[{"data":1,"prerenderedAt":112888},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-poptavka-nabidka":1626,"course-stats-imek":15861,"course-topics-imek":15865,"backlinks-poptavka-nabidka":112860,"related-poptavka-nabidka":112883},{"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":15860},{"id":1628,"title":802,"body":1629,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":15846,"navigation":664,"path":15847,"seo":15848,"sources":15849,"stem":15850,"tags":15851,"type":15858,"updated":677,"__hash__":15859},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":1630,"toc":15801},[1631,1634,1663,1667,1674,1839,1854,1857,1860,1956,1960,1999,2080,2102,2227,2238,2252,2256,2261,2292,2356,2366,2370,2432,2439,2460,2582,2660,2664,2667,2730,2850,2855,2888,2950,3001,3057,3061,3085,3109,3158,3162,3175,3179,3290,3294,3310,3351,3362,3523,3534,3539,3543,3669,3679,3688,3692,3770,3782,3862,3868,3875,4015,4022,4025,4083,4087,4167,4214,4258,4264,4377,4381,4384,4583,4587,4825,4828,4982,5135,5137,5140,5221,5224,5329,5399,5408,5412,5415,5476,5485,5489,5522,5600,5640,5644,5693,5747,5751,5782,5812,5865,5872,5926,6004,6008,6051,6118,6162,6267,6286,6288,6292,6400,6404,6472,6521,6528,6613,6617,6692,6697,6745,6937,6941,6946,7125,7130,7191,7297,7301,7328,7332,7339,7505,7592,7597,7599,7602,7704,7854,7926,8000,8002,8006,8020,8024,8159,8214,8327,8405,8409,8466,8573,8632,8794,8798,8873,8945,9044,9102,9196,9249,9270,9324,9329,9407,9457,9546,9584,9672,9825,9862,9916,9919,9921,9924,9975,9982,9990,10078,10087,10174,10181,10183,10187,10413,10415,10419,10423,10492,10543,10747,10753,10764,10833,10839,11263,11267,11332,11356,11552,11558,11572,11640,11643,11683,11908,11976,12279,12690,12767,12933,12939,12942,13017,13473,13524,13930,14035,14698,14701,14778,14786,14861,14892,14894,14898,14942,14944,14948,14952,15184,15188,15280,15285,15379,15384,15557,15562,15681,15686,15735,15737,15741],[12,1632,802],{"id":1633},"poptávka-nabídka-a-tržní-rovnováha",[1635,1636,1637],"blockquote",{},[724,1638,1639,1642,1643,1646,1647,1650,1651,1654,1655,1658,1659,1662],{},[883,1640,1641],{},"!info"," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,1644,1645],{},"poptávka",") a výrobce (",[38,1648,1649],{},"nabídka","), jejich interakci v ",[38,1652,1653],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,1656,1657],{},"multiplikátory","). Uzavírá ji pojem ",[38,1660,1661],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,1664,1666],{"id":1665},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,1668,1669,1670,1673],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,1671,1672],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,1675,1676,1694,1744,1761],{},[123,1677,1678,1679,1693],{},"cena ",[883,1680,1682],{"className":1681},[886],[888,1683,1684],{"xmlns":890},[892,1685,1686,1691],{},[895,1687,1688],{},[898,1689,1690],{},"P",[902,1692,1690],{"encoding":904}," zkoumaného zboží,",[123,1695,1696,1697,1719],{},"ceny alternativních zboží ",[883,1698,1700],{"className":1699},[886],[888,1701,1702],{"xmlns":890},[892,1703,1704,1741],{},[895,1705,1706,1715,1720,1727,1729,1732,1734],{},[1707,1708,1709,1711],"msub",{},[898,1710,1690],{},[1712,1713,1714],"mn",{},"1",[1716,1717,1719],"mo",{"separator":1718},"true",",",[1707,1721,1722,1724],{},[898,1723,1690],{},[1712,1725,1726],{},"2",[1716,1728,1719],{"separator":1718},[1716,1730,1731],{},"…",[1716,1733,1719],{"separator":1718},[1707,1735,1736,1738],{},[898,1737,1690],{},[898,1739,1740],{},"n",[902,1742,1743],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,1745,1746,1747,1719],{},"důchod ",[883,1748,1750],{"className":1749},[886],[888,1751,1752],{"xmlns":890},[892,1753,1754,1759],{},[895,1755,1756],{},[898,1757,1758],{},"Y",[902,1760,1758],{"encoding":904},[123,1762,1763,1764,1778,1779,1793,1794,1808,1809,1823,1824,1838],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,1765,1767],{"className":1766},[886],[888,1768,1769],{"xmlns":890},[892,1770,1771,1776],{},[895,1772,1773],{},[898,1774,1775],{},"L",[902,1777,1775],{"encoding":904},", kapitál ",[883,1780,1782],{"className":1781},[886],[888,1783,1784],{"xmlns":890},[892,1785,1786,1791],{},[895,1787,1788],{},[898,1789,1790],{},"K",[902,1792,1790],{"encoding":904},", půda ",[883,1795,1797],{"className":1796},[886],[888,1798,1799],{"xmlns":890},[892,1800,1801,1806],{},[895,1802,1803],{},[898,1804,1805],{},"E",[902,1807,1805],{"encoding":904},"), technologie, počet výrobců ",[883,1810,1812],{"className":1811},[886],[888,1813,1814],{"xmlns":890},[892,1815,1816,1821],{},[895,1817,1818],{},[898,1819,1820],{},"O",[902,1822,1820],{"encoding":904},", počasí ",[883,1825,1827],{"className":1826},[886],[888,1828,1829],{"xmlns":890},[892,1830,1831,1836],{},[895,1832,1833],{},[898,1834,1835],{},"W",[902,1837,1835],{"encoding":904}," atd.",[724,1840,1841,1842,1845,1846,1849,1850,1853],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,1843,1844],{},"ceteris paribus","), hovoříme o ",[38,1847,1848],{},"jednofaktorovém modelu","; jinak jde o model ",[38,1851,1852],{},"vícefaktorový",".",[1855,1856],"hr",{},[115,1858,1859],{"id":1645},"Poptávka",[1635,1861,1862],{},[724,1863,1864,1866,1867,1881,1882,1895,1896,1899,1900,1929,1930,1853],{},[883,1865,1641],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,1868,1870],{"className":1869},[886],[888,1871,1872],{"xmlns":890},[892,1873,1874,1879],{},[895,1875,1876],{},[898,1877,1878],{},"Q",[902,1880,1878],{"encoding":904}," na ceně ",[883,1883,1885],{"className":1884},[886],[888,1886,1887],{"xmlns":890},[892,1888,1889,1893],{},[895,1890,1891],{},[898,1892,1690],{},[902,1894,1690],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,1897,1898],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,1901,1903],{"className":1902},[886],[888,1904,1905],{"xmlns":890},[892,1906,1907,1926],{},[895,1908,1909,1911,1914,1917,1921,1923],{},[898,1910,1878],{},[1716,1912,1913],{},"=",[898,1915,1916],{},"D",[1716,1918,1920],{"stretchy":1919},"false","(",[898,1922,1690],{},[1716,1924,1925],{"stretchy":1919},")",[902,1927,1928],{"encoding":904},"Q = D(P)"," a jeho lineární verzí ",[883,1931,1933],{"className":1932},[886],[888,1934,1935],{"xmlns":890},[892,1936,1937,1953],{},[895,1938,1939,1941,1943,1945,1947,1950],{},[898,1940,1690],{},[1716,1942,1913],{},[898,1944,207],{},[898,1946,1878],{},[1716,1948,1949],{},"+",[898,1951,1952],{},"b",[902,1954,1955],{"encoding":904},"P = aQ + b",[198,1957,1959],{"id":1958},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,1961,1962,1963,1976,1977,1990,1991,1994,1995,1998],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,1964,1966],{"className":1965},[886],[888,1967,1968],{"xmlns":890},[892,1969,1970,1974],{},[895,1971,1972],{},[898,1973,1878],{},[902,1975,1878],{"encoding":904}," závisí na ceně ",[883,1978,1980],{"className":1979},[886],[888,1981,1982],{"xmlns":890},[892,1983,1984,1988],{},[895,1985,1986],{},[898,1987,1690],{},[902,1989,1690],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,1992,1993],{},"funkce poptávky"," (",[614,1996,1997],{},"demand function","):",[883,2000,2002],{"className":2001},[886],[888,2003,2005],{"xmlns":890,"display":2004},"block",[892,2006,2007,2077],{},[2008,2009,2011],"mtable",{"width":2010},"100%",[2012,2013,2014,2018,2069,2071],"mtr",{},[2015,2016],"mtd",{"width":2017},"50%",[2015,2019,2020],{},[895,2021,2022,2024,2026,2028,2030,2032,2034,2040,2042,2048,2050,2052,2054,2060,2062,2064,2066],{},[898,2023,1878],{},[1716,2025,1913],{},[898,2027,1916],{},[1716,2029,1920],{"stretchy":1919},[898,2031,1690],{},[1716,2033,1719],{"separator":1718},[1707,2035,2036,2038],{},[898,2037,1690],{},[1712,2039,1714],{},[1716,2041,1719],{"separator":1718},[1707,2043,2044,2046],{},[898,2045,1690],{},[1712,2047,1726],{},[1716,2049,1719],{"separator":1718},[1716,2051,1731],{},[1716,2053,1719],{"separator":1718},[1707,2055,2056,2058],{},[898,2057,1690],{},[898,2059,1740],{},[1716,2061,1719],{"separator":1718},[898,2063,1758],{},[1716,2065,1925],{"stretchy":1919},[898,2067,1853],{"mathvariant":2068},"normal",[2015,2070],{"width":2017},[2015,2072,2073],{},[2074,2075,2076],"mtext",{},"(2.1)",[902,2078,2079],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,2081,2082,2083,2086,2087,2101],{},"Důležitou vlastností je ",[38,2084,2085],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,2088,2090],{"className":2089},[886],[888,2091,2092],{"xmlns":890},[892,2093,2094,2099],{},[895,2095,2096],{},[898,2097,2098],{},"r",[902,2100,2098],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,2103,2105],{"className":2104},[886],[888,2106,2107],{"xmlns":890,"display":2004},[892,2108,2109,2224],{},[2008,2110,2111],{"width":2010},[2012,2112,2113,2115,2217,2219],{},[2015,2114],{"width":2017},[2015,2116,2117],{},[895,2118,2119,2121,2123,2125,2127,2129,2131,2133,2135,2141,2143,2145,2151,2153,2155,2157,2159,2165,2167,2169,2171,2173,2175,2177,2179,2181,2183,2189,2191,2197,2199,2201,2203,2209,2211,2213,2215],{},[898,2120,1878],{},[1716,2122,1913],{},[898,2124,1916],{},[1716,2126,1920],{"stretchy":1919},[898,2128,2098],{},[898,2130,1690],{},[1716,2132,1719],{"separator":1718},[898,2134,2098],{},[1707,2136,2137,2139],{},[898,2138,1690],{},[1712,2140,1714],{},[1716,2142,1719],{"separator":1718},[898,2144,2098],{},[1707,2146,2147,2149],{},[898,2148,1690],{},[1712,2150,1726],{},[1716,2152,1719],{"separator":1718},[1716,2154,1731],{},[1716,2156,1719],{"separator":1718},[898,2158,2098],{},[1707,2160,2161,2163],{},[898,2162,1690],{},[898,2164,1740],{},[1716,2166,1719],{"separator":1718},[898,2168,2098],{},[898,2170,1758],{},[1716,2172,1925],{"stretchy":1919},[1716,2174,1913],{},[898,2176,1916],{},[1716,2178,1920],{"stretchy":1919},[898,2180,1690],{},[1716,2182,1719],{"separator":1718},[1707,2184,2185,2187],{},[898,2186,1690],{},[1712,2188,1714],{},[1716,2190,1719],{"separator":1718},[1707,2192,2193,2195],{},[898,2194,1690],{},[1712,2196,1726],{},[1716,2198,1719],{"separator":1718},[1716,2200,1731],{},[1716,2202,1719],{"separator":1718},[1707,2204,2205,2207],{},[898,2206,1690],{},[898,2208,1740],{},[1716,2210,1719],{"separator":1718},[898,2212,1758],{},[1716,2214,1925],{"stretchy":1919},[898,2216,1853],{"mathvariant":2068},[2015,2218],{"width":2017},[2015,2220,2221],{},[2074,2222,2223],{},"(2.2)",[902,2225,2226],{"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}",[1635,2228,2229],{},[724,2230,2231,2234,2235,1853],{},[883,2232,2233],{},"!warning"," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,2236,2237],{},"v jednofaktorových modelech neplatí",[724,2239,2240,2241,1343,2244,2247,2248,2251],{},"Rozlišuje se poptávka ",[38,2242,2243],{},"individuální",[38,2245,2246],{},"tržní"," a ",[38,2249,2250],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,2253,2255],{"id":2254},"jednofaktorové-modely","Jednofaktorové modely",[2257,2258,2260],"h4",{"id":2259},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,2262,2263,2264,2277,2278,2291],{},"Poptávané množství ",[883,2265,2267],{"className":2266},[886],[888,2268,2269],{"xmlns":890},[892,2270,2271,2275],{},[895,2272,2273],{},[898,2274,1878],{},[902,2276,1878],{"encoding":904}," závisí pouze na ceně ",[883,2279,2281],{"className":2280},[886],[888,2282,2283],{"xmlns":890},[892,2284,2285,2289],{},[895,2286,2287],{},[898,2288,1690],{},[902,2290,1690],{"encoding":904},":",[883,2293,2295],{"className":2294},[886],[888,2296,2297],{"xmlns":890,"display":2004},[892,2298,2299,2353],{},[2008,2300,2301],{"width":2010},[2012,2302,2303,2305,2346,2348],{},[2015,2304],{"width":2017},[2015,2306,2307],{},[895,2308,2309,2311,2313,2315,2317,2319,2321,2323,2327,2330,2332,2334,2336,2338,2340,2342,2344],{},[898,2310,1878],{},[1716,2312,1913],{},[898,2314,1916],{},[1716,2316,1920],{"stretchy":1919},[898,2318,1690],{},[1716,2320,1925],{"stretchy":1919},[1716,2322,1719],{"separator":1718},[2324,2325],"mspace",{"width":2326},"2em",[2074,2328,2329],{},"resp.",[2324,2331],{"width":2326},[898,2333,1690],{},[1716,2335,1913],{},[898,2337,1916],{},[1716,2339,1920],{"stretchy":1919},[898,2341,1878],{},[1716,2343,1925],{"stretchy":1919},[898,2345,1853],{"mathvariant":2068},[2015,2347],{"width":2017},[2015,2349,2350],{},[2074,2351,2352],{},"(2.3)",[902,2354,2355],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,2357,2358,2359,1994,2362,2365],{},"Graf této funkce se nazývá ",[38,2360,2361],{},"křivka poptávky",[614,2363,2364],{},"demand curve",").",[2257,2367,2369],{"id":2368},"zákon-klesající-poptávky","Zákon klesající poptávky",[1635,2371,2372],{},[724,2373,2374],{},[38,2375,2376,2377,2390,2391,2404,2405,2390,2418,2431],{},"Roste-li cena ",[883,2378,2380],{"className":2379},[886],[888,2381,2382],{"xmlns":890},[892,2383,2384,2388],{},[895,2385,2386],{},[898,2387,1690],{},[902,2389,1690],{"encoding":904},", pak množství ",[883,2392,2394],{"className":2393},[886],[888,2395,2396],{"xmlns":890},[892,2397,2398,2402],{},[895,2399,2400],{},[898,2401,1878],{},[902,2403,1878],{"encoding":904}," klesá; klesá-li cena ",[883,2406,2408],{"className":2407},[886],[888,2409,2410],{"xmlns":890},[892,2411,2412,2416],{},[895,2413,2414],{},[898,2415,1690],{},[902,2417,1690],{"encoding":904},[883,2419,2421],{"className":2420},[886],[888,2422,2423],{"xmlns":890},[892,2424,2425,2429],{},[895,2426,2427],{},[898,2428,1878],{},[902,2430,1878],{"encoding":904}," roste.",[724,2433,2434,2435,2438],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,2436,2437],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1635,2440,2441,2446],{},[724,2442,2443,2445],{},[883,2444,1641],{}," Intuice — proč zákon platí",[120,2447,2448,2454],{},[123,2449,2450,2453],{},[38,2451,2452],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,2455,2456,2459],{},[38,2457,2458],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,2461,2462,2463,2476,2477,2490,2491,2520,2521,2547,2548,2574,2575,2578,2579,1853],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,2464,2466],{"className":2465},[886],[888,2467,2468],{"xmlns":890},[892,2469,2470,2474],{},[895,2471,2472],{},[898,2473,1690],{},[902,2475,1690],{"encoding":904}," se vynáší na svislou osu, množství ",[883,2478,2480],{"className":2479},[886],[888,2481,2482],{"xmlns":890},[892,2483,2484,2488],{},[895,2485,2486],{},[898,2487,1878],{},[902,2489,1878],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,2492,2494],{"className":2493},[886],[888,2495,2496],{"xmlns":890},[892,2497,2498,2517],{},[895,2499,2500,2503,2506,2508,2514],{},[1716,2501,2502],{"stretchy":1919},"[",[1712,2504,2505],{},"0",[1716,2507,1719],{"separator":1718},[1707,2509,2510,2512],{},[898,2511,1690],{},[1712,2513,2505],{},[1716,2515,2516],{"stretchy":1919},"]",[902,2518,2519],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,2522,2524],{"className":2523},[886],[888,2525,2526],{"xmlns":890},[892,2527,2528,2544],{},[895,2529,2530,2532,2538,2540,2542],{},[1716,2531,2502],{"stretchy":1919},[1707,2533,2534,2536],{},[898,2535,1878],{},[1712,2537,2505],{},[1716,2539,1719],{"separator":1718},[1712,2541,2505],{},[1716,2543,2516],{"stretchy":1919},[902,2545,2546],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,2549,2551],{"className":2550},[886],[888,2552,2553],{"xmlns":890},[892,2554,2555,2571],{},[895,2556,2557,2559,2561,2563,2569],{},[1716,2558,1920],{"stretchy":1919},[1712,2560,2505],{},[1716,2562,1719],{"separator":1718},[1707,2564,2565,2567],{},[898,2566,1690],{},[1712,2568,2505],{},[1716,2570,1925],{"stretchy":1919},[902,2572,2573],{"encoding":904},"(0, P_0)"," je ",[38,2576,2577],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,2580,2581],{},"konvexní",[724,2583,2584],{},[614,2585,2586,2587,2609,2610,2247,2635,1853],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,2588,2590],{"className":2589},[886],[888,2591,2592],{"xmlns":890},[892,2593,2594,2606],{},[895,2595,2596,2598,2600,2602,2604],{},[1716,2597,1920],{"stretchy":1919},[898,2599,1878],{},[1716,2601,1719],{"separator":1718},[898,2603,1690],{},[1716,2605,1925],{"stretchy":1919},[902,2607,2608],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,2611,2613],{"className":2612},[886],[888,2614,2615],{"xmlns":890},[892,2616,2617,2633],{},[895,2618,2619,2621,2623,2625,2631],{},[1716,2620,2502],{"stretchy":1919},[1712,2622,2505],{},[1716,2624,1719],{"separator":1718},[1707,2626,2627,2629],{},[898,2628,1690],{},[1712,2630,2505],{},[1716,2632,2516],{"stretchy":1919},[902,2634,2519],{"encoding":904},[883,2636,2638],{"className":2637},[886],[888,2639,2640],{"xmlns":890},[892,2641,2642,2658],{},[895,2643,2644,2646,2652,2654,2656],{},[1716,2645,2502],{"stretchy":1919},[1707,2647,2648,2650],{},[898,2649,1878],{},[1712,2651,2505],{},[1716,2653,1719],{"separator":1718},[1712,2655,2505],{},[1716,2657,2516],{"stretchy":1919},[902,2659,2546],{"encoding":904},[2257,2661,2663],{"id":2662},"lineární-model-poptávky","Lineární model poptávky",[724,2665,2666],{},"Nejjednodušší závislostí je",[883,2668,2670],{"className":2669},[886],[888,2671,2672],{"xmlns":890,"display":2004},[892,2673,2674,2727],{},[2008,2675,2676],{"width":2010},[2012,2677,2678,2680,2720,2722],{},[2015,2679],{"width":2017},[2015,2681,2682],{},[895,2683,2684,2686,2688,2690,2692,2694,2696,2698,2700,2702,2705,2707,2709,2712,2714,2717],{},[898,2685,1690],{},[1716,2687,1913],{},[898,2689,207],{},[898,2691,1878],{},[1716,2693,1949],{},[898,2695,1952],{},[1716,2697,1719],{"separator":1718},[2324,2699],{"width":2326},[898,2701,207],{},[1716,2703,2704],{},"\u003C",[1712,2706,2505],{},[1716,2708,1719],{"separator":1718},[2074,2710,2711],{}," ",[898,2713,1952],{},[1716,2715,2716],{},">",[1712,2718,2719],{},"0.",[2015,2721],{"width":2017},[2015,2723,2724],{},[2074,2725,2726],{},"(2.4)",[902,2728,2729],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,2731,2732,2733,2772,2773,2247,2797,2823,2824,2846,2847,1853],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,2734,2736],{"className":2735},[886],[888,2737,2738],{"xmlns":890},[892,2739,2740,2769],{},[895,2741,2742,2744,2746,2756,2758,2761],{},[898,2743,1878],{},[1716,2745,1913],{},[2747,2748,2749],"mstyle",{"scriptlevel":2505,"displaystyle":1919},[2750,2751,2752,2754],"mfrac",{},[1712,2753,1714],{},[898,2755,207],{},[898,2757,1690],{},[1716,2759,2760],{},"−",[2747,2762,2763],{"scriptlevel":2505,"displaystyle":1919},[2750,2764,2765,2767],{},[898,2766,1952],{},[898,2768,207],{},[902,2770,2771],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",", kde ",[883,2774,2776],{"className":2775},[886],[888,2777,2778],{"xmlns":890},[892,2779,2780,2794],{},[895,2781,2782,2790,2792],{},[2747,2783,2784],{"scriptlevel":2505,"displaystyle":1919},[2750,2785,2786,2788],{},[1712,2787,1714],{},[898,2789,207],{},[1716,2791,2704],{},[1712,2793,2505],{},[902,2795,2796],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,2798,2800],{"className":2799},[886],[888,2801,2802],{"xmlns":890},[892,2803,2804,2820],{},[895,2805,2806,2808,2816,2818],{},[1716,2807,2760],{},[2747,2809,2810],{"scriptlevel":2505,"displaystyle":1919},[2750,2811,2812,2814],{},[898,2813,1952],{},[898,2815,207],{},[1716,2817,2716],{},[1712,2819,2505],{},[902,2821,2822],{"encoding":904},"-\\tfrac{b}{a} > 0",". Reálné cenové rozpětí je ",[883,2825,2827],{"className":2826},[886],[888,2828,2829],{"xmlns":890},[892,2830,2831,2843],{},[895,2832,2833,2835,2837,2839,2841],{},[1716,2834,1920],{"stretchy":1919},[1712,2836,2505],{},[1716,2838,1719],{"separator":1718},[898,2840,1952],{},[1716,2842,1925],{"stretchy":1919},[902,2844,2845],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,2848,2849],{},"nedokonalé konkurenci",[2851,2852,2854],"h5",{"id":2853},"příklad-21","Příklad 2.1",[724,2856,2857,2860,2861,1853],{},[38,2858,2859],{},"Zadání:"," Lineární poptávka ",[883,2862,2864],{"className":2863},[886],[888,2865,2866],{"xmlns":890},[892,2867,2868,2885],{},[895,2869,2870,2872,2874,2876,2878,2880,2882],{},[898,2871,1690],{},[1716,2873,1913],{},[1716,2875,2760],{},[1712,2877,1726],{},[898,2879,1878],{},[1716,2881,1949],{},[1712,2883,2884],{},"60",[902,2886,2887],{"encoding":904},"P = -2Q + 60",[724,2889,2890,2893,2894,2916,2917,1853],{},[38,2891,2892],{},"Řešení:"," Reálné cenové rozpětí je ",[883,2895,2897],{"className":2896},[886],[888,2898,2899],{"xmlns":890},[892,2900,2901,2913],{},[895,2902,2903,2905,2907,2909,2911],{},[1716,2904,1920],{"stretchy":1919},[1712,2906,2505],{},[1716,2908,1719],{"separator":1718},[1712,2910,2884],{},[1716,2912,1925],{"stretchy":1919},[902,2914,2915],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,2918,2920],{"className":2919},[886],[888,2921,2922],{"xmlns":890},[892,2923,2924,2947],{},[895,2925,2926,2928,2930,2932,2940,2942,2944],{},[898,2927,1878],{},[1716,2929,1913],{},[1716,2931,2760],{},[2747,2933,2934],{"scriptlevel":2505,"displaystyle":1919},[2750,2935,2936,2938],{},[1712,2937,1714],{},[1712,2939,1726],{},[898,2941,1690],{},[1716,2943,1949],{},[1712,2945,2946],{},"30",[902,2948,2949],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,2951,2952,2977],{},[19,2953,2954],{},[22,2955,2956,2971,2974],{},[25,2957,2958],{},[883,2959,2961],{"className":2960},[886],[888,2962,2963],{"xmlns":890},[892,2964,2965,2969],{},[895,2966,2967],{},[898,2968,1690],{},[902,2970,1690],{"encoding":904},[25,2972,2973],{},"40",[25,2975,2976],{},"20",[30,2978,2979],{},[22,2980,2981,2996,2999],{},[35,2982,2983],{},[883,2984,2986],{"className":2985},[886],[888,2987,2988],{"xmlns":890},[892,2989,2990,2994],{},[895,2991,2992],{},[898,2993,1878],{},[902,2995,1878],{"encoding":904},[35,2997,2998],{},"10",[35,3000,2976],{},[724,3002,3003],{},[614,3004,3005,3006,2247,3028,1853],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,3007,3009],{"className":3008},[886],[888,3010,3011],{"xmlns":890},[892,3012,3013,3025],{},[895,3014,3015,3017,3019,3021,3023],{},[1716,3016,2502],{"stretchy":1919},[1712,3018,2505],{},[1716,3020,1719],{"separator":1718},[898,3022,1952],{},[1716,3024,2516],{"stretchy":1919},[902,3026,3027],{"encoding":904},"[0, b]",[883,3029,3031],{"className":3030},[886],[888,3032,3033],{"xmlns":890},[892,3034,3035,3054],{},[895,3036,3037,3039,3041,3043,3046,3048,3050,3052],{},[1716,3038,2502],{"stretchy":1919},[1716,3040,2760],{},[898,3042,1952],{},[898,3044,3045],{"mathvariant":2068},"\u002F",[898,3047,207],{},[1716,3049,1719],{"separator":1718},[1712,3051,2505],{},[1716,3053,2516],{"stretchy":1919},[902,3055,3056],{"encoding":904},"[-b\u002Fa, 0]",[2257,3058,3060],{"id":3059},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,3062,3063,3064,3084],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,3065,3067],{"className":3066},[886],[888,3068,3069],{"xmlns":890},[892,3070,3071,3081],{},[895,3072,3073],{},[3074,3075,3076,3078],"msup",{},[898,3077,1690],{},[1716,3079,3080],{},"∗",[902,3082,3083],{"encoding":904},"P^*",", je funkce poptávky konstantní:",[883,3086,3088],{"className":3087},[886],[888,3089,3090],{"xmlns":890,"display":2004},[892,3091,3092,3106],{},[895,3093,3094,3096,3098,3104],{},[898,3095,1690],{},[1716,3097,1913],{},[3074,3099,3100,3102],{},[898,3101,1690],{},[1716,3103,3080],{},[898,3105,1853],{"mathvariant":2068},[902,3107,3108],{"encoding":904},"P = P^*.",[724,3110,3111],{},[614,3112,3113,3114,3135,3136,1853],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,3115,3117],{"className":3116},[886],[888,3118,3119],{"xmlns":890},[892,3120,3121,3133],{},[895,3122,3123,3125,3127,3129,3131],{},[1716,3124,1920],{"stretchy":1919},[898,3126,1878],{},[1716,3128,1719],{"separator":1718},[898,3130,1690],{},[1716,3132,1925],{"stretchy":1919},[902,3134,2608],{"encoding":904}," na úrovni ",[883,3137,3139],{"className":3138},[886],[888,3140,3141],{"xmlns":890},[892,3142,3143,3155],{},[895,3144,3145,3147,3149],{},[898,3146,1690],{},[1716,3148,1913],{},[3074,3150,3151,3153],{},[898,3152,1690],{},[1716,3154,3080],{},[902,3156,3157],{"encoding":904},"P = P^*",[2257,3159,3161],{"id":3160},"giffenův-statek","Giffenův statek",[724,3163,3164,3165,3168,3169,3171,3172,1853],{},"Existují zboží, u nichž je křivka poptávky ",[38,3166,3167],{},"rostoucí"," — tzv. ",[38,3170,3161],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,3173,3174],{},"podřadnému zboží",[2851,3176,3178],{"id":3177},"příklad-22","Příklad 2.2",[724,3180,3181,3184,3185,3203,3204,3227,3228,3246,3247,3265,3266,3289],{},[38,3182,3183],{},"Zadání a popis:"," Křivka ",[883,3186,3188],{"className":3187},[886],[888,3189,3190],{"xmlns":890},[892,3191,3192,3200],{},[895,3193,3194],{},[1707,3195,3196,3198],{},[898,3197,1916],{},[1712,3199,1714],{},[902,3201,3202],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,3205,3207],{"className":3206},[886],[888,3208,3209],{"xmlns":890},[892,3210,3211,3224],{},[895,3212,3213,3215,3217,3219,3222],{},[1716,3214,1920],{"stretchy":1919},[1712,3216,2505],{},[1716,3218,1719],{"separator":1718},[1712,3220,3221],{},"15",[1716,3223,1925],{"stretchy":1919},[902,3225,3226],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,3229,3231],{"className":3230},[886],[888,3232,3233],{"xmlns":890},[892,3234,3235,3243],{},[895,3236,3237],{},[1707,3238,3239,3241],{},[898,3240,1878],{},[1712,3242,2505],{},[902,3244,3245],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,3248,3250],{"className":3249},[886],[888,3251,3252],{"xmlns":890},[892,3253,3254,3262],{},[895,3255,3256],{},[1707,3257,3258,3260],{},[898,3259,1916],{},[1712,3261,1726],{},[902,3263,3264],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,3267,3269],{"className":3268},[886],[888,3270,3271],{"xmlns":890},[892,3272,3273,3286],{},[895,3274,3275,3277,3279,3281,3284],{},[1716,3276,2502],{"stretchy":1919},[1712,3278,2505],{},[1716,3280,1719],{"separator":1718},[1712,3282,3283],{},"21",[1716,3285,2516],{"stretchy":1919},[902,3287,3288],{"encoding":904},"[0, 21]"," centů.",[198,3291,3293],{"id":3292},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,3295,3296,3297,2291],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,3298,3300],{"className":3299},[886],[888,3301,3302],{"xmlns":890},[892,3303,3304,3308],{},[895,3305,3306],{},[898,3307,1758],{},[902,3309,1758],{"encoding":904},[883,3311,3313],{"className":3312},[886],[888,3314,3315],{"xmlns":890,"display":2004},[892,3316,3317,3348],{},[2008,3318,3319],{"width":2010},[2012,3320,3321,3323,3341,3343],{},[2015,3322],{"width":2017},[2015,3324,3325],{},[895,3326,3327,3329,3331,3333,3335,3337,3339],{},[898,3328,1878],{},[1716,3330,1913],{},[898,3332,1805],{},[1716,3334,1920],{"stretchy":1919},[898,3336,1758],{},[1716,3338,1925],{"stretchy":1919},[898,3340,1853],{"mathvariant":2068},[2015,3342],{"width":2017},[2015,3344,3345],{},[2074,3346,3347],{},"(2.5)",[902,3349,3350],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,3352,3353,3354,3357,3358,3361],{},"Funkce se nazývá ",[38,3355,3356],{},"Engelova",", její graf ",[38,3359,3360],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,3363,3364,3498],{},[123,3365,3366,3369,3370,3383,3384,3397,3398,3415,3416],{},[38,3367,3368],{},"Normální (superior) zboží"," — ",[883,3371,3373],{"className":3372},[886],[888,3374,3375],{"xmlns":890},[892,3376,3377,3381],{},[895,3378,3379],{},[898,3380,1878],{},[902,3382,1878],{"encoding":904}," roste s ",[883,3385,3387],{"className":3386},[886],[888,3388,3389],{"xmlns":890},[892,3390,3391,3395],{},[895,3392,3393],{},[898,3394,1758],{},[902,3396,1758],{"encoding":904},", nepřesáhne hodnotu ",[883,3399,3401],{"className":3400},[886],[888,3402,3403],{"xmlns":890},[892,3404,3405,3413],{},[895,3406,3407],{},[1707,3408,3409,3411],{},[898,3410,1878],{},[1712,3412,2505],{},[902,3414,3245],{"encoding":904},":\n",[120,3417,3418,3450],{},[123,3419,3420,3423,3424,3427,3428,1853],{},[38,3421,3422],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,3425,3426],{},"konkávní"," křivka, autonomní spotřeba ",[883,3429,3431],{"className":3430},[886],[888,3432,3433],{"xmlns":890},[892,3434,3435,3447],{},[895,3436,3437,3443,3445],{},[1707,3438,3439,3441],{},[898,3440,1878],{},[1712,3442,1714],{},[1716,3444,2716],{},[1712,3446,2505],{},[902,3448,3449],{"encoding":904},"Q_1 > 0",[123,3451,3452,3455,3456,3474,3475,3477,3478,3495,3496,1853],{},[38,3453,3454],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,3457,3459],{"className":3458},[886],[888,3460,3461],{"xmlns":890},[892,3462,3463,3471],{},[895,3464,3465],{},[1707,3466,3467,3469],{},[898,3468,1758],{},[1712,3470,1714],{},[902,3472,3473],{"encoding":904},"Y_1",", křivka je nejprve ",[38,3476,2581],{}," a od ",[883,3479,3481],{"className":3480},[886],[888,3482,3483],{"xmlns":890},[892,3484,3485,3493],{},[895,3486,3487],{},[1707,3488,3489,3491],{},[898,3490,1758],{},[1712,3492,1714],{},[902,3494,3473],{"encoding":904}," ",[38,3497,3426],{},[123,3499,3500,3503,3504,3522],{},[38,3501,3502],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,3505,3507],{"className":3506},[886],[888,3508,3509],{"xmlns":890},[892,3510,3511,3519],{},[895,3512,3513],{},[1707,3514,3515,3517],{},[898,3516,1758],{},[1712,3518,2505],{},[902,3520,3521],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,3524,3525,3526,3529,3530,2365],{},"Mírou citlivosti je ",[614,3527,3528],{},"důchodová elasticita"," (viz ",[207,3531,3533],{"className":3532,"dataFsResolvedFilePath":848,"href":849},[210],"elasticita",[724,3535,3536],{},[614,3537,3538],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[2257,3540,3542],{"id":3541},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1635,3544,3545,3619,3663],{},[724,3546,3547,3549,3550,3495,3553,3495,3566,3569,3570,3583,3584,3587,3588,1853],{},[883,3548,2233],{}," Pozor — nezbytné ≠ podřadné\n",[38,3551,3552],{},"Nezbytné zboží:",[883,3554,3556],{"className":3555},[886],[888,3557,3558],{"xmlns":890},[892,3559,3560,3564],{},[895,3561,3562],{},[898,3563,1878],{},[902,3565,1878],{"encoding":904},[38,3567,3568],{},"roste"," s ",[883,3571,3573],{"className":3572},[886],[888,3574,3575],{"xmlns":890},[892,3576,3577,3581],{},[895,3578,3579],{},[898,3580,1758],{},[902,3582,1758],{"encoding":904},", ale ",[38,3585,3586],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,3589,3591],{"className":3590},[886],[888,3592,3593],{"xmlns":890},[892,3594,3595,3616],{},[895,3596,3597,3603,3606,3608,3610,3612,3614],{},[1707,3598,3599,3601],{},[898,3600,1805],{},[898,3602,1758],{},[1716,3604,3605],{},"∈",[1716,3607,1920],{"stretchy":1919},[1712,3609,2505],{},[1716,3611,1719],{"separator":1718},[1712,3613,1714],{},[1716,3615,1925],{"stretchy":1919},[902,3617,3618],{"encoding":904},"E_Y \\in (0, 1)",[724,3620,3621,3495,3624,3495,3637,3640,3641,1853],{},[38,3622,3623],{},"Podřadné zboží:",[883,3625,3627],{"className":3626},[886],[888,3628,3629],{"xmlns":890},[892,3630,3631,3635],{},[895,3632,3633],{},[898,3634,1878],{},[902,3636,1878],{"encoding":904},[38,3638,3639],{},"klesá"," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,3642,3644],{"className":3643},[886],[888,3645,3646],{"xmlns":890},[892,3647,3648,3660],{},[895,3649,3650,3656,3658],{},[1707,3651,3652,3654],{},[898,3653,1805],{},[898,3655,1758],{},[1716,3657,2704],{},[1712,3659,2505],{},[902,3661,3662],{"encoding":904},"E_Y \u003C 0",[724,3664,3665,3666,1853],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,3667,3668],{},"méně kusů, ne jen proporčně méně",[724,3670,3671,3674,3675,3678],{},[38,3672,3673],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,3676,3677],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,3680,3681],{},[3682,3683],"img",{"alt":3684,"className":3685,"src":3687},"imek-engelovy-krivky-3typy",[210,3686],"wikilink-broken","\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[2851,3689,3691],{"id":3690},"české-příklady","České příklady",[16,3693,3694,3704],{},[19,3695,3696],{},[22,3697,3698,3701],{},[25,3699,3700],{},"Podřadné",[25,3702,3703],{},"Nahradí se za",[30,3705,3706,3714,3722,3730,3738,3746,3754,3762],{},[22,3707,3708,3711],{},[35,3709,3710],{},"Instantní polévky, ramen",[35,3712,3713],{},"Čerstvé jídlo, restaurace",[22,3715,3716,3719],{},[35,3717,3718],{},"MHD (autobus, tramvaj)",[35,3720,3721],{},"Vlastní auto, Uber, taxi",[22,3723,3724,3727],{},[35,3725,3726],{},"Mražené polotovary, pizza z mrazáku",[35,3728,3729],{},"Čerstvé suroviny, hotovky",[22,3731,3732,3735],{},[35,3733,3734],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,3736,3737],{},"Značkové produkty",[22,3739,3740,3743],{},[35,3741,3742],{},"Paštika Májka, obyčejný měkký salám",[35,3744,3745],{},"Kvalitní uzeniny, šunka od kosti",[22,3747,3748,3751],{},[35,3749,3750],{},"Second hand oblečení",[35,3752,3753],{},"Nové oblečení, značky",[22,3755,3756,3759],{},[35,3757,3758],{},"Krabicové víno, nejlevnější pivo",[35,3760,3761],{},"Lahvové víno, řemeslná piva",[22,3763,3764,3767],{},[35,3765,3766],{},"Ojetá auta nižších tříd",[35,3768,3769],{},"Nová auta, prémiové značky",[1635,3771,3772],{},[724,3773,3774,3777,3778,3781],{},[883,3775,3776],{},"!tip"," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,3779,3780],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,3783,3784,3787,3788,1994,3791,3813,3814,1994,3817,3838,3839,3857,3858,3861],{},[38,3785,3786],{},"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 ",[38,3789,3790],{},"luxus",[883,3792,3794],{"className":3793},[886],[888,3795,3796],{"xmlns":890},[892,3797,3798,3810],{},[895,3799,3800,3806,3808],{},[1707,3801,3802,3804],{},[898,3803,1805],{},[898,3805,1758],{},[1716,3807,2716],{},[1712,3809,1714],{},[902,3811,3812],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,3815,3816],{},"podřadné",[883,3818,3820],{"className":3819},[886],[888,3821,3822],{"xmlns":890},[892,3823,3824,3836],{},[895,3825,3826,3832,3834],{},[1707,3827,3828,3830],{},[898,3829,1805],{},[898,3831,1758],{},[1716,3833,2704],{},[1712,3835,2505],{},[902,3837,3662],{"encoding":904},"). Proto je ",[883,3840,3842],{"className":3841},[886],[888,3843,3844],{"xmlns":890},[892,3845,3846,3854],{},[895,3847,3848],{},[1707,3849,3850,3852],{},[898,3851,1805],{},[898,3853,1758],{},[902,3855,3856],{"encoding":904},"E_Y"," vždy ",[38,3859,3860],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,3863,3864,3865,3867],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,3866,3161],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,3869,3871,3872,1925],{"id":3870},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,3873,3874],{},"shift of demand",[724,3876,3877,3878,3896,3897,3914,3915,3928,3929,3942,3943,3965,3966,3983,3984,4010,4011,4014],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,3879,3881],{"className":3880},[886],[888,3882,3883],{"xmlns":890},[892,3884,3885,3893],{},[895,3886,3887],{},[1707,3888,3889,3891],{},[898,3890,1690],{},[1712,3892,2505],{},[902,3894,3895],{"encoding":904},"P_0"," odpovídá množství ",[883,3898,3900],{"className":3899},[886],[888,3901,3902],{"xmlns":890},[892,3903,3904,3912],{},[895,3905,3906],{},[1707,3907,3908,3910],{},[898,3909,1878],{},[1712,3911,2505],{},[902,3913,3245],{"encoding":904}," na křivce ",[883,3916,3918],{"className":3917},[886],[888,3919,3920],{"xmlns":890},[892,3921,3922,3926],{},[895,3923,3924],{},[898,3925,1916],{},[902,3927,1916],{"encoding":904},"; vzroste-li důchod z ",[883,3930,3932],{"className":3931},[886],[888,3933,3934],{"xmlns":890},[892,3935,3936,3940],{},[895,3937,3938],{},[898,3939,1758],{},[902,3941,1758],{"encoding":904}," na ",[883,3944,3946],{"className":3945},[886],[888,3947,3948],{"xmlns":890},[892,3949,3950,3962],{},[895,3951,3952,3958,3960],{},[1707,3953,3954,3956],{},[898,3955,1758],{},[1712,3957,1714],{},[1716,3959,2716],{},[898,3961,1758],{},[902,3963,3964],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,3967,3969],{"className":3968},[886],[888,3970,3971],{"xmlns":890},[892,3972,3973,3981],{},[895,3974,3975],{},[1707,3976,3977,3979],{},[898,3978,1690],{},[1712,3980,2505],{},[902,3982,3895],{"encoding":904}," odpovídá vyšší ",[883,3985,3987],{"className":3986},[886],[888,3988,3989],{"xmlns":890},[892,3990,3991,4007],{},[895,3992,3993,3999,4001],{},[1707,3994,3995,3997],{},[898,3996,1878],{},[1712,3998,1714],{},[1716,4000,2716],{},[1707,4002,4003,4005],{},[898,4004,1878],{},[1712,4006,2505],{},[902,4008,4009],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,4012,4013],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,4016,4017],{},[3682,4018],{"alt":4019,"className":4020,"src":4021},"imek-posun-vs-pohyb-po-krivce",[210,3686],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,4023,4024],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,4026,4027],{},[614,4028,4029,4030,4060,4061,4082],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,4031,4033],{"className":4032},[886],[888,4034,4035],{"xmlns":890},[892,4036,4037,4057],{},[895,4038,4039,4045,4047,4049,4051],{},[1707,4040,4041,4043],{},[898,4042,1916],{},[1712,4044,1726],{},[1716,4046,1719],{"separator":1718},[898,4048,1916],{},[1716,4050,1719],{"separator":1718},[1707,4052,4053,4055],{},[898,4054,1916],{},[1712,4056,1714],{},[902,4058,4059],{"encoding":904},"D_2, D, D_1"," v rovině ",[883,4062,4064],{"className":4063},[886],[888,4065,4066],{"xmlns":890},[892,4067,4068,4080],{},[895,4069,4070,4072,4074,4076,4078],{},[1716,4071,1920],{"stretchy":1919},[898,4073,1878],{},[1716,4075,1719],{"separator":1718},[898,4077,1690],{},[1716,4079,1925],{"stretchy":1919},[902,4081,2608],{"encoding":904},", šipky naznačují posuny.",[2851,4084,4086],{"id":4085},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,4088,4089,4091,4092,4116,4117,4134,4135,4152,4153,1853],{},[38,4090,2859],{}," Poptávce ",[883,4093,4095],{"className":4094},[886],[888,4096,4097],{"xmlns":890},[892,4098,4099,4113],{},[895,4100,4101,4103,4105,4107,4109,4111],{},[898,4102,1690],{},[1716,4104,1913],{},[898,4106,1916],{},[1716,4108,1920],{"stretchy":1919},[898,4110,1878],{},[1716,4112,1925],{"stretchy":1919},[902,4114,4115],{"encoding":904},"P = D(Q)"," odpovídá ceně ",[883,4118,4120],{"className":4119},[886],[888,4121,4122],{"xmlns":890},[892,4123,4124,4132],{},[895,4125,4126],{},[1707,4127,4128,4130],{},[898,4129,1690],{},[1712,4131,2505],{},[902,4133,3895],{"encoding":904}," množství ",[883,4136,4138],{"className":4137},[886],[888,4139,4140],{"xmlns":890},[892,4141,4142,4150],{},[895,4143,4144],{},[1707,4145,4146,4148],{},[898,4147,1878],{},[1712,4149,2505],{},[902,4151,3245],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,4154,4156],{"className":4155},[886],[888,4157,4158],{"xmlns":890},[892,4159,4160,4165],{},[895,4161,4162],{},[898,4163,4164],{},"T",[902,4166,4164],{"encoding":904},[724,4168,4169,4171,4172,4190,4191,4213],{},[38,4170,2892],{}," Kupující nakupuje množství ",[883,4173,4175],{"className":4174},[886],[888,4176,4177],{"xmlns":890},[892,4178,4179,4187],{},[895,4180,4181],{},[1707,4182,4183,4185],{},[898,4184,1878],{},[1712,4186,1714],{},[902,4188,4189],{"encoding":904},"Q_1",", které odpovídá ceně ",[883,4192,4194],{"className":4193},[886],[888,4195,4196],{"xmlns":890},[892,4197,4198,4210],{},[895,4199,4200,4206,4208],{},[1707,4201,4202,4204],{},[898,4203,1690],{},[1712,4205,2505],{},[1716,4207,1949],{},[898,4209,4164],{},[902,4211,4212],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,4215,4217],{"className":4216},[886],[888,4218,4219],{"xmlns":890,"display":2004},[892,4220,4221,4255],{},[895,4222,4223,4225,4227,4233,4235,4237,4239,4241,4243,4245,4247,4249,4251,4253],{},[898,4224,1690],{},[1716,4226,1913],{},[1707,4228,4229,4231],{},[898,4230,1916],{},[1712,4232,1714],{},[1716,4234,1920],{"stretchy":1919},[898,4236,1878],{},[1716,4238,1925],{"stretchy":1919},[1716,4240,1913],{},[898,4242,1916],{},[1716,4244,1920],{"stretchy":1919},[898,4246,1878],{},[1716,4248,1925],{"stretchy":1919},[1716,4250,2760],{},[898,4252,4164],{},[1716,4254,1719],{"separator":1718},[902,4256,4257],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,4259,4260,4261,1853],{},"tj. dojde k ",[38,4262,4263],{},"posunu poptávky doleva",[724,4265,4266],{},[614,4267,4268,4269,4290,4291,1343,4308,1343,4321,4342,4343,2247,4360,1853],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,4270,4272],{"className":4271},[886],[888,4273,4274],{"xmlns":890},[892,4275,4276,4288],{},[895,4277,4278,4280,4282,4284,4286],{},[1716,4279,1920],{"stretchy":1919},[898,4281,1878],{},[1716,4283,1719],{"separator":1718},[898,4285,1690],{},[1716,4287,1925],{"stretchy":1919},[902,4289,2608],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,4292,4294],{"className":4293},[886],[888,4295,4296],{"xmlns":890},[892,4297,4298,4306],{},[895,4299,4300],{},[1707,4301,4302,4304],{},[898,4303,1690],{},[1712,4305,2505],{},[902,4307,3895],{"encoding":904},[883,4309,4311],{"className":4310},[886],[888,4312,4313],{"xmlns":890},[892,4314,4315,4319],{},[895,4316,4317],{},[898,4318,4164],{},[902,4320,4164],{"encoding":904},[883,4322,4324],{"className":4323},[886],[888,4325,4326],{"xmlns":890},[892,4327,4328,4340],{},[895,4329,4330,4336,4338],{},[1707,4331,4332,4334],{},[898,4333,1690],{},[1712,4335,2505],{},[1716,4337,1949],{},[898,4339,4164],{},[902,4341,4212],{"encoding":904},"; na vodorovné ",[883,4344,4346],{"className":4345},[886],[888,4347,4348],{"xmlns":890},[892,4349,4350,4358],{},[895,4351,4352],{},[1707,4353,4354,4356],{},[898,4355,1878],{},[1712,4357,1714],{},[902,4359,4189],{"encoding":904},[883,4361,4363],{"className":4362},[886],[888,4364,4365],{"xmlns":890},[892,4366,4367,4375],{},[895,4368,4369],{},[1707,4370,4371,4373],{},[898,4372,1878],{},[1712,4374,2505],{},[902,4376,3245],{"encoding":904},[198,4378,4380],{"id":4379},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,4382,4383],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,4385,4387],{"className":4386},[886],[888,4388,4389],{"xmlns":890,"display":2004},[892,4390,4391,4580],{},[2008,4392,4393],{"width":2010},[2012,4394,4395,4397,4573,4575],{},[2015,4396],{"width":2017},[2015,4398,4399],{},[2008,4400,4404,4489],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},"0.25em","right left","0em",[2012,4405,4406,4416],{},[2015,4407,4408],{},[2747,4409,4410],{"scriptlevel":2505,"displaystyle":1718},[1707,4411,4412,4414],{},[898,4413,1878],{},[1712,4415,1714],{},[2015,4417,4418],{},[2747,4419,4420],{"scriptlevel":2505,"displaystyle":1718},[895,4421,4422,4424,4426,4432,4434,4440,4442,4448,4450,4452,4458,4460,4466,4472,4474,4481,4487],{},[895,4423],{},[1716,4425,1913],{},[1707,4427,4428,4430],{},[898,4429,1916],{},[1712,4431,1714],{},[1716,4433,1920],{"stretchy":1919},[1707,4435,4436,4438],{},[898,4437,1690],{},[1712,4439,1714],{},[1716,4441,1719],{"separator":1718},[1707,4443,4444,4446],{},[898,4445,1690],{},[1712,4447,1726],{},[1716,4449,1925],{"stretchy":1919},[1716,4451,1913],{},[1707,4453,4454,4456],{},[898,4455,207],{},[1712,4457,1714],{},[1716,4459,1949],{},[1707,4461,4462,4464],{},[898,4463,1952],{},[1712,4465,1714],{},[1707,4467,4468,4470],{},[898,4469,1690],{},[1712,4471,1714],{},[1716,4473,1949],{},[1707,4475,4476,4479],{},[898,4477,4478],{},"c",[1712,4480,1714],{},[1707,4482,4483,4485],{},[898,4484,1690],{},[1712,4486,1726],{},[1716,4488,1719],{"separator":1718},[2012,4490,4491,4501],{},[2015,4492,4493],{},[2747,4494,4495],{"scriptlevel":2505,"displaystyle":1718},[1707,4496,4497,4499],{},[898,4498,1878],{},[1712,4500,1726],{},[2015,4502,4503],{},[2747,4504,4505],{"scriptlevel":2505,"displaystyle":1718},[895,4506,4507,4509,4511,4517,4519,4525,4527,4533,4535,4537,4543,4545,4551,4557,4559,4565,4571],{},[895,4508],{},[1716,4510,1913],{},[1707,4512,4513,4515],{},[898,4514,1916],{},[1712,4516,1726],{},[1716,4518,1920],{"stretchy":1919},[1707,4520,4521,4523],{},[898,4522,1690],{},[1712,4524,1714],{},[1716,4526,1719],{"separator":1718},[1707,4528,4529,4531],{},[898,4530,1690],{},[1712,4532,1726],{},[1716,4534,1925],{"stretchy":1919},[1716,4536,1913],{},[1707,4538,4539,4541],{},[898,4540,207],{},[1712,4542,1726],{},[1716,4544,1949],{},[1707,4546,4547,4549],{},[898,4548,1952],{},[1712,4550,1726],{},[1707,4552,4553,4555],{},[898,4554,1690],{},[1712,4556,1714],{},[1716,4558,1949],{},[1707,4560,4561,4563],{},[898,4562,4478],{},[1712,4564,1726],{},[1707,4566,4567,4569],{},[898,4568,1690],{},[1712,4570,1726],{},[898,4572,1853],{"mathvariant":2068},[2015,4574],{"width":2017},[2015,4576,4577],{},[2074,4578,4579],{},"(2.6)",[902,4581,4582],{"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}",[2257,4584,4586],{"id":4585},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,4588,4589,4636,4683],{},[123,4590,4591,1343,4613,4635],{},[883,4592,4594],{"className":4593},[886],[888,4595,4596],{"xmlns":890},[892,4597,4598,4610],{},[895,4599,4600,4606,4608],{},[1707,4601,4602,4604],{},[898,4603,207],{},[1712,4605,1714],{},[1716,4607,2716],{},[1712,4609,2505],{},[902,4611,4612],{"encoding":904},"a_1 > 0",[883,4614,4616],{"className":4615},[886],[888,4617,4618],{"xmlns":890},[892,4619,4620,4632],{},[895,4621,4622,4628,4630],{},[1707,4623,4624,4626],{},[898,4625,207],{},[1712,4627,1726],{},[1716,4629,2716],{},[1712,4631,2505],{},[902,4633,4634],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,4637,4638,1343,4660,4682],{},[883,4639,4641],{"className":4640},[886],[888,4642,4643],{"xmlns":890},[892,4644,4645,4657],{},[895,4646,4647,4653,4655],{},[1707,4648,4649,4651],{},[898,4650,1952],{},[1712,4652,1714],{},[1716,4654,2704],{},[1712,4656,2505],{},[902,4658,4659],{"encoding":904},"b_1 \u003C 0",[883,4661,4663],{"className":4662},[886],[888,4664,4665],{"xmlns":890},[892,4666,4667,4679],{},[895,4668,4669,4675,4677],{},[1707,4670,4671,4673],{},[898,4672,4478],{},[1712,4674,1726],{},[1716,4676,2704],{},[1712,4678,2505],{},[902,4680,4681],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,4684,4685,4686,1343,4704,4722,4723],{},"zkřížené koeficienty ",[883,4687,4689],{"className":4688},[886],[888,4690,4691],{"xmlns":890},[892,4692,4693,4701],{},[895,4694,4695],{},[1707,4696,4697,4699],{},[898,4698,4478],{},[1712,4700,1714],{},[902,4702,4703],{"encoding":904},"c_1",[883,4705,4707],{"className":4706},[886],[888,4708,4709],{"xmlns":890},[892,4710,4711,4719],{},[895,4712,4713],{},[1707,4714,4715,4717],{},[898,4716,1952],{},[1712,4718,1726],{},[902,4720,4721],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,4724,4725,4775],{},[123,4726,4727,4730,4731,1343,4753,1719],{},[38,4728,4729],{},"substituty"," (máslo vs. margarín): ",[883,4732,4734],{"className":4733},[886],[888,4735,4736],{"xmlns":890},[892,4737,4738,4750],{},[895,4739,4740,4746,4748],{},[1707,4741,4742,4744],{},[898,4743,4478],{},[1712,4745,1714],{},[1716,4747,2716],{},[1712,4749,2505],{},[902,4751,4752],{"encoding":904},"c_1 > 0",[883,4754,4756],{"className":4755},[886],[888,4757,4758],{"xmlns":890},[892,4759,4760,4772],{},[895,4761,4762,4768,4770],{},[1707,4763,4764,4766],{},[898,4765,1952],{},[1712,4767,1726],{},[1716,4769,2716],{},[1712,4771,2505],{},[902,4773,4774],{"encoding":904},"b_2 > 0",[123,4776,4777,4780,4781,1343,4803,1853],{},[38,4778,4779],{},"komplementy"," (auto vs. benzín): ",[883,4782,4784],{"className":4783},[886],[888,4785,4786],{"xmlns":890},[892,4787,4788,4800],{},[895,4789,4790,4796,4798],{},[1707,4791,4792,4794],{},[898,4793,4478],{},[1712,4795,1714],{},[1716,4797,2704],{},[1712,4799,2505],{},[902,4801,4802],{"encoding":904},"c_1 \u003C 0",[883,4804,4806],{"className":4805},[886],[888,4807,4808],{"xmlns":890},[892,4809,4810,4822],{},[895,4811,4812,4818,4820],{},[1707,4813,4814,4816],{},[898,4815,1952],{},[1712,4817,1726],{},[1716,4819,2704],{},[1712,4821,2505],{},[902,4823,4824],{"encoding":904},"b_2 \u003C 0",[724,4826,4827],{},"Schematicky:",[724,4829,4830,4833],{},[38,4831,4832],{},"Substituty",[883,4834,4836],{"className":4835},[886],[888,4837,4838],{"xmlns":890},[892,4839,4840,4979],{},[895,4841,4842,4848,4850,4865,4867,4887,4889,4909,4911,4913,4919,4921,4935,4937,4957,4959],{},[1707,4843,4844,4846],{},[898,4845,1878],{},[1712,4847,1714],{},[1716,4849,1913],{},[898,4851,4852],{},[4853,4854,4855,4863],"munder",{},[1716,4856,4857],{},[1707,4858,4859,4861],{},[898,4860,207],{},[1712,4862,1714],{},[1716,4864,1949],{"lspace":4403,"rspace":4403},[1716,4866,1949],{},[898,4868,4869],{},[4853,4870,4871,4885],{},[1716,4872,4873,4879],{},[1707,4874,4875,4877],{},[898,4876,1952],{},[1712,4878,1714],{},[1707,4880,4881,4883],{},[898,4882,1690],{},[1712,4884,1714],{},[1716,4886,2760],{"lspace":4403,"rspace":4403},[1716,4888,1949],{},[898,4890,4891],{},[4853,4892,4893,4907],{},[1716,4894,4895,4901],{},[1707,4896,4897,4899],{},[898,4898,4478],{},[1712,4900,1714],{},[1707,4902,4903,4905],{},[898,4904,1690],{},[1712,4906,1726],{},[1716,4908,1949],{"lspace":4403,"rspace":4403},[1716,4910,1719],{"separator":1718},[2324,4912],{"width":2326},[1707,4914,4915,4917],{},[898,4916,1878],{},[1712,4918,1726],{},[1716,4920,1913],{},[898,4922,4923],{},[4853,4924,4925,4933],{},[1716,4926,4927],{},[1707,4928,4929,4931],{},[898,4930,207],{},[1712,4932,1726],{},[1716,4934,1949],{"lspace":4403,"rspace":4403},[1716,4936,1949],{},[898,4938,4939],{},[4853,4940,4941,4955],{},[1716,4942,4943,4949],{},[1707,4944,4945,4947],{},[898,4946,1952],{},[1712,4948,1726],{},[1707,4950,4951,4953],{},[898,4952,1690],{},[1712,4954,1714],{},[1716,4956,1949],{"lspace":4403,"rspace":4403},[1716,4958,1949],{},[898,4960,4961],{},[4853,4962,4963,4977],{},[1716,4964,4965,4971],{},[1707,4966,4967,4969],{},[898,4968,4478],{},[1712,4970,1726],{},[1707,4972,4973,4975],{},[898,4974,1690],{},[1712,4976,1726],{},[1716,4978,2760],{"lspace":4403,"rspace":4403},[902,4980,4981],{"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}",[724,4983,4984,4987],{},[38,4985,4986],{},"Komplementy",[883,4988,4990],{"className":4989},[886],[888,4991,4992],{"xmlns":890},[892,4993,4994,5132],{},[895,4995,4996,5002,5004,5018,5020,5040,5042,5062,5064,5066,5072,5074,5088,5090,5110,5112],{},[1707,4997,4998,5000],{},[898,4999,1878],{},[1712,5001,1714],{},[1716,5003,1913],{},[898,5005,5006],{},[4853,5007,5008,5016],{},[1716,5009,5010],{},[1707,5011,5012,5014],{},[898,5013,207],{},[1712,5015,1714],{},[1716,5017,1949],{"lspace":4403,"rspace":4403},[1716,5019,1949],{},[898,5021,5022],{},[4853,5023,5024,5038],{},[1716,5025,5026,5032],{},[1707,5027,5028,5030],{},[898,5029,1952],{},[1712,5031,1714],{},[1707,5033,5034,5036],{},[898,5035,1690],{},[1712,5037,1714],{},[1716,5039,2760],{"lspace":4403,"rspace":4403},[1716,5041,1949],{},[898,5043,5044],{},[4853,5045,5046,5060],{},[1716,5047,5048,5054],{},[1707,5049,5050,5052],{},[898,5051,4478],{},[1712,5053,1714],{},[1707,5055,5056,5058],{},[898,5057,1690],{},[1712,5059,1726],{},[1716,5061,2760],{"lspace":4403,"rspace":4403},[1716,5063,1719],{"separator":1718},[2324,5065],{"width":2326},[1707,5067,5068,5070],{},[898,5069,1878],{},[1712,5071,1726],{},[1716,5073,1913],{},[898,5075,5076],{},[4853,5077,5078,5086],{},[1716,5079,5080],{},[1707,5081,5082,5084],{},[898,5083,207],{},[1712,5085,1726],{},[1716,5087,1949],{"lspace":4403,"rspace":4403},[1716,5089,1949],{},[898,5091,5092],{},[4853,5093,5094,5108],{},[1716,5095,5096,5102],{},[1707,5097,5098,5100],{},[898,5099,1952],{},[1712,5101,1726],{},[1707,5103,5104,5106],{},[898,5105,1690],{},[1712,5107,1714],{},[1716,5109,2760],{"lspace":4403,"rspace":4403},[1716,5111,1949],{},[898,5113,5114],{},[4853,5115,5116,5130],{},[1716,5117,5118,5124],{},[1707,5119,5120,5122],{},[898,5121,4478],{},[1712,5123,1726],{},[1707,5125,5126,5128],{},[898,5127,1690],{},[1712,5129,1726],{},[1716,5131,2760],{"lspace":4403,"rspace":4403},[902,5133,5134],{"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}",[1855,5136],{},[115,5138,5139],{"id":1649},"Nabídka",[1635,5141,5142],{},[724,5143,5144,5146,5147,1881,5160,1895,5173,5176,5177,3569,5202,5220],{},[883,5145,1641],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,5148,5150],{"className":5149},[886],[888,5151,5152],{"xmlns":890},[892,5153,5154,5158],{},[895,5155,5156],{},[898,5157,1878],{},[902,5159,1878],{"encoding":904},[883,5161,5163],{"className":5162},[886],[888,5164,5165],{"xmlns":890},[892,5166,5167,5171],{},[895,5168,5169],{},[898,5170,1690],{},[902,5172,1690],{"encoding":904},[38,5174,5175],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,5178,5180],{"className":5179},[886],[888,5181,5182],{"xmlns":890},[892,5183,5184,5199],{},[895,5185,5186,5188,5190,5192,5194,5196],{},[898,5187,1690],{},[1716,5189,1913],{},[898,5191,4478],{},[898,5193,1878],{},[1716,5195,1949],{},[898,5197,5198],{},"d",[902,5200,5201],{"encoding":904},"P = cQ + d",[883,5203,5205],{"className":5204},[886],[888,5206,5207],{"xmlns":890},[892,5208,5209,5217],{},[895,5210,5211,5213,5215],{},[898,5212,4478],{},[1716,5214,2716],{},[1712,5216,2505],{},[902,5218,5219],{"encoding":904},"c > 0"," je standardní aproximací.",[198,5222,1959],{"id":5223},"obecný-vícefaktorový-model-1",[724,5225,5226,1994,5229,5232,5233,5246,5247,1778,5260,1793,5273,5286,5287,5301,5302,1823,5315,5328],{},[38,5227,5228],{},"Nabízené množství",[614,5230,5231],{},"quantity supplied",") závisí na ceně ",[883,5234,5236],{"className":5235},[886],[888,5237,5238],{"xmlns":890},[892,5239,5240,5244],{},[895,5241,5242],{},[898,5243,1690],{},[902,5245,1690],{"encoding":904},", cenách výrobních faktorů (práce ",[883,5248,5250],{"className":5249},[886],[888,5251,5252],{"xmlns":890},[892,5253,5254,5258],{},[895,5255,5256],{},[898,5257,1775],{},[902,5259,1775],{"encoding":904},[883,5261,5263],{"className":5262},[886],[888,5264,5265],{"xmlns":890},[892,5266,5267,5271],{},[895,5268,5269],{},[898,5270,1790],{},[902,5272,1790],{"encoding":904},[883,5274,5276],{"className":5275},[886],[888,5277,5278],{"xmlns":890},[892,5279,5280,5284],{},[895,5281,5282],{},[898,5283,1805],{},[902,5285,1805],{"encoding":904},"), očekávání ",[883,5288,5290],{"className":5289},[886],[888,5291,5292],{"xmlns":890},[892,5293,5294,5299],{},[895,5295,5296],{},[898,5297,5298],{},"V",[902,5300,5298],{"encoding":904},", počtu výrobců ",[883,5303,5305],{"className":5304},[886],[888,5306,5307],{"xmlns":890},[892,5308,5309,5313],{},[895,5310,5311],{},[898,5312,1820],{},[902,5314,1820],{"encoding":904},[883,5316,5318],{"className":5317},[886],[888,5319,5320],{"xmlns":890},[892,5321,5322,5326],{},[895,5323,5324],{},[898,5325,1835],{},[902,5327,1835],{"encoding":904}," a dalších:",[883,5330,5332],{"className":5331},[886],[888,5333,5334],{"xmlns":890,"display":2004},[892,5335,5336,5396],{},[2008,5337,5338],{"width":2010},[2012,5339,5340,5342,5389,5391],{},[2015,5341],{"width":2017},[2015,5343,5344],{},[895,5345,5346,5348,5350,5353,5355,5357,5359,5361,5363,5365,5367,5369,5371,5373,5375,5377,5379,5381,5383,5385,5387],{},[898,5347,1878],{},[1716,5349,1913],{},[898,5351,5352],{},"S",[1716,5354,1920],{"stretchy":1919},[898,5356,1690],{},[1716,5358,1719],{"separator":1718},[898,5360,1775],{},[1716,5362,1719],{"separator":1718},[898,5364,1790],{},[1716,5366,1719],{"separator":1718},[898,5368,1805],{},[1716,5370,1719],{"separator":1718},[898,5372,5298],{},[1716,5374,1719],{"separator":1718},[898,5376,1820],{},[1716,5378,1719],{"separator":1718},[898,5380,1835],{},[1716,5382,1719],{"separator":1718},[1716,5384,1731],{},[1716,5386,1925],{"stretchy":1919},[898,5388,1853],{"mathvariant":2068},[2015,5390],{"width":2017},[2015,5392,5393],{},[2074,5394,5395],{},"(2.7)",[902,5397,5398],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,5400,3353,5401,1994,5404,5407],{},[38,5402,5403],{},"funkce nabídky",[614,5405,5406],{},"supply function",") v širším slova smyslu.",[198,5409,5411],{"id":5410},"jednofaktorový-model","Jednofaktorový model",[724,5413,5414],{},"V nejpřirozenějším jednofaktorovém modelu",[883,5416,5418],{"className":5417},[886],[888,5419,5420],{"xmlns":890,"display":2004},[892,5421,5422,5473],{},[2008,5423,5424],{"width":2010},[2012,5425,5426,5428,5466,5468],{},[2015,5427],{"width":2017},[2015,5429,5430],{},[895,5431,5432,5434,5436,5438,5440,5442,5444,5446,5448,5450,5452,5454,5456,5458,5460,5462,5464],{},[898,5433,1878],{},[1716,5435,1913],{},[898,5437,5352],{},[1716,5439,1920],{"stretchy":1919},[898,5441,1690],{},[1716,5443,1925],{"stretchy":1919},[1716,5445,1719],{"separator":1718},[2324,5447],{"width":2326},[2074,5449,2329],{},[2324,5451],{"width":2326},[898,5453,1690],{},[1716,5455,1913],{},[898,5457,5352],{},[1716,5459,1920],{"stretchy":1919},[898,5461,1878],{},[1716,5463,1925],{"stretchy":1919},[898,5465,1853],{"mathvariant":2068},[2015,5467],{"width":2017},[2015,5469,5470],{},[2074,5471,5472],{},"(2.8)",[902,5474,5475],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,5477,5478,5479,1994,5482,2365],{},"Graf je ",[38,5480,5481],{},"křivka nabídky",[614,5483,5484],{},"supply curve",[2257,5486,5488],{"id":5487},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1635,5490,5491],{},[724,5492,5493],{},[38,5494,2376,5495,5508,5509,2431],{},[883,5496,5498],{"className":5497},[886],[888,5499,5500],{"xmlns":890},[892,5501,5502,5506],{},[895,5503,5504],{},[898,5505,1690],{},[902,5507,1690],{"encoding":904},", pak nabízené množství ",[883,5510,5512],{"className":5511},[886],[888,5513,5514],{"xmlns":890},[892,5515,5516,5520],{},[895,5517,5518],{},[898,5519,1878],{},[902,5521,1878],{"encoding":904},[724,5523,5524,5525,5550,5551,5581,5582,5599],{},"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 ",[883,5526,5528],{"className":5527},[886],[888,5529,5530],{"xmlns":890},[892,5531,5532,5548],{},[895,5533,5534,5536,5538,5540,5546],{},[1716,5535,2502],{"stretchy":1919},[1712,5537,2505],{},[1716,5539,1719],{"separator":1718},[1707,5541,5542,5544],{},[898,5543,1690],{},[1712,5545,2505],{},[1716,5547,2516],{"stretchy":1919},[902,5549,2519],{"encoding":904}," na svislé ose (případně z ",[883,5552,5554],{"className":5553},[886],[888,5555,5556],{"xmlns":890},[892,5557,5558,5578],{},[895,5559,5560,5562,5568,5570,5576],{},[1716,5561,2502],{"stretchy":1919},[1707,5563,5564,5566],{},[898,5565,1878],{},[1712,5567,1714],{},[1716,5569,1719],{"separator":1718},[1707,5571,5572,5574],{},[898,5573,1690],{},[1712,5575,1714],{},[1716,5577,2516],{"stretchy":1919},[902,5579,5580],{"encoding":904},"[Q_1, P_1]","), kde ",[883,5583,5585],{"className":5584},[886],[888,5586,5587],{"xmlns":890},[892,5588,5589,5597],{},[895,5590,5591],{},[1707,5592,5593,5595],{},[898,5594,1690],{},[1712,5596,2505],{},[902,5598,3895],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,5601,5602],{},[614,5603,5604,5605,5618,5619,1853],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,5606,5608],{"className":5607},[886],[888,5609,5610],{"xmlns":890},[892,5611,5612,5616],{},[895,5613,5614],{},[898,5615,5352],{},[902,5617,5352],{"encoding":904}," v ",[883,5620,5622],{"className":5621},[886],[888,5623,5624],{"xmlns":890},[892,5625,5626,5638],{},[895,5627,5628,5630,5632,5634,5636],{},[1716,5629,1920],{"stretchy":1919},[898,5631,1878],{},[1716,5633,1719],{"separator":1718},[898,5635,1690],{},[1716,5637,1925],{"stretchy":1919},[902,5639,2608],{"encoding":904},[2257,5641,5643],{"id":5642},"lineární-model-nabídky","Lineární model nabídky",[883,5645,5647],{"className":5646},[886],[888,5648,5649],{"xmlns":890,"display":2004},[892,5650,5651,5690],{},[2008,5652,5653],{"width":2010},[2012,5654,5655,5657,5683,5685],{},[2015,5656],{"width":2017},[2015,5658,5659],{},[895,5660,5661,5663,5665,5667,5669,5671,5673,5675,5677,5679,5681],{},[898,5662,1690],{},[1716,5664,1913],{},[898,5666,4478],{},[898,5668,1878],{},[1716,5670,1949],{},[898,5672,5198],{},[1716,5674,1719],{"separator":1718},[2324,5676],{"width":2326},[898,5678,4478],{},[1716,5680,2716],{},[1712,5682,2719],{},[2015,5684],{"width":2017},[2015,5686,5687],{},[2074,5688,5689],{},"(2.9)",[902,5691,5692],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,5694,5695,5696,5732,5733,5746],{},"Alternativně ",[883,5697,5699],{"className":5698},[886],[888,5700,5701],{"xmlns":890},[892,5702,5703,5729],{},[895,5704,5705,5707,5709,5717,5719,5721],{},[898,5706,1878],{},[1716,5708,1913],{},[2747,5710,5711],{"scriptlevel":2505,"displaystyle":1919},[2750,5712,5713,5715],{},[1712,5714,1714],{},[898,5716,4478],{},[898,5718,1690],{},[1716,5720,2760],{},[2747,5722,5723],{"scriptlevel":2505,"displaystyle":1919},[2750,5724,5725,5727],{},[898,5726,5198],{},[898,5728,4478],{},[902,5730,5731],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,5734,5736],{"className":5735},[886],[888,5737,5738],{"xmlns":890},[892,5739,5740,5744],{},[895,5741,5742],{},[898,5743,1690],{},[902,5745,1690],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[2851,5748,5750],{"id":5749},"příklad-25","Příklad 2.5",[724,5752,5753,5755,5756,1853],{},[38,5754,2859],{}," Lineární nabídka ",[883,5757,5759],{"className":5758},[886],[888,5760,5761],{"xmlns":890},[892,5762,5763,5779],{},[895,5764,5765,5767,5769,5772,5774,5776],{},[898,5766,1690],{},[1716,5768,1913],{},[1712,5770,5771],{},"0,5",[898,5773,1878],{},[1716,5775,1949],{},[1712,5777,5778],{},"25",[902,5780,5781],{"encoding":904},"P = 0{,}5Q + 25",[724,5783,5784,5786,5787,1853],{},[38,5785,2892],{}," Alternativní tvar ",[883,5788,5790],{"className":5789},[886],[888,5791,5792],{"xmlns":890},[892,5793,5794,5809],{},[895,5795,5796,5798,5800,5802,5804,5806],{},[898,5797,1878],{},[1716,5799,1913],{},[1712,5801,1726],{},[898,5803,1690],{},[1716,5805,2760],{},[1712,5807,5808],{},"50",[902,5810,5811],{"encoding":904},"Q = 2P - 50",[16,5813,5814,5840],{},[19,5815,5816],{},[22,5817,5818,5833,5835,5838],{},[25,5819,5820],{},[883,5821,5823],{"className":5822},[886],[888,5824,5825],{"xmlns":890},[892,5826,5827,5831],{},[895,5828,5829],{},[898,5830,1690],{},[902,5832,1690],{"encoding":904},[25,5834,2946],{},[25,5836,5837],{},"35",[25,5839,2973],{},[30,5841,5842],{},[22,5843,5844,5859,5861,5863],{},[35,5845,5846],{},[883,5847,5849],{"className":5848},[886],[888,5850,5851],{"xmlns":890},[892,5852,5853,5857],{},[895,5854,5855],{},[898,5856,1878],{},[902,5858,1878],{"encoding":904},[35,5860,2998],{},[35,5862,2976],{},[35,5864,2946],{},[198,5866,5868,5869,1925],{"id":5867},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,5870,5871],{},"shift of supply",[724,5873,5874,5875,5878,5879,5896,5897,5922,5923,1853],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,5876,5877],{},"doprava",": při stejné ceně ",[883,5880,5882],{"className":5881},[886],[888,5883,5884],{"xmlns":890},[892,5885,5886,5894],{},[895,5887,5888],{},[1707,5889,5890,5892],{},[898,5891,1690],{},[1712,5893,2505],{},[902,5895,3895],{"encoding":904}," vyrobí výrobce větší ",[883,5898,5900],{"className":5899},[886],[888,5901,5902],{"xmlns":890},[892,5903,5904,5920],{},[895,5905,5906,5912,5914],{},[1707,5907,5908,5910],{},[898,5909,1878],{},[1712,5911,1714],{},[1716,5913,2716],{},[1707,5915,5916,5918],{},[898,5917,1878],{},[1712,5919,2505],{},[902,5921,4009],{"encoding":904},"); zdražení vstupů posune křivku ",[38,5924,5925],{},"doleva",[724,5927,5928],{},[614,5929,5930,5931,5944,5945,5963,5964,5982,5983,1853],{},"Obrázek 2.11: Původní ",[883,5932,5934],{"className":5933},[886],[888,5935,5936],{"xmlns":890},[892,5937,5938,5942],{},[895,5939,5940],{},[898,5941,5352],{},[902,5943,5352],{"encoding":904},", posunuté ",[883,5946,5948],{"className":5947},[886],[888,5949,5950],{"xmlns":890},[892,5951,5952,5960],{},[895,5953,5954],{},[1707,5955,5956,5958],{},[898,5957,5352],{},[1712,5959,1714],{},[902,5961,5962],{"encoding":904},"S_1"," (doprava) a ",[883,5965,5967],{"className":5966},[886],[888,5968,5969],{"xmlns":890},[892,5970,5971,5979],{},[895,5972,5973],{},[1707,5974,5975,5977],{},[898,5976,5352],{},[1712,5978,1726],{},[902,5980,5981],{"encoding":904},"S_2"," (doleva) v ",[883,5984,5986],{"className":5985},[886],[888,5987,5988],{"xmlns":890},[892,5989,5990,6002],{},[895,5991,5992,5994,5996,5998,6000],{},[1716,5993,1920],{"stretchy":1919},[898,5995,1878],{},[1716,5997,1719],{"separator":1718},[898,5999,1690],{},[1716,6001,1925],{"stretchy":1919},[902,6003,2608],{"encoding":904},[2851,6005,6007],{"id":6006},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,6009,6010,6012,6013,6037,6038,1853],{},[38,6011,2859],{}," Nabídka ",[883,6014,6016],{"className":6015},[886],[888,6017,6018],{"xmlns":890},[892,6019,6020,6034],{},[895,6021,6022,6024,6026,6028,6030,6032],{},[898,6023,1690],{},[1716,6025,1913],{},[898,6027,5352],{},[1716,6029,1920],{"stretchy":1919},[898,6031,1878],{},[1716,6033,1925],{"stretchy":1919},[902,6035,6036],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,6039,6041],{"className":6040},[886],[888,6042,6043],{"xmlns":890},[892,6044,6045,6049],{},[895,6046,6047],{},[898,6048,4164],{},[902,6050,4164],{"encoding":904},[724,6052,6053,6055,6056,6069,6070,6088,6089,6117],{},[38,6054,2892],{}," Spotřebitel zaplatí ",[883,6057,6059],{"className":6058},[886],[888,6060,6061],{"xmlns":890},[892,6062,6063,6067],{},[895,6064,6065],{},[898,6066,1690],{},[902,6068,1690],{"encoding":904},", výrobce obdrží ",[883,6071,6073],{"className":6072},[886],[888,6074,6075],{"xmlns":890},[892,6076,6077,6085],{},[895,6078,6079,6081,6083],{},[898,6080,1690],{},[1716,6082,2760],{},[898,6084,4164],{},[902,6086,6087],{"encoding":904},"P - T",". Z podmínky ",[883,6090,6092],{"className":6091},[886],[888,6093,6094],{"xmlns":890},[892,6095,6096,6114],{},[895,6097,6098,6100,6102,6104,6106,6108,6110,6112],{},[898,6099,1690],{},[1716,6101,2760],{},[898,6103,4164],{},[1716,6105,1913],{},[898,6107,5352],{},[1716,6109,1920],{"stretchy":1919},[898,6111,1878],{},[1716,6113,1925],{"stretchy":1919},[902,6115,6116],{"encoding":904},"P - T = S(Q)"," plyne",[883,6119,6121],{"className":6120},[886],[888,6122,6123],{"xmlns":890,"display":2004},[892,6124,6125,6159],{},[895,6126,6127,6129,6131,6137,6139,6141,6143,6145,6147,6149,6151,6153,6155,6157],{},[898,6128,1690],{},[1716,6130,1913],{},[1707,6132,6133,6135],{},[898,6134,5352],{},[1712,6136,1714],{},[1716,6138,1920],{"stretchy":1919},[898,6140,1878],{},[1716,6142,1925],{"stretchy":1919},[1716,6144,1913],{},[898,6146,5352],{},[1716,6148,1920],{"stretchy":1919},[898,6150,1878],{},[1716,6152,1925],{"stretchy":1919},[1716,6154,1949],{},[898,6156,4164],{},[898,6158,1853],{"mathvariant":2068},[902,6160,6161],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,6163,6164,6165,6178,6179,3495,6192,6195,6196,2247,6216,2574,6235,1853],{},"Křivka ",[883,6166,6168],{"className":6167},[886],[888,6169,6170],{"xmlns":890},[892,6171,6172,6176],{},[895,6173,6174],{},[898,6175,5352],{},[902,6177,5352],{"encoding":904}," se tedy posune o ",[883,6180,6182],{"className":6181},[886],[888,6183,6184],{"xmlns":890},[892,6185,6186,6190],{},[895,6187,6188],{},[898,6189,4164],{},[902,6191,4164],{"encoding":904},[38,6193,6194],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,6197,6199],{"className":6198},[886],[888,6200,6201],{"xmlns":890},[892,6202,6203,6213],{},[895,6204,6205,6207,6209,6211],{},[898,6206,1690],{},[1716,6208,1913],{},[1712,6210,1726],{},[898,6212,1878],{},[902,6214,6215],{"encoding":904},"P = 2Q",[883,6217,6219],{"className":6218},[886],[888,6220,6221],{"xmlns":890},[892,6222,6223,6232],{},[895,6224,6225,6227,6229],{},[898,6226,4164],{},[1716,6228,1913],{},[1712,6230,6231],{},"6",[902,6233,6234],{"encoding":904},"T = 6",[883,6236,6238],{"className":6237},[886],[888,6239,6240],{"xmlns":890},[892,6241,6242,6264],{},[895,6243,6244,6250,6252,6254,6256,6258,6260,6262],{},[1707,6245,6246,6248],{},[898,6247,5352],{},[1712,6249,1714],{},[1716,6251,2291],{},[898,6253,1690],{},[1716,6255,1913],{},[1712,6257,1726],{},[898,6259,1878],{},[1716,6261,1949],{},[1712,6263,6231],{},[902,6265,6266],{"encoding":904},"S_1: P = 2Q + 6",[724,6268,6269],{},[614,6270,6271,6272,6285],{},"Obrázek 2.12: Posun nabídky o ",[883,6273,6275],{"className":6274},[886],[888,6276,6277],{"xmlns":890},[892,6278,6279,6283],{},[895,6280,6281],{},[898,6282,4164],{},[902,6284,4164],{"encoding":904}," svisle nahoru.",[1855,6287],{},[115,6289,6291],{"id":6290},"tržní-rovnováha","Tržní rovnováha",[1635,6293,6294],{},[724,6295,6296,6298,6299,3495,6302,6334,6335,1343,6358,6381,6382,6385,6386,6399],{},[883,6297,1641],{}," TL;DR\nV ",[38,6300,6301],{},"rovnovážném bodě",[883,6303,6305],{"className":6304},[886],[888,6306,6307],{"xmlns":890},[892,6308,6309,6331],{},[895,6310,6311,6313,6315,6321,6323,6329],{},[898,6312,1805],{},[1716,6314,2502],{"stretchy":1919},[3074,6316,6317,6319],{},[898,6318,1878],{},[898,6320,1805],{},[1716,6322,1719],{"separator":1718},[3074,6324,6325,6327],{},[898,6326,1690],{},[898,6328,1805],{},[1716,6330,2516],{"stretchy":1919},[902,6332,6333],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,6336,6338],{"className":6337},[886],[888,6339,6340],{"xmlns":890},[892,6341,6342,6356],{},[895,6343,6344,6346,6348,6350,6352,6354],{},[898,6345,1690],{},[1716,6347,1913],{},[898,6349,1916],{},[1716,6351,1920],{"stretchy":1919},[898,6353,1878],{},[1716,6355,1925],{"stretchy":1919},[902,6357,4115],{"encoding":904},[883,6359,6361],{"className":6360},[886],[888,6362,6363],{"xmlns":890},[892,6364,6365,6379],{},[895,6366,6367,6369,6371,6373,6375,6377],{},[898,6368,1690],{},[1716,6370,1913],{},[898,6372,5352],{},[1716,6374,1920],{"stretchy":1919},[898,6376,1878],{},[1716,6378,1925],{"stretchy":1919},[902,6380,6036],{"encoding":904},". Čtyři ",[38,6383,6384],{},"pravidla komparativní statiky"," popisují, jak se ",[883,6387,6389],{"className":6388},[886],[888,6390,6391],{"xmlns":890},[892,6392,6393,6397],{},[895,6394,6395],{},[898,6396,1805],{},[902,6398,1805],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,6401,6403],{"id":6402},"definice","Definice",[724,6405,6406,1994,6408,6411,6412,3495,6415,6433,6434,6465,6466,1994,6469,2365],{},[38,6407,6291],{},[614,6409,6410],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,6413,6414],{},"rovnovážné ceně",[883,6416,6418],{"className":6417},[886],[888,6419,6420],{"xmlns":890},[892,6421,6422,6430],{},[895,6423,6424],{},[3074,6425,6426,6428],{},[898,6427,1690],{},[898,6429,1805],{},[902,6431,6432],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,6435,6437],{"className":6436},[886],[888,6438,6439],{"xmlns":890},[892,6440,6441,6463],{},[895,6442,6443,6445,6447,6453,6455,6461],{},[898,6444,1805],{},[1716,6446,2502],{"stretchy":1919},[3074,6448,6449,6451],{},[898,6450,1878],{},[898,6452,1805],{},[1716,6454,1719],{"separator":1718},[3074,6456,6457,6459],{},[898,6458,1690],{},[898,6460,1805],{},[1716,6462,2516],{"stretchy":1919},[902,6464,6333],{"encoding":904}," se nazývá ",[38,6467,6468],{},"rovnovážný bod",[614,6470,6471],{},"equilibrium point",[724,6473,6474,6475,1343,6498,1853],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,6476,6478],{"className":6477},[886],[888,6479,6480],{"xmlns":890},[892,6481,6482,6496],{},[895,6483,6484,6486,6488,6490,6492,6494],{},[898,6485,1690],{},[1716,6487,1913],{},[898,6489,1916],{},[1716,6491,1920],{"stretchy":1919},[898,6493,1878],{},[1716,6495,1925],{"stretchy":1919},[902,6497,4115],{"encoding":904},[883,6499,6501],{"className":6500},[886],[888,6502,6503],{"xmlns":890},[892,6504,6505,6519],{},[895,6506,6507,6509,6511,6513,6515,6517],{},[898,6508,1690],{},[1716,6510,1913],{},[898,6512,5352],{},[1716,6514,1920],{"stretchy":1919},[898,6516,1878],{},[1716,6518,1925],{"stretchy":1919},[902,6520,6036],{"encoding":904},[724,6522,6523],{},[3682,6524],{"alt":6525,"className":6526,"src":6527},"imek-poptavka-nabidka-rovnovaha",[210,3686],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,6529,6530],{},[614,6531,6532,6533,6546,6547,4060,6560,6581,6582,1853],{},"Obrázek 2.13: Klesající ",[883,6534,6536],{"className":6535},[886],[888,6537,6538],{"xmlns":890},[892,6539,6540,6544],{},[895,6541,6542],{},[898,6543,1916],{},[902,6545,1916],{"encoding":904}," a rostoucí ",[883,6548,6550],{"className":6549},[886],[888,6551,6552],{"xmlns":890},[892,6553,6554,6558],{},[895,6555,6556],{},[898,6557,5352],{},[902,6559,5352],{"encoding":904},[883,6561,6563],{"className":6562},[886],[888,6564,6565],{"xmlns":890},[892,6566,6567,6579],{},[895,6568,6569,6571,6573,6575,6577],{},[1716,6570,1920],{"stretchy":1919},[898,6572,1878],{},[1716,6574,1719],{"separator":1718},[898,6576,1690],{},[1716,6578,1925],{"stretchy":1919},[902,6580,2608],{"encoding":904}," protínající se v ",[883,6583,6585],{"className":6584},[886],[888,6586,6587],{"xmlns":890},[892,6588,6589,6611],{},[895,6590,6591,6593,6595,6601,6603,6609],{},[898,6592,1805],{},[1716,6594,2502],{"stretchy":1919},[3074,6596,6597,6599],{},[898,6598,1878],{},[898,6600,1805],{},[1716,6602,1719],{"separator":1718},[3074,6604,6605,6607],{},[898,6606,1690],{},[898,6608,1805],{},[1716,6610,2516],{"stretchy":1919},[902,6612,6333],{"encoding":904},[198,6614,6616],{"id":6615},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,6618,6619,6621,6622,6657,6658,1853],{},[38,6620,2859],{}," Poptávka ",[883,6623,6625],{"className":6624},[886],[888,6626,6627],{"xmlns":890},[892,6628,6629,6654],{},[895,6630,6631,6633,6635,6637,6643,6645,6647,6649,6651],{},[898,6632,1690],{},[1716,6634,1913],{},[1716,6636,2760],{},[3074,6638,6639,6641],{},[898,6640,1878],{},[1712,6642,1726],{},[1716,6644,2760],{},[1712,6646,2998],{},[898,6648,1878],{},[1716,6650,1949],{},[1712,6652,6653],{},"150",[902,6655,6656],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,6659,6661],{"className":6660},[886],[888,6662,6663],{"xmlns":890},[892,6664,6665,6689],{},[895,6666,6667,6669,6671,6677,6679,6682,6684,6686],{},[898,6668,1690],{},[1716,6670,1913],{},[3074,6672,6673,6675],{},[898,6674,1878],{},[1712,6676,1726],{},[1716,6678,1949],{},[1712,6680,6681],{},"14",[898,6683,1878],{},[1716,6685,1949],{},[1712,6687,6688],{},"22",[902,6690,6691],{"encoding":904},"P = Q^2 + 14Q + 22",[724,6693,6694,6696],{},[38,6695,2892],{}," Z rovnosti",[883,6698,6700],{"className":6699},[886],[888,6701,6702],{"xmlns":890,"display":2004},[892,6703,6704,6742],{},[895,6705,6706,6708,6714,6716,6718,6720,6722,6724,6726,6732,6734,6736,6738,6740],{},[1716,6707,2760],{},[3074,6709,6710,6712],{},[898,6711,1878],{},[1712,6713,1726],{},[1716,6715,2760],{},[1712,6717,2998],{},[898,6719,1878],{},[1716,6721,1949],{},[1712,6723,6653],{},[1716,6725,1913],{},[3074,6727,6728,6730],{},[898,6729,1878],{},[1712,6731,1726],{},[1716,6733,1949],{},[1712,6735,6681],{},[898,6737,1878],{},[1716,6739,1949],{},[1712,6741,6688],{},[902,6743,6744],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,6746,6747,6748,6784,6785,6819,6820,6837,6838,6852,6853,1343,6875,6912,6913,1853],{},"dostaneme ",[883,6749,6751],{"className":6750},[886],[888,6752,6753],{"xmlns":890},[892,6754,6755,6781],{},[895,6756,6757,6759,6765,6767,6770,6772,6774,6777,6779],{},[1712,6758,1726],{},[3074,6760,6761,6763],{},[898,6762,1878],{},[1712,6764,1726],{},[1716,6766,1949],{},[1712,6768,6769],{},"24",[898,6771,1878],{},[1716,6773,2760],{},[1712,6775,6776],{},"128",[1716,6778,1913],{},[1712,6780,2505],{},[902,6782,6783],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,6786,6788],{"className":6787},[886],[888,6789,6790],{"xmlns":890},[892,6791,6792,6816],{},[895,6793,6794,6800,6802,6805,6807,6809,6812,6814],{},[3074,6795,6796,6798],{},[898,6797,1878],{},[1712,6799,1726],{},[1716,6801,1949],{},[1712,6803,6804],{},"12",[898,6806,1878],{},[1716,6808,2760],{},[1712,6810,6811],{},"64",[1716,6813,1913],{},[1712,6815,2505],{},[902,6817,6818],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,6821,6823],{"className":6822},[886],[888,6824,6825],{"xmlns":890},[892,6826,6827,6834],{},[895,6828,6829,6831],{},[1716,6830,2760],{},[1712,6832,6833],{},"16",[902,6835,6836],{"encoding":904},"-16"," (nevyhovuje) a ",[883,6839,6841],{"className":6840},[886],[888,6842,6843],{"xmlns":890},[892,6844,6845,6850],{},[895,6846,6847],{},[1712,6848,6849],{},"4",[902,6851,6849],{"encoding":904},". Tedy ",[883,6854,6856],{"className":6855},[886],[888,6857,6858],{"xmlns":890},[892,6859,6860,6872],{},[895,6861,6862,6868,6870],{},[3074,6863,6864,6866],{},[898,6865,1878],{},[898,6867,1805],{},[1716,6869,1913],{},[1712,6871,6849],{},[902,6873,6874],{"encoding":904},"Q^E = 4",[883,6876,6878],{"className":6877},[886],[888,6879,6880],{"xmlns":890},[892,6881,6882,6909],{},[895,6883,6884,6890,6892,6894,6896,6898,6900,6902,6904,6906],{},[3074,6885,6886,6888],{},[898,6887,1690],{},[898,6889,1805],{},[1716,6891,1913],{},[1716,6893,2760],{},[1712,6895,6833],{},[1716,6897,2760],{},[1712,6899,2973],{},[1716,6901,1949],{},[1712,6903,6653],{},[1716,6905,1913],{},[1712,6907,6908],{},"94",[902,6910,6911],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,6914,6916],{"className":6915},[886],[888,6917,6918],{"xmlns":890},[892,6919,6920,6934],{},[895,6921,6922,6924,6926,6928,6930,6932],{},[898,6923,1805],{},[1716,6925,2502],{"stretchy":1919},[1712,6927,6849],{},[1716,6929,1719],{"separator":1718},[1712,6931,6908],{},[1716,6933,2516],{"stretchy":1919},[902,6935,6936],{"encoding":904},"E[4, 94]",[198,6938,6940],{"id":6939},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,6942,6943,6945],{},[38,6944,2859],{}," Poptávky a nabídky dvou zboží",[883,6947,6949],{"className":6948},[886],[888,6950,6951],{"xmlns":890,"display":2004},[892,6952,6953,7122],{},[2008,6954,6957,7046],{"rowspacing":4401,"columnalign":6955,"columnspacing":6956},"right left right left","0em 1em 0em",[2012,6958,6959,6969,7002,7012],{},[2015,6960,6961],{},[2747,6962,6963],{"scriptlevel":2505,"displaystyle":1718},[1707,6964,6965,6967],{},[898,6966,1878],{},[1712,6968,1714],{},[2015,6970,6971],{},[2747,6972,6973],{"scriptlevel":2505,"displaystyle":1718},[895,6974,6975,6977,6979,6981,6983,6986,6992,6994,7000],{},[895,6976],{},[1716,6978,1913],{},[1712,6980,2973],{},[1716,6982,2760],{},[1712,6984,6985],{},"5",[1707,6987,6988,6990],{},[898,6989,1690],{},[1712,6991,1714],{},[1716,6993,2760],{},[1707,6995,6996,6998],{},[898,6997,1690],{},[1712,6999,1726],{},[1716,7001,1719],{"separator":1718},[2015,7003,7004],{},[2747,7005,7006],{"scriptlevel":2505,"displaystyle":1718},[1707,7007,7008,7010],{},[898,7009,1878],{},[1712,7011,1726],{},[2015,7013,7014],{},[2747,7015,7016],{"scriptlevel":2505,"displaystyle":1718},[895,7017,7018,7020,7022,7024,7026,7028,7034,7036,7038,7044],{},[895,7019],{},[1716,7021,1913],{},[1712,7023,5808],{},[1716,7025,2760],{},[1712,7027,1726],{},[1707,7029,7030,7032],{},[898,7031,1690],{},[1712,7033,1714],{},[1716,7035,2760],{},[1712,7037,6849],{},[1707,7039,7040,7042],{},[898,7041,1690],{},[1712,7043,1726],{},[1716,7045,1719],{"separator":1718},[2012,7047,7048,7058,7085,7095],{},[2015,7049,7050],{},[2747,7051,7052],{"scriptlevel":2505,"displaystyle":1718},[1707,7053,7054,7056],{},[898,7055,1878],{},[1712,7057,1714],{},[2015,7059,7060],{},[2747,7061,7062],{"scriptlevel":2505,"displaystyle":1718},[895,7063,7064,7066,7068,7070,7073,7075,7077,7083],{},[895,7065],{},[1716,7067,1913],{},[1716,7069,2760],{},[1712,7071,7072],{},"3",[1716,7074,1949],{},[1712,7076,6849],{},[1707,7078,7079,7081],{},[898,7080,1690],{},[1712,7082,1714],{},[1716,7084,1719],{"separator":1718},[2015,7086,7087],{},[2747,7088,7089],{"scriptlevel":2505,"displaystyle":1718},[1707,7090,7091,7093],{},[898,7092,1878],{},[1712,7094,1726],{},[2015,7096,7097],{},[2747,7098,7099],{"scriptlevel":2505,"displaystyle":1718},[895,7100,7101,7103,7105,7107,7110,7112,7114,7120],{},[895,7102],{},[1716,7104,1913],{},[1716,7106,2760],{},[1712,7108,7109],{},"7",[1716,7111,1949],{},[1712,7113,7072],{},[1707,7115,7116,7118],{},[898,7117,1690],{},[1712,7119,1726],{},[898,7121,1853],{"mathvariant":2068},[902,7123,7124],{"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}",[724,7126,7127,7129],{},[38,7128,2892],{}," Z rovností poptávek a nabídek dostaneme",[883,7131,7133],{"className":7132},[886],[888,7134,7135],{"xmlns":890,"display":2004},[892,7136,7137,7188],{},[895,7138,7139,7142,7148,7150,7156,7158,7161,7163,7165,7167,7173,7175,7177,7183,7185],{},[1712,7140,7141],{},"9",[1707,7143,7144,7146],{},[898,7145,1690],{},[1712,7147,1714],{},[1716,7149,1949],{},[1707,7151,7152,7154],{},[898,7153,1690],{},[1712,7155,1726],{},[1716,7157,1913],{},[1712,7159,7160],{},"43",[1716,7162,1719],{"separator":1718},[2324,7164],{"width":2326},[1712,7166,1726],{},[1707,7168,7169,7171],{},[898,7170,1690],{},[1712,7172,1714],{},[1716,7174,1949],{},[1712,7176,7109],{},[1707,7178,7179,7181],{},[898,7180,1690],{},[1712,7182,1726],{},[1716,7184,1913],{},[1712,7186,7187],{},"57.",[902,7189,7190],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,7192,7193,7194,1343,7219,7243,7244,1343,7269,7293,7294,7296],{},"Řešením je ",[883,7195,7197],{"className":7196},[886],[888,7198,7199],{"xmlns":890},[892,7200,7201,7216],{},[895,7202,7203,7212,7214],{},[7204,7205,7206,7208,7210],"msubsup",{},[898,7207,1690],{},[1712,7209,1714],{},[898,7211,1805],{},[1716,7213,1913],{},[1712,7215,6849],{},[902,7217,7218],{"encoding":904},"P_1^E = 4",[883,7220,7222],{"className":7221},[886],[888,7223,7224],{"xmlns":890},[892,7225,7226,7240],{},[895,7227,7228,7236,7238],{},[7204,7229,7230,7232,7234],{},[898,7231,1690],{},[1712,7233,1726],{},[898,7235,1805],{},[1716,7237,1913],{},[1712,7239,7109],{},[902,7241,7242],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,7245,7247],{"className":7246},[886],[888,7248,7249],{"xmlns":890},[892,7250,7251,7266],{},[895,7252,7253,7261,7263],{},[7204,7254,7255,7257,7259],{},[898,7256,1878],{},[1712,7258,1714],{},[898,7260,1805],{},[1716,7262,1913],{},[1712,7264,7265],{},"13",[902,7267,7268],{"encoding":904},"Q_1^E = 13",[883,7270,7272],{"className":7271},[886],[888,7273,7274],{"xmlns":890},[892,7275,7276,7290],{},[895,7277,7278,7286,7288],{},[7204,7279,7280,7282,7284],{},[898,7281,1878],{},[1712,7283,1726],{},[898,7285,1805],{},[1716,7287,1913],{},[1712,7289,6681],{},[902,7291,7292],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,7295,4779],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,7298,7300],{"id":7299},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,7302,7303,7304,7321,7322,1994,7325,2365],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,7305,7307],{"className":7306},[886],[888,7308,7309],{"xmlns":890},[892,7310,7311,7319],{},[895,7312,7313],{},[3074,7314,7315,7317],{},[898,7316,1690],{},[898,7318,1805],{},[902,7320,6432],{"encoding":904},"; mechanismus popisuje ",[38,7323,7324],{},"teorém pavučiny",[614,7326,7327],{},"cobweb model",[198,7329,7331],{"id":7330},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,7333,7334],{},[3682,7335],{"alt":7336,"className":7337,"src":7338},"imek-komparativni-statika-4pripady",[210,3686],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1635,7340,7341,7383,7423,7464],{},[724,7342,7343,7346,7347,7364,7365,1853],{},[38,7344,7345],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,7348,7350],{"className":7349},[886],[888,7351,7352],{"xmlns":890},[892,7353,7354,7362],{},[895,7355,7356],{},[3074,7357,7358,7360],{},[898,7359,1690],{},[898,7361,1805],{},[902,7363,6432],{"encoding":904}," i ",[883,7366,7368],{"className":7367},[886],[888,7369,7370],{"xmlns":890},[892,7371,7372,7380],{},[895,7373,7374],{},[3074,7375,7376,7378],{},[898,7377,1878],{},[898,7379,1805],{},[902,7381,7382],{"encoding":904},"Q^E",[724,7384,7385,7388,7389,7364,7406,1853],{},[38,7386,7387],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,7390,7392],{"className":7391},[886],[888,7393,7394],{"xmlns":890},[892,7395,7396,7404],{},[895,7397,7398],{},[3074,7399,7400,7402],{},[898,7401,1690],{},[898,7403,1805],{},[902,7405,6432],{"encoding":904},[883,7407,7409],{"className":7408},[886],[888,7410,7411],{"xmlns":890},[892,7412,7413,7421],{},[895,7414,7415],{},[3074,7416,7417,7419],{},[898,7418,1878],{},[898,7420,1805],{},[902,7422,7382],{"encoding":904},[724,7424,7425,7428,7429,7446,7447,1853],{},[38,7426,7427],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,7430,7432],{"className":7431},[886],[888,7433,7434],{"xmlns":890},[892,7435,7436,7444],{},[895,7437,7438],{},[3074,7439,7440,7442],{},[898,7441,1690],{},[898,7443,1805],{},[902,7445,6432],{"encoding":904},", růst ",[883,7448,7450],{"className":7449},[886],[888,7451,7452],{"xmlns":890},[892,7453,7454,7462],{},[895,7455,7456],{},[3074,7457,7458,7460],{},[898,7459,1878],{},[898,7461,1805],{},[902,7463,7382],{"encoding":904},[724,7465,7466,7469,7470,7487,7488,1853],{},[38,7467,7468],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,7471,7473],{"className":7472},[886],[888,7474,7475],{"xmlns":890},[892,7476,7477,7485],{},[895,7478,7479],{},[3074,7480,7481,7483],{},[898,7482,1690],{},[898,7484,1805],{},[902,7486,6432],{"encoding":904},", pokles ",[883,7489,7491],{"className":7490},[886],[888,7492,7493],{"xmlns":890},[892,7494,7495,7503],{},[895,7496,7497],{},[3074,7498,7499,7501],{},[898,7500,1878],{},[898,7502,1805],{},[902,7504,7382],{"encoding":904},[16,7506,7507,7552],{},[19,7508,7509],{},[22,7510,7511,7514,7533],{},[25,7512,7513],{},"Změna",[25,7515,7516],{},[883,7517,7519],{"className":7518},[886],[888,7520,7521],{"xmlns":890},[892,7522,7523,7531],{},[895,7524,7525],{},[3074,7526,7527,7529],{},[898,7528,1690],{},[898,7530,1805],{},[902,7532,6432],{"encoding":904},[25,7534,7535],{},[883,7536,7538],{"className":7537},[886],[888,7539,7540],{"xmlns":890},[892,7541,7542,7550],{},[895,7543,7544],{},[3074,7545,7546,7548],{},[898,7547,1878],{},[898,7549,1805],{},[902,7551,7382],{"encoding":904},[30,7553,7554,7564,7574,7583],{},[22,7555,7556,7559,7562],{},[35,7557,7558],{},"Růst poptávky",[35,7560,7561],{},"↑",[35,7563,7561],{},[22,7565,7566,7569,7572],{},[35,7567,7568],{},"Pokles poptávky",[35,7570,7571],{},"↓",[35,7573,7571],{},[22,7575,7576,7579,7581],{},[35,7577,7578],{},"Růst nabídky",[35,7580,7571],{},[35,7582,7561],{},[22,7584,7585,7588,7590],{},[35,7586,7587],{},"Pokles nabídky",[35,7589,7561],{},[35,7591,7571],{},[724,7593,7594],{},[614,7595,7596],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[1855,7598],{},[115,7600,811],{"id":7601},"zdanění-trhu",[1635,7603,7604,7695],{},[724,7605,7606,7608,7609,7622,7623,7636,7637,7640,7641,1646,7664,7690,7691,7694],{},[883,7607,1641],{}," TL;DR\nJednotková daň ",[883,7610,7612],{"className":7611},[886],[888,7613,7614],{"xmlns":890},[892,7615,7616,7620],{},[895,7617,7618],{},[898,7619,4164],{},[902,7621,4164],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,7624,7626],{"className":7625},[886],[888,7627,7628],{"xmlns":890},[892,7629,7630,7634],{},[895,7631,7632],{},[898,7633,4164],{},[902,7635,4164],{"encoding":904},". ",[38,7638,7639],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,7642,7644],{"className":7643},[886],[888,7645,7646],{"xmlns":890},[892,7647,7648,7661],{},[895,7649,7650],{},[1707,7651,7652,7654],{},[898,7653,4164],{},[895,7655,7656,7659],{},[898,7657,7658],{},"s",[898,7660,724],{},[902,7662,7663],{"encoding":904},"T_{sp}",[883,7665,7667],{"className":7666},[886],[888,7668,7669],{"xmlns":890},[892,7670,7671,7687],{},[895,7672,7673],{},[1707,7674,7675,7677],{},[898,7676,4164],{},[895,7678,7679,7682,7685],{},[898,7680,7681],{},"v",[898,7683,7684],{},"y",[898,7686,2098],{},[902,7688,7689],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,7692,7693],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,7696,7697],{},[614,7698,7699,7700,1853],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,7701,7703],{"className":7702,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,7705,7706,7707,7710,7711,7737,7738,7741,7742,7768,7769,7786,7787,7827,7828,2247,7841,1853],{},"Existují dvě formy zdanění — daň uložená ",[38,7708,7709],{},"výrobci"," (posun nabídky ",[883,7712,7714],{"className":7713},[886],[888,7715,7716],{"xmlns":890},[892,7717,7718,7734],{},[895,7719,7720,7726,7728,7730,7732],{},[1707,7721,7722,7724],{},[898,7723,5352],{},[1712,7725,1714],{},[1716,7727,1913],{},[898,7729,5352],{},[1716,7731,1949],{},[898,7733,4164],{},[902,7735,7736],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,7739,7740],{},"spotřebiteli"," (posun poptávky ",[883,7743,7745],{"className":7744},[886],[888,7746,7747],{"xmlns":890},[892,7748,7749,7765],{},[895,7750,7751,7757,7759,7761,7763],{},[1707,7752,7753,7755],{},[898,7754,1916],{},[1712,7756,1726],{},[1716,7758,1913],{},[898,7760,1916],{},[1716,7762,2760],{},[898,7764,4164],{},[902,7766,7767],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,7770,7772],{"className":7771},[886],[888,7773,7774],{"xmlns":890},[892,7775,7776,7784],{},[895,7777,7778],{},[3074,7779,7780,7782],{},[898,7781,1878],{},[898,7783,1805],{},[902,7785,7382],{"encoding":904}," klesá a vzniká rozklad daně ",[883,7788,7790],{"className":7789},[886],[888,7791,7792],{"xmlns":890},[892,7793,7794,7824],{},[895,7795,7796,7798,7800,7810,7812],{},[898,7797,4164],{},[1716,7799,1913],{},[1707,7801,7802,7804],{},[898,7803,4164],{},[895,7805,7806,7808],{},[898,7807,7658],{},[898,7809,724],{},[1716,7811,1949],{},[1707,7813,7814,7816],{},[898,7815,4164],{},[895,7817,7818,7820,7822],{},[898,7819,7681],{},[898,7821,7684],{},[898,7823,2098],{},[902,7825,7826],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,7829,7831],{"className":7830},[886],[888,7832,7833],{"xmlns":890},[892,7834,7835,7839],{},[895,7836,7837],{},[898,7838,1916],{},[902,7840,1916],{"encoding":904},[883,7842,7844],{"className":7843},[886],[888,7845,7846],{"xmlns":890},[892,7847,7848,7852],{},[895,7849,7850],{},[898,7851,5352],{},[902,7853,5352],{"encoding":904},[724,7855,7856,7857,7860,7861,2247,7891,7925],{},"Zásadním výsledkem kapitoly je ",[38,7858,7859],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,7862,7864],{"className":7863},[886],[888,7865,7866],{"xmlns":890},[892,7867,7868,7888],{},[895,7869,7870,7878,7880],{},[7204,7871,7872,7874,7876],{},[898,7873,1878],{},[1712,7875,1714],{},[898,7877,1805],{},[1716,7879,1913],{},[7204,7881,7882,7884,7886],{},[898,7883,1878],{},[1712,7885,1726],{},[898,7887,1805],{},[902,7889,7890],{"encoding":904},"Q_1^E = Q_2^E",[883,7892,7894],{"className":7893},[886],[888,7895,7896],{"xmlns":890},[892,7897,7898,7922],{},[895,7899,7900,7908,7910,7912,7914],{},[7204,7901,7902,7904,7906],{},[898,7903,1690],{},[1712,7905,1714],{},[898,7907,1805],{},[1716,7909,2760],{},[898,7911,4164],{},[1716,7913,1913],{},[7204,7915,7916,7918,7920],{},[898,7917,1690],{},[1712,7919,1726],{},[898,7921,1805],{},[902,7923,7924],{"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.",[724,7927,7928,7929,7932,7933,7959,7960,7988,7989,7992,7993,7996,7997,1853],{},"Podrobný výklad, Příklady ",[38,7930,7931],{},"2.9"," (daň výrobci, ",[883,7934,7936],{"className":7935},[886],[888,7937,7938],{"xmlns":890},[892,7939,7940,7956],{},[895,7941,7942,7952,7954],{},[1707,7943,7944,7946],{},[898,7945,4164],{},[895,7947,7948,7950],{},[898,7949,7658],{},[898,7951,724],{},[1716,7953,1913],{},[1712,7955,1726],{},[902,7957,7958],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,7961,7963],{"className":7962},[886],[888,7964,7965],{"xmlns":890},[892,7966,7967,7985],{},[895,7968,7969,7981,7983],{},[1707,7970,7971,7973],{},[898,7972,4164],{},[895,7974,7975,7977,7979],{},[898,7976,7681],{},[898,7978,7684],{},[898,7980,2098],{},[1716,7982,1913],{},[1712,7984,6849],{},[902,7986,7987],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,7990,7991],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,7994,7995],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,7998,7703],{"className":7999,"dataFsResolvedFilePath":809,"href":810},[210],[1855,8001],{},[115,8003,8005],{"id":8004},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1635,8007,8008],{},[724,8009,8010,8012,8013,8016,8017,8019],{},[883,8011,1641],{}," TL;DR\nMultiplikátory jsou ",[38,8014,8015],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,8018,1844],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,8021,8023],{"id":8022},"redukovaný-tvar","Redukovaný tvar",[724,8025,8026,8027,1994,8050,1343,8068,8086,8087,1994,8110,8127,8128,8158],{},"Pro lineární model ",[883,8028,8030],{"className":8029},[886],[888,8031,8032],{"xmlns":890},[892,8033,8034,8048],{},[895,8035,8036,8038,8040,8042,8044,8046],{},[898,8037,1690],{},[1716,8039,1913],{},[898,8041,207],{},[898,8043,1878],{},[1716,8045,1949],{},[898,8047,1952],{},[902,8049,1955],{"encoding":904},[883,8051,8053],{"className":8052},[886],[888,8054,8055],{"xmlns":890},[892,8056,8057,8065],{},[895,8058,8059,8061,8063],{},[898,8060,207],{},[1716,8062,2704],{},[1712,8064,2505],{},[902,8066,8067],{"encoding":904},"a \u003C 0",[883,8069,8071],{"className":8070},[886],[888,8072,8073],{"xmlns":890},[892,8074,8075,8083],{},[895,8076,8077,8079,8081],{},[898,8078,1952],{},[1716,8080,2716],{},[1712,8082,2505],{},[902,8084,8085],{"encoding":904},"b > 0",") a ",[883,8088,8090],{"className":8089},[886],[888,8091,8092],{"xmlns":890},[892,8093,8094,8108],{},[895,8095,8096,8098,8100,8102,8104,8106],{},[898,8097,1690],{},[1716,8099,1913],{},[898,8101,4478],{},[898,8103,1878],{},[1716,8105,1949],{},[898,8107,5198],{},[902,8109,5201],{"encoding":904},[883,8111,8113],{"className":8112},[886],[888,8114,8115],{"xmlns":890},[892,8116,8117,8125],{},[895,8118,8119,8121,8123],{},[898,8120,4478],{},[1716,8122,2716],{},[1712,8124,2505],{},[902,8126,5219],{"encoding":904},") dává podmínka rovnováhy ",[883,8129,8131],{"className":8130},[886],[888,8132,8133],{"xmlns":890},[892,8134,8135,8155],{},[895,8136,8137,8139,8141,8143,8145,8147,8149,8151,8153],{},[898,8138,207],{},[898,8140,1878],{},[1716,8142,1949],{},[898,8144,1952],{},[1716,8146,1913],{},[898,8148,4478],{},[898,8150,1878],{},[1716,8152,1949],{},[898,8154,5198],{},[902,8156,8157],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,8160,8162],{"className":8161},[886],[888,8163,8164],{"xmlns":890,"display":2004},[892,8165,8166,8211],{},[2008,8167,8168],{"width":2010},[2012,8169,8170,8172,8204,8206],{},[2015,8171],{"width":2017},[2015,8173,8174],{},[895,8175,8176,8182,8184,8202],{},[3074,8177,8178,8180],{},[898,8179,1878],{},[898,8181,1805],{},[1716,8183,1913],{},[2750,8185,8186,8194],{},[895,8187,8188,8190,8192],{},[898,8189,1952],{},[1716,8191,2760],{},[898,8193,5198],{},[895,8195,8196,8198,8200],{},[898,8197,4478],{},[1716,8199,2760],{},[898,8201,207],{},[898,8203,1853],{"mathvariant":2068},[2015,8205],{"width":2017},[2015,8207,8208],{},[2074,8209,8210],{},"(2.10)",[902,8212,8213],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,8215,8216,8217,1994,8220,8223,8224,8241,8242,3495,8245,8271,8272,8285,8286,8304,8305,2365],{},"Vztah (2.10) je ",[38,8218,8219],{},"redukovaný tvar",[614,8221,8222],{},"reduced form",") pro ",[883,8225,8227],{"className":8226},[886],[888,8228,8229],{"xmlns":890},[892,8230,8231,8239],{},[895,8232,8233],{},[3074,8234,8235,8237],{},[898,8236,1878],{},[898,8238,1805],{},[902,8240,7382],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,8243,8244],{},"parametrů",[883,8246,8248],{"className":8247},[886],[888,8249,8250],{"xmlns":890},[892,8251,8252,8268],{},[895,8253,8254,8256,8258,8260,8262,8264,8266],{},[898,8255,207],{},[1716,8257,1719],{"separator":1718},[898,8259,1952],{},[1716,8261,1719],{"separator":1718},[898,8263,4478],{},[1716,8265,1719],{"separator":1718},[898,8267,5198],{},[902,8269,8270],{"encoding":904},"a, b, c, d",". Aby ",[883,8273,8275],{"className":8274},[886],[888,8276,8277],{"xmlns":890},[892,8278,8279,8283],{},[895,8280,8281],{},[898,8282,1805],{},[902,8284,1805],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,8287,8289],{"className":8288},[886],[888,8290,8291],{"xmlns":890},[892,8292,8293,8301],{},[895,8294,8295,8297,8299],{},[898,8296,1952],{},[1716,8298,2716],{},[898,8300,5198],{},[902,8302,8303],{"encoding":904},"b > d"," (neboť ",[883,8306,8308],{"className":8307},[886],[888,8309,8310],{"xmlns":890},[892,8311,8312,8324],{},[895,8313,8314,8316,8318,8320,8322],{},[898,8315,4478],{},[1716,8317,2760],{},[898,8319,207],{},[1716,8321,2716],{},[1712,8323,2505],{},[902,8325,8326],{"encoding":904},"c - a > 0",[724,8328,8329],{},[614,8330,8331,8332,8345,8346,8359,8360,8373,8374,6912,8391,8404],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,8333,8335],{"className":8334},[886],[888,8336,8337],{"xmlns":890},[892,8338,8339,8343],{},[895,8340,8341],{},[898,8342,1952],{},[902,8344,1952],{"encoding":904}," na ose ",[883,8347,8349],{"className":8348},[886],[888,8350,8351],{"xmlns":890},[892,8352,8353,8357],{},[895,8354,8355],{},[898,8356,1690],{},[902,8358,1690],{"encoding":904},") a nabídka (úsek ",[883,8361,8363],{"className":8362},[886],[888,8364,8365],{"xmlns":890},[892,8366,8367,8371],{},[895,8368,8369],{},[898,8370,5198],{},[902,8372,5198],{"encoding":904},"), ",[883,8375,8377],{"className":8376},[886],[888,8378,8379],{"xmlns":890},[892,8380,8381,8389],{},[895,8382,8383,8385,8387],{},[898,8384,1952],{},[1716,8386,2716],{},[898,8388,5198],{},[902,8390,8303],{"encoding":904},[883,8392,8394],{"className":8393},[886],[888,8395,8396],{"xmlns":890},[892,8397,8398,8402],{},[895,8399,8400],{},[898,8401,1805],{},[902,8403,1805],{"encoding":904}," v 1. kvadrantu.",[198,8406,8408],{"id":8407},"definice-multiplikátorů","Definice multiplikátorů",[724,8410,8411,8412,8437,8438,8451,8452,8465],{},"V komparativní statice jsou ",[883,8413,8415],{"className":8414},[886],[888,8416,8417],{"xmlns":890},[892,8418,8419,8435],{},[895,8420,8421,8423,8425,8427,8429,8431,8433],{},[898,8422,207],{},[1716,8424,1719],{"separator":1718},[898,8426,1952],{},[1716,8428,1719],{"separator":1718},[898,8430,4478],{},[1716,8432,1719],{"separator":1718},[898,8434,5198],{},[902,8436,8270],{"encoding":904}," exogenní proměnné a ",[883,8439,8441],{"className":8440},[886],[888,8442,8443],{"xmlns":890},[892,8444,8445,8449],{},[895,8446,8447],{},[898,8448,1878],{},[902,8450,1878],{"encoding":904}," endogenní. Přibližná změna ",[883,8453,8455],{"className":8454},[886],[888,8456,8457],{"xmlns":890},[892,8458,8459,8463],{},[895,8460,8461],{},[898,8462,1878],{},[902,8464,1878],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,8467,8469],{"className":8468},[886],[888,8470,8471],{"xmlns":890,"display":2004},[892,8472,8473,8570],{},[2008,8474,8475],{"width":2010},[2012,8476,8477,8479,8563,8565],{},[2015,8478],{"width":2017},[2015,8480,8481],{},[895,8482,8483,8486,8488,8491,8493,8495,8497,8506,8509,8511,8513,8515,8523,8525,8527,8529,8531,8539,8541,8543,8545,8547,8555,8557,8559,8561],{},[898,8484,8485],{"mathvariant":2068},"Δ",[898,8487,1878],{},[1716,8489,8490],{},"≈",[898,8492,5198],{},[898,8494,1878],{},[1716,8496,1913],{},[7204,8498,8499,8501,8503],{},[898,8500,1878],{},[898,8502,207],{},[1716,8504,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},"′",[2074,8507,8508],{}," ",[898,8510,5198],{},[898,8512,207],{},[1716,8514,1949],{},[7204,8516,8517,8519,8521],{},[898,8518,1878],{},[898,8520,1952],{},[1716,8522,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,8524,8508],{},[898,8526,5198],{},[898,8528,1952],{},[1716,8530,1949],{},[7204,8532,8533,8535,8537],{},[898,8534,1878],{},[898,8536,4478],{},[1716,8538,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,8540,8508],{},[898,8542,5198],{},[898,8544,4478],{},[1716,8546,1949],{},[7204,8548,8549,8551,8553],{},[898,8550,1878],{},[898,8552,5198],{},[1716,8554,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,8556,8508],{},[898,8558,5198],{},[898,8560,5198],{},[898,8562,1853],{"mathvariant":2068},[2015,8564],{"width":2017},[2015,8566,8567],{},[2074,8568,8569],{},"(2.11)",[902,8571,8572],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,8574,8575,8576,8626,8627,1994,8629,1998],{},"Parciální derivace ",[883,8577,8579],{"className":8578},[886],[888,8580,8581],{"xmlns":890},[892,8582,8583,8623],{},[895,8584,8585,8593,8595,8603,8605,8613,8615],{},[7204,8586,8587,8589,8591],{},[898,8588,1878],{},[898,8590,207],{},[1716,8592,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8594,1719],{"separator":1718},[7204,8596,8597,8599,8601],{},[898,8598,1878],{},[898,8600,1952],{},[1716,8602,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8604,1719],{"separator":1718},[7204,8606,8607,8609,8611],{},[898,8608,1878],{},[898,8610,4478],{},[1716,8612,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8614,1719],{"separator":1718},[7204,8616,8617,8619,8621],{},[898,8618,1878],{},[898,8620,5198],{},[1716,8622,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,8624,8625],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,8628,1657],{},[614,8630,8631],{},"multipliers",[883,8633,8635],{"className":8634},[886],[888,8636,8637],{"xmlns":890,"display":2004},[892,8638,8639,8791],{},[2008,8640,8641],{"width":2010},[2012,8642,8643,8645,8784,8786],{},[2015,8644],{"width":2017},[2015,8646,8647],{},[895,8648,8649,8657,8659,8685,8687,8690,8698,8700,8712,8714,8716,8724,8726,8728,8754,8756,8758,8766,8768,8770,8782],{},[7204,8650,8651,8653,8655],{},[898,8652,1878],{},[898,8654,207],{},[1716,8656,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8658,1913],{},[2750,8660,8661,8669],{},[895,8662,8663,8665,8667],{},[898,8664,1952],{},[1716,8666,2760],{},[898,8668,5198],{},[895,8670,8671,8673,8675,8677,8679],{},[1716,8672,1920],{"stretchy":1919},[898,8674,4478],{},[1716,8676,2760],{},[898,8678,207],{},[3074,8680,8681,8683],{},[1716,8682,1925],{"stretchy":1919},[1712,8684,1726],{},[1716,8686,1719],{"separator":1718},[2324,8688],{"width":8689},"1em",[7204,8691,8692,8694,8696],{},[898,8693,1878],{},[898,8695,1952],{},[1716,8697,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8699,1913],{},[2750,8701,8702,8704],{},[1712,8703,1714],{},[895,8705,8706,8708,8710],{},[898,8707,4478],{},[1716,8709,2760],{},[898,8711,207],{},[1716,8713,1719],{"separator":1718},[2324,8715],{"width":8689},[7204,8717,8718,8720,8722],{},[898,8719,1878],{},[898,8721,4478],{},[1716,8723,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8725,1913],{},[1716,8727,2760],{},[2750,8729,8730,8738],{},[895,8731,8732,8734,8736],{},[898,8733,1952],{},[1716,8735,2760],{},[898,8737,5198],{},[895,8739,8740,8742,8744,8746,8748],{},[1716,8741,1920],{"stretchy":1919},[898,8743,4478],{},[1716,8745,2760],{},[898,8747,207],{},[3074,8749,8750,8752],{},[1716,8751,1925],{"stretchy":1919},[1712,8753,1726],{},[1716,8755,1719],{"separator":1718},[2324,8757],{"width":8689},[7204,8759,8760,8762,8764],{},[898,8761,1878],{},[898,8763,5198],{},[1716,8765,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8767,1913],{},[1716,8769,2760],{},[2750,8771,8772,8774],{},[1712,8773,1714],{},[895,8775,8776,8778,8780],{},[898,8777,4478],{},[1716,8779,2760],{},[898,8781,207],{},[898,8783,1853],{"mathvariant":2068},[2015,8785],{"width":2017},[2015,8787,8788],{},[2074,8789,8790],{},"(2.12)",[902,8792,8793],{"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}",[198,8795,8797],{"id":8796},"znaménka-a-interpretace","Znaménka a interpretace",[724,8799,8800,8801,1343,8818,1343,8835,1343,8852,8869,8870,1998],{},"Za podmínek ",[883,8802,8804],{"className":8803},[886],[888,8805,8806],{"xmlns":890},[892,8807,8808,8816],{},[895,8809,8810,8812,8814],{},[898,8811,207],{},[1716,8813,2704],{},[1712,8815,2505],{},[902,8817,8067],{"encoding":904},[883,8819,8821],{"className":8820},[886],[888,8822,8823],{"xmlns":890},[892,8824,8825,8833],{},[895,8826,8827,8829,8831],{},[898,8828,1952],{},[1716,8830,2716],{},[1712,8832,2505],{},[902,8834,8085],{"encoding":904},[883,8836,8838],{"className":8837},[886],[888,8839,8840],{"xmlns":890},[892,8841,8842,8850],{},[895,8843,8844,8846,8848],{},[898,8845,4478],{},[1716,8847,2716],{},[1712,8849,2505],{},[902,8851,5219],{"encoding":904},[883,8853,8855],{"className":8854},[886],[888,8856,8857],{"xmlns":890},[892,8858,8859,8867],{},[895,8860,8861,8863,8865],{},[898,8862,1952],{},[1716,8864,2716],{},[898,8866,5198],{},[902,8868,8303],{"encoding":904}," platí (znaménka se ",[38,8871,8872],{},"nemění",[883,8874,8876],{"className":8875},[886],[888,8877,8878],{"xmlns":890,"display":2004},[892,8879,8880,8942],{},[895,8881,8882,8890,8892,8894,8896,8898,8906,8908,8910,8912,8914,8922,8924,8926,8928,8930,8938,8940],{},[7204,8883,8884,8886,8888],{},[898,8885,1878],{},[898,8887,207],{},[1716,8889,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8891,2716],{},[1712,8893,2505],{},[1716,8895,1719],{"separator":1718},[2324,8897],{"width":2326},[7204,8899,8900,8902,8904],{},[898,8901,1878],{},[898,8903,1952],{},[1716,8905,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8907,2716],{},[1712,8909,2505],{},[1716,8911,1719],{"separator":1718},[2324,8913],{"width":2326},[7204,8915,8916,8918,8920],{},[898,8917,1878],{},[898,8919,4478],{},[1716,8921,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8923,2704],{},[1712,8925,2505],{},[1716,8927,1719],{"separator":1718},[2324,8929],{"width":2326},[7204,8931,8932,8934,8936],{},[898,8933,1878],{},[898,8935,5198],{},[1716,8937,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,8939,2704],{},[1712,8941,2719],{},[902,8943,8944],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,8946,8947,9007],{},[123,8948,8949,3495,8952,8973,8974,8991,8992,1343,9005,1853],{},[38,8950,8951],{},"Kvantitativní smysl:",[883,8953,8955],{"className":8954},[886],[888,8956,8957],{"xmlns":890},[892,8958,8959,8970],{},[895,8960,8961],{},[7204,8962,8963,8965,8968],{},[898,8964,1878],{},[898,8966,8967],{},"x",[1716,8969,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,8971,8972],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,8975,8977],{"className":8976},[886],[888,8978,8979],{"xmlns":890},[892,8980,8981,8989],{},[895,8982,8983],{},[3074,8984,8985,8987],{},[898,8986,1878],{},[898,8988,1805],{},[902,8990,7382],{"encoding":904}," při jednotkové změně parametru ",[883,8993,8995],{"className":8994},[886],[888,8996,8997],{"xmlns":890},[892,8998,8999,9003],{},[895,9000,9001],{},[898,9002,8967],{},[902,9004,8967],{"encoding":904},[614,9006,1844],{},[123,9008,9009,9012,9013,9030,9031,1853],{},[38,9010,9011],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,9014,9016],{"className":9015},[886],[888,9017,9018],{"xmlns":890},[892,9019,9020,9028],{},[895,9021,9022],{},[3074,9023,9024,9026],{},[898,9025,1878],{},[898,9027,1805],{},[902,9029,7382],{"encoding":904}," na růst ",[883,9032,9034],{"className":9033},[886],[888,9035,9036],{"xmlns":890},[892,9037,9038,9042],{},[895,9039,9040],{},[898,9041,8967],{},[902,9043,8967],{"encoding":904},[724,9045,9046,9047,9060,9061,8304,9078,2365],{},"Např. růst ",[883,9048,9050],{"className":9049},[886],[888,9051,9052],{"xmlns":890},[892,9053,9054,9058],{},[895,9055,9056],{},[898,9057,4478],{},[902,9059,4478],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,9062,9064],{"className":9063},[886],[888,9065,9066],{"xmlns":890},[892,9067,9068,9076],{},[895,9069,9070],{},[3074,9071,9072,9074],{},[898,9073,1878],{},[898,9075,1805],{},[902,9077,7382],{"encoding":904},[883,9079,9081],{"className":9080},[886],[888,9082,9083],{"xmlns":890},[892,9084,9085,9099],{},[895,9086,9087,9095,9097],{},[7204,9088,9089,9091,9093],{},[898,9090,1878],{},[898,9092,4478],{},[1716,9094,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,9096,2704],{},[1712,9098,2505],{},[902,9100,9101],{"encoding":904},"Q'_c \u003C 0",[724,9103,9104],{},[614,9105,9106,9107,9127,9128,9152,9153,9175,9176,1853],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,9108,9110],{"className":9109},[886],[888,9111,9112],{"xmlns":890},[892,9113,9114,9124],{},[895,9115,9116,9118,9120,9122],{},[898,9117,4478],{},[898,9119,1878],{},[1716,9121,1949],{},[898,9123,5198],{},[902,9125,9126],{"encoding":904},"cQ + d"," na strmější ",[883,9129,9131],{"className":9130},[886],[888,9132,9133],{"xmlns":890},[892,9134,9135,9149],{},[895,9136,9137,9143,9145,9147],{},[1707,9138,9139,9141],{},[898,9140,4478],{},[1712,9142,1714],{},[898,9144,1878],{},[1716,9146,1949],{},[898,9148,5198],{},[902,9150,9151],{"encoding":904},"c_1 Q + d"," (při ",[883,9154,9156],{"className":9155},[886],[888,9157,9158],{"xmlns":890},[892,9159,9160,9172],{},[895,9161,9162,9168,9170],{},[1707,9163,9164,9166],{},[898,9165,4478],{},[1712,9167,1714],{},[1716,9169,2716],{},[898,9171,4478],{},[902,9173,9174],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,9177,9179],{"className":9178},[886],[888,9180,9181],{"xmlns":890},[892,9182,9183,9193],{},[895,9184,9185,9191],{},[3074,9186,9187,9189],{},[898,9188,1878],{},[898,9190,1805],{},[1716,9192,7571],{},[902,9194,9195],{"encoding":904},"Q^E \\downarrow",[724,9197,9198,9199,9231,9232,1853],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,9200,9202],{"className":9201},[886],[888,9203,9204],{"xmlns":890},[892,9205,9206,9228],{},[895,9207,9208,9210,9212,9214,9222,9224,9226],{},[898,9209,8485],{"mathvariant":2068},[898,9211,1878],{},[1716,9213,8490],{},[7204,9215,9216,9218,9220],{},[898,9217,1878],{},[898,9219,1952],{},[1716,9221,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,9223,8508],{},[898,9225,5198],{},[898,9227,1952],{},[902,9229,9230],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,9233,9235],{"className":9234},[886],[888,9236,9237],{"xmlns":890},[892,9238,9239,9247],{},[895,9240,9241],{},[3074,9242,9243,9245],{},[898,9244,1690],{},[898,9246,1805],{},[902,9248,6432],{"encoding":904},[198,9250,9252,9253],{"id":9251},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,9254,9256],{"className":9255},[886],[888,9257,9258],{"xmlns":890},[892,9259,9260,9268],{},[895,9261,9262],{},[3074,9263,9264,9266],{},[898,9265,1878],{},[898,9267,1805],{},[902,9269,7382],{"encoding":904},[724,9271,9272,6621,9274,6657,9300,1853],{},[38,9273,2859],{},[883,9275,9277],{"className":9276},[886],[888,9278,9279],{"xmlns":890},[892,9280,9281,9297],{},[895,9282,9283,9285,9287,9289,9291,9293,9295],{},[898,9284,1690],{},[1716,9286,1913],{},[1716,9288,2760],{},[1712,9290,7072],{},[898,9292,1878],{},[1716,9294,1949],{},[1712,9296,2973],{},[902,9298,9299],{"encoding":904},"P = -3Q + 40",[883,9301,9303],{"className":9302},[886],[888,9304,9305],{"xmlns":890},[892,9306,9307,9321],{},[895,9308,9309,9311,9313,9315,9317,9319],{},[898,9310,1690],{},[1716,9312,1913],{},[1712,9314,5771],{},[898,9316,1878],{},[1716,9318,1949],{},[1712,9320,2998],{},[902,9322,9323],{"encoding":904},"P = 0{,}5Q + 10",[724,9325,9326,9328],{},[38,9327,2892],{}," Rovnovážné množství",[883,9330,9332],{"className":9331},[886],[888,9333,9334],{"xmlns":890,"display":2004},[892,9335,9336,9404],{},[895,9337,9338,9344,9346,9364,9366,9390,9392,9399,9401],{},[3074,9339,9340,9342],{},[898,9341,1878],{},[898,9343,1805],{},[1716,9345,1913],{},[2750,9347,9348,9356],{},[895,9349,9350,9352,9354],{},[898,9351,1952],{},[1716,9353,2760],{},[898,9355,5198],{},[895,9357,9358,9360,9362],{},[898,9359,4478],{},[1716,9361,2760],{},[898,9363,207],{},[1716,9365,1913],{},[2750,9367,9368,9376],{},[895,9369,9370,9372,9374],{},[1712,9371,2973],{},[1716,9373,2760],{},[1712,9375,2998],{},[895,9377,9378,9380,9382,9384,9386,9388],{},[1712,9379,5771],{},[1716,9381,2760],{},[1716,9383,1920],{"stretchy":1919},[1716,9385,2760],{},[1712,9387,7072],{},[1716,9389,1925],{"stretchy":1919},[1716,9391,1913],{},[2750,9393,9394,9396],{},[1712,9395,2946],{},[1712,9397,9398],{},"3,5",[1716,9400,8490],{},[1712,9402,9403],{},"8,571.",[902,9405,9406],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,9408,9409,9456],{},[38,9410,9411,9412,9425,9426,3942,9440,9455],{},"(a) Změna ",[883,9413,9415],{"className":9414},[886],[888,9416,9417],{"xmlns":890},[892,9418,9419,9423],{},[895,9420,9421],{},[898,9422,4478],{},[902,9424,4478],{"encoding":904}," z ",[883,9427,9429],{"className":9428},[886],[888,9430,9431],{"xmlns":890},[892,9432,9433,9437],{},[895,9434,9435],{},[1712,9436,5771],{},[902,9438,9439],{"encoding":904},"0{,}5",[883,9441,9443],{"className":9442},[886],[888,9444,9445],{"xmlns":890},[892,9446,9447,9452],{},[895,9448,9449],{},[1712,9450,9451],{},"0,6",[902,9453,9454],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,9458,9460],{"className":9459},[886],[888,9461,9462],{"xmlns":890,"display":2004},[892,9463,9464,9543],{},[895,9465,9466,9474,9476,9478,9480,9482,9484,9510,9512,9514,9516,9518,9520,9530,9533,9536,9538,9540],{},[7204,9467,9468,9470,9472],{},[898,9469,1878],{},[898,9471,4478],{},[1716,9473,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,9475,8508],{},[898,9477,5198],{},[898,9479,4478],{},[1716,9481,1913],{},[1716,9483,2760],{},[2750,9485,9486,9494],{},[895,9487,9488,9490,9492],{},[898,9489,1952],{},[1716,9491,2760],{},[898,9493,5198],{},[895,9495,9496,9498,9500,9502,9504],{},[1716,9497,1920],{"stretchy":1919},[898,9499,4478],{},[1716,9501,2760],{},[898,9503,207],{},[3074,9505,9506,9508],{},[1716,9507,1925],{"stretchy":1919},[1712,9509,1726],{},[2074,9511,8508],{},[898,9513,5198],{},[898,9515,4478],{},[1716,9517,1913],{},[1716,9519,2760],{},[2750,9521,9522,9524],{},[1712,9523,2946],{},[3074,9525,9526,9528],{},[1712,9527,9398],{},[1712,9529,1726],{},[1716,9531,9532],{},"⋅",[1712,9534,9535],{},"0,1",[1716,9537,8490],{},[1716,9539,2760],{},[1712,9541,9542],{},"0,245.",[902,9544,9545],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,9547,9548,9549,1853],{},"Nové rovnovážné množství ",[883,9550,9552],{"className":9551},[886],[888,9553,9554],{"xmlns":890},[892,9555,9556,9581],{},[895,9557,9558,9566,9568,9571,9573,9576,9578],{},[7204,9559,9560,9562,9564],{},[898,9561,1878],{},[1712,9563,1714],{},[898,9565,1805],{},[1716,9567,8490],{},[1712,9569,9570],{},"8,571",[1716,9572,2760],{},[1712,9574,9575],{},"0,245",[1716,9577,1913],{},[1712,9579,9580],{},"8,326",[902,9582,9583],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,9585,9586,9671],{},[38,9587,9588,9589,1343,9609,1343,9631,1343,9651,1853],{},"(b) Současné změny ",[883,9590,9592],{"className":9591},[886],[888,9593,9594],{"xmlns":890},[892,9595,9596,9606],{},[895,9597,9598,9600,9602,9604],{},[898,9599,5198],{},[898,9601,207],{},[1716,9603,1913],{},[1712,9605,5771],{},[902,9607,9608],{"encoding":904},"da = 0{,}5",[883,9610,9612],{"className":9611},[886],[888,9613,9614],{"xmlns":890},[892,9615,9616,9628],{},[895,9617,9618,9620,9622,9624,9626],{},[898,9619,5198],{},[898,9621,1952],{},[1716,9623,1913],{},[1716,9625,2760],{},[1712,9627,6985],{},[902,9629,9630],{"encoding":904},"db = -5",[883,9632,9634],{"className":9633},[886],[888,9635,9636],{"xmlns":890},[892,9637,9638,9648],{},[895,9639,9640,9642,9644,9646],{},[898,9641,5198],{},[898,9643,4478],{},[1716,9645,1913],{},[1712,9647,9535],{},[902,9649,9650],{"encoding":904},"dc = 0{,}1",[883,9652,9654],{"className":9653},[886],[888,9655,9656],{"xmlns":890},[892,9657,9658,9668],{},[895,9659,9660,9662,9664,9666],{},[898,9661,5198],{},[898,9663,5198],{},[1716,9665,1913],{},[1712,9667,1714],{},[902,9669,9670],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,9673,9675],{"className":9674},[886],[888,9676,9677],{"xmlns":890,"display":2004},[892,9678,9679,9822],{},[2008,9680,9681,9763,9799],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,9682,9683,9693],{},[2015,9684,9685],{},[2747,9686,9687],{"scriptlevel":2505,"displaystyle":1718},[895,9688,9689,9691],{},[898,9690,8485],{"mathvariant":2068},[898,9692,1878],{},[2015,9694,9695],{},[2747,9696,9697],{"scriptlevel":2505,"displaystyle":1718},[895,9698,9699,9701,9703,9713,9715,9717,9719,9725,9727,9729,9731,9733,9735,9737,9747,9749,9751,9753,9759,9761],{},[895,9700],{},[1716,9702,8490],{},[2750,9704,9705,9707],{},[1712,9706,2946],{},[3074,9708,9709,9711],{},[1712,9710,9398],{},[1712,9712,1726],{},[1716,9714,9532],{},[1712,9716,5771],{},[1716,9718,1949],{},[2750,9720,9721,9723],{},[1712,9722,1714],{},[1712,9724,9398],{},[1716,9726,9532],{},[1716,9728,1920],{"stretchy":1919},[1716,9730,2760],{},[1712,9732,6985],{},[1716,9734,1925],{"stretchy":1919},[1716,9736,2760],{},[2750,9738,9739,9741],{},[1712,9740,2946],{},[3074,9742,9743,9745],{},[1712,9744,9398],{},[1712,9746,1726],{},[1716,9748,9532],{},[1712,9750,9535],{},[1716,9752,2760],{},[2750,9754,9755,9757],{},[1712,9756,1714],{},[1712,9758,9398],{},[1716,9760,9532],{},[1712,9762,1714],{},[2012,9764,9765,9771],{},[2015,9766,9767],{},[2747,9768,9769],{"scriptlevel":2505,"displaystyle":1718},[895,9770],{},[2015,9772,9773],{},[2747,9774,9775],{"scriptlevel":2505,"displaystyle":1718},[895,9776,9777,9779,9781,9784,9786,9789,9791,9794,9796],{},[895,9778],{},[1716,9780,1913],{},[1712,9782,9783],{},"1,2245",[1716,9785,2760],{},[1712,9787,9788],{},"1,4286",[1716,9790,2760],{},[1712,9792,9793],{},"0,2449",[1716,9795,2760],{},[1712,9797,9798],{},"0,2857",[2012,9800,9801,9807],{},[2015,9802,9803],{},[2747,9804,9805],{"scriptlevel":2505,"displaystyle":1718},[895,9806],{},[2015,9808,9809],{},[2747,9810,9811],{"scriptlevel":2505,"displaystyle":1718},[895,9812,9813,9815,9817,9819],{},[895,9814],{},[1716,9816,8490],{},[1716,9818,2760],{},[1712,9820,9821],{},"0,735.",[902,9823,9824],{"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}",[724,9826,9827,9828,1853],{},"Tedy ",[883,9829,9831],{"className":9830},[886],[888,9832,9833],{"xmlns":890},[892,9834,9835,9859],{},[895,9836,9837,9845,9847,9849,9851,9854,9856],{},[7204,9838,9839,9841,9843],{},[898,9840,1878],{},[1712,9842,1714],{},[898,9844,1805],{},[1716,9846,8490],{},[1712,9848,9570],{},[1716,9850,2760],{},[1712,9852,9853],{},"0,735",[1716,9855,1913],{},[1712,9857,9858],{},"7,836",[902,9860,9861],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1635,9863,9864],{},[724,9865,9866,9868,9869,9892,9893,9915],{},[883,9867,2233],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,9870,9872],{"className":9871},[886],[888,9873,9874],{"xmlns":890},[892,9875,9876,9889],{},[895,9877,9878,9880,9882,9884,9886],{},[898,9879,8485],{"mathvariant":2068},[898,9881,1878],{},[1716,9883,8490],{},[1716,9885,2760],{},[1712,9887,9888],{},"2,69",[902,9890,9891],{"encoding":904},"\\Delta Q \\approx -2{,}69",", ta však neodpovídá přepočtu parciálních derivací podle (2.11) a (2.12). Správná hodnota při uvedených změnách je ",[883,9894,9896],{"className":9895},[886],[888,9897,9898],{"xmlns":890},[892,9899,9900,9912],{},[895,9901,9902,9904,9906,9908,9910],{},[898,9903,8485],{"mathvariant":2068},[898,9905,1878],{},[1716,9907,8490],{},[1716,9909,2760],{},[1712,9911,9853],{},[902,9913,9914],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,9917,9918],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[1855,9920],{},[115,9922,820],{"id":9923},"přebytek-spotřebitele-a-výrobce",[1635,9925,9926],{},[724,9927,9928,9930,9931,1994,9934,8086,9951,1994,9954,9970,9971,1853],{},[883,9929,1641],{}," TL;DR\n",[38,9932,9933],{},"Přebytek spotřebitele",[883,9935,9937],{"className":9936},[886],[888,9938,9939],{"xmlns":890},[892,9940,9941,9948],{},[895,9942,9943,9946],{},[898,9944,9945],{},"C",[898,9947,5352],{},[902,9949,9950],{"encoding":904},"CS",[38,9952,9953],{},"přebytek výrobce",[883,9955,9957],{"className":9956},[886],[888,9958,9959],{"xmlns":890},[892,9960,9961,9967],{},[895,9962,9963,9965],{},[898,9964,1690],{},[898,9966,5352],{},[902,9968,9969],{"encoding":904},"PS",") jsou míry čistého prospěchu stran trhu, definované pomocí určitého integrálu a geometricky odpovídající plochám mezi rovnovážnou cenou a příslušnou křivkou. Podrobný výklad je na samostatné stránce ",[207,9972,9974],{"className":9973,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,9976,9977],{},[3682,9978],{"alt":9979,"className":9980,"src":9981},"imek-prebytky-cs-ps",[210,3686],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,9983,9984,1994,9986,9989],{},[38,9985,9933],{},[614,9987,9988],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,9991,9993],{"className":9992},[886],[888,9994,9995],{"xmlns":890,"display":2004},[892,9996,9997,10075],{},[2008,9998,9999],{"width":2010},[2012,10000,10001,10003,10068,10070],{},[2015,10002],{"width":2017},[2015,10004,10005],{},[895,10006,10007,10009,10011,10013,10019,10021,10023,10036,10038,10040,10042,10044,10046,10048,10050,10052,10058,10060,10066],{},[898,10008,9945],{},[898,10010,5352],{},[1716,10012,1920],{"stretchy":1919},[1707,10014,10015,10017],{},[898,10016,1878],{},[1712,10018,2505],{},[1716,10020,1925],{"stretchy":1919},[1716,10022,1913],{},[7204,10024,10025,10028,10030],{},[1716,10026,10027],{},"∫",[1712,10029,2505],{},[1707,10031,10032,10034],{},[898,10033,1878],{},[1712,10035,2505],{},[898,10037,1916],{},[1716,10039,1920],{"stretchy":1919},[898,10041,1878],{},[1716,10043,1925],{"stretchy":1919},[2074,10045,8508],{},[898,10047,5198],{},[898,10049,1878],{},[1716,10051,2760],{},[1707,10053,10054,10056],{},[898,10055,1690],{},[1712,10057,2505],{},[2074,10059,8508],{},[1707,10061,10062,10064],{},[898,10063,1878],{},[1712,10065,2505],{},[898,10067,1853],{"mathvariant":2068},[2015,10069],{"width":2017},[2015,10071,10072],{},[2074,10073,10074],{},"(2.14)",[902,10076,10077],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,10079,10080,1994,10083,10086],{},[38,10081,10082],{},"Přebytek výrobce",[614,10084,10085],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,10088,10090],{"className":10089},[886],[888,10091,10092],{"xmlns":890,"display":2004},[892,10093,10094,10171],{},[2008,10095,10096],{"width":2010},[2012,10097,10098,10100,10164,10166],{},[2015,10099],{"width":2017},[2015,10101,10102],{},[895,10103,10104,10106,10108,10110,10116,10118,10120,10126,10128,10134,10136,10148,10150,10152,10154,10156,10158,10160,10162],{},[898,10105,1690],{},[898,10107,5352],{},[1716,10109,1920],{"stretchy":1919},[1707,10111,10112,10114],{},[898,10113,1878],{},[1712,10115,2505],{},[1716,10117,1925],{"stretchy":1919},[1716,10119,1913],{},[1707,10121,10122,10124],{},[898,10123,1690],{},[1712,10125,2505],{},[2074,10127,8508],{},[1707,10129,10130,10132],{},[898,10131,1878],{},[1712,10133,2505],{},[1716,10135,2760],{},[7204,10137,10138,10140,10142],{},[1716,10139,10027],{},[1712,10141,2505],{},[1707,10143,10144,10146],{},[898,10145,1878],{},[1712,10147,2505],{},[898,10149,5352],{},[1716,10151,1920],{"stretchy":1919},[898,10153,1878],{},[1716,10155,1925],{"stretchy":1919},[2074,10157,8508],{},[898,10159,5198],{},[898,10161,1878],{},[898,10163,1853],{"mathvariant":2068},[2015,10165],{"width":2017},[2015,10167,10168],{},[2074,10169,10170],{},"(2.15)",[902,10172,10173],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,10175,10176,10177,1853],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,10178,10180],{"className":10179,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[1855,10182],{},[115,10184,10186],{"id":10185},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,10188,10189,10220,10225,10231,10259,10265,10294,10300,10381,10407],{},[123,10190,10191,10193,10194,10219],{},[38,10192,2854],{}," — lineární poptávka ",[883,10195,10197],{"className":10196},[886],[888,10198,10199],{"xmlns":890},[892,10200,10201,10217],{},[895,10202,10203,10205,10207,10209,10211,10213,10215],{},[898,10204,1690],{},[1716,10206,1913],{},[1716,10208,2760],{},[1712,10210,1726],{},[898,10212,1878],{},[1716,10214,1949],{},[1712,10216,2884],{},[902,10218,2887],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,10221,10222,10224],{},[38,10223,3178],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,10226,10227,10230],{},[38,10228,10229],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,10232,10233,10235,10236,1853],{},[38,10234,5750],{}," — lineární nabídka ",[883,10237,10239],{"className":10238},[886],[888,10240,10241],{"xmlns":890},[892,10242,10243,10257],{},[895,10244,10245,10247,10249,10251,10253,10255],{},[898,10246,1690],{},[1716,10248,1913],{},[1712,10250,5771],{},[898,10252,1878],{},[1716,10254,1949],{},[1712,10256,5778],{},[902,10258,5781],{"encoding":904},[123,10260,10261,10264],{},[38,10262,10263],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,10266,10267,10270,10271,1853],{},[38,10268,10269],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,10272,10274],{"className":10273},[886],[888,10275,10276],{"xmlns":890},[892,10277,10278,10292],{},[895,10279,10280,10282,10284,10286,10288,10290],{},[898,10281,1805],{},[1716,10283,2502],{"stretchy":1919},[1712,10285,6849],{},[1716,10287,1719],{"separator":1718},[1712,10289,6908],{},[1716,10291,2516],{"stretchy":1919},[902,10293,6936],{"encoding":904},[123,10295,10296,10299],{},[38,10297,10298],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,10301,10302,10305,10306,10323,10324,1343,10349,10376,10377,10380],{},[38,10303,10304],{},"Příklad 2.9"," — daň ",[883,10307,10309],{"className":10308},[886],[888,10310,10311],{"xmlns":890},[892,10312,10313,10321],{},[895,10314,10315,10317,10319],{},[898,10316,4164],{},[1716,10318,1913],{},[1712,10320,6231],{},[902,10322,6234],{"encoding":904}," na výrobce; rozklad ",[883,10325,10327],{"className":10326},[886],[888,10328,10329],{"xmlns":890},[892,10330,10331,10347],{},[895,10332,10333,10343,10345],{},[1707,10334,10335,10337],{},[898,10336,4164],{},[895,10338,10339,10341],{},[898,10340,7658],{},[898,10342,724],{},[1716,10344,1913],{},[1712,10346,1726],{},[902,10348,7958],{"encoding":904},[883,10350,10352],{"className":10351},[886],[888,10353,10354],{"xmlns":890},[892,10355,10356,10374],{},[895,10357,10358,10370,10372],{},[1707,10359,10360,10362],{},[898,10361,4164],{},[895,10363,10364,10366,10368],{},[898,10365,7681],{},[898,10367,7684],{},[898,10369,2098],{},[1716,10371,1913],{},[1712,10373,6849],{},[902,10375,7987],{"encoding":904},". (Viz ",[207,10378,7703],{"className":10379,"dataFsResolvedFilePath":809,"href":810},[210],".)",[123,10382,10383,10305,10386,10403,10404,10380],{},[38,10384,10385],{},"Příklad 2.10",[883,10387,10389],{"className":10388},[886],[888,10390,10391],{"xmlns":890},[892,10392,10393,10401],{},[895,10394,10395,10397,10399],{},[898,10396,4164],{},[1716,10398,1913],{},[1712,10400,6231],{},[902,10402,6234],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,10405,7703],{"className":10406,"dataFsResolvedFilePath":809,"href":810},[210],[123,10408,10409,10412],{},[38,10410,10411],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[1855,10414],{},[115,10416,10418],{"id":10417},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,10420,10422],{"id":10421},"základní-analýza-poptávky","Základní analýza poptávky",[724,10424,10425,10428,10429,10464,10465,10491],{},[38,10426,10427],{},"2.1"," Je dána poptávka ",[883,10430,10432],{"className":10431},[886],[888,10433,10434],{"xmlns":890},[892,10435,10436,10461],{},[895,10437,10438,10440,10442,10444,10446,10448,10450,10452,10455,10457,10459],{},[898,10439,1878],{},[1716,10441,1913],{},[898,10443,1916],{},[1716,10445,1920],{"stretchy":1919},[898,10447,1690],{},[1716,10449,1925],{"stretchy":1919},[1716,10451,1913],{},[1712,10453,10454],{},"75",[1716,10456,2760],{},[1712,10458,6985],{},[898,10460,1690],{},[902,10462,10463],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,10466,10468],{"className":10467},[886],[888,10469,10470],{"xmlns":890},[892,10471,10472,10488],{},[895,10473,10474,10476,10478,10480,10482,10484,10486],{},[1712,10475,2505],{},[1716,10477,1719],{"separator":1718},[1712,10479,6985],{},[1716,10481,1719],{"separator":1718},[1712,10483,2998],{},[1716,10485,1719],{"separator":1718},[1712,10487,3221],{},[902,10489,10490],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,10493,10494,10497,10498,10516,10517,1998],{},[38,10495,10496],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,10499,10501],{"className":10500},[886],[888,10502,10503],{"xmlns":890},[892,10504,10505,10513],{},[895,10506,10507,10509,10511],{},[898,10508,1690],{},[1716,10510,1719],{"separator":1718},[898,10512,1878],{},[902,10514,10515],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,10518,10520],{"className":10519},[886],[888,10521,10522],{"xmlns":890},[892,10523,10524,10540],{},[895,10525,10526,10528,10530,10532,10534,10536,10538],{},[898,10527,207],{},[1716,10529,1719],{"separator":1718},[898,10531,1952],{},[1716,10533,1719],{"separator":1718},[898,10535,4478],{},[1716,10537,2716],{},[1712,10539,2505],{},[902,10541,10542],{"encoding":904},"a, b, c > 0",[120,10544,10545,10578,10610,10645,10676,10711],{},[123,10546,10547,10548],{},"(a) ",[883,10549,10551],{"className":10550},[886],[888,10552,10553],{"xmlns":890},[892,10554,10555,10575],{},[895,10556,10557,10559,10561],{},[898,10558,1878],{},[1716,10560,1913],{},[2747,10562,10563],{"scriptlevel":2505,"displaystyle":1718},[2750,10564,10565,10567],{},[898,10566,207],{},[895,10568,10569,10571,10573],{},[898,10570,1690],{},[1716,10572,1949],{},[898,10574,4478],{},[902,10576,10577],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,10579,10580,10581],{},"(b) ",[883,10582,10584],{"className":10583},[886],[888,10585,10586],{"xmlns":890},[892,10587,10588,10607],{},[895,10589,10590,10592,10594],{},[898,10591,1878],{},[1716,10593,1913],{},[10595,10596,10597],"msqrt",{},[895,10598,10599,10601,10603,10605],{},[898,10600,207],{},[1716,10602,2760],{},[898,10604,1952],{},[898,10606,1878],{},[902,10608,10609],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,10611,10612,10613],{},"(c) ",[883,10614,10616],{"className":10615},[886],[888,10617,10618],{"xmlns":890},[892,10619,10620,10642],{},[895,10621,10622,10624,10626],{},[898,10623,1878],{},[1716,10625,1913],{},[2747,10627,10628],{"scriptlevel":2505,"displaystyle":1718},[2750,10629,10630,10640],{},[895,10631,10632,10634,10636],{},[898,10633,207],{},[1716,10635,2760],{},[10595,10637,10638],{},[898,10639,1690],{},[898,10641,1952],{},[902,10643,10644],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,10646,10647,10648],{},"(d) ",[883,10649,10651],{"className":10650},[886],[888,10652,10653],{"xmlns":890},[892,10654,10655,10673],{},[895,10656,10657,10659,10661,10663,10665,10667],{},[898,10658,1690],{},[1716,10660,1913],{},[898,10662,207],{},[1716,10664,2760],{},[898,10666,1952],{},[3074,10668,10669,10671],{},[898,10670,1878],{},[1712,10672,1726],{},[902,10674,10675],{"encoding":904},"P = a - bQ^2",[123,10677,10678,10679],{},"(e) ",[883,10680,10682],{"className":10681},[886],[888,10683,10684],{"xmlns":890},[892,10685,10686,10708],{},[895,10687,10688,10690,10692,10694,10704,10706],{},[898,10689,1878],{},[1716,10691,1913],{},[898,10693,1952],{},[3074,10695,10696,10698],{},[898,10697,1690],{},[895,10699,10700,10702],{},[1716,10701,2760],{},[898,10703,207],{},[1716,10705,1949],{},[898,10707,4478],{},[902,10709,10710],{"encoding":904},"Q = bP^{-a} + c",[123,10712,10713,10714],{},"(f) ",[883,10715,10717],{"className":10716},[886],[888,10718,10719],{"xmlns":890},[892,10720,10721,10744],{},[895,10722,10723,10725,10727,10729,10731],{},[898,10724,1878],{},[1716,10726,1913],{},[898,10728,207],{},[1716,10730,9532],{},[3074,10732,10733,10736],{},[898,10734,10735],{},"e",[895,10737,10738,10740,10742],{},[1716,10739,2760],{},[898,10741,1952],{},[898,10743,1690],{},[902,10745,10746],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,10748,10749,10752],{},[38,10750,10751],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,10754,10755,10758,10761],{},[123,10756,10757],{},"(a) Cena substitutu.",[123,10759,10760],{},"(b) Cena komplementu.",[123,10762,10763],{},"(c) Výdaje na reklamu.",[724,10765,10766,10428,10769,10803,10804,10832],{},[38,10767,10768],{},"2.4",[883,10770,10772],{"className":10771},[886],[888,10773,10774],{"xmlns":890},[892,10775,10776,10800],{},[895,10777,10778,10780,10782,10784,10786,10788,10790,10792,10794,10796,10798],{},[898,10779,1690],{},[1716,10781,1913],{},[898,10783,1916],{},[1716,10785,1920],{"stretchy":1919},[898,10787,1878],{},[1716,10789,1925],{"stretchy":1919},[1716,10791,1913],{},[1712,10793,6804],{},[1716,10795,2760],{},[1712,10797,1726],{},[898,10799,1878],{},[902,10801,10802],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,10805,10807],{"className":10806},[886],[888,10808,10809],{"xmlns":890},[892,10810,10811,10829],{},[895,10812,10813,10815,10817,10823,10825,10827],{},[898,10814,1690],{},[1716,10816,1913],{},[3074,10818,10819,10821],{},[898,10820,1916],{},[1716,10822,3080],{},[1716,10824,1920],{"stretchy":1919},[898,10826,1878],{},[1716,10828,1925],{"stretchy":1919},[902,10830,10831],{"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.",[724,10834,10835,10838],{},[38,10836,10837],{},"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:",[120,10840,10841,10927,11003,11089,11177],{},[123,10842,10547,10843,1343,10885,1853],{},[883,10844,10846],{"className":10845},[886],[888,10847,10848],{"xmlns":890},[892,10849,10850,10882],{},[895,10851,10852,10859,10861,10863,10865,10867,10874,10876],{},[1707,10853,10854,10857],{},[898,10855,10856],{},"B",[1712,10858,1714],{},[1716,10860,1913],{},[1712,10862,2976],{},[1716,10864,2760],{},[1712,10866,6849],{},[1707,10868,10869,10872],{},[898,10870,10871],{},"A",[1712,10873,1714],{},[1716,10875,1949],{},[1707,10877,10878,10880],{},[898,10879,10871],{},[1712,10881,1726],{},[902,10883,10884],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,10886,10888],{"className":10887},[886],[888,10889,10890],{"xmlns":890},[892,10891,10892,10924],{},[895,10893,10894,10900,10902,10904,10906,10908,10914,10916,10918],{},[1707,10895,10896,10898],{},[898,10897,10856],{},[1712,10899,1726],{},[1716,10901,1913],{},[1712,10903,2998],{},[1716,10905,1949],{},[1712,10907,1726],{},[1707,10909,10910,10912],{},[898,10911,10871],{},[1712,10913,1714],{},[1716,10915,2760],{},[1712,10917,6849],{},[1707,10919,10920,10922],{},[898,10921,10871],{},[1712,10923,1726],{},[902,10925,10926],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,10928,10580,10929,1343,10971,1853],{},[883,10930,10932],{"className":10931},[886],[888,10933,10934],{"xmlns":890},[892,10935,10936,10968],{},[895,10937,10938,10944,10946,10948,10950,10952,10958,10960,10962],{},[1707,10939,10940,10942],{},[898,10941,10856],{},[1712,10943,1714],{},[1716,10945,1913],{},[1712,10947,5808],{},[1716,10949,2760],{},[1712,10951,2998],{},[1707,10953,10954,10956],{},[898,10955,10871],{},[1712,10957,1714],{},[1716,10959,2760],{},[1712,10961,6231],{},[1707,10963,10964,10966],{},[898,10965,10871],{},[1712,10967,1726],{},[902,10969,10970],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,10972,10974],{"className":10973},[886],[888,10975,10976],{"xmlns":890},[892,10977,10978,11000],{},[895,10979,10980,10986,10988,10990,10992,10994],{},[1707,10981,10982,10984],{},[898,10983,10856],{},[1712,10985,1726],{},[1716,10987,1913],{},[1712,10989,3221],{},[1716,10991,2760],{},[1712,10993,2998],{},[1707,10995,10996,10998],{},[898,10997,10871],{},[1712,10999,1726],{},[902,11001,11002],{"encoding":904},"B_2 = 15 - 10A_2",[123,11004,10612,11005,1343,11047,1853],{},[883,11006,11008],{"className":11007},[886],[888,11009,11010],{"xmlns":890},[892,11011,11012,11044],{},[895,11013,11014,11020,11022,11024,11026,11028,11034,11036,11038],{},[1707,11015,11016,11018],{},[898,11017,10856],{},[1712,11019,1714],{},[1716,11021,1913],{},[1712,11023,2946],{},[1716,11025,2760],{},[1712,11027,1726],{},[1707,11029,11030,11032],{},[898,11031,10871],{},[1712,11033,1714],{},[1716,11035,2760],{},[1712,11037,6849],{},[1707,11039,11040,11042],{},[898,11041,10871],{},[1712,11043,1726],{},[902,11045,11046],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,11048,11050],{"className":11049},[886],[888,11051,11052],{"xmlns":890},[892,11053,11054,11086],{},[895,11055,11056,11062,11064,11066,11068,11070,11076,11078,11080],{},[1707,11057,11058,11060],{},[898,11059,10856],{},[1712,11061,1726],{},[1716,11063,1913],{},[1712,11065,3221],{},[1716,11067,1949],{},[1712,11069,1726],{},[1707,11071,11072,11074],{},[898,11073,10871],{},[1712,11075,1714],{},[1716,11077,2760],{},[1712,11079,1726],{},[1707,11081,11082,11084],{},[898,11083,10871],{},[1712,11085,1726],{},[902,11087,11088],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,11090,10647,11091,1343,11135,1853],{},[883,11092,11094],{"className":11093},[886],[888,11095,11096],{"xmlns":890},[892,11097,11098,11132],{},[895,11099,11100,11106,11108,11110,11112,11114,11116,11122,11124,11126],{},[1707,11101,11102,11104],{},[898,11103,10856],{},[1712,11105,1714],{},[1716,11107,1913],{},[1716,11109,2760],{},[1712,11111,2976],{},[1716,11113,2760],{},[1712,11115,1726],{},[1707,11117,11118,11120],{},[898,11119,10871],{},[1712,11121,1714],{},[1716,11123,1949],{},[1712,11125,7072],{},[1707,11127,11128,11130],{},[898,11129,10871],{},[1712,11131,1726],{},[902,11133,11134],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,11136,11138],{"className":11137},[886],[888,11139,11140],{"xmlns":890},[892,11141,11142,11174],{},[895,11143,11144,11150,11152,11154,11156,11158,11164,11166,11168],{},[1707,11145,11146,11148],{},[898,11147,10856],{},[1712,11149,1726],{},[1716,11151,1913],{},[1712,11153,2998],{},[1716,11155,1949],{},[1712,11157,1726],{},[1707,11159,11160,11162],{},[898,11161,10871],{},[1712,11163,1714],{},[1716,11165,2760],{},[1712,11167,1726],{},[1707,11169,11170,11172],{},[898,11171,10871],{},[1712,11173,1726],{},[902,11175,11176],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,11178,10678,11179,1343,11221,1853],{},[883,11180,11182],{"className":11181},[886],[888,11183,11184],{"xmlns":890},[892,11185,11186,11218],{},[895,11187,11188,11194,11196,11198,11200,11202,11208,11210,11212],{},[1707,11189,11190,11192],{},[898,11191,10856],{},[1712,11193,1714],{},[1716,11195,1913],{},[1712,11197,2976],{},[1716,11199,1949],{},[1712,11201,1726],{},[1707,11203,11204,11206],{},[898,11205,10871],{},[1712,11207,1714],{},[1716,11209,1949],{},[1712,11211,6849],{},[1707,11213,11214,11216],{},[898,11215,10871],{},[1712,11217,1726],{},[902,11219,11220],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,11222,11224],{"className":11223},[886],[888,11225,11226],{"xmlns":890},[892,11227,11228,11260],{},[895,11229,11230,11236,11238,11240,11242,11244,11250,11252,11254],{},[1707,11231,11232,11234],{},[898,11233,10856],{},[1712,11235,1726],{},[1716,11237,1913],{},[1712,11239,2973],{},[1716,11241,2760],{},[1712,11243,7072],{},[1707,11245,11246,11248],{},[898,11247,10871],{},[1712,11249,1714],{},[1716,11251,1949],{},[1712,11253,6985],{},[1707,11255,11256,11258],{},[898,11257,10871],{},[1712,11259,1726],{},[902,11261,11262],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,11264,11266],{"id":11265},"základní-analýza-nabídky","Základní analýza nabídky",[724,11268,11269,11272,11273,11308,11309,11331],{},[38,11270,11271],{},"2.6"," Je dána nabídka ",[883,11274,11276],{"className":11275},[886],[888,11277,11278],{"xmlns":890},[892,11279,11280,11305],{},[895,11281,11282,11284,11286,11288,11290,11292,11294,11296,11298,11300,11303],{},[898,11283,1690],{},[1716,11285,1913],{},[898,11287,5352],{},[1716,11289,1920],{"stretchy":1919},[898,11291,1878],{},[1716,11293,1925],{"stretchy":1919},[1716,11295,1913],{},[1712,11297,2976],{},[1716,11299,1949],{},[1712,11301,11302],{},"0,2",[898,11304,1878],{},[902,11306,11307],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,11310,11312],{"className":11311},[886],[888,11313,11314],{"xmlns":890},[892,11315,11316,11328],{},[895,11317,11318,11320,11322,11324,11326],{},[1712,11319,5778],{},[1716,11321,1719],{"separator":1718},[1712,11323,2946],{},[1716,11325,1719],{"separator":1718},[1712,11327,5837],{},[902,11329,11330],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,11333,11334,11337,11338,11355],{},[38,11335,11336],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,11339,11341],{"className":11340},[886],[888,11342,11343],{"xmlns":890},[892,11344,11345,11353],{},[895,11346,11347,11349,11351],{},[898,11348,1690],{},[1716,11350,1719],{"separator":1718},[898,11352,1878],{},[902,11354,10515],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,11357,11358,11384,11412,11445,11479,11515],{},[123,11359,10547,11360],{},[883,11361,11363],{"className":11362},[886],[888,11364,11365],{"xmlns":890},[892,11366,11367,11381],{},[895,11368,11369,11371,11373,11375,11377,11379],{},[898,11370,1690],{},[1716,11372,1913],{},[1712,11374,2946],{},[1716,11376,1949],{},[1712,11378,1726],{},[898,11380,1878],{},[902,11382,11383],{"encoding":904},"P = 30 + 2Q",[123,11385,10580,11386],{},[883,11387,11389],{"className":11388},[886],[888,11390,11391],{"xmlns":890},[892,11392,11393,11409],{},[895,11394,11395,11397,11399,11401,11403,11405,11407],{},[898,11396,1878],{},[1716,11398,1913],{},[1716,11400,2760],{},[1712,11402,7072],{},[1716,11404,1949],{},[1712,11406,6804],{},[898,11408,1690],{},[902,11410,11411],{"encoding":904},"Q = -3 + 12P",[123,11413,10612,11414],{},[883,11415,11417],{"className":11416},[886],[888,11418,11419],{"xmlns":890},[892,11420,11421,11443],{},[895,11422,11423,11425,11427,11433,11435,11437,11439,11441],{},[898,11424,1690],{},[1716,11426,1913],{},[3074,11428,11429,11431],{},[898,11430,1878],{},[1712,11432,1726],{},[1716,11434,1949],{},[1712,11436,6681],{},[898,11438,1878],{},[1716,11440,1949],{},[1712,11442,6688],{},[902,11444,6691],{"encoding":904},[123,11446,10647,11447],{},[883,11448,11450],{"className":11449},[886],[888,11451,11452],{"xmlns":890},[892,11453,11454,11476],{},[895,11455,11456,11458,11460,11466,11468,11470,11472,11474],{},[898,11457,1690],{},[1716,11459,1913],{},[3074,11461,11462,11464],{},[898,11463,1878],{},[1712,11465,1726],{},[1716,11467,1949],{},[1712,11469,1726],{},[898,11471,1878],{},[1716,11473,1949],{},[1712,11475,6804],{},[902,11477,11478],{"encoding":904},"P = Q^2 + 2Q + 12",[123,11480,10678,11481],{},[883,11482,11484],{"className":11483},[886],[888,11485,11486],{"xmlns":890},[892,11487,11488,11512],{},[895,11489,11490,11492,11494,11496,11498,11500,11502,11504,11506],{},[898,11491,1878],{},[1716,11493,1913],{},[1712,11495,6653],{},[1716,11497,1949],{},[1712,11499,6985],{},[898,11501,1690],{},[1716,11503,1949],{},[1712,11505,9535],{},[3074,11507,11508,11510],{},[898,11509,1690],{},[1712,11511,1726],{},[902,11513,11514],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,11516,10713,11517],{},[883,11518,11520],{"className":11519},[886],[888,11521,11522],{"xmlns":890},[892,11523,11524,11549],{},[895,11525,11526,11528,11530,11532,11534,11536,11538,11540,11543],{},[898,11527,1878],{},[1716,11529,1913],{},[1712,11531,7109],{},[1716,11533,1949],{},[1712,11535,9535],{},[898,11537,1690],{},[1716,11539,1949],{},[1712,11541,11542],{},"0,004",[3074,11544,11545,11547],{},[898,11546,1690],{},[1712,11548,1726],{},[902,11550,11551],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,11553,11554,11557],{},[38,11555,11556],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,11559,11560,11563,11566,11569],{},[123,11561,11562],{},"(a) Sníží ceny surovin — vstupů.",[123,11564,11565],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,11567,11568],{},"(c) Zvýší ceny všech energií.",[123,11570,11571],{},"(d) Sníží daňové odvody státu.",[724,11573,11574,11272,11576,11610,11611,11639],{},[38,11575,7931],{},[883,11577,11579],{"className":11578},[886],[888,11580,11581],{"xmlns":890},[892,11582,11583,11607],{},[895,11584,11585,11587,11589,11591,11593,11595,11597,11599,11601,11603,11605],{},[898,11586,1690],{},[1716,11588,1913],{},[898,11590,5352],{},[1716,11592,1920],{"stretchy":1919},[898,11594,1878],{},[1716,11596,1925],{"stretchy":1919},[1716,11598,1913],{},[1712,11600,5771],{},[898,11602,1878],{},[1716,11604,1949],{},[1712,11606,3221],{},[902,11608,11609],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,11612,11614],{"className":11613},[886],[888,11615,11616],{"xmlns":890},[892,11617,11618,11636],{},[895,11619,11620,11622,11624,11630,11632,11634],{},[898,11621,1690],{},[1716,11623,1913],{},[3074,11625,11626,11628],{},[898,11627,5352],{},[1716,11629,3080],{},[1716,11631,1920],{"stretchy":1919},[898,11633,1878],{},[1716,11635,1925],{"stretchy":1919},[902,11637,11638],{"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.",[198,11641,6291],{"id":11642},"tržní-rovnováha-1",[724,11644,11645,11647,11648,11665,11666,2291],{},[38,11646,7991],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,11649,11651],{"className":11650},[886],[888,11652,11653],{"xmlns":890},[892,11654,11655,11663],{},[895,11656,11657],{},[3074,11658,11659,11661],{},[898,11660,1878],{},[898,11662,1805],{},[902,11664,7382],{"encoding":904}," a rovnovážnou cenu ",[883,11667,11669],{"className":11668},[886],[888,11670,11671],{"xmlns":890},[892,11672,11673,11681],{},[895,11674,11675],{},[3074,11676,11677,11679],{},[898,11678,1690],{},[898,11680,1805],{},[902,11682,6432],{"encoding":904},[120,11684,11685,11738,11789,11849],{},[123,11686,10547,11687,1343,11714,1853],{},[883,11688,11690],{"className":11689},[886],[888,11691,11692],{"xmlns":890},[892,11693,11694,11711],{},[895,11695,11696,11698,11700,11702,11704,11706,11708],{},[898,11697,1690],{},[1716,11699,1913],{},[1716,11701,2760],{},[1712,11703,6985],{},[898,11705,1878],{},[1716,11707,1949],{},[1712,11709,11710],{},"80",[902,11712,11713],{"encoding":904},"P = -5Q + 80",[883,11715,11717],{"className":11716},[886],[888,11718,11719],{"xmlns":890},[892,11720,11721,11735],{},[895,11722,11723,11725,11727,11729,11731,11733],{},[898,11724,1690],{},[1716,11726,1913],{},[1712,11728,1726],{},[898,11730,1878],{},[1716,11732,1949],{},[1712,11734,2998],{},[902,11736,11737],{"encoding":904},"P = 2Q + 10",[123,11739,10580,11740,1343,11766,1853],{},[883,11741,11743],{"className":11742},[886],[888,11744,11745],{"xmlns":890},[892,11746,11747,11763],{},[895,11748,11749,11751,11753,11755,11757,11759,11761],{},[898,11750,1878],{},[1716,11752,1913],{},[1716,11754,2760],{},[1712,11756,5771],{},[898,11758,1690],{},[1716,11760,1949],{},[1712,11762,5778],{},[902,11764,11765],{"encoding":904},"Q = -0{,}5P + 25",[883,11767,11769],{"className":11768},[886],[888,11770,11771],{"xmlns":890},[892,11772,11773,11787],{},[895,11774,11775,11777,11779,11781,11783,11785],{},[898,11776,1878],{},[1716,11778,1913],{},[1712,11780,1726],{},[898,11782,1690],{},[1716,11784,2760],{},[1712,11786,5808],{},[902,11788,5811],{"encoding":904},[123,11790,10612,11791,1343,11818,1853],{},[883,11792,11794],{"className":11793},[886],[888,11795,11796],{"xmlns":890},[892,11797,11798,11815],{},[895,11799,11800,11802,11804,11806,11808,11810,11812],{},[898,11801,1690],{},[1716,11803,1913],{},[1716,11805,2760],{},[1712,11807,6849],{},[898,11809,1878],{},[1716,11811,1949],{},[1712,11813,11814],{},"120",[902,11816,11817],{"encoding":904},"P = -4Q + 120",[883,11819,11821],{"className":11820},[886],[888,11822,11823],{"xmlns":890},[892,11824,11825,11846],{},[895,11826,11827,11829,11831,11839,11841,11843],{},[898,11828,1690],{},[1716,11830,1913],{},[2747,11832,11833],{"scriptlevel":2505,"displaystyle":1919},[2750,11834,11835,11837],{},[1712,11836,1714],{},[1712,11838,7072],{},[898,11840,1878],{},[1716,11842,1949],{},[1712,11844,11845],{},"29",[902,11847,11848],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,11850,10647,11851,1343,11880,1853],{},[883,11852,11854],{"className":11853},[886],[888,11855,11856],{"xmlns":890},[892,11857,11858,11877],{},[895,11859,11860,11862,11864,11866,11872,11874],{},[898,11861,1690],{},[1716,11863,1913],{},[1716,11865,2760],{},[3074,11867,11868,11870],{},[898,11869,1878],{},[1712,11871,1726],{},[1716,11873,1949],{},[1712,11875,11876],{},"52",[902,11878,11879],{"encoding":904},"P = -Q^2 + 52",[883,11881,11883],{"className":11882},[886],[888,11884,11885],{"xmlns":890},[892,11886,11887,11905],{},[895,11888,11889,11891,11893,11895,11901,11903],{},[898,11890,1690],{},[1716,11892,1913],{},[1712,11894,1726],{},[3074,11896,11897,11899],{},[898,11898,1878],{},[1712,11900,1726],{},[1716,11902,1949],{},[1712,11904,2998],{},[902,11906,11907],{"encoding":904},"P = 2Q^2 + 10",[724,11909,11910,11913,11914,11944,11945,11975],{},[38,11911,11912],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,11915,11917],{"className":11916},[886],[888,11918,11919],{"xmlns":890},[892,11920,11921,11941],{},[895,11922,11923,11931,11933],{},[7204,11924,11925,11927,11929],{},[898,11926,1878],{},[1712,11928,1714],{},[898,11930,1805],{},[1716,11932,1719],{"separator":1718},[7204,11934,11935,11937,11939],{},[898,11936,1878],{},[1712,11938,1726],{},[898,11940,1805],{},[902,11942,11943],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,11946,11948],{"className":11947},[886],[888,11949,11950],{"xmlns":890},[892,11951,11952,11972],{},[895,11953,11954,11962,11964],{},[7204,11955,11956,11958,11960],{},[898,11957,1690],{},[1712,11959,1714],{},[898,11961,1805],{},[1716,11963,1719],{"separator":1718},[7204,11965,11966,11968,11970],{},[898,11967,1690],{},[1712,11969,1726],{},[898,11971,1805],{},[902,11973,11974],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,11977,11978,12130],{},[123,11979,10547,11980,1343,12020,1343,12062,1343,12096,1853],{},[883,11981,11983],{"className":11982},[886],[888,11984,11985],{"xmlns":890},[892,11986,11987,12017],{},[895,11988,11989,11995,11997,11999,12001,12003,12009,12011],{},[1707,11990,11991,11993],{},[898,11992,1878],{},[1712,11994,1714],{},[1716,11996,1913],{},[1712,11998,2998],{},[1716,12000,2760],{},[1712,12002,1726],{},[1707,12004,12005,12007],{},[898,12006,1690],{},[1712,12008,1714],{},[1716,12010,1949],{},[1707,12012,12013,12015],{},[898,12014,1690],{},[1712,12016,1726],{},[902,12018,12019],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,12021,12023],{"className":12022},[886],[888,12024,12025],{"xmlns":890},[892,12026,12027,12059],{},[895,12028,12029,12035,12037,12039,12041,12043,12049,12051,12053],{},[1707,12030,12031,12033],{},[898,12032,1878],{},[1712,12034,1726],{},[1716,12036,1913],{},[1712,12038,6985],{},[1716,12040,1949],{},[1712,12042,1726],{},[1707,12044,12045,12047],{},[898,12046,1690],{},[1712,12048,1714],{},[1716,12050,2760],{},[1712,12052,1726],{},[1707,12054,12055,12057],{},[898,12056,1690],{},[1712,12058,1726],{},[902,12060,12061],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,12063,12065],{"className":12064},[886],[888,12066,12067],{"xmlns":890},[892,12068,12069,12093],{},[895,12070,12071,12077,12079,12081,12083,12085,12087],{},[1707,12072,12073,12075],{},[898,12074,1878],{},[1712,12076,1714],{},[1716,12078,1913],{},[1716,12080,2760],{},[1712,12082,7072],{},[1716,12084,1949],{},[1712,12086,1726],{},[1707,12088,12089,12091],{},[898,12090,1690],{},[1712,12092,1714],{},[902,12094,12095],{"encoding":904},"Q_1 = -3 + 2P_1",[883,12097,12099],{"className":12098},[886],[888,12100,12101],{"xmlns":890},[892,12102,12103,12127],{},[895,12104,12105,12111,12113,12115,12117,12119,12121],{},[1707,12106,12107,12109],{},[898,12108,1878],{},[1712,12110,1726],{},[1716,12112,1913],{},[1716,12114,2760],{},[1712,12116,1726],{},[1716,12118,1949],{},[1712,12120,7072],{},[1707,12122,12123,12125],{},[898,12124,1690],{},[1712,12126,1726],{},[902,12128,12129],{"encoding":904},"Q_2 = -2 + 3P_2",[123,12131,10580,12132,1343,12173,1343,12215,1343,12247,1853],{},[883,12133,12135],{"className":12134},[886],[888,12136,12137],{"xmlns":890},[892,12138,12139,12170],{},[895,12140,12141,12147,12149,12152,12154,12156,12162,12164],{},[1707,12142,12143,12145],{},[898,12144,1878],{},[1712,12146,1714],{},[1716,12148,1913],{},[1712,12150,12151],{},"100",[1716,12153,2760],{},[1712,12155,1726],{},[1707,12157,12158,12160],{},[898,12159,1690],{},[1712,12161,1714],{},[1716,12163,1949],{},[1707,12165,12166,12168],{},[898,12167,1690],{},[1712,12169,1726],{},[902,12171,12172],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,12174,12176],{"className":12175},[886],[888,12177,12178],{"xmlns":890},[892,12179,12180,12212],{},[895,12181,12182,12188,12190,12192,12194,12196,12202,12204,12206],{},[1707,12183,12184,12186],{},[898,12185,1878],{},[1712,12187,1726],{},[1716,12189,1913],{},[1712,12191,6985],{},[1716,12193,1949],{},[1712,12195,1726],{},[1707,12197,12198,12200],{},[898,12199,1690],{},[1712,12201,1714],{},[1716,12203,2760],{},[1712,12205,7072],{},[1707,12207,12208,12210],{},[898,12209,1690],{},[1712,12211,1726],{},[902,12213,12214],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,12216,12218],{"className":12217},[886],[888,12219,12220],{"xmlns":890},[892,12221,12222,12244],{},[895,12223,12224,12230,12232,12234,12236,12238],{},[1707,12225,12226,12228],{},[898,12227,1878],{},[1712,12229,1714],{},[1716,12231,1913],{},[1716,12233,2760],{},[1712,12235,2998],{},[1716,12237,1949],{},[1707,12239,12240,12242],{},[898,12241,1690],{},[1712,12243,1714],{},[902,12245,12246],{"encoding":904},"Q_1 = -10 + P_1",[883,12248,12250],{"className":12249},[886],[888,12251,12252],{"xmlns":890},[892,12253,12254,12276],{},[895,12255,12256,12262,12264,12266,12268,12270],{},[1707,12257,12258,12260],{},[898,12259,1878],{},[1712,12261,1726],{},[1716,12263,1913],{},[1712,12265,6985],{},[1716,12267,1949],{},[1712,12269,6231],{},[1707,12271,12272,12274],{},[898,12273,1690],{},[1712,12275,1726],{},[902,12277,12278],{"encoding":904},"Q_2 = 5 + 6P_2",[724,12280,12281,12284,12285,1343,12333,1343,12379,12430,12431,1343,12463,1343,12497,2772,12531,2247,12550,12568,12569,12582,12583,12609,12610,11944,12650,1853],{},[38,12282,12283],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,12286,12288],{"className":12287},[886],[888,12289,12290],{"xmlns":890},[892,12291,12292,12330],{},[895,12293,12294,12300,12302,12304,12306,12312,12314,12316,12322,12324],{},[1707,12295,12296,12298],{},[898,12297,1878],{},[1712,12299,1714],{},[1716,12301,1913],{},[1712,12303,3221],{},[1716,12305,2760],{},[1707,12307,12308,12310],{},[898,12309,1690],{},[1712,12311,1714],{},[1716,12313,1949],{},[1712,12315,1726],{},[1707,12317,12318,12320],{},[898,12319,1690],{},[1712,12321,1726],{},[1716,12323,1949],{},[1707,12325,12326,12328],{},[898,12327,1690],{},[1712,12329,7072],{},[902,12331,12332],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,12334,12336],{"className":12335},[886],[888,12337,12338],{"xmlns":890},[892,12339,12340,12376],{},[895,12341,12342,12348,12350,12352,12354,12360,12362,12368,12370],{},[1707,12343,12344,12346],{},[898,12345,1878],{},[1712,12347,1726],{},[1716,12349,1913],{},[1712,12351,7141],{},[1716,12353,1949],{},[1707,12355,12356,12358],{},[898,12357,1690],{},[1712,12359,1714],{},[1716,12361,2760],{},[1707,12363,12364,12366],{},[898,12365,1690],{},[1712,12367,1726],{},[1716,12369,2760],{},[1707,12371,12372,12374],{},[898,12373,1690],{},[1712,12375,7072],{},[902,12377,12378],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,12380,12382],{"className":12381},[886],[888,12383,12384],{"xmlns":890},[892,12385,12386,12427],{},[895,12387,12388,12394,12396,12399,12401,12403,12409,12411,12417,12419,12421],{},[1707,12389,12390,12392],{},[898,12391,1878],{},[1712,12393,7072],{},[1716,12395,1913],{},[1712,12397,12398],{},"8",[1716,12400,1949],{},[1712,12402,1726],{},[1707,12404,12405,12407],{},[898,12406,1690],{},[1712,12408,1714],{},[1716,12410,2760],{},[1707,12412,12413,12415],{},[898,12414,1690],{},[1712,12416,1726],{},[1716,12418,2760],{},[1712,12420,6849],{},[1707,12422,12423,12425],{},[898,12424,1690],{},[1712,12426,7072],{},[902,12428,12429],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,12432,12434],{"className":12433},[886],[888,12435,12436],{"xmlns":890},[892,12437,12438,12460],{},[895,12439,12440,12446,12448,12450,12452,12454],{},[1707,12441,12442,12444],{},[898,12443,1878],{},[1712,12445,1714],{},[1716,12447,1913],{},[1716,12449,2760],{},[1712,12451,7109],{},[1716,12453,1949],{},[1707,12455,12456,12458],{},[898,12457,1690],{},[1712,12459,1714],{},[902,12461,12462],{"encoding":904},"Q_1 = -7 + P_1",[883,12464,12466],{"className":12465},[886],[888,12467,12468],{"xmlns":890},[892,12469,12470,12494],{},[895,12471,12472,12478,12480,12482,12484,12486,12488],{},[1707,12473,12474,12476],{},[898,12475,1878],{},[1712,12477,1726],{},[1716,12479,1913],{},[1716,12481,2760],{},[1712,12483,6849],{},[1716,12485,1949],{},[1712,12487,6849],{},[1707,12489,12490,12492],{},[898,12491,1690],{},[1712,12493,1726],{},[902,12495,12496],{"encoding":904},"Q_2 = -4 + 4P_2",[883,12498,12500],{"className":12499},[886],[888,12501,12502],{"xmlns":890},[892,12503,12504,12528],{},[895,12505,12506,12512,12514,12516,12518,12520,12522],{},[1707,12507,12508,12510],{},[898,12509,1878],{},[1712,12511,7072],{},[1716,12513,1913],{},[1716,12515,2760],{},[1712,12517,6985],{},[1716,12519,1949],{},[1712,12521,1726],{},[1707,12523,12524,12526],{},[898,12525,1690],{},[1712,12527,7072],{},[902,12529,12530],{"encoding":904},"Q_3 = -5 + 2P_3",[883,12532,12534],{"className":12533},[886],[888,12535,12536],{"xmlns":890},[892,12537,12538,12547],{},[895,12539,12540],{},[1707,12541,12542,12544],{},[898,12543,1878],{},[898,12545,12546],{},"i",[902,12548,12549],{"encoding":904},"Q_i",[883,12551,12553],{"className":12552},[886],[888,12554,12555],{"xmlns":890},[892,12556,12557,12565],{},[895,12558,12559],{},[1707,12560,12561,12563],{},[898,12562,1690],{},[898,12564,12546],{},[902,12566,12567],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,12570,12572],{"className":12571},[886],[888,12573,12574],{"xmlns":890},[892,12575,12576,12580],{},[895,12577,12578],{},[898,12579,12546],{},[902,12581,12546],{"encoding":904},"-tého zboží, ",[883,12584,12586],{"className":12585},[886],[888,12587,12588],{"xmlns":890},[892,12589,12590,12606],{},[895,12591,12592,12594,12596,12598,12600,12602,12604],{},[898,12593,12546],{},[1716,12595,1913],{},[1712,12597,1714],{},[1716,12599,1719],{"separator":1718},[1712,12601,1726],{},[1716,12603,1719],{"separator":1718},[1712,12605,7072],{},[902,12607,12608],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,12611,12613],{"className":12612},[886],[888,12614,12615],{"xmlns":890},[892,12616,12617,12647],{},[895,12618,12619,12627,12629,12637,12639],{},[7204,12620,12621,12623,12625],{},[898,12622,1878],{},[1712,12624,1714],{},[898,12626,1805],{},[1716,12628,1719],{"separator":1718},[7204,12630,12631,12633,12635],{},[898,12632,1878],{},[1712,12634,1726],{},[898,12636,1805],{},[1716,12638,1719],{"separator":1718},[7204,12640,12641,12643,12645],{},[898,12642,1878],{},[1712,12644,7072],{},[898,12646,1805],{},[902,12648,12649],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,12651,12653],{"className":12652},[886],[888,12654,12655],{"xmlns":890},[892,12656,12657,12687],{},[895,12658,12659,12667,12669,12677,12679],{},[7204,12660,12661,12663,12665],{},[898,12662,1690],{},[1712,12664,1714],{},[898,12666,1805],{},[1716,12668,1719],{"separator":1718},[7204,12670,12671,12673,12675],{},[898,12672,1690],{},[1712,12674,1726],{},[898,12676,1805],{},[1716,12678,1719],{"separator":1718},[7204,12680,12681,12683,12685],{},[898,12682,1690],{},[1712,12684,7072],{},[898,12686,1805],{},[902,12688,12689],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,12691,12692,12695,12696,12732,12733,1853],{},[38,12693,12694],{},"2.13"," Jsou dány poptávka ",[883,12697,12699],{"className":12698},[886],[888,12700,12701],{"xmlns":890},[892,12702,12703,12729],{},[895,12704,12705,12707,12709,12711,12713,12715,12717,12719,12721,12723,12725,12727],{},[898,12706,1690],{},[1716,12708,1913],{},[898,12710,1916],{},[1716,12712,1920],{"stretchy":1919},[898,12714,1878],{},[1716,12716,1925],{"stretchy":1919},[1716,12718,1913],{},[1716,12720,2760],{},[1712,12722,6849],{},[898,12724,1878],{},[1716,12726,1949],{},[1712,12728,11710],{},[902,12730,12731],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,12734,12736],{"className":12735},[886],[888,12737,12738],{"xmlns":890},[892,12739,12740,12764],{},[895,12741,12742,12744,12746,12748,12750,12752,12754,12756,12758,12760,12762],{},[898,12743,1690],{},[1716,12745,1913],{},[898,12747,5352],{},[1716,12749,1920],{"stretchy":1919},[898,12751,1878],{},[1716,12753,1925],{"stretchy":1919},[1716,12755,1913],{},[1712,12757,7072],{},[898,12759,1878],{},[1716,12761,1949],{},[1712,12763,2998],{},[902,12765,12766],{"encoding":904},"P = S(Q) = 3Q + 10",[120,12768,12769,12806,12870,12930],{},[123,12770,12771,12772,11665,12789,1853],{},"(a) Určete rovnovážné množství ",[883,12773,12775],{"className":12774},[886],[888,12776,12777],{"xmlns":890},[892,12778,12779,12787],{},[895,12780,12781],{},[3074,12782,12783,12785],{},[898,12784,1878],{},[898,12786,1805],{},[902,12788,7382],{"encoding":904},[883,12790,12792],{"className":12791},[886],[888,12793,12794],{"xmlns":890},[892,12795,12796,12804],{},[895,12797,12798],{},[3074,12799,12800,12802],{},[898,12801,1690],{},[898,12803,1805],{},[902,12805,6432],{"encoding":904},[123,12807,12808,12809,12827,12828,12848,12849,12869],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,12810,12812],{"className":12811},[886],[888,12813,12814],{"xmlns":890},[892,12815,12816,12824],{},[895,12817,12818,12820,12822],{},[898,12819,4164],{},[1716,12821,1913],{},[1712,12823,7109],{},[902,12825,12826],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,12829,12831],{"className":12830},[886],[888,12832,12833],{"xmlns":890},[892,12834,12835,12845],{},[895,12836,12837],{},[7204,12838,12839,12841,12843],{},[898,12840,1878],{},[1712,12842,1714],{},[898,12844,1805],{},[902,12846,12847],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,12850,12852],{"className":12851},[886],[888,12853,12854],{"xmlns":890},[892,12855,12856,12866],{},[895,12857,12858],{},[7204,12859,12860,12862,12864],{},[898,12861,1690],{},[1712,12863,1714],{},[898,12865,1805],{},[902,12867,12868],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,12871,12872,12873,12827,12890,12848,12910,12869],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,12874,12876],{"className":12875},[886],[888,12877,12878],{"xmlns":890},[892,12879,12880,12888],{},[895,12881,12882,12884,12886],{},[898,12883,4164],{},[1716,12885,1913],{},[1712,12887,7109],{},[902,12889,12826],{"encoding":904},[883,12891,12893],{"className":12892},[886],[888,12894,12895],{"xmlns":890},[892,12896,12897,12907],{},[895,12898,12899],{},[7204,12900,12901,12903,12905],{},[898,12902,1878],{},[1712,12904,1726],{},[898,12906,1805],{},[902,12908,12909],{"encoding":904},"Q_2^E",[883,12911,12913],{"className":12912},[886],[888,12914,12915],{"xmlns":890},[892,12916,12917,12927],{},[895,12918,12919],{},[7204,12920,12921,12923,12925],{},[898,12922,1690],{},[1712,12924,1726],{},[898,12926,1805],{},[902,12928,12929],{"encoding":904},"P_2^E",[123,12931,12932],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,12934,12935,12936,1853],{},"Viz též ",[207,12937,7703],{"className":12938,"dataFsResolvedFilePath":809,"href":810},[210],[198,12940,8005],{"id":12941},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,12943,12944,12695,12947,12732,12983,1853],{},[38,12945,12946],{},"2.14",[883,12948,12950],{"className":12949},[886],[888,12951,12952],{"xmlns":890},[892,12953,12954,12980],{},[895,12955,12956,12958,12960,12962,12964,12966,12968,12970,12972,12974,12976,12978],{},[898,12957,1690],{},[1716,12959,1913],{},[898,12961,207],{},[898,12963,1878],{},[1716,12965,1949],{},[898,12967,1952],{},[1716,12969,1913],{},[1716,12971,2760],{},[1712,12973,1726],{},[898,12975,1878],{},[1716,12977,1949],{},[1712,12979,5808],{},[902,12981,12982],{"encoding":904},"P = aQ + b = -2Q + 50",[883,12984,12986],{"className":12985},[886],[888,12987,12988],{"xmlns":890},[892,12989,12990,13014],{},[895,12991,12992,12994,12996,12998,13000,13002,13004,13006,13008,13010,13012],{},[898,12993,1690],{},[1716,12995,1913],{},[898,12997,4478],{},[898,12999,1878],{},[1716,13001,1949],{},[898,13003,5198],{},[1716,13005,1913],{},[1712,13007,9451],{},[898,13009,1878],{},[1716,13011,1949],{},[1712,13013,2976],{},[902,13015,13016],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,13018,13019,13055,13058,13144,13197,13278,13332],{},[123,13020,12771,13021,11665,13038,1853],{},[883,13022,13024],{"className":13023},[886],[888,13025,13026],{"xmlns":890},[892,13027,13028,13036],{},[895,13029,13030],{},[3074,13031,13032,13034],{},[898,13033,1878],{},[898,13035,1805],{},[902,13037,7382],{"encoding":904},[883,13039,13041],{"className":13040},[886],[888,13042,13043],{"xmlns":890},[892,13044,13045,13053],{},[895,13046,13047],{},[3074,13048,13049,13051],{},[898,13050,1690],{},[898,13052,1805],{},[902,13054,6432],{"encoding":904},[123,13056,13057],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,13059,13060,13061,13078,13079,9425,13092,3942,13108,13124,13125,1853],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,13062,13064],{"className":13063},[886],[888,13065,13066],{"xmlns":890},[892,13067,13068,13076],{},[895,13069,13070],{},[3074,13071,13072,13074],{},[898,13073,1878],{},[898,13075,1805],{},[902,13077,7382],{"encoding":904}," odpovídající změně ",[883,13080,13082],{"className":13081},[886],[888,13083,13084],{"xmlns":890},[892,13085,13086,13090],{},[895,13087,13088],{},[898,13089,207],{},[902,13091,207],{"encoding":904},[883,13093,13095],{"className":13094},[886],[888,13096,13097],{"xmlns":890},[892,13098,13099,13105],{},[895,13100,13101,13103],{},[1716,13102,2760],{},[1712,13104,1726],{},[902,13106,13107],{"encoding":904},"-2",[883,13109,13111],{"className":13110},[886],[888,13112,13113],{"xmlns":890},[892,13114,13115,13121],{},[895,13116,13117,13119],{},[1716,13118,2760],{},[1712,13120,7072],{},[902,13122,13123],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,13126,13128],{"className":13127},[886],[888,13129,13130],{"xmlns":890},[892,13131,13132,13142],{},[895,13133,13134],{},[7204,13135,13136,13138,13140],{},[898,13137,1878],{},[1712,13139,1714],{},[898,13141,1805],{},[902,13143,12847],{"encoding":904},[123,13145,13146,13147,13078,13164,13177,13178,1853],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,13148,13150],{"className":13149},[886],[888,13151,13152],{"xmlns":890},[892,13153,13154,13162],{},[895,13155,13156],{},[3074,13157,13158,13160],{},[898,13159,1878],{},[898,13161,1805],{},[902,13163,7382],{"encoding":904},[883,13165,13167],{"className":13166},[886],[888,13168,13169],{"xmlns":890},[892,13170,13171,13175],{},[895,13172,13173],{},[898,13174,1952],{},[902,13176,1952],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,13179,13181],{"className":13180},[886],[888,13182,13183],{"xmlns":890},[892,13184,13185,13195],{},[895,13186,13187],{},[7204,13188,13189,13191,13193],{},[898,13190,1878],{},[1712,13192,1726],{},[898,13194,1805],{},[902,13196,12909],{"encoding":904},[123,13198,13199,13200,13078,13217,9425,13230,3942,13243,13124,13258,1853],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,13201,13203],{"className":13202},[886],[888,13204,13205],{"xmlns":890},[892,13206,13207,13215],{},[895,13208,13209],{},[3074,13210,13211,13213],{},[898,13212,1878],{},[898,13214,1805],{},[902,13216,7382],{"encoding":904},[883,13218,13220],{"className":13219},[886],[888,13221,13222],{"xmlns":890},[892,13223,13224,13228],{},[895,13225,13226],{},[898,13227,4478],{},[902,13229,4478],{"encoding":904},[883,13231,13233],{"className":13232},[886],[888,13234,13235],{"xmlns":890},[892,13236,13237,13241],{},[895,13238,13239],{},[1712,13240,9451],{},[902,13242,9454],{"encoding":904},[883,13244,13246],{"className":13245},[886],[888,13247,13248],{"xmlns":890},[892,13249,13250,13255],{},[895,13251,13252],{},[1712,13253,13254],{},"0,8",[902,13256,13257],{"encoding":904},"0{,}8",[883,13259,13261],{"className":13260},[886],[888,13262,13263],{"xmlns":890},[892,13264,13265,13275],{},[895,13266,13267],{},[7204,13268,13269,13271,13273],{},[898,13270,1878],{},[1712,13272,7072],{},[898,13274,1805],{},[902,13276,13277],{"encoding":904},"Q_3^E",[123,13279,13280,13281,13078,13298,13311,13312,1853],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,13282,13284],{"className":13283},[886],[888,13285,13286],{"xmlns":890},[892,13287,13288,13296],{},[895,13289,13290],{},[3074,13291,13292,13294],{},[898,13293,1878],{},[898,13295,1805],{},[902,13297,7382],{"encoding":904},[883,13299,13301],{"className":13300},[886],[888,13302,13303],{"xmlns":890},[892,13304,13305,13309],{},[895,13306,13307],{},[898,13308,5198],{},[902,13310,5198],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,13313,13315],{"className":13314},[886],[888,13316,13317],{"xmlns":890},[892,13318,13319,13329],{},[895,13320,13321],{},[7204,13322,13323,13325,13327],{},[898,13324,1878],{},[1712,13326,6849],{},[898,13328,1805],{},[902,13330,13331],{"encoding":904},"Q_4^E",[123,13333,13334,13335,13352,13353,13366,13367,13380,13381,1343,13397,13380,13410,2247,13424,13380,13437,13452,13453,1853],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,13336,13338],{"className":13337},[886],[888,13339,13340],{"xmlns":890},[892,13341,13342,13350],{},[895,13343,13344],{},[3074,13345,13346,13348],{},[898,13347,1878],{},[898,13349,1805],{},[902,13351,7382],{"encoding":904}," odpovídající změnám ",[883,13354,13356],{"className":13355},[886],[888,13357,13358],{"xmlns":890},[892,13359,13360,13364],{},[895,13361,13362],{},[898,13363,207],{},[902,13365,207],{"encoding":904}," o 1, ",[883,13368,13370],{"className":13369},[886],[888,13371,13372],{"xmlns":890},[892,13373,13374,13378],{},[895,13375,13376],{},[898,13377,1952],{},[902,13379,1952],{"encoding":904}," o ",[883,13382,13384],{"className":13383},[886],[888,13385,13386],{"xmlns":890},[892,13387,13388,13394],{},[895,13389,13390,13392],{},[1716,13391,2760],{},[1712,13393,2998],{},[902,13395,13396],{"encoding":904},"-10",[883,13398,13400],{"className":13399},[886],[888,13401,13402],{"xmlns":890},[892,13403,13404,13408],{},[895,13405,13406],{},[898,13407,4478],{},[902,13409,4478],{"encoding":904},[883,13411,13413],{"className":13412},[886],[888,13414,13415],{"xmlns":890},[892,13416,13417,13421],{},[895,13418,13419],{},[1712,13420,9535],{},[902,13422,13423],{"encoding":904},"0{,}1",[883,13425,13427],{"className":13426},[886],[888,13428,13429],{"xmlns":890},[892,13430,13431,13435],{},[895,13432,13433],{},[898,13434,5198],{},[902,13436,5198],{"encoding":904},[883,13438,13440],{"className":13439},[886],[888,13441,13442],{"xmlns":890},[892,13443,13444,13450],{},[895,13445,13446,13448],{},[1716,13447,2760],{},[1712,13449,2998],{},[902,13451,13396],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,13454,13456],{"className":13455},[886],[888,13457,13458],{"xmlns":890},[892,13459,13460,13470],{},[895,13461,13462],{},[7204,13463,13464,13466,13468],{},[898,13465,1878],{},[1712,13467,6985],{},[898,13469,1805],{},[902,13471,13472],{"encoding":904},"Q_5^E",[724,13474,13475,12695,13478,12732,13501,1853],{},[38,13476,13477],{},"2.15",[883,13479,13481],{"className":13480},[886],[888,13482,13483],{"xmlns":890},[892,13484,13485,13499],{},[895,13486,13487,13489,13491,13493,13495,13497],{},[898,13488,1690],{},[1716,13490,1913],{},[898,13492,207],{},[898,13494,1878],{},[1716,13496,1949],{},[898,13498,1952],{},[902,13500,1955],{"encoding":904},[883,13502,13504],{"className":13503},[886],[888,13505,13506],{"xmlns":890},[892,13507,13508,13522],{},[895,13509,13510,13512,13514,13516,13518,13520],{},[898,13511,1690],{},[1716,13513,1913],{},[898,13515,4478],{},[898,13517,1878],{},[1716,13519,1949],{},[898,13521,5198],{},[902,13523,5201],{"encoding":904},[120,13525,13526,13601,13618,13727,13780,13834],{},[123,13527,13528,13529,13542,13543,13568,13569,13600],{},"(a) Odvoďte redukovaný tvar pro ",[883,13530,13532],{"className":13531},[886],[888,13533,13534],{"xmlns":890},[892,13535,13536,13540],{},[895,13537,13538],{},[898,13539,1690],{},[902,13541,1690],{"encoding":904},". Stanovte podmínky pro ",[883,13544,13546],{"className":13545},[886],[888,13547,13548],{"xmlns":890},[892,13549,13550,13566],{},[895,13551,13552,13554,13556,13558,13560,13562,13564],{},[898,13553,207],{},[1716,13555,1719],{"separator":1718},[898,13557,1952],{},[1716,13559,1719],{"separator":1718},[898,13561,4478],{},[1716,13563,1719],{"separator":1718},[898,13565,5198],{},[902,13567,8270],{"encoding":904}," tak, aby rovnovážný bod ",[883,13570,13572],{"className":13571},[886],[888,13573,13574],{"xmlns":890},[892,13575,13576,13598],{},[895,13577,13578,13580,13582,13588,13590,13596],{},[898,13579,1805],{},[1716,13581,2502],{"stretchy":1919},[3074,13583,13584,13586],{},[898,13585,1878],{},[898,13587,1805],{},[1716,13589,1719],{"separator":1718},[3074,13591,13592,13594],{},[898,13593,1690],{},[898,13595,1805],{},[1716,13597,2516],{"stretchy":1919},[902,13599,6333],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,13602,13603,13604,13617],{},"(b) Vypočtěte multiplikátory pro ",[883,13605,13607],{"className":13606},[886],[888,13608,13609],{"xmlns":890},[892,13610,13611,13615],{},[895,13612,13613],{},[898,13614,1690],{},[902,13616,1690],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,13619,13620,13621,1343,13641,1343,13659,1343,13677,13695,13696,13713,13714,1853],{},"(c) Pro hodnoty parametrů ",[883,13622,13624],{"className":13623},[886],[888,13625,13626],{"xmlns":890},[892,13627,13628,13638],{},[895,13629,13630,13632,13634,13636],{},[898,13631,207],{},[1716,13633,1913],{},[1716,13635,2760],{},[1712,13637,1726],{},[902,13639,13640],{"encoding":904},"a = -2",[883,13642,13644],{"className":13643},[886],[888,13645,13646],{"xmlns":890},[892,13647,13648,13656],{},[895,13649,13650,13652,13654],{},[898,13651,1952],{},[1716,13653,1913],{},[1712,13655,2973],{},[902,13657,13658],{"encoding":904},"b = 40",[883,13660,13662],{"className":13661},[886],[888,13663,13664],{"xmlns":890},[892,13665,13666,13674],{},[895,13667,13668,13670,13672],{},[898,13669,4478],{},[1716,13671,1913],{},[1712,13673,5771],{},[902,13675,13676],{"encoding":904},"c = 0{,}5",[883,13678,13680],{"className":13679},[886],[888,13681,13682],{"xmlns":890},[892,13683,13684,13692],{},[895,13685,13686,13688,13690],{},[898,13687,5198],{},[1716,13689,1913],{},[1712,13691,2998],{},[902,13693,13694],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,13697,13699],{"className":13698},[886],[888,13700,13701],{"xmlns":890},[892,13702,13703,13711],{},[895,13704,13705],{},[3074,13706,13707,13709],{},[898,13708,1690],{},[898,13710,1805],{},[902,13712,6432],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,13715,13717],{"className":13716},[886],[888,13718,13719],{"xmlns":890},[892,13720,13721,13725],{},[895,13722,13723],{},[898,13724,1690],{},[902,13726,1690],{"encoding":904},[123,13728,13729,13730,13078,13747,13760,13761,1853],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,13731,13733],{"className":13732},[886],[888,13734,13735],{"xmlns":890},[892,13736,13737,13745],{},[895,13738,13739],{},[3074,13740,13741,13743],{},[898,13742,1690],{},[898,13744,1805],{},[902,13746,6432],{"encoding":904},[883,13748,13750],{"className":13749},[886],[888,13751,13752],{"xmlns":890},[892,13753,13754,13758],{},[895,13755,13756],{},[898,13757,207],{},[902,13759,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,13762,13764],{"className":13763},[886],[888,13765,13766],{"xmlns":890},[892,13767,13768,13778],{},[895,13769,13770],{},[7204,13771,13772,13774,13776],{},[898,13773,1690],{},[1712,13775,1714],{},[898,13777,1805],{},[902,13779,12868],{"encoding":904},[123,13781,13782,13783,13800,13801,13814,13815,1853],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,13784,13786],{"className":13785},[886],[888,13787,13788],{"xmlns":890},[892,13789,13790,13798],{},[895,13791,13792],{},[3074,13793,13794,13796],{},[898,13795,1690],{},[898,13797,1805],{},[902,13799,6432],{"encoding":904}," odpovídající poklesu ",[883,13802,13804],{"className":13803},[886],[888,13805,13806],{"xmlns":890},[892,13807,13808,13812],{},[895,13809,13810],{},[898,13811,207],{},[902,13813,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,13816,13818],{"className":13817},[886],[888,13819,13820],{"xmlns":890},[892,13821,13822,13832],{},[895,13823,13824],{},[7204,13825,13826,13828,13830],{},[898,13827,1690],{},[1712,13829,1726],{},[898,13831,1805],{},[902,13833,12929],{"encoding":904},[123,13835,13836,13837,13352,13854,13867,13868,3942,13881,2247,13896,13909,13910,1853],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,13838,13840],{"className":13839},[886],[888,13841,13842],{"xmlns":890},[892,13843,13844,13852],{},[895,13845,13846],{},[3074,13847,13848,13850],{},[898,13849,1690],{},[898,13851,1805],{},[902,13853,6432],{"encoding":904},[883,13855,13857],{"className":13856},[886],[888,13858,13859],{"xmlns":890},[892,13860,13861,13865],{},[895,13862,13863],{},[898,13864,207],{},[902,13866,207],{"encoding":904}," na 35, ",[883,13869,13871],{"className":13870},[886],[888,13872,13873],{"xmlns":890},[892,13874,13875,13879],{},[895,13876,13877],{},[898,13878,4478],{},[902,13880,4478],{"encoding":904},[883,13882,13884],{"className":13883},[886],[888,13885,13886],{"xmlns":890},[892,13887,13888,13893],{},[895,13889,13890],{},[1712,13891,13892],{},"0,7",[902,13894,13895],{"encoding":904},"0{,}7",[883,13897,13899],{"className":13898},[886],[888,13900,13901],{"xmlns":890},[892,13902,13903,13907],{},[895,13904,13905],{},[898,13906,5198],{},[902,13908,5198],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,13911,13913],{"className":13912},[886],[888,13914,13915],{"xmlns":890},[892,13916,13917,13927],{},[895,13918,13919],{},[7204,13920,13921,13923,13925],{},[898,13922,1690],{},[1712,13924,7072],{},[898,13926,1805],{},[902,13928,13929],{"encoding":904},"P_3^E",[724,13931,13932,12695,13935,12732,13963,2772,13991,2247,14017,1853],{},[38,13933,13934],{},"2.16",[883,13936,13938],{"className":13937},[886],[888,13939,13940],{"xmlns":890},[892,13941,13942,13960],{},[895,13943,13944,13946,13948,13950,13952,13954],{},[898,13945,1690],{},[1716,13947,1913],{},[898,13949,207],{},[1716,13951,1949],{},[898,13953,1952],{},[3074,13955,13956,13958],{},[898,13957,1878],{},[1712,13959,1726],{},[902,13961,13962],{"encoding":904},"P = a + bQ^2",[883,13964,13966],{"className":13965},[886],[888,13967,13968],{"xmlns":890},[892,13969,13970,13988],{},[895,13971,13972,13974,13976,13978,13980,13982],{},[898,13973,1690],{},[1716,13975,1913],{},[898,13977,4478],{},[1716,13979,1949],{},[898,13981,5198],{},[3074,13983,13984,13986],{},[898,13985,1878],{},[1712,13987,1726],{},[902,13989,13990],{"encoding":904},"P = c + dQ^2",[883,13992,13994],{"className":13993},[886],[888,13995,13996],{"xmlns":890},[892,13997,13998,14014],{},[895,13999,14000,14002,14004,14006,14008,14010,14012],{},[898,14001,207],{},[1716,14003,1719],{"separator":1718},[898,14005,4478],{},[1716,14007,1719],{"separator":1718},[898,14009,5198],{},[1716,14011,2716],{},[1712,14013,2505],{},[902,14015,14016],{"encoding":904},"a, c, d > 0",[883,14018,14020],{"className":14019},[886],[888,14021,14022],{"xmlns":890},[892,14023,14024,14032],{},[895,14025,14026,14028,14030],{},[898,14027,1952],{},[1716,14029,2704],{},[1712,14031,2505],{},[902,14033,14034],{"encoding":904},"b \u003C 0",[120,14036,14037,14085,14101,14208,14260,14312,14421,14437,14536,14589],{},[123,14038,13528,14039,14052,14053,14084],{},[883,14040,14042],{"className":14041},[886],[888,14043,14044],{"xmlns":890},[892,14045,14046,14050],{},[895,14047,14048],{},[898,14049,1878],{},[902,14051,1878],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,14054,14056],{"className":14055},[886],[888,14057,14058],{"xmlns":890},[892,14059,14060,14082],{},[895,14061,14062,14064,14066,14072,14074,14080],{},[898,14063,1805],{},[1716,14065,2502],{"stretchy":1919},[3074,14067,14068,14070],{},[898,14069,1878],{},[898,14071,1805],{},[1716,14073,1719],{"separator":1718},[3074,14075,14076,14078],{},[898,14077,1690],{},[898,14079,1805],{},[1716,14081,2516],{"stretchy":1919},[902,14083,6333],{"encoding":904}," patřil do 1. kvadrantu.",[123,14086,13603,14087,14100],{},[883,14088,14090],{"className":14089},[886],[888,14091,14092],{"xmlns":890},[892,14093,14094,14098],{},[895,14095,14096],{},[898,14097,1878],{},[902,14099,1878],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,14102,13620,14103,1343,14121,1343,14141,1343,14159,14177,14178,13713,14195,1853],{},[883,14104,14106],{"className":14105},[886],[888,14107,14108],{"xmlns":890},[892,14109,14110,14118],{},[895,14111,14112,14114,14116],{},[898,14113,207],{},[1716,14115,1913],{},[1712,14117,12151],{},[902,14119,14120],{"encoding":904},"a = 100",[883,14122,14124],{"className":14123},[886],[888,14125,14126],{"xmlns":890},[892,14127,14128,14138],{},[895,14129,14130,14132,14134,14136],{},[898,14131,1952],{},[1716,14133,1913],{},[1716,14135,2760],{},[1712,14137,1714],{},[902,14139,14140],{"encoding":904},"b = -1",[883,14142,14144],{"className":14143},[886],[888,14145,14146],{"xmlns":890},[892,14147,14148,14156],{},[895,14149,14150,14152,14154],{},[898,14151,4478],{},[1716,14153,1913],{},[1712,14155,2976],{},[902,14157,14158],{"encoding":904},"c = 20",[883,14160,14162],{"className":14161},[886],[888,14163,14164],{"xmlns":890},[892,14165,14166,14174],{},[895,14167,14168,14170,14172],{},[898,14169,5198],{},[1716,14171,1913],{},[1712,14173,1714],{},[902,14175,14176],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,14179,14181],{"className":14180},[886],[888,14182,14183],{"xmlns":890},[892,14184,14185,14193],{},[895,14186,14187],{},[3074,14188,14189,14191],{},[898,14190,1878],{},[898,14192,1805],{},[902,14194,7382],{"encoding":904},[883,14196,14198],{"className":14197},[886],[888,14199,14200],{"xmlns":890},[892,14201,14202,14206],{},[895,14203,14204],{},[898,14205,1878],{},[902,14207,1878],{"encoding":904},[123,14209,13146,14210,13078,14227,14240,14241,1853],{},[883,14211,14213],{"className":14212},[886],[888,14214,14215],{"xmlns":890},[892,14216,14217,14225],{},[895,14218,14219],{},[3074,14220,14221,14223],{},[898,14222,1878],{},[898,14224,1805],{},[902,14226,7382],{"encoding":904},[883,14228,14230],{"className":14229},[886],[888,14231,14232],{"xmlns":890},[892,14233,14234,14238],{},[895,14235,14236],{},[898,14237,207],{},[902,14239,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,14242,14244],{"className":14243},[886],[888,14245,14246],{"xmlns":890},[892,14247,14248,14258],{},[895,14249,14250],{},[7204,14251,14252,14254,14256],{},[898,14253,1878],{},[1712,14255,1714],{},[898,14257,1805],{},[902,14259,12847],{"encoding":904},[123,14261,13199,14262,13078,14279,14292,14293,1853],{},[883,14263,14265],{"className":14264},[886],[888,14266,14267],{"xmlns":890},[892,14268,14269,14277],{},[895,14270,14271],{},[3074,14272,14273,14275],{},[898,14274,1878],{},[898,14276,1805],{},[902,14278,7382],{"encoding":904},[883,14280,14282],{"className":14281},[886],[888,14283,14284],{"xmlns":890},[892,14285,14286,14290],{},[895,14287,14288],{},[898,14289,4478],{},[902,14291,4478],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,14294,14296],{"className":14295},[886],[888,14297,14298],{"xmlns":890},[892,14299,14300,14310],{},[895,14301,14302],{},[7204,14303,14304,14306,14308],{},[898,14305,1878],{},[1712,14307,1726],{},[898,14309,1805],{},[902,14311,12909],{"encoding":904},[123,14313,13280,14314,13352,14331,14344,14345,3942,14358,14373,14374,14387,14388,14401,14402,1853],{},[883,14315,14317],{"className":14316},[886],[888,14318,14319],{"xmlns":890},[892,14320,14321,14329],{},[895,14322,14323],{},[3074,14324,14325,14327],{},[898,14326,1878],{},[898,14328,1805],{},[902,14330,7382],{"encoding":904},[883,14332,14334],{"className":14333},[886],[888,14335,14336],{"xmlns":890},[892,14337,14338,14342],{},[895,14339,14340],{},[898,14341,207],{},[902,14343,207],{"encoding":904}," na 110, poklesu ",[883,14346,14348],{"className":14347},[886],[888,14349,14350],{"xmlns":890},[892,14351,14352,14356],{},[895,14353,14354],{},[898,14355,1952],{},[902,14357,1952],{"encoding":904},[883,14359,14361],{"className":14360},[886],[888,14362,14363],{"xmlns":890},[892,14364,14365,14371],{},[895,14366,14367,14369],{},[1716,14368,2760],{},[1712,14370,1726],{},[902,14372,13107],{"encoding":904},", růstu ",[883,14375,14377],{"className":14376},[886],[888,14378,14379],{"xmlns":890},[892,14380,14381,14385],{},[895,14382,14383],{},[898,14384,4478],{},[902,14386,4478],{"encoding":904}," na 25 a růstu ",[883,14389,14391],{"className":14390},[886],[888,14392,14393],{"xmlns":890},[892,14394,14395,14399],{},[895,14396,14397],{},[898,14398,5198],{},[902,14400,5198],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,14403,14405],{"className":14404},[886],[888,14406,14407],{"xmlns":890},[892,14408,14409,14419],{},[895,14410,14411],{},[7204,14412,14413,14415,14417],{},[898,14414,1878],{},[1712,14416,7072],{},[898,14418,1805],{},[902,14420,13277],{"encoding":904},[123,14422,14423,14424,14100],{},"(i) Vypočtěte multiplikátory pro ",[883,14425,14427],{"className":14426},[886],[888,14428,14429],{"xmlns":890},[892,14430,14431,14435],{},[895,14432,14433],{},[898,14434,1690],{},[902,14436,1690],{"encoding":904},[123,14438,14439,14440,13713,14457,14470,14471,13078,14488,3942,14501,14516,14517,1853],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,14441,14443],{"className":14442},[886],[888,14444,14445],{"xmlns":890},[892,14446,14447,14455],{},[895,14448,14449],{},[3074,14450,14451,14453],{},[898,14452,1690],{},[898,14454,1805],{},[902,14456,6432],{"encoding":904},[883,14458,14460],{"className":14459},[886],[888,14461,14462],{"xmlns":890},[892,14463,14464,14468],{},[895,14465,14466],{},[898,14467,1690],{},[902,14469,1690],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,14472,14474],{"className":14473},[886],[888,14475,14476],{"xmlns":890},[892,14477,14478,14486],{},[895,14479,14480],{},[3074,14481,14482,14484],{},[898,14483,1690],{},[898,14485,1805],{},[902,14487,6432],{"encoding":904},[883,14489,14491],{"className":14490},[886],[888,14492,14493],{"xmlns":890},[892,14494,14495,14499],{},[895,14496,14497],{},[898,14498,207],{},[902,14500,207],{"encoding":904},[883,14502,14504],{"className":14503},[886],[888,14505,14506],{"xmlns":890},[892,14507,14508,14514],{},[895,14509,14510,14512],{},[1716,14511,2760],{},[1712,14513,7072],{},[902,14515,13123],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,14518,14520],{"className":14519},[886],[888,14521,14522],{"xmlns":890},[892,14523,14524,14534],{},[895,14525,14526],{},[7204,14527,14528,14530,14532],{},[898,14529,1690],{},[1712,14531,1714],{},[898,14533,1805],{},[902,14535,12868],{"encoding":904},[123,14537,14538,14539,13078,14556,14569,14570,1853],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,14540,14542],{"className":14541},[886],[888,14543,14544],{"xmlns":890},[892,14545,14546,14554],{},[895,14547,14548],{},[3074,14549,14550,14552],{},[898,14551,1690],{},[898,14553,1805],{},[902,14555,6432],{"encoding":904},[883,14557,14559],{"className":14558},[886],[888,14560,14561],{"xmlns":890},[892,14562,14563,14567],{},[895,14564,14565],{},[898,14566,207],{},[902,14568,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,14571,14573],{"className":14572},[886],[888,14574,14575],{"xmlns":890},[892,14576,14577,14587],{},[895,14578,14579],{},[7204,14580,14581,14583,14585],{},[898,14582,1690],{},[1712,14584,1726],{},[898,14586,1805],{},[902,14588,12929],{"encoding":904},[123,14590,14591,14592,13800,14609,14622,14623,3942,14636,14373,14651,14664,14665,14678,14679,1853],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,14593,14595],{"className":14594},[886],[888,14596,14597],{"xmlns":890},[892,14598,14599,14607],{},[895,14600,14601],{},[3074,14602,14603,14605],{},[898,14604,1690],{},[898,14606,1805],{},[902,14608,6432],{"encoding":904},[883,14610,14612],{"className":14611},[886],[888,14613,14614],{"xmlns":890},[892,14615,14616,14620],{},[895,14617,14618],{},[898,14619,207],{},[902,14621,207],{"encoding":904}," na 90, poklesu ",[883,14624,14626],{"className":14625},[886],[888,14627,14628],{"xmlns":890},[892,14629,14630,14634],{},[895,14631,14632],{},[898,14633,1952],{},[902,14635,1952],{"encoding":904},[883,14637,14639],{"className":14638},[886],[888,14640,14641],{"xmlns":890},[892,14642,14643,14649],{},[895,14644,14645,14647],{},[1716,14646,2760],{},[1712,14648,7072],{},[902,14650,13123],{"encoding":904},[883,14652,14654],{"className":14653},[886],[888,14655,14656],{"xmlns":890},[892,14657,14658,14662],{},[895,14659,14660],{},[898,14661,4478],{},[902,14663,4478],{"encoding":904}," na 30 a růstu ",[883,14666,14668],{"className":14667},[886],[888,14669,14670],{"xmlns":890},[892,14671,14672,14676],{},[895,14673,14674],{},[898,14675,5198],{},[902,14677,5198],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,14680,14682],{"className":14681},[886],[888,14683,14684],{"xmlns":890},[892,14685,14686,14696],{},[895,14687,14688],{},[7204,14689,14690,14692,14694],{},[898,14691,1690],{},[1712,14693,7072],{},[898,14695,1805],{},[902,14697,13929],{"encoding":904},[198,14699,820],{"id":14700},"přebytek-spotřebitele-a-výrobce-1",[724,14702,14703,12695,14706,12732,14742,1853],{},[38,14704,14705],{},"2.17",[883,14707,14709],{"className":14708},[886],[888,14710,14711],{"xmlns":890},[892,14712,14713,14739],{},[895,14714,14715,14717,14719,14721,14723,14725,14727,14729,14731,14733],{},[898,14716,1690],{},[1716,14718,1913],{},[898,14720,1916],{},[1716,14722,1920],{"stretchy":1919},[898,14724,1878],{},[1716,14726,1925],{"stretchy":1919},[1716,14728,1913],{},[1712,14730,5837],{},[1716,14732,2760],{},[3074,14734,14735,14737],{},[898,14736,1878],{},[1712,14738,1726],{},[902,14740,14741],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,14743,14745],{"className":14744},[886],[888,14746,14747],{"xmlns":890},[892,14748,14749,14775],{},[895,14750,14751,14753,14755,14757,14759,14761,14763,14765,14767,14769],{},[898,14752,1690],{},[1716,14754,1913],{},[898,14756,5352],{},[1716,14758,1920],{"stretchy":1919},[898,14760,1878],{},[1716,14762,1925],{"stretchy":1919},[1716,14764,1913],{},[1712,14766,7072],{},[1716,14768,1949],{},[3074,14770,14771,14773],{},[898,14772,1878],{},[1712,14774,1726],{},[902,14776,14777],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,14779,14780,14783],{},[123,14781,14782],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,14784,14785],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,14787,14788,12695,14791,12732,14826,1853],{},[38,14789,14790],{},"2.18",[883,14792,14794],{"className":14793},[886],[888,14795,14796],{"xmlns":890},[892,14797,14798,14823],{},[895,14799,14800,14802,14804,14806,14808,14810,14812,14814,14817,14819,14821],{},[898,14801,1690],{},[1716,14803,1913],{},[898,14805,1916],{},[1716,14807,1920],{"stretchy":1919},[898,14809,1878],{},[1716,14811,1925],{"stretchy":1919},[1716,14813,1913],{},[1712,14815,14816],{},"18",[1716,14818,2760],{},[1712,14820,1726],{},[898,14822,1878],{},[902,14824,14825],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,14827,14829],{"className":14828},[886],[888,14830,14831],{"xmlns":890},[892,14832,14833,14859],{},[895,14834,14835,14837,14839,14841,14843,14845,14847,14849,14851,14853],{},[898,14836,1690],{},[1716,14838,1913],{},[898,14840,5352],{},[1716,14842,1920],{"stretchy":1919},[898,14844,1878],{},[1716,14846,1925],{"stretchy":1919},[1716,14848,1913],{},[1712,14850,7072],{},[1716,14852,1949],{},[3074,14854,14855,14857],{},[898,14856,1878],{},[1712,14858,1726],{},[902,14860,14777],{"encoding":904},[120,14862,14863,14883,14886,14889],{},[123,14864,14865,14866,1853],{},"(a) Vypočtěte rovnovážné množství ",[883,14867,14869],{"className":14868},[886],[888,14870,14871],{"xmlns":890},[892,14872,14873,14881],{},[895,14874,14875],{},[3074,14876,14877,14879],{},[898,14878,1878],{},[898,14880,1805],{},[902,14882,7382],{"encoding":904},[123,14884,14885],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,14887,14888],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,14890,14891],{},"(c) Graficky interpretujte.",[1855,14893],{},[115,14895,14897],{"id":14896},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,14899,14900,14903,14906,14909,14912,14915,14918,14921,14924,14927,14930,14933,14936,14939],{},[123,14901,14902],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,14904,14905],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,14907,14908],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,14910,14911],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,14913,14914],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,14916,14917],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,14919,14920],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,14922,14923],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,14925,14926],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,14928,14929],{},"K čemu slouží multiplikátory?",[123,14931,14932],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,14934,14935],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,14937,14938],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,14940,14941],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[1855,14943],{},[115,14945,14947],{"id":14946},"klíčové-pojmy","Klíčové pojmy",[724,14949,14950],{},[38,14951,1859],{},[120,14953,14954,14989,14994,15024,15030,15093,15119,15124,15155,15164,15171,15177],{},[123,14955,14956,1994,14959,8373,14962,3495,14964,1343,14987],{},[38,14957,14958],{},"Poptávané množství",[614,14960,14961],{},"quantity demanded",[38,14963,1993],{},[883,14965,14967],{"className":14966},[886],[888,14968,14969],{"xmlns":890},[892,14970,14971,14985],{},[895,14972,14973,14975,14977,14979,14981,14983],{},[898,14974,1878],{},[1716,14976,1913],{},[898,14978,1916],{},[1716,14980,1920],{"stretchy":1919},[898,14982,1690],{},[1716,14984,1925],{"stretchy":1919},[902,14986,1928],{"encoding":904},[38,14988,2361],{},[123,14990,14991,14993],{},[38,14992,2369],{}," — substituční + důchodový efekt",[123,14995,14996,3495,14999],{},[38,14997,14998],{},"Reálné cenové rozpětí",[883,15000,15002],{"className":15001},[886],[888,15003,15004],{"xmlns":890},[892,15005,15006,15022],{},[895,15007,15008,15010,15012,15014,15020],{},[1716,15009,1920],{"stretchy":1919},[1712,15011,2505],{},[1716,15013,1719],{"separator":1718},[1707,15015,15016,15018],{},[898,15017,1690],{},[1712,15019,2505],{},[1716,15021,1925],{"stretchy":1919},[902,15023,2573],{"encoding":904},[123,15025,15026,15029],{},[38,15027,15028],{},"Homogenita poptávky"," (vícefaktorový model)",[123,15031,15032,3495,15035,1343,15058,1343,15075,15092],{},[38,15033,15034],{},"Lineární poptávka",[883,15036,15038],{"className":15037},[886],[888,15039,15040],{"xmlns":890},[892,15041,15042,15056],{},[895,15043,15044,15046,15048,15050,15052,15054],{},[898,15045,1690],{},[1716,15047,1913],{},[898,15049,207],{},[898,15051,1878],{},[1716,15053,1949],{},[898,15055,1952],{},[902,15057,1955],{"encoding":904},[883,15059,15061],{"className":15060},[886],[888,15062,15063],{"xmlns":890},[892,15064,15065,15073],{},[895,15066,15067,15069,15071],{},[898,15068,207],{},[1716,15070,2704],{},[1712,15072,2505],{},[902,15074,8067],{"encoding":904},[883,15076,15078],{"className":15077},[886],[888,15079,15080],{"xmlns":890},[892,15081,15082,15090],{},[895,15083,15084,15086,15088],{},[898,15085,1952],{},[1716,15087,2716],{},[1712,15089,2505],{},[902,15091,8085],{"encoding":904}," — nedokonalá konkurence",[123,15094,15095,3369,15098],{},[38,15096,15097],{},"Dokonalá konkurence",[883,15099,15101],{"className":15100},[886],[888,15102,15103],{"xmlns":890},[892,15104,15105,15117],{},[895,15106,15107,15109,15111],{},[898,15108,1690],{},[1716,15110,1913],{},[3074,15112,15113,15115],{},[898,15114,1690],{},[1716,15116,3080],{},[902,15118,3157],{"encoding":904},[123,15120,15121,15123],{},[38,15122,3161],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,15125,15126,3495,15129,1343,15153],{},[38,15127,15128],{},"Engelova funkce",[883,15130,15132],{"className":15131},[886],[888,15133,15134],{"xmlns":890},[892,15135,15136,15150],{},[895,15137,15138,15140,15142,15144,15146,15148],{},[898,15139,1878],{},[1716,15141,1913],{},[898,15143,1805],{},[1716,15145,1920],{"stretchy":1919},[898,15147,1758],{},[1716,15149,1925],{"stretchy":1919},[902,15151,15152],{"encoding":904},"Q = E(Y)",[38,15154,3360],{},[123,15156,15157,15160,15161,15163],{},[38,15158,15159],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,15162,3816],{}," zboží",[123,15165,15166,2247,15168,15170],{},[38,15167,4832],{},[38,15169,4779],{}," — znaménka zkřížených koeficientů",[123,15172,15173,15176],{},[38,15174,15175],{},"Dvoukomoditní trh"," (2.6)",[123,15178,15179,1994,15182,1925],{},[38,15180,15181],{},"Posun poptávky",[614,15183,3874],{},[724,15185,15186],{},[38,15187,5139],{},[120,15189,15190,15224,15228,15273],{},[123,15191,15192,1994,15194,8373,15196,3495,15198,1343,15222],{},[38,15193,5228],{},[614,15195,5231],{},[38,15197,5403],{},[883,15199,15201],{"className":15200},[886],[888,15202,15203],{"xmlns":890},[892,15204,15205,15219],{},[895,15206,15207,15209,15211,15213,15215,15217],{},[898,15208,1878],{},[1716,15210,1913],{},[898,15212,5352],{},[1716,15214,1920],{"stretchy":1919},[898,15216,1690],{},[1716,15218,1925],{"stretchy":1919},[902,15220,15221],{"encoding":904},"Q = S(P)",[38,15223,5481],{},[123,15225,15226],{},[38,15227,5488],{},[123,15229,15230,3495,15233,1343,15256],{},[38,15231,15232],{},"Lineární nabídka",[883,15234,15236],{"className":15235},[886],[888,15237,15238],{"xmlns":890},[892,15239,15240,15254],{},[895,15241,15242,15244,15246,15248,15250,15252],{},[898,15243,1690],{},[1716,15245,1913],{},[898,15247,4478],{},[898,15249,1878],{},[1716,15251,1949],{},[898,15253,5198],{},[902,15255,5201],{"encoding":904},[883,15257,15259],{"className":15258},[886],[888,15260,15261],{"xmlns":890},[892,15262,15263,15271],{},[895,15264,15265,15267,15269],{},[898,15266,4478],{},[1716,15268,2716],{},[1712,15270,2505],{},[902,15272,5219],{"encoding":904},[123,15274,15275,1994,15278,1925],{},[38,15276,15277],{},"Posun nabídky",[614,15279,5871],{},[724,15281,15282],{},[38,15283,15284],{},"Rovnováha a komparativní statika",[120,15286,15287,15366,15372],{},[123,15288,15289,1994,15291,8373,15293,3495,15296,1343,15313,3495,15316,1343,15333,3495,15335],{},[38,15290,6291],{},[614,15292,6410],{},[38,15294,15295],{},"rovnovážná cena",[883,15297,15299],{"className":15298},[886],[888,15300,15301],{"xmlns":890},[892,15302,15303,15311],{},[895,15304,15305],{},[3074,15306,15307,15309],{},[898,15308,1690],{},[898,15310,1805],{},[902,15312,6432],{"encoding":904},[38,15314,15315],{},"rovnovážné množství",[883,15317,15319],{"className":15318},[886],[888,15320,15321],{"xmlns":890},[892,15322,15323,15331],{},[895,15324,15325],{},[3074,15326,15327,15329],{},[898,15328,1878],{},[898,15330,1805],{},[902,15332,7382],{"encoding":904},[38,15334,6468],{},[883,15336,15338],{"className":15337},[886],[888,15339,15340],{"xmlns":890},[892,15341,15342,15364],{},[895,15343,15344,15346,15348,15354,15356,15362],{},[898,15345,1805],{},[1716,15347,2502],{"stretchy":1919},[3074,15349,15350,15352],{},[898,15351,1878],{},[898,15353,1805],{},[1716,15355,1719],{"separator":1718},[3074,15357,15358,15360],{},[898,15359,1690],{},[898,15361,1805],{},[1716,15363,2516],{"stretchy":1919},[902,15365,6333],{"encoding":904},[123,15367,15368,15371],{},[38,15369,15370],{},"Pravidla 1–4"," komparativní statiky",[123,15373,15374,1994,15377,1925],{},[38,15375,15376],{},"Teorém pavučiny",[614,15378,7327],{},[724,15380,15381],{},[38,15382,15383],{},"Zdanění",[120,15385,15386,15442,15490],{},[123,15387,15388,15390,15391,15416,15417,1925],{},[38,15389,15383],{}," — daň výrobci (",[883,15392,15394],{"className":15393},[886],[888,15395,15396],{"xmlns":890},[892,15397,15398,15414],{},[895,15399,15400,15406,15408,15410,15412],{},[1707,15401,15402,15404],{},[898,15403,5352],{},[1712,15405,1714],{},[1716,15407,1913],{},[898,15409,5352],{},[1716,15411,1949],{},[898,15413,4164],{},[902,15415,7736],{"encoding":904},") vs. daň spotřebiteli (",[883,15418,15420],{"className":15419},[886],[888,15421,15422],{"xmlns":890},[892,15423,15424,15440],{},[895,15425,15426,15432,15434,15436,15438],{},[1707,15427,15428,15430],{},[898,15429,1916],{},[1712,15431,1726],{},[1716,15433,1913],{},[898,15435,1916],{},[1716,15437,2760],{},[898,15439,4164],{},[902,15441,7767],{"encoding":904},[123,15443,15444,3495,15446,1343,15467],{},[38,15445,7639],{},[883,15447,15449],{"className":15448},[886],[888,15450,15451],{"xmlns":890},[892,15452,15453,15465],{},[895,15454,15455],{},[1707,15456,15457,15459],{},[898,15458,4164],{},[895,15460,15461,15463],{},[898,15462,7658],{},[898,15464,724],{},[902,15466,7663],{"encoding":904},[883,15468,15470],{"className":15469},[886],[888,15471,15472],{"xmlns":890},[892,15473,15474,15488],{},[895,15475,15476],{},[1707,15477,15478,15480],{},[898,15479,4164],{},[895,15481,15482,15484,15486],{},[898,15483,7681],{},[898,15485,7684],{},[898,15487,2098],{},[902,15489,7689],{"encoding":904},[123,15491,15492,3495,15495,1343,15524],{},[38,15493,15494],{},"Ekvivalence zdanění",[883,15496,15498],{"className":15497},[886],[888,15499,15500],{"xmlns":890},[892,15501,15502,15522],{},[895,15503,15504,15512,15514],{},[7204,15505,15506,15508,15510],{},[898,15507,1878],{},[1712,15509,1714],{},[898,15511,1805],{},[1716,15513,1913],{},[7204,15515,15516,15518,15520],{},[898,15517,1878],{},[1712,15519,1726],{},[898,15521,1805],{},[902,15523,7890],{"encoding":904},[883,15525,15527],{"className":15526},[886],[888,15528,15529],{"xmlns":890},[892,15530,15531,15555],{},[895,15532,15533,15541,15543,15545,15547],{},[7204,15534,15535,15537,15539],{},[898,15536,1690],{},[1712,15538,1714],{},[898,15540,1805],{},[1716,15542,2760],{},[898,15544,4164],{},[1716,15546,1913],{},[7204,15548,15549,15551,15553],{},[898,15550,1690],{},[1712,15552,1726],{},[898,15554,1805],{},[902,15556,7924],{"encoding":904},[724,15558,15559],{},[38,15560,15561],{},"Multiplikátory",[120,15563,15564,15610,15641,15646,15652,15659],{},[123,15565,15566,3495,15568],{},[38,15567,8023],{},[883,15569,15571],{"className":15570},[886],[888,15572,15573],{"xmlns":890},[892,15574,15575,15607],{},[895,15576,15577,15583,15585,15587,15589,15591,15593,15595,15597,15599,15601,15603,15605],{},[3074,15578,15579,15581],{},[898,15580,1878],{},[898,15582,1805],{},[1716,15584,1913],{},[1716,15586,1920],{"stretchy":1919},[898,15588,1952],{},[1716,15590,2760],{},[898,15592,5198],{},[1716,15594,1925],{"stretchy":1919},[898,15596,3045],{"mathvariant":2068},[1716,15598,1920],{"stretchy":1919},[898,15600,4478],{},[1716,15602,2760],{},[898,15604,207],{},[1716,15606,1925],{"stretchy":1919},[902,15608,15609],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,15611,15612,3495,15615,15640],{},[38,15613,15614],{},"Parametry",[883,15616,15618],{"className":15617},[886],[888,15619,15620],{"xmlns":890},[892,15621,15622,15638],{},[895,15623,15624,15626,15628,15630,15632,15634,15636],{},[898,15625,207],{},[1716,15627,1719],{"separator":1718},[898,15629,1952],{},[1716,15631,1719],{"separator":1718},[898,15633,4478],{},[1716,15635,1719],{"separator":1718},[898,15637,5198],{},[902,15639,8270],{"encoding":904}," — exogenní proměnné",[123,15642,15643],{},[38,15644,15645],{},"Endogenní \u002F exogenní proměnná",[123,15647,15648,15651],{},[38,15649,15650],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,15653,15654,1343,15657],{},[38,15655,15656],{},"Komparativní statika",[38,15658,1844],{},[123,15660,15661,3495,15664,15680],{},[38,15662,15663],{},"Diferenciál",[883,15665,15667],{"className":15666},[886],[888,15668,15669],{"xmlns":890},[892,15670,15671,15677],{},[895,15672,15673,15675],{},[898,15674,5198],{},[898,15676,1878],{},[902,15678,15679],{"encoding":904},"dQ"," (2.11)",[724,15682,15683],{},[38,15684,15685],{},"Přebytky a ostatní",[120,15687,15688,15726],{},[123,15689,15690,3495,15692,15707,15708,3495,15710,15725],{},[38,15691,9933],{},[883,15693,15695],{"className":15694},[886],[888,15696,15697],{"xmlns":890},[892,15698,15699,15705],{},[895,15700,15701,15703],{},[898,15702,9945],{},[898,15704,5352],{},[902,15706,9950],{"encoding":904}," (2.14), ",[38,15709,9953],{},[883,15711,15713],{"className":15712},[886],[888,15714,15715],{"xmlns":890},[892,15716,15717,15723],{},[895,15718,15719,15721],{},[898,15720,1690],{},[898,15722,5352],{},[902,15724,9969],{"encoding":904}," (2.15)",[123,15727,15728,1343,15731,15734],{},[38,15729,15730],{},"Homo economicus",[38,15732,15733],{},"Marshallova formulace"," (1890)",[1855,15736],{},[115,15738,15740],{"id":15739},"navigace","Navigace",[120,15742,15743,15781,15790],{},[123,15744,15745,3495,15748,15751,15752,1343,15755,15759,15760,15763,15764,15767,15768,15771,15772,15776,15777],{},[38,15746,15747],{},"Související témata:",[207,15749,811],{"className":15750,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,15753,820],{"className":15754,"dataFsResolvedFilePath":818,"href":819},[210],[207,15756,15758],{"className":15757,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace"," (zákon klesající\u002Frostoucí, monotonie), ",[207,15761,775],{"className":15762,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,15765,784],{"className":15766,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,15769,793],{"className":15770,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,15773,15775],{"className":15774,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (důchodová a cenová citlivost), ",[207,15778,15780],{"className":15779,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk",[123,15782,15783,3495,15786],{},[38,15784,15785],{},"Shrnutí přednášek:",[207,15787,15789],{"className":15788,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,15791,15792,3495,15795],{},[38,15793,15794],{},"Kurz:",[207,15796,15800],{"className":15797,"dataFsResolvedFilePath":15798,"href":15799},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",{"title":641,"searchDepth":642,"depth":642,"links":15802},[15803,15804,15812,15818,15825,15826,15833,15834,15835,15842,15843,15844],{"id":1665,"depth":642,"text":1666},{"id":1645,"depth":642,"text":1859,"children":15805},[15806,15807,15808,15809,15811],{"id":1958,"depth":649,"text":1959},{"id":2254,"depth":649,"text":2255},{"id":3292,"depth":649,"text":3293},{"id":3870,"depth":649,"text":15810},"Posun poptávky (shift of demand)",{"id":4379,"depth":649,"text":4380},{"id":1649,"depth":642,"text":5139,"children":15813},[15814,15815,15816],{"id":5223,"depth":649,"text":1959},{"id":5410,"depth":649,"text":5411},{"id":5867,"depth":649,"text":15817},"Posun nabídky (shift of supply)",{"id":6290,"depth":642,"text":6291,"children":15819},[15820,15821,15822,15823,15824],{"id":6402,"depth":649,"text":6403},{"id":6615,"depth":649,"text":6616},{"id":6939,"depth":649,"text":6940},{"id":7299,"depth":649,"text":7300},{"id":7330,"depth":649,"text":7331},{"id":7601,"depth":642,"text":811},{"id":8004,"depth":642,"text":8005,"children":15827},[15828,15829,15830,15831],{"id":8022,"depth":649,"text":8023},{"id":8407,"depth":649,"text":8408},{"id":8796,"depth":649,"text":8797},{"id":9251,"depth":649,"text":15832},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":9923,"depth":642,"text":820},{"id":10185,"depth":642,"text":10186},{"id":10417,"depth":642,"text":10418,"children":15836},[15837,15838,15839,15840,15841],{"id":10421,"depth":649,"text":10422},{"id":11265,"depth":649,"text":11266},{"id":11642,"depth":649,"text":6291},{"id":12941,"depth":649,"text":8005},{"id":14700,"depth":649,"text":820},{"id":14896,"depth":642,"text":14897},{"id":14946,"depth":642,"text":14947},{"id":15739,"depth":642,"text":15740},"2026-04-22",{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,15852,15853,15854,15855,15856,15857],"poptavka","nabidka","rovnovaha","multiplikator","zdaneni","prebytek","topic","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q","topics",{"zapisku":1625,"topics":15862,"summaries":15863,"outputs":15864},15,5,1,[15866,17709,23376,24928,25798,30068,31673,41534,50518,63580,67872,87216,99328,108287,108575],{"id":15867,"title":15868,"body":15869,"course":1128,"courses":659,"created":1129,"description":17698,"extension":661,"meta":17699,"navigation":664,"path":17700,"seo":17701,"sources":17702,"stem":17703,"tags":17704,"type":15858,"updated":677,"__hash__":17708},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":15870,"toc":17681},[15871,15874,15893,15897,15974,15977,16100,16243,16245,16325,16329,16388,16438,16445,16449,16582,16632,16636,16676,16743,16812,16819,16822,16860,16932,16936,17013,17061,17105,17109,17113,17183,17187,17237,17314,17321,17324,17376,17644,17646],[12,15872,15868],{"id":15873},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,15875,15876,15877,15881,15882,15885,15886,15889,15890,1853],{},"Matematický aparát kurzu ",[207,15878,15880],{"className":15879,"dataFsResolvedFilePath":15798,"href":15799},[210],"ImeK",". Bez derivace se neobejdou ",[38,15883,15884],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,15887,15888],{},"maximalizace zisku"," ani ",[38,15891,15892],{},"minimalizace nákladů",[115,15894,15896],{"id":15895},"funkce-a-polynomy","Funkce a polynomy",[724,15898,15899,15900,15925,15926,15939,15940,15953,15954,1853],{},"Funkce jedné proměnné ",[883,15901,15903],{"className":15902},[886],[888,15904,15905],{"xmlns":890},[892,15906,15907,15922],{},[895,15908,15909,15911,15913,15916,15918,15920],{},[898,15910,7684],{},[1716,15912,1913],{},[898,15914,15915],{},"f",[1716,15917,1920],{"stretchy":1919},[898,15919,8967],{},[1716,15921,1925],{"stretchy":1919},[902,15923,15924],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,15927,15929],{"className":15928},[886],[888,15930,15931],{"xmlns":890},[892,15932,15933,15937],{},[895,15934,15935],{},[898,15936,8967],{},[902,15938,8967],{"encoding":904}," (nezávislá) → ",[883,15941,15943],{"className":15942},[886],[888,15944,15945],{"xmlns":890},[892,15946,15947,15951],{},[895,15948,15949],{},[898,15950,7684],{},[902,15952,7684],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,15955,15957],{"className":15956},[886],[888,15958,15959],{"xmlns":890},[892,15960,15961,15971],{},[895,15962,15963,15965,15967,15969],{},[898,15964,15915],{},[1716,15966,1920],{"stretchy":1919},[898,15968,207],{},[1716,15970,1925],{"stretchy":1919},[902,15972,15973],{"encoding":904},"f(a)",[724,15975,15976],{},"Polynomy:",[120,15978,15979,16010,16050],{},[123,15980,15981],{},[152,15982,15983],{},[123,15984,15985,15986],{},"stupně: ",[883,15987,15989],{"className":15988},[886],[888,15990,15991],{"xmlns":890},[892,15992,15993,16007],{},[895,15994,15995,15997,15999,16001,16003,16005],{},[898,15996,7684],{},[1716,15998,1913],{},[898,16000,207],{},[898,16002,8967],{},[1716,16004,1949],{},[898,16006,1952],{},[902,16008,16009],{"encoding":904},"y = ax + b",[123,16011,16012],{},[152,16013,16014],{"start":642},[123,16015,15985,16016],{},[883,16017,16019],{"className":16018},[886],[888,16020,16021],{"xmlns":890},[892,16022,16023,16047],{},[895,16024,16025,16027,16029,16031,16037,16039,16041,16043,16045],{},[898,16026,7684],{},[1716,16028,1913],{},[898,16030,207],{},[3074,16032,16033,16035],{},[898,16034,8967],{},[1712,16036,1726],{},[1716,16038,1949],{},[898,16040,1952],{},[898,16042,8967],{},[1716,16044,1949],{},[898,16046,4478],{},[902,16048,16049],{"encoding":904},"y = ax^2 + bx + c",[123,16051,16052],{},[152,16053,16054],{"start":649},[123,16055,15985,16056],{},[883,16057,16059],{"className":16058},[886],[888,16060,16061],{"xmlns":890},[892,16062,16063,16097],{},[895,16064,16065,16067,16069,16071,16077,16079,16081,16087,16089,16091,16093,16095],{},[898,16066,7684],{},[1716,16068,1913],{},[898,16070,207],{},[3074,16072,16073,16075],{},[898,16074,8967],{},[1712,16076,7072],{},[1716,16078,1949],{},[898,16080,1952],{},[3074,16082,16083,16085],{},[898,16084,8967],{},[1712,16086,1726],{},[1716,16088,1949],{},[898,16090,4478],{},[898,16092,8967],{},[1716,16094,1949],{},[898,16096,5198],{},[902,16098,16099],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,16101,16102,3495,16105,16159,16160,16196,16197,1853],{},[38,16103,16104],{},"Příklad rozkladu:",[883,16106,16108],{"className":16107},[886],[888,16109,16110],{"xmlns":890},[892,16111,16112,16156],{},[895,16113,16114,16116,16118,16124,16126,16128,16130,16132,16134,16136,16138,16140,16142,16144,16146,16148,16150,16152,16154],{},[898,16115,7684],{},[1716,16117,1913],{},[3074,16119,16120,16122],{},[898,16121,8967],{},[1712,16123,1726],{},[1716,16125,2760],{},[1712,16127,6985],{},[898,16129,8967],{},[1716,16131,1949],{},[1712,16133,6231],{},[1716,16135,1913],{},[1716,16137,1920],{"stretchy":1919},[898,16139,8967],{},[1716,16141,2760],{},[1712,16143,1726],{},[1716,16145,1925],{"stretchy":1919},[1716,16147,1920],{"stretchy":1919},[898,16149,8967],{},[1716,16151,2760],{},[1712,16153,7072],{},[1716,16155,1925],{"stretchy":1919},[902,16157,16158],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,16161,16163],{"className":16162},[886],[888,16164,16165],{"xmlns":890},[892,16166,16167,16193],{},[895,16168,16169,16175,16177,16179,16181,16183,16189,16191],{},[1707,16170,16171,16173],{},[898,16172,8967],{},[1712,16174,1714],{},[1716,16176,1913],{},[1712,16178,1726],{},[1716,16180,1719],{"separator":1718},[2074,16182,2711],{},[1707,16184,16185,16187],{},[898,16186,8967],{},[1712,16188,1726],{},[1716,16190,1913],{},[1712,16192,7072],{},[902,16194,16195],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,16198,16200],{"className":16199},[886],[888,16201,16202],{"xmlns":890},[892,16203,16204,16240],{},[895,16205,16206,16208,16210,16212,16214,16216,16224,16230,16232],{},[898,16207,7684],{},[1716,16209,1913],{},[1716,16211,1920],{"stretchy":1919},[898,16213,8967],{},[1716,16215,2760],{},[2747,16217,16218],{"scriptlevel":2505,"displaystyle":1919},[2750,16219,16220,16222],{},[1712,16221,6985],{},[1712,16223,1726],{},[3074,16225,16226,16228],{},[1716,16227,1925],{"stretchy":1919},[1712,16229,1726],{},[1716,16231,2760],{},[2747,16233,16234],{"scriptlevel":2505,"displaystyle":1919},[2750,16235,16236,16238],{},[1712,16237,1714],{},[1712,16239,6849],{},[902,16241,16242],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,16244,15758],{"id":1145},[724,16246,16247,16248,1348,16272,16300,16301,1853],{},"Označení ",[883,16249,16251],{"className":16250},[886],[888,16252,16253],{"xmlns":890},[892,16254,16255,16269],{},[895,16256,16257,16263,16265,16267],{},[3074,16258,16259,16261],{},[898,16260,15915],{},[1716,16262,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16264,1920],{"stretchy":1919},[898,16266,8967],{},[1716,16268,1925],{"stretchy":1919},[902,16270,16271],{"encoding":904},"f'(x)",[883,16273,16275],{"className":16274},[886],[888,16276,16277],{"xmlns":890},[892,16278,16279,16297],{},[895,16280,16281],{},[2747,16282,16283],{"scriptlevel":2505,"displaystyle":1718},[2750,16284,16285,16291],{},[895,16286,16287,16289],{},[898,16288,5198],{},[898,16290,7684],{},[895,16292,16293,16295],{},[898,16294,5198],{},[898,16296,8967],{},[902,16298,16299],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,16302,16304],{"className":16303},[886],[888,16305,16306],{"xmlns":890},[892,16307,16308,16322],{},[895,16309,16310,16316,16318,16320],{},[3074,16311,16312,16314],{},[898,16313,15915],{},[1716,16315,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16317,1920],{"stretchy":1919},[898,16319,207],{},[1716,16321,1925],{"stretchy":1919},[902,16323,16324],{"encoding":904},"f'(a)",[198,16326,16328],{"id":16327},"geometrická-interpretace","Geometrická interpretace",[724,16330,16331,16354,16355,16358,16359,16387],{},[883,16332,16334],{"className":16333},[886],[888,16335,16336],{"xmlns":890},[892,16337,16338,16352],{},[895,16339,16340,16346,16348,16350],{},[3074,16341,16342,16344],{},[898,16343,15915],{},[1716,16345,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16347,1920],{"stretchy":1919},[898,16349,207],{},[1716,16351,1925],{"stretchy":1919},[902,16353,16324],{"encoding":904}," = ",[38,16356,16357],{},"sklon tečny"," ke grafu funkce v bodě ",[883,16360,16362],{"className":16361},[886],[888,16363,16364],{"xmlns":890},[892,16365,16366,16384],{},[895,16367,16368,16370,16372,16374,16376,16378,16380,16382],{},[1716,16369,2502],{"stretchy":1919},[898,16371,207],{},[1716,16373,1719],{"separator":1718},[898,16375,15915],{},[1716,16377,1920],{"stretchy":1919},[898,16379,207],{},[1716,16381,1925],{"stretchy":1919},[1716,16383,2516],{"stretchy":1919},[902,16385,16386],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,16389,16390],{},[883,16391,16393],{"className":16392},[886],[888,16394,16395],{"xmlns":890},[892,16396,16397,16435],{},[895,16398,16399,16401,16403,16405,16407,16409,16411,16413,16419,16421,16423,16425,16427,16429,16431,16433],{},[898,16400,7684],{},[1716,16402,2760],{},[898,16404,15915],{},[1716,16406,1920],{"stretchy":1919},[898,16408,207],{},[1716,16410,1925],{"stretchy":1919},[1716,16412,1913],{},[3074,16414,16415,16417],{},[898,16416,15915],{},[1716,16418,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16420,1920],{"stretchy":1919},[898,16422,207],{},[1716,16424,1925],{"stretchy":1919},[1716,16426,1920],{"stretchy":1919},[898,16428,8967],{},[1716,16430,2760],{},[898,16432,207],{},[1716,16434,1925],{"stretchy":1919},[902,16436,16437],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,16439,16440],{},[3682,16441],{"alt":16442,"className":16443,"src":16444},"imek-derivace-tecna",[210,3686],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,16446,16448],{"id":16447},"inženýrská-interpretace","Inženýrská interpretace",[724,16450,16451,16354,16474,3495,16477,16490,16491,16504,16505,16523,16524,16537,16538,9425,16551,3942,16564,2291],{},[883,16452,16454],{"className":16453},[886],[888,16455,16456],{"xmlns":890},[892,16457,16458,16472],{},[895,16459,16460,16466,16468,16470],{},[3074,16461,16462,16464],{},[898,16463,15915],{},[1716,16465,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16467,1920],{"stretchy":1919},[898,16469,207],{},[1716,16471,1925],{"stretchy":1919},[902,16473,16324],{"encoding":904},[38,16475,16476],{},"rychlost změny",[883,16478,16480],{"className":16479},[886],[888,16481,16482],{"xmlns":890},[892,16483,16484,16488],{},[895,16485,16486],{},[898,16487,7684],{},[902,16489,7684],{"encoding":904}," vzhledem k ",[883,16492,16494],{"className":16493},[886],[888,16495,16496],{"xmlns":890},[892,16497,16498,16502],{},[895,16499,16500],{},[898,16501,8967],{},[902,16503,8967],{"encoding":904}," v bodě ",[883,16506,16508],{"className":16507},[886],[888,16509,16510],{"xmlns":890},[892,16511,16512,16520],{},[895,16513,16514,16516,16518],{},[898,16515,8967],{},[1716,16517,1913],{},[898,16519,207],{},[902,16521,16522],{"encoding":904},"x = a","; přibližná změna ",[883,16525,16527],{"className":16526},[886],[888,16528,16529],{"xmlns":890},[892,16530,16531,16535],{},[895,16532,16533],{},[898,16534,7684],{},[902,16536,7684],{"encoding":904}," při změně ",[883,16539,16541],{"className":16540},[886],[888,16542,16543],{"xmlns":890},[892,16544,16545,16549],{},[895,16546,16547],{},[898,16548,8967],{},[902,16550,8967],{"encoding":904},[883,16552,16554],{"className":16553},[886],[888,16555,16556],{"xmlns":890},[892,16557,16558,16562],{},[895,16559,16560],{},[898,16561,207],{},[902,16563,207],{"encoding":904},[883,16565,16567],{"className":16566},[886],[888,16568,16569],{"xmlns":890},[892,16570,16571,16579],{},[895,16572,16573,16575,16577],{},[898,16574,207],{},[1716,16576,1949],{},[1712,16578,1714],{},[902,16580,16581],{"encoding":904},"a+1",[724,16583,16584],{},[883,16585,16587],{"className":16586},[886],[888,16588,16589],{"xmlns":890},[892,16590,16591,16629],{},[895,16592,16593,16595,16597,16599,16601,16603,16605,16607,16609,16611,16613,16615,16617,16623,16625,16627],{},[898,16594,15915],{},[1716,16596,1920],{"stretchy":1919},[898,16598,207],{},[1716,16600,1949],{},[1712,16602,1714],{},[1716,16604,1925],{"stretchy":1919},[1716,16606,8490],{},[898,16608,15915],{},[1716,16610,1920],{"stretchy":1919},[898,16612,207],{},[1716,16614,1925],{"stretchy":1919},[1716,16616,1949],{},[3074,16618,16619,16621],{},[898,16620,15915],{},[1716,16622,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16624,1920],{"stretchy":1919},[898,16626,207],{},[1716,16628,1925],{"stretchy":1919},[902,16630,16631],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,16633,16635],{"id":16634},"příklad-mezní-náklady","Příklad — mezní náklady",[724,16637,16638,16639,1853],{},"Celkové náklady ",[883,16640,16642],{"className":16641},[886],[888,16643,16644],{"xmlns":890},[892,16645,16646,16673],{},[895,16647,16648,16650,16652,16654,16657,16659,16661,16663,16665,16667],{},[898,16649,4164],{},[898,16651,9945],{},[1716,16653,1913],{},[1712,16655,16656],{},"1000",[1716,16658,1949],{},[1712,16660,1726],{},[898,16662,1878],{},[1716,16664,1949],{},[1712,16666,9535],{},[3074,16668,16669,16671],{},[898,16670,1878],{},[1712,16672,1726],{},[902,16674,16675],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,16677,16678,16679,16716,16717,1853],{},"Mezní náklady: ",[883,16680,16682],{"className":16681},[886],[888,16683,16684],{"xmlns":890},[892,16685,16686,16713],{},[895,16687,16688,16691,16693,16695,16697,16703,16705,16707,16709,16711],{},[898,16689,16690],{},"M",[898,16692,9945],{},[1716,16694,1913],{},[898,16696,4164],{},[3074,16698,16699,16701],{},[898,16700,9945],{},[1716,16702,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16704,1913],{},[1712,16706,1726],{},[1716,16708,1949],{},[1712,16710,11302],{},[898,16712,1878],{},[902,16714,16715],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,16718,16720],{"className":16719},[886],[888,16721,16722],{"xmlns":890},[892,16723,16724,16740],{},[895,16725,16726,16728,16730,16732,16734,16736,16738],{},[898,16727,16690],{},[898,16729,9945],{},[1716,16731,1920],{"stretchy":1919},[1712,16733,2998],{},[1716,16735,1925],{"stretchy":1919},[1716,16737,1913],{},[1712,16739,6849],{},[902,16741,16742],{"encoding":904},"MC(10) = 4",[724,16744,16745,3495,16748,7636,16796,3495,16799,1853],{},[38,16746,16747],{},"Skutečný přírůstek:",[883,16749,16751],{"className":16750},[886],[888,16752,16753],{"xmlns":890},[892,16754,16755,16793],{},[895,16756,16757,16759,16761,16763,16765,16767,16769,16771,16774,16776,16778,16780,16782,16784,16786,16788,16790],{},[898,16758,8485],{"mathvariant":2068},[898,16760,4164],{},[898,16762,9945],{},[1716,16764,1913],{},[898,16766,4164],{},[898,16768,9945],{},[1716,16770,1920],{"stretchy":1919},[1712,16772,16773],{},"11",[1716,16775,1925],{"stretchy":1919},[1716,16777,2760],{},[898,16779,4164],{},[898,16781,9945],{},[1716,16783,1920],{"stretchy":1919},[1712,16785,2998],{},[1716,16787,1925],{"stretchy":1919},[1716,16789,1913],{},[1712,16791,16792],{},"4,2",[902,16794,16795],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",[38,16797,16798],{},"Přibližný (lineární):",[883,16800,16802],{"className":16801},[886],[888,16803,16804],{"xmlns":890},[892,16805,16806,16810],{},[895,16807,16808],{},[1712,16809,6849],{},[902,16811,6849],{"encoding":904},[724,16813,16814,16815,10380],{},"(Viz aplikace v ",[207,16816,16818],{"className":16817,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk",[115,16820,15663],{"id":16821},"diferenciál",[724,16823,16824],{},[883,16825,16827],{"className":16826},[886],[888,16828,16829],{"xmlns":890},[892,16830,16831,16857],{},[895,16832,16833,16835,16837,16839,16845,16847,16849,16851,16853,16855],{},[898,16834,5198],{},[898,16836,15915],{},[1716,16838,1913],{},[3074,16840,16841,16843],{},[898,16842,15915],{},[1716,16844,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,16846,1920],{"stretchy":1919},[898,16848,8967],{},[1716,16850,1925],{"stretchy":1919},[2074,16852,8508],{},[898,16854,5198],{},[898,16856,8967],{},[902,16858,16859],{"encoding":904},"df = f'(x)\\, dx",[724,16861,16862,16863,16879,16880,16928,16929,1853],{},"Pro malá ",[883,16864,16866],{"className":16865},[886],[888,16867,16868],{"xmlns":890},[892,16869,16870,16876],{},[895,16871,16872,16874],{},[898,16873,5198],{},[898,16875,8967],{},[902,16877,16878],{"encoding":904},"dx"," platí: ",[883,16881,16883],{"className":16882},[886],[888,16884,16885],{"xmlns":890},[892,16886,16887,16925],{},[895,16888,16889,16891,16893,16895,16897,16899,16901,16903,16905,16907,16909,16911,16913,16915,16917,16919,16921,16923],{},[898,16890,8485],{"mathvariant":2068},[898,16892,15915],{},[1716,16894,1913],{},[898,16896,15915],{},[1716,16898,1920],{"stretchy":1919},[898,16900,8967],{},[1716,16902,1949],{},[898,16904,5198],{},[898,16906,8967],{},[1716,16908,1925],{"stretchy":1919},[1716,16910,2760],{},[898,16912,15915],{},[1716,16914,1920],{"stretchy":1919},[898,16916,8967],{},[1716,16918,1925],{"stretchy":1919},[1716,16920,8490],{},[898,16922,5198],{},[898,16924,15915],{},[902,16926,16927],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,16930,16931],{},"lineární odhad přírůstku",[198,16933,16935],{"id":16934},"příklad","Příklad",[724,16937,16938,16968,16969,16992,16993,1998],{},[883,16939,16941],{"className":16940},[886],[888,16942,16943],{"xmlns":890},[892,16944,16945,16965],{},[895,16946,16947,16949,16951,16953,16955,16957,16959],{},[898,16948,4164],{},[898,16950,9945],{},[1716,16952,1913],{},[1712,16954,12151],{},[1716,16956,1949],{},[1712,16958,9535],{},[3074,16960,16961,16963],{},[898,16962,1878],{},[1712,16964,1726],{},[902,16966,16967],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,16970,16972],{"className":16971},[886],[888,16973,16974],{"xmlns":890},[892,16975,16976,16989],{},[895,16977,16978,16980,16982,16984,16987],{},[898,16979,1878],{},[1716,16981,2291],{},[1712,16983,5808],{},[1716,16985,16986],{},"→",[1712,16988,2884],{},[902,16990,16991],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,16994,16996],{"className":16995},[886],[888,16997,16998],{"xmlns":890},[892,16999,17000,17010],{},[895,17001,17002,17004,17006,17008],{},[898,17003,5198],{},[898,17005,1878],{},[1716,17007,1913],{},[1712,17009,2998],{},[902,17011,17012],{"encoding":904},"dQ = 10",[724,17014,17015],{},[883,17016,17018],{"className":17017},[886],[888,17019,17020],{"xmlns":890},[892,17021,17022,17058],{},[895,17023,17024,17026,17028,17030,17032,17034,17036,17038,17040,17042,17044,17046,17048,17050,17052,17054,17056],{},[898,17025,5198],{},[898,17027,4164],{},[898,17029,9945],{},[1716,17031,1913],{},[1712,17033,11302],{},[898,17035,1878],{},[1716,17037,9532],{},[898,17039,5198],{},[898,17041,1878],{},[1716,17043,1913],{},[1712,17045,11302],{},[1716,17047,9532],{},[1712,17049,5808],{},[1716,17051,9532],{},[1712,17053,2998],{},[1716,17055,1913],{},[1712,17057,12151],{},[902,17059,17060],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,17062,17063,17064,17087,17088,17104],{},"Přesná změna: ",[883,17065,17067],{"className":17066},[886],[888,17068,17069],{"xmlns":890},[892,17070,17071,17084],{},[895,17072,17073,17075,17077,17079,17081],{},[898,17074,8485],{"mathvariant":2068},[898,17076,4164],{},[898,17078,9945],{},[1716,17080,1913],{},[1712,17082,17083],{},"110",[902,17085,17086],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,17089,17091],{"className":17090},[886],[888,17092,17093],{"xmlns":890},[892,17094,17095,17101],{},[895,17096,17097,17099],{},[898,17098,4164],{},[898,17100,9945],{},[902,17102,17103],{"encoding":904},"TC"," je konvexní.",[115,17106,17108],{"id":17107},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,17110,17112],{"id":17111},"nutná-podmínka","Nutná podmínka",[724,17114,17115,17116,16504,17136,17149,17150,17178,17179,17182],{},"Má-li ",[883,17117,17119],{"className":17118},[886],[888,17120,17121],{"xmlns":890},[892,17122,17123,17133],{},[895,17124,17125,17127,17129,17131],{},[898,17126,15915],{},[1716,17128,1920],{"stretchy":1919},[898,17130,8967],{},[1716,17132,1925],{"stretchy":1919},[902,17134,17135],{"encoding":904},"f(x)",[883,17137,17139],{"className":17138},[886],[888,17140,17141],{"xmlns":890},[892,17142,17143,17147],{},[895,17144,17145],{},[898,17146,207],{},[902,17148,207],{"encoding":904}," extrém, pak ",[883,17151,17153],{"className":17152},[886],[888,17154,17155],{"xmlns":890},[892,17156,17157,17175],{},[895,17158,17159,17165,17167,17169,17171,17173],{},[3074,17160,17161,17163],{},[898,17162,15915],{},[1716,17164,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,17166,1920],{"stretchy":1919},[898,17168,207],{},[1716,17170,1925],{"stretchy":1919},[1716,17172,1913],{},[1712,17174,2505],{},[902,17176,17177],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,17180,17181],{},"stacionární"," (podezřelé) body.",[198,17184,17186],{"id":17185},"postačující-podmínka","Postačující podmínka",[724,17188,17189,17190,17203,17204,2291],{},"Pro stacionární bod ",[883,17191,17193],{"className":17192},[886],[888,17194,17195],{"xmlns":890},[892,17196,17197,17201],{},[895,17198,17199],{},[898,17200,207],{},[902,17202,207],{"encoding":904},", je-li ",[883,17205,17207],{"className":17206},[886],[888,17208,17209],{"xmlns":890},[892,17210,17211,17234],{},[895,17212,17213,17223,17225,17227,17229,17232],{},[3074,17214,17215,17217],{},[898,17216,15915],{},[895,17218,17219,17221],{},[1716,17220,8505],{"mathvariant":2068},[1716,17222,8505],{"mathvariant":2068},[1716,17224,1920],{"stretchy":1919},[898,17226,207],{},[1716,17228,1925],{"stretchy":1919},[1716,17230,17231],{"mathvariant":2068},"≠",[1712,17233,2505],{},[902,17235,17236],{"encoding":904},"f''(a) \\neq 0",[120,17238,17239,17277],{},[123,17240,17241,17273,17274],{},[883,17242,17244],{"className":17243},[886],[888,17245,17246],{"xmlns":890},[892,17247,17248,17270],{},[895,17249,17250,17260,17262,17264,17266,17268],{},[3074,17251,17252,17254],{},[898,17253,15915],{},[895,17255,17256,17258],{},[1716,17257,8505],{"mathvariant":2068},[1716,17259,8505],{"mathvariant":2068},[1716,17261,1920],{"stretchy":1919},[898,17263,207],{},[1716,17265,1925],{"stretchy":1919},[1716,17267,2716],{},[1712,17269,2505],{},[902,17271,17272],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,17275,17276],{},"lokální minimum",[123,17278,17279,17273,17311],{},[883,17280,17282],{"className":17281},[886],[888,17283,17284],{"xmlns":890},[892,17285,17286,17308],{},[895,17287,17288,17298,17300,17302,17304,17306],{},[3074,17289,17290,17292],{},[898,17291,15915],{},[895,17293,17294,17296],{},[1716,17295,8505],{"mathvariant":2068},[1716,17297,8505],{"mathvariant":2068},[1716,17299,1920],{"stretchy":1919},[898,17301,207],{},[1716,17303,1925],{"stretchy":1919},[1716,17305,2704],{},[1712,17307,2505],{},[902,17309,17310],{"encoding":904},"f''(a) \u003C 0",[38,17312,17313],{},"lokální maximum",[724,17315,17316],{},[3682,17317],{"alt":17318,"className":17319,"src":17320},"imek-extremy-1d",[210,3686],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,17322,16935],{"id":17323},"příklad-1",[724,17325,17326],{},[883,17327,17329],{"className":17328},[886],[888,17330,17331],{"xmlns":890},[892,17332,17333,17373],{},[895,17334,17335,17337,17339,17341,17343,17345,17347,17353,17355,17357,17363,17365,17367,17369,17371],{},[898,17336,15915],{},[1716,17338,1920],{"stretchy":1919},[898,17340,8967],{},[1716,17342,1925],{"stretchy":1919},[1716,17344,1913],{},[1712,17346,1726],{},[3074,17348,17349,17351],{},[898,17350,8967],{},[1712,17352,7072],{},[1716,17354,2760],{},[1712,17356,7072],{},[3074,17358,17359,17361],{},[898,17360,8967],{},[1712,17362,1726],{},[1716,17364,2760],{},[1712,17366,6804],{},[898,17368,8967],{},[1716,17370,1949],{},[1712,17372,7072],{},[902,17374,17375],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,17377,17378,17489,17529,17590],{},[123,17379,17380,17452,17453],{},[883,17381,17383],{"className":17382},[886],[888,17384,17385],{"xmlns":890},[892,17386,17387,17449],{},[895,17388,17389,17395,17397,17399,17401,17403,17405,17411,17413,17415,17417,17419,17421,17423,17425,17427,17429,17431,17433,17435,17437,17439,17441,17443,17445,17447],{},[3074,17390,17391,17393],{},[898,17392,15915],{},[1716,17394,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,17396,1920],{"stretchy":1919},[898,17398,8967],{},[1716,17400,1925],{"stretchy":1919},[1716,17402,1913],{},[1712,17404,6231],{},[3074,17406,17407,17409],{},[898,17408,8967],{},[1712,17410,1726],{},[1716,17412,2760],{},[1712,17414,6231],{},[898,17416,8967],{},[1716,17418,2760],{},[1712,17420,6804],{},[1716,17422,1913],{},[1712,17424,6231],{},[1716,17426,1920],{"stretchy":1919},[898,17428,8967],{},[1716,17430,1949],{},[1712,17432,1714],{},[1716,17434,1925],{"stretchy":1919},[1716,17436,1920],{"stretchy":1919},[898,17438,8967],{},[1716,17440,2760],{},[1712,17442,1726],{},[1716,17444,1925],{"stretchy":1919},[1716,17446,1913],{},[1712,17448,2505],{},[902,17450,17451],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,17454,17456],{"className":17455},[886],[888,17457,17458],{"xmlns":890},[892,17459,17460,17486],{},[895,17461,17462,17468,17470,17472,17474,17476,17482,17484],{},[1707,17463,17464,17466],{},[898,17465,8967],{},[1712,17467,1714],{},[1716,17469,1913],{},[1716,17471,2760],{},[1712,17473,1714],{},[1716,17475,1719],{"separator":1718},[1707,17477,17478,17480],{},[898,17479,8967],{},[1712,17481,1726],{},[1716,17483,1913],{},[1712,17485,1726],{},[902,17487,17488],{"encoding":904},"x_1 = -1, x_2 = 2",[123,17490,17491],{},[883,17492,17494],{"className":17493},[886],[888,17495,17496],{"xmlns":890},[892,17497,17498,17526],{},[895,17499,17500,17510,17512,17514,17516,17518,17520,17522,17524],{},[3074,17501,17502,17504],{},[898,17503,15915],{},[895,17505,17506,17508],{},[1716,17507,8505],{"mathvariant":2068},[1716,17509,8505],{"mathvariant":2068},[1716,17511,1920],{"stretchy":1919},[898,17513,8967],{},[1716,17515,1925],{"stretchy":1919},[1716,17517,1913],{},[1712,17519,6804],{},[898,17521,8967],{},[1716,17523,2760],{},[1712,17525,6231],{},[902,17527,17528],{"encoding":904},"f''(x) = 12x - 6",[123,17530,17531,17273,17571,5618,17574],{},[883,17532,17534],{"className":17533},[886],[888,17535,17536],{"xmlns":890},[892,17537,17538,17568],{},[895,17539,17540,17550,17552,17554,17556,17558,17560,17562,17564,17566],{},[3074,17541,17542,17544],{},[898,17543,15915],{},[895,17545,17546,17548],{},[1716,17547,8505],{"mathvariant":2068},[1716,17549,8505],{"mathvariant":2068},[1716,17551,1920],{"stretchy":1919},[1716,17553,2760],{},[1712,17555,1714],{},[1716,17557,1925],{"stretchy":1919},[1716,17559,1913],{},[1716,17561,2760],{},[1712,17563,14816],{},[1716,17565,2704],{},[1712,17567,2505],{},[902,17569,17570],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,17572,17573],{},"maximum",[883,17575,17577],{"className":17576},[886],[888,17578,17579],{"xmlns":890},[892,17580,17581,17587],{},[895,17582,17583,17585],{},[1716,17584,2760],{},[1712,17586,1714],{},[902,17588,17589],{"encoding":904},"-1",[123,17591,17592,17273,17628,5618,17631],{},[883,17593,17595],{"className":17594},[886],[888,17596,17597],{"xmlns":890},[892,17598,17599,17625],{},[895,17600,17601,17611,17613,17615,17617,17619,17621,17623],{},[3074,17602,17603,17605],{},[898,17604,15915],{},[895,17606,17607,17609],{},[1716,17608,8505],{"mathvariant":2068},[1716,17610,8505],{"mathvariant":2068},[1716,17612,1920],{"stretchy":1919},[1712,17614,1726],{},[1716,17616,1925],{"stretchy":1919},[1716,17618,1913],{},[1712,17620,14816],{},[1716,17622,2716],{},[1712,17624,2505],{},[902,17626,17627],{"encoding":904},"f''(2) = 18 > 0",[38,17629,17630],{},"minimum",[883,17632,17634],{"className":17633},[886],[888,17635,17636],{"xmlns":890},[892,17637,17638,17642],{},[895,17639,17640],{},[1712,17641,1726],{},[902,17643,1726],{"encoding":904},[115,17645,15740],{"id":15739},[120,17647,17648,17656,17664],{},[123,17649,17650,3495,17653],{},[38,17651,17652],{},"Předchozí:",[207,17654,757],{"className":17655,"dataFsResolvedFilePath":755,"href":756},[210],[123,17657,17658,3495,17661],{},[38,17659,17660],{},"Navazující:",[207,17662,775],{"className":17663,"dataFsResolvedFilePath":773,"href":774},[210],[123,17665,17666,3495,17669,17672,17673,17676,17677,17680],{},[38,17667,17668],{},"Souvislosti:",[207,17670,784],{"className":17671,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,17674,15780],{"className":17675,"dataFsResolvedFilePath":827,"href":828},[210]," (aplikace mezních veličin), ",[207,17678,15775],{"className":17679,"dataFsResolvedFilePath":848,"href":849},[210]," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":17682},[17683,17684,17689,17692,17697],{"id":15895,"depth":642,"text":15896},{"id":1145,"depth":642,"text":15758,"children":17685},[17686,17687,17688],{"id":16327,"depth":649,"text":16328},{"id":16447,"depth":649,"text":16448},{"id":16634,"depth":649,"text":16635},{"id":16821,"depth":642,"text":15663,"children":17690},[17691],{"id":16934,"depth":649,"text":16935},{"id":17107,"depth":642,"text":17108,"children":17693},[17694,17695,17696],{"id":17111,"depth":649,"text":17112},{"id":17185,"depth":649,"text":17186},{"id":17323,"depth":649,"text":16935},{"id":15739,"depth":642,"text":15740},"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":15868,"description":17698},[1135],"topics\u002Fderivace",[1128,1145,17705,17706,17707],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":17710,"title":17711,"body":17712,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":23365,"navigation":664,"path":23366,"seo":23367,"sources":23368,"stem":23369,"tags":23370,"type":15858,"updated":677,"__hash__":23375},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":17713,"toc":23338},[17714,17717,17737,17741,17766,17770,17811,17900,17944,17948,17972,17979,17983,17993,18004,18008,18035,18044,18099,18105,18108,18114,18141,18147,18242,18401,18689,18693,18773,18779,18783,18879,18945,19112,19116,19194,19225,19252,19258,19290,19368,19453,19457,19519,19525,19528,19534,19648,19731,19775,19779,19825,19832,20148,20153,20177,20206,20273,20369,20373,20380,20387,20458,20578,20662,20665,20671,20997,21001,21162,21170,21306,21314,21552,21560,21563,21568,21824,21828,21999,22133,22170,22214,22217,22347,22437,22455,22459,22466,22472,22531,22534,22558,22561,22567,22570,22576,22579,22583,22620,22678,22866,22870,22942,22948,22955,22959,22965,23106,23110,23116,23152,23157,23333],[12,17715,17711],{"id":17716},"elasticita-poptávky-a-nabídky",[1635,17718,17719],{},[724,17720,17721,9930,17724,17726,17727,17730,17731,2247,17734,1853],{},[883,17722,17723],{},"!abstract",[38,17725,15775],{}," 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: ",[38,17728,17729],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,17732,17733],{},"křížově-cenovou elasticitu",[38,17735,17736],{},"důchodovou elasticitu",[115,17738,17740],{"id":17739},"úvod-motivace","Úvod — motivace",[724,17742,17743,17744,17746,17747,17750,17751,17754,17755,17758,17759,17762,17763,2365],{},"Termín ",[614,17745,3533],{}," (alternativně ",[614,17748,17749],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,17752,17753],{},"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 ",[614,17756,17757],{},"cenové elasticity poptávky"," (resp. ",[614,17760,17761],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,17764,15758],{"className":17765,"dataFsResolvedFilePath":764,"href":765},[210],[198,17767,17769],{"id":17768},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,17771,17772,17773,17791,17792,17810],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,17774,17776],{"className":17775},[886],[888,17777,17778],{"xmlns":890},[892,17779,17780,17788],{},[895,17781,17782,17784,17786],{},[898,17783,1690],{},[1716,17785,1913],{},[1712,17787,2998],{},[902,17789,17790],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,17793,17795],{"className":17794},[886],[888,17796,17797],{"xmlns":890},[892,17798,17799,17807],{},[895,17800,17801,17803,17805],{},[898,17802,1878],{},[1716,17804,1913],{},[1712,17806,12151],{},[902,17808,17809],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,17812,17813,17858],{},[123,17814,17815,17818,17819,17857],{},[38,17816,17817],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,17820,17822],{"className":17821},[886],[888,17823,17824],{"xmlns":890},[892,17825,17826,17854],{},[895,17827,17828,17831,17834,17836,17838,17841,17843,17845,17847,17849,17851],{},[2074,17829,17830],{},"  ",[1716,17832,17833],{},"⇒",[2074,17835,17830],{},[898,17837,4164],{},[898,17839,17840],{},"R",[1716,17842,1913],{},[1712,17844,7141],{},[1716,17846,9532],{},[1712,17848,17083],{},[1716,17850,1913],{},[1712,17852,17853],{},"990",[902,17855,17856],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,17859,17860,17863,17864,17899],{},[38,17861,17862],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,17865,17867],{"className":17866},[886],[888,17868,17869],{"xmlns":890},[892,17870,17871,17896],{},[895,17872,17873,17875,17877,17879,17881,17883,17885,17887,17889,17891,17893],{},[2074,17874,17830],{},[1716,17876,17833],{},[2074,17878,17830],{},[898,17880,4164],{},[898,17882,17840],{},[1716,17884,1913],{},[1712,17886,7141],{},[1716,17888,9532],{},[1712,17890,11814],{},[1716,17892,1913],{},[1712,17894,17895],{},"1080",[902,17897,17898],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,17901,17902,17903,17906,17907,17910,17911,17914,17915,17918,17919,17922,17923,17939,17940,17943],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,17904,17905],{},"nerozumné",", na Trhu 2 ",[38,17908,17909],{},"rozumné",". Trh 2 je ",[38,17912,17913],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,17916,17917],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,17920,17921],{},"neelastická"," a vyššího ",[883,17924,17926],{"className":17925},[886],[888,17927,17928],{"xmlns":890},[892,17929,17930,17936],{},[895,17931,17932,17934],{},[898,17933,4164],{},[898,17935,17840],{},[902,17937,17938],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,17941,17942],{},"zvýšením"," ceny.",[198,17945,17947],{"id":17946},"hypotéza-41","Hypotéza 4.1",[1635,17949,17950],{},[724,17951,17952,17953],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,17954,17956],{"className":17955},[886],[888,17957,17958],{"xmlns":890},[892,17959,17960,17969],{},[895,17961,17962,17964,17967],{},[1716,17963,1920],{"stretchy":1919},[1712,17965,17966],{},"4.1",[1716,17968,1925],{"stretchy":1919},[902,17970,17971],{"encoding":904},"(4.1)",[724,17973,17974,17975,17978],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,17976,17977],{},"procentní změny"," obou faktorů.",[115,17980,17982],{"id":17981},"pojem-elasticity","Pojem elasticity",[724,17984,17985,17986,17988,17989,17992],{},"Obecně ",[38,17987,3533],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,17990,17991],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1635,17994,17995],{},[724,17996,17997,17999,18000,18003],{},[883,17998,1641],{}," Intuice\nElasticitu lze číst jako ",[38,18001,18002],{},"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.",[115,18005,18007],{"id":18006},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,18009,18010,18011,18034],{},"Nechť ",[883,18012,18014],{"className":18013},[886],[888,18015,18016],{"xmlns":890},[892,18017,18018,18032],{},[895,18019,18020,18022,18024,18026,18028,18030],{},[898,18021,1878],{},[1716,18023,1913],{},[898,18025,1916],{},[1716,18027,1920],{"stretchy":1919},[898,18029,1690],{},[1716,18031,1925],{"stretchy":1919},[902,18033,1928],{"encoding":904}," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,18036,18037],{},[883,18038,18043],{"className":18039,"title":18041,"style":18042},[18040],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,18045,18046,18047,2247,18063,18079,18080,18098],{},"Znaménko minus je korekce: změny ",[883,18048,18050],{"className":18049},[886],[888,18051,18052],{"xmlns":890},[892,18053,18054,18060],{},[895,18055,18056,18058],{},[898,18057,8485],{"mathvariant":2068},[898,18059,1878],{},[902,18061,18062],{"encoding":904},"\\Delta Q",[883,18064,18066],{"className":18065},[886],[888,18067,18068],{"xmlns":890},[892,18069,18070,18076],{},[895,18071,18072,18074],{},[898,18073,8485],{"mathvariant":2068},[898,18075,1690],{},[902,18077,18078],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,18081,18083],{"className":18082},[886],[888,18084,18085],{"xmlns":890},[892,18086,18087,18095],{},[895,18088,18089],{},[3074,18090,18091,18093],{},[898,18092,1805],{},[898,18094,10871],{},[902,18096,18097],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,18100,18101],{},[883,18102,18104],{"className":18103,"title":18041,"style":18042},[18040],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,18106,18107],{},"Po dosazení:",[724,18109,18110],{},[883,18111,18113],{"className":18112,"title":18041,"style":18042},[18040],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,18115,18116,18117,18137,18138,18140],{},"Limitním přechodem ",[883,18118,18120],{"className":18119},[886],[888,18121,18122],{"xmlns":890},[892,18123,18124,18134],{},[895,18125,18126,18128,18130,18132],{},[898,18127,8485],{"mathvariant":2068},[898,18129,1690],{},[1716,18131,16986],{},[1712,18133,2505],{},[902,18135,18136],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,18139,17757],{}," (price elasticity of demand):",[724,18142,18143],{},[883,18144,18146],{"className":18145,"title":18041,"style":18042},[18040],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,18148,18149,18150,18173,18174,18195,18196,18220,18221,18241],{},"kde ",[883,18151,18153],{"className":18152},[886],[888,18154,18155],{"xmlns":890},[892,18156,18157,18171],{},[895,18158,18159,18161,18163,18165,18167,18169],{},[898,18160,1878],{},[1716,18162,1913],{},[898,18164,1916],{},[1716,18166,1920],{"stretchy":1919},[898,18168,1690],{},[1716,18170,1925],{"stretchy":1919},[902,18172,1928],{"encoding":904},". Pro pevnou cenu ",[883,18175,18177],{"className":18176},[886],[888,18178,18179],{"xmlns":890},[892,18180,18181,18193],{},[895,18182,18183,18185,18187],{},[898,18184,1690],{},[1716,18186,1913],{},[3074,18188,18189,18191],{},[898,18190,1690],{},[1716,18192,3080],{},[902,18194,3157],{"encoding":904}," se ",[883,18197,18199],{"className":18198},[886],[888,18200,18201],{"xmlns":890},[892,18202,18203,18217],{},[895,18204,18205,18207,18209,18215],{},[898,18206,1805],{},[1716,18208,1920],{"stretchy":1919},[3074,18210,18211,18213],{},[898,18212,1690],{},[1716,18214,3080],{},[1716,18216,1925],{"stretchy":1919},[902,18218,18219],{"encoding":904},"E(P^*)"," nazývá ",[614,18222,18223,18224],{},"elasticita poptávky při ceně ",[883,18225,18227],{"className":18226},[886],[888,18228,18229],{"xmlns":890},[892,18230,18231,18239],{},[895,18232,18233],{},[3074,18234,18235,18237],{},[898,18236,1690],{},[1716,18238,3080],{},[902,18240,3083],{"encoding":904}," a je to vždy nezáporné číslo.",[1635,18243,18244],{},[724,18245,18246,18248,18249,18267,18268,18296,18297,18326,18327,1343,18345,1343,18363,18381,18382,18397,18398,1853],{},[883,18247,2233],{}," Pozor na znaménko\nV (4.5) je ",[38,18250,18251,18252],{},"explicitní ",[883,18253,18255],{"className":18254},[886],[888,18256,18257],{"xmlns":890},[892,18258,18259,18265],{},[895,18260,18261,18263],{},[1716,18262,2760],{},[1712,18264,1714],{},[902,18266,17589],{"encoding":904}," právě proto, že ",[883,18269,18271],{"className":18270},[886],[888,18272,18273],{"xmlns":890},[892,18274,18275,18293],{},[895,18276,18277,18283,18285,18287,18289,18291],{},[3074,18278,18279,18281],{},[898,18280,1878],{},[1716,18282,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,18284,1920],{"stretchy":1919},[898,18286,1690],{},[1716,18288,1925],{"stretchy":1919},[1716,18290,2704],{},[1712,18292,2505],{},[902,18294,18295],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,18298,18300],{"className":18299},[886],[888,18301,18302],{"xmlns":890},[892,18303,18304,18323],{},[895,18305,18306,18308,18310,18316,18318,18321],{},[898,18307,1805],{},[1716,18309,1920],{"stretchy":1919},[3074,18311,18312,18314],{},[898,18313,1690],{},[1716,18315,3080],{},[1716,18317,1925],{"stretchy":1919},[1716,18319,18320],{},"≥",[1712,18322,2505],{},[902,18324,18325],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,18328,18330],{"className":18329},[886],[888,18331,18332],{"xmlns":890},[892,18333,18334,18342],{},[895,18335,18336,18338,18340],{},[898,18337,1805],{},[1716,18339,2716],{},[1712,18341,1714],{},[902,18343,18344],{"encoding":904},"E > 1",[883,18346,18348],{"className":18347},[886],[888,18349,18350],{"xmlns":890},[892,18351,18352,18360],{},[895,18353,18354,18356,18358],{},[898,18355,1805],{},[1716,18357,2704],{},[1712,18359,1714],{},[902,18361,18362],{"encoding":904},"E \u003C 1",[883,18364,18366],{"className":18365},[886],[888,18367,18368],{"xmlns":890},[892,18369,18370,18378],{},[895,18371,18372,18374,18376],{},[898,18373,1805],{},[1716,18375,1913],{},[1712,18377,1714],{},[902,18379,18380],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,18383,18385],{"className":18384},[886],[888,18386,18387],{"xmlns":890},[892,18388,18389,18395],{},[895,18390,18391,18393],{},[1716,18392,2760],{},[1712,18394,1714],{},[902,18396,17589],{"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 ",[38,18399,18400],{},"absolutní hodnotou",[1635,18402,18403,18422],{},[724,18404,18405,18407,18408,18421],{},[883,18406,3776],{}," Postup: jak spočítat ",[883,18409,18411],{"className":18410},[886],[888,18412,18413],{"xmlns":890},[892,18414,18415,18419],{},[895,18416,18417],{},[898,18418,1805],{},[902,18420,1805],{"encoding":904}," v bodě",[152,18423,18424,18475,18514,18567,18632],{},[123,18425,18426,18427,18450,18451,18474],{},"Zapište ",[883,18428,18430],{"className":18429},[886],[888,18431,18432],{"xmlns":890},[892,18433,18434,18448],{},[895,18435,18436,18438,18440,18442,18444,18446],{},[898,18437,1878],{},[1716,18439,1913],{},[898,18441,1916],{},[1716,18443,1920],{"stretchy":1919},[898,18445,1690],{},[1716,18447,1925],{"stretchy":1919},[902,18449,1928],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,18452,18454],{"className":18453},[886],[888,18455,18456],{"xmlns":890},[892,18457,18458,18472],{},[895,18459,18460,18462,18464,18466,18468,18470],{},[898,18461,1690],{},[1716,18463,1913],{},[898,18465,1916],{},[1716,18467,1920],{"stretchy":1919},[898,18469,1878],{},[1716,18471,1925],{"stretchy":1919},[902,18473,4115],{"encoding":904},", použijte vztah (4.9).",[123,18476,18477,18478,1853],{},"Spočítejte derivaci ",[883,18479,18481],{"className":18480},[886],[888,18482,18483],{"xmlns":890},[892,18484,18485,18511],{},[895,18486,18487,18493,18495,18497,18499,18501,18503,18505,18507,18509],{},[3074,18488,18489,18491],{},[898,18490,1878],{},[1716,18492,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,18494,1920],{"stretchy":1919},[898,18496,1690],{},[1716,18498,1925],{"stretchy":1919},[1716,18500,1913],{},[898,18502,5198],{"mathvariant":2068},[898,18504,1878],{},[898,18506,3045],{"mathvariant":2068},[898,18508,5198],{"mathvariant":2068},[898,18510,1690],{},[902,18512,18513],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,18515,18516,18517,18534,18535,1853],{},"Dosaďte zadanou cenu ",[883,18518,18520],{"className":18519},[886],[888,18521,18522],{"xmlns":890},[892,18523,18524,18532],{},[895,18525,18526],{},[3074,18527,18528,18530],{},[898,18529,1690],{},[1716,18531,3080],{},[902,18533,3083],{"encoding":904}," a dopočítejte odpovídající ",[883,18536,18538],{"className":18537},[886],[888,18539,18540],{"xmlns":890},[892,18541,18542,18564],{},[895,18543,18544,18550,18552,18554,18556,18562],{},[3074,18545,18546,18548],{},[898,18547,1878],{},[1716,18549,3080],{},[1716,18551,1913],{},[898,18553,1916],{},[1716,18555,1920],{"stretchy":1919},[3074,18557,18558,18560],{},[898,18559,1690],{},[1716,18561,3080],{},[1716,18563,1925],{"stretchy":1919},[902,18565,18566],{"encoding":904},"Q^* = D(P^*)",[123,18568,18569,18570,1853],{},"Dosaďte do (4.5): ",[883,18571,18573],{"className":18572},[886],[888,18574,18575],{"xmlns":890},[892,18576,18577,18629],{},[895,18578,18579,18581,18583,18589,18591,18593,18595,18611,18613,18619,18621,18627],{},[898,18580,1805],{},[1716,18582,1920],{"stretchy":1919},[3074,18584,18585,18587],{},[898,18586,1690],{},[1716,18588,3080],{},[1716,18590,1925],{"stretchy":1919},[1716,18592,1913],{},[1716,18594,2760],{},[2747,18596,18597],{"scriptlevel":2505,"displaystyle":1718},[2750,18598,18599,18605],{},[3074,18600,18601,18603],{},[898,18602,1690],{},[1716,18604,3080],{},[3074,18606,18607,18609],{},[898,18608,1878],{},[1716,18610,3080],{},[2074,18612,8508],{},[3074,18614,18615,18617],{},[898,18616,1878],{},[1716,18618,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,18620,1920],{"stretchy":1919},[3074,18622,18623,18625],{},[898,18624,1690],{},[1716,18626,3080],{},[1716,18628,1925],{"stretchy":1919},[902,18630,18631],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,18633,18634,18635,18652,18653,18670,18671,18688],{},"Klasifikujte: ",[883,18636,18638],{"className":18637},[886],[888,18639,18640],{"xmlns":890},[892,18641,18642,18650],{},[895,18643,18644,18646,18648],{},[898,18645,1805],{},[1716,18647,2716],{},[1712,18649,1714],{},[902,18651,18344],{"encoding":904}," elastická, ",[883,18654,18656],{"className":18655},[886],[888,18657,18658],{"xmlns":890},[892,18659,18660,18668],{},[895,18661,18662,18664,18666],{},[898,18663,1805],{},[1716,18665,1913],{},[1712,18667,1714],{},[902,18669,18380],{"encoding":904}," jednotková, ",[883,18672,18674],{"className":18673},[886],[888,18675,18676],{"xmlns":890},[892,18677,18678,18686],{},[895,18679,18680,18682,18684],{},[898,18681,1805],{},[1716,18683,2704],{},[1712,18685,1714],{},[902,18687,18362],{"encoding":904}," neelastická.",[198,18690,18692],{"id":18691},"interpretace-46","Interpretace (4.6)",[1635,18694,18695],{},[724,18696,18697,18698,18721,18722,18735,18736,18753,18754],{},"Číslo ",[883,18699,18701],{"className":18700},[886],[888,18702,18703],{"xmlns":890},[892,18704,18705,18719],{},[895,18706,18707,18709,18711,18717],{},[898,18708,1805],{},[1716,18710,1920],{"stretchy":1919},[3074,18712,18713,18715],{},[898,18714,1690],{},[1716,18716,3080],{},[1716,18718,1925],{"stretchy":1919},[902,18720,18219],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,18723,18725],{"className":18724},[886],[888,18726,18727],{"xmlns":890},[892,18728,18729,18733],{},[895,18730,18731],{},[898,18732,1878],{},[902,18734,1878],{"encoding":904},", jestliže se cena ",[883,18737,18739],{"className":18738},[886],[888,18740,18741],{"xmlns":890},[892,18742,18743,18751],{},[895,18744,18745],{},[3074,18746,18747,18749],{},[898,18748,1690],{},[1716,18750,3080],{},[902,18752,3083],{"encoding":904}," změní o 1 %. ",[883,18755,18757],{"className":18756},[886],[888,18758,18759],{"xmlns":890},[892,18760,18761,18770],{},[895,18762,18763,18765,18768],{},[1716,18764,1920],{"stretchy":1919},[1712,18766,18767],{},"4.6",[1716,18769,1925],{"stretchy":1919},[902,18771,18772],{"encoding":904},"(4.6)",[724,18774,18775,18778],{},[38,18776,18777],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,18780,18782],{"id":18781},"příklad-41","Příklad 4.1",[724,18784,18785,18786,18820,18821,1343,18845,2291],{},"Poptávka ",[883,18787,18789],{"className":18788},[886],[888,18790,18791],{"xmlns":890},[892,18792,18793,18817],{},[895,18794,18795,18797,18799,18801,18803,18805,18807,18809,18811,18813,18815],{},[898,18796,1690],{},[1716,18798,1913],{},[898,18800,1916],{},[1716,18802,1920],{"stretchy":1919},[898,18804,1878],{},[1716,18806,1925],{"stretchy":1919},[1716,18808,1913],{},[1712,18810,5808],{},[1716,18812,2760],{},[1712,18814,1726],{},[898,18816,1878],{},[902,18818,18819],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,18822,18824],{"className":18823},[886],[888,18825,18826],{"xmlns":890},[892,18827,18828,18842],{},[895,18829,18830,18832,18834,18836,18838,18840],{},[898,18831,1878],{},[1716,18833,1913],{},[1712,18835,5778],{},[1716,18837,2760],{},[1712,18839,5771],{},[898,18841,1690],{},[902,18843,18844],{"encoding":904},"Q = 25 - 0{,}5P",[883,18846,18848],{"className":18847},[886],[888,18849,18850],{"xmlns":890},[892,18851,18852,18876],{},[895,18853,18854,18870,18872,18874],{},[2747,18855,18856],{"scriptlevel":2505,"displaystyle":1718},[2750,18857,18858,18864],{},[895,18859,18860,18862],{},[898,18861,5198],{"mathvariant":2068},[898,18863,1878],{},[895,18865,18866,18868],{},[898,18867,5198],{"mathvariant":2068},[898,18869,1690],{},[1716,18871,1913],{},[1716,18873,2760],{},[1712,18875,5771],{},[902,18877,18878],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,18880,18881],{},[883,18882,18884],{"className":18883},[886],[888,18885,18886],{"xmlns":890},[892,18887,18888,18942],{},[895,18889,18890,18892,18894,18896,18910,18912,18914,18916,18918,18920,18922,18940],{},[898,18891,1805],{},[1716,18893,1913],{},[1716,18895,2760],{},[2750,18897,18898,18900],{},[898,18899,1690],{},[895,18901,18902,18904,18906,18908],{},[1712,18903,5778],{},[1716,18905,2760],{},[1712,18907,5771],{},[898,18909,1690],{},[1716,18911,9532],{},[1716,18913,1920],{"stretchy":1919},[1716,18915,2760],{},[1712,18917,5771],{},[1716,18919,1925],{"stretchy":1919},[1716,18921,1913],{},[2750,18923,18924,18930],{},[895,18925,18926,18928],{},[1712,18927,5771],{},[898,18929,1690],{},[895,18931,18932,18934,18936,18938],{},[1712,18933,5778],{},[1716,18935,2760],{},[1712,18937,5771],{},[898,18939,1690],{},[898,18941,1853],{"mathvariant":2068},[902,18943,18944],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,18946,18947,18948,1343,18972,1343,19002,1343,19026,19050,19051,19074,19075,3942,19093,2365],{},"Potom ",[883,18949,18951],{"className":18950},[886],[888,18952,18953],{"xmlns":890},[892,18954,18955,18969],{},[895,18956,18957,18959,18961,18963,18965,18967],{},[898,18958,1805],{},[1716,18960,1920],{"stretchy":1919},[1712,18962,2505],{},[1716,18964,1925],{"stretchy":1919},[1716,18966,1913],{},[1712,18968,2505],{},[902,18970,18971],{"encoding":904},"E(0)=0",[883,18973,18975],{"className":18974},[886],[888,18976,18977],{"xmlns":890},[892,18978,18979,18999],{},[895,18980,18981,18983,18985,18987,18989,18991],{},[898,18982,1805],{},[1716,18984,1920],{"stretchy":1919},[1712,18986,2998],{},[1716,18988,1925],{"stretchy":1919},[1716,18990,1913],{},[2747,18992,18993],{"scriptlevel":2505,"displaystyle":1919},[2750,18994,18995,18997],{},[1712,18996,1714],{},[1712,18998,6849],{},[902,19000,19001],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,19003,19005],{"className":19004},[886],[888,19006,19007],{"xmlns":890},[892,19008,19009,19023],{},[895,19010,19011,19013,19015,19017,19019,19021],{},[898,19012,1805],{},[1716,19014,1920],{"stretchy":1919},[1712,19016,5778],{},[1716,19018,1925],{"stretchy":1919},[1716,19020,1913],{},[1712,19022,1714],{},[902,19024,19025],{"encoding":904},"E(25)=1",[883,19027,19029],{"className":19028},[886],[888,19030,19031],{"xmlns":890},[892,19032,19033,19047],{},[895,19034,19035,19037,19039,19041,19043,19045],{},[898,19036,1805],{},[1716,19038,1920],{"stretchy":1919},[1712,19040,2973],{},[1716,19042,1925],{"stretchy":1919},[1716,19044,1913],{},[1712,19046,6849],{},[902,19048,19049],{"encoding":904},"E(40)=4",". Např. ",[883,19052,19054],{"className":19053},[886],[888,19055,19056],{"xmlns":890},[892,19057,19058,19072],{},[895,19059,19060,19062,19064,19066,19068,19070],{},[898,19061,1805],{},[1716,19063,1920],{"stretchy":1919},[1712,19065,2973],{},[1716,19067,1925],{"stretchy":1919},[1716,19069,1913],{},[1712,19071,6849],{},[902,19073,19049],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,19076,19078],{"className":19077},[886],[888,19079,19080],{"xmlns":890},[892,19081,19082,19090],{},[895,19083,19084,19086,19088],{},[898,19085,1878],{},[1716,19087,1913],{},[1712,19089,6985],{},[902,19091,19092],{"encoding":904},"Q=5",[883,19094,19096],{"className":19095},[886],[888,19097,19098],{"xmlns":890},[892,19099,19100,19109],{},[895,19101,19102,19104,19106],{},[898,19103,1878],{},[1716,19105,1913],{},[1712,19107,19108],{},"4,8",[902,19110,19111],{"encoding":904},"Q=4{,}8",[198,19113,19115],{"id":19114},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,19117,19118,19174],{},[123,19119,19120,19123,19124,19141,19142,1853],{},[38,19121,19122],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,19125,19127],{"className":19126},[886],[888,19128,19129],{"xmlns":890},[892,19130,19131,19139],{},[895,19132,19133],{},[3074,19134,19135,19137],{},[898,19136,1805],{},[898,19138,10871],{},[902,19140,18097],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,19143,19145],{"className":19144},[886],[888,19146,19147],{"xmlns":890},[892,19148,19149,19171],{},[895,19150,19151,19154,19156,19158,19160,19162,19164,19166,19168],{},[1716,19152,19153],{"stretchy":1919},"⟨",[898,19155,1690],{},[1716,19157,1719],{"separator":1718},[2074,19159,8508],{},[898,19161,1690],{},[1716,19163,1949],{},[898,19165,8485],{"mathvariant":2068},[898,19167,1690],{},[1716,19169,19170],{"stretchy":1919},"⟩",[902,19172,19173],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,19175,19176,19179,19180,19193],{},[38,19177,19178],{},"Bodová"," (okamžitá) elasticita: ",[883,19181,19183],{"className":19182},[886],[888,19184,19185],{"xmlns":890},[892,19186,19187,19191],{},[895,19188,19189],{},[898,19190,1805],{},[902,19192,1805],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,19195,19197,19198,19211,19212],{"id":19196},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,19199,19201],{"className":19200},[886],[888,19202,19203],{"xmlns":890},[892,19204,19205,19209],{},[895,19206,19207],{},[898,19208,1690],{},[902,19210,1690],{"encoding":904}," jako funkce ",[883,19213,19215],{"className":19214},[886],[888,19216,19217],{"xmlns":890},[892,19218,19219,19223],{},[895,19220,19221],{},[898,19222,1878],{},[902,19224,1878],{"encoding":904},[724,19226,19227,19228,19251],{},"Pokud je poptávka zadaná ve tvaru ",[883,19229,19231],{"className":19230},[886],[888,19232,19233],{"xmlns":890},[892,19234,19235,19249],{},[895,19236,19237,19239,19241,19243,19245,19247],{},[898,19238,1690],{},[1716,19240,1913],{},[898,19242,1916],{},[1716,19244,1920],{"stretchy":1919},[898,19246,1878],{},[1716,19248,1925],{"stretchy":1919},[902,19250,4115],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,19253,19254],{},[883,19255,19257],{"className":19256,"title":18041,"style":18042},[18040],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,19259,19260,3495,19263,19289],{},[38,19261,19262],{},"Příklad 4.3.",[883,19264,19266],{"className":19265},[886],[888,19267,19268],{"xmlns":890},[892,19269,19270,19286],{},[895,19271,19272,19274,19276,19278,19280],{},[898,19273,1690],{},[1716,19275,1913],{},[1712,19277,12151],{},[1716,19279,2760],{},[3074,19281,19282,19284],{},[898,19283,1878],{},[1712,19285,1726],{},[902,19287,19288],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,19291,19292],{},[883,19293,19295],{"className":19294},[886],[888,19296,19297],{"xmlns":890},[892,19298,19299,19365],{},[895,19300,19301,19303,19305,19307,19323,19325,19337,19339,19363],{},[898,19302,1805],{},[1716,19304,1913],{},[1716,19306,2760],{},[2750,19308,19309,19321],{},[895,19310,19311,19313,19315],{},[1712,19312,12151],{},[1716,19314,2760],{},[3074,19316,19317,19319],{},[898,19318,1878],{},[1712,19320,1726],{},[898,19322,1878],{},[1716,19324,9532],{},[2750,19326,19327,19329],{},[1712,19328,1714],{},[895,19330,19331,19333,19335],{},[1716,19332,2760],{},[1712,19334,1726],{},[898,19336,1878],{},[1716,19338,1913],{},[2750,19340,19341,19353],{},[895,19342,19343,19345,19347],{},[1712,19344,12151],{},[1716,19346,2760],{},[3074,19348,19349,19351],{},[898,19350,1878],{},[1712,19352,1726],{},[895,19354,19355,19357],{},[1712,19356,1726],{},[3074,19358,19359,19361],{},[898,19360,1878],{},[1712,19362,1726],{},[898,19364,1853],{"mathvariant":2068},[902,19366,19367],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,19369,19370,19371,19398,19399,19417,19418,1853],{},"Z rovnice ",[883,19372,19374],{"className":19373},[886],[888,19375,19376],{"xmlns":890},[892,19377,19378,19395],{},[895,19379,19380,19382,19384,19390,19392],{},[1712,19381,12151],{},[1716,19383,2760],{},[3074,19385,19386,19388],{},[898,19387,1878],{},[1712,19389,1726],{},[1716,19391,1913],{},[1712,19393,19394],{},"36",[902,19396,19397],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,19400,19402],{"className":19401},[886],[888,19403,19404],{"xmlns":890},[892,19405,19406,19414],{},[895,19407,19408,19410,19412],{},[898,19409,1878],{},[1716,19411,1913],{},[1712,19413,12398],{},[902,19415,19416],{"encoding":904},"Q = 8",", tedy ",[883,19419,19421],{"className":19420},[886],[888,19422,19423],{"xmlns":890},[892,19424,19425,19450],{},[895,19426,19427,19429,19431,19433,19435,19437,19445,19447],{},[898,19428,1805],{},[1716,19430,1920],{"stretchy":1919},[1712,19432,12398],{},[1716,19434,1925],{"stretchy":1919},[1716,19436,1913],{},[2747,19438,19439],{"scriptlevel":2505,"displaystyle":1919},[2750,19440,19441,19443],{},[1712,19442,19394],{},[1712,19444,6776],{},[1716,19446,1913],{},[1712,19448,19449],{},"0,281",[902,19451,19452],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,19454,19456],{"id":19455},"přibližné-změny","Přibližné změny",[724,19458,19459,19460,3569,19496,19518],{},"Diferenciál ",[883,19461,19463],{"className":19462},[886],[888,19464,19465],{"xmlns":890},[892,19466,19467,19493],{},[895,19468,19469,19471,19473,19475,19481,19483,19485,19487,19489,19491],{},[898,19470,5198],{"mathvariant":2068},[898,19472,1878],{},[1716,19474,1913],{},[3074,19476,19477,19479],{},[898,19478,1878],{},[1716,19480,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,19482,1920],{"stretchy":1919},[898,19484,1690],{},[1716,19486,1925],{"stretchy":1919},[2074,19488,8508],{},[898,19490,5198],{"mathvariant":2068},[898,19492,1690],{},[902,19494,19495],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P",[883,19497,19499],{"className":19498},[886],[888,19500,19501],{"xmlns":890},[892,19502,19503,19515],{},[895,19504,19505,19507,19509,19511,19513],{},[898,19506,5198],{"mathvariant":2068},[898,19508,1690],{},[1716,19510,1913],{},[898,19512,8485],{"mathvariant":2068},[898,19514,1690],{},[902,19516,19517],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,19520,19521],{},[883,19522,19524],{"className":19523,"title":18041,"style":18042},[18040],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,19526,19527],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,19529,19530],{},[883,19531,19533],{"className":19532,"title":18041,"style":18042},[18040],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,19535,19536,3495,19539,19574,19575,19594,19595,19629,19630,19647],{},[38,19537,19538],{},"Příklad 4.5.",[883,19540,19542],{"className":19541},[886],[888,19543,19544],{"xmlns":890},[892,19545,19546,19571],{},[895,19547,19548,19550,19552,19554,19560,19562,19564,19566,19568],{},[898,19549,1690],{},[1716,19551,1913],{},[1716,19553,2760],{},[3074,19555,19556,19558],{},[898,19557,1878],{},[1712,19559,1726],{},[1716,19561,2760],{},[1712,19563,6849],{},[898,19565,1878],{},[1716,19567,1949],{},[1712,19569,19570],{},"96",[902,19572,19573],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,19576,19578],{"className":19577},[886],[888,19579,19580],{"xmlns":890},[892,19581,19582,19591],{},[895,19583,19584,19586,19588],{},[898,19585,1690],{},[1716,19587,1913],{},[1712,19589,19590],{},"51",[902,19592,19593],{"encoding":904},"P=51",". Z rovnice ",[883,19596,19598],{"className":19597},[886],[888,19599,19600],{"xmlns":890},[892,19601,19602,19626],{},[895,19603,19604,19606,19608,19610,19616,19618,19620,19622,19624],{},[1712,19605,19590],{},[1716,19607,1913],{},[1716,19609,2760],{},[3074,19611,19612,19614],{},[898,19613,1878],{},[1712,19615,1726],{},[1716,19617,2760],{},[1712,19619,6849],{},[898,19621,1878],{},[1716,19623,1949],{},[1712,19625,19570],{},[902,19627,19628],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,19631,19633],{"className":19632},[886],[888,19634,19635],{"xmlns":890},[892,19636,19637,19645],{},[895,19638,19639,19641,19643],{},[898,19640,1878],{},[1716,19642,1913],{},[1712,19644,6985],{},[902,19646,19092],{"encoding":904},". Elasticita:",[724,19649,19650],{},[883,19651,19653],{"className":19652},[886],[888,19654,19655],{"xmlns":890},[892,19656,19657,19728],{},[895,19658,19659,19661,19663,19701,19703,19705,19707,19709,19711,19713,19715,19722,19725],{},[898,19660,1805],{},[1716,19662,1913],{},[2750,19664,19665,19685],{},[895,19666,19667,19669,19675,19677,19679,19681,19683],{},[1716,19668,2760],{},[3074,19670,19671,19673],{},[898,19672,1878],{},[1712,19674,1726],{},[1716,19676,2760],{},[1712,19678,6849],{},[898,19680,1878],{},[1716,19682,1949],{},[1712,19684,19570],{},[895,19686,19687,19689,19691,19693,19695,19697,19699],{},[898,19688,1878],{},[1716,19690,1920],{"stretchy":1919},[1712,19692,1726],{},[898,19694,1878],{},[1716,19696,1949],{},[1712,19698,6849],{},[1716,19700,1925],{"stretchy":1919},[1716,19702,1719],{"separator":1718},[2324,19704],{"width":2326},[898,19706,1805],{},[1716,19708,1920],{"stretchy":1919},[1712,19710,6985],{},[1716,19712,1925],{"stretchy":1919},[1716,19714,1913],{},[2750,19716,19717,19719],{},[1712,19718,19590],{},[1712,19720,19721],{},"70",[1716,19723,19724],{},"≐",[1712,19726,19727],{},"0,728.",[902,19729,19730],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,19732,19733,19734,1853],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,19735,19737],{"className":19736},[886],[888,19738,19739],{"xmlns":890},[892,19740,19741,19772],{},[895,19742,19743,19745,19747,19750,19752,19754,19757,19759,19761,19763,19765,19768,19770],{},[898,19744,8485],{"mathvariant":2068},[898,19746,1878],{},[898,19748,19749],{"mathvariant":2068},"%",[1716,19751,8490],{},[1716,19753,2760],{},[1712,19755,19756],{},"0,728",[1716,19758,9532],{},[1712,19760,1726],{},[1716,19762,1913],{},[1716,19764,2760],{},[1712,19766,19767],{},"1,456",[2074,19769,8508],{},[898,19771,19749],{"mathvariant":2068},[902,19773,19774],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,19776,19778],{"id":19777},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,19780,19781,19782,19805,19806,2291],{},"V závislosti na hodnotě ",[883,19783,19785],{"className":19784},[886],[888,19786,19787],{"xmlns":890},[892,19788,19789,19803],{},[895,19790,19791,19793,19795,19801],{},[898,19792,1805],{},[1716,19794,1920],{"stretchy":1919},[3074,19796,19797,19799],{},[898,19798,1690],{},[1716,19800,3080],{},[1716,19802,1925],{"stretchy":1919},[902,19804,18219],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,19807,19809],{"className":19808},[886],[888,19810,19811],{"xmlns":890},[892,19812,19813,19822],{},[895,19814,19815,19817,19820],{},[1716,19816,1920],{"stretchy":1919},[1712,19818,19819],{},"4.7",[1716,19821,1925],{"stretchy":1919},[902,19823,19824],{"encoding":904},"(4.7)",[724,19826,19827],{},[3682,19828],{"alt":19829,"className":19830,"src":19831},"imek-typy-elasticity-5panelu",[210,3686],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,19833,19834,19873],{},[19,19835,19836],{},[22,19837,19838,19864,19867,19870],{},[25,19839,19840,19841],{},"Hodnota ",[883,19842,19844],{"className":19843},[886],[888,19845,19846],{"xmlns":890},[892,19847,19848,19862],{},[895,19849,19850,19852,19854,19860],{},[898,19851,1805],{},[1716,19853,1920],{"stretchy":1919},[3074,19855,19856,19858],{},[898,19857,1690],{},[1716,19859,3080],{},[1716,19861,1925],{"stretchy":1919},[902,19863,18219],{"encoding":904},[25,19865,19866],{},"Typ poptávky",[25,19868,19869],{},"Termín",[25,19871,19872],{},"Význam",[30,19874,19875,19908,19970,20044,20101],{},[22,19876,19877,19897,19902,19905],{},[35,19878,19879],{},[883,19880,19882],{"className":19881},[886],[888,19883,19884],{"xmlns":890},[892,19885,19886,19894],{},[895,19887,19888,19890,19892],{},[898,19889,1805],{},[1716,19891,1913],{},[1712,19893,2505],{},[902,19895,19896],{"encoding":904},"E = 0",[35,19898,19899],{},[38,19900,19901],{},"dokonale neelastická",[35,19903,19904],{},"perfectly inelastic",[35,19906,19907],{},"množství se nemění bez ohledu na cenu",[22,19909,19910,19934,19938,19941],{},[35,19911,19912],{},[883,19913,19915],{"className":19914},[886],[888,19916,19917],{"xmlns":890},[892,19918,19919,19931],{},[895,19920,19921,19923,19925,19927,19929],{},[1712,19922,2505],{},[1716,19924,2704],{},[898,19926,1805],{},[1716,19928,2704],{},[1712,19930,1714],{},[902,19932,19933],{"encoding":904},"0 \u003C E \u003C 1",[35,19935,19936],{},[38,19937,17921],{},[35,19939,19940],{},"inelastic",[35,19942,19943,19956,19957],{},[883,19944,19946],{"className":19945},[886],[888,19947,19948],{"xmlns":890},[892,19949,19950,19954],{},[895,19951,19952],{},[898,19953,1878],{},[902,19955,1878],{"encoding":904}," se mění pomaleji než ",[883,19958,19960],{"className":19959},[886],[888,19961,19962],{"xmlns":890},[892,19963,19964,19968],{},[895,19965,19966],{},[898,19967,1690],{},[902,19969,1690],{"encoding":904},[22,19971,19972,19991,19996,19999],{},[35,19973,19974],{},[883,19975,19977],{"className":19976},[886],[888,19978,19979],{"xmlns":890},[892,19980,19981,19989],{},[895,19982,19983,19985,19987],{},[898,19984,1805],{},[1716,19986,1913],{},[1712,19988,1714],{},[902,19990,18380],{"encoding":904},[35,19992,19993],{},[38,19994,19995],{},"jednotkově elastická",[35,19997,19998],{},"unit elastic",[35,20000,20001,7364,20014,20027,20028,20043],{},[883,20002,20004],{"className":20003},[886],[888,20005,20006],{"xmlns":890},[892,20007,20008,20012],{},[895,20009,20010],{},[898,20011,1878],{},[902,20013,1878],{"encoding":904},[883,20015,20017],{"className":20016},[886],[888,20018,20019],{"xmlns":890},[892,20020,20021,20025],{},[895,20022,20023],{},[898,20024,1690],{},[902,20026,1690],{"encoding":904}," se mění stejně rychle; ",[883,20029,20031],{"className":20030},[886],[888,20032,20033],{"xmlns":890},[892,20034,20035,20041],{},[895,20036,20037,20039],{},[898,20038,4164],{},[898,20040,17840],{},[902,20042,17938],{"encoding":904}," má maximum",[22,20045,20046,20065,20069,20072],{},[35,20047,20048],{},[883,20049,20051],{"className":20050},[886],[888,20052,20053],{"xmlns":890},[892,20054,20055,20063],{},[895,20056,20057,20059,20061],{},[898,20058,1805],{},[1716,20060,2716],{},[1712,20062,1714],{},[902,20064,18344],{"encoding":904},[35,20066,20067],{},[38,20068,17917],{},[35,20070,20071],{},"elastic",[35,20073,20074,20087,20088],{},[883,20075,20077],{"className":20076},[886],[888,20078,20079],{"xmlns":890},[892,20080,20081,20085],{},[895,20082,20083],{},[898,20084,1878],{},[902,20086,1878],{"encoding":904}," se mění rychleji než ",[883,20089,20091],{"className":20090},[886],[888,20092,20093],{"xmlns":890},[892,20094,20095,20099],{},[895,20096,20097],{},[898,20098,1690],{},[902,20100,1690],{"encoding":904},[22,20102,20103,20124,20129,20132],{},[35,20104,20105],{},[883,20106,20108],{"className":20107},[886],[888,20109,20110],{"xmlns":890},[892,20111,20112,20121],{},[895,20113,20114,20116,20118],{},[898,20115,1805],{},[1716,20117,16986],{},[898,20119,20120],{"mathvariant":2068},"∞",[902,20122,20123],{"encoding":904},"E \\to \\infty",[35,20125,20126],{},[38,20127,20128],{},"dokonale elastická",[35,20130,20131],{},"perfectly elastic",[35,20133,20134,20135],{},"sebemenší změna ceny úplně mění ",[883,20136,20138],{"className":20137},[886],[888,20139,20140],{"xmlns":890},[892,20141,20142,20146],{},[895,20143,20144],{},[898,20145,1878],{},[902,20147,1878],{"encoding":904},[724,20149,20150],{},[38,20151,20152],{},"Pravidlo růstu elasticity s cenou:",[1635,20154,20155],{},[724,20156,20157,20158],{},"S rostoucí cenou elasticita poptávky roste. ",[883,20159,20161],{"className":20160},[886],[888,20162,20163],{"xmlns":890},[892,20164,20165,20174],{},[895,20166,20167,20169,20172],{},[1716,20168,1920],{"stretchy":1919},[1712,20170,20171],{},"4.8",[1716,20173,1925],{"stretchy":1919},[902,20175,20176],{"encoding":904},"(4.8)",[724,20178,20179,20180,20183,20184,20187,20188,20205],{},"Z toho plyne, že při ",[614,20181,20182],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,20185,20186],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,20189,20191],{"className":20190},[886],[888,20192,20193],{"xmlns":890},[892,20194,20195,20203],{},[895,20196,20197],{},[3074,20198,20199,20201],{},[898,20200,1690],{},[1716,20202,3080],{},[902,20204,3083],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1635,20207,20208,20213],{},[724,20209,20210,20212],{},[883,20211,3776],{}," Postup: jak klasifikovat poptávku",[152,20214,20215,20242,20245],{},[123,20216,20217,20218,20241],{},"Spočítejte ",[883,20219,20221],{"className":20220},[886],[888,20222,20223],{"xmlns":890},[892,20224,20225,20239],{},[895,20226,20227,20229,20231,20237],{},[898,20228,1805],{},[1716,20230,1920],{"stretchy":1919},[3074,20232,20233,20235],{},[898,20234,1690],{},[1716,20236,3080],{},[1716,20238,1925],{"stretchy":1919},[902,20240,18219],{"encoding":904}," dle (4.5).",[123,20243,20244],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,20246,20247,20248,20272],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,20249,20251],{"className":20250},[886],[888,20252,20253],{"xmlns":890},[892,20254,20255,20269],{},[895,20256,20257,20259,20261,20263,20265,20267],{},[898,20258,1805],{},[1716,20260,1920],{"stretchy":1919},[898,20262,1690],{},[1716,20264,1925],{"stretchy":1919},[1716,20266,1913],{},[1712,20268,1714],{},[902,20270,20271],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,20274,20275,20278,20279,20296,20297,20315,20316,20342,20343,1853],{},[38,20276,20277],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,20280,20282],{"className":20281},[886],[888,20283,20284],{"xmlns":890},[892,20285,20286,20294],{},[895,20287,20288,20290,20292],{},[898,20289,1805],{},[1716,20291,1913],{},[1712,20293,1714],{},[902,20295,18380],{"encoding":904}," pro ",[883,20298,20300],{"className":20299},[886],[888,20301,20302],{"xmlns":890},[892,20303,20304,20312],{},[895,20305,20306,20308,20310],{},[898,20307,1690],{},[1716,20309,1913],{},[1712,20311,5778],{},[902,20313,20314],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,20317,20319],{"className":20318},[886],[888,20320,20321],{"xmlns":890},[892,20322,20323,20339],{},[895,20324,20325,20327,20329,20331,20333,20335,20337],{},[898,20326,1690],{},[1716,20328,3605],{},[1716,20330,19153],{"stretchy":1919},[1712,20332,2505],{},[1716,20334,1719],{"separator":1718},[1712,20336,5778],{},[1716,20338,1925],{"stretchy":1919},[902,20340,20341],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,20344,20346],{"className":20345},[886],[888,20347,20348],{"xmlns":890},[892,20349,20350,20366],{},[895,20351,20352,20354,20356,20358,20360,20362,20364],{},[898,20353,1690],{},[1716,20355,3605],{},[1716,20357,1920],{"stretchy":1919},[1712,20359,5778],{},[1716,20361,1719],{"separator":1718},[1712,20363,5808],{},[1716,20365,19170],{"stretchy":1919},[902,20367,20368],{"encoding":904},"P \\in (25, 50\\rangle",[115,20370,20372],{"id":20371},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,20374,20375],{},[3682,20376],{"alt":20377,"className":20378,"src":20379},"imek-elasticita-tr",[210,3686],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,20381,20382],{},[3682,20383],{"alt":20384,"className":20385,"src":20386},"imek-elasticita-podel-linearni-poptavky",[210,3686],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,20388,20389,20390,20440,20441,20457],{},"Pro celkový příjem platí ",[883,20391,20393],{"className":20392},[886],[888,20394,20395],{"xmlns":890},[892,20396,20397,20437],{},[895,20398,20399,20401,20403,20405,20407,20409,20411,20413,20415,20417,20419,20421,20423,20425,20427,20429,20431,20433,20435],{},[898,20400,4164],{},[898,20402,17840],{},[1716,20404,1913],{},[898,20406,4164],{},[898,20408,17840],{},[1716,20410,1920],{"stretchy":1919},[898,20412,1878],{},[1716,20414,1925],{"stretchy":1919},[1716,20416,1913],{},[898,20418,1690],{},[1716,20420,9532],{},[898,20422,1878],{},[1716,20424,1913],{},[898,20426,1878],{},[1716,20428,9532],{},[898,20430,1916],{},[1716,20432,1920],{"stretchy":1919},[898,20434,1878],{},[1716,20436,1925],{"stretchy":1919},[902,20438,20439],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,20442,20444],{"className":20443},[886],[888,20445,20446],{"xmlns":890},[892,20447,20448,20454],{},[895,20449,20450,20452],{},[898,20451,16690],{},[898,20453,17840],{},[902,20455,20456],{"encoding":904},"MR"," odvodíme:",[724,20459,20460],{},[883,20461,20463],{"className":20462},[886],[888,20464,20465],{"xmlns":890},[892,20466,20467,20575],{},[895,20468,20469,20471,20473,20475,20477,20483,20485,20487,20489,20491,20493,20495,20497,20499,20501,20503,20505,20511,20513,20515,20517,20519,20521,20523,20525,20539,20541,20543],{},[898,20470,16690],{},[898,20472,17840],{},[1716,20474,1913],{},[898,20476,4164],{},[3074,20478,20479,20481],{},[898,20480,17840],{},[1716,20482,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,20484,1920],{"stretchy":1919},[898,20486,1878],{},[1716,20488,1925],{"stretchy":1919},[1716,20490,1913],{},[898,20492,1916],{},[1716,20494,1920],{"stretchy":1919},[898,20496,1878],{},[1716,20498,1925],{"stretchy":1919},[1716,20500,1949],{},[898,20502,1878],{},[2074,20504,8508],{},[3074,20506,20507,20509],{},[898,20508,1916],{},[1716,20510,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,20512,1920],{"stretchy":1919},[898,20514,1878],{},[1716,20516,1925],{"stretchy":1919},[1716,20518,1913],{},[898,20520,1690],{},[1716,20522,1949],{},[898,20524,1878],{},[2750,20526,20527,20533],{},[895,20528,20529,20531],{},[898,20530,5198],{"mathvariant":2068},[898,20532,1690],{},[895,20534,20535,20537],{},[898,20536,5198],{"mathvariant":2068},[898,20538,1878],{},[1716,20540,1913],{},[898,20542,1690],{},[895,20544,20545,20547,20549,20551,20557,20559,20573],{},[1716,20546,1920],{"fence":1718},[1712,20548,1714],{},[1716,20550,1949],{},[2750,20552,20553,20555],{},[898,20554,1878],{},[898,20556,1690],{},[1716,20558,9532],{},[2750,20560,20561,20567],{},[895,20562,20563,20565],{},[898,20564,5198],{"mathvariant":2068},[898,20566,1690],{},[895,20568,20569,20571],{},[898,20570,5198],{"mathvariant":2068},[898,20572,1878],{},[1716,20574,1925],{"fence":1718},[902,20576,20577],{"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)",[724,20579,20580],{},[883,20581,20583],{"className":20582},[886],[888,20584,20585],{"xmlns":890},[892,20586,20587,20659],{},[895,20588,20589,20591,20593,20635,20637,20639],{},[1716,20590,1913],{},[898,20592,1690],{},[895,20594,20595,20597,20599,20601,20633],{},[1716,20596,1920],{"fence":1718},[1712,20598,1714],{},[1716,20600,1949],{},[2750,20602,20603,20605],{},[1712,20604,1714],{},[895,20606,20607,20615,20617],{},[2747,20608,20609],{"scriptlevel":2505,"displaystyle":1919},[2750,20610,20611,20613],{},[898,20612,1690],{},[898,20614,1878],{},[1716,20616,9532],{},[2747,20618,20619],{"scriptlevel":2505,"displaystyle":1919},[2750,20620,20621,20627],{},[895,20622,20623,20625],{},[898,20624,5198],{"mathvariant":2068},[898,20626,1878],{},[895,20628,20629,20631],{},[898,20630,5198],{"mathvariant":2068},[898,20632,1690],{},[1716,20634,1925],{"fence":1718},[1716,20636,1913],{},[898,20638,1690],{},[895,20640,20641,20643,20645,20647,20657],{},[1716,20642,1920],{"fence":1718},[1712,20644,1714],{},[1716,20646,1949],{},[2750,20648,20649,20651],{},[1712,20650,1714],{},[895,20652,20653,20655],{},[1716,20654,2760],{},[898,20656,1805],{},[1716,20658,1925],{"fence":1718},[902,20660,20661],{"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)",[724,20663,20664],{},"a tedy",[724,20666,20667],{},[883,20668,20670],{"className":20669,"title":18041,"style":18042},[18040],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1635,20672,20673,20742,20991],{},[724,20674,20675,20677,20678,20712,20713,20728,20729,2291],{},[883,20676,1641],{}," Intuice: vztah ",[883,20679,20681],{"className":20680},[886],[888,20682,20683],{"xmlns":890},[892,20684,20685,20709],{},[895,20686,20687,20689,20691,20693,20695,20697,20699,20701,20703,20705,20707],{},[898,20688,16690],{},[898,20690,17840],{},[1716,20692,1913],{},[898,20694,1690],{},[1716,20696,1920],{"stretchy":1919},[1712,20698,1714],{},[1716,20700,2760],{},[1712,20702,1714],{},[898,20704,3045],{"mathvariant":2068},[898,20706,1805],{},[1716,20708,1925],{"stretchy":1919},[902,20710,20711],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,20714,20716],{"className":20715},[886],[888,20717,20718],{"xmlns":890},[892,20719,20720,20726],{},[895,20721,20722,20724],{},[898,20723,16690],{},[898,20725,17840],{},[902,20727,20456],{"encoding":904}," jednoznačně určuje hodnota ",[883,20730,20732],{"className":20731},[886],[888,20733,20734],{"xmlns":890},[892,20735,20736,20740],{},[895,20737,20738],{},[898,20739,1805],{},[902,20741,1805],{"encoding":904},[120,20743,20744,20853,20922],{},[123,20745,20746,20763,20764,3495,20778,3495,20804,3495,20817,3369,20837,20852],{},[883,20747,20749],{"className":20748},[886],[888,20750,20751],{"xmlns":890},[892,20752,20753,20761],{},[895,20754,20755,20757,20759],{},[898,20756,1805],{},[1716,20758,2716],{},[1712,20760,1714],{},[902,20762,18344],{"encoding":904}," (elastická) ",[883,20765,20767],{"className":20766},[886],[888,20768,20769],{"xmlns":890},[892,20770,20771,20775],{},[895,20772,20773],{},[1716,20774,17833],{},[902,20776,20777],{"encoding":904},"\\Rightarrow",[883,20779,20781],{"className":20780},[886],[888,20782,20783],{"xmlns":890},[892,20784,20785,20801],{},[895,20786,20787,20789,20791,20793,20795,20797,20799],{},[1712,20788,1714],{},[1716,20790,2760],{},[1712,20792,1714],{},[898,20794,3045],{"mathvariant":2068},[898,20796,1805],{},[1716,20798,2716],{},[1712,20800,2505],{},[902,20802,20803],{"encoding":904},"1 - 1\u002FE > 0",[883,20805,20807],{"className":20806},[886],[888,20808,20809],{"xmlns":890},[892,20810,20811,20815],{},[895,20812,20813],{},[1716,20814,17833],{},[902,20816,20777],{"encoding":904},[883,20818,20820],{"className":20819},[886],[888,20821,20822],{"xmlns":890},[892,20823,20824,20834],{},[895,20825,20826,20828,20830,20832],{},[898,20827,16690],{},[898,20829,17840],{},[1716,20831,2716],{},[1712,20833,2505],{},[902,20835,20836],{"encoding":904},"MR > 0",[883,20838,20840],{"className":20839},[886],[888,20841,20842],{"xmlns":890},[892,20843,20844,20850],{},[895,20845,20846,20848],{},[898,20847,4164],{},[898,20849,17840],{},[902,20851,17938],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,20854,20855,20872,20873,3495,20886,3369,20906,20921],{},[883,20856,20858],{"className":20857},[886],[888,20859,20860],{"xmlns":890},[892,20861,20862,20870],{},[895,20863,20864,20866,20868],{},[898,20865,1805],{},[1716,20867,1913],{},[1712,20869,1714],{},[902,20871,18380],{"encoding":904}," (jednotková) ",[883,20874,20876],{"className":20875},[886],[888,20877,20878],{"xmlns":890},[892,20879,20880,20884],{},[895,20881,20882],{},[1716,20883,17833],{},[902,20885,20777],{"encoding":904},[883,20887,20889],{"className":20888},[886],[888,20890,20891],{"xmlns":890},[892,20892,20893,20903],{},[895,20894,20895,20897,20899,20901],{},[898,20896,16690],{},[898,20898,17840],{},[1716,20900,1913],{},[1712,20902,2505],{},[902,20904,20905],{"encoding":904},"MR = 0",[883,20907,20909],{"className":20908},[886],[888,20910,20911],{"xmlns":890},[892,20912,20913,20919],{},[895,20914,20915,20917],{},[898,20916,4164],{},[898,20918,17840],{},[902,20920,17938],{"encoding":904}," je extrém (maximum).",[123,20923,20924,20941,20942,3495,20955,3369,20975,20990],{},[883,20925,20927],{"className":20926},[886],[888,20928,20929],{"xmlns":890},[892,20930,20931,20939],{},[895,20932,20933,20935,20937],{},[898,20934,1805],{},[1716,20936,2704],{},[1712,20938,1714],{},[902,20940,18362],{"encoding":904}," (neelastická) ",[883,20943,20945],{"className":20944},[886],[888,20946,20947],{"xmlns":890},[892,20948,20949,20953],{},[895,20950,20951],{},[1716,20952,17833],{},[902,20954,20777],{"encoding":904},[883,20956,20958],{"className":20957},[886],[888,20959,20960],{"xmlns":890},[892,20961,20962,20972],{},[895,20963,20964,20966,20968,20970],{},[898,20965,16690],{},[898,20967,17840],{},[1716,20969,2704],{},[1712,20971,2505],{},[902,20973,20974],{"encoding":904},"MR \u003C 0",[883,20976,20978],{"className":20977},[886],[888,20979,20980],{"xmlns":890},[892,20981,20982,20988],{},[895,20983,20984,20986],{},[898,20985,4164],{},[898,20987,17840],{},[902,20989,17938],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,20992,20993,20994,1853],{},"Viz také ",[207,20995,15780],{"className":20996,"dataFsResolvedFilePath":827,"href":828},[210],[198,20998,21000],{"id":20999},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,21002,21003,21023,21024,21050,21051,21066,21067,21080,21081,21094,21095,21108,21109,21125,21126,3495,21141,21143,21144,21125,21160,1853],{},[38,21004,21005,21006,2365],{},"(a) Poptávka elastická (",[883,21007,21009],{"className":21008},[886],[888,21010,21011],{"xmlns":890},[892,21012,21013,21021],{},[895,21014,21015,21017,21019],{},[898,21016,1805],{},[1716,21018,2716],{},[1712,21020,1714],{},[902,21022,18344],{"encoding":904}," Z (4.12) plyne ",[883,21025,21027],{"className":21026},[886],[888,21028,21029],{"xmlns":890},[892,21030,21031,21047],{},[895,21032,21033,21035,21037,21039,21041,21043,21045],{},[898,21034,16690],{},[898,21036,17840],{},[1716,21038,1920],{"stretchy":1919},[898,21040,1878],{},[1716,21042,1925],{"stretchy":1919},[1716,21044,2716],{},[1712,21046,2505],{},[902,21048,21049],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,21052,21054],{"className":21053},[886],[888,21055,21056],{"xmlns":890},[892,21057,21058,21064],{},[895,21059,21060,21062],{},[898,21061,4164],{},[898,21063,17840],{},[902,21065,17938],{"encoding":904}," je rostoucí funkcí ",[883,21068,21070],{"className":21069},[886],[888,21071,21072],{"xmlns":890},[892,21073,21074,21078],{},[895,21075,21076],{},[898,21077,1878],{},[902,21079,1878],{"encoding":904},". Avšak růst ",[883,21082,21084],{"className":21083},[886],[888,21085,21086],{"xmlns":890},[892,21087,21088,21092],{},[895,21089,21090],{},[898,21091,1878],{},[902,21093,1878],{"encoding":904}," je odezvou na pokles ceny ",[883,21096,21098],{"className":21097},[886],[888,21099,21100],{"xmlns":890},[892,21101,21102,21106],{},[895,21103,21104],{},[898,21105,1690],{},[902,21107,1690],{"encoding":904},". Tudíž s ",[614,21110,21111,21112],{},"poklesem ceny ",[883,21113,21115],{"className":21114},[886],[888,21116,21117],{"xmlns":890},[892,21118,21119,21123],{},[895,21120,21121],{},[898,21122,1690],{},[902,21124,1690],{"encoding":904}," celkový příjem ",[883,21127,21129],{"className":21128},[886],[888,21130,21131],{"xmlns":890},[892,21132,21133,21139],{},[895,21134,21135,21137],{},[898,21136,4164],{},[898,21138,17840],{},[902,21140,17938],{"encoding":904},[614,21142,3568],{}," a s ",[614,21145,21146,21147],{},"růstem ceny ",[883,21148,21150],{"className":21149},[886],[888,21151,21152],{"xmlns":890},[892,21153,21154,21158],{},[895,21155,21156],{},[898,21157,1690],{},[902,21159,1690],{"encoding":904},[614,21161,3639],{},[1635,21163,21164],{},[724,21165,21166,21169],{},[38,21167,21168],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,21171,21172,21023,21192,1343,21218,21233,21234,21247,21248,21261,21262,21275,21276,21125,21289,3495,21304,1853],{},[38,21173,21174,21175,2365],{},"(b) Poptávka neelastická (",[883,21176,21178],{"className":21177},[886],[888,21179,21180],{"xmlns":890},[892,21181,21182,21190],{},[895,21183,21184,21186,21188],{},[898,21185,1805],{},[1716,21187,2704],{},[1712,21189,1714],{},[902,21191,18362],{"encoding":904},[883,21193,21195],{"className":21194},[886],[888,21196,21197],{"xmlns":890},[892,21198,21199,21215],{},[895,21200,21201,21203,21205,21207,21209,21211,21213],{},[898,21202,16690],{},[898,21204,17840],{},[1716,21206,1920],{"stretchy":1919},[898,21208,1878],{},[1716,21210,1925],{"stretchy":1919},[1716,21212,2704],{},[1712,21214,2505],{},[902,21216,21217],{"encoding":904},"MR(Q) \u003C 0",[883,21219,21221],{"className":21220},[886],[888,21222,21223],{"xmlns":890},[892,21224,21225,21231],{},[895,21226,21227,21229],{},[898,21228,4164],{},[898,21230,17840],{},[902,21232,17938],{"encoding":904}," je klesající funkce ",[883,21235,21237],{"className":21236},[886],[888,21238,21239],{"xmlns":890},[892,21240,21241,21245],{},[895,21242,21243],{},[898,21244,1878],{},[902,21246,1878],{"encoding":904},", tj. s růstem ",[883,21249,21251],{"className":21250},[886],[888,21252,21253],{"xmlns":890},[892,21254,21255,21259],{},[895,21256,21257],{},[898,21258,1878],{},[902,21260,1878],{"encoding":904}," (s poklesem ceny ",[883,21263,21265],{"className":21264},[886],[888,21266,21267],{"xmlns":890},[892,21268,21269,21273],{},[895,21270,21271],{},[898,21272,1690],{},[902,21274,1690],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,21277,21279],{"className":21278},[886],[888,21280,21281],{"xmlns":890},[892,21282,21283,21287],{},[895,21284,21285],{},[898,21286,1690],{},[902,21288,1690],{"encoding":904},[883,21290,21292],{"className":21291},[886],[888,21293,21294],{"xmlns":890},[892,21295,21296,21302],{},[895,21297,21298,21300],{},[898,21299,4164],{},[898,21301,17840],{},[902,21303,17938],{"encoding":904},[614,21305,3568],{},[1635,21307,21308],{},[724,21309,21310,21313],{},[38,21311,21312],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,21315,21316,21023,21336,21355,21356,21371,21372,21442,21443,2247,21471,21504,21505,19417,21533,21548,21549,1853],{},[38,21317,21318,21319,2365],{},"(c) Jednotková elasticita (",[883,21320,21322],{"className":21321},[886],[888,21323,21324],{"xmlns":890},[892,21325,21326,21334],{},[895,21327,21328,21330,21332],{},[898,21329,1805],{},[1716,21331,1913],{},[1712,21333,1714],{},[902,21335,18380],{"encoding":904},[883,21337,21339],{"className":21338},[886],[888,21340,21341],{"xmlns":890},[892,21342,21343,21353],{},[895,21344,21345,21347,21349,21351],{},[898,21346,16690],{},[898,21348,17840],{},[1716,21350,1913],{},[1712,21352,2505],{},[902,21354,20905],{"encoding":904}," — nutná podmínka extrému ",[883,21357,21359],{"className":21358},[886],[888,21360,21361],{"xmlns":890},[892,21362,21363,21369],{},[895,21364,21365,21367],{},[898,21366,4164],{},[898,21368,17840],{},[902,21370,17938],{"encoding":904},". Dále ",[883,21373,21375],{"className":21374},[886],[888,21376,21377],{"xmlns":890},[892,21378,21379,21439],{},[895,21380,21381,21383,21393,21395,21397,21403,21405,21411,21413,21415,21417,21419,21421,21423,21433,21435,21437],{},[898,21382,4164],{},[3074,21384,21385,21387],{},[898,21386,17840],{},[895,21388,21389,21391],{},[1716,21390,8505],{"mathvariant":2068},[1716,21392,8505],{"mathvariant":2068},[1716,21394,1913],{},[898,21396,16690],{},[3074,21398,21399,21401],{},[898,21400,17840],{},[1716,21402,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,21404,1913],{},[3074,21406,21407,21409],{},[898,21408,1916],{},[1716,21410,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,21412,1920],{"stretchy":1919},[898,21414,1878],{},[1716,21416,1925],{"stretchy":1919},[1716,21418,1949],{},[898,21420,1878],{},[2074,21422,8508],{},[3074,21424,21425,21427],{},[898,21426,1916],{},[895,21428,21429,21431],{},[1716,21430,8505],{"mathvariant":2068},[1716,21432,8505],{"mathvariant":2068},[1716,21434,1920],{"stretchy":1919},[898,21436,1878],{},[1716,21438,1925],{"stretchy":1919},[902,21440,21441],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,21444,21446],{"className":21445},[886],[888,21447,21448],{"xmlns":890},[892,21449,21450,21468],{},[895,21451,21452,21458,21460,21462,21464,21466],{},[3074,21453,21454,21456],{},[898,21455,1916],{},[1716,21457,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,21459,1920],{"stretchy":1919},[898,21461,1878],{},[1716,21463,1925],{"stretchy":1919},[1716,21465,2704],{},[1712,21467,2505],{},[902,21469,21470],{"encoding":904},"D'(Q) \u003C 0",[883,21472,21474],{"className":21473},[886],[888,21475,21476],{"xmlns":890},[892,21477,21478,21501],{},[895,21479,21480,21490,21492,21494,21496,21499],{},[3074,21481,21482,21484],{},[898,21483,1916],{},[895,21485,21486,21488],{},[1716,21487,8505],{"mathvariant":2068},[1716,21489,8505],{"mathvariant":2068},[1716,21491,1920],{"stretchy":1919},[898,21493,1878],{},[1716,21495,1925],{"stretchy":1919},[1716,21497,21498],{},"≤",[1712,21500,2505],{},[902,21502,21503],{"encoding":904},"D''(Q) \\le 0",", odkud ",[883,21506,21508],{"className":21507},[886],[888,21509,21510],{"xmlns":890},[892,21511,21512,21530],{},[895,21513,21514,21516,21526,21528],{},[898,21515,4164],{},[3074,21517,21518,21520],{},[898,21519,17840],{},[895,21521,21522,21524],{},[1716,21523,8505],{"mathvariant":2068},[1716,21525,8505],{"mathvariant":2068},[1716,21527,2704],{},[1712,21529,2505],{},[902,21531,21532],{"encoding":904},"TR'' \u003C 0",[883,21534,21536],{"className":21535},[886],[888,21537,21538],{"xmlns":890},[892,21539,21540,21546],{},[895,21541,21542,21544],{},[898,21543,4164],{},[898,21545,17840],{},[902,21547,17938],{"encoding":904}," nabývá ",[38,21550,21551],{},"maxima",[1635,21553,21554],{},[724,21555,21556,21559],{},[38,21557,21558],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,21561,21562],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,21564,21565],{},[38,21566,21567],{},"Souhrnná tabulka Pravidel 1–3:",[16,21569,21570,21674],{},[19,21571,21572],{},[22,21573,21574,21577,21592,21609,21640,21671],{},[25,21575,21576],{},"Charakter poptávky",[25,21578,21579],{},[883,21580,21582],{"className":21581},[886],[888,21583,21584],{"xmlns":890},[892,21585,21586,21590],{},[895,21587,21588],{},[898,21589,1805],{},[902,21591,1805],{"encoding":904},[25,21593,21594],{},[883,21595,21597],{"className":21596},[886],[888,21598,21599],{"xmlns":890},[892,21600,21601,21607],{},[895,21602,21603,21605],{},[898,21604,16690],{},[898,21606,17840],{},[902,21608,20456],{"encoding":904},[25,21610,21611,21612,3495,21625],{},"Pokles ceny ",[883,21613,21615],{"className":21614},[886],[888,21616,21617],{"xmlns":890},[892,21618,21619,21623],{},[895,21620,21621],{},[1716,21622,17833],{},[902,21624,20777],{"encoding":904},[883,21626,21628],{"className":21627},[886],[888,21629,21630],{"xmlns":890},[892,21631,21632,21638],{},[895,21633,21634,21636],{},[898,21635,4164],{},[898,21637,17840],{},[902,21639,17938],{"encoding":904},[25,21641,21642,21643,3495,21656],{},"Růst ceny ",[883,21644,21646],{"className":21645},[886],[888,21647,21648],{"xmlns":890},[892,21649,21650,21654],{},[895,21651,21652],{},[1716,21653,17833],{},[902,21655,20777],{"encoding":904},[883,21657,21659],{"className":21658},[886],[888,21660,21661],{"xmlns":890},[892,21662,21663,21669],{},[895,21664,21665,21667],{},[898,21666,4164],{},[898,21668,17840],{},[902,21670,17938],{"encoding":904},[25,21672,21673],{},"Doporučení",[30,21675,21676,21725,21775],{},[22,21677,21678,21680,21698,21716,21718,21720],{},[35,21679,17917],{},[35,21681,21682],{},[883,21683,21685],{"className":21684},[886],[888,21686,21687],{"xmlns":890},[892,21688,21689,21695],{},[895,21690,21691,21693],{},[1716,21692,2716],{},[1712,21694,1714],{},[902,21696,21697],{"encoding":904},"> 1",[35,21699,21700],{},[883,21701,21703],{"className":21702},[886],[888,21704,21705],{"xmlns":890},[892,21706,21707,21713],{},[895,21708,21709,21711],{},[1716,21710,2716],{},[1712,21712,2505],{},[902,21714,21715],{"encoding":904},"> 0",[35,21717,3568],{},[35,21719,3639],{},[35,21721,21722],{},[38,21723,21724],{},"snížit cenu",[22,21726,21727,21730,21748,21766,21768,21770],{},[35,21728,21729],{},"jednotková",[35,21731,21732],{},[883,21733,21735],{"className":21734},[886],[888,21736,21737],{"xmlns":890},[892,21738,21739,21745],{},[895,21740,21741,21743],{},[1716,21742,1913],{},[1712,21744,1714],{},[902,21746,21747],{"encoding":904},"= 1",[35,21749,21750],{},[883,21751,21753],{"className":21752},[886],[888,21754,21755],{"xmlns":890},[892,21756,21757,21763],{},[895,21758,21759,21761],{},[1716,21760,1913],{},[1712,21762,2505],{},[902,21764,21765],{"encoding":904},"= 0",[35,21767,17573],{},[35,21769,17573],{},[35,21771,21772],{},[38,21773,21774],{},"držet cenu",[22,21776,21777,21779,21797,21815,21817,21819],{},[35,21778,17921],{},[35,21780,21781],{},[883,21782,21784],{"className":21783},[886],[888,21785,21786],{"xmlns":890},[892,21787,21788,21794],{},[895,21789,21790,21792],{},[1716,21791,2704],{},[1712,21793,1714],{},[902,21795,21796],{"encoding":904},"\u003C 1",[35,21798,21799],{},[883,21800,21802],{"className":21801},[886],[888,21803,21804],{"xmlns":890},[892,21805,21806,21812],{},[895,21807,21808,21810],{},[1716,21809,2704],{},[1712,21811,2505],{},[902,21813,21814],{"encoding":904},"\u003C 0",[35,21816,3639],{},[35,21818,3568],{},[35,21820,21821],{},[38,21822,21823],{},"zvýšit cenu",[198,21825,21827],{"id":21826},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,21829,21830,21831,2823,21856,21878,21879,21892,21893,21906,21907,2574,21920,19417,21946,21998],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,21832,21834],{"className":21833},[886],[888,21835,21836],{"xmlns":890},[892,21837,21838,21854],{},[895,21839,21840,21842,21844,21846,21848],{},[898,21841,1690],{},[1716,21843,1913],{},[1712,21845,12151],{},[1716,21847,2760],{},[3074,21849,21850,21852],{},[898,21851,1878],{},[1712,21853,1726],{},[902,21855,19288],{"encoding":904},[883,21857,21859],{"className":21858},[886],[888,21860,21861],{"xmlns":890},[892,21862,21863,21875],{},[895,21864,21865,21867,21869,21871,21873],{},[1716,21866,19153],{"stretchy":1919},[1712,21868,1714],{},[1716,21870,1719],{"separator":1718},[1712,21872,12151],{},[1716,21874,19170],{"stretchy":1919},[902,21876,21877],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,21880,21882],{"className":21881},[886],[888,21883,21884],{"xmlns":890},[892,21885,21886,21890],{},[895,21887,21888],{},[898,21889,1878],{},[902,21891,1878],{"encoding":904}," jako funkci ",[883,21894,21896],{"className":21895},[886],[888,21897,21898],{"xmlns":890},[892,21899,21900,21904],{},[895,21901,21902],{},[898,21903,1690],{},[902,21905,1690],{"encoding":904},"; pro nezáporné ",[883,21908,21910],{"className":21909},[886],[888,21911,21912],{"xmlns":890},[892,21913,21914,21918],{},[895,21915,21916],{},[898,21917,1878],{},[902,21919,1878],{"encoding":904},[883,21921,21923],{"className":21922},[886],[888,21924,21925],{"xmlns":890},[892,21926,21927,21943],{},[895,21928,21929,21931,21933],{},[898,21930,1878],{},[1716,21932,1913],{},[10595,21934,21935],{},[895,21936,21937,21939,21941],{},[1712,21938,12151],{},[1716,21940,2760],{},[898,21942,1690],{},[902,21944,21945],{"encoding":904},"Q = \\sqrt{100 - P}",[883,21947,21949],{"className":21948},[886],[888,21950,21951],{"xmlns":890},[892,21952,21953,21995],{},[895,21954,21955,21971,21973,21975],{},[2747,21956,21957],{"scriptlevel":2505,"displaystyle":1718},[2750,21958,21959,21965],{},[895,21960,21961,21963],{},[898,21962,5198],{"mathvariant":2068},[898,21964,1878],{},[895,21966,21967,21969],{},[898,21968,5198],{"mathvariant":2068},[898,21970,1690],{},[1716,21972,1913],{},[1716,21974,2760],{},[2747,21976,21977],{"scriptlevel":2505,"displaystyle":1718},[2750,21978,21979,21981],{},[1712,21980,1714],{},[895,21982,21983,21985],{},[1712,21984,1726],{},[10595,21986,21987],{},[895,21988,21989,21991,21993],{},[1712,21990,12151],{},[1716,21992,2760],{},[898,21994,1690],{},[902,21996,21997],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,22000,22001],{},[883,22002,22004],{"className":22003},[886],[888,22005,22006],{"xmlns":890},[892,22007,22008,22130],{},[895,22009,22010,22012,22014,22016,22018,22020,22022,22028,22030,22044,22046,22048,22062,22064,22090,22092,22110,22112,22128],{},[898,22011,1805],{},[1716,22013,1920],{"stretchy":1919},[898,22015,1690],{},[1716,22017,1925],{"stretchy":1919},[1716,22019,1913],{},[1716,22021,2760],{},[2750,22023,22024,22026],{},[898,22025,1690],{},[898,22027,1878],{},[1716,22029,9532],{},[2750,22031,22032,22038],{},[895,22033,22034,22036],{},[898,22035,5198],{"mathvariant":2068},[898,22037,1878],{},[895,22039,22040,22042],{},[898,22041,5198],{"mathvariant":2068},[898,22043,1690],{},[1716,22045,1913],{},[1716,22047,2760],{},[2750,22049,22050,22052],{},[898,22051,1690],{},[10595,22053,22054],{},[895,22055,22056,22058,22060],{},[1712,22057,12151],{},[1716,22059,2760],{},[898,22061,1690],{},[1716,22063,9532],{},[895,22065,22066,22068,22070,22088],{},[1716,22067,1920],{"fence":1718},[1716,22069,2760],{},[2750,22071,22072,22074],{},[1712,22073,1714],{},[895,22075,22076,22078],{},[1712,22077,1726],{},[10595,22079,22080],{},[895,22081,22082,22084,22086],{},[1712,22083,12151],{},[1716,22085,2760],{},[898,22087,1690],{},[1716,22089,1925],{"fence":1718},[1716,22091,1913],{},[2750,22093,22094,22096],{},[898,22095,1690],{},[895,22097,22098,22100,22102,22104,22106,22108],{},[1712,22099,1726],{},[1716,22101,1920],{"stretchy":1919},[1712,22103,12151],{},[1716,22105,2760],{},[898,22107,1690],{},[1716,22109,1925],{"stretchy":1919},[1716,22111,1913],{},[2750,22113,22114,22120],{},[895,22115,22116,22118],{},[1712,22117,5771],{},[898,22119,1690],{},[895,22121,22122,22124,22126],{},[1712,22123,12151],{},[1716,22125,2760],{},[898,22127,1690],{},[898,22129,1853],{"mathvariant":2068},[902,22131,22132],{"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}.",[724,22134,22135,22136,2291],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,22137,22139],{"className":22138},[886],[888,22140,22141],{"xmlns":890},[892,22142,22143,22167],{},[895,22144,22145,22163,22165],{},[2747,22146,22147],{"scriptlevel":2505,"displaystyle":1718},[2750,22148,22149,22155],{},[895,22150,22151,22153],{},[1712,22152,5771],{},[898,22154,1690],{},[895,22156,22157,22159,22161],{},[1712,22158,12151],{},[1716,22160,2760],{},[898,22162,1690],{},[1716,22164,1913],{},[1712,22166,1714],{},[902,22168,22169],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,22171,22172],{},[883,22173,22175],{"className":22174},[886],[888,22176,22177],{"xmlns":890},[892,22178,22179,22211],{},[895,22180,22181,22187,22189,22196,22198,22201,22209],{},[3074,22182,22183,22185],{},[898,22184,1690],{},[1716,22186,3080],{},[1716,22188,1913],{},[2750,22190,22191,22194],{},[1712,22192,22193],{},"200",[1712,22195,7072],{},[1716,22197,19724],{},[1712,22199,22200],{},"66,",[22202,22203,22204,22206],"mover",{"accent":1718},[1712,22205,6231],{},[1716,22207,22208],{"stretchy":1718},"‾",[898,22210,1853],{"mathvariant":2068},[902,22212,22213],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,22215,22216],{},"S využitím vlastnosti (4.8):",[120,22218,22219,22265,22307],{},[123,22220,22221,22222,22257,22258,22260,22261,22264],{},"Při cenách ",[883,22223,22225],{"className":22224},[886],[888,22226,22227],{"xmlns":890},[892,22228,22229,22254],{},[895,22230,22231,22233,22235,22237,22239,22242,22244,22246,22252],{},[898,22232,1690],{},[1716,22234,3605],{},[1716,22236,19153],{"stretchy":1919},[1712,22238,1714],{},[1716,22240,22241],{"separator":1718},";",[2074,22243,8508],{},[1712,22245,22200],{},[22202,22247,22248,22250],{"accent":1718},[1712,22249,6231],{},[1716,22251,22208],{"stretchy":1718},[1716,22253,1925],{"stretchy":1919},[902,22255,22256],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,22259,17921],{}," — dle ",[614,22262,22263],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,22266,22221,22267,22257,22301,22260,22303,22306],{},[883,22268,22270],{"className":22269},[886],[888,22271,22272],{"xmlns":890},[892,22273,22274,22298],{},[895,22275,22276,22278,22280,22282,22284,22290,22292,22294,22296],{},[898,22277,1690],{},[1716,22279,3605],{},[1716,22281,1920],{"stretchy":1919},[1712,22283,22200],{},[22202,22285,22286,22288],{"accent":1718},[1712,22287,6231],{},[1716,22289,22208],{"stretchy":1718},[1716,22291,22241],{"separator":1718},[2074,22293,8508],{},[1712,22295,12151],{},[1716,22297,19170],{"stretchy":1919},[902,22299,22300],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,22302,17917],{},[614,22304,22305],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,22308,22309,22310,22313,22314,22342,22343,22346],{},"Dle ",[614,22311,22312],{},"Pravidla 3"," je při ceně ",[883,22315,22317],{"className":22316},[886],[888,22318,22319],{"xmlns":890},[892,22320,22321,22339],{},[895,22322,22323,22329,22331,22333],{},[3074,22324,22325,22327],{},[898,22326,1690],{},[1716,22328,3080],{},[1716,22330,1913],{},[1712,22332,22200],{},[22202,22334,22335,22337],{"accent":1718},[1712,22336,6231],{},[1716,22338,22208],{"stretchy":1718},[902,22340,22341],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,22344,22345],{},"maxima celkového příjmu"," ve výši",[724,22348,22349],{},[883,22350,22352],{"className":22351},[886],[888,22353,22354],{"xmlns":890},[892,22355,22356,22434],{},[895,22357,22358,22360,22362,22364,22370,22372,22374,22380,22382,22396,22398,22404,22406,22414,22416,22429,22431],{},[898,22359,4164],{},[898,22361,17840],{},[1716,22363,1920],{"stretchy":1919},[3074,22365,22366,22368],{},[898,22367,1690],{},[1716,22369,3080],{},[1716,22371,1925],{"stretchy":1919},[1716,22373,1913],{},[3074,22375,22376,22378],{},[898,22377,1690],{},[1716,22379,3080],{},[1716,22381,9532],{},[10595,22383,22384],{},[895,22385,22386,22388,22390],{},[1712,22387,12151],{},[1716,22389,2760],{},[3074,22391,22392,22394],{},[898,22393,1690],{},[1716,22395,3080],{},[1716,22397,1913],{},[2750,22399,22400,22402],{},[1712,22401,22193],{},[1712,22403,7072],{},[1716,22405,9532],{},[10595,22407,22408],{},[2750,22409,22410,22412],{},[1712,22411,12151],{},[1712,22413,7072],{},[1716,22415,1913],{},[2750,22417,22418,22421],{},[1712,22419,22420],{},"2000",[895,22422,22423,22425],{},[1712,22424,7072],{},[10595,22426,22427],{},[1712,22428,7072],{},[1716,22430,19724],{},[1712,22432,22433],{},"384,9.",[902,22435,22436],{"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.",[724,22438,22439,22440,1853],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,22441,22443],{"className":22442},[886],[888,22444,22445],{"xmlns":890},[892,22446,22447,22453],{},[895,22448,22449,22451],{},[898,22450,4164],{},[898,22452,17840],{},[902,22454,17938],{"encoding":904},[115,22456,22458],{"id":22457},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,22460,22461,22462,22465],{},"Analogicky se definuje ",[38,22463,22464],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,22467,22468],{},[883,22469,22471],{"className":22470,"title":18041,"style":18042},[18040],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,22473,18149,22474,22497,22498,22530],{},[883,22475,22477],{"className":22476},[886],[888,22478,22479],{"xmlns":890},[892,22480,22481,22495],{},[895,22482,22483,22485,22487,22489,22491,22493],{},[898,22484,1878],{},[1716,22486,1913],{},[898,22488,5352],{},[1716,22490,1920],{"stretchy":1919},[898,22492,1690],{},[1716,22494,1925],{"stretchy":1919},[902,22496,15221],{"encoding":904}," je funkce nabídky. Protože nabídka je rostoucí, ",[883,22499,22501],{"className":22500},[886],[888,22502,22503],{"xmlns":890},[892,22504,22505,22527],{},[895,22506,22507,22523,22525],{},[2747,22508,22509],{"scriptlevel":2505,"displaystyle":1718},[2750,22510,22511,22517],{},[895,22512,22513,22515],{},[898,22514,5198],{"mathvariant":2068},[898,22516,1878],{},[895,22518,22519,22521],{},[898,22520,5198],{"mathvariant":2068},[898,22522,1690],{},[1716,22524,2716],{},[1712,22526,2505],{},[902,22528,22529],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,22532,22533],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1635,22535,22536],{},[724,22537,22538,22539],{},"S rostoucí cenou elasticita nabídky roste. ",[883,22540,22542],{"className":22541},[886],[888,22543,22544],{"xmlns":890},[892,22545,22546,22555],{},[895,22547,22548,22550,22553],{},[1716,22549,1920],{"stretchy":1919},[1712,22551,22552],{},"4.14",[1716,22554,1925],{"stretchy":1919},[902,22556,22557],{"encoding":904},"(4.14)",[724,22559,22560],{},"Pro nominální změny platí",[724,22562,22563],{},[883,22564,22566],{"className":22565,"title":18041,"style":18042},[18040],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,22568,22569],{},"a pro procentní změny",[724,22571,22572],{},[883,22573,22575],{"className":22574,"title":18041,"style":18042},[18040],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,22577,22578],{},"(bez znaménka minus).",[198,22580,22582],{"id":22581},"příklad-47","Příklad 4.7",[724,22584,22585,22586,2291],{},"Nabídka ",[883,22587,22589],{"className":22588},[886],[888,22590,22591],{"xmlns":890},[892,22592,22593,22617],{},[895,22594,22595,22597,22599,22601,22607,22609,22611,22613,22615],{},[898,22596,1878],{},[1716,22598,1913],{},[1712,22600,9535],{},[3074,22602,22603,22605],{},[898,22604,1690],{},[1712,22606,1726],{},[1716,22608,1949],{},[1712,22610,6985],{},[898,22612,1690],{},[1716,22614,1949],{},[1712,22616,6653],{},[902,22618,22619],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,22621,22622],{},[883,22623,22625],{"className":22624},[886],[888,22626,22627],{"xmlns":890},[892,22628,22629,22675],{},[895,22630,22631,22633,22635,22659,22661,22663,22665,22667,22669,22671,22673],{},[898,22632,1805],{},[1716,22634,1913],{},[2750,22636,22637,22639],{},[898,22638,1690],{},[895,22640,22641,22643,22649,22651,22653,22655,22657],{},[1712,22642,9535],{},[3074,22644,22645,22647],{},[898,22646,1690],{},[1712,22648,1726],{},[1716,22650,1949],{},[1712,22652,6985],{},[898,22654,1690],{},[1716,22656,1949],{},[1712,22658,6653],{},[2074,22660,8508],{},[1716,22662,1920],{"stretchy":1919},[1712,22664,11302],{},[898,22666,1690],{},[1716,22668,1949],{},[1712,22670,6985],{},[1716,22672,1925],{"stretchy":1919},[898,22674,1853],{"mathvariant":2068},[902,22676,22677],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,22679,18947,22680,1343,22710,1343,22737,22773,22774,22799,22800,22818,22819,1853],{},[883,22681,22683],{"className":22682},[886],[888,22684,22685],{"xmlns":890},[892,22686,22687,22707],{},[895,22688,22689,22691,22693,22695,22697,22699],{},[898,22690,1805],{},[1716,22692,1920],{"stretchy":1919},[1712,22694,2998],{},[1716,22696,1925],{"stretchy":1919},[1716,22698,1913],{},[2747,22700,22701],{"scriptlevel":2505,"displaystyle":1919},[2750,22702,22703,22705],{},[1712,22704,1714],{},[1712,22706,7072],{},[902,22708,22709],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,22711,22713],{"className":22712},[886],[888,22714,22715],{"xmlns":890},[892,22716,22717,22734],{},[895,22718,22719,22721,22723,22728,22730,22732],{},[898,22720,1805],{},[1716,22722,1920],{"stretchy":1919},[10595,22724,22725],{},[1712,22726,22727],{},"1500",[1716,22729,1925],{"stretchy":1919},[1716,22731,1913],{},[1712,22733,1714],{},[902,22735,22736],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,22738,22740],{"className":22739},[886],[888,22741,22742],{"xmlns":890},[892,22743,22744,22770],{},[895,22745,22746,22748,22750,22752,22754,22756,22765,22767],{},[898,22747,1805],{},[1716,22749,1920],{"stretchy":1919},[1712,22751,12151],{},[1716,22753,1925],{"stretchy":1919},[1716,22755,1913],{},[2747,22757,22758],{"scriptlevel":2505,"displaystyle":1919},[2750,22759,22760,22762],{},[1712,22761,5808],{},[1712,22763,22764],{},"33",[1716,22766,19724],{},[1712,22768,22769],{},"1,515",[902,22771,22772],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,22775,22777],{"className":22776},[886],[888,22778,22779],{"xmlns":890},[892,22780,22781,22796],{},[895,22782,22783,22785,22787,22791,22793],{},[898,22784,1690],{},[1716,22786,2716],{},[10595,22788,22789],{},[1712,22790,22727],{},[1716,22792,8490],{},[1712,22794,22795],{},"38,7",[902,22797,22798],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,22801,22803],{"className":22802},[886],[888,22804,22805],{"xmlns":890},[892,22806,22807,22815],{},[895,22808,22809,22811,22813],{},[898,22810,1690],{},[1716,22812,2704],{},[1712,22814,22795],{},[902,22816,22817],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,22820,22822],{"className":22821},[886],[888,22823,22824],{"xmlns":890},[892,22825,22826,22863],{},[895,22827,22828,22830,22832,22834,22836,22844,22846,22848,22850,22853,22859,22861],{},[898,22829,8485],{"mathvariant":2068},[898,22831,1878],{},[898,22833,19749],{"mathvariant":2068},[1716,22835,8490],{},[2747,22837,22838],{"scriptlevel":2505,"displaystyle":1919},[2750,22839,22840,22842],{},[1712,22841,1714],{},[1712,22843,7072],{},[1716,22845,9532],{},[1712,22847,2976],{},[1716,22849,1913],{},[1712,22851,22852],{},"6,",[22202,22854,22855,22857],{"accent":1718},[1712,22856,6231],{},[1716,22858,22208],{"stretchy":1718},[2074,22860,8508],{},[898,22862,19749],{"mathvariant":2068},[902,22864,22865],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,22867,22869],{"id":22868},"vícefaktorový-model","Vícefaktorový model",[724,22871,22872,22873,22886,22887,3495,22890,22903,22904,3495,22907,22925,22926,3495,22929,2291],{},"Předpokládejme, že poptávané množství ",[883,22874,22876],{"className":22875},[886],[888,22877,22878],{"xmlns":890},[892,22879,22880,22884],{},[895,22881,22882],{},[898,22883,1878],{},[902,22885,1878],{"encoding":904}," závisí na ",[38,22888,22889],{},"ceně základního zboží",[883,22891,22893],{"className":22892},[886],[888,22894,22895],{"xmlns":890},[892,22896,22897,22901],{},[895,22898,22899],{},[898,22900,1690],{},[902,22902,1690],{"encoding":904},", na ",[38,22905,22906],{},"ceně alternativního zboží",[883,22908,22910],{"className":22909},[886],[888,22911,22912],{"xmlns":890},[892,22913,22914,22922],{},[895,22915,22916],{},[1707,22917,22918,22920],{},[898,22919,1690],{},[898,22921,10871],{},[902,22923,22924],{"encoding":904},"P_A"," a na ",[38,22927,22928],{},"důchodu",[883,22930,22932],{"className":22931},[886],[888,22933,22934],{"xmlns":890},[892,22935,22936,22940],{},[895,22937,22938],{},[898,22939,1758],{},[902,22941,1758],{"encoding":904},[724,22943,22944],{},[883,22945,22947],{"className":22946,"title":18041,"style":18042},[18040],"Q = D(P, P_A, Y). \\tag{4.17}",[724,22949,22950,22951,22954],{},"V analogii jednofaktorového modelu pracujeme s ",[38,22952,22953],{},"parciálními derivacemi"," funkce poptávky.",[198,22956,22958],{"id":22957},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,22960,22961],{},[883,22962,22964],{"className":22963,"title":18041,"style":18042},[18040],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,22966,18149,22967,22987,22988,23001,23002,7636,23024,3495,23027,23073,23074,23087,23088,23105],{},[883,22968,22970],{"className":22969},[886],[888,22971,22972],{"xmlns":890},[892,22973,22974,22984],{},[895,22975,22976],{},[7204,22977,22978,22980,22982],{},[898,22979,1878],{},[898,22981,1690],{},[1716,22983,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,22985,22986],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,22989,22991],{"className":22990},[886],[888,22992,22993],{"xmlns":890},[892,22994,22995,22999],{},[895,22996,22997],{},[898,22998,1690],{},[902,23000,1690],{"encoding":904},". Vždy ",[883,23003,23005],{"className":23004},[886],[888,23006,23007],{"xmlns":890},[892,23008,23009,23021],{},[895,23010,23011,23017,23019],{},[1707,23012,23013,23015],{},[898,23014,1805],{},[898,23016,1690],{},[1716,23018,18320],{},[1712,23020,2505],{},[902,23022,23023],{"encoding":904},"E_P \\ge 0",[614,23025,23026],{},"Interpretace:",[883,23028,23030],{"className":23029},[886],[888,23031,23032],{"xmlns":890},[892,23033,23034,23070],{},[895,23035,23036,23042,23044,23050,23052,23060,23062,23068],{},[1707,23037,23038,23040],{},[898,23039,1805],{},[898,23041,1690],{},[1716,23043,1920],{"stretchy":1919},[3074,23045,23046,23048],{},[898,23047,1690],{},[1716,23049,3080],{},[1716,23051,1719],{"separator":1718},[7204,23053,23054,23056,23058],{},[898,23055,1690],{},[898,23057,10871],{},[1716,23059,3080],{},[1716,23061,1719],{"separator":1718},[3074,23063,23064,23066],{},[898,23065,1758],{},[1716,23067,3080],{},[1716,23069,1925],{"stretchy":1919},[902,23071,23072],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,23075,23077],{"className":23076},[886],[888,23078,23079],{"xmlns":890},[892,23080,23081,23085],{},[895,23082,23083],{},[898,23084,1878],{},[902,23086,1878],{"encoding":904}," při 1% změně ",[883,23089,23091],{"className":23090},[886],[888,23092,23093],{"xmlns":890},[892,23094,23095,23103],{},[895,23096,23097],{},[3074,23098,23099,23101],{},[898,23100,1690],{},[1716,23102,3080],{},[902,23104,3083],{"encoding":904},", ceteris paribus.",[198,23107,23109],{"id":23108},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,23111,23112],{},[883,23113,23115],{"className":23114,"title":18041,"style":18042},[18040],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,23117,23118,23073,23120,23133,23134,23151],{},[614,23119,23026],{},[883,23121,23123],{"className":23122},[886],[888,23124,23125],{"xmlns":890},[892,23126,23127,23131],{},[895,23128,23129],{},[898,23130,1878],{},[902,23132,1878],{"encoding":904}," základního zboží při 1% změně ceny ",[883,23135,23137],{"className":23136},[886],[888,23138,23139],{"xmlns":890},[892,23140,23141,23149],{},[895,23142,23143],{},[1707,23144,23145,23147],{},[898,23146,1690],{},[898,23148,10871],{},[902,23150,22924],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,23153,23154],{},[38,23155,23156],{},"Znaménko závisí na povaze alternativního zboží:",[120,23158,23159,23246],{},[123,23160,23161,23162,7446,23165,23182,23183,3495,23196,1853],{},"Je-li alternativní zboží ",[38,23163,23164],{},"komplement",[883,23166,23168],{"className":23167},[886],[888,23169,23170],{"xmlns":890},[892,23171,23172,23180],{},[895,23173,23174],{},[1707,23175,23176,23178],{},[898,23177,1690],{},[898,23179,10871],{},[902,23181,22924],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,23184,23186],{"className":23185},[886],[888,23187,23188],{"xmlns":890},[892,23189,23190,23194],{},[895,23191,23192],{},[898,23193,1878],{},[902,23195,1878],{"encoding":904},[883,23197,23199],{"className":23198},[886],[888,23200,23201],{"xmlns":890},[892,23202,23203,23243],{},[895,23204,23205,23207,23209,23221,23223,23225,23227,23229,23239,23241],{},[1716,23206,17833],{},[2074,23208,17830],{},[7204,23210,23211,23213,23219],{},[898,23212,1878],{},[1707,23214,23215,23217],{},[898,23216,1690],{},[898,23218,10871],{},[1716,23220,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,23222,2704],{},[1712,23224,2505],{},[1716,23226,1719],{"separator":1718},[2074,23228,17830],{},[1707,23230,23231,23233],{},[898,23232,1805],{},[1707,23234,23235,23237],{},[898,23236,1690],{},[898,23238,10871],{},[1716,23240,2704],{},[1712,23242,2505],{},[902,23244,23245],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,23247,23161,23248,7446,23251,23268,23269,23282,23283,1853],{},[38,23249,23250],{},"substitut",[883,23252,23254],{"className":23253},[886],[888,23255,23256],{"xmlns":890},[892,23257,23258,23266],{},[895,23259,23260],{},[1707,23261,23262,23264],{},[898,23263,1690],{},[898,23265,10871],{},[902,23267,22924],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,23270,23272],{"className":23271},[886],[888,23273,23274],{"xmlns":890},[892,23275,23276,23280],{},[895,23277,23278],{},[898,23279,1878],{},[902,23281,1878],{"encoding":904}," roste ",[883,23284,23286],{"className":23285},[886],[888,23287,23288],{"xmlns":890},[892,23289,23290,23330],{},[895,23291,23292,23294,23296,23308,23310,23312,23314,23316,23326,23328],{},[1716,23293,17833],{},[2074,23295,17830],{},[7204,23297,23298,23300,23306],{},[898,23299,1878],{},[1707,23301,23302,23304],{},[898,23303,1690],{},[898,23305,10871],{},[1716,23307,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,23309,2716],{},[1712,23311,2505],{},[1716,23313,1719],{"separator":1718},[2074,23315,17830],{},[1707,23317,23318,23320],{},[898,23319,1805],{},[1707,23321,23322,23324],{},[898,23323,1690],{},[898,23325,10871],{},[1716,23327,2716],{},[1712,23329,2505],{},[902,23331,23332],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,23334,23337],{"className":23335,"title":23336,"style":18042},[18040],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":23339},[23340,23344,23345,23353,23354,23358,23361],{"id":17739,"depth":642,"text":17740,"children":23341},[23342,23343],{"id":17768,"depth":649,"text":17769},{"id":17946,"depth":649,"text":17947},{"id":17981,"depth":642,"text":17982},{"id":18006,"depth":642,"text":18007,"children":23346},[23347,23348,23349,23350,23352],{"id":18691,"depth":649,"text":18692},{"id":18781,"depth":649,"text":18782},{"id":19114,"depth":649,"text":19115},{"id":19196,"depth":649,"text":23351},"Výpočet, je-li dáno PP jako funkce QQ",{"id":19455,"depth":649,"text":19456},{"id":19777,"depth":642,"text":19778},{"id":20371,"depth":642,"text":20372,"children":23355},[23356,23357],{"id":20999,"depth":649,"text":21000},{"id":21826,"depth":649,"text":21827},{"id":22457,"depth":642,"text":22458,"children":23359},[23360],{"id":22581,"depth":649,"text":22582},{"id":22868,"depth":642,"text":22869,"children":23362},[23363,23364],{"id":22957,"depth":649,"text":22958},{"id":23108,"depth":649,"text":23109},{},"\u002Ftopics\u002Felasticita",{"title":17711,"description":641},[1138,1136],"topics\u002Felasticita",[1128,3533,23371,23372,23373,23374],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":23377,"title":23378,"body":23379,"course":1128,"courses":659,"created":1129,"description":24916,"extension":661,"meta":24917,"navigation":664,"path":24918,"seo":24919,"sources":24920,"stem":24921,"tags":24922,"type":15858,"updated":677,"__hash__":24927},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":23380,"toc":24901},[23381,23384,23457,23464,23468,23532,23619,23623,23650,23717,23772,23776,23803,23895,23897,23929,24100,24104,24174,24222,24226,24287,24393,24408,24412,24414,24442,24507,24509,24516,24604,24629,24827,24831,24867,24869],[12,23382,23378],{"id":23383},"kalkul-funkcí-více-proměnných",[724,23385,23386,23387,23390,23391,1343,23420,1853],{},"Většina ekonomických veličin závisí na ",[38,23388,23389],{},"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 ",[883,23392,23394],{"className":23393},[886],[888,23395,23396],{"xmlns":890},[892,23397,23398,23417],{},[895,23399,23400,23403,23405,23407,23409,23411,23413,23415],{},[898,23401,23402],{},"z",[1716,23404,1913],{},[898,23406,15915],{},[1716,23408,1920],{"stretchy":1919},[898,23410,8967],{},[1716,23412,1719],{"separator":1718},[898,23414,7684],{},[1716,23416,1925],{"stretchy":1919},[902,23418,23419],{"encoding":904},"z = f(x, y)",[883,23421,23423],{"className":23422},[886],[888,23424,23425],{"xmlns":890},[892,23426,23427,23454],{},[895,23428,23429,23432,23434,23436,23438,23440,23442,23444,23446,23448,23450,23452],{},[898,23430,23431],{},"w",[1716,23433,1913],{},[898,23435,15915],{},[1716,23437,1920],{"stretchy":1919},[898,23439,8967],{},[1716,23441,1719],{"separator":1718},[898,23443,7684],{},[1716,23445,1719],{"separator":1718},[898,23447,23402],{},[1716,23449,1925],{"stretchy":1919},[1716,23451,1719],{"separator":1718},[1716,23453,1731],{},[902,23455,23456],{"encoding":904},"w = f(x, y, z), \\ldots",[724,23458,23459],{},[3682,23460],{"alt":23461,"className":23462,"src":23463},"imek-funkce-2d-vrstevnice",[210,3686],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,23465,23467],{"id":23466},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,23469,23470,23471,23498,23499,23527,23528,23531],{},"Pro ",[883,23472,23474],{"className":23473},[886],[888,23475,23476],{"xmlns":890},[892,23477,23478,23496],{},[895,23479,23480,23482,23484,23486,23488,23490,23492,23494],{},[898,23481,23402],{},[1716,23483,1913],{},[898,23485,15915],{},[1716,23487,1920],{"stretchy":1919},[898,23489,8967],{},[1716,23491,1719],{"separator":1718},[898,23493,7684],{},[1716,23495,1925],{"stretchy":1919},[902,23497,23419],{"encoding":904}," se křivkou s předpisem ",[883,23500,23502],{"className":23501},[886],[888,23503,23504],{"xmlns":890},[892,23505,23506,23524],{},[895,23507,23508,23510,23512,23514,23516,23518,23520,23522],{},[898,23509,15915],{},[1716,23511,1920],{"stretchy":1919},[898,23513,8967],{},[1716,23515,1719],{"separator":1718},[898,23517,7684],{},[1716,23519,1925],{"stretchy":1919},[1716,23521,1913],{},[898,23523,4478],{},[902,23525,23526],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,23529,23530],{},"vrstevnice"," funkce. V ekonomii:",[120,23533,23534,23581],{},[123,23535,23536,23539,23540,23576,23577,1853],{},[38,23537,23538],{},"Indiferenční křivky"," užitečnosti ",[883,23541,23543],{"className":23542},[886],[888,23544,23545],{"xmlns":890},[892,23546,23547,23573],{},[895,23548,23549,23551,23553,23559,23561,23567,23569,23571],{},[898,23550,900],{},[1716,23552,1920],{"stretchy":1919},[1707,23554,23555,23557],{},[898,23556,1878],{},[1712,23558,1714],{},[1716,23560,1719],{"separator":1718},[1707,23562,23563,23565],{},[898,23564,1878],{},[1712,23566,1726],{},[1716,23568,1925],{"stretchy":1919},[1716,23570,1913],{},[898,23572,4478],{},[902,23574,23575],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,23578,23580],{"className":23579,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,23582,23583,23586,23587,23576,23615,1853],{},[38,23584,23585],{},"Izokvanty"," produkce ",[883,23588,23590],{"className":23589},[886],[888,23591,23592],{"xmlns":890},[892,23593,23594,23612],{},[895,23595,23596,23598,23600,23602,23604,23606,23608,23610],{},[898,23597,1878],{},[1716,23599,1920],{"stretchy":1919},[898,23601,1775],{},[1716,23603,1719],{"separator":1718},[898,23605,1790],{},[1716,23607,1925],{"stretchy":1919},[1716,23609,1913],{},[898,23611,4478],{},[902,23613,23614],{"encoding":904},"Q(L, K) = c",[207,23616,23618],{"className":23617,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,23620,23622],{"id":23621},"parciální-derivace","Parciální derivace",[724,23624,23470,23625,23649],{},[883,23626,23628],{"className":23627},[886],[888,23629,23630],{"xmlns":890},[892,23631,23632,23646],{},[895,23633,23634,23636,23638,23640,23642,23644],{},[898,23635,15915],{},[1716,23637,1920],{"stretchy":1919},[898,23639,8967],{},[1716,23641,1719],{"separator":1718},[898,23643,7684],{},[1716,23645,1925],{"stretchy":1919},[902,23647,23648],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,23651,23652],{},[883,23653,23655],{"className":23654},[886],[888,23656,23657],{"xmlns":890},[892,23658,23659,23714],{},[895,23660,23661,23669,23671,23686,23688,23690,23698,23700],{},[7204,23662,23663,23665,23667],{},[898,23664,15915],{},[898,23666,8967],{},[1716,23668,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,23670,1913],{},[2750,23672,23673,23680],{},[895,23674,23675,23678],{},[898,23676,23677],{"mathvariant":2068},"∂",[898,23679,15915],{},[895,23681,23682,23684],{},[898,23683,23677],{"mathvariant":2068},[898,23685,8967],{},[1716,23687,1719],{"separator":1718},[2324,23689],{"width":2326},[7204,23691,23692,23694,23696],{},[898,23693,15915],{},[898,23695,7684],{},[1716,23697,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,23699,1913],{},[2750,23701,23702,23708],{},[895,23703,23704,23706],{},[898,23705,23677],{"mathvariant":2068},[898,23707,15915],{},[895,23709,23710,23712],{},[898,23711,23677],{"mathvariant":2068},[898,23713,7684],{},[902,23715,23716],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,23718,23719,23720,1853],{},"Hodnoty v bodě: ",[883,23721,23723],{"className":23722},[886],[888,23724,23725],{"xmlns":890},[892,23726,23727,23769],{},[895,23728,23729,23737,23739,23741,23743,23745,23747,23749,23751,23759,23761,23763,23765,23767],{},[7204,23730,23731,23733,23735],{},[898,23732,15915],{},[898,23734,8967],{},[1716,23736,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,23738,1920],{"stretchy":1919},[898,23740,207],{},[1716,23742,1719],{"separator":1718},[898,23744,1952],{},[1716,23746,1925],{"stretchy":1919},[1716,23748,1719],{"separator":1718},[2074,23750,2711],{},[7204,23752,23753,23755,23757],{},[898,23754,15915],{},[898,23756,7684],{},[1716,23758,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,23760,1920],{"stretchy":1919},[898,23762,207],{},[1716,23764,1719],{"separator":1718},[898,23766,1952],{},[1716,23768,1925],{"stretchy":1919},[902,23770,23771],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,23773,23775],{"id":23774},"ekonomické-značení","Ekonomické značení",[724,23777,23778,23779,2291],{},"Pro produkční funkci ",[883,23780,23782],{"className":23781},[886],[888,23783,23784],{"xmlns":890},[892,23785,23786,23800],{},[895,23787,23788,23790,23792,23794,23796,23798],{},[898,23789,1878],{},[1716,23791,1920],{"stretchy":1919},[898,23793,1775],{},[1716,23795,1719],{"separator":1718},[898,23797,1790],{},[1716,23799,1925],{"stretchy":1919},[902,23801,23802],{"encoding":904},"Q(L, K)",[120,23804,23805,23850],{},[123,23806,23807,16354,23827,1994,23830,1925],{},[883,23808,23810],{"className":23809},[886],[888,23811,23812],{"xmlns":890},[892,23813,23814,23824],{},[895,23815,23816],{},[7204,23817,23818,23820,23822],{},[898,23819,1878],{},[898,23821,1775],{},[1716,23823,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,23825,23826],{"encoding":904},"Q'_L",[38,23828,23829],{},"mezní produkt práce",[883,23831,23833],{"className":23832},[886],[888,23834,23835],{"xmlns":890},[892,23836,23837,23847],{},[895,23838,23839,23841],{},[898,23840,16690],{},[1707,23842,23843,23845],{},[898,23844,1690],{},[898,23846,1775],{},[902,23848,23849],{"encoding":904},"MP_L",[123,23851,23852,16354,23872,1994,23875,1925],{},[883,23853,23855],{"className":23854},[886],[888,23856,23857],{"xmlns":890},[892,23858,23859,23869],{},[895,23860,23861],{},[7204,23862,23863,23865,23867],{},[898,23864,1878],{},[898,23866,1790],{},[1716,23868,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,23870,23871],{"encoding":904},"Q'_K",[38,23873,23874],{},"mezní produkt kapitálu",[883,23876,23878],{"className":23877},[886],[888,23879,23880],{"xmlns":890},[892,23881,23882,23892],{},[895,23883,23884,23886],{},[898,23885,16690],{},[1707,23887,23888,23890],{},[898,23889,1690],{},[898,23891,1790],{},[902,23893,23894],{"encoding":904},"MP_K",[198,23896,16448],{"id":16447},[724,23898,23899,2291],{},[883,23900,23902],{"className":23901},[886],[888,23903,23904],{"xmlns":890},[892,23905,23906,23926],{},[895,23907,23908,23916,23918,23920,23922,23924],{},[7204,23909,23910,23912,23914],{},[898,23911,15915],{},[898,23913,8967],{},[1716,23915,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,23917,1920],{"stretchy":1919},[898,23919,207],{},[1716,23921,1719],{"separator":1718},[898,23923,1952],{},[1716,23925,1925],{"stretchy":1919},[902,23927,23928],{"encoding":904},"f'_x(a, b)",[120,23930,23931,23989],{},[123,23932,23933,23934,23947,23948,23961,23962,23988],{},"rychlost změny ",[883,23935,23937],{"className":23936},[886],[888,23938,23939],{"xmlns":890},[892,23940,23941,23945],{},[895,23942,23943],{},[898,23944,15915],{},[902,23946,15915],{"encoding":904}," vůči ",[883,23949,23951],{"className":23950},[886],[888,23952,23953],{"xmlns":890},[892,23954,23955,23959],{},[895,23956,23957],{},[898,23958,8967],{},[902,23960,8967],{"encoding":904}," při ",[883,23963,23965],{"className":23964},[886],[888,23966,23967],{"xmlns":890},[892,23968,23969,23985],{},[895,23970,23971,23973,23975,23977,23979,23981,23983],{},[898,23972,8967],{},[1716,23974,1913],{},[898,23976,207],{},[1716,23978,1719],{"separator":1718},[898,23980,7684],{},[1716,23982,1913],{},[898,23984,1952],{},[902,23986,23987],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,23990,23991,23992,16537,24005,24018,24019,24037,24038,1853],{},"přibližná změna ",[883,23993,23995],{"className":23994},[886],[888,23996,23997],{"xmlns":890},[892,23998,23999,24003],{},[895,24000,24001],{},[898,24002,15915],{},[902,24004,15915],{"encoding":904},[883,24006,24008],{"className":24007},[886],[888,24009,24010],{"xmlns":890},[892,24011,24012,24016],{},[895,24013,24014],{},[898,24015,8967],{},[902,24017,8967],{"encoding":904}," o 1 (a pevném ",[883,24020,24022],{"className":24021},[886],[888,24023,24024],{"xmlns":890},[892,24025,24026,24034],{},[895,24027,24028,24030,24032],{},[898,24029,7684],{},[1716,24031,1913],{},[898,24033,1952],{},[902,24035,24036],{"encoding":904},"y = b","): ",[883,24039,24041],{"className":24040},[886],[888,24042,24043],{"xmlns":890},[892,24044,24045,24097],{},[895,24046,24047,24049,24051,24053,24055,24057,24059,24061,24063,24065,24067,24069,24071,24073,24075,24077,24079,24087,24089,24091,24093,24095],{},[898,24048,15915],{},[1716,24050,1920],{"stretchy":1919},[898,24052,207],{},[1716,24054,1949],{},[1712,24056,1714],{},[1716,24058,1719],{"separator":1718},[898,24060,1952],{},[1716,24062,1925],{"stretchy":1919},[1716,24064,8490],{},[898,24066,15915],{},[1716,24068,1920],{"stretchy":1919},[898,24070,207],{},[1716,24072,1719],{"separator":1718},[898,24074,1952],{},[1716,24076,1925],{"stretchy":1919},[1716,24078,1949],{},[7204,24080,24081,24083,24085],{},[898,24082,15915],{},[898,24084,8967],{},[1716,24086,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24088,1920],{"stretchy":1919},[898,24090,207],{},[1716,24092,1719],{"separator":1718},[898,24094,1952],{},[1716,24096,1925],{"stretchy":1919},[902,24098,24099],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,24101,24103],{"id":24102},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,24105,24106],{},[883,24107,24109],{"className":24108},[886],[888,24110,24111],{"xmlns":890},[892,24112,24113,24171],{},[895,24114,24115,24117,24119,24121,24129,24131,24133,24135,24137,24139,24141,24143,24145,24147,24155,24157,24159,24161,24163,24165,24167,24169],{},[898,24116,5198],{},[898,24118,15915],{},[1716,24120,1913],{},[7204,24122,24123,24125,24127],{},[898,24124,15915],{},[898,24126,8967],{},[1716,24128,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24130,1920],{"stretchy":1919},[898,24132,8967],{},[1716,24134,1719],{"separator":1718},[898,24136,7684],{},[1716,24138,1925],{"stretchy":1919},[2074,24140,8508],{},[898,24142,5198],{},[898,24144,8967],{},[1716,24146,1949],{},[7204,24148,24149,24151,24153],{},[898,24150,15915],{},[898,24152,7684],{},[1716,24154,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24156,1920],{"stretchy":1919},[898,24158,8967],{},[1716,24160,1719],{"separator":1718},[898,24162,7684],{},[1716,24164,1925],{"stretchy":1919},[2074,24166,8508],{},[898,24168,5198],{},[898,24170,7684],{},[902,24172,24173],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,24175,16862,24176,24198,24199,24221],{},[883,24177,24179],{"className":24178},[886],[888,24180,24181],{"xmlns":890},[892,24182,24183,24195],{},[895,24184,24185,24187,24189,24191,24193],{},[898,24186,5198],{},[898,24188,8967],{},[1716,24190,1719],{"separator":1718},[898,24192,5198],{},[898,24194,7684],{},[902,24196,24197],{"encoding":904},"dx, dy"," platí ",[883,24200,24202],{"className":24201},[886],[888,24203,24204],{"xmlns":890},[892,24205,24206,24218],{},[895,24207,24208,24210,24212,24214,24216],{},[898,24209,8485],{"mathvariant":2068},[898,24211,15915],{},[1716,24213,8490],{},[898,24215,5198],{},[898,24217,15915],{},[902,24219,24220],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,24223,24225],{"id":24224},"implicitní-funkce","Implicitní funkce",[724,24227,24228,24229,24258,24259,24272,24273,24286],{},"Je-li vztah dán rovnicí ",[883,24230,24232],{"className":24231},[886],[888,24233,24234],{"xmlns":890},[892,24235,24236,24255],{},[895,24237,24238,24241,24243,24245,24247,24249,24251,24253],{},[898,24239,24240],{},"F",[1716,24242,1920],{"stretchy":1919},[898,24244,8967],{},[1716,24246,1719],{"separator":1718},[898,24248,7684],{},[1716,24250,1925],{"stretchy":1919},[1716,24252,1913],{},[1712,24254,2505],{},[902,24256,24257],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,24260,24262],{"className":24261},[886],[888,24263,24264],{"xmlns":890},[892,24265,24266,24270],{},[895,24267,24268],{},[898,24269,7684],{},[902,24271,7684],{"encoding":904}," podle ",[883,24274,24276],{"className":24275},[886],[888,24277,24278],{"xmlns":890},[892,24279,24280,24284],{},[895,24281,24282],{},[898,24283,8967],{},[902,24285,8967],{"encoding":904}," (nebo naopak):",[724,24288,24289],{},[883,24290,24292],{"className":24291},[886],[888,24293,24294],{"xmlns":890},[892,24295,24296,24390],{},[895,24297,24298,24304,24306,24320,24322,24324,24342,24344,24346,24352,24354,24368,24370,24372],{},[3074,24299,24300,24302],{},[898,24301,7684],{},[1716,24303,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24305,1913],{},[2750,24307,24308,24314],{},[895,24309,24310,24312],{},[898,24311,5198],{},[898,24313,7684],{},[895,24315,24316,24318],{},[898,24317,5198],{},[898,24319,8967],{},[1716,24321,1913],{},[1716,24323,2760],{},[2750,24325,24326,24334],{},[7204,24327,24328,24330,24332],{},[898,24329,24240],{},[898,24331,8967],{},[1716,24333,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,24335,24336,24338,24340],{},[898,24337,24240],{},[898,24339,7684],{},[1716,24341,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24343,1719],{"separator":1718},[2324,24345],{"width":2326},[3074,24347,24348,24350],{},[898,24349,8967],{},[1716,24351,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24353,1913],{},[2750,24355,24356,24362],{},[895,24357,24358,24360],{},[898,24359,5198],{},[898,24361,8967],{},[895,24363,24364,24366],{},[898,24365,5198],{},[898,24367,7684],{},[1716,24369,1913],{},[1716,24371,2760],{},[2750,24373,24374,24382],{},[7204,24375,24376,24378,24380],{},[898,24377,24240],{},[898,24379,7684],{},[1716,24381,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,24383,24384,24386,24388],{},[898,24385,24240],{},[898,24387,8967],{},[1716,24389,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,24391,24392],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,24394,24395,24396,24399,24400,2247,24404,1853],{},"Tato vzorec dává ",[38,24397,24398],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,24401,24403],{"className":24402,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,24405,24407],{"className":24406,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,24409,24411],{"id":24410},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,24413,17112],{"id":17111},[724,24415,24416,24417,24441],{},"V bodě extrému ",[883,24418,24420],{"className":24419},[886],[888,24421,24422],{"xmlns":890},[892,24423,24424,24438],{},[895,24425,24426,24428,24430,24432,24434,24436],{},[898,24427,10871],{},[1716,24429,2502],{"stretchy":1919},[898,24431,207],{},[1716,24433,1719],{"separator":1718},[898,24435,1952],{},[1716,24437,2516],{"stretchy":1919},[902,24439,24440],{"encoding":904},"A[a, b]"," musí platit současně:",[724,24443,24444],{},[883,24445,24447],{"className":24446},[886],[888,24448,24449],{"xmlns":890},[892,24450,24451,24504],{},[895,24452,24453,24461,24463,24465,24467,24469,24471,24473,24475,24477,24480,24482,24490,24492,24494,24496,24498,24500,24502],{},[7204,24454,24455,24457,24459],{},[898,24456,15915],{},[898,24458,8967],{},[1716,24460,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24462,1920],{"stretchy":1919},[898,24464,207],{},[1716,24466,1719],{"separator":1718},[898,24468,1952],{},[1716,24470,1925],{"stretchy":1919},[1716,24472,1913],{},[1712,24474,2505],{},[2074,24476,17830],{},[1716,24478,24479],{},"∧",[2074,24481,17830],{},[7204,24483,24484,24486,24488],{},[898,24485,15915],{},[898,24487,7684],{},[1716,24489,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,24491,1920],{"stretchy":1919},[898,24493,207],{},[1716,24495,1719],{"separator":1718},[898,24497,1952],{},[1716,24499,1925],{"stretchy":1919},[1716,24501,1913],{},[1712,24503,2505],{},[902,24505,24506],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,24508,17186],{"id":17185},[724,24510,24511,24512,24515],{},"Definujeme ",[38,24513,24514],{},"diskriminant"," (Hessián zjednodušeně):",[724,24517,24518],{},[883,24519,24521],{"className":24520},[886],[888,24522,24523],{"xmlns":890},[892,24524,24525,24601],{},[895,24526,24527,24529,24531,24533,24535,24537,24539,24541,24557,24559,24575,24577,24579,24595],{},[898,24528,1916],{},[1716,24530,1920],{"stretchy":1919},[898,24532,8967],{},[1716,24534,1719],{"separator":1718},[898,24536,7684],{},[1716,24538,1925],{"stretchy":1919},[1716,24540,1913],{},[7204,24542,24543,24545,24551],{},[898,24544,15915],{},[895,24546,24547,24549],{},[898,24548,8967],{},[898,24550,8967],{},[895,24552,24553,24555],{},[1716,24554,8505],{"mathvariant":2068},[1716,24556,8505],{"mathvariant":2068},[1716,24558,9532],{},[7204,24560,24561,24563,24569],{},[898,24562,15915],{},[895,24564,24565,24567],{},[898,24566,7684],{},[898,24568,7684],{},[895,24570,24571,24573],{},[1716,24572,8505],{"mathvariant":2068},[1716,24574,8505],{"mathvariant":2068},[1716,24576,2760],{},[1716,24578,1920],{"stretchy":1919},[7204,24580,24581,24583,24589],{},[898,24582,15915],{},[895,24584,24585,24587],{},[898,24586,8967],{},[898,24588,7684],{},[895,24590,24591,24593],{},[1716,24592,8505],{"mathvariant":2068},[1716,24594,8505],{"mathvariant":2068},[3074,24596,24597,24599],{},[1716,24598,1925],{"stretchy":1919},[1712,24600,1726],{},[902,24602,24603],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,24605,24606,24607,2291],{},"V podezřelém bodě ",[883,24608,24610],{"className":24609},[886],[888,24611,24612],{"xmlns":890},[892,24613,24614,24626],{},[895,24615,24616,24618,24620,24622,24624],{},[1716,24617,2502],{"stretchy":1919},[898,24619,207],{},[1716,24621,1719],{"separator":1718},[898,24623,1952],{},[1716,24625,2516],{"stretchy":1919},[902,24627,24628],{"encoding":904},"[a, b]",[152,24630,24631,24758,24794],{},[123,24632,24633,24663,24664],{},[38,24634,24635,2291],{},[883,24636,24638],{"className":24637},[886],[888,24639,24640],{"xmlns":890},[892,24641,24642,24660],{},[895,24643,24644,24646,24648,24650,24652,24654,24656,24658],{},[898,24645,1916],{},[1716,24647,1920],{"stretchy":1919},[898,24649,207],{},[1716,24651,1719],{"separator":1718},[898,24653,1952],{},[1716,24655,1925],{"stretchy":1919},[1716,24657,2716],{},[1712,24659,2505],{},[902,24661,24662],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,24665,24666,24712],{},[123,24667,24668,17273,24710],{},[883,24669,24671],{"className":24670},[886],[888,24672,24673],{"xmlns":890},[892,24674,24675,24707],{},[895,24676,24677,24693,24695,24697,24699,24701,24703,24705],{},[7204,24678,24679,24681,24687],{},[898,24680,15915],{},[895,24682,24683,24685],{},[898,24684,8967],{},[898,24686,8967],{},[895,24688,24689,24691],{},[1716,24690,8505],{"mathvariant":2068},[1716,24692,8505],{"mathvariant":2068},[1716,24694,1920],{"stretchy":1919},[898,24696,207],{},[1716,24698,1719],{"separator":1718},[898,24700,1952],{},[1716,24702,1925],{"stretchy":1919},[1716,24704,2716],{},[1712,24706,2505],{},[902,24708,24709],{"encoding":904},"f''_{xx}(a, b) > 0",[38,24711,17630],{},[123,24713,24714,17273,24756],{},[883,24715,24717],{"className":24716},[886],[888,24718,24719],{"xmlns":890},[892,24720,24721,24753],{},[895,24722,24723,24739,24741,24743,24745,24747,24749,24751],{},[7204,24724,24725,24727,24733],{},[898,24726,15915],{},[895,24728,24729,24731],{},[898,24730,8967],{},[898,24732,8967],{},[895,24734,24735,24737],{},[1716,24736,8505],{"mathvariant":2068},[1716,24738,8505],{"mathvariant":2068},[1716,24740,1920],{"stretchy":1919},[898,24742,207],{},[1716,24744,1719],{"separator":1718},[898,24746,1952],{},[1716,24748,1925],{"stretchy":1919},[1716,24750,2704],{},[1712,24752,2505],{},[902,24754,24755],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,24757,17573],{},[123,24759,24760,3495,24790,24793],{},[38,24761,24762,2291],{},[883,24763,24765],{"className":24764},[886],[888,24766,24767],{"xmlns":890},[892,24768,24769,24787],{},[895,24770,24771,24773,24775,24777,24779,24781,24783,24785],{},[898,24772,1916],{},[1716,24774,1920],{"stretchy":1919},[898,24776,207],{},[1716,24778,1719],{"separator":1718},[898,24780,1952],{},[1716,24782,1925],{"stretchy":1919},[1716,24784,2704],{},[1712,24786,2505],{},[902,24788,24789],{"encoding":904},"D(a, b) \u003C 0",[38,24791,24792],{},"sedlo"," (v daném bodě extrém není).",[123,24795,24796,24826],{},[38,24797,24798,2291],{},[883,24799,24801],{"className":24800},[886],[888,24802,24803],{"xmlns":890},[892,24804,24805,24823],{},[895,24806,24807,24809,24811,24813,24815,24817,24819,24821],{},[898,24808,1916],{},[1716,24810,1920],{"stretchy":1919},[898,24812,207],{},[1716,24814,1719],{"separator":1718},[898,24816,1952],{},[1716,24818,1925],{"stretchy":1919},[1716,24820,1913],{},[1712,24822,2505],{},[902,24824,24825],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,24828,24830],{"id":24829},"vázané-extrémy","Vázané extrémy",[724,24832,24833,24834,24863,24864,1853],{},"Pro extrémy s omezující podmínkou ",[883,24835,24837],{"className":24836},[886],[888,24838,24839],{"xmlns":890},[892,24840,24841,24860],{},[895,24842,24843,24846,24848,24850,24852,24854,24856,24858],{},[898,24844,24845],{},"g",[1716,24847,1920],{"stretchy":1919},[898,24849,8967],{},[1716,24851,1719],{"separator":1718},[898,24853,7684],{},[1716,24855,1925],{"stretchy":1919},[1716,24857,1913],{},[1712,24859,2505],{},[902,24861,24862],{"encoding":904},"g(x, y) = 0"," se používá ",[207,24865,793],{"className":24866,"dataFsResolvedFilePath":791,"href":792},[210],[115,24868,15740],{"id":15739},[120,24870,24871,24878,24885],{},[123,24872,24873,3495,24875],{},[38,24874,17652],{},[207,24876,775],{"className":24877,"dataFsResolvedFilePath":773,"href":774},[210],[123,24879,24880,3495,24882],{},[38,24881,17660],{},[207,24883,793],{"className":24884,"dataFsResolvedFilePath":791,"href":792},[210],[123,24886,24887,3495,24889,24893,24894,24897,24898,15029],{},[38,24888,17668],{},[207,24890,24892],{"className":24891,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,24895,880],{"className":24896,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,24899,15775],{"className":24900,"dataFsResolvedFilePath":848,"href":849},[210],{"title":641,"searchDepth":642,"depth":642,"links":24902},[24903,24904,24908,24909,24910,24914,24915],{"id":23466,"depth":642,"text":23467},{"id":23621,"depth":642,"text":23622,"children":24905},[24906,24907],{"id":23774,"depth":649,"text":23775},{"id":16447,"depth":649,"text":16448},{"id":24102,"depth":642,"text":24103},{"id":24224,"depth":642,"text":24225},{"id":24410,"depth":642,"text":24411,"children":24911},[24912,24913],{"id":17111,"depth":649,"text":17112},{"id":17185,"depth":649,"text":17186},{"id":24829,"depth":642,"text":24830},{"id":15739,"depth":642,"text":15740},"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":23378,"description":24916},[1135],"topics\u002Ffunkce-vice-promennych",[1128,24923,17705,24924,24925,24926],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":24929,"title":775,"body":24930,"course":1128,"courses":659,"created":1129,"description":25784,"extension":661,"meta":25785,"navigation":664,"path":25786,"seo":25787,"sources":25788,"stem":25789,"tags":25790,"type":15858,"updated":677,"__hash__":25797},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":24931,"toc":25774},[24932,24935,24946,24950,24994,25074,25078,25154,25196,25203,25207,25211,25240,25298,25345,25383,25387,25437,25489,25541,25585,25587,25590,25662,25665,25737,25744,25746],[12,24933,775],{"id":24934},"integrál",[724,24936,24937,24938,24941,24942,24945],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,24939,24940],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,24943,24944],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,24947,24949],{"id":24948},"neurčitý-integrál","Neurčitý integrál",[724,24951,24952],{},[883,24953,24955],{"className":24954},[886],[888,24956,24957],{"xmlns":890},[892,24958,24959,24991],{},[895,24960,24961,24963,24965,24967,24969,24971,24973,24975,24977,24979,24981,24983,24985,24987,24989],{},[898,24962,24240],{},[1716,24964,1920],{"stretchy":1919},[898,24966,8967],{},[1716,24968,1925],{"stretchy":1919},[1716,24970,1913],{},[1716,24972,10027],{},[898,24974,15915],{},[1716,24976,1920],{"stretchy":1919},[898,24978,8967],{},[1716,24980,1925],{"stretchy":1919},[2074,24982,8508],{},[898,24984,5198],{},[898,24986,8967],{},[1716,24988,1949],{},[898,24990,9945],{},[902,24992,24993],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,24995,18149,24996,7636,25030,2574,25043,25046,25047,1343,25060,25073],{},[883,24997,24999],{"className":24998},[886],[888,25000,25001],{"xmlns":890},[892,25002,25003,25027],{},[895,25004,25005,25011,25013,25015,25017,25019,25021,25023,25025],{},[3074,25006,25007,25009],{},[898,25008,24240],{},[1716,25010,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,25012,1920],{"stretchy":1919},[898,25014,8967],{},[1716,25016,1925],{"stretchy":1919},[1716,25018,1913],{},[898,25020,15915],{},[1716,25022,1920],{"stretchy":1919},[898,25024,8967],{},[1716,25026,1925],{"stretchy":1919},[902,25028,25029],{"encoding":904},"F'(x) = f(x)",[883,25031,25033],{"className":25032},[886],[888,25034,25035],{"xmlns":890},[892,25036,25037,25041],{},[895,25038,25039],{},[898,25040,24240],{},[902,25042,24240],{"encoding":904},[38,25044,25045],{},"primitivní funkce"," k ",[883,25048,25050],{"className":25049},[886],[888,25051,25052],{"xmlns":890},[892,25053,25054,25058],{},[895,25055,25056],{},[898,25057,15915],{},[902,25059,15915],{"encoding":904},[883,25061,25063],{"className":25062},[886],[888,25064,25065],{"xmlns":890},[892,25066,25067,25071],{},[895,25068,25069],{},[898,25070,9945],{},[902,25072,9945],{"encoding":904}," konstanta.",[115,25075,25077],{"id":25076},"určitý-integrál","Určitý integrál",[724,25079,25080],{},[883,25081,25083],{"className":25082},[886],[888,25084,25085],{"xmlns":890},[892,25086,25087,25151],{},[895,25088,25089,25097,25099,25101,25103,25105,25107,25109,25111,25113,25115,25117,25119,25121,25123,25131,25133,25135,25137,25139,25141,25143,25145,25147,25149],{},[7204,25090,25091,25093,25095],{},[1716,25092,10027],{},[898,25094,207],{},[898,25096,1952],{},[898,25098,15915],{},[1716,25100,1920],{"stretchy":1919},[898,25102,8967],{},[1716,25104,1925],{"stretchy":1919},[2074,25106,8508],{},[898,25108,5198],{},[898,25110,8967],{},[1716,25112,1913],{},[1716,25114,2502],{"stretchy":1919},[898,25116,24240],{},[1716,25118,1920],{"stretchy":1919},[898,25120,8967],{},[1716,25122,1925],{"stretchy":1919},[7204,25124,25125,25127,25129],{},[1716,25126,2516],{"stretchy":1919},[898,25128,207],{},[898,25130,1952],{},[1716,25132,1913],{},[898,25134,24240],{},[1716,25136,1920],{"stretchy":1919},[898,25138,1952],{},[1716,25140,1925],{"stretchy":1919},[1716,25142,2760],{},[898,25144,24240],{},[1716,25146,1920],{"stretchy":1919},[898,25148,207],{},[1716,25150,1925],{"stretchy":1919},[902,25152,25153],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,25155,25156,25157,3495,25160,25173,25174,25195],{},"Geometricky ",[38,25158,25159],{},"plocha pod grafem",[883,25161,25163],{"className":25162},[886],[888,25164,25165],{"xmlns":890},[892,25166,25167,25171],{},[895,25168,25169],{},[898,25170,15915],{},[902,25172,15915],{"encoding":904}," na intervalu ",[883,25175,25177],{"className":25176},[886],[888,25178,25179],{"xmlns":890},[892,25180,25181,25193],{},[895,25182,25183,25185,25187,25189,25191],{},[1716,25184,2502],{"stretchy":1919},[898,25186,207],{},[1716,25188,1719],{"separator":1718},[898,25190,1952],{},[1716,25192,2516],{"stretchy":1919},[902,25194,24628],{"encoding":904}," (orientovaná).",[724,25197,25198],{},[3682,25199],{"alt":25200,"className":25201,"src":25202},"imek-integral-plocha",[210,3686],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,25204,25206],{"id":25205},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,25208,25210],{"id":25209},"příklad-tr-z-mr","Příklad — TR z MR",[724,25212,25213,25214,1853],{},"Mezní příjem ",[883,25215,25217],{"className":25216},[886],[888,25218,25219],{"xmlns":890},[892,25220,25221,25237],{},[895,25222,25223,25225,25227,25229,25231,25233,25235],{},[898,25224,16690],{},[898,25226,17840],{},[1716,25228,1913],{},[1712,25230,12151],{},[1716,25232,2760],{},[1712,25234,1726],{},[898,25236,1878],{},[902,25238,25239],{"encoding":904},"MR = 100 - 2Q",[724,25241,25242],{},[883,25243,25245],{"className":25244},[886],[888,25246,25247],{"xmlns":890},[892,25248,25249,25295],{},[895,25250,25251,25253,25255,25257,25259,25261,25263,25265,25267,25269,25271,25273,25275,25277,25279,25281,25283,25285,25291,25293],{},[898,25252,4164],{},[898,25254,17840],{},[1716,25256,1913],{},[1716,25258,10027],{},[1716,25260,1920],{"stretchy":1919},[1712,25262,12151],{},[1716,25264,2760],{},[1712,25266,1726],{},[898,25268,1878],{},[1716,25270,1925],{"stretchy":1919},[2074,25272,8508],{},[898,25274,5198],{},[898,25276,1878],{},[1716,25278,1913],{},[1712,25280,12151],{},[898,25282,1878],{},[1716,25284,2760],{},[3074,25286,25287,25289],{},[898,25288,1878],{},[1712,25290,1726],{},[1716,25292,1949],{},[898,25294,4478],{},[902,25296,25297],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,25299,25300,25301,17273,25327,2291],{},"Okrajová podmínka ",[883,25302,25304],{"className":25303},[886],[888,25305,25306],{"xmlns":890},[892,25307,25308,25324],{},[895,25309,25310,25312,25314,25316,25318,25320,25322],{},[898,25311,4164],{},[898,25313,17840],{},[1716,25315,1920],{"stretchy":1919},[1712,25317,2505],{},[1716,25319,1925],{"stretchy":1919},[1716,25321,1913],{},[1712,25323,2505],{},[902,25325,25326],{"encoding":904},"TR(0) = 0",[883,25328,25330],{"className":25329},[886],[888,25331,25332],{"xmlns":890},[892,25333,25334,25342],{},[895,25335,25336,25338,25340],{},[898,25337,4478],{},[1716,25339,1913],{},[1712,25341,2505],{},[902,25343,25344],{"encoding":904},"c = 0",[724,25346,25347],{},[883,25348,25350],{"className":25349},[886],[888,25351,25352],{"xmlns":890},[892,25353,25354,25380],{},[895,25355,25356,25358,25360,25362,25364,25366,25368,25370,25372,25374],{},[898,25357,4164],{},[898,25359,17840],{},[1716,25361,1920],{"stretchy":1919},[898,25363,1878],{},[1716,25365,1925],{"stretchy":1919},[1716,25367,1913],{},[1712,25369,12151],{},[898,25371,1878],{},[1716,25373,2760],{},[3074,25375,25376,25378],{},[898,25377,1878],{},[1712,25379,1726],{},[902,25381,25382],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,25384,25386],{"id":25385},"příklad-tc-z-mc","Příklad — TC z MC",[724,25388,25389,25390,25416,25417,1853],{},"Mezní náklady ",[883,25391,25393],{"className":25392},[886],[888,25394,25395],{"xmlns":890},[892,25396,25397,25413],{},[895,25398,25399,25401,25403,25405,25407,25409,25411],{},[898,25400,16690],{},[898,25402,9945],{},[1716,25404,1913],{},[1712,25406,1726],{},[1716,25408,1949],{},[1712,25410,11302],{},[898,25412,1878],{},[902,25414,25415],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,25418,25420],{"className":25419},[886],[888,25421,25422],{"xmlns":890},[892,25423,25424,25434],{},[895,25425,25426,25428,25430,25432],{},[898,25427,24240],{},[898,25429,9945],{},[1716,25431,1913],{},[1712,25433,12151],{},[902,25435,25436],{"encoding":904},"FC = 100",[724,25438,25439],{},[883,25440,25442],{"className":25441},[886],[888,25443,25444],{"xmlns":890},[892,25445,25446,25486],{},[895,25447,25448,25450,25452,25454,25456,25458,25460,25462,25464,25466,25468,25470,25472,25474,25476,25482,25484],{},[898,25449,4164],{},[898,25451,9945],{},[1716,25453,1913],{},[1716,25455,10027],{},[898,25457,16690],{},[898,25459,9945],{},[2074,25461,8508],{},[898,25463,5198],{},[898,25465,1878],{},[1716,25467,1913],{},[1712,25469,1726],{},[898,25471,1878],{},[1716,25473,1949],{},[1712,25475,9535],{},[3074,25477,25478,25480],{},[898,25479,1878],{},[1712,25481,1726],{},[1716,25483,1949],{},[898,25485,4478],{},[902,25487,25488],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,25490,25300,25491,17273,25523,2291],{},[883,25492,25494],{"className":25493},[886],[888,25495,25496],{"xmlns":890},[892,25497,25498,25520],{},[895,25499,25500,25502,25504,25506,25508,25510,25512,25514,25516,25518],{},[898,25501,4164],{},[898,25503,9945],{},[1716,25505,1920],{"stretchy":1919},[1712,25507,2505],{},[1716,25509,1925],{"stretchy":1919},[1716,25511,1913],{},[898,25513,24240],{},[898,25515,9945],{},[1716,25517,1913],{},[1712,25519,12151],{},[902,25521,25522],{"encoding":904},"TC(0) = FC = 100",[883,25524,25526],{"className":25525},[886],[888,25527,25528],{"xmlns":890},[892,25529,25530,25538],{},[895,25531,25532,25534,25536],{},[898,25533,4478],{},[1716,25535,1913],{},[1712,25537,12151],{},[902,25539,25540],{"encoding":904},"c = 100",[724,25542,25543],{},[883,25544,25546],{"className":25545},[886],[888,25547,25548],{"xmlns":890},[892,25549,25550,25582],{},[895,25551,25552,25554,25556,25558,25560,25562,25564,25566,25568,25570,25572,25574,25576],{},[898,25553,4164],{},[898,25555,9945],{},[1716,25557,1920],{"stretchy":1919},[898,25559,1878],{},[1716,25561,1925],{"stretchy":1919},[1716,25563,1913],{},[1712,25565,12151],{},[1716,25567,1949],{},[1712,25569,1726],{},[898,25571,1878],{},[1716,25573,1949],{},[1712,25575,9535],{},[3074,25577,25578,25580],{},[898,25579,1878],{},[1712,25581,1726],{},[902,25583,25584],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,25586,820],{"id":9923},[724,25588,25589],{},"Přebytek spotřebitele:",[724,25591,25592],{},[883,25593,25595],{"className":25594},[886],[888,25596,25597],{"xmlns":890},[892,25598,25599,25659],{},[895,25600,25601,25603,25605,25607,25613,25615,25617,25629,25631,25633,25635,25637,25639,25641,25643,25645,25651,25653],{},[898,25602,9945],{},[898,25604,5352],{},[1716,25606,1920],{"stretchy":1919},[1707,25608,25609,25611],{},[898,25610,1878],{},[1712,25612,2505],{},[1716,25614,1925],{"stretchy":1919},[1716,25616,1913],{},[7204,25618,25619,25621,25623],{},[1716,25620,10027],{},[1712,25622,2505],{},[1707,25624,25625,25627],{},[898,25626,1878],{},[1712,25628,2505],{},[898,25630,1916],{},[1716,25632,1920],{"stretchy":1919},[898,25634,1878],{},[1716,25636,1925],{"stretchy":1919},[2074,25638,8508],{},[898,25640,5198],{},[898,25642,1878],{},[1716,25644,2760],{},[1707,25646,25647,25649],{},[898,25648,1690],{},[1712,25650,2505],{},[2074,25652,8508],{},[1707,25654,25655,25657],{},[898,25656,1878],{},[1712,25658,2505],{},[902,25660,25661],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,25663,25664],{},"Přebytek výrobce:",[724,25666,25667],{},[883,25668,25670],{"className":25669},[886],[888,25671,25672],{"xmlns":890},[892,25673,25674,25734],{},[895,25675,25676,25678,25680,25682,25688,25690,25692,25698,25700,25706,25708,25720,25722,25724,25726,25728,25730,25732],{},[898,25677,1690],{},[898,25679,5352],{},[1716,25681,1920],{"stretchy":1919},[1707,25683,25684,25686],{},[898,25685,1878],{},[1712,25687,2505],{},[1716,25689,1925],{"stretchy":1919},[1716,25691,1913],{},[1707,25693,25694,25696],{},[898,25695,1690],{},[1712,25697,2505],{},[2074,25699,8508],{},[1707,25701,25702,25704],{},[898,25703,1878],{},[1712,25705,2505],{},[1716,25707,2760],{},[7204,25709,25710,25712,25714],{},[1716,25711,10027],{},[1712,25713,2505],{},[1707,25715,25716,25718],{},[898,25717,1878],{},[1712,25719,2505],{},[898,25721,5352],{},[1716,25723,1920],{"stretchy":1919},[898,25725,1878],{},[1716,25727,1925],{"stretchy":1919},[2074,25729,8508],{},[898,25731,5198],{},[898,25733,1878],{},[902,25735,25736],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,25738,25739,25740,1853],{},"Detailně viz ",[207,25741,25743],{"className":25742,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,25745,15740],{"id":15739},[120,25747,25748,25755,25762],{},[123,25749,25750,3495,25752],{},[38,25751,17652],{},[207,25753,766],{"className":25754,"dataFsResolvedFilePath":764,"href":765},[210],[123,25756,25757,3495,25759],{},[38,25758,17660],{},[207,25760,784],{"className":25761,"dataFsResolvedFilePath":782,"href":783},[210],[123,25763,25764,3495,25766,25769,25770,25773],{},[38,25765,17668],{},[207,25767,15780],{"className":25768,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,25771,25743],{"className":25772,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":25775},[25776,25777,25778,25783],{"id":24948,"depth":642,"text":24949},{"id":25076,"depth":642,"text":25077},{"id":25205,"depth":642,"text":25206,"children":25779},[25780,25781,25782],{"id":25209,"depth":649,"text":25210},{"id":25385,"depth":649,"text":25386},{"id":9923,"depth":649,"text":820},{"id":15739,"depth":642,"text":15740},"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":25784},[1135],"topics\u002Fintegral",[1128,25791,25792,25793,25794,25795,25796],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":25799,"title":25800,"body":25801,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":30056,"navigation":664,"path":30057,"seo":30058,"sources":30059,"stem":30060,"tags":30061,"type":15858,"updated":677,"__hash__":30067},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":25802,"toc":30044},[25803,25806,25810,25952,25959,25963,26033,26071,26174,26178,26208,26273,26320,26323,26392,26395,26430,26466,26470,26518,26525,26571,26617,26620,26699,26796,26879,26883,26926,26956,26961,26990,27012,27062,27115,27181,27184,27250,27279,27338,27354,27441,27538,27669,27673,27829,27978,28358,28362,28365,28423,28426,28512,28540,28578,28581,28618,28658,28692,28694,28731,28763,28860,28865,28989,29041,29122,29261,29265,29385,29392,29503,29510,29512,29987,29989],[12,25804,25800],{"id":25805},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,25807,25809],{"id":25808},"tldr","TL;DR",[724,25811,25812,25815,25816,1994,25819,25832,25833,25846,25847,25850,25851,1343,25854,25857,25858,1343,25861,25864,25865,3495,25868,25898,25899,25902,25903,1343,25917,8086,25930,25933,25934,2365],{},[38,25813,25814],{},"IS-LM"," je makroekonomický model se ",[38,25817,25818],{},"dvěma neznámými",[883,25820,25822],{"className":25821},[886],[888,25823,25824],{"xmlns":890},[892,25825,25826,25830],{},[895,25827,25828],{},[898,25829,1758],{},[902,25831,1758],{"encoding":904}," — národní důchod a ",[883,25834,25836],{"className":25835},[886],[888,25837,25838],{"xmlns":890},[892,25839,25840,25844],{},[895,25841,25842],{},[898,25843,2098],{},[902,25845,2098],{"encoding":904}," — úroková míra) a ",[38,25848,25849],{},"dvěma trhy",": trhem zboží (křivka ",[38,25852,25853],{},"IS",[614,25855,25856],{},"Investment = Savings",") a trhem peněz (křivka ",[38,25859,25860],{},"LM",[614,25862,25863],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[38,25866,25867],{},"simultánní rovnováhu",[883,25869,25871],{"className":25870},[886],[888,25872,25873],{"xmlns":890},[892,25874,25875,25895],{},[895,25876,25877,25879,25885,25887,25893],{},[1716,25878,1920],{"stretchy":1919},[3074,25880,25881,25883],{},[898,25882,1758],{},[898,25884,1805],{},[1716,25886,1719],{"separator":1718},[3074,25888,25889,25891],{},[898,25890,2098],{},[898,25892,1805],{},[1716,25894,1925],{"stretchy":1919},[902,25896,25897],{"encoding":904},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,25900,25901],{},"fiskální politiky"," (posun IS změnou ",[883,25904,25906],{"className":25905},[886],[888,25907,25908],{"xmlns":890},[892,25909,25910,25915],{},[895,25911,25912],{},[898,25913,25914],{},"G",[902,25916,25914],{"encoding":904},[883,25918,25920],{"className":25919},[886],[888,25921,25922],{"xmlns":890},[892,25923,25924,25928],{},[895,25925,25926],{},[898,25927,4164],{},[902,25929,4164],{"encoding":904},[38,25931,25932],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[883,25935,25937],{"className":25936},[886],[888,25938,25939],{"xmlns":890},[892,25940,25941,25949],{},[895,25942,25943],{},[3074,25944,25945,25947],{},[898,25946,16690],{},[1716,25948,3080],{},[902,25950,25951],{"encoding":904},"M^*",[724,25953,25954],{},[3682,25955],{"alt":25956,"className":25957,"src":25958},"imek-is-lm-model",[210,3686],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,25960,25962],{"id":25961},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,25964,25965,25966,25970,25971,1994,25974,25997,25998,26001,26002,26018,26019,26032],{},"V modelech ",[207,25967,25969],{"className":25968,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X"," byly ",[38,25972,25973],{},"investice pokládány za konstantní",[883,25975,25977],{"className":25976},[886],[888,25978,25979],{"xmlns":890},[892,25980,25981,25994],{},[895,25982,25983,25986,25988],{},[898,25984,25985],{},"I",[1716,25987,1913],{},[3074,25989,25990,25992],{},[898,25991,25985],{},[1716,25993,3080],{},[902,25995,25996],{"encoding":904},"I = I^*","). To není realistické — investice firem závisejí na ",[38,25999,26000],{},"ceně peněz",", tedy na ",[38,26003,26004,26005],{},"úrokové míře ",[883,26006,26008],{"className":26007},[886],[888,26009,26010],{"xmlns":890},[892,26011,26012,26016],{},[895,26013,26014],{},[898,26015,2098],{},[902,26017,2098],{"encoding":904},": čím vyšší ",[883,26020,26022],{"className":26021},[886],[888,26023,26024],{"xmlns":890},[892,26025,26026,26030],{},[895,26027,26028],{},[898,26029,2098],{},[902,26031,2098],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,26034,26035,26065],{},[123,26036,26037,3495,26040,26064],{},[38,26038,26039],{},"funkci investic",[883,26041,26043],{"className":26042},[886],[888,26044,26045],{"xmlns":890},[892,26046,26047,26061],{},[895,26048,26049,26051,26053,26055,26057,26059],{},[898,26050,25985],{},[1716,26052,1913],{},[898,26054,25985],{},[1716,26056,1920],{"stretchy":1919},[898,26058,2098],{},[1716,26060,1925],{"stretchy":1919},[902,26062,26063],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,26066,26067,26070],{},[38,26068,26069],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1635,26072,26073],{},[724,26074,26075,26077,26078,26097,26098,26125,26126,26139,26140,26169,26170,26173],{},[883,26076,2233],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,26079,26081],{"className":26080},[886],[888,26082,26083],{"xmlns":890},[892,26084,26085,26094],{},[895,26086,26087,26089,26092],{},[898,26088,9945],{},[2074,26090,26091],{},"-",[898,26093,25985],{},[902,26095,26096],{"encoding":904},"C\\text{-}I"," až ",[883,26099,26101],{"className":26100},[886],[888,26102,26103],{"xmlns":890},[892,26104,26105,26122],{},[895,26106,26107,26109,26111,26113,26115,26117,26119],{},[898,26108,9945],{},[2074,26110,26091],{},[898,26112,25985],{},[2074,26114,26091],{},[898,26116,25914],{},[2074,26118,26091],{},[898,26120,26121],{},"X",[902,26123,26124],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[883,26127,26129],{"className":26128},[886],[888,26130,26131],{"xmlns":890},[892,26132,26133,26137],{},[895,26134,26135],{},[898,26136,1758],{},[902,26138,1758],{"encoding":904},". V IS-LM jsou ",[38,26141,26142,26143,2247,26156],{},"dvě neznámé ",[883,26144,26146],{"className":26145},[886],[888,26147,26148],{"xmlns":890},[892,26149,26150,26154],{},[895,26151,26152],{},[898,26153,1758],{},[902,26155,1758],{"encoding":904},[883,26157,26159],{"className":26158},[886],[888,26160,26161],{"xmlns":890},[892,26162,26163,26167],{},[895,26164,26165],{},[898,26166,2098],{},[902,26168,2098],{"encoding":904},", a proto potřebujeme ",[38,26171,26172],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,26175,26177],{"id":26176},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,26179,26180,26181,26194,26195,2291],{},"Lineární závislost investic ",[883,26182,26184],{"className":26183},[886],[888,26185,26186],{"xmlns":890},[892,26187,26188,26192],{},[895,26189,26190],{},[898,26191,25985],{},[902,26193,25985],{"encoding":904}," na úrokové míře ",[883,26196,26198],{"className":26197},[886],[888,26199,26200],{"xmlns":890},[892,26201,26202,26206],{},[895,26203,26204],{},[898,26205,2098],{},[902,26207,2098],{"encoding":904},[724,26209,26210],{},[883,26211,26213],{"className":26212},[886],[888,26214,26215],{"xmlns":890},[892,26216,26217,26270],{},[895,26218,26219,26221,26223,26225,26227,26229,26231,26233,26235,26237,26239,26241,26243,26245,26247,26249,26251,26253,26255,26257,26259,26261,26263,26265,26268],{},[898,26220,25985],{},[1716,26222,1913],{},[898,26224,25985],{},[1716,26226,1920],{"stretchy":1919},[898,26228,2098],{},[1716,26230,1925],{"stretchy":1919},[1716,26232,1913],{},[898,26234,4478],{},[898,26236,2098],{},[1716,26238,1949],{},[898,26240,5198],{},[1716,26242,1719],{"separator":1718},[2324,26244],{"width":2326},[898,26246,4478],{},[1716,26248,2704],{},[1712,26250,2505],{},[1716,26252,1719],{"separator":1718},[2074,26254,2711],{},[898,26256,5198],{},[1716,26258,2716],{},[1712,26260,2719],{},[2324,26262],{"width":2326},[1716,26264,1920],{"stretchy":1919},[1712,26266,26267],{},"7.11",[1716,26269,1925],{"stretchy":1919},[902,26271,26272],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,26274,26275,26296],{},[123,26276,26277,26295],{},[883,26278,26280],{"className":26279},[886],[888,26281,26282],{"xmlns":890},[892,26283,26284,26292],{},[895,26285,26286,26288,26290],{},[898,26287,5198],{},[1716,26289,2716],{},[1712,26291,2505],{},[902,26293,26294],{"encoding":904},"d > 0"," zřejmé,",[123,26297,26298,26316,26317,1853],{},[883,26299,26301],{"className":26300},[886],[888,26302,26303],{"xmlns":890},[892,26304,26305,26313],{},[895,26306,26307,26309,26311],{},[898,26308,4478],{},[1716,26310,2704],{},[1712,26312,2505],{},[902,26314,26315],{"encoding":904},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[38,26318,26319],{},"klesající",[724,26321,26322],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,26324,26325],{},[883,26326,26328],{"className":26327},[886],[888,26329,26330],{"xmlns":890},[892,26331,26332,26389],{},[895,26333,26334,26336,26338,26340,26342,26344,26346,26348,26350,26352,26354,26356,26358,26360,26362,26364,26366,26368,26370,26372,26374,26376,26378,26380,26382,26384,26387],{},[898,26335,9945],{},[1716,26337,1913],{},[898,26339,9945],{},[1716,26341,1920],{"stretchy":1919},[898,26343,1758],{},[1716,26345,1925],{"stretchy":1919},[1716,26347,1913],{},[898,26349,207],{},[898,26351,1758],{},[1716,26353,1949],{},[898,26355,1952],{},[1716,26357,1719],{"separator":1718},[2324,26359],{"width":2326},[1712,26361,2505],{},[1716,26363,2704],{},[898,26365,207],{},[1716,26367,2704],{},[1712,26369,1714],{},[1716,26371,1719],{"separator":1718},[2074,26373,2711],{},[898,26375,1952],{},[1716,26377,2716],{},[1712,26379,2719],{},[2324,26381],{"width":2326},[1716,26383,1920],{"stretchy":1919},[1712,26385,26386],{},"7.12",[1716,26388,1925],{"stretchy":1919},[902,26390,26391],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,26393,26394],{},"Podmínka rovnováhy na trhu zboží:",[724,26396,26397],{},[883,26398,26400],{"className":26399},[886],[888,26401,26402],{"xmlns":890},[892,26403,26404,26427],{},[895,26405,26406,26408,26410,26412,26414,26416,26418,26420,26422,26425],{},[898,26407,1758],{},[1716,26409,1913],{},[898,26411,9945],{},[1716,26413,1949],{},[898,26415,25985],{},[898,26417,1853],{"mathvariant":2068},[2324,26419],{"width":2326},[1716,26421,1920],{"stretchy":1919},[1712,26423,26424],{},"7.13",[1716,26426,1925],{"stretchy":1919},[902,26428,26429],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,26431,26432,26433,3495,26436,26462,26463,1853],{},"To dává ",[38,26434,26435],{},"tři rovnice o čtyřech neznámých",[883,26437,26439],{"className":26438},[886],[888,26440,26441],{"xmlns":890},[892,26442,26443,26459],{},[895,26444,26445,26447,26449,26451,26453,26455,26457],{},[898,26446,1758],{},[1716,26448,1719],{"separator":1718},[898,26450,9945],{},[1716,26452,1719],{"separator":1718},[898,26454,25985],{},[1716,26456,1719],{"separator":1718},[898,26458,2098],{},[902,26460,26461],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,26464,26465],{},"rovnováhy na trhu peněz",[115,26467,26469],{"id":26468},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,26471,26472,26473,19398,26495,26513,26514,26517],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,26474,26476],{"className":26475},[886],[888,26477,26478],{"xmlns":890},[892,26479,26480,26492],{},[895,26481,26482,26484,26486,26488,26490],{},[898,26483,1758],{},[1716,26485,1913],{},[898,26487,9945],{},[1716,26489,1949],{},[898,26491,5352],{},[902,26493,26494],{"encoding":904},"Y = C + S",[883,26496,26498],{"className":26497},[886],[888,26499,26500],{"xmlns":890},[892,26501,26502,26510],{},[895,26503,26504,26506,26508],{},[898,26505,25985],{},[1716,26507,1913],{},[898,26509,5352],{},[902,26511,26512],{"encoding":904},"I = S"," (plánované ",[38,26515,26516],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,26519,26520],{},[3682,26521],{"alt":26522,"className":26523,"src":26524},"imek-odvozeni-is-4panelu",[210,3686],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,26526,26527],{},[883,26528,26530],{"className":26529},[886],[888,26531,26532],{"xmlns":890},[892,26533,26534,26568],{},[895,26535,26536,26538,26540,26542,26544,26546,26548,26550,26552,26554,26556,26558,26560,26562,26564,26566],{},[898,26537,1758],{},[1716,26539,1913],{},[1716,26541,1920],{"stretchy":1919},[898,26543,207],{},[898,26545,1758],{},[1716,26547,1949],{},[898,26549,1952],{},[1716,26551,1925],{"stretchy":1919},[1716,26553,1949],{},[1716,26555,1920],{"stretchy":1919},[898,26557,4478],{},[898,26559,2098],{},[1716,26561,1949],{},[898,26563,5198],{},[1716,26565,1925],{"stretchy":1919},[1716,26567,1719],{"separator":1718},[902,26569,26570],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,26572,26573],{},[883,26574,26576],{"className":26575},[886],[888,26577,26578],{"xmlns":890},[892,26579,26580,26614],{},[895,26581,26582,26584,26586,26588,26590,26592,26594,26596,26598,26600,26602,26604,26606,26608,26610,26612],{},[1716,26583,1920],{"stretchy":1919},[1712,26585,1714],{},[1716,26587,2760],{},[898,26589,207],{},[1716,26591,1925],{"stretchy":1919},[898,26593,1758],{},[1716,26595,2760],{},[898,26597,4478],{},[898,26599,2098],{},[1716,26601,2760],{},[898,26603,1952],{},[1716,26605,2760],{},[898,26607,5198],{},[1716,26609,1913],{},[1712,26611,2505],{},[1716,26613,1719],{"separator":1718},[902,26615,26616],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,26618,26619],{},"odkud",[724,26621,26622],{},[883,26623,26625],{"className":26624},[886],[888,26626,26627],{"xmlns":890},[892,26628,26629,26696],{},[895,26630,26631,26687,26689,26691,26694],{},[26632,26633,26635],"menclose",{"notation":26634},"box",[2747,26636,26637],{"scriptlevel":2505,"displaystyle":1919},[2747,26638,26639],{"scriptlevel":2505,"displaystyle":1919},[2747,26640,26641],{"scriptlevel":2505,"displaystyle":1718},[895,26642,26643,26645,26647,26649,26661,26663,26665,26667,26685],{},[2074,26644,8508],{},[898,26646,1758],{},[1716,26648,1913],{},[2750,26650,26651,26653],{},[898,26652,4478],{},[895,26654,26655,26657,26659],{},[1712,26656,1714],{},[1716,26658,2760],{},[898,26660,207],{},[2074,26662,8508],{},[898,26664,2098],{},[1716,26666,1949],{},[2750,26668,26669,26677],{},[895,26670,26671,26673,26675],{},[898,26672,1952],{},[1716,26674,1949],{},[898,26676,5198],{},[895,26678,26679,26681,26683],{},[1712,26680,1714],{},[1716,26682,2760],{},[898,26684,207],{},[2074,26686,8508],{},[2324,26688],{"width":2326},[1716,26690,1920],{"stretchy":1919},[1712,26692,26693],{},"7.14",[1716,26695,1925],{"stretchy":1919},[902,26697,26698],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,26700,26701,26702,1994,26705,26708,26709,26712,26713,26715,26716,26738,26739,26767,26768,26789,26790,26792,26793,26795],{},"Tento vztah se nazývá ",[38,26703,26704],{},"funkce IS",[614,26706,26707],{},"IS schedule",") a její graf ",[38,26710,26711],{},"křivka IS",". Křivka je ",[38,26714,26319],{}," přímka v rovině ",[883,26717,26719],{"className":26718},[886],[888,26720,26721],{"xmlns":890},[892,26722,26723,26735],{},[895,26724,26725,26727,26729,26731,26733],{},[1716,26726,1920],{"stretchy":1919},[898,26728,2098],{},[1716,26730,1719],{"separator":1718},[898,26732,1758],{},[1716,26734,1925],{"stretchy":1919},[902,26736,26737],{"encoding":904},"(r, Y)",", neboť ",[883,26740,26742],{"className":26741},[886],[888,26743,26744],{"xmlns":890},[892,26745,26746,26764],{},[895,26747,26748,26760,26762],{},[2750,26749,26750,26752],{},[898,26751,4478],{},[895,26753,26754,26756,26758],{},[1712,26755,1714],{},[1716,26757,2760],{},[898,26759,207],{},[1716,26761,2704],{},[1712,26763,2505],{},[902,26765,26766],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,26769,26771],{"className":26770},[886],[888,26772,26773],{"xmlns":890},[892,26774,26775,26787],{},[895,26776,26777,26779,26781,26783,26785],{},[1716,26778,1920],{"stretchy":1919},[898,26780,2098],{},[1716,26782,1719],{"separator":1718},[898,26784,1758],{},[1716,26786,1925],{"stretchy":1919},[902,26788,26737],{"encoding":904},", pro které plánované ",[38,26791,25985],{},"nvestment = ",[38,26794,5352],{},"avings.",[1635,26797,26798],{},[724,26799,26800,26802,26803,26816,26817,3495,26820,26833,26834,26847,26848,2247,26861,26874,26875,26878],{},[883,26801,1641],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,26804,26806],{"className":26805},[886],[888,26807,26808],{"xmlns":890},[892,26809,26810,26814],{},[895,26811,26812],{},[898,26813,2098],{},[902,26815,2098],{"encoding":904}," → levnější úvěr → ",[38,26818,26819],{},"více investic",[883,26821,26823],{"className":26822},[886],[888,26824,26825],{"xmlns":890},[892,26826,26827,26831],{},[895,26828,26829],{},[898,26830,25985],{},[902,26832,25985],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,26835,26837],{"className":26836},[886],[888,26838,26839],{"xmlns":890},[892,26840,26841,26845],{},[895,26842,26843],{},[898,26844,1758],{},[902,26846,1758],{"encoding":904},". Vztah mezi ",[883,26849,26851],{"className":26850},[886],[888,26852,26853],{"xmlns":890},[892,26854,26855,26859],{},[895,26856,26857],{},[898,26858,2098],{},[902,26860,2098],{"encoding":904},[883,26862,26864],{"className":26863},[886],[888,26865,26866],{"xmlns":890},[892,26867,26868,26872],{},[895,26869,26870],{},[898,26871,1758],{},[902,26873,1758],{"encoding":904}," na trhu zboží je proto ",[38,26876,26877],{},"nepřímý"," (klesající křivka).",[115,26880,26882],{"id":26881},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,26884,26885,26886,26904,26905,7636,26923,26925],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,26887,26889],{"className":26888},[886],[888,26890,26891],{"xmlns":890},[892,26892,26893,26901],{},[895,26894,26895],{},[3074,26896,26897,26899],{},[898,26898,16690],{},[898,26900,1916],{},[902,26902,26903],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,26906,26908],{"className":26907},[886],[888,26909,26910],{"xmlns":890},[892,26911,26912,26920],{},[895,26913,26914],{},[3074,26915,26916,26918],{},[898,26917,16690],{},[898,26919,5352],{},[902,26921,26922],{"encoding":904},"M^S",[38,26924,5139],{}," je pod kontrolou národní banky a je pevně zadána:",[724,26927,26928],{},[883,26929,26931],{"className":26930},[886],[888,26932,26933],{"xmlns":890},[892,26934,26935,26953],{},[895,26936,26937,26943,26945,26951],{},[3074,26938,26939,26941],{},[898,26940,16690],{},[898,26942,5352],{},[1716,26944,1913],{},[3074,26946,26947,26949],{},[898,26948,16690],{},[1716,26950,3080],{},[898,26952,1853],{"mathvariant":2068},[902,26954,26955],{"encoding":904},"M^S = M^*.",[724,26957,26958,26960],{},[38,26959,1859],{}," po penězích má tři zdroje:",[120,26962,26963,26972,26981],{},[123,26964,26965,1994,26968,26971],{},[38,26966,26967],{},"transakční poptávka",[614,26969,26970],{},"transactions demand",") — peníze pro nákup zboží,",[123,26973,26974,1994,26977,26980],{},[38,26975,26976],{},"opatrnostní poptávka",[614,26978,26979],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,26982,26983,1994,26986,26989],{},[38,26984,26985],{},"spekulační poptávka",[614,26987,26988],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,26991,26992,26993,27011],{},"Součet transakční a opatrnostní poptávky ",[883,26994,26996],{"className":26995},[886],[888,26997,26998],{"xmlns":890},[892,26999,27000,27008],{},[895,27001,27002],{},[1707,27003,27004,27006],{},[898,27005,1775],{},[1712,27007,1714],{},[902,27009,27010],{"encoding":904},"L_1"," je úměrný důchodu:",[724,27013,27014],{},[883,27015,27017],{"className":27016},[886],[888,27018,27019],{"xmlns":890},[892,27020,27021,27059],{},[895,27022,27023,27029,27031,27038,27040,27042,27044,27046,27048,27054,27056],{},[1707,27024,27025,27027],{},[898,27026,1775],{},[1712,27028,1714],{},[1716,27030,1913],{},[1707,27032,27033,27036],{},[898,27034,27035],{},"k",[1712,27037,1714],{},[898,27039,1758],{},[1716,27041,1719],{"separator":1718},[2324,27043],{"width":2326},[1712,27045,2505],{},[1716,27047,2704],{},[1707,27049,27050,27052],{},[898,27051,27035],{},[1712,27053,1714],{},[1716,27055,2704],{},[1712,27057,27058],{},"1.",[902,27060,27061],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,27063,27064,27065,27083,27084,1343,27097,27114],{},"Spekulační poptávka ",[883,27066,27068],{"className":27067},[886],[888,27069,27070],{"xmlns":890},[892,27071,27072,27080],{},[895,27073,27074],{},[1707,27075,27076,27078],{},[898,27077,1775],{},[1712,27079,1726],{},[902,27081,27082],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,27085,27087],{"className":27086},[886],[888,27088,27089],{"xmlns":890},[892,27090,27091,27095],{},[895,27092,27093],{},[898,27094,2098],{},[902,27096,2098],{"encoding":904},[883,27098,27100],{"className":27099},[886],[888,27101,27102],{"xmlns":890},[892,27103,27104,27112],{},[895,27105,27106],{},[1707,27107,27108,27110],{},[898,27109,1775],{},[1712,27111,1726],{},[902,27113,27082],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,27116,27117],{},[883,27118,27120],{"className":27119},[886],[888,27121,27122],{"xmlns":890},[892,27123,27124,27178],{},[895,27125,27126,27132,27134,27140,27142,27144,27150,27152,27154,27160,27162,27164,27166,27168,27174,27176],{},[1707,27127,27128,27130],{},[898,27129,1775],{},[1712,27131,1726],{},[1716,27133,1913],{},[1707,27135,27136,27138],{},[898,27137,27035],{},[1712,27139,1726],{},[898,27141,2098],{},[1716,27143,1949],{},[1707,27145,27146,27148],{},[898,27147,27035],{},[1712,27149,7072],{},[1716,27151,1719],{"separator":1718},[2324,27153],{"width":2326},[1707,27155,27156,27158],{},[898,27157,27035],{},[1712,27159,1726],{},[1716,27161,2704],{},[1712,27163,2505],{},[1716,27165,1719],{"separator":1718},[2074,27167,2711],{},[1707,27169,27170,27172],{},[898,27171,27035],{},[1712,27173,7072],{},[1716,27175,2716],{},[1712,27177,2719],{},[902,27179,27180],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,27182,27183],{},"Celková poptávka po penězích:",[724,27185,27186],{},[883,27187,27189],{"className":27188},[886],[888,27190,27191],{"xmlns":890},[892,27192,27193,27247],{},[895,27194,27195,27201,27203,27209,27211,27217,27219,27225,27227,27229,27235,27237,27239,27245],{},[3074,27196,27197,27199],{},[898,27198,16690],{},[898,27200,1916],{},[1716,27202,1913],{},[1707,27204,27205,27207],{},[898,27206,1775],{},[1712,27208,1714],{},[1716,27210,1949],{},[1707,27212,27213,27215],{},[898,27214,1775],{},[1712,27216,1726],{},[1716,27218,1913],{},[1707,27220,27221,27223],{},[898,27222,27035],{},[1712,27224,1714],{},[898,27226,1758],{},[1716,27228,1949],{},[1707,27230,27231,27233],{},[898,27232,27035],{},[1712,27234,1726],{},[898,27236,2098],{},[1716,27238,1949],{},[1707,27240,27241,27243],{},[898,27242,27035],{},[1712,27244,7072],{},[898,27246,1853],{"mathvariant":2068},[902,27248,27249],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,27251,27252,27253,2291],{},"Podmínka rovnováhy na trhu peněz ",[883,27254,27256],{"className":27255},[886],[888,27257,27258],{"xmlns":890},[892,27259,27260,27276],{},[895,27261,27262,27268,27270],{},[3074,27263,27264,27266],{},[898,27265,16690],{},[898,27267,1916],{},[1716,27269,1913],{},[3074,27271,27272,27274],{},[898,27273,16690],{},[1716,27275,3080],{},[902,27277,27278],{"encoding":904},"M^D = M^*",[724,27280,27281],{},[883,27282,27284],{"className":27283},[886],[888,27285,27286],{"xmlns":890},[892,27287,27288,27335],{},[895,27289,27290,27296,27298,27304,27306,27308,27314,27316,27318,27324,27326,27328,27330,27333],{},[3074,27291,27292,27294],{},[898,27293,16690],{},[1716,27295,3080],{},[1716,27297,1913],{},[1707,27299,27300,27302],{},[898,27301,27035],{},[1712,27303,1714],{},[898,27305,1758],{},[1716,27307,1949],{},[1707,27309,27310,27312],{},[898,27311,27035],{},[1712,27313,1726],{},[898,27315,2098],{},[1716,27317,1949],{},[1707,27319,27320,27322],{},[898,27321,27035],{},[1712,27323,7072],{},[1716,27325,1719],{"separator":1718},[2324,27327],{"width":2326},[1716,27329,1920],{"stretchy":1919},[1712,27331,27332],{},"7.15",[1716,27334,1925],{"stretchy":1919},[902,27336,27337],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,27339,27340,27341,1998],{},"po úpravě (vyjádření ",[883,27342,27344],{"className":27343},[886],[888,27345,27346],{"xmlns":890},[892,27347,27348,27352],{},[895,27349,27350],{},[898,27351,1758],{},[902,27353,1758],{"encoding":904},[724,27355,27356],{},[883,27357,27359],{"className":27358},[886],[888,27360,27361],{"xmlns":890},[892,27362,27363,27438],{},[895,27364,27365,27429,27431,27433,27436],{},[26632,27366,27367],{"notation":26634},[2747,27368,27369],{"scriptlevel":2505,"displaystyle":1919},[2747,27370,27371],{"scriptlevel":2505,"displaystyle":1919},[2747,27372,27373],{"scriptlevel":2505,"displaystyle":1718},[895,27374,27375,27377,27379,27381,27383,27397,27399,27401,27403,27427],{},[2074,27376,8508],{},[898,27378,1758],{},[1716,27380,1913],{},[1716,27382,2760],{},[2750,27384,27385,27391],{},[1707,27386,27387,27389],{},[898,27388,27035],{},[1712,27390,1726],{},[1707,27392,27393,27395],{},[898,27394,27035],{},[1712,27396,1714],{},[2074,27398,8508],{},[898,27400,2098],{},[1716,27402,1949],{},[2750,27404,27405,27421],{},[895,27406,27407,27413,27415],{},[3074,27408,27409,27411],{},[898,27410,16690],{},[1716,27412,3080],{},[1716,27414,2760],{},[1707,27416,27417,27419],{},[898,27418,27035],{},[1712,27420,7072],{},[1707,27422,27423,27425],{},[898,27424,27035],{},[1712,27426,1714],{},[2074,27428,8508],{},[2324,27430],{"width":2326},[1716,27432,1920],{"stretchy":1919},[1712,27434,27435],{},"7.16",[1716,27437,1925],{"stretchy":1919},[902,27439,27440],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,27442,26701,27443,1994,27446,27449,27450,26712,27453,26715,27455,26738,27476,27508,27509,27531,27532,27534,27535,27537],{},[38,27444,27445],{},"funkce LM",[614,27447,27448],{},"LM schedule","), její graf ",[38,27451,27452],{},"křivka LM",[38,27454,3167],{},[883,27456,27458],{"className":27457},[886],[888,27459,27460],{"xmlns":890},[892,27461,27462,27474],{},[895,27463,27464,27466,27468,27470,27472],{},[1716,27465,1920],{"stretchy":1919},[898,27467,2098],{},[1716,27469,1719],{"separator":1718},[898,27471,1758],{},[1716,27473,1925],{"stretchy":1919},[902,27475,26737],{"encoding":904},[883,27477,27479],{"className":27478},[886],[888,27480,27481],{"xmlns":890},[892,27482,27483,27505],{},[895,27484,27485,27487,27501,27503],{},[1716,27486,2760],{},[2750,27488,27489,27495],{},[1707,27490,27491,27493],{},[898,27492,27035],{},[1712,27494,1726],{},[1707,27496,27497,27499],{},[898,27498,27035],{},[1712,27500,1714],{},[1716,27502,2716],{},[1712,27504,2505],{},[902,27506,27507],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,27510,27512],{"className":27511},[886],[888,27513,27514],{"xmlns":890},[892,27515,27516,27528],{},[895,27517,27518,27524,27526],{},[1707,27519,27520,27522],{},[898,27521,27035],{},[1712,27523,1726],{},[1716,27525,2704],{},[1712,27527,2505],{},[902,27529,27530],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,27533,1775],{},"iquidity of ",[38,27536,16690],{},"oney.",[1635,27539,27540],{},[724,27541,27542,27544,27545,27558,27559,27587,27588,27605,27606,27619,27620,27637,27638,2247,27651,27664,27665,27668],{},[883,27543,1641],{}," Intuice — proč LM roste\nVyšší důchod ",[883,27546,27548],{"className":27547},[886],[888,27549,27550],{"xmlns":890},[892,27551,27552,27556],{},[895,27553,27554],{},[898,27555,1758],{},[902,27557,1758],{"encoding":904}," → větší transakční poptávka po penězích ",[883,27560,27562],{"className":27561},[886],[888,27563,27564],{"xmlns":890},[892,27565,27566,27584],{},[895,27567,27568,27574,27576,27582],{},[1707,27569,27570,27572],{},[898,27571,1775],{},[1712,27573,1714],{},[1716,27575,1913],{},[1707,27577,27578,27580],{},[898,27579,27035],{},[1712,27581,1714],{},[898,27583,1758],{},[902,27585,27586],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,27589,27591],{"className":27590},[886],[888,27592,27593],{"xmlns":890},[892,27594,27595,27603],{},[895,27596,27597],{},[3074,27598,27599,27601],{},[898,27600,16690],{},[1716,27602,3080],{},[902,27604,25951],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,27607,27609],{"className":27608},[886],[888,27610,27611],{"xmlns":890},[892,27612,27613,27617],{},[895,27614,27615],{},[898,27616,2098],{},[902,27618,2098],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,27621,27623],{"className":27622},[886],[888,27624,27625],{"xmlns":890},[892,27626,27627,27635],{},[895,27628,27629],{},[1707,27630,27631,27633],{},[898,27632,1775],{},[1712,27634,1726],{},[902,27636,27082],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,27639,27641],{"className":27640},[886],[888,27642,27643],{"xmlns":890},[892,27644,27645,27649],{},[895,27646,27647],{},[898,27648,1758],{},[902,27650,1758],{"encoding":904},[883,27652,27654],{"className":27653},[886],[888,27655,27656],{"xmlns":890},[892,27657,27658,27662],{},[895,27659,27660],{},[898,27661,2098],{},[902,27663,2098],{"encoding":904}," na trhu peněz je proto ",[38,27666,27667],{},"přímý"," (rostoucí křivka).",[115,27670,27672],{"id":27671},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,27674,27675,27676,27679,27680,3495,27683,2247,27701,3495,27704,27722,27723,27741,27742,27760,27761,27777,27778,2247,27793,4060,27808,1853],{},"Řešením ",[38,27677,27678],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,27681,27682],{},"rovnovážný důchod",[883,27684,27686],{"className":27685},[886],[888,27687,27688],{"xmlns":890},[892,27689,27690,27698],{},[895,27691,27692],{},[3074,27693,27694,27696],{},[898,27695,1758],{},[898,27697,1805],{},[902,27699,27700],{"encoding":904},"Y^E",[38,27702,27703],{},"rovnovážnou úrokovou míru",[883,27705,27707],{"className":27706},[886],[888,27708,27709],{"xmlns":890},[892,27710,27711,27719],{},[895,27712,27713],{},[3074,27714,27715,27717],{},[898,27716,2098],{},[898,27718,1805],{},[902,27720,27721],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,27724,27726],{"className":27725},[886],[888,27727,27728],{"xmlns":890},[892,27729,27730,27738],{},[895,27731,27732],{},[3074,27733,27734,27736],{},[898,27735,25985],{},[898,27737,1805],{},[902,27739,27740],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,27743,27745],{"className":27744},[886],[888,27746,27747],{"xmlns":890},[892,27748,27749,27757],{},[895,27750,27751],{},[3074,27752,27753,27755],{},[898,27754,9945],{},[898,27756,1805],{},[902,27758,27759],{"encoding":904},"C^E",". Graficky jde o ",[38,27762,27763,27764],{},"průsečík ",[883,27765,27767],{"className":27766},[886],[888,27768,27769],{"xmlns":890},[892,27770,27771,27775],{},[895,27772,27773],{},[898,27774,1805],{},[902,27776,1805],{"encoding":904}," křivek ",[883,27779,27781],{"className":27780},[886],[888,27782,27783],{"xmlns":890},[892,27784,27785,27791],{},[895,27786,27787,27789],{},[898,27788,25985],{},[898,27790,5352],{},[902,27792,25853],{"encoding":904},[883,27794,27796],{"className":27795},[886],[888,27797,27798],{"xmlns":890},[892,27799,27800,27806],{},[895,27801,27802,27804],{},[898,27803,1775],{},[898,27805,16690],{},[902,27807,25860],{"encoding":904},[883,27809,27811],{"className":27810},[886],[888,27812,27813],{"xmlns":890},[892,27814,27815,27827],{},[895,27816,27817,27819,27821,27823,27825],{},[1716,27818,1920],{"stretchy":1919},[898,27820,2098],{},[1716,27822,1719],{"separator":1718},[898,27824,1758],{},[1716,27826,1925],{"stretchy":1919},[902,27828,26737],{"encoding":904},[724,27830,27831],{},[614,27832,27833,27834,27855,27856,27871,27872,27887,27888,27901,27902,27919,27920,8086,27933,27919,27950,27963,27964,27977],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,27835,27837],{"className":27836},[886],[888,27838,27839],{"xmlns":890},[892,27840,27841,27853],{},[895,27842,27843,27845,27847,27849,27851],{},[1716,27844,1920],{"stretchy":1919},[898,27846,2098],{},[1716,27848,1719],{"separator":1718},[898,27850,1758],{},[1716,27852,1925],{"stretchy":1919},[902,27854,26737],{"encoding":904},". Rostoucí přímka ",[883,27857,27859],{"className":27858},[886],[888,27860,27861],{"xmlns":890},[892,27862,27863,27869],{},[895,27864,27865,27867],{},[898,27866,1775],{},[898,27868,16690],{},[902,27870,25860],{"encoding":904}," a klesající přímka ",[883,27873,27875],{"className":27874},[886],[888,27876,27877],{"xmlns":890},[892,27878,27879,27885],{},[895,27880,27881,27883],{},[898,27882,25985],{},[898,27884,5352],{},[902,27886,25853],{"encoding":904}," se protínají v bodě ",[883,27889,27891],{"className":27890},[886],[888,27892,27893],{"xmlns":890},[892,27894,27895,27899],{},[895,27896,27897],{},[898,27898,1805],{},[902,27900,1805],{"encoding":904}," se souřadnicemi ",[883,27903,27905],{"className":27904},[886],[888,27906,27907],{"xmlns":890},[892,27908,27909,27917],{},[895,27910,27911],{},[3074,27912,27913,27915],{},[898,27914,2098],{},[898,27916,1805],{},[902,27918,27721],{"encoding":904}," (na ose ",[883,27921,27923],{"className":27922},[886],[888,27924,27925],{"xmlns":890},[892,27926,27927,27931],{},[895,27928,27929],{},[898,27930,2098],{},[902,27932,2098],{"encoding":904},[883,27934,27936],{"className":27935},[886],[888,27937,27938],{"xmlns":890},[892,27939,27940,27948],{},[895,27941,27942],{},[3074,27943,27944,27946],{},[898,27945,1758],{},[898,27947,1805],{},[902,27949,27700],{"encoding":904},[883,27951,27953],{"className":27952},[886],[888,27954,27955],{"xmlns":890},[892,27956,27957,27961],{},[895,27958,27959],{},[898,27960,1758],{},[902,27962,1758],{"encoding":904},"); tečkované čáry z ",[883,27965,27967],{"className":27966},[886],[888,27968,27969],{"xmlns":890},[892,27970,27971,27975],{},[895,27972,27973],{},[898,27974,1805],{},[902,27976,1805],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1635,27979,27980,27985],{},[724,27981,27982,27984],{},[883,27983,3776],{}," Postup — jak najít IS-LM rovnováhu",[152,27986,27987,28063,28131,28189,28262],{},[123,27988,27989,27992,27993,2247,28013,28033,28034,2247,28047,28060,28061,1853],{},[38,27990,27991],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,27994,27996],{"className":27995},[886],[888,27997,27998],{"xmlns":890},[892,27999,28000,28010],{},[895,28001,28002,28004,28006,28008],{},[898,28003,9945],{},[1716,28005,1920],{"stretchy":1919},[898,28007,1758],{},[1716,28009,1925],{"stretchy":1919},[902,28011,28012],{"encoding":904},"C(Y)",[883,28014,28016],{"className":28015},[886],[888,28017,28018],{"xmlns":890},[892,28019,28020,28030],{},[895,28021,28022,28024,28026,28028],{},[898,28023,25985],{},[1716,28025,1920],{"stretchy":1919},[898,28027,2098],{},[1716,28029,1925],{"stretchy":1919},[902,28031,28032],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,28035,28037],{"className":28036},[886],[888,28038,28039],{"xmlns":890},[892,28040,28041,28045],{},[895,28042,28043],{},[898,28044,1758],{},[902,28046,1758],{"encoding":904},[883,28048,28050],{"className":28049},[886],[888,28051,28052],{"xmlns":890},[892,28053,28054,28058],{},[895,28055,28056],{},[898,28057,2098],{},[902,28059,2098],{"encoding":904}," — dostaneš rovnici ",[38,28062,25853],{},[123,28064,28065,28068,28069,2247,28086,28103,28104,28060,28129,1853],{},[38,28066,28067],{},"Z trhu peněz (7.15)"," dosaď ",[883,28070,28072],{"className":28071},[886],[888,28073,28074],{"xmlns":890},[892,28075,28076,28084],{},[895,28077,28078],{},[1707,28079,28080,28082],{},[898,28081,1775],{},[1712,28083,1714],{},[902,28085,27010],{"encoding":904},[883,28087,28089],{"className":28088},[886],[888,28090,28091],{"xmlns":890},[892,28092,28093,28101],{},[895,28094,28095],{},[1707,28096,28097,28099],{},[898,28098,1775],{},[1712,28100,1726],{},[902,28102,27082],{"encoding":904}," a vztah ",[883,28105,28107],{"className":28106},[886],[888,28108,28109],{"xmlns":890},[892,28110,28111,28127],{},[895,28112,28113,28119,28121],{},[3074,28114,28115,28117],{},[898,28116,16690],{},[898,28118,1916],{},[1716,28120,1913],{},[3074,28122,28123,28125],{},[898,28124,16690],{},[1716,28126,3080],{},[902,28128,27278],{"encoding":904},[38,28130,25860],{},[123,28132,28133,28136,28137,2247,28150,28163,28164,28188],{},[38,28134,28135],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,28138,28140],{"className":28139},[886],[888,28141,28142],{"xmlns":890},[892,28143,28144,28148],{},[895,28145,28146],{},[898,28147,1758],{},[902,28149,1758],{"encoding":904},[883,28151,28153],{"className":28152},[886],[888,28154,28155],{"xmlns":890},[892,28156,28157,28161],{},[895,28158,28159],{},[898,28160,2098],{},[902,28162,2098],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,28165,28167],{"className":28166},[886],[888,28168,28169],{"xmlns":890},[892,28170,28171,28185],{},[895,28172,28173,28175,28177,28179,28181,28183],{},[898,28174,1758],{},[1716,28176,1913],{},[898,28178,15915],{},[1716,28180,1920],{"stretchy":1919},[898,28182,2098],{},[1716,28184,1925],{"stretchy":1919},[902,28186,28187],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,28190,28191,3495,28194,2247,28228,1853],{},[38,28192,28193],{},"Zpětně dopočítej",[883,28195,28197],{"className":28196},[886],[888,28198,28199],{"xmlns":890},[892,28200,28201,28225],{},[895,28202,28203,28209,28211,28213,28215,28221,28223],{},[3074,28204,28205,28207],{},[898,28206,9945],{},[898,28208,1805],{},[1716,28210,1913],{},[898,28212,207],{},[2074,28214,8508],{},[3074,28216,28217,28219],{},[898,28218,1758],{},[898,28220,1805],{},[1716,28222,1949],{},[898,28224,1952],{},[902,28226,28227],{"encoding":904},"C^E = a\\,Y^E + b",[883,28229,28231],{"className":28230},[886],[888,28232,28233],{"xmlns":890},[892,28234,28235,28259],{},[895,28236,28237,28243,28245,28247,28249,28255,28257],{},[3074,28238,28239,28241],{},[898,28240,25985],{},[898,28242,1805],{},[1716,28244,1913],{},[898,28246,4478],{},[2074,28248,8508],{},[3074,28250,28251,28253],{},[898,28252,2098],{},[898,28254,1805],{},[1716,28256,1949],{},[898,28258,5198],{},[902,28260,28261],{"encoding":904},"I^E = c\\,r^E + d",[123,28263,28264,28267,28268,28302,28303,28357],{},[38,28265,28266],{},"Ověř:"," musí platit ",[883,28269,28271],{"className":28270},[886],[888,28272,28273],{"xmlns":890},[892,28274,28275,28299],{},[895,28276,28277,28283,28285,28291,28293],{},[3074,28278,28279,28281],{},[898,28280,1758],{},[898,28282,1805],{},[1716,28284,1913],{},[3074,28286,28287,28289],{},[898,28288,9945],{},[898,28290,1805],{},[1716,28292,1949],{},[3074,28294,28295,28297],{},[898,28296,25985],{},[898,28298,1805],{},[902,28300,28301],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,28304,28306],{"className":28305},[886],[888,28307,28308],{"xmlns":890},[892,28309,28310,28354],{},[895,28311,28312,28318,28320,28326,28332,28334,28340,28346,28348],{},[3074,28313,28314,28316],{},[898,28315,16690],{},[1716,28317,3080],{},[1716,28319,1913],{},[1707,28321,28322,28324],{},[898,28323,27035],{},[1712,28325,1714],{},[3074,28327,28328,28330],{},[898,28329,1758],{},[898,28331,1805],{},[1716,28333,1949],{},[1707,28335,28336,28338],{},[898,28337,27035],{},[1712,28339,1726],{},[3074,28341,28342,28344],{},[898,28343,2098],{},[898,28345,1805],{},[1716,28347,1949],{},[1707,28349,28350,28352],{},[898,28351,27035],{},[1712,28353,7072],{},[902,28355,28356],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,28359,28361],{"id":28360},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,28363,28364],{},"Pro trh zboží jsou dány:",[120,28366,28367,28394],{},[123,28368,28369,28370,1719],{},"spotřeba ",[883,28371,28373],{"className":28372},[886],[888,28374,28375],{"xmlns":890},[892,28376,28377,28391],{},[895,28378,28379,28381,28383,28385,28387,28389],{},[898,28380,9945],{},[1716,28382,1913],{},[1712,28384,13254],{},[898,28386,1758],{},[1716,28388,1949],{},[1712,28390,12151],{},[902,28392,28393],{"encoding":904},"C = 0{,}8Y + 100",[123,28395,28396,28397,1853],{},"investice ",[883,28398,28400],{"className":28399},[886],[888,28401,28402],{"xmlns":890},[892,28403,28404,28420],{},[895,28405,28406,28408,28410,28412,28414,28416,28418],{},[898,28407,25985],{},[1716,28409,1913],{},[1716,28411,2760],{},[1712,28413,2976],{},[898,28415,2098],{},[1716,28417,1949],{},[1712,28419,16656],{},[902,28421,28422],{"encoding":904},"I = -20r + 1000",[724,28424,28425],{},"Pro trh peněz:",[120,28427,28428,28454,28486],{},[123,28429,28430,1719],{},[883,28431,28433],{"className":28432},[886],[888,28434,28435],{"xmlns":890},[892,28436,28437,28451],{},[895,28438,28439,28445,28447,28449],{},[1707,28440,28441,28443],{},[898,28442,1775],{},[1712,28444,1714],{},[1716,28446,1913],{},[1712,28448,9535],{},[898,28450,1758],{},[902,28452,28453],{"encoding":904},"L_1 = 0{,}1Y",[123,28455,28456,1719],{},[883,28457,28459],{"className":28458},[886],[888,28460,28461],{"xmlns":890},[892,28462,28463,28483],{},[895,28464,28465,28471,28473,28475,28477,28479,28481],{},[1707,28466,28467,28469],{},[898,28468,1775],{},[1712,28470,1726],{},[1716,28472,1913],{},[1716,28474,2760],{},[1712,28476,5778],{},[898,28478,2098],{},[1716,28480,1949],{},[1712,28482,22420],{},[902,28484,28485],{"encoding":904},"L_2 = -25r + 2000",[123,28487,28488,28489,1853],{},"nabídka peněz ",[883,28490,28492],{"className":28491},[886],[888,28493,28494],{"xmlns":890},[892,28495,28496,28509],{},[895,28497,28498,28504,28506],{},[3074,28499,28500,28502],{},[898,28501,16690],{},[1716,28503,3080],{},[1716,28505,1913],{},[1712,28507,28508],{},"2375",[902,28510,28511],{"encoding":904},"M^* = 2375",[724,28513,28514,28517,28518,2291],{},[38,28515,28516],{},"Funkce IS"," — dosazením do (7.13) ",[883,28519,28521],{"className":28520},[886],[888,28522,28523],{"xmlns":890},[892,28524,28525,28537],{},[895,28526,28527,28529,28531,28533,28535],{},[898,28528,1758],{},[1716,28530,1913],{},[898,28532,9945],{},[1716,28534,1949],{},[898,28536,25985],{},[902,28538,28539],{"encoding":904},"Y = C + I",[724,28541,28542],{},[883,28543,28545],{"className":28544},[886],[888,28546,28547],{"xmlns":890},[892,28548,28549,28575],{},[895,28550,28551,28553,28555,28557,28559,28561,28563,28565,28567,28569,28571,28573],{},[898,28552,1758],{},[1716,28554,1913],{},[1712,28556,13254],{},[898,28558,1758],{},[1716,28560,1949],{},[1712,28562,12151],{},[1716,28564,2760],{},[1712,28566,2976],{},[898,28568,2098],{},[1716,28570,1949],{},[1712,28572,16656],{},[1716,28574,1719],{"separator":1718},[902,28576,28577],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,28579,28580],{},"tj.",[724,28582,28583],{},[883,28584,28586],{"className":28585},[886],[888,28587,28588],{"xmlns":890},[892,28589,28590,28615],{},[895,28591,28592,28594,28596,28598,28600,28602,28604,28607,28609,28611,28613],{},[1712,28593,11302],{},[898,28595,1758],{},[1716,28597,1949],{},[1712,28599,2976],{},[898,28601,2098],{},[1716,28603,1913],{},[1712,28605,28606],{},"1100.",[2324,28608],{"width":2326},[1716,28610,1920],{"stretchy":1919},[2074,28612,25853],{},[1716,28614,1925],{"stretchy":1919},[902,28616,28617],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,28619,28620,28623,28624,2291],{},[38,28621,28622],{},"Funkce LM"," — dosazením do (7.15) ",[883,28625,28627],{"className":28626},[886],[888,28628,28629],{"xmlns":890},[892,28630,28631,28655],{},[895,28632,28633,28639,28641,28647,28649],{},[3074,28634,28635,28637],{},[898,28636,16690],{},[1716,28638,3080],{},[1716,28640,1913],{},[1707,28642,28643,28645],{},[898,28644,1775],{},[1712,28646,1714],{},[1716,28648,1949],{},[1707,28650,28651,28653],{},[898,28652,1775],{},[1712,28654,1726],{},[902,28656,28657],{"encoding":904},"M^* = L_1 + L_2",[724,28659,28660],{},[883,28661,28663],{"className":28662},[886],[888,28664,28665],{"xmlns":890},[892,28666,28667,28689],{},[895,28668,28669,28671,28673,28675,28677,28679,28681,28683,28685,28687],{},[1712,28670,28508],{},[1716,28672,1913],{},[1712,28674,9535],{},[898,28676,1758],{},[1716,28678,2760],{},[1712,28680,5778],{},[898,28682,2098],{},[1716,28684,1949],{},[1712,28686,22420],{},[1716,28688,1719],{"separator":1718},[902,28690,28691],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,28693,28580],{},[724,28695,28696],{},[883,28697,28699],{"className":28698},[886],[888,28700,28701],{"xmlns":890},[892,28702,28703,28728],{},[895,28704,28705,28707,28709,28711,28713,28715,28717,28720,28722,28724,28726],{},[1712,28706,9535],{},[898,28708,1758],{},[1716,28710,2760],{},[1712,28712,5778],{},[898,28714,2098],{},[1716,28716,1913],{},[1712,28718,28719],{},"375.",[2324,28721],{"width":2326},[1716,28723,1920],{"stretchy":1919},[2074,28725,25860],{},[1716,28727,1925],{"stretchy":1919},[902,28729,28730],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,28732,28733,28736,28737,28762],{},[38,28734,28735],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,28738,28740],{"className":28739},[886],[888,28741,28742],{"xmlns":890},[892,28743,28744,28759],{},[895,28745,28746,28748,28750,28753,28755,28757],{},[898,28747,1758],{},[1716,28749,1913],{},[1712,28751,28752],{},"5500",[1716,28754,2760],{},[1712,28756,12151],{},[898,28758,2098],{},[902,28760,28761],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,28764,28765],{},[883,28766,28768],{"className":28767},[886],[888,28769,28770],{"xmlns":890},[892,28771,28772,28857],{},[895,28773,28774,28776,28778,28780,28782,28784,28786,28788,28790,28792,28794,28796,28799,28801,28804,28806,28809,28811,28813,28815,28817,28819,28821,28823,28825,28827,28829,28831,28833,28835,28837,28840,28842,28844,28846,28852,28854],{},[1712,28775,9535],{},[1716,28777,1920],{"stretchy":1919},[1712,28779,28752],{},[1716,28781,2760],{},[1712,28783,12151],{},[898,28785,2098],{},[1716,28787,1925],{"stretchy":1919},[1716,28789,2760],{},[1712,28791,5778],{},[898,28793,2098],{},[1716,28795,1913],{},[1712,28797,28798],{},"375",[2074,28800,17830],{},[1716,28802,28803],{},"⟹",[2074,28805,17830],{},[1712,28807,28808],{},"550",[1716,28810,2760],{},[1712,28812,2998],{},[898,28814,2098],{},[1716,28816,2760],{},[1712,28818,5778],{},[898,28820,2098],{},[1716,28822,1913],{},[1712,28824,28798],{},[2074,28826,17830],{},[1716,28828,28803],{},[2074,28830,17830],{},[1712,28832,5837],{},[898,28834,2098],{},[1716,28836,1913],{},[1712,28838,28839],{},"175",[2074,28841,17830],{},[1716,28843,28803],{},[2074,28845,17830],{},[3074,28847,28848,28850],{},[898,28849,2098],{},[898,28851,1805],{},[1716,28853,1913],{},[1712,28855,28856],{},"5.",[902,28858,28859],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,28861,28862],{},[38,28863,28864],{},"Zpětné dosazení:",[120,28866,28867,28913,28950],{},[123,28868,28869,1719],{},[883,28870,28872],{"className":28871},[886],[888,28873,28874],{"xmlns":890},[892,28875,28876,28910],{},[895,28877,28878,28884,28886,28888,28890,28892,28894,28896,28898,28900,28902,28905,28907],{},[3074,28879,28880,28882],{},[898,28881,1758],{},[898,28883,1805],{},[1716,28885,1913],{},[1712,28887,28752],{},[1716,28889,2760],{},[1712,28891,12151],{},[1716,28893,9532],{},[1712,28895,6985],{},[1716,28897,1913],{},[1712,28899,28752],{},[1716,28901,2760],{},[1712,28903,28904],{},"500",[1716,28906,1913],{},[1712,28908,28909],{},"5000",[902,28911,28912],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,28914,28915,1719],{},[883,28916,28918],{"className":28917},[886],[888,28919,28920],{"xmlns":890},[892,28921,28922,28947],{},[895,28923,28924,28930,28932,28934,28936,28938,28940,28942,28944],{},[3074,28925,28926,28928],{},[898,28927,9945],{},[898,28929,1805],{},[1716,28931,1913],{},[1712,28933,13254],{},[1716,28935,9532],{},[1712,28937,28909],{},[1716,28939,1949],{},[1712,28941,12151],{},[1716,28943,1913],{},[1712,28945,28946],{},"4100",[902,28948,28949],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,28951,28952,1853],{},[883,28953,28955],{"className":28954},[886],[888,28956,28957],{"xmlns":890},[892,28958,28959,28986],{},[895,28960,28961,28967,28969,28971,28973,28975,28977,28979,28981,28983],{},[3074,28962,28963,28965],{},[898,28964,25985],{},[898,28966,1805],{},[1716,28968,1913],{},[1716,28970,2760],{},[1712,28972,2976],{},[1716,28974,9532],{},[1712,28976,6985],{},[1716,28978,1949],{},[1712,28980,16656],{},[1716,28982,1913],{},[1712,28984,28985],{},"900",[902,28987,28988],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,28990,28991,3495,28994,29040],{},[38,28992,28993],{},"Ověření:",[883,28995,28997],{"className":28996},[886],[888,28998,28999],{"xmlns":890},[892,29000,29001,29037],{},[895,29002,29003,29009,29011,29017,29019,29021,29023,29025,29027,29029,29031],{},[3074,29004,29005,29007],{},[898,29006,9945],{},[898,29008,1805],{},[1716,29010,1949],{},[3074,29012,29013,29015],{},[898,29014,25985],{},[898,29016,1805],{},[1716,29018,1913],{},[1712,29020,28946],{},[1716,29022,1949],{},[1712,29024,28985],{},[1716,29026,1913],{},[1712,29028,28909],{},[1716,29030,1913],{},[3074,29032,29033,29035],{},[898,29034,1758],{},[898,29036,1805],{},[902,29038,29039],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,29042,29043],{},[883,29044,29046],{"className":29045},[886],[888,29047,29048],{"xmlns":890},[892,29049,29050,29119],{},[895,29051,29052],{},[26632,29053,29054],{"notation":26634},[2747,29055,29056],{"scriptlevel":2505,"displaystyle":1919},[2747,29057,29058],{"scriptlevel":2505,"displaystyle":1919},[2747,29059,29060],{"scriptlevel":2505,"displaystyle":1718},[895,29061,29062,29064,29070,29072,29074,29076,29078,29084,29086,29088,29090,29092,29098,29100,29102,29104,29106,29112,29114,29117],{},[2074,29063,8508],{},[3074,29065,29066,29068],{},[898,29067,1758],{},[898,29069,1805],{},[1716,29071,1913],{},[1712,29073,28909],{},[1716,29075,1719],{"separator":1718},[2324,29077],{"width":8689},[3074,29079,29080,29082],{},[898,29081,2098],{},[898,29083,1805],{},[1716,29085,1913],{},[1712,29087,6985],{},[1716,29089,1719],{"separator":1718},[2324,29091],{"width":8689},[3074,29093,29094,29096],{},[898,29095,9945],{},[898,29097,1805],{},[1716,29099,1913],{},[1712,29101,28946],{},[1716,29103,1719],{"separator":1718},[2324,29105],{"width":8689},[3074,29107,29108,29110],{},[898,29109,25985],{},[898,29111,1805],{},[1716,29113,1913],{},[1712,29115,29116],{},"900.",[2074,29118,8508],{},[902,29120,29121],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,29123,29124],{},[614,29125,29126,29127,29140,29141,29154,29155,29170,29171,29184,29185,29200,29201,29214,29215,29228,29229,1853],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,29128,29130],{"className":29129},[886],[888,29131,29132],{"xmlns":890},[892,29133,29134,29138],{},[895,29135,29136],{},[898,29137,1758],{},[902,29139,1758],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,29142,29144],{"className":29143},[886],[888,29145,29146],{"xmlns":890},[892,29147,29148,29152],{},[895,29149,29150],{},[898,29151,2098],{},[902,29153,2098],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,29156,29158],{"className":29157},[886],[888,29159,29160],{"xmlns":890},[892,29161,29162,29168],{},[895,29163,29164,29166],{},[898,29165,1775],{},[898,29167,16690],{},[902,29169,25860],{"encoding":904}," stoupá z oblasti nízkých ",[883,29172,29174],{"className":29173},[886],[888,29175,29176],{"xmlns":890},[892,29177,29178,29182],{},[895,29179,29180],{},[898,29181,2098],{},[902,29183,2098],{"encoding":904},", přímka ",[883,29186,29188],{"className":29187},[886],[888,29189,29190],{"xmlns":890},[892,29191,29192,29198],{},[895,29193,29194,29196],{},[898,29195,25985],{},[898,29197,5352],{},[902,29199,25853],{"encoding":904}," klesá a protíná osu ",[883,29202,29204],{"className":29203},[886],[888,29205,29206],{"xmlns":890},[892,29207,29208,29212],{},[895,29209,29210],{},[898,29211,2098],{},[902,29213,2098],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,29216,29218],{"className":29217},[886],[888,29219,29220],{"xmlns":890},[892,29221,29222,29226],{},[895,29223,29224],{},[898,29225,1805],{},[902,29227,1805],{"encoding":904}," leží v bodě ",[883,29230,29232],{"className":29231},[886],[888,29233,29234],{"xmlns":890},[892,29235,29236,29258],{},[895,29237,29238,29240,29242,29244,29246,29248,29250,29252,29254,29256],{},[1716,29239,2502],{"stretchy":1919},[898,29241,2098],{},[1716,29243,1913],{},[1712,29245,6985],{},[1716,29247,1719],{"separator":1718},[2074,29249,2711],{},[898,29251,1758],{},[1716,29253,1913],{},[1712,29255,28909],{},[1716,29257,2516],{"stretchy":1919},[902,29259,29260],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,29262,29264],{"id":29263},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,29266,29267,29270,29271,29284,29285,3369,29298,29301,29302,29320,29321,29338,29339,29356,29357,29370,29371,29384],{},[38,29268,29269],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,29272,29274],{"className":29273},[886],[888,29275,29276],{"xmlns":890},[892,29277,29278,29282],{},[895,29279,29280],{},[898,29281,25914],{},[902,29283,25914],{"encoding":904}," nebo snížení daní ",[883,29286,29288],{"className":29287},[886],[888,29289,29290],{"xmlns":890},[892,29291,29292,29296],{},[895,29293,29294],{},[898,29295,4164],{},[902,29297,4164],{"encoding":904},[38,29299,29300],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,29303,29305],{"className":29304},[886],[888,29306,29307],{"xmlns":890},[892,29308,29309,29317],{},[895,29310,29311],{},[3074,29312,29313,29315],{},[898,29314,1805],{},[1716,29316,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,29318,29319],{"encoding":904},"E'"," má vyšší ",[883,29322,29324],{"className":29323},[886],[888,29325,29326],{"xmlns":890},[892,29327,29328,29336],{},[895,29329,29330],{},[3074,29331,29332,29334],{},[898,29333,1758],{},[898,29335,1805],{},[902,29337,27700],{"encoding":904}," i vyšší ",[883,29340,29342],{"className":29341},[886],[888,29343,29344],{"xmlns":890},[892,29345,29346,29354],{},[895,29347,29348],{},[3074,29349,29350,29352],{},[898,29351,2098],{},[898,29353,1805],{},[902,29355,27721],{"encoding":904}," (vyšší ",[883,29358,29360],{"className":29359},[886],[888,29361,29362],{"xmlns":890},[892,29363,29364,29368],{},[895,29365,29366],{},[898,29367,1758],{},[902,29369,1758],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,29372,29374],{"className":29373},[886],[888,29375,29376],{"xmlns":890},[892,29377,29378,29382],{},[895,29379,29380],{},[898,29381,2098],{},[902,29383,2098],{"encoding":904}," nahoru).",[724,29386,29387],{},[3682,29388],{"alt":29389,"className":29390,"src":29391},"imek-posun-is-lm-politiky",[210,3686],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,29393,29394,29397,29398,29415,29416,29419,29420,29437,29438,29455,29456,29469,29470,29489,29490,2365],{},[38,29395,29396],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,29399,29401],{"className":29400},[886],[888,29402,29403],{"xmlns":890},[892,29404,29405,29413],{},[895,29406,29407],{},[3074,29408,29409,29411],{},[898,29410,16690],{},[1716,29412,3080],{},[902,29414,25951],{"encoding":904}," národní bankou — ",[38,29417,29418],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,29421,29423],{"className":29422},[886],[888,29424,29425],{"xmlns":890},[892,29426,29427,29435],{},[895,29428,29429],{},[3074,29430,29431,29433],{},[898,29432,2098],{},[898,29434,1805],{},[902,29436,27721],{"encoding":904}," a vyšší ",[883,29439,29441],{"className":29440},[886],[888,29442,29443],{"xmlns":890},[892,29444,29445,29453],{},[895,29446,29447],{},[3074,29448,29449,29451],{},[898,29450,1758],{},[898,29452,1805],{},[902,29454,27700],{"encoding":904}," (nižší ",[883,29457,29459],{"className":29458},[886],[888,29460,29461],{"xmlns":890},[892,29462,29463,29467],{},[895,29464,29465],{},[898,29466,2098],{},[902,29468,2098],{"encoding":904}," povzbuzuje investice ",[883,29471,29473],{"className":29472},[886],[888,29474,29475],{"xmlns":890},[892,29476,29477,29487],{},[895,29478,29479,29481,29483,29485],{},[898,29480,25985],{},[1716,29482,1920],{"stretchy":1919},[898,29484,2098],{},[1716,29486,1925],{"stretchy":1919},[902,29488,28032],{"encoding":904},", ty zvedají ",[883,29491,29493],{"className":29492},[886],[888,29494,29495],{"xmlns":890},[892,29496,29497,29501],{},[895,29498,29499],{},[898,29500,1758],{},[902,29502,1758],{"encoding":904},[724,29504,29505,29506,29509],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,29507,29508],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,29511,14947],{"id":14946},[120,29513,29514,29587,29633,29715,29765,29832,29889,29930,29963],{},[123,29515,29516,3369,29549,1343,29566,29583,29584,29586],{},[38,29517,29518,29519],{},"Funkce investic ",[883,29520,29522],{"className":29521},[886],[888,29523,29524],{"xmlns":890},[892,29525,29526,29546],{},[895,29527,29528,29530,29532,29534,29536,29538,29540,29542,29544],{},[898,29529,25985],{},[1716,29531,1920],{"stretchy":1919},[898,29533,2098],{},[1716,29535,1925],{"stretchy":1919},[1716,29537,1913],{},[898,29539,4478],{},[898,29541,2098],{},[1716,29543,1949],{},[898,29545,5198],{},[902,29547,29548],{"encoding":904},"I(r) = cr + d",[883,29550,29552],{"className":29551},[886],[888,29553,29554],{"xmlns":890},[892,29555,29556,29564],{},[895,29557,29558,29560,29562],{},[898,29559,4478],{},[1716,29561,2704],{},[1712,29563,2505],{},[902,29565,26315],{"encoding":904},[883,29567,29569],{"className":29568},[886],[888,29570,29571],{"xmlns":890},[892,29572,29573,29581],{},[895,29574,29575,29577,29579],{},[898,29576,5198],{},[1716,29578,2716],{},[1712,29580,2505],{},[902,29582,26294],{"encoding":904},"; ",[38,29585,26319],{}," funkce úrokové míry.",[123,29588,29589,29592,29593,29614,29615,29632],{},[38,29590,29591],{},"Trh zboží"," — rovnováha ",[883,29594,29596],{"className":29595},[886],[888,29597,29598],{"xmlns":890},[892,29599,29600,29612],{},[895,29601,29602,29604,29606,29608,29610],{},[898,29603,1758],{},[1716,29605,1913],{},[898,29607,9945],{},[1716,29609,1949],{},[898,29611,25985],{},[902,29613,28539],{"encoding":904},", ekvivalentně ",[883,29616,29618],{"className":29617},[886],[888,29619,29620],{"xmlns":890},[892,29621,29622,29630],{},[895,29623,29624,29626,29628],{},[898,29625,25985],{},[1716,29627,1913],{},[898,29629,5352],{},[902,29631,26512],{"encoding":904}," (investice = úspory).",[123,29634,29635,1994,29638,29640,29641,29691,29692,26715,29694,1853],{},[38,29636,29637],{},"Křivka IS",[614,29639,25856],{},") — ",[883,29642,29644],{"className":29643},[886],[888,29645,29646],{"xmlns":890},[892,29647,29648,29688],{},[895,29649,29650,29652,29654,29666,29668,29670],{},[898,29651,1758],{},[1716,29653,1913],{},[2750,29655,29656,29658],{},[898,29657,4478],{},[895,29659,29660,29662,29664],{},[1712,29661,1714],{},[1716,29663,2760],{},[898,29665,207],{},[898,29667,2098],{},[1716,29669,1949],{},[2750,29671,29672,29680],{},[895,29673,29674,29676,29678],{},[898,29675,1952],{},[1716,29677,1949],{},[898,29679,5198],{},[895,29681,29682,29684,29686],{},[1712,29683,1714],{},[1716,29685,2760],{},[898,29687,207],{},[902,29689,29690],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[38,29693,26319],{},[883,29695,29697],{"className":29696},[886],[888,29698,29699],{"xmlns":890},[892,29700,29701,29713],{},[895,29702,29703,29705,29707,29709,29711],{},[1716,29704,1920],{"stretchy":1919},[898,29706,2098],{},[1716,29708,1719],{"separator":1718},[898,29710,1758],{},[1716,29712,1925],{"stretchy":1919},[902,29714,26737],{"encoding":904},[123,29716,29717,29592,29720,29746,29747,1853],{},[38,29718,29719],{},"Trh peněz",[883,29721,29723],{"className":29722},[886],[888,29724,29725],{"xmlns":890},[892,29726,29727,29743],{},[895,29728,29729,29735,29737],{},[3074,29730,29731,29733],{},[898,29732,16690],{},[898,29734,1916],{},[1716,29736,1913],{},[3074,29738,29739,29741],{},[898,29740,16690],{},[898,29742,5352],{},[902,29744,29745],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,29748,29750],{"className":29749},[886],[888,29751,29752],{"xmlns":890},[892,29753,29754,29762],{},[895,29755,29756],{},[3074,29757,29758,29760],{},[898,29759,16690],{},[1716,29761,3080],{},[902,29763,29764],{"encoding":904},"M^* ",[123,29766,29767,3369,29770,1853],{},[38,29768,29769],{},"Transakční, opatrnostní, spekulační poptávka",[883,29771,29773],{"className":29772},[886],[888,29774,29775],{"xmlns":890},[892,29776,29777,29829],{},[895,29778,29779,29785,29787,29793,29795,29801,29803,29809,29811,29813,29819,29821,29823],{},[3074,29780,29781,29783],{},[898,29782,16690],{},[898,29784,1916],{},[1716,29786,1913],{},[1707,29788,29789,29791],{},[898,29790,1775],{},[1712,29792,1714],{},[1716,29794,1949],{},[1707,29796,29797,29799],{},[898,29798,1775],{},[1712,29800,1726],{},[1716,29802,1913],{},[1707,29804,29805,29807],{},[898,29806,27035],{},[1712,29808,1714],{},[898,29810,1758],{},[1716,29812,1949],{},[1707,29814,29815,29817],{},[898,29816,27035],{},[1712,29818,1726],{},[898,29820,2098],{},[1716,29822,1949],{},[1707,29824,29825,29827],{},[898,29826,27035],{},[1712,29828,7072],{},[902,29830,29831],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,29833,29834,1994,29837,29640,29839,29885,29886,29888],{},[38,29835,29836],{},"Křivka LM",[614,29838,25863],{},[883,29840,29842],{"className":29841},[886],[888,29843,29844],{"xmlns":890},[892,29845,29846,29882],{},[895,29847,29848,29854,29856,29862,29864,29866,29872,29874,29876],{},[3074,29849,29850,29852],{},[898,29851,16690],{},[1716,29853,3080],{},[1716,29855,1913],{},[1707,29857,29858,29860],{},[898,29859,27035],{},[1712,29861,1714],{},[898,29863,1758],{},[1716,29865,1949],{},[1707,29867,29868,29870],{},[898,29869,27035],{},[1712,29871,1726],{},[898,29873,2098],{},[1716,29875,1949],{},[1707,29877,29878,29880],{},[898,29879,27035],{},[1712,29881,7072],{},[902,29883,29884],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[38,29887,3167],{}," přímka.",[123,29890,29891,29894,29895,29929],{},[38,29892,29893],{},"Simultánní rovnováha"," — průsečík ",[883,29896,29898],{"className":29897},[886],[888,29899,29900],{"xmlns":890},[892,29901,29902,29926],{},[895,29903,29904,29906,29908,29910,29916,29918,29924],{},[898,29905,1805],{},[1716,29907,1913],{},[1716,29909,1920],{"stretchy":1919},[3074,29911,29912,29914],{},[898,29913,2098],{},[898,29915,1805],{},[1716,29917,1719],{"separator":1718},[3074,29919,29920,29922],{},[898,29921,1758],{},[898,29923,1805],{},[1716,29925,1925],{"stretchy":1919},[902,29927,29928],{"encoding":904},"E = (r^E, Y^E)"," křivek IS a LM.",[123,29931,29932,29935,29936,1343,29949,29962],{},[38,29933,29934],{},"Fiskální politika"," — nástroje ",[883,29937,29939],{"className":29938},[886],[888,29940,29941],{"xmlns":890},[892,29942,29943,29947],{},[895,29944,29945],{},[898,29946,25914],{},[902,29948,25914],{"encoding":904},[883,29950,29952],{"className":29951},[886],[888,29953,29954],{"xmlns":890},[892,29955,29956,29960],{},[895,29957,29958],{},[898,29959,4164],{},[902,29961,4164],{"encoding":904}," posouvající křivku IS.",[123,29964,29965,29968,29969,29986],{},[38,29966,29967],{},"Monetární politika"," — nástroj ",[883,29970,29972],{"className":29971},[886],[888,29973,29974],{"xmlns":890},[892,29975,29976,29984],{},[895,29977,29978],{},[3074,29979,29980,29982],{},[898,29981,16690],{},[1716,29983,3080],{},[902,29985,25951],{"encoding":904}," posouvající křivku LM.",[115,29988,15740],{"id":15739},[120,29990,29991,29998,30007,30017],{},[123,29992,29993,3495,29995],{},[38,29994,15794],{},[207,29996,15800],{"className":29997,"dataFsResolvedFilePath":15798,"href":15799},[210],[123,29999,30000,3495,30003],{},[38,30001,30002],{},"Přednáška:",[207,30004,30006],{"className":30005,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,30008,30009,3495,30012,30016],{},[38,30010,30011],{},"Nadřazené téma:",[207,30013,30015],{"className":30014,"dataFsResolvedFilePath":934,"href":935},[210],"narodni-duchod"," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,30018,30019,30022],{},[38,30020,30021],{},"Související:",[120,30023,30024,30031,30037],{},[123,30025,30026,30030],{},[207,30027,30029],{"className":30028,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,30032,30033,30036],{},[207,30034,1145],{"className":30035,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,30038,30039,30043],{},[207,30040,30042],{"className":30041,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":30045},[30046,30047,30048,30049,30050,30051,30052,30053,30054,30055],{"id":25808,"depth":642,"text":25809},{"id":25961,"depth":642,"text":25962},{"id":26176,"depth":642,"text":26177},{"id":26468,"depth":642,"text":26469},{"id":26881,"depth":642,"text":26882},{"id":27671,"depth":642,"text":27672},{"id":28360,"depth":642,"text":28361},{"id":29263,"depth":642,"text":29264},{"id":14946,"depth":642,"text":14947},{"id":15739,"depth":642,"text":15740},{},"\u002Ftopics\u002Fis-lm",{"title":25800,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,30062,1143,30063,30064,30065,30066,30015],"is-lm","trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":30069,"title":30070,"body":30071,"course":659,"courses":31663,"created":1129,"description":31664,"extension":661,"meta":31665,"navigation":664,"path":31666,"seo":31667,"sources":31668,"stem":31669,"tags":31670,"type":15858,"updated":677,"__hash__":31672},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":30072,"toc":31651},[30073,30076,30172,30179,30199,30203,30208,30271,30290,30292,30295,30431,30433,30643,30677,30814,30818,30882,30898,30926,30930,31028,31032,31036,31089,31195,31409,31413,31456,31562,31613,31615],[12,30074,30070],{"id":30075},"lagrangeova-metoda-vázané-extrémy",[724,30077,30078,30079,17758,30102,30134,30135,30138,30139,30166,30167,30171],{},"Hledáme extrém funkce ",[883,30080,30082],{"className":30081},[886],[888,30083,30084],{"xmlns":890},[892,30085,30086,30100],{},[895,30087,30088,30090,30092,30094,30096,30098],{},[898,30089,15915],{},[1716,30091,1920],{"stretchy":1919},[898,30093,8967],{},[1716,30095,1719],{"separator":1718},[898,30097,7684],{},[1716,30099,1925],{"stretchy":1919},[902,30101,23648],{"encoding":904},[883,30103,30105],{"className":30104},[886],[888,30106,30107],{"xmlns":890},[892,30108,30109,30131],{},[895,30110,30111,30113,30115,30121,30123,30129],{},[898,30112,900],{},[1716,30114,1920],{"stretchy":1919},[1707,30116,30117,30119],{},[898,30118,1878],{},[1712,30120,1714],{},[1716,30122,1719],{"separator":1718},[1707,30124,30125,30127],{},[898,30126,1878],{},[1712,30128,1726],{},[1716,30130,1925],{"stretchy":1919},[902,30132,30133],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,30136,30137],{},"podmíněný"," rovnicí ",[883,30140,30142],{"className":30141},[886],[888,30143,30144],{"xmlns":890},[892,30145,30146,30164],{},[895,30147,30148,30150,30152,30154,30156,30158,30160,30162],{},[898,30149,24845],{},[1716,30151,1920],{"stretchy":1919},[898,30153,8967],{},[1716,30155,1719],{"separator":1718},[898,30157,7684],{},[1716,30159,1925],{"stretchy":1919},[1716,30161,1913],{},[1712,30163,2505],{},[902,30165,24862],{"encoding":904},". V ",[207,30168,30170],{"className":30169,"dataFsResolvedFilePath":15798,"href":15799},[210],"matematické ekonomii"," se používá pro:",[724,30173,30174],{},[3682,30175],{"alt":30176,"className":30177,"src":30178},"imek-lagrange-tecnost",[210,3686],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,30180,30181,30190,30196],{},[123,30182,30183,30186,30187,1925],{},[38,30184,30185],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,30188,23580],{"className":30189,"dataFsResolvedFilePath":878,"href":879},[210],[123,30191,30192,30195],{},[38,30193,30194],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,30197,30198],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,30200,30202],{"id":30201},"princip","Princip",[724,30204,24511,30205,2291],{},[38,30206,30207],{},"Lagrangeovu funkci",[724,30209,30210],{},[883,30211,30213],{"className":30212},[886],[888,30214,30215],{"xmlns":890},[892,30216,30217,30268],{},[895,30218,30219,30221,30223,30225,30227,30229,30231,30234,30236,30238,30240,30242,30244,30246,30248,30250,30252,30254,30256,30258,30260,30262,30264,30266],{},[898,30220,1775],{},[1716,30222,1920],{"stretchy":1919},[898,30224,8967],{},[1716,30226,1719],{"separator":1718},[898,30228,7684],{},[1716,30230,1719],{"separator":1718},[898,30232,30233],{},"λ",[1716,30235,1925],{"stretchy":1919},[1716,30237,1913],{},[898,30239,15915],{},[1716,30241,1920],{"stretchy":1919},[898,30243,8967],{},[1716,30245,1719],{"separator":1718},[898,30247,7684],{},[1716,30249,1925],{"stretchy":1919},[1716,30251,1949],{},[898,30253,30233],{},[2074,30255,8508],{},[898,30257,24845],{},[1716,30259,1920],{"stretchy":1919},[898,30261,8967],{},[1716,30263,1719],{"separator":1718},[898,30265,7684],{},[1716,30267,1925],{"stretchy":1919},[902,30269,30270],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,30272,18149,30273,2574,30287,1853],{},[883,30274,30276],{"className":30275},[886],[888,30277,30278],{"xmlns":890},[892,30279,30280,30284],{},[895,30281,30282],{},[898,30283,30233],{},[902,30285,30286],{"encoding":904},"\\lambda",[38,30288,30289],{},"Lagrangeův