791],{},[38,98785,98786],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,98789,98790],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,98793,98794,4088,98797,98837],{},[38,98795,98796],{},"Funkce užitečnosti",[883,98798,98800],{"className":98799},[886],[888,98801,98802],{"xmlns":890},[892,98803,98804,98834],{},[895,98805,98806,98808,98810,98812,98814,98820,98822,98824,98826,98832],{},[898,98807,900],{},[1701,98809,1792],{},[898,98811,900],{},[1701,98813,1799],{"stretchy":1798},[1845,98815,98816,98818],{},[898,98817,1802],{},[1850,98819,4062],{},[1701,98821,2012],{"separator":2011},[1701,98823,13704],{},[1701,98825,2012],{"separator":2011},[1845,98827,98828,98830],{},[898,98829,1802],{},[898,98831,40890],{},[1701,98833,1805],{"stretchy":1798},[902,98835,98836],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,98839,98840,4088,98843,98872,98873,4088,98876,98892],{},[38,98841,98842],{},"Mezní užitečnost",[883,98844,98846],{"className":98845},[886],[888,98847,98848],{"xmlns":890},[892,98849,98850,98870],{},[895,98851,98852,98854,98860,98862],{},[898,98853,6909],{},[1845,98855,98856,98858],{},[898,98857,900],{},[898,98859,21836],{},[1701,98861,1792],{},[2287,98863,98864,98866,98868],{},[898,98865,900],{},[898,98867,21836],{},[1701,98869,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[902,98871,90399],{"encoding":904}," — vzorec (6.2); ",[38,98874,98875],{},"totální diferenciál",[883,98877,98879],{"className":98878},[886],[888,98880,98881],{"xmlns":890},[892,98882,98883,98889],{},[895,98884,98885,98887],{},[898,98886,2312],{"mathvariant":2334},[898,98888,900],{},[902,98890,98891],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,98894,98895,98897,98898,98922,98923,98955],{},[38,98896,92578],{}," — (6.4) ",[883,98899,98901],{"className":98900},[886],[888,98902,98903],{"xmlns":890},[892,98904,98905,98919],{},[895,98906,98907,98915,98917],{},[2287,98908,98909,98911,98913],{},[898,98910,900],{},[898,98912,21836],{},[1701,98914,4783],{"mathvariant":2334,"lspace":4782,"rspace":4782},[1701,98916,7491],{},[1850,98918,1852],{},[902,98920,98921],{"encoding":904},"U'_i > 0",", (6.5) ",[883,98924,98926],{"className":98925},[886],[888,98927,98928],{"xmlns":890},[892,98929,98930,98952],{},[895,98931,98932,98948,98950],{},[2287,98933,98934,98936,98942],{},[898,98935,900],{},[895,98937,98938,98940],{},[898,98939,21836],{},[898,98941,21836],{},[895,98943,98944,98946],{},[1701,98945,4783],{"mathvariant":2334},[1701,98947,4783],{"mathvariant":2334},[1701,98949,7530],{},[1850,98951,1852],{},[902,98953,98954],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,98957,98958,4088,98960,98991,98992,1715],{},[38,98959,94366],{},[883,98961,98963],{"className":98962},[886],[888,98964,98965],{"xmlns":890},[892,98966,98967,98989],{},[895,98968,98969,98971,98973,98981],{},[898,98970,900],{},[1701,98972,1792],{},[2287,98974,98975,98977,98979],{},[898,98976,1802],{},[1850,98978,4062],{},[898,98980,207],{},[2287,98982,98983,98985,98987],{},[898,98984,1802],{},[1850,98986,3938],{},[898,98988,3598],{},[902,98990,39834],{"encoding":904}," — (6.6), speciálně ",[883,98993,98995],{"className":98994},[886],[888,98996,98997],{"xmlns":890},[892,98998,98999,99011],{},[895,99000,99001,99003,99005,99007,99009],{},[898,99002,3598],{},[1701,99004,1792],{},[1850,99006,4062],{},[1701,99008,2317],{},[898,99010,207],{},[902,99012,94520],{"encoding":904},[123,99014,99015,4088,99018,99053,99054,99067],{},[38,99016,99017],{},"Křivky užitečnosti (indiferenční)",[883,99019,99021],{"className":99020},[886],[888,99022,99023],{"xmlns":890},[892,99024,99025,99051],{},[895,99026,99027,99029,99031,99037,99039,99045,99047,99049],{},[898,99028,900],{},[1701,99030,1799],{"stretchy":1798},[1845,99032,99033,99035],{},[898,99034,1802],{},[1850,99036,4062],{},[1701,99038,2012],{"separator":2011},[1845,99040,99041,99043],{},[898,99042,1802],{},[1850,99044,3938],{},[1701,99046,1805],{"stretchy":1798},[1701,99048,1792],{},[898,99050,3618],{},[902,99052,13826],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,99055,99057],{"className":99056},[886],[888,99058,99059],{"xmlns":890},[892,99060,99061,99065],{},[895,99062,99063],{},[898,99064,900],{},[902,99066,900],{"encoding":904},", konvexní.",[123,99069,99070,4088,99072,99106],{},[38,99071,95911],{},[883,99073,99075],{"className":99074},[886],[888,99076,99077],{"xmlns":890},[892,99078,99079,99103],{},[895,99080,99081,99083,99085,99087,99093,99095,99097],{},[1939,99082,14659],{},[1701,99084,1792],{},[898,99086,6909],{},[1845,99088,99089,99091],{},[898,99090,900],{},[1850,99092,4062],{},[898,99094,8741],{"mathvariant":2334},[898,99096,6909],{},[1845,99098,99099,99101],{},[898,99100,900],{},[1850,99102,3938],{},[902,99104,99105],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,99108,99109,4088,99112,13827,99141,99144],{},[38,99110,99111],{},"Podmínka optimality",[883,99113,99115],{"className":99114},[886],[888,99116,99117],{"xmlns":890},[892,99118,99119,99139],{},[895,99120,99121,99123,99125,99131,99133],{},[1939,99122,14659],{},[1701,99124,1792],{},[1845,99126,99127,99129],{},[898,99128,1680],{},[1850,99130,4062],{},[898,99132,8741],{"mathvariant":2334},[1845,99134,99135,99137],{},[898,99136,1680],{},[1850,99138,3938],{},[902,99140,32035],{"encoding":904},[207,99142,40784],{"className":99143,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,99146,5984],{"id":5983},[120,99148,99149,99186,99227,99237],{},[123,99150,99151,4088,99154,99157,99158,99171,99172,99185],{},[38,99152,99153],{},"Navazující téma:",[207,99155,913],{"className":99156,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,99159,99161],{"className":99160},[886],[888,99162,99163],{"xmlns":890},[892,99164,99165,99169],{},[895,99166,99167],{},[898,99168,900],{},[902,99170,900],{"encoding":904},", min ",[883,99173,99175],{"className":99174},[886],[888,99176,99177],{"xmlns":890},[892,99178,99179,99183],{},[895,99180,99181],{},[898,99182,3249],{},[902,99184,3249],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,99187,99188,4088,99191,15149,99194,90154,99197,99200,99201,99204,99205,22694,99223,99226],{},[38,99189,99190],{},"Související pojmy:",[207,99192,784],{"className":99193,"dataFsResolvedFilePath":782,"href":783},[210],[207,99195,6007],{"className":99196,"dataFsResolvedFilePath":764,"href":765},[210],[207,99198,15144],{"className":99199,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,99202,15996],{"className":99203,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,99206,99208],{"className":99207},[886],[888,99209,99210],{"xmlns":890},[892,99211,99212,99220],{},[895,99213,99214],{},[1845,99215,99216,99218],{},[898,99217,1795],{},[898,99219,21836],{},[902,99221,99222],{"encoding":904},"D_i",[207,99224,793],{"className":99225,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,99228,99229,4088,99231,1343,99234],{},[38,99230,40733],{},[207,99232,1094],{"className":99233,"dataFsResolvedFilePath":838,"href":839},[210],[207,99235,1101],{"className":99236,"dataFsResolvedFilePath":868,"href":869},[210],[123,99238,99239,4088,99241],{},[38,99240,6031],{},[207,99242,6037],{"className":99243,"dataFsResolvedFilePath":6035,"href":6036},[210],{"title":641,"searchDepth":642,"depth":642,"links":99245},[99246,99247,99248,99251,99252,99255,99259,99260,99263,99264,99265,99266,99267,99268,99269],{"id":16060,"depth":642,"text":16061},{"id":90538,"depth":642,"text":90539},{"id":90598,"depth":642,"text":90599,"children":99249},[99250],{"id":90614,"depth":649,"text":90615},{"id":90921,"depth":642,"text":90922},{"id":91781,"depth":642,"text":91782,"children":99253},[99254],{"id":92328,"depth":649,"text":83957},{"id":92577,"depth":642,"text":92578,"children":99256},[99257],{"id":93450,"depth":649,"text":99258},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":94365,"depth":642,"text":94366},{"id":94901,"depth":642,"text":94902,"children":99261},[99262],{"id":95675,"depth":649,"text":95676},{"id":95905,"depth":642,"text":95906},{"id":96666,"depth":642,"text":96667},{"id":97204,"depth":642,"text":97205},{"id":53868,"depth":642,"text":53869},{"id":97340,"depth":642,"text":97341},{"id":5577,"depth":642,"text":5578},{"id":5983,"depth":642,"text":5984},{},"\u002Ftopics\u002Fuzitecnost",{"title":90322,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,13831,99276,90316,15179,99277],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":99280,"title":757,"body":99281,"course":1128,"courses":659,"created":1129,"description":99554,"extension":661,"meta":99555,"navigation":664,"path":99556,"seo":99557,"sources":99558,"stem":99559,"tags":99560,"type":6074,"updated":677,"__hash__":99566},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":99282,"toc":99546},[99283,99286,99293,99300,99304,99314,99316,99350,99354,99397,99400,99458,99462,99492,99496,99517,99519],[12,99284,757],{"id":99285},"základy-matematické-ekonomie",[724,99287,99288,99289,99292],{},"Úvodní pojmy a princip modelování v ",[207,99290,20426],{"className":99291,"dataFsResolvedFilePath":6035,"href":6036},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,99294,99295],{},[2139,99296],{"alt":99297,"className":99298,"src":99299},"imek-model-promenne",[210,2143],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,99301,99303],{"id":99302},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,99305,99306,99309,99310,99313],{},[38,99307,99308],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,99311,99312],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,99315,5578],{"id":5577},[120,99317,99318,99324,99330,99336,99345],{},[123,99319,99320,99323],{},[38,99321,99322],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,99325,99326,99329],{},[38,99327,99328],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,99331,99332,99335],{},[38,99333,99334],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,99337,99338,2979,99341,99344],{},[38,99339,99340],{},"Ceteris