multiplikátor",[115,30291,17112],{"id":17111},[724,30293,30294],{},"Řešíme soustavu:",[724,30296,30297,30345,30393],{},[883,30298,30300],{"className":30299},[886],[888,30301,30302],{"xmlns":890},[892,30303,30304,30342],{},[895,30305,30306,30314,30316,30324,30326,30328,30330,30338,30340],{},[7204,30307,30308,30310,30312],{},[898,30309,1775],{},[898,30311,8967],{},[1716,30313,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30315,1913],{},[7204,30317,30318,30320,30322],{},[898,30319,15915],{},[898,30321,8967],{},[1716,30323,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30325,1949],{},[898,30327,30233],{},[2074,30329,8508],{},[7204,30331,30332,30334,30336],{},[898,30333,24845],{},[898,30335,8967],{},[1716,30337,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30339,1913],{},[1712,30341,2505],{},[902,30343,30344],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,30346,30348],{"className":30347},[886],[888,30349,30350],{"xmlns":890},[892,30351,30352,30390],{},[895,30353,30354,30362,30364,30372,30374,30376,30378,30386,30388],{},[7204,30355,30356,30358,30360],{},[898,30357,1775],{},[898,30359,7684],{},[1716,30361,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30363,1913],{},[7204,30365,30366,30368,30370],{},[898,30367,15915],{},[898,30369,7684],{},[1716,30371,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30373,1949],{},[898,30375,30233],{},[2074,30377,8508],{},[7204,30379,30380,30382,30384],{},[898,30381,24845],{},[898,30383,7684],{},[1716,30385,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30387,1913],{},[1712,30389,2505],{},[902,30391,30392],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,30394,30396],{"className":30395},[886],[888,30397,30398],{"xmlns":890},[892,30399,30400,30428],{},[895,30401,30402,30410,30412,30414,30416,30418,30420,30422,30424,30426],{},[7204,30403,30404,30406,30408],{},[898,30405,1775],{},[898,30407,30233],{},[1716,30409,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30411,1913],{},[898,30413,24845],{},[1716,30415,1920],{"stretchy":1919},[898,30417,8967],{},[1716,30419,1719],{"separator":1718},[898,30421,7684],{},[1716,30423,1925],{"stretchy":1919},[1716,30425,1913],{},[1712,30427,2505],{},[902,30429,30430],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,30432,17186],{"id":17185},[724,30434,30435],{},[883,30436,30438],{"className":30437},[886],[888,30439,30440],{"xmlns":890},[892,30441,30442,30640],{},[895,30443,30444,30446,30448,30450,30452,30454,30456,30458,30460,30462,30464,30480,30482,30484,30500,30502,30504,30512,30518,30520,30522,30538,30540,30542,30558,30560,30562,30570,30576,30578,30580,30582,30598,30600,30602,30618,30620,30622,30630,30632],{},[898,30445,1916],{},[1716,30447,1920],{"stretchy":1919},[898,30449,8967],{},[1716,30451,1719],{"separator":1718},[898,30453,7684],{},[1716,30455,1719],{"separator":1718},[898,30457,30233],{},[1716,30459,1925],{"stretchy":1919},[1716,30461,1913],{},[1716,30463,1920],{"stretchy":1919},[7204,30465,30466,30468,30474],{},[898,30467,15915],{},[895,30469,30470,30472],{},[898,30471,8967],{},[898,30473,8967],{},[895,30475,30476,30478],{},[1716,30477,8505],{"mathvariant":2068},[1716,30479,8505],{"mathvariant":2068},[1716,30481,1949],{},[898,30483,30233],{},[7204,30485,30486,30488,30494],{},[898,30487,24845],{},[895,30489,30490,30492],{},[898,30491,8967],{},[898,30493,8967],{},[895,30495,30496,30498],{},[1716,30497,8505],{"mathvariant":2068},[1716,30499,8505],{"mathvariant":2068},[1716,30501,1925],{"stretchy":1919},[1716,30503,1920],{"stretchy":1919},[7204,30505,30506,30508,30510],{},[898,30507,24845],{},[898,30509,7684],{},[1716,30511,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[3074,30513,30514,30516],{},[1716,30515,1925],{"stretchy":1919},[1712,30517,1726],{},[1716,30519,1949],{},[1716,30521,1920],{"stretchy":1919},[7204,30523,30524,30526,30532],{},[898,30525,15915],{},[895,30527,30528,30530],{},[898,30529,7684],{},[898,30531,7684],{},[895,30533,30534,30536],{},[1716,30535,8505],{"mathvariant":2068},[1716,30537,8505],{"mathvariant":2068},[1716,30539,1949],{},[898,30541,30233],{},[7204,30543,30544,30546,30552],{},[898,30545,24845],{},[895,30547,30548,30550],{},[898,30549,7684],{},[898,30551,7684],{},[895,30553,30554,30556],{},[1716,30555,8505],{"mathvariant":2068},[1716,30557,8505],{"mathvariant":2068},[1716,30559,1925],{"stretchy":1919},[1716,30561,1920],{"stretchy":1919},[7204,30563,30564,30566,30568],{},[898,30565,24845],{},[898,30567,8967],{},[1716,30569,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[3074,30571,30572,30574],{},[1716,30573,1925],{"stretchy":1919},[1712,30575,1726],{},[1716,30577,2760],{},[1712,30579,1726],{},[1716,30581,1920],{"stretchy":1919},[7204,30583,30584,30586,30592],{},[898,30585,15915],{},[895,30587,30588,30590],{},[898,30589,8967],{},[898,30591,7684],{},[895,30593,30594,30596],{},[1716,30595,8505],{"mathvariant":2068},[1716,30597,8505],{"mathvariant":2068},[1716,30599,1949],{},[898,30601,30233],{},[7204,30603,30604,30606,30612],{},[898,30605,24845],{},[895,30607,30608,30610],{},[898,30609,8967],{},[898,30611,7684],{},[895,30613,30614,30616],{},[1716,30615,8505],{"mathvariant":2068},[1716,30617,8505],{"mathvariant":2068},[1716,30619,1925],{"stretchy":1919},[2074,30621,8508],{},[7204,30623,30624,30626,30628],{},[898,30625,24845],{},[898,30627,8967],{},[1716,30629,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,30631,8508],{},[7204,30633,30634,30636,30638],{},[898,30635,24845],{},[898,30637,7684],{},[1716,30639,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,30641,30642],{"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",[724,30644,30645,30646,30676],{},"Je-li ",[883,30647,30649],{"className":30648},[886],[888,30650,30651],{"xmlns":890},[892,30652,30653,30673],{},[895,30654,30655,30657,30659,30661,30663,30665,30671],{},[1716,30656,2502],{"stretchy":1919},[898,30658,207],{},[1716,30660,1719],{"separator":1718},[898,30662,1952],{},[1716,30664,1719],{"separator":1718},[1707,30666,30667,30669],{},[898,30668,30233],{},[1712,30670,2505],{},[1716,30672,2516],{"stretchy":1919},[902,30674,30675],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,30678,30679,30747],{},[123,30680,30681,17273,30717,30719,30720],{},[883,30682,30684],{"className":30683},[886],[888,30685,30686],{"xmlns":890},[892,30687,30688,30714],{},[895,30689,30690,30692,30694,30696,30698,30700,30702,30708,30710,30712],{},[898,30691,1916],{},[1716,30693,1920],{"stretchy":1919},[898,30695,207],{},[1716,30697,1719],{"separator":1718},[898,30699,1952],{},[1716,30701,1719],{"separator":1718},[1707,30703,30704,30706],{},[898,30705,30233],{},[1712,30707,2505],{},[1716,30709,1925],{"stretchy":1919},[1716,30711,2704],{},[1712,30713,2505],{},[902,30715,30716],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,30718,17573],{}," vázané podmínkou ",[883,30721,30723],{"className":30722},[886],[888,30724,30725],{"xmlns":890},[892,30726,30727,30745],{},[895,30728,30729,30731,30733,30735,30737,30739,30741,30743],{},[898,30730,24845],{},[1716,30732,1920],{"stretchy":1919},[898,30734,8967],{},[1716,30736,1719],{"separator":1718},[898,30738,7684],{},[1716,30740,1925],{"stretchy":1919},[1716,30742,1913],{},[1712,30744,2505],{},[902,30746,24862],{"encoding":904},[123,30748,30749,17273,30785,30719,30787],{},[883,30750,30752],{"className":30751},[886],[888,30753,30754],{"xmlns":890},[892,30755,30756,30782],{},[895,30757,30758,30760,30762,30764,30766,30768,30770,30776,30778,30780],{},[898,30759,1916],{},[1716,30761,1920],{"stretchy":1919},[898,30763,207],{},[1716,30765,1719],{"separator":1718},[898,30767,1952],{},[1716,30769,1719],{"separator":1718},[1707,30771,30772,30774],{},[898,30773,30233],{},[1712,30775,2505],{},[1716,30777,1925],{"stretchy":1919},[1716,30779,2716],{},[1712,30781,2505],{},[902,30783,30784],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,30786,17630],{},[883,30788,30790],{"className":30789},[886],[888,30791,30792],{"xmlns":890},[892,30793,30794,30812],{},[895,30795,30796,30798,30800,30802,30804,30806,30808,30810],{},[898,30797,24845],{},[1716,30799,1920],{"stretchy":1919},[898,30801,8967],{},[1716,30803,1719],{"separator":1718},[898,30805,7684],{},[1716,30807,1925],{"stretchy":1919},[1716,30809,1913],{},[1712,30811,2505],{},[902,30813,24862],{"encoding":904},[115,30815,30817],{"id":30816},"význam-multiplikátoru","Význam multiplikátoru",[724,30819,30820],{},[883,30821,30823],{"className":30822},[886],[888,30824,30825],{"xmlns":890},[892,30826,30827,30879],{},[895,30828,30829,30831,30833,30855,30857],{},[898,30830,30233],{},[1716,30832,1913],{},[2750,30834,30835,30843],{},[7204,30836,30837,30839,30841],{},[898,30838,15915],{},[898,30840,8967],{},[1716,30842,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[895,30844,30845,30847],{},[1716,30846,2760],{},[7204,30848,30849,30851,30853],{},[898,30850,24845],{},[898,30852,8967],{},[1716,30854,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,30856,1913],{},[2750,30858,30859,30867],{},[7204,30860,30861,30863,30865],{},[898,30862,15915],{},[898,30864,7684],{},[1716,30866,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[895,30868,30869,30871],{},[1716,30870,2760],{},[7204,30872,30873,30875,30877],{},[898,30874,24845],{},[898,30876,7684],{},[1716,30878,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,30880,30881],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,30883,30884,30897],{},[883,30885,30887],{"className":30886},[886],[888,30888,30889],{"xmlns":890},[892,30890,30891,30895],{},[895,30892,30893],{},[898,30894,30233],{},[902,30896,30286],{"encoding":904}," udává:",[120,30899,30900,30906],{},[123,30901,30902,30903],{},"konstantní ",[38,30904,30905],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,30907,30908,30911,30912,30925],{},[38,30909,30910],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,30913,30915],{"className":30914},[886],[888,30916,30917],{"xmlns":890},[892,30918,30919,30923],{},[895,30920,30921],{},[898,30922,15915],{},[902,30924,15915],{"encoding":904},", uvolní-li se omezení o jednotku",[115,30927,30929],{"id":30928},"alternativní-postup","Alternativní postup",[724,30931,30932,30933,30960,30961,30985,30986,31010,31011,31024,31025,1853],{},"Lze-li z ",[883,30934,30936],{"className":30935},[886],[888,30937,30938],{"xmlns":890},[892,30939,30940,30958],{},[895,30941,30942,30944,30946,30948,30950,30952,30954,30956],{},[898,30943,24845],{},[1716,30945,1920],{"stretchy":1919},[898,30947,8967],{},[1716,30949,1719],{"separator":1718},[898,30951,7684],{},[1716,30953,1925],{"stretchy":1919},[1716,30955,1913],{},[1712,30957,2505],{},[902,30959,24862],{"encoding":904}," vyjádřit ",[883,30962,30964],{"className":30963},[886],[888,30965,30966],{"xmlns":890},[892,30967,30968,30982],{},[895,30969,30970,30972,30974,30976,30978,30980],{},[898,30971,7684],{},[1716,30973,1913],{},[898,30975,7684],{},[1716,30977,1920],{"stretchy":1919},[898,30979,8967],{},[1716,30981,1925],{"stretchy":1919},[902,30983,30984],{"encoding":904},"y = y(x)"," (nebo ",[883,30987,30989],{"className":30988},[886],[888,30990,30991],{"xmlns":890},[892,30992,30993,31007],{},[895,30994,30995,30997,30999,31001,31003,31005],{},[898,30996,8967],{},[1716,30998,1913],{},[898,31000,8967],{},[1716,31002,1920],{"stretchy":1919},[898,31004,7684],{},[1716,31006,1925],{"stretchy":1919},[902,31008,31009],{"encoding":904},"x = x(y)","), dosadíme do ",[883,31012,31014],{"className":31013},[886],[888,31015,31016],{"xmlns":890},[892,31017,31018,31022],{},[895,31019,31020],{},[898,31021,15915],{},[902,31023,15915],{"encoding":904}," a převedeme na ",[38,31026,31027],{},"extrém funkce jedné proměnné",[115,31029,31031],{"id":31030},"použití-v-imek","Použití v ImeK",[198,31033,31035],{"id":31034},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,31037,31038,31039,1853],{},"Rozpočtové omezení: ",[883,31040,31042],{"className":31041},[886],[888,31043,31044],{"xmlns":890},[892,31045,31046,31086],{},[895,31047,31048,31054,31056,31064,31070,31072,31080],{},[3074,31049,31050,31052],{},[898,31051,1758],{},[1716,31053,3080],{},[1716,31055,1913],{},[7204,31057,31058,31060,31062],{},[898,31059,1690],{},[1712,31061,1714],{},[1716,31063,3080],{},[1707,31065,31066,31068],{},[898,31067,1878],{},[1712,31069,1714],{},[1716,31071,1949],{},[7204,31073,31074,31076,31078],{},[898,31075,1690],{},[1712,31077,1726],{},[1716,31079,3080],{},[1707,31081,31082,31084],{},[898,31083,1878],{},[1712,31085,1726],{},[902,31087,31088],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,31090,31091],{},[883,31092,31094],{"className":31093},[886],[888,31095,31096],{"xmlns":890},[892,31097,31098,31192],{},[895,31099,31100,31102,31104,31110,31112,31118,31120,31122,31124,31126,31128,31130,31136,31138,31144,31146,31148,31150,31152,31158,31160,31168,31174,31176,31184,31190],{},[898,31101,1775],{},[1716,31103,1920],{"stretchy":1919},[1707,31105,31106,31108],{},[898,31107,1878],{},[1712,31109,1714],{},[1716,31111,1719],{"separator":1718},[1707,31113,31114,31116],{},[898,31115,1878],{},[1712,31117,1726],{},[1716,31119,1719],{"separator":1718},[898,31121,30233],{},[1716,31123,1925],{"stretchy":1919},[1716,31125,1913],{},[898,31127,900],{},[1716,31129,1920],{"stretchy":1919},[1707,31131,31132,31134],{},[898,31133,1878],{},[1712,31135,1714],{},[1716,31137,1719],{"separator":1718},[1707,31139,31140,31142],{},[898,31141,1878],{},[1712,31143,1726],{},[1716,31145,1925],{"stretchy":1919},[1716,31147,1949],{},[898,31149,30233],{},[1716,31151,1920],{"stretchy":1919},[3074,31153,31154,31156],{},[898,31155,1758],{},[1716,31157,3080],{},[1716,31159,2760],{},[7204,31161,31162,31164,31166],{},[898,31163,1690],{},[1712,31165,1714],{},[1716,31167,3080],{},[1707,31169,31170,31172],{},[898,31171,1878],{},[1712,31173,1714],{},[1716,31175,2760],{},[7204,31177,31178,31180,31182],{},[898,31179,1690],{},[1712,31181,1726],{},[1716,31183,3080],{},[1707,31185,31186,31188],{},[898,31187,1878],{},[1712,31189,1726],{},[1716,31191,1925],{"stretchy":1919},[902,31193,31194],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,31196,31197,31198,1343,31230,1343,31262,31311,31312,31366,31367,1853],{},"Soustava: ",[883,31199,31201],{"className":31200},[886],[888,31202,31203],{"xmlns":890},[892,31204,31205,31227],{},[895,31206,31207,31215,31217,31219],{},[7204,31208,31209,31211,31213],{},[898,31210,900],{},[1712,31212,1714],{},[1716,31214,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,31216,1913],{},[898,31218,30233],{},[7204,31220,31221,31223,31225],{},[898,31222,1690],{},[1712,31224,1714],{},[1716,31226,3080],{},[902,31228,31229],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,31231,31233],{"className":31232},[886],[888,31234,31235],{"xmlns":890},[892,31236,31237,31259],{},[895,31238,31239,31247,31249,31251],{},[7204,31240,31241,31243,31245],{},[898,31242,900],{},[1712,31244,1726],{},[1716,31246,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,31248,1913],{},[898,31250,30233],{},[7204,31252,31253,31255,31257],{},[898,31254,1690],{},[1712,31256,1726],{},[1716,31258,3080],{},[902,31260,31261],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,31263,31265],{"className":31264},[886],[888,31266,31267],{"xmlns":890},[892,31268,31269,31309],{},[895,31270,31271,31277,31279,31287,31293,31295,31303],{},[3074,31272,31273,31275],{},[898,31274,1758],{},[1716,31276,3080],{},[1716,31278,1913],{},[7204,31280,31281,31283,31285],{},[898,31282,1690],{},[1712,31284,1714],{},[1716,31286,3080],{},[1707,31288,31289,31291],{},[898,31290,1878],{},[1712,31292,1714],{},[1716,31294,1949],{},[7204,31296,31297,31299,31301],{},[898,31298,1690],{},[1712,31300,1726],{},[1716,31302,3080],{},[1707,31304,31305,31307],{},[898,31306,1878],{},[1712,31308,1726],{},[902,31310,31088],{"encoding":904},". Z prvních dvou: ",[883,31313,31315],{"className":31314},[886],[888,31316,31317],{"xmlns":890},[892,31318,31319,31363],{},[895,31320,31321,31341,31343],{},[2747,31322,31323],{"scriptlevel":2505,"displaystyle":1919},[2750,31324,31325,31333],{},[7204,31326,31327,31329,31331],{},[898,31328,900],{},[1712,31330,1714],{},[1716,31332,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,31334,31335,31337,31339],{},[898,31336,900],{},[1712,31338,1726],{},[1716,31340,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,31342,1913],{},[2747,31344,31345],{"scriptlevel":2505,"displaystyle":1919},[2750,31346,31347,31355],{},[7204,31348,31349,31351,31353],{},[898,31350,1690],{},[1712,31352,1714],{},[1716,31354,3080],{},[7204,31356,31357,31359,31361],{},[898,31358,1690],{},[1712,31360,1726],{},[1716,31362,3080],{},[902,31364,31365],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,31368,31370],{"className":31369},[886],[888,31371,31372],{"xmlns":890},[892,31373,31374,31406],{},[895,31375,31376,31378,31380,31382,31384,31386],{},[898,31377,16690],{},[898,31379,17840],{},[898,31381,9945],{},[898,31383,5352],{},[1716,31385,1913],{},[2747,31387,31388],{"scriptlevel":2505,"displaystyle":1919},[2750,31389,31390,31398],{},[7204,31391,31392,31394,31396],{},[898,31393,1690],{},[1712,31395,1714],{},[1716,31397,3080],{},[7204,31399,31400,31402,31404],{},[898,31401,1690],{},[1712,31403,1726],{},[1716,31405,3080],{},[902,31407,31408],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,31410,31412],{"id":31411},"minimalizace-výdajů","Minimalizace výdajů",[724,31414,31415,31416,1853],{},"Podmínka dané užitečnosti ",[883,31417,31419],{"className":31418},[886],[888,31420,31421],{"xmlns":890},[892,31422,31423,31453],{},[895,31424,31425,31431,31433,31435,31437,31443,31445,31451],{},[3074,31426,31427,31429],{},[898,31428,900],{},[1716,31430,3080],{},[1716,31432,1913],{},[898,31434,900],{},[1716,31436,1920],{"stretchy":1919},[1707,31438,31439,31441],{},[898,31440,1878],{},[1712,31442,1714],{},[1716,31444,1719],{"separator":1718},[1707,31446,31447,31449],{},[898,31448,1878],{},[1712,31450,1726],{},[1716,31452,1925],{"stretchy":1919},[902,31454,31455],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,31457,31458],{},[883,31459,31461],{"className":31460},[886],[888,31462,31463],{"xmlns":890},[892,31464,31465,31559],{},[895,31466,31467,31469,31471,31477,31479,31485,31487,31489,31491,31493,31501,31507,31509,31517,31523,31525,31527,31529,31535,31537,31539,31541,31547,31549,31555,31557],{},[898,31468,1775],{},[1716,31470,1920],{"stretchy":1919},[1707,31472,31473,31475],{},[898,31474,1878],{},[1712,31476,1714],{},[1716,31478,1719],{"separator":1718},[1707,31480,31481,31483],{},[898,31482,1878],{},[1712,31484,1726],{},[1716,31486,1719],{"separator":1718},[898,31488,30233],{},[1716,31490,1925],{"stretchy":1919},[1716,31492,1913],{},[7204,31494,31495,31497,31499],{},[898,31496,1690],{},[1712,31498,1714],{},[1716,31500,3080],{},[1707,31502,31503,31505],{},[898,31504,1878],{},[1712,31506,1714],{},[1716,31508,1949],{},[7204,31510,31511,31513,31515],{},[898,31512,1690],{},[1712,31514,1726],{},[1716,31516,3080],{},[1707,31518,31519,31521],{},[898,31520,1878],{},[1712,31522,1726],{},[1716,31524,1949],{},[898,31526,30233],{},[1716,31528,1920],{"stretchy":1919},[3074,31530,31531,31533],{},[898,31532,900],{},[1716,31534,3080],{},[1716,31536,2760],{},[898,31538,900],{},[1716,31540,1920],{"stretchy":1919},[1707,31542,31543,31545],{},[898,31544,1878],{},[1712,31546,1714],{},[1716,31548,1719],{"separator":1718},[1707,31550,31551,31553],{},[898,31552,1878],{},[1712,31554,1726],{},[1716,31556,1925],{"stretchy":1919},[1716,31558,1925],{"stretchy":1919},[902,31560,31561],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,31563,31564,31565,1853],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,31566,31568],{"className":31567},[886],[888,31569,31570],{"xmlns":890},[892,31571,31572,31610],{},[895,31573,31574,31580,31582,31588,31590,31596,31598,31604,31606,31608],{},[1707,31575,31576,31578],{},[898,31577,1878],{},[898,31579,12546],{},[1716,31581,1913],{},[1707,31583,31584,31586],{},[898,31585,1916],{},[898,31587,12546],{},[1716,31589,1920],{"stretchy":1919},[1707,31591,31592,31594],{},[898,31593,1690],{},[1712,31595,1714],{},[1716,31597,1719],{"separator":1718},[1707,31599,31600,31602],{},[898,31601,1690],{},[1712,31603,1726],{},[1716,31605,1719],{"separator":1718},[898,31607,900],{},[1716,31609,1925],{"stretchy":1919},[902,31611,31612],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,31614,15740],{"id":15739},[120,31616,31617,31624,31631,31640],{},[123,31618,31619,3495,31621],{},[38,31620,17652],{},[207,31622,784],{"className":31623,"dataFsResolvedFilePath":782,"href":783},[210],[123,31625,31626,3495,31628],{},[38,31627,17660],{},[207,31629,25743],{"className":31630,"dataFsResolvedFilePath":800,"href":801},[210],[123,31632,31633,3495,31636,31639],{},[38,31634,31635],{},"Aplikace v kurzu:",[207,31637,880],{"className":31638,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,31641,31642,3495,31644,1343,31647,31650],{},[38,31643,17668],{},[207,31645,936],{"className":31646,"dataFsResolvedFilePath":934,"href":935},[210],[207,31648,1400],{"className":31649,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":31652},[31653,31654,31655,31656,31657,31658,31662],{"id":30201,"depth":642,"text":30202},{"id":17111,"depth":642,"text":17112},{"id":17185,"depth":642,"text":17186},{"id":30816,"depth":642,"text":30817},{"id":30928,"depth":642,"text":30929},{"id":31030,"depth":642,"text":31031,"children":31659},[31660,31661],{"id":31034,"depth":649,"text":31035},{"id":31411,"depth":649,"text":31412},{"id":15739,"depth":642,"text":15740},[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":30070,"description":31664},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,31671,15855],"vazane-extremy","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":31674,"title":936,"body":31675,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":41524,"navigation":664,"path":41525,"seo":41526,"sources":41527,"stem":41528,"tags":41529,"type":15858,"updated":677,"__hash__":41533},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":31676,"toc":41486},[31677,31680,31682,31804,31939,31943,31946,32059,32063,32091,32138,32141,32207,32252,32255,32281,32312,32316,32320,32364,32408,32469,32524,32527,32531,32534,32581,32677,32783,32789,32866,32895,33034,33038,33067,33116,33262,33352,33356,33382,33420,33447,33485,33547,33622,33700,33758,33824,33868,33872,33930,33979,34024,34237,34357,34363,34367,34390,34394,34401,34405,34436,34471,34475,34525,34608,34650,34671,34732,34792,34796,34867,34935,35006,35121,35169,35173,35176,35216,35255,35278,35391,35555,35563,35590,35620,35623,35700,35853,35937,36276,36280,36404,36540,36676,36728,36731,36981,37061,37065,37068,37126,37158,37161,37210,37213,37284,37480,37484,37635,37865,37903,37956,38001,38004,38060,38109,38313,38403,38407,38422,38429,38598,38602,38673,38754,38835,38914,39060,39148,39152,39335,39466,39511,39608,39612,40350,40352,41403,41405],[12,31678,936],{"id":31679},"národní-důchod",[115,31681,25809],{"id":25808},[724,31683,31684,31685,3495,31689,31692,31693,3495,31696,31709,31710,31713,31714,31717,31718,31721,31722,31724,31725,3495,31727,31744,31745,31762,31763,31765,31766,2365],{},"Kapitola 7 ",[207,31686,31688],{"className":31687,"dataFsResolvedFilePath":15798,"href":15799},[210],"Matematické ekonomie",[38,31690,31691],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,31694,31695],{},"národním důchodem",[883,31697,31699],{"className":31698},[886],[888,31700,31701],{"xmlns":890},[892,31702,31703,31707],{},[895,31704,31705],{},[898,31706,1758],{},[902,31708,1758],{"encoding":904},". Budují se postupně bohatší modely — ",[38,31711,31712],{},"C-I"," (jen spotřeba a investice) → ",[38,31715,31716],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,31719,31720],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,31723,25814],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,31726,27682],{},[883,31728,31730],{"className":31729},[886],[888,31731,31732],{"xmlns":890},[892,31733,31734,31742],{},[895,31735,31736],{},[3074,31737,31738,31740],{},[898,31739,1758],{},[898,31741,1805],{},[902,31743,27700],{"encoding":904}," jako řešení soustavy lineárních rovnic; citlivost ",[883,31746,31748],{"className":31747},[886],[888,31749,31750],{"xmlns":890},[892,31751,31752,31760],{},[895,31753,31754],{},[3074,31755,31756,31758],{},[898,31757,1758],{},[898,31759,1805],{},[902,31761,27700],{"encoding":904}," na exogenní veličiny popisují ",[38,31764,1657],{}," (zejména Keynesův multiplikátor investic ",[883,31767,31769],{"className":31768},[886],[888,31770,31771],{"xmlns":890},[892,31772,31773,31801],{},[895,31774,31775,31777,31779,31781,31783,31785,31787,31789,31791,31793,31795,31797,31799],{},[1712,31776,1714],{},[898,31778,3045],{"mathvariant":2068},[1716,31780,1920],{"stretchy":1919},[1712,31782,1714],{},[1716,31784,2760],{},[898,31786,207],{},[1716,31788,1925],{"stretchy":1919},[1716,31790,1913],{},[1712,31792,1714],{},[898,31794,3045],{"mathvariant":2068},[898,31796,16690],{},[898,31798,1690],{},[898,31800,5352],{},[902,31802,31803],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",[1635,31805,31806],{},[724,31807,31808,31810,31811,31814,31815,31833,31834,31864,31865,31912,31913,31915,31916,31938],{},[883,31809,1641],{}," Intuice\n",[38,31812,31813],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,31816,31818],{"className":31817},[886],[888,31819,31820],{"xmlns":890},[892,31821,31822,31830],{},[895,31823,31824,31826,31828],{},[898,31825,16690],{},[898,31827,1690],{},[898,31829,9945],{},[902,31831,31832],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,31835,31837],{"className":31836},[886],[888,31838,31839],{"xmlns":890},[892,31840,31841,31861],{},[895,31842,31843,31845,31847,31849,31851,31853,31855,31857,31859],{},[898,31844,16690],{},[898,31846,1690],{},[898,31848,5352],{},[1716,31850,1913],{},[1712,31852,1714],{},[1716,31854,2760],{},[898,31856,16690],{},[898,31858,1690],{},[898,31860,9945],{},[902,31862,31863],{"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 ",[883,31866,31868],{"className":31867},[886],[888,31869,31870],{"xmlns":890},[892,31871,31872,31909],{},[895,31873,31874,31876,31878,31880,31882,31888,31890,31893,31895,31897,31899,31901,31903,31905,31907],{},[1712,31875,1714],{},[1716,31877,1949],{},[898,31879,207],{},[1716,31881,1949],{},[3074,31883,31884,31886],{},[898,31885,207],{},[1712,31887,1726],{},[1716,31889,1949],{},[1716,31891,31892],{},"⋯",[1716,31894,1913],{},[1712,31896,1714],{},[898,31898,3045],{"mathvariant":2068},[1716,31900,1920],{"stretchy":1919},[1712,31902,1714],{},[1716,31904,2760],{},[898,31906,207],{},[1716,31908,1925],{"stretchy":1919},[902,31910,31911],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,31914,25814],{}," 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 ",[883,31917,31919],{"className":31918},[886],[888,31920,31921],{"xmlns":890},[892,31922,31923,31935],{},[895,31924,31925,31927,31929,31931,31933],{},[1716,31926,1920],{"stretchy":1919},[898,31928,1758],{},[1716,31930,1719],{"separator":1718},[898,31932,2098],{},[1716,31934,1925],{"stretchy":1919},[902,31936,31937],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,31940,31942],{"id":31941},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,31944,31945],{},"Po prostudování kapitoly by čtenář měl umět:",[120,31947,31948,31951,31954,31957,31960,31963,31966,32056],{},[123,31949,31950],{},"popsat zjednodušený model národní ekonomiky,",[123,31952,31953],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,31955,31956],{},"popsat lineární model spotřeby a úspor,",[123,31958,31959],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,31961,31962],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,31964,31965],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,31967,31968,31969,1343,31986,1343,32008,2247,32033,32055],{},"popsat modely ",[883,31970,31972],{"className":31971},[886],[888,31973,31974],{"xmlns":890},[892,31975,31976,31984],{},[895,31977,31978,31980,31982],{},[898,31979,9945],{},[2074,31981,26091],{},[898,31983,25985],{},[902,31985,26096],{"encoding":904},[883,31987,31989],{"className":31988},[886],[888,31990,31991],{"xmlns":890},[892,31992,31993,32005],{},[895,31994,31995,31997,31999,32001,32003],{},[898,31996,9945],{},[2074,31998,26091],{},[898,32000,25985],{},[2074,32002,26091],{},[898,32004,25914],{},[902,32006,32007],{"encoding":904},"C\\text{-}I\\text{-}G",[883,32009,32011],{"className":32010},[886],[888,32012,32013],{"xmlns":890},[892,32014,32015,32031],{},[895,32016,32017,32019,32021,32023,32025,32027,32029],{},[898,32018,9945],{},[2074,32020,26091],{},[898,32022,25985],{},[2074,32024,26091],{},[898,32026,25914],{},[2074,32028,26091],{},[898,32030,26121],{},[902,32032,26124],{"encoding":904},[883,32034,32036],{"className":32035},[886],[888,32037,32038],{"xmlns":890},[892,32039,32040,32052],{},[895,32041,32042,32044,32046,32048,32050],{},[898,32043,25985],{},[898,32045,5352],{},[2074,32047,26091],{},[898,32049,1775],{},[898,32051,16690],{},[902,32053,32054],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,32057,32058],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,32060,32062],{"id":32061},"gnp-a-národní-důchod","GNP a národní důchod",[724,32064,32065,3495,32068,1994,32087,32090],{},[38,32066,32067],{},"Hrubý národní produkt",[883,32069,32071],{"className":32070},[886],[888,32072,32073],{"xmlns":890},[892,32074,32075,32084],{},[895,32076,32077,32079,32082],{},[898,32078,25914],{},[898,32080,32081],{},"N",[898,32083,1690],{},[902,32085,32086],{"encoding":904},"GNP",[614,32088,32089],{},"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:",[724,32092,32093],{},[883,32094,32096],{"className":32095},[886],[888,32097,32098],{"xmlns":890},[892,32099,32100,32135],{},[895,32101,32102,32104,32106,32108,32110,32112,32114,32116,32118,32120,32122,32124,32126,32128,32130,32133],{},[898,32103,25914],{},[898,32105,32081],{},[898,32107,1690],{},[1716,32109,1913],{},[898,32111,9945],{},[1716,32113,1949],{},[898,32115,25985],{},[1716,32117,1949],{},[898,32119,25914],{},[1716,32121,1949],{},[898,32123,26121],{},[1716,32125,1719],{"separator":1718},[2324,32127],{"width":2326},[1716,32129,1920],{"stretchy":1919},[1712,32131,32132],{},"7.1",[1716,32134,1925],{"stretchy":1919},[902,32136,32137],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,32139,32140],{},"kde",[120,32142,32143,32159,32175,32191],{},[123,32144,32145,32158],{},[883,32146,32148],{"className":32147},[886],[888,32149,32150],{"xmlns":890},[892,32151,32152,32156],{},[895,32153,32154],{},[898,32155,9945],{},[902,32157,9945],{"encoding":904}," — výdaje domácností na spotřebu,",[123,32160,32161,32174],{},[883,32162,32164],{"className":32163},[886],[888,32165,32166],{"xmlns":890},[892,32167,32168,32172],{},[895,32169,32170],{},[898,32171,25985],{},[902,32173,25985],{"encoding":904}," — hrubé domácí investice,",[123,32176,32177,32190],{},[883,32178,32180],{"className":32179},[886],[888,32181,32182],{"xmlns":890},[892,32183,32184,32188],{},[895,32185,32186],{},[898,32187,25914],{},[902,32189,25914],{"encoding":904}," — vládní výdaje,",[123,32192,32193,32206],{},[883,32194,32196],{"className":32195},[886],[888,32197,32198],{"xmlns":890},[892,32199,32200,32204],{},[895,32201,32202],{},[898,32203,26121],{},[902,32205,26121],{"encoding":904}," — čistý export.",[724,32208,32209,32210,32227,32228,32231,32232,3495,32235,1994,32248,32251],{},"K měření ",[883,32211,32213],{"className":32212},[886],[888,32214,32215],{"xmlns":890},[892,32216,32217,32225],{},[895,32218,32219,32221,32223],{},[898,32220,25914],{},[898,32222,32081],{},[898,32224,1690],{},[902,32226,32086],{"encoding":904}," se užívá ",[38,32229,32230],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,32233,32234],{},"národní důchod",[883,32236,32238],{"className":32237},[886],[888,32239,32240],{"xmlns":890},[892,32241,32242,32246],{},[895,32243,32244],{},[898,32245,1758],{},[902,32247,1758],{"encoding":904},[614,32249,32250],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,32253,32254],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,32256,32257],{},[883,32258,32260],{"className":32259},[886],[888,32261,32262],{"xmlns":890},[892,32263,32264,32278],{},[895,32265,32266,32268,32270,32272,32274,32276],{},[898,32267,25914],{},[898,32269,32081],{},[898,32271,1690],{},[1716,32273,8490],{},[898,32275,1758],{},[1716,32277,1719],{"separator":1718},[902,32279,32280],{"encoding":904},"GNP \\approx Y,",[724,32282,32283,32284,1994,32287,32290,32291,32304,32305,32308,32309,1853],{},"a užívá se společného názvu ",[38,32285,32286],{},"důchod",[614,32288,32289],{},"income",") s označením ",[883,32292,32294],{"className":32293},[886],[888,32295,32296],{"xmlns":890},[892,32297,32298,32302],{},[895,32299,32300],{},[898,32301,1758],{},[902,32303,1758],{"encoding":904},". Domácnosti důchod použijí ke ",[38,32306,32307],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,32310,32311],{},"úspor",[115,32313,32315],{"id":32314},"spotřeba-a-úspory","Spotřeba a úspory",[198,32317,32319],{"id":32318},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,32321,32322,32323,32336,32337,32350,32351,2291],{},"Jak spotřeba ",[883,32324,32326],{"className":32325},[886],[888,32327,32328],{"xmlns":890},[892,32329,32330,32334],{},[895,32331,32332],{},[898,32333,9945],{},[902,32335,9945],{"encoding":904},", tak úspory ",[883,32338,32340],{"className":32339},[886],[888,32341,32342],{"xmlns":890},[892,32343,32344,32348],{},[895,32345,32346],{},[898,32347,5352],{},[902,32349,5352],{"encoding":904}," závisejí na důchodu ",[883,32352,32354],{"className":32353},[886],[888,32355,32356],{"xmlns":890},[892,32357,32358,32362],{},[895,32359,32360],{},[898,32361,1758],{},[902,32363,1758],{"encoding":904},[724,32365,32366],{},[883,32367,32369],{"className":32368},[886],[888,32370,32371],{"xmlns":890},[892,32372,32373,32405],{},[895,32374,32375,32377,32379,32381,32383,32385,32387,32389,32391,32393,32395,32397,32399,32401,32403],{},[898,32376,9945],{},[1716,32378,1913],{},[898,32380,9945],{},[1716,32382,1920],{"stretchy":1919},[898,32384,1758],{},[1716,32386,1925],{"stretchy":1919},[1716,32388,1719],{"separator":1718},[2324,32390],{"width":2326},[898,32392,5352],{},[1716,32394,1913],{},[898,32396,5352],{},[1716,32398,1920],{"stretchy":1919},[898,32400,1758],{},[1716,32402,1925],{"stretchy":1919},[898,32404,1853],{"mathvariant":2068},[902,32406,32407],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,32409,32410,2574,32429,1994,32432,8373,32435,2574,32455,1994,32458,32461,32462,2247,32465,32468],{},[883,32411,32413],{"className":32412},[886],[888,32414,32415],{"xmlns":890},[892,32416,32417,32427],{},[895,32418,32419,32421,32423,32425],{},[898,32420,9945],{},[1716,32422,1920],{"stretchy":1919},[898,32424,1758],{},[1716,32426,1925],{"stretchy":1919},[902,32428,28012],{"encoding":904},[38,32430,32431],{},"funkce spotřeby",[614,32433,32434],{},"consumption function",[883,32436,32438],{"className":32437},[886],[888,32439,32440],{"xmlns":890},[892,32441,32442,32452],{},[895,32443,32444,32446,32448,32450],{},[898,32445,5352],{},[1716,32447,1920],{"stretchy":1919},[898,32449,1758],{},[1716,32451,1925],{"stretchy":1919},[902,32453,32454],{"encoding":904},"S(Y)",[38,32456,32457],{},"funkce úspor",[614,32459,32460],{},"savings function","); jejich grafy se nazývají ",[38,32463,32464],{},"křivka spotřeby",[38,32466,32467],{},"křivka úspor",". Platí základní identita",[724,32470,32471],{},[883,32472,32474],{"className":32473},[886],[888,32475,32476],{"xmlns":890},[892,32477,32478,32521],{},[895,32479,32480,32482,32484,32486,32488,32490,32492,32494,32496,32498,32500,32502,32504,32506,32508,32510,32512,32514,32516,32519],{},[898,32481,1758],{},[1716,32483,1913],{},[898,32485,9945],{},[1716,32487,1949],{},[898,32489,5352],{},[1716,32491,1913],{},[898,32493,9945],{},[1716,32495,1920],{"stretchy":1919},[898,32497,1758],{},[1716,32499,1925],{"stretchy":1919},[1716,32501,1949],{},[898,32503,5352],{},[1716,32505,1920],{"stretchy":1919},[898,32507,1758],{},[1716,32509,1925],{"stretchy":1919},[898,32511,1853],{"mathvariant":2068},[2324,32513],{"width":2326},[1716,32515,1920],{"stretchy":1919},[1712,32517,32518],{},"7.2",[1716,32520,1925],{"stretchy":1919},[902,32522,32523],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,32525,32526],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,32528,32530],{"id":32529},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,32532,32533],{},"Nejjednodušší model předpokládá lineární tvar",[724,32535,32536],{},[883,32537,32539],{"className":32538},[886],[888,32540,32541],{"xmlns":890},[892,32542,32543,32578],{},[895,32544,32545,32547,32549,32551,32553,32555,32557,32559,32561,32563,32565,32567,32569,32571,32573,32576],{},[898,32546,9945],{},[1716,32548,1913],{},[898,32550,9945],{},[1716,32552,1920],{"stretchy":1919},[898,32554,1758],{},[1716,32556,1925],{"stretchy":1919},[1716,32558,1913],{},[898,32560,207],{},[898,32562,1758],{},[1716,32564,1949],{},[898,32566,1952],{},[1716,32568,1719],{"separator":1718},[2324,32570],{"width":2326},[1716,32572,1920],{"stretchy":1919},[1712,32574,32575],{},"7.3",[1716,32577,1925],{"stretchy":1919},[902,32579,32580],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,32582,18149,32583,2247,32600,32622,32623,32663,32664,1853],{},[883,32584,32586],{"className":32585},[886],[888,32587,32588],{"xmlns":890},[892,32589,32590,32598],{},[895,32591,32592,32594,32596],{},[898,32593,1952],{},[1716,32595,2716],{},[1712,32597,2505],{},[902,32599,8085],{"encoding":904},[883,32601,32603],{"className":32602},[886],[888,32604,32605],{"xmlns":890},[892,32606,32607,32619],{},[895,32608,32609,32611,32613,32615,32617],{},[1712,32610,2505],{},[1716,32612,2704],{},[898,32614,207],{},[1716,32616,2704],{},[1712,32618,1714],{},[902,32620,32621],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,32624,32626],{"className":32625},[886],[888,32627,32628],{"xmlns":890},[892,32629,32630,32660],{},[895,32631,32632,32634,32636,32643,32645,32648,32650,32652,32654,32656,32658],{},[898,32633,207],{},[1716,32635,1913],{},[895,32637,32638,32641],{},[898,32639,32640],{"mathvariant":2068},"t",[898,32642,24845],{"mathvariant":2068},[2074,32644,8508],{},[898,32646,32647],{},"α",[1716,32649,1913],{},[898,32651,8485],{"mathvariant":2068},[898,32653,9945],{},[898,32655,3045],{"mathvariant":2068},[898,32657,8485],{"mathvariant":2068},[898,32659,1758],{},[902,32661,32662],{"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 ",[883,32665,32667],{"className":32666},[886],[888,32668,32669],{"xmlns":890},[892,32670,32671,32675],{},[895,32672,32673],{},[898,32674,1758],{},[902,32676,1758],{"encoding":904},[724,32678,32679],{},[614,32680,32681,32682,32706,32707,32745,32746,32762,32763,1853],{},"Obrázek 7.1 — Přímka spotřeby ",[883,32683,32685],{"className":32684},[886],[888,32686,32687],{"xmlns":890},[892,32688,32689,32703],{},[895,32690,32691,32693,32695,32697,32699,32701],{},[898,32692,9945],{},[1716,32694,1913],{},[898,32696,207],{},[898,32698,1758],{},[1716,32700,1949],{},[898,32702,1952],{},[902,32704,32705],{"encoding":904},"C = aY + b"," se směrnicí ",[883,32708,32710],{"className":32709},[886],[888,32711,32712],{"xmlns":890},[892,32713,32714,32742],{},[895,32715,32716,32718,32720,32726,32728,32730,32732,32734,32736,32738,32740],{},[898,32717,207],{},[1716,32719,1913],{},[895,32721,32722,32724],{},[898,32723,32640],{"mathvariant":2068},[898,32725,24845],{"mathvariant":2068},[2074,32727,8508],{},[898,32729,32647],{},[1716,32731,1913],{},[898,32733,8485],{"mathvariant":2068},[898,32735,9945],{},[898,32737,3045],{"mathvariant":2068},[898,32739,8485],{"mathvariant":2068},[898,32741,1758],{},[902,32743,32744],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,32747,32749],{"className":32748},[886],[888,32750,32751],{"xmlns":890},[892,32752,32753,32759],{},[895,32754,32755,32757],{},[898,32756,8485],{"mathvariant":2068},[898,32758,9945],{},[902,32760,32761],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,32764,32766],{"className":32765},[886],[888,32767,32768],{"xmlns":890},[892,32769,32770,32780],{},[895,32771,32772,32774,32776,32778],{},[898,32773,8485],{"mathvariant":2068},[898,32775,1758],{},[1716,32777,1913],{},[1712,32779,1714],{},[902,32781,32782],{"encoding":904},"\\Delta Y = 1",[724,32784,32785,32786,2291],{},"Dosazením do (7.2) plyne ",[38,32787,32788],{},"lineární model úspor",[724,32790,32791],{},[883,32792,32794],{"className":32793},[886],[888,32795,32796],{"xmlns":890},[892,32797,32798,32863],{},[895,32799,32800,32802,32804,32806,32808,32810,32812,32814,32816,32818,32820,32822,32824,32826,32828,32830,32832,32834,32836,32838,32840,32842,32844,32846,32848,32850,32852,32854,32856,32858,32861],{},[898,32801,5352],{},[1716,32803,1913],{},[898,32805,1758],{},[1716,32807,2760],{},[898,32809,9945],{},[1716,32811,1920],{"stretchy":1919},[898,32813,1758],{},[1716,32815,1925],{"stretchy":1919},[1716,32817,1913],{},[898,32819,1758],{},[1716,32821,2760],{},[1716,32823,1920],{"stretchy":1919},[898,32825,207],{},[898,32827,1758],{},[1716,32829,1949],{},[898,32831,1952],{},[1716,32833,1925],{"stretchy":1919},[1716,32835,1913],{},[1716,32837,1920],{"stretchy":1919},[1712,32839,1714],{},[1716,32841,2760],{},[898,32843,207],{},[1716,32845,1925],{"stretchy":1919},[898,32847,1758],{},[1716,32849,2760],{},[898,32851,1952],{},[898,32853,1853],{"mathvariant":2068},[2324,32855],{"width":2326},[1716,32857,1920],{"stretchy":1919},[1712,32859,32860],{},"7.4",[1716,32862,1925],{"stretchy":1919},[902,32864,32865],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,32867,32868,32869,2365],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,32870,32872],{"className":32871},[886],[888,32873,32874],{"xmlns":890},[892,32875,32876,32892],{},[895,32877,32878,32880,32882,32884,32886,32888,32890],{},[1712,32879,2505],{},[1716,32881,2704],{},[1712,32883,1714],{},[1716,32885,2760],{},[898,32887,207],{},[1716,32889,2704],{},[1712,32891,1714],{},[902,32893,32894],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,32896,32897],{},[614,32898,32899,32900,2247,32923,32955,32956,16504,32969,32999,33000,16504,33018,1853],{},"Obrázek 7.2 — Přímky ",[883,32901,32903],{"className":32902},[886],[888,32904,32905],{"xmlns":890},[892,32906,32907,32921],{},[895,32908,32909,32911,32913,32915,32917,32919],{},[898,32910,9945],{},[1716,32912,1913],{},[898,32914,207],{},[898,32916,1758],{},[1716,32918,1949],{},[898,32920,1952],{},[902,32922,32705],{"encoding":904},[883,32924,32926],{"className":32925},[886],[888,32927,32928],{"xmlns":890},[892,32929,32930,32952],{},[895,32931,32932,32934,32936,32938,32940,32942,32944,32946,32948,32950],{},[898,32933,5352],{},[1716,32935,1913],{},[1716,32937,1920],{"stretchy":1919},[1712,32939,1714],{},[1716,32941,2760],{},[898,32943,207],{},[1716,32945,1925],{"stretchy":1919},[898,32947,1758],{},[1716,32949,2760],{},[898,32951,1952],{},[902,32953,32954],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,32957,32959],{"className":32958},[886],[888,32960,32961],{"xmlns":890},[892,32962,32963,32967],{},[895,32964,32965],{},[898,32966,1758],{},[902,32968,1758],{"encoding":904},[883,32970,32972],{"className":32971},[886],[888,32973,32974],{"xmlns":890},[892,32975,32976,32996],{},[895,32977,32978,32980,32982,32984,32986,32988,32990,32992,32994],{},[898,32979,1758],{},[1716,32981,1913],{},[898,32983,1952],{},[898,32985,3045],{"mathvariant":2068},[1716,32987,1920],{"stretchy":1919},[1712,32989,1714],{},[1716,32991,2760],{},[898,32993,207],{},[1716,32995,1925],{"stretchy":1919},[902,32997,32998],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,33001,33003],{"className":33002},[886],[888,33004,33005],{"xmlns":890},[892,33006,33007,33015],{},[895,33008,33009,33011,33013],{},[898,33010,9945],{},[1716,33012,1719],{"separator":1718},[898,33014,5352],{},[902,33016,33017],{"encoding":904},"C, S",[883,33019,33021],{"className":33020},[886],[888,33022,33023],{"xmlns":890},[892,33024,33025,33031],{},[895,33026,33027,33029],{},[1716,33028,2760],{},[898,33030,1952],{},[902,33032,33033],{"encoding":904},"-b",[198,33035,33037],{"id":33036},"příklad-71","Příklad 7.1",[724,33039,33040,33041,33066],{},"Pro spotřebu ",[883,33042,33044],{"className":33043},[886],[888,33045,33046],{"xmlns":890},[892,33047,33048,33063],{},[895,33049,33050,33052,33054,33057,33059,33061],{},[898,33051,9945],{},[1716,33053,1913],{},[1712,33055,33056],{},"0,4",[898,33058,1758],{},[1716,33060,1949],{},[1712,33062,2998],{},[902,33064,33065],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,33068,33069],{},[883,33070,33072],{"className":33071},[886],[888,33073,33074],{"xmlns":890},[892,33075,33076,33113],{},[895,33077,33078,33080,33082,33084,33086,33088,33090,33092,33094,33096,33098,33100,33102,33104,33106,33108,33110],{},[898,33079,5352],{},[1716,33081,1913],{},[898,33083,1758],{},[1716,33085,2760],{},[898,33087,9945],{},[1716,33089,1913],{},[898,33091,1758],{},[1716,33093,2760],{},[1712,33095,33056],{},[898,33097,1758],{},[1716,33099,2760],{},[1712,33101,2998],{},[1716,33103,1913],{},[1712,33105,9451],{},[898,33107,1758],{},[1716,33109,2760],{},[1712,33111,33112],{},"10.",[902,33114,33115],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,33117,33118],{},[614,33119,33120,33121,2247,33144,33168,33169,2574,33182,33206,33207,2574,33224,33239,33240,1853],{},"Obrázek 7.3 — Přímky ",[883,33122,33124],{"className":33123},[886],[888,33125,33126],{"xmlns":890},[892,33127,33128,33142],{},[895,33129,33130,33132,33134,33136,33138,33140],{},[898,33131,9945],{},[1716,33133,1913],{},[1712,33135,33056],{},[898,33137,1758],{},[1716,33139,1949],{},[1712,33141,2998],{},[902,33143,33065],{"encoding":904},[883,33145,33147],{"className":33146},[886],[888,33148,33149],{"xmlns":890},[892,33150,33151,33165],{},[895,33152,33153,33155,33157,33159,33161,33163],{},[898,33154,5352],{},[1716,33156,1913],{},[1712,33158,9451],{},[898,33160,1758],{},[1716,33162,2760],{},[1712,33164,2998],{},[902,33166,33167],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,33170,33172],{"className":33171},[886],[888,33173,33174],{"xmlns":890},[892,33175,33176,33180],{},[895,33177,33178],{},[898,33179,1758],{},[902,33181,1758],{"encoding":904},[883,33183,33185],{"className":33184},[886],[888,33186,33187],{"xmlns":890},[892,33188,33189,33203],{},[895,33190,33191,33193,33196],{},[1716,33192,8490],{},[1712,33194,33195],{},"16,",[22202,33197,33198,33200],{"accent":1718},[1712,33199,6231],{},[1716,33201,33202],{},"ˉ",[902,33204,33205],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,33208,33210],{"className":33209},[886],[888,33211,33212],{"xmlns":890},[892,33213,33214,33222],{},[895,33215,33216,33218,33220],{},[898,33217,9945],{},[1716,33219,1719],{"separator":1718},[898,33221,5352],{},[902,33223,33017],{"encoding":904},[883,33225,33227],{"className":33226},[886],[888,33228,33229],{"xmlns":890},[892,33230,33231,33237],{},[895,33232,33233,33235],{},[1716,33234,2760],{},[1712,33236,2998],{},[902,33238,13396],{"encoding":904},"; přímka spotřeby prochází bodem ",[883,33241,33243],{"className":33242},[886],[888,33244,33245],{"xmlns":890},[892,33246,33247,33259],{},[895,33248,33249,33251,33253,33255,33257],{},[1716,33250,1920],{"stretchy":1919},[1712,33252,2505],{},[1716,33254,1719],{"separator":1718},[1712,33256,2998],{},[1716,33258,1925],{"stretchy":1919},[902,33260,33261],{"encoding":904},"(0, 10)",[724,33263,33264,33265,2574,33283,33313,33314,1994,33317,33320,33321,2574,33345,1994,33348,33351],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,33266,33268],{"className":33267},[886],[888,33269,33270],{"xmlns":890},[892,33271,33272,33280],{},[895,33273,33274,33276,33278],{},[898,33275,1758],{},[1716,33277,1913],{},[1712,33279,2505],{},[902,33281,33282],{"encoding":904},"Y = 0",[883,33284,33286],{"className":33285},[886],[888,33287,33288],{"xmlns":890},[892,33289,33290,33310],{},[895,33291,33292,33294,33296,33298,33300,33302,33304,33306,33308],{},[898,33293,5352],{},[1716,33295,1920],{"stretchy":1919},[1712,33297,2505],{},[1716,33299,1925],{"stretchy":1919},[1716,33301,1913],{},[1716,33303,2760],{},[898,33305,1952],{},[1716,33307,2704],{},[1712,33309,2505],{},[902,33311,33312],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,33315,33316],{},"autonomních úsporách",[614,33318,33319],{},"autonomous savings","). Analogicky ",[883,33322,33324],{"className":33323},[886],[888,33325,33326],{"xmlns":890},[892,33327,33328,33342],{},[895,33329,33330,33332,33334,33336,33338,33340],{},[898,33331,9945],{},[1716,33333,1920],{"stretchy":1919},[1712,33335,2505],{},[1716,33337,1925],{"stretchy":1919},[1716,33339,1913],{},[898,33341,1952],{},[902,33343,33344],{"encoding":904},"C(0) = b",[38,33346,33347],{},"autonomní spotřeba",[614,33349,33350],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,33353,33355],{"id":33354},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,33357,33358,3495,33361,1994,33378,33381],{},[38,33359,33360],{},"Mezní sklon ke spotřebě",[883,33362,33364],{"className":33363},[886],[888,33365,33366],{"xmlns":890},[892,33367,33368,33376],{},[895,33369,33370,33372,33374],{},[898,33371,16690],{},[898,33373,1690],{},[898,33375,9945],{},[902,33377,31832],{"encoding":904},[614,33379,33380],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,33383,33384],{},[883,33385,33387],{"className":33386},[886],[888,33388,33389],{"xmlns":890},[892,33390,33391,33417],{},[895,33392,33393,33395,33397,33399,33401,33415],{},[898,33394,16690],{},[898,33396,1690],{},[898,33398,9945],{},[1716,33400,1913],{},[2750,33402,33403,33409],{},[895,33404,33405,33407],{},[898,33406,5198],{"mathvariant":2068},[898,33408,9945],{},[895,33410,33411,33413],{},[898,33412,5198],{"mathvariant":2068},[898,33414,1758],{},[898,33416,1853],{"mathvariant":2068},[902,33418,33419],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,33421,33422,3495,33425,1994,33443,33446],{},[38,33423,33424],{},"Mezní sklon k úsporám",[883,33426,33428],{"className":33427},[886],[888,33429,33430],{"xmlns":890},[892,33431,33432,33440],{},[895,33433,33434,33436,33438],{},[898,33435,16690],{},[898,33437,1690],{},[898,33439,5352],{},[902,33441,33442],{"encoding":904},"MPS",[614,33444,33445],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,33448,33449],{},[883,33450,33452],{"className":33451},[886],[888,33453,33454],{"xmlns":890},[892,33455,33456,33482],{},[895,33457,33458,33460,33462,33464,33466,33480],{},[898,33459,16690],{},[898,33461,1690],{},[898,33463,5352],{},[1716,33465,1913],{},[2750,33467,33468,33474],{},[895,33469,33470,33472],{},[898,33471,5198],{"mathvariant":2068},[898,33473,5352],{},[895,33475,33476,33478],{},[898,33477,5198],{"mathvariant":2068},[898,33479,1758],{},[898,33481,1853],{"mathvariant":2068},[902,33483,33484],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,33486,33487,33488,33546],{},"Z (7.2) plyne ",[883,33489,33491],{"className":33490},[886],[888,33492,33493],{"xmlns":890},[892,33494,33495,33543],{},[895,33496,33497,33511,33513,33527,33529],{},[2750,33498,33499,33505],{},[895,33500,33501,33503],{},[898,33502,5198],{"mathvariant":2068},[898,33504,1758],{},[895,33506,33507,33509],{},[898,33508,5198],{"mathvariant":2068},[898,33510,1758],{},[1716,33512,1913],{},[2750,33514,33515,33521],{},[895,33516,33517,33519],{},[898,33518,5198],{"mathvariant":2068},[898,33520,9945],{},[895,33522,33523,33525],{},[898,33524,5198],{"mathvariant":2068},[898,33526,1758],{},[1716,33528,1949],{},[2750,33530,33531,33537],{},[895,33532,33533,33535],{},[898,33534,5198],{"mathvariant":2068},[898,33536,5352],{},[895,33538,33539,33541],{},[898,33540,5198],{"mathvariant":2068},[898,33542,1758],{},[902,33544,33545],{"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",[724,33548,33549],{},[883,33550,33552],{"className":33551},[886],[888,33553,33554],{"xmlns":890},[892,33555,33556,33619],{},[895,33557,33558,33610,33612,33614,33617],{},[26632,33559,33560],{"notation":26634},[2747,33561,33562],{"scriptlevel":2505,"displaystyle":1919},[2747,33563,33564],{"scriptlevel":2505,"displaystyle":1919},[2747,33565,33566],{"scriptlevel":2505,"displaystyle":1718},[895,33567,33568,33570,33572,33574,33576,33578,33580,33582,33584,33586,33588,33590,33592,33594,33596,33598,33600,33602,33604,33606,33608],{},[898,33569,16690],{},[898,33571,1690],{},[898,33573,9945],{},[1716,33575,1949],{},[898,33577,16690],{},[898,33579,1690],{},[898,33581,5352],{},[1716,33583,1913],{},[1712,33585,1714],{},[1716,33587,1719],{"separator":1718},[2324,33589],{"width":2326},[898,33591,16690],{},[898,33593,1690],{},[898,33595,5352],{},[1716,33597,1913],{},[1712,33599,1714],{},[1716,33601,2760],{},[898,33603,16690],{},[898,33605,1690],{},[898,33607,9945],{},[898,33609,1853],{"mathvariant":2068},[2324,33611],{"width":2326},[1716,33613,1920],{"stretchy":1919},[1712,33615,33616],{},"7.5",[1716,33618,1925],{"stretchy":1919},[902,33620,33621],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,33623,33624,3495,33627,33650,33651,2247,33673,33699],{},[38,33625,33626],{},"Pro lineární model",[883,33628,33630],{"className":33629},[886],[888,33631,33632],{"xmlns":890},[892,33633,33634,33648],{},[895,33635,33636,33638,33640,33642,33644,33646],{},[898,33637,9945],{},[1716,33639,1913],{},[898,33641,207],{},[898,33643,1758],{},[1716,33645,1949],{},[898,33647,1952],{},[902,33649,32705],{"encoding":904}," vychází ",[883,33652,33654],{"className":33653},[886],[888,33655,33656],{"xmlns":890},[892,33657,33658,33670],{},[895,33659,33660,33662,33664,33666,33668],{},[898,33661,16690],{},[898,33663,1690],{},[898,33665,9945],{},[1716,33667,1913],{},[898,33669,207],{},[902,33671,33672],{"encoding":904},"MPC = a",[883,33674,33676],{"className":33675},[886],[888,33677,33678],{"xmlns":890},[892,33679,33680,33696],{},[895,33681,33682,33684,33686,33688,33690,33692,33694],{},[898,33683,16690],{},[898,33685,1690],{},[898,33687,5352],{},[1716,33689,1913],{},[1712,33691,1714],{},[1716,33693,2760],{},[898,33695,207],{},[902,33697,33698],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,33701,33702,33705,33706,33728,33729,33757],{},[38,33703,33704],{},"Interpretace diferenciálem."," Pro pevné ",[883,33707,33709],{"className":33708},[886],[888,33710,33711],{"xmlns":890},[892,33712,33713,33725],{},[895,33714,33715,33717,33719],{},[898,33716,1758],{},[1716,33718,1913],{},[3074,33720,33721,33723],{},[898,33722,1758],{},[1716,33724,3080],{},[902,33726,33727],{"encoding":904},"Y = Y^*"," udává ",[883,33730,33732],{"className":33731},[886],[888,33733,33734],{"xmlns":890},[892,33735,33736,33754],{},[895,33737,33738,33740,33742,33744,33746,33752],{},[898,33739,16690],{},[898,33741,1690],{},[898,33743,9945],{},[1716,33745,1920],{"stretchy":1919},[3074,33747,33748,33750],{},[898,33749,1758],{},[1716,33751,3080],{},[1716,33753,1925],{"stretchy":1919},[902,33755,33756],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,33759,33760],{},[883,33761,33763],{"className":33762},[886],[888,33764,33765],{"xmlns":890},[892,33766,33767,33821],{},[895,33768,33769,33771,33773,33775,33777,33779,33781,33787,33789,33791,33793,33795,33797,33799,33801,33803,33805,33807,33809,33811,33813,33815,33817,33819],{},[898,33770,8485],{"mathvariant":2068},[898,33772,9945],{},[1716,33774,8490],{},[898,33776,5198],{"mathvariant":2068},[898,33778,9945],{},[1716,33780,1913],{},[3074,33782,33783,33785],{},[898,33784,9945],{},[1716,33786,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,33788,1920],{"stretchy":1919},[898,33790,1758],{},[1716,33792,1925],{"stretchy":1919},[2074,33794,8508],{},[898,33796,5198],{"mathvariant":2068},[898,33798,1758],{},[1716,33800,1913],{},[898,33802,16690],{},[898,33804,1690],{},[898,33806,9945],{},[1716,33808,1920],{"stretchy":1919},[898,33810,1758],{},[1716,33812,1925],{"stretchy":1919},[2074,33814,8508],{},[898,33816,5198],{"mathvariant":2068},[898,33818,1758],{},[898,33820,1853],{"mathvariant":2068},[902,33822,33823],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,33825,33826,33827,33863,33864,33867],{},"Analogicky ",[883,33828,33830],{"className":33829},[886],[888,33831,33832],{"xmlns":890},[892,33833,33834,33860],{},[895,33835,33836,33838,33840,33842,33844,33846,33848,33850,33852,33854,33856,33858],{},[898,33837,8485],{"mathvariant":2068},[898,33839,5352],{},[1716,33841,8490],{},[898,33843,16690],{},[898,33845,1690],{},[898,33847,5352],{},[1716,33849,1920],{"stretchy":1919},[898,33851,1758],{},[1716,33853,1925],{"stretchy":1919},[2074,33855,8508],{},[898,33857,5198],{"mathvariant":2068},[898,33859,1758],{},[902,33861,33862],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,33865,1145],{"className":33866,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,33869,33871],{"id":33870},"příklad-72","Příklad 7.2",[724,33873,33040,33874,33909,33910,33929],{},[883,33875,33877],{"className":33876},[886],[888,33878,33879],{"xmlns":890},[892,33880,33881,33906],{},[895,33882,33883,33885,33887,33890,33896,33898,33900,33902,33904],{},[898,33884,9945],{},[1716,33886,1913],{},[1712,33888,33889],{},"0,001",[3074,33891,33892,33894],{},[898,33893,1758],{},[1712,33895,1726],{},[1716,33897,1949],{},[1712,33899,11302],{},[898,33901,1758],{},[1716,33903,1949],{},[1712,33905,5808],{},[902,33907,33908],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,33911,33913],{"className":33912},[886],[888,33914,33915],{"xmlns":890},[892,33916,33917,33926],{},[895,33918,33919,33921,33923],{},[898,33920,1758],{},[1716,33922,2704],{},[1712,33924,33925],{},"400",[902,33927,33928],{"encoding":904},"Y \u003C 400",") platí",[724,33931,33932],{},[883,33933,33935],{"className":33934},[886],[888,33936,33937],{"xmlns":890},[892,33938,33939,33976],{},[895,33940,33941,33943,33945,33947,33949,33963,33965,33968,33970,33972,33974],{},[898,33942,16690],{},[898,33944,1690],{},[898,33946,9945],{},[1716,33948,1913],{},[2750,33950,33951,33957],{},[895,33952,33953,33955],{},[898,33954,5198],{"mathvariant":2068},[898,33956,9945],{},[895,33958,33959,33961],{},[898,33960,5198],{"mathvariant":2068},[898,33962,1758],{},[1716,33964,1913],{},[1712,33966,33967],{},"0,002",[898,33969,1758],{},[1716,33971,1949],{},[1712,33973,11302],{},[1716,33975,1719],{"separator":1718},[902,33977,33978],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,33980,33981],{},[883,33982,33984],{"className":33983},[886],[888,33985,33986],{"xmlns":890},[892,33987,33988,34021],{},[895,33989,33990,33992,33994,33996,33998,34000,34002,34004,34006,34008,34010,34012,34014,34016,34018],{},[898,33991,16690],{},[898,33993,1690],{},[898,33995,5352],{},[1716,33997,1913],{},[1712,33999,1714],{},[1716,34001,2760],{},[898,34003,16690],{},[898,34005,1690],{},[898,34007,9945],{},[1716,34009,1913],{},[1716,34011,2760],{},[1712,34013,33967],{},[898,34015,1758],{},[1716,34017,1949],{},[1712,34019,34020],{},"0,8.",[902,34022,34023],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,34025,34026,34106,34185],{},[123,34027,34028,1343,34056,34084,34085,2574,34103,1853],{},[883,34029,34031],{"className":34030},[886],[888,34032,34033],{"xmlns":890},[892,34034,34035,34053],{},[895,34036,34037,34039,34041,34043,34045,34047,34049,34051],{},[898,34038,16690],{},[898,34040,1690],{},[898,34042,9945],{},[1716,34044,1920],{"stretchy":1919},[1712,34046,12151],{},[1716,34048,1925],{"stretchy":1919},[1716,34050,1913],{},[1712,34052,33056],{},[902,34054,34055],{"encoding":904},"MPC(100) = 0{,}4",[883,34057,34059],{"className":34058},[886],[888,34060,34061],{"xmlns":890},[892,34062,34063,34081],{},[895,34064,34065,34067,34069,34071,34073,34075,34077,34079],{},[898,34066,16690],{},[898,34068,1690],{},[898,34070,5352],{},[1716,34072,1920],{"stretchy":1919},[1712,34074,12151],{},[1716,34076,1925],{"stretchy":1919},[1716,34078,1913],{},[1712,34080,9451],{},[902,34082,34083],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,34086,34088],{"className":34087},[886],[888,34089,34090],{"xmlns":890},[892,34091,34092,34100],{},[895,34093,34094,34096,34098],{},[898,34095,1758],{},[1716,34097,1913],{},[1712,34099,12151],{},[902,34101,34102],{"encoding":904},"Y = 100",[38,34104,34105],{},"větší sklon k úsporám",[123,34107,34108,1343,34136,34084,34164,2574,34182,1853],{},[883,34109,34111],{"className":34110},[886],[888,34112,34113],{"xmlns":890},[892,34114,34115,34133],{},[895,34116,34117,34119,34121,34123,34125,34127,34129,34131],{},[898,34118,16690],{},[898,34120,1690],{},[898,34122,9945],{},[1716,34124,1920],{"stretchy":1919},[1712,34126,22193],{},[1716,34128,1925],{"stretchy":1919},[1716,34130,1913],{},[1712,34132,9451],{},[902,34134,34135],{"encoding":904},"MPC(200) = 0{,}6",[883,34137,34139],{"className":34138},[886],[888,34140,34141],{"xmlns":890},[892,34142,34143,34161],{},[895,34144,34145,34147,34149,34151,34153,34155,34157,34159],{},[898,34146,16690],{},[898,34148,1690],{},[898,34150,5352],{},[1716,34152,1920],{"stretchy":1919},[1712,34154,22193],{},[1716,34156,1925],{"stretchy":1919},[1716,34158,1913],{},[1712,34160,33056],{},[902,34162,34163],{"encoding":904},"MPS(200) = 0{,}4",[883,34165,34167],{"className":34166},[886],[888,34168,34169],{"xmlns":890},[892,34170,34171,34179],{},[895,34172,34173,34175,34177],{},[898,34174,1758],{},[1716,34176,1913],{},[1712,34178,22193],{},[902,34180,34181],{"encoding":904},"Y = 200",[38,34183,34184],{},"větší sklon ke spotřebě",[123,34186,34187,34188,34206,34207,2365],{},"Přesně při ",[883,34189,34191],{"className":34190},[886],[888,34192,34193],{"xmlns":890},[892,34194,34195,34203],{},[895,34196,34197,34199,34201],{},[898,34198,1758],{},[1716,34200,1913],{},[1712,34202,6653],{},[902,34204,34205],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,34208,34210],{"className":34209},[886],[888,34211,34212],{"xmlns":890},[892,34213,34214,34234],{},[895,34215,34216,34218,34220,34222,34224,34226,34228,34230,34232],{},[898,34217,16690],{},[898,34219,1690],{},[898,34221,9945],{},[1716,34223,1913],{},[898,34225,16690],{},[898,34227,1690],{},[898,34229,5352],{},[1716,34231,1913],{},[1712,34233,5771],{},[902,34235,34236],{"encoding":904},"MPC = MPS = 0{,}5",[724,34238,34239,34240,34257,34258,34272,34273,3942,34286,34300,34301,34314,34315,34356],{},"Interpretace: při ",[883,34241,34243],{"className":34242},[886],[888,34244,34245],{"xmlns":890},[892,34246,34247,34255],{},[895,34248,34249,34251,34253],{},[898,34250,1758],{},[1716,34252,1913],{},[1712,34254,12151],{},[902,34256,34102],{"encoding":904}," se spotřeba mění ",[883,34259,34261],{"className":34260},[886],[888,34262,34263],{"xmlns":890},[892,34264,34265,34269],{},[895,34266,34267],{},[1712,34268,33056],{},[902,34270,34271],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,34274,34276],{"className":34275},[886],[888,34277,34278],{"xmlns":890},[892,34279,34280,34284],{},[895,34281,34282],{},[1712,34283,12151],{},[902,34285,12151],{"encoding":904},[883,34287,34289],{"className":34288},[886],[888,34290,34291],{"xmlns":890},[892,34292,34293,34298],{},[895,34294,34295],{},[1712,34296,34297],{},"101",[902,34299,34297],{"encoding":904},", změní se spotřeba přibližně o ",[883,34302,34304],{"className":34303},[886],[888,34305,34306],{"xmlns":890},[892,34307,34308,34312],{},[895,34309,34310],{},[1712,34311,33056],{},[902,34313,34271],{"encoding":904},". Skutečná změna ",[883,34316,34318],{"className":34317},[886],[888,34319,34320],{"xmlns":890},[892,34321,34322,34353],{},[895,34323,34324,34326,34328,34330,34332,34334,34336,34338,34340,34342,34344,34346,34348,34350],{},[898,34325,8485],{"mathvariant":2068},[898,34327,9945],{},[1716,34329,1913],{},[898,34331,9945],{},[1716,34333,1920],{"stretchy":1919},[1712,34335,34297],{},[1716,34337,1925],{"stretchy":1919},[1716,34339,2760],{},[898,34341,9945],{},[1716,34343,1920],{"stretchy":1919},[1712,34345,12151],{},[1716,34347,1925],{"stretchy":1919},[1716,34349,1913],{},[1712,34351,34352],{},"0,401",[902,34354,34355],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,34358,34359,34360],{},"Obecný trend: ",[38,34361,34362],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,34364,34366],{"id":34365},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,34368,34369,34370,1994,34373,34376,34377,1994,34380,8086,34383,1994,34386,34389],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,34371,34372],{},"makroekonomická rovnováha",[614,34374,34375],{},"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 ",[38,34378,34379],{},"agregátní poptávky",[614,34381,34382],{},"aggregate demand",[38,34384,34385],{},"agregátní nabídky",[614,34387,34388],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,34391,34393],{"id":34392},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,34395,34396],{},[3682,34397],{"alt":34398,"className":34399,"src":34400},"imek-keynesian-kriz",[210,3686],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,34402,34404],{"id":34403},"zadání-modelu","Zadání modelu",[724,34406,34407,34408,34421,34422,34435],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,34409,34411],{"className":34410},[886],[888,34412,34413],{"xmlns":890},[892,34414,34415,34419],{},[895,34416,34417],{},[898,34418,9945],{},[902,34420,9945],{"encoding":904}," a investice ",[883,34423,34425],{"className":34424},[886],[888,34426,34427],{"xmlns":890},[892,34428,34429,34433],{},[895,34430,34431],{},[898,34432,25985],{},[902,34434,25985],{"encoding":904},". Podmínka rovnováhy:",[724,34437,34438],{},[883,34439,34441],{"className":34440},[886],[888,34442,34443],{"xmlns":890},[892,34444,34445,34468],{},[895,34446,34447,34449,34451,34453,34455,34457,34459,34461,34463,34466],{},[898,34448,1758],{},[1716,34450,1913],{},[898,34452,9945],{},[1716,34454,1949],{},[898,34456,25985],{},[898,34458,1853],{"mathvariant":2068},[2324,34460],{"width":2326},[1716,34462,1920],{"stretchy":1919},[1712,34464,34465],{},"7.6",[1716,34467,1925],{"stretchy":1919},[902,34469,34470],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,34472,34474],{"id":34473},"soustava-rovnic","Soustava rovnic",[724,34476,34477,34478,34499,34500,34524],{},"Pro pevně zadané (plánované) investice ",[883,34479,34481],{"className":34480},[886],[888,34482,34483],{"xmlns":890},[892,34484,34485,34497],{},[895,34486,34487,34489,34491],{},[898,34488,25985],{},[1716,34490,1913],{},[3074,34492,34493,34495],{},[898,34494,25985],{},[1716,34496,3080],{},[902,34498,25996],{"encoding":904}," a funkci spotřeby ",[883,34501,34503],{"className":34502},[886],[888,34504,34505],{"xmlns":890},[892,34506,34507,34521],{},[895,34508,34509,34511,34513,34515,34517,34519],{},[898,34510,9945],{},[1716,34512,1913],{},[898,34514,9945],{},[1716,34516,1920],{"stretchy":1919},[898,34518,1758],{},[1716,34520,1925],{"stretchy":1919},[902,34522,34523],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,34526,34527],{},[883,34528,34530],{"className":34529},[886],[888,34531,34532],{"xmlns":890},[892,34533,34534,34605],{},[895,34535,34536,34596,34598,34600,34603],{},[2008,34537,34538,34568],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,34539,34540,34546],{},[2015,34541,34542],{},[2747,34543,34544],{"scriptlevel":2505,"displaystyle":1718},[898,34545,1758],{},[2015,34547,34548],{},[2747,34549,34550],{"scriptlevel":2505,"displaystyle":1718},[895,34551,34552,34554,34556,34558,34560,34566],{},[895,34553],{},[1716,34555,1913],{},[898,34557,9945],{},[1716,34559,1949],{},[3074,34561,34562,34564],{},[898,34563,25985],{},[1716,34565,3080],{},[1716,34567,1719],{"separator":1718},[2012,34569,34570,34576],{},[2015,34571,34572],{},[2747,34573,34574],{"scriptlevel":2505,"displaystyle":1718},[898,34575,9945],{},[2015,34577,34578],{},[2747,34579,34580],{"scriptlevel":2505,"displaystyle":1718},[895,34581,34582,34584,34586,34588,34590,34592,34594],{},[895,34583],{},[1716,34585,1913],{},[898,34587,9945],{},[1716,34589,1920],{"stretchy":1919},[898,34591,1758],{},[1716,34593,1925],{"stretchy":1919},[1716,34595,1719],{"separator":1718},[2324,34597],{"width":2326},[1716,34599,1920],{"stretchy":1919},[1712,34601,34602],{},"7.7",[1716,34604,1925],{"stretchy":1919},[902,34606,34607],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,34609,34610,34611,3495,34613,2247,34630,3495,34633,1853],{},"jejímž řešením jsou ",[38,34612,27682],{},[883,34614,34616],{"className":34615},[886],[888,34617,34618],{"xmlns":890},[892,34619,34620,34628],{},[895,34621,34622],{},[3074,34623,34624,34626],{},[898,34625,1758],{},[898,34627,1805],{},[902,34629,27700],{"encoding":904},[38,34631,34632],{},"rovnovážná spotřeba",[883,34634,34636],{"className":34635},[886],[888,34637,34638],{"xmlns":890},[892,34639,34640,34648],{},[895,34641,34642],{},[3074,34643,34644,34646],{},[898,34645,9945],{},[898,34647,1805],{},[902,34649,27759],{"encoding":904},[198,34651,34653,34654],{"id":34652},"výpočet-yeye","Výpočet ",[883,34655,34657],{"className":34656},[886],[888,34658,34659],{"xmlns":890},[892,34660,34661,34669],{},[895,34662,34663],{},[3074,34664,34665,34667],{},[898,34666,1758],{},[898,34668,1805],{},[902,34670,27700],{"encoding":904},[724,34672,34673,34674,34697,34698,21504,34730],{},"Pro lineární spotřebu ",[883,34675,34677],{"className":34676},[886],[888,34678,34679],{"xmlns":890},[892,34680,34681,34695],{},[895,34682,34683,34685,34687,34689,34691,34693],{},[898,34684,9945],{},[1716,34686,1913],{},[898,34688,207],{},[898,34690,1758],{},[1716,34692,1949],{},[898,34694,1952],{},[902,34696,32705],{"encoding":904}," plyne z (7.7) rovnice ",[883,34699,34701],{"className":34700},[886],[888,34702,34703],{"xmlns":890},[892,34704,34705,34727],{},[895,34706,34707,34709,34711,34713,34715,34717,34719,34721],{},[898,34708,1758],{},[1716,34710,1913],{},[898,34712,207],{},[898,34714,1758],{},[1716,34716,1949],{},[898,34718,1952],{},[1716,34720,1949],{},[3074,34722,34723,34725],{},[898,34724,25985],{},[1716,34726,3080],{},[902,34728,34729],{"encoding":904},"Y = aY + b + I^*",[38,34731,8219],{},[724,34733,34734],{},[883,34735,34737],{"className":34736},[886],[888,34738,34739],{"xmlns":890},[892,34740,34741,34789],{},[895,34742,34743],{},[26632,34744,34745],{"notation":26634},[2747,34746,34747],{"scriptlevel":2505,"displaystyle":1919},[2747,34748,34749],{"scriptlevel":2505,"displaystyle":1919},[2747,34750,34751],{"scriptlevel":2505,"displaystyle":1718},[895,34752,34753,34755,34761,34763,34785,34787],{},[2074,34754,8508],{},[3074,34756,34757,34759],{},[898,34758,1758],{},[898,34760,1805],{},[1716,34762,1913],{},[2750,34764,34765,34777],{},[895,34766,34767,34769,34771],{},[898,34768,1952],{},[1716,34770,1949],{},[3074,34772,34773,34775],{},[898,34774,25985],{},[1716,34776,3080],{},[895,34778,34779,34781,34783],{},[1712,34780,1714],{},[1716,34782,2760],{},[898,34784,207],{},[898,34786,1853],{"mathvariant":2068},[2074,34788,8508],{},[902,34790,34791],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,34793,34795],{"id":34794},"příklad-73","Příklad 7.3",[724,34797,34798,34799,2574,34816,2247,34840,34866],{},"V modelu ",[883,34800,34802],{"className":34801},[886],[888,34803,34804],{"xmlns":890},[892,34805,34806,34814],{},[895,34807,34808,34810,34812],{},[898,34809,9945],{},[2074,34811,26091],{},[898,34813,25985],{},[902,34815,26096],{"encoding":904},[883,34817,34819],{"className":34818},[886],[888,34820,34821],{"xmlns":890},[892,34822,34823,34837],{},[895,34824,34825,34827,34829,34831,34833,34835],{},[898,34826,9945],{},[1716,34828,1913],{},[1712,34830,9451],{},[898,34832,1758],{},[1716,34834,1949],{},[1712,34836,2998],{},[902,34838,34839],{"encoding":904},"C = 0{,}6Y + 10",[883,34841,34843],{"className":34842},[886],[888,34844,34845],{"xmlns":890},[892,34846,34847,34863],{},[895,34848,34849,34851,34853,34855,34857],{},[898,34850,25985],{},[1716,34852,1913],{},[1712,34854,6804],{},[1716,34856,1913],{},[3074,34858,34859,34861],{},[898,34860,25985],{},[1716,34862,3080],{},[902,34864,34865],{"encoding":904},"I = 12 = I^*",". Soustava",[724,34868,34869],{},[883,34870,34872],{"className":34871},[886],[888,34873,34874],{"xmlns":890},[892,34875,34876,34932],{},[2008,34877,34878,34904],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,34879,34880,34886],{},[2015,34881,34882],{},[2747,34883,34884],{"scriptlevel":2505,"displaystyle":1718},[898,34885,1758],{},[2015,34887,34888],{},[2747,34889,34890],{"scriptlevel":2505,"displaystyle":1718},[895,34891,34892,34894,34896,34898,34900,34902],{},[895,34893],{},[1716,34895,1913],{},[898,34897,9945],{},[1716,34899,1949],{},[1712,34901,6804],{},[1716,34903,1719],{"separator":1718},[2012,34905,34906,34912],{},[2015,34907,34908],{},[2747,34909,34910],{"scriptlevel":2505,"displaystyle":1718},[898,34911,9945],{},[2015,34913,34914],{},[2747,34915,34916],{"scriptlevel":2505,"displaystyle":1718},[895,34917,34918,34920,34922,34924,34926,34928,34930],{},[895,34919],{},[1716,34921,1913],{},[1712,34923,9451],{},[898,34925,1758],{},[1716,34927,1949],{},[1712,34929,2998],{},[1716,34931,1719],{"separator":1718},[902,34933,34934],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,34936,34937,34938,1343,34961,34983,34984,2365],{},"má řešení ",[883,34939,34941],{"className":34940},[886],[888,34942,34943],{"xmlns":890},[892,34944,34945,34958],{},[895,34946,34947,34953,34955],{},[3074,34948,34949,34951],{},[898,34950,1758],{},[898,34952,1805],{},[1716,34954,1913],{},[1712,34956,34957],{},"55",[902,34959,34960],{"encoding":904},"Y^E = 55",[883,34962,34964],{"className":34963},[886],[888,34965,34966],{"xmlns":890},[892,34967,34968,34980],{},[895,34969,34970,34976,34978],{},[3074,34971,34972,34974],{},[898,34973,9945],{},[898,34975,1805],{},[1716,34977,1913],{},[1712,34979,7160],{},[902,34981,34982],{"encoding":904},"C^E = 43"," (a ",[883,34985,34987],{"className":34986},[886],[888,34988,34989],{"xmlns":890},[892,34990,34991,35003],{},[895,34992,34993,34999,35001],{},[3074,34994,34995,34997],{},[898,34996,5352],{},[898,34998,1805],{},[1716,35000,1913],{},[1712,35002,6804],{},[902,35004,35005],{"encoding":904},"S^E = 12",[724,35007,35008],{},[614,35009,35010,35011,35033,35034,8086,35055,35078,35079,1853],{},"Obrázek 7.5 — Přímky ",[883,35012,35014],{"className":35013},[886],[888,35015,35016],{"xmlns":890},[892,35017,35018,35030],{},[895,35019,35020,35022,35024,35026,35028],{},[898,35021,9945],{},[1716,35023,1913],{},[898,35025,1758],{},[1716,35027,2760],{},[1712,35029,6804],{},[902,35031,35032],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,35035,35037],{"className":35036},[886],[888,35038,35039],{"xmlns":890},[892,35040,35041,35053],{},[895,35042,35043,35045,35047,35049,35051],{},[898,35044,1758],{},[1716,35046,1913],{},[898,35048,9945],{},[1716,35050,1949],{},[898,35052,25985],{},[902,35054,28539],{"encoding":904},[883,35056,35058],{"className":35057},[886],[888,35059,35060],{"xmlns":890},[892,35061,35062,35076],{},[895,35063,35064,35066,35068,35070,35072,35074],{},[898,35065,9945],{},[1716,35067,1913],{},[1712,35069,9451],{},[898,35071,1758],{},[1716,35073,1949],{},[1712,35075,2998],{},[902,35077,34839],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,35080,35082],{"className":35081},[886],[888,35083,35084],{"xmlns":890},[892,35085,35086,35118],{},[895,35087,35088,35090,35096,35098,35104,35106,35108,35110,35112,35114,35116],{},[1716,35089,2502],{"stretchy":1919},[3074,35091,35092,35094],{},[898,35093,1758],{},[898,35095,1805],{},[1716,35097,1719],{"separator":1718},[3074,35099,35100,35102],{},[898,35101,9945],{},[898,35103,1805],{},[1716,35105,2516],{"stretchy":1919},[1716,35107,1913],{},[1716,35109,2502],{"stretchy":1919},[1712,35111,34957],{},[1716,35113,1719],{"separator":1718},[1712,35115,7160],{},[1716,35117,2516],{"stretchy":1919},[902,35119,35120],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,35122,35123,35126,35127,35144,35145,1853],{},[38,35124,35125],{},"Komentář k přechodu."," Model ",[883,35128,35130],{"className":35129},[886],[888,35131,35132],{"xmlns":890},[892,35133,35134,35142],{},[895,35135,35136,35138,35140],{},[898,35137,9945],{},[2074,35139,26091],{},[898,35141,25985],{},[902,35143,26096],{"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 ",[38,35146,35147,35148],{},"model ",[883,35149,35151],{"className":35150},[886],[888,35152,35153],{"xmlns":890},[892,35154,35155,35167],{},[895,35156,35157,35159,35161,35163,35165],{},[898,35158,9945],{},[2074,35160,26091],{},[898,35162,25985],{},[2074,35164,26091],{},[898,35166,25914],{},[902,35168,32007],{"encoding":904},[115,35170,35172],{"id":35171},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,35174,34404],{"id":35175},"zadání-modelu-1",[724,35177,35178,35179,13380,35196,3495,35199,1994,35212,35215],{},"Rozšíření modelu ",[883,35180,35182],{"className":35181},[886],[888,35183,35184],{"xmlns":890},[892,35185,35186,35194],{},[895,35187,35188,35190,35192],{},[898,35189,9945],{},[2074,35191,26091],{},[898,35193,25985],{},[902,35195,26096],{"encoding":904},[38,35197,35198],{},"vládní výdaje",[883,35200,35202],{"className":35201},[886],[888,35203,35204],{"xmlns":890},[892,35205,35206,35210],{},[895,35207,35208],{},[898,35209,25914],{},[902,35211,25914],{"encoding":904},[614,35213,35214],{},"government expenditure","). Podmínka rovnováhy:",[724,35217,35218],{},[883,35219,35221],{"className":35220},[886],[888,35222,35223],{"xmlns":890},[892,35224,35225,35252],{},[895,35226,35227,35229,35231,35233,35235,35237,35239,35241,35243,35245,35247,35250],{},[898,35228,1758],{},[1716,35230,1913],{},[898,35232,9945],{},[1716,35234,1949],{},[898,35236,25985],{},[1716,35238,1949],{},[898,35240,25914],{},[898,35242,1853],{"mathvariant":2068},[2324,35244],{"width":2326},[1716,35246,1920],{"stretchy":1919},[1712,35248,35249],{},"7.8",[1716,35251,1925],{"stretchy":1919},[902,35253,35254],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,35256,35257,35258,3495,35261,1994,35274,35277],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,35259,35260],{},"zdaněním domácností",[883,35262,35264],{"className":35263},[886],[888,35265,35266],{"xmlns":890},[892,35267,35268,35272],{},[895,35269,35270],{},[898,35271,4164],{},[902,35273,4164],{"encoding":904},[614,35275,35276],{},"taxation","). Zdanění bývá:",[120,35279,35280,35313,35338],{},[123,35281,35282,35283,1719],{},"úměrné důchodu: ",[883,35284,35286],{"className":35285},[886],[888,35287,35288],{"xmlns":890},[892,35289,35290,35310],{},[895,35291,35292,35294,35296,35298,35300,35302,35304,35306,35308],{},[898,35293,4164],{},[1716,35295,1913],{},[898,35297,4164],{},[1716,35299,1920],{"stretchy":1919},[898,35301,1758],{},[1716,35303,1925],{"stretchy":1919},[1716,35305,1913],{},[898,35307,32640],{},[898,35309,1758],{},[902,35311,35312],{"encoding":904},"T = T(Y) = tY",[123,35314,35315,35316,1719],{},"fixní: ",[883,35317,35319],{"className":35318},[886],[888,35320,35321],{"xmlns":890},[892,35322,35323,35335],{},[895,35324,35325,35327,35329],{},[898,35326,4164],{},[1716,35328,1913],{},[3074,35330,35331,35333],{},[898,35332,4164],{},[1716,35334,3080],{},[902,35336,35337],{"encoding":904},"T = T^*",[123,35339,35340,35341,2772,35369,1853],{},"kombinované: ",[883,35342,35344],{"className":35343},[886],[888,35345,35346],{"xmlns":890},[892,35347,35348,35366],{},[895,35349,35350,35352,35354,35360,35362,35364],{},[898,35351,4164],{},[1716,35353,1913],{},[3074,35355,35356,35358],{},[898,35357,4164],{},[1716,35359,3080],{},[1716,35361,1949],{},[898,35363,32640],{},[898,35365,1758],{},[902,35367,35368],{"encoding":904},"T = T^* + tY",[883,35370,35372],{"className":35371},[886],[888,35373,35374],{"xmlns":890},[892,35375,35376,35388],{},[895,35377,35378,35380,35382,35384,35386],{},[1712,35379,2505],{},[1716,35381,21498],{},[898,35383,32640],{},[1716,35385,2704],{},[1712,35387,1714],{},[902,35389,35390],{"encoding":904},"0 \\le t \u003C 1",[1635,35392,35393],{},[724,35394,35395,35397,35398,35419,35420,35423,35424,35437,35438,8086,35464,3495,35467,35493,35494,35522,35523,2247,35536,35554],{},[883,35396,2233],{}," Pozor na disponibilní důchod\nV modelu ",[883,35399,35401],{"className":35400},[886],[888,35402,35403],{"xmlns":890},[892,35404,35405,35417],{},[895,35406,35407,35409,35411,35413,35415],{},[898,35408,9945],{},[2074,35410,26091],{},[898,35412,25985],{},[2074,35414,26091],{},[898,35416,25914],{},[902,35418,32007],{"encoding":904}," je nutné ",[38,35421,35422],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,35425,35427],{"className":35426},[886],[888,35428,35429],{"xmlns":890},[892,35430,35431,35435],{},[895,35432,35433],{},[898,35434,1758],{},[902,35436,1758],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,35439,35441],{"className":35440},[886],[888,35442,35443],{"xmlns":890},[892,35444,35445,35461],{},[895,35446,35447,35449,35451,35453,35455,35457,35459],{},[898,35448,1758],{},[1716,35450,1913],{},[898,35452,9945],{},[1716,35454,1949],{},[898,35456,25985],{},[1716,35458,1949],{},[898,35460,25914],{},[902,35462,35463],{"encoding":904},"Y = C + I + G",[38,35465,35466],{},"disponibilní důchod",[883,35468,35470],{"className":35469},[886],[888,35471,35472],{"xmlns":890},[892,35473,35474,35490],{},[895,35475,35476,35482,35484,35486,35488],{},[1707,35477,35478,35480],{},[898,35479,1758],{},[898,35481,1916],{},[1716,35483,1913],{},[898,35485,1758],{},[1716,35487,2760],{},[898,35489,4164],{},[902,35491,35492],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,35495,35497],{"className":35496},[886],[888,35498,35499],{"xmlns":890},[892,35500,35501,35519],{},[895,35502,35503,35505,35507,35509,35511,35517],{},[898,35504,9945],{},[1716,35506,1913],{},[898,35508,9945],{},[1716,35510,1920],{"stretchy":1919},[1707,35512,35513,35515],{},[898,35514,1758],{},[898,35516,1916],{},[1716,35518,1925],{"stretchy":1919},[902,35520,35521],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,35524,35526],{"className":35525},[886],[888,35527,35528],{"xmlns":890},[892,35529,35530,35534],{},[895,35531,35532],{},[898,35533,1758],{},[902,35535,1758],{"encoding":904},[883,35537,35539],{"className":35538},[886],[888,35540,35541],{"xmlns":890},[892,35542,35543,35551],{},[895,35544,35545],{},[1707,35546,35547,35549],{},[898,35548,1758],{},[898,35550,1916],{},[902,35552,35553],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,35556,35557,1994,35560,1925],{},[38,35558,35559],{},"Disponibilní důchod",[614,35561,35562],{},"disposable income",[724,35564,35565],{},[883,35566,35568],{"className":35567},[886],[888,35569,35570],{"xmlns":890},[892,35571,35572,35588],{},[895,35573,35574,35580,35582,35584,35586],{},[1707,35575,35576,35578],{},[898,35577,1758],{},[898,35579,1916],{},[1716,35581,1913],{},[898,35583,1758],{},[1716,35585,2760],{},[898,35587,4164],{},[902,35589,35492],{"encoding":904},[724,35591,35592,35593,1853],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,35594,35596],{"className":35595},[886],[888,35597,35598],{"xmlns":890},[892,35599,35600,35618],{},[895,35601,35602,35604,35606,35608,35610,35616],{},[898,35603,9945],{},[1716,35605,1913],{},[898,35607,9945],{},[1716,35609,1920],{"stretchy":1919},[1707,35611,35612,35614],{},[898,35613,1758],{},[898,35615,1916],{},[1716,35617,1925],{"stretchy":1919},[902,35619,35521],{"encoding":904},[198,35621,34474],{"id":35622},"soustava-rovnic-1",[724,35624,35625,35626,1343,35647,35669,35670,2291],{},"Pro pevně zadané ",[883,35627,35629],{"className":35628},[886],[888,35630,35631],{"xmlns":890},[892,35632,35633,35645],{},[895,35634,35635,35637,35639],{},[898,35636,25985],{},[1716,35638,1913],{},[3074,35640,35641,35643],{},[898,35642,25985],{},[1716,35644,3080],{},[902,35646,25996],{"encoding":904},[883,35648,35650],{"className":35649},[886],[888,35651,35652],{"xmlns":890},[892,35653,35654,35666],{},[895,35655,35656,35658,35660],{},[898,35657,25914],{},[1716,35659,1913],{},[3074,35661,35662,35664],{},[898,35663,25914],{},[1716,35665,3080],{},[902,35667,35668],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,35671,35673],{"className":35672},[886],[888,35674,35675],{"xmlns":890},[892,35676,35677,35697],{},[895,35678,35679,35681,35683,35685,35687,35693,35695],{},[898,35680,1758],{},[1716,35682,1719],{"separator":1718},[898,35684,9945],{},[1716,35686,1719],{"separator":1718},[1707,35688,35689,35691],{},[898,35690,1758],{},[898,35692,1916],{},[1716,35694,1719],{"separator":1718},[898,35696,4164],{},[902,35698,35699],{"encoding":904},"Y, C, Y_D, T",[724,35701,35702],{},[883,35703,35705],{"className":35704},[886],[888,35706,35707],{"xmlns":890},[892,35708,35709,35850],{},[895,35710,35711,35841,35843,35845,35848],{},[2008,35712,35713,35751,35779,35811],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,35714,35715,35721],{},[2015,35716,35717],{},[2747,35718,35719],{"scriptlevel":2505,"displaystyle":1718},[898,35720,1758],{},[2015,35722,35723],{},[2747,35724,35725],{"scriptlevel":2505,"displaystyle":1718},[895,35726,35727,35729,35731,35733,35735,35741,35743,35749],{},[895,35728],{},[1716,35730,1913],{},[898,35732,9945],{},[1716,35734,1949],{},[3074,35736,35737,35739],{},[898,35738,25985],{},[1716,35740,3080],{},[1716,35742,1949],{},[3074,35744,35745,35747],{},[898,35746,25914],{},[1716,35748,3080],{},[1716,35750,1719],{"separator":1718},[2012,35752,35753,35759],{},[2015,35754,35755],{},[2747,35756,35757],{"scriptlevel":2505,"displaystyle":1718},[898,35758,4164],{},[2015,35760,35761],{},[2747,35762,35763],{"scriptlevel":2505,"displaystyle":1718},[895,35764,35765,35767,35769,35771,35773,35775,35777],{},[895,35766],{},[1716,35768,1913],{},[898,35770,4164],{},[1716,35772,1920],{"stretchy":1919},[898,35774,1758],{},[1716,35776,1925],{"stretchy":1919},[1716,35778,1719],{"separator":1718},[2012,35780,35781,35787],{},[2015,35782,35783],{},[2747,35784,35785],{"scriptlevel":2505,"displaystyle":1718},[898,35786,9945],{},[2015,35788,35789],{},[2747,35790,35791],{"scriptlevel":2505,"displaystyle":1718},[895,35792,35793,35795,35797,35799,35801,35807,35809],{},[895,35794],{},[1716,35796,1913],{},[898,35798,9945],{},[1716,35800,1920],{"stretchy":1919},[1707,35802,35803,35805],{},[898,35804,1758],{},[898,35806,1916],{},[1716,35808,1925],{"stretchy":1919},[1716,35810,1719],{"separator":1718},[2012,35812,35813,35823],{},[2015,35814,35815],{},[2747,35816,35817],{"scriptlevel":2505,"displaystyle":1718},[1707,35818,35819,35821],{},[898,35820,1758],{},[898,35822,1916],{},[2015,35824,35825],{},[2747,35826,35827],{"scriptlevel":2505,"displaystyle":1718},[895,35828,35829,35831,35833,35835,35837,35839],{},[895,35830],{},[1716,35832,1913],{},[898,35834,1758],{},[1716,35836,2760],{},[898,35838,4164],{},[1716,35840,1719],{"separator":1718},[2324,35842],{"width":2326},[1716,35844,1920],{"stretchy":1919},[1712,35846,35847],{},"7.9",[1716,35849,1925],{"stretchy":1919},[902,35851,35852],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,35854,35855,35856,35900,35901,1853],{},"s řešeními ",[883,35857,35859],{"className":35858},[886],[888,35860,35861],{"xmlns":890},[892,35862,35863,35897],{},[895,35864,35865,35871,35873,35879,35881,35887,35889],{},[3074,35866,35867,35869],{},[898,35868,1758],{},[898,35870,1805],{},[1716,35872,1719],{"separator":1718},[3074,35874,35875,35877],{},[898,35876,9945],{},[898,35878,1805],{},[1716,35880,1719],{"separator":1718},[3074,35882,35883,35885],{},[898,35884,4164],{},[898,35886,1805],{},[1716,35888,1719],{"separator":1718},[7204,35890,35891,35893,35895],{},[898,35892,1758],{},[898,35894,1916],{},[898,35896,1805],{},[902,35898,35899],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,35902,35904],{"className":35903},[886],[888,35905,35906],{"xmlns":890},[892,35907,35908,35934],{},[895,35909,35910,35916,35918,35926,35928],{},[3074,35911,35912,35914],{},[898,35913,5352],{},[898,35915,1805],{},[1716,35917,1913],{},[7204,35919,35920,35922,35924],{},[898,35921,1758],{},[898,35923,1916],{},[898,35925,1805],{},[1716,35927,2760],{},[3074,35929,35930,35932],{},[898,35931,9945],{},[898,35933,1805],{},[902,35935,35936],{"encoding":904},"S^E = Y_D^E - C^E",[1635,35938,35939,35944],{},[724,35940,35941,35943],{},[883,35942,3776],{}," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,35945,35946,35969,36052,36107,36197],{},[123,35947,35948,35951,35952,1853],{},[38,35949,35950],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,35953,35955],{"className":35954},[886],[888,35956,35957],{"xmlns":890},[892,35958,35959,35967],{},[895,35960,35961],{},[1707,35962,35963,35965],{},[898,35964,1758],{},[898,35966,1916],{},[902,35968,35553],{"encoding":904},[123,35970,35971,36020,36021,36038,36039,1853],{},[38,35972,35973,35974,35994,35995],{},"Dosaď ",[883,35975,35977],{"className":35976},[886],[888,35978,35979],{"xmlns":890},[892,35980,35981,35991],{},[895,35982,35983,35985,35987,35989],{},[898,35984,4164],{},[1716,35986,1920],{"stretchy":1919},[898,35988,1758],{},[1716,35990,1925],{"stretchy":1919},[902,35992,35993],{"encoding":904},"T(Y)"," do ",[883,35996,35998],{"className":35997},[886],[888,35999,36000],{"xmlns":890},[892,36001,36002,36018],{},[895,36003,36004,36010,36012,36014,36016],{},[1707,36005,36006,36008],{},[898,36007,1758],{},[898,36009,1916],{},[1716,36011,1913],{},[898,36013,1758],{},[1716,36015,2760],{},[898,36017,4164],{},[902,36019,35492],{"encoding":904}," — dostaneš ",[883,36022,36024],{"className":36023},[886],[888,36025,36026],{"xmlns":890},[892,36027,36028,36036],{},[895,36029,36030],{},[1707,36031,36032,36034],{},[898,36033,1758],{},[898,36035,1916],{},[902,36037,35553],{"encoding":904}," jako lineární funkci ",[883,36040,36042],{"className":36041},[886],[888,36043,36044],{"xmlns":890},[892,36045,36046,36050],{},[895,36047,36048],{},[898,36049,1758],{},[902,36051,1758],{"encoding":904},[123,36053,36054,36020,36081,36038,36094,1853],{},[38,36055,35973,36056,36080],{},[883,36057,36059],{"className":36058},[886],[888,36060,36061],{"xmlns":890},[892,36062,36063,36077],{},[895,36064,36065,36071,36073,36075],{},[1707,36066,36067,36069],{},[898,36068,1758],{},[898,36070,1916],{},[1716,36072,1920],{"stretchy":1919},[898,36074,1758],{},[1716,36076,1925],{"stretchy":1919},[902,36078,36079],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,36082,36084],{"className":36083},[886],[888,36085,36086],{"xmlns":890},[892,36087,36088,36092],{},[895,36089,36090],{},[898,36091,9945],{},[902,36093,9945],{"encoding":904},[883,36095,36097],{"className":36096},[886],[888,36098,36099],{"xmlns":890},[892,36100,36101,36105],{},[895,36102,36103],{},[898,36104,1758],{},[902,36106,1758],{"encoding":904},[123,36108,36109,3495,36131,36165,36166,36179,36180,1853],{},[38,36110,35973,36111,36130],{},[883,36112,36114],{"className":36113},[886],[888,36115,36116],{"xmlns":890},[892,36117,36118,36128],{},[895,36119,36120,36122,36124,36126],{},[898,36121,9945],{},[1716,36123,1920],{"stretchy":1919},[898,36125,1758],{},[1716,36127,1925],{"stretchy":1919},[902,36129,28012],{"encoding":904}," do podmínky rovnováhy",[883,36132,36134],{"className":36133},[886],[888,36135,36136],{"xmlns":890},[892,36137,36138,36162],{},[895,36139,36140,36142,36144,36146,36148,36154,36156],{},[898,36141,1758],{},[1716,36143,1913],{},[898,36145,9945],{},[1716,36147,1949],{},[3074,36149,36150,36152],{},[898,36151,25985],{},[1716,36153,3080],{},[1716,36155,1949],{},[3074,36157,36158,36160],{},[898,36159,25914],{},[1716,36161,3080],{},[902,36163,36164],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,36167,36169],{"className":36168},[886],[888,36170,36171],{"xmlns":890},[892,36172,36173,36177],{},[895,36174,36175],{},[898,36176,1758],{},[902,36178,1758],{"encoding":904},", odtud ",[883,36181,36183],{"className":36182},[886],[888,36184,36185],{"xmlns":890},[892,36186,36187,36195],{},[895,36188,36189],{},[3074,36190,36191,36193],{},[898,36192,1758],{},[898,36194,1805],{},[902,36196,27700],{"encoding":904},[123,36198,36199,36202,36203,1343,36221,1343,36241,1343,36258,1853],{},[38,36200,36201],{},"Zpětným dosazením"," dopočítej ",[883,36204,36206],{"className":36205},[886],[888,36207,36208],{"xmlns":890},[892,36209,36210,36218],{},[895,36211,36212],{},[3074,36213,36214,36216],{},[898,36215,4164],{},[898,36217,1805],{},[902,36219,36220],{"encoding":904},"T^E",[883,36222,36224],{"className":36223},[886],[888,36225,36226],{"xmlns":890},[892,36227,36228,36238],{},[895,36229,36230],{},[7204,36231,36232,36234,36236],{},[898,36233,1758],{},[898,36235,1916],{},[898,36237,1805],{},[902,36239,36240],{"encoding":904},"Y_D^E",[883,36242,36244],{"className":36243},[886],[888,36245,36246],{"xmlns":890},[892,36247,36248,36256],{},[895,36249,36250],{},[3074,36251,36252,36254],{},[898,36253,9945],{},[898,36255,1805],{},[902,36257,27759],{"encoding":904},[883,36259,36261],{"className":36260},[886],[888,36262,36263],{"xmlns":890},[892,36264,36265,36273],{},[895,36266,36267],{},[3074,36268,36269,36271],{},[898,36270,5352],{},[898,36272,1805],{},[902,36274,36275],{"encoding":904},"S^E",[198,36277,36279],{"id":36278},"příklad-74","Příklad 7.4",[724,36281,34798,36282,36303,36304,1343,36335,1343,36359,1343,36381,36403],{},[883,36283,36285],{"className":36284},[886],[888,36286,36287],{"xmlns":890},[892,36288,36289,36301],{},[895,36290,36291,36293,36295,36297,36299],{},[898,36292,9945],{},[2074,36294,26091],{},[898,36296,25985],{},[2074,36298,26091],{},[898,36300,25914],{},[902,36302,32007],{"encoding":904}," jsou dány ",[883,36305,36307],{"className":36306},[886],[888,36308,36309],{"xmlns":890},[892,36310,36311,36332],{},[895,36312,36313,36315,36317,36320,36322,36328,36330],{},[898,36314,9945],{},[1716,36316,1913],{},[1712,36318,36319],{},"0,9",[2074,36321,8508],{},[1707,36323,36324,36326],{},[898,36325,1758],{},[898,36327,1916],{},[1716,36329,1949],{},[1712,36331,19721],{},[902,36333,36334],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,36336,36338],{"className":36337},[886],[888,36339,36340],{"xmlns":890},[892,36341,36342,36356],{},[895,36343,36344,36346,36348,36350,36352,36354],{},[898,36345,4164],{},[1716,36347,1913],{},[1712,36349,11302],{},[898,36351,1758],{},[1716,36353,1949],{},[1712,36355,5778],{},[902,36357,36358],{"encoding":904},"T = 0{,}2Y + 25",[883,36360,36362],{"className":36361},[886],[888,36363,36364],{"xmlns":890},[892,36365,36366,36378],{},[895,36367,36368,36374,36376],{},[3074,36369,36370,36372],{},[898,36371,25985],{},[1716,36373,3080],{},[1716,36375,1913],{},[1712,36377,5837],{},[902,36379,36380],{"encoding":904},"I^* = 35",[883,36382,36384],{"className":36383},[886],[888,36385,36386],{"xmlns":890},[892,36387,36388,36400],{},[895,36389,36390,36396,36398],{},[3074,36391,36392,36394],{},[898,36393,25914],{},[1716,36395,3080],{},[1716,36397,1913],{},[1712,36399,2976],{},[902,36401,36402],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,36405,36406],{},[883,36407,36409],{"className":36408},[886],[888,36410,36411],{"xmlns":890},[892,36412,36413,36537],{},[2008,36414,36415,36445,36473,36507],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,36416,36417,36423],{},[2015,36418,36419],{},[2747,36420,36421],{"scriptlevel":2505,"displaystyle":1718},[898,36422,1758],{},[2015,36424,36425],{},[2747,36426,36427],{"scriptlevel":2505,"displaystyle":1718},[895,36428,36429,36431,36433,36435,36437,36439,36441,36443],{},[895,36430],{},[1716,36432,1913],{},[898,36434,9945],{},[1716,36436,1949],{},[1712,36438,5837],{},[1716,36440,1949],{},[1712,36442,2976],{},[1716,36444,1719],{"separator":1718},[2012,36446,36447,36453],{},[2015,36448,36449],{},[2747,36450,36451],{"scriptlevel":2505,"displaystyle":1718},[898,36452,4164],{},[2015,36454,36455],{},[2747,36456,36457],{"scriptlevel":2505,"displaystyle":1718},[895,36458,36459,36461,36463,36465,36467,36469,36471],{},[895,36460],{},[1716,36462,1913],{},[1712,36464,11302],{},[898,36466,1758],{},[1716,36468,1949],{},[1712,36470,5778],{},[1716,36472,1719],{"separator":1718},[2012,36474,36475,36481],{},[2015,36476,36477],{},[2747,36478,36479],{"scriptlevel":2505,"displaystyle":1718},[898,36480,9945],{},[2015,36482,36483],{},[2747,36484,36485],{"scriptlevel":2505,"displaystyle":1718},[895,36486,36487,36489,36491,36493,36495,36501,36503,36505],{},[895,36488],{},[1716,36490,1913],{},[1712,36492,36319],{},[2074,36494,8508],{},[1707,36496,36497,36499],{},[898,36498,1758],{},[898,36500,1916],{},[1716,36502,1949],{},[1712,36504,19721],{},[1716,36506,1719],{"separator":1718},[2012,36508,36509,36519],{},[2015,36510,36511],{},[2747,36512,36513],{"scriptlevel":2505,"displaystyle":1718},[1707,36514,36515,36517],{},[898,36516,1758],{},[898,36518,1916],{},[2015,36520,36521],{},[2747,36522,36523],{"scriptlevel":2505,"displaystyle":1718},[895,36524,36525,36527,36529,36531,36533,36535],{},[895,36526],{},[1716,36528,1913],{},[898,36530,1758],{},[1716,36532,2760],{},[898,36534,4164],{},[898,36536,1853],{"mathvariant":2068},[902,36538,36539],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,36541,36542,36545,36546,36600,36601,36647,36648,2291],{},[38,36543,36544],{},"Řešení."," Z definice ",[883,36547,36549],{"className":36548},[886],[888,36550,36551],{"xmlns":890},[892,36552,36553,36597],{},[895,36554,36555,36561,36563,36565,36567,36569,36571,36573,36575,36577,36579,36581,36583,36585,36587,36589,36591,36593,36595],{},[1707,36556,36557,36559],{},[898,36558,1758],{},[898,36560,1916],{},[1716,36562,1913],{},[898,36564,1758],{},[1716,36566,2760],{},[898,36568,4164],{},[1716,36570,1913],{},[898,36572,1758],{},[1716,36574,2760],{},[1716,36576,1920],{"stretchy":1919},[1712,36578,11302],{},[898,36580,1758],{},[1716,36582,1949],{},[1712,36584,5778],{},[1716,36586,1925],{"stretchy":1919},[1716,36588,1913],{},[1712,36590,13254],{},[898,36592,1758],{},[1716,36594,2760],{},[1712,36596,5778],{},[902,36598,36599],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,36602,36604],{"className":36603},[886],[888,36605,36606],{"xmlns":890},[892,36607,36608,36644],{},[895,36609,36610,36612,36614,36616,36618,36620,36622,36624,36626,36628,36630,36632,36634,36637,36639,36641],{},[898,36611,9945],{},[1716,36613,1913],{},[1712,36615,36319],{},[1716,36617,1920],{"stretchy":1919},[1712,36619,13254],{},[898,36621,1758],{},[1716,36623,2760],{},[1712,36625,5778],{},[1716,36627,1925],{"stretchy":1919},[1716,36629,1949],{},[1712,36631,19721],{},[1716,36633,1913],{},[1712,36635,36636],{},"0,72",[898,36638,1758],{},[1716,36640,1949],{},[1712,36642,36643],{},"47,5",[902,36645,36646],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,36649,36651],{"className":36650},[886],[888,36652,36653],{"xmlns":890},[892,36654,36655,36673],{},[895,36656,36657,36659,36661,36663,36665,36667,36669,36671],{},[898,36658,1758],{},[1716,36660,1913],{},[1712,36662,36636],{},[898,36664,1758],{},[1716,36666,1949],{},[1712,36668,36643],{},[1716,36670,1949],{},[1712,36672,34957],{},[902,36674,36675],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,36677,36678],{},[883,36679,36681],{"className":36680},[886],[888,36682,36683],{"xmlns":890},[892,36684,36685,36725],{},[895,36686,36687,36690,36692,36694,36697,36699,36701,36703,36709,36711,36720,36722],{},[1712,36688,36689],{},"0,28",[898,36691,1758],{},[1716,36693,1913],{},[1712,36695,36696],{},"102,5",[2074,36698,17830],{},[1716,36700,28803],{},[2074,36702,17830],{},[3074,36704,36705,36707],{},[898,36706,1758],{},[898,36708,1805],{},[1716,36710,1913],{},[2747,36712,36713],{"scriptlevel":2505,"displaystyle":1919},[2750,36714,36715,36718],{},[1712,36716,36717],{},"5125",[1712,36719,6681],{},[1716,36721,19724],{},[1712,36723,36724],{},"366,071.",[902,36726,36727],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,36729,36730],{},"Rovnovážné veličiny:",[120,36732,36733,36768,36820,36874,36922],{},[123,36734,36735,1719],{},[883,36736,36738],{"className":36737},[886],[888,36739,36740],{"xmlns":890},[892,36741,36742,36765],{},[895,36743,36744,36750,36752,36760,36762],{},[3074,36745,36746,36748],{},[898,36747,1758],{},[898,36749,1805],{},[1716,36751,1913],{},[2747,36753,36754],{"scriptlevel":2505,"displaystyle":1919},[2750,36755,36756,36758],{},[1712,36757,36717],{},[1712,36759,6681],{},[1716,36761,19724],{},[1712,36763,36764],{},"366,071",[902,36766,36767],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,36769,36770,1719],{},[883,36771,36773],{"className":36772},[886],[888,36774,36775],{"xmlns":890},[892,36776,36777,36817],{},[895,36778,36779,36785,36787,36789,36791,36797,36799,36801,36803,36812,36814],{},[3074,36780,36781,36783],{},[898,36782,4164],{},[898,36784,1805],{},[1716,36786,1913],{},[1712,36788,11302],{},[2074,36790,8508],{},[3074,36792,36793,36795],{},[898,36794,1758],{},[898,36796,1805],{},[1716,36798,1949],{},[1712,36800,5778],{},[1716,36802,1913],{},[2747,36804,36805],{"scriptlevel":2505,"displaystyle":1919},[2750,36806,36807,36810],{},[1712,36808,36809],{},"1375",[1712,36811,6681],{},[1716,36813,19724],{},[1712,36815,36816],{},"98,214",[902,36818,36819],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,36821,36822,1719],{},[883,36823,36825],{"className":36824},[886],[888,36826,36827],{"xmlns":890},[892,36828,36829,36871],{},[895,36830,36831,36839,36841,36847,36849,36855,36857,36866,36868],{},[7204,36832,36833,36835,36837],{},[898,36834,1758],{},[898,36836,1916],{},[898,36838,1805],{},[1716,36840,1913],{},[3074,36842,36843,36845],{},[898,36844,1758],{},[898,36846,1805],{},[1716,36848,2760],{},[3074,36850,36851,36853],{},[898,36852,4164],{},[898,36854,1805],{},[1716,36856,1913],{},[2747,36858,36859],{"scriptlevel":2505,"displaystyle":1919},[2750,36860,36861,36864],{},[1712,36862,36863],{},"3750",[1712,36865,6681],{},[1716,36867,19724],{},[1712,36869,36870],{},"267,857",[902,36872,36873],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,36875,36876,1719],{},[883,36877,36879],{"className":36878},[886],[888,36880,36881],{"xmlns":890},[892,36882,36883,36919],{},[895,36884,36885,36891,36893,36899,36901,36903,36905,36914,36916],{},[3074,36886,36887,36889],{},[898,36888,9945],{},[898,36890,1805],{},[1716,36892,1913],{},[3074,36894,36895,36897],{},[898,36896,1758],{},[898,36898,1805],{},[1716,36900,2760],{},[1712,36902,34957],{},[1716,36904,1913],{},[2747,36906,36907],{"scriptlevel":2505,"displaystyle":1919},[2750,36908,36909,36912],{},[1712,36910,36911],{},"4355",[1712,36913,6681],{},[1716,36915,19724],{},[1712,36917,36918],{},"311,071",[902,36920,36921],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,36923,36924,36980],{},[883,36925,36927],{"className":36926},[886],[888,36928,36929],{"xmlns":890},[892,36930,36931,36977],{},[895,36932,36933,36939,36941,36949,36951,36957,36959,36961,36970,36972,36974],{},[3074,36934,36935,36937],{},[898,36936,5352],{},[898,36938,1805],{},[1716,36940,1913],{},[7204,36942,36943,36945,36947],{},[898,36944,1758],{},[898,36946,1916],{},[898,36948,1805],{},[1716,36950,2760],{},[3074,36952,36953,36955],{},[898,36954,9945],{},[898,36956,1805],{},[1716,36958,1913],{},[1716,36960,2760],{},[2747,36962,36963],{"scriptlevel":2505,"displaystyle":1919},[2750,36964,36965,36968],{},[1712,36966,36967],{},"605",[1712,36969,6681],{},[1716,36971,19724],{},[1716,36973,2760],{},[1712,36975,36976],{},"43,214",[902,36978,36979],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,36982,36983,35126,36985,37006,37007,37010,37011,37033,37034,1853],{},[38,36984,35125],{},[883,36986,36988],{"className":36987},[886],[888,36989,36990],{"xmlns":890},[892,36991,36992,37004],{},[895,36993,36994,36996,36998,37000,37002],{},[898,36995,9945],{},[2074,36997,26091],{},[898,36999,25985],{},[2074,37001,26091],{},[898,37003,25914],{},[902,37005,32007],{"encoding":904}," stále uvažuje ",[38,37008,37009],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,37012,37014],{"className":37013},[886],[888,37015,37016],{"xmlns":890},[892,37017,37018,37030],{},[895,37019,37020,37022,37024,37026,37028],{},[898,37021,26121],{},[1716,37023,1913],{},[898,37025,10856],{},[1716,37027,2760],{},[898,37029,16690],{},[902,37031,37032],{"encoding":904},"X = B - M"," dává ",[38,37035,35147,37036],{},[883,37037,37039],{"className":37038},[886],[888,37040,37041],{"xmlns":890},[892,37042,37043,37059],{},[895,37044,37045,37047,37049,37051,37053,37055,37057],{},[898,37046,9945],{},[2074,37048,26091],{},[898,37050,25985],{},[2074,37052,26091],{},[898,37054,25914],{},[2074,37056,26091],{},[898,37058,26121],{},[902,37060,26124],{"encoding":904},[115,37062,37064],{"id":37063},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,37066,34404],{"id":37067},"zadání-modelu-2",[724,37069,37070,37071,3495,37074,2772,37095,37108,37109,8086,37112,37125],{},"Rozšíření o ",[38,37072,37073],{},"čistý export",[883,37075,37077],{"className":37076},[886],[888,37078,37079],{"xmlns":890},[892,37080,37081,37093],{},[895,37082,37083,37085,37087,37089,37091],{},[898,37084,26121],{},[1716,37086,1913],{},[898,37088,10856],{},[1716,37090,2760],{},[898,37092,16690],{},[902,37094,37032],{"encoding":904},[883,37096,37098],{"className":37097},[886],[888,37099,37100],{"xmlns":890},[892,37101,37102,37106],{},[895,37103,37104],{},[898,37105,10856],{},[902,37107,10856],{"encoding":904}," je hrubý export (",[614,37110,37111],{},"brutto export",[883,37113,37115],{"className":37114},[886],[888,37116,37117],{"xmlns":890},[892,37118,37119,37123],{},[895,37120,37121],{},[898,37122,16690],{},[902,37124,16690],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,37127,37128],{},[883,37129,37131],{"className":37130},[886],[888,37132,37133],{"xmlns":890},[892,37134,37135,37155],{},[895,37136,37137,37139,37141,37143,37145,37151,37153],{},[898,37138,16690],{},[1716,37140,1913],{},[898,37142,16690],{},[1716,37144,1920],{"stretchy":1919},[1707,37146,37147,37149],{},[898,37148,1758],{},[898,37150,1916],{},[1716,37152,1925],{"stretchy":1919},[898,37154,1853],{"mathvariant":2068},[902,37156,37157],{"encoding":904},"M = M(Y_D).",[724,37159,37160],{},"Podmínka rovnováhy:",[724,37162,37163],{},[883,37164,37166],{"className":37165},[886],[888,37167,37168],{"xmlns":890},[892,37169,37170,37207],{},[895,37171,37172,37174,37176,37178,37180,37182,37184,37186,37188,37190,37192,37194,37196,37198,37200,37203,37205],{},[898,37173,1758],{},[1716,37175,1913],{},[898,37177,9945],{},[1716,37179,1949],{},[898,37181,25985],{},[1716,37183,1949],{},[898,37185,25914],{},[1716,37187,1949],{},[898,37189,10856],{},[1716,37191,2760],{},[898,37193,16690],{},[898,37195,1853],{"mathvariant":2068},[2324,37197],{"width":2326},[1716,37199,1920],{"stretchy":1919},[1712,37201,37202],{},"7.10",[2074,37204,207],{},[1716,37206,1925],{"stretchy":1919},[902,37208,37209],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,37211,34474],{"id":37212},"soustava-rovnic-2",[724,37214,35625,37215,37249,37250,2291],{},[883,37216,37218],{"className":37217},[886],[888,37219,37220],{"xmlns":890},[892,37221,37222,37246],{},[895,37223,37224,37230,37232,37238,37240],{},[3074,37225,37226,37228],{},[898,37227,25985],{},[1716,37229,3080],{},[1716,37231,1719],{"separator":1718},[3074,37233,37234,37236],{},[898,37235,25914],{},[1716,37237,3080],{},[1716,37239,1719],{"separator":1718},[3074,37241,37242,37244],{},[898,37243,10856],{},[1716,37245,3080],{},[902,37247,37248],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,37251,37253],{"className":37252},[886],[888,37254,37255],{"xmlns":890},[892,37256,37257,37281],{},[895,37258,37259,37261,37263,37265,37267,37269,37271,37277,37279],{},[898,37260,1758],{},[1716,37262,1719],{"separator":1718},[898,37264,9945],{},[1716,37266,1719],{"separator":1718},[898,37268,4164],{},[1716,37270,1719],{"separator":1718},[1707,37272,37273,37275],{},[898,37274,1758],{},[898,37276,1916],{},[1716,37278,1719],{"separator":1718},[898,37280,16690],{},[902,37282,37283],{"encoding":904},"Y, C, T, Y_D, M",[724,37285,37286],{},[883,37287,37289],{"className":37288},[886],[888,37290,37291],{"xmlns":890},[892,37292,37293,37477],{},[895,37294,37295,37469,37471,37473,37475],{},[2008,37296,37297,37329,37359,37387,37419],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,37298,37299,37305],{},[2015,37300,37301],{},[2747,37302,37303],{"scriptlevel":2505,"displaystyle":1718},[898,37304,9945],{},[2015,37306,37307],{},[2747,37308,37309],{"scriptlevel":2505,"displaystyle":1718},[895,37310,37311,37313,37315,37317,37319,37325,37327],{},[895,37312],{},[1716,37314,1913],{},[898,37316,9945],{},[1716,37318,1920],{"stretchy":1919},[1707,37320,37321,37323],{},[898,37322,1758],{},[898,37324,1916],{},[1716,37326,1925],{"stretchy":1919},[1716,37328,1719],{"separator":1718},[2012,37330,37331,37341],{},[2015,37332,37333],{},[2747,37334,37335],{"scriptlevel":2505,"displaystyle":1718},[1707,37336,37337,37339],{},[898,37338,1758],{},[898,37340,1916],{},[2015,37342,37343],{},[2747,37344,37345],{"scriptlevel":2505,"displaystyle":1718},[895,37346,37347,37349,37351,37353,37355,37357],{},[895,37348],{},[1716,37350,1913],{},[898,37352,1758],{},[1716,37354,2760],{},[898,37356,4164],{},[1716,37358,1719],{"separator":1718},[2012,37360,37361,37367],{},[2015,37362,37363],{},[2747,37364,37365],{"scriptlevel":2505,"displaystyle":1718},[898,37366,4164],{},[2015,37368,37369],{},[2747,37370,37371],{"scriptlevel":2505,"displaystyle":1718},[895,37372,37373,37375,37377,37379,37381,37383,37385],{},[895,37374],{},[1716,37376,1913],{},[898,37378,4164],{},[1716,37380,1920],{"stretchy":1919},[898,37382,1758],{},[1716,37384,1925],{"stretchy":1919},[1716,37386,1719],{"separator":1718},[2012,37388,37389,37395],{},[2015,37390,37391],{},[2747,37392,37393],{"scriptlevel":2505,"displaystyle":1718},[898,37394,16690],{},[2015,37396,37397],{},[2747,37398,37399],{"scriptlevel":2505,"displaystyle":1718},[895,37400,37401,37403,37405,37407,37409,37415,37417],{},[895,37402],{},[1716,37404,1913],{},[898,37406,16690],{},[1716,37408,1920],{"stretchy":1919},[1707,37410,37411,37413],{},[898,37412,1758],{},[898,37414,1916],{},[1716,37416,1925],{"stretchy":1919},[1716,37418,1719],{"separator":1718},[2012,37420,37421,37427],{},[2015,37422,37423],{},[2747,37424,37425],{"scriptlevel":2505,"displaystyle":1718},[898,37426,1758],{},[2015,37428,37429],{},[2747,37430,37431],{"scriptlevel":2505,"displaystyle":1718},[895,37432,37433,37435,37437,37439,37441,37447,37449,37455,37457,37463,37465,37467],{},[895,37434],{},[1716,37436,1913],{},[898,37438,9945],{},[1716,37440,1949],{},[3074,37442,37443,37445],{},[898,37444,25985],{},[1716,37446,3080],{},[1716,37448,1949],{},[3074,37450,37451,37453],{},[898,37452,25914],{},[1716,37454,3080],{},[1716,37456,1949],{},[3074,37458,37459,37461],{},[898,37460,10856],{},[1716,37462,3080],{},[1716,37464,2760],{},[898,37466,16690],{},[898,37468,1853],{"mathvariant":2068},[2324,37470],{"width":2326},[1716,37472,1920],{"stretchy":1919},[1712,37474,37202],{},[1716,37476,1925],{"stretchy":1919},[902,37478,37479],{"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)",[198,37481,37483],{"id":37482},"příklad-75","Příklad 7.5",[724,37485,37486,37487,1343,37519,1343,37546,1343,37567,1343,37589,1343,37611,37634],{},"Dáno: ",[883,37488,37490],{"className":37489},[886],[888,37491,37492],{"xmlns":890},[892,37493,37494,37516],{},[895,37495,37496,37498,37500,37503,37505,37511,37513],{},[898,37497,9945],{},[1716,37499,1913],{},[1712,37501,37502],{},"0,75",[2074,37504,8508],{},[1707,37506,37507,37509],{},[898,37508,1758],{},[898,37510,1916],{},[1716,37512,1949],{},[1712,37514,37515],{},"750",[902,37517,37518],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,37520,37522],{"className":37521},[886],[888,37523,37524],{"xmlns":890},[892,37525,37526,37543],{},[895,37527,37528,37530,37532,37535,37537],{},[898,37529,16690],{},[1716,37531,1913],{},[1712,37533,37534],{},"0,15",[2074,37536,8508],{},[1707,37538,37539,37541],{},[898,37540,1758],{},[898,37542,1916],{},[902,37544,37545],{"encoding":904},"M = 0{,}15\\,Y_D",[883,37547,37549],{"className":37548},[886],[888,37550,37551],{"xmlns":890},[892,37552,37553,37564],{},[895,37554,37555,37557,37559,37562],{},[898,37556,4164],{},[1716,37558,1913],{},[1712,37560,37561],{},"0,25",[898,37563,1758],{},[902,37565,37566],{"encoding":904},"T = 0{,}25Y",[883,37568,37570],{"className":37569},[886],[888,37571,37572],{"xmlns":890},[892,37573,37574,37586],{},[895,37575,37576,37582,37584],{},[3074,37577,37578,37580],{},[898,37579,25985],{},[1716,37581,3080],{},[1716,37583,1913],{},[1712,37585,28904],{},[902,37587,37588],{"encoding":904},"I^* = 500",[883,37590,37592],{"className":37591},[886],[888,37593,37594],{"xmlns":890},[892,37595,37596,37608],{},[895,37597,37598,37604,37606],{},[3074,37599,37600,37602],{},[898,37601,25914],{},[1716,37603,3080],{},[1716,37605,1913],{},[1712,37607,6653],{},[902,37609,37610],{"encoding":904},"G^* = 150",[883,37612,37614],{"className":37613},[886],[888,37615,37616],{"xmlns":890},[892,37617,37618,37631],{},[895,37619,37620,37626,37628],{},[3074,37621,37622,37624],{},[898,37623,10856],{},[1716,37625,3080],{},[1716,37627,1913],{},[1712,37629,37630],{},"800",[902,37632,37633],{"encoding":904},"B^* = 800",". Soustava:",[724,37636,37637],{},[883,37638,37640],{"className":37639},[886],[888,37641,37642],{"xmlns":890},[892,37643,37644,37862],{},[2008,37645,37646,37692,37734,37770,37812],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,37647,37648,37664],{},[2015,37649,37650],{},[2747,37651,37652],{"scriptlevel":2505,"displaystyle":1718},[895,37653,37654,37656,37658,37660,37662],{},[1716,37655,1920],{"stretchy":1919},[898,37657,2098],{},[1712,37659,1714],{},[1716,37661,1925],{"stretchy":1919},[2074,37663,2711],{},[2015,37665,37666],{},[2747,37667,37668],{"scriptlevel":2505,"displaystyle":1718},[895,37669,37670,37672,37674,37676,37678,37680,37686,37688,37690],{},[895,37671],{},[898,37673,9945],{},[1716,37675,1913],{},[1712,37677,37502],{},[2074,37679,8508],{},[1707,37681,37682,37684],{},[898,37683,1758],{},[898,37685,1916],{},[1716,37687,1949],{},[1712,37689,37515],{},[1716,37691,1719],{"separator":1718},[2012,37693,37694,37710],{},[2015,37695,37696],{},[2747,37697,37698],{"scriptlevel":2505,"displaystyle":1718},[895,37699,37700,37702,37704,37706,37708],{},[1716,37701,1920],{"stretchy":1919},[898,37703,2098],{},[1712,37705,1726],{},[1716,37707,1925],{"stretchy":1919},[2074,37709,2711],{},[2015,37711,37712],{},[2747,37713,37714],{"scriptlevel":2505,"displaystyle":1718},[895,37715,37716,37718,37724,37726,37728,37730,37732],{},[895,37717],{},[1707,37719,37720,37722],{},[898,37721,1758],{},[898,37723,1916],{},[1716,37725,1913],{},[898,37727,1758],{},[1716,37729,2760],{},[898,37731,4164],{},[1716,37733,1719],{"separator":1718},[2012,37735,37736,37752],{},[2015,37737,37738],{},[2747,37739,37740],{"scriptlevel":2505,"displaystyle":1718},[895,37741,37742,37744,37746,37748,37750],{},[1716,37743,1920],{"stretchy":1919},[898,37745,2098],{},[1712,37747,7072],{},[1716,37749,1925],{"stretchy":1919},[2074,37751,2711],{},[2015,37753,37754],{},[2747,37755,37756],{"scriptlevel":2505,"displaystyle":1718},[895,37757,37758,37760,37762,37764,37766,37768],{},[895,37759],{},[898,37761,4164],{},[1716,37763,1913],{},[1712,37765,37561],{},[898,37767,1758],{},[1716,37769,1719],{"separator":1718},[2012,37771,37772,37788],{},[2015,37773,37774],{},[2747,37775,37776],{"scriptlevel":2505,"displaystyle":1718},[895,37777,37778,37780,37782,37784,37786],{},[1716,37779,1920],{"stretchy":1919},[898,37781,2098],{},[1712,37783,6849],{},[1716,37785,1925],{"stretchy":1919},[2074,37787,2711],{},[2015,37789,37790],{},[2747,37791,37792],{"scriptlevel":2505,"displaystyle":1718},[895,37793,37794,37796,37798,37800,37802,37804,37810],{},[895,37795],{},[898,37797,16690],{},[1716,37799,1913],{},[1712,37801,37534],{},[2074,37803,8508],{},[1707,37805,37806,37808],{},[898,37807,1758],{},[898,37809,1916],{},[1716,37811,1719],{"separator":1718},[2012,37813,37814,37830],{},[2015,37815,37816],{},[2747,37817,37818],{"scriptlevel":2505,"displaystyle":1718},[895,37819,37820,37822,37824,37826,37828],{},[1716,37821,1920],{"stretchy":1919},[898,37823,2098],{},[1712,37825,6985],{},[1716,37827,1925],{"stretchy":1919},[2074,37829,2711],{},[2015,37831,37832],{},[2747,37833,37834],{"scriptlevel":2505,"displaystyle":1718},[895,37835,37836,37838,37840,37842,37844,37846,37848,37850,37852,37854,37856,37858,37860],{},[895,37837],{},[898,37839,1758],{},[1716,37841,1913],{},[898,37843,9945],{},[1716,37845,1949],{},[1712,37847,28904],{},[1716,37849,1949],{},[1712,37851,6653],{},[1716,37853,1949],{},[1712,37855,37630],{},[1716,37857,2760],{},[898,37859,16690],{},[898,37861,1853],{"mathvariant":2068},[902,37863,37864],{"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}",[724,37866,37867,37868,37902],{},"Postupná substituce — z (r3) do (r2): ",[883,37869,37871],{"className":37870},[886],[888,37872,37873],{"xmlns":890},[892,37874,37875,37899],{},[895,37876,37877,37883,37885,37887,37889,37891,37893,37895,37897],{},[1707,37878,37879,37881],{},[898,37880,1758],{},[898,37882,1916],{},[1716,37884,1913],{},[898,37886,1758],{},[1716,37888,2760],{},[1712,37890,37561],{},[898,37892,1758],{},[1716,37894,1913],{},[1712,37896,37502],{},[898,37898,1758],{},[902,37900,37901],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,37904,37905],{},[883,37906,37908],{"className":37907},[886],[888,37909,37910],{"xmlns":890},[892,37911,37912,37953],{},[895,37913,37914,37916,37918,37920,37922,37924,37926,37928,37930,37932,37934,37936,37938,37940,37942,37945,37947,37949,37951],{},[1716,37915,1920],{"stretchy":1919},[898,37917,2098],{},[1712,37919,6231],{},[1716,37921,1925],{"stretchy":1919},[2074,37923,2711],{},[898,37925,9945],{},[1716,37927,1913],{},[1712,37929,37502],{},[1716,37931,9532],{},[1712,37933,37502],{},[898,37935,1758],{},[1716,37937,1949],{},[1712,37939,37515],{},[1716,37941,1913],{},[1712,37943,37944],{},"0,5625",[898,37946,1758],{},[1716,37948,1949],{},[1712,37950,37515],{},[1716,37952,1719],{"separator":1718},[902,37954,37955],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,37957,37958],{},[883,37959,37961],{"className":37960},[886],[888,37962,37963],{"xmlns":890},[892,37964,37965,37998],{},[895,37966,37967,37969,37971,37973,37975,37977,37979,37981,37983,37985,37987,37989,37991,37994,37996],{},[1716,37968,1920],{"stretchy":1919},[898,37970,2098],{},[1712,37972,7109],{},[1716,37974,1925],{"stretchy":1919},[2074,37976,2711],{},[898,37978,16690],{},[1716,37980,1913],{},[1712,37982,37534],{},[1716,37984,9532],{},[1712,37986,37502],{},[898,37988,1758],{},[1716,37990,1913],{},[1712,37992,37993],{},"0,1125",[898,37995,1758],{},[898,37997,1853],{"mathvariant":2068},[902,37999,38000],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,38002,38003],{},"Dosazením do (r5):",[724,38005,38006],{},[883,38007,38009],{"className":38008},[886],[888,38010,38011],{"xmlns":890},[892,38012,38013,38057],{},[895,38014,38015,38017,38019,38021,38023,38025,38027,38029,38031,38033,38035,38037,38039,38041,38043,38045,38047,38050,38052,38054],{},[898,38016,1758],{},[1716,38018,1913],{},[1712,38020,37944],{},[898,38022,1758],{},[1716,38024,1949],{},[1712,38026,37515],{},[1716,38028,1949],{},[1712,38030,28904],{},[1716,38032,1949],{},[1712,38034,6653],{},[1716,38036,1949],{},[1712,38038,37630],{},[1716,38040,2760],{},[1712,38042,37993],{},[898,38044,1758],{},[1716,38046,1913],{},[1712,38048,38049],{},"0,45",[898,38051,1758],{},[1716,38053,1949],{},[1712,38055,38056],{},"2200.",[902,38058,38059],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,38061,38062,38063,19417,38085,38108],{},"Odtud ",[883,38064,38066],{"className":38065},[886],[888,38067,38068],{"xmlns":890},[892,38069,38070,38082],{},[895,38071,38072,38075,38077,38079],{},[1712,38073,38074],{},"0,55",[898,38076,1758],{},[1716,38078,1913],{},[1712,38080,38081],{},"2200",[902,38083,38084],{"encoding":904},"0{,}55Y = 2200",[883,38086,38088],{"className":38087},[886],[888,38089,38090],{"xmlns":890},[892,38091,38092,38105],{},[895,38093,38094,38100,38102],{},[3074,38095,38096,38098],{},[898,38097,1758],{},[898,38099,1805],{},[1716,38101,1913],{},[1712,38103,38104],{},"4000",[902,38106,38107],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,38110,38111,38134,38166,38201,38234,38270],{},[123,38112,38113,1719],{},[883,38114,38116],{"className":38115},[886],[888,38117,38118],{"xmlns":890},[892,38119,38120,38132],{},[895,38121,38122,38128,38130],{},[3074,38123,38124,38126],{},[898,38125,1758],{},[898,38127,1805],{},[1716,38129,1913],{},[1712,38131,38104],{},[902,38133,38107],{"encoding":904},[123,38135,38136,1719],{},[883,38137,38139],{"className":38138},[886],[888,38140,38141],{"xmlns":890},[892,38142,38143,38163],{},[895,38144,38145,38151,38153,38155,38157,38159,38161],{},[3074,38146,38147,38149],{},[898,38148,4164],{},[898,38150,1805],{},[1716,38152,1913],{},[1712,38154,37561],{},[1716,38156,9532],{},[1712,38158,38104],{},[1716,38160,1913],{},[1712,38162,16656],{},[902,38164,38165],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,38167,38168,1719],{},[883,38169,38171],{"className":38170},[886],[888,38172,38173],{"xmlns":890},[892,38174,38175,38198],{},[895,38176,38177,38185,38187,38189,38191,38193,38195],{},[7204,38178,38179,38181,38183],{},[898,38180,1758],{},[898,38182,1916],{},[898,38184,1805],{},[1716,38186,1913],{},[1712,38188,37502],{},[1716,38190,9532],{},[1712,38192,38104],{},[1716,38194,1913],{},[1712,38196,38197],{},"3000",[902,38199,38200],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,38202,38203,1719],{},[883,38204,38206],{"className":38205},[886],[888,38207,38208],{"xmlns":890},[892,38209,38210,38231],{},[895,38211,38212,38218,38220,38222,38224,38226,38228],{},[3074,38213,38214,38216],{},[898,38215,16690],{},[898,38217,1805],{},[1716,38219,1913],{},[1712,38221,37534],{},[1716,38223,9532],{},[1712,38225,38197],{},[1716,38227,1913],{},[1712,38229,38230],{},"450",[902,38232,38233],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,38235,38236,1719],{},[883,38237,38239],{"className":38238},[886],[888,38240,38241],{"xmlns":890},[892,38242,38243,38267],{},[895,38244,38245,38251,38253,38255,38257,38259,38261,38263,38265],{},[3074,38246,38247,38249],{},[898,38248,9945],{},[898,38250,1805],{},[1716,38252,1913],{},[1712,38254,37502],{},[1716,38256,9532],{},[1712,38258,38197],{},[1716,38260,1949],{},[1712,38262,37515],{},[1716,38264,1913],{},[1712,38266,38197],{},[902,38268,38269],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,38271,38272,38312],{},[883,38273,38275],{"className":38274},[886],[888,38276,38277],{"xmlns":890},[892,38278,38279,38309],{},[895,38280,38281,38287,38289,38297,38299,38305,38307],{},[3074,38282,38283,38285],{},[898,38284,5352],{},[898,38286,1805],{},[1716,38288,1913],{},[7204,38290,38291,38293,38295],{},[898,38292,1758],{},[898,38294,1916],{},[898,38296,1805],{},[1716,38298,2760],{},[3074,38300,38301,38303],{},[898,38302,9945],{},[898,38304,1805],{},[1716,38306,1913],{},[1712,38308,2505],{},[902,38310,38311],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,38314,38315,38317,38318,1343,38335,2247,38356,38381,38382,38385,38386,38399,38400,1853],{},[38,38316,35125],{}," Modely ",[883,38319,38321],{"className":38320},[886],[888,38322,38323],{"xmlns":890},[892,38324,38325,38333],{},[895,38326,38327,38329,38331],{},[898,38328,9945],{},[2074,38330,26091],{},[898,38332,25985],{},[902,38334,26096],{"encoding":904},[883,38336,38338],{"className":38337},[886],[888,38339,38340],{"xmlns":890},[892,38341,38342,38354],{},[895,38343,38344,38346,38348,38350,38352],{},[898,38345,9945],{},[2074,38347,26091],{},[898,38349,25985],{},[2074,38351,26091],{},[898,38353,25914],{},[902,38355,32007],{"encoding":904},[883,38357,38359],{"className":38358},[886],[888,38360,38361],{"xmlns":890},[892,38362,38363,38379],{},[895,38364,38365,38367,38369,38371,38373,38375,38377],{},[898,38366,9945],{},[2074,38368,26091],{},[898,38370,25985],{},[2074,38372,26091],{},[898,38374,25914],{},[2074,38376,26091],{},[898,38378,26121],{},[902,38380,26124],{"encoding":904}," pokládají investice za ",[38,38383,38384],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,38387,38389],{"className":38388},[886],[888,38390,38391],{"xmlns":890},[892,38392,38393,38397],{},[895,38394,38395],{},[898,38396,2098],{},[902,38398,2098],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,38401,38402],{},"model IS-LM",[115,38404,38406],{"id":38405},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,38408,38409,38410,38413,38414,38417,38418,38421],{},"V článku ",[207,38411,10768],{"className":38412,"dataFsResolvedFilePath":827,"href":828},[210]," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,38415,38416],{},"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 ",[38,38419,38420],{},"výraznější"," než v mikroekonomických modelech.",[724,38423,38424],{},[3682,38425],{"alt":38426,"className":38427,"src":38428},"imek-multiplikatorovy-efekt-chain",[210,3686],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,38430,25965,38431,1343,38448,1343,38469,38494,38495,38498,38499,38517,38518,38536,38537,38555,38556,38559,38560,1343,38577,38594,38595,38597],{},[883,38432,38434],{"className":38433},[886],[888,38435,38436],{"xmlns":890},[892,38437,38438,38446],{},[895,38439,38440,38442,38444],{},[898,38441,9945],{},[2074,38443,26091],{},[898,38445,25985],{},[902,38447,26096],{"encoding":904},[883,38449,38451],{"className":38450},[886],[888,38452,38453],{"xmlns":890},[892,38454,38455,38467],{},[895,38456,38457,38459,38461,38463,38465],{},[898,38458,9945],{},[2074,38460,26091],{},[898,38462,25985],{},[2074,38464,26091],{},[898,38466,25914],{},[902,38468,32007],{"encoding":904},[883,38470,38472],{"className":38471},[886],[888,38473,38474],{"xmlns":890},[892,38475,38476,38492],{},[895,38477,38478,38480,38482,38484,38486,38488,38490],{},[898,38479,9945],{},[2074,38481,26091],{},[898,38483,25985],{},[2074,38485,26091],{},[898,38487,25914],{},[2074,38489,26091],{},[898,38491,26121],{},[902,38493,26124],{"encoding":904}," se vyšetřuje vliv změn ",[38,38496,38497],{},"exogenních"," veličin (plánovaných investic ",[883,38500,38502],{"className":38501},[886],[888,38503,38504],{"xmlns":890},[892,38505,38506,38514],{},[895,38507,38508],{},[3074,38509,38510,38512],{},[898,38511,25985],{},[1716,38513,3080],{},[902,38515,38516],{"encoding":904},"I^*",", vládních výdajů ",[883,38519,38521],{"className":38520},[886],[888,38522,38523],{"xmlns":890},[892,38524,38525,38533],{},[895,38526,38527],{},[3074,38528,38529,38531],{},[898,38530,25914],{},[1716,38532,3080],{},[902,38534,38535],{"encoding":904},"G^*",", exportu ",[883,38538,38540],{"className":38539},[886],[888,38541,38542],{"xmlns":890},[892,38543,38544,38552],{},[895,38545,38546],{},[3074,38547,38548,38550],{},[898,38549,10856],{},[1716,38551,3080],{},[902,38553,38554],{"encoding":904},"B^*",") na změny ",[38,38557,38558],{},"endogenních"," rovnovážných veličin (",[883,38561,38563],{"className":38562},[886],[888,38564,38565],{"xmlns":890},[892,38566,38567,38575],{},[895,38568,38569],{},[3074,38570,38571,38573],{},[898,38572,1758],{},[898,38574,1805],{},[902,38576,27700],{"encoding":904},[883,38578,38580],{"className":38579},[886],[888,38581,38582],{"xmlns":890},[892,38583,38584,38592],{},[895,38585,38586],{},[3074,38587,38588,38590],{},[898,38589,9945],{},[898,38591,1805],{},[902,38593,27759],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,38596,1657],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,38599,38601],{"id":38600},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,38603,34673,38604,38627,38628,38672],{},[883,38605,38607],{"className":38606},[886],[888,38608,38609],{"xmlns":890},[892,38610,38611,38625],{},[895,38612,38613,38615,38617,38619,38621,38623],{},[898,38614,9945],{},[1716,38616,1913],{},[898,38618,207],{},[898,38620,1758],{},[1716,38622,1949],{},[898,38624,1952],{},[902,38626,32705],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,38629,38631],{"className":38630},[886],[888,38632,38633],{"xmlns":890},[892,38634,38635,38669],{},[895,38636,38637,38643,38645],{},[3074,38638,38639,38641],{},[898,38640,1758],{},[898,38642,1805],{},[1716,38644,1913],{},[2747,38646,38647],{"scriptlevel":2505,"displaystyle":1718},[2750,38648,38649,38661],{},[895,38650,38651,38653,38655],{},[898,38652,1952],{},[1716,38654,1949],{},[3074,38656,38657,38659],{},[898,38658,25985],{},[1716,38660,3080],{},[895,38662,38663,38665,38667],{},[1712,38664,1714],{},[1716,38666,2760],{},[898,38668,207],{},[902,38670,38671],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,38674,38675],{},[883,38676,38678],{"className":38677},[886],[888,38679,38680],{"xmlns":890},[892,38681,38682,38751],{},[895,38683,38684,38702,38704,38734,38736],{},[2750,38685,38686,38696],{},[895,38687,38688,38690],{},[898,38689,23677],{"mathvariant":2068},[3074,38691,38692,38694],{},[898,38693,1758],{},[898,38695,1805],{},[895,38697,38698,38700],{},[898,38699,23677],{"mathvariant":2068},[898,38701,207],{},[1716,38703,1913],{},[2750,38705,38706,38718],{},[895,38707,38708,38710,38712],{},[898,38709,1952],{},[1716,38711,1949],{},[3074,38713,38714,38716],{},[898,38715,25985],{},[1716,38717,3080],{},[895,38719,38720,38722,38724,38726,38728],{},[1716,38721,1920],{"stretchy":1919},[1712,38723,1714],{},[1716,38725,2760],{},[898,38727,207],{},[3074,38729,38730,38732],{},[1716,38731,1925],{"stretchy":1919},[1712,38733,1726],{},[2324,38735],{"width":2326},[895,38737,38738,38741,38748],{},[2074,38739,38740],{},"(multiplik",[22202,38742,38743,38745],{"accent":1718},[2074,38744,207],{},[1716,38746,38747],{},"ˊ",[2074,38749,38750],{},"tor MPC)",[902,38752,38753],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,38755,38756],{},[883,38757,38759],{"className":38758},[886],[888,38760,38761],{"xmlns":890},[892,38762,38763,38832],{},[895,38764,38765,38783,38785,38797,38799],{},[2750,38766,38767,38777],{},[895,38768,38769,38771],{},[898,38770,23677],{"mathvariant":2068},[3074,38772,38773,38775],{},[898,38774,1758],{},[898,38776,1805],{},[895,38778,38779,38781],{},[898,38780,23677],{"mathvariant":2068},[898,38782,1952],{},[1716,38784,1913],{},[2750,38786,38787,38789],{},[1712,38788,1714],{},[895,38790,38791,38793,38795],{},[1712,38792,1714],{},[1716,38794,2760],{},[898,38796,207],{},[2324,38798],{"width":2326},[895,38800,38801,38803,38809,38812,38819,38822,38829],{},[2074,38802,38740],{},[22202,38804,38805,38807],{"accent":1718},[2074,38806,207],{},[1716,38808,38747],{},[2074,38810,38811],{},"tor autonomn",[22202,38813,38814,38817],{"accent":1718},[2074,38815,38816],{},"ı",[1716,38818,38747],{},[2074,38820,38821],{}," spot",[22202,38823,38824,38826],{"accent":1718},[2074,38825,2098],{},[1716,38827,38828],{},"ˇ",[2074,38830,38831],{},"eby)",[902,38833,38834],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,38836,38837],{},[883,38838,38840],{"className":38839},[886],[888,38841,38842],{"xmlns":890},[892,38843,38844,38911],{},[895,38845,38846,38868,38870,38882,38884,38896,38898],{},[2750,38847,38848,38858],{},[895,38849,38850,38852],{},[898,38851,23677],{"mathvariant":2068},[3074,38853,38854,38856],{},[898,38855,1758],{},[898,38857,1805],{},[895,38859,38860,38862],{},[898,38861,23677],{"mathvariant":2068},[3074,38863,38864,38866],{},[898,38865,25985],{},[1716,38867,3080],{},[1716,38869,1913],{},[2750,38871,38872,38874],{},[1712,38873,1714],{},[895,38875,38876,38878,38880],{},[1712,38877,1714],{},[1716,38879,2760],{},[898,38881,207],{},[1716,38883,1913],{},[2750,38885,38886,38888],{},[1712,38887,1714],{},[895,38889,38890,38892,38894],{},[898,38891,16690],{},[898,38893,1690],{},[898,38895,5352],{},[2324,38897],{"width":2326},[895,38899,38900,38902,38908],{},[2074,38901,38740],{},[22202,38903,38904,38906],{"accent":1718},[2074,38905,207],{},[1716,38907,38747],{},[2074,38909,38910],{},"tor investic)",[902,38912,38913],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1635,38915,38916],{},[724,38917,38918,38920,38921,38924,38925,38938,38939,38956,38957,38975,38976,39020,39021,13380,39038,39041,39042,39059],{},[883,38919,1641],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,38922,38923],{},"důchodem","; z něj se utratí ",[883,38926,38928],{"className":38927},[886],[888,38929,38930],{"xmlns":890},[892,38931,38932,38936],{},[895,38933,38934],{},[898,38935,207],{},[902,38937,207],{"encoding":904}," Kč (= ",[883,38940,38942],{"className":38941},[886],[888,38943,38944],{"xmlns":890},[892,38945,38946,38954],{},[895,38947,38948,38950,38952],{},[898,38949,16690],{},[898,38951,1690],{},[898,38953,9945],{},[902,38955,31832],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,38958,38960],{"className":38959},[886],[888,38961,38962],{"xmlns":890},[892,38963,38964,38972],{},[895,38965,38966],{},[3074,38967,38968,38970],{},[898,38969,207],{},[1712,38971,1726],{},[902,38973,38974],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,38977,38979],{"className":38978},[886],[888,38980,38981],{"xmlns":890},[892,38982,38983,39017],{},[895,38984,38985,38987,38989,38991,38993,38999,39001,39003,39005],{},[1712,38986,1714],{},[1716,38988,1949],{},[898,38990,207],{},[1716,38992,1949],{},[3074,38994,38995,38997],{},[898,38996,207],{},[1712,38998,1726],{},[1716,39000,1949],{},[1716,39002,31892],{},[1716,39004,1913],{},[2750,39006,39007,39009],{},[1712,39008,1714],{},[895,39010,39011,39013,39015],{},[1712,39012,1714],{},[1716,39014,2760],{},[898,39016,207],{},[902,39018,39019],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,39022,39024],{"className":39023},[886],[888,39025,39026],{"xmlns":890},[892,39027,39028,39036],{},[895,39029,39030],{},[3074,39031,39032,39034],{},[898,39033,1758],{},[898,39035,1805],{},[902,39037,27700],{"encoding":904},[38,39039,39040],{},"více"," než korunu — čím vyšší ",[883,39043,39045],{"className":39044},[886],[888,39046,39047],{"xmlns":890},[892,39048,39049,39057],{},[895,39050,39051,39053,39055],{},[898,39052,16690],{},[898,39054,1690],{},[898,39056,9945],{},[902,39058,31832],{"encoding":904},", tím silnější multiplikační efekt.",[724,39061,39062,39065,39066,39092,39093,39096,39097,2247,39118,39143,39144,1853],{},[38,39063,39064],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,39067,39069],{"className":39068},[886],[888,39070,39071],{"xmlns":890},[892,39072,39073,39089],{},[895,39074,39075],{},[2747,39076,39077],{"scriptlevel":2505,"displaystyle":1919},[2750,39078,39079,39081],{},[1712,39080,1714],{},[895,39082,39083,39085,39087],{},[1712,39084,1714],{},[1716,39086,2760],{},[898,39088,207],{},[902,39090,39091],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,39094,39095],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,39098,39100],{"className":39099},[886],[888,39101,39102],{"xmlns":890},[892,39103,39104,39116],{},[895,39105,39106,39108,39110,39112,39114],{},[898,39107,9945],{},[2074,39109,26091],{},[898,39111,25985],{},[2074,39113,26091],{},[898,39115,25914],{},[902,39117,32007],{"encoding":904},[883,39119,39121],{"className":39120},[886],[888,39122,39123],{"xmlns":890},[892,39124,39125,39141],{},[895,39126,39127,39129,39131,39133,39135,39137,39139],{},[898,39128,9945],{},[2074,39130,26091],{},[898,39132,25985],{},[2074,39134,26091],{},[898,39136,25914],{},[2074,39138,26091],{},[898,39140,26121],{},[902,39142,26124],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,39145,39147],{"className":39146,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,39149,39151],{"id":39150},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,39153,25965,39154,1343,39171,2247,39192,25970,39217,1994,39220,39241,39242,3495,39245,39258,39259,3569,39288,39305,39306,39309,39310,39312,39313,39334],{},[883,39155,39157],{"className":39156},[886],[888,39158,39159],{"xmlns":890},[892,39160,39161,39169],{},[895,39162,39163,39165,39167],{},[898,39164,9945],{},[2074,39166,26091],{},[898,39168,25985],{},[902,39170,26096],{"encoding":904},[883,39172,39174],{"className":39173},[886],[888,39175,39176],{"xmlns":890},[892,39177,39178,39190],{},[895,39179,39180,39182,39184,39186,39188],{},[898,39181,9945],{},[2074,39183,26091],{},[898,39185,25985],{},[2074,39187,26091],{},[898,39189,25914],{},[902,39191,32007],{"encoding":904},[883,39193,39195],{"className":39194},[886],[888,39196,39197],{"xmlns":890},[892,39198,39199,39215],{},[895,39200,39201,39203,39205,39207,39209,39211,39213],{},[898,39202,9945],{},[2074,39204,26091],{},[898,39206,25985],{},[2074,39208,26091],{},[898,39210,25914],{},[2074,39212,26091],{},[898,39214,26121],{},[902,39216,26124],{"encoding":904},[38,39218,39219],{},"investice konstantní",[883,39221,39223],{"className":39222},[886],[888,39224,39225],{"xmlns":890},[892,39226,39227,39239],{},[895,39228,39229,39231,39233],{},[898,39230,25985],{},[1716,39232,1913],{},[3074,39234,39235,39237],{},[898,39236,25985],{},[1716,39238,3080],{},[902,39240,25996],{"encoding":904},"). Reálnější je předpoklad, že ",[38,39243,39244],{},"investice závisejí na úrokové míře",[883,39246,39248],{"className":39247},[886],[888,39249,39250],{"xmlns":890},[892,39251,39252,39256],{},[895,39253,39254],{},[898,39255,2098],{},[902,39257,2098],{"encoding":904}," — klesající funkce ",[883,39260,39262],{"className":39261},[886],[888,39263,39264],{"xmlns":890},[892,39265,39266,39286],{},[895,39267,39268,39270,39272,39274,39276,39278,39280,39282,39284],{},[898,39269,25985],{},[1716,39271,1920],{"stretchy":1919},[898,39273,2098],{},[1716,39275,1925],{"stretchy":1919},[1716,39277,1913],{},[898,39279,4478],{},[898,39281,2098],{},[1716,39283,1949],{},[898,39285,5198],{},[902,39287,29548],{"encoding":904},[883,39289,39291],{"className":39290},[886],[888,39292,39293],{"xmlns":890},[892,39294,39295,39303],{},[895,39296,39297,39299,39301],{},[898,39298,4478],{},[1716,39300,2704],{},[1712,39302,2505],{},[902,39304,26315],{"encoding":904},". Přidáním ",[38,39307,39308],{},"trhu peněz"," k trhu zboží vzniká model ",[38,39311,25814],{}," se dvěma neznámými ",[883,39314,39316],{"className":39315},[886],[888,39317,39318],{"xmlns":890},[892,39319,39320,39332],{},[895,39321,39322,39324,39326,39328,39330],{},[1716,39323,1920],{"stretchy":1919},[898,39325,1758],{},[1716,39327,1719],{"separator":1718},[898,39329,2098],{},[1716,39331,1925],{"stretchy":1919},[902,39333,31937],{"encoding":904}," a dvěma rovnicemi:",[120,39336,39337,39387],{},[123,39338,39339,1994,39341,39343,39344,39365,39366,1853],{},[38,39340,29637],{},[614,39342,25856],{},") — klesající přímka v rovině ",[883,39345,39347],{"className":39346},[886],[888,39348,39349],{"xmlns":890},[892,39350,39351,39363],{},[895,39352,39353,39355,39357,39359,39361],{},[1716,39354,1920],{"stretchy":1919},[898,39356,2098],{},[1716,39358,1719],{"separator":1718},[898,39360,1758],{},[1716,39362,1925],{"stretchy":1919},[902,39364,26737],{"encoding":904},", odvozená z rovnováhy trhu zboží ",[883,39367,39369],{"className":39368},[886],[888,39370,39371],{"xmlns":890},[892,39372,39373,39385],{},[895,39374,39375,39377,39379,39381,39383],{},[898,39376,1758],{},[1716,39378,1913],{},[898,39380,9945],{},[1716,39382,1949],{},[898,39384,25985],{},[902,39386,28539],{"encoding":904},[123,39388,39389,1994,39391,39393,39394,2772,39419,39465],{},[38,39390,29836],{},[614,39392,25863],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,39395,39397],{"className":39396},[886],[888,39398,39399],{"xmlns":890},[892,39400,39401,39417],{},[895,39402,39403,39409,39411],{},[3074,39404,39405,39407],{},[898,39406,16690],{},[898,39408,1916],{},[1716,39410,1913],{},[3074,39412,39413,39415],{},[898,39414,16690],{},[1716,39416,3080],{},[902,39418,27278],{"encoding":904},[883,39420,39422],{"className":39421},[886],[888,39423,39424],{"xmlns":890},[892,39425,39426,39462],{},[895,39427,39428,39434,39436,39442,39444,39446,39452,39454,39456],{},[3074,39429,39430,39432],{},[898,39431,16690],{},[898,39433,1916],{},[1716,39435,1913],{},[1707,39437,39438,39440],{},[898,39439,27035],{},[1712,39441,1714],{},[898,39443,1758],{},[1716,39445,1949],{},[1707,39447,39448,39450],{},[898,39449,27035],{},[1712,39451,1726],{},[898,39453,2098],{},[1716,39455,1949],{},[1707,39457,39458,39460],{},[898,39459,27035],{},[1712,39461,7072],{},[902,39463,39464],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,39467,39468,3495,39471,39504,39505,39507,39508,39510],{},[38,39469,39470],{},"Simultánní rovnovážný bod",[883,39472,39474],{"className":39473},[886],[888,39475,39476],{"xmlns":890},[892,39477,39478,39502],{},[895,39479,39480,39482,39484,39486,39492,39494,39500],{},[898,39481,1805],{},[1716,39483,1913],{},[1716,39485,1920],{"stretchy":1919},[3074,39487,39488,39490],{},[898,39489,2098],{},[898,39491,1805],{},[1716,39493,1719],{"separator":1718},[3074,39495,39496,39498],{},[898,39497,1758],{},[898,39499,1805],{},[1716,39501,1925],{"stretchy":1919},[902,39503,29928],{"encoding":904}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,39506,25901],{}," (posun IS) a ",[38,39509,25932],{}," (posun LM).",[724,39512,39513],{},[38,39514,39515,39516,1343,39538,1343,39560,1343,39582,39604,39605,1853],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,39517,39519],{"className":39518},[886],[888,39520,39521],{"xmlns":890},[892,39522,39523,39535],{},[895,39524,39525,39531,39533],{},[3074,39526,39527,39529],{},[898,39528,1758],{},[898,39530,1805],{},[1716,39532,1913],{},[1712,39534,28909],{},[902,39536,39537],{"encoding":904},"Y^E = 5000",[883,39539,39541],{"className":39540},[886],[888,39542,39543],{"xmlns":890},[892,39544,39545,39557],{},[895,39546,39547,39553,39555],{},[3074,39548,39549,39551],{},[898,39550,2098],{},[898,39552,1805],{},[1716,39554,1913],{},[1712,39556,6985],{},[902,39558,39559],{"encoding":904},"r^E = 5",[883,39561,39563],{"className":39562},[886],[888,39564,39565],{"xmlns":890},[892,39566,39567,39579],{},[895,39568,39569,39575,39577],{},[3074,39570,39571,39573],{},[898,39572,9945],{},[898,39574,1805],{},[1716,39576,1913],{},[1712,39578,28946],{},[902,39580,39581],{"encoding":904},"C^E = 4100",[883,39583,39585],{"className":39584},[886],[888,39586,39587],{"xmlns":890},[892,39588,39589,39601],{},[895,39590,39591,39597,39599],{},[3074,39592,39593,39595],{},[898,39594,25985],{},[898,39596,1805],{},[1716,39598,1913],{},[1712,39600,28985],{},[902,39602,39603],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,39606,945],{"className":39607,"dataFsResolvedFilePath":943,"href":944},[210],[115,39609,39611],{"id":39610},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,39613,39614,39678,39789,39932,40174,40241],{},[123,39615,39616,39619,39620,39642,39643,39677],{},[38,39617,39618],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,39621,39623],{"className":39622},[886],[888,39624,39625],{"xmlns":890},[892,39626,39627,39639],{},[895,39628,39629,39631,39633,39635,39637],{},[898,39630,25914],{},[898,39632,32081],{},[898,39634,1690],{},[1716,39636,8490],{},[898,39638,1758],{},[902,39640,39641],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,39644,39646],{"className":39645},[886],[888,39647,39648],{"xmlns":890},[892,39649,39650,39674],{},[895,39651,39652,39654,39656,39658,39660,39662,39664,39666,39668,39670,39672],{},[898,39653,25914],{},[898,39655,32081],{},[898,39657,1690],{},[1716,39659,1913],{},[898,39661,9945],{},[1716,39663,1949],{},[898,39665,25985],{},[1716,39667,1949],{},[898,39669,25914],{},[1716,39671,1949],{},[898,39673,26121],{},[902,39675,39676],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,39679,39680,39682,39683,39704,39705,1343,39728,39759,39760,39773,39774,1853],{},[38,39681,32315],{}," splňují ",[883,39684,39686],{"className":39685},[886],[888,39687,39688],{"xmlns":890},[892,39689,39690,39702],{},[895,39691,39692,39694,39696,39698,39700],{},[898,39693,1758],{},[1716,39695,1913],{},[898,39697,9945],{},[1716,39699,1949],{},[898,39701,5352],{},[902,39703,26494],{"encoding":904}," (7.2); lineární model ",[883,39706,39708],{"className":39707},[886],[888,39709,39710],{"xmlns":890},[892,39711,39712,39726],{},[895,39713,39714,39716,39718,39720,39722,39724],{},[898,39715,9945],{},[1716,39717,1913],{},[898,39719,207],{},[898,39721,1758],{},[1716,39723,1949],{},[898,39725,1952],{},[902,39727,32705],{"encoding":904},[883,39729,39731],{"className":39730},[886],[888,39732,39733],{"xmlns":890},[892,39734,39735,39757],{},[895,39736,39737,39739,39741,39743,39745,39747,39749,39751,39753,39755],{},[898,39738,5352],{},[1716,39740,1913],{},[1716,39742,1920],{"stretchy":1919},[1712,39744,1714],{},[1716,39746,2760],{},[898,39748,207],{},[1716,39750,1925],{"stretchy":1919},[898,39752,1758],{},[1716,39754,2760],{},[898,39756,1952],{},[902,39758,32954],{"encoding":904}," s autonomní spotřebou ",[883,39761,39763],{"className":39762},[886],[888,39764,39765],{"xmlns":890},[892,39766,39767,39771],{},[895,39768,39769],{},[898,39770,1952],{},[902,39772,1952],{"encoding":904}," a autonomními úsporami ",[883,39775,39777],{"className":39776},[886],[888,39778,39779],{"xmlns":890},[892,39780,39781,39787],{},[895,39782,39783,39785],{},[1716,39784,2760],{},[898,39786,1952],{},[902,39788,33033],{"encoding":904},[123,39790,39791,3495,39794,1343,39824,39854,39855,39885,39886,1343,39907,1853],{},[38,39792,39793],{},"Mezní sklony",[883,39795,39797],{"className":39796},[886],[888,39798,39799],{"xmlns":890},[892,39800,39801,39821],{},[895,39802,39803,39805,39807,39809,39811,39813,39815,39817,39819],{},[898,39804,16690],{},[898,39806,1690],{},[898,39808,9945],{},[1716,39810,1913],{},[898,39812,5198],{"mathvariant":2068},[898,39814,9945],{},[898,39816,3045],{"mathvariant":2068},[898,39818,5198],{"mathvariant":2068},[898,39820,1758],{},[902,39822,39823],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,39825,39827],{"className":39826},[886],[888,39828,39829],{"xmlns":890},[892,39830,39831,39851],{},[895,39832,39833,39835,39837,39839,39841,39843,39845,39847,39849],{},[898,39834,16690],{},[898,39836,1690],{},[898,39838,5352],{},[1716,39840,1913],{},[898,39842,5198],{"mathvariant":2068},[898,39844,5352],{},[898,39846,3045],{"mathvariant":2068},[898,39848,5198],{"mathvariant":2068},[898,39850,1758],{},[902,39852,39853],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,39856,39858],{"className":39857},[886],[888,39859,39860],{"xmlns":890},[892,39861,39862,39882],{},[895,39863,39864,39866,39868,39870,39872,39874,39876,39878,39880],{},[898,39865,16690],{},[898,39867,1690],{},[898,39869,9945],{},[1716,39871,1949],{},[898,39873,16690],{},[898,39875,1690],{},[898,39877,5352],{},[1716,39879,1913],{},[1712,39881,1714],{},[902,39883,39884],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,39887,39889],{"className":39888},[886],[888,39890,39891],{"xmlns":890},[892,39892,39893,39905],{},[895,39894,39895,39897,39899,39901,39903],{},[898,39896,16690],{},[898,39898,1690],{},[898,39900,9945],{},[1716,39902,1913],{},[898,39904,207],{},[902,39906,33672],{"encoding":904},[883,39908,39910],{"className":39909},[886],[888,39911,39912],{"xmlns":890},[892,39913,39914,39930],{},[895,39915,39916,39918,39920,39922,39924,39926,39928],{},[898,39917,16690],{},[898,39919,1690],{},[898,39921,5352],{},[1716,39923,1913],{},[1712,39925,1714],{},[1716,39927,2760],{},[898,39929,207],{},[902,39931,33698],{"encoding":904},[123,39933,39934,39937,39938],{},[38,39935,39936],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,39939,39940,40028,40097],{},[123,39941,39942,39959,39960,39981,39982,1719],{},[883,39943,39945],{"className":39944},[886],[888,39946,39947],{"xmlns":890},[892,39948,39949,39957],{},[895,39950,39951,39953,39955],{},[898,39952,9945],{},[2074,39954,26091],{},[898,39956,25985],{},[902,39958,26096],{"encoding":904},": ",[883,39961,39963],{"className":39962},[886],[888,39964,39965],{"xmlns":890},[892,39966,39967,39979],{},[895,39968,39969,39971,39973,39975,39977],{},[898,39970,1758],{},[1716,39972,1913],{},[898,39974,9945],{},[1716,39976,1949],{},[898,39978,25985],{},[902,39980,28539],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,39983,39985],{"className":39984},[886],[888,39986,39987],{"xmlns":890},[892,39988,39989,40025],{},[895,39990,39991,39997,39999,40001,40003,40005,40011,40013,40015,40017,40019,40021,40023],{},[3074,39992,39993,39995],{},[898,39994,1758],{},[898,39996,1805],{},[1716,39998,1913],{},[1716,40000,1920],{"stretchy":1919},[898,40002,1952],{},[1716,40004,1949],{},[3074,40006,40007,40009],{},[898,40008,25985],{},[1716,40010,3080],{},[1716,40012,1925],{"stretchy":1919},[898,40014,3045],{"mathvariant":2068},[1716,40016,1920],{"stretchy":1919},[1712,40018,1714],{},[1716,40020,2760],{},[898,40022,207],{},[1716,40024,1925],{"stretchy":1919},[902,40026,40027],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,40029,40030,40051,40052,40071,40072,1719],{},[883,40031,40033],{"className":40032},[886],[888,40034,40035],{"xmlns":890},[892,40036,40037,40049],{},[895,40038,40039,40041,40043,40045,40047],{},[898,40040,9945],{},[2074,40042,26091],{},[898,40044,25985],{},[2074,40046,26091],{},[898,40048,25914],{},[902,40050,32007],{"encoding":904},": přidává vládu, zdanění ",[883,40053,40055],{"className":40054},[886],[888,40056,40057],{"xmlns":890},[892,40058,40059,40069],{},[895,40060,40061,40063,40065,40067],{},[898,40062,4164],{},[1716,40064,1920],{"stretchy":1919},[898,40066,1758],{},[1716,40068,1925],{"stretchy":1919},[902,40070,35993],{"encoding":904}," a disponibilní důchod ",[883,40073,40075],{"className":40074},[886],[888,40076,40077],{"xmlns":890},[892,40078,40079,40095],{},[895,40080,40081,40087,40089,40091,40093],{},[1707,40082,40083,40085],{},[898,40084,1758],{},[898,40086,1916],{},[1716,40088,1913],{},[898,40090,1758],{},[1716,40092,2760],{},[898,40094,4164],{},[902,40096,35492],{"encoding":904},[123,40098,40099,40124,40125,2772,40146,1853],{},[883,40100,40102],{"className":40101},[886],[888,40103,40104],{"xmlns":890},[892,40105,40106,40122],{},[895,40107,40108,40110,40112,40114,40116,40118,40120],{},[898,40109,9945],{},[2074,40111,26091],{},[898,40113,25985],{},[2074,40115,26091],{},[898,40117,25914],{},[2074,40119,26091],{},[898,40121,26121],{},[902,40123,26124],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,40126,40128],{"className":40127},[886],[888,40129,40130],{"xmlns":890},[892,40131,40132,40144],{},[895,40133,40134,40136,40138,40140,40142],{},[898,40135,26121],{},[1716,40137,1913],{},[898,40139,10856],{},[1716,40141,2760],{},[898,40143,16690],{},[902,40145,37032],{"encoding":904},[883,40147,40149],{"className":40148},[886],[888,40150,40151],{"xmlns":890},[892,40152,40153,40171],{},[895,40154,40155,40157,40159,40161,40163,40169],{},[898,40156,16690],{},[1716,40158,1913],{},[898,40160,16690],{},[1716,40162,1920],{"stretchy":1919},[1707,40164,40165,40167],{},[898,40166,1758],{},[898,40168,1916],{},[1716,40170,1925],{"stretchy":1919},[902,40172,40173],{"encoding":904},"M = M(Y_D)",[123,40175,40176,40178,40179,3495,40182,40240],{},[38,40177,15561],{}," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,40180,40181],{},"multiplikátor investic",[883,40183,40185],{"className":40184},[886],[888,40186,40187],{"xmlns":890},[892,40188,40189,40237],{},[895,40190,40191,40193,40199,40201,40203,40209,40211,40213,40215,40217,40219,40221,40223,40225,40227,40229,40231,40233,40235],{},[898,40192,23677],{"mathvariant":2068},[3074,40194,40195,40197],{},[898,40196,1758],{},[898,40198,1805],{},[898,40200,3045],{"mathvariant":2068},[898,40202,23677],{"mathvariant":2068},[3074,40204,40205,40207],{},[898,40206,25985],{},[1716,40208,3080],{},[1716,40210,1913],{},[1712,40212,1714],{},[898,40214,3045],{"mathvariant":2068},[1716,40216,1920],{"stretchy":1919},[1712,40218,1714],{},[1716,40220,2760],{},[898,40222,207],{},[1716,40224,1925],{"stretchy":1919},[1716,40226,1913],{},[1712,40228,1714],{},[898,40230,3045],{"mathvariant":2068},[898,40232,16690],{},[898,40234,1690],{},[898,40236,5352],{},[902,40238,40239],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,40242,40243,40245,40246,40261,40262,8373,40279,40294,40295,40320,40321,1853],{},[38,40244,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,40247,40249],{"className":40248},[886],[888,40250,40251],{"xmlns":890},[892,40252,40253,40259],{},[895,40254,40255,40257],{},[898,40256,25985],{},[898,40258,5352],{},[902,40260,25853],{"encoding":904}," popisuje rovnováhu trhu zboží (",[883,40263,40265],{"className":40264},[886],[888,40266,40267],{"xmlns":890},[892,40268,40269,40277],{},[895,40270,40271,40273,40275],{},[898,40272,25985],{},[1716,40274,1913],{},[898,40276,5352],{},[902,40278,26512],{"encoding":904},[883,40280,40282],{"className":40281},[886],[888,40283,40284],{"xmlns":890},[892,40285,40286,40292],{},[895,40287,40288,40290],{},[898,40289,1775],{},[898,40291,16690],{},[902,40293,25860],{"encoding":904}," rovnováhu trhu peněz (",[883,40296,40298],{"className":40297},[886],[888,40299,40300],{"xmlns":890},[892,40301,40302,40318],{},[895,40303,40304,40310,40312],{},[3074,40305,40306,40308],{},[898,40307,16690],{},[898,40309,1916],{},[1716,40311,1913],{},[3074,40313,40314,40316],{},[898,40315,16690],{},[1716,40317,3080],{},[902,40319,27278],{"encoding":904},"); průsečík dává ",[883,40322,40324],{"className":40323},[886],[888,40325,40326],{"xmlns":890},[892,40327,40328,40348],{},[895,40329,40330,40332,40338,40340,40346],{},[1716,40331,1920],{"stretchy":1919},[3074,40333,40334,40336],{},[898,40335,1758],{},[898,40337,1805],{},[1716,40339,1719],{"separator":1718},[3074,40341,40342,40344],{},[898,40343,2098],{},[898,40345,1805],{},[1716,40347,1925],{"stretchy":1919},[902,40349,25897],{"encoding":904},[115,40351,14947],{"id":14946},[120,40353,40354,40392,40432,40522,40604,40658,40714,40773,40808,40813,40885,40960,41046,41108,41176,41234,41287,41326],{},[123,40355,40356,3369,40359,39677],{},[38,40357,40358],{},"Hrubý národní produkt (GNP)",[883,40360,40362],{"className":40361},[886],[888,40363,40364],{"xmlns":890},[892,40365,40366,40390],{},[895,40367,40368,40370,40372,40374,40376,40378,40380,40382,40384,40386,40388],{},[898,40369,25914],{},[898,40371,32081],{},[898,40373,1690],{},[1716,40375,1913],{},[898,40377,9945],{},[1716,40379,1949],{},[898,40381,25985],{},[1716,40383,1949],{},[898,40385,25914],{},[1716,40387,1949],{},[898,40389,26121],{},[902,40391,39676],{"encoding":904},[123,40393,40394,40410,40411,1853],{},[38,40395,40396,40397],{},"Národní důchod ",[883,40398,40400],{"className":40399},[886],[888,40401,40402],{"xmlns":890},[892,40403,40404,40408],{},[895,40405,40406],{},[898,40407,1758],{},[902,40409,1758],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,40412,40414],{"className":40413},[886],[888,40415,40416],{"xmlns":890},[892,40417,40418,40430],{},[895,40419,40420,40422,40424,40426,40428],{},[898,40421,25914],{},[898,40423,32081],{},[898,40425,1690],{},[1716,40427,8490],{},[898,40429,1758],{},[902,40431,39641],{"encoding":904},[123,40433,40434,40460,40461,1343,40484,1343,40505,1853],{},[38,40435,40436,40437],{},"Funkce spotřeby ",[883,40438,40440],{"className":40439},[886],[888,40441,40442],{"xmlns":890},[892,40443,40444,40458],{},[895,40445,40446,40448,40450,40452,40454,40456],{},[898,40447,9945],{},[1716,40449,1913],{},[898,40451,9945],{},[1716,40453,1920],{"stretchy":1919},[898,40455,1758],{},[1716,40457,1925],{"stretchy":1919},[902,40459,34523],{"encoding":904}," — lineární model ",[883,40462,40464],{"className":40463},[886],[888,40465,40466],{"xmlns":890},[892,40467,40468,40482],{},[895,40469,40470,40472,40474,40476,40478,40480],{},[898,40471,9945],{},[1716,40473,1913],{},[898,40475,207],{},[898,40477,1758],{},[1716,40479,1949],{},[898,40481,1952],{},[902,40483,32705],{"encoding":904},[883,40485,40487],{"className":40486},[886],[888,40488,40489],{"xmlns":890},[892,40490,40491,40503],{},[895,40492,40493,40495,40497,40499,40501],{},[1712,40494,2505],{},[1716,40496,2704],{},[898,40498,207],{},[1716,40500,2704],{},[1712,40502,1714],{},[902,40504,32621],{"encoding":904},[883,40506,40508],{"className":40507},[886],[888,40509,40510],{"xmlns":890},[892,40511,40512,40520],{},[895,40513,40514,40516,40518],{},[898,40515,1952],{},[1716,40517,2716],{},[1712,40519,2505],{},[902,40521,8085],{"encoding":904},[123,40523,40524,3369,40551,40572,40573,1853],{},[38,40525,40526,40527],{},"Funkce úspor ",[883,40528,40530],{"className":40529},[886],[888,40531,40532],{"xmlns":890},[892,40533,40534,40548],{},[895,40535,40536,40538,40540,40542,40544,40546],{},[898,40537,5352],{},[1716,40539,1913],{},[898,40541,5352],{},[1716,40543,1920],{"stretchy":1919},[898,40545,1758],{},[1716,40547,1925],{"stretchy":1919},[902,40549,40550],{"encoding":904},"S = S(Y)",[883,40552,40554],{"className":40553},[886],[888,40555,40556],{"xmlns":890},[892,40557,40558,40570],{},[895,40559,40560,40562,40564,40566,40568],{},[898,40561,1758],{},[1716,40563,1913],{},[898,40565,9945],{},[1716,40567,1949],{},[898,40569,5352],{},[902,40571,26494],{"encoding":904},"; lineární ",[883,40574,40576],{"className":40575},[886],[888,40577,40578],{"xmlns":890},[892,40579,40580,40602],{},[895,40581,40582,40584,40586,40588,40590,40592,40594,40596,40598,40600],{},[898,40583,5352],{},[1716,40585,1913],{},[1716,40587,1920],{"stretchy":1919},[1712,40589,1714],{},[1716,40591,2760],{},[898,40593,207],{},[1716,40595,1925],{"stretchy":1919},[898,40597,1758],{},[1716,40599,2760],{},[898,40601,1952],{},[902,40603,32954],{"encoding":904},[123,40605,40606,3369,40609,1343,40632,1853],{},[38,40607,40608],{},"Autonomní spotřeba\u002Fúspory",[883,40610,40612],{"className":40611},[886],[888,40613,40614],{"xmlns":890},[892,40615,40616,40630],{},[895,40617,40618,40620,40622,40624,40626,40628],{},[898,40619,9945],{},[1716,40621,1920],{"stretchy":1919},[1712,40623,2505],{},[1716,40625,1925],{"stretchy":1919},[1716,40627,1913],{},[898,40629,1952],{},[902,40631,33344],{"encoding":904},[883,40633,40635],{"className":40634},[886],[888,40636,40637],{"xmlns":890},[892,40638,40639,40655],{},[895,40640,40641,40643,40645,40647,40649,40651,40653],{},[898,40642,5352],{},[1716,40644,1920],{"stretchy":1919},[1712,40646,2505],{},[1716,40648,1925],{"stretchy":1919},[1716,40650,1913],{},[1716,40652,2760],{},[898,40654,1952],{},[902,40656,40657],{"encoding":904},"S(0) = -b",[123,40659,40660,40692,40693,2365],{},[38,40661,40662,40663],{},"Mezní sklon ke spotřebě ",[883,40664,40666],{"className":40665},[886],[888,40667,40668],{"xmlns":890},[892,40669,40670,40690],{},[895,40671,40672,40674,40676,40678,40680,40682,40684,40686,40688],{},[898,40673,16690],{},[898,40675,1690],{},[898,40677,9945],{},[1716,40679,1913],{},[898,40681,5198],{"mathvariant":2068},[898,40683,9945],{},[898,40685,3045],{"mathvariant":2068},[898,40687,5198],{"mathvariant":2068},[898,40689,1758],{},[902,40691,39823],{"encoding":904}," (v lineárním modelu ",[883,40694,40696],{"className":40695},[886],[888,40697,40698],{"xmlns":890},[892,40699,40700,40712],{},[895,40701,40702,40704,40706,40708,40710],{},[898,40703,16690],{},[898,40705,1690],{},[898,40707,9945],{},[1716,40709,1913],{},[898,40711,207],{},[902,40713,33672],{"encoding":904},[123,40715,40716,40692,40748,2365],{},[38,40717,40718,40719],{},"Mezní sklon k úsporám ",[883,40720,40722],{"className":40721},[886],[888,40723,40724],{"xmlns":890},[892,40725,40726,40746],{},[895,40727,40728,40730,40732,40734,40736,40738,40740,40742,40744],{},[898,40729,16690],{},[898,40731,1690],{},[898,40733,5352],{},[1716,40735,1913],{},[898,40737,5198],{"mathvariant":2068},[898,40739,5352],{},[898,40741,3045],{"mathvariant":2068},[898,40743,5198],{"mathvariant":2068},[898,40745,1758],{},[902,40747,39853],{"encoding":904},[883,40749,40751],{"className":40750},[886],[888,40752,40753],{"xmlns":890},[892,40754,40755,40771],{},[895,40756,40757,40759,40761,40763,40765,40767,40769],{},[898,40758,16690],{},[898,40760,1690],{},[898,40762,5352],{},[1716,40764,1913],{},[1712,40766,1714],{},[1716,40768,2760],{},[898,40770,207],{},[902,40772,33698],{"encoding":904},[123,40774,40775,3495,40778,40807],{},[38,40776,40777],{},"Vztah",[883,40779,40781],{"className":40780},[886],[888,40782,40783],{"xmlns":890},[892,40784,40785,40805],{},[895,40786,40787,40789,40791,40793,40795,40797,40799,40801,40803],{},[898,40788,16690],{},[898,40790,1690],{},[898,40792,9945],{},[1716,40794,1949],{},[898,40796,16690],{},[898,40798,1690],{},[898,40800,5352],{},[1716,40802,1913],{},[1712,40804,1714],{},[902,40806,39884],{"encoding":904}," (7.5).",[123,40809,40810,40812],{},[38,40811,34366],{}," — rovnováha agregátní poptávky a nabídky.",[123,40814,40815,40818,40819,29583,40840,1853],{},[38,40816,40817],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,40820,40822],{"className":40821},[886],[888,40823,40824],{"xmlns":890},[892,40825,40826,40838],{},[895,40827,40828,40830,40832,40834,40836],{},[898,40829,1758],{},[1716,40831,1913],{},[898,40833,9945],{},[1716,40835,1949],{},[898,40837,25985],{},[902,40839,28539],{"encoding":904},[883,40841,40843],{"className":40842},[886],[888,40844,40845],{"xmlns":890},[892,40846,40847,40883],{},[895,40848,40849,40855,40857,40859,40861,40863,40869,40871,40873,40875,40877,40879,40881],{},[3074,40850,40851,40853],{},[898,40852,1758],{},[898,40854,1805],{},[1716,40856,1913],{},[1716,40858,1920],{"stretchy":1919},[898,40860,1952],{},[1716,40862,1949],{},[3074,40864,40865,40867],{},[898,40866,25985],{},[1716,40868,3080],{},[1716,40870,1925],{"stretchy":1919},[898,40872,3045],{"mathvariant":2068},[1716,40874,1920],{"stretchy":1919},[1712,40876,1714],{},[1716,40878,2760],{},[898,40880,207],{},[1716,40882,1925],{"stretchy":1919},[902,40884,40027],{"encoding":904},[123,40886,40887,40890,40891,1343,40910,29583,40935,1853],{},[38,40888,40889],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,40892,40894],{"className":40893},[886],[888,40895,40896],{"xmlns":890},[892,40897,40898,40908],{},[895,40899,40900,40902,40904,40906],{},[898,40901,4164],{},[1716,40903,1920],{"stretchy":1919},[898,40905,1758],{},[1716,40907,1925],{"stretchy":1919},[902,40909,35993],{"encoding":904},[883,40911,40913],{"className":40912},[886],[888,40914,40915],{"xmlns":890},[892,40916,40917,40933],{},[895,40918,40919,40925,40927,40929,40931],{},[1707,40920,40921,40923],{},[898,40922,1758],{},[898,40924,1916],{},[1716,40926,1913],{},[898,40928,1758],{},[1716,40930,2760],{},[898,40932,4164],{},[902,40934,35492],{"encoding":904},[883,40936,40938],{"className":40937},[886],[888,40939,40940],{"xmlns":890},[892,40941,40942,40958],{},[895,40943,40944,40946,40948,40950,40952,40954,40956],{},[898,40945,1758],{},[1716,40947,1913],{},[898,40949,9945],{},[1716,40951,1949],{},[898,40953,25985],{},[1716,40955,1949],{},[898,40957,25914],{},[902,40959,35463],{"encoding":904},[123,40961,40962,40965,40966,40987,40988,29583,41012,1853],{},[38,40963,40964],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,40967,40969],{"className":40968},[886],[888,40970,40971],{"xmlns":890},[892,40972,40973,40985],{},[895,40974,40975,40977,40979,40981,40983],{},[898,40976,26121],{},[1716,40978,1913],{},[898,40980,10856],{},[1716,40982,2760],{},[898,40984,16690],{},[902,40986,37032],{"encoding":904},", importem ",[883,40989,40991],{"className":40990},[886],[888,40992,40993],{"xmlns":890},[892,40994,40995,41009],{},[895,40996,40997,40999,41001,41007],{},[898,40998,16690],{},[1716,41000,1920],{"stretchy":1919},[1707,41002,41003,41005],{},[898,41004,1758],{},[898,41006,1916],{},[1716,41008,1925],{"stretchy":1919},[902,41010,41011],{"encoding":904},"M(Y_D)",[883,41013,41015],{"className":41014},[886],[888,41016,41017],{"xmlns":890},[892,41018,41019,41043],{},[895,41020,41021,41023,41025,41027,41029,41031,41033,41035,41037,41039,41041],{},[898,41022,1758],{},[1716,41024,1913],{},[898,41026,9945],{},[1716,41028,1949],{},[898,41030,25985],{},[1716,41032,1949],{},[898,41034,25914],{},[1716,41036,1949],{},[898,41038,10856],{},[1716,41040,2760],{},[898,41042,16690],{},[902,41044,41045],{"encoding":904},"Y = C + I + G + B - M",[123,41047,41048,3369,41051,40240],{},[38,41049,41050],{},"Multiplikátor investic",[883,41052,41054],{"className":41053},[886],[888,41055,41056],{"xmlns":890},[892,41057,41058,41106],{},[895,41059,41060,41062,41068,41070,41072,41078,41080,41082,41084,41086,41088,41090,41092,41094,41096,41098,41100,41102,41104],{},[898,41061,23677],{"mathvariant":2068},[3074,41063,41064,41066],{},[898,41065,1758],{},[898,41067,1805],{},[898,41069,3045],{"mathvariant":2068},[898,41071,23677],{"mathvariant":2068},[3074,41073,41074,41076],{},[898,41075,25985],{},[1716,41077,3080],{},[1716,41079,1913],{},[1712,41081,1714],{},[898,41083,3045],{"mathvariant":2068},[1716,41085,1920],{"stretchy":1919},[1712,41087,1714],{},[1716,41089,2760],{},[898,41091,207],{},[1716,41093,1925],{"stretchy":1919},[1716,41095,1913],{},[1712,41097,1714],{},[898,41099,3045],{"mathvariant":2068},[898,41101,16690],{},[898,41103,1690],{},[898,41105,5352],{},[902,41107,40239],{"encoding":904},[123,41109,41110,3369,41141,1343,41158,41175],{},[38,41111,29518,41112],{},[883,41113,41115],{"className":41114},[886],[888,41116,41117],{"xmlns":890},[892,41118,41119,41139],{},[895,41120,41121,41123,41125,41127,41129,41131,41133,41135,41137],{},[898,41122,25985],{},[1716,41124,1920],{"stretchy":1919},[898,41126,2098],{},[1716,41128,1925],{"stretchy":1919},[1716,41130,1913],{},[898,41132,4478],{},[898,41134,2098],{},[1716,41136,1949],{},[898,41138,5198],{},[902,41140,29548],{"encoding":904},[883,41142,41144],{"className":41143},[886],[888,41145,41146],{"xmlns":890},[892,41147,41148,41156],{},[895,41149,41150,41152,41154],{},[898,41151,4478],{},[1716,41153,2704],{},[1712,41155,2505],{},[902,41157,26315],{"encoding":904},[883,41159,41161],{"className":41160},[886],[888,41162,41163],{"xmlns":890},[892,41164,41165,41173],{},[895,41166,41167,41169,41171],{},[898,41168,5198],{},[1716,41170,2716],{},[1712,41172,2505],{},[902,41174,26294],{"encoding":904},"; klesající.",[123,41177,41178,41180,41181,41183,41184,41233],{},[38,41179,29637],{}," — rovnováha na trhu zboží (",[614,41182,25856],{},"); ",[883,41185,41187],{"className":41186},[886],[888,41188,41189],{"xmlns":890},[892,41190,41191,41231],{},[895,41192,41193,41195,41197,41209,41211,41213],{},[898,41194,1758],{},[1716,41196,1913],{},[2750,41198,41199,41201],{},[898,41200,4478],{},[895,41202,41203,41205,41207],{},[1712,41204,1714],{},[1716,41206,2760],{},[898,41208,207],{},[898,41210,2098],{},[1716,41212,1949],{},[2750,41214,41215,41223],{},[895,41216,41217,41219,41221],{},[898,41218,1952],{},[1716,41220,1949],{},[898,41222,5198],{},[895,41224,41225,41227,41229],{},[1712,41226,1714],{},[1716,41228,2760],{},[898,41230,207],{},[902,41232,29690],{"encoding":904}," (7.14); klesající.",[123,41235,41236,41238,41239,41183,41241,41286],{},[38,41237,29836],{}," — rovnováha na trhu peněz (",[614,41240,25863],{},[883,41242,41244],{"className":41243},[886],[888,41245,41246],{"xmlns":890},[892,41247,41248,41284],{},[895,41249,41250,41256,41258,41264,41266,41268,41274,41276,41278],{},[3074,41251,41252,41254],{},[898,41253,16690],{},[1716,41255,3080],{},[1716,41257,1913],{},[1707,41259,41260,41262],{},[898,41261,27035],{},[1712,41263,1714],{},[898,41265,1758],{},[1716,41267,1949],{},[1707,41269,41270,41272],{},[898,41271,27035],{},[1712,41273,1726],{},[898,41275,2098],{},[1716,41277,1949],{},[1707,41279,41280,41282],{},[898,41281,27035],{},[1712,41283,7072],{},[902,41285,29884],{"encoding":904}," (7.15); rostoucí.",[123,41288,41289,3369,41292,1853],{},[38,41290,41291],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,41293,41295],{"className":41294},[886],[888,41296,41297],{"xmlns":890},[892,41298,41299,41323],{},[895,41300,41301,41307,41309,41315,41317],{},[3074,41302,41303,41305],{},[898,41304,16690],{},[898,41306,1916],{},[1716,41308,1913],{},[1707,41310,41311,41313],{},[898,41312,1775],{},[1712,41314,1714],{},[1716,41316,1949],{},[1707,41318,41319,41321],{},[898,41320,1775],{},[1712,41322,1726],{},[902,41324,41325],{"encoding":904},"M^D = L_1 + L_2",[123,41327,41328,29894,41330,27777,41343,2247,41358,41373,41374,1853],{},[38,41329,945],{},[883,41331,41333],{"className":41332},[886],[888,41334,41335],{"xmlns":890},[892,41336,41337,41341],{},[895,41338,41339],{},[898,41340,1805],{},[902,41342,1805],{"encoding":904},[883,41344,41346],{"className":41345},[886],[888,41347,41348],{"xmlns":890},[892,41349,41350,41356],{},[895,41351,41352,41354],{},[898,41353,25985],{},[898,41355,5352],{},[902,41357,25853],{"encoding":904},[883,41359,41361],{"className":41360},[886],[888,41362,41363],{"xmlns":890},[892,41364,41365,41371],{},[895,41366,41367,41369],{},[898,41368,1775],{},[898,41370,16690],{},[902,41372,25860],{"encoding":904}," určuje ",[883,41375,41377],{"className":41376},[886],[888,41378,41379],{"xmlns":890},[892,41380,41381,41401],{},[895,41382,41383,41385,41391,41393,41399],{},[1716,41384,1920],{"stretchy":1919},[3074,41386,41387,41389],{},[898,41388,1758],{},[898,41390,1805],{},[1716,41392,1719],{"separator":1718},[3074,41394,41395,41397],{},[898,41396,2098],{},[898,41398,1805],{},[1716,41400,1925],{"stretchy":1919},[902,41402,25897],{"encoding":904},[115,41404,15740],{"id":15739},[120,41406,41407,41414,41421],{},[123,41408,41409,3495,41411],{},[38,41410,15794],{},[207,41412,15800],{"className":41413,"dataFsResolvedFilePath":15798,"href":15799},[210],[123,41415,41416,3495,41418],{},[38,41417,30002],{},[207,41419,30006],{"className":41420,"dataFsResolvedFilePath":868,"href":869},[210],[123,41422,41423,41425],{},[38,41424,30021],{},[120,41426,41427,41433,41439,41445],{},[123,41428,41429,41432],{},[207,41430,30062],{"className":41431,"dataFsResolvedFilePath":943,"href":944},[210]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,41434,41435,41438],{},[207,41436,30029],{"className":41437,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,41440,41441,41444],{},[207,41442,16818],{"className":41443,"dataFsResolvedFilePath":827,"href":828},[210]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,41446,41447,41450,41451,1343,41468,41485],{},[207,41448,1145],{"className":41449,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,41452,41454],{"className":41453},[886],[888,41455,41456],{"xmlns":890},[892,41457,41458,41466],{},[895,41459,41460,41462,41464],{},[898,41461,16690],{},[898,41463,1690],{},[898,41465,9945],{},[902,41467,31832],{"encoding":904},[883,41469,41471],{"className":41470},[886],[888,41472,41473],{"xmlns":890},[892,41474,41475,41483],{},[895,41476,41477,41479,41481],{},[898,41478,16690],{},[898,41480,1690],{},[898,41482,5352],{},[902,41484,33442],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":41487},[41488,41489,41490,41491,41496,41499,41500,41507,41512,41517,41520,41521,41522,41523],{"id":25808,"depth":642,"text":25809},{"id":31941,"depth":642,"text":31942},{"id":32061,"depth":642,"text":32062},{"id":32314,"depth":642,"text":32315,"children":41492},[41493,41494,41495],{"id":32318,"depth":649,"text":32319},{"id":32529,"depth":649,"text":32530},{"id":33036,"depth":649,"text":33037},{"id":33354,"depth":642,"text":33355,"children":41497},[41498],{"id":33870,"depth":649,"text":33871},{"id":34365,"depth":642,"text":34366},{"id":34392,"depth":642,"text":34393,"children":41501},[41502,41503,41504,41506],{"id":34403,"depth":649,"text":34404},{"id":34473,"depth":649,"text":34474},{"id":34652,"depth":649,"text":41505},"Výpočet YEY^E",{"id":34794,"depth":649,"text":34795},{"id":35171,"depth":642,"text":35172,"children":41508},[41509,41510,41511],{"id":35175,"depth":649,"text":34404},{"id":35622,"depth":649,"text":34474},{"id":36278,"depth":649,"text":36279},{"id":37063,"depth":642,"text":37064,"children":41513},[41514,41515,41516],{"id":37067,"depth":649,"text":34404},{"id":37212,"depth":649,"text":34474},{"id":37482,"depth":649,"text":37483},{"id":38405,"depth":642,"text":38406,"children":41518},[41519],{"id":38600,"depth":649,"text":38601},{"id":39150,"depth":642,"text":39151},{"id":39610,"depth":642,"text":39611},{"id":14946,"depth":642,"text":14947},{"id":15739,"depth":642,"text":15740},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,30015,1143,41530,41531,41532,30062,15855],"gnp","mpc","mps","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU",{"id":41535,"title":41536,"body":41537,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":50507,"navigation":664,"path":50508,"seo":50509,"sources":50510,"stem":50511,"tags":50512,"type":15858,"updated":677,"__hash__":50517},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":41538,"toc":50476},[41539,41542,41544,41772,41776,41829,41896,42008,42167,42171,42287,42291,42294,42416,42419,42612,42636,42704,42867,42885,42951,43329,43333,43340,43583,43639,43643,43708,43826,43957,43989,44109,44191,44194,44316,44509,44730,44734,44774,44879,44936,45036,45213,45343,45396,45399,45486,45489,45665,45669,45672,45757,45760,45817,45922,45926,46047,46050,46233,46236,46343,46552,46872,46920,46993,47067,47069,47293,47528,47796,47800,47803,47908,47965,47999,48046,48079,48163,48165,48397,48530,48607,48729,48884,48888,49029,49036,49260,49271,49275,49279,49384,49526,49636,49735,49739,49898,50007,50009,50402,50404],[12,41540,41536],{"id":41541},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,41543,25809],{"id":25808},[724,41545,41546,41548,41549,41583,41584,41587,41588,41619,41620,41666,41667,41670,41671,41713,41714,41732,41733,41737,41738,41768,41769,41771],{},[38,41547,913],{}," řeší, jaký svazek zboží ",[883,41550,41552],{"className":41551},[886],[888,41553,41554],{"xmlns":890},[892,41555,41556,41580],{},[895,41557,41558,41560,41568,41570,41578],{},[1716,41559,2502],{"stretchy":1919},[7204,41561,41562,41564,41566],{},[898,41563,1878],{},[1712,41565,1714],{},[1716,41567,3080],{},[1716,41569,1719],{"separator":1718},[7204,41571,41572,41574,41576],{},[898,41573,1878],{},[1712,41575,1726],{},[1716,41577,3080],{},[1716,41579,2516],{"stretchy":1919},[902,41581,41582],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,41585,41586],{},"primární úloha"," — maximalizace užitečnosti ",[883,41589,41591],{"className":41590},[886],[888,41592,41593],{"xmlns":890},[892,41594,41595,41617],{},[895,41596,41597,41599,41601,41607,41609,41615],{},[898,41598,900],{},[1716,41600,1920],{"stretchy":1919},[1707,41602,41603,41605],{},[898,41604,1878],{},[1712,41606,1714],{},[1716,41608,1719],{"separator":1718},[1707,41610,41611,41613],{},[898,41612,1878],{},[1712,41614,1726],{},[1716,41616,1925],{"stretchy":1919},[902,41618,30133],{"encoding":904}," při rozpočtovém omezení ",[883,41621,41623],{"className":41622},[886],[888,41624,41625],{"xmlns":890},[892,41626,41627,41663],{},[895,41628,41629,41635,41637,41643,41649,41651,41657],{},[3074,41630,41631,41633],{},[898,41632,1758],{},[1716,41634,3080],{},[1716,41636,1913],{},[1707,41638,41639,41641],{},[898,41640,1690],{},[1712,41642,1714],{},[1707,41644,41645,41647],{},[898,41646,1878],{},[1712,41648,1714],{},[1716,41650,1949],{},[1707,41652,41653,41655],{},[898,41654,1690],{},[1712,41656,1726],{},[1707,41658,41659,41661],{},[898,41660,1878],{},[1712,41662,1726],{},[902,41664,41665],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,41668,41669],{},"duální úloha"," — minimalizace výdajů ",[883,41672,41674],{"className":41673},[886],[888,41675,41676],{"xmlns":890},[892,41677,41678,41710],{},[895,41679,41680,41682,41684,41690,41696,41698,41704],{},[898,41681,1805],{},[1716,41683,1913],{},[1707,41685,41686,41688],{},[898,41687,1690],{},[1712,41689,1714],{},[1707,41691,41692,41694],{},[898,41693,1878],{},[1712,41695,1714],{},[1716,41697,1949],{},[1707,41699,41700,41702],{},[898,41701,1690],{},[1712,41703,1726],{},[1707,41705,41706,41708],{},[898,41707,1878],{},[1712,41709,1726],{},[902,41711,41712],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,41715,41717],{"className":41716},[886],[888,41718,41719],{"xmlns":890},[892,41720,41721,41729],{},[895,41722,41723],{},[3074,41724,41725,41727],{},[898,41726,900],{},[1716,41728,3080],{},[902,41730,41731],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,41734,41736],{"className":41735,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,41739,41741],{"className":41740},[886],[888,41742,41743],{"xmlns":890},[892,41744,41745,41765],{},[895,41746,41747,41749,41751,41757,41759],{},[2074,41748,24407],{},[1716,41750,1913],{},[1707,41752,41753,41755],{},[898,41754,1690],{},[1712,41756,1714],{},[898,41758,3045],{"mathvariant":2068},[1707,41760,41761,41763],{},[898,41762,1690],{},[1712,41764,1726],{},[902,41766,41767],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,41770,1993],{}," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,41773,41775],{"id":41774},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,41777,41778,41779,41797,41798,41828],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,41780,41782],{"className":41781},[886],[888,41783,41784],{"xmlns":890},[892,41785,41786,41794],{},[895,41787,41788],{},[3074,41789,41790,41792],{},[898,41791,1758],{},[1716,41793,3080],{},[902,41795,41796],{"encoding":904},"Y^*"," a ceny ",[883,41799,41801],{"className":41800},[886],[888,41802,41803],{"xmlns":890},[892,41804,41805,41825],{},[895,41806,41807,41815,41817],{},[7204,41808,41809,41811,41813],{},[898,41810,1690],{},[1712,41812,1714],{},[1716,41814,3080],{},[1716,41816,1719],{"separator":1718},[7204,41818,41819,41821,41823],{},[898,41820,1690],{},[1712,41822,1726],{},[1716,41824,3080],{},[902,41826,41827],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,41830,41832],{"className":41831},[886],[888,41833,41834],{"xmlns":890,"display":2004},[892,41835,41836,41893],{},[2008,41837,41838],{"width":2010},[2012,41839,41840,41842,41886,41888],{},[2015,41841],{"width":2017},[2015,41843,41844],{},[895,41845,41846,41852,41854,41862,41868,41870,41878,41884],{},[3074,41847,41848,41850],{},[898,41849,1758],{},[1716,41851,3080],{},[1716,41853,1913],{},[7204,41855,41856,41858,41860],{},[898,41857,1690],{},[1712,41859,1714],{},[1716,41861,3080],{},[1707,41863,41864,41866],{},[898,41865,1878],{},[1712,41867,1714],{},[1716,41869,1949],{},[7204,41871,41872,41874,41876],{},[898,41873,1690],{},[1712,41875,1726],{},[1716,41877,3080],{},[1707,41879,41880,41882],{},[898,41881,1878],{},[1712,41883,1726],{},[1716,41885,1719],{"separator":1718},[2015,41887],{"width":2017},[2015,41889,41890],{},[2074,41891,41892],{},"(6.12)",[902,41894,41895],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,41897,41898,41899,41902,41903,2247,41939,41975,41976,41989,41990,42004,42005,1853],{},"geometricky ",[38,41900,41901],{},"rozpočtová přímka (budget line)"," procházející body ",[883,41904,41906],{"className":41905},[886],[888,41907,41908],{"xmlns":890},[892,41909,41910,41936],{},[895,41911,41912,41914,41920,41922,41930,41932,41934],{},[1716,41913,2502],{"stretchy":1919},[3074,41915,41916,41918],{},[898,41917,1758],{},[1716,41919,3080],{},[898,41921,3045],{"mathvariant":2068},[7204,41923,41924,41926,41928],{},[898,41925,1690],{},[1712,41927,1714],{},[1716,41929,3080],{},[1716,41931,1719],{"separator":1718},[1712,41933,2505],{},[1716,41935,2516],{"stretchy":1919},[902,41937,41938],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,41940,41942],{"className":41941},[886],[888,41943,41944],{"xmlns":890},[892,41945,41946,41972],{},[895,41947,41948,41950,41952,41954,41960,41962,41970],{},[1716,41949,2502],{"stretchy":1919},[1712,41951,2505],{},[1716,41953,1719],{"separator":1718},[3074,41955,41956,41958],{},[898,41957,1758],{},[1716,41959,3080],{},[898,41961,3045],{"mathvariant":2068},[7204,41963,41964,41966,41968],{},[898,41965,1690],{},[1712,41967,1726],{},[1716,41969,3080],{},[1716,41971,2516],{"stretchy":1919},[902,41973,41974],{"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 ",[883,41977,41979],{"className":41978},[886],[888,41980,41981],{"xmlns":890},[892,41982,41983,41987],{},[895,41984,41985],{},[898,41986,900],{},[902,41988,900],{"encoding":904},", indiferenční křivky a ",[883,41991,41993],{"className":41992},[886],[888,41994,41995],{"xmlns":890},[892,41996,41997,42001],{},[895,41998,41999],{},[2074,42000,24407],{},[902,42002,42003],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,42006,880],{"className":42007,"dataFsResolvedFilePath":878,"href":879},[210],[1635,42009,42010],{},[724,42011,42012,42014,42015,42018,42019,42032,42033,42035,42036,42049,42050,3495,42053,42093,42094,42111,42112,42129,42130,42147,42148,42166],{},[883,42013,2233],{}," Pozor — dvě úlohy, totéž řešení\n",[38,42016,42017],{},"Primární úloha"," (max ",[883,42020,42022],{"className":42021},[886],[888,42023,42024],{"xmlns":890},[892,42025,42026,42030],{},[895,42027,42028],{},[898,42029,900],{},[902,42031,900],{"encoding":904}," při pevném rozpočtu) a ",[38,42034,41669],{}," (min ",[883,42037,42039],{"className":42038},[886],[888,42040,42041],{"xmlns":890},[892,42042,42043,42047],{},[895,42044,42045],{},[898,42046,1805],{},[902,42048,1805],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,42051,42052],{},"tentýž bod",[883,42054,42056],{"className":42055},[886],[888,42057,42058],{"xmlns":890},[892,42059,42060,42090],{},[895,42061,42062,42068,42070,42078,42080,42088],{},[3074,42063,42064,42066],{},[898,42065,1878],{},[1716,42067,3080],{},[1716,42069,2502],{"stretchy":1919},[7204,42071,42072,42074,42076],{},[898,42073,1878],{},[1712,42075,1714],{},[1716,42077,3080],{},[1716,42079,1719],{"separator":1718},[7204,42081,42082,42084,42086],{},[898,42083,1878],{},[1712,42085,1726],{},[1716,42087,3080],{},[1716,42089,2516],{"stretchy":1919},[902,42091,42092],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,42095,42097],{"className":42096},[886],[888,42098,42099],{"xmlns":890},[892,42100,42101,42109],{},[895,42102,42103],{},[3074,42104,42105,42107],{},[898,42106,1758],{},[1716,42108,3080],{},[902,42110,41796],{"encoding":904}," a hledáme maximální ",[883,42113,42115],{"className":42114},[886],[888,42116,42117],{"xmlns":890},[892,42118,42119,42127],{},[895,42120,42121],{},[3074,42122,42123,42125],{},[898,42124,900],{},[1716,42126,3080],{},[902,42128,41731],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,42131,42133],{"className":42132},[886],[888,42134,42135],{"xmlns":890},[892,42136,42137,42145],{},[895,42138,42139],{},[3074,42140,42141,42143],{},[898,42142,900],{},[1716,42144,3080],{},[902,42146,41731],{"encoding":904}," a hledáme minimální ",[883,42149,42151],{"className":42150},[886],[888,42152,42153],{"xmlns":890},[892,42154,42155,42163],{},[895,42156,42157],{},[3074,42158,42159,42161],{},[898,42160,1805],{},[1716,42162,3080],{},[902,42164,42165],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,42168,42170],{"id":42169},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,42172,42173,42174,42205,42206,42282,42283,1853],{},"Úlohou je najít maximum ",[883,42175,42177],{"className":42176},[886],[888,42178,42179],{"xmlns":890},[892,42180,42181,42203],{},[895,42182,42183,42185,42187,42193,42195,42201],{},[898,42184,900],{},[1716,42186,1920],{"stretchy":1919},[1707,42188,42189,42191],{},[898,42190,1878],{},[1712,42192,1714],{},[1716,42194,1719],{"separator":1718},[1707,42196,42197,42199],{},[898,42198,1878],{},[1712,42200,1726],{},[1716,42202,1925],{"stretchy":1919},[902,42204,30133],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,42207,42209],{"className":42208},[886],[888,42210,42211],{"xmlns":890},[892,42212,42213,42279],{},[895,42214,42215,42217,42219,42225,42227,42233,42235,42237,42243,42245,42253,42259,42261,42269,42275,42277],{},[898,42216,24845],{},[1716,42218,1920],{"stretchy":1919},[1707,42220,42221,42223],{},[898,42222,1878],{},[1712,42224,1714],{},[1716,42226,1719],{"separator":1718},[1707,42228,42229,42231],{},[898,42230,1878],{},[1712,42232,1726],{},[1716,42234,1925],{"stretchy":1919},[1716,42236,1913],{},[3074,42238,42239,42241],{},[898,42240,1758],{},[1716,42242,3080],{},[1716,42244,2760],{},[7204,42246,42247,42249,42251],{},[898,42248,1690],{},[1712,42250,1714],{},[1716,42252,3080],{},[1707,42254,42255,42257],{},[898,42256,1878],{},[1712,42258,1714],{},[1716,42260,2760],{},[7204,42262,42263,42265,42267],{},[898,42264,1690],{},[1712,42266,1726],{},[1716,42268,3080],{},[1707,42270,42271,42273],{},[898,42272,1878],{},[1712,42274,1726],{},[1716,42276,1913],{},[1712,42278,2505],{},[902,42280,42281],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,42284,42286],{"className":42285,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,42288,42290],{"id":42289},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,42292,42293],{},"Sestavíme",[883,42295,42297],{"className":42296},[886],[888,42298,42299],{"xmlns":890,"display":2004},[892,42300,42301,42413],{},[2008,42302,42303],{"width":2010},[2012,42304,42305,42307,42406,42408],{},[2015,42306],{"width":2017},[2015,42308,42309],{},[895,42310,42311,42314,42316,42322,42324,42330,42332,42334,42336,42338,42340,42342,42348,42350,42356,42358,42360,42362,42364,42370,42372,42380,42386,42388,42396,42402,42404],{},[898,42312,1775],{"mathvariant":42313},"script",[1716,42315,1920],{"stretchy":1919},[1707,42317,42318,42320],{},[898,42319,1878],{},[1712,42321,1714],{},[1716,42323,1719],{"separator":1718},[1707,42325,42326,42328],{},[898,42327,1878],{},[1712,42329,1726],{},[1716,42331,1719],{"separator":1718},[898,42333,30233],{},[1716,42335,1925],{"stretchy":1919},[1716,42337,1913],{},[898,42339,900],{},[1716,42341,1920],{"stretchy":1919},[1707,42343,42344,42346],{},[898,42345,1878],{},[1712,42347,1714],{},[1716,42349,1719],{"separator":1718},[1707,42351,42352,42354],{},[898,42353,1878],{},[1712,42355,1726],{},[1716,42357,1925],{"stretchy":1919},[1716,42359,1949],{},[898,42361,30233],{},[1716,42363,1920],{"stretchy":1919},[3074,42365,42366,42368],{},[898,42367,1758],{},[1716,42369,3080],{},[1716,42371,2760],{},[7204,42373,42374,42376,42378],{},[898,42375,1690],{},[1712,42377,1714],{},[1716,42379,3080],{},[1707,42381,42382,42384],{},[898,42383,1878],{},[1712,42385,1714],{},[1716,42387,2760],{},[7204,42389,42390,42392,42394],{},[898,42391,1690],{},[1712,42393,1726],{},[1716,42395,3080],{},[1707,42397,42398,42400],{},[898,42399,1878],{},[1712,42401,1726],{},[1716,42403,1925],{"stretchy":1919},[898,42405,1853],{"mathvariant":2068},[2015,42407],{"width":2017},[2015,42409,42410],{},[2074,42411,42412],{},"(6.13)",[902,42414,42415],{"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}",[724,42417,42418],{},"Soustava prvního řádu:",[883,42420,42422],{"className":42421},[886],[888,42423,42424],{"xmlns":890,"display":2004},[892,42425,42426,42609],{},[2008,42427,42428],{"width":2010},[2012,42429,42430,42432,42602,42604],{},[2015,42431],{"width":2017},[2015,42433,42434],{},[2008,42435,42436,42486,42536],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,42437,42438,42450],{},[2015,42439,42440],{},[2747,42441,42442],{"scriptlevel":2505,"displaystyle":1718},[7204,42443,42444,42446,42448],{},[898,42445,1775],{"mathvariant":42313},[1712,42447,1714],{},[1716,42449,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,42451,42452],{},[2747,42453,42454],{"scriptlevel":2505,"displaystyle":1718},[895,42455,42456,42458,42460,42468,42470,42472,42480,42482,42484],{},[895,42457],{},[1716,42459,1913],{},[7204,42461,42462,42464,42466],{},[898,42463,900],{},[1712,42465,1714],{},[1716,42467,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,42469,2760],{},[898,42471,30233],{},[7204,42473,42474,42476,42478],{},[898,42475,1690],{},[1712,42477,1714],{},[1716,42479,3080],{},[1716,42481,1913],{},[1712,42483,2505],{},[1716,42485,1719],{"separator":1718},[2012,42487,42488,42500],{},[2015,42489,42490],{},[2747,42491,42492],{"scriptlevel":2505,"displaystyle":1718},[7204,42493,42494,42496,42498],{},[898,42495,1775],{"mathvariant":42313},[1712,42497,1726],{},[1716,42499,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,42501,42502],{},[2747,42503,42504],{"scriptlevel":2505,"displaystyle":1718},[895,42505,42506,42508,42510,42518,42520,42522,42530,42532,42534],{},[895,42507],{},[1716,42509,1913],{},[7204,42511,42512,42514,42516],{},[898,42513,900],{},[1712,42515,1726],{},[1716,42517,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,42519,2760],{},[898,42521,30233],{},[7204,42523,42524,42526,42528],{},[898,42525,1690],{},[1712,42527,1726],{},[1716,42529,3080],{},[1716,42531,1913],{},[1712,42533,2505],{},[1716,42535,1719],{"separator":1718},[2012,42537,42538,42550],{},[2015,42539,42540],{},[2747,42541,42542],{"scriptlevel":2505,"displaystyle":1718},[7204,42543,42544,42546,42548],{},[898,42545,1775],{"mathvariant":42313},[898,42547,30233],{},[1716,42549,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,42551,42552],{},[2747,42553,42554],{"scriptlevel":2505,"displaystyle":1718},[895,42555,42556,42558,42560,42566,42568,42576,42582,42584,42592,42598,42600],{},[895,42557],{},[1716,42559,1913],{},[3074,42561,42562,42564],{},[898,42563,1758],{},[1716,42565,3080],{},[1716,42567,2760],{},[7204,42569,42570,42572,42574],{},[898,42571,1690],{},[1712,42573,1714],{},[1716,42575,3080],{},[1707,42577,42578,42580],{},[898,42579,1878],{},[1712,42581,1714],{},[1716,42583,2760],{},[7204,42585,42586,42588,42590],{},[898,42587,1690],{},[1712,42589,1726],{},[1716,42591,3080],{},[1707,42593,42594,42596],{},[898,42595,1878],{},[1712,42597,1726],{},[1716,42599,1913],{},[1712,42601,2719],{},[2015,42603],{"width":2017},[2015,42605,42606],{},[2074,42607,42608],{},"(6.14)",[902,42610,42611],{"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}",[724,42613,42614,42615,42618,42619,42632,42633,2291],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,42616,42617],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,42620,42622],{"className":42621},[886],[888,42623,42624],{"xmlns":890},[892,42625,42626,42630],{},[895,42627,42628],{},[898,42629,30233],{},[902,42631,30286],{"encoding":904}," dostáváme ",[38,42634,42635],{},"podmínku optimality",[883,42637,42639],{"className":42638},[886],[888,42640,42641],{"xmlns":890,"display":2004},[892,42642,42643,42701],{},[895,42644,42645],{},[26632,42646,42647],{"notation":26634},[2747,42648,42649],{"scriptlevel":2505,"displaystyle":1919},[2747,42650,42651],{"scriptlevel":2505,"displaystyle":1919},[2747,42652,42653],{"scriptlevel":2505,"displaystyle":1718},[895,42654,42655,42657,42659,42661,42679,42681,42699],{},[2074,42656,17830],{},[2074,42658,24407],{},[1716,42660,1913],{},[2750,42662,42663,42671],{},[7204,42664,42665,42667,42669],{},[898,42666,900],{},[1712,42668,1714],{},[1716,42670,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,42672,42673,42675,42677],{},[898,42674,900],{},[1712,42676,1726],{},[1716,42678,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,42680,1913],{},[2750,42682,42683,42691],{},[7204,42684,42685,42687,42689],{},[898,42686,1690],{},[1712,42688,1714],{},[1716,42690,3080],{},[7204,42692,42693,42695,42697],{},[898,42694,1690],{},[1712,42696,1726],{},[1716,42698,3080],{},[2074,42700,17830],{},[902,42702,42703],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1635,42705,42706],{},[724,42707,42708,42710,42711,42745,42746,42749,42750,42767,42768,42786,42787,42817,42818,42835,42836,42866],{},[883,42709,1641],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,42712,42714],{"className":42713},[886],[888,42715,42716],{"xmlns":890},[892,42717,42718,42742],{},[895,42719,42720,42722,42724,42732,42734],{},[2074,42721,24407],{},[1716,42723,1913],{},[7204,42725,42726,42728,42730],{},[898,42727,1690],{},[1712,42729,1714],{},[1716,42731,3080],{},[898,42733,3045],{"mathvariant":2068},[7204,42735,42736,42738,42740],{},[898,42737,1690],{},[1712,42739,1726],{},[1716,42741,3080],{},[902,42743,42744],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,42747,42748],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,42751,42753],{"className":42752},[886],[888,42754,42755],{"xmlns":890},[892,42756,42757,42765],{},[895,42758,42759],{},[1707,42760,42761,42763],{},[898,42762,1878],{},[1712,42764,1714],{},[902,42766,4189],{"encoding":904}," za ",[883,42769,42771],{"className":42770},[886],[888,42772,42773],{"xmlns":890},[892,42774,42775,42783],{},[895,42776,42777],{},[1707,42778,42779,42781],{},[898,42780,1878],{},[1712,42782,1726],{},[902,42784,42785],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,42788,42790],{"className":42789},[886],[888,42791,42792],{"xmlns":890},[892,42793,42794,42814],{},[895,42795,42796,42798,42800,42806,42808],{},[2074,42797,24407],{},[1716,42799,2716],{},[1707,42801,42802,42804],{},[898,42803,1690],{},[1712,42805,1714],{},[898,42807,3045],{"mathvariant":2068},[1707,42809,42810,42812],{},[898,42811,1690],{},[1712,42813,1726],{},[902,42815,42816],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,42819,42821],{"className":42820},[886],[888,42822,42823],{"xmlns":890},[892,42824,42825,42833],{},[895,42826,42827],{},[1707,42828,42829,42831],{},[898,42830,1878],{},[1712,42832,1714],{},[902,42834,4189],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,42837,42839],{"className":42838},[886],[888,42840,42841],{"xmlns":890},[892,42842,42843,42863],{},[895,42844,42845,42847,42849,42855,42857],{},[2074,42846,24407],{},[1716,42848,2704],{},[1707,42850,42851,42853],{},[898,42852,1690],{},[1712,42854,1714],{},[898,42856,3045],{"mathvariant":2068},[1707,42858,42859,42861],{},[898,42860,1690],{},[1712,42862,1726],{},[902,42864,42865],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,42868,42870,42871,42884],{"id":42869},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,42872,42874],{"className":42873},[886],[888,42875,42876],{"xmlns":890},[892,42877,42878,42882],{},[895,42879,42880],{},[898,42881,30233],{},[902,42883,30286],{"encoding":904}," — mezní užitečnost důchodu",[724,42886,42887,42888,42906,42907,42910,42911,42928,42929,42946,42947,42950],{},"Lagrangeův multiplikátor ",[883,42889,42891],{"className":42890},[886],[888,42892,42893],{"xmlns":890},[892,42894,42895,42903],{},[895,42896,42897],{},[3074,42898,42899,42901],{},[898,42900,30233],{},[1716,42902,3080],{},[902,42904,42905],{"encoding":904},"\\lambda^*"," představuje ",[38,42908,42909],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,42912,42914],{"className":42913},[886],[888,42915,42916],{"xmlns":890},[892,42917,42918,42926],{},[895,42919,42920],{},[3074,42921,42922,42924],{},[898,42923,900],{},[1716,42925,3080],{},[902,42927,41731],{"encoding":904}," při jednotkové změně důchodu ",[883,42930,42932],{"className":42931},[886],[888,42933,42934],{"xmlns":890},[892,42935,42936,42944],{},[895,42937,42938],{},[3074,42939,42940,42942],{},[898,42941,1758],{},[1716,42943,3080],{},[902,42945,41796],{"encoding":904},". Je to ",[38,42948,42949],{},"stínová cena"," rozpočtového omezení.",[1635,42952,42953,42958],{},[724,42954,42955,42957],{},[883,42956,3776],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,42959,42960,43020,43107,43143,43230],{},[123,42961,42962,42965,42966,1853],{},[38,42963,42964],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,42967,42969],{"className":42968},[886],[888,42970,42971],{"xmlns":890},[892,42972,42973,43017],{},[895,42974,42975,42981,42983,42991,42997,42999,43007,43013,43015],{},[3074,42976,42977,42979],{},[898,42978,1758],{},[1716,42980,3080],{},[1716,42982,2760],{},[7204,42984,42985,42987,42989],{},[898,42986,1690],{},[1712,42988,1714],{},[1716,42990,3080],{},[1707,42992,42993,42995],{},[898,42994,1878],{},[1712,42996,1714],{},[1716,42998,2760],{},[7204,43000,43001,43003,43005],{},[898,43002,1690],{},[1712,43004,1726],{},[1716,43006,3080],{},[1707,43008,43009,43011],{},[898,43010,1878],{},[1712,43012,1726],{},[1716,43014,1913],{},[1712,43016,2505],{},[902,43018,43019],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,43021,43022,3495,43025,1853],{},[38,43023,43024],{},"Sestav Lagrangeovu funkci",[883,43026,43028],{"className":43027},[886],[888,43029,43030],{"xmlns":890},[892,43031,43032,43104],{},[895,43033,43034,43036,43038,43040,43042,43048,43050,43056,43058,43060,43062,43064,43070,43072,43080,43086,43088,43096,43102],{},[898,43035,1775],{"mathvariant":42313},[1716,43037,1913],{},[898,43039,900],{},[1716,43041,1920],{"stretchy":1919},[1707,43043,43044,43046],{},[898,43045,1878],{},[1712,43047,1714],{},[1716,43049,1719],{"separator":1718},[1707,43051,43052,43054],{},[898,43053,1878],{},[1712,43055,1726],{},[1716,43057,1925],{"stretchy":1919},[1716,43059,1949],{},[898,43061,30233],{},[1716,43063,1920],{"stretchy":1919},[3074,43065,43066,43068],{},[898,43067,1758],{},[1716,43069,3080],{},[1716,43071,2760],{},[7204,43073,43074,43076,43078],{},[898,43075,1690],{},[1712,43077,1714],{},[1716,43079,3080],{},[1707,43081,43082,43084],{},[898,43083,1878],{},[1712,43085,1714],{},[1716,43087,2760],{},[7204,43089,43090,43092,43094],{},[898,43091,1690],{},[1712,43093,1726],{},[1716,43095,3080],{},[1707,43097,43098,43100],{},[898,43099,1878],{},[1712,43101,1726],{},[1716,43103,1925],{"stretchy":1919},[902,43105,43106],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,43108,43109,24272,43112,43142],{},[38,43110,43111],{},"Spočítej parciální derivace",[883,43113,43115],{"className":43114},[886],[888,43116,43117],{"xmlns":890},[892,43118,43119,43139],{},[895,43120,43121,43127,43129,43135,43137],{},[1707,43122,43123,43125],{},[898,43124,1878],{},[1712,43126,1714],{},[1716,43128,1719],{"separator":1718},[1707,43130,43131,43133],{},[898,43132,1878],{},[1712,43134,1726],{},[1716,43136,1719],{"separator":1718},[898,43138,30233],{},[902,43140,43141],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,43144,43145,43161,43162,43195,43196,2247,43213,1853],{},[38,43146,43147,43148],{},"Vyluč ",[883,43149,43151],{"className":43150},[886],[888,43152,43153],{"xmlns":890},[892,43154,43155,43159],{},[895,43156,43157],{},[898,43158,30233],{},[902,43160,30286],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,43163,43165],{"className":43164},[886],[888,43166,43167],{"xmlns":890},[892,43168,43169,43193],{},[895,43170,43171,43173,43175,43183,43185],{},[2074,43172,24407],{},[1716,43174,1913],{},[7204,43176,43177,43179,43181],{},[898,43178,1690],{},[1712,43180,1714],{},[1716,43182,3080],{},[898,43184,3045],{"mathvariant":2068},[7204,43186,43187,43189,43191],{},[898,43188,1690],{},[1712,43190,1726],{},[1716,43192,3080],{},[902,43194,42744],{"encoding":904},", která dá vztah mezi ",[883,43197,43199],{"className":43198},[886],[888,43200,43201],{"xmlns":890},[892,43202,43203,43211],{},[895,43204,43205],{},[1707,43206,43207,43209],{},[898,43208,1878],{},[1712,43210,1714],{},[902,43212,4189],{"encoding":904},[883,43214,43216],{"className":43215},[886],[888,43217,43218],{"xmlns":890},[892,43219,43220,43228],{},[895,43221,43222],{},[1707,43223,43224,43226],{},[898,43225,1878],{},[1712,43227,1726],{},[902,43229,42785],{"encoding":904},[123,43231,43232,43235,43236,43266,43267,43284,43285,1853],{},[38,43233,43234],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,43237,43239],{"className":43238},[886],[888,43240,43241],{"xmlns":890},[892,43242,43243,43263],{},[895,43244,43245,43253,43255],{},[7204,43246,43247,43249,43251],{},[898,43248,1878],{},[1712,43250,1714],{},[1716,43252,3080],{},[1716,43254,1719],{"separator":1718},[7204,43256,43257,43259,43261],{},[898,43258,1878],{},[1712,43260,1726],{},[1716,43262,3080],{},[902,43264,43265],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,43268,43270],{"className":43269},[886],[888,43271,43272],{"xmlns":890},[892,43273,43274,43282],{},[895,43275,43276],{},[3074,43277,43278,43280],{},[898,43279,30233],{},[1716,43281,3080],{},[902,43283,42905],{"encoding":904}," a maximální užitečnost ",[883,43286,43288],{"className":43287},[886],[888,43289,43290],{"xmlns":890},[892,43291,43292,43326],{},[895,43293,43294,43300,43302,43304,43306,43314,43316,43324],{},[3074,43295,43296,43298],{},[898,43297,900],{},[1716,43299,3080],{},[1716,43301,1913],{},[898,43303,900],{},[1716,43305,1920],{"stretchy":1919},[7204,43307,43308,43310,43312],{},[898,43309,1878],{},[1712,43311,1714],{},[1716,43313,3080],{},[1716,43315,1719],{"separator":1718},[7204,43317,43318,43320,43322],{},[898,43319,1878],{},[1712,43321,1726],{},[1716,43323,3080],{},[1716,43325,1925],{"stretchy":1919},[902,43327,43328],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,43330,43332],{"id":43331},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,43334,43335],{},[3682,43336],{"alt":43337,"className":43338,"src":43339},"imek-uzitecnost-optimum",[210,3686],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,43341,43342],{},[614,43343,43344,43345,43394,43395,2247,43423,43451,43452,43486,43487,43526,43527,43545,43546,43563,43564,43582],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,43346,43348],{"className":43347},[886],[888,43349,43350],{"xmlns":890},[892,43351,43352,43392],{},[895,43353,43354,43360,43362,43370,43376,43378,43386],{},[3074,43355,43356,43358],{},[898,43357,1758],{},[1716,43359,3080],{},[1716,43361,1913],{},[7204,43363,43364,43366,43368],{},[898,43365,1690],{},[1712,43367,1714],{},[1716,43369,3080],{},[1707,43371,43372,43374],{},[898,43373,1878],{},[1712,43375,1714],{},[1716,43377,1949],{},[7204,43379,43380,43382,43384],{},[898,43381,1690],{},[1712,43383,1726],{},[1716,43385,3080],{},[1707,43387,43388,43390],{},[898,43389,1878],{},[1712,43391,1726],{},[902,43393,31088],{"encoding":904}," protíná osy v ",[883,43396,43398],{"className":43397},[886],[888,43399,43400],{"xmlns":890},[892,43401,43402,43420],{},[895,43403,43404,43410,43412],{},[3074,43405,43406,43408],{},[898,43407,1758],{},[1716,43409,3080],{},[898,43411,3045],{"mathvariant":2068},[7204,43413,43414,43416,43418],{},[898,43415,1690],{},[1712,43417,1714],{},[1716,43419,3080],{},[902,43421,43422],{"encoding":904},"Y^*\u002FP_1^*",[883,43424,43426],{"className":43425},[886],[888,43427,43428],{"xmlns":890},[892,43429,43430,43448],{},[895,43431,43432,43438,43440],{},[3074,43433,43434,43436],{},[898,43435,1758],{},[1716,43437,3080],{},[898,43439,3045],{"mathvariant":2068},[7204,43441,43442,43444,43446],{},[898,43443,1690],{},[1712,43445,1726],{},[1716,43447,3080],{},[902,43449,43450],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,43453,43455],{"className":43454},[886],[888,43456,43457],{"xmlns":890},[892,43458,43459,43483],{},[895,43460,43461,43467,43469,43475,43477],{},[1707,43462,43463,43465],{},[898,43464,4478],{},[1712,43466,1714],{},[1716,43468,2704],{},[3074,43470,43471,43473],{},[898,43472,4478],{},[1716,43474,3080],{},[1716,43476,2704],{},[1707,43478,43479,43481],{},[898,43480,4478],{},[1712,43482,1726],{},[902,43484,43485],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,43488,43490],{"className":43489},[886],[888,43491,43492],{"xmlns":890},[892,43493,43494,43524],{},[895,43495,43496,43502,43504,43512,43514,43522],{},[3074,43497,43498,43500],{},[898,43499,1878],{},[1716,43501,3080],{},[1716,43503,2502],{"stretchy":1919},[7204,43505,43506,43508,43510],{},[898,43507,1878],{},[1712,43509,1714],{},[1716,43511,3080],{},[1716,43513,1719],{"separator":1718},[7204,43515,43516,43518,43520],{},[898,43517,1878],{},[1712,43519,1726],{},[1716,43521,3080],{},[1716,43523,2516],{"stretchy":1919},[902,43525,42092],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,43528,43530],{"className":43529},[886],[888,43531,43532],{"xmlns":890},[892,43533,43534,43542],{},[895,43535,43536],{},[3074,43537,43538,43540],{},[898,43539,4478],{},[1716,43541,3080],{},[902,43543,43544],{"encoding":904},"c^*",". Křivka ",[883,43547,43549],{"className":43548},[886],[888,43550,43551],{"xmlns":890},[892,43552,43553,43561],{},[895,43554,43555],{},[1707,43556,43557,43559],{},[898,43558,4478],{},[1712,43560,1714],{},[902,43562,4703],{"encoding":904}," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,43565,43567],{"className":43566},[886],[888,43568,43569],{"xmlns":890},[892,43570,43571,43579],{},[895,43572,43573],{},[1707,43574,43575,43577],{},[898,43576,4478],{},[1712,43578,1726],{},[902,43580,43581],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,43584,43585,43586,43589,43590,43608,43609,43638],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,43587,43588],{},"dotýkají",", tj. mají v bodě ",[883,43591,43593],{"className":43592},[886],[888,43594,43595],{"xmlns":890},[892,43596,43597,43605],{},[895,43598,43599],{},[3074,43600,43601,43603],{},[898,43602,1878],{},[1716,43604,3080],{},[902,43606,43607],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,43610,43612],{"className":43611},[886],[888,43613,43614],{"xmlns":890},[892,43615,43616,43636],{},[895,43617,43618,43620,43622,43628,43630],{},[2074,43619,24407],{},[1716,43621,1913],{},[1707,43623,43624,43626],{},[898,43625,1690],{},[1712,43627,1714],{},[898,43629,3045],{"mathvariant":2068},[1707,43631,43632,43634],{},[898,43633,1690],{},[1712,43635,1726],{},[902,43637,41767],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,43640,43642],{"id":43641},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,43644,23470,43645,43707],{},[883,43646,43648],{"className":43647},[886],[888,43649,43650],{"xmlns":890},[892,43651,43652,43704],{},[895,43653,43654,43656,43658,43664,43666,43672,43674,43676,43690],{},[898,43655,900],{},[1716,43657,1920],{"stretchy":1919},[1707,43659,43660,43662],{},[898,43661,1878],{},[1712,43663,1714],{},[1716,43665,1719],{"separator":1718},[1707,43667,43668,43670],{},[898,43669,1878],{},[1712,43671,1726],{},[1716,43673,1925],{"stretchy":1919},[1716,43675,1913],{},[7204,43677,43678,43680,43682],{},[898,43679,1878],{},[1712,43681,1714],{},[895,43683,43684,43686,43688],{},[1712,43685,1714],{},[898,43687,3045],{"mathvariant":2068},[1712,43689,1726],{},[7204,43691,43692,43694,43696],{},[898,43693,1878],{},[1712,43695,1726],{},[895,43697,43698,43700,43702],{},[1712,43699,1714],{},[898,43701,3045],{"mathvariant":2068},[1712,43703,1726],{},[902,43705,43706],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,43709,43710],{},[883,43711,43713],{"className":43712},[886],[888,43714,43715],{"xmlns":890},[892,43716,43717,43823],{},[895,43718,43719,43721,43723,43805,43807,43821],{},[2074,43720,24407],{},[1716,43722,1913],{},[2750,43724,43725,43765],{},[895,43726,43727,43735,43751],{},[2747,43728,43729],{"scriptlevel":2505,"displaystyle":1919},[2750,43730,43731,43733],{},[1712,43732,1714],{},[1712,43734,1726],{},[7204,43736,43737,43739,43741],{},[898,43738,1878],{},[1712,43740,1714],{},[895,43742,43743,43745,43747,43749],{},[1716,43744,2760],{},[1712,43746,1714],{},[898,43748,3045],{"mathvariant":2068},[1712,43750,1726],{},[7204,43752,43753,43755,43757],{},[898,43754,1878],{},[1712,43756,1726],{},[895,43758,43759,43761,43763],{},[1712,43760,1714],{},[898,43762,3045],{"mathvariant":2068},[1712,43764,1726],{},[895,43766,43767,43775,43789],{},[2747,43768,43769],{"scriptlevel":2505,"displaystyle":1919},[2750,43770,43771,43773],{},[1712,43772,1714],{},[1712,43774,1726],{},[7204,43776,43777,43779,43781],{},[898,43778,1878],{},[1712,43780,1714],{},[895,43782,43783,43785,43787],{},[1712,43784,1714],{},[898,43786,3045],{"mathvariant":2068},[1712,43788,1726],{},[7204,43790,43791,43793,43795],{},[898,43792,1878],{},[1712,43794,1726],{},[895,43796,43797,43799,43801,43803],{},[1716,43798,2760],{},[1712,43800,1714],{},[898,43802,3045],{"mathvariant":2068},[1712,43804,1726],{},[1716,43806,1913],{},[2750,43808,43809,43815],{},[1707,43810,43811,43813],{},[898,43812,1878],{},[1712,43814,1726],{},[1707,43816,43817,43819],{},[898,43818,1878],{},[1712,43820,1714],{},[898,43822,1853],{"mathvariant":2068},[902,43824,43825],{"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}.",[724,43827,9827,43828,7636,43873,43875,43876,43896,43897,43927,43928,1853],{},[883,43829,43831],{"className":43830},[886],[888,43832,43833],{"xmlns":890},[892,43834,43835,43870],{},[895,43836,43837,43839,43841,43844,43846,43848,43850,43852,43860,43862],{},[2074,43838,24407],{},[1716,43840,1920],{"stretchy":1919},[1712,43842,43843],{},"300",[1716,43845,1719],{"separator":1718},[1712,43847,28904],{},[1716,43849,1925],{"stretchy":1919},[1716,43851,1913],{},[2747,43853,43854],{"scriptlevel":2505,"displaystyle":1919},[2750,43855,43856,43858],{},[1712,43857,28904],{},[1712,43859,43843],{},[1716,43861,1913],{},[2747,43863,43864],{"scriptlevel":2505,"displaystyle":1919},[2750,43865,43866,43868],{},[1712,43867,6985],{},[1712,43869,7072],{},[902,43871,43872],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,43874,23026],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,43877,43879],{"className":43878},[886],[888,43880,43881],{"xmlns":890},[892,43882,43883,43893],{},[895,43884,43885],{},[2747,43886,43887],{"scriptlevel":2505,"displaystyle":1919},[2750,43888,43889,43891],{},[1712,43890,6985],{},[1712,43892,7072],{},[902,43894,43895],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,43898,43900],{"className":43899},[886],[888,43901,43902],{"xmlns":890},[892,43903,43904,43924],{},[895,43905,43906,43908,43910,43916,43918],{},[2074,43907,24407],{},[1716,43909,1913],{},[1707,43911,43912,43914],{},[898,43913,1878],{},[1712,43915,1726],{},[898,43917,3045],{"mathvariant":2068},[1707,43919,43920,43922],{},[898,43921,1878],{},[1712,43923,1714],{},[902,43925,43926],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,43929,43931],{"className":43930},[886],[888,43932,43933],{"xmlns":890},[892,43934,43935,43955],{},[895,43936,43937,43939,43941,43947,43949],{},[2074,43938,24407],{},[1716,43940,1913],{},[1707,43942,43943,43945],{},[898,43944,1690],{},[1712,43946,1714],{},[898,43948,3045],{"mathvariant":2068},[1707,43950,43951,43953],{},[898,43952,1690],{},[1712,43954,1726],{},[902,43956,41767],{"encoding":904},[115,43958,43960,43961],{"id":43959},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,43962,43964],{"className":43963},[886],[888,43965,43966],{"xmlns":890},[892,43967,43968,43986],{},[895,43969,43970,43972,43974,43980],{},[898,43971,900],{},[1716,43973,1913],{},[1707,43975,43976,43978],{},[898,43977,1878],{},[1712,43979,1714],{},[1707,43981,43982,43984],{},[898,43983,1878],{},[1712,43985,1726],{},[902,43987,43988],{"encoding":904},"U = Q_1 Q_2",[724,43990,43991,43992,1343,44038,1343,44062,1343,44086,44108],{},"Je dána ",[883,43993,43995],{"className":43994},[886],[888,43996,43997],{"xmlns":890},[892,43998,43999,44035],{},[895,44000,44001,44003,44005,44011,44013,44019,44021,44023,44029],{},[898,44002,900],{},[1716,44004,1920],{"stretchy":1919},[1707,44006,44007,44009],{},[898,44008,1878],{},[1712,44010,1714],{},[1716,44012,1719],{"separator":1718},[1707,44014,44015,44017],{},[898,44016,1878],{},[1712,44018,1726],{},[1716,44020,1925],{"stretchy":1919},[1716,44022,1913],{},[1707,44024,44025,44027],{},[898,44026,1878],{},[1712,44028,1714],{},[1707,44030,44031,44033],{},[898,44032,1878],{},[1712,44034,1726],{},[902,44036,44037],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,44039,44041],{"className":44040},[886],[888,44042,44043],{"xmlns":890},[892,44044,44045,44059],{},[895,44046,44047,44055,44057],{},[7204,44048,44049,44051,44053],{},[898,44050,1690],{},[1712,44052,1714],{},[1716,44054,3080],{},[1716,44056,1913],{},[1712,44058,1726],{},[902,44060,44061],{"encoding":904},"P_1^* = 2",[883,44063,44065],{"className":44064},[886],[888,44066,44067],{"xmlns":890},[892,44068,44069,44083],{},[895,44070,44071,44079,44081],{},[7204,44072,44073,44075,44077],{},[898,44074,1690],{},[1712,44076,1726],{},[1716,44078,3080],{},[1716,44080,1913],{},[1712,44082,6985],{},[902,44084,44085],{"encoding":904},"P_2^* = 5",[883,44087,44089],{"className":44088},[886],[888,44090,44091],{"xmlns":890},[892,44092,44093,44105],{},[895,44094,44095,44101,44103],{},[3074,44096,44097,44099],{},[898,44098,1758],{},[1716,44100,3080],{},[1716,44102,1913],{},[1712,44104,12151],{},[902,44106,44107],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,44110,44112],{"className":44111},[886],[888,44113,44114],{"xmlns":890,"display":2004},[892,44115,44116,44188],{},[895,44117,44118,44120,44122,44128,44130,44136,44138,44140,44142,44144,44150,44156,44158,44160,44162,44164,44166,44168,44174,44176,44178,44184,44186],{},[898,44119,1775],{"mathvariant":42313},[1716,44121,1920],{"stretchy":1919},[1707,44123,44124,44126],{},[898,44125,1878],{},[1712,44127,1714],{},[1716,44129,1719],{"separator":1718},[1707,44131,44132,44134],{},[898,44133,1878],{},[1712,44135,1726],{},[1716,44137,1719],{"separator":1718},[898,44139,30233],{},[1716,44141,1925],{"stretchy":1919},[1716,44143,1913],{},[1707,44145,44146,44148],{},[898,44147,1878],{},[1712,44149,1714],{},[1707,44151,44152,44154],{},[898,44153,1878],{},[1712,44155,1726],{},[1716,44157,1949],{},[898,44159,30233],{},[1716,44161,1920],{"stretchy":1919},[1712,44163,12151],{},[1716,44165,2760],{},[1712,44167,1726],{},[1707,44169,44170,44172],{},[898,44171,1878],{},[1712,44173,1714],{},[1716,44175,2760],{},[1712,44177,6985],{},[1707,44179,44180,44182],{},[898,44181,1878],{},[1712,44183,1726],{},[1716,44185,1925],{"stretchy":1919},[898,44187,1853],{"mathvariant":2068},[902,44189,44190],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,44192,44193],{},"Soustava:",[883,44195,44197],{"className":44196},[886],[888,44198,44199],{"xmlns":890,"display":2004},[892,44200,44201,44313],{},[2008,44202,44203,44237,44271],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,44204,44205,44223],{},[2015,44206,44207],{},[2747,44208,44209],{"scriptlevel":2505,"displaystyle":1718},[895,44210,44211,44217,44219,44221],{},[1707,44212,44213,44215],{},[898,44214,1878],{},[1712,44216,1726],{},[1716,44218,2760],{},[1712,44220,1726],{},[898,44222,30233],{},[2015,44224,44225],{},[2747,44226,44227],{"scriptlevel":2505,"displaystyle":1718},[895,44228,44229,44231,44233,44235],{},[895,44230],{},[1716,44232,1913],{},[1712,44234,2505],{},[1716,44236,1719],{"separator":1718},[2012,44238,44239,44257],{},[2015,44240,44241],{},[2747,44242,44243],{"scriptlevel":2505,"displaystyle":1718},[895,44244,44245,44251,44253,44255],{},[1707,44246,44247,44249],{},[898,44248,1878],{},[1712,44250,1714],{},[1716,44252,2760],{},[1712,44254,6985],{},[898,44256,30233],{},[2015,44258,44259],{},[2747,44260,44261],{"scriptlevel":2505,"displaystyle":1718},[895,44262,44263,44265,44267,44269],{},[895,44264],{},[1716,44266,1913],{},[1712,44268,2505],{},[1716,44270,1719],{"separator":1718},[2012,44272,44273,44301],{},[2015,44274,44275],{},[2747,44276,44277],{"scriptlevel":2505,"displaystyle":1718},[895,44278,44279,44281,44283,44285,44291,44293,44295],{},[1712,44280,12151],{},[1716,44282,2760],{},[1712,44284,1726],{},[1707,44286,44287,44289],{},[898,44288,1878],{},[1712,44290,1714],{},[1716,44292,2760],{},[1712,44294,6985],{},[1707,44296,44297,44299],{},[898,44298,1878],{},[1712,44300,1726],{},[2015,44302,44303],{},[2747,44304,44305],{"scriptlevel":2505,"displaystyle":1718},[895,44306,44307,44309,44311],{},[895,44308],{},[1716,44310,1913],{},[1712,44312,2719],{},[902,44314,44315],{"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}",[724,44317,44318,44319,1343,44343,44367,44368,19417,44408,44426,44427,44477,44478,1853],{},"Z prvních dvou rovnic ",[883,44320,44322],{"className":44321},[886],[888,44323,44324],{"xmlns":890},[892,44325,44326,44340],{},[895,44327,44328,44334,44336,44338],{},[1707,44329,44330,44332],{},[898,44331,1878],{},[1712,44333,1726],{},[1716,44335,1913],{},[1712,44337,1726],{},[898,44339,30233],{},[902,44341,44342],{"encoding":904},"Q_2 = 2\\lambda",[883,44344,44346],{"className":44345},[886],[888,44347,44348],{"xmlns":890},[892,44349,44350,44364],{},[895,44351,44352,44358,44360,44362],{},[1707,44353,44354,44356],{},[898,44355,1878],{},[1712,44357,1714],{},[1716,44359,1913],{},[1712,44361,6985],{},[898,44363,30233],{},[902,44365,44366],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,44369,44371],{"className":44370},[886],[888,44372,44373],{"xmlns":890},[892,44374,44375,44405],{},[895,44376,44377,44379,44381,44383,44385,44387,44389,44391,44393,44395,44397,44399,44401,44403],{},[1712,44378,12151],{},[1716,44380,1913],{},[1712,44382,1726],{},[1716,44384,9532],{},[1712,44386,6985],{},[898,44388,30233],{},[1716,44390,1949],{},[1712,44392,6985],{},[1716,44394,9532],{},[1712,44396,1726],{},[898,44398,30233],{},[1716,44400,1913],{},[1712,44402,2976],{},[898,44404,30233],{},[902,44406,44407],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,44409,44411],{"className":44410},[886],[888,44412,44413],{"xmlns":890},[892,44414,44415,44423],{},[895,44416,44417,44419,44421],{},[898,44418,30233],{},[1716,44420,1913],{},[1712,44422,6985],{},[902,44424,44425],{"encoding":904},"\\lambda = 5",". Odtud ",[38,44428,44429,1343,44453],{},[883,44430,44432],{"className":44431},[886],[888,44433,44434],{"xmlns":890},[892,44435,44436,44450],{},[895,44437,44438,44446,44448],{},[7204,44439,44440,44442,44444],{},[898,44441,1878],{},[1712,44443,1714],{},[1716,44445,3080],{},[1716,44447,1913],{},[1712,44449,5778],{},[902,44451,44452],{"encoding":904},"Q_1^* = 25",[883,44454,44456],{"className":44455},[886],[888,44457,44458],{"xmlns":890},[892,44459,44460,44474],{},[895,44461,44462,44470,44472],{},[7204,44463,44464,44466,44468],{},[898,44465,1878],{},[1712,44467,1726],{},[1716,44469,3080],{},[1716,44471,1913],{},[1712,44473,2998],{},[902,44475,44476],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,44479,44481],{"className":44480},[886],[888,44482,44483],{"xmlns":890},[892,44484,44485,44506],{},[895,44486,44487,44493,44495,44497,44499,44501,44503],{},[3074,44488,44489,44491],{},[898,44490,900],{},[1716,44492,3080],{},[1716,44494,1913],{},[1712,44496,5778],{},[1716,44498,9532],{},[1712,44500,2998],{},[1716,44502,1913],{},[1712,44504,44505],{},"250",[902,44507,44508],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,44510,44511],{},[614,44512,44513,44514,41902,44552,2247,44576,44600,44601,44631,44632,44656,44657,44679,44680,1853],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,44515,44517],{"className":44516},[886],[888,44518,44519],{"xmlns":890},[892,44520,44521,44549],{},[895,44522,44523,44525,44527,44529,44535,44537,44539,44545,44547],{},[1712,44524,12151],{},[1716,44526,2760],{},[1712,44528,1726],{},[1707,44530,44531,44533],{},[898,44532,1878],{},[1712,44534,1714],{},[1716,44536,2760],{},[1712,44538,6985],{},[1707,44540,44541,44543],{},[898,44542,1878],{},[1712,44544,1726],{},[1716,44546,1913],{},[1712,44548,2505],{},[902,44550,44551],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,44553,44555],{"className":44554},[886],[888,44556,44557],{"xmlns":890},[892,44558,44559,44573],{},[895,44560,44561,44563,44565,44567,44569,44571],{},[898,44562,10871],{},[1716,44564,2502],{"stretchy":1919},[1712,44566,2505],{},[1716,44568,1719],{"separator":1718},[1712,44570,2976],{},[1716,44572,2516],{"stretchy":1919},[902,44574,44575],{"encoding":904},"A[0, 20]",[883,44577,44579],{"className":44578},[886],[888,44580,44581],{"xmlns":890},[892,44582,44583,44597],{},[895,44584,44585,44587,44589,44591,44593,44595],{},[898,44586,10856],{},[1716,44588,2502],{"stretchy":1919},[1712,44590,5808],{},[1716,44592,1719],{"separator":1718},[1712,44594,2505],{},[1716,44596,2516],{"stretchy":1919},[902,44598,44599],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,44602,44604],{"className":44603},[886],[888,44605,44606],{"xmlns":890},[892,44607,44608,44628],{},[895,44609,44610,44616,44618,44620,44622],{},[1707,44611,44612,44614],{},[898,44613,1878],{},[1712,44615,1726],{},[1716,44617,1913],{},[1712,44619,44505],{},[898,44621,3045],{"mathvariant":2068},[1707,44623,44624,44626],{},[898,44625,1878],{},[1712,44627,1714],{},[902,44629,44630],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,44633,44635],{"className":44634},[886],[888,44636,44637],{"xmlns":890},[892,44638,44639,44653],{},[895,44640,44641,44643,44645,44647,44649,44651],{},[898,44642,1805],{},[1716,44644,2502],{"stretchy":1919},[1712,44646,5778],{},[1716,44648,1719],{"separator":1718},[1712,44650,2998],{},[1716,44652,2516],{"stretchy":1919},[902,44654,44655],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,44658,44660],{"className":44659},[886],[888,44661,44662],{"xmlns":890},[892,44663,44664,44676],{},[895,44665,44666,44668],{},[1716,44667,2760],{},[2747,44669,44670],{"scriptlevel":2505,"displaystyle":1919},[2750,44671,44672,44674],{},[1712,44673,1726],{},[1712,44675,6985],{},[902,44677,44678],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,44681,44683],{"className":44682},[886],[888,44684,44685],{"xmlns":890},[892,44686,44687,44727],{},[895,44688,44689,44691,44693,44695,44697,44699,44701,44703,44705,44707,44715,44717,44719],{},[1716,44690,2760],{},[2074,44692,24407],{},[1716,44694,1920],{"stretchy":1919},[1712,44696,5778],{},[1716,44698,1719],{"separator":1718},[1712,44700,2998],{},[1716,44702,1925],{"stretchy":1919},[1716,44704,1913],{},[1716,44706,2760],{},[2747,44708,44709],{"scriptlevel":2505,"displaystyle":1919},[2750,44710,44711,44713],{},[1712,44712,2998],{},[1712,44714,5778],{},[1716,44716,1913],{},[1716,44718,2760],{},[2747,44720,44721],{"scriptlevel":2505,"displaystyle":1919},[2750,44722,44723,44725],{},[1712,44724,1726],{},[1712,44726,6985],{},[902,44728,44729],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,44731,44733],{"id":44732},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,44735,44736,44737,42767,44767,44770,44771,2291],{},"Považujeme-li v úloze ",[883,44738,44740],{"className":44739},[886],[888,44741,44742],{"xmlns":890},[892,44743,44744,44764],{},[895,44745,44746,44752,44754,44760,44762],{},[1707,44747,44748,44750],{},[898,44749,1690],{},[1712,44751,1714],{},[1716,44753,1719],{"separator":1718},[1707,44755,44756,44758],{},[898,44757,1690],{},[1712,44759,1726],{},[1716,44761,1719],{"separator":1718},[898,44763,1758],{},[902,44765,44766],{"encoding":904},"P_1, P_2, Y",[38,44768,44769],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,44772,44773],{},"Marshallovy poptávkové funkce",[883,44775,44777],{"className":44776},[886],[888,44778,44779],{"xmlns":890,"display":2004},[892,44780,44781,44876],{},[2008,44782,44783],{"width":2010},[2012,44784,44785,44787,44869,44871],{},[2015,44786],{"width":2017},[2015,44788,44789],{},[895,44790,44791,44797,44799,44805,44807,44813,44815,44821,44823,44825,44827,44829,44831,44837,44839,44845,44847,44853,44855,44861,44863,44865,44867],{},[1707,44792,44793,44795],{},[898,44794,1878],{},[1712,44796,1714],{},[1716,44798,1913],{},[1707,44800,44801,44803],{},[898,44802,1916],{},[1712,44804,1714],{},[1716,44806,1920],{"stretchy":1919},[1707,44808,44809,44811],{},[898,44810,1690],{},[1712,44812,1714],{},[1716,44814,1719],{"separator":1718},[1707,44816,44817,44819],{},[898,44818,1690],{},[1712,44820,1726],{},[1716,44822,1719],{"separator":1718},[898,44824,1758],{},[1716,44826,1925],{"stretchy":1919},[1716,44828,1719],{"separator":1718},[2324,44830],{"width":8689},[1707,44832,44833,44835],{},[898,44834,1878],{},[1712,44836,1726],{},[1716,44838,1913],{},[1707,44840,44841,44843],{},[898,44842,1916],{},[1712,44844,1726],{},[1716,44846,1920],{"stretchy":1919},[1707,44848,44849,44851],{},[898,44850,1690],{},[1712,44852,1714],{},[1716,44854,1719],{"separator":1718},[1707,44856,44857,44859],{},[898,44858,1690],{},[1712,44860,1726],{},[1716,44862,1719],{"separator":1718},[898,44864,1758],{},[1716,44866,1925],{"stretchy":1919},[1716,44868,1719],{"separator":1718},[2015,44870],{"width":2017},[2015,44872,44873],{},[2074,44874,44875],{},"(6.15)",[902,44877,44878],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,44880,44882],{"className":44881},[886],[888,44883,44884],{"xmlns":890,"display":2004},[892,44885,44886,44933],{},[2008,44887,44888],{"width":2010},[2012,44889,44890,44892,44926,44928],{},[2015,44891],{"width":2017},[2015,44893,44894],{},[895,44895,44896,44898,44900,44902,44904,44910,44912,44918,44920,44922,44924],{},[898,44897,30233],{},[1716,44899,1913],{},[898,44901,30233],{},[1716,44903,1920],{"stretchy":1919},[1707,44905,44906,44908],{},[898,44907,1690],{},[1712,44909,1714],{},[1716,44911,1719],{"separator":1718},[1707,44913,44914,44916],{},[898,44915,1690],{},[1712,44917,1726],{},[1716,44919,1719],{"separator":1718},[898,44921,1758],{},[1716,44923,1925],{"stretchy":1919},[898,44925,1853],{"mathvariant":2068},[2015,44927],{"width":2017},[2015,44929,44930],{},[2074,44931,44932],{},"(6.16)",[902,44934,44935],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,44937,44938,44968,44969,45035],{},[38,44939,44940,44941,1853],{},"Odvození pro ",[883,44942,44944],{"className":44943},[886],[888,44945,44946],{"xmlns":890},[892,44947,44948,44966],{},[895,44949,44950,44952,44954,44960],{},[898,44951,900],{},[1716,44953,1913],{},[1707,44955,44956,44958],{},[898,44957,1878],{},[1712,44959,1714],{},[1707,44961,44962,44964],{},[898,44963,1878],{},[1712,44965,1726],{},[902,44967,43988],{"encoding":904}," Lagrangeova funkce ",[883,44970,44972],{"className":44971},[886],[888,44973,44974],{"xmlns":890},[892,44975,44976,45032],{},[895,44977,44978,44980,44982,44988,44994,44996,44998,45000,45002,45004,45010,45016,45018,45024,45030],{},[898,44979,1775],{"mathvariant":42313},[1716,44981,1913],{},[1707,44983,44984,44986],{},[898,44985,1878],{},[1712,44987,1714],{},[1707,44989,44990,44992],{},[898,44991,1878],{},[1712,44993,1726],{},[1716,44995,1949],{},[898,44997,30233],{},[1716,44999,1920],{"stretchy":1919},[898,45001,1758],{},[1716,45003,2760],{},[1707,45005,45006,45008],{},[898,45007,1690],{},[1712,45009,1714],{},[1707,45011,45012,45014],{},[898,45013,1878],{},[1712,45015,1714],{},[1716,45017,2760],{},[1707,45019,45020,45022],{},[898,45021,1690],{},[1712,45023,1726],{},[1707,45025,45026,45028],{},[898,45027,1878],{},[1712,45029,1726],{},[1716,45031,1925],{"stretchy":1919},[902,45033,45034],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,45037,45039],{"className":45038},[886],[888,45040,45041],{"xmlns":890,"display":2004},[892,45042,45043,45210],{},[2008,45044,45045],{"width":2010},[2012,45046,45047,45049,45203,45205],{},[2015,45048],{"width":2017},[2015,45050,45051],{},[2008,45052,45053,45099,45145],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,45054,45055,45067],{},[2015,45056,45057],{},[2747,45058,45059],{"scriptlevel":2505,"displaystyle":1718},[7204,45060,45061,45063,45065],{},[898,45062,1775],{"mathvariant":42313},[1712,45064,1714],{},[1716,45066,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,45068,45069],{},[2747,45070,45071],{"scriptlevel":2505,"displaystyle":1718},[895,45072,45073,45075,45077,45083,45085,45087,45093,45095,45097],{},[895,45074],{},[1716,45076,1913],{},[1707,45078,45079,45081],{},[898,45080,1878],{},[1712,45082,1726],{},[1716,45084,2760],{},[898,45086,30233],{},[1707,45088,45089,45091],{},[898,45090,1690],{},[1712,45092,1714],{},[1716,45094,1913],{},[1712,45096,2505],{},[1716,45098,1719],{"separator":1718},[2012,45100,45101,45113],{},[2015,45102,45103],{},[2747,45104,45105],{"scriptlevel":2505,"displaystyle":1718},[7204,45106,45107,45109,45111],{},[898,45108,1775],{"mathvariant":42313},[1712,45110,1726],{},[1716,45112,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,45114,45115],{},[2747,45116,45117],{"scriptlevel":2505,"displaystyle":1718},[895,45118,45119,45121,45123,45129,45131,45133,45139,45141,45143],{},[895,45120],{},[1716,45122,1913],{},[1707,45124,45125,45127],{},[898,45126,1878],{},[1712,45128,1714],{},[1716,45130,2760],{},[898,45132,30233],{},[1707,45134,45135,45137],{},[898,45136,1690],{},[1712,45138,1726],{},[1716,45140,1913],{},[1712,45142,2505],{},[1716,45144,1719],{"separator":1718},[2012,45146,45147,45159],{},[2015,45148,45149],{},[2747,45150,45151],{"scriptlevel":2505,"displaystyle":1718},[7204,45152,45153,45155,45157],{},[898,45154,1775],{"mathvariant":42313},[898,45156,30233],{},[1716,45158,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,45160,45161],{},[2747,45162,45163],{"scriptlevel":2505,"displaystyle":1718},[895,45164,45165,45167,45169,45171,45173,45179,45185,45187,45193,45199,45201],{},[895,45166],{},[1716,45168,1913],{},[898,45170,1758],{},[1716,45172,2760],{},[1707,45174,45175,45177],{},[898,45176,1690],{},[1712,45178,1714],{},[1707,45180,45181,45183],{},[898,45182,1878],{},[1712,45184,1714],{},[1716,45186,2760],{},[1707,45188,45189,45191],{},[898,45190,1690],{},[1712,45192,1726],{},[1707,45194,45195,45197],{},[898,45196,1878],{},[1712,45198,1726],{},[1716,45200,1913],{},[1712,45202,2719],{},[2015,45204],{"width":2017},[2015,45206,45207],{},[2074,45208,45209],{},"(6.17)",[902,45211,45212],{"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}",[724,45214,45215,45216,45244,45245,45273,45274,45342],{},"Z prvních dvou: ",[883,45217,45219],{"className":45218},[886],[888,45220,45221],{"xmlns":890},[892,45222,45223,45241],{},[895,45224,45225,45231,45233,45239],{},[1707,45226,45227,45229],{},[898,45228,1878],{},[1712,45230,1726],{},[1716,45232,1913],{},[1707,45234,45235,45237],{},[898,45236,1690],{},[1712,45238,1714],{},[898,45240,30233],{},[902,45242,45243],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,45246,45248],{"className":45247},[886],[888,45249,45250],{"xmlns":890},[892,45251,45252,45270],{},[895,45253,45254,45260,45262,45268],{},[1707,45255,45256,45258],{},[898,45257,1878],{},[1712,45259,1714],{},[1716,45261,1913],{},[1707,45263,45264,45266],{},[898,45265,1690],{},[1712,45267,1726],{},[898,45269,30233],{},[902,45271,45272],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,45275,45277],{"className":45276},[886],[888,45278,45279],{"xmlns":890},[892,45280,45281,45339],{},[895,45282,45283,45285,45287,45293,45295,45301,45303,45305,45311,45313,45319,45321,45323,45325,45331,45337],{},[898,45284,1758],{},[1716,45286,1913],{},[1707,45288,45289,45291],{},[898,45290,1690],{},[1712,45292,1714],{},[1716,45294,9532],{},[1707,45296,45297,45299],{},[898,45298,1690],{},[1712,45300,1726],{},[898,45302,30233],{},[1716,45304,1949],{},[1707,45306,45307,45309],{},[898,45308,1690],{},[1712,45310,1726],{},[1716,45312,9532],{},[1707,45314,45315,45317],{},[898,45316,1690],{},[1712,45318,1714],{},[898,45320,30233],{},[1716,45322,1913],{},[1712,45324,1726],{},[1707,45326,45327,45329],{},[898,45328,1690],{},[1712,45330,1714],{},[1707,45332,45333,45335],{},[898,45334,1690],{},[1712,45336,1726],{},[898,45338,30233],{},[902,45340,45341],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,45344,45346],{"className":45345},[886],[888,45347,45348],{"xmlns":890,"display":2004},[892,45349,45350,45393],{},[2008,45351,45352],{"width":2010},[2012,45353,45354,45356,45386,45388],{},[2015,45355],{"width":2017},[2015,45357,45358],{},[895,45359,45360,45362,45364,45384],{},[898,45361,30233],{},[1716,45363,1913],{},[2750,45365,45366,45368],{},[898,45367,1758],{},[895,45369,45370,45372,45378],{},[1712,45371,1726],{},[1707,45373,45374,45376],{},[898,45375,1690],{},[1712,45377,1714],{},[1707,45379,45380,45382],{},[898,45381,1690],{},[1712,45383,1726],{},[898,45385,1853],{"mathvariant":2068},[2015,45387],{"width":2017},[2015,45389,45390],{},[2074,45391,45392],{},"(6.20)",[902,45394,45395],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,45397,45398],{},"Zpětně:",[883,45400,45402],{"className":45401},[886],[888,45403,45404],{"xmlns":890,"display":2004},[892,45405,45406,45483],{},[2008,45407,45408],{"width":2010},[2012,45409,45410,45412,45476,45478],{},[2015,45411],{"width":2017},[2015,45413,45414],{},[26632,45415,45416],{"notation":26634},[2747,45417,45418],{"scriptlevel":2505,"displaystyle":1919},[2747,45419,45420],{"scriptlevel":2505,"displaystyle":1919},[2747,45421,45422],{"scriptlevel":2505,"displaystyle":1718},[895,45423,45424,45426,45432,45434,45448,45450,45452,45458,45460,45474],{},[2074,45425,17830],{},[1707,45427,45428,45430],{},[898,45429,1878],{},[1712,45431,1714],{},[1716,45433,1913],{},[2750,45435,45436,45438],{},[898,45437,1758],{},[895,45439,45440,45442],{},[1712,45441,1726],{},[1707,45443,45444,45446],{},[898,45445,1690],{},[1712,45447,1714],{},[1716,45449,1719],{"separator":1718},[2324,45451],{"width":8689},[1707,45453,45454,45456],{},[898,45455,1878],{},[1712,45457,1726],{},[1716,45459,1913],{},[2750,45461,45462,45464],{},[898,45463,1758],{},[895,45465,45466,45468],{},[1712,45467,1726],{},[1707,45469,45470,45472],{},[898,45471,1690],{},[1712,45473,1726],{},[2074,45475,17830],{},[2015,45477],{"width":2017},[2015,45479,45480],{},[2074,45481,45482],{},"(6.21)",[902,45484,45485],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,45487,15128],{"id":45488},"engelova-funkce",[724,45490,23470,45491,45494,45495,45498,45499,33650,45516,1343,45546,45576,45577,45611,45612,1343,45638,45664],{},[38,45492,45493],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,45496,45497],{},"Engelovou funkcí",": pro ",[883,45500,45502],{"className":45501},[886],[888,45503,45504],{"xmlns":890},[892,45505,45506,45514],{},[895,45507,45508,45510,45512],{},[898,45509,1758],{},[1716,45511,1913],{},[1712,45513,12151],{},[902,45515,34102],{"encoding":904},[883,45517,45519],{"className":45518},[886],[888,45520,45521],{"xmlns":890},[892,45522,45523,45543],{},[895,45524,45525,45531,45533,45535,45537],{},[1707,45526,45527,45529],{},[898,45528,1878],{},[1712,45530,1714],{},[1716,45532,1913],{},[1712,45534,5808],{},[898,45536,3045],{"mathvariant":2068},[1707,45538,45539,45541],{},[898,45540,1690],{},[1712,45542,1714],{},[902,45544,45545],{"encoding":904},"Q_1 = 50\u002FP_1",[883,45547,45549],{"className":45548},[886],[888,45550,45551],{"xmlns":890},[892,45552,45553,45573],{},[895,45554,45555,45561,45563,45565,45567],{},[1707,45556,45557,45559],{},[898,45558,1878],{},[1712,45560,1726],{},[1716,45562,1913],{},[1712,45564,5808],{},[898,45566,3045],{"mathvariant":2068},[1707,45568,45569,45571],{},[898,45570,1690],{},[1712,45572,1726],{},[902,45574,45575],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,45578,45580],{"className":45579},[886],[888,45581,45582],{"xmlns":890},[892,45583,45584,45608],{},[895,45585,45586,45592,45594,45596,45598,45604,45606],{},[1707,45587,45588,45590],{},[898,45589,1690],{},[1712,45591,1714],{},[1716,45593,1913],{},[1712,45595,2998],{},[1716,45597,1719],{"separator":1718},[1707,45599,45600,45602],{},[898,45601,1690],{},[1712,45603,1726],{},[1716,45605,1913],{},[1712,45607,2976],{},[902,45609,45610],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,45613,45615],{"className":45614},[886],[888,45616,45617],{"xmlns":890},[892,45618,45619,45635],{},[895,45620,45621,45627,45629,45631,45633],{},[1707,45622,45623,45625],{},[898,45624,1878],{},[1712,45626,1714],{},[1716,45628,1913],{},[898,45630,1758],{},[898,45632,3045],{"mathvariant":2068},[1712,45634,2976],{},[902,45636,45637],{"encoding":904},"Q_1 = Y\u002F20",[883,45639,45641],{"className":45640},[886],[888,45642,45643],{"xmlns":890},[892,45644,45645,45661],{},[895,45646,45647,45653,45655,45657,45659],{},[1707,45648,45649,45651],{},[898,45650,1878],{},[1712,45652,1726],{},[1716,45654,1913],{},[898,45656,1758],{},[898,45658,3045],{"mathvariant":2068},[1712,45660,2973],{},[902,45662,45663],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,45666,45668],{"id":45667},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,45670,45671],{},"Výdaje spotřebitele jsou",[883,45673,45675],{"className":45674},[886],[888,45676,45677],{"xmlns":890,"display":2004},[892,45678,45679,45754],{},[2008,45680,45681],{"width":2010},[2012,45682,45683,45685,45747,45749],{},[2015,45684],{"width":2017},[2015,45686,45687],{},[895,45688,45689,45691,45693,45695,45697,45703,45705,45711,45713,45715,45723,45729,45731,45739,45745],{},[898,45690,1805],{},[1716,45692,1913],{},[898,45694,1805],{},[1716,45696,1920],{"stretchy":1919},[1707,45698,45699,45701],{},[898,45700,1878],{},[1712,45702,1714],{},[1716,45704,1719],{"separator":1718},[1707,45706,45707,45709],{},[898,45708,1878],{},[1712,45710,1726],{},[1716,45712,1925],{"stretchy":1919},[1716,45714,1913],{},[7204,45716,45717,45719,45721],{},[898,45718,1690],{},[1712,45720,1714],{},[1716,45722,3080],{},[1707,45724,45725,45727],{},[898,45726,1878],{},[1712,45728,1714],{},[1716,45730,1949],{},[7204,45732,45733,45735,45737],{},[898,45734,1690],{},[1712,45736,1726],{},[1716,45738,3080],{},[1707,45740,45741,45743],{},[898,45742,1878],{},[1712,45744,1726],{},[1716,45746,1719],{"separator":1718},[2015,45748],{"width":2017},[2015,45750,45751],{},[2074,45752,45753],{},"(6.22)",[902,45755,45756],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,45758,45759],{},"a je pevně zadána hladina užitečnosti",[883,45761,45763],{"className":45762},[886],[888,45764,45765],{"xmlns":890,"display":2004},[892,45766,45767,45814],{},[2008,45768,45769],{"width":2010},[2012,45770,45771,45773,45807,45809],{},[2015,45772],{"width":2017},[2015,45774,45775],{},[895,45776,45777,45783,45785,45787,45789,45795,45797,45803,45805],{},[3074,45778,45779,45781],{},[898,45780,900],{},[1716,45782,3080],{},[1716,45784,1913],{},[898,45786,900],{},[1716,45788,1920],{"stretchy":1919},[1707,45790,45791,45793],{},[898,45792,1878],{},[1712,45794,1714],{},[1716,45796,1719],{"separator":1718},[1707,45798,45799,45801],{},[898,45800,1878],{},[1712,45802,1726],{},[1716,45804,1925],{"stretchy":1919},[898,45806,1853],{"mathvariant":2068},[2015,45808],{"width":2017},[2015,45810,45811],{},[2074,45812,45813],{},"(6.23)",[902,45815,45816],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,45818,45819,45822,45823,45855,45856,1853],{},[38,45820,45821],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,45824,45826],{"className":45825},[886],[888,45827,45828],{"xmlns":890},[892,45829,45830,45852],{},[895,45831,45832,45834,45836,45842,45844,45850],{},[898,45833,1805],{},[1716,45835,1920],{"stretchy":1919},[1707,45837,45838,45840],{},[898,45839,1878],{},[1712,45841,1714],{},[1716,45843,1719],{"separator":1718},[1707,45845,45846,45848],{},[898,45847,1878],{},[1712,45849,1726],{},[1716,45851,1925],{"stretchy":1919},[902,45853,45854],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,45857,45859],{"className":45858},[886],[888,45860,45861],{"xmlns":890},[892,45862,45863,45919],{},[895,45864,45865,45867,45869,45875,45877,45883,45885,45887,45893,45895,45897,45899,45905,45907,45913,45915,45917],{},[898,45866,24845],{},[1716,45868,1920],{"stretchy":1919},[1707,45870,45871,45873],{},[898,45872,1878],{},[1712,45874,1714],{},[1716,45876,1719],{"separator":1718},[1707,45878,45879,45881],{},[898,45880,1878],{},[1712,45882,1726],{},[1716,45884,1925],{"stretchy":1919},[1716,45886,1913],{},[3074,45888,45889,45891],{},[898,45890,900],{},[1716,45892,3080],{},[1716,45894,2760],{},[898,45896,900],{},[1716,45898,1920],{"stretchy":1919},[1707,45900,45901,45903],{},[898,45902,1878],{},[1712,45904,1714],{},[1716,45906,1719],{"separator":1718},[1707,45908,45909,45911],{},[898,45910,1878],{},[1712,45912,1726],{},[1716,45914,1925],{"stretchy":1919},[1716,45916,1913],{},[1712,45918,2505],{},[902,45920,45921],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,45923,45925],{"id":45924},"lagrangeova-funkce","Lagrangeova funkce",[883,45927,45929],{"className":45928},[886],[888,45930,45931],{"xmlns":890,"display":2004},[892,45932,45933,46044],{},[2008,45934,45935],{"width":2010},[2012,45936,45937,45939,46037,46039],{},[2015,45938],{"width":2017},[2015,45940,45941],{},[895,45942,45943,45945,45947,45953,45955,45961,45963,45965,45967,45969,45977,45983,45985,45993,45999,46001,46003,46005,46011,46013,46015,46017,46023,46025,46031,46033,46035],{},[898,45944,1775],{"mathvariant":42313},[1716,45946,1920],{"stretchy":1919},[1707,45948,45949,45951],{},[898,45950,1878],{},[1712,45952,1714],{},[1716,45954,1719],{"separator":1718},[1707,45956,45957,45959],{},[898,45958,1878],{},[1712,45960,1726],{},[1716,45962,1719],{"separator":1718},[898,45964,30233],{},[1716,45966,1925],{"stretchy":1919},[1716,45968,1913],{},[7204,45970,45971,45973,45975],{},[898,45972,1690],{},[1712,45974,1714],{},[1716,45976,3080],{},[1707,45978,45979,45981],{},[898,45980,1878],{},[1712,45982,1714],{},[1716,45984,1949],{},[7204,45986,45987,45989,45991],{},[898,45988,1690],{},[1712,45990,1726],{},[1716,45992,3080],{},[1707,45994,45995,45997],{},[898,45996,1878],{},[1712,45998,1726],{},[1716,46000,1949],{},[898,46002,30233],{},[1716,46004,1920],{"stretchy":1919},[3074,46006,46007,46009],{},[898,46008,900],{},[1716,46010,3080],{},[1716,46012,2760],{},[898,46014,900],{},[1716,46016,1920],{"stretchy":1919},[1707,46018,46019,46021],{},[898,46020,1878],{},[1712,46022,1714],{},[1716,46024,1719],{"separator":1718},[1707,46026,46027,46029],{},[898,46028,1878],{},[1712,46030,1726],{},[1716,46032,1925],{"stretchy":1919},[1716,46034,1925],{"stretchy":1919},[898,46036,1853],{"mathvariant":2068},[2015,46038],{"width":2017},[2015,46040,46041],{},[2074,46042,46043],{},"(6.24)",[902,46045,46046],{"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}",[724,46048,46049],{},"Soustava podmínek prvního řádu:",[883,46051,46053],{"className":46052},[886],[888,46054,46055],{"xmlns":890,"display":2004},[892,46056,46057,46230],{},[2008,46058,46059],{"width":2010},[2012,46060,46061,46063,46223,46225],{},[2015,46062],{"width":2017},[2015,46064,46065],{},[2008,46066,46067,46117,46167],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,46068,46069,46081],{},[2015,46070,46071],{},[2747,46072,46073],{"scriptlevel":2505,"displaystyle":1718},[7204,46074,46075,46077,46079],{},[898,46076,1775],{"mathvariant":42313},[1712,46078,1714],{},[1716,46080,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,46082,46083],{},[2747,46084,46085],{"scriptlevel":2505,"displaystyle":1718},[895,46086,46087,46089,46091,46099,46101,46103,46111,46113,46115],{},[895,46088],{},[1716,46090,1913],{},[7204,46092,46093,46095,46097],{},[898,46094,1690],{},[1712,46096,1714],{},[1716,46098,3080],{},[1716,46100,2760],{},[898,46102,30233],{},[7204,46104,46105,46107,46109],{},[898,46106,900],{},[1712,46108,1714],{},[1716,46110,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,46112,1913],{},[1712,46114,2505],{},[1716,46116,1719],{"separator":1718},[2012,46118,46119,46131],{},[2015,46120,46121],{},[2747,46122,46123],{"scriptlevel":2505,"displaystyle":1718},[7204,46124,46125,46127,46129],{},[898,46126,1775],{"mathvariant":42313},[1712,46128,1726],{},[1716,46130,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,46132,46133],{},[2747,46134,46135],{"scriptlevel":2505,"displaystyle":1718},[895,46136,46137,46139,46141,46149,46151,46153,46161,46163,46165],{},[895,46138],{},[1716,46140,1913],{},[7204,46142,46143,46145,46147],{},[898,46144,1690],{},[1712,46146,1726],{},[1716,46148,3080],{},[1716,46150,2760],{},[898,46152,30233],{},[7204,46154,46155,46157,46159],{},[898,46156,900],{},[1712,46158,1726],{},[1716,46160,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,46162,1913],{},[1712,46164,2505],{},[1716,46166,1719],{"separator":1718},[2012,46168,46169,46181],{},[2015,46170,46171],{},[2747,46172,46173],{"scriptlevel":2505,"displaystyle":1718},[7204,46174,46175,46177,46179],{},[898,46176,1775],{"mathvariant":42313},[898,46178,30233],{},[1716,46180,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,46182,46183],{},[2747,46184,46185],{"scriptlevel":2505,"displaystyle":1718},[895,46186,46187,46189,46191,46197,46199,46201,46203,46209,46211,46217,46219,46221],{},[895,46188],{},[1716,46190,1913],{},[3074,46192,46193,46195],{},[898,46194,900],{},[1716,46196,3080],{},[1716,46198,2760],{},[898,46200,900],{},[1716,46202,1920],{"stretchy":1919},[1707,46204,46205,46207],{},[898,46206,1878],{},[1712,46208,1714],{},[1716,46210,1719],{"separator":1718},[1707,46212,46213,46215],{},[898,46214,1878],{},[1712,46216,1726],{},[1716,46218,1925],{"stretchy":1919},[1716,46220,1913],{},[1712,46222,2719],{},[2015,46224],{"width":2017},[2015,46226,46227],{},[2074,46228,46229],{},"(6.25)",[902,46231,46232],{"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}",[724,46234,46235],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,46237,46239],{"className":46238},[886],[888,46240,46241],{"xmlns":890,"display":2004},[892,46242,46243,46340],{},[2008,46244,46245],{"width":2010},[2012,46246,46247,46249,46333,46335],{},[2015,46248],{"width":2017},[2015,46250,46251],{},[895,46252,46253,46255,46257,46263,46265,46271,46273,46275,46277,46279,46281,46283,46331],{},[898,46254,1916],{},[1716,46256,1920],{"stretchy":1919},[1707,46258,46259,46261],{},[898,46260,1878],{},[1712,46262,1714],{},[1716,46264,1719],{"separator":1718},[1707,46266,46267,46269],{},[898,46268,1878],{},[1712,46270,1726],{},[1716,46272,1719],{"separator":1718},[898,46274,30233],{},[1716,46276,1925],{"stretchy":1919},[1716,46278,1913],{},[1716,46280,2760],{},[898,46282,30233],{},[895,46284,46285,46287,46299,46301,46313,46315,46317,46329],{},[1716,46286,1920],{"fence":1718},[7204,46288,46289,46291,46293],{},[898,46290,900],{},[1712,46292,16773],{},[895,46294,46295,46297],{},[1716,46296,8505],{"mathvariant":2068},[1716,46298,8505],{"mathvariant":2068},[1716,46300,1949],{},[7204,46302,46303,46305,46307],{},[898,46304,900],{},[1712,46306,6688],{},[895,46308,46309,46311],{},[1716,46310,8505],{"mathvariant":2068},[1716,46312,8505],{"mathvariant":2068},[1716,46314,1949],{},[1712,46316,1726],{},[7204,46318,46319,46321,46323],{},[898,46320,900],{},[1712,46322,6804],{},[895,46324,46325,46327],{},[1716,46326,8505],{"mathvariant":2068},[1716,46328,8505],{"mathvariant":2068},[1716,46330,1925],{"fence":1718},[898,46332,1853],{"mathvariant":2068},[2015,46334],{"width":2017},[2015,46336,46337],{},[2074,46338,46339],{},"(6.26)",[902,46341,46342],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,46344,46345,46348,46349,46388,46389,46428,46429,46479,46480,46506,46507,46524,46525,46551],{},[38,46346,46347],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,46350,46352],{"className":46351},[886],[888,46353,46354],{"xmlns":890},[892,46355,46356,46386],{},[895,46357,46358,46364,46366,46374,46376,46384],{},[3074,46359,46360,46362],{},[898,46361,1878],{},[1716,46363,3080],{},[1716,46365,2502],{"stretchy":1919},[7204,46367,46368,46370,46372],{},[898,46369,1878],{},[1712,46371,1714],{},[1716,46373,3080],{},[1716,46375,1719],{"separator":1718},[7204,46377,46378,46380,46382],{},[898,46379,1878],{},[1712,46381,1726],{},[1716,46383,3080],{},[1716,46385,2516],{"stretchy":1919},[902,46387,42092],{"encoding":904}," dotyku křivky užitečnosti ",[883,46390,46392],{"className":46391},[886],[888,46393,46394],{"xmlns":890},[892,46395,46396,46426],{},[895,46397,46398,46404,46406,46408,46410,46416,46418,46424],{},[3074,46399,46400,46402],{},[898,46401,900],{},[1716,46403,3080],{},[1716,46405,1913],{},[898,46407,900],{},[1716,46409,1920],{"stretchy":1919},[1707,46411,46412,46414],{},[898,46413,1878],{},[1712,46415,1714],{},[1716,46417,1719],{"separator":1718},[1707,46419,46420,46422],{},[898,46421,1878],{},[1712,46423,1726],{},[1716,46425,1925],{"stretchy":1919},[902,46427,31455],{"encoding":904}," s přímkou výdajů ",[883,46430,46432],{"className":46431},[886],[888,46433,46434],{"xmlns":890},[892,46435,46436,46476],{},[895,46437,46438,46444,46446,46454,46460,46462,46470],{},[3074,46439,46440,46442],{},[898,46441,1805],{},[1716,46443,3080],{},[1716,46445,1913],{},[7204,46447,46448,46450,46452],{},[898,46449,1690],{},[1712,46451,1714],{},[1716,46453,3080],{},[1707,46455,46456,46458],{},[898,46457,1878],{},[1712,46459,1714],{},[1716,46461,1949],{},[7204,46463,46464,46466,46468],{},[898,46465,1690],{},[1712,46467,1726],{},[1716,46469,3080],{},[1707,46471,46472,46474],{},[898,46473,1878],{},[1712,46475,1726],{},[902,46477,46478],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,46481,46483],{"className":46482},[886],[888,46484,46485],{"xmlns":890},[892,46486,46487,46503],{},[895,46488,46489,46495,46497],{},[1707,46490,46491,46493],{},[898,46492,1805],{},[1712,46494,2505],{},[1716,46496,2704],{},[3074,46498,46499,46501],{},[898,46500,1805],{},[1716,46502,3080],{},[902,46504,46505],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,46508,46510],{"className":46509},[886],[888,46511,46512],{"xmlns":890},[892,46513,46514,46522],{},[895,46515,46516],{},[3074,46517,46518,46520],{},[898,46519,900],{},[1716,46521,3080],{},[902,46523,41731],{"encoding":904},", hladina ",[883,46526,46528],{"className":46527},[886],[888,46529,46530],{"xmlns":890},[892,46531,46532,46548],{},[895,46533,46534,46540,46542],{},[1707,46535,46536,46538],{},[898,46537,1805],{},[1712,46539,1714],{},[1716,46541,2716],{},[3074,46543,46544,46546],{},[898,46545,1805],{},[1716,46547,3080],{},[902,46549,46550],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1635,46553,46554,46559],{},[724,46555,46556,46558],{},[883,46557,3776],{}," Postup — duální úloha (minimalizace výdajů)",[152,46560,46561,46611,46697,46737,46812],{},[123,46562,46563,3495,46566,46610],{},[38,46564,46565],{},"Zapiš vazbu",[883,46567,46569],{"className":46568},[886],[888,46570,46571],{"xmlns":890},[892,46572,46573,46607],{},[895,46574,46575,46581,46583,46585,46587,46593,46595,46601,46603,46605],{},[3074,46576,46577,46579],{},[898,46578,900],{},[1716,46580,3080],{},[1716,46582,2760],{},[898,46584,900],{},[1716,46586,1920],{"stretchy":1919},[1707,46588,46589,46591],{},[898,46590,1878],{},[1712,46592,1714],{},[1716,46594,1719],{"separator":1718},[1707,46596,46597,46599],{},[898,46598,1878],{},[1712,46600,1726],{},[1716,46602,1925],{"stretchy":1919},[1716,46604,1913],{},[1712,46606,2505],{},[902,46608,46609],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,46612,46613,3495,46615,1853],{},[38,46614,43024],{},[883,46616,46618],{"className":46617},[886],[888,46619,46620],{"xmlns":890},[892,46621,46622,46694],{},[895,46623,46624,46626,46628,46636,46642,46644,46652,46658,46660,46662,46664,46670,46672,46674,46676,46682,46684,46690,46692],{},[898,46625,1775],{"mathvariant":42313},[1716,46627,1913],{},[7204,46629,46630,46632,46634],{},[898,46631,1690],{},[1712,46633,1714],{},[1716,46635,3080],{},[1707,46637,46638,46640],{},[898,46639,1878],{},[1712,46641,1714],{},[1716,46643,1949],{},[7204,46645,46646,46648,46650],{},[898,46647,1690],{},[1712,46649,1726],{},[1716,46651,3080],{},[1707,46653,46654,46656],{},[898,46655,1878],{},[1712,46657,1726],{},[1716,46659,1949],{},[898,46661,30233],{},[1716,46663,1920],{"stretchy":1919},[3074,46665,46666,46668],{},[898,46667,900],{},[1716,46669,3080],{},[1716,46671,2760],{},[898,46673,900],{},[1716,46675,1920],{"stretchy":1919},[1707,46677,46678,46680],{},[898,46679,1878],{},[1712,46681,1714],{},[1716,46683,1719],{"separator":1718},[1707,46685,46686,46688],{},[898,46687,1878],{},[1712,46689,1726],{},[1716,46691,1925],{"stretchy":1919},[1716,46693,1925],{"stretchy":1919},[902,46695,46696],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,46698,46699,46702,46703,46736],{},[38,46700,46701],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,46704,46706],{"className":46705},[886],[888,46707,46708],{"xmlns":890},[892,46709,46710,46734],{},[895,46711,46712,46714,46716,46724,46726],{},[2074,46713,24407],{},[1716,46715,1913],{},[7204,46717,46718,46720,46722],{},[898,46719,1690],{},[1712,46721,1714],{},[1716,46723,3080],{},[898,46725,3045],{"mathvariant":2068},[7204,46727,46728,46730,46732],{},[898,46729,1690],{},[1712,46731,1726],{},[1716,46733,3080],{},[902,46735,42744],{"encoding":904}," (stejná jako u maximalizace!).",[123,46738,46739,3495,46742,46782,46783,1853],{},[38,46740,46741],{},"Dosaď do vazby",[883,46743,46745],{"className":46744},[886],[888,46746,46747],{"xmlns":890},[892,46748,46749,46779],{},[895,46750,46751,46753,46755,46761,46763,46769,46771,46773],{},[898,46752,900],{},[1716,46754,1920],{"stretchy":1919},[1707,46756,46757,46759],{},[898,46758,1878],{},[1712,46760,1714],{},[1716,46762,1719],{"separator":1718},[1707,46764,46765,46767],{},[898,46766,1878],{},[1712,46768,1726],{},[1716,46770,1925],{"stretchy":1919},[1716,46772,1913],{},[3074,46774,46775,46777],{},[898,46776,900],{},[1716,46778,3080],{},[902,46780,46781],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,46784,46786],{"className":46785},[886],[888,46787,46788],{"xmlns":890},[892,46789,46790,46810],{},[895,46791,46792,46800,46802],{},[7204,46793,46794,46796,46798],{},[898,46795,1878],{},[1712,46797,1714],{},[1716,46799,3080],{},[1716,46801,1719],{"separator":1718},[7204,46803,46804,46806,46808],{},[898,46805,1878],{},[1712,46807,1726],{},[1716,46809,3080],{},[902,46811,43265],{"encoding":904},[123,46813,46814,3495,46817,46871],{},[38,46815,46816],{},"Vypočítej minimální výdaje",[883,46818,46820],{"className":46819},[886],[888,46821,46822],{"xmlns":890},[892,46823,46824,46868],{},[895,46825,46826,46832,46834,46842,46850,46852,46860],{},[3074,46827,46828,46830],{},[898,46829,1805],{},[1716,46831,3080],{},[1716,46833,1913],{},[7204,46835,46836,46838,46840],{},[898,46837,1690],{},[1712,46839,1714],{},[1716,46841,3080],{},[7204,46843,46844,46846,46848],{},[898,46845,1878],{},[1712,46847,1714],{},[1716,46849,3080],{},[1716,46851,1949],{},[7204,46853,46854,46856,46858],{},[898,46855,1690],{},[1712,46857,1726],{},[1716,46859,3080],{},[7204,46861,46862,46864,46866],{},[898,46863,1878],{},[1712,46865,1726],{},[1716,46867,3080],{},[902,46869,46870],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,46873,46875,46876],{"id":46874},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,46877,46879],{"className":46878},[886],[888,46880,46881],{"xmlns":890},[892,46882,46883,46917],{},[895,46884,46885,46887,46889,46903],{},[898,46886,900],{},[1716,46888,1913],{},[7204,46890,46891,46893,46895],{},[898,46892,1878],{},[1712,46894,1714],{},[895,46896,46897,46899,46901],{},[1712,46898,1714],{},[898,46900,3045],{"mathvariant":2068},[1712,46902,1726],{},[7204,46904,46905,46907,46909],{},[898,46906,1878],{},[1712,46908,1726],{},[895,46910,46911,46913,46915],{},[1712,46912,1714],{},[898,46914,3045],{"mathvariant":2068},[1712,46916,1726],{},[902,46918,46919],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,46921,46922,46923,1343,46945,1343,46969,44108],{},"Dáno ",[883,46924,46926],{"className":46925},[886],[888,46927,46928],{"xmlns":890},[892,46929,46930,46942],{},[895,46931,46932,46938,46940],{},[3074,46933,46934,46936],{},[898,46935,900],{},[1716,46937,3080],{},[1716,46939,1913],{},[1712,46941,1726],{},[902,46943,46944],{"encoding":904},"U^* = 2",[883,46946,46948],{"className":46947},[886],[888,46949,46950],{"xmlns":890},[892,46951,46952,46966],{},[895,46953,46954,46962,46964],{},[7204,46955,46956,46958,46960],{},[898,46957,1690],{},[1712,46959,1714],{},[1716,46961,3080],{},[1716,46963,1913],{},[1712,46965,37561],{},[902,46967,46968],{"encoding":904},"P_1^* = 0{,}25",[883,46970,46972],{"className":46971},[886],[888,46973,46974],{"xmlns":890},[892,46975,46976,46990],{},[895,46977,46978,46986,46988],{},[7204,46979,46980,46982,46984],{},[898,46981,1690],{},[1712,46983,1726],{},[1716,46985,3080],{},[1716,46987,1913],{},[1712,46989,1714],{},[902,46991,46992],{"encoding":904},"P_2^* = 1",[883,46994,46996],{"className":46995},[886],[888,46997,46998],{"xmlns":890,"display":2004},[892,46999,47000,47064],{},[895,47001,47002,47004,47006,47008,47014,47016,47022,47024,47026,47028,47030,47032,47046,47060,47062],{},[898,47003,1775],{"mathvariant":42313},[1716,47005,1913],{},[1712,47007,37561],{},[1707,47009,47010,47012],{},[898,47011,1878],{},[1712,47013,1714],{},[1716,47015,1949],{},[1707,47017,47018,47020],{},[898,47019,1878],{},[1712,47021,1726],{},[1716,47023,1949],{},[898,47025,30233],{},[1716,47027,1920],{"stretchy":1919},[1712,47029,1726],{},[1716,47031,2760],{},[7204,47033,47034,47036,47038],{},[898,47035,1878],{},[1712,47037,1714],{},[895,47039,47040,47042,47044],{},[1712,47041,1714],{},[898,47043,3045],{"mathvariant":2068},[1712,47045,1726],{},[7204,47047,47048,47050,47052],{},[898,47049,1878],{},[1712,47051,1726],{},[895,47053,47054,47056,47058],{},[1712,47055,1714],{},[898,47057,3045],{"mathvariant":2068},[1712,47059,1726],{},[1716,47061,1925],{"stretchy":1919},[898,47063,1853],{"mathvariant":2068},[902,47065,47066],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,47068,44193],{},[883,47070,47072],{"className":47071},[886],[888,47073,47074],{"xmlns":890,"display":2004},[892,47075,47076,47290],{},[2008,47077,47078,47154,47230],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,47079,47080,47092],{},[2015,47081,47082],{},[2747,47083,47084],{"scriptlevel":2505,"displaystyle":1718},[7204,47085,47086,47088,47090],{},[898,47087,1775],{"mathvariant":42313},[1712,47089,1714],{},[1716,47091,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,47093,47094],{},[2747,47095,47096],{"scriptlevel":2505,"displaystyle":1718},[895,47097,47098,47100,47102,47104,47106,47108,47110,47118,47134,47148,47150,47152],{},[895,47099],{},[1716,47101,1913],{},[1712,47103,37561],{},[1716,47105,2760],{},[898,47107,30233],{},[1716,47109,9532],{},[2747,47111,47112],{"scriptlevel":2505,"displaystyle":1919},[2750,47113,47114,47116],{},[1712,47115,1714],{},[1712,47117,1726],{},[7204,47119,47120,47122,47124],{},[898,47121,1878],{},[1712,47123,1714],{},[895,47125,47126,47128,47130,47132],{},[1716,47127,2760],{},[1712,47129,1714],{},[898,47131,3045],{"mathvariant":2068},[1712,47133,1726],{},[7204,47135,47136,47138,47140],{},[898,47137,1878],{},[1712,47139,1726],{},[895,47141,47142,47144,47146],{},[1712,47143,1714],{},[898,47145,3045],{"mathvariant":2068},[1712,47147,1726],{},[1716,47149,1913],{},[1712,47151,2505],{},[1716,47153,1719],{"separator":1718},[2012,47155,47156,47168],{},[2015,47157,47158],{},[2747,47159,47160],{"scriptlevel":2505,"displaystyle":1718},[7204,47161,47162,47164,47166],{},[898,47163,1775],{"mathvariant":42313},[1712,47165,1726],{},[1716,47167,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,47169,47170],{},[2747,47171,47172],{"scriptlevel":2505,"displaystyle":1718},[895,47173,47174,47176,47178,47180,47182,47184,47186,47194,47208,47224,47226,47228],{},[895,47175],{},[1716,47177,1913],{},[1712,47179,1714],{},[1716,47181,2760],{},[898,47183,30233],{},[1716,47185,9532],{},[2747,47187,47188],{"scriptlevel":2505,"displaystyle":1919},[2750,47189,47190,47192],{},[1712,47191,1714],{},[1712,47193,1726],{},[7204,47195,47196,47198,47200],{},[898,47197,1878],{},[1712,47199,1714],{},[895,47201,47202,47204,47206],{},[1712,47203,1714],{},[898,47205,3045],{"mathvariant":2068},[1712,47207,1726],{},[7204,47209,47210,47212,47214],{},[898,47211,1878],{},[1712,47213,1726],{},[895,47215,47216,47218,47220,47222],{},[1716,47217,2760],{},[1712,47219,1714],{},[898,47221,3045],{"mathvariant":2068},[1712,47223,1726],{},[1716,47225,1913],{},[1712,47227,2505],{},[1716,47229,1719],{"separator":1718},[2012,47231,47232,47244],{},[2015,47233,47234],{},[2747,47235,47236],{"scriptlevel":2505,"displaystyle":1718},[7204,47237,47238,47240,47242],{},[898,47239,1775],{"mathvariant":42313},[898,47241,30233],{},[1716,47243,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,47245,47246],{},[2747,47247,47248],{"scriptlevel":2505,"displaystyle":1718},[895,47249,47250,47252,47254,47256,47258,47272,47286,47288],{},[895,47251],{},[1716,47253,1913],{},[1712,47255,1726],{},[1716,47257,2760],{},[7204,47259,47260,47262,47264],{},[898,47261,1878],{},[1712,47263,1714],{},[895,47265,47266,47268,47270],{},[1712,47267,1714],{},[898,47269,3045],{"mathvariant":2068},[1712,47271,1726],{},[7204,47273,47274,47276,47278],{},[898,47275,1878],{},[1712,47277,1726],{},[895,47279,47280,47282,47284],{},[1712,47281,1714],{},[898,47283,3045],{"mathvariant":2068},[1712,47285,1726],{},[1716,47287,1913],{},[1712,47289,2719],{},[902,47291,47292],{"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}",[724,47294,47295,47296,31366,47326,47354,47355,19417,47417,1343,47467,47489,47490,1853],{},"Podílem prvních dvou rovnic: ",[883,47297,47299],{"className":47298},[886],[888,47300,47301],{"xmlns":890},[892,47302,47303,47323],{},[895,47304,47305,47307,47309,47315,47317],{},[1712,47306,37561],{},[1716,47308,1913],{},[1707,47310,47311,47313],{},[898,47312,1878],{},[1712,47314,1726],{},[898,47316,3045],{"mathvariant":2068},[1707,47318,47319,47321],{},[898,47320,1878],{},[1712,47322,1714],{},[902,47324,47325],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,47327,47329],{"className":47328},[886],[888,47330,47331],{"xmlns":890},[892,47332,47333,47351],{},[895,47334,47335,47341,47343,47345],{},[1707,47336,47337,47339],{},[898,47338,1878],{},[1712,47340,1726],{},[1716,47342,1913],{},[1712,47344,37561],{},[1707,47346,47347,47349],{},[898,47348,1878],{},[1712,47350,1714],{},[902,47352,47353],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,47356,47358],{"className":47357},[886],[888,47359,47360],{"xmlns":890},[892,47361,47362,47414],{},[895,47363,47364,47378,47380,47382,47388,47400,47402,47404,47410,47412],{},[7204,47365,47366,47368,47370],{},[898,47367,1878],{},[1712,47369,1714],{},[895,47371,47372,47374,47376],{},[1712,47373,1714],{},[898,47375,3045],{"mathvariant":2068},[1712,47377,1726],{},[1716,47379,1920],{"stretchy":1919},[1712,47381,37561],{},[1707,47383,47384,47386],{},[898,47385,1878],{},[1712,47387,1714],{},[3074,47389,47390,47392],{},[1716,47391,1925],{"stretchy":1919},[895,47393,47394,47396,47398],{},[1712,47395,1714],{},[898,47397,3045],{"mathvariant":2068},[1712,47399,1726],{},[1716,47401,1913],{},[1712,47403,5771],{},[1707,47405,47406,47408],{},[898,47407,1878],{},[1712,47409,1714],{},[1716,47411,1913],{},[1712,47413,1726],{},[902,47415,47416],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,47418,47419,1343,47443],{},[883,47420,47422],{"className":47421},[886],[888,47423,47424],{"xmlns":890},[892,47425,47426,47440],{},[895,47427,47428,47436,47438],{},[7204,47429,47430,47432,47434],{},[898,47431,1878],{},[1712,47433,1714],{},[1716,47435,3080],{},[1716,47437,1913],{},[1712,47439,6849],{},[902,47441,47442],{"encoding":904},"Q_1^* = 4",[883,47444,47446],{"className":47445},[886],[888,47447,47448],{"xmlns":890},[892,47449,47450,47464],{},[895,47451,47452,47460,47462],{},[7204,47453,47454,47456,47458],{},[898,47455,1878],{},[1712,47457,1726],{},[1716,47459,3080],{},[1716,47461,1913],{},[1712,47463,1714],{},[902,47465,47466],{"encoding":904},"Q_2^* = 1",[883,47468,47470],{"className":47469},[886],[888,47471,47472],{"xmlns":890},[892,47473,47474,47486],{},[895,47475,47476,47482,47484],{},[3074,47477,47478,47480],{},[898,47479,30233],{},[1716,47481,3080],{},[1716,47483,1913],{},[1712,47485,1714],{},[902,47487,47488],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,47491,47493],{"className":47492},[886],[888,47494,47495],{"xmlns":890},[892,47496,47497,47525],{},[895,47498,47499,47505,47507,47509,47511,47513,47515,47517,47519,47521,47523],{},[3074,47500,47501,47503],{},[898,47502,1805],{},[1716,47504,3080],{},[1716,47506,1913],{},[1712,47508,37561],{},[1716,47510,9532],{},[1712,47512,6849],{},[1716,47514,1949],{},[1712,47516,1714],{},[1716,47518,9532],{},[1712,47520,1714],{},[1716,47522,1913],{},[1712,47524,1726],{},[902,47526,47527],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,47529,47530,47533,47534,1343,47600,1343,47666,47732,47733,47770,47771,47793,47794,1853],{},[614,47531,47532],{},"Ověření postačující podmínky"," (6.26): ",[883,47535,47537],{"className":47536},[886],[888,47538,47539],{"xmlns":890},[892,47540,47541,47597],{},[895,47542,47543,47555,47557,47559,47567,47583],{},[7204,47544,47545,47547,47549],{},[898,47546,900],{},[1712,47548,16773],{},[895,47550,47551,47553],{},[1716,47552,8505],{"mathvariant":2068},[1716,47554,8505],{"mathvariant":2068},[1716,47556,1913],{},[1716,47558,2760],{},[2747,47560,47561],{"scriptlevel":2505,"displaystyle":1919},[2750,47562,47563,47565],{},[1712,47564,1714],{},[1712,47566,6849],{},[7204,47568,47569,47571,47573],{},[898,47570,1878],{},[1712,47572,1714],{},[895,47574,47575,47577,47579,47581],{},[1716,47576,2760],{},[1712,47578,7072],{},[898,47580,3045],{"mathvariant":2068},[1712,47582,1726],{},[7204,47584,47585,47587,47589],{},[898,47586,1878],{},[1712,47588,1726],{},[895,47590,47591,47593,47595],{},[1712,47592,1714],{},[898,47594,3045],{"mathvariant":2068},[1712,47596,1726],{},[902,47598,47599],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,47601,47603],{"className":47602},[886],[888,47604,47605],{"xmlns":890},[892,47606,47607,47663],{},[895,47608,47609,47621,47623,47625,47633,47647],{},[7204,47610,47611,47613,47615],{},[898,47612,900],{},[1712,47614,6688],{},[895,47616,47617,47619],{},[1716,47618,8505],{"mathvariant":2068},[1716,47620,8505],{"mathvariant":2068},[1716,47622,1913],{},[1716,47624,2760],{},[2747,47626,47627],{"scriptlevel":2505,"displaystyle":1919},[2750,47628,47629,47631],{},[1712,47630,1714],{},[1712,47632,6849],{},[7204,47634,47635,47637,47639],{},[898,47636,1878],{},[1712,47638,1714],{},[895,47640,47641,47643,47645],{},[1712,47642,1714],{},[898,47644,3045],{"mathvariant":2068},[1712,47646,1726],{},[7204,47648,47649,47651,47653],{},[898,47650,1878],{},[1712,47652,1726],{},[895,47654,47655,47657,47659,47661],{},[1716,47656,2760],{},[1712,47658,7072],{},[898,47660,3045],{"mathvariant":2068},[1712,47662,1726],{},[902,47664,47665],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,47667,47669],{"className":47668},[886],[888,47670,47671],{"xmlns":890},[892,47672,47673,47729],{},[895,47674,47675,47687,47689,47697,47713],{},[7204,47676,47677,47679,47681],{},[898,47678,900],{},[1712,47680,6804],{},[895,47682,47683,47685],{},[1716,47684,8505],{"mathvariant":2068},[1716,47686,8505],{"mathvariant":2068},[1716,47688,1913],{},[2747,47690,47691],{"scriptlevel":2505,"displaystyle":1919},[2750,47692,47693,47695],{},[1712,47694,1714],{},[1712,47696,6849],{},[7204,47698,47699,47701,47703],{},[898,47700,1878],{},[1712,47702,1714],{},[895,47704,47705,47707,47709,47711],{},[1716,47706,2760],{},[1712,47708,1714],{},[898,47710,3045],{"mathvariant":2068},[1712,47712,1726],{},[7204,47714,47715,47717,47719],{},[898,47716,1878],{},[1712,47718,1726],{},[895,47720,47721,47723,47725,47727],{},[1716,47722,2760],{},[1712,47724,1714],{},[898,47726,3045],{"mathvariant":2068},[1712,47728,1726],{},[902,47730,47731],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,47734,47736],{"className":47735},[886],[888,47737,47738],{"xmlns":890},[892,47739,47740,47767],{},[895,47741,47742,47744,47746,47748,47750,47752,47754,47756,47758,47760,47763,47765],{},[898,47743,1916],{},[1716,47745,1920],{"stretchy":1919},[1712,47747,6849],{},[1716,47749,1719],{"separator":1718},[1712,47751,1714],{},[1716,47753,1719],{"separator":1718},[1712,47755,1714],{},[1716,47757,1925],{"stretchy":1919},[1716,47759,1913],{},[1712,47761,47762],{},"0,28125",[1716,47764,2716],{},[1712,47766,2505],{},[902,47768,47769],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,47772,47774],{"className":47773},[886],[888,47775,47776],{"xmlns":890},[892,47777,47778,47790],{},[895,47779,47780,47782,47784,47786,47788],{},[1716,47781,2502],{"stretchy":1919},[1712,47783,6849],{},[1716,47785,1719],{"separator":1718},[1712,47787,1714],{},[1716,47789,2516],{"stretchy":1919},[902,47791,47792],{"encoding":904},"[4, 1]"," je vázané ",[38,47795,17630],{},[115,47797,47799],{"id":47798},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,47801,47802],{},"Obecně:",[883,47804,47806],{"className":47805},[886],[888,47807,47808],{"xmlns":890,"display":2004},[892,47809,47810,47905],{},[2008,47811,47812],{"width":2010},[2012,47813,47814,47816,47898,47900],{},[2015,47815],{"width":2017},[2015,47817,47818],{},[895,47819,47820,47826,47828,47834,47836,47842,47844,47850,47852,47854,47856,47858,47860,47866,47868,47874,47876,47882,47884,47890,47892,47894,47896],{},[1707,47821,47822,47824],{},[898,47823,1878],{},[1712,47825,1714],{},[1716,47827,1913],{},[1707,47829,47830,47832],{},[898,47831,1916],{},[1712,47833,1714],{},[1716,47835,1920],{"stretchy":1919},[1707,47837,47838,47840],{},[898,47839,1690],{},[1712,47841,1714],{},[1716,47843,1719],{"separator":1718},[1707,47845,47846,47848],{},[898,47847,1690],{},[1712,47849,1726],{},[1716,47851,1719],{"separator":1718},[898,47853,900],{},[1716,47855,1925],{"stretchy":1919},[1716,47857,1719],{"separator":1718},[2324,47859],{"width":8689},[1707,47861,47862,47864],{},[898,47863,1878],{},[1712,47865,1726],{},[1716,47867,1913],{},[1707,47869,47870,47872],{},[898,47871,1916],{},[1712,47873,1726],{},[1716,47875,1920],{"stretchy":1919},[1707,47877,47878,47880],{},[898,47879,1690],{},[1712,47881,1714],{},[1716,47883,1719],{"separator":1718},[1707,47885,47886,47888],{},[898,47887,1690],{},[1712,47889,1726],{},[1716,47891,1719],{"separator":1718},[898,47893,900],{},[1716,47895,1925],{"stretchy":1919},[1716,47897,1719],{"separator":1718},[2015,47899],{"width":2017},[2015,47901,47902],{},[2074,47903,47904],{},"(6.27)",[902,47906,47907],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,47909,47911],{"className":47910},[886],[888,47912,47913],{"xmlns":890,"display":2004},[892,47914,47915,47962],{},[2008,47916,47917],{"width":2010},[2012,47918,47919,47921,47955,47957],{},[2015,47920],{"width":2017},[2015,47922,47923],{},[895,47924,47925,47927,47929,47931,47933,47939,47941,47947,47949,47951,47953],{},[898,47926,30233],{},[1716,47928,1913],{},[898,47930,30233],{},[1716,47932,1920],{"stretchy":1919},[1707,47934,47935,47937],{},[898,47936,1690],{},[1712,47938,1714],{},[1716,47940,1719],{"separator":1718},[1707,47942,47943,47945],{},[898,47944,1690],{},[1712,47946,1726],{},[1716,47948,1719],{"separator":1718},[898,47950,900],{},[1716,47952,1925],{"stretchy":1919},[898,47954,1853],{"mathvariant":2068},[2015,47956],{"width":2017},[2015,47958,47959],{},[2074,47960,47961],{},"(6.28)",[902,47963,47964],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,47966,47967,47968,3495,47971,47984,47985,47998],{},"Hicksova poptávka závisí na ",[38,47969,47970],{},"hladině užitečnosti",[883,47972,47974],{"className":47973},[886],[888,47975,47976],{"xmlns":890},[892,47977,47978,47982],{},[895,47979,47980],{},[898,47981,900],{},[902,47983,900],{"encoding":904}," (nikoli na důchodu ",[883,47986,47988],{"className":47987},[886],[888,47989,47990],{"xmlns":890},[892,47991,47992,47996],{},[895,47993,47994],{},[898,47995,1758],{},[902,47997,1758],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,48000,48002,48003],{"id":48001},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,48004,48006],{"className":48005},[886],[888,48007,48008],{"xmlns":890},[892,48009,48010,48044],{},[895,48011,48012,48014,48016,48030],{},[898,48013,900],{},[1716,48015,1913],{},[7204,48017,48018,48020,48022],{},[898,48019,1878],{},[1712,48021,1714],{},[895,48023,48024,48026,48028],{},[1712,48025,1714],{},[898,48027,3045],{"mathvariant":2068},[1712,48029,1726],{},[7204,48031,48032,48034,48036],{},[898,48033,1878],{},[1712,48035,1726],{},[895,48037,48038,48040,48042],{},[1712,48039,1714],{},[898,48041,3045],{"mathvariant":2068},[1712,48043,1726],{},[902,48045,46919],{"encoding":904},[724,48047,48048,48078],{},[883,48049,48051],{"className":48050},[886],[888,48052,48053],{"xmlns":890},[892,48054,48055,48075],{},[895,48056,48057,48063,48065,48071,48073],{},[1707,48058,48059,48061],{},[898,48060,1690],{},[1712,48062,1714],{},[1716,48064,1719],{"separator":1718},[1707,48066,48067,48069],{},[898,48068,1690],{},[1712,48070,1726],{},[1716,48072,1719],{"separator":1718},[898,48074,900],{},[902,48076,48077],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,48080,48082],{"className":48081},[886],[888,48083,48084],{"xmlns":890,"display":2004},[892,48085,48086,48160],{},[895,48087,48088,48090,48092,48098,48104,48106,48112,48118,48120,48122,48124,48126,48128,48142,48156,48158],{},[898,48089,1775],{"mathvariant":42313},[1716,48091,1913],{},[1707,48093,48094,48096],{},[898,48095,1690],{},[1712,48097,1714],{},[1707,48099,48100,48102],{},[898,48101,1878],{},[1712,48103,1714],{},[1716,48105,1949],{},[1707,48107,48108,48110],{},[898,48109,1690],{},[1712,48111,1726],{},[1707,48113,48114,48116],{},[898,48115,1878],{},[1712,48117,1726],{},[1716,48119,1949],{},[898,48121,30233],{},[1716,48123,1920],{"stretchy":1919},[898,48125,900],{},[1716,48127,2760],{},[7204,48129,48130,48132,48134],{},[898,48131,1878],{},[1712,48133,1714],{},[895,48135,48136,48138,48140],{},[1712,48137,1714],{},[898,48139,3045],{"mathvariant":2068},[1712,48141,1726],{},[7204,48143,48144,48146,48148],{},[898,48145,1878],{},[1712,48147,1726],{},[895,48149,48150,48152,48154],{},[1712,48151,1714],{},[898,48153,3045],{"mathvariant":2068},[1712,48155,1726],{},[1716,48157,1925],{"stretchy":1919},[898,48159,1853],{"mathvariant":2068},[902,48161,48162],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,48164,44193],{},[883,48166,48168],{"className":48167},[886],[888,48169,48170],{"xmlns":890,"display":2004},[892,48171,48172,48394],{},[2008,48173,48174,48254,48334],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,48175,48176,48188],{},[2015,48177,48178],{},[2747,48179,48180],{"scriptlevel":2505,"displaystyle":1718},[7204,48181,48182,48184,48186],{},[898,48183,1775],{"mathvariant":42313},[1712,48185,1714],{},[1716,48187,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,48189,48190],{},[2747,48191,48192],{"scriptlevel":2505,"displaystyle":1718},[895,48193,48194,48196,48198,48204,48206,48208,48210,48218,48234,48248,48250,48252],{},[895,48195],{},[1716,48197,1913],{},[1707,48199,48200,48202],{},[898,48201,1690],{},[1712,48203,1714],{},[1716,48205,2760],{},[898,48207,30233],{},[1716,48209,9532],{},[2747,48211,48212],{"scriptlevel":2505,"displaystyle":1919},[2750,48213,48214,48216],{},[1712,48215,1714],{},[1712,48217,1726],{},[7204,48219,48220,48222,48224],{},[898,48221,1878],{},[1712,48223,1714],{},[895,48225,48226,48228,48230,48232],{},[1716,48227,2760],{},[1712,48229,1714],{},[898,48231,3045],{"mathvariant":2068},[1712,48233,1726],{},[7204,48235,48236,48238,48240],{},[898,48237,1878],{},[1712,48239,1726],{},[895,48241,48242,48244,48246],{},[1712,48243,1714],{},[898,48245,3045],{"mathvariant":2068},[1712,48247,1726],{},[1716,48249,1913],{},[1712,48251,2505],{},[1716,48253,1719],{"separator":1718},[2012,48255,48256,48268],{},[2015,48257,48258],{},[2747,48259,48260],{"scriptlevel":2505,"displaystyle":1718},[7204,48261,48262,48264,48266],{},[898,48263,1775],{"mathvariant":42313},[1712,48265,1726],{},[1716,48267,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,48269,48270],{},[2747,48271,48272],{"scriptlevel":2505,"displaystyle":1718},[895,48273,48274,48276,48278,48284,48286,48288,48290,48298,48312,48328,48330,48332],{},[895,48275],{},[1716,48277,1913],{},[1707,48279,48280,48282],{},[898,48281,1690],{},[1712,48283,1726],{},[1716,48285,2760],{},[898,48287,30233],{},[1716,48289,9532],{},[2747,48291,48292],{"scriptlevel":2505,"displaystyle":1919},[2750,48293,48294,48296],{},[1712,48295,1714],{},[1712,48297,1726],{},[7204,48299,48300,48302,48304],{},[898,48301,1878],{},[1712,48303,1714],{},[895,48305,48306,48308,48310],{},[1712,48307,1714],{},[898,48309,3045],{"mathvariant":2068},[1712,48311,1726],{},[7204,48313,48314,48316,48318],{},[898,48315,1878],{},[1712,48317,1726],{},[895,48319,48320,48322,48324,48326],{},[1716,48321,2760],{},[1712,48323,1714],{},[898,48325,3045],{"mathvariant":2068},[1712,48327,1726],{},[1716,48329,1913],{},[1712,48331,2505],{},[1716,48333,1719],{"separator":1718},[2012,48335,48336,48348],{},[2015,48337,48338],{},[2747,48339,48340],{"scriptlevel":2505,"displaystyle":1718},[7204,48341,48342,48344,48346],{},[898,48343,1775],{"mathvariant":42313},[898,48345,30233],{},[1716,48347,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2015,48349,48350],{},[2747,48351,48352],{"scriptlevel":2505,"displaystyle":1718},[895,48353,48354,48356,48358,48360,48362,48376,48390,48392],{},[895,48355],{},[1716,48357,1913],{},[898,48359,900],{},[1716,48361,2760],{},[7204,48363,48364,48366,48368],{},[898,48365,1878],{},[1712,48367,1714],{},[895,48369,48370,48372,48374],{},[1712,48371,1714],{},[898,48373,3045],{"mathvariant":2068},[1712,48375,1726],{},[7204,48377,48378,48380,48382],{},[898,48379,1878],{},[1712,48381,1726],{},[895,48383,48384,48386,48388],{},[1712,48385,1714],{},[898,48387,3045],{"mathvariant":2068},[1712,48389,1726],{},[1716,48391,1913],{},[1712,48393,2719],{},[902,48395,48396],{"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}",[724,48398,48399,48400,48470,48471,48529],{},"Podílem rovnic: ",[883,48401,48403],{"className":48402},[886],[888,48404,48405],{"xmlns":890},[892,48406,48407,48467],{},[895,48408,48409,48415,48417,48423,48425,48431,48433,48439,48441,48447,48453,48455,48461],{},[1707,48410,48411,48413],{},[898,48412,1690],{},[1712,48414,1714],{},[898,48416,3045],{"mathvariant":2068},[1707,48418,48419,48421],{},[898,48420,1690],{},[1712,48422,1726],{},[1716,48424,1913],{},[1707,48426,48427,48429],{},[898,48428,1878],{},[1712,48430,1726],{},[898,48432,3045],{"mathvariant":2068},[1707,48434,48435,48437],{},[898,48436,1878],{},[1712,48438,1714],{},[1716,48440,17833],{},[1707,48442,48443,48445],{},[898,48444,1690],{},[1712,48446,1714],{},[1707,48448,48449,48451],{},[898,48450,1878],{},[1712,48452,1714],{},[1716,48454,1913],{},[1707,48456,48457,48459],{},[898,48458,1690],{},[1712,48460,1726],{},[1707,48462,48463,48465],{},[898,48464,1878],{},[1712,48466,1726],{},[902,48468,48469],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,48472,48474],{"className":48473},[886],[888,48475,48476],{"xmlns":890},[892,48477,48478,48526],{},[895,48479,48480,48482,48484,48490,48496,48498,48504,48510,48512,48514,48520],{},[898,48481,1805],{},[1716,48483,1913],{},[1707,48485,48486,48488],{},[898,48487,1690],{},[1712,48489,1714],{},[1707,48491,48492,48494],{},[898,48493,1878],{},[1712,48495,1714],{},[1716,48497,1949],{},[1707,48499,48500,48502],{},[898,48501,1690],{},[1712,48503,1726],{},[1707,48505,48506,48508],{},[898,48507,1878],{},[1712,48509,1726],{},[1716,48511,1913],{},[1712,48513,1726],{},[1707,48515,48516,48518],{},[898,48517,1690],{},[1712,48519,1714],{},[1707,48521,48522,48524],{},[898,48523,1878],{},[1712,48525,1714],{},[902,48527,48528],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,48531,48533],{"className":48532},[886],[888,48534,48535],{"xmlns":890,"display":2004},[892,48536,48537,48604],{},[2008,48538,48539],{"width":2010},[2012,48540,48541,48543,48597,48599],{},[2015,48542],{"width":2017},[2015,48544,48545],{},[895,48546,48547,48553,48555,48569,48571,48573,48579,48581,48595],{},[1707,48548,48549,48551],{},[898,48550,1878],{},[1712,48552,1714],{},[1716,48554,1913],{},[2750,48556,48557,48559],{},[898,48558,1805],{},[895,48560,48561,48563],{},[1712,48562,1726],{},[1707,48564,48565,48567],{},[898,48566,1690],{},[1712,48568,1714],{},[1716,48570,1719],{"separator":1718},[2324,48572],{"width":8689},[1707,48574,48575,48577],{},[898,48576,1878],{},[1712,48578,1726],{},[1716,48580,1913],{},[2750,48582,48583,48585],{},[898,48584,1805],{},[895,48586,48587,48589],{},[1712,48588,1726],{},[1707,48590,48591,48593],{},[898,48592,1690],{},[1712,48594,1726],{},[898,48596,1853],{"mathvariant":2068},[2015,48598],{"width":2017},[2015,48600,48601],{},[2074,48602,48603],{},"(6.29)",[902,48605,48606],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,48608,48609,48610,31366,48692,48728],{},"Ze třetí rovnice ",[883,48611,48613],{"className":48612},[886],[888,48614,48615],{"xmlns":890},[892,48616,48617,48689],{},[895,48618,48619,48621,48623,48661,48663],{},[898,48620,900],{},[1716,48622,1913],{},[10595,48624,48625],{},[895,48626,48627,48643,48645],{},[2747,48628,48629],{"scriptlevel":2505,"displaystyle":1919},[2750,48630,48631,48633],{},[898,48632,1805],{},[895,48634,48635,48637],{},[1712,48636,1726],{},[1707,48638,48639,48641],{},[898,48640,1690],{},[1712,48642,1714],{},[1716,48644,9532],{},[2747,48646,48647],{"scriptlevel":2505,"displaystyle":1919},[2750,48648,48649,48651],{},[898,48650,1805],{},[895,48652,48653,48655],{},[1712,48654,1726],{},[1707,48656,48657,48659],{},[898,48658,1690],{},[1712,48660,1726],{},[1716,48662,1913],{},[2747,48664,48665],{"scriptlevel":2505,"displaystyle":1919},[2750,48666,48667,48669],{},[898,48668,1805],{},[895,48670,48671,48673],{},[1712,48672,1726],{},[10595,48674,48675],{},[895,48676,48677,48683],{},[1707,48678,48679,48681],{},[898,48680,1690],{},[1712,48682,1714],{},[1707,48684,48685,48687],{},[898,48686,1690],{},[1712,48688,1726],{},[902,48690,48691],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,48693,48695],{"className":48694},[886],[888,48696,48697],{"xmlns":890},[892,48698,48699,48725],{},[895,48700,48701,48703,48705,48707,48709],{},[898,48702,1805],{},[1716,48704,1913],{},[1712,48706,1726],{},[898,48708,900],{},[10595,48710,48711],{},[895,48712,48713,48719],{},[1707,48714,48715,48717],{},[898,48716,1690],{},[1712,48718,1714],{},[1707,48720,48721,48723],{},[898,48722,1690],{},[1712,48724,1726],{},[902,48726,48727],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,48730,48732],{"className":48731},[886],[888,48733,48734],{"xmlns":890,"display":2004},[892,48735,48736,48881],{},[2008,48737,48738],{"width":2010},[2012,48739,48740,48742,48874,48876],{},[2015,48741],{"width":2017},[2015,48743,48744],{},[26632,48745,48746],{"notation":26634},[2747,48747,48748],{"scriptlevel":2505,"displaystyle":1919},[2747,48749,48750],{"scriptlevel":2505,"displaystyle":1919},[2747,48751,48752],{"scriptlevel":2505,"displaystyle":1718},[895,48753,48754,48756,48762,48764,48766,48782,48784,48790,48792,48798,48800,48806,48808,48810,48812,48814,48816,48822,48824,48826,48842,48844,48850,48852,48858,48860,48866,48868,48870,48872],{},[2074,48755,17830],{},[1707,48757,48758,48760],{},[898,48759,1878],{},[1712,48761,1714],{},[1716,48763,1913],{},[898,48765,900],{},[10595,48767,48768],{},[2750,48769,48770,48776],{},[1707,48771,48772,48774],{},[898,48773,1690],{},[1712,48775,1726],{},[1707,48777,48778,48780],{},[898,48779,1690],{},[1712,48781,1714],{},[1716,48783,1913],{},[1707,48785,48786,48788],{},[898,48787,1916],{},[1712,48789,1714],{},[1716,48791,1920],{"stretchy":1919},[1707,48793,48794,48796],{},[898,48795,1690],{},[1712,48797,1714],{},[1716,48799,1719],{"separator":1718},[1707,48801,48802,48804],{},[898,48803,1690],{},[1712,48805,1726],{},[1716,48807,1719],{"separator":1718},[898,48809,900],{},[1716,48811,1925],{"stretchy":1919},[1716,48813,1719],{"separator":1718},[2324,48815],{"width":8689},[1707,48817,48818,48820],{},[898,48819,1878],{},[1712,48821,1726],{},[1716,48823,1913],{},[898,48825,900],{},[10595,48827,48828],{},[2750,48829,48830,48836],{},[1707,48831,48832,48834],{},[898,48833,1690],{},[1712,48835,1714],{},[1707,48837,48838,48840],{},[898,48839,1690],{},[1712,48841,1726],{},[1716,48843,1913],{},[1707,48845,48846,48848],{},[898,48847,1916],{},[1712,48849,1726],{},[1716,48851,1920],{"stretchy":1919},[1707,48853,48854,48856],{},[898,48855,1690],{},[1712,48857,1714],{},[1716,48859,1719],{"separator":1718},[1707,48861,48862,48864],{},[898,48863,1690],{},[1712,48865,1726],{},[1716,48867,1719],{"separator":1718},[898,48869,900],{},[1716,48871,1925],{"stretchy":1919},[2074,48873,17830],{},[2015,48875],{"width":2017},[2015,48877,48878],{},[2074,48879,48880],{},"(6.30)",[902,48882,48883],{"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}",[115,48885,48887],{"id":48886},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,48889,48890,48891,48904,48905,48922,48923,48936,48937,48954,48955,48958,48959,48998,48999,49028],{},"Primární (max ",[883,48892,48894],{"className":48893},[886],[888,48895,48896],{"xmlns":890},[892,48897,48898,48902],{},[895,48899,48900],{},[898,48901,900],{},[902,48903,900],{"encoding":904}," při rozpočtu ",[883,48906,48908],{"className":48907},[886],[888,48909,48910],{"xmlns":890},[892,48911,48912,48920],{},[895,48913,48914],{},[3074,48915,48916,48918],{},[898,48917,1758],{},[1716,48919,3080],{},[902,48921,41796],{"encoding":904},") a duální (min ",[883,48924,48926],{"className":48925},[886],[888,48927,48928],{"xmlns":890},[892,48929,48930,48934],{},[895,48931,48932],{},[898,48933,1805],{},[902,48935,1805],{"encoding":904}," při užitečnosti ",[883,48938,48940],{"className":48939},[886],[888,48941,48942],{"xmlns":890},[892,48943,48944,48952],{},[895,48945,48946],{},[3074,48947,48948,48950],{},[898,48949,900],{},[1716,48951,3080],{},[902,48953,41731],{"encoding":904},") úloha jsou ",[38,48956,48957],{},"ekvivalentní",": mají tentýž bod optima ",[883,48960,48962],{"className":48961},[886],[888,48963,48964],{"xmlns":890},[892,48965,48966,48996],{},[895,48967,48968,48974,48976,48984,48986,48994],{},[3074,48969,48970,48972],{},[898,48971,1878],{},[1716,48973,3080],{},[1716,48975,2502],{"stretchy":1919},[7204,48977,48978,48980,48982],{},[898,48979,1878],{},[1712,48981,1714],{},[1716,48983,3080],{},[1716,48985,1719],{"separator":1718},[7204,48987,48988,48990,48992],{},[898,48989,1878],{},[1712,48991,1726],{},[1716,48993,3080],{},[1716,48995,2516],{"stretchy":1919},[902,48997,42092],{"encoding":904}," a v obou platí ",[883,49000,49002],{"className":49001},[886],[888,49003,49004],{"xmlns":890},[892,49005,49006,49026],{},[895,49007,49008,49010,49012,49018,49020],{},[2074,49009,24407],{},[1716,49011,1913],{},[1707,49013,49014,49016],{},[898,49015,1690],{},[1712,49017,1714],{},[898,49019,3045],{"mathvariant":2068},[1707,49021,49022,49024],{},[898,49023,1690],{},[1712,49025,1726],{},[902,49027,41767],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,49030,49031],{},[3682,49032],{"alt":49033,"className":49034,"src":49035},"imek-primarni-vs-dualni",[210,3686],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,49037,49038,49149],{},[123,49039,49040,49043,49044,49057,49058,49098,49099,1853],{},[38,49041,49042],{},"Primární"," (Marshall): zadáno ",[883,49045,49047],{"className":49046},[886],[888,49048,49049],{"xmlns":890},[892,49050,49051,49055],{},[895,49052,49053],{},[898,49054,1758],{},[902,49056,1758],{"encoding":904},", hledáme maximální ",[883,49059,49061],{"className":49060},[886],[888,49062,49063],{"xmlns":890},[892,49064,49065,49095],{},[895,49066,49067,49073,49075,49081,49083,49089,49091,49093],{},[3074,49068,49069,49071],{},[898,49070,900],{},[1716,49072,3080],{},[1716,49074,1920],{"stretchy":1919},[1707,49076,49077,49079],{},[898,49078,1690],{},[1712,49080,1714],{},[1716,49082,1719],{"separator":1718},[1707,49084,49085,49087],{},[898,49086,1690],{},[1712,49088,1726],{},[1716,49090,1719],{"separator":1718},[898,49092,1758],{},[1716,49094,1925],{"stretchy":1919},[902,49096,49097],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,49100,49102],{"className":49101},[886],[888,49103,49104],{"xmlns":890},[892,49105,49106,49146],{},[895,49107,49108,49114,49116,49124,49126,49132,49134,49140,49142,49144],{},[1707,49109,49110,49112],{},[898,49111,1878],{},[898,49113,12546],{},[1716,49115,1913],{},[7204,49117,49118,49120,49122],{},[898,49119,1916],{},[898,49121,12546],{},[898,49123,16690],{},[1716,49125,1920],{"stretchy":1919},[1707,49127,49128,49130],{},[898,49129,1690],{},[1712,49131,1714],{},[1716,49133,1719],{"separator":1718},[1707,49135,49136,49138],{},[898,49137,1690],{},[1712,49139,1726],{},[1716,49141,1719],{"separator":1718},[898,49143,1758],{},[1716,49145,1925],{"stretchy":1919},[902,49147,49148],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,49150,49151,49154,49155,49168,49169,49098,49209,1853],{},[38,49152,49153],{},"Duální"," (Hicks): zadáno ",[883,49156,49158],{"className":49157},[886],[888,49159,49160],{"xmlns":890},[892,49161,49162,49166],{},[895,49163,49164],{},[898,49165,900],{},[902,49167,900],{"encoding":904},", hledáme minimální ",[883,49170,49172],{"className":49171},[886],[888,49173,49174],{"xmlns":890},[892,49175,49176,49206],{},[895,49177,49178,49184,49186,49192,49194,49200,49202,49204],{},[3074,49179,49180,49182],{},[898,49181,1805],{},[1716,49183,3080],{},[1716,49185,1920],{"stretchy":1919},[1707,49187,49188,49190],{},[898,49189,1690],{},[1712,49191,1714],{},[1716,49193,1719],{"separator":1718},[1707,49195,49196,49198],{},[898,49197,1690],{},[1712,49199,1726],{},[1716,49201,1719],{"separator":1718},[898,49203,900],{},[1716,49205,1925],{"stretchy":1919},[902,49207,49208],{"encoding":904},"E^*(P_1, P_2, U)",[883,49210,49212],{"className":49211},[886],[888,49213,49214],{"xmlns":890},[892,49215,49216,49257],{},[895,49217,49218,49224,49226,49235,49237,49243,49245,49251,49253,49255],{},[1707,49219,49220,49222],{},[898,49221,1878],{},[898,49223,12546],{},[1716,49225,1913],{},[7204,49227,49228,49230,49232],{},[898,49229,1916],{},[898,49231,12546],{},[898,49233,49234],{},"H",[1716,49236,1920],{"stretchy":1919},[1707,49238,49239,49241],{},[898,49240,1690],{},[1712,49242,1714],{},[1716,49244,1719],{"separator":1718},[1707,49246,49247,49249],{},[898,49248,1690],{},[1712,49250,1726],{},[1716,49252,1719],{"separator":1718},[898,49254,900],{},[1716,49256,1925],{"stretchy":1919},[902,49258,49259],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,49261,49262,49263,49266,49267,49270],{},"Proč se studují obě? Marshallova poptávka je ",[38,49264,49265],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,49268,49269],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,49272,49274],{"id":49273},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,49276,49278],{"id":49277},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,49280,49281,49284,49285,49317,49318,49356,49357,49383],{},[38,49282,49283],{},"6.8"," Jsou dány užitečnost ",[883,49286,49288],{"className":49287},[886],[888,49289,49290],{"xmlns":890},[892,49291,49292,49314],{},[895,49293,49294,49296,49298,49306],{},[898,49295,900],{},[1716,49297,1913],{},[7204,49299,49300,49302,49304],{},[898,49301,1878],{},[1712,49303,1714],{},[1712,49305,5771],{},[7204,49307,49308,49310,49312],{},[898,49309,1878],{},[1712,49311,1726],{},[1712,49313,5771],{},[902,49315,49316],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,49319,49321],{"className":49320},[886],[888,49322,49323],{"xmlns":890},[892,49324,49325,49353],{},[895,49326,49327,49335,49337,49339,49341,49349,49351],{},[7204,49328,49329,49331,49333],{},[898,49330,1690],{},[1712,49332,1714],{},[1716,49334,3080],{},[1716,49336,1913],{},[1712,49338,6849],{},[1716,49340,1719],{"separator":1718},[7204,49342,49343,49345,49347],{},[898,49344,1690],{},[1712,49346,1726],{},[1716,49348,3080],{},[1716,49350,1913],{},[1712,49352,2998],{},[902,49354,49355],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,49358,49360],{"className":49359},[886],[888,49361,49362],{"xmlns":890},[892,49363,49364,49380],{},[895,49365,49366,49372,49374],{},[1707,49367,49368,49370],{},[898,49369,1878],{},[1712,49371,1714],{},[1716,49373,1719],{"separator":1718},[1707,49375,49376,49378],{},[898,49377,1878],{},[1712,49379,1726],{},[902,49381,49382],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,49385,49386,49389,49390,49432,49433,49464,49465,49487,49488,1853],{},[38,49387,49388],{},"6.9"," Jsou dány rozpočtové omezení ",[883,49391,49393],{"className":49392},[886],[888,49394,49395],{"xmlns":890},[892,49396,49397,49429],{},[895,49398,49399,49401,49403,49409,49415,49417,49423],{},[898,49400,1758],{},[1716,49402,1913],{},[1707,49404,49405,49407],{},[898,49406,1690],{},[1712,49408,1714],{},[1707,49410,49411,49413],{},[898,49412,1878],{},[1712,49414,1714],{},[1716,49416,1949],{},[1707,49418,49419,49421],{},[898,49420,1690],{},[1712,49422,1726],{},[1707,49424,49425,49427],{},[898,49426,1878],{},[1712,49428,1726],{},[902,49430,49431],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,49434,49436],{"className":49435},[886],[888,49437,49438],{"xmlns":890},[892,49439,49440,49462],{},[895,49441,49442,49444,49446,49454],{},[898,49443,900],{},[1716,49445,1913],{},[7204,49447,49448,49450,49452],{},[898,49449,1878],{},[1712,49451,1714],{},[1712,49453,5771],{},[7204,49455,49456,49458,49460],{},[898,49457,1878],{},[1712,49459,1726],{},[1712,49461,5771],{},[902,49463,49316],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,49466,49468],{"className":49467},[886],[888,49469,49470],{"xmlns":890},[892,49471,49472,49484],{},[895,49473,49474,49480,49482],{},[3074,49475,49476,49478],{},[898,49477,1758],{},[1716,49479,3080],{},[1716,49481,1913],{},[1712,49483,28904],{},[902,49485,49486],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,49489,49491],{"className":49490},[886],[888,49492,49493],{"xmlns":890},[892,49494,49495,49523],{},[895,49496,49497,49505,49507,49509,49511,49519,49521],{},[7204,49498,49499,49501,49503],{},[898,49500,1690],{},[1712,49502,1714],{},[1716,49504,3080],{},[1716,49506,1913],{},[1712,49508,6985],{},[1716,49510,1719],{"separator":1718},[7204,49512,49513,49515,49517],{},[898,49514,1690],{},[1712,49516,1726],{},[1716,49518,3080],{},[1716,49520,1913],{},[1712,49522,2998],{},[902,49524,49525],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,49527,49528,49531,49532,2772,49564,49594,49595,1853],{},[38,49529,49530],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,49533,49535],{"className":49534},[886],[888,49536,49537],{"xmlns":890},[892,49538,49539,49561],{},[895,49540,49541,49543,49545,49553],{},[898,49542,900],{},[1716,49544,1913],{},[7204,49546,49547,49549,49551],{},[898,49548,1878],{},[1712,49550,1714],{},[898,49552,207],{},[7204,49554,49555,49557,49559],{},[898,49556,1878],{},[1712,49558,1726],{},[898,49560,1952],{},[902,49562,49563],{"encoding":904},"U = Q_1^a Q_2^b",[883,49565,49567],{"className":49566},[886],[888,49568,49569],{"xmlns":890},[892,49570,49571,49591],{},[895,49572,49573,49575,49577,49579,49581,49583,49585,49587,49589],{},[898,49574,207],{},[1716,49576,1719],{"separator":1718},[898,49578,1952],{},[1716,49580,3605],{},[1716,49582,19153],{"stretchy":1919},[1712,49584,2505],{},[1716,49586,1719],{"separator":1718},[1712,49588,1714],{},[1716,49590,19170],{"stretchy":1919},[902,49592,49593],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,49596,49598],{"className":49597},[886],[888,49599,49600],{"xmlns":890},[892,49601,49602,49634],{},[895,49603,49604,49606,49608,49614,49620,49622,49628],{},[898,49605,1758],{},[1716,49607,1913],{},[1707,49609,49610,49612],{},[898,49611,1690],{},[1712,49613,1714],{},[1707,49615,49616,49618],{},[898,49617,1878],{},[1712,49619,1714],{},[1716,49621,1949],{},[1707,49623,49624,49626],{},[898,49625,1690],{},[1712,49627,1726],{},[1707,49629,49630,49632],{},[898,49631,1878],{},[1712,49633,1726],{},[902,49635,49431],{"encoding":904},[724,49637,49638,49641,49642,2772,49676,49594,49694,1853],{},[38,49639,49640],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,49643,49645],{"className":49644},[886],[888,49646,49647],{"xmlns":890},[892,49648,49649,49673],{},[895,49650,49651,49653,49655,49663,49665],{},[898,49652,900],{},[1716,49654,1913],{},[7204,49656,49657,49659,49661],{},[898,49658,1878],{},[1712,49660,1714],{},[898,49662,207],{},[1716,49664,1949],{},[7204,49666,49667,49669,49671],{},[898,49668,1878],{},[1712,49670,1726],{},[898,49672,207],{},[902,49674,49675],{"encoding":904},"U = Q_1^a + Q_2^a",[883,49677,49679],{"className":49678},[886],[888,49680,49681],{"xmlns":890},[892,49682,49683,49691],{},[895,49684,49685,49687,49689],{},[898,49686,207],{},[1716,49688,17231],{"mathvariant":2068},[1712,49690,2505],{},[902,49692,49693],{"encoding":904},"a \\neq 0",[883,49695,49697],{"className":49696},[886],[888,49698,49699],{"xmlns":890},[892,49700,49701,49733],{},[895,49702,49703,49705,49707,49713,49719,49721,49727],{},[898,49704,1758],{},[1716,49706,1913],{},[1707,49708,49709,49711],{},[898,49710,1690],{},[1712,49712,1714],{},[1707,49714,49715,49717],{},[898,49716,1878],{},[1712,49718,1714],{},[1716,49720,1949],{},[1707,49722,49723,49725],{},[898,49724,1690],{},[1712,49726,1726],{},[1707,49728,49729,49731],{},[898,49730,1878],{},[1712,49732,1726],{},[902,49734,49431],{"encoding":904},[198,49736,49738],{"id":49737},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,49740,49741,49284,49744,1343,49771,49793,49794,1343,49817,49841,49842,49867,49868,1853],{},[38,49742,49743],{},"6.12",[883,49745,49747],{"className":49746},[886],[888,49748,49749],{"xmlns":890},[892,49750,49751,49769],{},[895,49752,49753,49755,49757,49763],{},[898,49754,900],{},[1716,49756,1913],{},[1707,49758,49759,49761],{},[898,49760,1878],{},[1712,49762,1714],{},[1707,49764,49765,49767],{},[898,49766,1878],{},[1712,49768,1726],{},[902,49770,43988],{"encoding":904},[883,49772,49774],{"className":49773},[886],[888,49775,49776],{"xmlns":890},[892,49777,49778,49790],{},[895,49779,49780,49786,49788],{},[3074,49781,49782,49784],{},[898,49783,900],{},[1716,49785,3080],{},[1716,49787,1913],{},[1712,49789,2998],{},[902,49791,49792],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,49795,49797],{"className":49796},[886],[888,49798,49799],{"xmlns":890},[892,49800,49801,49815],{},[895,49802,49803,49811,49813],{},[7204,49804,49805,49807,49809],{},[898,49806,1690],{},[1712,49808,1714],{},[1716,49810,3080],{},[1716,49812,1913],{},[1712,49814,1726],{},[902,49816,44061],{"encoding":904},[883,49818,49820],{"className":49819},[886],[888,49821,49822],{"xmlns":890},[892,49823,49824,49838],{},[895,49825,49826,49834,49836],{},[7204,49827,49828,49830,49832],{},[898,49829,1690],{},[1712,49831,1726],{},[1716,49833,3080],{},[1716,49835,1913],{},[1712,49837,6849],{},[902,49839,49840],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,49843,49845],{"className":49844},[886],[888,49846,49847],{"xmlns":890},[892,49848,49849,49865],{},[895,49850,49851,49857,49859],{},[1707,49852,49853,49855],{},[898,49854,1878],{},[1712,49856,1714],{},[1716,49858,1719],{"separator":1718},[1707,49860,49861,49863],{},[898,49862,1878],{},[1712,49864,1726],{},[902,49866,49382],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,49869,49871],{"className":49870},[886],[888,49872,49873],{"xmlns":890},[892,49874,49875,49895],{},[895,49876,49877,49879,49881,49887,49889],{},[898,49878,900],{},[1716,49880,1913],{},[1707,49882,49883,49885],{},[898,49884,1878],{},[1712,49886,1714],{},[1716,49888,9532],{},[1707,49890,49891,49893],{},[898,49892,1878],{},[1712,49894,1726],{},[902,49896,49897],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,49899,49900,49903,49904,49945,49946,49968,49969,1853],{},[38,49901,49902],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,49905,49907],{"className":49906},[886],[888,49908,49909],{"xmlns":890},[892,49910,49911,49943],{},[895,49912,49913,49915,49917,49923,49929,49931,49937],{},[898,49914,1805],{},[1716,49916,1913],{},[1707,49918,49919,49921],{},[898,49920,1690],{},[1712,49922,1714],{},[1707,49924,49925,49927],{},[898,49926,1878],{},[1712,49928,1714],{},[1716,49930,1949],{},[1707,49932,49933,49935],{},[898,49934,1690],{},[1712,49936,1726],{},[1707,49938,49939,49941],{},[898,49940,1878],{},[1712,49942,1726],{},[902,49944,41712],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,49947,49949],{"className":49948},[886],[888,49950,49951],{"xmlns":890},[892,49952,49953,49965],{},[895,49954,49955,49961,49963],{},[3074,49956,49957,49959],{},[898,49958,900],{},[1716,49960,3080],{},[1716,49962,1913],{},[1712,49964,5778],{},[902,49966,49967],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,49970,49972],{"className":49971},[886],[888,49973,49974],{"xmlns":890},[892,49975,49976,50004],{},[895,49977,49978,49986,49988,49990,49992,50000,50002],{},[7204,49979,49980,49982,49984],{},[898,49981,1690],{},[1712,49983,1714],{},[1716,49985,3080],{},[1716,49987,1913],{},[1712,49989,2976],{},[1716,49991,1719],{"separator":1718},[7204,49993,49994,49996,49998],{},[898,49995,1690],{},[1712,49997,1726],{},[1716,49999,3080],{},[1716,50001,1913],{},[1712,50003,3221],{},[902,50005,50006],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,50008,14947],{"id":14946},[120,50010,50011,50068,50107,50127,50162,50216,50221,50227,50323,50368],{},[123,50012,50013,3495,50016,50065,50066,1853],{},[38,50014,50015],{},"Rozpočtové omezení (budget constraint)",[883,50017,50019],{"className":50018},[886],[888,50020,50021],{"xmlns":890},[892,50022,50023,50063],{},[895,50024,50025,50031,50033,50041,50047,50049,50057],{},[3074,50026,50027,50029],{},[898,50028,1758],{},[1716,50030,3080],{},[1716,50032,1913],{},[7204,50034,50035,50037,50039],{},[898,50036,1690],{},[1712,50038,1714],{},[1716,50040,3080],{},[1707,50042,50043,50045],{},[898,50044,1878],{},[1712,50046,1714],{},[1716,50048,1949],{},[7204,50050,50051,50053,50055],{},[898,50052,1690],{},[1712,50054,1726],{},[1716,50056,3080],{},[1707,50058,50059,50061],{},[898,50060,1878],{},[1712,50062,1726],{},[902,50064,31088],{"encoding":904}," — (6.12); ",[38,50067,41901],{},[123,50069,50070,50073,50074,1853],{},[38,50071,50072],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,50075,50077],{"className":50076},[886],[888,50078,50079],{"xmlns":890},[892,50080,50081,50105],{},[895,50082,50083,50085,50087,50095,50097],{},[2074,50084,24407],{},[1716,50086,1913],{},[7204,50088,50089,50091,50093],{},[898,50090,1690],{},[1712,50092,1714],{},[1716,50094,3080],{},[898,50096,3045],{"mathvariant":2068},[7204,50098,50099,50101,50103],{},[898,50100,1690],{},[1712,50102,1726],{},[1716,50104,3080],{},[902,50106,42744],{"encoding":904},[123,50108,50109,50124,50125,1853],{},[38,50110,42887,50111],{},[883,50112,50114],{"className":50113},[886],[888,50115,50116],{"xmlns":890},[892,50117,50118,50122],{},[895,50119,50120],{},[898,50121,30233],{},[902,50123,30286],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,50126,42909],{},[123,50128,50129,50132,50133,1853],{},[38,50130,50131],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,50134,50136],{"className":50135},[886],[888,50137,50138],{"xmlns":890},[892,50139,50140,50160],{},[895,50141,50142,50144,50146,50152,50154],{},[2074,50143,24407],{},[1716,50145,1913],{},[1707,50147,50148,50150],{},[898,50149,1690],{},[1712,50151,1714],{},[898,50153,3045],{"mathvariant":2068},[1707,50155,50156,50158],{},[898,50157,1690],{},[1712,50159,1726],{},[902,50161,41767],{"encoding":904},[123,50163,50164,3369,50167,50215],{},[38,50165,50166],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,50168,50170],{"className":50169},[886],[888,50171,50172],{"xmlns":890},[892,50173,50174,50212],{},[895,50175,50176,50182,50184,50190,50192,50198,50200,50206,50208,50210],{},[1707,50177,50178,50180],{},[898,50179,1878],{},[898,50181,12546],{},[1716,50183,1913],{},[1707,50185,50186,50188],{},[898,50187,1916],{},[898,50189,12546],{},[1716,50191,1920],{"stretchy":1919},[1707,50193,50194,50196],{},[898,50195,1690],{},[1712,50197,1714],{},[1716,50199,1719],{"separator":1718},[1707,50201,50202,50204],{},[898,50203,1690],{},[1712,50205,1726],{},[1716,50207,1719],{"separator":1718},[898,50209,1758],{},[1716,50211,1925],{"stretchy":1919},[902,50213,50214],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,50217,50218,50220],{},[38,50219,15128],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,50222,50223,50226],{},[38,50224,50225],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,50228,50229,3369,50231,50278,50279,50322],{},[38,50230,47799],{},[883,50232,50234],{"className":50233},[886],[888,50235,50236],{"xmlns":890},[892,50237,50238,50276],{},[895,50239,50240,50246,50248,50254,50256,50262,50264,50270,50272,50274],{},[1707,50241,50242,50244],{},[898,50243,1878],{},[898,50245,12546],{},[1716,50247,1913],{},[1707,50249,50250,50252],{},[898,50251,1916],{},[898,50253,12546],{},[1716,50255,1920],{"stretchy":1919},[1707,50257,50258,50260],{},[898,50259,1690],{},[1712,50261,1714],{},[1716,50263,1719],{"separator":1718},[1707,50265,50266,50268],{},[898,50267,1690],{},[1712,50269,1726],{},[1716,50271,1719],{"separator":1718},[898,50273,900],{},[1716,50275,1925],{"stretchy":1919},[902,50277,31612],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,50280,50282],{"className":50281},[886],[888,50283,50284],{"xmlns":890},[892,50285,50286,50320],{},[895,50287,50288,50290,50292,50306],{},[898,50289,900],{},[1716,50291,1913],{},[7204,50293,50294,50296,50298],{},[898,50295,1878],{},[1712,50297,1714],{},[895,50299,50300,50302,50304],{},[1712,50301,1714],{},[898,50303,3045],{"mathvariant":2068},[1712,50305,1726],{},[7204,50307,50308,50310,50312],{},[898,50309,1878],{},[1712,50311,1726],{},[895,50313,50314,50316,50318],{},[1712,50315,1714],{},[898,50317,3045],{"mathvariant":2068},[1712,50319,1726],{},[902,50321,46919],{"encoding":904},": (6.30).",[123,50324,50325,50367],{},[38,50326,50327,50328],{},"Bod dotyku ",[883,50329,50331],{"className":50330},[886],[888,50332,50333],{"xmlns":890},[892,50334,50335,50365],{},[895,50336,50337,50343,50345,50353,50355,50363],{},[3074,50338,50339,50341],{},[898,50340,1878],{},[1716,50342,3080],{},[1716,50344,2502],{"stretchy":1919},[7204,50346,50347,50349,50351],{},[898,50348,1878],{},[1712,50350,1714],{},[1716,50352,3080],{},[1716,50354,1719],{"separator":1718},[7204,50356,50357,50359,50361],{},[898,50358,1878],{},[1712,50360,1726],{},[1716,50362,3080],{},[1716,50364,2516],{"stretchy":1919},[902,50366,42092],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,50369,50370,50373,50374,50387,50388,50401],{},[38,50371,50372],{},"Dualita"," — ekvivalence max ",[883,50375,50377],{"className":50376},[886],[888,50378,50379],{"xmlns":890},[892,50380,50381,50385],{},[895,50382,50383],{},[898,50384,900],{},[902,50386,900],{"encoding":904}," a min ",[883,50389,50391],{"className":50390},[886],[888,50392,50393],{"xmlns":890},[892,50394,50395,50399],{},[895,50396,50397],{},[898,50398,1805],{},[902,50400,1805],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,50403,15740],{"id":15739},[120,50405,50406,50429,50445,50458,50469],{},[123,50407,50408,3495,50411,50414,50415,50428],{},[38,50409,50410],{},"Teorie před optimalizací:",[207,50412,880],{"className":50413,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,50416,50418],{"className":50417},[886],[888,50419,50420],{"xmlns":890},[892,50421,50422,50426],{},[895,50423,50424],{},[898,50425,900],{},[902,50427,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,50430,50431,3495,50434,50437,50438,50441,50442,1853],{},[38,50432,50433],{},"Matematický aparát:",[207,50435,793],{"className":50436,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,50439,784],{"className":50440,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,50443,15758],{"className":50444,"dataFsResolvedFilePath":764,"href":765},[210],[123,50446,50447,3495,50450,50453,50454,50457],{},[38,50448,50449],{},"Paralely:",[207,50451,24892],{"className":50452,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,50455,25743],{"className":50456,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,50459,50460,3495,50463,1343,50466],{},[38,50461,50462],{},"Přednášky:",[207,50464,1094],{"className":50465,"dataFsResolvedFilePath":838,"href":839},[210],[207,50467,1101],{"className":50468,"dataFsResolvedFilePath":868,"href":869},[210],[123,50470,50471,3495,50473],{},[38,50472,15794],{},[207,50474,15800],{"className":50475,"dataFsResolvedFilePath":15798,"href":15799},[210],{"title":641,"searchDepth":642,"depth":642,"links":50477},[50478,50479,50480,50485,50486,50487,50489,50492,50495,50497,50498,50500,50501,50505,50506],{"id":25808,"depth":642,"text":25809},{"id":41774,"depth":642,"text":41775},{"id":42169,"depth":642,"text":42170,"children":50481},[50482,50483],{"id":42289,"depth":649,"text":42290},{"id":42869,"depth":649,"text":50484},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":43331,"depth":642,"text":43332},{"id":43641,"depth":642,"text":43642},{"id":43959,"depth":642,"text":50488},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":44732,"depth":642,"text":44733,"children":50490},[50491],{"id":45488,"depth":649,"text":15128},{"id":45667,"depth":642,"text":45668,"children":50493},[50494],{"id":45924,"depth":649,"text":45925},{"id":46874,"depth":642,"text":50496},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":47798,"depth":642,"text":47799},{"id":48001,"depth":642,"text":50499},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} 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je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,63611,10082],{},[883,63613,63615],{"className":63614},[886],[888,63616,63617],{"xmlns":890},[892,63618,63619,63625],{},[895,63620,63621,63623],{},[898,63622,1690],{},[898,63624,5352],{},[902,63626,9969],{"encoding":904},") je rozdíl mezi tím, co výrobce dostal, a minimální cenou, za kterou by byl ochoten prodávat. Geometricky jsou to plochy mezi křivkou poptávky \u002F nabídky a rovnovážnou cenou; početně určité integrály. Součet ",[883,63629,63631],{"className":63630},[886],[888,63632,63633],{"xmlns":890},[892,63634,63635,63647],{},[895,63636,63637,63639,63641,63643,63645],{},[898,63638,9945],{},[898,63640,5352],{},[1716,63642,1949],{},[898,63644,1690],{},[898,63646,5352],{},[902,63648,63649],{"encoding":904},"CS + PS"," měří ",[38,63652,63653],{},"celkový blahobyt trhu",[724,63655,63656,1994,63658,1343,63660,8086,63675,1994,63677,1343,63679,63694,63695,63699,63700,1853],{},[38,63657,9933],{},[614,63659,9988],{},[883,63661,63663],{"className":63662},[886],[888,63664,63665],{"xmlns":890},[892,63666,63667,63673],{},[895,63668,63669,63671],{},[898,63670,9945],{},[898,63672,5352],{},[902,63674,9950],{"encoding":904},[38,63676,9953],{},[614,63678,10085],{},[883,63680,63682],{"className":63681},[886],[888,63683,63684],{"xmlns":890},[892,63685,63686,63692],{},[895,63687,63688,63690],{},[898,63689,1690],{},[898,63691,5352],{},[902,63693,9969],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,63696,63698],{"className":63697,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,63701,63703],{"className":63702,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[1855,63705],{},[115,63707,1241],{"id":63708},"úvod",[724,63710,63711,63712,63735,63736,63759,63760,63777,63778,17758,63810,63842,63843,63869,63870,63873,63874,63877,63878,4060,63912,2772,63933,1853],{},"Je dána funkce poptávky ",[883,63713,63715],{"className":63714},[886],[888,63716,63717],{"xmlns":890},[892,63718,63719,63733],{},[895,63720,63721,63723,63725,63727,63729,63731],{},[898,63722,1690],{},[1716,63724,1913],{},[898,63726,1916],{},[1716,63728,1920],{"stretchy":1919},[898,63730,1878],{},[1716,63732,1925],{"stretchy":1919},[902,63734,4115],{"encoding":904},", resp. funkce nabídky ",[883,63737,63739],{"className":63738},[886],[888,63740,63741],{"xmlns":890},[892,63742,63743,63757],{},[895,63744,63745,63747,63749,63751,63753,63755],{},[898,63746,1690],{},[1716,63748,1913],{},[898,63750,5352],{},[1716,63752,1920],{"stretchy":1919},[898,63754,1878],{},[1716,63756,1925],{"stretchy":1919},[902,63758,6036],{"encoding":904},". Pro pevně zadané množství ",[883,63761,63763],{"className":63762},[886],[888,63764,63765],{"xmlns":890},[892,63766,63767,63775],{},[895,63768,63769],{},[1707,63770,63771,63773],{},[898,63772,1878],{},[1712,63774,2505],{},[902,63776,3245],{"encoding":904}," je odpovídající cena ",[883,63779,63781],{"className":63780},[886],[888,63782,63783],{"xmlns":890},[892,63784,63785,63807],{},[895,63786,63787,63793,63795,63797,63799,63805],{},[1707,63788,63789,63791],{},[898,63790,1690],{},[1712,63792,2505],{},[1716,63794,1913],{},[898,63796,1916],{},[1716,63798,1920],{"stretchy":1919},[1707,63800,63801,63803],{},[898,63802,1878],{},[1712,63804,2505],{},[1716,63806,1925],{"stretchy":1919},[902,63808,63809],{"encoding":904},"P_0 = D(Q_0)",[883,63811,63813],{"className":63812},[886],[888,63814,63815],{"xmlns":890},[892,63816,63817,63839],{},[895,63818,63819,63825,63827,63829,63831,63837],{},[1707,63820,63821,63823],{},[898,63822,1690],{},[1712,63824,2505],{},[1716,63826,1913],{},[898,63828,5352],{},[1716,63830,1920],{"stretchy":1919},[1707,63832,63833,63835],{},[898,63834,1878],{},[1712,63836,2505],{},[1716,63838,1925],{"stretchy":1919},[902,63840,63841],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,63844,63846],{"className":63845},[886],[888,63847,63848],{"xmlns":890},[892,63849,63850,63866],{},[895,63851,63852,63858,63860],{},[1707,63853,63854,63856],{},[898,63855,1690],{},[1712,63857,2505],{},[2074,63859,8508],{},[1707,63861,63862,63864],{},[898,63863,1878],{},[1712,63865,2505],{},[902,63867,63868],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,63871,63872],{},"výdaje spotřebitele",", nebo ",[38,63875,63876],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,63879,63881],{"className":63880},[886],[888,63882,63883],{"xmlns":890},[892,63884,63885,63909],{},[895,63886,63887,63889,63891,63897,63899,63901,63903],{},[1712,63888,2505],{},[2074,63890,8508],{},[1707,63892,63893,63895],{},[898,63894,1878],{},[1712,63896,2505],{},[2074,63898,8508],{},[898,63900,10871],{},[2074,63902,8508],{},[1707,63904,63905,63907],{},[898,63906,1690],{},[1712,63908,2505],{},[902,63910,63911],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,63913,63915],{"className":63914},[886],[888,63916,63917],{"xmlns":890},[892,63918,63919,63931],{},[895,63920,63921,63923,63925,63927,63929],{},[1716,63922,1920],{"stretchy":1919},[898,63924,1878],{},[1716,63926,1719],{"separator":1718},[898,63928,1690],{},[1716,63930,1925],{"stretchy":1919},[902,63932,2608],{"encoding":904},[883,63934,63936],{"className":63935},[886],[888,63937,63938],{"xmlns":890},[892,63939,63940,63964],{},[895,63941,63942,63944,63946,63948,63954,63956,63962],{},[898,63943,10871],{},[1716,63945,1913],{},[1716,63947,2502],{"stretchy":1919},[1707,63949,63950,63952],{},[898,63951,1878],{},[1712,63953,2505],{},[1716,63955,1719],{"separator":1718},[1707,63957,63958,63960],{},[898,63959,1690],{},[1712,63961,2505],{},[1716,63963,2516],{"stretchy":1919},[902,63965,63966],{"encoding":904},"A = [Q_0, P_0]",[1635,63968,63969,63974,64032],{},[724,63970,63971,63973],{},[883,63972,1641],{}," Intuice",[120,63975,63976,64004],{},[123,63977,63978,63979,63982,63983,63985,63986,64003],{},"Za jednotky zboží nakoupené ",[38,63980,63981],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,63984,39040],{}," než ",[883,63987,63989],{"className":63988},[886],[888,63990,63991],{"xmlns":890},[892,63992,63993,64001],{},[895,63994,63995],{},[1707,63996,63997,63999],{},[898,63998,1690],{},[1712,64000,2505],{},[902,64002,3895],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,64005,64006,64007,64009,64010,64013,64014,64031],{},"Za jednotky zboží prodané ",[38,64008,63981],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,64011,64012],{},"nižší"," cenu než ",[883,64015,64017],{"className":64016},[886],[888,64018,64019],{"xmlns":890},[892,64020,64021,64029],{},[895,64022,64023],{},[1707,64024,64025,64027],{},[898,64026,1690],{},[1712,64028,2505],{},[902,64030,3895],{"encoding":904}," — rozdíl je jeho přebytek.",[724,64033,64034,64035,64038,64039,64042],{},"Přebytek je tedy rozdíl mezi ",[614,64036,64037],{},"ochotou"," (platit \u002F prodávat) a ",[614,64040,64041],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,64044,64045],{},[3682,64046],{"alt":9979,"className":64047,"src":9981},[210,3686],[1855,64049],{},[115,64051,64053,64054,1925],{"id":64052},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,64055,64057],{"className":64056},[886],[888,64058,64059],{"xmlns":890},[892,64060,64061,64067],{},[895,64062,64063,64065],{},[898,64064,9945],{},[898,64066,5352],{},[902,64068,9950],{"encoding":904},[198,64070,64072],{"id":64071},"definice-vzorec-214","Definice (vzorec 2.14)",[724,64074,64075,64076,64099,64100,64117,64118,2291],{},"Pro poptávku ",[883,64077,64079],{"className":64078},[886],[888,64080,64081],{"xmlns":890},[892,64082,64083,64097],{},[895,64084,64085,64087,64089,64091,64093,64095],{},[898,64086,1690],{},[1716,64088,1913],{},[898,64090,1916],{},[1716,64092,1920],{"stretchy":1919},[898,64094,1878],{},[1716,64096,1925],{"stretchy":1919},[902,64098,4115],{"encoding":904}," a pevně zadané ",[883,64101,64103],{"className":64102},[886],[888,64104,64105],{"xmlns":890},[892,64106,64107,64115],{},[895,64108,64109],{},[1707,64110,64111,64113],{},[898,64112,1878],{},[1712,64114,2505],{},[902,64116,3245],{"encoding":904}," s cenou ",[883,64119,64121],{"className":64120},[886],[888,64122,64123],{"xmlns":890},[892,64124,64125,64147],{},[895,64126,64127,64133,64135,64137,64139,64145],{},[1707,64128,64129,64131],{},[898,64130,1690],{},[1712,64132,2505],{},[1716,64134,1913],{},[898,64136,1916],{},[1716,64138,1920],{"stretchy":1919},[1707,64140,64141,64143],{},[898,64142,1878],{},[1712,64144,2505],{},[1716,64146,1925],{"stretchy":1919},[902,64148,63809],{"encoding":904},[883,64150,64152],{"className":64151},[886],[888,64153,64154],{"xmlns":890,"display":2004},[892,64155,64156,64232],{},[2008,64157,64158],{"width":2010},[2012,64159,64160,64162,64226,64228],{},[2015,64161],{"width":2017},[2015,64163,64164],{},[895,64165,64166,64168,64170,64172,64178,64180,64182,64194,64196,64198,64200,64202,64204,64206,64208,64210,64216,64218,64224],{},[898,64167,9945],{},[898,64169,5352],{},[1716,64171,1920],{"stretchy":1919},[1707,64173,64174,64176],{},[898,64175,1878],{},[1712,64177,2505],{},[1716,64179,1925],{"stretchy":1919},[1716,64181,1913],{},[7204,64183,64184,64186,64188],{},[1716,64185,10027],{},[1712,64187,2505],{},[1707,64189,64190,64192],{},[898,64191,1878],{},[1712,64193,2505],{},[898,64195,1916],{},[1716,64197,1920],{"stretchy":1919},[898,64199,1878],{},[1716,64201,1925],{"stretchy":1919},[2074,64203,8508],{},[898,64205,5198],{},[898,64207,1878],{},[1716,64209,2760],{},[1707,64211,64212,64214],{},[898,64213,1690],{},[1712,64215,2505],{},[2074,64217,8508],{},[1707,64219,64220,64222],{},[898,64221,1878],{},[1712,64223,2505],{},[898,64225,1853],{"mathvariant":2068},[2015,64227],{"width":2017},[2015,64229,64230],{},[2074,64231,10074],{},[902,64233,10077],{"encoding":904},[198,64235,16328],{"id":16327},[120,64237,64238,64330,64392],{},[123,64239,64240,64280,64281,64307,64308,64311,64312,64329],{},[883,64241,64243],{"className":64242},[886],[888,64244,64245],{"xmlns":890},[892,64246,64247,64277],{},[895,64248,64249],{},[2747,64250,64251,64263,64265,64267,64269,64271,64273,64275],{"scriptlevel":2505,"displaystyle":1718},[7204,64252,64253,64255,64257],{},[1716,64254,10027],{},[1712,64256,2505],{},[1707,64258,64259,64261],{},[898,64260,1878],{},[1712,64262,2505],{},[898,64264,1916],{},[1716,64266,1920],{"stretchy":1919},[898,64268,1878],{},[1716,64270,1925],{"stretchy":1919},[2074,64272,8508],{},[898,64274,5198],{},[898,64276,1878],{},[902,64278,64279],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,64282,64284],{"className":64283},[886],[888,64285,64286],{"xmlns":890},[892,64287,64288,64304],{},[895,64289,64290,64292,64294,64296,64302],{},[1716,64291,2502],{"stretchy":1919},[1712,64293,2505],{},[1716,64295,1719],{"separator":1718},[1707,64297,64298,64300],{},[898,64299,1878],{},[1712,64301,2505],{},[1716,64303,2516],{"stretchy":1919},[902,64305,64306],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,64309,64310],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,64313,64315],{"className":64314},[886],[888,64316,64317],{"xmlns":890},[892,64318,64319,64327],{},[895,64320,64321],{},[1707,64322,64323,64325],{},[898,64324,1878],{},[1712,64326,2505],{},[902,64328,3245],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,64331,64332,64358,64359,2365],{},[883,64333,64335],{"className":64334},[886],[888,64336,64337],{"xmlns":890},[892,64338,64339,64355],{},[895,64340,64341,64347,64349],{},[1707,64342,64343,64345],{},[898,64344,1690],{},[1712,64346,2505],{},[2074,64348,8508],{},[1707,64350,64351,64353],{},[898,64352,1878],{},[1712,64354,2505],{},[902,64356,64357],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,64360,64362],{"className":64361},[886],[888,64363,64364],{"xmlns":890},[892,64365,64366,64390],{},[895,64367,64368,64370,64372,64378,64380,64382,64384],{},[1712,64369,2505],{},[2074,64371,8508],{},[1707,64373,64374,64376],{},[898,64375,1878],{},[1712,64377,2505],{},[2074,64379,8508],{},[898,64381,10871],{},[2074,64383,8508],{},[1707,64385,64386,64388],{},[898,64387,1690],{},[1712,64389,2505],{},[902,64391,63911],{"encoding":904},[123,64393,64394,64409,64410,64432,64433,64458,64459,2772,64485,2247,64517,1853],{},[883,64395,64397],{"className":64396},[886],[888,64398,64399],{"xmlns":890},[892,64400,64401,64407],{},[895,64402,64403,64405],{},[898,64404,9945],{},[898,64406,5352],{},[902,64408,9950],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,64411,64413],{"className":64412},[886],[888,64414,64415],{"xmlns":890},[892,64416,64417,64429],{},[895,64418,64419,64421,64423],{},[898,64420,1690],{},[1716,64422,1913],{},[1707,64424,64425,64427],{},[898,64426,1690],{},[1712,64428,2505],{},[902,64430,64431],{"encoding":904},"P = P_0"," v pásu ",[883,64434,64436],{"className":64435},[886],[888,64437,64438],{"xmlns":890},[892,64439,64440,64456],{},[895,64441,64442,64444,64446,64448,64454],{},[1716,64443,2502],{"stretchy":1919},[1712,64445,2505],{},[1716,64447,1719],{"separator":1718},[1707,64449,64450,64452],{},[898,64451,1878],{},[1712,64453,2505],{},[1716,64455,2516],{"stretchy":1919},[902,64457,64306],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,64460,64462],{"className":64461},[886],[888,64463,64464],{"xmlns":890},[892,64465,64466,64482],{},[895,64467,64468,64474,64476,64478,64480],{},[1707,64469,64470,64472],{},[898,64471,1690],{},[1712,64473,2505],{},[2074,64475,8508],{},[898,64477,10856],{},[2074,64479,8508],{},[898,64481,10871],{},[902,64483,64484],{"encoding":904},"P_0\\,B\\,A",[883,64486,64488],{"className":64487},[886],[888,64489,64490],{"xmlns":890},[892,64491,64492,64514],{},[895,64493,64494,64496,64498,64500,64502,64504,64506,64508,64510,64512],{},[898,64495,10856],{},[1716,64497,1913],{},[1716,64499,2502],{"stretchy":1919},[1712,64501,2505],{},[1716,64503,1719],{"separator":1718},[898,64505,1916],{},[1716,64507,1920],{"stretchy":1919},[1712,64509,2505],{},[1716,64511,1925],{"stretchy":1919},[1716,64513,2516],{"stretchy":1919},[902,64515,64516],{"encoding":904},"B = [0, D(0)]",[883,64518,64520],{"className":64519},[886],[888,64521,64522],{"xmlns":890},[892,64523,64524,64548],{},[895,64525,64526,64528,64530,64532,64538,64540,64546],{},[898,64527,10871],{},[1716,64529,1913],{},[1716,64531,2502],{"stretchy":1919},[1707,64533,64534,64536],{},[898,64535,1878],{},[1712,64537,2505],{},[1716,64539,1719],{"separator":1718},[1707,64541,64542,64544],{},[898,64543,1690],{},[1712,64545,2505],{},[1716,64547,2516],{"stretchy":1919},[902,64549,63966],{"encoding":904},[724,64551,64552],{},[614,64553,64554,64555,64568,64569,64602,64603,42906,64628,1853],{},"Obrázek 2.24: Křivka poptávky ",[883,64556,64558],{"className":64557},[886],[888,64559,64560],{"xmlns":890},[892,64561,64562,64566],{},[895,64563,64564],{},[898,64565,1916],{},[902,64567,1916],{"encoding":904},", bod ",[883,64570,64572],{"className":64571},[886],[888,64573,64574],{"xmlns":890},[892,64575,64576,64600],{},[895,64577,64578,64580,64582,64584,64590,64592,64598],{},[898,64579,10871],{},[1716,64581,1913],{},[1716,64583,2502],{"stretchy":1919},[1707,64585,64586,64588],{},[898,64587,1878],{},[1712,64589,2505],{},[1716,64591,1719],{"separator":1718},[1707,64593,64594,64596],{},[898,64595,1690],{},[1712,64597,2505],{},[1716,64599,2516],{"stretchy":1919},[902,64601,63966],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,64604,64606],{"className":64605},[886],[888,64607,64608],{"xmlns":890},[892,64609,64610,64626],{},[895,64611,64612,64618,64620,64622,64624],{},[1707,64613,64614,64616],{},[898,64615,1690],{},[1712,64617,2505],{},[2074,64619,8508],{},[898,64621,10856],{},[2074,64623,8508],{},[898,64625,10871],{},[902,64627,64484],{"encoding":904},[883,64629,64631],{"className":64630},[886],[888,64632,64633],{"xmlns":890},[892,64634,64635,64641],{},[895,64636,64637,64639],{},[898,64638,9945],{},[898,64640,5352],{},[902,64642,9950],{"encoding":904},[1855,64644],{},[115,64646,64648,64649,1925],{"id":64647},"přebytek-výrobce-psps","Přebytek výrobce (",[883,64650,64652],{"className":64651},[886],[888,64653,64654],{"xmlns":890},[892,64655,64656,64662],{},[895,64657,64658,64660],{},[898,64659,1690],{},[898,64661,5352],{},[902,64663,9969],{"encoding":904},[198,64665,64667],{"id":64666},"definice-vzorec-215","Definice (vzorec 2.15)",[724,64669,64670,64671,64099,64694,64117,64711,2291],{},"Analogicky — pro nabídku ",[883,64672,64674],{"className":64673},[886],[888,64675,64676],{"xmlns":890},[892,64677,64678,64692],{},[895,64679,64680,64682,64684,64686,64688,64690],{},[898,64681,1690],{},[1716,64683,1913],{},[898,64685,5352],{},[1716,64687,1920],{"stretchy":1919},[898,64689,1878],{},[1716,64691,1925],{"stretchy":1919},[902,64693,6036],{"encoding":904},[883,64695,64697],{"className":64696},[886],[888,64698,64699],{"xmlns":890},[892,64700,64701,64709],{},[895,64702,64703],{},[1707,64704,64705,64707],{},[898,64706,1878],{},[1712,64708,2505],{},[902,64710,3245],{"encoding":904},[883,64712,64714],{"className":64713},[886],[888,64715,64716],{"xmlns":890},[892,64717,64718,64740],{},[895,64719,64720,64726,64728,64730,64732,64738],{},[1707,64721,64722,64724],{},[898,64723,1690],{},[1712,64725,2505],{},[1716,64727,1913],{},[898,64729,5352],{},[1716,64731,1920],{"stretchy":1919},[1707,64733,64734,64736],{},[898,64735,1878],{},[1712,64737,2505],{},[1716,64739,1925],{"stretchy":1919},[902,64741,63841],{"encoding":904},[883,64743,64745],{"className":64744},[886],[888,64746,64747],{"xmlns":890,"display":2004},[892,64748,64749,64825],{},[2008,64750,64751],{"width":2010},[2012,64752,64753,64755,64819,64821],{},[2015,64754],{"width":2017},[2015,64756,64757],{},[895,64758,64759,64761,64763,64765,64771,64773,64775,64781,64783,64789,64791,64803,64805,64807,64809,64811,64813,64815,64817],{},[898,64760,1690],{},[898,64762,5352],{},[1716,64764,1920],{"stretchy":1919},[1707,64766,64767,64769],{},[898,64768,1878],{},[1712,64770,2505],{},[1716,64772,1925],{"stretchy":1919},[1716,64774,1913],{},[1707,64776,64777,64779],{},[898,64778,1690],{},[1712,64780,2505],{},[2074,64782,8508],{},[1707,64784,64785,64787],{},[898,64786,1878],{},[1712,64788,2505],{},[1716,64790,2760],{},[7204,64792,64793,64795,64797],{},[1716,64794,10027],{},[1712,64796,2505],{},[1707,64798,64799,64801],{},[898,64800,1878],{},[1712,64802,2505],{},[898,64804,5352],{},[1716,64806,1920],{"stretchy":1919},[898,64808,1878],{},[1716,64810,1925],{"stretchy":1919},[2074,64812,8508],{},[898,64814,5198],{},[898,64816,1878],{},[898,64818,1853],{"mathvariant":2068},[2015,64820],{"width":2017},[2015,64822,64823],{},[2074,64824,10170],{},[902,64826,10173],{"encoding":904},[198,64828,16328],{"id":64829},"geometrická-interpretace-1",[120,64831,64832,64880,64941],{},[123,64833,64834,3369,64859,64862,64863,1853],{},[883,64835,64837],{"className":64836},[886],[888,64838,64839],{"xmlns":890},[892,64840,64841,64857],{},[895,64842,64843,64849,64851],{},[1707,64844,64845,64847],{},[898,64846,1690],{},[1712,64848,2505],{},[2074,64850,8508],{},[1707,64852,64853,64855],{},[898,64854,1878],{},[1712,64856,2505],{},[902,64858,64357],{"encoding":904},[38,64860,64861],{},"tržba"," výrobce za prodané množství ",[883,64864,64866],{"className":64865},[886],[888,64867,64868],{"xmlns":890},[892,64869,64870,64878],{},[895,64871,64872],{},[1707,64873,64874,64876],{},[898,64875,1878],{},[1712,64877,2505],{},[902,64879,3245],{"encoding":904},[123,64881,64882,64922,64923,64940],{},[883,64883,64885],{"className":64884},[886],[888,64886,64887],{"xmlns":890},[892,64888,64889,64919],{},[895,64890,64891],{},[2747,64892,64893,64905,64907,64909,64911,64913,64915,64917],{"scriptlevel":2505,"displaystyle":1718},[7204,64894,64895,64897,64899],{},[1716,64896,10027],{},[1712,64898,2505],{},[1707,64900,64901,64903],{},[898,64902,1878],{},[1712,64904,2505],{},[898,64906,5352],{},[1716,64908,1920],{"stretchy":1919},[898,64910,1878],{},[1716,64912,1925],{"stretchy":1919},[2074,64914,8508],{},[898,64916,5198],{},[898,64918,1878],{},[902,64920,64921],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,64924,64926],{"className":64925},[886],[888,64927,64928],{"xmlns":890},[892,64929,64930,64938],{},[895,64931,64932],{},[1707,64933,64934,64936],{},[898,64935,1878],{},[1712,64937,2505],{},[902,64939,3245],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,64942,64943,64958,64959,64980,64981,1853],{},[883,64944,64946],{"className":64945},[886],[888,64947,64948],{"xmlns":890},[892,64949,64950,64956],{},[895,64951,64952,64954],{},[898,64953,1690],{},[898,64955,5352],{},[902,64957,9969],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,64960,64962],{"className":64961},[886],[888,64963,64964],{"xmlns":890},[892,64965,64966,64978],{},[895,64967,64968,64970,64972],{},[898,64969,1690],{},[1716,64971,1913],{},[1707,64973,64974,64976],{},[898,64975,1690],{},[1712,64977,2505],{},[902,64979,64431],{"encoding":904}," a křivkou nabídky v pásu ",[883,64982,64984],{"className":64983},[886],[888,64985,64986],{"xmlns":890},[892,64987,64988,65004],{},[895,64989,64990,64992,64994,64996,65002],{},[1716,64991,2502],{"stretchy":1919},[1712,64993,2505],{},[1716,64995,1719],{"separator":1718},[1707,64997,64998,65000],{},[898,64999,1878],{},[1712,65001,2505],{},[1716,65003,2516],{"stretchy":1919},[902,65005,64306],{"encoding":904},[724,65007,65008],{},[614,65009,65010],{},"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.",[1855,65012],{},[1635,65014,65015,65020],{},[724,65016,65017,65019],{},[883,65018,3776],{}," Postup výpočtu CS a PS",[152,65021,65022,65153,65263,65292,65426],{},[123,65023,65024,65025,65042,65043,65074,65075,65106,65107,1853],{},"Zjisti (nebo si zvol) množství ",[883,65026,65028],{"className":65027},[886],[888,65029,65030],{"xmlns":890},[892,65031,65032,65040],{},[895,65033,65034],{},[1707,65035,65036,65038],{},[898,65037,1878],{},[1712,65039,2505],{},[902,65041,3245],{"encoding":904}," a odpovídající cenu ",[883,65044,65046],{"className":65045},[886],[888,65047,65048],{"xmlns":890},[892,65049,65050,65072],{},[895,65051,65052,65058,65060,65062,65064,65070],{},[1707,65053,65054,65056],{},[898,65055,1690],{},[1712,65057,2505],{},[1716,65059,1913],{},[898,65061,1916],{},[1716,65063,1920],{"stretchy":1919},[1707,65065,65066,65068],{},[898,65067,1878],{},[1712,65069,2505],{},[1716,65071,1925],{"stretchy":1919},[902,65073,63809],{"encoding":904}," resp. ",[883,65076,65078],{"className":65077},[886],[888,65079,65080],{"xmlns":890},[892,65081,65082,65104],{},[895,65083,65084,65090,65092,65094,65096,65102],{},[1707,65085,65086,65088],{},[898,65087,1690],{},[1712,65089,2505],{},[1716,65091,1913],{},[898,65093,5352],{},[1716,65095,1920],{"stretchy":1919},[1707,65097,65098,65100],{},[898,65099,1878],{},[1712,65101,2505],{},[1716,65103,1925],{"stretchy":1919},[902,65105,63841],{"encoding":904},". V rovnováze platí ",[883,65108,65110],{"className":65109},[886],[888,65111,65112],{"xmlns":890},[892,65113,65114,65150],{},[895,65115,65116,65118,65120,65126,65128,65130,65132,65134,65140,65142,65144],{},[898,65117,1916],{},[1716,65119,1920],{"stretchy":1919},[3074,65121,65122,65124],{},[898,65123,1878],{},[898,65125,1805],{},[1716,65127,1925],{"stretchy":1919},[1716,65129,1913],{},[898,65131,5352],{},[1716,65133,1920],{"stretchy":1919},[3074,65135,65136,65138],{},[898,65137,1878],{},[898,65139,1805],{},[1716,65141,1925],{"stretchy":1919},[1716,65143,1913],{},[3074,65145,65146,65148],{},[898,65147,1690],{},[898,65149,1805],{},[902,65151,65152],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,65154,65155,65156,33909,65194,65209,65210,33909,65248,2365],{},"Spočti určitý integrál ",[883,65157,65159],{"className":65158},[886],[888,65160,65161],{"xmlns":890},[892,65162,65163,65191],{},[895,65164,65165,65177,65179,65181,65183,65185,65187,65189],{},[7204,65166,65167,65169,65171],{},[1716,65168,10027],{},[1712,65170,2505],{},[1707,65172,65173,65175],{},[898,65174,1878],{},[1712,65176,2505],{},[898,65178,1916],{},[1716,65180,1920],{"stretchy":1919},[898,65182,1878],{},[1716,65184,1925],{"stretchy":1919},[2074,65186,8508],{},[898,65188,5198],{},[898,65190,1878],{},[902,65192,65193],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,65195,65197],{"className":65196},[886],[888,65198,65199],{"xmlns":890},[892,65200,65201,65207],{},[895,65202,65203,65205],{},[898,65204,9945],{},[898,65206,5352],{},[902,65208,9950],{"encoding":904},") nebo ",[883,65211,65213],{"className":65212},[886],[888,65214,65215],{"xmlns":890},[892,65216,65217,65245],{},[895,65218,65219,65231,65233,65235,65237,65239,65241,65243],{},[7204,65220,65221,65223,65225],{},[1716,65222,10027],{},[1712,65224,2505],{},[1707,65226,65227,65229],{},[898,65228,1878],{},[1712,65230,2505],{},[898,65232,5352],{},[1716,65234,1920],{"stretchy":1919},[898,65236,1878],{},[1716,65238,1925],{"stretchy":1919},[2074,65240,8508],{},[898,65242,5198],{},[898,65244,1878],{},[902,65246,65247],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,65249,65251],{"className":65250},[886],[888,65252,65253],{"xmlns":890},[892,65254,65255,65261],{},[895,65256,65257,65259],{},[898,65258,1690],{},[898,65260,5352],{},[902,65262,9969],{"encoding":904},[123,65264,65265,65266,1853],{},"Sestav obdélník ",[883,65267,65269],{"className":65268},[886],[888,65270,65271],{"xmlns":890},[892,65272,65273,65289],{},[895,65274,65275,65281,65283],{},[1707,65276,65277,65279],{},[898,65278,1690],{},[1712,65280,2505],{},[1716,65282,9532],{},[1707,65284,65285,65287],{},[898,65286,1878],{},[1712,65288,2505],{},[902,65290,65291],{"encoding":904},"P_0 \\cdot Q_0",[123,65293,65294,65295],{},"Dosaď:\n",[120,65296,65297,65362],{},[123,65298,65299,65357,65358,65361],{},[883,65300,65302],{"className":65301},[886],[888,65303,65304],{"xmlns":890},[892,65305,65306,65354],{},[895,65307,65308,65310,65312,65314,65326,65328,65330,65332,65334,65336,65338,65340,65342,65348],{},[898,65309,9945],{},[898,65311,5352],{},[1716,65313,1913],{},[7204,65315,65316,65318,65320],{},[1716,65317,10027],{},[1712,65319,2505],{},[1707,65321,65322,65324],{},[898,65323,1878],{},[1712,65325,2505],{},[898,65327,1916],{},[1716,65329,1920],{"stretchy":1919},[898,65331,1878],{},[1716,65333,1925],{"stretchy":1919},[2074,65335,8508],{},[898,65337,5198],{},[898,65339,1878],{},[1716,65341,2760],{},[1707,65343,65344,65346],{},[898,65345,1690],{},[1712,65347,2505],{},[1707,65349,65350,65352],{},[898,65351,1878],{},[1712,65353,2505],{},[902,65355,65356],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,65359,65360],{},"mínus"," obdélník)",[123,65363,65364,65422,65423,65425],{},[883,65365,65367],{"className":65366},[886],[888,65368,65369],{"xmlns":890},[892,65370,65371,65419],{},[895,65372,65373,65375,65377,65379,65385,65391,65393,65405,65407,65409,65411,65413,65415,65417],{},[898,65374,1690],{},[898,65376,5352],{},[1716,65378,1913],{},[1707,65380,65381,65383],{},[898,65382,1690],{},[1712,65384,2505],{},[1707,65386,65387,65389],{},[898,65388,1878],{},[1712,65390,2505],{},[1716,65392,2760],{},[7204,65394,65395,65397,65399],{},[1716,65396,10027],{},[1712,65398,2505],{},[1707,65400,65401,65403],{},[898,65402,1878],{},[1712,65404,2505],{},[898,65406,5352],{},[1716,65408,1920],{"stretchy":1919},[898,65410,1878],{},[1716,65412,1925],{"stretchy":1919},[2074,65414,8508],{},[898,65416,5198],{},[898,65418,1878],{},[902,65420,65421],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,65424,65360],{}," integrál)",[123,65427,65428,65429,65432],{},"Kontrola znaménka: obě hodnoty musí být ",[38,65430,65431],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[1855,65434],{},[115,65436,65438],{"id":65437},"příklady","Příklady",[198,65440,65442],{"id":65441},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1635,65444,65445],{},[724,65446,65447,65450,65451,12732,65474,65497,65498,1343,65518,1343,65535,1343,65552,65569,65570,65646,65647,65664,65665,65678],{},[883,65448,65449],{},"!example"," Zadání\nJsou dány poptávka ",[883,65452,65454],{"className":65453},[886],[888,65455,65456],{"xmlns":890},[892,65457,65458,65472],{},[895,65459,65460,65462,65464,65466,65468,65470],{},[898,65461,1690],{},[1716,65463,1913],{},[898,65465,207],{},[898,65467,1878],{},[1716,65469,1949],{},[898,65471,1952],{},[902,65473,1955],{"encoding":904},[883,65475,65477],{"className":65476},[886],[888,65478,65479],{"xmlns":890},[892,65480,65481,65495],{},[895,65482,65483,65485,65487,65489,65491,65493],{},[898,65484,1690],{},[1716,65486,1913],{},[898,65488,4478],{},[898,65490,1878],{},[1716,65492,1949],{},[898,65494,5198],{},[902,65496,5201],{"encoding":904}," s hodnotami ",[883,65499,65501],{"className":65500},[886],[888,65502,65503],{"xmlns":890},[892,65504,65505,65515],{},[895,65506,65507,65509,65511,65513],{},[898,65508,207],{},[1716,65510,1913],{},[1716,65512,2760],{},[1712,65514,7072],{},[902,65516,65517],{"encoding":904},"a = -3",[883,65519,65521],{"className":65520},[886],[888,65522,65523],{"xmlns":890},[892,65524,65525,65533],{},[895,65526,65527,65529,65531],{},[898,65528,1952],{},[1716,65530,1913],{},[1712,65532,2973],{},[902,65534,13658],{"encoding":904},[883,65536,65538],{"className":65537},[886],[888,65539,65540],{"xmlns":890},[892,65541,65542,65550],{},[895,65543,65544,65546,65548],{},[898,65545,4478],{},[1716,65547,1913],{},[1712,65549,5771],{},[902,65551,13676],{"encoding":904},[883,65553,65555],{"className":65554},[886],[888,65556,65557],{"xmlns":890},[892,65558,65559,65567],{},[895,65560,65561,65563,65565],{},[898,65562,5198],{},[1716,65564,1913],{},[1712,65566,2998],{},[902,65568,13694],{"encoding":904},".\nRovnovážné množství:\n",[883,65571,65573],{"className":65572},[886],[888,65574,65575],{"xmlns":890},[892,65576,65577,65643],{},[895,65578,65579,65585,65587,65605,65607,65631,65633,65639,65641],{},[3074,65580,65581,65583],{},[898,65582,1878],{},[898,65584,1805],{},[1716,65586,1913],{},[2750,65588,65589,65597],{},[895,65590,65591,65593,65595],{},[898,65592,1952],{},[1716,65594,2760],{},[898,65596,5198],{},[895,65598,65599,65601,65603],{},[898,65600,4478],{},[1716,65602,2760],{},[898,65604,207],{},[1716,65606,1913],{},[2750,65608,65609,65617],{},[895,65610,65611,65613,65615],{},[1712,65612,2973],{},[1716,65614,2760],{},[1712,65616,2998],{},[895,65618,65619,65621,65623,65625,65627,65629],{},[1712,65620,5771],{},[1716,65622,2760],{},[1716,65624,1920],{"stretchy":1919},[1716,65626,2760],{},[1712,65628,7072],{},[1716,65630,1925],{"stretchy":1919},[1716,65632,1913],{},[2750,65634,65635,65637],{},[1712,65636,2946],{},[1712,65638,9398],{},[1716,65640,19724],{},[1712,65642,9403],{},[902,65644,65645],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,65648,65650],{"className":65649},[886],[888,65651,65652],{"xmlns":890},[892,65653,65654,65662],{},[895,65655,65656],{},[3074,65657,65658,65660],{},[898,65659,1878],{},[898,65661,1805],{},[902,65663,7382],{"encoding":904}," (a) při změně samotného parametru ",[883,65666,65668],{"className":65667},[886],[888,65669,65670],{"xmlns":890},[892,65671,65672,65676],{},[895,65673,65674],{},[898,65675,4478],{},[902,65677,4478],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,65680,65681],{},[38,65682,65683,65684,9425,65697,3942,65710,23105],{},"Řešení (a) — změna ",[883,65685,65687],{"className":65686},[886],[888,65688,65689],{"xmlns":890},[892,65690,65691,65695],{},[895,65692,65693],{},[898,65694,4478],{},[902,65696,4478],{"encoding":904},[883,65698,65700],{"className":65699},[886],[888,65701,65702],{"xmlns":890},[892,65703,65704,65708],{},[895,65705,65706],{},[1712,65707,5771],{},[902,65709,9439],{"encoding":904},[883,65711,65713],{"className":65712},[886],[888,65714,65715],{"xmlns":890},[892,65716,65717,65721],{},[895,65718,65719],{},[1712,65720,9451],{},[902,65722,9454],{"encoding":904},[724,65724,65725,65726,65790,65791,2291],{},"Pomocí vzorce (2.13) pro ",[883,65727,65729],{"className":65728},[886],[888,65730,65731],{"xmlns":890},[892,65732,65733,65787],{},[895,65734,65735,65755,65757,65759],{},[2747,65736,65737],{"scriptlevel":2505,"displaystyle":1718},[2750,65738,65739,65749],{},[895,65740,65741,65743],{},[898,65742,23677],{"mathvariant":2068},[3074,65744,65745,65747],{},[898,65746,1878],{},[898,65748,1805],{},[895,65750,65751,65753],{},[898,65752,23677],{"mathvariant":2068},[898,65754,4478],{},[1716,65756,1913],{},[1716,65758,2760],{},[2747,65760,65761],{"scriptlevel":2505,"displaystyle":1718},[2750,65762,65763,65771],{},[895,65764,65765,65767,65769],{},[898,65766,1952],{},[1716,65768,2760],{},[898,65770,5198],{},[895,65772,65773,65775,65777,65779,65781],{},[1716,65774,1920],{"stretchy":1919},[898,65776,4478],{},[1716,65778,2760],{},[898,65780,207],{},[3074,65782,65783,65785],{},[1716,65784,1925],{"stretchy":1919},[1712,65786,1726],{},[902,65788,65789],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,65792,65794],{"className":65793},[886],[888,65795,65796],{"xmlns":890},[892,65797,65798,65820],{},[895,65799,65800,65802],{},[1716,65801,2760],{},[2747,65803,65804],{"scriptlevel":2505,"displaystyle":1718},[2750,65805,65806,65812],{},[3074,65807,65808,65810],{},[898,65809,1878],{},[898,65811,1805],{},[895,65813,65814,65816,65818],{},[898,65815,4478],{},[1716,65817,2760],{},[898,65819,207],{},[902,65821,65822],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,65824,65826],{"className":65825},[886],[888,65827,65828],{"xmlns":890,"display":2004},[892,65829,65830,65886],{},[895,65831,65832,65834,65840,65842,65844,65860,65862,65864,65866,65868,65870,65876,65878,65880,65882,65884],{},[898,65833,5198],{},[3074,65835,65836,65838],{},[898,65837,1878],{},[898,65839,1805],{},[1716,65841,1913],{},[1716,65843,2760],{},[2750,65845,65846,65852],{},[3074,65847,65848,65850],{},[898,65849,1878],{},[898,65851,1805],{},[895,65853,65854,65856,65858],{},[898,65855,4478],{},[1716,65857,2760],{},[898,65859,207],{},[2074,65861,8508],{},[898,65863,5198],{},[898,65865,4478],{},[1716,65867,1913],{},[1716,65869,2760],{},[2750,65871,65872,65874],{},[1712,65873,9570],{},[1712,65875,9398],{},[1716,65877,9532],{},[1712,65879,9535],{},[1716,65881,19724],{},[1716,65883,2760],{},[1712,65885,9542],{},[902,65887,65888],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,65890,65891],{},"Nové rovnovážné množství:",[883,65893,65895],{"className":65894},[886],[888,65896,65897],{"xmlns":890,"display":2004},[892,65898,65899,65922],{},[895,65900,65901,65909,65911,65913,65915,65917,65919],{},[7204,65902,65903,65905,65907],{},[898,65904,1878],{},[1712,65906,1714],{},[898,65908,1805],{},[1716,65910,8490],{},[1712,65912,9570],{},[1716,65914,2760],{},[1712,65916,9575],{},[1716,65918,1913],{},[1712,65920,65921],{},"8,326.",[902,65923,65924],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,65926,65927,3495,65930,1343,65957,1343,65979,1343,66001,19417,66023,1343,66042,1343,66063,1343,66082,1853],{},[38,65928,65929],{},"Řešení (b) — současná změna všech parametrů:",[883,65931,65933],{"className":65932},[886],[888,65934,65935],{"xmlns":890},[892,65936,65937,65954],{},[895,65938,65939,65941,65943,65945,65947,65949,65951],{},[898,65940,207],{},[1716,65942,2291],{},[1716,65944,2760],{},[1712,65946,7072],{},[1716,65948,16986],{},[1716,65950,2760],{},[1712,65952,65953],{},"2,5",[902,65955,65956],{"encoding":904},"a: -3 \\to -2{,}5",[883,65958,65960],{"className":65959},[886],[888,65961,65962],{"xmlns":890},[892,65963,65964,65976],{},[895,65965,65966,65968,65970,65972,65974],{},[898,65967,1952],{},[1716,65969,2291],{},[1712,65971,2973],{},[1716,65973,16986],{},[1712,65975,5837],{},[902,65977,65978],{"encoding":904},"b: 40 \\to 35",[883,65980,65982],{"className":65981},[886],[888,65983,65984],{"xmlns":890},[892,65985,65986,65998],{},[895,65987,65988,65990,65992,65994,65996],{},[898,65989,4478],{},[1716,65991,2291],{},[1712,65993,5771],{},[1716,65995,16986],{},[1712,65997,9451],{},[902,65999,66000],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,66002,66004],{"className":66003},[886],[888,66005,66006],{"xmlns":890},[892,66007,66008,66020],{},[895,66009,66010,66012,66014,66016,66018],{},[898,66011,5198],{},[1716,66013,2291],{},[1712,66015,2998],{},[1716,66017,16986],{},[1712,66019,16773],{},[902,66021,66022],{"encoding":904},"d: 10 \\to 11",[883,66024,66026],{"className":66025},[886],[888,66027,66028],{"xmlns":890},[892,66029,66030,66040],{},[895,66031,66032,66034,66036,66038],{},[898,66033,5198],{},[898,66035,207],{},[1716,66037,1913],{},[1712,66039,5771],{},[902,66041,9608],{"encoding":904},[883,66043,66045],{"className":66044},[886],[888,66046,66047],{"xmlns":890},[892,66048,66049,66061],{},[895,66050,66051,66053,66055,66057,66059],{},[898,66052,5198],{},[898,66054,1952],{},[1716,66056,1913],{},[1716,66058,2760],{},[1712,66060,6985],{},[902,66062,9630],{"encoding":904},[883,66064,66066],{"className":66065},[886],[888,66067,66068],{"xmlns":890},[892,66069,66070,66080],{},[895,66071,66072,66074,66076,66078],{},[898,66073,5198],{},[898,66075,4478],{},[1716,66077,1913],{},[1712,66079,9535],{},[902,66081,9650],{"encoding":904},[883,66083,66085],{"className":66084},[886],[888,66086,66087],{"xmlns":890},[892,66088,66089,66099],{},[895,66090,66091,66093,66095,66097],{},[898,66092,5198],{},[898,66094,5198],{},[1716,66096,1913],{},[1712,66098,1714],{},[902,66100,9670],{"encoding":904},[724,66102,66103,66104,66162],{},"Totální diferenciál ",[883,66105,66107],{"className":66106},[886],[888,66108,66109],{"xmlns":890},[892,66110,66111,66159],{},[895,66112,66113,66119,66121,66123,66125,66127,66129,66131,66133,66135,66137,66139],{},[3074,66114,66115,66117],{},[898,66116,1878],{},[898,66118,1805],{},[1716,66120,1920],{"stretchy":1919},[898,66122,207],{},[1716,66124,1719],{"separator":1718},[898,66126,1952],{},[1716,66128,1719],{"separator":1718},[898,66130,4478],{},[1716,66132,1719],{"separator":1718},[898,66134,5198],{},[1716,66136,1925],{"stretchy":1919},[1716,66138,1913],{},[2747,66140,66141],{"scriptlevel":2505,"displaystyle":1718},[2750,66142,66143,66151],{},[895,66144,66145,66147,66149],{},[898,66146,1952],{},[1716,66148,2760],{},[898,66150,5198],{},[895,66152,66153,66155,66157],{},[898,66154,4478],{},[1716,66156,2760],{},[898,66158,207],{},[902,66160,66161],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,66164,66166],{"className":66165},[886],[888,66167,66168],{"xmlns":890,"display":2004},[892,66169,66170,66290],{},[895,66171,66172,66174,66180,66182,66208,66210,66212,66214,66216,66228,66230,66232,66234,66236,66262,66264,66266,66268,66270,66282,66284,66286,66288],{},[898,66173,5198],{},[3074,66175,66176,66178],{},[898,66177,1878],{},[898,66179,1805],{},[1716,66181,1913],{},[2750,66183,66184,66192],{},[895,66185,66186,66188,66190],{},[898,66187,1952],{},[1716,66189,2760],{},[898,66191,5198],{},[895,66193,66194,66196,66198,66200,66202],{},[1716,66195,1920],{"stretchy":1919},[898,66197,4478],{},[1716,66199,2760],{},[898,66201,207],{},[3074,66203,66204,66206],{},[1716,66205,1925],{"stretchy":1919},[1712,66207,1726],{},[2074,66209,8508],{},[898,66211,5198],{},[898,66213,207],{},[1716,66215,1949],{},[2750,66217,66218,66220],{},[1712,66219,1714],{},[895,66221,66222,66224,66226],{},[898,66223,4478],{},[1716,66225,2760],{},[898,66227,207],{},[2074,66229,8508],{},[898,66231,5198],{},[898,66233,1952],{},[1716,66235,2760],{},[2750,66237,66238,66246],{},[895,66239,66240,66242,66244],{},[898,66241,1952],{},[1716,66243,2760],{},[898,66245,5198],{},[895,66247,66248,66250,66252,66254,66256],{},[1716,66249,1920],{"stretchy":1919},[898,66251,4478],{},[1716,66253,2760],{},[898,66255,207],{},[3074,66257,66258,66260],{},[1716,66259,1925],{"stretchy":1919},[1712,66261,1726],{},[2074,66263,8508],{},[898,66265,5198],{},[898,66267,4478],{},[1716,66269,2760],{},[2750,66271,66272,66274],{},[1712,66273,1714],{},[895,66275,66276,66278,66280],{},[898,66277,4478],{},[1716,66279,2760],{},[898,66281,207],{},[2074,66283,8508],{},[898,66285,5198],{},[898,66287,5198],{},[898,66289,1853],{"mathvariant":2068},[902,66291,66292],{"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.",[724,66294,66295,66296,1343,66318,1343,66349,1998],{},"Dosazením číselných hodnot (",[883,66297,66299],{"className":66298},[886],[888,66300,66301],{"xmlns":890},[892,66302,66303,66315],{},[895,66304,66305,66307,66309,66311,66313],{},[898,66306,4478],{},[1716,66308,2760],{},[898,66310,207],{},[1716,66312,1913],{},[1712,66314,9398],{},[902,66316,66317],{"encoding":904},"c - a = 3{,}5",[883,66319,66321],{"className":66320},[886],[888,66322,66323],{"xmlns":890},[892,66324,66325,66346],{},[895,66326,66327,66329,66331,66333,66335,66341,66343],{},[1716,66328,1920],{"stretchy":1919},[898,66330,4478],{},[1716,66332,2760],{},[898,66334,207],{},[3074,66336,66337,66339],{},[1716,66338,1925],{"stretchy":1919},[1712,66340,1726],{},[1716,66342,1913],{},[1712,66344,66345],{},"12,25",[902,66347,66348],{"encoding":904},"(c-a)^2 = 12{,}25",[883,66350,66352],{"className":66351},[886],[888,66353,66354],{"xmlns":890},[892,66355,66356,66368],{},[895,66357,66358,66360,66362,66364,66366],{},[898,66359,1952],{},[1716,66361,2760],{},[898,66363,5198],{},[1716,66365,1913],{},[1712,66367,2946],{},[902,66369,66370],{"encoding":904},"b - d = 30",[883,66372,66374],{"className":66373},[886],[888,66375,66376],{"xmlns":890,"display":2004},[892,66377,66378,66479],{},[895,66379,66380,66382,66388,66390,66398,66400,66402,66404,66406,66414,66416,66418,66420,66422,66424,66432,66434,66436,66438,66440,66448,66450,66452,66454,66456,66459,66461,66464,66466,66468,66470,66473,66475,66477],{},[898,66381,5198],{},[3074,66383,66384,66386],{},[898,66385,1878],{},[898,66387,1805],{},[1716,66389,8490],{},[2747,66391,66392],{"scriptlevel":2505,"displaystyle":1919},[2750,66393,66394,66396],{},[1712,66395,2946],{},[1712,66397,66345],{},[1716,66399,1920],{"stretchy":1919},[1712,66401,5771],{},[1716,66403,1925],{"stretchy":1919},[1716,66405,1949],{},[2747,66407,66408],{"scriptlevel":2505,"displaystyle":1919},[2750,66409,66410,66412],{},[1712,66411,1714],{},[1712,66413,9398],{},[1716,66415,1920],{"stretchy":1919},[1716,66417,2760],{},[1712,66419,6985],{},[1716,66421,1925],{"stretchy":1919},[1716,66423,2760],{},[2747,66425,66426],{"scriptlevel":2505,"displaystyle":1919},[2750,66427,66428,66430],{},[1712,66429,2946],{},[1712,66431,66345],{},[1716,66433,1920],{"stretchy":1919},[1712,66435,9535],{},[1716,66437,1925],{"stretchy":1919},[1716,66439,2760],{},[2747,66441,66442],{"scriptlevel":2505,"displaystyle":1919},[2750,66443,66444,66446],{},[1712,66445,1714],{},[1712,66447,9398],{},[1716,66449,1920],{"stretchy":1919},[1712,66451,1714],{},[1716,66453,1925],{"stretchy":1919},[1716,66455,19724],{},[1712,66457,66458],{},"1,224",[1716,66460,2760],{},[1712,66462,66463],{},"1,429",[1716,66465,2760],{},[1712,66467,9575],{},[1716,66469,2760],{},[1712,66471,66472],{},"0,286",[1716,66474,19724],{},[1716,66476,2760],{},[1712,66478,9821],{},[902,66480,66481],{"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.",[724,66483,9827,66484,1853],{},[883,66485,66487],{"className":66486},[886],[888,66488,66489],{"xmlns":890},[892,66490,66491,66513],{},[895,66492,66493,66501,66503,66505,66507,66509,66511],{},[7204,66494,66495,66497,66499],{},[898,66496,1878],{},[1712,66498,1714],{},[898,66500,1805],{},[1716,66502,8490],{},[1712,66504,9570],{},[1716,66506,2760],{},[1712,66508,9853],{},[1716,66510,19724],{},[1712,66512,9858],{},[902,66514,66515],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1635,66517,66518],{},[724,66519,66520,66522,66523,66544,66545,66571,66572,66575,66576,66672,66673,66696,66697,66713],{},[883,66521,2233],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,66524,66526],{"className":66525},[886],[888,66527,66528],{"xmlns":890},[892,66529,66530,66542],{},[895,66531,66532,66534,66536,66538,66540],{},[898,66533,8485],{"mathvariant":2068},[898,66535,1878],{},[1716,66537,8490],{},[1716,66539,2760],{},[1712,66541,9888],{},[902,66543,9891],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,66546,66548],{"className":66547},[886],[888,66549,66550],{"xmlns":890},[892,66551,66552,66568],{},[895,66553,66554,66556,66562,66564,66566],{},[898,66555,5198],{},[3074,66557,66558,66560],{},[898,66559,1878],{},[898,66561,1805],{},[1716,66563,19724],{},[1716,66565,2760],{},[1712,66567,9853],{},[902,66569,66570],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,66573,66574],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,66577,66579],{"className":66578},[886],[888,66580,66581],{"xmlns":890},[892,66582,66583,66669],{},[895,66584,66585,66593,66595,66629,66631,66655,66657,66664,66666],{},[7204,66586,66587,66589,66591],{},[898,66588,1878],{},[1712,66590,1714],{},[898,66592,1805],{},[1716,66594,1913],{},[2750,66596,66597,66613],{},[895,66598,66599,66605,66607],{},[3074,66600,66601,66603],{},[898,66602,1952],{},[1716,66604,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,66606,2760],{},[3074,66608,66609,66611],{},[898,66610,5198],{},[1716,66612,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[895,66614,66615,66621,66623],{},[3074,66616,66617,66619],{},[898,66618,4478],{},[1716,66620,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,66622,2760],{},[3074,66624,66625,66627],{},[898,66626,207],{},[1716,66628,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,66630,1913],{},[2750,66632,66633,66641],{},[895,66634,66635,66637,66639],{},[1712,66636,5837],{},[1716,66638,2760],{},[1712,66640,16773],{},[895,66642,66643,66645,66647,66649,66651,66653],{},[1712,66644,9451],{},[1716,66646,2760],{},[1716,66648,1920],{"stretchy":1919},[1716,66650,2760],{},[1712,66652,65953],{},[1716,66654,1925],{"stretchy":1919},[1716,66656,1913],{},[2750,66658,66659,66661],{},[1712,66660,6769],{},[1712,66662,66663],{},"3,1",[1716,66665,19724],{},[1712,66667,66668],{},"7,742",[902,66670,66671],{"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 ",[883,66674,66676],{"className":66675},[886],[888,66677,66678],{"xmlns":890},[892,66679,66680,66693],{},[895,66681,66682,66684,66686,66688,66690],{},[898,66683,8485],{"mathvariant":2068},[898,66685,1878],{},[1716,66687,19724],{},[1716,66689,2760],{},[1712,66691,66692],{},"0,829",[902,66694,66695],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,66698,66700],{"className":66699},[886],[888,66701,66702],{"xmlns":890},[892,66703,66704,66710],{},[895,66705,66706,66708],{},[1716,66707,2760],{},[1712,66709,9888],{},[902,66711,66712],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,66715,66716],{},[614,66717,66718,66719,66732],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,66720,66722],{"className":66721},[886],[888,66723,66724],{"xmlns":890},[892,66725,66726,66730],{},[895,66727,66728],{},[898,66729,1878],{},[902,66731,1878],{"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.",[198,66734,66736,66737],{"id":66735},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,66738,66740],{"className":66739},[886],[888,66741,66742],{"xmlns":890},[892,66743,66744,66750],{},[895,66745,66746,66748],{},[898,66747,1690],{},[898,66749,5352],{},[902,66751,9969],{"encoding":904},[1635,66753,66754],{},[724,66755,66756,66758,66759,66793,66794,66816],{},[883,66757,65449],{}," Zadání\nPro nabídku ",[883,66760,66762],{"className":66761},[886],[888,66763,66764],{"xmlns":890},[892,66765,66766,66790],{},[895,66767,66768,66770,66772,66774,66776,66778,66780,66782,66784,66786,66788],{},[898,66769,1690],{},[1716,66771,1913],{},[898,66773,5352],{},[1716,66775,1920],{"stretchy":1919},[898,66777,1878],{},[1716,66779,1925],{"stretchy":1919},[1716,66781,1913],{},[1712,66783,2998],{},[1716,66785,1949],{},[1712,66787,1726],{},[898,66789,1878],{},[902,66791,66792],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,66795,66797],{"className":66796},[886],[888,66798,66799],{"xmlns":890},[892,66800,66801,66813],{},[895,66802,66803,66809,66811],{},[1707,66804,66805,66807],{},[898,66806,1878],{},[1712,66808,2505],{},[1716,66810,1913],{},[1712,66812,2998],{},[902,66814,66815],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,66818,66819],{},[38,66820,36544],{},[724,66822,66823],{},"Odpovídající cena:",[883,66825,66827],{"className":66826},[886],[888,66828,66829],{"xmlns":890,"display":2004},[892,66830,66831,66866],{},[895,66832,66833,66839,66841,66843,66845,66847,66849,66851,66853,66855,66857,66859,66861,66863],{},[1707,66834,66835,66837],{},[898,66836,1690],{},[1712,66838,2505],{},[1716,66840,1913],{},[898,66842,5352],{},[1716,66844,1920],{"stretchy":1919},[1712,66846,2998],{},[1716,66848,1925],{"stretchy":1919},[1716,66850,1913],{},[1712,66852,2998],{},[1716,66854,1949],{},[1712,66856,1726],{},[1716,66858,9532],{},[1712,66860,2998],{},[1716,66862,1913],{},[1712,66864,66865],{},"30.",[902,66867,66868],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,66870,66871],{},"Dle vzorce (2.15):",[883,66873,66875],{"className":66874},[886],[888,66876,66877],{"xmlns":890,"display":2004},[892,66878,66879,66987],{},[895,66880,66881,66883,66885,66887,66889,66891,66893,66899,66905,66907,66915,66917,66919,66921,66923,66925,66927,66929,66931,66933,66935,66937,66939,66941,66943,66946,66948,66950,66952,66958,66966,66968,66970,66972,66974,66976,66978,66980,66982,66984],{},[898,66882,1690],{},[898,66884,5352],{},[1716,66886,1920],{"stretchy":1919},[1712,66888,2998],{},[1716,66890,1925],{"stretchy":1919},[1716,66892,1913],{},[1707,66894,66895,66897],{},[898,66896,1690],{},[1712,66898,2505],{},[1707,66900,66901,66903],{},[898,66902,1878],{},[1712,66904,2505],{},[1716,66906,2760],{},[7204,66908,66909,66911,66913],{},[1716,66910,10027],{},[1712,66912,2505],{},[1712,66914,2998],{},[1716,66916,1920],{"stretchy":1919},[1712,66918,2998],{},[1716,66920,1949],{},[1712,66922,1726],{},[898,66924,1878],{},[1716,66926,1925],{"stretchy":1919},[2074,66928,8508],{},[898,66930,5198],{},[898,66932,1878],{},[1716,66934,1913],{},[1712,66936,2998],{},[1716,66938,9532],{},[1712,66940,2946],{},[1716,66942,2760],{},[1716,66944,2502],{"fence":1919,"stretchy":1718,"minsize":66945,"maxsize":66945},"1.8em",[1712,66947,2998],{},[898,66949,1878],{},[1716,66951,1949],{},[3074,66953,66954,66956],{},[898,66955,1878],{},[1712,66957,1726],{},[7204,66959,66960,66962,66964],{},[1716,66961,2516],{"fence":1919,"stretchy":1718,"minsize":66945,"maxsize":66945},[1712,66963,2505],{},[1712,66965,2998],{},[1716,66967,1913],{},[1712,66969,43843],{},[1716,66971,2760],{},[1716,66973,1920],{"stretchy":1919},[1712,66975,12151],{},[1716,66977,1949],{},[1712,66979,12151],{},[1716,66981,1925],{"stretchy":1919},[1716,66983,1913],{},[1712,66985,66986],{},"100.",[902,66988,66989],{"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.",[724,66991,66992,66993,67014,67015,67035],{},"Přebytek výrobce při množství ",[883,66994,66996],{"className":66995},[886],[888,66997,66998],{"xmlns":890},[892,66999,67000,67012],{},[895,67001,67002,67008,67010],{},[1707,67003,67004,67006],{},[898,67005,1878],{},[1712,67007,2505],{},[1716,67009,1913],{},[1712,67011,2998],{},[902,67013,66815],{"encoding":904}," je tedy ",[883,67016,67018],{"className":67017},[886],[888,67019,67020],{"xmlns":890},[892,67021,67022,67032],{},[895,67023,67024,67026,67028,67030],{},[898,67025,1690],{},[898,67027,5352],{},[1716,67029,1913],{},[1712,67031,12151],{},[902,67033,67034],{"encoding":904},"PS = 100"," (peněžních jednotek).",[1855,67037],{},[115,67039,67041],{"id":67040},"cheat-sheet","Cheat sheet",[16,67043,67044,67057],{},[19,67045,67046],{},[22,67047,67048,67051,67054],{},[25,67049,67050],{},"Veličina",[25,67052,67053],{},"Vzorec",[25,67055,67056],{},"Geometrie",[30,67058,67059,67177,67291,67359],{},[22,67060,67061,67089,67145],{},[35,67062,67063],{},[883,67064,67066],{"className":67065},[886],[888,67067,67068],{"xmlns":890},[892,67069,67070,67086],{},[895,67071,67072,67074,67076,67078,67084],{},[898,67073,9945],{},[898,67075,5352],{},[1716,67077,1920],{"stretchy":1919},[1707,67079,67080,67082],{},[898,67081,1878],{},[1712,67083,2505],{},[1716,67085,1925],{"stretchy":1919},[902,67087,67088],{"encoding":904},"CS(Q_0)",[35,67090,67091],{},[883,67092,67094],{"className":67093},[886],[888,67095,67096],{"xmlns":890},[892,67097,67098,67142],{},[895,67099,67100],{},[2747,67101,67102,67114,67116,67118,67120,67122,67124,67126,67128,67130,67136],{"scriptlevel":2505,"displaystyle":1718},[7204,67103,67104,67106,67108],{},[1716,67105,10027],{},[1712,67107,2505],{},[1707,67109,67110,67112],{},[898,67111,1878],{},[1712,67113,2505],{},[898,67115,1916],{},[1716,67117,1920],{"stretchy":1919},[898,67119,1878],{},[1716,67121,1925],{"stretchy":1919},[2074,67123,8508],{},[898,67125,5198],{},[898,67127,1878],{},[1716,67129,2760],{},[1707,67131,67132,67134],{},[898,67133,1690],{},[1712,67135,2505],{},[1707,67137,67138,67140],{},[898,67139,1878],{},[1712,67141,2505],{},[902,67143,67144],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,67146,67147,67148,67151,67152,67155,67156],{},"plocha ",[38,67149,67150],{},"pod"," křivkou poptávky, ",[38,67153,67154],{},"nad"," čárou ",[883,67157,67159],{"className":67158},[886],[888,67160,67161],{"xmlns":890},[892,67162,67163,67175],{},[895,67164,67165,67167,67169],{},[898,67166,1690],{},[1716,67168,1913],{},[1707,67170,67171,67173],{},[898,67172,1690],{},[1712,67174,2505],{},[902,67176,64431],{"encoding":904},[22,67178,67179,67207,67263],{},[35,67180,67181],{},[883,67182,67184],{"className":67183},[886],[888,67185,67186],{"xmlns":890},[892,67187,67188,67204],{},[895,67189,67190,67192,67194,67196,67202],{},[898,67191,1690],{},[898,67193,5352],{},[1716,67195,1920],{"stretchy":1919},[1707,67197,67198,67200],{},[898,67199,1878],{},[1712,67201,2505],{},[1716,67203,1925],{"stretchy":1919},[902,67205,67206],{"encoding":904},"PS(Q_0)",[35,67208,67209],{},[883,67210,67212],{"className":67211},[886],[888,67213,67214],{"xmlns":890},[892,67215,67216,67260],{},[895,67217,67218],{},[2747,67219,67220,67226,67232,67234,67246,67248,67250,67252,67254,67256,67258],{"scriptlevel":2505,"displaystyle":1718},[1707,67221,67222,67224],{},[898,67223,1690],{},[1712,67225,2505],{},[1707,67227,67228,67230],{},[898,67229,1878],{},[1712,67231,2505],{},[1716,67233,2760],{},[7204,67235,67236,67238,67240],{},[1716,67237,10027],{},[1712,67239,2505],{},[1707,67241,67242,67244],{},[898,67243,1878],{},[1712,67245,2505],{},[898,67247,5352],{},[1716,67249,1920],{"stretchy":1919},[898,67251,1878],{},[1716,67253,1925],{"stretchy":1919},[2074,67255,8508],{},[898,67257,5198],{},[898,67259,1878],{},[902,67261,67262],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,67264,67147,67265,67267,67268,67155,67270],{},[38,67266,67154],{}," křivkou nabídky, ",[38,67269,67150],{},[883,67271,67273],{"className":67272},[886],[888,67274,67275],{"xmlns":890},[892,67276,67277,67289],{},[895,67278,67279,67281,67283],{},[898,67280,1690],{},[1716,67282,1913],{},[1707,67284,67285,67287],{},[898,67286,1690],{},[1712,67288,2505],{},[902,67290,64431],{"encoding":904},[22,67292,67293,67296,67323],{},[35,67294,67295],{},"Výdaje \u002F tržby",[35,67297,67298],{},[883,67299,67301],{"className":67300},[886],[888,67302,67303],{"xmlns":890},[892,67304,67305,67321],{},[895,67306,67307,67313,67315],{},[1707,67308,67309,67311],{},[898,67310,1690],{},[1712,67312,2505],{},[1716,67314,9532],{},[1707,67316,67317,67319],{},[898,67318,1878],{},[1712,67320,2505],{},[902,67322,65291],{"encoding":904},[35,67324,67325,67326],{},"obdélník ",[883,67327,67329],{"className":67328},[886],[888,67330,67331],{"xmlns":890},[892,67332,67333,67357],{},[895,67334,67335,67337,67339,67345,67347,67349,67351],{},[1712,67336,2505],{},[2074,67338,8508],{},[1707,67340,67341,67343],{},[898,67342,1878],{},[1712,67344,2505],{},[2074,67346,8508],{},[898,67348,10871],{},[2074,67350,8508],{},[1707,67352,67353,67355],{},[898,67354,1690],{},[1712,67356,2505],{},[902,67358,63911],{"encoding":904},[22,67360,67361,67364,67387],{},[35,67362,67363],{},"Celkový přebytek",[35,67365,67366],{},[883,67367,67369],{"className":67368},[886],[888,67370,67371],{"xmlns":890},[892,67372,67373,67385],{},[895,67374,67375,67377,67379,67381,67383],{},[898,67376,9945],{},[898,67378,5352],{},[1716,67380,1949],{},[898,67382,1690],{},[898,67384,5352],{},[902,67386,63649],{"encoding":904},[35,67388,67389],{},"součet obou ploch v rovnováze",[1855,67391],{},[115,67393,14947],{"id":14946},[120,67395,67396,67418,67440,67484,67528,67591,67619],{},[123,67397,67398,1994,67400,1343,67415,67417],{},[38,67399,9933],{},[883,67401,67403],{"className":67402},[886],[888,67404,67405],{"xmlns":890},[892,67406,67407,67413],{},[895,67408,67409,67411],{},[898,67410,9945],{},[898,67412,5352],{},[902,67414,9950],{"encoding":904},[614,67416,9988],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,67419,67420,1994,67422,1343,67437,67439],{},[38,67421,10082],{},[883,67423,67425],{"className":67424},[886],[888,67426,67427],{"xmlns":890},[892,67428,67429,67435],{},[895,67430,67431,67433],{},[898,67432,1690],{},[898,67434,5352],{},[902,67436,9969],{"encoding":904},[614,67438,10085],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,67441,67442,3369,67445,1853],{},[38,67443,67444],{},"Ochota platit",[883,67446,67448],{"className":67447},[886],[888,67449,67450],{"xmlns":890},[892,67451,67452,67482],{},[895,67453,67454],{},[2747,67455,67456,67468,67470,67472,67474,67476,67478,67480],{"scriptlevel":2505,"displaystyle":1718},[7204,67457,67458,67460,67462],{},[1716,67459,10027],{},[1712,67461,2505],{},[1707,67463,67464,67466],{},[898,67465,1878],{},[1712,67467,2505],{},[898,67469,1916],{},[1716,67471,1920],{"stretchy":1919},[898,67473,1878],{},[1716,67475,1925],{"stretchy":1919},[2074,67477,8508],{},[898,67479,5198],{},[898,67481,1878],{},[902,67483,64279],{"encoding":904},[123,67485,67486,3369,67489,1853],{},[38,67487,67488],{},"Minimální cena výrobce",[883,67490,67492],{"className":67491},[886],[888,67493,67494],{"xmlns":890},[892,67495,67496,67526],{},[895,67497,67498],{},[2747,67499,67500,67512,67514,67516,67518,67520,67522,67524],{"scriptlevel":2505,"displaystyle":1718},[7204,67501,67502,67504,67506],{},[1716,67503,10027],{},[1712,67505,2505],{},[1707,67507,67508,67510],{},[898,67509,1878],{},[1712,67511,2505],{},[898,67513,5352],{},[1716,67515,1920],{"stretchy":1919},[898,67517,1878],{},[1716,67519,1925],{"stretchy":1919},[2074,67521,8508],{},[898,67523,5198],{},[898,67525,1878],{},[902,67527,64921],{"encoding":904},[123,67529,67530,3369,67533,65422,67558,2365],{},[38,67531,67532],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,67534,67536],{"className":67535},[886],[888,67537,67538],{"xmlns":890},[892,67539,67540,67556],{},[895,67541,67542,67548,67550],{},[1707,67543,67544,67546],{},[898,67545,1690],{},[1712,67547,2505],{},[2074,67549,8508],{},[1707,67551,67552,67554],{},[898,67553,1878],{},[1712,67555,2505],{},[902,67557,64357],{"encoding":904},[883,67559,67561],{"className":67560},[886],[888,67562,67563],{"xmlns":890},[892,67564,67565,67589],{},[895,67566,67567,67569,67571,67577,67579,67581,67583],{},[1712,67568,2505],{},[2074,67570,8508],{},[1707,67572,67573,67575],{},[898,67574,1878],{},[1712,67576,2505],{},[2074,67578,8508],{},[898,67580,10871],{},[2074,67582,8508],{},[1707,67584,67585,67587],{},[898,67586,1690],{},[1712,67588,2505],{},[902,67590,63911],{"encoding":904},[123,67592,67593,67596,67597,67618],{},[38,67594,67595],{},"Celkový přebytek trhu"," — součet ",[883,67598,67600],{"className":67599},[886],[888,67601,67602],{"xmlns":890},[892,67603,67604,67616],{},[895,67605,67606,67608,67610,67612,67614],{},[898,67607,9945],{},[898,67609,5352],{},[1716,67611,1949],{},[898,67613,1690],{},[898,67615,5352],{},[902,67617,63649],{"encoding":904}," v rovnovážném bodě.",[123,67620,67621,67623,67624,1343,67637,67650,67651,1853],{},[38,67622,16328],{}," — plochy ohraničené křivkami ",[883,67625,67627],{"className":67626},[886],[888,67628,67629],{"xmlns":890},[892,67630,67631,67635],{},[895,67632,67633],{},[898,67634,1916],{},[902,67636,1916],{"encoding":904},[883,67638,67640],{"className":67639},[886],[888,67641,67642],{"xmlns":890},[892,67643,67644,67648],{},[895,67645,67646],{},[898,67647,5352],{},[902,67649,5352],{"encoding":904}," a přímkou ",[883,67652,67654],{"className":67653},[886],[888,67655,67656],{"xmlns":890},[892,67657,67658,67670],{},[895,67659,67660,67662,67664],{},[898,67661,1690],{},[1716,67663,1913],{},[1707,67665,67666,67668],{},[898,67667,1690],{},[1712,67669,2505],{},[902,67671,64431],{"encoding":904},[1855,67673],{},[115,67675,67677],{"id":67676},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,67679,67680,67681,67694,67695,67712],{},"Uvalení jednotkové daně ",[883,67682,67684],{"className":67683},[886],[888,67685,67686],{"xmlns":890},[892,67687,67688,67692],{},[895,67689,67690],{},[898,67691,4164],{},[902,67693,4164],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,67696,67698],{"className":67697},[886],[888,67699,67700],{"xmlns":890},[892,67701,67702,67710],{},[895,67703,67704],{},[3074,67705,67706,67708],{},[898,67707,1878],{},[898,67709,1805],{},[902,67711,7382],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,67714,67715],{},[3682,67716],{"alt":67717,"className":67718,"src":67719},"imek-prebytky-s-dani-deadweight",[210,3686],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,67721,67722,67723,67738,67739,67754,67755,65422,67758,67782,67783,1994,67786,67789,67790,1853],{},"Přebytek spotřebitele ",[883,67724,67726],{"className":67725},[886],[888,67727,67728],{"xmlns":890},[892,67729,67730,67736],{},[895,67731,67732,67734],{},[898,67733,9945],{},[898,67735,5352],{},[902,67737,9950],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,67740,67742],{"className":67741},[886],[888,67743,67744],{"xmlns":890},[892,67745,67746,67752],{},[895,67747,67748,67750],{},[898,67749,1690],{},[898,67751,5352],{},[902,67753,9969],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,67756,67757],{},"daňový příjem",[883,67759,67761],{"className":67760},[886],[888,67762,67763],{"xmlns":890},[892,67764,67765,67779],{},[895,67766,67767,67769,67771],{},[898,67768,4164],{},[1716,67770,9532],{},[7204,67772,67773,67775,67777],{},[898,67774,1878],{},[1712,67776,1714],{},[898,67778,1805],{},[902,67780,67781],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,67784,67785],{},"mrtvá ztráta",[614,67787,67788],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,67791,811],{"className":67792,"dataFsResolvedFilePath":809,"href":810},[210],[1855,67794],{},[115,67796,15740],{"id":15739},[120,67798,67799,67806,67818,67825,67832],{},[123,67800,67801,3495,67803],{},[38,67802,30011],{},[207,67804,802],{"className":67805,"dataFsResolvedFilePath":800,"href":801},[210],[123,67807,67808,3495,67810,67813,67814,67817],{},[38,67809,50433],{},[207,67811,775],{"className":67812,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,67815,15758],{"className":67816,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,67819,67820,3495,67822],{},[38,67821,30021],{},[207,67823,15780],{"className":67824,"dataFsResolvedFilePath":827,"href":828},[210],[123,67826,67827,3495,67829],{},[38,67828,15785],{},[207,67830,15789],{"className":67831,"dataFsResolvedFilePath":745,"href":746},[210],[123,67833,67834,3495,67836],{},[38,67835,15794],{},[207,67837,15800],{"className":67838,"dataFsResolvedFilePath":15798,"href":15799},[210],{"title":641,"searchDepth":642,"depth":642,"links":67840},[67841,67842,67847,67852,67857,67858,67859,67860],{"id":63708,"depth":642,"text":1241},{"id":64052,"depth":642,"text":67843,"children":67844},"Přebytek spotřebitele (CSCS)",[67845,67846],{"id":64071,"depth":649,"text":64072},{"id":16327,"depth":649,"text":16328},{"id":64647,"depth":642,"text":67848,"children":67849},"Přebytek výrobce (PSPS)",[67850,67851],{"id":64666,"depth":649,"text":64667},{"id":64829,"depth":649,"text":16328},{"id":65437,"depth":642,"text":65438,"children":67853},[67854,67855],{"id":65441,"depth":649,"text":65442},{"id":66735,"depth":649,"text":67856},"Příklad 2.13 — numerický výpočet PSPS",{"id":67040,"depth":642,"text":67041},{"id":14946,"depth":642,"text":14947},{"id":67676,"depth":642,"text":67677},{"id":15739,"depth":642,"text":15740},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,15857,67867,67868,25791,30029,67869,67870],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":67873,"title":67874,"body":67875,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":87204,"navigation":664,"path":87205,"seo":87206,"sources":87207,"stem":87208,"tags":87209,"type":15858,"updated":677,"__hash__":87215},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":67876,"toc":87168},[67877,67880,68066,68068,68159,68164,68490,68494,68501,68505,68550,68617,68648,68698,68733,68737,68796,68801,68867,68985,69087,69091,69114,69192,69235,69239,69268,69335,69341,69455,69459,69539,69576,69628,69826,69890,69977,69981,69984,70063,70066,70184,70203,70268,70272,70364,70432,70473,70527,70595,70632,70636,70694,70724,70935,71007,71059,71225,71318,71353,71357,71361,71398,71463,71518,71522,71545,71634,71738,71807,71811,71908,72021,72077,72131,72189,72250,72253,72289,72354,72384,72613,72671,72705,72709,72736,72815,72929,72950,73029,73031,73139,73143,73281,73603,73607,73610,73614,73663,73667,73921,74073,74080,74153,74337,74342,74685,74689,74712,74714,74735,74794,74804,74853,74995,75069,75164,75279,75377,75495,75499,75568,75573,75685,75830,75881,75993,76035,76039,76059,76120,76147,76209,76213,76235,76304,76584,76591,76621,76628,76821,76825,76903,76908,76984,76987,77075,77151,77218,77267,77370,77443,77564,77915,78028,78130,78134,78137,78144,78147,78183,78242,78251,78400,78624,78628,78691,78870,78962,79017,79021,79077,79147,79199,79220,79301,79304,79379,79423,79427,79468,79511,79537,79541,79612,79708,79770,79822,79925,80003,80026,80055,80059,80225,80342,80414,80729,80889,80893,80944,81006,81041,81071,81171,81213,81382,81387,81483,81521,81525,81644,81945,81947,81982,81986,81990,82118,82250,82572,82760,82838,82842,83147,83260,83406,83591,83697,83929,84044,84126,84245,84343,84384,84388,84443,84587,84741,84901,84994,85188,85500,85631,85760,85764,85836,85878,85929,85931,87126,87128],[12,67878,67874],{"id":67879},"příjem-náklady-zisk-a-nabídka-firmy",[1635,67881,67882],{},[724,67883,67884,9930,67886,3495,67889,67904,67905,3495,67908,67923,67924,3495,67927,67955,67956,67978,67979,68003,68004,68026,68027,68030,68031,68047,68048,1853],{},[883,67885,17723],{},[38,67887,67888],{},"Příjem",[883,67890,67892],{"className":67891},[886],[888,67893,67894],{"xmlns":890},[892,67895,67896,67902],{},[895,67897,67898,67900],{},[898,67899,4164],{},[898,67901,17840],{},[902,67903,17938],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,67906,67907],{},"náklady",[883,67909,67911],{"className":67910},[886],[888,67912,67913],{"xmlns":890},[892,67914,67915,67921],{},[895,67916,67917,67919],{},[898,67918,4164],{},[898,67920,9945],{},[902,67922,17103],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,67925,67926],{},"zisk",[883,67928,67930],{"className":67929},[886],[888,67931,67932],{"xmlns":890},[892,67933,67934,67952],{},[895,67935,67936,67938,67940,67942,67944,67946,67948,67950],{},[898,67937,1690],{},[898,67939,17840],{},[1716,67941,1913],{},[898,67943,4164],{},[898,67945,17840],{},[1716,67947,2760],{},[898,67949,4164],{},[898,67951,9945],{},[902,67953,67954],{"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: ",[883,67957,67959],{"className":67958},[886],[888,67960,67961],{"xmlns":890},[892,67962,67963,67975],{},[895,67964,67965,67967,67969,67971,67973],{},[898,67966,10871],{},[898,67968,9945],{},[1716,67970,1913],{},[898,67972,16690],{},[898,67974,9945],{},[902,67976,67977],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,67980,67982],{"className":67981},[886],[888,67983,67984],{"xmlns":890},[892,67985,67986,68000],{},[895,67987,67988,67990,67992,67994,67996,67998],{},[898,67989,10871],{},[898,67991,5298],{},[898,67993,9945],{},[1716,67995,1913],{},[898,67997,16690],{},[898,67999,9945],{},[902,68001,68002],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,68005,68007],{"className":68006},[886],[888,68008,68009],{"xmlns":890},[892,68010,68011,68023],{},[895,68012,68013,68015,68017,68019,68021],{},[898,68014,16690],{},[898,68016,17840],{},[1716,68018,1913],{},[898,68020,16690],{},[898,68022,9945],{},[902,68024,68025],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,68028,68029],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,68032,68034],{"className":68033},[886],[888,68035,68036],{"xmlns":890},[892,68037,68038,68044],{},[895,68039,68040,68042],{},[898,68041,16690],{},[898,68043,9945],{},[902,68045,68046],{"encoding":904},"MC"," nad bodem minima ",[883,68049,68051],{"className":68050},[886],[888,68052,68053],{"xmlns":890},[892,68054,68055,68063],{},[895,68056,68057,68059,68061],{},[898,68058,10871],{},[898,68060,5298],{},[898,68062,9945],{},[902,68064,68065],{"encoding":904},"AVC",[115,68067,1241],{"id":63708},[724,68069,68070,68071,68074,68075,68077,68078,1343,68081,1343,68084,68086,68087,68090,68091,68094,68095,68098,68099,9425,68114,1348,68129,9425,68144,2365],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,68072,68073],{},"příjmem"," (revenue) a ",[38,68076,67907],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,68079,68080],{},"zisku",[38,68082,68083],{},"bodů zvratu",[38,68085,15888],{}," a konstrukcí ",[38,68088,68089],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,68092,1145],{"className":68093,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,68096,24934],{"className":68097,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,68100,68102],{"className":68101},[886],[888,68103,68104],{"xmlns":890},[892,68105,68106,68112],{},[895,68107,68108,68110],{},[898,68109,4164],{},[898,68111,17840],{},[902,68113,17938],{"encoding":904},[883,68115,68117],{"className":68116},[886],[888,68118,68119],{"xmlns":890},[892,68120,68121,68127],{},[895,68122,68123,68125],{},[898,68124,16690],{},[898,68126,17840],{},[902,68128,20456],{"encoding":904},[883,68130,68132],{"className":68131},[886],[888,68133,68134],{"xmlns":890},[892,68135,68136,68142],{},[895,68137,68138,68140],{},[898,68139,4164],{},[898,68141,9945],{},[902,68143,17103],{"encoding":904},[883,68145,68147],{"className":68146},[886],[888,68148,68149],{"xmlns":890},[892,68150,68151,68157],{},[895,68152,68153,68155],{},[898,68154,16690],{},[898,68156,9945],{},[902,68158,68046],{"encoding":904},[724,68160,68161],{},[38,68162,68163],{},"Cílové znalosti:",[120,68165,68166,68330,68333,68336,68429,68476,68483],{},[123,68167,68168,68169,1343,68184,1343,68200,2247,68215,1343,68230,1343,68246,1343,68264,1343,68282,1343,68299,1343,68315,22241],{},"odvodit a interpretovat funkce ",[883,68170,68172],{"className":68171},[886],[888,68173,68174],{"xmlns":890},[892,68175,68176,68182],{},[895,68177,68178,68180],{},[898,68179,4164],{},[898,68181,17840],{},[902,68183,17938],{"encoding":904},[883,68185,68187],{"className":68186},[886],[888,68188,68189],{"xmlns":890},[892,68190,68191,68197],{},[895,68192,68193,68195],{},[898,68194,10871],{},[898,68196,17840],{},[902,68198,68199],{"encoding":904},"AR",[883,68201,68203],{"className":68202},[886],[888,68204,68205],{"xmlns":890},[892,68206,68207,68213],{},[895,68208,68209,68211],{},[898,68210,16690],{},[898,68212,17840],{},[902,68214,20456],{"encoding":904},[883,68216,68218],{"className":68217},[886],[888,68219,68220],{"xmlns":890},[892,68221,68222,68228],{},[895,68223,68224,68226],{},[898,68225,4164],{},[898,68227,9945],{},[902,68229,17103],{"encoding":904},[883,68231,68233],{"className":68232},[886],[888,68234,68235],{"xmlns":890},[892,68236,68237,68243],{},[895,68238,68239,68241],{},[898,68240,24240],{},[898,68242,9945],{},[902,68244,68245],{"encoding":904},"FC",[883,68247,68249],{"className":68248},[886],[888,68250,68251],{"xmlns":890},[892,68252,68253,68261],{},[895,68254,68255,68257,68259],{},[898,68256,4164],{},[898,68258,5298],{},[898,68260,9945],{},[902,68262,68263],{"encoding":904},"TVC",[883,68265,68267],{"className":68266},[886],[888,68268,68269],{"xmlns":890},[892,68270,68271,68279],{},[895,68272,68273,68275,68277],{},[898,68274,10871],{},[898,68276,24240],{},[898,68278,9945],{},[902,68280,68281],{"encoding":904},"AFC",[883,68283,68285],{"className":68284},[886],[888,68286,68287],{"xmlns":890},[892,68288,68289,68297],{},[895,68290,68291,68293,68295],{},[898,68292,10871],{},[898,68294,5298],{},[898,68296,9945],{},[902,68298,68065],{"encoding":904},[883,68300,68302],{"className":68301},[886],[888,68303,68304],{"xmlns":890},[892,68305,68306,68312],{},[895,68307,68308,68310],{},[898,68309,10871],{},[898,68311,9945],{},[902,68313,68314],{"encoding":904},"AC",[883,68316,68318],{"className":68317},[886],[888,68319,68320],{"xmlns":890},[892,68321,68322,68328],{},[895,68323,68324,68326],{},[898,68325,16690],{},[898,68327,9945],{},[902,68329,68046],{"encoding":904},[123,68331,68332],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,68334,68335],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,68337,68338,68339,68342,68343,6784,68385,22241],{},"osvojit si ",[38,68340,68341],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,68344,68346],{"className":68345},[886],[888,68347,68348],{"xmlns":890},[892,68349,68350,68382],{},[895,68351,68352,68354,68356,68358,68364,68366,68368,68370,68372,68374,68380],{},[898,68353,10871],{},[898,68355,9945],{},[1716,68357,1920],{"stretchy":1919},[1707,68359,68360,68362],{},[898,68361,1878],{},[1712,68363,2505],{},[1716,68365,1925],{"stretchy":1919},[1716,68367,1913],{},[898,68369,16690],{},[898,68371,9945],{},[1716,68373,1920],{"stretchy":1919},[1707,68375,68376,68378],{},[898,68377,1878],{},[1712,68379,2505],{},[1716,68381,1925],{"stretchy":1919},[902,68383,68384],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,68386,68388],{"className":68387},[886],[888,68389,68390],{"xmlns":890},[892,68391,68392,68426],{},[895,68393,68394,68396,68398,68400,68402,68408,68410,68412,68414,68416,68418,68424],{},[898,68395,10871],{},[898,68397,5298],{},[898,68399,9945],{},[1716,68401,1920],{"stretchy":1919},[1707,68403,68404,68406],{},[898,68405,1878],{},[1712,68407,2505],{},[1716,68409,1925],{"stretchy":1919},[1716,68411,1913],{},[898,68413,16690],{},[898,68415,9945],{},[1716,68417,1920],{"stretchy":1919},[1707,68419,68420,68422],{},[898,68421,1878],{},[1712,68423,2505],{},[1716,68425,1925],{"stretchy":1919},[902,68427,68428],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,68430,68338,68431,68342,68434,22241],{},[38,68432,68433],{},"princip maximalizace zisku",[883,68435,68437],{"className":68436},[886],[888,68438,68439],{"xmlns":890},[892,68440,68441,68473],{},[895,68442,68443,68445,68447,68449,68455,68457,68459,68461,68463,68465,68471],{},[898,68444,16690],{},[898,68446,17840],{},[1716,68448,1920],{"stretchy":1919},[1707,68450,68451,68453],{},[898,68452,1878],{},[1712,68454,2505],{},[1716,68456,1925],{"stretchy":1919},[1716,68458,1913],{},[898,68460,16690],{},[898,68462,9945],{},[1716,68464,1920],{"stretchy":1919},[1707,68466,68467,68469],{},[898,68468,1878],{},[1712,68470,2505],{},[1716,68472,1925],{"stretchy":1919},[902,68474,68475],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,68477,68478,68479,68482],{},"stanovit ",[38,68480,68481],{},"body zvratu"," a interval zisku;",[123,68484,68485,68486,68489],{},"zkonstruovat ",[38,68487,68488],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,68491,68493],{"id":68492},"příjem-firmy","Příjem firmy",[724,68495,68496],{},[3682,68497],{"alt":68498,"className":68499,"src":68500},"imek-ar-mr-dvojnasobny-sklon",[210,3686],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,68502,68504],{"id":68503},"celkový-příjem","Celkový příjem",[724,68506,68507,68508,1994,68523,68526,68527,43707],{},"Celkový příjem ",[883,68509,68511],{"className":68510},[886],[888,68512,68513],{"xmlns":890},[892,68514,68515,68521],{},[895,68516,68517,68519],{},[898,68518,4164],{},[898,68520,17840],{},[902,68522,17938],{"encoding":904},[38,68524,68525],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,68528,68530],{"className":68529},[886],[888,68531,68532],{"xmlns":890},[892,68533,68534,68548],{},[895,68535,68536,68538,68540,68542,68544,68546],{},[898,68537,1690],{},[1716,68539,1913],{},[898,68541,1916],{},[1716,68543,1920],{"stretchy":1919},[898,68545,1878],{},[1716,68547,1925],{"stretchy":1919},[902,68549,4115],{"encoding":904},[883,68551,68553],{"className":68552},[886],[888,68554,68555],{"xmlns":890,"display":2004},[892,68556,68557,68614],{},[2008,68558,68559],{"width":2010},[2012,68560,68561,68563,68607,68609],{},[2015,68562],{"width":2017},[2015,68564,68565],{},[895,68566,68567,68569,68571,68573,68575,68577,68579,68581,68583,68585,68587,68589,68591,68593,68595,68597,68599,68601,68603,68605],{},[898,68568,4164],{},[898,68570,17840],{},[1716,68572,1913],{},[898,68574,4164],{},[898,68576,17840],{},[1716,68578,1920],{"stretchy":1919},[898,68580,1878],{},[1716,68582,1925],{"stretchy":1919},[1716,68584,1913],{},[898,68586,1690],{},[1716,68588,9532],{},[898,68590,1878],{},[1716,68592,1913],{},[898,68594,1916],{},[1716,68596,1920],{"stretchy":1919},[898,68598,1878],{},[1716,68600,1925],{"stretchy":1919},[1716,68602,9532],{},[898,68604,1878],{},[898,68606,1853],{"mathvariant":2068},[2015,68608],{"width":2017},[2015,68610,68611],{},[2074,68612,68613],{},"(3.1)",[902,68615,68616],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,68618,68619,68620,68623,68624,68647],{},"Graf funkce se nazývá ",[38,68621,68622],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,68625,68627],{"className":68626},[886],[888,68628,68629],{"xmlns":890},[892,68630,68631,68645],{},[895,68632,68633,68635,68637,68639,68641,68643],{},[898,68634,1690],{},[1716,68636,1913],{},[898,68638,207],{},[898,68640,1878],{},[1716,68642,1949],{},[898,68644,1952],{},[902,68646,1955],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,68649,68651],{"className":68650},[886],[888,68652,68653],{"xmlns":890,"display":2004},[892,68654,68655,68695],{},[895,68656,68657,68659,68661,68663,68665,68667,68669,68671,68673,68675,68677,68679,68681,68687,68689,68691,68693],{},[898,68658,4164],{},[898,68660,17840],{},[1716,68662,1913],{},[898,68664,1878],{},[1716,68666,1920],{"stretchy":1919},[898,68668,207],{},[898,68670,1878],{},[1716,68672,1949],{},[898,68674,1952],{},[1716,68676,1925],{"stretchy":1919},[1716,68678,1913],{},[898,68680,207],{},[3074,68682,68683,68685],{},[898,68684,1878],{},[1712,68686,1726],{},[1716,68688,1949],{},[898,68690,1952],{},[898,68692,1878],{},[1716,68694,1719],{"separator":1718},[902,68696,68697],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,68699,68700,68701,68714,68715,68732],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,68702,68704],{"className":68703},[886],[888,68705,68706],{"xmlns":890},[892,68707,68708,68712],{},[895,68709,68710],{},[898,68711,900],{},[902,68713,900],{"encoding":904}," (jelikož ",[883,68716,68718],{"className":68717},[886],[888,68719,68720],{"xmlns":890},[892,68721,68722,68730],{},[895,68723,68724,68726,68728],{},[898,68725,207],{},[1716,68727,2704],{},[1712,68729,2505],{},[902,68731,8067],{"encoding":904},") procházející počátkem.",[2257,68734,68736],{"id":68735},"příklad-31","Příklad 3.1",[724,68738,68739,68742,68743,68779,68780,68795],{},[38,68740,68741],{},"Zadání."," Pro poptávku ",[883,68744,68746],{"className":68745},[886],[888,68747,68748],{"xmlns":890},[892,68749,68750,68776],{},[895,68751,68752,68754,68756,68758,68760,68762,68764,68766,68768,68770,68772,68774],{},[898,68753,1690],{},[1716,68755,1913],{},[898,68757,1916],{},[1716,68759,1920],{"stretchy":1919},[898,68761,1878],{},[1716,68763,1925],{"stretchy":1919},[1716,68765,1913],{},[1716,68767,2760],{},[1712,68769,1726],{},[898,68771,1878],{},[1716,68773,1949],{},[1712,68775,12151],{},[902,68777,68778],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,68781,68783],{"className":68782},[886],[888,68784,68785],{"xmlns":890},[892,68786,68787,68793],{},[895,68788,68789,68791],{},[898,68790,4164],{},[898,68792,17840],{},[902,68794,17938],{"encoding":904}," a charakterizujte jeho křivku.",[724,68797,68798,68800],{},[38,68799,36544],{}," Celkový příjem je",[883,68802,68804],{"className":68803},[886],[888,68805,68806],{"xmlns":890,"display":2004},[892,68807,68808,68864],{},[895,68809,68810,68812,68814,68816,68818,68820,68822,68824,68826,68828,68830,68832,68834,68836,68838,68840,68842,68844,68846,68848,68850,68856,68858,68860,68862],{},[898,68811,4164],{},[898,68813,17840],{},[1716,68815,1913],{},[898,68817,4164],{},[898,68819,17840],{},[1716,68821,1920],{"stretchy":1919},[898,68823,1878],{},[1716,68825,1925],{"stretchy":1919},[1716,68827,1913],{},[898,68829,1878],{},[1716,68831,1920],{"stretchy":1919},[1716,68833,2760],{},[1712,68835,1726],{},[898,68837,1878],{},[1716,68839,1949],{},[1712,68841,12151],{},[1716,68843,1925],{"stretchy":1919},[1716,68845,1913],{},[1716,68847,2760],{},[1712,68849,1726],{},[3074,68851,68852,68854],{},[898,68853,1878],{},[1712,68855,1726],{},[1716,68857,1949],{},[1712,68859,12151],{},[898,68861,1878],{},[898,68863,1853],{"mathvariant":2068},[902,68865,68866],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,68868,68869,68870,2247,68892,68914,68915,68933,68934,1853],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,68871,68873],{"className":68872},[886],[888,68874,68875],{"xmlns":890},[892,68876,68877,68889],{},[895,68878,68879,68885,68887],{},[1707,68880,68881,68883],{},[898,68882,1878],{},[1712,68884,1714],{},[1716,68886,1913],{},[1712,68888,2505],{},[902,68890,68891],{"encoding":904},"Q_1 = 0",[883,68893,68895],{"className":68894},[886],[888,68896,68897],{"xmlns":890},[892,68898,68899,68911],{},[895,68900,68901,68907,68909],{},[1707,68902,68903,68905],{},[898,68904,1878],{},[1712,68906,1726],{},[1716,68908,1913],{},[1712,68910,5808],{},[902,68912,68913],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,68916,68918],{"className":68917},[886],[888,68919,68920],{"xmlns":890},[892,68921,68922,68930],{},[895,68923,68924,68926,68928],{},[898,68925,1878],{},[1716,68927,1913],{},[1712,68929,5778],{},[902,68931,68932],{"encoding":904},"Q = 25"," ve výši ",[883,68935,68937],{"className":68936},[886],[888,68938,68939],{"xmlns":890},[892,68940,68941,68982],{},[895,68942,68943,68945,68955,68957,68959,68961,68963,68966,68968,68970,68972,68974,68976,68978,68980],{},[898,68944,4164],{},[1707,68946,68947,68949,68952],{},[898,68948,17840],{},[898,68950,68951],{},"max",[1716,68953,68954],{},"⁡",[1716,68956,1913],{},[1716,68958,2760],{},[1712,68960,1726],{},[1716,68962,9532],{},[1712,68964,68965],{},"625",[1716,68967,1949],{},[1712,68969,12151],{},[1716,68971,9532],{},[1712,68973,5778],{},[1716,68975,1913],{},[1712,68977,1714],{},[2074,68979,8508],{},[1712,68981,44505],{},[902,68983,68984],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,68986,68987],{},[614,68988,68989,68990,69024,69025,2247,69038,69051,69052,16504,69070,1853],{},"Obrázek 3.1: Parabola ",[883,68991,68993],{"className":68992},[886],[888,68994,68995],{"xmlns":890},[892,68996,68997,69021],{},[895,68998,68999,69001,69003,69005,69007,69009,69015,69017,69019],{},[898,69000,4164],{},[898,69002,17840],{},[1716,69004,1913],{},[1716,69006,2760],{},[1712,69008,1726],{},[3074,69010,69011,69013],{},[898,69012,1878],{},[1712,69014,1726],{},[1716,69016,1949],{},[1712,69018,12151],{},[898,69020,1878],{},[902,69022,69023],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,69026,69028],{"className":69027},[886],[888,69029,69030],{"xmlns":890},[892,69031,69032,69036],{},[895,69033,69034],{},[1712,69035,2505],{},[902,69037,2505],{"encoding":904},[883,69039,69041],{"className":69040},[886],[888,69042,69043],{"xmlns":890},[892,69044,69045,69049],{},[895,69046,69047],{},[1712,69048,5808],{},[902,69050,5808],{"encoding":904}," a maximem ",[883,69053,69055],{"className":69054},[886],[888,69056,69057],{"xmlns":890},[892,69058,69059,69067],{},[895,69060,69061,69063,69065],{},[1712,69062,1714],{},[2074,69064,8508],{},[1712,69066,44505],{},[902,69068,69069],{"encoding":904},"1\\,250",[883,69071,69073],{"className":69072},[886],[888,69074,69075],{"xmlns":890},[892,69076,69077,69085],{},[895,69078,69079,69081,69083],{},[898,69080,1878],{},[1716,69082,1913],{},[1712,69084,5778],{},[902,69086,68932],{"encoding":904},[198,69088,69090],{"id":69089},"průměrný-příjem","Průměrný příjem",[724,69092,69093,3495,69095,1994,69110,69113],{},[38,69094,69090],{},[883,69096,69098],{"className":69097},[886],[888,69099,69100],{"xmlns":890},[892,69101,69102,69108],{},[895,69103,69104,69106],{},[898,69105,10871],{},[898,69107,17840],{},[902,69109,68199],{"encoding":904},[38,69111,69112],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,69115,69117],{"className":69116},[886],[888,69118,69119],{"xmlns":890,"display":2004},[892,69120,69121,69189],{},[895,69122,69123,69125,69127,69129,69131,69133,69135,69137,69139,69141,69157,69159,69177,69179,69181,69183,69185,69187],{},[898,69124,10871],{},[898,69126,17840],{},[1716,69128,1913],{},[898,69130,10871],{},[898,69132,17840],{},[1716,69134,1920],{"stretchy":1919},[898,69136,1878],{},[1716,69138,1925],{"stretchy":1919},[1716,69140,1913],{},[2750,69142,69143,69155],{},[895,69144,69145,69147,69149,69151,69153],{},[898,69146,4164],{},[898,69148,17840],{},[1716,69150,1920],{"stretchy":1919},[898,69152,1878],{},[1716,69154,1925],{"stretchy":1919},[898,69156,1878],{},[1716,69158,1913],{},[2750,69160,69161,69175],{},[895,69162,69163,69165,69167,69169,69171,69173],{},[898,69164,1878],{},[2074,69166,8508],{},[898,69168,1916],{},[1716,69170,1920],{"stretchy":1919},[898,69172,1878],{},[1716,69174,1925],{"stretchy":1919},[898,69176,1878],{},[1716,69178,1913],{},[898,69180,1916],{},[1716,69182,1920],{"stretchy":1919},[898,69184,1878],{},[1716,69186,1925],{"stretchy":1919},[898,69188,1853],{"mathvariant":2068},[902,69190,69191],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1635,69193,69194],{},[724,69195,69196,69199,69200,1343,69203,1853],{},[883,69197,69198],{},"!note"," Klíčové pozorování\n",[38,69201,69202],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,69204,69206],{"className":69205},[886],[888,69207,69208],{"xmlns":890},[892,69209,69210,69232],{},[895,69211,69212,69214,69216,69218,69220,69222,69224,69226,69228,69230],{},[898,69213,10871],{},[898,69215,17840],{},[1716,69217,1920],{"stretchy":1919},[898,69219,1878],{},[1716,69221,1925],{"stretchy":1919},[1716,69223,1913],{},[898,69225,1916],{},[1716,69227,1920],{"stretchy":1919},[898,69229,1878],{},[1716,69231,1925],{"stretchy":1919},[902,69233,69234],{"encoding":904},"AR(Q) = D(Q)",[198,69236,69238],{"id":69237},"mezní-příjem","Mezní příjem",[724,69240,69241,69242,3495,69245,1994,69260,69263,69264,69267],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,69243,69244],{},"mezní příjem",[883,69246,69248],{"className":69247},[886],[888,69249,69250],{"xmlns":890},[892,69251,69252,69258],{},[895,69253,69254,69256],{},[898,69255,16690],{},[898,69257,17840],{},[902,69259,20456],{"encoding":904},[38,69261,69262],{},"marginal revenue","), definovaný jako ",[207,69265,1145],{"className":69266,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,69269,69271],{"className":69270},[886],[888,69272,69273],{"xmlns":890,"display":2004},[892,69274,69275,69332],{},[2008,69276,69277],{"width":2010},[2012,69278,69279,69281,69325,69327],{},[2015,69280],{"width":2017},[2015,69282,69283],{},[895,69284,69285,69287,69289,69291,69307,69309,69311,69317,69319,69321,69323],{},[898,69286,16690],{},[898,69288,17840],{},[1716,69290,1913],{},[2750,69292,69293,69301],{},[895,69294,69295,69297,69299],{},[898,69296,5198],{"mathvariant":2068},[898,69298,4164],{},[898,69300,17840],{},[895,69302,69303,69305],{},[898,69304,5198],{"mathvariant":2068},[898,69306,1878],{},[1716,69308,1913],{},[898,69310,4164],{},[3074,69312,69313,69315],{},[898,69314,17840],{},[1716,69316,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,69318,1920],{"stretchy":1919},[898,69320,1878],{},[1716,69322,1925],{"stretchy":1919},[898,69324,1853],{"mathvariant":2068},[2015,69326],{"width":2017},[2015,69328,69329],{},[2074,69330,69331],{},"(3.2)",[902,69333,69334],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,69336,69337,69338,69340],{},"Mezní příjem udává ",[38,69339,16476],{}," celkového příjmu vzhledem k množství.",[1635,69342,69343],{},[724,69344,69345,69347,69348,69374,69375,69392,69393,1853],{},[883,69346,1641],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,69349,69351],{"className":69350},[886],[888,69352,69353],{"xmlns":890},[892,69354,69355,69371],{},[895,69356,69357,69359,69361,69363,69369],{},[898,69358,16690],{},[898,69360,17840],{},[1716,69362,1920],{"stretchy":1919},[3074,69364,69365,69367],{},[898,69366,1878],{},[1716,69368,3080],{},[1716,69370,1925],{"stretchy":1919},[902,69372,69373],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,69376,69378],{"className":69377},[886],[888,69379,69380],{"xmlns":890},[892,69381,69382,69390],{},[895,69383,69384],{},[3074,69385,69386,69388],{},[898,69387,1878],{},[1716,69389,3080],{},[902,69391,43607],{"encoding":904},". Jinak řečeno: ",[883,69394,69396],{"className":69395},[886],[888,69397,69398],{"xmlns":890},[892,69399,69400,69452],{},[895,69401,69402,69404,69406,69408,69414,69416,69418,69420,69422,69424,69430,69432,69434,69436,69438,69440,69442,69444,69450],{},[898,69403,16690],{},[898,69405,17840],{},[1716,69407,1920],{"stretchy":1919},[3074,69409,69410,69412],{},[898,69411,1878],{},[1716,69413,3080],{},[1716,69415,1925],{"stretchy":1919},[1716,69417,8490],{},[898,69419,4164],{},[898,69421,17840],{},[1716,69423,1920],{"stretchy":1919},[3074,69425,69426,69428],{},[898,69427,1878],{},[1716,69429,3080],{},[1716,69431,1949],{},[1712,69433,1714],{},[1716,69435,1925],{"stretchy":1919},[1716,69437,2760],{},[898,69439,4164],{},[898,69441,17840],{},[1716,69443,1920],{"stretchy":1919},[3074,69445,69446,69448],{},[898,69447,1878],{},[1716,69449,3080],{},[1716,69451,1925],{"stretchy":1919},[902,69453,69454],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[2257,69456,69458],{"id":69457},"příklad-32","Příklad 3.2",[724,69460,69461,68742,69463,68779,69497,69512,69513,1853],{},[38,69462,68741],{},[883,69464,69466],{"className":69465},[886],[888,69467,69468],{"xmlns":890},[892,69469,69470,69494],{},[895,69471,69472,69474,69476,69478,69480,69482,69484,69486,69488,69490,69492],{},[898,69473,1690],{},[1716,69475,1913],{},[898,69477,1916],{},[1716,69479,1920],{"stretchy":1919},[898,69481,1878],{},[1716,69483,1925],{"stretchy":1919},[1716,69485,1913],{},[1712,69487,12151],{},[1716,69489,2760],{},[1712,69491,1726],{},[898,69493,1878],{},[902,69495,69496],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,69498,69500],{"className":69499},[886],[888,69501,69502],{"xmlns":890},[892,69503,69504,69510],{},[895,69505,69506,69508],{},[898,69507,16690],{},[898,69509,17840],{},[902,69511,20456],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,69514,69516],{"className":69515},[886],[888,69517,69518],{"xmlns":890},[892,69519,69520,69536],{},[895,69521,69522,69524,69526,69528,69530,69532,69534],{},[898,69523,1878],{},[1716,69525,1913],{},[1712,69527,3221],{},[1716,69529,1719],{"separator":1718},[1712,69531,6833],{},[1716,69533,1719],{"separator":1718},[1712,69535,2976],{},[902,69537,69538],{"encoding":904},"Q = 15, 16, 20",[724,69540,69541,3495,69543,69575],{},[38,69542,36544],{},[883,69544,69546],{"className":69545},[886],[888,69547,69548],{"xmlns":890},[892,69549,69550,69572],{},[895,69551,69552,69554,69556,69558,69560,69562,69564,69566],{},[898,69553,4164],{},[898,69555,17840],{},[1716,69557,1913],{},[1712,69559,12151],{},[898,69561,1878],{},[1716,69563,2760],{},[1712,69565,1726],{},[3074,69567,69568,69570],{},[898,69569,1878],{},[1712,69571,1726],{},[902,69573,69574],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,69577,69579],{"className":69578},[886],[888,69580,69581],{"xmlns":890,"display":2004},[892,69582,69583,69625],{},[895,69584,69585,69587,69589,69591,69593,69595,69597,69599,69601,69607,69613,69615,69617,69619,69621,69623],{},[898,69586,16690],{},[898,69588,17840],{},[1716,69590,1913],{},[1716,69592,1920],{"stretchy":1919},[1712,69594,12151],{},[898,69596,1878],{},[1716,69598,2760],{},[1712,69600,1726],{},[3074,69602,69603,69605],{},[898,69604,1878],{},[1712,69606,1726],{},[3074,69608,69609,69611],{},[1716,69610,1925],{"stretchy":1919},[1716,69612,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,69614,1913],{},[1712,69616,12151],{},[1716,69618,2760],{},[1712,69620,6849],{},[898,69622,1878],{},[898,69624,1853],{"mathvariant":2068},[902,69626,69627],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,69629,23470,69630,2574,69648,69674,69675,18195,69688,69703,69704,69717,69718,13380,69731,18195,69744,69759,69760,69773,69774,69805,69806,69825],{},[883,69631,69633],{"className":69632},[886],[888,69634,69635],{"xmlns":890},[892,69636,69637,69645],{},[895,69638,69639,69641,69643],{},[898,69640,1878],{},[1716,69642,1913],{},[1712,69644,3221],{},[902,69646,69647],{"encoding":904},"Q = 15",[883,69649,69651],{"className":69650},[886],[888,69652,69653],{"xmlns":890},[892,69654,69655,69671],{},[895,69656,69657,69659,69661,69663,69665,69667,69669],{},[898,69658,16690],{},[898,69660,17840],{},[1716,69662,1920],{"stretchy":1919},[1712,69664,3221],{},[1716,69666,1925],{"stretchy":1919},[1716,69668,1913],{},[1712,69670,2973],{},[902,69672,69673],{"encoding":904},"MR(15) = 40",": při množství ",[883,69676,69678],{"className":69677},[886],[888,69679,69680],{"xmlns":890},[892,69681,69682,69686],{},[895,69683,69684],{},[1712,69685,3221],{},[902,69687,3221],{"encoding":904},[883,69689,69691],{"className":69690},[886],[888,69692,69693],{"xmlns":890},[892,69694,69695,69701],{},[895,69696,69697,69699],{},[898,69698,4164],{},[898,69700,17840],{},[902,69702,17938],{"encoding":904}," mění asi ",[883,69705,69707],{"className":69706},[886],[888,69708,69709],{"xmlns":890},[892,69710,69711,69715],{},[895,69712,69713],{},[1712,69714,2973],{},[902,69716,2973],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,69719,69721],{"className":69720},[886],[888,69722,69723],{"xmlns":890},[892,69724,69725,69729],{},[895,69726,69727],{},[898,69728,1878],{},[902,69730,1878],{"encoding":904},[883,69732,69734],{"className":69733},[886],[888,69735,69736],{"xmlns":890},[892,69737,69738,69742],{},[895,69739,69740],{},[1712,69741,1714],{},[902,69743,1714],{"encoding":904},[883,69745,69747],{"className":69746},[886],[888,69748,69749],{"xmlns":890},[892,69750,69751,69757],{},[895,69752,69753,69755],{},[898,69754,4164],{},[898,69756,17840],{},[902,69758,17938],{"encoding":904}," zvýší přibližně o ",[883,69761,69763],{"className":69762},[886],[888,69764,69765],{"xmlns":890},[892,69766,69767,69771],{},[895,69768,69769],{},[1712,69770,2973],{},[902,69772,2973],{"encoding":904},", tj. ze skutečné hodnoty ",[883,69775,69777],{"className":69776},[886],[888,69778,69779],{"xmlns":890},[892,69780,69781,69802],{},[895,69782,69783,69785,69787,69789,69791,69793,69795,69797,69799],{},[898,69784,4164],{},[898,69786,17840],{},[1716,69788,1920],{"stretchy":1919},[1712,69790,3221],{},[1716,69792,1925],{"stretchy":1919},[1716,69794,1913],{},[1712,69796,1714],{},[2074,69798,8508],{},[1712,69800,69801],{},"050",[902,69803,69804],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,69807,69809],{"className":69808},[886],[888,69810,69811],{"xmlns":890},[892,69812,69813,69822],{},[895,69814,69815,69817,69819],{},[1712,69816,1714],{},[2074,69818,8508],{},[1712,69820,69821],{},"090",[902,69823,69824],{"encoding":904},"1\\,090",". Skutečná změna je",[883,69827,69829],{"className":69828},[886],[888,69830,69831],{"xmlns":890,"display":2004},[892,69832,69833,69887],{},[895,69834,69835,69837,69839,69841,69843,69845,69847,69849,69851,69853,69855,69857,69859,69861,69863,69865,69867,69869,69871,69874,69876,69878,69880,69882,69884],{},[898,69836,8485],{"mathvariant":2068},[898,69838,4164],{},[898,69840,17840],{},[1716,69842,1913],{},[898,69844,4164],{},[898,69846,17840],{},[1716,69848,1920],{"stretchy":1919},[1712,69850,6833],{},[1716,69852,1925],{"stretchy":1919},[1716,69854,2760],{},[898,69856,4164],{},[898,69858,17840],{},[1716,69860,1920],{"stretchy":1919},[1712,69862,3221],{},[1716,69864,1925],{"stretchy":1919},[1716,69866,1913],{},[1712,69868,1714],{},[2074,69870,8508],{},[1712,69872,69873],{},"088",[1716,69875,2760],{},[1712,69877,1714],{},[2074,69879,8508],{},[1712,69881,69801],{},[1716,69883,1913],{},[1712,69885,69886],{},"38.",[902,69888,69889],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,69891,69892,69893,1343,69919,7636,69945,69960,69961,69976],{},"Podobně ",[883,69894,69896],{"className":69895},[886],[888,69897,69898],{"xmlns":890},[892,69899,69900,69916],{},[895,69901,69902,69904,69906,69908,69910,69912,69914],{},[898,69903,16690],{},[898,69905,17840],{},[1716,69907,1920],{"stretchy":1919},[1712,69909,6833],{},[1716,69911,1925],{"stretchy":1919},[1716,69913,1913],{},[1712,69915,19394],{},[902,69917,69918],{"encoding":904},"MR(16) = 36",[883,69920,69922],{"className":69921},[886],[888,69923,69924],{"xmlns":890},[892,69925,69926,69942],{},[895,69927,69928,69930,69932,69934,69936,69938,69940],{},[898,69929,16690],{},[898,69931,17840],{},[1716,69933,1920],{"stretchy":1919},[1712,69935,2976],{},[1716,69937,1925],{"stretchy":1919},[1716,69939,1913],{},[1712,69941,2976],{},[902,69943,69944],{"encoding":904},"MR(20) = 20",[883,69946,69948],{"className":69947},[886],[888,69949,69950],{"xmlns":890},[892,69951,69952,69958],{},[895,69953,69954,69956],{},[898,69955,16690],{},[898,69957,17840],{},[902,69959,20456],{"encoding":904}," je klesající funkce — rychlost změny ",[883,69962,69964],{"className":69963},[886],[888,69965,69966],{"xmlns":890},[892,69967,69968,69974],{},[895,69969,69970,69972],{},[898,69971,4164],{},[898,69973,17840],{},[902,69975,17938],{"encoding":904}," s růstem množství klesá.",[198,69978,69980],{"id":69979},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,69982,69983],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,69985,69987],{"className":69986},[886],[888,69988,69989],{"xmlns":890,"display":2004},[892,69990,69991,70060],{},[2008,69992,69993],{"width":2010},[2012,69994,69995,69997,70053,70055],{},[2015,69996],{"width":2017},[2015,69998,69999],{},[895,70000,70001,70003,70005,70007,70009,70011,70013,70015,70017,70019,70021,70023,70025,70027,70033,70035,70037,70039,70041,70043,70045,70047,70049,70051],{},[898,70002,8485],{"mathvariant":2068},[898,70004,4164],{},[898,70006,17840],{},[2074,70008,17830],{},[1716,70010,8490],{},[2074,70012,17830],{},[898,70014,5198],{"mathvariant":2068},[898,70016,4164],{},[898,70018,17840],{},[1716,70020,1913],{},[1716,70022,1920],{"stretchy":1919},[898,70024,4164],{},[898,70026,17840],{},[3074,70028,70029,70031],{},[1716,70030,1925],{"stretchy":1919},[1716,70032,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,70034,8508],{},[898,70036,5198],{"mathvariant":2068},[898,70038,1878],{},[1716,70040,1913],{},[898,70042,16690],{},[898,70044,17840],{},[2074,70046,8508],{},[898,70048,5198],{"mathvariant":2068},[898,70050,1878],{},[1716,70052,1719],{"separator":1718},[2015,70054],{"width":2017},[2015,70056,70057],{},[2074,70058,70059],{},"(3.3)",[902,70061,70062],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,70064,70065],{},"schematicky:",[883,70067,70069],{"className":70068},[886],[888,70070,70071],{"xmlns":890,"display":2004},[892,70072,70073,70181],{},[895,70074,70075,70113,70115,70117,70119,70148,70151,70179],{},[895,70076,70077,70080,70086,70089,70095,70098,70104,70110],{},[2074,70078,70079],{},"zm",[22202,70081,70082,70084],{"accent":1718},[2074,70083,10735],{},[1716,70085,38828],{},[2074,70087,70088],{},"na celkov",[22202,70090,70091,70093],{"accent":1718},[2074,70092,10735],{},[1716,70094,38747],{},[2074,70096,70097],{},"ho p",[22202,70099,70100,70102],{"accent":1718},[2074,70101,2098],{},[1716,70103,38828],{},[22202,70105,70106,70108],{"accent":1718},[2074,70107,38816],{},[1716,70109,38747],{},[2074,70111,70112],{},"jmu",[2074,70114,17830],{},[1716,70116,8490],{},[2074,70118,17830],{},[895,70120,70121,70124,70130,70133,70139,70145],{},[2074,70122,70123],{},"mezn",[22202,70125,70126,70128],{"accent":1718},[2074,70127,38816],{},[1716,70129,38747],{},[2074,70131,70132],{}," p",[22202,70134,70135,70137],{"accent":1718},[2074,70136,2098],{},[1716,70138,38828],{},[22202,70140,70141,70143],{"accent":1718},[2074,70142,38816],{},[1716,70144,38747],{},[2074,70146,70147],{},"jem",[1716,70149,70150],{},"×",[895,70152,70153,70155,70161,70164,70170,70173],{},[2074,70154,70079],{},[22202,70156,70157,70159],{"accent":1718},[2074,70158,10735],{},[1716,70160,38828],{},[2074,70162,70163],{},"na mno",[22202,70165,70166,70168],{"accent":1718},[2074,70167,23402],{},[1716,70169,38828],{},[2074,70171,70172],{},"stv",[22202,70174,70175,70177],{"accent":1718},[2074,70176,38816],{},[1716,70178,38747],{},[898,70180,1853],{"mathvariant":2068},[902,70182,70183],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,70185,70186,70187,70202],{},"Pro porovnání skutečná změna ",[883,70188,70190],{"className":70189},[886],[888,70191,70192],{"xmlns":890},[892,70193,70194,70200],{},[895,70195,70196,70198],{},[898,70197,4164],{},[898,70199,17840],{},[902,70201,17938],{"encoding":904}," je",[883,70204,70206],{"className":70205},[886],[888,70207,70208],{"xmlns":890,"display":2004},[892,70209,70210,70265],{},[2008,70211,70212],{"width":2010},[2012,70213,70214,70216,70258,70260],{},[2015,70215],{"width":2017},[2015,70217,70218],{},[895,70219,70220,70222,70224,70226,70228,70230,70232,70234,70236,70238,70240,70242,70244,70246,70248,70250,70252,70254,70256],{},[898,70221,8485],{"mathvariant":2068},[898,70223,4164],{},[898,70225,17840],{},[1716,70227,1913],{},[898,70229,4164],{},[898,70231,17840],{},[1716,70233,1920],{"stretchy":1919},[898,70235,1878],{},[1716,70237,1949],{},[898,70239,5198],{"mathvariant":2068},[898,70241,1878],{},[1716,70243,1925],{"stretchy":1919},[1716,70245,2760],{},[898,70247,4164],{},[898,70249,17840],{},[1716,70251,1920],{"stretchy":1919},[898,70253,1878],{},[1716,70255,1925],{"stretchy":1919},[898,70257,1853],{"mathvariant":2068},[2015,70259],{"width":2017},[2015,70261,70262],{},[2074,70263,70264],{},"(3.4)",[902,70266,70267],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[2257,70269,70271],{"id":70270},"příklad-33","Příklad 3.3",[724,70273,70274,70276,70277,70307,70308,16537,70323,9425,70336,3942,70349,70363],{},[38,70275,68741],{}," Pro ",[883,70278,70280],{"className":70279},[886],[888,70281,70282],{"xmlns":890},[892,70283,70284,70304],{},[895,70285,70286,70288,70290,70292,70294,70296,70298],{},[898,70287,4164],{},[898,70289,17840],{},[1716,70291,1913],{},[1712,70293,12151],{},[898,70295,1878],{},[1716,70297,2760],{},[3074,70299,70300,70302],{},[898,70301,1878],{},[1712,70303,1726],{},[902,70305,70306],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,70309,70311],{"className":70310},[886],[888,70312,70313],{"xmlns":890},[892,70314,70315,70321],{},[895,70316,70317,70319],{},[898,70318,4164],{},[898,70320,17840],{},[902,70322,17938],{"encoding":904},[883,70324,70326],{"className":70325},[886],[888,70327,70328],{"xmlns":890},[892,70329,70330,70334],{},[895,70331,70332],{},[898,70333,1878],{},[902,70335,1878],{"encoding":904},[883,70337,70339],{"className":70338},[886],[888,70340,70341],{"xmlns":890},[892,70342,70343,70347],{},[895,70344,70345],{},[1712,70346,2884],{},[902,70348,2884],{"encoding":904},[883,70350,70352],{"className":70351},[886],[888,70353,70354],{"xmlns":890},[892,70355,70356,70361],{},[895,70357,70358],{},[1712,70359,70360],{},"63",[902,70362,70360],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,70365,70366,3495,70368,70393,70394,1343,70412,2291],{},[38,70367,36544],{},[883,70369,70371],{"className":70370},[886],[888,70372,70373],{"xmlns":890},[892,70374,70375,70391],{},[895,70376,70377,70379,70381,70383,70385,70387,70389],{},[898,70378,16690],{},[898,70380,17840],{},[1716,70382,1913],{},[1712,70384,12151],{},[1716,70386,2760],{},[1712,70388,1726],{},[898,70390,1878],{},[902,70392,25239],{"encoding":904},", tedy při ",[883,70395,70397],{"className":70396},[886],[888,70398,70399],{"xmlns":890},[892,70400,70401,70409],{},[895,70402,70403,70405,70407],{},[898,70404,1878],{},[1716,70406,1913],{},[1712,70408,2884],{},[902,70410,70411],{"encoding":904},"Q = 60",[883,70413,70415],{"className":70414},[886],[888,70416,70417],{"xmlns":890},[892,70418,70419,70429],{},[895,70420,70421,70423,70425,70427],{},[898,70422,5198],{"mathvariant":2068},[898,70424,1878],{},[1716,70426,1913],{},[1712,70428,7072],{},[902,70430,70431],{"encoding":904},"\\mathrm{d}Q = 3",[883,70433,70435],{"className":70434},[886],[888,70436,70437],{"xmlns":890,"display":2004},[892,70438,70439,70470],{},[895,70440,70441,70443,70445,70447,70449,70451,70453,70455,70457,70459,70461,70463,70465,70467],{},[898,70442,5198],{"mathvariant":2068},[898,70444,4164],{},[898,70446,17840],{},[1716,70448,1913],{},[1716,70450,1920],{"stretchy":1919},[1712,70452,12151],{},[1716,70454,2760],{},[1712,70456,11814],{},[1716,70458,1925],{"stretchy":1919},[1716,70460,9532],{},[1712,70462,7072],{},[1716,70464,1913],{},[1716,70466,2760],{},[1712,70468,70469],{},"60.",[902,70471,70472],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,70474,70475,70476,70506,70507,70526],{},"Celkový příjem klesne z ",[883,70477,70479],{"className":70478},[886],[888,70480,70481],{"xmlns":890},[892,70482,70483,70503],{},[895,70484,70485,70487,70489,70491,70493,70495,70497,70499,70501],{},[898,70486,4164],{},[898,70488,17840],{},[1716,70490,1920],{"stretchy":1919},[1712,70492,2884],{},[1716,70494,1925],{"stretchy":1919},[1716,70496,1913],{},[1712,70498,1726],{},[2074,70500,8508],{},[1712,70502,33925],{},[902,70504,70505],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,70508,70510],{"className":70509},[886],[888,70511,70512],{"xmlns":890},[892,70513,70514,70523],{},[895,70515,70516,70518,70520],{},[1712,70517,1726],{},[2074,70519,8508],{},[1712,70521,70522],{},"340",[902,70524,70525],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,70528,70530],{"className":70529},[886],[888,70531,70532],{"xmlns":890,"display":2004},[892,70533,70534,70592],{},[895,70535,70536,70538,70540,70542,70544,70546,70548,70550,70552,70554,70556,70558,70560,70562,70564,70566,70568,70570,70572,70575,70577,70579,70581,70583,70585,70587,70590],{},[898,70537,8485],{"mathvariant":2068},[898,70539,4164],{},[898,70541,17840],{},[1716,70543,1913],{},[898,70545,4164],{},[898,70547,17840],{},[1716,70549,1920],{"stretchy":1919},[1712,70551,70360],{},[1716,70553,1925],{"stretchy":1919},[1716,70555,2760],{},[898,70557,4164],{},[898,70559,17840],{},[1716,70561,1920],{"stretchy":1919},[1712,70563,2884],{},[1716,70565,1925],{"stretchy":1919},[1716,70567,1913],{},[1712,70569,1726],{},[2074,70571,8508],{},[1712,70573,70574],{},"331",[1716,70576,2760],{},[1712,70578,1726],{},[2074,70580,8508],{},[1712,70582,33925],{},[1716,70584,1913],{},[1716,70586,2760],{},[1712,70588,70589],{},"69",[1716,70591,1719],{"separator":1718},[902,70593,70594],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,70596,70597,70598,70613,70614,1853],{},"tj. ",[883,70599,70601],{"className":70600},[886],[888,70602,70603],{"xmlns":890},[892,70604,70605,70611],{},[895,70606,70607,70609],{},[898,70608,4164],{},[898,70610,17840],{},[902,70612,17938],{"encoding":904}," klesne na ",[883,70615,70617],{"className":70616},[886],[888,70618,70619],{"xmlns":890},[892,70620,70621,70629],{},[895,70622,70623,70625,70627],{},[1712,70624,1726],{},[2074,70626,8508],{},[1712,70628,70574],{},[902,70630,70631],{"encoding":904},"2\\,331",[198,70633,70635],{"id":70634},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,70637,70638,70639,24198,70662,45342],{},"Obecně pro lineární poptávku ",[883,70640,70642],{"className":70641},[886],[888,70643,70644],{"xmlns":890},[892,70645,70646,70660],{},[895,70647,70648,70650,70652,70654,70656,70658],{},[898,70649,1690],{},[1716,70651,1913],{},[898,70653,207],{},[898,70655,1878],{},[1716,70657,1949],{},[898,70659,1952],{},[902,70661,1955],{"encoding":904},[883,70663,70665],{"className":70664},[886],[888,70666,70667],{"xmlns":890},[892,70668,70669,70691],{},[895,70670,70671,70673,70675,70677,70679,70685,70687,70689],{},[898,70672,4164],{},[898,70674,17840],{},[1716,70676,1913],{},[898,70678,207],{},[3074,70680,70681,70683],{},[898,70682,1878],{},[1712,70684,1726],{},[1716,70686,1949],{},[898,70688,1952],{},[898,70690,1878],{},[902,70692,70693],{"encoding":904},"TR = aQ^2 + bQ",[883,70695,70697],{"className":70696},[886],[888,70698,70699],{"xmlns":890,"display":2004},[892,70700,70701,70721],{},[895,70702,70703,70705,70707,70709,70711,70713,70715,70717,70719],{},[898,70704,16690],{},[898,70706,17840],{},[1716,70708,1913],{},[1712,70710,1726],{},[898,70712,207],{},[898,70714,1878],{},[1716,70716,1949],{},[898,70718,1952],{},[898,70720,1853],{"mathvariant":2068},[902,70722,70723],{"encoding":904},"MR = 2aQ + b.",[724,70725,70726,70727,70742,70743,70758,70759,70772,70773,1994,70776,70792,70793,70806,70807,70822,70823,70838,70839,70854,70855,16504,70868,70898,70899,70918,70919,70934],{},"Křivky ",[883,70728,70730],{"className":70729},[886],[888,70731,70732],{"xmlns":890},[892,70733,70734,70740],{},[895,70735,70736,70738],{},[898,70737,16690],{},[898,70739,17840],{},[902,70741,20456],{"encoding":904}," a poptávky (resp. ",[883,70744,70746],{"className":70745},[886],[888,70747,70748],{"xmlns":890},[892,70749,70750,70756],{},[895,70751,70752,70754],{},[898,70753,10871],{},[898,70755,17840],{},[902,70757,68199],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,70760,70762],{"className":70761},[886],[888,70763,70764],{"xmlns":890},[892,70765,70766,70770],{},[895,70767,70768],{},[898,70769,1952],{},[902,70771,1952],{"encoding":904},", přičemž ",[38,70774,70775],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,70777,70779],{"className":70778},[886],[888,70780,70781],{"xmlns":890},[892,70782,70783,70789],{},[895,70784,70785,70787],{},[1712,70786,1726],{},[898,70788,207],{},[902,70790,70791],{"encoding":904},"2a"," vs. ",[883,70794,70796],{"className":70795},[886],[888,70797,70798],{"xmlns":890},[892,70799,70800,70804],{},[895,70801,70802],{},[898,70803,207],{},[902,70805,207],{"encoding":904},", obrázek 3.2). ",[883,70808,70810],{"className":70809},[886],[888,70811,70812],{"xmlns":890},[892,70813,70814,70820],{},[895,70815,70816,70818],{},[898,70817,16690],{},[898,70819,17840],{},[902,70821,20456],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,70824,70826],{"className":70825},[886],[888,70827,70828],{"xmlns":890},[892,70829,70830,70836],{},[895,70831,70832,70834],{},[898,70833,4164],{},[898,70835,17840],{},[902,70837,17938],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,70840,70842],{"className":70841},[886],[888,70843,70844],{"xmlns":890},[892,70845,70846,70852],{},[895,70847,70848,70850],{},[898,70849,16690],{},[898,70851,17840],{},[902,70853,20456],{"encoding":904}," osu ",[883,70856,70858],{"className":70857},[886],[888,70859,70860],{"xmlns":890},[892,70861,70862,70866],{},[895,70863,70864],{},[898,70865,1878],{},[902,70867,1878],{"encoding":904},[883,70869,70871],{"className":70870},[886],[888,70872,70873],{"xmlns":890},[892,70874,70875,70895],{},[895,70876,70877,70879,70881,70883],{},[898,70878,1878],{},[1716,70880,1913],{},[1716,70882,2760],{},[2747,70884,70885],{"scriptlevel":2505,"displaystyle":1919},[2750,70886,70887,70889],{},[898,70888,1952],{},[895,70890,70891,70893],{},[1712,70892,1726],{},[898,70894,207],{},[902,70896,70897],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,70900,70902],{"className":70901},[886],[888,70903,70904],{"xmlns":890},[892,70905,70906,70916],{},[895,70907,70908,70910,70912,70914],{},[898,70909,16690],{},[898,70911,17840],{},[1716,70913,1913],{},[1712,70915,2505],{},[902,70917,20905],{"encoding":904},", a dále ",[883,70920,70922],{"className":70921},[886],[888,70923,70924],{"xmlns":890},[892,70925,70926,70932],{},[895,70927,70928,70930],{},[898,70929,4164],{},[898,70931,17840],{},[902,70933,17938],{"encoding":904}," klesá.",[724,70936,70937,70938,70944,70945,70977,70978,71006],{},"V případě ",[38,70939,70940],{},[207,70941,70943],{"className":70942,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,70946,70948],{"className":70947},[886],[888,70949,70950],{"xmlns":890},[892,70951,70952,70974],{},[895,70953,70954,70956,70958,70960,70962,70964,70966,70968],{},[898,70955,1690],{},[1716,70957,1913],{},[898,70959,1916],{},[1716,70961,1920],{"stretchy":1919},[898,70963,1878],{},[1716,70965,1925],{"stretchy":1919},[1716,70967,1913],{},[3074,70969,70970,70972],{},[898,70971,1690],{},[1716,70973,3080],{},[902,70975,70976],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,70979,70981],{"className":70980},[886],[888,70982,70983],{"xmlns":890},[892,70984,70985,71003],{},[895,70986,70987,70989,70991,70993,70995,70997],{},[898,70988,4164],{},[898,70990,17840],{},[1716,70992,1913],{},[898,70994,1878],{},[1716,70996,9532],{},[3074,70998,70999,71001],{},[898,71000,1690],{},[1716,71002,3080],{},[902,71004,71005],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,71008,71010],{"className":71009},[886],[888,71011,71012],{"xmlns":890,"display":2004},[892,71013,71014,71056],{},[895,71015,71016,71018,71020,71022,71024,71026,71028,71034,71036,71038,71052,71054],{},[898,71017,16690],{},[898,71019,17840],{},[1716,71021,1913],{},[898,71023,10871],{},[898,71025,17840],{},[1716,71027,1913],{},[3074,71029,71030,71032],{},[898,71031,1690],{},[1716,71033,3080],{},[2324,71035],{"width":8689},[1716,71037,1920],{"stretchy":1919},[895,71039,71040,71043,71049],{},[2074,71041,71042],{},"obr",[22202,71044,71045,71047],{"accent":1718},[2074,71046,207],{},[1716,71048,38747],{},[2074,71050,71051],{},"zek 3.4",[1716,71053,1925],{"stretchy":1919},[898,71055,1853],{"mathvariant":2068},[902,71057,71058],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,71060,71061],{},[614,71062,71063,71064,2247,71090,71118,71119,71132,71133,71148,71149,5618,71162,1343,71188,5618,71203,1853],{},"Obrázek 3.2: Přímky ",[883,71065,71067],{"className":71066},[886],[888,71068,71069],{"xmlns":890},[892,71070,71071,71087],{},[895,71072,71073,71075,71077,71079,71081,71083,71085],{},[898,71074,10871],{},[898,71076,17840],{},[1716,71078,1913],{},[898,71080,207],{},[898,71082,1878],{},[1716,71084,1949],{},[898,71086,1952],{},[902,71088,71089],{"encoding":904},"AR = aQ + b",[883,71091,71093],{"className":71092},[886],[888,71094,71095],{"xmlns":890},[892,71096,71097,71115],{},[895,71098,71099,71101,71103,71105,71107,71109,71111,71113],{},[898,71100,16690],{},[898,71102,17840],{},[1716,71104,1913],{},[1712,71106,1726],{},[898,71108,207],{},[898,71110,1878],{},[1716,71112,1949],{},[898,71114,1952],{},[902,71116,71117],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,71120,71122],{"className":71121},[886],[888,71123,71124],{"xmlns":890},[892,71125,71126,71130],{},[895,71127,71128],{},[898,71129,1952],{},[902,71131,1952],{"encoding":904}," se svislou osou, ",[883,71134,71136],{"className":71135},[886],[888,71137,71138],{"xmlns":890},[892,71139,71140,71146],{},[895,71141,71142,71144],{},[898,71143,16690],{},[898,71145,17840],{},[902,71147,20456],{"encoding":904}," protíná osu ",[883,71150,71152],{"className":71151},[886],[888,71153,71154],{"xmlns":890},[892,71155,71156,71160],{},[895,71157,71158],{},[898,71159,1878],{},[902,71161,1878],{"encoding":904},[883,71163,71165],{"className":71164},[886],[888,71166,71167],{"xmlns":890},[892,71168,71169,71185],{},[895,71170,71171,71173],{},[1716,71172,2760],{},[2747,71174,71175],{"scriptlevel":2505,"displaystyle":1919},[2750,71176,71177,71179],{},[898,71178,1952],{},[895,71180,71181,71183],{},[1712,71182,1726],{},[898,71184,207],{},[902,71186,71187],{"encoding":904},"-\\tfrac{b}{2a}",[883,71189,71191],{"className":71190},[886],[888,71192,71193],{"xmlns":890},[892,71194,71195,71201],{},[895,71196,71197,71199],{},[898,71198,10871],{},[898,71200,17840],{},[902,71202,68199],{"encoding":904},[883,71204,71206],{"className":71205},[886],[888,71207,71208],{"xmlns":890},[892,71209,71210,71222],{},[895,71211,71212,71214],{},[1716,71213,2760],{},[2747,71215,71216],{"scriptlevel":2505,"displaystyle":1919},[2750,71217,71218,71220],{},[898,71219,1952],{},[898,71221,207],{},[902,71223,71224],{"encoding":904},"-\\tfrac{b}{a}",[724,71226,71227],{},[614,71228,71229,71230,71261,71262,71291,71292,1853],{},"Obrázek 3.3: Parabola ",[883,71231,71233],{"className":71232},[886],[888,71234,71235],{"xmlns":890},[892,71236,71237,71259],{},[895,71238,71239,71241,71243,71245,71247,71253,71255,71257],{},[898,71240,4164],{},[898,71242,17840],{},[1716,71244,1913],{},[898,71246,207],{},[3074,71248,71249,71251],{},[898,71250,1878],{},[1712,71252,1726],{},[1716,71254,1949],{},[898,71256,1952],{},[898,71258,1878],{},[902,71260,70693],{"encoding":904}," s maximem v ",[883,71263,71265],{"className":71264},[886],[888,71266,71267],{"xmlns":890},[892,71268,71269,71289],{},[895,71270,71271,71273,71275,71277],{},[898,71272,1878],{},[1716,71274,1913],{},[1716,71276,2760],{},[2747,71278,71279],{"scriptlevel":2505,"displaystyle":1919},[2750,71280,71281,71283],{},[898,71282,1952],{},[895,71284,71285,71287],{},[1712,71286,1726],{},[898,71288,207],{},[902,71290,70897],{"encoding":904}," a nulou v ",[883,71293,71295],{"className":71294},[886],[888,71296,71297],{"xmlns":890},[892,71298,71299,71315],{},[895,71300,71301,71303,71305,71307],{},[898,71302,1878],{},[1716,71304,1913],{},[1716,71306,2760],{},[2747,71308,71309],{"scriptlevel":2505,"displaystyle":1919},[2750,71310,71311,71313],{},[898,71312,1952],{},[898,71314,207],{},[902,71316,71317],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,71319,71320],{},[614,71321,71322,71323,1853],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,71324,71326],{"className":71325},[886],[888,71327,71328],{"xmlns":890},[892,71329,71330,71350],{},[895,71331,71332,71334,71336,71338,71340,71342,71344],{},[898,71333,10871],{},[898,71335,17840],{},[1716,71337,1913],{},[898,71339,16690],{},[898,71341,17840],{},[1716,71343,1913],{},[3074,71345,71346,71348],{},[898,71347,1690],{},[1716,71349,3080],{},[902,71351,71352],{"encoding":904},"AR = MR = P^*",[115,71354,71356],{"id":71355},"náklady-firmy","Náklady firmy",[198,71358,71360],{"id":71359},"celkové-náklady","Celkové náklady",[724,71362,71363,3495,71365,1994,71380,71383,71384,71397],{},[38,71364,71360],{},[883,71366,71368],{"className":71367},[886],[888,71369,71370],{"xmlns":890},[892,71371,71372,71378],{},[895,71373,71374,71376],{},[898,71375,4164],{},[898,71377,9945],{},[902,71379,17103],{"encoding":904},[38,71381,71382],{},"total cost",") jsou veškeré náklady na realizaci ",[883,71385,71387],{"className":71386},[886],[888,71388,71389],{"xmlns":890},[892,71390,71391,71395],{},[895,71392,71393],{},[898,71394,1878],{},[902,71396,1878],{"encoding":904}," jednotek produkce:",[883,71399,71401],{"className":71400},[886],[888,71402,71403],{"xmlns":890,"display":2004},[892,71404,71405,71460],{},[2008,71406,71407],{"width":2010},[2012,71408,71409,71411,71453,71455],{},[2015,71410],{"width":2017},[2015,71412,71413],{},[895,71414,71415,71417,71419,71421,71423,71425,71427,71429,71431,71433,71435,71437,71439,71441,71443,71445,71447,71449,71451],{},[898,71416,4164],{},[898,71418,9945],{},[1716,71420,1913],{},[898,71422,4164],{},[898,71424,9945],{},[1716,71426,1920],{"stretchy":1919},[898,71428,1878],{},[1716,71430,1925],{"stretchy":1919},[1716,71432,1913],{},[898,71434,24240],{},[898,71436,9945],{},[1716,71438,1949],{},[898,71440,4164],{},[898,71442,5298],{},[898,71444,9945],{},[1716,71446,1920],{"stretchy":1919},[898,71448,1878],{},[1716,71450,1925],{"stretchy":1919},[1716,71452,1719],{"separator":1718},[2015,71454],{"width":2017},[2015,71456,71457],{},[2074,71458,71459],{},"(3.5)",[902,71461,71462],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,71464,18149,71465,71480,71481,1994,71484,8086,71487,71480,71511,1994,71514,71517],{},[883,71466,71468],{"className":71467},[886],[888,71469,71470],{"xmlns":890},[892,71471,71472,71478],{},[895,71473,71474,71476],{},[898,71475,24240],{},[898,71477,9945],{},[902,71479,68245],{"encoding":904}," jsou ",[38,71482,71483],{},"fixní náklady",[38,71485,71486],{},"fixed cost",[883,71488,71490],{"className":71489},[886],[888,71491,71492],{"xmlns":890},[892,71493,71494,71508],{},[895,71495,71496,71498,71500,71502,71504,71506],{},[898,71497,4164],{},[898,71499,5298],{},[898,71501,9945],{},[1716,71503,1920],{"stretchy":1919},[898,71505,1878],{},[1716,71507,1925],{"stretchy":1919},[902,71509,71510],{"encoding":904},"TVC(Q)",[38,71512,71513],{},"celkové variabilní náklady",[38,71515,71516],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,71519,71521],{"id":71520},"průměrné-náklady","Průměrné náklady",[724,71523,71524,3495,71526,1994,71541,71544],{},[38,71525,71521],{},[883,71527,71529],{"className":71528},[886],[888,71530,71531],{"xmlns":890},[892,71532,71533,71539],{},[895,71534,71535,71537],{},[898,71536,10871],{},[898,71538,9945],{},[902,71540,68314],{"encoding":904},[38,71542,71543],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,71546,71548],{"className":71547},[886],[888,71549,71550],{"xmlns":890,"display":2004},[892,71551,71552,71631],{},[2008,71553,71554],{"width":2010},[2012,71555,71556,71558,71624,71626],{},[2015,71557],{"width":2017},[2015,71559,71560],{},[895,71561,71562,71564,71566,71568,71570,71572,71574,71576,71578,71580,71590,71592,71602,71604,71622],{},[898,71563,10871],{},[898,71565,9945],{},[1716,71567,1913],{},[898,71569,10871],{},[898,71571,9945],{},[1716,71573,1920],{"stretchy":1919},[898,71575,1878],{},[1716,71577,1925],{"stretchy":1919},[1716,71579,1913],{},[2750,71581,71582,71588],{},[895,71583,71584,71586],{},[898,71585,4164],{},[898,71587,9945],{},[898,71589,1878],{},[1716,71591,1913],{},[2750,71593,71594,71600],{},[895,71595,71596,71598],{},[898,71597,24240],{},[898,71599,9945],{},[898,71601,1878],{},[1716,71603,1949],{},[2750,71605,71606,71620],{},[895,71607,71608,71610,71612,71614,71616,71618],{},[898,71609,4164],{},[898,71611,5298],{},[898,71613,9945],{},[1716,71615,1920],{"stretchy":1919},[898,71617,1878],{},[1716,71619,1925],{"stretchy":1919},[898,71621,1878],{},[1716,71623,1719],{"separator":1718},[2015,71625],{"width":2017},[2015,71627,71628],{},[2074,71629,71630],{},"(3.6)",[902,71632,71633],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,71635,18149,71636,71480,71660,3495,71663,1994,71680,8086,71683,71480,71715,3495,71718,1994,71735,1998],{},[883,71637,71639],{"className":71638},[886],[888,71640,71641],{"xmlns":890},[892,71642,71643,71657],{},[895,71644,71645],{},[2747,71646,71647],{"scriptlevel":2505,"displaystyle":1919},[2750,71648,71649,71655],{},[895,71650,71651,71653],{},[898,71652,24240],{},[898,71654,9945],{},[898,71656,1878],{},[902,71658,71659],{"encoding":904},"\\tfrac{FC}{Q}",[38,71661,71662],{},"průměrné fixní náklady",[883,71664,71666],{"className":71665},[886],[888,71667,71668],{"xmlns":890},[892,71669,71670,71678],{},[895,71671,71672,71674,71676],{},[898,71673,10871],{},[898,71675,24240],{},[898,71677,9945],{},[902,71679,68281],{"encoding":904},[38,71681,71682],{},"average fixed cost",[883,71684,71686],{"className":71685},[886],[888,71687,71688],{"xmlns":890},[892,71689,71690,71712],{},[895,71691,71692],{},[2747,71693,71694],{"scriptlevel":2505,"displaystyle":1919},[2750,71695,71696,71710],{},[895,71697,71698,71700,71702,71704,71706,71708],{},[898,71699,4164],{},[898,71701,5298],{},[898,71703,9945],{},[1716,71705,1920],{"stretchy":1919},[898,71707,1878],{},[1716,71709,1925],{"stretchy":1919},[898,71711,1878],{},[902,71713,71714],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,71716,71717],{},"průměrné variabilní náklady",[883,71719,71721],{"className":71720},[886],[888,71722,71723],{"xmlns":890},[892,71724,71725,71733],{},[895,71726,71727,71729,71731],{},[898,71728,10871],{},[898,71730,5298],{},[898,71732,9945],{},[902,71734,68065],{"encoding":904},[38,71736,71737],{},"average