paribus",[614,99342,99343],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,99346,99347,99349],{},[38,99348,54622],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,99351,99353],{"id":99352},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,99355,99356,99396],{},[883,99357,99359],{"className":99358},[886],[888,99360,99361],{"xmlns":890},[892,99362,99363,99393],{},[895,99364,99365,99367,99369,99371,99373,99375,99377,99379,99381,99383,99385,99387,99389,99391],{},[898,99366,1802],{},[1701,99368,1792],{},[898,99370,1795],{},[1701,99372,1799],{"stretchy":1798},[898,99374,1680],{},[1701,99376,2012],{"separator":2011},[898,99378,13189],{},[1701,99380,2012],{"separator":2011},[898,99382,22340],{},[1701,99384,2012],{"separator":2011},[898,99386,900],{},[1701,99388,2012],{"separator":2011},[1701,99390,13704],{},[1701,99392,1805],{"stretchy":1798},[902,99394,99395],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,99398,99399],{},"Zjednodušení:",[120,99401,99402,99430],{},[123,99403,99404,4088,99407],{},[38,99405,99406],{},"Jednofaktorový model:",[883,99408,99410],{"className":99409},[886],[888,99411,99412],{"xmlns":890},[892,99413,99414,99428],{},[895,99415,99416,99418,99420,99422,99424,99426],{},[898,99417,1802],{},[1701,99419,1792],{},[898,99421,1795],{},[1701,99423,1799],{"stretchy":1798},[898,99425,1680],{},[1701,99427,1805],{"stretchy":1798},[902,99429,8264],{"encoding":904},[123,99431,99432,4088,99435],{},[38,99433,99434],{},"Inverzní zápis:",[883,99436,99438],{"className":99437},[886],[888,99439,99440],{"xmlns":890},[892,99441,99442,99456],{},[895,99443,99444,99446,99448,99450,99452,99454],{},[898,99445,1680],{},[1701,99447,1792],{},[898,99449,1795],{},[1701,99451,1799],{"stretchy":1798},[898,99453,1802],{},[1701,99455,1805],{"stretchy":1798},[902,99457,1808],{"encoding":904},[115,99459,99461],{"id":99460},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,99463,99464,99473],{},[123,99465,99466,99469,99470,2506],{},[38,99467,99468],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,99471,6071],{"className":99472,"dataFsResolvedFilePath":800,"href":801},[210],[123,99474,99475,99478,99479,99482,99483,99486,99487,99491],{},[38,99476,99477],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,99480,1145],{"className":99481,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,99484,20298],{"className":99485,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,99488,99490],{"className":99489,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,99493,99495],{"id":99494},"konvence-z-přednášek","Konvence z přednášek",[120,99497,99498,99505,99511],{},[123,99499,99500,99501,99504],{},"Symbol ",[99502,99503,4067],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,99506,99507,99508,1715],{},"Numerické výsledky ",[38,99509,99510],{},"na 3 desetinná místa",[123,99512,7971,99513,99516],{},[614,99514,99515],{},"jednotková změna"," má standardní význam (změna o 1).",[115,99518,5984],{"id":5983},[120,99520,99521,99526,99534],{},[123,99522,99523,99525],{},[38,99524,7880],{}," —",[123,99527,99528,4088,99530],{},[38,99529,7888],{},[207,99531,99533],{"className":99532,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,99535,99536,4088,99538,1343,99542],{},[38,99537,7896],{},[207,99539,99541],{"className":99540,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,99543,99545],{"className":99544,"dataFsResolvedFilePath":6035,"href":6036},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":99547},[99548,99549,99550,99551,99552,99553],{"id":99302,"depth":642,"text":99303},{"id":5577,"depth":642,"text":5578},{"id":99352,"depth":642,"text":99353},{"id":99460,"depth":642,"text":99461},{"id":99494,"depth":642,"text":99495},{"id":5983,"depth":642,"text":5984},"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":99554},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,99561,99562,99563,99564,99565],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":99568,"title":99569,"body":99570,"course":1128,"courses":659,"created":6060,"description":641,"extension":661,"meta":103842,"navigation":664,"path":103843,"seo":103844,"sources":103845,"stem":103846,"tags":103847,"type":6074,"updated":677,"__hash__":103851},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":99571,"toc":103825},[99572,99575,99669,99673,99695,99709,99761,99763,99767,99830,99873,99892,100055,100154,100157,100224,100228,100357,100396,100426,100538,100583,100649,100702,100778,100834,100836,100840,100904,100948,100968,101129,101132,101216,101313,101316,101382,101386,101435,101461,101566,101630,101635,101731,101778,101780,101783,101805,101847,101854,101887,101889,101960,102014,102123,102127,102216,102292,102556,102594,102596,102600,102603,102610,102921,102924,102982,103162,103191,103193,103197,103203,103341,103350,103352,103354,103779,103781,103783],[12,99573,99569],{"id":99574},"zdanění-trhu-dopady-daně-na-rovnováhu",[1635,99576,99577],{},[724,99578,99579,46648,99581,99594,99595,99598,99599,99601,99602,99605,99606,99627,99628,99651,99652,99655,99656,1715],{},[883,99580,2063],{},[883,99582,99584],{"className":99583},[886],[888,99585,99586],{"xmlns":890},[892,99587,99588,99592],{},[895,99589,99590],{},[898,99591,5877],{},[902,99593,5877],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,99596,99597],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,99600,90606],{}," (je-li uložena spotřebiteli). Výsledné ",[38,99603,99604],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,99607,99609],{"className":99608},[886],[888,99610,99611],{"xmlns":890},[892,99612,99613,99625],{},[895,99614,99615],{},[1845,99616,99617,99619],{},[898,99618,5877],{},[895,99620,99621,99623],{},[898,99622,46697],{},[898,99624,724],{},[902,99626,46702],{"encoding":904}," (spotřebitel) a ",[883,99629,99631],{"className":99630},[886],[888,99632,99633],{"xmlns":890},[892,99634,99635,99649],{},[895,99636,99637],{},[1845,99638,99639,99641],{},[898,99640,5877],{},[895,99642,99643,99645,99647],{},[898,99644,46720],{},[898,99646,6127],{},[898,99648,16096],{},[902,99650,46727],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,99653,99654],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,99657,99659],{"className":99658},[886],[888,99660,99661],{"xmlns":890},[892,99662,99663,99667],{},[895,99664,99665],{},[898,99666,5877],{},[902,99668,5877],{"encoding":904},[115,99670,99672],{"id":99671},"dvě-formy-zdanění","Dvě formy zdanění",[724,99674,99675,99676,99694],{},"Uvažujme jednotkovou daň ",[883,99677,99679],{"className":99678},[886],[888,99680,99681],{"xmlns":890},[892,99682,99683,99691],{},[895,99684,99685,99687,99689],{},[898,99686,5877],{},[1701,99688,7491],{},[1850,99690,1852],{},[902,99692,99693],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,99696,99697,99703],{},[123,99698,99699,99702],{},[38,99700,99701],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,99704,99705,99708],{},[38,99706,99707],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,99710,99711,99712,99725,99726,99729,99730,1715],{},"V obou případech dochází k posunu jedné z křivek o ",[883,99713,99715],{"className":99714},[886],[888,99716,99717],{"xmlns":890},[892,99718,99719,99723],{},[895,99720,99721],{},[898,99722,5877],{},[902,99724,5877],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,99727,99728],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,99731,99733],{"className":99732},[886],[888,99734,99735],{"xmlns":890},[892,99736,99737,99759],{},[895,99738,99739,99741,99743,99749,99751,99757],{},[898,99740,3249],{},[1701,99742,2036],{"stretchy":1798},[3243,99744,99745,99747],{},[898,99746,1802],{},[898,99748,3249],{},[1701,99750,2012],{"separator":2011},[3243,99752,99753,99755],{},[898,99754,1680],{},[898,99756,3249],{},[1701,99758,2053],{"stretchy":1798},[902,99760,45389],{"encoding":904},[1771,99762],{},[115,99764,99766],{"id":99765},"daň-uložená-výrobci","Daň uložená výrobci",[724,99768,99769,99770,99783,99784,99801,99802,99829],{},"Je-li daň ",[883,99771,99773],{"className":99772},[886],[888,99774,99775],{"xmlns":890},[892,99776,99777,99781],{},[895,99778,99779],{},[898,99780,5877],{},[902,99782,5877],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,99785,99787],{"className":99786},[886],[888,99788,99789],{"xmlns":890},[892,99790,99791,99799],{},[895,99792,99793,99795,99797],{},[898,99794,1680],{},[1701,99796,2317],{},[898,99798,5877],{},[902,99800,45144],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,99803,99805],{"className":99804},[886],[888,99806,99807],{"xmlns":890},[892,99808,99809,99827],{},[895,99810,99811,99813,99815,99817,99819,99821,99823,99825],{},[898,99812,1680],{},[1701,99814,2317],{},[898,99816,5877],{},[1701,99818,1792],{},[898,99820,1661],{},[1701,99822,1799],{"stretchy":1798},[898,99824,1802],{},[1701,99826,1805],{"stretchy":1798},[902,99828,45173],{"encoding":904}," nová funkce nabídky:",[883,99831,99833],{"className":99832},[886],[888,99834,99835],{"xmlns":890,"display":2252},[892,99836,99837,99871],{},[895,99838,99839,99841,99843,99849,99851,99853,99855,99857,99859,99861,99863,99865,99867,99869],{},[898,99840,1680],{},[1701,99842,1792],{},[1845,99844,99845,99847],{},[898,99846,1661],{},[1850,99848,4062],{},[1701,99850,1799],{"stretchy":1798},[898,99852,1802],{},[1701,99854,1805],{"stretchy":1798},[1701,99856,1792],{},[898,99858,1661],{},[1701,99860,1799],{"stretchy":1798},[898,99862,1802],{},[1701,99864,1805],{"stretchy":1798},[1701,99866,1703],{},[898,99868,5877],{},[898,99870,1715],{"mathvariant":2334},[902,99872,45218],{"encoding":904},[724,99874,99875,99876,4088,99889,99891],{},"Nabídka se tedy posouvá o ",[883,99877,99879],{"className":99878},[886],[888,99880,99881],{"xmlns":890},[892,99882,99883,99887],{},[895,99884,99885],{},[898,99886,5877],{},[902,99888,5877],{"encoding":904},[38,99890,45251],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,99893,99894,99895,99935,99936,2633,99964,99992,99993,100012,100013,100037,100038,2506],{},"Nový rovnovážný bod ",[883,99896,99898],{"className":99897},[886],[888,99899,99900],{"xmlns":890},[892,99901,99902,99932],{},[895,99903,99904,99910,99912,99920,99922,99930],{},[1845,99905,99906,99908],{},[898,99907,3249],{},[1850,99909,4062],{},[1701,99911,2036],{"stretchy":1798},[2287,99913,99914,99916,99918],{},[898,99915,1802],{},[1850,99917,4062],{},[898,99919,3249],{},[1701,99921,2012],{"separator":2011},[2287,99923,99924,99926,99928],{},[898,99925,1680],{},[1850,99927,4062],{},[898,99929,3249],{},[1701,99931,2053],{"stretchy":1798},[902,99933,99934],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,99937,99939],{"className":99938},[886],[888,99940,99941],{"xmlns":890},[892,99942,99943,99961],{},[895,99944,99945,99953,99955],{},[2287,99946,99947,99949,99951],{},[898,99948,1802],{},[1850,99950,4062],{},[898,99952,3249],{},[1701,99954,7530],{},[3243,99956,99957,99959],{},[898,99958,1802],{},[898,99960,3249],{},[902,99962,99963],{"encoding":904},"Q_1^E \u003C Q^E",[883,99965,99967],{"className":99966},[886],[888,99968,99969],{"xmlns":890},[892,99970,99971,99989],{},[895,99972,99973,99981,99983],{},[2287,99974,99975,99977,99979],{},[898,99976,1680],{},[1850,99978,4062],{},[898,99980,3249],{},[1701,99982,7491],{},[3243,99984,99985,99987],{},[898,99986,1680],{},[898,99988,3249],{},[902,99990,99991],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,99994,99996],{"className":99995},[886],[888,99997,99998],{"xmlns":890},[892,99999,100000,100010],{},[895,100001,100002],{},[2287,100003,100004,100006,100008],{},[898,100005,1680],{},[1850,100007,4062],{},[898,100009,3249],{},[902,100011,51847],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,100014,100016],{"className":100015},[886],[888,100017,100018],{"xmlns":890},[892,100019,100020,100034],{},[895,100021,100022,100030,100032],{},[2287,100023,100024,100026,100028],{},[898,100025,1680],{},[1850,100027,4062],{},[898,100029,3249],{},[1701,100031,2317],{},[898,100033,5877],{},[902,100035,100036],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,100039,100041],{"className":100040},[886],[888,100042,100043],{"xmlns":890},[892,100044,100045,100053],{},[895,100046,100047],{},[3243,100048,100049,100051],{},[898,100050,1680],{},[898,100052,3249],{},[902,100054,45488],{"encoding":904},[724,100056,100057],{},[614,100058,100059,100060,100090,100091,100104,100105,9733,100122,100135,100136,1715],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,100061,100063],{"className":100062},[886],[888,100064,100065],{"xmlns":890},[892,100066,100067,100087],{},[895,100068,100069,100071,100073,100079,100081,100083,100085],{},[898,100070,1661],{},[1701,100072,4108],{},[1845,100074,100075,100077],{},[898,100076,1661],{},[1850,100078,4062],{},[1701,100080,1792],{},[898,100082,1661],{},[1701,100084,1703],{},[898,100086,5877],{},[902,100088,100089],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,100092,100094],{"className":100093},[886],[888,100095,100096],{"xmlns":890},[892,100097,100098,100102],{},[895,100099,100100],{},[898,100101,5877],{},[902,100103,5877],{"encoding":904},". Průsečík ",[883,100106,100108],{"className":100107},[886],[888,100109,100110],{"xmlns":890},[892,100111,100112,100120],{},[895,100113,100114],{},[1845,100115,100116,100118],{},[898,100117,1661],{},[1850,100119,4062],{},[902,100121,45020],{"encoding":904},[883,100123,100125],{"className":100124},[886],[888,100126,100127],{"xmlns":890},[892,100128,100129,100133],{},[895,100130,100131],{},[898,100132,1795],{},[902,100134,1795],{"encoding":904}," je nový rovnovážný bod ",[883,100137,100139],{"className":100138},[886],[888,100140,100141],{"xmlns":890},[892,100142,100143,100151],{},[895,100144,100145],{},[1845,100146,100147,100149],{},[898,100148,3249],{},[1850,100150,4062],{},[902,100152,100153],{"encoding":904},"E_1",[198,100155,49294],{"id":100156},"příklad-29",[724,100158,100159,45677,100161,45712,100185,100205,100206,100223],{},[38,100160,41960],{},[883,100162,100164],{"className":100163},[886],[888,100165,100166],{"xmlns":890},[892,100167,100168,100182],{},[895,100169,100170,100172,100174,100176,100178,100180],{},[898,100171,1680],{},[1701,100173,1792],{},[1850,100175,7592],{},[1701,100177,2317],{},[1850,100179,3938],{},[898,100181,1802],{},[902,100183,100184],{"encoding":904},"P = 12 - 2Q",[883,100186,100188],{"className":100187},[886],[888,100189,100190],{"xmlns":890},[892,100191,100192,100202],{},[895,100193,100194,100196,100198,100200],{},[898,100195,1680],{},[1701,100197,1792],{},[1850,100199,6460],{},[898,100201,1802],{},[902,100203,100204],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,100207,100209],{"className":100208},[886],[888,100210,100211],{"xmlns":890},[892,100212,100213,100221],{},[895,100214,100215,100217,100219],{},[898,100216,5877],{},[1701,100218,1792],{},[1850,100220,6352],{},[902,100222,45290],{"encoding":904}," Kč.",[724,100225,100226],{},[38,100227,41992],{},[724,100229,100230,100233,100234,9634,100260,4185,100280,1343,100302,100332,100333,1715],{},[614,100231,100232],{},"Bez daně."," Z rovnosti ",[883,100235,100237],{"className":100236},[886],[888,100238,100239],{"xmlns":890},[892,100240,100241,100257],{},[895,100242,100243,100245,100247,100249,100251,100253,100255],{},[1850,100244,7592],{},[1701,100246,2317],{},[1850,100248,3938],{},[898,100250,1802],{},[1701,100252,1792],{},[1850,100254,6460],{},[898,100256,1802],{},[902,100258,100259],{"encoding":904},"12 - 2Q = 4Q",[883,100261,100263],{"className":100262},[886],[888,100264,100265],{"xmlns":890},[892,100266,100267,100277],{},[895,100268,100269,100271,100273,100275],{},[1850,100270,6352],{},[898,100272,1802],{},[1701,100274,1792],{},[1850,100276,7592],{},[902,100278,100279],{"encoding":904},"6Q = 12",[883,100281,100283],{"className":100282},[886],[888,100284,100285],{"xmlns":890},[892,100286,100287,100299],{},[895,100288,100289,100295,100297],{},[3243,100290,100291,100293],{},[898,100292,1802],{},[898,100294,3249],{},[1701,100296,1792],{},[1850,100298,3938],{},[902,100300,100301],{"encoding":904},"Q^E = 2",[883,100303,100305],{"className":100304},[886],[888,100306,100307],{"xmlns":890},[892,100308,100309,100329],{},[895,100310,100311,100317,100319,100321,100323,100325,100327],{},[3243,100312,100313,100315],{},[898,100314,1680],{},[898,100316,3249],{},[1701,100318,1792],{},[1850,100320,6460],{},[1701,100322,3408],{},[1850,100324,3938],{},[1701,100326,1792],{},[1850,100328,9650],{},[902,100330,100331],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,100334,100336],{"className":100335},[886],[888,100337,100338],{"xmlns":890},[892,100339,100340,100354],{},[895,100341,100342,100344,100346,100348,100350,100352],{},[898,100343,3249],{},[1701,100345,2036],{"stretchy":1798},[1850,100347,3938],{},[1701,100349,2012],{"separator":2011},[1850,100351,9650],{},[1701,100353,2053],{"stretchy":1798},[902,100355,100356],{"encoding":904},"E[2, 8]",[724,100358,100359,100362,100363,100395],{},[614,100360,100361],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,100364,100366],{"className":100365},[886],[888,100367,100368],{"xmlns":890},[892,100369,100370,100392],{},[895,100371,100372,100378,100380,100382,100384,100386,100388,100390],{},[1845,100373,100374,100376],{},[898,100375,1661],{},[1850,100377,4062],{},[1701,100379,2246],{},[898,100381,1680],{},[1701,100383,1792],{},[1850,100385,6460],{},[898,100387,1802],{},[1701,100389,1703],{},[1850,100391,6352],{},[902,100393,100394],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,100397,100399],{"className":100398},[886],[888,100400,100401],{"xmlns":890,"display":2252},[892,100402,100403,100423],{},[895,100404,100405,100407,100409,100411,100413,100415,100417,100419,100421],{},[1850,100406,7592],{},[1701,100408,2317],{},[1850,100410,3938],{},[898,100412,1802],{},[1701,100414,1792],{},[1850,100416,6460],{},[898,100418,1802],{},[1701,100420,1703],{},[1850,100422,6352],{},[902,100424,100425],{"encoding":904},"12 - 2Q = 4Q + 6",[724,100427,100428,100429,4185,100449,1343,100473,100509,100510,1715],{},"plyne ",[883,100430,100432],{"className":100431},[886],[888,100433,100434],{"xmlns":890},[892,100435,100436,100446],{},[895,100437,100438,100440,100442,100444],{},[1850,100439,6352],{},[898,100441,1802],{},[1701,100443,1792],{},[1850,100445,6352],{},[902,100447,100448],{"encoding":904},"6Q = 6",[883,100450,100452],{"className":100451},[886],[888,100453,100454],{"xmlns":890},[892,100455,100456,100470],{},[895,100457,100458,100466,100468],{},[2287,100459,100460,100462,100464],{},[898,100461,1802],{},[1850,100463,4062],{},[898,100465,3249],{},[1701,100467,1792],{},[1850,100469,4062],{},[902,100471,100472],{"encoding":904},"Q_1^E = 1",[883,100474,100476],{"className":100475},[886],[888,100477,100478],{"xmlns":890},[892,100479,100480,100506],{},[895,100481,100482,100490,100492,100494,100496,100498,100500,100502,100504],{},[2287,100483,100484,100486,100488],{},[898,100485,1680],{},[1850,100487,4062],{},[898,100489,3249],{},[1701,100491,1792],{},[1850,100493,6460],{},[1701,100495,3408],{},[1850,100497,4062],{},[1701,100499,1703],{},[1850,100501,6352],{},[1701,100503,1792],{},[1850,100505,3703],{},[902,100507,100508],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,100511,100513],{"className":100512},[886],[888,100514,100515],{"xmlns":890},[892,100516,100517,100535],{},[895,100518,100519,100525,100527,100529,100531,100533],{},[1845,100520,100521,100523],{},[898,100522,3249],{},[1850,100524,4062],{},[1701,100526,2036],{"stretchy":1798},[1850,100528,4062],{},[1701,100530,2012],{"separator":2011},[1850,100532,3703],{},[1701,100534,2053],{"stretchy":1798},[902,100536,100537],{"encoding":904},"E_1[1, 10]",[724,100539,100540,100543,100544,100568,100569,100582],{},[614,100541,100542],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,100545,100547],{"className":100546},[886],[888,100548,100549],{"xmlns":890},[892,100550,100551,100565],{},[895,100552,100553,100561,100563],{},[2287,100554,100555,100557,100559],{},[898,100556,1680],{},[1850,100558,4062],{},[898,100560,3249],{},[1701,100562,1792],{},[1850,100564,3703],{},[902,100566,100567],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,100570,100572],{"className":100571},[886],[888,100573,100574],{"xmlns":890},[892,100575,100576,100580],{},[895,100577,100578],{},[1850,100579,9650],{},[902,100581,9650],{"encoding":904},", navýšení je",[883,100584,100586],{"className":100585},[886],[888,100587,100588],{"xmlns":890,"display":2252},[892,100589,100590,100646],{},[895,100591,100592,100602,100604,100612,100614,100620,100622,100624,100626,100628,100630,100632,100634,100644],{},[1845,100593,100594,100596],{},[898,100595,5877],{},[895,100597,100598,100600],{},[898,100599,46697],{},[898,100601,724],{},[1701,100603,1792],{},[2287,100605,100606,100608,100610],{},[898,100607,1680],{},[1850,100609,4062],{},[898,100611,3249],{},[1701,100613,2317],{},[3243,100615,100616,100618],{},[898,100617,1680],{},[898,100619,3249],{},[1701,100621,1792],{},[1850,100623,3703],{},[1701,100625,2317],{},[1850,100627,9650],{},[1701,100629,1792],{},[1850,100631,3938],{},[1939,100633,6402],{},[895,100635,100636,100638],{},[1939,100637,13858],{},[12448,100639,100640,100642],{"accent":2011},[1939,100641,3618],{},[1701,100643,29096],{},[898,100645,1715],{"mathvariant":2334},[902,100647,100648],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,100650,100651,100652,100568,100688,100701],{},"Výrobci zůstává čistá cena ",[883,100653,100655],{"className":100654},[886],[888,100656,100657],{"xmlns":890},[892,100658,100659,100685],{},[895,100660,100661,100669,100671,100673,100675,100677,100679,100681,100683],{},[2287,100662,100663,100665,100667],{},[898,100664,1680],{},[1850,100666,4062],{},[898,100668,3249],{},[1701,100670,2317],{},[898,100672,5877],{},[1701,100674,1792],{},[1850,100676,3703],{},[1701,100678,2317],{},[1850,100680,6352],{},[1701,100682,1792],{},[1850,100684,6460],{},[902,100686,100687],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,100689,100691],{"className":100690},[886],[888,100692,100693],{"xmlns":890},[892,100694,100695,100699],{},[895,100696,100697],{},[1850,100698,9650],{},[902,100700,9650],{"encoding":904},", pokles je",[883,100703,100705],{"className":100704},[886],[888,100706,100707],{"xmlns":890,"display":2252},[892,100708,100709,100775],{},[895,100710,100711,100723,100725,100731,100733,100735,100743,100745,100747,100749,100751,100753,100755,100757,100759,100761,100763,100773],{},[1845,100712,100713,100715],{},[898,100714,5877],{},[895,100716,100717,100719,100721],{},[898,100718,46720],{},[898,100720,6127],{},[898,100722,16096],{},[1701,100724,1792],{},[3243,100726,100727,100729],{},[898,100728,1680],{},[898,100730,3249],{},[1701,100732,2317],{},[1701,100734,1799],{"stretchy":1798},[2287,100736,100737,100739,100741],{},[898,100738,1680],{},[1850,100740,4062],{},[898,100742,3249],{},[1701,100744,2317],{},[898,100746,5877],{},[1701,100748,1805],{"stretchy":1798},[1701,100750,1792],{},[1850,100752,9650],{},[1701,100754,2317],{},[1850,100756,6460],{},[1701,100758,1792],{},[1850,100760,6460],{},[1939,100762,6402],{},[895,100764,100765,100767],{},[1939,100766,13858],{},[12448,100768,100769,100771],{"accent":2011},[1939,100770,3618],{},[1701,100772,29096],{},[898,100774,1715],{"mathvariant":2334},[902,100776,100777],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,100779,100780,100781,100833],{},"Kontrola: ",[883,100782,100784],{"className":100783},[886],[888,100785,100786],{"xmlns":890},[892,100787,100788,100830],{},[895,100789,100790,100800,100802,100814,100816,100818,100820,100822,100824,100826,100828],{},[1845,100791,100792,100794],{},[898,100793,5877],{},[895,100795,100796,100798],{},[898,100797,46697],{},[898,100799,724],{},[1701,100801,1703],{},[1845,100803,100804,100806],{},[898,100805,5877],{},[895,100807,100808,100810,100812],{},[898,100809,46720],{},[898,100811,6127],{},[898,100813,16096],{},[1701,100815,1792],{},[1850,100817,3938],{},[1701,100819,1703],{},[1850,100821,6460],{},[1701,100823,1792],{},[1850,100825,6352],{},[1701,100827,1792],{},[898,100829,5877],{},[902,100831,100832],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[1771,100835],{},[115,100837,100839],{"id":100838},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,100841,99769,100842,100855,100856,100874,100875,100903],{},[883,100843,100845],{"className":100844},[886],[888,100846,100847],{"xmlns":890},[892,100848,100849,100853],{},[895,100850,100851],{},[898,100852,5877],{},[902,100854,5877],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,100857,100859],{"className":100858},[886],[888,100860,100861],{"xmlns":890},[892,100862,100863,100871],{},[895,100864,100865,100867,100869],{},[898,100866,1680],{},[1701,100868,1703],{},[898,100870,5877],{},[902,100872,100873],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,100876,100878],{"className":100877},[886],[888,100879,100880],{"xmlns":890},[892,100881,100882,100900],{},[895,100883,100884,100886,100888,100890,100892,100894,100896,100898],{},[898,100885,1680],{},[1701,100887,1703],{},[898,100889,5877],{},[1701,100891,1792],{},[898,100893,1795],{},[1701,100895,1799],{"stretchy":1798},[898,100897,1802],{},[1701,100899,1805],{"stretchy":1798},[902,100901,100902],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,100905,100907],{"className":100906},[886],[888,100908,100909],{"xmlns":890,"display":2252},[892,100910,100911,100945],{},[895,100912,100913,100915,100917,100923,100925,100927,100929,100931,100933,100935,100937,100939,100941,100943],{},[898,100914,1680],{},[1701,100916,1792],{},[1845,100918,100919,100921],{},[898,100920,1795],{},[1850,100922,3938],{},[1701,100924,1799],{"stretchy":1798},[898,100926,1802],{},[1701,100928,1805],{"stretchy":1798},[1701,100930,1792],{},[898,100932,1795],{},[1701,100934,1799],{"stretchy":1798},[898,100936,1802],{},[1701,100938,1805],{"stretchy":1798},[1701,100940,2317],{},[898,100942,5877],{},[898,100944,1715],{"mathvariant":2334},[902,100946,100947],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,100949,100950,100951,4088,100964,100967],{},"Poptávka se tedy posouvá o ",[883,100952,100954],{"className":100953},[886],[888,100955,100956],{"xmlns":890},[892,100957,100958,100962],{},[895,100959,100960],{},[898,100961,5877],{},[902,100963,5877],{"encoding":904},[38,100965,100966],{},"svisle dolů",". Nabídka se nemění.",[724,100969,99894,100970,99935,101010,2633,101038,101066,101067,101086,101087,101111,101112,2506],{},[883,100971,100973],{"className":100972},[886],[888,100974,100975],{"xmlns":890},[892,100976,100977,101007],{},[895,100978,100979,100985,100987,100995,100997,101005],{},[1845,100980,100981,100983],{},[898,100982,3249],{},[1850,100984,3938],{},[1701,100986,2036],{"stretchy":1798},[2287,100988,100989,100991,100993],{},[898,100990,1802],{},[1850,100992,3938],{},[898,100994,3249],{},[1701,100996,2012],{"separator":2011},[2287,100998,100999,101001,101003],{},[898,101000,1680],{},[1850,101002,3938],{},[898,101004,3249],{},[1701,101006,2053],{"stretchy":1798},[902,101008,101009],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,101011,101013],{"className":101012},[886],[888,101014,101015],{"xmlns":890},[892,101016,101017,101035],{},[895,101018,101019,101027,101029],{},[2287,101020,101021,101023,101025],{},[898,101022,1802],{},[1850,101024,3938],{},[898,101026,3249],{},[1701,101028,7530],{},[3243,101030,101031,101033],{},[898,101032,1802],{},[898,101034,3249],{},[902,101036,101037],{"encoding":904},"Q_2^E \u003C Q^E",[883,101039,101041],{"className":101040},[886],[888,101042,101043],{"xmlns":890},[892,101044,101045,101063],{},[895,101046,101047,101055,101057],{},[2287,101048,101049,101051,101053],{},[898,101050,1680],{},[1850,101052,3938],{},[898,101054,3249],{},[1701,101056,7530],{},[3243,101058,101059,101061],{},[898,101060,1680],{},[898,101062,3249],{},[902,101064,101065],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,101068,101070],{"className":101069},[886],[888,101071,101072],{"xmlns":890},[892,101073,101074,101084],{},[895,101075,101076],{},[2287,101077,101078,101080,101082],{},[898,101079,1680],{},[1850,101081,3938],{},[898,101083,3249],{},[902,101085,51908],{"encoding":904},", spotřebitel platí celkem ",[883,101088,101090],{"className":101089},[886],[888,101091,101092],{"xmlns":890},[892,101093,101094,101108],{},[895,101095,101096,101104,101106],{},[2287,101097,101098,101100,101102],{},[898,101099,1680],{},[1850,101101,3938],{},[898,101103,3249],{},[1701,101105,1703],{},[898,101107,5877],{},[902,101109,101110],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,101113,101115],{"className":101114},[886],[888,101116,101117],{"xmlns":890},[892,101118,101119,101127],{},[895,101120,101121],{},[3243,101122,101123,101125],{},[898,101124,1680],{},[898,101126,3249],{},[902,101128,45488],{"encoding":904},[724,101130,101131],{},"Daňové břemeno:",[883,101133,101135],{"className":101134},[886],[888,101136,101137],{"xmlns":890,"display":2252},[892,101138,101139,101213],{},[895,101140,101141,101151,101153,101155,101163,101165,101167,101169,101171,101177,101179,101181,101193,101195,101201,101203,101211],{},[1845,101142,101143,101145],{},[898,101144,5877],{},[895,101146,101147,101149],{},[898,101148,46697],{},[898,101150,724],{},[1701,101152,1792],{},[1701,101154,1799],{"stretchy":1798},[2287,101156,101157,101159,101161],{},[898,101158,1680],{},[1850,101160,3938],{},[898,101162,3249],{},[1701,101164,1703],{},[898,101166,5877],{},[1701,101168,1805],{"stretchy":1798},[1701,101170,2317],{},[3243,101172,101173,101175],{},[898,101174,1680],{},[898,101176,3249],{},[1701,101178,2012],{"separator":2011},[9942,101180],{"width":9944},[1845,101182,101183,101185],{},[898,101184,5877],{},[895,101186,101187,101189,101191],{},[898,101188,46720],{},[898,101190,6127],{},[898,101192,16096],{},[1701,101194,1792],{},[3243,101196,101197,101199],{},[898,101198,1680],{},[898,101200,3249],{},[1701,101202,2317],{},[2287,101204,101205,101207,101209],{},[898,101206,1680],{},[1850,101208,3938],{},[898,101210,3249],{},[898,101212,1715],{"mathvariant":2334},[902,101214,101215],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,101217,101218],{},[614,101219,101220,101221,101251,101252,100104,101265,9733,101282,100135,101295,1715],{},"Obrázek 2.19: Posun ",[883,101222,101224],{"className":101223},[886],[888,101225,101226],{"xmlns":890},[892,101227,101228,101248],{},[895,101229,101230,101232,101234,101240,101242,101244,101246],{},[898,101231,1795],{},[1701,101233,4108],{},[1845,101235,101236,101238],{},[898,101237,1795],{},[1850,101239,3938],{},[1701,101241,1792],{},[898,101243,1795],{},[1701,101245,2317],{},[898,101247,5877],{},[902,101249,101250],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,101253,101255],{"className":101254},[886],[888,101256,101257],{"xmlns":890},[892,101258,101259,101263],{},[895,101260,101261],{},[898,101262,5877],{},[902,101264,5877],{"encoding":904},[883,101266,101268],{"className":101267},[886],[888,101269,101270],{"xmlns":890},[892,101271,101272,101280],{},[895,101273,101274],{},[1845,101275,101276,101278],{},[898,101277,1795],{},[1850,101279,3938],{},[902,101281,42352],{"encoding":904},[883,101283,101285],{"className":101284},[886],[888,101286,101287],{"xmlns":890},[892,101288,101289,101293],{},[895,101290,101291],{},[898,101292,1661],{},[902,101294,1661],{"encoding":904},[883,101296,101298],{"className":101297},[886],[888,101299,101300],{"xmlns":890},[892,101301,101302,101310],{},[895,101303,101304],{},[1845,101305,101306,101308],{},[898,101307,3249],{},[1850,101309,3938],{},[902,101311,101312],{"encoding":904},"E_2",[198,101314,49374],{"id":101315},"příklad-210",[724,101317,101318,101320,101321,45712,101344,101363,101364,101381],{},[38,101319,41960],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,101322,101324],{"className":101323},[886],[888,101325,101326],{"xmlns":890},[892,101327,101328,101342],{},[895,101329,101330,101332,101334,101336,101338,101340],{},[898,101331,1680],{},[1701,101333,1792],{},[1850,101335,7592],{},[1701,101337,2317],{},[1850,101339,3938],{},[898,101341,1802],{},[902,101343,100184],{"encoding":904},[883,101345,101347],{"className":101346},[886],[888,101348,101349],{"xmlns":890},[892,101350,101351,101361],{},[895,101352,101353,101355,101357,101359],{},[898,101354,1680],{},[1701,101356,1792],{},[1850,101358,6460],{},[898,101360,1802],{},[902,101362,100204],{"encoding":904},". Daň ",[883,101365,101367],{"className":101366},[886],[888,101368,101369],{"xmlns":890},[892,101370,101371,101379],{},[895,101372,101373,101375,101377],{},[898,101374,5877],{},[1701,101376,1792],{},[1850,101378,6352],{},[902,101380,45290],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,101383,101384],{},[38,101385,41992],{},[724,101387,101388,101389,100395],{},"Nová poptávka je ",[883,101390,101392],{"className":101391},[886],[888,101393,101394],{"xmlns":890},[892,101395,101396,101432],{},[895,101397,101398,101404,101406,101408,101410,101412,101414,101416,101418,101420,101422,101424,101426,101428,101430],{},[1845,101399,101400,101402],{},[898,101401,1795],{},[1850,101403,3938],{},[1701,101405,2246],{},[898,101407,1680],{},[1701,101409,1792],{},[1850,101411,7592],{},[1701,101413,2317],{},[1850,101415,3938],{},[898,101417,1802],{},[1701,101419,2317],{},[1850,101421,6352],{},[1701,101423,1792],{},[1850,101425,6352],{},[1701,101427,2317],{},[1850,101429,3938],{},[898,101431,1802],{},[902,101433,101434],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,101436,101438],{"className":101437},[886],[888,101439,101440],{"xmlns":890,"display":2252},[892,101441,101442,101458],{},[895,101443,101444,101446,101448,101450,101452,101454,101456],{},[1850,101445,6352],{},[1701,101447,2317],{},[1850,101449,3938],{},[898,101451,1802],{},[1701,101453,1792],{},[1850,101455,6460],{},[898,101457,1802],{},[902,101459,101460],{"encoding":904},"6 - 2Q = 4Q",[724,101462,100428,101463,4185,101482,1343,101506,100509,101538,1715],{},[883,101464,101466],{"className":101465},[886],[888,101467,101468],{"xmlns":890},[892,101469,101470,101480],{},[895,101471,101472,101474,101476,101478],{},[1850,101473,6352],{},[898,101475,1802],{},[1701,101477,1792],{},[1850,101479,6352],{},[902,101481,100448],{"encoding":904},[883,101483,101485],{"className":101484},[886],[888,101486,101487],{"xmlns":890},[892,101488,101489,101503],{},[895,101490,101491,101499,101501],{},[2287,101492,101493,101495,101497],{},[898,101494,1802],{},[1850,101496,3938],{},[898,101498,3249],{},[1701,101500,1792],{},[1850,101502,4062],{},[902,101504,101505],{"encoding":904},"Q_2^E = 1",[883,101507,101509],{"className":101508},[886],[888,101510,101511],{"xmlns":890},[892,101512,101513,101535],{},[895,101514,101515,101523,101525,101527,101529,101531,101533],{},[2287,101516,101517,101519,101521],{},[898,101518,1680],{},[1850,101520,3938],{},[898,101522,3249],{},[1701,101524,1792],{},[1850,101526,6460],{},[1701,101528,3408],{},[1850,101530,4062],{},[1701,101532,1792],{},[1850,101534,6460],{},[902,101536,101537],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,101539,101541],{"className":101540},[886],[888,101542,101543],{"xmlns":890},[892,101544,101545,101563],{},[895,101546,101547,101553,101555,101557,101559,101561],{},[1845,101548,101549,101551],{},[898,101550,3249],{},[1850,101552,3938],{},[1701,101554,2036],{"stretchy":1798},[1850,101556,4062],{},[1701,101558,2012],{"separator":2011},[1850,101560,6460],{},[1701,101562,2053],{"stretchy":1798},[902,101564,101565],{"encoding":904},"E_2[1, 4]",[724,101567,101568,101569,101605,101606,100223],{},"Spotřebitel platí celkem ",[883,101570,101572],{"className":101571},[886],[888,101573,101574],{"xmlns":890},[892,101575,101576,101602],{},[895,101577,101578,101586,101588,101590,101592,101594,101596,101598,101600],{},[2287,101579,101580,101582,101584],{},[898,101581,1680],{},[1850,101583,3938],{},[898,101585,3249],{},[1701,101587,1703],{},[898,101589,5877],{},[1701,101591,1792],{},[1850,101593,6460],{},[1701,101595,1703],{},[1850,101597,6352],{},[1701,101599,1792],{},[1850,101601,3703],{},[902,101603,101604],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,101607,101609],{"className":101608},[886],[888,101610,101611],{"xmlns":890},[892,101612,101613,101627],{},[895,101614,101615,101623,101625],{},[2287,101616,101617,101619,101621],{},[898,101618,1680],{},[1850,101620,3938],{},[898,101622,3249],{},[1701,101624,1792],{},[1850,101626,6460],{},[902,101628,101629],{"encoding":904},"P_2^E = 4",[724,101631,101632],{},[614,101633,101634],{},"Rozklad daňového břemene:",[883,101636,101638],{"className":101637},[886],[888,101639,101640],{"xmlns":890,"display":2252},[892,101641,101642,101728],{},[895,101643,101644,101654,101656,101658,101660,101662,101664,101666,101668,101670,101672,101674,101676,101686,101688,101690,101702,101704,101706,101708,101710,101712,101714,101716,101726],{},[1845,101645,101646,101648],{},[898,101647,5877],{},[895,101649,101650,101652],{},[898,101651,46697],{},[898,101653,724],{},[1701,101655,1792],{},[1701,101657,1799],{"stretchy":1798},[1850,101659,6460],{},[1701,101661,1703],{},[1850,101663,6352],{},[1701,101665,1805],{"stretchy":1798},[1701,101667,2317],{},[1850,101669,9650],{},[1701,101671,1792],{},[1850,101673,3938],{},[1939,101675,6402],{},[895,101677,101678,101680],{},[1939,101679,13858],{},[12448,101681,101682,101684],{"accent":2011},[1939,101683,3618],{},[1701,101685,29096],{},[1701,101687,2012],{"separator":2011},[9942,101689],{"width":9944},[1845,101691,101692,101694],{},[898,101693,5877],{},[895,101695,101696,101698,101700],{},[898,101697,46720],{},[898,101699,6127],{},[898,101701,16096],{},[1701,101703,1792],{},[1850,101705,9650],{},[1701,101707,2317],{},[1850,101709,6460],{},[1701,101711,1792],{},[1850,101713,6460],{},[1939,101715,6402],{},[895,101717,101718,101720],{},[1939,101719,13858],{},[12448,101721,101722,101724],{"accent":2011},[1939,101723,3618],{},[1701,101725,29096],{},[898,101727,1715],{"mathvariant":2334},[902,101729,101730],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,101732,101733,101734,1715],{},"Opět ",[883,101735,101737],{"className":101736},[886],[888,101738,101739],{"xmlns":890},[892,101740,101741,101775],{},[895,101742,101743,101753,101755,101767,101769,101771,101773],{},[1845,101744,101745,101747],{},[898,101746,5877],{},[895,101748,101749,101751],{},[898,101750,46697],{},[898,101752,724],{},[1701,101754,1703],{},[1845,101756,101757,101759],{},[898,101758,5877],{},[895,101760,101761,101763,101765],{},[898,101762,46720],{},[898,101764,6127],{},[898,101766,16096],{},[1701,101768,1792],{},[1850,101770,6352],{},[1701,101772,1792],{},[898,101774,5877],{},[902,101776,101777],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[1771,101779],{},[115,101781,46678],{"id":101782},"daňové-břemeno",[724,101784,101785,1646,101787,101790,101791,101804],{},[38,101786,46678],{},[614,101788,101789],{},"tax burden",") je rozdělení zaplacené daně ",[883,101792,101794],{"className":101793},[886],[888,101795,101796],{"xmlns":890},[892,101797,101798,101802],{},[895,101799,101800],{},[898,101801,5877],{},[902,101803,5877],{"encoding":904}," mezi spotřebitele a výrobce:",[883,101806,101808],{"className":101807},[886],[888,101809,101810],{"xmlns":890,"display":2252},[892,101811,101812,101844],{},[895,101813,101814,101816,101818,101828,101830,101842],{},[898,101815,5877],{},[1701,101817,1792],{},[1845,101819,101820,101822],{},[898,101821,5877],{},[895,101823,101824,101826],{},[898,101825,46697],{},[898,101827,724],{},[1701,101829,1703],{},[1845,101831,101832,101834],{},[898,101833,5877],{},[895,101835,101836,101838,101840],{},[898,101837,46720],{},[898,101839,6127],{},[898,101841,16096],{},[898,101843,1715],{"mathvariant":2334},[902,101845,101846],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,101848,101849],{},[2139,101850],{"alt":101851,"className":101852,"src":101853},"imek-dan-rozklad-bremene-sklony",[210,2143],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1635,101855,101856],{},[724,101857,101858,101860,101861,2633,101874,1715],{},[883,101859,2063],{}," 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 ",[883,101862,101864],{"className":101863},[886],[888,101865,101866],{"xmlns":890},[892,101867,101868,101872],{},[895,101869,101870],{},[898,101871,1795],{},[902,101873,1795],{"encoding":904},[883,101875,101877],{"className":101876},[886],[888,101878,101879],{"xmlns":890},[892,101880,101881,101885],{},[895,101882,101883],{},[898,101884,1661],{},[902,101886,1661],{"encoding":904},[198,101888,2348],{"id":2347},[724,101890,101891,101892,101913,101914,101927,101928,101945,101946,101959],{},"V grafu ",[883,101893,101895],{"className":101894},[886],[888,101896,101897],{"xmlns":890},[892,101898,101899,101911],{},[895,101900,101901,101903,101905,101907,101909],{},[1701,101902,1799],{"stretchy":1798},[898,101904,1802],{},[1701,101906,2012],{"separator":2011},[898,101908,1680],{},[1701,101910,1805],{"stretchy":1798},[902,101912,2019],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,101915,101917],{"className":101916},[886],[888,101918,101919],{"xmlns":890},[892,101920,101921,101925],{},[895,101922,101923],{},[898,101924,5877],{},[902,101926,5877],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,101929,101931],{"className":101930},[886],[888,101932,101933],{"xmlns":890},[892,101934,101935,101943],{},[895,101936,101937],{},[3243,101938,101939,101941],{},[898,101940,1680],{},[898,101942,3249],{},[902,101944,45488],{"encoding":904},", rozdělí se úsečka ",[883,101947,101949],{"className":101948},[886],[888,101950,101951],{"xmlns":890},[892,101952,101953,101957],{},[895,101954,101955],{},[898,101956,5877],{},[902,101958,5877],{"encoding":904}," na dvě části:",[120,101961,101962,101987],{},[123,101963,101964,101965,101986],{},"horní část odpovídá ",[883,101966,101968],{"className":101967},[886],[888,101969,101970],{"xmlns":890},[892,101971,101972,101984],{},[895,101973,101974],{},[1845,101975,101976,101978],{},[898,101977,5877],{},[895,101979,101980,101982],{},[898,101981,46697],{},[898,101983,724],{},[902,101985,46702],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,101988,101989,101990,102013],{},"dolní část odpovídá ",[883,101991,101993],{"className":101992},[886],[888,101994,101995],{"xmlns":890},[892,101996,101997,102011],{},[895,101998,101999],{},[1845,102000,102001,102003],{},[898,102002,5877],{},[895,102004,102005,102007,102009],{},[898,102006,46720],{},[898,102008,6127],{},[898,102010,16096],{},[902,102012,46727],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,102015,102016],{},[614,102017,102018,102019,3856,102032,102053,102054,102077,102078,2633,102099,102122],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,102020,102022],{"className":102021},[886],[888,102023,102024],{"xmlns":890},[892,102025,102026,102030],{},[895,102027,102028],{},[898,102029,5877],{},[902,102031,5877],{"encoding":904},[883,102033,102035],{"className":102034},[886],[888,102036,102037],{"xmlns":890},[892,102038,102039,102051],{},[895,102040,102041],{},[1845,102042,102043,102045],{},[898,102044,5877],{},[895,102046,102047,102049],{},[898,102048,46697],{},[898,102050,724],{},[902,102052,46702],{"encoding":904}," (nahoře) a ",[883,102055,102057],{"className":102056},[886],[888,102058,102059],{"xmlns":890},[892,102060,102061,102075],{},[895,102062,102063],{},[1845,102064,102065,102067],{},[898,102066,5877],{},[895,102068,102069,102071,102073],{},[898,102070,46720],{},[898,102072,6127],{},[898,102074,16096],{},[902,102076,46727],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,102079,102081],{"className":102080},[886],[888,102082,102083],{"xmlns":890},[892,102084,102085,102097],{},[895,102086,102087],{},[1845,102088,102089,102091],{},[898,102090,5877],{},[895,102092,102093,102095],{},[898,102094,46697],{},[898,102096,724],{},[902,102098,46702],{"encoding":904},[883,102100,102102],{"className":102101},[886],[888,102103,102104],{"xmlns":890},[892,102105,102106,102120],{},[895,102107,102108],{},[1845,102109,102110,102112],{},[898,102111,5877],{},[895,102113,102114,102116,102118],{},[898,102115,46720],{},[898,102117,6127],{},[898,102119,16096],{},[902,102121,46727],{"encoding":904}," je v obou případech stejná.",[198,102124,102126],{"id":102125},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,102128,102129,102130,102133,102134,1646,102157,102174,102175,1646,102198,102215],{},"Platí obecně: ",[38,102131,102132],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,102135,102137],{"className":102136},[886],[888,102138,102139],{"xmlns":890},[892,102140,102141,102155],{},[895,102142,102143,102145,102147,102149,102151,102153],{},[898,102144,1680],{},[1701,102146,1792],{},[898,102148,207],{},[898,102150,1802],{},[1701,102152,1703],{},[898,102154,3598],{},[902,102156,3601],{"encoding":904},[883,102158,102160],{"className":102159},[886],[888,102161,102162],{"xmlns":890},[892,102163,102164,102172],{},[895,102165,102166,102168,102170],{},[898,102167,207],{},[1701,102169,7530],{},[1850,102171,1852],{},[902,102173,47105],{"encoding":904},") a lineární nabídku ",[883,102176,102178],{"className":102177},[886],[888,102179,102180],{"xmlns":890},[892,102181,102182,102196],{},[895,102183,102184,102186,102188,102190,102192,102194],{},[898,102185,1680],{},[1701,102187,1792],{},[898,102189,3618],{},[898,102191,1802],{},[1701,102193,1703],{},[898,102195,2312],{},[902,102197,3627],{"encoding":904},[883,102199,102201],{"className":102200},[886],[888,102202,102203],{"xmlns":890},[892,102204,102205,102213],{},[895,102206,102207,102209,102211],{},[898,102208,3618],{},[1701,102210,7491],{},[1850,102212,1852],{},[902,102214,44283],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,102217,102219],{"className":102218},[886],[888,102220,102221],{"xmlns":890,"display":2252},[892,102222,102223,102289],{},[895,102224,102225,102249,102251,102261,102263,102287],{},[3726,102226,102227,102237],{},[1845,102228,102229,102231],{},[898,102230,5877],{},[895,102232,102233,102235],{},[898,102234,46697],{},[898,102236,724],{},[1845,102238,102239,102241],{},[898,102240,5877],{},[895,102242,102243,102245,102247],{},[898,102244,46720],{},[898,102246,6127],{},[898,102248,16096],{},[1701,102250,1792],{},[3726,102252,102253,102255],{},[898,102254,3618],{},[895,102256,102257,102259],{},[1701,102258,2317],{},[898,102260,207],{},[1701,102262,1792],{},[3726,102264,102265,102277],{},[895,102266,102267,102270,102273,102275],{},[898,102268,102269],{"mathvariant":2334},"∣",[1939,102271,102272],{},"sklon ",[898,102274,1661],{},[898,102276,102269],{"mathvariant":2334},[895,102278,102279,102281,102283,102285],{},[898,102280,102269],{"mathvariant":2334},[1939,102282,102272],{},[898,102284,1795],{},[898,102286,102269],{"mathvariant":2334},[898,102288,1715],{"mathvariant":2334},[902,102290,102291],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1635,102293,102294,102299],{},[724,102295,102296,102298],{},[883,102297,3140],{}," Postup výpočtu rozkladu",[152,102300,102301,102336,102389,102468],{},[123,102302,102303,102304,102335],{},"Spočti rovnovážný bod ",[883,102305,102307],{"className":102306},[886],[888,102308,102309],{"xmlns":890},[892,102310,102311,102333],{},[895,102312,102313,102315,102317,102323,102325,102331],{},[898,102314,3249],{},[1701,102316,2036],{"stretchy":1798},[3243,102318,102319,102321],{},[898,102320,1802],{},[898,102322,3249],{},[1701,102324,2012],{"separator":2011},[3243,102326,102327,102329],{},[898,102328,1680],{},[898,102330,3249],{},[1701,102332,2053],{"stretchy":1798},[902,102334,45389],{"encoding":904}," bez daně.",[123,102337,102338,102339,1348,102364,2506],{},"Urči posunutou křivku (",[883,102340,102342],{"className":102341},[886],[888,102343,102344],{"xmlns":890},[892,102345,102346,102362],{},[895,102347,102348,102354,102356,102358,102360],{},[1845,102349,102350,102352],{},[898,102351,1661],{},[1850,102353,4062],{},[1701,102355,1792],{},[898,102357,1661],{},[1701,102359,1703],{},[898,102361,5877],{},[902,102363,46774],{"encoding":904},[883,102365,102367],{"className":102366},[886],[888,102368,102369],{"xmlns":890},[892,102370,102371,102387],{},[895,102372,102373,102379,102381,102383,102385],{},[1845,102374,102375,102377],{},[898,102376,1795],{},[1850,102378,3938],{},[1701,102380,1792],{},[898,102382,1795],{},[1701,102384,2317],{},[898,102386,5877],{},[902,102388,46805],{"encoding":904},[123,102390,102391,102392,1889,102411,1738,102430,1889,102449,2506],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,102393,102395],{"className":102394},[886],[888,102396,102397],{"xmlns":890},[892,102398,102399,102409],{},[895,102400,102401],{},[2287,102402,102403,102405,102407],{},[898,102404,1802],{},[1850,102406,4062],{},[898,102408,3249],{},[902,102410,51826],{"encoding":904},[883,102412,102414],{"className":102413},[886],[888,102415,102416],{"xmlns":890},[892,102417,102418,102428],{},[895,102419,102420],{},[2287,102421,102422,102424,102426],{},[898,102423,1802],{},[1850,102425,3938],{},[898,102427,3249],{},[902,102429,51888],{"encoding":904},[883,102431,102433],{"className":102432},[886],[888,102434,102435],{"xmlns":890},[892,102436,102437,102447],{},[895,102438,102439],{},[2287,102440,102441,102443,102445],{},[898,102442,1680],{},[1850,102444,4062],{},[898,102446,3249],{},[902,102448,51847],{"encoding":904},[883,102450,102452],{"className":102451},[886],[888,102453,102454],{"xmlns":890},[892,102455,102456,102466],{},[895,102457,102458],{},[2287,102459,102460,102462,102464],{},[898,102461,1680],{},[1850,102463,3938],{},[898,102465,3249],{},[902,102467,51908],{"encoding":904},[123,102469,102470,102471,2633,102492,102515,102516,1715],{},"Dopočítej ",[883,102472,102474],{"className":102473},[886],[888,102475,102476],{"xmlns":890},[892,102477,102478,102490],{},[895,102479,102480],{},[1845,102481,102482,102484],{},[898,102483,5877],{},[895,102485,102486,102488],{},[898,102487,46697],{},[898,102489,724],{},[902,102491,46702],{"encoding":904},[883,102493,102495],{"className":102494},[886],[888,102496,102497],{"xmlns":890},[892,102498,102499,102513],{},[895,102500,102501],{},[1845,102502,102503,102505],{},[898,102504,5877],{},[895,102506,102507,102509,102511],{},[898,102508,46720],{},[898,102510,6127],{},[898,102512,16096],{},[902,102514,46727],{"encoding":904}," z definice, vždy ověř ",[883,102517,102519],{"className":102518},[886],[888,102520,102521],{"xmlns":890},[892,102522,102523,102553],{},[895,102524,102525,102535,102537,102549,102551],{},[1845,102526,102527,102529],{},[898,102528,5877],{},[895,102530,102531,102533],{},[898,102532,46697],{},[898,102534,724],{},[1701,102536,1703],{},[1845,102538,102539,102541],{},[898,102540,5877],{},[895,102542,102543,102545,102547],{},[898,102544,46720],{},[898,102546,6127],{},[898,102548,16096],{},[1701,102550,1792],{},[898,102552,5877],{},[902,102554,102555],{"encoding":904},"T_{sp} + T_{vyr} = T",[1635,102557,102558],{},[724,102559,102560,102562,102563,102566,102567,2633,102580,102593],{},[883,102561,4695],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,102564,102565],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,102568,102570],{"className":102569},[886],[888,102571,102572],{"xmlns":890},[892,102573,102574,102578],{},[895,102575,102576],{},[898,102577,1795],{},[902,102579,1795],{"encoding":904},[883,102581,102583],{"className":102582},[886],[888,102584,102585],{"xmlns":890},[892,102586,102587,102591],{},[895,102588,102589],{},[898,102590,1661],{},[902,102592,1661],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[1771,102595],{},[115,102597,102599],{"id":102598},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,102601,102602],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,102604,102605],{},[2139,102606],{"alt":102607,"className":102608,"src":102609},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,2143],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,102611,102612,102624],{},[19,102613,102614],{},[22,102615,102616,102618,102621],{},[25,102617,5233],{},[25,102619,102620],{},"(a) daň výrobci",[25,102622,102623],{},"(b) daň spotřebiteli",[30,102625,102626,102681,102748,102808],{},[22,102627,102628,102631,102656],{},[35,102629,102630],{},"Rovnovážné množství",[35,102632,102633],{},[883,102634,102636],{"className":102635},[886],[888,102637,102638],{"xmlns":890},[892,102639,102640,102654],{},[895,102641,102642,102650,102652],{},[2287,102643,102644,102646,102648],{},[898,102645,1802],{},[1850,102647,4062],{},[898,102649,3249],{},[1701,102651,1792],{},[1850,102653,4062],{},[902,102655,100472],{"encoding":904},[35,102657,102658],{},[883,102659,102661],{"className":102660},[886],[888,102662,102663],{"xmlns":890},[892,102664,102665,102679],{},[895,102666,102667,102675,102677],{},[2287,102668,102669,102671,102673],{},[898,102670,1802],{},[1850,102672,3938],{},[898,102674,3249],{},[1701,102676,1792],{},[1850,102678,4062],{},[902,102680,101505],{"encoding":904},[22,102682,102683,102686,102711],{},[35,102684,102685],{},"Cena