variable cost",[883,71739,71741],{"className":71740},[886],[888,71742,71743],{"xmlns":890,"display":2004},[892,71744,71745,71804],{},[2008,71746,71747],{"width":2010},[2012,71748,71749,71751,71797,71799],{},[2015,71750],{"width":2017},[2015,71752,71753],{},[895,71754,71755,71757,71759,71761,71763,71765,71767,71769,71771,71773,71775,71777,71795],{},[898,71756,10871],{},[898,71758,5298],{},[898,71760,9945],{},[1716,71762,1913],{},[898,71764,10871],{},[898,71766,5298],{},[898,71768,9945],{},[1716,71770,1920],{"stretchy":1919},[898,71772,1878],{},[1716,71774,1925],{"stretchy":1919},[1716,71776,1913],{},[2750,71778,71779,71793],{},[895,71780,71781,71783,71785,71787,71789,71791],{},[898,71782,4164],{},[898,71784,5298],{},[898,71786,9945],{},[1716,71788,1920],{"stretchy":1919},[898,71790,1878],{},[1716,71792,1925],{"stretchy":1919},[898,71794,1878],{},[898,71796,1853],{"mathvariant":2068},[2015,71798],{"width":2017},[2015,71800,71801],{},[2074,71802,71803],{},"(3.7)",[902,71805,71806],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[2257,71808,71810],{"id":71809},"příklad-34","Příklad 3.4",[724,71812,71813,70276,71815,2247,71840,68779,71864,2247,71879,71894,71895,1853],{},[38,71814,68741],{},[883,71816,71818],{"className":71817},[886],[888,71819,71820],{"xmlns":890},[892,71821,71822,71837],{},[895,71823,71824,71826,71828,71830,71832,71834],{},[898,71825,24240],{},[898,71827,9945],{},[1716,71829,1913],{},[1712,71831,1714],{},[2074,71833,8508],{},[1712,71835,71836],{},"000",[902,71838,71839],{"encoding":904},"FC = 1\\,000",[883,71841,71843],{"className":71842},[886],[888,71844,71845],{"xmlns":890},[892,71846,71847,71861],{},[895,71848,71849,71851,71853,71855,71857,71859],{},[898,71850,4164],{},[898,71852,5298],{},[898,71854,9945],{},[1716,71856,1913],{},[1712,71858,6849],{},[898,71860,1878],{},[902,71862,71863],{"encoding":904},"TVC = 4Q",[883,71865,71867],{"className":71866},[886],[888,71868,71869],{"xmlns":890},[892,71870,71871,71877],{},[895,71872,71873,71875],{},[898,71874,4164],{},[898,71876,9945],{},[902,71878,17103],{"encoding":904},[883,71880,71882],{"className":71881},[886],[888,71883,71884],{"xmlns":890},[892,71885,71886,71892],{},[895,71887,71888,71890],{},[898,71889,10871],{},[898,71891,9945],{},[902,71893,68314],{"encoding":904}," a jejich chování s rostoucím ",[883,71896,71898],{"className":71897},[886],[888,71899,71900],{"xmlns":890},[892,71901,71902,71906],{},[895,71903,71904],{},[898,71905,1878],{},[902,71907,1878],{"encoding":904},[724,71909,71910,3495,71912,2247,71942,71978,71979,18195,71992,72007,72008,2291],{},[38,71911,36544],{},[883,71913,71915],{"className":71914},[886],[888,71916,71917],{"xmlns":890},[892,71918,71919,71939],{},[895,71920,71921,71923,71925,71927,71929,71931,71933,71935,71937],{},[898,71922,4164],{},[898,71924,9945],{},[1716,71926,1913],{},[1712,71928,1714],{},[2074,71930,8508],{},[1712,71932,71836],{},[1716,71934,1949],{},[1712,71936,6849],{},[898,71938,1878],{},[902,71940,71941],{"encoding":904},"TC = 1\\,000 + 4Q",[883,71943,71945],{"className":71944},[886],[888,71946,71947],{"xmlns":890},[892,71948,71949,71975],{},[895,71950,71951,71953,71955,71957,71971,71973],{},[898,71952,10871],{},[898,71954,9945],{},[1716,71956,1913],{},[2747,71958,71959],{"scriptlevel":2505,"displaystyle":1919},[2750,71960,71961,71969],{},[895,71962,71963,71965,71967],{},[1712,71964,1714],{},[2074,71966,8508],{},[1712,71968,71836],{},[898,71970,1878],{},[1716,71972,1949],{},[1712,71974,6849],{},[902,71976,71977],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,71980,71982],{"className":71981},[886],[888,71983,71984],{"xmlns":890},[892,71985,71986,71990],{},[895,71987,71988],{},[898,71989,1878],{},[902,71991,1878],{"encoding":904},[883,71993,71995],{"className":71994},[886],[888,71996,71997],{"xmlns":890},[892,71998,71999,72005],{},[895,72000,72001,72003],{},[898,72002,10871],{},[898,72004,9945],{},[902,72006,68314],{"encoding":904}," blíží ",[883,72009,72011],{"className":72010},[886],[888,72012,72013],{"xmlns":890},[892,72014,72015,72019],{},[895,72016,72017],{},[1712,72018,6849],{},[902,72020,6849],{"encoding":904},[883,72022,72024],{"className":72023},[886],[888,72025,72026],{"xmlns":890,"display":2004},[892,72027,72028,72074],{},[895,72029,72030,72047,72069,72071],{},[4853,72031,72032,72039],{},[895,72033,72034,72037],{},[898,72035,72036],{},"lim",[1716,72038,68954],{},[895,72040,72041,72043,72045],{},[898,72042,1878],{},[1716,72044,16986],{},[898,72046,20120],{"mathvariant":2068},[895,72048,72049,72051,72063,72065,72067],{},[1716,72050,1920],{"fence":1718},[2750,72052,72053,72061],{},[895,72054,72055,72057,72059],{},[1712,72056,1714],{},[2074,72058,8508],{},[1712,72060,71836],{},[898,72062,1878],{},[1716,72064,1949],{},[1712,72066,6849],{},[1716,72068,1925],{"fence":1718},[1716,72070,1913],{},[1712,72072,72073],{},"4.",[902,72075,72076],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,72078,72079,72117,72118,1853],{},[883,72080,72082],{"className":72081},[886],[888,72083,72084],{"xmlns":890},[892,72085,72086,72114],{},[895,72087,72088,72090,72092,72094,72096,72110,72112],{},[898,72089,10871],{},[898,72091,24240],{},[898,72093,9945],{},[1716,72095,1913],{},[2747,72097,72098],{"scriptlevel":2505,"displaystyle":1919},[2750,72099,72100,72108],{},[895,72101,72102,72104,72106],{},[1712,72103,1714],{},[2074,72105,8508],{},[1712,72107,71836],{},[898,72109,1878],{},[1716,72111,16986],{},[1712,72113,2505],{},[902,72115,72116],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,72119,72121],{"className":72120},[886],[888,72122,72123],{"xmlns":890},[892,72124,72125,72129],{},[895,72126,72127],{},[898,72128,1878],{},[902,72130,1878],{"encoding":904},[724,72132,72133],{},[614,72134,72135,72136,72165,72166,1853],{},"Obrázek 3.5: Přímka ",[883,72137,72139],{"className":72138},[886],[888,72140,72141],{"xmlns":890},[892,72142,72143,72163],{},[895,72144,72145,72147,72149,72151,72153,72155,72157,72159,72161],{},[898,72146,4164],{},[898,72148,9945],{},[1716,72150,1913],{},[1712,72152,1714],{},[2074,72154,8508],{},[1712,72156,71836],{},[1716,72158,1949],{},[1712,72160,6849],{},[898,72162,1878],{},[902,72164,71941],{"encoding":904}," protínající svislou osu ve výši ",[883,72167,72169],{"className":72168},[886],[888,72170,72171],{"xmlns":890},[892,72172,72173,72187],{},[895,72174,72175,72177,72179,72181,72183,72185],{},[898,72176,24240],{},[898,72178,9945],{},[1716,72180,1913],{},[1712,72182,1714],{},[2074,72184,8508],{},[1712,72186,71836],{},[902,72188,71839],{"encoding":904},[724,72190,72191],{},[614,72192,72193,72194,72229,72230,1853],{},"Obrázek 3.6: Hyperbola ",[883,72195,72197],{"className":72196},[886],[888,72198,72199],{"xmlns":890},[892,72200,72201,72227],{},[895,72202,72203,72205,72207,72209,72223,72225],{},[898,72204,10871],{},[898,72206,9945],{},[1716,72208,1913],{},[2747,72210,72211],{"scriptlevel":2505,"displaystyle":1919},[2750,72212,72213,72221],{},[895,72214,72215,72217,72219],{},[1712,72216,1714],{},[2074,72218,8508],{},[1712,72220,71836],{},[898,72222,1878],{},[1716,72224,1949],{},[1712,72226,6849],{},[902,72228,71977],{"encoding":904}," s vodorovnou asymptotou ",[883,72231,72233],{"className":72232},[886],[888,72234,72235],{"xmlns":890},[892,72236,72237,72247],{},[895,72238,72239,72241,72243,72245],{},[898,72240,10871],{},[898,72242,9945],{},[1716,72244,1913],{},[1712,72246,6849],{},[902,72248,72249],{"encoding":904},"AC = 4",[724,72251,72252],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,72254,72256],{"className":72255},[886],[888,72257,72258],{"xmlns":890,"display":2004},[892,72259,72260,72286],{},[895,72261,72262,72264,72266,72268,72270,72272,72274,72276,72278,72280,72282,72284],{},[898,72263,4164],{},[898,72265,5298],{},[898,72267,9945],{},[1716,72269,1913],{},[898,72271,1878],{},[1716,72273,9532],{},[898,72275,5298],{},[898,72277,9945],{},[1716,72279,1920],{"stretchy":1919},[898,72281,1878],{},[1716,72283,1925],{"stretchy":1919},[1716,72285,1719],{"separator":1718},[902,72287,72288],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,72290,18149,72291,71480,72319,72322,72323,72353],{},[883,72292,72294],{"className":72293},[886],[888,72295,72296],{"xmlns":890},[892,72297,72298,72316],{},[895,72299,72300,72302,72304,72306,72308,72310,72312,72314],{},[898,72301,5298],{},[898,72303,9945],{},[1716,72305,1913],{},[898,72307,5298],{},[898,72309,9945],{},[1716,72311,1920],{"stretchy":1919},[898,72313,1878],{},[1716,72315,1925],{"stretchy":1919},[902,72317,72318],{"encoding":904},"VC = VC(Q)",[38,72320,72321],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,72324,72326],{"className":72325},[886],[888,72327,72328],{"xmlns":890},[892,72329,72330,72350],{},[895,72331,72332,72334,72336,72338,72340,72342,72344,72346,72348],{},[898,72333,4164],{},[898,72335,5298],{},[898,72337,9945],{},[1716,72339,1920],{"stretchy":1919},[898,72341,1878],{},[1716,72343,1925],{"stretchy":1919},[1716,72345,1913],{},[898,72347,207],{},[898,72349,1878],{},[902,72351,72352],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,72355,72357],{"className":72356},[886],[888,72358,72359],{"xmlns":890,"display":2004},[892,72360,72361,72381],{},[895,72362,72363,72365,72367,72369,72371,72373,72375,72377,72379],{},[898,72364,4164],{},[898,72366,9945],{},[1716,72368,1913],{},[898,72370,24240],{},[898,72372,9945],{},[1716,72374,1949],{},[898,72376,207],{},[898,72378,1878],{},[898,72380,1853],{"mathvariant":2068},[902,72382,72383],{"encoding":904},"TC = FC + aQ.",[724,72385,72386,72387,72402,72403,72418,72419,72442,72443,72477,72478,72229,72491,72504,72505,2247,72553,72597,72598,1853],{},"Křivkou ",[883,72388,72390],{"className":72389},[886],[888,72391,72392],{"xmlns":890},[892,72393,72394,72400],{},[895,72395,72396,72398],{},[898,72397,4164],{},[898,72399,9945],{},[902,72401,17103],{"encoding":904}," je přímka se svislým průsečíkem ",[883,72404,72406],{"className":72405},[886],[888,72407,72408],{"xmlns":890},[892,72409,72410,72416],{},[895,72411,72412,72414],{},[898,72413,24240],{},[898,72415,9945],{},[902,72417,68245],{"encoding":904}," a sklonem ",[883,72420,72422],{"className":72421},[886],[888,72423,72424],{"xmlns":890},[892,72425,72426,72439],{},[895,72427,72428,72431,72433,72435,72437],{},[898,72429,72430],{},"tan",[1716,72432,68954],{},[898,72434,32647],{},[1716,72436,1913],{},[898,72438,207],{},[902,72440,72441],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,72444,72446],{"className":72445},[886],[888,72447,72448],{"xmlns":890},[892,72449,72450,72474],{},[895,72451,72452,72454,72456,72458,72470,72472],{},[898,72453,10871],{},[898,72455,9945],{},[1716,72457,1913],{},[2747,72459,72460],{"scriptlevel":2505,"displaystyle":1919},[2750,72461,72462,72468],{},[895,72463,72464,72466],{},[898,72465,24240],{},[898,72467,9945],{},[898,72469,1878],{},[1716,72471,1949],{},[898,72473,207],{},[902,72475,72476],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,72479,72481],{"className":72480},[886],[888,72482,72483],{"xmlns":890},[892,72484,72485,72489],{},[895,72486,72487],{},[898,72488,1775],{},[902,72490,1775],{"encoding":904},[883,72492,72494],{"className":72493},[886],[888,72495,72496],{"xmlns":890},[892,72497,72498,72502],{},[895,72499,72500],{},[898,72501,207],{},[902,72503,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,72506,72508],{"className":72507},[886],[888,72509,72510],{"xmlns":890},[892,72511,72512,72550],{},[895,72513,72514,72534,72546,72548],{},[1707,72515,72516,72522],{},[895,72517,72518,72520],{},[898,72519,72036],{},[1716,72521,68954],{},[895,72523,72524,72526,72528],{},[898,72525,1878],{},[1716,72527,16986],{},[3074,72529,72530,72532],{},[1712,72531,2505],{},[1716,72533,1949],{},[2747,72535,72536],{"scriptlevel":2505,"displaystyle":1919},[2750,72537,72538,72544],{},[895,72539,72540,72542],{},[898,72541,24240],{},[898,72543,9945],{},[898,72545,1878],{},[1716,72547,1913],{},[898,72549,20120],{"mathvariant":2068},[902,72551,72552],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,72554,72556],{"className":72555},[886],[888,72557,72558],{"xmlns":890},[892,72559,72560,72594],{},[895,72561,72562,72578,72590,72592],{},[1707,72563,72564,72570],{},[895,72565,72566,72568],{},[898,72567,72036],{},[1716,72569,68954],{},[895,72571,72572,72574,72576],{},[898,72573,1878],{},[1716,72575,16986],{},[898,72577,20120],{"mathvariant":2068},[2747,72579,72580],{"scriptlevel":2505,"displaystyle":1919},[2750,72581,72582,72588],{},[895,72583,72584,72586],{},[898,72585,24240],{},[898,72587,9945],{},[898,72589,1878],{},[1716,72591,1913],{},[1712,72593,2505],{},[902,72595,72596],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,72599,72601],{"className":72600},[886],[888,72602,72603],{"xmlns":890},[892,72604,72605,72611],{},[895,72606,72607,72609],{},[898,72608,10871],{},[898,72610,9945],{},[902,72612,68314],{"encoding":904},[724,72614,72615],{},[614,72616,72617,72618,72633,72634,72649,72650,1853],{},"Obrázek 3.7: Přímka ",[883,72619,72621],{"className":72620},[886],[888,72622,72623],{"xmlns":890},[892,72624,72625,72631],{},[895,72626,72627,72629],{},[898,72628,4164],{},[898,72630,9945],{},[902,72632,17103],{"encoding":904}," s osovým průsečíkem ve výši ",[883,72635,72637],{"className":72636},[886],[888,72638,72639],{"xmlns":890},[892,72640,72641,72647],{},[895,72642,72643,72645],{},[898,72644,24240],{},[898,72646,9945],{},[902,72648,68245],{"encoding":904}," a se sklonem ",[883,72651,72653],{"className":72652},[886],[888,72654,72655],{"xmlns":890},[892,72656,72657,72669],{},[895,72658,72659,72661,72663,72665,72667],{},[898,72660,72430],{},[1716,72662,68954],{},[898,72664,32647],{},[1716,72666,1913],{},[898,72668,207],{},[902,72670,72441],{"encoding":904},[724,72672,72673],{},[614,72674,72675,72676,72691,72692,1853],{},"Obrázek 3.8: Klesající hyperbola ",[883,72677,72679],{"className":72678},[886],[888,72680,72681],{"xmlns":890},[892,72682,72683,72689],{},[895,72684,72685,72687],{},[898,72686,10871],{},[898,72688,9945],{},[902,72690,68314],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,72693,72695],{"className":72694},[886],[888,72696,72697],{"xmlns":890},[892,72698,72699,72703],{},[895,72700,72701],{},[898,72702,207],{},[902,72704,207],{"encoding":904},[198,72706,72708],{"id":72707},"mezní-náklady","Mezní náklady",[724,72710,72711,3495,72713,1994,72728,72731,72732,72735],{},[38,72712,72708],{},[883,72714,72716],{"className":72715},[886],[888,72717,72718],{"xmlns":890},[892,72719,72720,72726],{},[895,72721,72722,72724],{},[898,72723,16690],{},[898,72725,9945],{},[902,72727,68046],{"encoding":904},[38,72729,72730],{},"marginal cost",") jsou ",[207,72733,1145],{"className":72734,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,72737,72739],{"className":72738},[886],[888,72740,72741],{"xmlns":890,"display":2004},[892,72742,72743,72812],{},[2008,72744,72745],{"width":2010},[2012,72746,72747,72749,72805,72807],{},[2015,72748],{"width":2017},[2015,72750,72751],{},[895,72752,72753,72755,72757,72759,72761,72763,72765,72767,72769,72771,72787,72789,72791,72797,72799,72801,72803],{},[898,72754,16690],{},[898,72756,9945],{},[1716,72758,1913],{},[898,72760,16690],{},[898,72762,9945],{},[1716,72764,1920],{"stretchy":1919},[898,72766,1878],{},[1716,72768,1925],{"stretchy":1919},[1716,72770,1913],{},[2750,72772,72773,72781],{},[895,72774,72775,72777,72779],{},[898,72776,5198],{"mathvariant":2068},[898,72778,4164],{},[898,72780,9945],{},[895,72782,72783,72785],{},[898,72784,5198],{"mathvariant":2068},[898,72786,1878],{},[1716,72788,1913],{},[898,72790,4164],{},[3074,72792,72793,72795],{},[898,72794,9945],{},[1716,72796,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,72798,1920],{"stretchy":1919},[898,72800,1878],{},[1716,72802,1925],{"stretchy":1919},[898,72804,1853],{"mathvariant":2068},[2015,72806],{"width":2017},[2015,72808,72809],{},[2074,72810,72811],{},"(3.8)",[902,72813,72814],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1635,72816,72817],{},[724,72818,72819,72821,72822,72848,72849,72866,72867,1853],{},[883,72820,1641],{}," Intuice — „kolik stojí další kus\"\n",[883,72823,72825],{"className":72824},[886],[888,72826,72827],{"xmlns":890},[892,72828,72829,72845],{},[895,72830,72831,72833,72835,72837,72843],{},[898,72832,16690],{},[898,72834,9945],{},[1716,72836,1920],{"stretchy":1919},[3074,72838,72839,72841],{},[898,72840,1878],{},[1716,72842,3080],{},[1716,72844,1925],{"stretchy":1919},[902,72846,72847],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,72850,72852],{"className":72851},[886],[888,72853,72854],{"xmlns":890},[892,72855,72856,72864],{},[895,72857,72858],{},[3074,72859,72860,72862],{},[898,72861,1878],{},[1716,72863,3080],{},[902,72865,43607],{"encoding":904},". Formálně ",[883,72868,72870],{"className":72869},[886],[888,72871,72872],{"xmlns":890},[892,72873,72874,72926],{},[895,72875,72876,72878,72880,72882,72888,72890,72892,72894,72896,72898,72904,72906,72908,72910,72912,72914,72916,72918,72924],{},[898,72877,16690],{},[898,72879,9945],{},[1716,72881,1920],{"stretchy":1919},[3074,72883,72884,72886],{},[898,72885,1878],{},[1716,72887,3080],{},[1716,72889,1925],{"stretchy":1919},[1716,72891,8490],{},[898,72893,4164],{},[898,72895,9945],{},[1716,72897,1920],{"stretchy":1919},[3074,72899,72900,72902],{},[898,72901,1878],{},[1716,72903,3080],{},[1716,72905,1949],{},[1712,72907,1714],{},[1716,72909,1925],{"stretchy":1919},[1716,72911,2760],{},[898,72913,4164],{},[898,72915,9945],{},[1716,72917,1920],{"stretchy":1919},[3074,72919,72920,72922],{},[898,72921,1878],{},[1716,72923,3080],{},[1716,72925,1925],{"stretchy":1919},[902,72927,72928],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,72930,72931,72932,2291],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,72933,72935],{"className":72934},[886],[888,72936,72937],{"xmlns":890},[892,72938,72939,72947],{},[895,72940,72941,72943,72945],{},[898,72942,8485],{"mathvariant":2068},[898,72944,4164],{},[898,72946,9945],{},[902,72948,72949],{"encoding":904},"\\Delta TC",[883,72951,72953],{"className":72952},[886],[888,72954,72955],{"xmlns":890,"display":2004},[892,72956,72957,73026],{},[2008,72958,72959],{"width":2010},[2012,72960,72961,72963,73019,73021],{},[2015,72962],{"width":2017},[2015,72964,72965],{},[895,72966,72967,72969,72971,72973,72975,72977,72979,72981,72983,72985,72987,72989,72991,72993,72999,73001,73003,73005,73007,73009,73011,73013,73015,73017],{},[898,72968,8485],{"mathvariant":2068},[898,72970,4164],{},[898,72972,9945],{},[2074,72974,17830],{},[1716,72976,8490],{},[2074,72978,17830],{},[898,72980,5198],{"mathvariant":2068},[898,72982,4164],{},[898,72984,9945],{},[1716,72986,1913],{},[1716,72988,1920],{"stretchy":1919},[898,72990,4164],{},[898,72992,9945],{},[3074,72994,72995,72997],{},[1716,72996,1925],{"stretchy":1919},[1716,72998,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,73000,8508],{},[898,73002,5198],{"mathvariant":2068},[898,73004,1878],{},[1716,73006,1913],{},[898,73008,16690],{},[898,73010,9945],{},[2074,73012,8508],{},[898,73014,5198],{"mathvariant":2068},[898,73016,1878],{},[1716,73018,1719],{"separator":1718},[2015,73020],{"width":2017},[2015,73022,73023],{},[2074,73024,73025],{},"(3.9)",[902,73027,73028],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,73030,70065],{},[883,73032,73034],{"className":73033},[886],[888,73035,73036],{"xmlns":890,"display":2004},[892,73037,73038,73136],{},[895,73039,73040,73078,73080,73082,73084,73106,73108,73134],{},[895,73041,73042,73044,73050,73052,73058,73061,73067,73070],{},[2074,73043,70079],{},[22202,73045,73046,73048],{"accent":1718},[2074,73047,10735],{},[1716,73049,38828],{},[2074,73051,70088],{},[22202,73053,73054,73056],{"accent":1718},[2074,73055,7684],{},[1716,73057,38747],{},[2074,73059,73060],{},"ch n",[22202,73062,73063,73065],{"accent":1718},[2074,73064,207],{},[1716,73066,38747],{},[2074,73068,73069],{},"klad",[22202,73071,73072,73075],{"accent":1718},[2074,73073,73074],{},"u",[1716,73076,73077],{},"˚",[2074,73079,17830],{},[1716,73081,8490],{},[2074,73083,17830],{},[895,73085,73086,73088,73094,73097,73103],{},[2074,73087,70123],{},[22202,73089,73090,73092],{"accent":1718},[2074,73091,38816],{},[1716,73093,38747],{},[2074,73095,73096],{}," n",[22202,73098,73099,73101],{"accent":1718},[2074,73100,207],{},[1716,73102,38747],{},[2074,73104,73105],{},"klady",[1716,73107,70150],{},[895,73109,73110,73112,73118,73120,73126,73128],{},[2074,73111,70079],{},[22202,73113,73114,73116],{"accent":1718},[2074,73115,10735],{},[1716,73117,38828],{},[2074,73119,70163],{},[22202,73121,73122,73124],{"accent":1718},[2074,73123,23402],{},[1716,73125,38828],{},[2074,73127,70172],{},[22202,73129,73130,73132],{"accent":1718},[2074,73131,38816],{},[1716,73133,38747],{},[898,73135,1853],{"mathvariant":2068},[902,73137,73138],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[2257,73140,73142],{"id":73141},"příklad-35","Příklad 3.5",[724,73144,73145,70276,73147,68779,73183,73198,73199,73214,73215,9425,73228,3942,73241,73254,73255,3942,73268,1853],{},[38,73146,68741],{},[883,73148,73150],{"className":73149},[886],[888,73151,73152],{"xmlns":890},[892,73153,73154,73180],{},[895,73155,73156,73158,73160,73162,73164,73166,73168,73170,73172,73174],{},[898,73157,4164],{},[898,73159,9945],{},[1716,73161,1913],{},[1712,73163,22193],{},[1716,73165,1949],{},[1712,73167,6231],{},[898,73169,1878],{},[1716,73171,1949],{},[1712,73173,1726],{},[3074,73175,73176,73178],{},[898,73177,1878],{},[1712,73179,1726],{},[902,73181,73182],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,73184,73186],{"className":73185},[886],[888,73187,73188],{"xmlns":890},[892,73189,73190,73196],{},[895,73191,73192,73194],{},[898,73193,16690],{},[898,73195,9945],{},[902,73197,68046],{"encoding":904}," a odhadněte změny ",[883,73200,73202],{"className":73201},[886],[888,73203,73204],{"xmlns":890},[892,73205,73206,73212],{},[895,73207,73208,73210],{},[898,73209,4164],{},[898,73211,9945],{},[902,73213,17103],{"encoding":904}," při změnách ",[883,73216,73218],{"className":73217},[886],[888,73219,73220],{"xmlns":890},[892,73221,73222,73226],{},[895,73223,73224],{},[898,73225,1878],{},[902,73227,1878],{"encoding":904},[883,73229,73231],{"className":73230},[886],[888,73232,73233],{"xmlns":890},[892,73234,73235,73239],{},[895,73236,73237],{},[1712,73238,3221],{},[902,73240,3221],{"encoding":904},[883,73242,73244],{"className":73243},[886],[888,73245,73246],{"xmlns":890},[892,73247,73248,73252],{},[895,73249,73250],{},[1712,73251,6833],{},[902,73253,6833],{"encoding":904}," a z ",[883,73256,73258],{"className":73257},[886],[888,73259,73260],{"xmlns":890},[892,73261,73262,73266],{},[895,73263,73264],{},[1712,73265,3221],{},[902,73267,3221],{"encoding":904},[883,73269,73271],{"className":73270},[886],[888,73272,73273],{"xmlns":890},[892,73274,73275,73279],{},[895,73276,73277],{},[1712,73278,6804],{},[902,73280,6804],{"encoding":904},[724,73282,73283,3495,73285,7636,73311,1343,73338,73365,73366,73381,73382,73397,73398,73425,73426,73446,73447,34314,73468,73524,73525,9425,73538,3942,73551,2574,73564,1853],{},[38,73284,36544],{},[883,73286,73288],{"className":73287},[886],[888,73289,73290],{"xmlns":890},[892,73291,73292,73308],{},[895,73293,73294,73296,73298,73300,73302,73304,73306],{},[898,73295,16690],{},[898,73297,9945],{},[1716,73299,1913],{},[1712,73301,6231],{},[1716,73303,1949],{},[1712,73305,6849],{},[898,73307,1878],{},[902,73309,73310],{"encoding":904},"MC = 6 + 4Q",[883,73312,73314],{"className":73313},[886],[888,73315,73316],{"xmlns":890},[892,73317,73318,73335],{},[895,73319,73320,73322,73324,73326,73328,73330,73332],{},[898,73321,16690],{},[898,73323,9945],{},[1716,73325,1920],{"stretchy":1919},[1712,73327,3221],{},[1716,73329,1925],{"stretchy":1919},[1716,73331,1913],{},[1712,73333,73334],{},"66",[902,73336,73337],{"encoding":904},"MC(15) = 66",[883,73339,73341],{"className":73340},[886],[888,73342,73343],{"xmlns":890},[892,73344,73345,73362],{},[895,73346,73347,73349,73351,73353,73355,73357,73359],{},[898,73348,16690],{},[898,73350,9945],{},[1716,73352,1920],{"stretchy":1919},[1712,73354,2976],{},[1716,73356,1925],{"stretchy":1919},[1716,73358,1913],{},[1712,73360,73361],{},"86",[902,73363,73364],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,73367,73369],{"className":73368},[886],[888,73370,73371],{"xmlns":890},[892,73372,73373,73379],{},[895,73374,73375,73377],{},[898,73376,4164],{},[898,73378,9945],{},[902,73380,17103],{"encoding":904}," zvyšuje (",[883,73383,73385],{"className":73384},[886],[888,73386,73387],{"xmlns":890},[892,73388,73389,73395],{},[895,73390,73391,73393],{},[898,73392,16690],{},[898,73394,9945],{},[902,73396,68046],{"encoding":904}," je rostoucí). Z ",[883,73399,73401],{"className":73400},[886],[888,73402,73403],{"xmlns":890},[892,73404,73405,73422],{},[895,73406,73407,73409,73411,73413,73415,73417,73419],{},[898,73408,4164],{},[898,73410,9945],{},[1716,73412,1920],{"stretchy":1919},[1712,73414,3221],{},[1716,73416,1925],{"stretchy":1919},[1716,73418,1913],{},[1712,73420,73421],{},"740",[902,73423,73424],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,73427,73429],{"className":73428},[886],[888,73430,73431],{"xmlns":890},[892,73432,73433,73443],{},[895,73434,73435,73437,73439,73441],{},[898,73436,5198],{"mathvariant":2068},[898,73438,1878],{},[1716,73440,1913],{},[1712,73442,1714],{},[902,73444,73445],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,73448,73450],{"className":73449},[886],[888,73451,73452],{"xmlns":890},[892,73453,73454,73465],{},[895,73455,73456,73458,73460,73462],{},[898,73457,4164],{},[898,73459,9945],{},[1716,73461,8490],{},[1712,73463,73464],{},"806",[902,73466,73467],{"encoding":904},"TC \\approx 806",[883,73469,73471],{"className":73470},[886],[888,73472,73473],{"xmlns":890},[892,73474,73475,73521],{},[895,73476,73477,73479,73481,73483,73485,73487,73489,73491,73493,73495,73497,73499,73501,73503,73505,73507,73509,73512,73514,73516,73518],{},[898,73478,8485],{"mathvariant":2068},[898,73480,4164],{},[898,73482,9945],{},[1716,73484,1913],{},[898,73486,4164],{},[898,73488,9945],{},[1716,73490,1920],{"stretchy":1919},[1712,73492,6833],{},[1716,73494,1925],{"stretchy":1919},[1716,73496,2760],{},[898,73498,4164],{},[898,73500,9945],{},[1716,73502,1920],{"stretchy":1919},[1712,73504,3221],{},[1716,73506,1925],{"stretchy":1919},[1716,73508,1913],{},[1712,73510,73511],{},"808",[1716,73513,2760],{},[1712,73515,73421],{},[1716,73517,1913],{},[1712,73519,73520],{},"68",[902,73522,73523],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,73526,73528],{"className":73527},[886],[888,73529,73530],{"xmlns":890},[892,73531,73532,73536],{},[895,73533,73534],{},[898,73535,1878],{},[902,73537,1878],{"encoding":904},[883,73539,73541],{"className":73540},[886],[888,73542,73543],{"xmlns":890},[892,73544,73545,73549],{},[895,73546,73547],{},[1712,73548,3221],{},[902,73550,3221],{"encoding":904},[883,73552,73554],{"className":73553},[886],[888,73555,73556],{"xmlns":890},[892,73557,73558,73562],{},[895,73559,73560],{},[1712,73561,6804],{},[902,73563,6804],{"encoding":904},[883,73565,73567],{"className":73566},[886],[888,73568,73569],{"xmlns":890},[892,73570,73571,73600],{},[895,73572,73573,73575,73577,73579,73581,73583,73585,73587,73589,73591,73593,73595,73597],{},[898,73574,8485],{"mathvariant":2068},[898,73576,4164],{},[898,73578,9945],{},[1716,73580,8490],{},[1712,73582,73334],{},[1716,73584,9532],{},[1716,73586,1920],{"stretchy":1919},[1716,73588,2760],{},[1712,73590,7072],{},[1716,73592,1925],{"stretchy":1919},[1716,73594,1913],{},[1716,73596,2760],{},[1712,73598,73599],{},"198",[902,73601,73602],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,73604,73606],{"id":73605},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,73608,73609],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[2257,73611,73613],{"id":73612},"příklad-36","Příklad 3.6",[724,73615,73616,70276,73618,73662],{},[38,73617,68741],{},[883,73619,73621],{"className":73620},[886],[888,73622,73623],{"xmlns":890},[892,73624,73625,73659],{},[895,73626,73627,73629,73631,73633,73635,73637,73639,73641,73643,73645,73651,73653],{},[898,73628,4164],{},[898,73630,9945],{},[1716,73632,1913],{},[1712,73634,12151],{},[1716,73636,1949],{},[1712,73638,5778],{},[898,73640,1878],{},[1716,73642,2760],{},[1712,73644,6985],{},[3074,73646,73647,73649],{},[898,73648,1878],{},[1712,73650,1726],{},[1716,73652,1949],{},[3074,73654,73655,73657],{},[898,73656,1878],{},[1712,73658,7072],{},[902,73660,73661],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,73664,73665],{},[38,73666,36544],{},[883,73668,73670],{"className":73669},[886],[888,73671,73672],{"xmlns":890,"display":2004},[892,73673,73674,73918],{},[2008,73675,73676,73702,73750,73784,73826,73876],{"rowspacing":4401,"columnalign":4402,"columnspacing":4403},[2012,73677,73678,73688],{},[2015,73679,73680],{},[2747,73681,73682],{"scriptlevel":2505,"displaystyle":1718},[895,73683,73684,73686],{},[898,73685,24240],{},[898,73687,9945],{},[2015,73689,73690],{},[2747,73691,73692],{"scriptlevel":2505,"displaystyle":1718},[895,73693,73694,73696,73698,73700],{},[895,73695],{},[1716,73697,1913],{},[1712,73699,12151],{},[1716,73701,1719],{"separator":1718},[2012,73703,73704,73716],{},[2015,73705,73706],{},[2747,73707,73708],{"scriptlevel":2505,"displaystyle":1718},[895,73709,73710,73712,73714],{},[898,73711,4164],{},[898,73713,5298],{},[898,73715,9945],{},[2015,73717,73718],{},[2747,73719,73720],{"scriptlevel":2505,"displaystyle":1718},[895,73721,73722,73724,73726,73728,73730,73732,73734,73740,73742,73748],{},[895,73723],{},[1716,73725,1913],{},[1712,73727,5778],{},[898,73729,1878],{},[1716,73731,2760],{},[1712,73733,6985],{},[3074,73735,73736,73738],{},[898,73737,1878],{},[1712,73739,1726],{},[1716,73741,1949],{},[3074,73743,73744,73746],{},[898,73745,1878],{},[1712,73747,7072],{},[1716,73749,1719],{"separator":1718},[2012,73751,73752,73764],{},[2015,73753,73754],{},[2747,73755,73756],{"scriptlevel":2505,"displaystyle":1718},[895,73757,73758,73760,73762],{},[898,73759,10871],{},[898,73761,24240],{},[898,73763,9945],{},[2015,73765,73766],{},[2747,73767,73768],{"scriptlevel":2505,"displaystyle":1718},[895,73769,73770,73772,73774,73782],{},[895,73771],{},[1716,73773,1913],{},[2747,73775,73776],{"scriptlevel":2505,"displaystyle":1919},[2750,73777,73778,73780],{},[1712,73779,12151],{},[898,73781,1878],{},[1716,73783,1719],{"separator":1718},[2012,73785,73786,73798],{},[2015,73787,73788],{},[2747,73789,73790],{"scriptlevel":2505,"displaystyle":1718},[895,73791,73792,73794,73796],{},[898,73793,10871],{},[898,73795,5298],{},[898,73797,9945],{},[2015,73799,73800],{},[2747,73801,73802],{"scriptlevel":2505,"displaystyle":1718},[895,73803,73804,73806,73808,73810,73812,73814,73816,73818,73824],{},[895,73805],{},[1716,73807,1913],{},[1712,73809,5778],{},[1716,73811,2760],{},[1712,73813,6985],{},[898,73815,1878],{},[1716,73817,1949],{},[3074,73819,73820,73822],{},[898,73821,1878],{},[1712,73823,1726],{},[1716,73825,1719],{"separator":1718},[2012,73827,73828,73838],{},[2015,73829,73830],{},[2747,73831,73832],{"scriptlevel":2505,"displaystyle":1718},[895,73833,73834,73836],{},[898,73835,10871],{},[898,73837,9945],{},[2015,73839,73840],{},[2747,73841,73842],{"scriptlevel":2505,"displaystyle":1718},[895,73843,73844,73846,73848,73856,73858,73860,73862,73864,73866,73868,73874],{},[895,73845],{},[1716,73847,1913],{},[2747,73849,73850],{"scriptlevel":2505,"displaystyle":1919},[2750,73851,73852,73854],{},[1712,73853,12151],{},[898,73855,1878],{},[1716,73857,1949],{},[1712,73859,5778],{},[1716,73861,2760],{},[1712,73863,6985],{},[898,73865,1878],{},[1716,73867,1949],{},[3074,73869,73870,73872],{},[898,73871,1878],{},[1712,73873,1726],{},[1716,73875,1719],{"separator":1718},[2012,73877,73878,73888],{},[2015,73879,73880],{},[2747,73881,73882],{"scriptlevel":2505,"displaystyle":1718},[895,73883,73884,73886],{},[898,73885,16690],{},[898,73887,9945],{},[2015,73889,73890],{},[2747,73891,73892],{"scriptlevel":2505,"displaystyle":1718},[895,73893,73894,73896,73898,73900,73902,73904,73906,73908,73910,73916],{},[895,73895],{},[1716,73897,1913],{},[1712,73899,5778],{},[1716,73901,2760],{},[1712,73903,2998],{},[898,73905,1878],{},[1716,73907,1949],{},[1712,73909,7072],{},[3074,73911,73912,73914],{},[898,73913,1878],{},[1712,73915,1726],{},[898,73917,1853],{"mathvariant":2068},[902,73919,73920],{"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}",[724,73922,73923,73924,29583,73939,29583,73954,73969,73970,73985,73986,1343,74004,73985,74021,1343,74039,73985,74054,74072],{},"Význačné body ",[883,73925,73927],{"className":73926},[886],[888,73928,73929],{"xmlns":890},[892,73930,73931,73936],{},[895,73932,73933],{},[1712,73934,73935],{},"1,67",[902,73937,73938],{"encoding":904},"1{,}67",[883,73940,73942],{"className":73941},[886],[888,73943,73944],{"xmlns":890},[892,73945,73946,73951],{},[895,73947,73948],{},[1712,73949,73950],{},"2,50",[902,73952,73953],{"encoding":904},"2{,}50",[883,73955,73957],{"className":73956},[886],[888,73958,73959],{"xmlns":890},[892,73960,73961,73966],{},[895,73962,73963],{},[1712,73964,73965],{},"4,73",[902,73967,73968],{"encoding":904},"4{,}73"," odpovídají: ",[883,73971,73973],{"className":73972},[886],[888,73974,73975],{"xmlns":890},[892,73976,73977,73983],{},[895,73978,73979,73981],{},[898,73980,16690],{},[898,73982,9945],{},[902,73984,68046],{"encoding":904}," minimum v ",[883,73987,73989],{"className":73988},[886],[888,73990,73991],{"xmlns":890},[892,73992,73993,74001],{},[895,73994,73995,73997,73999],{},[898,73996,1878],{},[1716,73998,19724],{},[1712,74000,73935],{},[902,74002,74003],{"encoding":904},"Q \\doteq 1{,}67",[883,74005,74007],{"className":74006},[886],[888,74008,74009],{"xmlns":890},[892,74010,74011,74019],{},[895,74012,74013,74015,74017],{},[898,74014,10871],{},[898,74016,5298],{},[898,74018,9945],{},[902,74020,68065],{"encoding":904},[883,74022,74024],{"className":74023},[886],[888,74025,74026],{"xmlns":890},[892,74027,74028,74036],{},[895,74029,74030,74032,74034],{},[898,74031,1878],{},[1716,74033,1913],{},[1712,74035,73950],{},[902,74037,74038],{"encoding":904},"Q = 2{,}50",[883,74040,74042],{"className":74041},[886],[888,74043,74044],{"xmlns":890},[892,74045,74046,74052],{},[895,74047,74048,74050],{},[898,74049,10871],{},[898,74051,9945],{},[902,74053,68314],{"encoding":904},[883,74055,74057],{"className":74056},[886],[888,74058,74059],{"xmlns":890},[892,74060,74061,74069],{},[895,74062,74063,74065,74067],{},[898,74064,1878],{},[1716,74066,19724],{},[1712,74068,73965],{},[902,74070,74071],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,74074,74075],{},[3682,74076],{"alt":74077,"className":74078,"src":74079},"imek-ac-avc-mc",[210,3686],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,74081,74082],{},[614,74083,74084,74085,2247,74100,74117,74118,29583,74137,74152],{},"Obrázek 3.9: Kubické křivky ",[883,74086,74088],{"className":74087},[886],[888,74089,74090],{"xmlns":890},[892,74091,74092,74098],{},[895,74093,74094,74096],{},[898,74095,4164],{},[898,74097,9945],{},[902,74099,17103],{"encoding":904},[883,74101,74103],{"className":74102},[886],[888,74104,74105],{"xmlns":890},[892,74106,74107,74115],{},[895,74108,74109,74111,74113],{},[898,74110,4164],{},[898,74112,5298],{},[898,74114,9945],{},[902,74116,68263],{"encoding":904}," rostoucí od bodu ",[883,74119,74121],{"className":74120},[886],[888,74122,74123],{"xmlns":890},[892,74124,74125,74135],{},[895,74126,74127,74129,74131,74133],{},[898,74128,24240],{},[898,74130,9945],{},[1716,74132,1913],{},[1712,74134,12151],{},[902,74136,25436],{"encoding":904},[883,74138,74140],{"className":74139},[886],[888,74141,74142],{"xmlns":890},[892,74143,74144,74150],{},[895,74145,74146,74148],{},[898,74147,24240],{},[898,74149,9945],{},[902,74151,68245],{"encoding":904}," je vodorovná přímka.",[724,74154,74155],{},[614,74156,74157,74158,1343,74173,1343,74190,42965,74205,74218,74219,7636,74236,74251,74252,7364,74269,74284,74285,39959,74298,1343,74311,1343,74324,1853],{},"Obrázek 3.10: Křivky ",[883,74159,74161],{"className":74160},[886],[888,74162,74163],{"xmlns":890},[892,74164,74165,74171],{},[895,74166,74167,74169],{},[898,74168,10871],{},[898,74170,9945],{},[902,74172,68314],{"encoding":904},[883,74174,74176],{"className":74175},[886],[888,74177,74178],{"xmlns":890},[892,74179,74180,74188],{},[895,74181,74182,74184,74186],{},[898,74183,10871],{},[898,74185,5298],{},[898,74187,9945],{},[902,74189,68065],{"encoding":904},[883,74191,74193],{"className":74192},[886],[888,74194,74195],{"xmlns":890},[892,74196,74197,74203],{},[895,74198,74199,74201],{},[898,74200,16690],{},[898,74202,9945],{},[902,74204,68046],{"encoding":904},[883,74206,74208],{"className":74207},[886],[888,74209,74210],{"xmlns":890},[892,74211,74212,74216],{},[895,74213,74214],{},[898,74215,900],{},[902,74217,900],{"encoding":904}," a klesající hyperbola ",[883,74220,74222],{"className":74221},[886],[888,74223,74224],{"xmlns":890},[892,74225,74226,74234],{},[895,74227,74228,74230,74232],{},[898,74229,10871],{},[898,74231,24240],{},[898,74233,9945],{},[902,74235,68281],{"encoding":904},[883,74237,74239],{"className":74238},[886],[888,74240,74241],{"xmlns":890},[892,74242,74243,74249],{},[895,74244,74245,74247],{},[898,74246,16690],{},[898,74248,9945],{},[902,74250,68046],{"encoding":904}," protíná ",[883,74253,74255],{"className":74254},[886],[888,74256,74257],{"xmlns":890},[892,74258,74259,74267],{},[895,74260,74261,74263,74265],{},[898,74262,10871],{},[898,74264,5298],{},[898,74266,9945],{},[902,74268,68065],{"encoding":904},[883,74270,74272],{"className":74271},[886],[888,74273,74274],{"xmlns":890},[892,74275,74276,74282],{},[895,74277,74278,74280],{},[898,74279,10871],{},[898,74281,9945],{},[902,74283,68314],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,74286,74288],{"className":74287},[886],[888,74289,74290],{"xmlns":890},[892,74291,74292,74296],{},[895,74293,74294],{},[898,74295,1878],{},[902,74297,1878],{"encoding":904},[883,74299,74301],{"className":74300},[886],[888,74302,74303],{"xmlns":890},[892,74304,74305,74309],{},[895,74306,74307],{},[1712,74308,73935],{},[902,74310,73938],{"encoding":904},[883,74312,74314],{"className":74313},[886],[888,74315,74316],{"xmlns":890},[892,74317,74318,74322],{},[895,74319,74320],{},[1712,74321,73950],{},[902,74323,73953],{"encoding":904},[883,74325,74327],{"className":74326},[886],[888,74328,74329],{"xmlns":890},[892,74330,74331,74335],{},[895,74332,74333],{},[1712,74334,73965],{},[902,74336,73968],{"encoding":904},[724,74338,74339],{},[38,74340,74341],{},"Standardní vlastnosti:",[120,74343,74344,74379,74443,74511,74561,74581],{},[123,74345,74346,2247,74361,74378],{},[883,74347,74349],{"className":74348},[886],[888,74350,74351],{"xmlns":890},[892,74352,74353,74359],{},[895,74354,74355,74357],{},[898,74356,4164],{},[898,74358,9945],{},[902,74360,17103],{"encoding":904},[883,74362,74364],{"className":74363},[886],[888,74365,74366],{"xmlns":890},[892,74367,74368,74376],{},[895,74369,74370,74372,74374],{},[898,74371,4164],{},[898,74373,5298],{},[898,74375,9945],{},[902,74377,68263],{"encoding":904}," jsou kubické funkce;",[123,74380,74381,1343,74396,1343,74413,74428,74429,74442],{},[883,74382,74384],{"className":74383},[886],[888,74385,74386],{"xmlns":890},[892,74387,74388,74394],{},[895,74389,74390,74392],{},[898,74391,10871],{},[898,74393,9945],{},[902,74395,68314],{"encoding":904},[883,74397,74399],{"className":74398},[886],[888,74400,74401],{"xmlns":890},[892,74402,74403,74411],{},[895,74404,74405,74407,74409],{},[898,74406,10871],{},[898,74408,5298],{},[898,74410,9945],{},[902,74412,68065],{"encoding":904},[883,74414,74416],{"className":74415},[886],[888,74417,74418],{"xmlns":890},[892,74419,74420,74426],{},[895,74421,74422,74424],{},[898,74423,16690],{},[898,74425,9945],{},[902,74427,68046],{"encoding":904}," jsou křivky tvaru ",[883,74430,74432],{"className":74431},[886],[888,74433,74434],{"xmlns":890},[892,74435,74436,74440],{},[895,74437,74438],{},[898,74439,900],{},[902,74441,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,74444,74445,74460,74461,1343,74478,74495,74496,22241],{},[883,74446,74448],{"className":74447},[886],[888,74449,74450],{"xmlns":890},[892,74451,74452,74458],{},[895,74453,74454,74456],{},[898,74455,16690],{},[898,74457,9945],{},[902,74459,68046],{"encoding":904}," nabývá minima před ",[883,74462,74464],{"className":74463},[886],[888,74465,74466],{"xmlns":890},[892,74467,74468,74476],{},[895,74469,74470,74472,74474],{},[898,74471,10871],{},[898,74473,5298],{},[898,74475,9945],{},[902,74477,68065],{"encoding":904},[883,74479,74481],{"className":74480},[886],[888,74482,74483],{"xmlns":890},[892,74484,74485,74493],{},[895,74486,74487,74489,74491],{},[898,74488,10871],{},[898,74490,5298],{},[898,74492,9945],{},[902,74494,68065],{"encoding":904}," před ",[883,74497,74499],{"className":74498},[886],[888,74500,74501],{"xmlns":890},[892,74502,74503,74509],{},[895,74504,74505,74507],{},[898,74506,10871],{},[898,74508,9945],{},[902,74510,68314],{"encoding":904},[123,74512,74513,74251,74528,2247,74543,74560],{},[883,74514,74516],{"className":74515},[886],[888,74517,74518],{"xmlns":890},[892,74519,74520,74526],{},[895,74521,74522,74524],{},[898,74523,16690],{},[898,74525,9945],{},[902,74527,68046],{"encoding":904},[883,74529,74531],{"className":74530},[886],[888,74532,74533],{"xmlns":890},[892,74534,74535,74541],{},[895,74536,74537,74539],{},[898,74538,10871],{},[898,74540,9945],{},[902,74542,68314],{"encoding":904},[883,74544,74546],{"className":74545},[886],[888,74547,74548],{"xmlns":890},[892,74549,74550,74558],{},[895,74551,74552,74554,74556],{},[898,74553,10871],{},[898,74555,5298],{},[898,74557,9945],{},[902,74559,68065],{"encoding":904}," zdola právě v jejich minimech;",[123,74562,74563,74580],{},[883,74564,74566],{"className":74565},[886],[888,74567,74568],{"xmlns":890},[892,74569,74570,74578],{},[895,74571,74572,74574,74576],{},[898,74573,10871],{},[898,74575,24240],{},[898,74577,9945],{},[902,74579,68281],{"encoding":904}," je hyperbola, stále klesající;",[123,74582,74583,74615,74616,2247,74631,74648,74649,74662,74663,2365],{},[883,74584,74586],{"className":74585},[886],[888,74587,74588],{"xmlns":890},[892,74589,74590,74612],{},[895,74591,74592,74594,74596,74598,74600,74602,74604,74606,74608,74610],{},[898,74593,10871],{},[898,74595,9945],{},[1716,74597,1913],{},[898,74599,10871],{},[898,74601,24240],{},[898,74603,9945],{},[1716,74605,1949],{},[898,74607,10871],{},[898,74609,5298],{},[898,74611,9945],{},[902,74613,74614],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,74617,74619],{"className":74618},[886],[888,74620,74621],{"xmlns":890},[892,74622,74623,74629],{},[895,74624,74625,74627],{},[898,74626,10871],{},[898,74628,9945],{},[902,74630,68314],{"encoding":904},[883,74632,74634],{"className":74633},[886],[888,74635,74636],{"xmlns":890},[892,74637,74638,74646],{},[895,74639,74640,74642,74644],{},[898,74641,10871],{},[898,74643,5298],{},[898,74645,9945],{},[902,74647,68065],{"encoding":904}," klesá s rostoucím ",[883,74650,74652],{"className":74651},[886],[888,74653,74654],{"xmlns":890},[892,74655,74656,74660],{},[895,74657,74658],{},[898,74659,1878],{},[902,74661,1878],{"encoding":904}," (protože ",[883,74664,74666],{"className":74665},[886],[888,74667,74668],{"xmlns":890},[892,74669,74670,74682],{},[895,74671,74672,74674,74676,74678,74680],{},[898,74673,10871],{},[898,74675,24240],{},[898,74677,9945],{},[1716,74679,16986],{},[1712,74681,2505],{},[902,74683,74684],{"encoding":904},"AFC \\to 0",[115,74686,74688],{"id":74687},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,74690,74691,74692,74695,74696,74711],{},"Častou optimalizační úlohou je ",[38,74693,74694],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,74697,74699],{"className":74698},[886],[888,74700,74701],{"xmlns":890},[892,74702,74703,74709],{},[895,74704,74705,74707],{},[898,74706,10871],{},[898,74708,9945],{},[902,74710,68314],{"encoding":904}," minimální.",[198,74713,30202],{"id":30201},[724,74715,74716,74717,74734],{},"Mají-li průměrné náklady minimum v bodě ",[883,74718,74720],{"className":74719},[886],[888,74721,74722],{"xmlns":890},[892,74723,74724,74732],{},[895,74725,74726],{},[1707,74727,74728,74730],{},[898,74729,1878],{},[1712,74731,2505],{},[902,74733,3245],{"encoding":904},", pak platí",[883,74736,74738],{"className":74737},[886],[888,74739,74740],{"xmlns":890,"display":2004},[892,74741,74742,74791],{},[2008,74743,74744],{"width":2010},[2012,74745,74746,74748,74784,74786],{},[2015,74747],{"width":2017},[2015,74749,74750],{},[895,74751,74752,74754,74756,74758,74764,74766,74768,74770,74772,74774,74780,74782],{},[898,74753,10871],{},[898,74755,9945],{},[1716,74757,1920],{"stretchy":1919},[1707,74759,74760,74762],{},[898,74761,1878],{},[1712,74763,2505],{},[1716,74765,1925],{"stretchy":1919},[1716,74767,1913],{},[898,74769,16690],{},[898,74771,9945],{},[1716,74773,1920],{"stretchy":1919},[1707,74775,74776,74778],{},[898,74777,1878],{},[1712,74779,2505],{},[1716,74781,1925],{"stretchy":1919},[898,74783,1853],{"mathvariant":2068},[2015,74785],{"width":2017},[2015,74787,74788],{},[2074,74789,74790],{},"(3.10)",[902,74792,74793],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1635,74795,74796],{},[724,74797,74798,74800,74801],{},[883,74799,69198],{}," Princip\n",[38,74802,74803],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,74805,74806,74809,74810,74852],{},[38,74807,74808],{},"Odvození."," Z ",[883,74811,74813],{"className":74812},[886],[888,74814,74815],{"xmlns":890},[892,74816,74817,74849],{},[895,74818,74819,74821,74823,74825,74827,74829,74831],{},[898,74820,10871],{},[898,74822,9945],{},[1716,74824,1920],{"stretchy":1919},[898,74826,1878],{},[1716,74828,1925],{"stretchy":1919},[1716,74830,1913],{},[2747,74832,74833],{"scriptlevel":2505,"displaystyle":1919},[2750,74834,74835,74847],{},[895,74836,74837,74839,74841,74843,74845],{},[898,74838,4164],{},[898,74840,9945],{},[1716,74842,1920],{"stretchy":1919},[898,74844,1878],{},[1716,74846,1925],{"stretchy":1919},[898,74848,1878],{},[902,74850,74851],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,74854,74856],{"className":74855},[886],[888,74857,74858],{"xmlns":890,"display":2004},[892,74859,74860,74992],{},[895,74861,74862,74864,74870,74872,74874,74876,74878,74918,74920,74960,74962,74990],{},[898,74863,10871],{},[3074,74865,74866,74868],{},[898,74867,9945],{},[1716,74869,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,74871,1920],{"stretchy":1919},[898,74873,1878],{},[1716,74875,1925],{"stretchy":1919},[1716,74877,1913],{},[2750,74879,74880,74912],{},[895,74881,74882,74884,74890,74892,74894,74896,74898,74900,74902,74904,74906,74908,74910],{},[898,74883,4164],{},[3074,74885,74886,74888],{},[898,74887,9945],{},[1716,74889,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,74891,1920],{"stretchy":1919},[898,74893,1878],{},[1716,74895,1925],{"stretchy":1919},[1716,74897,9532],{},[898,74899,1878],{},[1716,74901,2760],{},[898,74903,4164],{},[898,74905,9945],{},[1716,74907,1920],{"stretchy":1919},[898,74909,1878],{},[1716,74911,1925],{"stretchy":1919},[3074,74913,74914,74916],{},[898,74915,1878],{},[1712,74917,1726],{},[1716,74919,1913],{},[2750,74921,74922,74954],{},[895,74923,74924,74926,74928,74930,74932,74934,74936,74938,74940,74942,74944,74946,74948,74950,74952],{},[898,74925,16690],{},[898,74927,9945],{},[1716,74929,1920],{"stretchy":1919},[898,74931,1878],{},[1716,74933,1925],{"stretchy":1919},[1716,74935,9532],{},[898,74937,1878],{},[1716,74939,2760],{},[898,74941,10871],{},[898,74943,9945],{},[1716,74945,1920],{"stretchy":1919},[898,74947,1878],{},[1716,74949,1925],{"stretchy":1919},[1716,74951,9532],{},[898,74953,1878],{},[3074,74955,74956,74958],{},[898,74957,1878],{},[1712,74959,1726],{},[1716,74961,1913],{},[2750,74963,74964,74988],{},[895,74965,74966,74968,74970,74972,74974,74976,74978,74980,74982,74984,74986],{},[898,74967,16690],{},[898,74969,9945],{},[1716,74971,1920],{"stretchy":1919},[898,74973,1878],{},[1716,74975,1925],{"stretchy":1919},[1716,74977,2760],{},[898,74979,10871],{},[898,74981,9945],{},[1716,74983,1920],{"stretchy":1919},[898,74985,1878],{},[1716,74987,1925],{"stretchy":1919},[898,74989,1878],{},[898,74991,1853],{"mathvariant":2068},[902,74993,74994],{"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}.",[724,74996,74997,74998,16504,75013,2574,75035,69575],{},"Nutnou podmínkou minima ",[883,74999,75001],{"className":75000},[886],[888,75002,75003],{"xmlns":890},[892,75004,75005,75011],{},[895,75006,75007,75009],{},[898,75008,10871],{},[898,75010,9945],{},[902,75012,68314],{"encoding":904},[883,75014,75016],{"className":75015},[886],[888,75017,75018],{"xmlns":890},[892,75019,75020,75032],{},[895,75021,75022,75028,75030],{},[1707,75023,75024,75026],{},[898,75025,1878],{},[1712,75027,2505],{},[1716,75029,2716],{},[1712,75031,2505],{},[902,75033,75034],{"encoding":904},"Q_0 > 0",[883,75036,75038],{"className":75037},[886],[888,75039,75040],{"xmlns":890},[892,75041,75042,75066],{},[895,75043,75044,75046,75052,75054,75060,75062,75064],{},[898,75045,10871],{},[3074,75047,75048,75050],{},[898,75049,9945],{},[1716,75051,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,75053,1920],{"stretchy":1919},[1707,75055,75056,75058],{},[898,75057,1878],{},[1712,75059,2505],{},[1716,75061,1925],{"stretchy":1919},[1716,75063,1913],{},[1712,75065,2505],{},[902,75067,75068],{"encoding":904},"AC'(Q_0) = 0",[883,75070,75072],{"className":75071},[886],[888,75073,75074],{"xmlns":890,"display":2004},[892,75075,75076,75161],{},[895,75077,75078,75118,75120,75122,75124,75127,75129,75131,75133,75135,75141,75143,75145,75147,75149,75151,75157,75159],{},[2750,75079,75080,75112],{},[895,75081,75082,75084,75086,75088,75094,75096,75098,75100,75102,75104,75110],{},[898,75083,16690],{},[898,75085,9945],{},[1716,75087,1920],{"stretchy":1919},[1707,75089,75090,75092],{},[898,75091,1878],{},[1712,75093,2505],{},[1716,75095,1925],{"stretchy":1919},[1716,75097,2760],{},[898,75099,10871],{},[898,75101,9945],{},[1716,75103,1920],{"stretchy":1919},[1707,75105,75106,75108],{},[898,75107,1878],{},[1712,75109,2505],{},[1716,75111,1925],{"stretchy":1919},[1707,75113,75114,75116],{},[898,75115,1878],{},[1712,75117,2505],{},[1716,75119,1913],{},[1712,75121,2505],{},[2324,75123],{"width":8689},[1716,75125,75126],{},"⟺",[2324,75128],{"width":8689},[898,75130,16690],{},[898,75132,9945],{},[1716,75134,1920],{"stretchy":1919},[1707,75136,75137,75139],{},[898,75138,1878],{},[1712,75140,2505],{},[1716,75142,1925],{"stretchy":1919},[1716,75144,1913],{},[898,75146,10871],{},[898,75148,9945],{},[1716,75150,1920],{"stretchy":1919},[1707,75152,75153,75155],{},[898,75154,1878],{},[1712,75156,2505],{},[1716,75158,1925],{"stretchy":1919},[898,75160,1853],{"mathvariant":2068},[902,75162,75163],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,75165,75166,3495,75169,74251,75184,75199,75200,75215,75216,2574,75233,75255,75256,75278],{},[38,75167,75168],{},"Geometrická interpretace.",[883,75170,75172],{"className":75171},[886],[888,75173,75174],{"xmlns":890},[892,75175,75176,75182],{},[895,75177,75178,75180],{},[898,75179,16690],{},[898,75181,9945],{},[902,75183,68046],{"encoding":904},[883,75185,75187],{"className":75186},[886],[888,75188,75189],{"xmlns":890},[892,75190,75191,75197],{},[895,75192,75193,75195],{},[898,75194,10871],{},[898,75196,9945],{},[902,75198,68314],{"encoding":904}," právě v bodě minima ",[883,75201,75203],{"className":75202},[886],[888,75204,75205],{"xmlns":890},[892,75206,75207,75213],{},[895,75208,75209,75211],{},[898,75210,10871],{},[898,75212,9945],{},[902,75214,68314],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,75217,75219],{"className":75218},[886],[888,75220,75221],{"xmlns":890},[892,75222,75223,75231],{},[895,75224,75225],{},[1707,75226,75227,75229],{},[898,75228,1878],{},[1712,75230,2505],{},[902,75232,3245],{"encoding":904},[883,75234,75236],{"className":75235},[886],[888,75237,75238],{"xmlns":890},[892,75239,75240,75252],{},[895,75241,75242,75244,75246,75248,75250],{},[898,75243,16690],{},[898,75245,9945],{},[1716,75247,2704],{},[898,75249,10871],{},[898,75251,9945],{},[902,75253,75254],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,75257,75259],{"className":75258},[886],[888,75260,75261],{"xmlns":890},[892,75262,75263,75275],{},[895,75264,75265,75267,75269,75271,75273],{},[898,75266,16690],{},[898,75268,9945],{},[1716,75270,2716],{},[898,75272,10871],{},[898,75274,9945],{},[902,75276,75277],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,75280,75281,75282,75324,75325,75342,75343,1853],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,75283,75285],{"className":75284},[886],[888,75286,75287],{"xmlns":890},[892,75288,75289,75321],{},[895,75290,75291,75293,75295,75297,75303,75305,75307,75309,75311,75313,75319],{},[898,75292,10871],{},[898,75294,9945],{},[1716,75296,1920],{"stretchy":1919},[1707,75298,75299,75301],{},[898,75300,1878],{},[1712,75302,2505],{},[1716,75304,1925],{"stretchy":1919},[1716,75306,1913],{},[898,75308,16690],{},[898,75310,9945],{},[1716,75312,1920],{"stretchy":1919},[1707,75314,75315,75317],{},[898,75316,1878],{},[1712,75318,2505],{},[1716,75320,1925],{"stretchy":1919},[902,75322,75323],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,75326,75328],{"className":75327},[886],[888,75329,75330],{"xmlns":890},[892,75331,75332,75340],{},[895,75333,75334],{},[1707,75335,75336,75338],{},[898,75337,1878],{},[1712,75339,2505],{},[902,75341,3245],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,75344,75346],{"className":75345},[886],[888,75347,75348],{"xmlns":890},[892,75349,75350,75374],{},[895,75351,75352,75354,75356,75358,75360,75362,75364,75366,75368,75370,75372],{},[898,75353,10871],{},[898,75355,9945],{},[1716,75357,1920],{"stretchy":1919},[898,75359,1878],{},[1716,75361,1925],{"stretchy":1919},[1716,75363,1913],{},[898,75365,16690],{},[898,75367,9945],{},[1716,75369,1920],{"stretchy":1919},[898,75371,1878],{},[1716,75373,1925],{"stretchy":1919},[902,75375,75376],{"encoding":904},"AC(Q) = MC(Q)",[1635,75378,75379],{},[724,75380,75381,75383,75384,24198,75402,75423,75424,24198,75427,75448,75449,75464,75465,70792,75480,2365],{},[883,75382,2233],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,75385,75386,75387],{},"minimum ",[883,75388,75390],{"className":75389},[886],[888,75391,75392],{"xmlns":890},[892,75393,75394,75400],{},[895,75395,75396,75398],{},[898,75397,10871],{},[898,75399,9945],{},[902,75401,68314],{"encoding":904},[883,75403,75405],{"className":75404},[886],[888,75406,75407],{"xmlns":890},[892,75408,75409,75421],{},[895,75410,75411,75413,75415,75417,75419],{},[898,75412,10871],{},[898,75414,9945],{},[1716,75416,1913],{},[898,75418,16690],{},[898,75420,9945],{},[902,75422,67977],{"encoding":904},", pro ",[38,75425,75426],{},"maximum zisku",[883,75428,75430],{"className":75429},[886],[888,75431,75432],{"xmlns":890},[892,75433,75434,75446],{},[895,75435,75436,75438,75440,75442,75444],{},[898,75437,16690],{},[898,75439,17840],{},[1716,75441,1913],{},[898,75443,16690],{},[898,75445,9945],{},[902,75447,68025],{"encoding":904},". Obě podmínky využívají ",[883,75450,75452],{"className":75451},[886],[888,75453,75454],{"xmlns":890},[892,75455,75456,75462],{},[895,75457,75458,75460],{},[898,75459,16690],{},[898,75461,9945],{},[902,75463,68046],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,75466,75468],{"className":75467},[886],[888,75469,75470],{"xmlns":890},[892,75471,75472,75478],{},[895,75473,75474,75476],{},[898,75475,10871],{},[898,75477,9945],{},[902,75479,68314],{"encoding":904},[883,75481,75483],{"className":75482},[886],[888,75484,75485],{"xmlns":890},[892,75486,75487,75493],{},[895,75488,75489,75491],{},[898,75490,16690],{},[898,75492,17840],{},[902,75494,20456],{"encoding":904},[2257,75496,75498],{"id":75497},"příklad-37","Příklad 3.7",[724,75500,75501,70276,75503,75537,75538,75551,75552,75567],{},[38,75502,68741],{},[883,75504,75506],{"className":75505},[886],[888,75507,75508],{"xmlns":890},[892,75509,75510,75534],{},[895,75511,75512,75514,75516,75518,75524,75526,75528,75530,75532],{},[898,75513,4164],{},[898,75515,9945],{},[1716,75517,1913],{},[3074,75519,75520,75522],{},[898,75521,1878],{},[1712,75523,1726],{},[1716,75525,1949],{},[1712,75527,7072],{},[898,75529,1878],{},[1716,75531,1949],{},[1712,75533,19394],{},[902,75535,75536],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,75539,75541],{"className":75540},[886],[888,75542,75543],{"xmlns":890},[892,75544,75545,75549],{},[895,75546,75547],{},[898,75548,1878],{},[902,75550,1878],{"encoding":904}," minimalizující ",[883,75553,75555],{"className":75554},[886],[888,75556,75557],{"xmlns":890},[892,75558,75559,75565],{},[895,75560,75561,75563],{},[898,75562,10871],{},[898,75564,9945],{},[902,75566,68314],{"encoding":904}," a ověřte princip (3.10).",[724,75569,75570,75572],{},[38,75571,36544],{}," Přímý výpočet:",[883,75574,75576],{"className":75575},[886],[888,75577,75578],{"xmlns":890,"display":2004},[892,75579,75580,75682],{},[895,75581,75582,75584,75586,75588,75610,75612,75614,75616,75618,75620,75626,75628,75630,75632,75634,75636,75642,75644,75646,75648,75658,75660,75680],{},[898,75583,10871],{},[898,75585,9945],{},[1716,75587,1913],{},[2750,75589,75590,75608],{},[895,75591,75592,75598,75600,75602,75604,75606],{},[3074,75593,75594,75596],{},[898,75595,1878],{},[1712,75597,1726],{},[1716,75599,1949],{},[1712,75601,7072],{},[898,75603,1878],{},[1716,75605,1949],{},[1712,75607,19394],{},[898,75609,1878],{},[1716,75611,1913],{},[898,75613,1878],{},[1716,75615,1949],{},[1712,75617,7072],{},[1716,75619,1949],{},[2750,75621,75622,75624],{},[1712,75623,19394],{},[898,75625,1878],{},[1716,75627,1719],{"separator":1718},[2324,75629],{"width":2326},[1716,75631,1920],{"stretchy":1919},[898,75633,10871],{},[898,75635,9945],{},[3074,75637,75638,75640],{},[1716,75639,1925],{"stretchy":1919},[1716,75641,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,75643,1913],{},[1712,75645,1714],{},[1716,75647,2760],{},[2750,75649,75650,75652],{},[1712,75651,19394],{},[3074,75653,75654,75656],{},[898,75655,1878],{},[1712,75657,1726],{},[1716,75659,1913],{},[2750,75661,75662,75674],{},[895,75663,75664,75670,75672],{},[3074,75665,75666,75668],{},[898,75667,1878],{},[1712,75669,1726],{},[1716,75671,2760],{},[1712,75673,19394],{},[3074,75675,75676,75678],{},[898,75677,1878],{},[1712,75679,1726],{},[898,75681,1853],{"mathvariant":2068},[902,75683,75684],{"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}.",[724,75686,75687,75727,75728,75752,75753,75803,75804,1853],{},[883,75688,75690],{"className":75689},[886],[888,75691,75692],{"xmlns":890},[892,75693,75694,75724],{},[895,75695,75696,75698,75700,75702,75708,75710,75712,75714,75720,75722],{},[1716,75697,1920],{"stretchy":1919},[898,75699,10871],{},[898,75701,9945],{},[3074,75703,75704,75706],{},[1716,75705,1925],{"stretchy":1919},[1716,75707,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,75709,1913],{},[1712,75711,2505],{},[1716,75713,17833],{},[1707,75715,75716,75718],{},[898,75717,1878],{},[1712,75719,1714],{},[1716,75721,1913],{},[1712,75723,6231],{},[902,75725,75726],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,75729,75731],{"className":75730},[886],[888,75732,75733],{"xmlns":890},[892,75734,75735,75749],{},[895,75736,75737,75743,75745,75747],{},[1707,75738,75739,75741],{},[898,75740,1878],{},[1712,75742,1726],{},[1716,75744,1913],{},[1716,75746,2760],{},[1712,75748,6231],{},[902,75750,75751],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,75754,75756],{"className":75755},[886],[888,75757,75758],{"xmlns":890},[892,75759,75760,75800],{},[895,75761,75762,75764,75766,75768,75778,75780,75782,75784,75786,75794,75796,75798],{},[1716,75763,1920],{"stretchy":1919},[898,75765,10871],{},[898,75767,9945],{},[3074,75769,75770,75772],{},[1716,75771,1925],{"stretchy":1919},[895,75773,75774,75776],{},[1716,75775,8505],{"mathvariant":2068},[1716,75777,8505],{"mathvariant":2068},[1716,75779,1920],{"stretchy":1919},[1712,75781,6231],{},[1716,75783,1925],{"stretchy":1919},[1716,75785,1913],{},[2747,75787,75788],{"scriptlevel":2505,"displaystyle":1919},[2750,75789,75790,75792],{},[1712,75791,1714],{},[1712,75793,7072],{},[1716,75795,2716],{},[1712,75797,2505],{},[1716,75799,17833],{},[902,75801,75802],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,75805,75807],{"className":75806},[886],[888,75808,75809],{"xmlns":890},[892,75810,75811,75827],{},[895,75812,75813,75815,75817,75819,75821,75823,75825],{},[898,75814,10871],{},[898,75816,9945],{},[1716,75818,1920],{"stretchy":1919},[1712,75820,6231],{},[1716,75822,1925],{"stretchy":1919},[1716,75824,1913],{},[1712,75826,3221],{},[902,75828,75829],{"encoding":904},"AC(6) = 15",[724,75831,75832,75833,75859,75860,2291],{},"Pomocí principu: ",[883,75834,75836],{"className":75835},[886],[888,75837,75838],{"xmlns":890},[892,75839,75840,75856],{},[895,75841,75842,75844,75846,75848,75850,75852,75854],{},[898,75843,16690],{},[898,75845,9945],{},[1716,75847,1913],{},[1712,75849,1726],{},[898,75851,1878],{},[1716,75853,1949],{},[1712,75855,7072],{},[902,75857,75858],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,75861,75863],{"className":75862},[886],[888,75864,75865],{"xmlns":890},[892,75866,75867,75879],{},[895,75868,75869,75871,75873,75875,75877],{},[898,75870,10871],{},[898,75872,9945],{},[1716,75874,1913],{},[898,75876,16690],{},[898,75878,9945],{},[902,75880,67977],{"encoding":904},[883,75882,75884],{"className":75883},[886],[888,75885,75886],{"xmlns":890,"display":2004},[892,75887,75888,75990],{},[895,75889,75890,75912,75914,75916,75918,75920,75922,75924,75926,75928,75934,75936,75938,75940,75942,75944,75946,75948,75954,75956,75958,75960,75962,75964,75966,75972,75974,75976,75978,75980,75982,75984,75986,75988],{},[2750,75891,75892,75910],{},[895,75893,75894,75900,75902,75904,75906,75908],{},[3074,75895,75896,75898],{},[898,75897,1878],{},[1712,75899,1726],{},[1716,75901,1949],{},[1712,75903,7072],{},[898,75905,1878],{},[1716,75907,1949],{},[1712,75909,19394],{},[898,75911,1878],{},[1716,75913,1913],{},[1712,75915,1726],{},[898,75917,1878],{},[1716,75919,1949],{},[1712,75921,7072],{},[2074,75923,17830],{},[1716,75925,17833],{},[2074,75927,17830],{},[3074,75929,75930,75932],{},[898,75931,1878],{},[1712,75933,1726],{},[1716,75935,1949],{},[1712,75937,7072],{},[898,75939,1878],{},[1716,75941,1949],{},[1712,75943,19394],{},[1716,75945,1913],{},[1712,75947,1726],{},[3074,75949,75950,75952],{},[898,75951,1878],{},[1712,75953,1726],{},[1716,75955,1949],{},[1712,75957,7072],{},[898,75959,1878],{},[2074,75961,17830],{},[1716,75963,17833],{},[2074,75965,17830],{},[3074,75967,75968,75970],{},[898,75969,1878],{},[1712,75971,1726],{},[1716,75973,1913],{},[1712,75975,19394],{},[2074,75977,17830],{},[1716,75979,17833],{},[2074,75981,17830],{},[898,75983,1878],{},[1716,75985,1913],{},[1712,75987,6231],{},[1716,75989,1719],{"separator":1718},[902,75991,75992],{"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,",[724,75994,75995,75996,76034],{},"a ",[883,75997,75999],{"className":75998},[886],[888,76000,76001],{"xmlns":890},[892,76002,76003,76031],{},[895,76004,76005,76007,76009,76011,76013,76015,76017,76019,76021,76023,76025,76027,76029],{},[898,76006,10871],{},[898,76008,9945],{},[1716,76010,1920],{"stretchy":1919},[1712,76012,6231],{},[1716,76014,1925],{"stretchy":1919},[1716,76016,1913],{},[898,76018,16690],{},[898,76020,9945],{},[1716,76022,1920],{"stretchy":1919},[1712,76024,6231],{},[1716,76026,1925],{"stretchy":1919},[1716,76028,1913],{},[1712,76030,3221],{},[902,76032,76033],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,76036,76038],{"id":76037},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,76040,76041,76042,2291],{},"Analogicky pro ",[883,76043,76045],{"className":76044},[886],[888,76046,76047],{"xmlns":890},[892,76048,76049,76057],{},[895,76050,76051,76053,76055],{},[898,76052,10871],{},[898,76054,5298],{},[898,76056,9945],{},[902,76058,68065],{"encoding":904},[883,76060,76062],{"className":76061},[886],[888,76063,76064],{"xmlns":890,"display":2004},[892,76065,76066,76117],{},[2008,76067,76068],{"width":2010},[2012,76069,76070,76072,76110,76112],{},[2015,76071],{"width":2017},[2015,76073,76074],{},[895,76075,76076,76078,76080,76082,76084,76090,76092,76094,76096,76098,76100,76106,76108],{},[898,76077,10871],{},[898,76079,5298],{},[898,76081,9945],{},[1716,76083,1920],{"stretchy":1919},[1707,76085,76086,76088],{},[898,76087,1878],{},[1712,76089,2505],{},[1716,76091,1925],{"stretchy":1919},[1716,76093,1913],{},[898,76095,16690],{},[898,76097,9945],{},[1716,76099,1920],{"stretchy":1919},[1707,76101,76102,76104],{},[898,76103,1878],{},[1712,76105,2505],{},[1716,76107,1925],{"stretchy":1919},[898,76109,1853],{"mathvariant":2068},[2015,76111],{"width":2017},[2015,76113,76114],{},[2074,76115,76116],{},"(3.11)",[902,76118,76119],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1635,76121,76122],{},[724,76123,76124,74800,76126],{},[883,76125,69198],{},[38,76127,76128,76129,76146],{},"V bodě minima průměrných variabilních nákladů se ",[883,76130,76132],{"className":76131},[886],[888,76133,76134],{"xmlns":890},[892,76135,76136,76144],{},[895,76137,76138,76140,76142],{},[898,76139,10871],{},[898,76141,5298],{},[898,76143,9945],{},[902,76145,68065],{"encoding":904}," rovnají mezním nákladům.",[724,76148,76149,76150,76172,76173,1853],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,76151,76153],{"className":76152},[886],[888,76154,76155],{"xmlns":890},[892,76156,76157,76169],{},[895,76158,76159,76165,76167],{},[1707,76160,76161,76163],{},[898,76162,1878],{},[1712,76164,2505],{},[1716,76166,1913],{},[1712,76168,65953],{},[902,76170,76171],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,76174,76176],{"className":76175},[886],[888,76177,76178],{"xmlns":890},[892,76179,76180,76206],{},[895,76181,76182,76184,76186,76188,76190,76192,76194,76196,76198,76200,76202,76204],{},[898,76183,10871],{},[898,76185,5298],{},[898,76187,9945],{},[1716,76189,1920],{"stretchy":1919},[898,76191,1878],{},[1716,76193,1925],{"stretchy":1919},[1716,76195,1913],{},[898,76197,16690],{},[898,76199,9945],{},[1716,76201,1920],{"stretchy":1919},[898,76203,1878],{},[1716,76205,1925],{"stretchy":1919},[902,76207,76208],{"encoding":904},"AVC(Q) = MC(Q)",[115,76210,76212],{"id":76211},"zisk-a-body-zvratu","Zisk a body zvratu",[724,76214,76215,3495,76218,76234],{},[38,76216,76217],{},"Zisk",[883,76219,76221],{"className":76220},[886],[888,76222,76223],{"xmlns":890},[892,76224,76225,76231],{},[895,76226,76227,76229],{},[898,76228,1690],{},[898,76230,17840],{},[902,76232,76233],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,76236,76238],{"className":76237},[886],[888,76239,76240],{"xmlns":890,"display":2004},[892,76241,76242,76301],{},[2008,76243,76244],{"width":2010},[2012,76245,76246,76248,76294,76296],{},[2015,76247],{"width":2017},[2015,76249,76250],{},[895,76251,76252,76254,76256,76258,76260,76262,76264,76266,76268,76270,76272,76274,76276,76278,76280,76282,76284,76286,76288,76290,76292],{},[898,76253,1690],{},[898,76255,17840],{},[1716,76257,1913],{},[898,76259,1690],{},[898,76261,17840],{},[1716,76263,1920],{"stretchy":1919},[898,76265,1878],{},[1716,76267,1925],{"stretchy":1919},[1716,76269,1913],{},[898,76271,4164],{},[898,76273,17840],{},[1716,76275,1920],{"stretchy":1919},[898,76277,1878],{},[1716,76279,1925],{"stretchy":1919},[1716,76281,2760],{},[898,76283,4164],{},[898,76285,9945],{},[1716,76287,1920],{"stretchy":1919},[898,76289,1878],{},[1716,76291,1925],{"stretchy":1919},[898,76293,1853],{"mathvariant":2068},[2015,76295],{"width":2017},[2015,76297,76298],{},[2074,76299,76300],{},"(3.12)",[902,76302,76303],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,76305,76306,76307,2247,76322,8626,76337,76339,76340,76343,76344,76360,76361,76376,76377,76392,76393,1343,76406,76419,76420,1343,76438,76456,76457,1994,76460,76463,76464,1348,76486,2574,76508,76530,76531,2574,76561,76583],{},"Body rovnosti ",[883,76308,76310],{"className":76309},[886],[888,76311,76312],{"xmlns":890},[892,76313,76314,76320],{},[895,76315,76316,76318],{},[898,76317,4164],{},[898,76319,17840],{},[902,76321,17938],{"encoding":904},[883,76323,76325],{"className":76324},[886],[888,76326,76327],{"xmlns":890},[892,76328,76329,76335],{},[895,76330,76331,76333],{},[898,76332,4164],{},[898,76334,9945],{},[902,76336,17103],{"encoding":904},[38,76338,68481],{}," (též vyrovnání, ",[614,76341,76342],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,76345,76347],{"className":76346},[886],[888,76348,76349],{"xmlns":890},[892,76350,76351,76357],{},[895,76352,76353,76355],{},[898,76354,5298],{},[898,76356,9945],{},[902,76358,76359],{"encoding":904},"VC",") je ",[883,76362,76364],{"className":76363},[886],[888,76365,76366],{"xmlns":890},[892,76367,76368,76374],{},[895,76369,76370,76372],{},[898,76371,4164],{},[898,76373,17840],{},[902,76375,17938],{"encoding":904}," kvadratická a ",[883,76378,76380],{"className":76379},[886],[888,76381,76382],{"xmlns":890},[892,76383,76384,76390],{},[895,76385,76386,76388],{},[898,76387,4164],{},[898,76389,9945],{},[902,76391,17103],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,76394,76396],{"className":76395},[886],[888,76397,76398],{"xmlns":890},[892,76399,76400,76404],{},[895,76401,76402],{},[898,76403,10871],{},[902,76405,10871],{"encoding":904},[883,76407,76409],{"className":76408},[886],[888,76410,76411],{"xmlns":890},[892,76412,76413,76417],{},[895,76414,76415],{},[898,76416,10856],{},[902,76418,10856],{"encoding":904}," odpovídajících množstvím ",[883,76421,76423],{"className":76422},[886],[888,76424,76425],{"xmlns":890},[892,76426,76427,76435],{},[895,76428,76429],{},[1707,76430,76431,76433],{},[898,76432,1878],{},[898,76434,10871],{},[902,76436,76437],{"encoding":904},"Q_A",[883,76439,76441],{"className":76440},[886],[888,76442,76443],{"xmlns":890},[892,76444,76445,76453],{},[895,76446,76447],{},[1707,76448,76449,76451],{},[898,76450,1878],{},[898,76452,10856],{},[902,76454,76455],{"encoding":904},"Q_B"," — firma je na ",[38,76458,76459],{},"prahu rentability",[614,76461,76462],{},"break even","). Pro ",[883,76465,76467],{"className":76466},[886],[888,76468,76469],{"xmlns":890},[892,76470,76471,76483],{},[895,76472,76473,76475,76477],{},[898,76474,1878],{},[1716,76476,2704],{},[1707,76478,76479,76481],{},[898,76480,1878],{},[898,76482,10871],{},[902,76484,76485],{"encoding":904},"Q \u003C Q_A",[883,76487,76489],{"className":76488},[886],[888,76490,76491],{"xmlns":890},[892,76492,76493,76505],{},[895,76494,76495,76497,76499],{},[898,76496,1878],{},[1716,76498,2716],{},[1707,76500,76501,76503],{},[898,76502,1878],{},[898,76504,10856],{},[902,76506,76507],{"encoding":904},"Q > Q_B",[883,76509,76511],{"className":76510},[886],[888,76512,76513],{"xmlns":890},[892,76514,76515,76527],{},[895,76516,76517,76519,76521,76523,76525],{},[898,76518,4164],{},[898,76520,9945],{},[1716,76522,2716],{},[898,76524,4164],{},[898,76526,17840],{},[902,76528,76529],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,76532,76534],{"className":76533},[886],[888,76535,76536],{"xmlns":890},[892,76537,76538,76558],{},[895,76539,76540,76546,76548,76550,76552],{},[1707,76541,76542,76544],{},[898,76543,1878],{},[898,76545,10871],{},[1716,76547,2704],{},[898,76549,1878],{},[1716,76551,2704],{},[1707,76553,76554,76556],{},[898,76555,1878],{},[898,76557,10856],{},[902,76559,76560],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,76562,76564],{"className":76563},[886],[888,76565,76566],{"xmlns":890},[892,76567,76568,76580],{},[895,76569,76570,76572,76574,76576,76578],{},[898,76571,4164],{},[898,76573,17840],{},[1716,76575,2716],{},[898,76577,4164],{},[898,76579,9945],{},[902,76581,76582],{"encoding":904},"TR > TC"," (zisk).",[1635,76585,76586],{},[724,76587,76588,76590],{},[883,76589,1641],{}," 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.",[724,76592,76593,76594,76620],{},"Body zvratu jsou řešení rovnice ",[883,76595,76597],{"className":76596},[886],[888,76598,76599],{"xmlns":890},[892,76600,76601,76617],{},[895,76602,76603,76605,76607,76609,76611,76613,76615],{},[898,76604,1690],{},[898,76606,17840],{},[1716,76608,1920],{"stretchy":1919},[898,76610,1878],{},[1716,76612,1925],{"stretchy":1919},[1716,76614,1913],{},[1712,76616,2505],{},[902,76618,76619],{"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.",[724,76622,76623],{},[3682,76624],{"alt":76625,"className":76626,"src":76627},"imek-tr-tc-body-zvratu",[210,3686],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,76629,76630],{},[614,76631,76632,76633,76648,76649,76664,76665,2247,76678,8345,76691,76704,76705,2247,76722,76739,76740,76760,76761,2247,76776,20296,76791,76820],{},"Obrázek 3.11: Body zvratu — křivky ",[883,76634,76636],{"className":76635},[886],[888,76637,76638],{"xmlns":890},[892,76639,76640,76646],{},[895,76641,76642,76644],{},[898,76643,4164],{},[898,76645,17840],{},[902,76647,17938],{"encoding":904}," (obrácená parabola) a ",[883,76650,76652],{"className":76651},[886],[888,76653,76654],{"xmlns":890},[892,76655,76656,76662],{},[895,76657,76658,76660],{},[898,76659,4164],{},[898,76661,9945],{},[902,76663,17103],{"encoding":904}," (přímka) se protínají v bodech ",[883,76666,76668],{"className":76667},[886],[888,76669,76670],{"xmlns":890},[892,76671,76672,76676],{},[895,76673,76674],{},[898,76675,10871],{},[902,76677,10871],{"encoding":904},[883,76679,76681],{"className":76680},[886],[888,76682,76683],{"xmlns":890},[892,76684,76685,76689],{},[895,76686,76687],{},[898,76688,10856],{},[902,76690,10856],{"encoding":904},[883,76692,76694],{"className":76693},[886],[888,76695,76696],{"xmlns":890},[892,76697,76698,76702],{},[895,76699,76700],{},[898,76701,1878],{},[902,76703,1878],{"encoding":904}," v hodnotách ",[883,76706,76708],{"className":76707},[886],[888,76709,76710],{"xmlns":890},[892,76711,76712,76720],{},[895,76713,76714],{},[1707,76715,76716,76718],{},[898,76717,1878],{},[898,76719,10871],{},[902,76721,76437],{"encoding":904},[883,76723,76725],{"className":76724},[886],[888,76726,76727],{"xmlns":890},[892,76728,76729,76737],{},[895,76730,76731],{},[1707,76732,76733,76735],{},[898,76734,1878],{},[898,76736,10856],{},[902,76738,76455],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,76741,76743],{"className":76742},[886],[888,76744,76745],{"xmlns":890},[892,76746,76747,76757],{},[895,76748,76749],{},[1707,76750,76751,76753,76755],{},[898,76752,1878],{},[898,76754,68951],{},[1716,76756,68954],{},[902,76758,76759],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,76762,76764],{"className":76763},[886],[888,76765,76766],{"xmlns":890},[892,76767,76768,76774],{},[895,76769,76770,76772],{},[898,76771,4164],{},[898,76773,17840],{},[902,76775,17938],{"encoding":904},[883,76777,76779],{"className":76778},[886],[888,76780,76781],{"xmlns":890},[892,76782,76783,76789],{},[895,76784,76785,76787],{},[898,76786,4164],{},[898,76788,9945],{},[902,76790,17103],{"encoding":904},[883,76792,76794],{"className":76793},[886],[888,76795,76796],{"xmlns":890},[892,76797,76798,76818],{},[895,76799,76800,76806,76808,76810,76812],{},[1707,76801,76802,76804],{},[898,76803,1878],{},[898,76805,10871],{},[1716,76807,2704],{},[898,76809,1878],{},[1716,76811,2704],{},[1707,76813,76814,76816],{},[898,76815,1878],{},[898,76817,10856],{},[902,76819,76560],{"encoding":904}," vyznačuje zisk.",[2257,76822,76824],{"id":76823},"příklad-38","Příklad 3.8",[724,76826,76827,76829,76830,1343,76850,1343,76876,76902],{},[38,76828,68741],{}," Dáno ",[883,76831,76833],{"className":76832},[886],[888,76834,76835],{"xmlns":890},[892,76836,76837,76847],{},[895,76838,76839,76841,76843,76845],{},[898,76840,24240],{},[898,76842,9945],{},[1716,76844,1913],{},[1712,76846,6849],{},[902,76848,76849],{"encoding":904},"FC = 4",[883,76851,76853],{"className":76852},[886],[888,76854,76855],{"xmlns":890},[892,76856,76857,76873],{},[895,76858,76859,76861,76863,76865,76867],{},[898,76860,4164],{},[898,76862,5298],{},[898,76864,9945],{},[1716,76866,1913],{},[3074,76868,76869,76871],{},[898,76870,1878],{},[1712,76872,1726],{},[902,76874,76875],{"encoding":904},"TVC = Q^2",[883,76877,76879],{"className":76878},[886],[888,76880,76881],{"xmlns":890},[892,76882,76883,76899],{},[895,76884,76885,76887,76889,76891,76893,76895,76897],{},[898,76886,1690],{},[1716,76888,1913],{},[1716,76890,2760],{},[1712,76892,1726],{},[898,76894,1878],{},[1716,76896,1949],{},[1712,76898,7141],{},[902,76900,76901],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,76904,76905,76907],{},[38,76906,36544],{}," Celkové náklady a příjem:",[883,76909,76911],{"className":76910},[886],[888,76912,76913],{"xmlns":890,"display":2004},[892,76914,76915,76981],{},[895,76916,76917,76919,76921,76923,76925,76927,76933,76935,76937,76939,76941,76943,76945,76947,76949,76951,76953,76955,76957,76959,76961,76963,76965,76967,76973,76975,76977,76979],{},[898,76918,4164],{},[898,76920,9945],{},[1716,76922,1913],{},[1712,76924,6849],{},[1716,76926,1949],{},[3074,76928,76929,76931],{},[898,76930,1878],{},[1712,76932,1726],{},[1716,76934,1719],{"separator":1718},[2324,76936],{"width":2326},[898,76938,4164],{},[898,76940,17840],{},[1716,76942,1913],{},[898,76944,1878],{},[1716,76946,9532],{},[1716,76948,1920],{"stretchy":1919},[1716,76950,2760],{},[1712,76952,1726],{},[898,76954,1878],{},[1716,76956,1949],{},[1712,76958,7141],{},[1716,76960,1925],{"stretchy":1919},[1716,76962,1913],{},[1716,76964,2760],{},[1712,76966,1726],{},[3074,76968,76969,76971],{},[898,76970,1878],{},[1712,76972,1726],{},[1716,76974,1949],{},[1712,76976,7141],{},[898,76978,1878],{},[898,76980,1853],{"mathvariant":2068},[902,76982,76983],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,76985,76986],{},"Zisk dle (3.12):",[883,76988,76990],{"className":76989},[886],[888,76991,76992],{"xmlns":890,"display":2004},[892,76993,76994,77072],{},[895,76995,76996,76998,77000,77002,77004,77006,77008,77010,77012,77014,77016,77018,77020,77026,77028,77030,77032,77034,77036,77038,77040,77042,77048,77050,77052,77054,77056,77062,77064,77066,77068,77070],{},[898,76997,1690],{},[898,76999,17840],{},[1716,77001,1913],{},[898,77003,4164],{},[898,77005,17840],{},[1716,77007,2760],{},[898,77009,4164],{},[898,77011,9945],{},[1716,77013,1913],{},[1716,77015,1920],{"stretchy":1919},[1716,77017,2760],{},[1712,77019,1726],{},[3074,77021,77022,77024],{},[898,77023,1878],{},[1712,77025,1726],{},[1716,77027,1949],{},[1712,77029,7141],{},[898,77031,1878],{},[1716,77033,1925],{"stretchy":1919},[1716,77035,2760],{},[1716,77037,1920],{"stretchy":1919},[1712,77039,6849],{},[1716,77041,1949],{},[3074,77043,77044,77046],{},[898,77045,1878],{},[1712,77047,1726],{},[1716,77049,1925],{"stretchy":1919},[1716,77051,1913],{},[1716,77053,2760],{},[1712,77055,7072],{},[3074,77057,77058,77060],{},[898,77059,1878],{},[1712,77061,1726],{},[1716,77063,1949],{},[1712,77065,7141],{},[898,77067,1878],{},[1716,77069,2760],{},[1712,77071,72073],{},[902,77073,77074],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,77076,77077,77080,77081,31366,77117,2291],{},[38,77078,77079],{},"Body zvratu"," jsou kořeny rovnice ",[883,77082,77084],{"className":77083},[886],[888,77085,77086],{"xmlns":890},[892,77087,77088,77114],{},[895,77089,77090,77092,77094,77100,77102,77104,77106,77108,77110,77112],{},[1716,77091,2760],{},[1712,77093,7072],{},[3074,77095,77096,77098],{},[898,77097,1878],{},[1712,77099,1726],{},[1716,77101,1949],{},[1712,77103,7141],{},[898,77105,1878],{},[1716,77107,2760],{},[1712,77109,6849],{},[1716,77111,1913],{},[1712,77113,2505],{},[902,77115,77116],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,77118,77120],{"className":77119},[886],[888,77121,77122],{"xmlns":890},[892,77123,77124,77148],{},[895,77125,77126,77128,77134,77136,77138,77140,77142,77144,77146],{},[1712,77127,7072],{},[3074,77129,77130,77132],{},[898,77131,1878],{},[1712,77133,1726],{},[1716,77135,2760],{},[1712,77137,7141],{},[898,77139,1878],{},[1716,77141,1949],{},[1712,77143,6849],{},[1716,77145,1913],{},[1712,77147,2505],{},[902,77149,77150],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,77152,77154],{"className":77153},[886],[888,77155,77156],{"xmlns":890,"display":2004},[892,77157,77158,77215],{},[895,77159,77160,77172,77174,77197,77199,77213],{},[1707,77161,77162,77164],{},[898,77163,1878],{},[895,77165,77166,77168,77170],{},[1712,77167,1714],{},[1716,77169,1719],{"separator":1718},[1712,77171,1726],{},[1716,77173,1913],{},[2750,77175,77176,77195],{},[895,77177,77178,77180,77183],{},[1712,77179,7141],{},[1716,77181,77182],{},"±",[10595,77184,77185],{},[895,77186,77187,77190,77192],{},[1712,77188,77189],{},"81",[1716,77191,2760],{},[1712,77193,77194],{},"48",[1712,77196,6231],{},[1716,77198,1913],{},[2750,77200,77201,77211],{},[895,77202,77203,77205,77207],{},[1712,77204,7141],{},[1716,77206,77182],{},[10595,77208,77209],{},[1712,77210,22764],{},[1712,77212,6231],{},[1716,77214,1719],{"separator":1718},[902,77216,77217],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,77219,77220,77221,2247,77244,1853],{},"numericky ",[883,77222,77224],{"className":77223},[886],[888,77225,77226],{"xmlns":890},[892,77227,77228,77241],{},[895,77229,77230,77236,77238],{},[1707,77231,77232,77234],{},[898,77233,1878],{},[1712,77235,1714],{},[1716,77237,19724],{},[1712,77239,77240],{},"0,543",[902,77242,77243],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,77245,77247],{"className":77246},[886],[888,77248,77249],{"xmlns":890},[892,77250,77251,77264],{},[895,77252,77253,77259,77261],{},[1707,77254,77255,77257],{},[898,77256,1878],{},[1712,77258,1726],{},[1716,77260,19724],{},[1712,77262,77263],{},"2,457",[902,77265,77266],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,77268,77269,3495,77272,21371,77317,31366,77351,77369],{},[38,77270,77271],{},"Maximum zisku.",[883,77273,77275],{"className":77274},[886],[888,77276,77277],{"xmlns":890},[892,77278,77279,77314],{},[895,77280,77281,77283,77289,77291,77293,77295,77297,77299,77301,77303,77305,77307,77309,77311],{},[898,77282,1690],{},[3074,77284,77285,77287],{},[898,77286,17840],{},[1716,77288,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,77290,1913],{},[1716,77292,2760],{},[1712,77294,6231],{},[898,77296,1878],{},[1716,77298,1949],{},[1712,77300,7141],{},[1716,77302,1913],{},[1712,77304,2505],{},[1716,77306,17833],{},[898,77308,1878],{},[1716,77310,1913],{},[1712,77312,77313],{},"1,5",[902,77315,77316],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,77318,77320],{"className":77319},[886],[888,77321,77322],{"xmlns":890},[892,77323,77324,77348],{},[895,77325,77326,77328,77338,77340,77342,77344,77346],{},[898,77327,1690],{},[3074,77329,77330,77332],{},[898,77331,17840],{},[895,77333,77334,77336],{},[1716,77335,8505],{"mathvariant":2068},[1716,77337,8505],{"mathvariant":2068},[1716,77339,1913],{},[1716,77341,2760],{},[1712,77343,6231],{},[1716,77345,2704],{},[1712,77347,2505],{},[902,77349,77350],{"encoding":904},"PR'' = -6 \u003C 0",[883,77352,77354],{"className":77353},[886],[888,77355,77356],{"xmlns":890},[892,77357,77358,77366],{},[895,77359,77360,77362,77364],{},[898,77361,1878],{},[1716,77363,1913],{},[1712,77365,77313],{},[902,77367,77368],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,77371,77373],{"className":77372},[886],[888,77374,77375],{"xmlns":890,"display":2004},[892,77376,77377,77440],{},[895,77378,77379,77381,77383,77385,77387,77389,77391,77393,77395,77397,77399,77401,77407,77409,77411,77413,77415,77417,77419,77421,77423,77426,77428,77431,77433,77435,77437],{},[898,77380,1690],{},[898,77382,17840],{},[1716,77384,1920],{"stretchy":1919},[1712,77386,77313],{},[1716,77388,1925],{"stretchy":1919},[1716,77390,1913],{},[1716,77392,2760],{},[1712,77394,7072],{},[1716,77396,9532],{},[1716,77398,1920],{"stretchy":1919},[1712,77400,77313],{},[3074,77402,77403,77405],{},[1716,77404,1925],{"stretchy":1919},[1712,77406,1726],{},[1716,77408,1949],{},[1712,77410,7141],{},[1716,77412,9532],{},[1712,77414,77313],{},[1716,77416,2760],{},[1712,77418,6849],{},[1716,77420,1913],{},[1716,77422,2760],{},[1712,77424,77425],{},"6,75",[1716,77427,1949],{},[1712,77429,77430],{},"13,5",[1716,77432,2760],{},[1712,77434,6849],{},[1716,77436,1913],{},[1712,77438,77439],{},"2,75.",[902,77441,77442],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,77444,77445,77446,1343,77491,77544,77545,77563],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,77447,77449],{"className":77448},[886],[888,77450,77451],{"xmlns":890},[892,77452,77453,77488],{},[895,77454,77455,77457,77463,77465,77467,77469,77471,77473,77475,77477,77479,77481,77483,77485],{},[898,77456,4164],{},[3074,77458,77459,77461],{},[898,77460,17840],{},[1716,77462,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,77464,1913],{},[1716,77466,2760],{},[1712,77468,6849],{},[898,77470,1878],{},[1716,77472,1949],{},[1712,77474,7141],{},[1716,77476,1913],{},[1712,77478,2505],{},[1716,77480,17833],{},[898,77482,1878],{},[1716,77484,1913],{},[1712,77486,77487],{},"2,25",[902,77489,77490],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,77492,77494],{"className":77493},[886],[888,77495,77496],{"xmlns":890},[892,77497,77498,77541],{},[895,77499,77500,77502,77510,77512,77514,77516,77518,77520,77522,77528,77530,77532,77534,77536,77538],{},[898,77501,4164],{},[1707,77503,77504,77506,77508],{},[898,77505,17840],{},[898,77507,68951],{},[1716,77509,68954],{},[1716,77511,1913],{},[1716,77513,2760],{},[1712,77515,1726],{},[1716,77517,9532],{},[1716,77519,1920],{"stretchy":1919},[1712,77521,77487],{},[3074,77523,77524,77526],{},[1716,77525,1925],{"stretchy":1919},[1712,77527,1726],{},[1716,77529,1949],{},[1712,77531,7141],{},[1716,77533,9532],{},[1712,77535,77487],{},[1716,77537,1913],{},[1712,77539,77540],{},"10,125",[902,77542,77543],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,77546,77548],{"className":77547},[886],[888,77549,77550],{"xmlns":890},[892,77551,77552,77560],{},[895,77553,77554,77556,77558],{},[898,77555,1878],{},[1716,77557,1913],{},[1712,77559,77487],{},[902,77561,77562],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1635,77565,77566],{},[724,77567,77568,77570,77571,1343,77593,77615,77616,1343,77633,77654,77655,77687,77688,77726,77727,9425,77745,77762,77763,2247,77791,77825,77826,21504,77864,2247,77888,1853],{},[883,77569,2233],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,77572,77574],{"className":77573},[886],[888,77575,77576],{"xmlns":890},[892,77577,77578,77590],{},[895,77579,77580,77586,77588],{},[1707,77581,77582,77584],{},[898,77583,1878],{},[1712,77585,1714],{},[1716,77587,1913],{},[1712,77589,5771],{},[902,77591,77592],{"encoding":904},"Q_1 = 0{,}5",[883,77594,77596],{"className":77595},[886],[888,77597,77598],{"xmlns":890},[892,77599,77600,77612],{},[895,77601,77602,77608,77610],{},[1707,77603,77604,77606],{},[898,77605,1878],{},[1712,77607,1726],{},[1716,77609,1913],{},[1712,77611,6849],{},[902,77613,77614],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,77617,77619],{"className":77618},[886],[888,77620,77621],{"xmlns":890},[892,77622,77623,77631],{},[895,77624,77625,77627,77629],{},[898,77626,1878],{},[1716,77628,1913],{},[1712,77630,77487],{},[902,77632,77562],{"encoding":904},[883,77634,77636],{"className":77635},[886],[888,77637,77638],{"xmlns":890},[892,77639,77640,77651],{},[895,77641,77642,77644,77646,77648],{},[898,77643,1690],{},[898,77645,17840],{},[1716,77647,1913],{},[1712,77649,77650],{},"6,125",[902,77652,77653],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,77656,77658],{"className":77657},[886],[888,77659,77660],{"xmlns":890},[892,77661,77662,77684],{},[895,77663,77664,77666,77672,77674,77676,77678,77680,77682],{},[898,77665,1690],{},[3074,77667,77668,77670],{},[898,77669,17840],{},[1716,77671,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,77673,1913],{},[1716,77675,2760],{},[1712,77677,6849],{},[898,77679,1878],{},[1716,77681,1949],{},[1712,77683,7141],{},[902,77685,77686],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,77689,77691],{"className":77690},[886],[888,77692,77693],{"xmlns":890},[892,77694,77695,77723],{},[895,77696,77697,77699,77701,77703,77705,77707,77713,77715,77717,77719,77721],{},[898,77698,1690],{},[898,77700,17840],{},[1716,77702,1913],{},[1716,77704,2760],{},[1712,77706,1726],{},[3074,77708,77709,77711],{},[898,77710,1878],{},[1712,77712,1726],{},[1716,77714,1949],{},[1712,77716,7141],{},[898,77718,1878],{},[1716,77720,2760],{},[1712,77722,6849],{},[902,77724,77725],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,77728,77730],{"className":77729},[886],[888,77731,77732],{"xmlns":890},[892,77733,77734,77742],{},[895,77735,77736],{},[3074,77737,77738,77740],{},[898,77739,1878],{},[1712,77741,1726],{},[902,77743,77744],{"encoding":904},"Q^2",[883,77746,77748],{"className":77747},[886],[888,77749,77750],{"xmlns":890},[892,77751,77752,77760],{},[895,77753,77754,77756,77758],{},[898,77755,4164],{},[898,77757,5298],{},[898,77759,9945],{},[902,77761,68263],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,77764,77766],{"className":77765},[886],[888,77767,77768],{"xmlns":890},[892,77769,77770,77788],{},[895,77771,77772,77774,77776,77778,77780,77782],{},[898,77773,4164],{},[898,77775,9945],{},[1716,77777,1913],{},[1712,77779,6849],{},[1716,77781,1949],{},[3074,77783,77784,77786],{},[898,77785,1878],{},[1712,77787,1726],{},[902,77789,77790],{"encoding":904},"TC = 4 + Q^2",[883,77792,77794],{"className":77793},[886],[888,77795,77796],{"xmlns":890},[892,77797,77798,77822],{},[895,77799,77800,77802,77804,77806,77808,77810,77816,77818,77820],{},[898,77801,4164],{},[898,77803,17840],{},[1716,77805,1913],{},[1716,77807,2760],{},[1712,77809,1726],{},[3074,77811,77812,77814],{},[898,77813,1878],{},[1712,77815,1726],{},[1716,77817,1949],{},[1712,77819,7141],{},[898,77821,1878],{},[902,77823,77824],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,77827,77829],{"className":77828},[886],[888,77830,77831],{"xmlns":890},[892,77832,77833,77861],{},[895,77834,77835,77837,77839,77841,77843,77845,77851,77853,77855,77857,77859],{},[898,77836,1690],{},[898,77838,17840],{},[1716,77840,1913],{},[1716,77842,2760],{},[1712,77844,7072],{},[3074,77846,77847,77849],{},[898,77848,1878],{},[1712,77850,1726],{},[1716,77852,1949],{},[1712,77854,7141],{},[898,77856,1878],{},[1716,77858,2760],{},[1712,77860,6849],{},[902,77862,77863],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,77865,77867],{"className":77866},[886],[888,77868,77869],{"xmlns":890},[892,77870,77871,77885],{},[895,77872,77873,77881,77883],{},[1707,77874,77875,77877,77879],{},[898,77876,1878],{},[898,77878,68951],{},[1716,77880,68954],{},[1716,77882,1913],{},[1712,77884,77313],{},[902,77886,77887],{"encoding":904},"Q_{\\max} = 1{,}5",[883,77889,77891],{"className":77890},[886],[888,77892,77893],{"xmlns":890},[892,77894,77895,77912],{},[895,77896,77897,77899,77907,77909],{},[898,77898,1690],{},[1707,77900,77901,77903,77905],{},[898,77902,17840],{},[898,77904,68951],{},[1716,77906,68954],{},[1716,77908,1913],{},[1712,77910,77911],{},"2,75",[902,77913,77914],{"encoding":904},"PR_{\\max} = 2{,}75",[724,77916,77917],{},[614,77918,77919,77920,77947,77948,77981,77982,1343,78005,1853],{},"Obrázek 3.12: Graf ",[883,77921,77923],{"className":77922},[886],[888,77924,77925],{"xmlns":890},[892,77926,77927,77945],{},[895,77928,77929,77931,77933,77935,77937,77939],{},[898,77930,4164],{},[898,77932,9945],{},[1716,77934,1913],{},[1712,77936,6849],{},[1716,77938,1949],{},[3074,77940,77941,77943],{},[898,77942,1878],{},[1712,77944,1726],{},[902,77946,77790],{"encoding":904}," (parabola) a ",[883,77949,77951],{"className":77950},[886],[888,77952,77953],{"xmlns":890},[892,77954,77955,77979],{},[895,77956,77957,77959,77961,77963,77965,77967,77973,77975,77977],{},[898,77958,4164],{},[898,77960,17840],{},[1716,77962,1913],{},[1716,77964,2760],{},[1712,77966,1726],{},[3074,77968,77969,77971],{},[898,77970,1878],{},[1712,77972,1726],{},[1716,77974,1949],{},[1712,77976,7141],{},[898,77978,1878],{},[902,77980,77824],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,77983,77985],{"className":77984},[886],[888,77986,77987],{"xmlns":890},[892,77988,77989,78002],{},[895,77990,77991,77997,77999],{},[1707,77992,77993,77995],{},[898,77994,1878],{},[1712,77996,1714],{},[1716,77998,19724],{},[1712,78000,78001],{},"0,54",[902,78003,78004],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,78006,78008],{"className":78007},[886],[888,78009,78010],{"xmlns":890},[892,78011,78012,78025],{},[895,78013,78014,78020,78022],{},[1707,78015,78016,78018],{},[898,78017,1878],{},[1712,78019,1726],{},[1716,78021,19724],{},[1712,78023,78024],{},"2,46",[902,78026,78027],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,78029,78030],{},[614,78031,78032,78033,71261,78070,78087,78088,1343,78109,1853],{},"Obrázek 3.13: Graf zisku ",[883,78034,78036],{"className":78035},[886],[888,78037,78038],{"xmlns":890},[892,78039,78040,78068],{},[895,78041,78042,78044,78046,78048,78050,78052,78058,78060,78062,78064,78066],{},[898,78043,1690],{},[898,78045,17840],{},[1716,78047,1913],{},[1716,78049,2760],{},[1712,78051,7072],{},[3074,78053,78054,78056],{},[898,78055,1878],{},[1712,78057,1726],{},[1716,78059,1949],{},[1712,78061,7141],{},[898,78063,1878],{},[1716,78065,2760],{},[1712,78067,6849],{},[902,78069,77863],{"encoding":904},[883,78071,78073],{"className":78072},[886],[888,78074,78075],{"xmlns":890},[892,78076,78077,78085],{},[895,78078,78079,78081,78083],{},[898,78080,1878],{},[1716,78082,1913],{},[1712,78084,77313],{},[902,78086,77368],{"encoding":904}," a nulami ",[883,78089,78091],{"className":78090},[886],[888,78092,78093],{"xmlns":890},[892,78094,78095,78107],{},[895,78096,78097,78103,78105],{},[1707,78098,78099,78101],{},[898,78100,1878],{},[1712,78102,1714],{},[1716,78104,19724],{},[1712,78106,78001],{},[902,78108,78004],{"encoding":904},[883,78110,78112],{"className":78111},[886],[888,78113,78114],{"xmlns":890},[892,78115,78116,78128],{},[895,78117,78118,78124,78126],{},[1707,78119,78120,78122],{},[898,78121,1878],{},[1712,78123,1726],{},[1716,78125,19724],{},[1712,78127,78024],{},[902,78129,78027],{"encoding":904},[115,78131,78133],{"id":78132},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,78135,78136],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,78138,78139],{},[3682,78140],{"alt":78141,"className":78142,"src":78143},"imek-max-zisku-dva-pohledy",[210,3686],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,78145,30202],{"id":78146},"princip-1",[724,78148,78149,78150,16504,78165,78182],{},"Má-li zisk ",[883,78151,78153],{"className":78152},[886],[888,78154,78155],{"xmlns":890},[892,78156,78157,78163],{},[895,78158,78159,78161],{},[898,78160,1690],{},[898,78162,17840],{},[902,78164,76233],{"encoding":904},[883,78166,78168],{"className":78167},[886],[888,78169,78170],{"xmlns":890},[892,78171,78172,78180],{},[895,78173,78174],{},[1707,78175,78176,78178],{},[898,78177,1878],{},[1712,78179,2505],{},[902,78181,3245],{"encoding":904}," maximum, pak platí",[883,78184,78186],{"className":78185},[886],[888,78187,78188],{"xmlns":890,"display":2004},[892,78189,78190,78239],{},[2008,78191,78192],{"width":2010},[2012,78193,78194,78196,78232,78234],{},[2015,78195],{"width":2017},[2015,78197,78198],{},[895,78199,78200,78202,78204,78206,78212,78214,78216,78218,78220,78222,78228,78230],{},[898,78201,16690],{},[898,78203,17840],{},[1716,78205,1920],{"stretchy":1919},[1707,78207,78208,78210],{},[898,78209,1878],{},[1712,78211,2505],{},[1716,78213,1925],{"stretchy":1919},[1716,78215,1913],{},[898,78217,16690],{},[898,78219,9945],{},[1716,78221,1920],{"stretchy":1919},[1707,78223,78224,78226],{},[898,78225,1878],{},[1712,78227,2505],{},[1716,78229,1925],{"stretchy":1919},[898,78231,1853],{"mathvariant":2068},[2015,78233],{"width":2017},[2015,78235,78236],{},[2074,78237,78238],{},"(3.13)",[902,78240,78241],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1635,78243,78244],{},[724,78245,78246,74800,78248],{},[883,78247,69198],{},[38,78249,78250],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,78252,78253,78256,78257,2574,78284,31366,78358,1853],{},[38,78254,78255],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,78258,78260],{"className":78259},[886],[888,78261,78262],{"xmlns":890},[892,78263,78264,78282],{},[895,78265,78266,78268,78270,78272,78274,78276,78278,78280],{},[898,78267,1690],{},[898,78269,17840],{},[1716,78271,1913],{},[898,78273,4164],{},[898,78275,17840],{},[1716,78277,2760],{},[898,78279,4164],{},[898,78281,9945],{},[902,78283,67954],{"encoding":904},[883,78285,78287],{"className":78286},[886],[888,78288,78289],{"xmlns":890},[892,78290,78291,78355],{},[895,78292,78293,78295,78301,78303,78309,78311,78313,78315,78321,78323,78329,78331,78333,78335,78341,78343,78349,78351,78353],{},[898,78294,1690],{},[3074,78296,78297,78299],{},[898,78298,17840],{},[1716,78300,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,78302,1920],{"stretchy":1919},[1707,78304,78305,78307],{},[898,78306,1878],{},[1712,78308,2505],{},[1716,78310,1925],{"stretchy":1919},[1716,78312,1913],{},[898,78314,4164],{},[3074,78316,78317,78319],{},[898,78318,17840],{},[1716,78320,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,78322,1920],{"stretchy":1919},[1707,78324,78325,78327],{},[898,78326,1878],{},[1712,78328,2505],{},[1716,78330,1925],{"stretchy":1919},[1716,78332,2760],{},[898,78334,4164],{},[3074,78336,78337,78339],{},[898,78338,9945],{},[1716,78340,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,78342,1920],{"stretchy":1919},[1707,78344,78345,78347],{},[898,78346,1878],{},[1712,78348,2505],{},[1716,78350,1925],{"stretchy":1919},[1716,78352,1913],{},[1712,78354,2505],{},[902,78356,78357],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,78359,78361],{"className":78360},[886],[888,78362,78363],{"xmlns":890},[892,78364,78365,78397],{},[895,78366,78367,78369,78371,78373,78379,78381,78383,78385,78387,78389,78395],{},[898,78368,16690],{},[898,78370,17840],{},[1716,78372,1920],{"stretchy":1919},[1707,78374,78375,78377],{},[898,78376,1878],{},[1712,78378,2505],{},[1716,78380,1925],{"stretchy":1919},[1716,78382,1913],{},[898,78384,16690],{},[898,78386,9945],{},[1716,78388,1920],{"stretchy":1919},[1707,78390,78391,78393],{},[898,78392,1878],{},[1712,78394,2505],{},[1716,78396,1925],{"stretchy":1919},[902,78398,78399],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1635,78401,78402,78407],{},[724,78403,78404,78406],{},[883,78405,3776],{}," Postup — jak najít maximum zisku",[152,78408,78409,78473,78528,78565,78593],{},[123,78410,78411,78412,2247,78427,78442,78443,2365],{},"Sestavte ",[883,78413,78415],{"className":78414},[886],[888,78416,78417],{"xmlns":890},[892,78418,78419,78425],{},[895,78420,78421,78423],{},[898,78422,4164],{},[898,78424,17840],{},[902,78426,17938],{"encoding":904},[883,78428,78430],{"className":78429},[886],[888,78431,78432],{"xmlns":890},[892,78433,78434,78440],{},[895,78435,78436,78438],{},[898,78437,4164],{},[898,78439,9945],{},[902,78441,17103],{"encoding":904}," ze zadání (typicky ",[883,78444,78446],{"className":78445},[886],[888,78447,78448],{"xmlns":890},[892,78449,78450,78470],{},[895,78451,78452,78454,78456,78458,78460,78462,78464,78466,78468],{},[898,78453,4164],{},[898,78455,17840],{},[1716,78457,1913],{},[898,78459,1690],{},[1716,78461,1920],{"stretchy":1919},[898,78463,1878],{},[1716,78465,1925],{"stretchy":1919},[1716,78467,9532],{},[898,78469,1878],{},[902,78471,78472],{"encoding":904},"TR = P(Q) \\cdot Q",[123,78474,78475,78476,2247,78502,1853],{},"Vypočtěte ",[883,78477,78479],{"className":78478},[886],[888,78480,78481],{"xmlns":890},[892,78482,78483,78499],{},[895,78484,78485,78487,78489,78491,78493],{},[898,78486,16690],{},[898,78488,17840],{},[1716,78490,1913],{},[898,78492,4164],{},[3074,78494,78495,78497],{},[898,78496,17840],{},[1716,78498,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,78500,78501],{"encoding":904},"MR = TR'",[883,78503,78505],{"className":78504},[886],[888,78506,78507],{"xmlns":890},[892,78508,78509,78525],{},[895,78510,78511,78513,78515,78517,78519],{},[898,78512,16690],{},[898,78514,9945],{},[1716,78516,1913],{},[898,78518,4164],{},[3074,78520,78521,78523],{},[898,78522,9945],{},[1716,78524,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,78526,78527],{"encoding":904},"MC = TC'",[123,78529,78530,78531,1853],{},"Řešte rovnici ",[883,78532,78534],{"className":78533},[886],[888,78535,78536],{"xmlns":890},[892,78537,78538,78562],{},[895,78539,78540,78542,78544,78546,78548,78550,78552,78554,78556,78558,78560],{},[898,78541,16690],{},[898,78543,17840],{},[1716,78545,1920],{"stretchy":1919},[898,78547,1878],{},[1716,78549,1925],{"stretchy":1919},[1716,78551,1913],{},[898,78553,16690],{},[898,78555,9945],{},[1716,78557,1920],{"stretchy":1919},[898,78559,1878],{},[1716,78561,1925],{"stretchy":1919},[902,78563,78564],{"encoding":904},"MR(Q) = MC(Q)",[123,78566,78567,78568,78592],{},"Ověřte druhou derivaci ",[883,78569,78571],{"className":78570},[886],[888,78572,78573],{"xmlns":890},[892,78574,78575,78589],{},[895,78576,78577,78579],{},[898,78578,1690],{},[3074,78580,78581,78583],{},[898,78582,17840],{},[895,78584,78585,78587],{},[1716,78586,8505],{"mathvariant":2068},[1716,78588,8505],{"mathvariant":2068},[902,78590,78591],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,78594,78595,78596,78623],{},"Dosaďte do ",[883,78597,78599],{"className":78598},[886],[888,78600,78601],{"xmlns":890},[892,78602,78603,78621],{},[895,78604,78605,78607,78609,78611,78613,78615,78617,78619],{},[898,78606,1690],{},[898,78608,17840],{},[1716,78610,1913],{},[898,78612,4164],{},[898,78614,17840],{},[1716,78616,2760],{},[898,78618,4164],{},[898,78620,9945],{},[902,78622,67954],{"encoding":904}," pro hodnotu maxima.",[2257,78625,78627],{"id":78626},"příklad-39","Příklad 3.9",[724,78629,78630,68742,78632,2247,78654,78690],{},[38,78631,68741],{},[883,78633,78635],{"className":78634},[886],[888,78636,78637],{"xmlns":890},[892,78638,78639,78651],{},[895,78640,78641,78643,78645,78647,78649],{},[898,78642,1690],{},[1716,78644,1913],{},[1712,78646,2946],{},[1716,78648,2760],{},[898,78650,1878],{},[902,78652,78653],{"encoding":904},"P = 30 - Q",[883,78655,78657],{"className":78656},[886],[888,78658,78659],{"xmlns":890},[892,78660,78661,78687],{},[895,78662,78663,78665,78667,78669,78671,78677,78679,78681,78683,78685],{},[898,78664,4164],{},[898,78666,9945],{},[1716,78668,1913],{},[1712,78670,5771],{},[3074,78672,78673,78675],{},[898,78674,1878],{},[1712,78676,1726],{},[1716,78678,1949],{},[1712,78680,6231],{},[898,78682,1878],{},[1716,78684,1949],{},[1712,78686,7109],{},[902,78688,78689],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,78692,78693,3495,78695,1343,78725,78763,78764,29583,78808,78842,78843,1853],{},[38,78694,36544],{},[883,78696,78698],{"className":78697},[886],[888,78699,78700],{"xmlns":890},[892,78701,78702,78722],{},[895,78703,78704,78706,78708,78710,78712,78714,78716],{},[898,78705,4164],{},[898,78707,17840],{},[1716,78709,1913],{},[1712,78711,2946],{},[898,78713,1878],{},[1716,78715,2760],{},[3074,78717,78718,78720],{},[898,78719,1878],{},[1712,78721,1726],{},[902,78723,78724],{"encoding":904},"TR = 30Q - Q^2",[883,78726,78728],{"className":78727},[886],[888,78729,78730],{"xmlns":890},[892,78731,78732,78760],{},[895,78733,78734,78736,78738,78740,78742,78744,78750,78752,78754,78756,78758],{},[898,78735,1690],{},[898,78737,17840],{},[1716,78739,1913],{},[1716,78741,2760],{},[1712,78743,77313],{},[3074,78745,78746,78748],{},[898,78747,1878],{},[1712,78749,1726],{},[1716,78751,1949],{},[1712,78753,6769],{},[898,78755,1878],{},[1716,78757,2760],{},[1712,78759,7109],{},[902,78761,78762],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,78765,78767],{"className":78766},[886],[888,78768,78769],{"xmlns":890},[892,78770,78771,78805],{},[895,78772,78773,78775,78781,78783,78785,78787,78789,78791,78793,78795,78797,78799,78801,78803],{},[898,78774,1690],{},[3074,78776,78777,78779],{},[898,78778,17840],{},[1716,78780,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,78782,1913],{},[1716,78784,2760],{},[1712,78786,7072],{},[898,78788,1878],{},[1716,78790,1949],{},[1712,78792,6769],{},[1716,78794,1913],{},[1712,78796,2505],{},[1716,78798,17833],{},[898,78800,1878],{},[1716,78802,1913],{},[1712,78804,12398],{},[902,78806,78807],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,78809,78811],{"className":78810},[886],[888,78812,78813],{"xmlns":890},[892,78814,78815,78839],{},[895,78816,78817,78819,78829,78831,78833,78835,78837],{},[898,78818,1690],{},[3074,78820,78821,78823],{},[898,78822,17840],{},[895,78824,78825,78827],{},[1716,78826,8505],{"mathvariant":2068},[1716,78828,8505],{"mathvariant":2068},[1716,78830,1913],{},[1716,78832,2760],{},[1712,78834,7072],{},[1716,78836,2704],{},[1712,78838,2505],{},[902,78840,78841],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,78844,78846],{"className":78845},[886],[888,78847,78848],{"xmlns":890},[892,78849,78850,78867],{},[895,78851,78852,78854,78856,78858,78860,78862,78864],{},[898,78853,1690],{},[898,78855,17840],{},[1716,78857,1920],{"stretchy":1919},[1712,78859,12398],{},[1716,78861,1925],{"stretchy":1919},[1716,78863,1913],{},[1712,78865,78866],{},"89",[902,78868,78869],{"encoding":904},"PR(8) = 89",[724,78871,78872,78873,1343,78899,29583,78923,78961],{},"Ověření principu: ",[883,78874,78876],{"className":78875},[886],[888,78877,78878],{"xmlns":890},[892,78879,78880,78896],{},[895,78881,78882,78884,78886,78888,78890,78892,78894],{},[898,78883,16690],{},[898,78885,17840],{},[1716,78887,1913],{},[1712,78889,2946],{},[1716,78891,2760],{},[1712,78893,1726],{},[898,78895,1878],{},[902,78897,78898],{"encoding":904},"MR = 30 - 2Q",[883,78900,78902],{"className":78901},[886],[888,78903,78904],{"xmlns":890},[892,78905,78906,78920],{},[895,78907,78908,78910,78912,78914,78916,78918],{},[898,78909,16690],{},[898,78911,9945],{},[1716,78913,1913],{},[898,78915,1878],{},[1716,78917,1949],{},[1712,78919,6231],{},[902,78921,78922],{"encoding":904},"MC = Q + 6",[883,78924,78926],{"className":78925},[886],[888,78927,78928],{"xmlns":890},[892,78929,78930,78958],{},[895,78931,78932,78934,78936,78938,78940,78942,78944,78946,78948,78950,78952,78954,78956],{},[898,78933,16690],{},[898,78935,17840],{},[1716,78937,1920],{"stretchy":1919},[1712,78939,12398],{},[1716,78941,1925],{"stretchy":1919},[1716,78943,1913],{},[1712,78945,6681],{},[1716,78947,1913],{},[898,78949,16690],{},[898,78951,9945],{},[1716,78953,1920],{"stretchy":1919},[1712,78955,12398],{},[1716,78957,1925],{"stretchy":1919},[902,78959,78960],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,78963,78964,78965,78998,78999,79016],{},"V řadě případů — má-li rovnice ",[883,78966,78968],{"className":78967},[886],[888,78969,78970],{"xmlns":890},[892,78971,78972,78996],{},[895,78973,78974,78976,78978,78980,78982,78984,78986,78988,78990,78992,78994],{},[898,78975,16690],{},[898,78977,17840],{},[1716,78979,1920],{"stretchy":1919},[898,78981,1878],{},[1716,78983,1925],{"stretchy":1919},[1716,78985,1913],{},[898,78987,16690],{},[898,78989,9945],{},[1716,78991,1920],{"stretchy":1919},[898,78993,1878],{},[1716,78995,1925],{"stretchy":1919},[902,78997,78564],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,79000,79002],{"className":79001},[886],[888,79003,79004],{"xmlns":890},[892,79005,79006,79014],{},[895,79007,79008],{},[1707,79009,79010,79012],{},[898,79011,1878],{},[1712,79013,2505],{},[902,79015,3245],{"encoding":904}," — není třeba provádět test druhé derivace.",[2257,79018,79020],{"id":79019},"příklad-310","Příklad 3.10",[724,79022,79023,79025,79026,79030,79031,79044,79045,79076],{},[38,79024,68741],{}," Firma vyrábí minipočítače v ",[207,79027,79029],{"className":79028,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,79032,79034],{"className":79033},[886],[888,79035,79036],{"xmlns":890},[892,79037,79038,79042],{},[895,79039,79040],{},[1712,79041,28985],{},[902,79043,28985],{"encoding":904}," EUR\u002Fks. ",[883,79046,79048],{"className":79047},[886],[888,79049,79050],{"xmlns":890},[892,79051,79052,79073],{},[895,79053,79054,79056,79058,79060,79062,79064,79067],{},[898,79055,4164],{},[898,79057,9945],{},[1716,79059,1913],{},[1712,79061,5808],{},[1716,79063,1949],{},[1712,79065,79066],{},"28",[3074,79068,79069,79071],{},[898,79070,1878],{},[1712,79072,1726],{},[902,79074,79075],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,79078,79079,3495,79081,1343,79103,1343,79123,79146],{},[38,79080,36544],{},[883,79082,79084],{"className":79083},[886],[888,79085,79086],{"xmlns":890},[892,79087,79088,79100],{},[895,79089,79090,79092,79094,79096,79098],{},[898,79091,4164],{},[898,79093,17840],{},[1716,79095,1913],{},[1712,79097,28985],{},[898,79099,1878],{},[902,79101,79102],{"encoding":904},"TR = 900Q",[883,79104,79106],{"className":79105},[886],[888,79107,79108],{"xmlns":890},[892,79109,79110,79120],{},[895,79111,79112,79114,79116,79118],{},[898,79113,16690],{},[898,79115,17840],{},[1716,79117,1913],{},[1712,79119,28985],{},[902,79121,79122],{"encoding":904},"MR = 900",[883,79124,79126],{"className":79125},[886],[888,79127,79128],{"xmlns":890},[892,79129,79130,79143],{},[895,79131,79132,79134,79136,79138,79141],{},[898,79133,16690],{},[898,79135,9945],{},[1716,79137,1913],{},[1712,79139,79140],{},"56",[898,79142,1878],{},[902,79144,79145],{"encoding":904},"MC = 56Q",". Z principu:",[883,79148,79150],{"className":79149},[886],[888,79151,79152],{"xmlns":890,"display":2004},[892,79153,79154,79196],{},[895,79155,79156,79158,79160,79162,79164,79166,79168,79170,79172,79174,79182,79184,79187,79189,79191,79193],{},[1712,79157,28985],{},[1716,79159,1913],{},[1712,79161,79140],{},[898,79163,1878],{},[2074,79165,17830],{},[1716,79167,17833],{},[2074,79169,17830],{},[898,79171,1878],{},[1716,79173,1913],{},[2747,79175,79176],{"scriptlevel":2505,"displaystyle":1919},[2750,79177,79178,79180],{},[1712,79179,28985],{},[1712,79181,79140],{},[1716,79183,19724],{},[1712,79185,79186],{},"16,07",[2074,79188,17830],{},[1716,79190,8490],{},[2074,79192,17830],{},[1712,79194,79195],{},"16.",[902,79197,79198],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,79200,79201,79202,2291],{},"Zisk při ",[883,79203,79205],{"className":79204},[886],[888,79206,79207],{"xmlns":890},[892,79208,79209,79217],{},[895,79210,79211,79213,79215],{},[898,79212,1878],{},[1716,79214,1913],{},[1712,79216,6833],{},[902,79218,79219],{"encoding":904},"Q = 16",[883,79221,79223],{"className":79222},[886],[888,79224,79225],{"xmlns":890,"display":2004},[892,79226,79227,79298],{},[895,79228,79229,79231,79233,79235,79237,79239,79241,79243,79245,79247,79249,79251,79253,79255,79257,79259,79265,79267,79269,79271,79273,79275,79277,79279,79281,79284,79286,79288,79290,79293,79296],{},[898,79230,1690],{},[898,79232,17840],{},[1716,79234,1920],{"stretchy":1919},[1712,79236,6833],{},[1716,79238,1925],{"stretchy":1919},[1716,79240,1913],{},[1712,79242,28985],{},[1716,79244,9532],{},[1712,79246,6833],{},[1716,79248,2760],{},[1716,79250,1920],{"stretchy":1919},[1712,79252,5808],{},[1716,79254,1949],{},[1712,79256,79066],{},[1716,79258,9532],{},[3074,79260,79261,79263],{},[1712,79262,6833],{},[1712,79264,1726],{},[1716,79266,1925],{"stretchy":1919},[1716,79268,1913],{},[1712,79270,6681],{},[2074,79272,8508],{},[1712,79274,33925],{},[1716,79276,2760],{},[1712,79278,7109],{},[2074,79280,8508],{},[1712,79282,79283],{},"218",[1716,79285,1913],{},[1712,79287,7109],{},[2074,79289,8508],{},[1712,79291,79292],{},"182",[2074,79294,79295],{}," EUR",[898,79297,1853],{"mathvariant":2068},[902,79299,79300],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,79302,79303],{},"Pro srovnání při původních 30 ks:",[883,79305,79307],{"className":79306},[886],[888,79308,79309],{"xmlns":890,"display":2004},[892,79310,79311,79376],{},[895,79312,79313,79315,79317,79319,79321,79323,79325,79327,79329,79331,79333,79335,79337,79339,79341,79343,79345,79347,79349,79352,79354,79356,79358,79360,79362,79364,79366,79368,79370,79372,79374],{},[898,79314,1690],{},[898,79316,17840],{},[1716,79318,1920],{"stretchy":1919},[1712,79320,2946],{},[1716,79322,1925],{"stretchy":1919},[1716,79324,1913],{},[1712,79326,28985],{},[1716,79328,9532],{},[1712,79330,2946],{},[1716,79332,2760],{},[1716,79334,1920],{"stretchy":1919},[1712,79336,5808],{},[1716,79338,1949],{},[1712,79340,79066],{},[1716,79342,9532],{},[1712,79344,28985],{},[1716,79346,1925],{"stretchy":1919},[1716,79348,1913],{},[1712,79350,79351],{},"27",[2074,79353,8508],{},[1712,79355,71836],{},[1716,79357,2760],{},[1712,79359,5778],{},[2074,79361,8508],{},[1712,79363,44505],{},[1716,79365,1913],{},[1712,79367,1714],{},[2074,79369,8508],{},[1712,79371,37515],{},[2074,79373,79295],{},[898,79375,1853],{"mathvariant":2068},[902,79377,79378],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,79380,79381,79384,79385,79403,79404,79422],{},[38,79382,79383],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,79386,79388],{"className":79387},[886],[888,79389,79390],{"xmlns":890},[892,79391,79392,79400],{},[895,79393,79394,79396,79398],{},[1712,79395,7109],{},[2074,79397,8508],{},[1712,79399,79292],{},[902,79401,79402],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,79405,79407],{"className":79406},[886],[888,79408,79409],{"xmlns":890},[892,79410,79411,79419],{},[895,79412,79413,79415,79417],{},[1712,79414,1714],{},[2074,79416,8508],{},[1712,79418,37515],{},[902,79420,79421],{"encoding":904},"1\\,750"," EUR.",[198,79424,79426],{"id":79425},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,79428,79429,79430,75324,79443,79467],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,79431,79433],{"className":79432},[886],[888,79434,79435],{"xmlns":890},[892,79436,79437,79441],{},[895,79438,79439],{},[898,79440,1690],{},[902,79442,1690],{"encoding":904},[883,79444,79446],{"className":79445},[886],[888,79447,79448],{"xmlns":890},[892,79449,79450,79464],{},[895,79451,79452,79454,79456,79458,79460,79462],{},[898,79453,4164],{},[898,79455,17840],{},[1716,79457,1913],{},[898,79459,1690],{},[1716,79461,9532],{},[898,79463,1878],{},[902,79465,79466],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,79469,79471],{"className":79470},[886],[888,79472,79473],{"xmlns":890,"display":2004},[892,79474,79475,79508],{},[2008,79476,79477],{"width":2010},[2012,79478,79479,79481,79501,79503],{},[2015,79480],{"width":2017},[2015,79482,79483],{},[895,79484,79485,79487,79489,79491,79493,79495,79497,79499],{},[898,79486,1690],{},[1716,79488,1913],{},[898,79490,16690],{},[898,79492,9945],{},[1716,79494,1920],{"stretchy":1919},[898,79496,1878],{},[1716,79498,1925],{"stretchy":1919},[898,79500,1853],{"mathvariant":2068},[2015,79502],{"width":2017},[2015,79504,79505],{},[2074,79506,79507],{},"(3.14)",[902,79509,79510],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,79512,79513,79514,1853],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,79515,79517],{"className":79516},[886],[888,79518,79519],{"xmlns":890},[892,79520,79521,79535],{},[895,79522,79523,79525],{},[898,79524,1690],{},[3074,79526,79527,79529],{},[898,79528,17840],{},[895,79530,79531,79533],{},[1716,79532,8505],{"mathvariant":2068},[1716,79534,8505],{"mathvariant":2068},[902,79536,78591],{"encoding":904},[2257,79538,79540],{"id":79539},"příklad-311","Příklad 3.11",[724,79542,79543,70276,79545,79592,79593,79611],{},[38,79544,68741],{},[883,79546,79548],{"className":79547},[886],[888,79549,79550],{"xmlns":890},[892,79551,79552,79589],{},[895,79553,79554,79556,79558,79560,79563,79569,79571,79573,79579,79581,79583,79585,79587],{},[898,79555,4164],{},[898,79557,9945],{},[1716,79559,1913],{},[1712,79561,79562],{},"0,04",[3074,79564,79565,79567],{},[898,79566,1878],{},[1712,79568,7072],{},[1716,79570,2760],{},[1712,79572,36319],{},[3074,79574,79575,79577],{},[898,79576,1878],{},[1712,79578,1726],{},[1716,79580,1949],{},[1712,79582,2998],{},[898,79584,1878],{},[1716,79586,1949],{},[1712,79588,6985],{},[902,79590,79591],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,79594,79596],{"className":79595},[886],[888,79597,79598],{"xmlns":890},[892,79599,79600,79608],{},[895,79601,79602,79604,79606],{},[898,79603,1690],{},[1716,79605,1913],{},[1712,79607,6849],{},[902,79609,79610],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,79613,79614,79616,79617,31366,79659,79693,79694,2291],{},[38,79615,36544],{}," Z (3.14): ",[883,79618,79620],{"className":79619},[886],[888,79621,79622],{"xmlns":890},[892,79623,79624,79656],{},[895,79625,79626,79628,79630,79632,79635,79641,79643,79646,79648,79650,79652,79654],{},[898,79627,16690],{},[898,79629,9945],{},[1716,79631,1913],{},[1712,79633,79634],{},"0,12",[3074,79636,79637,79639],{},[898,79638,1878],{},[1712,79640,1726],{},[1716,79642,2760],{},[1712,79644,79645],{},"1,8",[898,79647,1878],{},[1716,79649,1949],{},[1712,79651,2998],{},[1716,79653,1913],{},[1712,79655,6849],{},[902,79657,79658],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,79660,79662],{"className":79661},[886],[888,79663,79664],{"xmlns":890},[892,79665,79666,79690],{},[895,79667,79668,79670,79676,79678,79680,79682,79684,79686,79688],{},[1712,79669,79634],{},[3074,79671,79672,79674],{},[898,79673,1878],{},[1712,79675,1726],{},[1716,79677,2760],{},[1712,79679,79645],{},[898,79681,1878],{},[1716,79683,1949],{},[1712,79685,6231],{},[1716,79687,1913],{},[1712,79689,2505],{},[902,79691,79692],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,79695,79697],{"className":79696},[886],[888,79698,79699],{"xmlns":890},[892,79700,79701,79705],{},[895,79702,79703],{},[1712,79704,79634],{},[902,79706,79707],{"encoding":904},"0{,}12",[883,79709,79711],{"className":79710},[886],[888,79712,79713],{"xmlns":890,"display":2004},[892,79714,79715,79767],{},[895,79716,79717,79723,79725,79727,79729,79731,79733,79735,79737,79739,79741,79743,79749,79751,79753,79755,79757,79763,79765],{},[3074,79718,79719,79721],{},[898,79720,1878],{},[1712,79722,1726],{},[1716,79724,2760],{},[1712,79726,3221],{},[898,79728,1878],{},[1716,79730,1949],{},[1712,79732,5808],{},[1716,79734,1913],{},[1712,79736,2505],{},[2074,79738,17830],{},[1716,79740,17833],{},[2074,79742,17830],{},[1707,79744,79745,79747],{},[898,79746,1878],{},[1712,79748,1714],{},[1716,79750,1913],{},[1712,79752,6985],{},[1716,79754,1719],{"separator":1718},[2074,79756,17830],{},[1707,79758,79759,79761],{},[898,79760,1878],{},[1712,79762,1726],{},[1716,79764,1913],{},[1712,79766,33112],{},[902,79768,79769],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,79771,79772,79773,2291],{},"Dále ",[883,79774,79776],{"className":79775},[886],[888,79777,79778],{"xmlns":890},[892,79779,79780,79819],{},[895,79781,79782,79784,79794,79796,79798,79800,79806,79808,79810,79813,79815,79817],{},[898,79783,1690],{},[3074,79785,79786,79788],{},[898,79787,17840],{},[895,79789,79790,79792],{},[1716,79791,8505],{"mathvariant":2068},[1716,79793,8505],{"mathvariant":2068},[1716,79795,1913],{},[1716,79797,2760],{},[898,79799,16690],{},[3074,79801,79802,79804],{},[898,79803,9945],{},[1716,79805,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,79807,1913],{},[1716,79809,2760],{},[1712,79811,79812],{},"0,24",[898,79814,1878],{},[1716,79816,1949],{},[1712,79818,79645],{},[902,79820,79821],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,79823,79824,79874],{},[123,79825,79826,79870,79871,79873],{},[883,79827,79829],{"className":79828},[886],[888,79830,79831],{"xmlns":890},[892,79832,79833,79867],{},[895,79834,79835,79837,79847,79849,79851,79853,79855,79857,79859,79861,79863,79865],{},[898,79836,1690],{},[3074,79838,79839,79841],{},[898,79840,17840],{},[895,79842,79843,79845],{},[1716,79844,8505],{"mathvariant":2068},[1716,79846,8505],{"mathvariant":2068},[1716,79848,1920],{"stretchy":1919},[1712,79850,6985],{},[1716,79852,1925],{"stretchy":1919},[1716,79854,1913],{},[1712,79856,9451],{},[1716,79858,2716],{},[1712,79860,2505],{},[2074,79862,17830],{},[1716,79864,17833],{},[2074,79866,17830],{},[902,79868,79869],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,79872,17630],{}," zisku (minimalizace ztráty);",[123,79875,79876,79870,79922,79924],{},[883,79877,79879],{"className":79878},[886],[888,79880,79881],{"xmlns":890},[892,79882,79883,79919],{},[895,79884,79885,79887,79897,79899,79901,79903,79905,79907,79909,79911,79913,79915,79917],{},[898,79886,1690],{},[3074,79888,79889,79891],{},[898,79890,17840],{},[895,79892,79893,79895],{},[1716,79894,8505],{"mathvariant":2068},[1716,79896,8505],{"mathvariant":2068},[1716,79898,1920],{"stretchy":1919},[1712,79900,2998],{},[1716,79902,1925],{"stretchy":1919},[1716,79904,1913],{},[1716,79906,2760],{},[1712,79908,9451],{},[1716,79910,2704],{},[1712,79912,2505],{},[2074,79914,17830],{},[1716,79916,17833],{},[2074,79918,17830],{},[902,79920,79921],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,79923,17573],{}," zisku, avšak",[883,79926,79928],{"className":79927},[886],[888,79929,79930],{"xmlns":890,"display":2004},[892,79931,79932,80000],{},[895,79933,79934,79936,79938,79940,79942,79944,79946,79948,79950,79952,79954,79956,79958,79960,79962,79964,79966,79968,79970,79972,79974,79976,79978,79980,79982,79984,79986,79988,79990,79992,79994,79996,79998],{},[898,79935,1690],{},[898,79937,17840],{},[1716,79939,1920],{"stretchy":1919},[1712,79941,2998],{},[1716,79943,1925],{"stretchy":1919},[1716,79945,1913],{},[1712,79947,6849],{},[1716,79949,9532],{},[1712,79951,2998],{},[1716,79953,2760],{},[1716,79955,1920],{"stretchy":1919},[1712,79957,79562],{},[1716,79959,9532],{},[1712,79961,1714],{},[2074,79963,8508],{},[1712,79965,71836],{},[1716,79967,2760],{},[1712,79969,36319],{},[1716,79971,9532],{},[1712,79973,12151],{},[1716,79975,1949],{},[1712,79977,12151],{},[1716,79979,1949],{},[1712,79981,6985],{},[1716,79983,1925],{"stretchy":1919},[1716,79985,1913],{},[1712,79987,2973],{},[1716,79989,2760],{},[1712,79991,34957],{},[1716,79993,1913],{},[1716,79995,2760],{},[1712,79997,3221],{},[1716,79999,1719],{"separator":1718},[902,80001,80002],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,80004,80005,80006,1853],{},"tj. ztráta větší než ",[883,80007,80009],{"className":80008},[886],[888,80010,80011],{"xmlns":890},[892,80012,80013,80023],{},[895,80014,80015,80017,80019,80021],{},[898,80016,24240],{},[898,80018,9945],{},[1716,80020,1913],{},[1712,80022,6985],{},[902,80024,80025],{"encoding":904},"FC = 5",[724,80027,80028,80031,80032,80035,80036,1853],{},[38,80029,80030],{},"Závěr:"," firma by měla ",[38,80033,80034],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,80037,80039],{"className":80038},[886],[888,80040,80041],{"xmlns":890},[892,80042,80043,80053],{},[895,80044,80045,80047,80049,80051],{},[898,80046,24240],{},[898,80048,9945],{},[1716,80050,1913],{},[1712,80052,6985],{},[902,80054,80025],{"encoding":904},[115,80056,80058],{"id":80057},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,80060,80061,80062,80064,80065,80080,80081,80094,80095,80121,80122,80135,80136,80153,80154,16504,80171,80174,80175,80195,80196,80211,80212,2291],{},"Důležitým završením analýzy je konstrukce ",[38,80063,68029],{},". S nabízeným množstvím rostou mezní náklady ",[883,80066,80068],{"className":80067},[886],[888,80069,80070],{"xmlns":890},[892,80071,80072,80078],{},[895,80073,80074,80076],{},[898,80075,16690],{},[898,80077,9945],{},[902,80079,68046],{"encoding":904}," a tyto určují cenu ",[883,80082,80084],{"className":80083},[886],[888,80085,80086],{"xmlns":890},[892,80087,80088,80092],{},[895,80089,80090],{},[898,80091,1690],{},[902,80093,1690],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,80096,80098],{"className":80097},[886],[888,80099,80100],{"xmlns":890},[892,80101,80102,80118],{},[895,80103,80104,80106,80108,80110,80112,80114,80116],{},[898,80105,1690],{},[1716,80107,1913],{},[898,80109,16690],{},[898,80111,9945],{},[1716,80113,1920],{"stretchy":1919},[898,80115,1878],{},[1716,80117,1925],{"stretchy":1919},[902,80119,80120],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,80123,80125],{"className":80124},[886],[888,80126,80127],{"xmlns":890},[892,80128,80129,80133],{},[895,80130,80131],{},[898,80132,1690],{},[902,80134,1690],{"encoding":904}," však nemůže být nižší než ",[883,80137,80139],{"className":80138},[886],[888,80140,80141],{"xmlns":890},[892,80142,80143,80151],{},[895,80144,80145],{},[3074,80146,80147,80149],{},[898,80148,1690],{},[1716,80150,3080],{},[902,80152,3083],{"encoding":904}," odpovídající množství ",[883,80155,80157],{"className":80156},[886],[888,80158,80159],{"xmlns":890},[892,80160,80161,80169],{},[895,80162,80163],{},[3074,80164,80165,80167],{},[898,80166,1878],{},[1716,80168,3080],{},[902,80170,43607],{"encoding":904},[38,80172,80173],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,80176,80178],{"className":80177},[886],[888,80179,80180],{"xmlns":890},[892,80181,80182,80192],{},[895,80183,80184,80186],{},[1712,80185,2505],{},[3074,80187,80188,80190],{},[898,80189,1878],{},[1716,80191,3080],{},[902,80193,80194],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,80197,80199],{"className":80198},[886],[888,80200,80201],{"xmlns":890},[892,80202,80203,80209],{},[895,80204,80205,80207],{},[898,80206,16690],{},[898,80208,9945],{},[902,80210,68046],{"encoding":904}," nad bodem ",[883,80213,80215],{"className":80214},[886],[888,80216,80217],{"xmlns":890},[892,80218,80219,80223],{},[895,80220,80221],{},[898,80222,10871],{},[902,80224,10871],{"encoding":904},[883,80226,80228],{"className":80227},[886],[888,80229,80230],{"xmlns":890,"display":2004},[892,80231,80232,80339],{},[2008,80233,80234],{"width":2010},[2012,80235,80236,80238,80332,80334],{},[2015,80237],{"width":2017},[2015,80239,80240],{},[895,80241,80242,80244,80246,80248,80250,80252,80254,80256],{},[898,80243,1690],{},[1716,80245,1913],{},[898,80247,5352],{},[1716,80249,1920],{"stretchy":1919},[898,80251,1878],{},[1716,80253,1925],{"stretchy":1919},[1716,80255,1913],{},[895,80257,80258,80261],{},[1716,80259,80260],{"fence":1718},"{",[2008,80262,80265,80304],{"rowspacing":80263,"columnalign":80264,"columnspacing":8689},"0.36em","left left",[2012,80266,80267,80283],{},[2015,80268,80269],{},[2747,80270,80271],{"scriptlevel":2505,"displaystyle":1919},[895,80272,80273,80275,80277,80279,80281],{},[898,80274,16690],{},[898,80276,9945],{},[1716,80278,1920],{"stretchy":1919},[898,80280,1878],{},[1716,80282,1925],{"stretchy":1919},[2015,80284,80285],{},[2747,80286,80287],{"scriptlevel":2505,"displaystyle":1919},[895,80288,80289,80292,80294,80296,80302],{},[2074,80290,80291],{},"pro ",[898,80293,1878],{},[1716,80295,18320],{},[3074,80297,80298,80300],{},[898,80299,1878],{},[1716,80301,3080],{},[1716,80303,1719],{"separator":1718},[2012,80305,80306,80312],{},[2015,80307,80308],{},[2747,80309,80310],{"scriptlevel":2505,"displaystyle":1919},[1712,80311,2505],{},[2015,80313,80314],{},[2747,80315,80316],{"scriptlevel":2505,"displaystyle":1919},[895,80317,80318,80320,80322,80324,80330],{},[2074,80319,80291],{},[898,80321,1878],{},[1716,80323,2704],{},[3074,80325,80326,80328],{},[898,80327,1878],{},[1716,80329,3080],{},[1716,80331,1719],{"separator":1718},[2015,80333],{"width":2017},[2015,80335,80336],{},[2074,80337,80338],{},"(3.15)",[902,80340,80341],{"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}",[724,80343,18149,80344,80361,80362,80379,80380,6465,80410,80413],{},[883,80345,80347],{"className":80346},[886],[888,80348,80349],{"xmlns":890},[892,80350,80351,80359],{},[895,80352,80353],{},[3074,80354,80355,80357],{},[898,80356,1878],{},[1716,80358,3080],{},[902,80360,43607],{"encoding":904}," je bod minima ",[883,80363,80365],{"className":80364},[886],[888,80366,80367],{"xmlns":890},[892,80368,80369,80377],{},[895,80370,80371,80373,80375],{},[898,80372,10871],{},[898,80374,5298],{},[898,80376,9945],{},[902,80378,68065],{"encoding":904},". Bod ",[883,80381,80383],{"className":80382},[886],[888,80384,80385],{"xmlns":890},[892,80386,80387,80407],{},[895,80388,80389,80391,80397,80399,80405],{},[1716,80390,1920],{"stretchy":1919},[3074,80392,80393,80395],{},[898,80394,1878],{},[1716,80396,3080],{},[1716,80398,1719],{"separator":1718},[3074,80400,80401,80403],{},[898,80402,1690],{},[1716,80404,3080],{},[1716,80406,1925],{"stretchy":1919},[902,80408,80409],{"encoding":904},"(Q^*, P^*)",[38,80411,80412],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1635,80415,80416,80421],{},[724,80417,80418,80420],{},[883,80419,3776],{}," Postup — jak odvodit nabídku firmy",[152,80422,80423,80472,80567,80622,80693],{},[123,80424,80425,80426,2247,80448,1853],{},"Ze zadaných nákladů určete ",[883,80427,80429],{"className":80428},[886],[888,80430,80431],{"xmlns":890},[892,80432,80433,80445],{},[895,80434,80435,80437,80439,80441,80443],{},[898,80436,16690],{},[898,80438,9945],{},[1716,80440,1920],{"stretchy":1919},[898,80442,1878],{},[1716,80444,1925],{"stretchy":1919},[902,80446,80447],{"encoding":904},"MC(Q)",[883,80449,80451],{"className":80450},[886],[888,80452,80453],{"xmlns":890},[892,80454,80455,80469],{},[895,80456,80457,80459,80461,80463,80465,80467],{},[898,80458,10871],{},[898,80460,5298],{},[898,80462,9945],{},[1716,80464,1920],{"stretchy":1919},[898,80466,1878],{},[1716,80468,1925],{"stretchy":1919},[902,80470,80471],{"encoding":904},"AVC(Q)",[123,80473,80474,80475,80492,80493,80510,80511,80543,80544,2365],{},"Najděte ",[883,80476,80478],{"className":80477},[886],[888,80479,80480],{"xmlns":890},[892,80481,80482,80490],{},[895,80483,80484],{},[3074,80485,80486,80488],{},[898,80487,1878],{},[1716,80489,3080],{},[902,80491,43607],{"encoding":904}," jako bod minima ",[883,80494,80496],{"className":80495},[886],[888,80497,80498],{"xmlns":890},[892,80499,80500,80508],{},[895,80501,80502,80504,80506],{},[898,80503,10871],{},[898,80505,5298],{},[898,80507,9945],{},[902,80509,68065],{"encoding":904}," (řešením ",[883,80512,80514],{"className":80513},[886],[888,80515,80516],{"xmlns":890},[892,80517,80518,80540],{},[895,80519,80520,80522,80524,80530,80532,80534,80536,80538],{},[898,80521,10871],{},[898,80523,5298],{},[3074,80525,80526,80528],{},[898,80527,9945],{},[1716,80529,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,80531,1920],{"stretchy":1919},[898,80533,1878],{},[1716,80535,1925],{"stretchy":1919},[1716,80537,1913],{},[1712,80539,2505],{},[902,80541,80542],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,80545,80547],{"className":80546},[886],[888,80548,80549],{"xmlns":890},[892,80550,80551,80565],{},[895,80552,80553,80555,80557,80559,80561,80563],{},[898,80554,10871],{},[898,80556,5298],{},[898,80558,9945],{},[1716,80560,1913],{},[898,80562,16690],{},[898,80564,9945],{},[902,80566,68002],{"encoding":904},[123,80568,78475,80569,80621],{},[883,80570,80572],{"className":80571},[886],[888,80573,80574],{"xmlns":890},[892,80575,80576,80618],{},[895,80577,80578,80584,80586,80588,80590,80592,80598,80600,80602,80604,80606,80608,80610,80616],{},[3074,80579,80580,80582],{},[898,80581,1690],{},[1716,80583,3080],{},[1716,80585,1913],{},[898,80587,16690],{},[898,80589,9945],{},[1716,80591,1920],{"stretchy":1919},[3074,80593,80594,80596],{},[898,80595,1878],{},[1716,80597,3080],{},[1716,80599,1925],{"stretchy":1919},[1716,80601,1913],{},[898,80603,10871],{},[898,80605,5298],{},[898,80607,9945],{},[1716,80609,1920],{"stretchy":1919},[3074,80611,80612,80614],{},[898,80613,1878],{},[1716,80615,3080],{},[1716,80617,1925],{"stretchy":1919},[902,80619,80620],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,80623,80624,80625,20296,80657,80679,80680,1853],{},"Zapište nabídku: ",[883,80626,80628],{"className":80627},[886],[888,80629,80630],{"xmlns":890},[892,80631,80632,80654],{},[895,80633,80634,80636,80638,80640,80642,80644,80646,80648,80650,80652],{},[898,80635,5352],{},[1716,80637,1920],{"stretchy":1919},[898,80639,1878],{},[1716,80641,1925],{"stretchy":1919},[1716,80643,1913],{},[898,80645,16690],{},[898,80647,9945],{},[1716,80649,1920],{"stretchy":1919},[898,80651,1878],{},[1716,80653,1925],{"stretchy":1919},[902,80655,80656],{"encoding":904},"S(Q) = MC(Q)",[883,80658,80660],{"className":80659},[886],[888,80661,80662],{"xmlns":890},[892,80663,80664,80676],{},[895,80665,80666,80668,80670],{},[898,80667,1878],{},[1716,80669,18320],{},[3074,80671,80672,80674],{},[898,80673,1878],{},[1716,80675,3080],{},[902,80677,80678],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,80681,80683],{"className":80682},[886],[888,80684,80685],{"xmlns":890},[892,80686,80687,80691],{},[895,80688,80689],{},[1712,80690,2505],{},[902,80692,2505],{"encoding":904},[123,80694,80695,80696,80728],{},"V případě potřeby vyjádřete inverzi ",[883,80697,80699],{"className":80698},[886],[888,80700,80701],{"xmlns":890},[892,80702,80703,80725],{},[895,80704,80705,80707,80709,80719,80721,80723],{},[898,80706,1878],{},[1716,80708,1913],{},[3074,80710,80711,80713],{},[898,80712,5352],{},[895,80714,80715,80717],{},[1716,80716,2760],{},[1712,80718,1714],{},[1716,80720,1920],{"stretchy":1919},[898,80722,1690],{},[1716,80724,1925],{"stretchy":1919},[902,80726,80727],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,80730,80731],{},[614,80732,80733,80734,1343,80749,2247,80766,42965,80781,80794,80795,80820,80821,80834,80835,80852,80853,80870,80871,80888],{},"Obrázek 3.14: Křivky ",[883,80735,80737],{"className":80736},[886],[888,80738,80739],{"xmlns":890},[892,80740,80741,80747],{},[895,80742,80743,80745],{},[898,80744,10871],{},[898,80746,9945],{},[902,80748,68314],{"encoding":904},[883,80750,80752],{"className":80751},[886],[888,80753,80754],{"xmlns":890},[892,80755,80756,80764],{},[895,80757,80758,80760,80762],{},[898,80759,10871],{},[898,80761,5298],{},[898,80763,9945],{},[902,80765,68065],{"encoding":904},[883,80767,80769],{"className":80768},[886],[888,80770,80771],{"xmlns":890},[892,80772,80773,80779],{},[895,80774,80775,80777],{},[898,80776,16690],{},[898,80778,9945],{},[902,80780,68046],{"encoding":904},[883,80782,80784],{"className":80783},[886],[888,80785,80786],{"xmlns":890},[892,80787,80788,80792],{},[895,80789,80790],{},[898,80791,900],{},[902,80793,900],{"encoding":904},"; křivka nabídky ",[883,80796,80798],{"className":80797},[886],[888,80799,80800],{"xmlns":890},[892,80801,80802,80818],{},[895,80803,80804,80806,80808,80810,80812,80814,80816],{},[898,80805,1690],{},[1716,80807,1913],{},[898,80809,16690],{},[898,80811,9945],{},[1716,80813,1920],{"stretchy":1919},[898,80815,1878],{},[1716,80817,1925],{"stretchy":1919},[902,80819,80120],{"encoding":904}," začíná v bodě ",[883,80822,80824],{"className":80823},[886],[888,80825,80826],{"xmlns":890},[892,80827,80828,80832],{},[895,80829,80830],{},[898,80831,10871],{},[902,80833,10871],{"encoding":904}," odpovídajícím minimu ",[883,80836,80838],{"className":80837},[886],[888,80839,80840],{"xmlns":890},[892,80841,80842,80850],{},[895,80843,80844,80846,80848],{},[898,80845,10871],{},[898,80847,5298],{},[898,80849,9945],{},[902,80851,68065],{"encoding":904}," při ceně ",[883,80854,80856],{"className":80855},[886],[888,80857,80858],{"xmlns":890},[892,80859,80860,80868],{},[895,80861,80862],{},[3074,80863,80864,80866],{},[898,80865,1690],{},[1716,80867,3080],{},[902,80869,3083],{"encoding":904}," (minimální cena nabídky); pod ",[883,80872,80874],{"className":80873},[886],[888,80875,80876],{"xmlns":890},[892,80877,80878,80886],{},[895,80879,80880],{},[3074,80881,80882,80884],{},[898,80883,1878],{},[1716,80885,3080],{},[902,80887,43607],{"encoding":904}," je nabídka nulová.",[2257,80890,80892],{"id":80891},"příklad-312","Příklad 3.12",[724,80894,80895,70276,80897,80943],{},[38,80896,68741],{},[883,80898,80900],{"className":80899},[886],[888,80901,80902],{"xmlns":890},[892,80903,80904,80940],{},[895,80905,80906,80908,80910,80912,80914,80920,80922,80924,80930,80932,80934,80936,80938],{},[898,80907,4164],{},[898,80909,9945],{},[1716,80911,1913],{},[1712,80913,9535],{},[3074,80915,80916,80918],{},[898,80917,1878],{},[1712,80919,7072],{},[1716,80921,2760],{},[1712,80923,1726],{},[3074,80925,80926,80928],{},[898,80927,1878],{},[1712,80929,1726],{},[1716,80931,1949],{},[1712,80933,3221],{},[898,80935,1878],{},[1716,80937,1949],{},[1712,80939,2998],{},[902,80941,80942],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,80945,80946,3495,80948,80985,80986,2291],{},[38,80947,36544],{},[883,80949,80951],{"className":80950},[886],[888,80952,80953],{"xmlns":890},[892,80954,80955,80982],{},[895,80956,80957,80959,80961,80963,80966,80972,80974,80976,80978,80980],{},[898,80958,16690],{},[898,80960,9945],{},[1716,80962,1913],{},[1712,80964,80965],{},"0,3",[3074,80967,80968,80970],{},[898,80969,1878],{},[1712,80971,1726],{},[1716,80973,2760],{},[1712,80975,6849],{},[898,80977,1878],{},[1716,80979,1949],{},[1712,80981,3221],{},[902,80983,80984],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,80987,80989],{"className":80988},[886],[888,80990,80991],{"xmlns":890},[892,80992,80993,81003],{},[895,80994,80995,80997,80999,81001],{},[898,80996,1690],{},[1716,80998,1913],{},[898,81000,16690],{},[898,81002,9945],{},[902,81004,81005],{"encoding":904},"P = MC",[883,81007,81009],{"className":81008},[886],[888,81010,81011],{"xmlns":890,"display":2004},[892,81012,81013,81038],{},[895,81014,81015,81017,81019,81021,81027,81029,81031,81033,81035],{},[898,81016,1690],{},[1716,81018,1913],{},[1712,81020,80965],{},[3074,81022,81023,81025],{},[898,81024,1878],{},[1712,81026,1726],{},[1716,81028,2760],{},[1712,81030,6849],{},[898,81032,1878],{},[1716,81034,1949],{},[1712,81036,81037],{},"15.",[902,81039,81040],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,81042,81043,81044,19211,81057,81070],{},"Vyjádření ",[883,81045,81047],{"className":81046},[886],[888,81048,81049],{"xmlns":890},[892,81050,81051,81055],{},[895,81052,81053],{},[898,81054,1878],{},[902,81056,1878],{"encoding":904},[883,81058,81060],{"className":81059},[886],[888,81061,81062],{"xmlns":890},[892,81063,81064,81068],{},[895,81065,81066],{},[898,81067,1690],{},[902,81069,1690],{"encoding":904}," doplněním na čtverec:",[883,81072,81074],{"className":81073},[886],[888,81075,81076],{"xmlns":890,"display":2004},[892,81077,81078,81168],{},[895,81079,81080,81082,81084,81086,81124,81126,81128,81150,81152,81166],{},[898,81081,1690],{},[1716,81083,1913],{},[1712,81085,80965],{},[895,81087,81088,81090,81112,81114,81122],{},[1716,81089,1920],{"fence":1718},[3074,81091,81092,81110],{},[895,81093,81094,81096,81098,81100,81108],{},[1716,81095,1920],{"fence":1718},[898,81097,1878],{},[1716,81099,2760],{},[2747,81101,81102],{"scriptlevel":2505,"displaystyle":1919},[2750,81103,81104,81106],{},[1712,81105,2976],{},[1712,81107,7072],{},[1716,81109,1925],{"fence":1718},[1712,81111,1726],{},[1716,81113,1949],{},[2747,81115,81116],{"scriptlevel":2505,"displaystyle":1919},[2750,81117,81118,81120],{},[1712,81119,5808],{},[1712,81121,7141],{},[1716,81123,1925],{"fence":1718},[1716,81125,1719],{"separator":1718},[2324,81127],{"width":2326},[3074,81129,81130,81148],{},[895,81131,81132,81134,81136,81138,81146],{},[1716,81133,1920],{"fence":1718},[898,81135,1878],{},[1716,81137,2760],{},[2747,81139,81140],{"scriptlevel":2505,"displaystyle":1919},[2750,81141,81142,81144],{},[1712,81143,2976],{},[1712,81145,7072],{},[1716,81147,1925],{"fence":1718},[1712,81149,1726],{},[1716,81151,1913],{},[2750,81153,81154,81164],{},[895,81155,81156,81158,81160,81162],{},[1712,81157,2946],{},[898,81159,1690],{},[1716,81161,2760],{},[1712,81163,5808],{},[1712,81165,7141],{},[1716,81167,1719],{"separator":1718},[902,81169,81170],{"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},",[883,81172,81174],{"className":81173},[886],[888,81175,81176],{"xmlns":890,"display":2004},[892,81177,81178,81210],{},[895,81179,81180,81182,81184,81190,81192,81208],{},[898,81181,1878],{},[1716,81183,1913],{},[2750,81185,81186,81188],{},[1712,81187,2976],{},[1712,81189,7072],{},[1716,81191,1949],{},[2750,81193,81194,81206],{},[10595,81195,81196],{},[895,81197,81198,81200,81202,81204],{},[1712,81199,2946],{},[898,81201,1690],{},[1716,81203,2760],{},[1712,81205,5808],{},[1712,81207,7072],{},[898,81209,1853],{"mathvariant":2068},[902,81211,81212],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,81214,79772,81215,1343,81253,1343,81301,81335,81336,1853],{},[883,81216,81218],{"className":81217},[886],[888,81219,81220],{"xmlns":890},[892,81221,81222,81250],{},[895,81223,81224,81226,81228,81230,81232,81234,81240,81242,81244,81246,81248],{},[898,81225,10871],{},[898,81227,5298],{},[898,81229,9945],{},[1716,81231,1913],{},[1712,81233,9535],{},[3074,81235,81236,81238],{},[898,81237,1878],{},[1712,81239,1726],{},[1716,81241,2760],{},[1712,81243,1726],{},[898,81245,1878],{},[1716,81247,1949],{},[1712,81249,3221],{},[902,81251,81252],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,81254,81256],{"className":81255},[886],[888,81257,81258],{"xmlns":890},[892,81259,81260,81298],{},[895,81261,81262,81264,81266,81272,81274,81276,81278,81280,81282,81284,81286,81288,81294,81296],{},[898,81263,10871],{},[898,81265,5298],{},[3074,81267,81268,81270],{},[898,81269,9945],{},[1716,81271,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,81273,1913],{},[1712,81275,11302],{},[898,81277,1878],{},[1716,81279,2760],{},[1712,81281,1726],{},[1716,81283,1913],{},[1712,81285,2505],{},[1716,81287,17833],{},[3074,81289,81290,81292],{},[898,81291,1878],{},[1716,81293,3080],{},[1716,81295,1913],{},[1712,81297,2998],{},[902,81299,81300],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,81302,81304],{"className":81303},[886],[888,81305,81306],{"xmlns":890},[892,81307,81308,81332],{},[895,81309,81310,81312,81314,81324,81326,81328,81330],{},[898,81311,10871],{},[898,81313,5298],{},[3074,81315,81316,81318],{},[898,81317,9945],{},[895,81319,81320,81322],{},[1716,81321,8505],{"mathvariant":2068},[1716,81323,8505],{"mathvariant":2068},[1716,81325,1913],{},[1712,81327,11302],{},[1716,81329,2716],{},[1712,81331,2505],{},[902,81333,81334],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,81337,81339],{"className":81338},[886],[888,81340,81341],{"xmlns":890},[892,81342,81343,81379],{},[895,81344,81345,81351,81353,81355,81357,81359,81361,81363,81365,81367,81369,81371,81373,81375,81377],{},[3074,81346,81347,81349],{},[898,81348,1690],{},[1716,81350,3080],{},[1716,81352,1913],{},[898,81354,16690],{},[898,81356,9945],{},[1716,81358,1920],{"stretchy":1919},[1712,81360,2998],{},[1716,81362,1925],{"stretchy":1919},[1716,81364,1913],{},[1712,81366,2946],{},[1716,81368,2760],{},[1712,81370,2973],{},[1716,81372,1949],{},[1712,81374,3221],{},[1716,81376,1913],{},[1712,81378,6985],{},[902,81380,81381],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,81383,81384],{},[38,81385,81386],{},"Závěr.",[883,81388,81390],{"className":81389},[886],[888,81391,81392],{"xmlns":890,"display":2004},[892,81393,81394,81480],{},[895,81395,81396,81398,81400,81402,81404,81406,81408,81410],{},[898,81397,1690],{},[1716,81399,1913],{},[898,81401,5352],{},[1716,81403,1920],{"stretchy":1919},[898,81405,1878],{},[1716,81407,1925],{"stretchy":1919},[1716,81409,1913],{},[895,81411,81412,81414],{},[1716,81413,80260],{"fence":1718},[2008,81415,81416,81458],{"rowspacing":80263,"columnalign":80264,"columnspacing":8689},[2012,81417,81418,81442],{},[2015,81419,81420],{},[2747,81421,81422],{"scriptlevel":2505,"displaystyle":1919},[895,81423,81424,81426,81432,81434,81436,81438,81440],{},[1712,81425,80965],{},[3074,81427,81428,81430],{},[898,81429,1878],{},[1712,81431,1726],{},[1716,81433,2760],{},[1712,81435,6849],{},[898,81437,1878],{},[1716,81439,1949],{},[1712,81441,3221],{},[2015,81443,81444],{},[2747,81445,81446],{"scriptlevel":2505,"displaystyle":1919},[895,81447,81448,81450,81452,81454,81456],{},[2074,81449,80291],{},[898,81451,1878],{},[1716,81453,18320],{},[1712,81455,2998],{},[1716,81457,1719],{"separator":1718},[2012,81459,81460,81466],{},[2015,81461,81462],{},[2747,81463,81464],{"scriptlevel":2505,"displaystyle":1919},[1712,81465,2505],{},[2015,81467,81468],{},[2747,81469,81470],{"scriptlevel":2505,"displaystyle":1919},[895,81471,81472,81474,81476,81478],{},[2074,81473,80291],{},[898,81475,1878],{},[1716,81477,2704],{},[1712,81479,33112],{},[902,81481,81482],{"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}",[724,81484,81485],{},[614,81486,81487,81488,81503,81504,1853],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,81489,81491],{"className":81490},[886],[888,81492,81493],{"xmlns":890},[892,81494,81495,81501],{},[895,81496,81497,81499],{},[898,81498,16690],{},[898,81500,9945],{},[902,81502,68046],{"encoding":904}," ležící