placená spotřebitelem",[35,102687,102688],{},[883,102689,102691],{"className":102690},[886],[888,102692,102693],{"xmlns":890},[892,102694,102695,102709],{},[895,102696,102697,102705,102707],{},[2287,102698,102699,102701,102703],{},[898,102700,1680],{},[1850,102702,4062],{},[898,102704,3249],{},[1701,102706,1792],{},[1850,102708,3703],{},[902,102710,100567],{"encoding":904},[35,102712,102713],{},[883,102714,102716],{"className":102715},[886],[888,102717,102718],{"xmlns":890},[892,102719,102720,102746],{},[895,102721,102722,102730,102732,102734,102736,102738,102740,102742,102744],{},[2287,102723,102724,102726,102728],{},[898,102725,1680],{},[1850,102727,3938],{},[898,102729,3249],{},[1701,102731,1703],{},[898,102733,5877],{},[1701,102735,1792],{},[1850,102737,6460],{},[1701,102739,1703],{},[1850,102741,6352],{},[1701,102743,1792],{},[1850,102745,3703],{},[902,102747,101604],{"encoding":904},[22,102749,102750,102753,102783],{},[35,102751,102752],{},"Cena přijímaná výrobcem",[35,102754,102755],{},[883,102756,102758],{"className":102757},[886],[888,102759,102760],{"xmlns":890},[892,102761,102762,102780],{},[895,102763,102764,102772,102774,102776,102778],{},[2287,102765,102766,102768,102770],{},[898,102767,1680],{},[1850,102769,4062],{},[898,102771,3249],{},[1701,102773,2317],{},[898,102775,5877],{},[1701,102777,1792],{},[1850,102779,6460],{},[902,102781,102782],{"encoding":904},"P_1^E - T = 4",[35,102784,102785],{},[883,102786,102788],{"className":102787},[886],[888,102789,102790],{"xmlns":890},[892,102791,102792,102806],{},[895,102793,102794,102802,102804],{},[2287,102795,102796,102798,102800],{},[898,102797,1680],{},[1850,102799,3938],{},[898,102801,3249],{},[1701,102803,1792],{},[1850,102805,6460],{},[902,102807,101629],{"encoding":904},[22,102809,102810,102813,102867],{},[35,102811,102812],{},"Rozklad břemene",[35,102814,102815,1343,102840],{},[883,102816,102818],{"className":102817},[886],[888,102819,102820],{"xmlns":890},[892,102821,102822,102838],{},[895,102823,102824,102834,102836],{},[1845,102825,102826,102828],{},[898,102827,5877],{},[895,102829,102830,102832],{},[898,102831,46697],{},[898,102833,724],{},[1701,102835,1792],{},[1850,102837,3938],{},[902,102839,46996],{"encoding":904},[883,102841,102843],{"className":102842},[886],[888,102844,102845],{"xmlns":890},[892,102846,102847,102865],{},[895,102848,102849,102861,102863],{},[1845,102850,102851,102853],{},[898,102852,5877],{},[895,102854,102855,102857,102859],{},[898,102856,46720],{},[898,102858,6127],{},[898,102860,16096],{},[1701,102862,1792],{},[1850,102864,6460],{},[902,102866,47025],{"encoding":904},[35,102868,102869,1343,102894],{},[883,102870,102872],{"className":102871},[886],[888,102873,102874],{"xmlns":890},[892,102875,102876,102892],{},[895,102877,102878,102888,102890],{},[1845,102879,102880,102882],{},[898,102881,5877],{},[895,102883,102884,102886],{},[898,102885,46697],{},[898,102887,724],{},[1701,102889,1792],{},[1850,102891,3938],{},[902,102893,46996],{"encoding":904},[883,102895,102897],{"className":102896},[886],[888,102898,102899],{"xmlns":890},[892,102900,102901,102919],{},[895,102902,102903,102915,102917],{},[1845,102904,102905,102907],{},[898,102906,5877],{},[895,102908,102909,102911,102913],{},[898,102910,46720],{},[898,102912,6127],{},[898,102914,16096],{},[1701,102916,1792],{},[1850,102918,6460],{},[902,102920,47025],{"encoding":904},[724,102922,102923],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,102925,102927],{"className":102926},[886],[888,102928,102929],{"xmlns":890,"display":2252},[892,102930,102931,102979],{},[895,102932,102933,102941,102943,102951,102953,102955,102963,102965,102967,102969,102977],{},[2287,102934,102935,102937,102939],{},[898,102936,1802],{},[1850,102938,4062],{},[898,102940,3249],{},[1701,102942,1792],{},[2287,102944,102945,102947,102949],{},[898,102946,1802],{},[1850,102948,3938],{},[898,102950,3249],{},[1701,102952,2012],{"separator":2011},[9942,102954],{"width":9944},[2287,102956,102957,102959,102961],{},[898,102958,1680],{},[1850,102960,4062],{},[898,102962,3249],{},[1701,102964,2317],{},[898,102966,5877],{},[1701,102968,1792],{},[2287,102970,102971,102973,102975],{},[898,102972,1680],{},[1850,102974,3938],{},[898,102976,3249],{},[898,102978,1715],{"mathvariant":2334},[902,102980,102981],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1635,102983,102984,103003,103157],{},[724,102985,102986,102988,102989,103002],{},[883,102987,3140],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,102990,102992],{"className":102991},[886],[888,102993,102994],{"xmlns":890},[892,102995,102996,103000],{},[895,102997,102998],{},[898,102999,5877],{},[902,103001,5877],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,103004,103005,103037,103073,103110],{},[123,103006,103007,103008,2012],{},"rovnovážná množství obou režimů, ",[883,103009,103011],{"className":103010},[886],[888,103012,103013],{"xmlns":890},[892,103014,103015,103035],{},[895,103016,103017,103025,103027],{},[2287,103018,103019,103021,103023],{},[898,103020,1802],{},[1850,103022,4062],{},[898,103024,3249],{},[1701,103026,1792],{},[2287,103028,103029,103031,103033],{},[898,103030,1802],{},[1850,103032,3938],{},[898,103034,3249],{},[902,103036,46928],{"encoding":904},[123,103038,103039,103040,2012],{},"čistá cena přijímaná výrobcem, ",[883,103041,103043],{"className":103042},[886],[888,103044,103045],{"xmlns":890},[892,103046,103047,103071],{},[895,103048,103049,103057,103059,103061,103063],{},[2287,103050,103051,103053,103055],{},[898,103052,1680],{},[1850,103054,4062],{},[898,103056,3249],{},[1701,103058,2317],{},[898,103060,5877],{},[1701,103062,1792],{},[2287,103064,103065,103067,103069],{},[898,103066,1680],{},[1850,103068,3938],{},[898,103070,3249],{},[902,103072,46962],{"encoding":904},[123,103074,103075,103076,2012],{},"celková cena placená spotřebitelem, ",[883,103077,103079],{"className":103078},[886],[888,103080,103081],{"xmlns":890},[892,103082,103083,103107],{},[895,103084,103085,103093,103095,103103,103105],{},[2287,103086,103087,103089,103091],{},[898,103088,1680],{},[1850,103090,4062],{},[898,103092,3249],{},[1701,103094,1792],{},[2287,103096,103097,103099,103101],{},[898,103098,1680],{},[1850,103100,3938],{},[898,103102,3249],{},[1701,103104,1703],{},[898,103106,5877],{},[902,103108,103109],{"encoding":904},"P_1^E = P_2^E + T",[123,103111,103112,103113,2633,103134,1715],{},"rozklad daňového břemene ",[883,103114,103116],{"className":103115},[886],[888,103117,103118],{"xmlns":890},[892,103119,103120,103132],{},[895,103121,103122],{},[1845,103123,103124,103126],{},[898,103125,5877],{},[895,103127,103128,103130],{},[898,103129,46697],{},[898,103131,724],{},[902,103133,46702],{"encoding":904},[883,103135,103137],{"className":103136},[886],[888,103138,103139],{"xmlns":890},[892,103140,103141,103155],{},[895,103142,103143],{},[1845,103144,103145,103147],{},[898,103146,5877],{},[895,103148,103149,103151,103153],{},[898,103150,46720],{},[898,103152,6127],{},[898,103154,16096],{},[902,103156,46727],{"encoding":904},[724,103158,103159,103160,1715],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,103161,39228],{},[724,103163,103164,103165,2633,103178,2506],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,103166,103168],{"className":103167},[886],[888,103169,103170],{"xmlns":890},[892,103171,103172,103176],{},[895,103173,103174],{},[898,103175,1795],{},[902,103177,1795],{"encoding":904},[883,103179,103181],{"className":103180},[886],[888,103182,103183],{"xmlns":890},[892,103184,103185,103189],{},[895,103186,103187],{},[898,103188,1661],{},[902,103190,1661],{"encoding":904},[1771,103192],{},[115,103194,103196],{"id":103195},"úlohy","Úlohy",[724,103198,103199,103200,4539],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,103201,6071],{"className":103202,"dataFsResolvedFilePath":800,"href":801},[210],[120,103204,103205,103235,103266],{},[123,103206,103207,103210,103211,103234],{},[38,103208,103209],{},"Úloha 2.4"," — Poptávka ",[883,103212,103214],{"className":103213},[886],[888,103215,103216],{"xmlns":890},[892,103217,103218,103232],{},[895,103219,103220,103222,103224,103226,103228,103230],{},[898,103221,1680],{},[1701,103223,1792],{},[1850,103225,7592],{},[1701,103227,2317],{},[1850,103229,3938],{},[898,103231,1802],{},[902,103233,100184],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,103236,103237,103240,103241,103265],{},[38,103238,103239],{},"Úloha 2.9"," — Nabídka ",[883,103242,103244],{"className":103243},[886],[888,103245,103246],{"xmlns":890},[892,103247,103248,103262],{},[895,103249,103250,103252,103254,103256,103258,103260],{},[898,103251,1680],{},[1701,103253,1792],{},[1850,103255,3684],{},[898,103257,1802],{},[1701,103259,1703],{},[1850,103261,40275],{},[902,103263,103264],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,103267,103268,103271,103272,2633,103298,103322,103323,103340],{},[38,103269,103270],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,103273,103275],{"className":103274},[886],[888,103276,103277],{"xmlns":890},[892,103278,103279,103295],{},[895,103280,103281,103283,103285,103287,103289,103291,103293],{},[898,103282,1680],{},[1701,103284,1792],{},[1701,103286,2317],{},[1850,103288,6460],{},[898,103290,1802],{},[1701,103292,1703],{},[1850,103294,50694],{},[902,103296,103297],{"encoding":904},"P = -4Q + 80",[883,103299,103301],{"className":103300},[886],[888,103302,103303],{"xmlns":890},[892,103304,103305,103319],{},[895,103306,103307,103309,103311,103313,103315,103317],{},[898,103308,1680],{},[1701,103310,1792],{},[1850,103312,3646],{},[898,103314,1802],{},[1701,103316,1703],{},[1850,103318,3703],{},[902,103320,103321],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,103324,103326],{"className":103325},[886],[888,103327,103328],{"xmlns":890},[892,103329,103330,103338],{},[895,103331,103332,103334,103336],{},[898,103333,5877],{},[1701,103335,1792],{},[1850,103337,28239],{},[902,103339,51805],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,103342,103343,103344,103346,103347,103349],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,103345,49219],{}," (posun poptávky při zdanění kupujícího) a ",[38,103348,49253],{}," (posun nabídky při zdanění výrobce).",[1771,103351],{},[115,103353,5578],{"id":5577},[120,103355,103356,103375,103433,103490,103573,103619,103662,103707,103773],{},[123,103357,103358,4088,103361,103374],{},[38,103359,103360],{},"Jednotková daň",[883,103362,103364],{"className":103363},[886],[888,103365,103366],{"xmlns":890},[892,103367,103368,103372],{},[895,103369,103370],{},[898,103371,5877],{},[902,103373,5877],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,103376,103377,103379,103380,103418,103419,103432],{},[38,103378,99766],{}," — posun nabídky ",[883,103381,103383],{"className":103382},[886],[888,103384,103385],{"xmlns":890},[892,103386,103387,103415],{},[895,103388,103389,103395,103397,103399,103401,103403,103405,103407,103409,103411,103413],{},[1845,103390,103391,103393],{},[898,103392,1661],{},[1850,103394,4062],{},[1701,103396,1799],{"stretchy":1798},[898,103398,1802],{},[1701,103400,1805],{"stretchy":1798},[1701,103402,1792],{},[898,103404,1661],{},[1701,103406,1799],{"stretchy":1798},[898,103408,1802],{},[1701,103410,1805],{"stretchy":1798},[1701,103412,1703],{},[898,103414,5877],{},[902,103416,103417],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,103420,103422],{"className":103421},[886],[888,103423,103424],{"xmlns":890},[892,103425,103426,103430],{},[895,103427,103428],{},[898,103429,5877],{},[902,103431,5877],{"encoding":904}," svisle nahoru)",[123,103434,103435,103437,103438,103418,103476,103489],{},[38,103436,100839],{}," — posun poptávky ",[883,103439,103441],{"className":103440},[886],[888,103442,103443],{"xmlns":890},[892,103444,103445,103473],{},[895,103446,103447,103453,103455,103457,103459,103461,103463,103465,103467,103469,103471],{},[1845,103448,103449,103451],{},[898,103450,1795],{},[1850,103452,3938],{},[1701,103454,1799],{"stretchy":1798},[898,103456,1802],{},[1701,103458,1805],{"stretchy":1798},[1701,103460,1792],{},[898,103462,1795],{},[1701,103464,1799],{"stretchy":1798},[898,103466,1802],{},[1701,103468,1805],{"stretchy":1798},[1701,103470,2317],{},[898,103472,5877],{},[902,103474,103475],{"encoding":904},"D_2(Q) = D(Q) - T",[883,103477,103479],{"className":103478},[886],[888,103480,103481],{"xmlns":890},[892,103482,103483,103487],{},[895,103484,103485],{},[898,103486,5877],{},[902,103488,5877],{"encoding":904}," svisle dolů)",[123,103491,103492,2979,103495,45835,103534],{},[38,103493,103494],{},"Rovnovážný bod s daní",[883,103496,103498],{"className":103497},[886],[888,103499,103500],{"xmlns":890},[892,103501,103502,103532],{},[895,103503,103504,103510,103512,103520,103522,103530],{},[1845,103505,103506,103508],{},[898,103507,3249],{},[1850,103509,4062],{},[1701,103511,2036],{"stretchy":1798},[2287,103513,103514,103516,103518],{},[898,103515,1802],{},[1850,103517,4062],{},[898,103519,3249],{},[1701,103521,2012],{"separator":2011},[2287,103523,103524,103526,103528],{},[898,103525,1680],{},[1850,103527,4062],{},[898,103529,3249],{},[1701,103531,2053],{"stretchy":1798},[902,103533,99934],{"encoding":904},[883,103535,103537],{"className":103536},[886],[888,103538,103539],{"xmlns":890},[892,103540,103541,103571],{},[895,103542,103543,103549,103551,103559,103561,103569],{},[1845,103544,103545,103547],{},[898,103546,3249],{},[1850,103548,3938],{},[1701,103550,2036],{"stretchy":1798},[2287,103552,103553,103555,103557],{},[898,103554,1802],{},[1850,103556,3938],{},[898,103558,3249],{},[1701,103560,2012],{"separator":2011},[2287,103562,103563,103565,103567],{},[898,103564,1680],{},[1850,103566,3938],{},[898,103568,3249],{},[1701,103570,2053],{"stretchy":1798},[902,103572,101009],{"encoding":904},[123,103574,103575,1646,103577,103579,103580],{},[38,103576,46678],{},[614,103578,101789],{},") — rozklad ",[883,103581,103583],{"className":103582},[886],[888,103584,103585],{"xmlns":890},[892,103586,103587,103617],{},[895,103588,103589,103591,103593,103603,103605],{},[898,103590,5877],{},[1701,103592,1792],{},[1845,103594,103595,103597],{},[898,103596,5877],{},[895,103598,103599,103601],{},[898,103600,46697],{},[898,103602,724],{},[1701,103604,1703],{},[1845,103606,103607,103609],{},[898,103608,5877],{},[895,103610,103611,103613,103615],{},[898,103612,46720],{},[898,103614,6127],{},[898,103616,16096],{},[902,103618,46864],{"encoding":904},[123,103620,103621,103644,103645,1805],{},[38,103622,103623],{},[883,103624,103626],{"className":103625},[886],[888,103627,103628],{"xmlns":890},[892,103629,103630,103642],{},[895,103631,103632],{},[1845,103633,103634,103636],{},[898,103635,5877],{},[895,103637,103638,103640],{},[898,103639,46697],{},[898,103641,724],{},[902,103643,46702],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,103646,103648],{"className":103647},[886],[888,103649,103650],{"xmlns":890},[892,103651,103652,103660],{},[895,103653,103654],{},[3243,103655,103656,103658],{},[898,103657,1680],{},[898,103659,3249],{},[902,103661,45488],{"encoding":904},[123,103663,103664,103689,103690,1805],{},[38,103665,103666],{},[883,103667,103669],{"className":103668},[886],[888,103670,103671],{"xmlns":890},[892,103672,103673,103687],{},[895,103674,103675],{},[1845,103676,103677,103679],{},[898,103678,5877],{},[895,103680,103681,103683,103685],{},[898,103682,46720],{},[898,103684,6127],{},[898,103686,16096],{},[902,103688,46727],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,103691,103693],{"className":103692},[886],[888,103694,103695],{"xmlns":890},[892,103696,103697,103705],{},[895,103698,103699],{},[3243,103700,103701,103703],{},[898,103702,1680],{},[898,103704,3249],{},[902,103706,45488],{"encoding":904},[123,103708,103709,2979,103711,1343,103740],{},[38,103710,54461],{},[883,103712,103714],{"className":103713},[886],[888,103715,103716],{"xmlns":890},[892,103717,103718,103738],{},[895,103719,103720,103728,103730],{},[2287,103721,103722,103724,103726],{},[898,103723,1802],{},[1850,103725,4062],{},[898,103727,3249],{},[1701,103729,1792],{},[2287,103731,103732,103734,103736],{},[898,103733,1802],{},[1850,103735,3938],{},[898,103737,3249],{},[902,103739,46928],{"encoding":904},[883,103741,103743],{"className":103742},[886],[888,103744,103745],{"xmlns":890},[892,103746,103747,103771],{},[895,103748,103749,103757,103759,103761,103763],{},[2287,103750,103751,103753,103755],{},[898,103752,1680],{},[1850,103754,4062],{},[898,103756,3249],{},[1701,103758,2317],{},[898,103760,5877],{},[1701,103762,1792],{},[2287,103764,103765,103767,103769],{},[898,103766,1680],{},[1850,103768,3938],{},[898,103770,3249],{},[902,103772,46962],{"encoding":904},[123,103774,103775,103778],{},[38,103776,103777],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[1771,103780],{},[115,103782,5984],{"id":5983},[120,103784,103785,103793,103811,103818],{},[123,103786,103787,4088,103790],{},[38,103788,103789],{},"Kontext (hub):",[207,103791,802],{"className":103792,"dataFsResolvedFilePath":800,"href":801},[210],[123,103794,103795,4088,103797,103800,103801,22694,103803,103806,103807,103810],{},[38,103796,54710],{},[207,103798,820],{"className":103799,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,103802,5974],{},[207,103804,6007],{"className":103805,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,103808,7908],{"className":103809,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,103812,103813,4088,103815],{},[38,103814,6022],{},[207,103816,6026],{"className":103817,"dataFsResolvedFilePath":745,"href":746},[210],[123,103819,103820,4088,103822],{},[38,103821,6031],{},[207,103823,6037],{"className":103824,"dataFsResolvedFilePath":6035,"href":6036},[210],{"title":641,"searchDepth":642,"depth":642,"links":103826},[103827,103828,103831,103834,103838,103839,103840,103841],{"id":99671,"depth":642,"text":99672},{"id":99765,"depth":642,"text":99766,"children":103829},[103830],{"id":100156,"depth":649,"text":49294},{"id":100838,"depth":642,"text":100839,"children":103832},[103833],{"id":101315,"depth":649,"text":49374},{"id":101782,"depth":642,"text":46678,"children":103835},[103836,103837],{"id":2347,"depth":649,"text":2348},{"id":102125,"depth":649,"text":102126},{"id":102598,"depth":642,"text":102599},{"id":103195,"depth":642,"text":103196},{"id":5577,"depth":642,"text":5578},{"id":5983,"depth":642,"text":5984},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":99569,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,54808,103848,103849,103850,6071],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[103853,103855,103859,103863,103865],{"slug":1128,"path":6036,"title":681,"snippet":103854},"… hu|Zdanění trhu]] — daň výrobci vs. spotřebiteli, rozklad daňového břemene, ekvivalence - \u003C\u003Cprebytek-spotrebitele-vyrobce>> — CS, PS, plochy pod\u002Fnad křivkami - Příjem, náklady a zisk — TR, …",{"slug":103856,"path":1109,"title":103857,"snippet":103858},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… obce. Obsahuje **Příklady 2.1–2.13** a **Úlohy 2.1–2.18**. Topiky: poptavka-nabidka, \u003C\u003Cprebytek-spotrebitele-vyrobce>>. ### Kapitola 3 — Příjem, náklady, zisk, nabídka firmy *(str. 66–81)* Celkový, průměrný …",{"slug":103860,"path":959,"title":103861,"snippet":103862},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… očtové přímky (tečnost). --- ## 11. Přebytky spotřebitele a výrobce **Základní téma:** \u003C\u003Cprebytek-spotrebitele-vyrobce>> ### Přebytek spotřebitele $$CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0 \\cdot Q_0$$ **Původ: …",{"slug":6071,"path":801,"title":802,"snippet":103864},"… hám mezi rovnovážnou cenou a příslušnou křivkou. Podrobný výklad je na samostatné stránce \u003C\u003Cprebytek-spotrebitele-vyrobce>>. přebytek spotřebitele a výrobce **Přebytek spotřebitele* …",{"slug":46741,"path":810,"title":99569,"snippet":103866},"… ub):** Poptávka, nabídka a tržní rovnováha - **Související témata:** \u003C\u003Cprebytek-spotrebitele-vyrobce>> (daň vyvolává ztrátu blahobytu — *deadweight loss*), Derivace (sklony křivek …",[103868,103871,103872,103873],{"slug":103869,"title":103870,"path":746,"sharedTags":649},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie",{"slug":6070,"title":775,"path":774,"sharedTags":642},{"slug":6071,"title":802,"path":801,"sharedTags":642},{"slug":46741,"title":99569,"path":810,"sharedTags":642},1777154968631]