nad minimem ",[883,81505,81507],{"className":81506},[886],[888,81508,81509],{"xmlns":890},[892,81510,81511,81519],{},[895,81512,81513,81515,81517],{},[898,81514,10871],{},[898,81516,5298],{},[898,81518,9945],{},[902,81520,68065],{"encoding":904},[115,81522,81524],{"id":81523},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,81526,81527,81528,81532,81533,81548,81549,81569,81570,2247,81573,81576,81577,81579,81580,33728,81602,81604,81605,2247,81607,71480,81610,3495,81613,6784,81628,81643],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,81529,81531],{"className":81530,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,81534,81536],{"className":81535},[886],[888,81537,81538],{"xmlns":890},[892,81539,81540,81546],{},[895,81541,81542,81544],{},[898,81543,4164],{},[898,81545,17840],{},[902,81547,17938],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,81550,81552],{"className":81551},[886],[888,81553,81554],{"xmlns":890},[892,81555,81556,81566],{},[895,81557,81558,81560,81562,81564],{},[898,81559,4164],{},[898,81561,17840],{},[898,81563,3045],{"mathvariant":2068},[898,81565,1878],{},[902,81567,81568],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,81571,81572],{},"fixních",[38,81574,81575],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,81578,77079],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,81581,81583],{"className":81582},[886],[888,81584,81585],{"xmlns":890},[892,81586,81587,81599],{},[895,81588,81589,81591,81593,81595,81597],{},[898,81590,4164],{},[898,81592,17840],{},[1716,81594,2760],{},[898,81596,4164],{},[898,81598,9945],{},[902,81600,81601],{"encoding":904},"TR - TC",[38,81603,67926],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,81606,69238],{},[38,81608,81609],{},"mezní náklady",[207,81611,1145],{"className":81612,"dataFsResolvedFilePath":764,"href":765},[210],[883,81614,81616],{"className":81615},[886],[888,81617,81618],{"xmlns":890},[892,81619,81620,81626],{},[895,81621,81622,81624],{},[898,81623,4164],{},[898,81625,17840],{},[902,81627,17938],{"encoding":904},[883,81629,81631],{"className":81630},[886],[888,81632,81633],{"xmlns":890},[892,81634,81635,81641],{},[895,81636,81637,81639],{},[898,81638,4164],{},[898,81640,9945],{},[902,81642,17103],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,81645,81646,81708,81774,81836],{},[123,81647,81648,81651,81652,24198,81667,1853],{},[38,81649,81650],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,81653,81655],{"className":81654},[886],[888,81656,81657],{"xmlns":890},[892,81658,81659,81665],{},[895,81660,81661,81663],{},[898,81662,10871],{},[898,81664,9945],{},[902,81666,68314],{"encoding":904},[883,81668,81670],{"className":81669},[886],[888,81671,81672],{"xmlns":890},[892,81673,81674,81706],{},[895,81675,81676,81678,81680,81682,81688,81690,81692,81694,81696,81698,81704],{},[898,81677,10871],{},[898,81679,9945],{},[1716,81681,1920],{"stretchy":1919},[1707,81683,81684,81686],{},[898,81685,1878],{},[1712,81687,2505],{},[1716,81689,1925],{"stretchy":1919},[1716,81691,1913],{},[898,81693,16690],{},[898,81695,9945],{},[1716,81697,1920],{"stretchy":1919},[1707,81699,81700,81702],{},[898,81701,1878],{},[1712,81703,2505],{},[1716,81705,1925],{"stretchy":1919},[902,81707,75323],{"encoding":904},[123,81709,81710,81651,81713,24198,81730,1853],{},[38,81711,81712],{},"Princip minimalizace průměrných variabilních nákladů:",[883,81714,81716],{"className":81715},[886],[888,81717,81718],{"xmlns":890},[892,81719,81720,81728],{},[895,81721,81722,81724,81726],{},[898,81723,10871],{},[898,81725,5298],{},[898,81727,9945],{},[902,81729,68065],{"encoding":904},[883,81731,81733],{"className":81732},[886],[888,81734,81735],{"xmlns":890},[892,81736,81737,81771],{},[895,81738,81739,81741,81743,81745,81747,81753,81755,81757,81759,81761,81763,81769],{},[898,81740,10871],{},[898,81742,5298],{},[898,81744,9945],{},[1716,81746,1920],{"stretchy":1919},[1707,81748,81749,81751],{},[898,81750,1878],{},[1712,81752,2505],{},[1716,81754,1925],{"stretchy":1919},[1716,81756,1913],{},[898,81758,16690],{},[898,81760,9945],{},[1716,81762,1920],{"stretchy":1919},[1707,81764,81765,81767],{},[898,81766,1878],{},[1712,81768,2505],{},[1716,81770,1925],{"stretchy":1919},[902,81772,81773],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,81775,81776,81779,81780,24198,81795,1853],{},[38,81777,81778],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,81781,81783],{"className":81782},[886],[888,81784,81785],{"xmlns":890},[892,81786,81787,81793],{},[895,81788,81789,81791],{},[898,81790,1690],{},[898,81792,17840],{},[902,81794,76233],{"encoding":904},[883,81796,81798],{"className":81797},[886],[888,81799,81800],{"xmlns":890},[892,81801,81802,81834],{},[895,81803,81804,81806,81808,81810,81816,81818,81820,81822,81824,81826,81832],{},[898,81805,16690],{},[898,81807,17840],{},[1716,81809,1920],{"stretchy":1919},[1707,81811,81812,81814],{},[898,81813,1878],{},[1712,81815,2505],{},[1716,81817,1925],{"stretchy":1919},[1716,81819,1913],{},[898,81821,16690],{},[898,81823,9945],{},[1716,81825,1920],{"stretchy":1919},[1707,81827,81828,81830],{},[898,81829,1878],{},[1712,81831,2505],{},[1716,81833,1925],{"stretchy":1919},[902,81835,78399],{"encoding":904},[123,81837,81838,3495,81841,20296,81877,80679,81898,2772,81911,80361,81928,1853],{},[38,81839,81840],{},"Funkce nabídky firmy:",[883,81842,81844],{"className":81843},[886],[888,81845,81846],{"xmlns":890},[892,81847,81848,81874],{},[895,81849,81850,81852,81854,81856,81858,81860,81862,81864,81866,81868,81870,81872],{},[898,81851,1690],{},[1716,81853,1913],{},[898,81855,5352],{},[1716,81857,1920],{"stretchy":1919},[898,81859,1878],{},[1716,81861,1925],{"stretchy":1919},[1716,81863,1913],{},[898,81865,16690],{},[898,81867,9945],{},[1716,81869,1920],{"stretchy":1919},[898,81871,1878],{},[1716,81873,1925],{"stretchy":1919},[902,81875,81876],{"encoding":904},"P = S(Q) = MC(Q)",[883,81878,81880],{"className":81879},[886],[888,81881,81882],{"xmlns":890},[892,81883,81884,81896],{},[895,81885,81886,81888,81890],{},[898,81887,1878],{},[1716,81889,18320],{},[3074,81891,81892,81894],{},[898,81893,1878],{},[1716,81895,3080],{},[902,81897,80678],{"encoding":904},[883,81899,81901],{"className":81900},[886],[888,81902,81903],{"xmlns":890},[892,81904,81905,81909],{},[895,81906,81907],{},[1712,81908,2505],{},[902,81910,2505],{"encoding":904},[883,81912,81914],{"className":81913},[886],[888,81915,81916],{"xmlns":890},[892,81917,81918,81926],{},[895,81919,81920],{},[3074,81921,81922,81924],{},[898,81923,1878],{},[1716,81925,3080],{},[902,81927,43607],{"encoding":904},[883,81929,81931],{"className":81930},[886],[888,81932,81933],{"xmlns":890},[892,81934,81935,81943],{},[895,81936,81937,81939,81941],{},[898,81938,10871],{},[898,81940,5298],{},[898,81942,9945],{},[902,81944,68065],{"encoding":904},[115,81946,14897],{"id":14896},[152,81948,81949,81952,81955,81958,81961,81964,81967,81970,81973,81976,81979],{},[123,81950,81951],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,81953,81954],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,81956,81957],{},"Jak se vypočte mezní příjem a co udává?",[123,81959,81960],{},"Z jakých složek se skládají celkové náklady?",[123,81962,81963],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,81965,81966],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,81968,81969],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,81971,81972],{},"Jak se vypočte zisk?",[123,81974,81975],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,81977,81978],{},"Co jsou body zvratu? Jak se najdou?",[123,81980,81981],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,81983,81985],{"id":81984},"úlohy-31328","Úlohy 3.1–3.28",[198,81987,81989],{"id":81988},"příjem-3135","Příjem (3.1–3.5)",[724,81991,81992,10428,81995,82023,82024,82039,82040,82055,82056,82071,82072,1343,82087,1343,82102,82117],{},[38,81993,81994],{},"3.1",[883,81996,81998],{"className":81997},[886],[888,81999,82000],{"xmlns":890},[892,82001,82002,82020],{},[895,82003,82004,82006,82008,82010,82012,82014,82016,82018],{},[898,82005,1690],{},[1716,82007,1913],{},[898,82009,1916],{},[1716,82011,1920],{"stretchy":1919},[898,82013,1878],{},[1716,82015,1925],{"stretchy":1919},[1716,82017,1913],{},[1712,82019,12151],{},[902,82021,82022],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,82025,82027],{"className":82026},[886],[888,82028,82029],{"xmlns":890},[892,82030,82031,82037],{},[895,82032,82033,82035],{},[898,82034,4164],{},[898,82036,17840],{},[902,82038,17938],{"encoding":904},", průměrný příjem ",[883,82041,82043],{"className":82042},[886],[888,82044,82045],{"xmlns":890},[892,82046,82047,82053],{},[895,82048,82049,82051],{},[898,82050,10871],{},[898,82052,17840],{},[902,82054,68199],{"encoding":904}," a mezní příjem ",[883,82057,82059],{"className":82058},[886],[888,82060,82061],{"xmlns":890},[892,82062,82063,82069],{},[895,82064,82065,82067],{},[898,82066,16690],{},[898,82068,17840],{},[902,82070,20456],{"encoding":904},". (c) Vypočtěte ",[883,82073,82075],{"className":82074},[886],[888,82076,82077],{"xmlns":890},[892,82078,82079,82085],{},[895,82080,82081,82083],{},[898,82082,4164],{},[898,82084,17840],{},[902,82086,17938],{"encoding":904},[883,82088,82090],{"className":82089},[886],[888,82091,82092],{"xmlns":890},[892,82093,82094,82100],{},[895,82095,82096,82098],{},[898,82097,10871],{},[898,82099,17840],{},[902,82101,68199],{"encoding":904},[883,82103,82105],{"className":82104},[886],[888,82106,82107],{"xmlns":890},[892,82108,82109,82115],{},[895,82110,82111,82113],{},[898,82112,16690],{},[898,82114,17840],{},[902,82116,20456],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,82119,82120,10428,82123,82023,82159,82039,82174,82055,82189,82071,82204,1343,82219,1343,82234,82249],{},[38,82121,82122],{},"3.2",[883,82124,82126],{"className":82125},[886],[888,82127,82128],{"xmlns":890},[892,82129,82130,82156],{},[895,82131,82132,82134,82136,82138,82140,82142,82144,82146,82148,82150,82152,82154],{},[898,82133,1690],{},[1716,82135,1913],{},[898,82137,1916],{},[1716,82139,1920],{"stretchy":1919},[898,82141,1878],{},[1716,82143,1925],{"stretchy":1919},[1716,82145,1913],{},[1716,82147,2760],{},[1712,82149,5771],{},[898,82151,1878],{},[1716,82153,1949],{},[1712,82155,2976],{},[902,82157,82158],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,82160,82162],{"className":82161},[886],[888,82163,82164],{"xmlns":890},[892,82165,82166,82172],{},[895,82167,82168,82170],{},[898,82169,4164],{},[898,82171,17840],{},[902,82173,17938],{"encoding":904},[883,82175,82177],{"className":82176},[886],[888,82178,82179],{"xmlns":890},[892,82180,82181,82187],{},[895,82182,82183,82185],{},[898,82184,10871],{},[898,82186,17840],{},[902,82188,68199],{"encoding":904},[883,82190,82192],{"className":82191},[886],[888,82193,82194],{"xmlns":890},[892,82195,82196,82202],{},[895,82197,82198,82200],{},[898,82199,16690],{},[898,82201,17840],{},[902,82203,20456],{"encoding":904},[883,82205,82207],{"className":82206},[886],[888,82208,82209],{"xmlns":890},[892,82210,82211,82217],{},[895,82212,82213,82215],{},[898,82214,4164],{},[898,82216,17840],{},[902,82218,17938],{"encoding":904},[883,82220,82222],{"className":82221},[886],[888,82223,82224],{"xmlns":890},[892,82225,82226,82232],{},[895,82227,82228,82230],{},[898,82229,10871],{},[898,82231,17840],{},[902,82233,68199],{"encoding":904},[883,82235,82237],{"className":82236},[886],[888,82238,82239],{"xmlns":890},[892,82240,82241,82247],{},[895,82242,82243,82245],{},[898,82244,16690],{},[898,82246,17840],{},[902,82248,20456],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,82251,82252,10428,82255,82292,82293,82039,82308,82055,82323,82338,82339,20296,82354,82380,82381,82396,82397,1343,82412,20296,82427,82380,82452,82467,82468,82481,82482,82497,82498,82513,82514,1343,82527,1343,82542,1343,82557,1853],{},[38,82253,82254],{},"3.3",[883,82256,82258],{"className":82257},[886],[888,82259,82260],{"xmlns":890},[892,82261,82262,82289],{},[895,82263,82264,82266,82268,82270,82272,82274,82276,82278,82281,82283],{},[898,82265,1690],{},[1716,82267,1913],{},[898,82269,1916],{},[1716,82271,1920],{"stretchy":1919},[898,82273,1878],{},[1716,82275,1925],{"stretchy":1919},[1716,82277,1913],{},[1712,82279,82280],{},"1200",[1716,82282,2760],{},[3074,82284,82285,82287],{},[898,82286,1878],{},[1712,82288,1726],{},[902,82290,82291],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,82294,82296],{"className":82295},[886],[888,82297,82298],{"xmlns":890},[892,82299,82300,82306],{},[895,82301,82302,82304],{},[898,82303,4164],{},[898,82305,17840],{},[902,82307,17938],{"encoding":904},[883,82309,82311],{"className":82310},[886],[888,82312,82313],{"xmlns":890},[892,82314,82315,82321],{},[895,82316,82317,82319],{},[898,82318,10871],{},[898,82320,17840],{},[902,82322,68199],{"encoding":904},[883,82324,82326],{"className":82325},[886],[888,82327,82328],{"xmlns":890},[892,82329,82330,82336],{},[895,82331,82332,82334],{},[898,82333,16690],{},[898,82335,17840],{},[902,82337,20456],{"encoding":904},". (b) Vypočtěte ",[883,82340,82342],{"className":82341},[886],[888,82343,82344],{"xmlns":890},[892,82345,82346,82352],{},[895,82347,82348,82350],{},[898,82349,4164],{},[898,82351,17840],{},[902,82353,17938],{"encoding":904},[883,82355,82357],{"className":82356},[886],[888,82358,82359],{"xmlns":890},[892,82360,82361,82377],{},[895,82362,82363,82365,82367,82369,82371,82373,82375],{},[898,82364,1878],{},[1716,82366,1913],{},[1712,82368,2998],{},[1716,82370,1719],{"separator":1718},[1712,82372,2976],{},[1716,82374,1719],{"separator":1718},[1712,82376,2946],{},[902,82378,82379],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,82382,82384],{"className":82383},[886],[888,82385,82386],{"xmlns":890},[892,82387,82388,82394],{},[895,82389,82390,82392],{},[898,82391,4164],{},[898,82393,17840],{},[902,82395,17938],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,82398,82400],{"className":82399},[886],[888,82401,82402],{"xmlns":890},[892,82403,82404,82410],{},[895,82405,82406,82408],{},[898,82407,10871],{},[898,82409,17840],{},[902,82411,68199],{"encoding":904},[883,82413,82415],{"className":82414},[886],[888,82416,82417],{"xmlns":890},[892,82418,82419,82425],{},[895,82420,82421,82423],{},[898,82422,16690],{},[898,82424,17840],{},[902,82426,20456],{"encoding":904},[883,82428,82430],{"className":82429},[886],[888,82431,82432],{"xmlns":890},[892,82433,82434,82450],{},[895,82435,82436,82438,82440,82442,82444,82446,82448],{},[898,82437,1878],{},[1716,82439,1913],{},[1712,82441,2998],{},[1716,82443,1719],{"separator":1718},[1712,82445,2976],{},[1716,82447,1719],{"separator":1718},[1712,82449,2946],{},[902,82451,82379],{"encoding":904},[883,82453,82455],{"className":82454},[886],[888,82456,82457],{"xmlns":890},[892,82458,82459,82465],{},[895,82460,82461,82463],{},[898,82462,16690],{},[898,82464,17840],{},[902,82466,20456],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,82469,82471],{"className":82470},[886],[888,82472,82473],{"xmlns":890},[892,82474,82475,82479],{},[895,82476,82477],{},[898,82478,1878],{},[902,82480,1878],{"encoding":904},", které maximalizuje ",[883,82483,82485],{"className":82484},[886],[888,82486,82487],{"xmlns":890},[892,82488,82489,82495],{},[895,82490,82491,82493],{},[898,82492,4164],{},[898,82494,17840],{},[902,82496,17938],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,82499,82501],{"className":82500},[886],[888,82502,82503],{"xmlns":890},[892,82504,82505,82511],{},[895,82506,82507,82509],{},[898,82508,4164],{},[898,82510,17840],{},[902,82512,17938],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,82515,82517],{"className":82516},[886],[888,82518,82519],{"xmlns":890},[892,82520,82521,82525],{},[895,82522,82523],{},[898,82524,1916],{},[902,82526,1916],{"encoding":904},[883,82528,82530],{"className":82529},[886],[888,82531,82532],{"xmlns":890},[892,82533,82534,82540],{},[895,82535,82536,82538],{},[898,82537,4164],{},[898,82539,17840],{},[902,82541,17938],{"encoding":904},[883,82543,82545],{"className":82544},[886],[888,82546,82547],{"xmlns":890},[892,82548,82549,82555],{},[895,82550,82551,82553],{},[898,82552,10871],{},[898,82554,17840],{},[902,82556,68199],{"encoding":904},[883,82558,82560],{"className":82559},[886],[888,82561,82562],{"xmlns":890},[892,82563,82564,82570],{},[895,82565,82566,82568],{},[898,82567,16690],{},[898,82569,17840],{},[902,82571,20456],{"encoding":904},[724,82573,82574,82577,82578,82608,82609,82624,82625,23961,82638,1343,82656,1343,82673,82691,82692,82714,82715,82730,82731,82744,82745,1853],{},[38,82575,82576],{},"3.4"," Je dán celkový příjem ",[883,82579,82581],{"className":82580},[886],[888,82582,82583],{"xmlns":890},[892,82584,82585,82605],{},[895,82586,82587,82589,82591,82593,82595,82597,82599],{},[898,82588,4164],{},[898,82590,17840],{},[1716,82592,1913],{},[1712,82594,82280],{},[898,82596,1878],{},[1716,82598,2760],{},[3074,82600,82601,82603],{},[898,82602,1878],{},[1712,82604,7072],{},[902,82606,82607],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,82610,82612],{"className":82611},[886],[888,82613,82614],{"xmlns":890},[892,82615,82616,82622],{},[895,82617,82618,82620],{},[898,82619,4164],{},[898,82621,17840],{},[902,82623,17938],{"encoding":904}," vzhledem ke ",[883,82626,82628],{"className":82627},[886],[888,82629,82630],{"xmlns":890},[892,82631,82632,82636],{},[895,82633,82634],{},[898,82635,1878],{},[902,82637,1878],{"encoding":904},[883,82639,82641],{"className":82640},[886],[888,82642,82643],{"xmlns":890},[892,82644,82645,82653],{},[895,82646,82647,82649,82651],{},[898,82648,1878],{},[1716,82650,1913],{},[1712,82652,6985],{},[902,82654,82655],{"encoding":904},"Q = 5",[883,82657,82659],{"className":82658},[886],[888,82660,82661],{"xmlns":890},[892,82662,82663,82671],{},[895,82664,82665,82667,82669],{},[898,82666,1878],{},[1716,82668,1913],{},[1712,82670,12398],{},[902,82672,19416],{"encoding":904},[883,82674,82676],{"className":82675},[886],[888,82677,82678],{"xmlns":890},[892,82679,82680,82688],{},[895,82681,82682,82684,82686],{},[898,82683,1878],{},[1716,82685,1913],{},[1712,82687,6804],{},[902,82689,82690],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,82693,82695],{"className":82694},[886],[888,82696,82697],{"xmlns":890},[892,82698,82699,82711],{},[895,82700,82701,82703,82705,82707,82709],{},[898,82702,16690],{},[898,82704,17840],{},[1716,82706,1920],{"stretchy":1919},[1712,82708,2998],{},[1716,82710,1925],{"stretchy":1919},[902,82712,82713],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,82716,82718],{"className":82717},[886],[888,82719,82720],{"xmlns":890},[892,82721,82722,82728],{},[895,82723,82724,82726],{},[898,82725,4164],{},[898,82727,17840],{},[902,82729,17938],{"encoding":904},", jestliže se ",[883,82732,82734],{"className":82733},[886],[888,82735,82736],{"xmlns":890},[892,82737,82738,82742],{},[895,82739,82740],{},[898,82741,1878],{},[902,82743,1878],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,82746,82748],{"className":82747},[886],[888,82749,82750],{"xmlns":890},[892,82751,82752,82758],{},[895,82753,82754,82756],{},[898,82755,4164],{},[898,82757,17840],{},[902,82759,17938],{"encoding":904},[724,82761,82762,82765,82766,82792,82793,82808,82809,82730,82824,82837],{},[38,82763,82764],{},"3.5"," Je dán mezní příjem ",[883,82767,82769],{"className":82768},[886],[888,82770,82771],{"xmlns":890},[892,82772,82773,82789],{},[895,82774,82775,82777,82779,82781,82783,82785,82787],{},[898,82776,16690],{},[898,82778,17840],{},[1716,82780,1913],{},[1716,82782,2760],{},[898,82784,1878],{},[1716,82786,1949],{},[1712,82788,2976],{},[902,82790,82791],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,82794,82796],{"className":82795},[886],[888,82797,82798],{"xmlns":890},[892,82799,82800,82806],{},[895,82801,82802,82804],{},[898,82803,4164],{},[898,82805,17840],{},[902,82807,17938],{"encoding":904},". (b) Vypočtěte změnu ",[883,82810,82812],{"className":82811},[886],[888,82813,82814],{"xmlns":890},[892,82815,82816,82822],{},[895,82817,82818,82820],{},[898,82819,4164],{},[898,82821,17840],{},[902,82823,17938],{"encoding":904},[883,82825,82827],{"className":82826},[886],[888,82828,82829],{"xmlns":890},[892,82830,82831,82835],{},[895,82832,82833],{},[898,82834,1878],{},[902,82836,1878],{"encoding":904}," změní z 8 na 12.",[198,82839,82841],{"id":82840},"náklady-36316","Náklady (3.6–3.16)",[724,82843,82844,82847,82848,82888,82889,82904,82905,82922,82923,82940,82941,82956,82957,82972,82973,82338,82988,1343,83003,1343,83020,1343,83037,1343,83052,1343,83067,20296,83082,83100,83101,1343,83116,1343,83131,83146],{},[38,82845,82846],{},"3.6"," Jsou dány celkové náklady ",[883,82849,82851],{"className":82850},[886],[888,82852,82853],{"xmlns":890},[892,82854,82855,82885],{},[895,82856,82857,82859,82861,82863,82865,82867,82869,82871,82873],{},[898,82858,4164],{},[898,82860,9945],{},[1716,82862,1913],{},[1712,82864,12151],{},[1716,82866,1949],{},[1712,82868,1726],{},[898,82870,1878],{},[1716,82872,1949],{},[2747,82874,82875],{"scriptlevel":2505,"displaystyle":1919},[2750,82876,82877,82883],{},[3074,82878,82879,82881],{},[898,82880,1878],{},[1712,82882,1726],{},[1712,82884,2998],{},[902,82886,82887],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,82890,82892],{"className":82891},[886],[888,82893,82894],{"xmlns":890},[892,82895,82896,82902],{},[895,82897,82898,82900],{},[898,82899,24240],{},[898,82901,9945],{},[902,82903,68245],{"encoding":904},", celkové variabilní náklady ",[883,82906,82908],{"className":82907},[886],[888,82909,82910],{"xmlns":890},[892,82911,82912,82920],{},[895,82913,82914,82916,82918],{},[898,82915,4164],{},[898,82917,5298],{},[898,82919,9945],{},[902,82921,68263],{"encoding":904},", průměrné variabilní náklady ",[883,82924,82926],{"className":82925},[886],[888,82927,82928],{"xmlns":890},[892,82929,82930,82938],{},[895,82931,82932,82934,82936],{},[898,82933,10871],{},[898,82935,5298],{},[898,82937,9945],{},[902,82939,68065],{"encoding":904},", variabilní náklady na jednotku ",[883,82942,82944],{"className":82943},[886],[888,82945,82946],{"xmlns":890},[892,82947,82948,82954],{},[895,82949,82950,82952],{},[898,82951,5298],{},[898,82953,9945],{},[902,82955,76359],{"encoding":904},", průměrné náklady ",[883,82958,82960],{"className":82959},[886],[888,82961,82962],{"xmlns":890},[892,82963,82964,82970],{},[895,82965,82966,82968],{},[898,82967,10871],{},[898,82969,9945],{},[902,82971,68314],{"encoding":904}," a mezní náklady ",[883,82974,82976],{"className":82975},[886],[888,82977,82978],{"xmlns":890},[892,82979,82980,82986],{},[895,82981,82982,82984],{},[898,82983,16690],{},[898,82985,9945],{},[902,82987,68046],{"encoding":904},[883,82989,82991],{"className":82990},[886],[888,82992,82993],{"xmlns":890},[892,82994,82995,83001],{},[895,82996,82997,82999],{},[898,82998,4164],{},[898,83000,9945],{},[902,83002,17103],{"encoding":904},[883,83004,83006],{"className":83005},[886],[888,83007,83008],{"xmlns":890},[892,83009,83010,83018],{},[895,83011,83012,83014,83016],{},[898,83013,4164],{},[898,83015,5298],{},[898,83017,9945],{},[902,83019,68263],{"encoding":904},[883,83021,83023],{"className":83022},[886],[888,83024,83025],{"xmlns":890},[892,83026,83027,83035],{},[895,83028,83029,83031,83033],{},[898,83030,10871],{},[898,83032,5298],{},[898,83034,9945],{},[902,83036,68065],{"encoding":904},[883,83038,83040],{"className":83039},[886],[888,83041,83042],{"xmlns":890},[892,83043,83044,83050],{},[895,83045,83046,83048],{},[898,83047,5298],{},[898,83049,9945],{},[902,83051,76359],{"encoding":904},[883,83053,83055],{"className":83054},[886],[888,83056,83057],{"xmlns":890},[892,83058,83059,83065],{},[895,83060,83061,83063],{},[898,83062,10871],{},[898,83064,9945],{},[902,83066,68314],{"encoding":904},[883,83068,83070],{"className":83069},[886],[888,83071,83072],{"xmlns":890},[892,83073,83074,83080],{},[895,83075,83076,83078],{},[898,83077,16690],{},[898,83079,9945],{},[902,83081,68046],{"encoding":904},[883,83083,83085],{"className":83084},[886],[888,83086,83087],{"xmlns":890},[892,83088,83089,83097],{},[895,83090,83091,83093,83095],{},[898,83092,1878],{},[1716,83094,1913],{},[1712,83096,5808],{},[902,83098,83099],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,83102,83104],{"className":83103},[886],[888,83105,83106],{"xmlns":890},[892,83107,83108,83114],{},[895,83109,83110,83112],{},[898,83111,4164],{},[898,83113,9945],{},[902,83115,17103],{"encoding":904},[883,83117,83119],{"className":83118},[886],[888,83120,83121],{"xmlns":890},[892,83122,83123,83129],{},[895,83124,83125,83127],{},[898,83126,10871],{},[898,83128,9945],{},[902,83130,68314],{"encoding":904},[883,83132,83134],{"className":83133},[886],[888,83135,83136],{"xmlns":890},[892,83137,83138,83144],{},[895,83139,83140,83142],{},[898,83141,16690],{},[898,83143,9945],{},[902,83145,68046],{"encoding":904}," rostou, resp. klesají.",[724,83148,83149,83152,83153,82972,83183,83198,83199,83214,83215,1343,83230,1343,83245,1853],{},[38,83150,83151],{},"3.7"," Jsou dány průměrné náklady ",[883,83154,83156],{"className":83155},[886],[888,83157,83158],{"xmlns":890},[892,83159,83160,83180],{},[895,83161,83162,83164,83166,83168,83176,83178],{},[898,83163,10871],{},[898,83165,9945],{},[1716,83167,1913],{},[2747,83169,83170],{"scriptlevel":2505,"displaystyle":1919},[2750,83171,83172,83174],{},[1712,83173,12151],{},[898,83175,1878],{},[1716,83177,1949],{},[1712,83179,2976],{},[902,83181,83182],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,83184,83186],{"className":83185},[886],[888,83187,83188],{"xmlns":890},[892,83189,83190,83196],{},[895,83191,83192,83194],{},[898,83193,16690],{},[898,83195,9945],{},[902,83197,68046],{"encoding":904},". (a) Určete celkové náklady ",[883,83200,83202],{"className":83201},[886],[888,83203,83204],{"xmlns":890},[892,83205,83206,83212],{},[895,83207,83208,83210],{},[898,83209,4164],{},[898,83211,9945],{},[902,83213,17103],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,83216,83218],{"className":83217},[886],[888,83219,83220],{"xmlns":890},[892,83221,83222,83228],{},[895,83223,83224,83226],{},[898,83225,10871],{},[898,83227,9945],{},[902,83229,68314],{"encoding":904},[883,83231,83233],{"className":83232},[886],[888,83234,83235],{"xmlns":890},[892,83236,83237,83243],{},[895,83238,83239,83241],{},[898,83240,4164],{},[898,83242,9945],{},[902,83244,17103],{"encoding":904},[883,83246,83248],{"className":83247},[886],[888,83249,83250],{"xmlns":890},[892,83251,83252,83258],{},[895,83253,83254,83256],{},[898,83255,16690],{},[898,83257,9945],{},[902,83259,68046],{"encoding":904},[724,83261,83262,82847,83265,83309,83310,1343,83327,1343,83342,1343,83359,1343,83374,1343,83391,1853],{},[38,83263,83264],{},"3.8",[883,83266,83268],{"className":83267},[886],[888,83269,83270],{"xmlns":890},[892,83271,83272,83306],{},[895,83273,83274,83276,83278,83280,83282,83284,83286,83288,83290,83292,83298,83300],{},[898,83275,4164],{},[898,83277,9945],{},[1716,83279,1913],{},[1712,83281,11710],{},[1716,83283,1949],{},[1712,83285,2946],{},[898,83287,1878],{},[1716,83289,2760],{},[1712,83291,6231],{},[3074,83293,83294,83296],{},[898,83295,1878],{},[1712,83297,1726],{},[1716,83299,1949],{},[3074,83301,83302,83304],{},[898,83303,1878],{},[1712,83305,7072],{},[902,83307,83308],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,83311,83313],{"className":83312},[886],[888,83314,83315],{"xmlns":890},[892,83316,83317,83325],{},[895,83318,83319,83321,83323],{},[898,83320,4164],{},[898,83322,5298],{},[898,83324,9945],{},[902,83326,68263],{"encoding":904},[883,83328,83330],{"className":83329},[886],[888,83331,83332],{"xmlns":890},[892,83333,83334,83340],{},[895,83335,83336,83338],{},[898,83337,24240],{},[898,83339,9945],{},[902,83341,68245],{"encoding":904},[883,83343,83345],{"className":83344},[886],[888,83346,83347],{"xmlns":890},[892,83348,83349,83357],{},[895,83350,83351,83353,83355],{},[898,83352,10871],{},[898,83354,5298],{},[898,83356,9945],{},[902,83358,68065],{"encoding":904},[883,83360,83362],{"className":83361},[886],[888,83363,83364],{"xmlns":890},[892,83365,83366,83372],{},[895,83367,83368,83370],{},[898,83369,10871],{},[898,83371,9945],{},[902,83373,68314],{"encoding":904},[883,83375,83377],{"className":83376},[886],[888,83378,83379],{"xmlns":890},[892,83380,83381,83389],{},[895,83382,83383,83385,83387],{},[898,83384,10871],{},[898,83386,24240],{},[898,83388,9945],{},[902,83390,68281],{"encoding":904},[883,83392,83394],{"className":83393},[886],[888,83395,83396],{"xmlns":890},[892,83397,83398,83404],{},[895,83399,83400,83402],{},[898,83401,16690],{},[898,83403,9945],{},[902,83405,68046],{"encoding":904},[724,83407,83408,82847,83411,83441,83442,82624,83457,20296,83470,1343,83488,1343,83506,82691,83524,82714,83546,83561,83562,83575,83576,1853],{},[38,83409,83410],{},"3.9",[883,83412,83414],{"className":83413},[886],[888,83415,83416],{"xmlns":890},[892,83417,83418,83438],{},[895,83419,83420,83422,83424,83426,83428,83430,83432],{},[898,83421,4164],{},[898,83423,9945],{},[1716,83425,1913],{},[1712,83427,28904],{},[1716,83429,1949],{},[1712,83431,9451],{},[3074,83433,83434,83436],{},[898,83435,1878],{},[1712,83437,1726],{},[902,83439,83440],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,83443,83445],{"className":83444},[886],[888,83446,83447],{"xmlns":890},[892,83448,83449,83455],{},[895,83450,83451,83453],{},[898,83452,4164],{},[898,83454,9945],{},[902,83456,17103],{"encoding":904},[883,83458,83460],{"className":83459},[886],[888,83461,83462],{"xmlns":890},[892,83463,83464,83468],{},[895,83465,83466],{},[898,83467,1878],{},[902,83469,1878],{"encoding":904},[883,83471,83473],{"className":83472},[886],[888,83474,83475],{"xmlns":890},[892,83476,83477,83485],{},[895,83478,83479,83481,83483],{},[898,83480,1878],{},[1716,83482,1913],{},[1712,83484,2998],{},[902,83486,83487],{"encoding":904},"Q = 10",[883,83489,83491],{"className":83490},[886],[888,83492,83493],{"xmlns":890},[892,83494,83495,83503],{},[895,83496,83497,83499,83501],{},[898,83498,1878],{},[1716,83500,1913],{},[1712,83502,2976],{},[902,83504,83505],{"encoding":904},"Q = 20",[883,83507,83509],{"className":83508},[886],[888,83510,83511],{"xmlns":890},[892,83512,83513,83521],{},[895,83514,83515,83517,83519],{},[898,83516,1878],{},[1716,83518,1913],{},[1712,83520,2946],{},[902,83522,83523],{"encoding":904},"Q = 30",[883,83525,83527],{"className":83526},[886],[888,83528,83529],{"xmlns":890},[892,83530,83531,83543],{},[895,83532,83533,83535,83537,83539,83541],{},[898,83534,16690],{},[898,83536,9945],{},[1716,83538,1920],{"stretchy":1919},[1712,83540,3221],{},[1716,83542,1925],{"stretchy":1919},[902,83544,83545],{"encoding":904},"MC(15)",[883,83547,83549],{"className":83548},[886],[888,83550,83551],{"xmlns":890},[892,83552,83553,83559],{},[895,83554,83555,83557],{},[898,83556,4164],{},[898,83558,9945],{},[902,83560,17103],{"encoding":904}," v důsledku změny ",[883,83563,83565],{"className":83564},[886],[888,83566,83567],{"xmlns":890},[892,83568,83569,83573],{},[895,83570,83571],{},[898,83572,1878],{},[902,83574,1878],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,83577,83579],{"className":83578},[886],[888,83580,83581],{"xmlns":890},[892,83582,83583,83589],{},[895,83584,83585,83587],{},[898,83586,4164],{},[898,83588,9945],{},[902,83590,17103],{"encoding":904},[724,83592,83593,83596,83597,83198,83633,83648,83649,82808,83668,83561,83683,83696],{},[38,83594,83595],{},"3.10"," Jsou dány mezní náklady ",[883,83598,83600],{"className":83599},[886],[888,83601,83602],{"xmlns":890},[892,83603,83604,83630],{},[895,83605,83606,83608,83610,83612,83614,83616,83618,83620,83622,83624],{},[898,83607,16690],{},[898,83609,9945],{},[1716,83611,1913],{},[1712,83613,2884],{},[1716,83615,2760],{},[1712,83617,6833],{},[898,83619,1878],{},[1716,83621,1949],{},[1712,83623,77313],{},[3074,83625,83626,83628],{},[898,83627,1878],{},[1712,83629,1726],{},[902,83631,83632],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,83634,83636],{"className":83635},[886],[888,83637,83638],{"xmlns":890},[892,83639,83640,83646],{},[895,83641,83642,83644],{},[898,83643,4164],{},[898,83645,9945],{},[902,83647,17103],{"encoding":904},", jestliže fixní náklady ",[883,83650,83652],{"className":83651},[886],[888,83653,83654],{"xmlns":890},[892,83655,83656,83666],{},[895,83657,83658,83660,83662,83664],{},[898,83659,24240],{},[898,83661,9945],{},[1716,83663,1913],{},[1712,83665,12151],{},[902,83667,25436],{"encoding":904},[883,83669,83671],{"className":83670},[886],[888,83672,83673],{"xmlns":890},[892,83674,83675,83681],{},[895,83676,83677,83679],{},[898,83678,4164],{},[898,83680,9945],{},[902,83682,17103],{"encoding":904},[883,83684,83686],{"className":83685},[886],[888,83687,83688],{"xmlns":890},[892,83689,83690,83694],{},[895,83691,83692],{},[898,83693,1878],{},[902,83695,1878],{"encoding":904}," z 15 na 20.",[724,83698,83699,82847,83702,83745,83746,83759,83760,83775,83776,83791,83792,83759,83805,83775,83822,83839,83840,83759,83853,83775,83868,83883,83884,83904,83905,83928],{},[38,83700,83701],{},"3.11",[883,83703,83705],{"className":83704},[886],[888,83706,83707],{"xmlns":890},[892,83708,83709,83743],{},[895,83710,83711,83713,83715,83717,83719,83721,83723,83725,83727,83729,83735,83737],{},[898,83712,4164],{},[898,83714,9945],{},[1716,83716,1913],{},[1712,83718,12151],{},[1716,83720,1949],{},[1712,83722,5778],{},[898,83724,1878],{},[1716,83726,2760],{},[1712,83728,6985],{},[3074,83730,83731,83733],{},[898,83732,1878],{},[1712,83734,1726],{},[1716,83736,1949],{},[3074,83738,83739,83741],{},[898,83740,1878],{},[1712,83742,7072],{},[902,83744,73661],{"encoding":904},". (a) Určete ",[883,83747,83749],{"className":83748},[886],[888,83750,83751],{"xmlns":890},[892,83752,83753,83757],{},[895,83754,83755],{},[898,83756,1878],{},[902,83758,1878],{"encoding":904},", které minimalizuje ",[883,83761,83763],{"className":83762},[886],[888,83764,83765],{"xmlns":890},[892,83766,83767,83773],{},[895,83768,83769,83771],{},[898,83770,16690],{},[898,83772,9945],{},[902,83774,68046],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,83777,83779],{"className":83778},[886],[888,83780,83781],{"xmlns":890},[892,83782,83783,83789],{},[895,83784,83785,83787],{},[898,83786,16690],{},[898,83788,9945],{},[902,83790,68046],{"encoding":904},". (b) Určete ",[883,83793,83795],{"className":83794},[886],[888,83796,83797],{"xmlns":890},[892,83798,83799,83803],{},[895,83800,83801],{},[898,83802,1878],{},[902,83804,1878],{"encoding":904},[883,83806,83808],{"className":83807},[886],[888,83809,83810],{"xmlns":890},[892,83811,83812,83820],{},[895,83813,83814,83816,83818],{},[898,83815,10871],{},[898,83817,5298],{},[898,83819,9945],{},[902,83821,68065],{"encoding":904},[883,83823,83825],{"className":83824},[886],[888,83826,83827],{"xmlns":890},[892,83828,83829,83837],{},[895,83830,83831,83833,83835],{},[898,83832,10871],{},[898,83834,5298],{},[898,83836,9945],{},[902,83838,68065],{"encoding":904},". (c) Určete ",[883,83841,83843],{"className":83842},[886],[888,83844,83845],{"xmlns":890},[892,83846,83847,83851],{},[895,83848,83849],{},[898,83850,1878],{},[902,83852,1878],{"encoding":904},[883,83854,83856],{"className":83855},[886],[888,83857,83858],{"xmlns":890},[892,83859,83860,83866],{},[895,83861,83862,83864],{},[898,83863,10871],{},[898,83865,9945],{},[902,83867,68314],{"encoding":904},[883,83869,83871],{"className":83870},[886],[888,83872,83873],{"xmlns":890},[892,83874,83875,83881],{},[895,83876,83877,83879],{},[898,83878,10871],{},[898,83880,9945],{},[902,83882,68314],{"encoding":904}," (rada: hledaný kořen ",[883,83885,83887],{"className":83886},[886],[888,83888,83889],{"xmlns":890},[892,83890,83891,83901],{},[895,83892,83893,83895],{},[898,83894,10871],{},[3074,83896,83897,83899],{},[898,83898,9945],{},[1716,83900,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,83902,83903],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,83906,83908],{"className":83907},[886],[888,83909,83910],{"xmlns":890},[892,83911,83912,83925],{},[895,83913,83914,83916,83919,83921,83923],{},[1716,83915,1920],{"stretchy":1919},[1712,83917,83918],{},"4,7",[1716,83920,22241],{"separator":1718},[1712,83922,19108],{},[1716,83924,1925],{"stretchy":1919},[902,83926,83927],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,83930,83931,83934,83935,16504,83963,83980,83981,2772,84022,84043],{},[38,83932,83933],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,83936,83938],{"className":83937},[886],[888,83939,83940],{"xmlns":890},[892,83941,83942,83960],{},[895,83943,83944,83946,83948,83950,83952,83954,83956,83958],{},[898,83945,10871],{},[898,83947,9945],{},[1716,83949,1913],{},[898,83951,10871],{},[898,83953,9945],{},[1716,83955,1920],{"stretchy":1919},[898,83957,1878],{},[1716,83959,1925],{"stretchy":1919},[902,83961,83962],{"encoding":904},"AC = AC(Q)",[883,83964,83966],{"className":83965},[886],[888,83967,83968],{"xmlns":890},[892,83969,83970,83978],{},[895,83971,83972],{},[1707,83973,83974,83976],{},[898,83975,1878],{},[1712,83977,2505],{},[902,83979,3245],{"encoding":904}," minimum, pak platí ",[883,83982,83984],{"className":83983},[886],[888,83985,83986],{"xmlns":890},[892,83987,83988,84020],{},[895,83989,83990,83992,83994,83996,84002,84004,84006,84008,84010,84012,84018],{},[898,83991,10871],{},[898,83993,9945],{},[1716,83995,1920],{"stretchy":1919},[1707,83997,83998,84000],{},[898,83999,1878],{},[1712,84001,2505],{},[1716,84003,1925],{"stretchy":1919},[1716,84005,1913],{},[898,84007,16690],{},[898,84009,9945],{},[1716,84011,1920],{"stretchy":1919},[1707,84013,84014,84016],{},[898,84015,1878],{},[1712,84017,2505],{},[1716,84019,1925],{"stretchy":1919},[902,84021,75323],{"encoding":904},[883,84023,84025],{"className":84024},[886],[888,84026,84027],{"xmlns":890},[892,84028,84029,84041],{},[895,84030,84031,84033,84035,84037,84039],{},[898,84032,16690],{},[898,84034,9945],{},[1716,84036,1920],{"stretchy":1919},[898,84038,1878],{},[1716,84040,1925],{"stretchy":1919},[902,84042,80447],{"encoding":904}," jsou mezní náklady.",[724,84045,84046,82847,84049,83309,84083,83759,84096,83775,84111,1853],{},[38,84047,84048],{},"3.13",[883,84050,84052],{"className":84051},[886],[888,84053,84054],{"xmlns":890},[892,84055,84056,84080],{},[895,84057,84058,84060,84062,84064,84070,84072,84074,84076,84078],{},[898,84059,4164],{},[898,84061,9945],{},[1716,84063,1913],{},[3074,84065,84066,84068],{},[898,84067,1878],{},[1712,84069,1726],{},[1716,84071,1949],{},[1712,84073,1726],{},[898,84075,1878],{},[1716,84077,1949],{},[1712,84079,5778],{},[902,84081,84082],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,84084,84086],{"className":84085},[886],[888,84087,84088],{"xmlns":890},[892,84089,84090,84094],{},[895,84091,84092],{},[898,84093,1878],{},[902,84095,1878],{"encoding":904},[883,84097,84099],{"className":84098},[886],[888,84100,84101],{"xmlns":890},[892,84102,84103,84109],{},[895,84104,84105,84107],{},[898,84106,10871],{},[898,84108,9945],{},[902,84110,68314],{"encoding":904},[883,84112,84114],{"className":84113},[886],[888,84115,84116],{"xmlns":890},[892,84117,84118,84124],{},[895,84119,84120,84122],{},[898,84121,10871],{},[898,84123,9945],{},[902,84125,68314],{"encoding":904},[724,84127,84128,84131,84132,16504,84164,83980,84181,2772,84224,84043],{},[38,84129,84130],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,84133,84135],{"className":84134},[886],[888,84136,84137],{"xmlns":890},[892,84138,84139,84161],{},[895,84140,84141,84143,84145,84147,84149,84151,84153,84155,84157,84159],{},[898,84142,10871],{},[898,84144,5298],{},[898,84146,9945],{},[1716,84148,1913],{},[898,84150,10871],{},[898,84152,5298],{},[898,84154,9945],{},[1716,84156,1920],{"stretchy":1919},[898,84158,1878],{},[1716,84160,1925],{"stretchy":1919},[902,84162,84163],{"encoding":904},"AVC = AVC(Q)",[883,84165,84167],{"className":84166},[886],[888,84168,84169],{"xmlns":890},[892,84170,84171,84179],{},[895,84172,84173],{},[1707,84174,84175,84177],{},[898,84176,1878],{},[1712,84178,2505],{},[902,84180,3245],{"encoding":904},[883,84182,84184],{"className":84183},[886],[888,84185,84186],{"xmlns":890},[892,84187,84188,84222],{},[895,84189,84190,84192,84194,84196,84198,84204,84206,84208,84210,84212,84214,84220],{},[898,84191,10871],{},[898,84193,5298],{},[898,84195,9945],{},[1716,84197,1920],{"stretchy":1919},[1707,84199,84200,84202],{},[898,84201,1878],{},[1712,84203,2505],{},[1716,84205,1925],{"stretchy":1919},[1716,84207,1913],{},[898,84209,16690],{},[898,84211,9945],{},[1716,84213,1920],{"stretchy":1919},[1707,84215,84216,84218],{},[898,84217,1878],{},[1712,84219,2505],{},[1716,84221,1925],{"stretchy":1919},[902,84223,81773],{"encoding":904},[883,84225,84227],{"className":84226},[886],[888,84228,84229],{"xmlns":890},[892,84230,84231,84243],{},[895,84232,84233,84235,84237,84239,84241],{},[898,84234,16690],{},[898,84236,9945],{},[1716,84238,1920],{"stretchy":1919},[898,84240,1878],{},[1716,84242,1925],{"stretchy":1919},[902,84244,80447],{"encoding":904},[724,84246,84247,82847,84250,83309,84296,83759,84309,83775,84326,1853],{},[38,84248,84249],{},"3.15",[883,84251,84253],{"className":84252},[886],[888,84254,84255],{"xmlns":890},[892,84256,84257,84293],{},[895,84258,84259,84261,84263,84265,84267,84269,84271,84273,84275,84277,84283,84285,84287],{},[898,84260,4164],{},[898,84262,9945],{},[1716,84264,1913],{},[1712,84266,5808],{},[1716,84268,1949],{},[1712,84270,3221],{},[898,84272,1878],{},[1716,84274,2760],{},[1712,84276,1726],{},[3074,84278,84279,84281],{},[898,84280,1878],{},[1712,84282,1726],{},[1716,84284,1949],{},[1712,84286,11302],{},[3074,84288,84289,84291],{},[898,84290,1878],{},[1712,84292,7072],{},[902,84294,84295],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,84297,84299],{"className":84298},[886],[888,84300,84301],{"xmlns":890},[892,84302,84303,84307],{},[895,84304,84305],{},[898,84306,1878],{},[902,84308,1878],{"encoding":904},[883,84310,84312],{"className":84311},[886],[888,84313,84314],{"xmlns":890},[892,84315,84316,84324],{},[895,84317,84318,84320,84322],{},[898,84319,10871],{},[898,84321,5298],{},[898,84323,9945],{},[902,84325,68065],{"encoding":904},[883,84327,84329],{"className":84328},[886],[888,84330,84331],{"xmlns":890},[892,84332,84333,84341],{},[895,84334,84335,84337,84339],{},[898,84336,10871],{},[898,84338,5298],{},[898,84340,9945],{},[902,84342,68065],{"encoding":904},[724,84344,84345,84348,84349,84362,84363,84383],{},[38,84346,84347],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,84350,84352],{"className":84351},[886],[888,84353,84354],{"xmlns":890},[892,84355,84356,84360],{},[895,84357,84358],{},[898,84359,8967],{},[902,84361,8967],{"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 ",[883,84364,84366],{"className":84365},[886],[888,84367,84368],{"xmlns":890},[892,84369,84370,84380],{},[895,84371,84372,84374,84376,84378],{},[1712,84373,2998],{},[2074,84375,8508],{},[1712,84377,71836],{},[898,84379,8967],{},[902,84381,84382],{"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.",[198,84385,84387],{"id":84386},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,84389,84390,84393,84394,2247,84416,84442],{},[38,84391,84392],{},"3.17"," Jsou dány ",[883,84395,84397],{"className":84396},[886],[888,84398,84399],{"xmlns":890},[892,84400,84401,84413],{},[895,84402,84403,84405,84407,84409,84411],{},[898,84404,4164],{},[898,84406,17840],{},[1716,84408,1913],{},[1712,84410,2998],{},[898,84412,1878],{},[902,84414,84415],{"encoding":904},"TR = 10Q",[883,84417,84419],{"className":84418},[886],[888,84420,84421],{"xmlns":890},[892,84422,84423,84439],{},[895,84424,84425,84427,84429,84431,84433,84435,84437],{},[898,84426,4164],{},[898,84428,9945],{},[1716,84430,1913],{},[1712,84432,12151],{},[1716,84434,1949],{},[1712,84436,6985],{},[898,84438,1878],{},[902,84440,84441],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,84444,84445,84448,84449,7364,84464,84479,84480,1343,84502,2772,84529,84551,84552,84586],{},[38,84446,84447],{},"3.18"," Odvoďte, že jestliže ",[883,84450,84452],{"className":84451},[886],[888,84453,84454],{"xmlns":890},[892,84455,84456,84462],{},[895,84457,84458,84460],{},[898,84459,4164],{},[898,84461,17840],{},[902,84463,17938],{"encoding":904},[883,84465,84467],{"className":84466},[886],[888,84468,84469],{"xmlns":890},[892,84470,84471,84477],{},[895,84472,84473,84475],{},[898,84474,4164],{},[898,84476,9945],{},[902,84478,17103],{"encoding":904}," jsou lineární tvaru ",[883,84481,84483],{"className":84482},[886],[888,84484,84485],{"xmlns":890},[892,84486,84487,84499],{},[895,84488,84489,84491,84493,84495,84497],{},[898,84490,4164],{},[898,84492,17840],{},[1716,84494,1913],{},[898,84496,724],{},[898,84498,1878],{},[902,84500,84501],{"encoding":904},"TR = pQ",[883,84503,84505],{"className":84504},[886],[888,84506,84507],{"xmlns":890},[892,84508,84509,84526],{},[895,84510,84511,84513,84515,84517,84520,84522,84524],{},[898,84512,4164],{},[898,84514,9945],{},[1716,84516,1913],{},[898,84518,84519],{},"m",[1716,84521,1949],{},[898,84523,1740],{},[898,84525,1878],{},[902,84527,84528],{"encoding":904},"TC = m + nQ",[883,84530,84532],{"className":84531},[886],[888,84533,84534],{"xmlns":890},[892,84535,84536,84548],{},[895,84537,84538,84540,84542,84544,84546],{},[898,84539,84519],{},[1716,84541,1719],{"separator":1718},[898,84543,1740],{},[1716,84545,1719],{"separator":1718},[898,84547,724],{},[902,84549,84550],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,84553,84555],{"className":84554},[886],[888,84556,84557],{"xmlns":890},[892,84558,84559,84583],{},[895,84560,84561,84567,84569],{},[3074,84562,84563,84565],{},[898,84564,1878],{},[1716,84566,3080],{},[1716,84568,1913],{},[2747,84570,84571],{"scriptlevel":2505,"displaystyle":1919},[2750,84572,84573,84575],{},[898,84574,84519],{},[895,84576,84577,84579,84581],{},[898,84578,724],{},[1716,84580,2760],{},[898,84582,1740],{},[902,84584,84585],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,84588,84589,84393,84592,2247,84626,83745,84652,84665,84666,82497,84681,84696,84697,82481,84710,82497,84725,84740],{},[38,84590,84591],{},"3.19",[883,84593,84595],{"className":84594},[886],[888,84596,84597],{"xmlns":890},[892,84598,84599,84623],{},[895,84600,84601,84603,84605,84607,84609,84611,84617,84619,84621],{},[898,84602,4164],{},[898,84604,17840],{},[1716,84606,1913],{},[1716,84608,2760],{},[1712,84610,1726],{},[3074,84612,84613,84615],{},[898,84614,1878],{},[1712,84616,1726],{},[1716,84618,1949],{},[1712,84620,6681],{},[898,84622,1878],{},[902,84624,84625],{"encoding":904},"TR = -2Q^2 + 14Q",[883,84627,84629],{"className":84628},[886],[888,84630,84631],{"xmlns":890},[892,84632,84633,84649],{},[895,84634,84635,84637,84639,84641,84643,84645,84647],{},[898,84636,4164],{},[898,84638,9945],{},[1716,84640,1913],{},[1712,84642,1726],{},[898,84644,1878],{},[1716,84646,1949],{},[1712,84648,2998],{},[902,84650,84651],{"encoding":904},"TC = 2Q + 10",[883,84653,84655],{"className":84654},[886],[888,84656,84657],{"xmlns":890},[892,84658,84659,84663],{},[895,84660,84661],{},[898,84662,1878],{},[902,84664,1878],{"encoding":904},", které maximalizuje zisk ",[883,84667,84669],{"className":84668},[886],[888,84670,84671],{"xmlns":890},[892,84672,84673,84679],{},[895,84674,84675,84677],{},[898,84676,1690],{},[898,84678,17840],{},[902,84680,76233],{"encoding":904},[883,84682,84684],{"className":84683},[886],[888,84685,84686],{"xmlns":890},[892,84687,84688,84694],{},[895,84689,84690,84692],{},[898,84691,1690],{},[898,84693,17840],{},[902,84695,76233],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,84698,84700],{"className":84699},[886],[888,84701,84702],{"xmlns":890},[892,84703,84704,84708],{},[895,84705,84706],{},[898,84707,1878],{},[902,84709,1878],{"encoding":904},[883,84711,84713],{"className":84712},[886],[888,84714,84715],{"xmlns":890},[892,84716,84717,84723],{},[895,84718,84719,84721],{},[898,84720,4164],{},[898,84722,17840],{},[902,84724,17938],{"encoding":904},[883,84726,84728],{"className":84727},[886],[888,84729,84730],{"xmlns":890},[892,84731,84732,84738],{},[895,84733,84734,84736],{},[898,84735,4164],{},[898,84737,17840],{},[902,84739,17938],{"encoding":904},". (d) Graficky interpretujte.",[724,84742,84743,12695,84746,1343,84772,1343,84791,83745,84811,84665,84824,82497,84839,84854,84855,84877,84878,83928],{},[38,84744,84745],{},"3.20",[883,84747,84749],{"className":84748},[886],[888,84750,84751],{"xmlns":890},[892,84752,84753,84769],{},[895,84754,84755,84757,84759,84761,84763],{},[898,84756,1690],{},[1716,84758,1913],{},[1712,84760,33925],{},[1716,84762,2760],{},[3074,84764,84765,84767],{},[898,84766,1878],{},[1712,84768,1726],{},[902,84770,84771],{"encoding":904},"P = 400 - Q^2",[883,84773,84775],{"className":84774},[886],[888,84776,84777],{"xmlns":890},[892,84778,84779,84789],{},[895,84780,84781,84783,84785,84787],{},[898,84782,24240],{},[898,84784,9945],{},[1716,84786,1913],{},[1712,84788,12151],{},[902,84790,25436],{"encoding":904},[883,84792,84794],{"className":84793},[886],[888,84795,84796],{"xmlns":890},[892,84797,84798,84808],{},[895,84799,84800,84802,84804,84806],{},[898,84801,16690],{},[898,84803,9945],{},[1716,84805,1913],{},[1712,84807,2976],{},[902,84809,84810],{"encoding":904},"MC = 20",[883,84812,84814],{"className":84813},[886],[888,84815,84816],{"xmlns":890},[892,84817,84818,84822],{},[895,84819,84820],{},[898,84821,1878],{},[902,84823,1878],{"encoding":904},[883,84825,84827],{"className":84826},[886],[888,84828,84829],{"xmlns":890},[892,84830,84831,84837],{},[895,84832,84833,84835],{},[898,84834,1690],{},[898,84836,17840],{},[902,84838,76233],{"encoding":904},[883,84840,84842],{"className":84841},[886],[888,84843,84844],{"xmlns":890},[892,84845,84846,84852],{},[895,84847,84848,84850],{},[898,84849,1690],{},[898,84851,17840],{},[902,84853,76233],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,84856,84858],{"className":84857},[886],[888,84859,84860],{"xmlns":890},[892,84861,84862,84874],{},[895,84863,84864,84866,84868,84870,84872],{},[1716,84865,1920],{"stretchy":1919},[1712,84867,2505],{},[1716,84869,1719],{"separator":1718},[1712,84871,1714],{},[1716,84873,1925],{"stretchy":1919},[902,84875,84876],{"encoding":904},"(0, 1)",", druhý do ",[883,84879,84881],{"className":84880},[886],[888,84882,84883],{"xmlns":890},[892,84884,84885,84898],{},[895,84886,84887,84889,84892,84894,84896],{},[1716,84888,1920],{"stretchy":1919},[1712,84890,84891],{},"19",[1716,84893,1719],{"separator":1718},[1712,84895,2976],{},[1716,84897,1925],{"stretchy":1919},[902,84899,84900],{"encoding":904},"(19, 20)",[724,84902,84903,84906,84907,16504,84935,84952,84953,1853],{},[38,84904,84905],{},"3.21"," Dokažte, že má-li zisk ",[883,84908,84910],{"className":84909},[886],[888,84911,84912],{"xmlns":890},[892,84913,84914,84932],{},[895,84915,84916,84918,84920,84922,84924,84926,84928,84930],{},[898,84917,1690],{},[898,84919,17840],{},[1716,84921,1913],{},[898,84923,1690],{},[898,84925,17840],{},[1716,84927,1920],{"stretchy":1919},[898,84929,1878],{},[1716,84931,1925],{"stretchy":1919},[902,84933,84934],{"encoding":904},"PR = PR(Q)",[883,84936,84938],{"className":84937},[886],[888,84939,84940],{"xmlns":890},[892,84941,84942,84950],{},[895,84943,84944],{},[1707,84945,84946,84948],{},[898,84947,1878],{},[1712,84949,2505],{},[902,84951,3245],{"encoding":904}," maximum, pak platí ",[883,84954,84956],{"className":84955},[886],[888,84957,84958],{"xmlns":890},[892,84959,84960,84992],{},[895,84961,84962,84964,84966,84968,84974,84976,84978,84980,84982,84984,84990],{},[898,84963,16690],{},[898,84965,17840],{},[1716,84967,1920],{"stretchy":1919},[1707,84969,84970,84972],{},[898,84971,1878],{},[1712,84973,2505],{},[1716,84975,1925],{"stretchy":1919},[1716,84977,1913],{},[898,84979,16690],{},[898,84981,9945],{},[1716,84983,1920],{"stretchy":1919},[1707,84985,84986,84988],{},[898,84987,1878],{},[1712,84989,2505],{},[1716,84991,1925],{"stretchy":1919},[902,84993,78399],{"encoding":904},[724,84995,84996,84999,85000,2247,85015,68779,85030,84665,85043,85058,85059,1343,85086,85123,85124,1343,85151,1853],{},[38,84997,84998],{},"3.22"," Pro zadané ",[883,85001,85003],{"className":85002},[886],[888,85004,85005],{"xmlns":890},[892,85006,85007,85013],{},[895,85008,85009,85011],{},[898,85010,16690],{},[898,85012,17840],{},[902,85014,20456],{"encoding":904},[883,85016,85018],{"className":85017},[886],[888,85019,85020],{"xmlns":890},[892,85021,85022,85028],{},[895,85023,85024,85026],{},[898,85025,16690],{},[898,85027,9945],{},[902,85029,68046],{"encoding":904},[883,85031,85033],{"className":85032},[886],[888,85034,85035],{"xmlns":890},[892,85036,85037,85041],{},[895,85038,85039],{},[898,85040,1878],{},[902,85042,1878],{"encoding":904},[883,85044,85046],{"className":85045},[886],[888,85047,85048],{"xmlns":890},[892,85049,85050,85056],{},[895,85051,85052,85054],{},[898,85053,1690],{},[898,85055,17840],{},[902,85057,76233],{"encoding":904},". (a) ",[883,85060,85062],{"className":85061},[886],[888,85063,85064],{"xmlns":890},[892,85065,85066,85083],{},[895,85067,85068,85070,85072,85074,85077,85079,85081],{},[898,85069,16690],{},[898,85071,17840],{},[1716,85073,1913],{},[1712,85075,85076],{},"236",[1716,85078,2760],{},[1712,85080,6833],{},[898,85082,1878],{},[902,85084,85085],{"encoding":904},"MR = 236 - 16Q",[883,85087,85089],{"className":85088},[886],[888,85090,85091],{"xmlns":890},[892,85092,85093,85120],{},[895,85094,85095,85097,85099,85101,85103,85109,85111,85114,85116,85118],{},[898,85096,16690],{},[898,85098,9945],{},[1716,85100,1913],{},[1712,85102,7072],{},[3074,85104,85105,85107],{},[898,85106,1878],{},[1712,85108,1726],{},[1716,85110,2760],{},[1712,85112,85113],{},"32",[898,85115,1878],{},[1716,85117,1949],{},[1712,85119,19570],{},[902,85121,85122],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,85125,85127],{"className":85126},[886],[888,85128,85129],{"xmlns":890},[892,85130,85131,85148],{},[895,85132,85133,85135,85137,85139,85142,85144,85146],{},[898,85134,16690],{},[898,85136,17840],{},[1716,85138,1913],{},[1712,85140,85141],{},"280",[1716,85143,2760],{},[1712,85145,2976],{},[898,85147,1878],{},[902,85149,85150],{"encoding":904},"MR = 280 - 20Q",[883,85152,85154],{"className":85153},[886],[888,85155,85156],{"xmlns":890},[892,85157,85158,85185],{},[895,85159,85160,85162,85164,85166,85169,85175,85177,85179,85181,85183],{},[898,85161,16690],{},[898,85163,9945],{},[1716,85165,1913],{},[1712,85167,85168],{},"1,6",[3074,85170,85171,85173],{},[898,85172,1878],{},[1712,85174,1726],{},[1716,85176,2760],{},[1712,85178,3221],{},[898,85180,1878],{},[1716,85182,1949],{},[1712,85184,2884],{},[902,85186,85187],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,85189,85190,84999,85193,2247,85208,68779,85223,82481,85236,82497,85251,85058,85266,1343,85297,85123,85333,1343,85365,85409,85410,1343,85442,1853],{},[38,85191,85192],{},"3.23",[883,85194,85196],{"className":85195},[886],[888,85197,85198],{"xmlns":890},[892,85199,85200,85206],{},[895,85201,85202,85204],{},[898,85203,4164],{},[898,85205,17840],{},[902,85207,17938],{"encoding":904},[883,85209,85211],{"className":85210},[886],[888,85212,85213],{"xmlns":890},[892,85214,85215,85221],{},[895,85216,85217,85219],{},[898,85218,4164],{},[898,85220,9945],{},[902,85222,17103],{"encoding":904},[883,85224,85226],{"className":85225},[886],[888,85227,85228],{"xmlns":890},[892,85229,85230,85234],{},[895,85231,85232],{},[898,85233,1878],{},[902,85235,1878],{"encoding":904},[883,85237,85239],{"className":85238},[886],[888,85240,85241],{"xmlns":890},[892,85242,85243,85249],{},[895,85244,85245,85247],{},[898,85246,1690],{},[898,85248,17840],{},[902,85250,76233],{"encoding":904},[883,85252,85254],{"className":85253},[886],[888,85255,85256],{"xmlns":890},[892,85257,85258,85264],{},[895,85259,85260,85262],{},[898,85261,1690],{},[898,85263,17840],{},[902,85265,76233],{"encoding":904},[883,85267,85269],{"className":85268},[886],[888,85270,85271],{"xmlns":890},[892,85272,85273,85294],{},[895,85274,85275,85277,85279,85281,85284,85286,85288],{},[898,85276,4164],{},[898,85278,17840],{},[1716,85280,1913],{},[1712,85282,85283],{},"125",[898,85285,1878],{},[1716,85287,2760],{},[3074,85289,85290,85292],{},[898,85291,1878],{},[1712,85293,1726],{},[902,85295,85296],{"encoding":904},"TR = 125Q - Q^2",[883,85298,85300],{"className":85299},[886],[888,85301,85302],{"xmlns":890},[892,85303,85304,85330],{},[895,85305,85306,85308,85310,85312,85314,85316,85318,85320,85322,85324],{},[898,85307,4164],{},[898,85309,9945],{},[1716,85311,1913],{},[1712,85313,28904],{},[1716,85315,1949],{},[1712,85317,6985],{},[898,85319,1878],{},[1716,85321,1949],{},[1712,85323,5771],{},[3074,85325,85326,85328],{},[898,85327,1878],{},[1712,85329,1726],{},[902,85331,85332],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,85334,85336],{"className":85335},[886],[888,85337,85338],{"xmlns":890},[892,85339,85340,85362],{},[895,85341,85342,85344,85346,85348,85350,85352,85354,85356],{},[898,85343,4164],{},[898,85345,17840],{},[1716,85347,1913],{},[1712,85349,2976],{},[898,85351,1878],{},[1716,85353,2760],{},[1712,85355,1726],{},[3074,85357,85358,85360],{},[898,85359,1878],{},[1712,85361,1726],{},[902,85363,85364],{"encoding":904},"TR = 20Q - 2Q^2",[883,85366,85368],{"className":85367},[886],[888,85369,85370],{"xmlns":890},[892,85371,85372,85406],{},[895,85373,85374,85376,85378,85380,85382,85384,85386,85388,85390,85392,85398,85400],{},[898,85375,4164],{},[898,85377,9945],{},[1716,85379,1913],{},[1712,85381,1726],{},[1716,85383,1949],{},[1712,85385,2976],{},[898,85387,1878],{},[1716,85389,2760],{},[1712,85391,12398],{},[3074,85393,85394,85396],{},[898,85395,1878],{},[1712,85397,1726],{},[1716,85399,1949],{},[3074,85401,85402,85404],{},[898,85403,1878],{},[1712,85405,7072],{},[902,85407,85408],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,85411,85413],{"className":85412},[886],[888,85414,85415],{"xmlns":890},[892,85416,85417,85439],{},[895,85418,85419,85421,85423,85425,85427,85429,85431,85433],{},[898,85420,4164],{},[898,85422,17840],{},[1716,85424,1913],{},[1712,85426,6849],{},[898,85428,1878],{},[1716,85430,2760],{},[1712,85432,37561],{},[3074,85434,85435,85437],{},[898,85436,1878],{},[1712,85438,1726],{},[902,85440,85441],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,85443,85445],{"className":85444},[886],[888,85446,85447],{"xmlns":890},[892,85448,85449,85497],{},[895,85450,85451,85453,85455,85457,85459,85461,85463,85465,85467,85483,85485],{},[898,85452,4164],{},[898,85454,9945],{},[1716,85456,1913],{},[1712,85458,6849],{},[1716,85460,1949],{},[1712,85462,1726],{},[898,85464,1878],{},[1716,85466,2760],{},[2747,85468,85469],{"scriptlevel":2505,"displaystyle":1919},[2750,85470,85471,85481],{},[895,85472,85473,85475],{},[1712,85474,7072],{},[3074,85476,85477,85479],{},[898,85478,1878],{},[1712,85480,1726],{},[1712,85482,2998],{},[1716,85484,1949],{},[2747,85486,85487],{"scriptlevel":2505,"displaystyle":1919},[2750,85488,85489,85495],{},[3074,85490,85491,85493],{},[898,85492,1878],{},[1712,85494,7072],{},[1712,85496,2976],{},[902,85498,85499],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,85501,85502,85505,85506,85536,85537,85569,85570,2772,85600,85630],{},[38,85503,85504],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,85507,85509],{"className":85508},[886],[888,85510,85511],{"xmlns":890},[892,85512,85513,85533],{},[895,85514,85515,85521,85523,85525,85527],{},[1707,85516,85517,85519],{},[898,85518,1690],{},[1712,85520,1714],{},[1716,85522,1913],{},[1712,85524,28904],{},[1716,85526,2760],{},[1707,85528,85529,85531],{},[898,85530,1878],{},[1712,85532,1714],{},[902,85534,85535],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,85538,85540],{"className":85539},[886],[888,85541,85542],{"xmlns":890},[892,85543,85544,85566],{},[895,85545,85546,85552,85554,85556,85558,85560],{},[1707,85547,85548,85550],{},[898,85549,1690],{},[1712,85551,1726],{},[1716,85553,1913],{},[1712,85555,43843],{},[1716,85557,2760],{},[1712,85559,77313],{},[1707,85561,85562,85564],{},[898,85563,1878],{},[1712,85565,1726],{},[902,85567,85568],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,85571,85573],{"className":85572},[886],[888,85574,85575],{"xmlns":890},[892,85576,85577,85597],{},[895,85578,85579,85581,85583,85585,85587,85589,85591,85593,85595],{},[898,85580,4164],{},[898,85582,9945],{},[1716,85584,1913],{},[1712,85586,5808],{},[2074,85588,8508],{},[1712,85590,71836],{},[1716,85592,1949],{},[1712,85594,2976],{},[898,85596,1878],{},[902,85598,85599],{"encoding":904},"TC = 50\\,000 + 20Q",[883,85601,85603],{"className":85602},[886],[888,85604,85605],{"xmlns":890},[892,85606,85607,85627],{},[895,85608,85609,85611,85613,85619,85621],{},[898,85610,1878],{},[1716,85612,1913],{},[1707,85614,85615,85617],{},[898,85616,1878],{},[1712,85618,1714],{},[1716,85620,1949],{},[1707,85622,85623,85625],{},[898,85624,1878],{},[1712,85626,1726],{},[902,85628,85629],{"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.",[724,85632,85633,85636,85637,85667,85668,85569,85700,2772,85730,85759],{},[38,85634,85635],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,85638,85640],{"className":85639},[886],[888,85641,85642],{"xmlns":890},[892,85643,85644,85664],{},[895,85645,85646,85652,85654,85656,85658],{},[1707,85647,85648,85650],{},[898,85649,1690],{},[1712,85651,1714],{},[1716,85653,1913],{},[1712,85655,43843],{},[1716,85657,2760],{},[1707,85659,85660,85662],{},[898,85661,1878],{},[1712,85663,1714],{},[902,85665,85666],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,85669,85671],{"className":85670},[886],[888,85672,85673],{"xmlns":890},[892,85674,85675,85697],{},[895,85676,85677,85683,85685,85687,85689,85691],{},[1707,85678,85679,85681],{},[898,85680,1690],{},[1712,85682,1726],{},[1716,85684,1913],{},[1712,85686,22193],{},[1716,85688,2760],{},[1712,85690,5771],{},[1707,85692,85693,85695],{},[898,85694,1878],{},[1712,85696,1726],{},[902,85698,85699],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,85701,85703],{"className":85702},[886],[888,85704,85705],{"xmlns":890},[892,85706,85707,85727],{},[895,85708,85709,85711,85713,85715,85717,85719,85721,85723,85725],{},[898,85710,4164],{},[898,85712,9945],{},[1716,85714,1913],{},[1712,85716,6985],{},[2074,85718,8508],{},[1712,85720,71836],{},[1716,85722,1949],{},[1712,85724,12151],{},[898,85726,1878],{},[902,85728,85729],{"encoding":904},"TC = 5\\,000 + 100Q",[883,85731,85733],{"className":85732},[886],[888,85734,85735],{"xmlns":890},[892,85736,85737,85757],{},[895,85738,85739,85741,85743,85749,85751],{},[898,85740,1878],{},[1716,85742,1913],{},[1707,85744,85745,85747],{},[898,85746,1878],{},[1712,85748,1714],{},[1716,85750,1949],{},[1707,85752,85753,85755],{},[898,85754,1878],{},[1712,85756,1726],{},[902,85758,85629],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,85761,85763],{"id":85762},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,85765,85766,85769,85770,85817,85818,85835],{},[38,85767,85768],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,85771,85773],{"className":85772},[886],[888,85774,85775],{"xmlns":890},[892,85776,85777,85814],{},[895,85778,85779,85781,85783,85785,85787,85790,85796,85798,85801,85807,85809,85812],{},[898,85780,4164],{},[898,85782,5298],{},[898,85784,9945],{},[1716,85786,1913],{},[1712,85788,85789],{},"0,85",[3074,85791,85792,85794],{},[898,85793,1878],{},[1712,85795,7072],{},[1716,85797,2760],{},[1712,85799,85800],{},"11,9",[3074,85802,85803,85805],{},[898,85804,1878],{},[1712,85806,1726],{},[1716,85808,1949],{},[1712,85810,85811],{},"102",[898,85813,1878],{},[902,85815,85816],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,85819,85821],{"className":85820},[886],[888,85822,85823],{"xmlns":890},[892,85824,85825,85833],{},[895,85826,85827],{},[3074,85828,85829,85831],{},[898,85830,1690],{},[1716,85832,3080],{},[902,85834,3083],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,85837,85838,83596,85841,85877],{},[38,85839,85840],{},"3.27",[883,85842,85844],{"className":85843},[886],[888,85845,85846],{"xmlns":890},[892,85847,85848,85874],{},[895,85849,85850,85852,85854,85856,85858,85864,85866,85868,85870,85872],{},[898,85851,16690],{},[898,85853,9945],{},[1716,85855,1913],{},[1712,85857,16792],{},[3074,85859,85860,85862],{},[898,85861,1878],{},[1712,85863,1726],{},[1716,85865,2760],{},[1712,85867,77194],{},[898,85869,1878],{},[1716,85871,1949],{},[1712,85873,44505],{},[902,85875,85876],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,85879,85880,82847,85883,85877],{},[38,85881,85882],{},"3.28",[883,85884,85886],{"className":85885},[886],[888,85887,85888],{"xmlns":890},[892,85889,85890,85926],{},[895,85891,85892,85894,85896,85898,85900,85906,85908,85910,85916,85918,85920,85922,85924],{},[898,85893,4164],{},[898,85895,9945],{},[1716,85897,1913],{},[1712,85899,5771],{},[3074,85901,85902,85904],{},[898,85903,1878],{},[1712,85905,7072],{},[1716,85907,2760],{},[1712,85909,7109],{},[3074,85911,85912,85914],{},[898,85913,1878],{},[1712,85915,1726],{},[1716,85917,1949],{},[1712,85919,2884],{},[898,85921,1878],{},[1716,85923,1949],{},[1712,85925,28904],{},[902,85927,85928],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,85930,14947],{"id":14946},[120,85932,85933,85961,86006,86078,86143,86183,86275,86381,86421,86535,86628,86692,86724,86784,86790,86854,86903,86957,87065,87120],{},[123,85934,85935,3495,85937,85960],{},[38,85936,68504],{},[883,85938,85940],{"className":85939},[886],[888,85941,85942],{"xmlns":890},[892,85943,85944,85958],{},[895,85945,85946,85948,85950,85952,85954,85956],{},[898,85947,4164],{},[898,85949,17840],{},[1716,85951,1913],{},[898,85953,1690],{},[1716,85955,9532],{},[898,85957,1878],{},[902,85959,79466],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,85962,85963,3495,85965,86005],{},[38,85964,69090],{},[883,85966,85968],{"className":85967},[886],[888,85969,85970],{"xmlns":890},[892,85971,85972,86002],{},[895,85973,85974,85976,85978,85980,85992,85994,85996,85998,86000],{},[898,85975,10871],{},[898,85977,17840],{},[1716,85979,1913],{},[2747,85981,85982],{"scriptlevel":2505,"displaystyle":1919},[2750,85983,85984,85990],{},[895,85985,85986,85988],{},[898,85987,4164],{},[898,85989,17840],{},[898,85991,1878],{},[1716,85993,1913],{},[898,85995,1916],{},[1716,85997,1920],{"stretchy":1919},[898,85999,1878],{},[1716,86001,1925],{"stretchy":1919},[902,86003,86004],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,86007,86008,3495,86010,86046,86047,86062,86063,1853],{},[38,86009,69238],{},[883,86011,86013],{"className":86012},[886],[888,86014,86015],{"xmlns":890},[892,86016,86017,86043],{},[895,86018,86019,86021,86023,86025],{},[898,86020,16690],{},[898,86022,17840],{},[1716,86024,1913],{},[2747,86026,86027],{"scriptlevel":2505,"displaystyle":1919},[2750,86028,86029,86037],{},[895,86030,86031,86033,86035],{},[898,86032,5198],{"mathvariant":2068},[898,86034,4164],{},[898,86036,17840],{},[895,86038,86039,86041],{},[898,86040,5198],{"mathvariant":2068},[898,86042,1878],{},[902,86044,86045],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,86048,86050],{"className":86049},[886],[888,86051,86052],{"xmlns":890},[892,86053,86054,86060],{},[895,86055,86056,86058],{},[898,86057,4164],{},[898,86059,17840],{},[902,86061,17938],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,86064,86066],{"className":86065},[886],[888,86067,86068],{"xmlns":890},[892,86069,86070,86076],{},[895,86071,86072,86074],{},[898,86073,10871],{},[898,86075,17840],{},[902,86077,68199],{"encoding":904},[123,86079,86080,3495,86083,1343,86113,1853],{},[38,86081,86082],{},"Diferenciál příjmu\u002Fnákladů",[883,86084,86086],{"className":86085},[886],[888,86087,86088],{"xmlns":890},[892,86089,86090,86110],{},[895,86091,86092,86094,86096,86098,86100,86102,86104,86106,86108],{},[898,86093,8485],{"mathvariant":2068},[898,86095,4164],{},[898,86097,17840],{},[1716,86099,8490],{},[898,86101,16690],{},[898,86103,17840],{},[2074,86105,8508],{},[898,86107,5198],{"mathvariant":2068},[898,86109,1878],{},[902,86111,86112],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,86114,86116],{"className":86115},[886],[888,86117,86118],{"xmlns":890},[892,86119,86120,86140],{},[895,86121,86122,86124,86126,86128,86130,86132,86134,86136,86138],{},[898,86123,8485],{"mathvariant":2068},[898,86125,4164],{},[898,86127,9945],{},[1716,86129,8490],{},[898,86131,16690],{},[898,86133,9945],{},[2074,86135,8508],{},[898,86137,5198],{"mathvariant":2068},[898,86139,1878],{},[902,86141,86142],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,86144,86145,3495,86147,1853],{},[38,86146,71360],{},[883,86148,86150],{"className":86149},[886],[888,86151,86152],{"xmlns":890},[892,86153,86154,86180],{},[895,86155,86156,86158,86160,86162,86164,86166,86168,86170,86172,86174,86176,86178],{},[898,86157,4164],{},[898,86159,9945],{},[1716,86161,1913],{},[898,86163,24240],{},[898,86165,9945],{},[1716,86167,1949],{},[898,86169,4164],{},[898,86171,5298],{},[898,86173,9945],{},[1716,86175,1920],{"stretchy":1919},[898,86177,1878],{},[1716,86179,1925],{"stretchy":1919},[902,86181,86182],{"encoding":904},"TC = FC + TVC(Q)",[123,86184,86185,3495,86188,1343,86203,3495,86205,1343,86228,3495,86231,1853],{},[38,86186,86187],{},"Fixní náklady",[883,86189,86191],{"className":86190},[886],[888,86192,86193],{"xmlns":890},[892,86194,86195,86201],{},[895,86196,86197,86199],{},[898,86198,24240],{},[898,86200,9945],{},[902,86202,68245],{"encoding":904},[38,86204,71513],{},[883,86206,86208],{"className":86207},[886],[888,86209,86210],{"xmlns":890},[892,86211,86212,86226],{},[895,86213,86214,86216,86218,86220,86222,86224],{},[898,86215,4164],{},[898,86217,5298],{},[898,86219,9945],{},[1716,86221,1920],{"stretchy":1919},[898,86223,1878],{},[1716,86225,1925],{"stretchy":1919},[902,86227,71510],{"encoding":904},[38,86229,86230],{},"variabilní náklady na jednotku",[883,86232,86234],{"className":86233},[886],[888,86235,86236],{"xmlns":890},[892,86237,86238,86272],{},[895,86239,86240,86242,86244,86246,86248,86250,86252],{},[898,86241,5298],{},[898,86243,9945],{},[1716,86245,1920],{"stretchy":1919},[898,86247,1878],{},[1716,86249,1925],{"stretchy":1919},[1716,86251,1913],{},[2747,86253,86254],{"scriptlevel":2505,"displaystyle":1919},[2750,86255,86256,86270],{},[895,86257,86258,86260,86262,86264,86266,86268],{},[898,86259,4164],{},[898,86261,5298],{},[898,86263,9945],{},[1716,86265,1920],{"stretchy":1919},[898,86267,1878],{},[1716,86269,1925],{"stretchy":1919},[898,86271,1878],{},[902,86273,86274],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,86276,86277,3495,86279,1343,86309,3495,86312,1343,86344,3495,86347,1853],{},[38,86278,71521],{},[883,86280,86282],{"className":86281},[886],[888,86283,86284],{"xmlns":890},[892,86285,86286,86306],{},[895,86287,86288,86290,86292,86294],{},[898,86289,10871],{},[898,86291,9945],{},[1716,86293,1913],{},[2747,86295,86296],{"scriptlevel":2505,"displaystyle":1919},[2750,86297,86298,86304],{},[895,86299,86300,86302],{},[898,86301,4164],{},[898,86303,9945],{},[898,86305,1878],{},[902,86307,86308],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,86310,86311],{},"průměrné fixní",[883,86313,86315],{"className":86314},[886],[888,86316,86317],{"xmlns":890},[892,86318,86319,86341],{},[895,86320,86321,86323,86325,86327,86329],{},[898,86322,10871],{},[898,86324,24240],{},[898,86326,9945],{},[1716,86328,1913],{},[2747,86330,86331],{"scriptlevel":2505,"displaystyle":1919},[2750,86332,86333,86339],{},[895,86334,86335,86337],{},[898,86336,24240],{},[898,86338,9945],{},[898,86340,1878],{},[902,86342,86343],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,86345,86346],{},"průměrné variabilní",[883,86348,86350],{"className":86349},[886],[888,86351,86352],{"xmlns":890},[892,86353,86354,86378],{},[895,86355,86356,86358,86360,86362,86364],{},[898,86357,10871],{},[898,86359,5298],{},[898,86361,9945],{},[1716,86363,1913],{},[2747,86365,86366],{"scriptlevel":2505,"displaystyle":1919},[2750,86367,86368,86376],{},[895,86369,86370,86372,86374],{},[898,86371,4164],{},[898,86373,5298],{},[898,86375,9945],{},[898,86377,1878],{},[902,86379,86380],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,86382,86383,3495,86385,1853],{},[38,86384,72708],{},[883,86386,86388],{"className":86387},[886],[888,86389,86390],{"xmlns":890},[892,86391,86392,86418],{},[895,86393,86394,86396,86398,86400],{},[898,86395,16690],{},[898,86397,9945],{},[1716,86399,1913],{},[2747,86401,86402],{"scriptlevel":2505,"displaystyle":1919},[2750,86403,86404,86412],{},[895,86405,86406,86408,86410],{},[898,86407,5198],{"mathvariant":2068},[898,86409,4164],{},[898,86411,9945],{},[895,86413,86414,86416],{},[898,86415,5198],{"mathvariant":2068},[898,86417,1878],{},[902,86419,86420],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,86422,86423,3495,86425,86473,86474,86487,86488,1343,86503,1343,86520,1853],{},[38,86424,73606],{},[883,86426,86428],{"className":86427},[886],[888,86429,86430],{"xmlns":890},[892,86431,86432,86470],{},[895,86433,86434,86436,86438,86440,86442,86444,86446,86448,86450,86452,86454,86460,86462,86464],{},[898,86435,4164],{},[898,86437,9945],{},[1716,86439,1913],{},[898,86441,24240],{},[898,86443,9945],{},[1716,86445,1949],{},[898,86447,207],{},[898,86449,1878],{},[1716,86451,1949],{},[898,86453,1952],{},[3074,86455,86456,86458],{},[898,86457,1878],{},[1712,86459,1726],{},[1716,86461,1949],{},[898,86463,4478],{},[3074,86465,86466,86468],{},[898,86467,1878],{},[1712,86469,7072],{},[902,86471,86472],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,86475,86477],{"className":86476},[886],[888,86478,86479],{"xmlns":890},[892,86480,86481,86485],{},[895,86482,86483],{},[898,86484,900],{},[902,86486,900],{"encoding":904},"-průběhem ",[883,86489,86491],{"className":86490},[886],[888,86492,86493],{"xmlns":890},[892,86494,86495,86501],{},[895,86496,86497,86499],{},[898,86498,10871],{},[898,86500,9945],{},[902,86502,68314],{"encoding":904},[883,86504,86506],{"className":86505},[886],[888,86507,86508],{"xmlns":890},[892,86509,86510,86518],{},[895,86511,86512,86514,86516],{},[898,86513,10871],{},[898,86515,5298],{},[898,86517,9945],{},[902,86519,68065],{"encoding":904},[883,86521,86523],{"className":86522},[886],[888,86524,86525],{"xmlns":890},[892,86526,86527,86533],{},[895,86528,86529,86531],{},[898,86530,16690],{},[898,86532,9945],{},[902,86534,68046],{"encoding":904},[123,86536,86537,86539,86540,24198,86555,86596,86597,74251,86612,86627],{},[38,86538,74688],{},": v bodě minima ",[883,86541,86543],{"className":86542},[886],[888,86544,86545],{"xmlns":890},[892,86546,86547,86553],{},[895,86548,86549,86551],{},[898,86550,10871],{},[898,86552,9945],{},[902,86554,68314],{"encoding":904},[883,86556,86558],{"className":86557},[886],[888,86559,86560],{"xmlns":890},[892,86561,86562,86594],{},[895,86563,86564,86566,86568,86570,86576,86578,86580,86582,86584,86586,86592],{},[898,86565,10871],{},[898,86567,9945],{},[1716,86569,1920],{"stretchy":1919},[1707,86571,86572,86574],{},[898,86573,1878],{},[1712,86575,2505],{},[1716,86577,1925],{"stretchy":1919},[1716,86579,1913],{},[898,86581,16690],{},[898,86583,9945],{},[1716,86585,1920],{"stretchy":1919},[1707,86587,86588,86590],{},[898,86589,1878],{},[1712,86591,2505],{},[1716,86593,1925],{"stretchy":1919},[902,86595,75323],{"encoding":904},"; geometricky ",[883,86598,86600],{"className":86599},[886],[888,86601,86602],{"xmlns":890},[892,86603,86604,86610],{},[895,86605,86606,86608],{},[898,86607,16690],{},[898,86609,9945],{},[902,86611,68046],{"encoding":904},[883,86613,86615],{"className":86614},[886],[888,86616,86617],{"xmlns":890},[892,86618,86619,86625],{},[895,86620,86621,86623],{},[898,86622,10871],{},[898,86624,9945],{},[902,86626,68314],{"encoding":904}," v jejím minimu.",[123,86629,86630,86539,86632,24198,86649,1853],{},[38,86631,76038],{},[883,86633,86635],{"className":86634},[886],[888,86636,86637],{"xmlns":890},[892,86638,86639,86647],{},[895,86640,86641,86643,86645],{},[898,86642,10871],{},[898,86644,5298],{},[898,86646,9945],{},[902,86648,68065],{"encoding":904},[883,86650,86652],{"className":86651},[886],[888,86653,86654],{"xmlns":890},[892,86655,86656,86690],{},[895,86657,86658,86660,86662,86664,86666,86672,86674,86676,86678,86680,86682,86688],{},[898,86659,10871],{},[898,86661,5298],{},[898,86663,9945],{},[1716,86665,1920],{"stretchy":1919},[1707,86667,86668,86670],{},[898,86669,1878],{},[1712,86671,2505],{},[1716,86673,1925],{"stretchy":1919},[1716,86675,1913],{},[898,86677,16690],{},[898,86679,9945],{},[1716,86681,1920],{"stretchy":1919},[1707,86683,86684,86686],{},[898,86685,1878],{},[1712,86687,2505],{},[1716,86689,1925],{"stretchy":1919},[902,86691,81773],{"encoding":904},[123,86693,86694,3495,86696,86723],{},[38,86695,76217],{},[883,86697,86699],{"className":86698},[886],[888,86700,86701],{"xmlns":890},[892,86702,86703,86721],{},[895,86704,86705,86707,86709,86711,86713,86715,86717,86719],{},[898,86706,1690],{},[898,86708,17840],{},[1716,86710,1913],{},[898,86712,4164],{},[898,86714,17840],{},[1716,86716,2760],{},[898,86718,4164],{},[898,86720,9945],{},[902,86722,67954],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,86725,86726,1994,86728,86730,86731,86757,86758,86783],{},[38,86727,77079],{},[614,86729,76342],{},") — hodnoty ",[883,86732,86734],{"className":86733},[886],[888,86735,86736],{"xmlns":890},[892,86737,86738,86754],{},[895,86739,86740,86746,86748],{},[1707,86741,86742,86744],{},[898,86743,1878],{},[898,86745,10871],{},[1716,86747,1719],{"separator":1718},[1707,86749,86750,86752],{},[898,86751,1878],{},[898,86753,10856],{},[902,86755,86756],{"encoding":904},"Q_A, Q_B"," splňující ",[883,86759,86761],{"className":86760},[886],[888,86762,86763],{"xmlns":890},[892,86764,86765,86781],{},[895,86766,86767,86769,86771,86773,86775,86777,86779],{},[898,86768,1690],{},[898,86770,17840],{},[1716,86772,1920],{"stretchy":1919},[898,86774,1878],{},[1716,86776,1925],{"stretchy":1919},[1716,86778,1913],{},[1712,86780,2505],{},[902,86782,76619],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,86785,86786,86789],{},[38,86787,86788],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,86791,86792,86794,86795,24198,86812,86853],{},[38,86793,78133],{}," — v bodě maxima zisku ",[883,86796,86798],{"className":86797},[886],[888,86799,86800],{"xmlns":890},[892,86801,86802,86810],{},[895,86803,86804],{},[1707,86805,86806,86808],{},[898,86807,1878],{},[1712,86809,2505],{},[902,86811,3245],{"encoding":904},[883,86813,86815],{"className":86814},[886],[888,86816,86817],{"xmlns":890},[892,86818,86819,86851],{},[895,86820,86821,86823,86825,86827,86833,86835,86837,86839,86841,86843,86849],{},[898,86822,16690],{},[898,86824,17840],{},[1716,86826,1920],{"stretchy":1919},[1707,86828,86829,86831],{},[898,86830,1878],{},[1712,86832,2505],{},[1716,86834,1925],{"stretchy":1919},[1716,86836,1913],{},[898,86838,16690],{},[898,86840,9945],{},[1716,86842,1920],{"stretchy":1919},[1707,86844,86845,86847],{},[898,86846,1878],{},[1712,86848,2505],{},[1716,86850,1925],{"stretchy":1919},[902,86852,78399],{"encoding":904}," (3.13).",[123,86855,86856,34084,86858,24198,86877,86902],{},[38,86857,79426],{},[883,86859,86861],{"className":86860},[886],[888,86862,86863],{"xmlns":890},[892,86864,86865,86874],{},[895,86866,86867,86869,86871],{},[898,86868,1690],{},[1716,86870,1913],{},[2074,86872,86873],{},"konst",[902,86875,86876],{"encoding":904},"P = \\text{konst}",[883,86878,86880],{"className":86879},[886],[888,86881,86882],{"xmlns":890},[892,86883,86884,86900],{},[895,86885,86886,86888,86890,86892,86894,86896,86898],{},[898,86887,1690],{},[1716,86889,1913],{},[898,86891,16690],{},[898,86893,9945],{},[1716,86895,1920],{"stretchy":1919},[898,86897,1878],{},[1716,86899,1925],{"stretchy":1919},[902,86901,80120],{"encoding":904}," (3.14).",[123,86904,86905,86908,86909,86938,86939,86956],{},[38,86906,86907],{},"Shutdown point"," — bod ",[883,86910,86912],{"className":86911},[886],[888,86913,86914],{"xmlns":890},[892,86915,86916,86936],{},[895,86917,86918,86920,86926,86928,86934],{},[1716,86919,1920],{"stretchy":1919},[3074,86921,86922,86924],{},[898,86923,1878],{},[1716,86925,3080],{},[1716,86927,1719],{"separator":1718},[3074,86929,86930,86932],{},[898,86931,1690],{},[1716,86933,3080],{},[1716,86935,1925],{"stretchy":1919},[902,86937,80409],{"encoding":904}," v minimu ",[883,86940,86942],{"className":86941},[886],[888,86943,86944],{"xmlns":890},[892,86945,86946,86954],{},[895,86947,86948,86950,86952],{},[898,86949,10871],{},[898,86951,5298],{},[898,86953,9945],{},[902,86955,68065],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,86958,86959,3495,86962,20296,86997,80679,87018,87031,87032,87047,87048,1853],{},[38,86960,86961],{},"Funkce nabídky firmy",[883,86963,86965],{"className":86964},[886],[888,86966,86967],{"xmlns":890},[892,86968,86969,86995],{},[895,86970,86971,86973,86975,86977,86979,86981,86983,86985,86987,86989,86991,86993],{},[898,86972,1690],{},[1716,86974,1913],{},[898,86976,5352],{},[1716,86978,1920],{"stretchy":1919},[898,86980,1878],{},[1716,86982,1925],{"stretchy":1919},[1716,86984,1913],{},[898,86986,16690],{},[898,86988,9945],{},[1716,86990,1920],{"stretchy":1919},[898,86992,1878],{},[1716,86994,1925],{"stretchy":1919},[902,86996,81876],{"encoding":904},[883,86998,87000],{"className":86999},[886],[888,87001,87002],{"xmlns":890},[892,87003,87004,87016],{},[895,87005,87006,87008,87010],{},[898,87007,1878],{},[1716,87009,18320],{},[3074,87011,87012,87014],{},[898,87013,1878],{},[1716,87015,3080],{},[902,87017,80678],{"encoding":904},[883,87019,87021],{"className":87020},[886],[888,87022,87023],{"xmlns":890},[892,87024,87025,87029],{},[895,87026,87027],{},[1712,87028,2505],{},[902,87030,2505],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,87033,87035],{"className":87034},[886],[888,87036,87037],{"xmlns":890},[892,87038,87039,87045],{},[895,87040,87041,87043],{},[898,87042,16690],{},[898,87044,9945],{},[902,87046,68046],{"encoding":904}," nad minimem ",[883,87049,87051],{"className":87050},[886],[888,87052,87053],{"xmlns":890},[892,87054,87055,87063],{},[895,87056,87057,87059,87061],{},[898,87058,10871],{},[898,87060,5298],{},[898,87062,9945],{},[902,87064,68065],{"encoding":904},[123,87066,87067,3369,87069,87090,87091,1853],{},[38,87068,15097],{},[883,87070,87072],{"className":87071},[886],[888,87073,87074],{"xmlns":890},[892,87075,87076,87088],{},[895,87077,87078,87080,87082],{},[898,87079,1690],{},[1716,87081,1913],{},[3074,87083,87084,87086],{},[898,87085,1690],{},[1716,87087,3080],{},[902,87089,3157],{"encoding":904}," konstantní ⇒ ",[883,87092,87094],{"className":87093},[886],[888,87095,87096],{"xmlns":890},[892,87097,87098,87118],{},[895,87099,87100,87102,87104,87106,87108,87110,87112],{},[898,87101,10871],{},[898,87103,17840],{},[1716,87105,1913],{},[898,87107,16690],{},[898,87109,17840],{},[1716,87111,1913],{},[3074,87113,87114,87116],{},[898,87115,1690],{},[1716,87117,3080],{},[902,87119,71352],{"encoding":904},[123,87121,87122,87125],{},[38,87123,87124],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,87127,15740],{"id":15739},[120,87129,87130,87149,87161],{},[123,87131,87132,3495,87134,1343,87137,1343,87140,1343,87143,1343,87146],{},[38,87133,15747],{},[207,87135,25743],{"className":87136,"dataFsResolvedFilePath":800,"href":801},[210],[207,87138,15775],{"className":87139,"dataFsResolvedFilePath":848,"href":849},[210],[207,87141,15758],{"className":87142,"dataFsResolvedFilePath":764,"href":765},[210],[207,87144,775],{"className":87145,"dataFsResolvedFilePath":773,"href":774},[210],[207,87147,859],{"className":87148,"dataFsResolvedFilePath":857,"href":858},[210],[123,87150,87151,3495,87153,1343,87157],{},[38,87152,50462],{},[207,87154,87156],{"className":87155,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,87158,87160],{"className":87159,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,87162,87163,3495,87165],{},[38,87164,15794],{},[207,87166,15800],{"className":87167,"dataFsResolvedFilePath":15798,"href":15799},[210],{"title":641,"searchDepth":642,"depth":642,"links":87169},[87170,87171,87178,87184,87188,87189,87193,87194,87195,87196,87202,87203],{"id":63708,"depth":642,"text":1241},{"id":68492,"depth":642,"text":68493,"children":87172},[87173,87174,87175,87176,87177],{"id":68503,"depth":649,"text":68504},{"id":69089,"depth":649,"text":69090},{"id":69237,"depth":649,"text":69238},{"id":69979,"depth":649,"text":69980},{"id":70634,"depth":649,"text":70635},{"id":71355,"depth":642,"text":71356,"children":87179},[87180,87181,87182,87183],{"id":71359,"depth":649,"text":71360},{"id":71520,"depth":649,"text":71521},{"id":72707,"depth":649,"text":72708},{"id":73605,"depth":649,"text":73606},{"id":74687,"depth":642,"text":74688,"children":87185},[87186,87187],{"id":30201,"depth":649,"text":30202},{"id":76037,"depth":649,"text":76038},{"id":76211,"depth":642,"text":76212},{"id":78132,"depth":642,"text":78133,"children":87190},[87191,87192],{"id":78146,"depth":649,"text":30202},{"id":79425,"depth":649,"text":79426},{"id":80057,"depth":642,"text":80058},{"id":81523,"depth":642,"text":81524},{"id":14896,"depth":642,"text":14897},{"id":81984,"depth":642,"text":81985,"children":87197},[87198,87199,87200,87201],{"id":81988,"depth":649,"text":81989},{"id":82840,"depth":649,"text":82841},{"id":84386,"depth":649,"text":84387},{"id":85762,"depth":649,"text":85763},{"id":14946,"depth":642,"text":14947},{"id":15739,"depth":642,"text":15740},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":67874,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,87210,87211,67926,87212,87213,87214],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":87217,"title":87218,"body":87219,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":99316,"navigation":664,"path":99317,"seo":99318,"sources":99319,"stem":99320,"tags":99321,"type":15858,"updated":677,"__hash__":99327},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":87220,"toc":99273},[87221,87224,87580,87584,87587,87655,87707,87717,87721,87755,87796,87820,87843,87872,87939,88046,88089,88146,88221,88266,88270,88278,88286,88289,88554,88605,88685,88755,88778,88806,88851,88873,88877,88884,88933,88959,89110,89113,89150,89313,89421,89425,89462,89537,89606,89725,89847,89928,89934,89975,90048,90141,90145,90181,90269,90383,90488,90573,90713,90717,90765,90810,90816,90820,90823,90874,90924,90931,90997,91130,91175,91179,91200,91579,91674,91691,91745,91749,91831,91915,92085,92088,92131,92198,92272,92276,92281,92350,92358,92367,92445,92511,92516,92611,92654,92659,92707,92712,92760,92878,92961,92999,93102,93161,93302,93306,93349,93422,93446,93500,93507,93509,93554,93599,93610,93615,93651,93713,93736,93745,93846,93913,93986,93993,94084,94146,94182,94239,94298,94483,94579,94583,94587,94666,94671,94795,94881,94887,94997,95034,95125,95223,95226,95230,95296,95333,95455,95507,95511,95539,95591,95665,95770,95794,95853,95857,95875,96018,96166,96168,96203,96207,96209,96299,96429,96555,96647,96722,96726,96842,96946,97136,97172,97266,97272,97385,97688,97694,97812,97911,97987,97989,99151,99153],[12,87222,87218],{"id":87223},"produkce-produkční-funkce-cobb-douglas-mrts",[1635,87225,87226],{},[724,87227,87228,9930,87230,87232,87233,1778,87246,87259,87260,30166,87273,1994,87275,87299,87300,3495,87302,2247,87336,3495,87339,87367,87368,24198,87388,87418,87419,1994,87422,87450,87451,87454,87455,87485,87486,87516,87517,3495,87520,87560,87561,87579],{},[883,87229,17723],{},[38,87231,859],{}," popisuje vztah mezi vstupy (práce ",[883,87234,87236],{"className":87235},[886],[888,87237,87238],{"xmlns":890},[892,87239,87240,87244],{},[895,87241,87242],{},[898,87243,1775],{},[902,87245,1775],{"encoding":904},[883,87247,87249],{"className":87248},[886],[888,87250,87251],{"xmlns":890},[892,87252,87253,87257],{},[895,87254,87255],{},[898,87256,1790],{},[902,87258,1790],{"encoding":904},") a výstupem ",[883,87261,87263],{"className":87262},[886],[888,87264,87265],{"xmlns":890},[892,87266,87267,87271],{},[895,87268,87269],{},[898,87270,1878],{},[902,87272,1878],{"encoding":904},[38,87274,1848],{},[883,87276,87278],{"className":87277},[886],[888,87279,87280],{"xmlns":890},[892,87281,87282,87296],{},[895,87283,87284,87286,87288,87290,87292,87294],{},[898,87285,1878],{},[1716,87287,1913],{},[898,87289,1878],{},[1716,87291,1920],{"stretchy":1919},[898,87293,1775],{},[1716,87295,1925],{"stretchy":1919},[902,87297,87298],{"encoding":904},"Q = Q(L)",") studujeme ",[614,87301,23829],{},[883,87303,87305],{"className":87304},[886],[888,87306,87307],{"xmlns":890},[892,87308,87309,87333],{},[895,87310,87311,87313,87319,87321,87327,87329,87331],{},[898,87312,16690],{},[1707,87314,87315,87317],{},[898,87316,1690],{},[898,87318,1775],{},[1716,87320,1913],{},[3074,87322,87323,87325],{},[898,87324,1878],{},[1716,87326,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,87328,1920],{"stretchy":1919},[898,87330,1775],{},[1716,87332,1925],{"stretchy":1919},[902,87334,87335],{"encoding":904},"MP_L = Q'(L)",[614,87337,87338],{},"průměrný produkt",[883,87340,87342],{"className":87341},[886],[888,87343,87344],{"xmlns":890},[892,87345,87346,87364],{},[895,87347,87348,87350,87356,87358,87360,87362],{},[898,87349,10871],{},[1707,87351,87352,87354],{},[898,87353,1690],{},[898,87355,1775],{},[1716,87357,1913],{},[898,87359,1878],{},[898,87361,3045],{"mathvariant":2068},[898,87363,1775],{},[902,87365,87366],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,87369,87371],{"className":87370},[886],[888,87372,87373],{"xmlns":890},[892,87374,87375,87385],{},[895,87376,87377,87379],{},[898,87378,10871],{},[1707,87380,87381,87383],{},[898,87382,1690],{},[898,87384,1775],{},[902,87386,87387],{"encoding":904},"AP_L",[883,87389,87391],{"className":87390},[886],[888,87392,87393],{"xmlns":890},[892,87394,87395,87415],{},[895,87396,87397,87399,87405,87407,87409],{},[898,87398,16690],{},[1707,87400,87401,87403],{},[898,87402,1690],{},[898,87404,1775],{},[1716,87406,1913],{},[898,87408,10871],{},[1707,87410,87411,87413],{},[898,87412,1690],{},[898,87414,1775],{},[902,87416,87417],{"encoding":904},"MP_L = AP_L",". Ve ",[38,87420,87421],{},"dvoufaktorovém modelu",[883,87423,87425],{"className":87424},[886],[888,87426,87427],{"xmlns":890},[892,87428,87429,87447],{},[895,87430,87431,87433,87435,87437,87439,87441,87443,87445],{},[898,87432,1878],{},[1716,87434,1913],{},[898,87436,1878],{},[1716,87438,1920],{"stretchy":1919},[898,87440,1775],{},[1716,87442,1719],{"separator":1718},[898,87444,1790],{},[1716,87446,1925],{"stretchy":1919},[902,87448,87449],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,87452,87453],{},"Cobb-Douglasovy"," funkce ",[883,87456,87458],{"className":87457},[886],[888,87459,87460],{"xmlns":890},[892,87461,87462,87482],{},[895,87463,87464,87466,87468,87470,87476],{},[898,87465,1878],{},[1716,87467,1913],{},[898,87469,10871],{},[3074,87471,87472,87474],{},[898,87473,1775],{},[898,87475,207],{},[3074,87477,87478,87480],{},[898,87479,1790],{},[898,87481,1952],{},[902,87483,87484],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,87487,87489],{"className":87488},[886],[888,87490,87491],{"xmlns":890},[892,87492,87493,87513],{},[895,87494,87495,87497,87503,87505,87507],{},[898,87496,16690],{},[1707,87498,87499,87501],{},[898,87500,1690],{},[898,87502,1775],{},[1716,87504,1719],{"separator":1718},[898,87506,16690],{},[1707,87508,87509,87511],{},[898,87510,1690],{},[898,87512,1790],{},[902,87514,87515],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,87518,87519],{},"mezní míru technické substituce",[883,87521,87523],{"className":87522},[886],[888,87524,87525],{"xmlns":890},[892,87526,87527,87557],{},[895,87528,87529,87531,87533,87535,87537,87539,87541,87547,87549,87551],{},[898,87530,16690],{},[898,87532,17840],{},[898,87534,4164],{},[898,87536,5352],{},[1716,87538,1913],{},[898,87540,16690],{},[1707,87542,87543,87545],{},[898,87544,1690],{},[898,87546,1775],{},[898,87548,3045],{"mathvariant":2068},[898,87550,16690],{},[1707,87552,87553,87555],{},[898,87554,1690],{},[898,87556,1790],{},[902,87558,87559],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,87562,87564],{"className":87563},[886],[888,87565,87566],{"xmlns":890},[892,87567,87568,87576],{},[895,87569,87570,87572,87574],{},[898,87571,207],{},[1716,87573,1949],{},[898,87575,1952],{},[902,87577,87578],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,87581,87583],{"id":87582},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,87585,87586],{},"Po prostudování kapitoly 5 student umí:",[120,87588,87589,87595,87605,87611,87617,87622,87628,87638,87643,87649],{},[123,87590,87591,87592,1719],{},"popsat ",[38,87593,87594],{},"jednofaktorový model produkce",[123,87596,87597,87598,2247,87601,87604],{},"vypočítat ",[38,87599,87600],{},"mezní",[38,87602,87603],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,87606,87607,87608,1719],{},"charakterizovat průběh ",[38,87609,87610],{},"křivky produkce",[123,87612,87613,87614,1719],{},"formulovat ",[38,87615,87616],{},"princip maximalizace průměrného produktu práce",[123,87618,87591,87619,1719],{},[38,87620,87621],{},"dvoufaktorový model produkce",[123,87623,87624,87625,1719],{},"uvést tvar ",[38,87626,87627],{},"Cobb–Douglasových produkčních funkcí",[123,87629,87630,87631,1343,87633,1343,87635,1719],{},"vyložit, co jsou ",[38,87632,38384],{},[38,87634,3167],{},[38,87636,87637],{},"klesající výnosy z rozsahu",[123,87639,87597,87640,87604],{},[38,87641,87642],{},"mezní produkty práce a kapitálu",[123,87644,87645,87646,1719],{},"najít ",[38,87647,87648],{},"izokvanty",[123,87650,87597,87651,87654],{},[38,87652,87653],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,87656,87657,87658,87661,87662,87665,87666,3495,87669,1343,87682,3495,87685,2247,87698,87701,87702,87704,87705,1853],{},"Každý proces produkce je určován ",[38,87659,87660],{},"faktory"," (též ",[38,87663,87664],{},"vstupy",") produkce. K hlavním patří ",[38,87667,87668],{},"práce",[883,87670,87672],{"className":87671},[886],[888,87673,87674],{"xmlns":890},[892,87675,87676,87680],{},[895,87677,87678],{},[898,87679,1775],{},[902,87681,1775],{"encoding":904},[38,87683,87684],{},"kapitál",[883,87686,87688],{"className":87687},[886],[888,87689,87690],{"xmlns":890},[892,87691,87692,87696],{},[895,87693,87694],{},[898,87695,1790],{},[902,87697,1790],{"encoding":904},[38,87699,87700],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,87703,1848],{}," (produkce závisí jen na práci); v opačném případě o ",[38,87706,87421],{},[724,87708,87709,87710,1343,87713,87716],{},"Související matematický aparát: ",[207,87711,15758],{"className":87712,"dataFsResolvedFilePath":764,"href":765},[210],[207,87714,784],{"className":87715,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,87718,87720],{"id":87719},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,87722,87723,87724,87737,87738,87751,87752],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,87725,87727],{"className":87726},[886],[888,87728,87729],{"xmlns":890},[892,87730,87731,87735],{},[895,87732,87733],{},[898,87734,1878],{},[902,87736,1878],{"encoding":904}," na práci ",[883,87739,87741],{"className":87740},[886],[888,87742,87743],{"xmlns":890},[892,87744,87745,87749],{},[895,87746,87747],{},[898,87748,1775],{},[902,87750,1775],{"encoding":904}," vyjadřuje ",[38,87753,87754],{},"produkční funkce",[883,87756,87758],{"className":87757},[886],[888,87759,87760],{"xmlns":890,"display":2004},[892,87761,87762,87793],{},[2008,87763,87764],{"width":2010},[2012,87765,87766,87768,87786,87788],{},[2015,87767],{"width":2017},[2015,87769,87770],{},[895,87771,87772,87774,87776,87778,87780,87782,87784],{},[898,87773,1878],{},[1716,87775,1913],{},[898,87777,1878],{},[1716,87779,1920],{"stretchy":1919},[898,87781,1775],{},[1716,87783,1925],{"stretchy":1919},[1716,87785,1719],{"separator":1718},[2015,87787],{"width":2017},[2015,87789,87790],{},[2074,87791,87792],{},"(5.1)",[902,87794,87795],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,87797,87798,87799,1994,87802,87805,87806,87819],{},"jejíž graf se nazývá ",[38,87800,87801],{},"křivka produkce",[614,87803,87804],{},"production curve","). Práce ",[883,87807,87809],{"className":87808},[886],[888,87810,87811],{"xmlns":890},[892,87812,87813,87817],{},[895,87814,87815],{},[898,87816,1775],{},[902,87818,1775],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,87821,87823,87824,1925],{"id":87822},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,87825,87827],{"className":87826},[886],[888,87828,87829],{"xmlns":890},[892,87830,87831,87841],{},[895,87832,87833,87835],{},[898,87834,16690],{},[1707,87836,87837,87839],{},[898,87838,1690],{},[898,87840,1775],{},[902,87842,23849],{"encoding":904},[724,87844,87845,1994,87848,87851,87852,87871],{},[38,87846,87847],{},"Mezní produkt práce",[614,87849,87850],{},"marginal product of labour",") ",[883,87853,87855],{"className":87854},[886],[888,87856,87857],{"xmlns":890},[892,87858,87859,87869],{},[895,87860,87861,87863],{},[898,87862,16690],{},[1707,87864,87865,87867],{},[898,87866,1690],{},[898,87868,1775],{},[902,87870,23849],{"encoding":904}," je derivace produkce podle práce:",[883,87873,87875],{"className":87874},[886],[888,87876,87877],{"xmlns":890,"display":2004},[892,87878,87879,87936],{},[2008,87880,87881],{"width":2010},[2012,87882,87883,87885,87929,87931],{},[2015,87884],{"width":2017},[2015,87886,87887],{},[895,87888,87889,87891,87897,87899,87913,87915,87921,87923,87925,87927],{},[898,87890,16690],{},[1707,87892,87893,87895],{},[898,87894,1690],{},[898,87896,1775],{},[1716,87898,1913],{},[2750,87900,87901,87907],{},[895,87902,87903,87905],{},[898,87904,5198],{},[898,87906,1878],{},[895,87908,87909,87911],{},[898,87910,5198],{},[898,87912,1775],{},[1716,87914,1913],{},[3074,87916,87917,87919],{},[898,87918,1878],{},[1716,87920,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,87922,1920],{"stretchy":1919},[898,87924,1775],{},[1716,87926,1925],{"stretchy":1919},[898,87928,1853],{"mathvariant":2068},[2015,87930],{"width":2017},[2015,87932,87933],{},[2074,87934,87935],{},"(5.2)",[902,87937,87938],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,87940,87941,87942,33728,87960,87988,87989,88006,88007,3942,88024,2365],{},"Pro pevnou hodnotu ",[883,87943,87945],{"className":87944},[886],[888,87946,87947],{"xmlns":890},[892,87948,87949,87957],{},[895,87950,87951],{},[3074,87952,87953,87955],{},[898,87954,1775],{},[1716,87956,3080],{},[902,87958,87959],{"encoding":904},"L^*",[883,87961,87963],{"className":87962},[886],[888,87964,87965],{"xmlns":890},[892,87966,87967,87985],{},[895,87968,87969,87975,87977,87983],{},[3074,87970,87971,87973],{},[898,87972,1878],{},[1716,87974,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,87976,1920],{"stretchy":1919},[3074,87978,87979,87981],{},[898,87980,1775],{},[1716,87982,3080],{},[1716,87984,1925],{"stretchy":1919},[902,87986,87987],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,87990,87992],{"className":87991},[886],[888,87993,87994],{"xmlns":890},[892,87995,87996,88004],{},[895,87997,87998],{},[3074,87999,88000,88002],{},[898,88001,1775],{},[1716,88003,3080],{},[902,88005,87959],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,88008,88010],{"className":88009},[886],[888,88011,88012],{"xmlns":890},[892,88013,88014,88022],{},[895,88015,88016],{},[3074,88017,88018,88020],{},[898,88019,1775],{},[1716,88021,3080],{},[902,88023,87959],{"encoding":904},[883,88025,88027],{"className":88026},[886],[888,88028,88029],{"xmlns":890},[892,88030,88031,88043],{},[895,88032,88033,88039,88041],{},[3074,88034,88035,88037],{},[898,88036,1775],{},[1716,88038,3080],{},[1716,88040,1949],{},[1712,88042,1714],{},[902,88044,88045],{"encoding":904},"L^*+1",[1635,88047,88048],{},[724,88049,88050,31810,88052,88071,88072,88075,88076,1853],{},[883,88051,1641],{},[883,88053,88055],{"className":88054},[886],[888,88056,88057],{"xmlns":890},[892,88058,88059,88069],{},[895,88060,88061,88063],{},[898,88062,16690],{},[1707,88064,88065,88067],{},[898,88066,1690],{},[898,88068,1775],{},[902,88070,23849],{"encoding":904}," odpovídá na otázku „",[38,88073,88074],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,88077,88079],{"className":88078},[886],[888,88080,88081],{"xmlns":890},[892,88082,88083,88087],{},[895,88084,88085],{},[898,88086,1775],{},[902,88088,1775],{"encoding":904},[724,88090,88091,88094,88095,88111,88112,3942,88125,88145],{},[38,88092,88093],{},"Přibližná změna produkce"," pro změnu práce o ",[883,88096,88098],{"className":88097},[886],[888,88099,88100],{"xmlns":890},[892,88101,88102,88108],{},[895,88103,88104,88106],{},[898,88105,5198],{},[898,88107,1775],{},[902,88109,88110],{"encoding":904},"dL"," (z ",[883,88113,88115],{"className":88114},[886],[888,88116,88117],{"xmlns":890},[892,88118,88119,88123],{},[895,88120,88121],{},[898,88122,1775],{},[902,88124,1775],{"encoding":904},[883,88126,88128],{"className":88127},[886],[888,88129,88130],{"xmlns":890},[892,88131,88132,88142],{},[895,88133,88134,88136,88138,88140],{},[898,88135,1775],{},[1716,88137,1949],{},[898,88139,5198],{},[898,88141,1775],{},[902,88143,88144],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,88147,88149],{"className":88148},[886],[888,88150,88151],{"xmlns":890,"display":2004},[892,88152,88153,88218],{},[2008,88154,88155],{"width":2010},[2012,88156,88157,88159,88211,88213],{},[2015,88158],{"width":2017},[2015,88160,88161],{},[895,88162,88163,88165,88167,88169,88171,88173,88175,88181,88183,88185,88187,88189,88191,88193,88195,88197,88203,88205,88207,88209],{},[898,88164,8485],{"mathvariant":2068},[898,88166,1878],{},[1716,88168,8490],{},[898,88170,5198],{},[898,88172,1878],{},[1716,88174,1913],{},[3074,88176,88177,88179],{},[898,88178,1878],{},[1716,88180,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,88182,1920],{"stretchy":1919},[898,88184,1775],{},[1716,88186,1925],{"stretchy":1919},[2074,88188,8508],{},[898,88190,5198],{},[898,88192,1775],{},[1716,88194,1913],{},[898,88196,16690],{},[1707,88198,88199,88201],{},[898,88200,1690],{},[898,88202,1775],{},[2074,88204,8508],{},[898,88206,5198],{},[898,88208,1775],{},[898,88210,1853],{"mathvariant":2068},[2015,88212],{"width":2017},[2015,88214,88215],{},[2074,88216,88217],{},"(5.3)",[902,88219,88220],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,88222,88223,88224,1853],{},"Skutečná změna je ",[883,88225,88227],{"className":88226},[886],[888,88228,88229],{"xmlns":890},[892,88230,88231,88263],{},[895,88232,88233,88235,88237,88239,88241,88243,88245,88247,88249,88251,88253,88255,88257,88259,88261],{},[898,88234,8485],{"mathvariant":2068},[898,88236,1878],{},[1716,88238,1913],{},[898,88240,1878],{},[1716,88242,1920],{"stretchy":1919},[898,88244,1775],{},[1716,88246,1949],{},[898,88248,5198],{},[898,88250,1775],{},[1716,88252,1925],{"stretchy":1919},[1716,88254,2760],{},[898,88256,1878],{},[1716,88258,1920],{"stretchy":1919},[898,88260,1775],{},[1716,88262,1925],{"stretchy":1919},[902,88264,88265],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,88267,88269],{"id":88268},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,88271,88272,1994,88275,1998],{},[38,88273,88274],{},"Zákon klesajících výnosů",[614,88276,88277],{},"law of diminishing marginal productivity",[1635,88279,88280],{},[724,88281,88282,88283,88285],{},"Roste-li postupně některý ze vstupů (",[614,88284,1844],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,88287,88288],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,88290,88291,88292,3495,88313,88332,88333,88383,88384,88386,88387,3495,88407,88426,88427,88383,88459,7636,88461,88480,88481,2772,88498,88532,88533,2574,88550,88553],{},"1° ",[38,88293,88294,88295,2291],{},"Do bodu ",[883,88296,88298],{"className":88297},[886],[888,88299,88300],{"xmlns":890},[892,88301,88302,88310],{},[895,88303,88304],{},[1707,88305,88306,88308],{},[898,88307,1775],{},[1712,88309,2505],{},[902,88311,88312],{"encoding":904},"L_0",[883,88314,88316],{"className":88315},[886],[888,88317,88318],{"xmlns":890},[892,88319,88320,88330],{},[895,88321,88322,88324],{},[898,88323,16690],{},[1707,88325,88326,88328],{},[898,88327,1690],{},[898,88329,1775],{},[902,88331,23849],{"encoding":904}," roste, tj. ",[883,88334,88336],{"className":88335},[886],[888,88337,88338],{"xmlns":890},[892,88339,88340,88380],{},[895,88341,88342,88344,88346,88352,88358,88360,88370,88372,88374,88376,88378],{},[1716,88343,1920],{"stretchy":1919},[898,88345,16690],{},[1707,88347,88348,88350],{},[898,88349,1690],{},[898,88351,1775],{},[3074,88353,88354,88356],{},[1716,88355,1925],{"stretchy":1919},[1716,88357,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,88359,1913],{},[3074,88361,88362,88364],{},[898,88363,1878],{},[895,88365,88366,88368],{},[1716,88367,8505],{"mathvariant":2068},[1716,88369,8505],{"mathvariant":2068},[1716,88371,1920],{"stretchy":1919},[898,88373,1775],{},[1716,88375,1925],{"stretchy":1919},[1716,88377,2716],{},[1712,88379,2505],{},[902,88381,88382],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,88385,2581],{},".\n2° ",[38,88388,88389,88390,2291],{},"Od bodu ",[883,88391,88393],{"className":88392},[886],[888,88394,88395],{"xmlns":890},[892,88396,88397,88405],{},[895,88398,88399],{},[1707,88400,88401,88403],{},[898,88402,1775],{},[1712,88404,2505],{},[902,88406,88312],{"encoding":904},[883,88408,88410],{"className":88409},[886],[888,88411,88412],{"xmlns":890},[892,88413,88414,88424],{},[895,88415,88416,88418],{},[898,88417,16690],{},[1707,88419,88420,88422],{},[898,88421,1690],{},[898,88423,1775],{},[902,88425,23849],{"encoding":904}," klesá, ",[883,88428,88430],{"className":88429},[886],[888,88431,88432],{"xmlns":890},[892,88433,88434,88456],{},[895,88435,88436,88446,88448,88450,88452,88454],{},[3074,88437,88438,88440],{},[898,88439,1878],{},[895,88441,88442,88444],{},[1716,88443,8505],{"mathvariant":2068},[1716,88445,8505],{"mathvariant":2068},[1716,88447,1920],{"stretchy":1919},[898,88449,1775],{},[1716,88451,1925],{"stretchy":1919},[1716,88453,2704],{},[1712,88455,2505],{},[902,88457,88458],{"encoding":904},"Q''(L) \u003C 0",[38,88460,3426],{},[883,88462,88464],{"className":88463},[886],[888,88465,88466],{"xmlns":890},[892,88467,88468,88478],{},[895,88469,88470,88472],{},[898,88471,16690],{},[1707,88473,88474,88476],{},[898,88475,1690],{},[898,88477,1775],{},[902,88479,23849],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,88482,88484],{"className":88483},[886],[888,88485,88486],{"xmlns":890},[892,88487,88488,88496],{},[895,88489,88490],{},[1707,88491,88492,88494],{},[898,88493,1775],{},[1712,88495,1714],{},[902,88497,27010],{"encoding":904},[883,88499,88501],{"className":88500},[886],[888,88502,88503],{"xmlns":890},[892,88504,88505,88529],{},[895,88506,88507,88509,88515,88517,88523,88525,88527],{},[898,88508,16690],{},[1707,88510,88511,88513],{},[898,88512,1690],{},[898,88514,1775],{},[1716,88516,1920],{"stretchy":1919},[1707,88518,88519,88521],{},[898,88520,1775],{},[1712,88522,1714],{},[1716,88524,1925],{"stretchy":1919},[1716,88526,1913],{},[1712,88528,2505],{},[902,88530,88531],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,88534,88536],{"className":88535},[886],[888,88537,88538],{"xmlns":890},[892,88539,88540,88548],{},[895,88541,88542],{},[1707,88543,88544,88546],{},[898,88545,1775],{},[1712,88547,2505],{},[902,88549,88312],{"encoding":904},[38,88551,88552],{},"inflexním bodem"," produkční funkce.",[724,88555,88556,88557,24198,88574,1853],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,88558,88560],{"className":88559},[886],[888,88561,88562],{"xmlns":890},[892,88563,88564,88572],{},[895,88565,88566],{},[1707,88567,88568,88570],{},[898,88569,1775],{},[1712,88571,2505],{},[902,88573,88312],{"encoding":904},[883,88575,88577],{"className":88576},[886],[888,88578,88579],{"xmlns":890},[892,88580,88581,88603],{},[895,88582,88583,88593,88595,88597,88599,88601],{},[3074,88584,88585,88587],{},[898,88586,1878],{},[895,88588,88589,88591],{},[1716,88590,8505],{"mathvariant":2068},[1716,88592,8505],{"mathvariant":2068},[1716,88594,1920],{"stretchy":1919},[898,88596,1775],{},[1716,88598,1925],{"stretchy":1919},[1716,88600,2704],{},[1712,88602,2505],{},[902,88604,88458],{"encoding":904},[724,88606,88607,3495,88610,3569,88650,1343,88667,88684],{},[38,88608,88609],{},"Typický polynom třetího stupně:",[883,88611,88613],{"className":88612},[886],[888,88614,88615],{"xmlns":890},[892,88616,88617,88647],{},[895,88618,88619,88621,88623,88625,88627,88629,88631,88637,88639,88641],{},[898,88620,1878],{},[1716,88622,1920],{"stretchy":1919},[898,88624,1775],{},[1716,88626,1925],{"stretchy":1919},[1716,88628,1913],{},[898,88630,207],{},[3074,88632,88633,88635],{},[898,88634,1775],{},[1712,88636,7072],{},[1716,88638,1949],{},[898,88640,1952],{},[3074,88642,88643,88645],{},[898,88644,1775],{},[1712,88646,1726],{},[902,88648,88649],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,88651,88653],{"className":88652},[886],[888,88654,88655],{"xmlns":890},[892,88656,88657,88665],{},[895,88658,88659,88661,88663],{},[898,88660,207],{},[1716,88662,2704],{},[1712,88664,2505],{},[902,88666,8067],{"encoding":904},[883,88668,88670],{"className":88669},[886],[888,88671,88672],{"xmlns":890},[892,88673,88674,88682],{},[895,88675,88676,88678,88680],{},[898,88677,1952],{},[1716,88679,2716],{},[1712,88681,2505],{},[902,88683,8085],{"encoding":904},". Pak",[883,88686,88688],{"className":88687},[886],[888,88689,88690],{"xmlns":890,"display":2004},[892,88691,88692,88752],{},[895,88693,88694,88700,88702,88704,88712,88720,88722,88724,88730,88732,88734,88742,88750],{},[1707,88695,88696,88698],{},[898,88697,1775],{},[1712,88699,2505],{},[1716,88701,1913],{},[1716,88703,2760],{},[2747,88705,88706],{"scriptlevel":2505,"displaystyle":1919},[2750,88707,88708,88710],{},[1712,88709,1714],{},[1712,88711,7072],{},[2747,88713,88714],{"scriptlevel":2505,"displaystyle":1919},[2750,88715,88716,88718],{},[898,88717,1952],{},[898,88719,207],{},[1716,88721,1719],{"separator":1718},[2324,88723],{"width":2326},[1707,88725,88726,88728],{},[898,88727,1775],{},[1712,88729,1714],{},[1716,88731,1913],{},[1716,88733,2760],{},[2747,88735,88736],{"scriptlevel":2505,"displaystyle":1919},[2750,88737,88738,88740],{},[1712,88739,1726],{},[1712,88741,7072],{},[2747,88743,88744],{"scriptlevel":2505,"displaystyle":1919},[2750,88745,88746,88748],{},[898,88747,1952],{},[898,88749,207],{},[898,88751,1853],{"mathvariant":2068},[902,88753,88754],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,88756,88758,88759,1925],{"id":88757},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,88760,88762],{"className":88761},[886],[888,88763,88764],{"xmlns":890},[892,88765,88766,88776],{},[895,88767,88768,88770],{},[898,88769,10871],{},[1707,88771,88772,88774],{},[898,88773,1690],{},[898,88775,1775],{},[902,88777,87387],{"encoding":904},[724,88779,88780,1994,88783,87851,88786,88805],{},[38,88781,88782],{},"Průměrný produkt práce",[614,88784,88785],{},"average product of labour",[883,88787,88789],{"className":88788},[886],[888,88790,88791],{"xmlns":890},[892,88792,88793,88803],{},[895,88794,88795,88797],{},[898,88796,10871],{},[1707,88798,88799,88801],{},[898,88800,1690],{},[898,88802,1775],{},[902,88804,87387],{"encoding":904}," je podíl produkce a práce:",[883,88807,88809],{"className":88808},[886],[888,88810,88811],{"xmlns":890,"display":2004},[892,88812,88813,88848],{},[2008,88814,88815],{"width":2010},[2012,88816,88817,88819,88841,88843],{},[2015,88818],{"width":2017},[2015,88820,88821],{},[895,88822,88823,88825,88831,88833,88839],{},[898,88824,10871],{},[1707,88826,88827,88829],{},[898,88828,1690],{},[898,88830,1775],{},[1716,88832,1913],{},[2750,88834,88835,88837],{},[898,88836,1878],{},[898,88838,1775],{},[898,88840,1853],{"mathvariant":2068},[2015,88842],{"width":2017},[2015,88844,88845],{},[2074,88846,88847],{},"(5.4)",[902,88849,88850],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,88852,88853,88854,1853],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,88855,88857],{"className":88856},[886],[888,88858,88859],{"xmlns":890},[892,88860,88861,88871],{},[895,88862,88863,88865],{},[898,88864,10871],{},[1707,88866,88867,88869],{},[898,88868,1690],{},[898,88870,1775],{},[902,88872,87387],{"encoding":904},[115,88874,88876],{"id":88875},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,88878,88879],{},[3682,88880],{"alt":88881,"className":88882,"src":88883},"imek-q-mpl-apl-tripanel",[210,3686],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1635,88885,88886],{},[724,88887,88888,88891,88892,16504,88911,88928,88929],{},[38,88889,88890],{},"Princip:"," Má-li ",[883,88893,88895],{"className":88894},[886],[888,88896,88897],{"xmlns":890},[892,88898,88899,88909],{},[895,88900,88901,88903],{},[898,88902,10871],{},[1707,88904,88905,88907],{},[898,88906,1690],{},[898,88908,1775],{},[902,88910,87387],{"encoding":904},[883,88912,88914],{"className":88913},[886],[888,88915,88916],{"xmlns":890},[892,88917,88918,88926],{},[895,88919,88920],{},[1707,88921,88922,88924],{},[898,88923,1775],{},[1712,88925,2505],{},[902,88927,88312],{"encoding":904}," maximum, pak platí\n",[883,88930,88932],{"className":88931,"title":18041,"style":18042},[18040],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,88934,88935,88936,88939,88940,3495,88944,1853],{},"Slovně: ",[38,88937,88938],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,88941,88943],{"className":88942,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,88945,88947],{"className":88946},[886],[888,88948,88949],{"xmlns":890},[892,88950,88951,88957],{},[895,88952,88953,88955],{},[898,88954,10871],{},[898,88956,9945],{},[902,88958,68314],{"encoding":904},[1635,88960,88961,88985],{},[724,88962,88963,88965,88966],{},[883,88964,3776],{}," Postup — jak najít max ",[883,88967,88969],{"className":88968},[886],[888,88970,88971],{"xmlns":890},[892,88972,88973,88983],{},[895,88974,88975,88977],{},[898,88976,10871],{},[1707,88978,88979,88981],{},[898,88980,1690],{},[898,88982,1775],{},[902,88984,87387],{"encoding":904},[152,88986,88987,89025,89107],{},[123,88988,88989,88990,89024],{},"Napište ",[883,88991,88993],{"className":88992},[886],[888,88994,88995],{"xmlns":890},[892,88996,88997,89021],{},[895,88998,88999,89001,89007,89009,89011,89013,89015,89017,89019],{},[898,89000,10871],{},[1707,89002,89003,89005],{},[898,89004,1690],{},[898,89006,1775],{},[1716,89008,1913],{},[898,89010,1878],{},[1716,89012,1920],{"stretchy":1919},[898,89014,1775],{},[1716,89016,1925],{"stretchy":1919},[898,89018,3045],{"mathvariant":2068},[898,89020,1775],{},[902,89022,89023],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,89026,89027,89028,89060,89061,89064,89065,1853],{},"Položte ",[883,89029,89031],{"className":89030},[886],[888,89032,89033],{"xmlns":890},[892,89034,89035,89057],{},[895,89036,89037,89039,89041,89047,89053,89055],{},[1716,89038,1920],{"stretchy":1919},[898,89040,10871],{},[1707,89042,89043,89045],{},[898,89044,1690],{},[898,89046,1775],{},[3074,89048,89049,89051],{},[1716,89050,1925],{"stretchy":1919},[1716,89052,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,89054,1913],{},[1712,89056,2505],{},[902,89058,89059],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,89062,89063],{},"Zkratka:"," můžete rovnou řešit ",[883,89066,89068],{"className":89067},[886],[888,89069,89070],{"xmlns":890},[892,89071,89072,89104],{},[895,89073,89074,89076,89082,89084,89086,89088,89090,89092,89098,89100,89102],{},[898,89075,16690],{},[1707,89077,89078,89080],{},[898,89079,1690],{},[898,89081,1775],{},[1716,89083,1920],{"stretchy":1919},[898,89085,1775],{},[1716,89087,1925],{"stretchy":1919},[1716,89089,1913],{},[898,89091,10871],{},[1707,89093,89094,89096],{},[898,89095,1690],{},[898,89097,1775],{},[1716,89099,1920],{"stretchy":1919},[898,89101,1775],{},[1716,89103,1925],{"stretchy":1919},[902,89105,89106],{"encoding":904},"MP_L(L) = AP_L(L)",[123,89108,89109],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,89111,78255],{"id":89112},"odvození",[724,89114,89115,89116,89149],{},"Z ",[883,89117,89119],{"className":89118},[886],[888,89120,89121],{"xmlns":890},[892,89122,89123,89147],{},[895,89124,89125,89127,89133,89135,89137,89139,89141,89143,89145],{},[898,89126,10871],{},[1707,89128,89129,89131],{},[898,89130,1690],{},[898,89132,1775],{},[1716,89134,1913],{},[898,89136,1878],{},[1716,89138,1920],{"stretchy":1919},[898,89140,1775],{},[1716,89142,1925],{"stretchy":1919},[898,89144,3045],{"mathvariant":2068},[898,89146,1775],{},[902,89148,89023],{"encoding":904}," a derivace podílu:",[883,89151,89153],{"className":89152},[886],[888,89154,89155],{"xmlns":890,"display":2004},[892,89156,89157,89310],{},[895,89158,89159,89161,89163,89169,89175,89177,89179,89181,89183,89223,89225,89231,89265,89267,89273,89276,89278,89284,89286,89288,89290,89292,89294,89300,89302,89304,89306,89308],{},[1716,89160,1920],{"stretchy":1919},[898,89162,10871],{},[1707,89164,89165,89167],{},[898,89166,1690],{},[898,89168,1775],{},[3074,89170,89171,89173],{},[1716,89172,1925],{"stretchy":1919},[1716,89174,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,89176,1920],{"stretchy":1919},[898,89178,1775],{},[1716,89180,1925],{"stretchy":1919},[1716,89182,1913],{},[2750,89184,89185,89217],{},[895,89186,89187,89193,89195,89197,89199,89201,89203,89205,89207,89209,89211,89213,89215],{},[3074,89188,89189,89191],{},[898,89190,1878],{},[1716,89192,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,89194,1920],{"stretchy":1919},[898,89196,1775],{},[1716,89198,1925],{"stretchy":1919},[1716,89200,9532],{},[898,89202,1775],{},[1716,89204,2760],{},[898,89206,1878],{},[1716,89208,1920],{"stretchy":1919},[898,89210,1775],{},[1716,89212,1925],{"stretchy":1919},[1716,89214,9532],{},[1712,89216,1714],{},[3074,89218,89219,89221],{},[898,89220,1775],{},[1712,89222,1726],{},[1716,89224,1913],{},[2750,89226,89227,89229],{},[1712,89228,1714],{},[898,89230,1775],{},[895,89232,89233,89235,89241,89243,89245,89247,89249,89263],{},[1716,89234,1920],{"fence":1718},[3074,89236,89237,89239],{},[898,89238,1878],{},[1716,89240,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,89242,1920],{"stretchy":1919},[898,89244,1775],{},[1716,89246,1925],{"stretchy":1919},[1716,89248,2760],{},[2750,89250,89251,89261],{},[895,89252,89253,89255,89257,89259],{},[898,89254,1878],{},[1716,89256,1920],{"stretchy":1919},[898,89258,1775],{},[1716,89260,1925],{"stretchy":1919},[898,89262,1775],{},[1716,89264,1925],{"fence":1718},[1716,89266,1913],{},[2750,89268,89269,89271],{},[1712,89270,1714],{},[898,89272,1775],{},[1716,89274,1920],{"fence":1718,"stretchy":1718,"minsize":89275,"maxsize":89275},"1.2em",[898,89277,16690],{},[1707,89279,89280,89282],{},[898,89281,1690],{},[898,89283,1775],{},[1716,89285,1920],{"stretchy":1919},[898,89287,1775],{},[1716,89289,1925],{"stretchy":1919},[1716,89291,2760],{},[898,89293,10871],{},[1707,89295,89296,89298],{},[898,89297,1690],{},[898,89299,1775],{},[1716,89301,1920],{"stretchy":1919},[898,89303,1775],{},[1716,89305,1925],{"stretchy":1919},[1716,89307,1925],{"fence":1718,"stretchy":1718,"minsize":89275,"maxsize":89275},[898,89309,1853],{"mathvariant":2068},[902,89311,89312],{"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).",[724,89314,23470,89315,2574,89337,89420],{},[883,89316,89318],{"className":89317},[886],[888,89319,89320],{"xmlns":890},[892,89321,89322,89334],{},[895,89323,89324,89330,89332],{},[1707,89325,89326,89328],{},[898,89327,1775],{},[1712,89329,2505],{},[1716,89331,2716],{},[1712,89333,2505],{},[902,89335,89336],{"encoding":904},"L_0 > 0",[883,89338,89340],{"className":89339},[886],[888,89341,89342],{"xmlns":890},[892,89343,89344,89417],{},[895,89345,89346,89348,89350,89356,89362,89364,89370,89372,89374,89376,89379,89381,89387,89389,89395,89397,89399,89401,89407,89409,89415],{},[1716,89347,1920],{"stretchy":1919},[898,89349,10871],{},[1707,89351,89352,89354],{},[898,89353,1690],{},[898,89355,1775],{},[3074,89357,89358,89360],{},[1716,89359,1925],{"stretchy":1919},[1716,89361,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,89363,1920],{"stretchy":1919},[1707,89365,89366,89368],{},[898,89367,1775],{},[1712,89369,2505],{},[1716,89371,1925],{"stretchy":1919},[1716,89373,1913],{},[1712,89375,2505],{},[1716,89377,89378],{},"⇔",[898,89380,16690],{},[1707,89382,89383,89385],{},[898,89384,1690],{},[898,89386,1775],{},[1716,89388,1920],{"stretchy":1919},[1707,89390,89391,89393],{},[898,89392,1775],{},[1712,89394,2505],{},[1716,89396,1925],{"stretchy":1919},[1716,89398,1913],{},[898,89400,10871],{},[1707,89402,89403,89405],{},[898,89404,1690],{},[898,89406,1775],{},[1716,89408,1920],{"stretchy":1919},[1707,89410,89411,89413],{},[898,89412,1775],{},[1712,89414,2505],{},[1716,89416,1925],{"stretchy":1919},[902,89418,89419],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,89422,89424],{"id":89423},"příklad-51","Příklad 5.1",[724,89426,89427,89428,1853],{},"Je dána produkce ",[883,89429,89431],{"className":89430},[886],[888,89432,89433],{"xmlns":890},[892,89434,89435,89459],{},[895,89436,89437,89439,89441,89443,89449,89451,89453],{},[898,89438,1878],{},[1716,89440,1913],{},[1712,89442,6231],{},[3074,89444,89445,89447],{},[898,89446,1775],{},[1712,89448,1726],{},[1716,89450,2760],{},[1712,89452,11302],{},[3074,89454,89455,89457],{},[898,89456,1775],{},[1712,89458,7072],{},[902,89460,89461],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,89463,89464,70276,89467,89517,89518,1853],{},[38,89465,89466],{},"(a)",[883,89468,89470],{"className":89469},[886],[888,89471,89472],{"xmlns":890},[892,89473,89474,89514],{},[895,89475,89476,89478,89480,89482,89484,89486,89488,89490,89492,89494,89496,89498,89500,89502,89504,89506,89508,89510,89512],{},[898,89477,1775],{},[1716,89479,1913],{},[1712,89481,1726],{},[1716,89483,1719],{"separator":1718},[1712,89485,6985],{},[1716,89487,1719],{"separator":1718},[1712,89489,12398],{},[1716,89491,1719],{"separator":1718},[1712,89493,2998],{},[1716,89495,1719],{"separator":1718},[1712,89497,6681],{},[1716,89499,1719],{"separator":1718},[1712,89501,14816],{},[1716,89503,1719],{"separator":1718},[1712,89505,2976],{},[1716,89507,1719],{"separator":1718},[1712,89509,3283],{},[1716,89511,1719],{"separator":1718},[1712,89513,5778],{},[902,89515,89516],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,89519,89521],{"className":89520},[886],[888,89522,89523],{"xmlns":890},[892,89524,89525,89535],{},[895,89526,89527,89529],{},[898,89528,16690],{},[1707,89530,89531,89533],{},[898,89532,1690],{},[898,89534,1775],{},[902,89536,23849],{"encoding":904},[724,89538,89539,89540,48728],{},"Podle (5.2): ",[883,89541,89543],{"className":89542},[886],[888,89544,89545],{"xmlns":890},[892,89546,89547,89603],{},[895,89548,89549,89551,89557,89559,89565,89567,89569,89571,89573,89575,89577,89579,89581,89587,89589,89591,89593,89595,89597,89599,89601],{},[898,89550,16690],{},[1707,89552,89553,89555],{},[898,89554,1690],{},[898,89556,1775],{},[1716,89558,1913],{},[3074,89560,89561,89563],{},[898,89562,1878],{},[1716,89564,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,89566,1920],{"stretchy":1919},[898,89568,1775],{},[1716,89570,1925],{"stretchy":1919},[1716,89572,1913],{},[1712,89574,6804],{},[898,89576,1775],{},[1716,89578,2760],{},[1712,89580,9451],{},[3074,89582,89583,89585],{},[898,89584,1775],{},[1712,89586,1726],{},[1716,89588,1913],{},[898,89590,1775],{},[1716,89592,1920],{"stretchy":1919},[1712,89594,6804],{},[1716,89596,2760],{},[1712,89598,9451],{},[898,89600,1775],{},[1716,89602,1925],{"stretchy":1919},[902,89604,89605],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,89607,89608,89645],{},[19,89609,89610],{},[22,89611,89612,89627,89629,89631,89633,89635,89637,89639,89641,89643],{},[25,89613,89614],{},[883,89615,89617],{"className":89616},[886],[888,89618,89619],{"xmlns":890},[892,89620,89621,89625],{},[895,89622,89623],{},[898,89624,1775],{},[902,89626,1775],{"encoding":904},[25,89628,1726],{},[25,89630,6985],{},[25,89632,12398],{},[25,89634,2998],{},[25,89636,6681],{},[25,89638,14816],{},[25,89640,2976],{},[25,89642,3283],{},[25,89644,5778],{},[30,89646,89647],{},[22,89648,89649,89670,89673,89676,89679,89681,89684,89686,89688,89707],{},[35,89650,89651],{},[883,89652,89654],{"className":89653},[886],[888,89655,89656],{"xmlns":890},[892,89657,89658,89668],{},[895,89659,89660,89662],{},[898,89661,16690],{},[1707,89663,89664,89666],{},[898,89665,1690],{},[898,89667,1775],{},[902,89669,23849],{"encoding":904},[35,89671,89672],{},"21,6",[35,89674,89675],{},"45",[35,89677,89678],{},"57,6",[35,89680,2884],{},[35,89682,89683],{},"50,4",[35,89685,89672],{},[35,89687,2505],{},[35,89689,89690],{},[883,89691,89693],{"className":89692},[886],[888,89694,89695],{"xmlns":890},[892,89696,89697,89704],{},[895,89698,89699,89701],{},[1716,89700,2760],{},[1712,89702,89703],{},"12,6",[902,89705,89706],{"encoding":904},"-12{,}6",[35,89708,89709],{},[883,89710,89712],{"className":89711},[886],[888,89713,89714],{"xmlns":890},[892,89715,89716,89722],{},[895,89717,89718,89720],{},[1716,89719,2760],{},[1712,89721,10454],{},[902,89723,89724],{"encoding":904},"-75",[724,89726,89727,89746,89747,89765,89766,89783,89784,89802,89803,89827,89828,89846],{},[883,89728,89730],{"className":89729},[886],[888,89731,89732],{"xmlns":890},[892,89733,89734,89744],{},[895,89735,89736,89738],{},[898,89737,16690],{},[1707,89739,89740,89742],{},[898,89741,1690],{},[898,89743,1775],{},[902,89745,23849],{"encoding":904}," nabývá maxima pro ",[883,89748,89750],{"className":89749},[886],[888,89751,89752],{"xmlns":890},[892,89753,89754,89762],{},[895,89755,89756,89758,89760],{},[898,89757,1775],{},[1716,89759,1913],{},[1712,89761,2998],{},[902,89763,89764],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,89767,89769],{"className":89768},[886],[888,89770,89771],{"xmlns":890},[892,89772,89773,89781],{},[895,89774,89775,89777,89779],{},[898,89776,1775],{},[1716,89778,1913],{},[1712,89780,2998],{},[902,89782,89764],{"encoding":904}," přírůstky klesají, v ",[883,89785,89787],{"className":89786},[886],[888,89788,89789],{"xmlns":890},[892,89790,89791,89799],{},[895,89792,89793,89795,89797],{},[898,89794,1775],{},[1716,89796,1913],{},[1712,89798,2976],{},[902,89800,89801],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,89804,89806],{"className":89805},[886],[888,89807,89808],{"xmlns":890},[892,89809,89810,89824],{},[895,89811,89812,89814,89816,89818,89820,89822],{},[898,89813,1878],{},[1716,89815,1920],{"stretchy":1919},[1712,89817,2976],{},[1716,89819,1925],{"stretchy":1919},[1716,89821,1913],{},[1712,89823,37630],{},[902,89825,89826],{"encoding":904},"Q(20) = 800","), od ",[883,89829,89831],{"className":89830},[886],[888,89832,89833],{"xmlns":890},[892,89834,89835,89843],{},[895,89836,89837,89839,89841],{},[898,89838,1775],{},[1716,89840,2716],{},[1712,89842,2976],{},[902,89844,89845],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,89848,89849],{},[614,89850,89851,89852,89892,89893,16504,89911,1853],{},"Obrázek 5.1 — graf produkce ",[883,89853,89855],{"className":89854},[886],[888,89856,89857],{"xmlns":890},[892,89858,89859,89889],{},[895,89860,89861,89863,89865,89867,89869,89871,89873,89879,89881,89883],{},[898,89862,1878],{},[1716,89864,1920],{"stretchy":1919},[898,89866,1775],{},[1716,89868,1925],{"stretchy":1919},[1716,89870,1913],{},[1712,89872,6231],{},[3074,89874,89875,89877],{},[898,89876,1775],{},[1712,89878,1726],{},[1716,89880,2760],{},[1712,89882,11302],{},[3074,89884,89885,89887],{},[898,89886,1775],{},[1712,89888,7072],{},[902,89890,89891],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,89894,89896],{"className":89895},[886],[888,89897,89898],{"xmlns":890},[892,89899,89900,89908],{},[895,89901,89902,89904,89906],{},[898,89903,1878],{},[1716,89905,1913],{},[1712,89907,37630],{},[902,89909,89910],{"encoding":904},"Q = 800",[883,89912,89914],{"className":89913},[886],[888,89915,89916],{"xmlns":890},[892,89917,89918,89926],{},[895,89919,89920,89922,89924],{},[898,89921,1775],{},[1716,89923,1913],{},[1712,89925,2976],{},[902,89927,89801],{"encoding":904},[724,89929,89930,89933],{},[38,89931,89932],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,89935,89936,89937,1343,89955,2291],{},"Podle (5.3) s ",[883,89938,89940],{"className":89939},[886],[888,89941,89942],{"xmlns":890},[892,89943,89944,89952],{},[895,89945,89946,89948,89950],{},[898,89947,1775],{},[1716,89949,1913],{},[1712,89951,6231],{},[902,89953,89954],{"encoding":904},"L = 6",[883,89956,89958],{"className":89957},[886],[888,89959,89960],{"xmlns":890},[892,89961,89962,89972],{},[895,89963,89964,89966,89968,89970],{},[898,89965,5198],{},[898,89967,1775],{},[1716,89969,1913],{},[1712,89971,7072],{},[902,89973,89974],{"encoding":904},"dL = 3",[883,89976,89978],{"className":89977},[886],[888,89979,89980],{"xmlns":890,"display":2004},[892,89981,89982,90045],{},[895,89983,89984,89986,89988,89990,89992,89998,90000,90002,90004,90006,90008,90010,90012,90014,90016,90018,90020,90022,90024,90026,90028,90030,90032,90034,90036,90038,90040,90042],{},[898,89985,5198],{},[898,89987,1878],{},[1716,89989,1913],{},[898,89991,16690],{},[1707,89993,89994,89996],{},[898,89995,1690],{},[898,89997,1775],{},[1716,89999,1920],{"stretchy":1919},[1712,90001,6231],{},[1716,90003,1925],{"stretchy":1919},[1716,90005,9532],{},[1712,90007,7072],{},[1716,90009,1913],{},[1716,90011,1920],{"stretchy":1919},[1712,90013,6804],{},[1716,90015,9532],{},[1712,90017,6231],{},[1716,90019,2760],{},[1712,90021,9451],{},[1716,90023,9532],{},[1712,90025,19394],{},[1716,90027,1925],{"stretchy":1919},[1716,90029,9532],{},[1712,90031,7072],{},[1716,90033,1913],{},[1712,90035,89683],{},[1716,90037,9532],{},[1712,90039,7072],{},[1716,90041,1913],{},[1712,90043,90044],{},"151,2.",[902,90046,90047],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,90049,90050,90051,70506,90076,90090,90091,1853],{},"Produkce vzroste z ",[883,90052,90054],{"className":90053},[886],[888,90055,90056],{"xmlns":890},[892,90057,90058,90073],{},[895,90059,90060,90062,90064,90066,90068,90070],{},[898,90061,1878],{},[1716,90063,1920],{"stretchy":1919},[1712,90065,6231],{},[1716,90067,1925],{"stretchy":1919},[1716,90069,1913],{},[1712,90071,90072],{},"172,8",[902,90074,90075],{"encoding":904},"Q(6) = 172{,}8",[883,90077,90079],{"className":90078},[886],[888,90080,90081],{"xmlns":890},[892,90082,90083,90088],{},[895,90084,90085],{},[1712,90086,90087],{},"324",[902,90089,90087],{"encoding":904},". Skutečná hodnota: ",[883,90092,90094],{"className":90093},[886],[888,90095,90096],{"xmlns":890},[892,90097,90098,90138],{},[895,90099,90100,90102,90104,90106,90108,90110,90112,90114,90116,90118,90120,90122,90124,90126,90129,90131,90133,90135],{},[898,90101,8485],{"mathvariant":2068},[898,90103,1878],{},[1716,90105,1913],{},[898,90107,1878],{},[1716,90109,1920],{"stretchy":1919},[1712,90111,7141],{},[1716,90113,1925],{"stretchy":1919},[1716,90115,2760],{},[898,90117,1878],{},[1716,90119,1920],{"stretchy":1919},[1712,90121,6231],{},[1716,90123,1925],{"stretchy":1919},[1716,90125,1913],{},[1712,90127,90128],{},"340,2",[1716,90130,2760],{},[1712,90132,90072],{},[1716,90134,1913],{},[1712,90136,90137],{},"167,4",[902,90139,90140],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,90142,90144],{"id":90143},"příklad-52","Příklad 5.2",[724,90146,90147,90148,1853],{},"Ověříme princip (5.5) pro ",[883,90149,90151],{"className":90150},[886],[888,90152,90153],{"xmlns":890},[892,90154,90155,90179],{},[895,90156,90157,90159,90161,90163,90169,90171,90173],{},[898,90158,1878],{},[1716,90160,1913],{},[1712,90162,6231],{},[3074,90164,90165,90167],{},[898,90166,1775],{},[1712,90168,1726],{},[1716,90170,2760],{},[1712,90172,11302],{},[3074,90174,90175,90177],{},[898,90176,1775],{},[1712,90178,7072],{},[902,90180,89461],{"encoding":904},[883,90182,90184],{"className":90183},[886],[888,90185,90186],{"xmlns":890,"display":2004},[892,90187,90188,90266],{},[895,90189,90190,90192,90198,90200,90206,90208,90210,90212,90214,90216,90222,90224,90226,90228,90236,90238,90240,90242,90244,90246,90248,90250,90252,90254,90256,90262,90264],{},[898,90191,10871],{},[1707,90193,90194,90196],{},[898,90195,1690],{},[898,90197,1775],{},[1716,90199,1913],{},[2750,90201,90202,90204],{},[898,90203,1878],{},[898,90205,1775],{},[1716,90207,1913],{},[1712,90209,6231],{},[898,90211,1775],{},[1716,90213,2760],{},[1712,90215,11302],{},[3074,90217,90218,90220],{},[898,90219,1775],{},[1712,90221,1726],{},[1716,90223,1719],{"separator":1718},[2324,90225],{"width":8689},[898,90227,10871],{},[7204,90229,90230,90232,90234],{},[898,90231,1690],{},[898,90233,1775],{},[1716,90235,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,90237,1913],{},[1712,90239,6231],{},[1716,90241,2760],{},[1712,90243,33056],{},[898,90245,1775],{},[1716,90247,1913],{},[1712,90249,2505],{},[2074,90251,17830],{},[1716,90253,17833],{},[2074,90255,17830],{},[1707,90257,90258,90260],{},[898,90259,1775],{},[1712,90261,2505],{},[1716,90263,1913],{},[1712,90265,81037],{},[902,90267,90268],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,90270,90271,90307,90308,90326,90327,1853],{},[883,90272,90274],{"className":90273},[886],[888,90275,90276],{"xmlns":890},[892,90277,90278,90304],{},[895,90279,90280,90282,90294,90296,90298,90300,90302],{},[898,90281,10871],{},[7204,90283,90284,90286,90288],{},[898,90285,1690],{},[898,90287,1775],{},[895,90289,90290,90292],{},[1716,90291,8505],{"mathvariant":2068},[1716,90293,8505],{"mathvariant":2068},[1716,90295,1913],{},[1716,90297,2760],{},[1712,90299,33056],{},[1716,90301,2704],{},[1712,90303,2505],{},[902,90305,90306],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,90309,90311],{"className":90310},[886],[888,90312,90313],{"xmlns":890},[892,90314,90315,90323],{},[895,90316,90317,90319,90321],{},[898,90318,1775],{},[1716,90320,1913],{},[1712,90322,3221],{},[902,90324,90325],{"encoding":904},"L = 15"," je maximum, ",[883,90328,90330],{"className":90329},[886],[888,90331,90332],{"xmlns":890},[892,90333,90334,90380],{},[895,90335,90336,90338,90344,90346,90348,90350,90352,90354,90356,90358,90360,90362,90364,90367,90369,90372,90374,90376,90378],{},[898,90337,10871],{},[1707,90339,90340,90342],{},[898,90341,1690],{},[898,90343,1775],{},[1716,90345,1920],{"stretchy":1919},[1712,90347,3221],{},[1716,90349,1925],{"stretchy":1919},[1716,90351,1913],{},[1712,90353,6231],{},[1716,90355,9532],{},[1712,90357,3221],{},[1716,90359,2760],{},[1712,90361,11302],{},[1716,90363,9532],{},[1712,90365,90366],{},"225",[1716,90368,1913],{},[1712,90370,90371],{},"90",[1716,90373,2760],{},[1712,90375,89675],{},[1716,90377,1913],{},[1712,90379,89675],{},[902,90381,90382],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,90384,90385,6852,90441,90487],{},[883,90386,90388],{"className":90387},[886],[888,90389,90390],{"xmlns":890},[892,90391,90392,90438],{},[895,90393,90394,90396,90402,90404,90406,90408,90410,90412,90414,90416,90418,90420,90422,90424,90426,90429,90431,90434,90436],{},[898,90395,16690],{},[1707,90397,90398,90400],{},[898,90399,1690],{},[898,90401,1775],{},[1716,90403,1920],{"stretchy":1919},[1712,90405,3221],{},[1716,90407,1925],{"stretchy":1919},[1716,90409,1913],{},[1712,90411,6804],{},[1716,90413,9532],{},[1712,90415,3221],{},[1716,90417,2760],{},[1712,90419,9451],{},[1716,90421,9532],{},[1712,90423,90366],{},[1716,90425,1913],{},[1712,90427,90428],{},"180",[1716,90430,2760],{},[1712,90432,90433],{},"135",[1716,90435,1913],{},[1712,90437,89675],{},[902,90439,90440],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,90442,90444],{"className":90443},[886],[888,90445,90446],{"xmlns":890},[892,90447,90448,90484],{},[895,90449,90450,90452,90458,90460,90462,90464,90466,90468,90474,90476,90478,90480,90482],{},[898,90451,16690],{},[1707,90453,90454,90456],{},[898,90455,1690],{},[898,90457,1775],{},[1716,90459,1920],{"stretchy":1919},[1712,90461,3221],{},[1716,90463,1925],{"stretchy":1919},[1716,90465,1913],{},[898,90467,10871],{},[1707,90469,90470,90472],{},[898,90471,1690],{},[898,90473,1775],{},[1716,90475,1920],{"stretchy":1919},[1712,90477,3221],{},[1716,90479,1925],{"stretchy":1919},[1716,90481,1913],{},[1712,90483,89675],{},[902,90485,90486],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,90489,90490,90493,90494,31366,90523,1853],{},[38,90491,90492],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,90495,90497],{"className":90496},[886],[888,90498,90499],{"xmlns":890},[892,90500,90501,90521],{},[895,90502,90503,90505,90511,90513,90515],{},[898,90504,16690],{},[1707,90506,90507,90509],{},[898,90508,1690],{},[898,90510,1775],{},[1716,90512,1913],{},[898,90514,10871],{},[1707,90516,90517,90519],{},[898,90518,1690],{},[898,90520,1775],{},[902,90522,87417],{"encoding":904},[883,90524,90526],{"className":90525},[886],[888,90527,90528],{"xmlns":890},[892,90529,90530,90570],{},[895,90531,90532,90534,90536,90538,90540,90546,90548,90550,90552,90554,90556,90562,90564,90566,90568],{},[1712,90533,6804],{},[898,90535,1775],{},[1716,90537,2760],{},[1712,90539,9451],{},[3074,90541,90542,90544],{},[898,90543,1775],{},[1712,90545,1726],{},[1716,90547,1913],{},[1712,90549,6231],{},[898,90551,1775],{},[1716,90553,2760],{},[1712,90555,11302],{},[3074,90557,90558,90560],{},[898,90559,1775],{},[1712,90561,1726],{},[1716,90563,17833],{},[898,90565,1775],{},[1716,90567,1913],{},[1712,90569,3221],{},[902,90571,90572],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,90574,90575],{},[614,90576,90577,90578,90597,90598,8086,90616,90635,90636,90654,90655,90672,90673,90692,90693,90712],{},"Obrázek 5.3 — křivky ",[883,90579,90581],{"className":90580},[886],[888,90582,90583],{"xmlns":890},[892,90584,90585,90595],{},[895,90586,90587,90589],{},[898,90588,16690],{},[1707,90590,90591,90593],{},[898,90592,1690],{},[898,90594,1775],{},[902,90596,23849],{"encoding":904}," (max 60 při ",[883,90599,90601],{"className":90600},[886],[888,90602,90603],{"xmlns":890},[892,90604,90605,90613],{},[895,90606,90607,90609,90611],{},[898,90608,1775],{},[1716,90610,1913],{},[1712,90612,2998],{},[902,90614,90615],{"encoding":904},"L=10",[883,90617,90619],{"className":90618},[886],[888,90620,90621],{"xmlns":890},[892,90622,90623,90633],{},[895,90624,90625,90627],{},[898,90626,10871],{},[1707,90628,90629,90631],{},[898,90630,1690],{},[898,90632,1775],{},[902,90634,87387],{"encoding":904}," (max 45 při ",[883,90637,90639],{"className":90638},[886],[888,90640,90641],{"xmlns":890},[892,90642,90643,90651],{},[895,90644,90645,90647,90649],{},[898,90646,1775],{},[1716,90648,1913],{},[1712,90650,3221],{},[902,90652,90653],{"encoding":904},"L=15","), průsečík v ",[883,90656,90658],{"className":90657},[886],[888,90659,90660],{"xmlns":890},[892,90661,90662,90670],{},[895,90663,90664,90666,90668],{},[898,90665,1775],{},[1716,90667,1913],{},[1712,90669,3221],{},[902,90671,90325],{"encoding":904},". Nalevo od 15 leží ",[883,90674,90676],{"className":90675},[886],[888,90677,90678],{"xmlns":890},[892,90679,90680,90690],{},[895,90681,90682,90684],{},[898,90683,16690],{},[1707,90685,90686,90688],{},[898,90687,1690],{},[898,90689,1775],{},[902,90691,23849],{"encoding":904}," nad ",[883,90694,90696],{"className":90695},[886],[888,90697,90698],{"xmlns":890},[892,90699,90700,90710],{},[895,90701,90702,90704],{},[898,90703,10871],{},[1707,90705,90706,90708],{},[898,90707,1690],{},[898,90709,1775],{},[902,90711,87387],{"encoding":904},", napravo pod ní.",[115,90714,90716],{"id":90715},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,90718,90719,90720,3942,90733,3495,90736,7364,90749,3495,90752,2291],{},"V dvoufaktorovém modelu závisí produkce ",[883,90721,90723],{"className":90722},[886],[888,90724,90725],{"xmlns":890},[892,90726,90727,90731],{},[895,90728,90729],{},[898,90730,1878],{},[902,90732,1878],{"encoding":904},[38,90734,90735],{},"práci",[883,90737,90739],{"className":90738},[886],[888,90740,90741],{"xmlns":890},[892,90742,90743,90747],{},[895,90744,90745],{},[898,90746,1775],{},[902,90748,1775],{"encoding":904},[38,90750,90751],{},"kapitálu",[883,90753,90755],{"className":90754},[886],[888,90756,90757],{"xmlns":890},[892,90758,90759,90763],{},[895,90760,90761],{},[898,90762,1790],{},[902,90764,1790],{"encoding":904},[883,90766,90768],{"className":90767},[886],[888,90769,90770],{"xmlns":890,"display":2004},[892,90771,90772,90807],{},[2008,90773,90774],{"width":2010},[2012,90775,90776,90778,90800,90802],{},[2015,90777],{"width":2017},[2015,90779,90780],{},[895,90781,90782,90784,90786,90788,90790,90792,90794,90796,90798],{},[898,90783,1878],{},[1716,90785,1913],{},[898,90787,1878],{},[1716,90789,1920],{"stretchy":1919},[898,90791,1775],{},[1716,90793,1719],{"separator":1718},[898,90795,1790],{},[1716,90797,1925],{"stretchy":1919},[898,90799,1853],{"mathvariant":2068},[2015,90801],{"width":2017},[2015,90803,90804],{},[2074,90805,90806],{},"(5.6)",[902,90808,90809],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,90811,90812,90813,90815],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,90814,87754],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,90817,90819],{"id":90818},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,90821,90822],{},"Široce používané produkční funkce mají tvar",[883,90824,90826],{"className":90825},[886],[888,90827,90828],{"xmlns":890,"display":2004},[892,90829,90830,90871],{},[2008,90831,90832],{"width":2010},[2012,90833,90834,90836,90864,90866],{},[2015,90835],{"width":2017},[2015,90837,90838],{},[895,90839,90840,90842,90844,90846,90848,90854,90856,90862],{},[898,90841,1878],{},[1716,90843,1913],{},[898,90845,10871],{},[2074,90847,8508],{},[3074,90849,90850,90852],{},[898,90851,1775],{},[898,90853,207],{},[2074,90855,8508],{},[3074,90857,90858,90860],{},[898,90859,1790],{},[898,90861,1952],{},[1716,90863,1719],{"separator":1718},[2015,90865],{"width":2017},[2015,90867,90868],{},[2074,90869,90870],{},"(5.7)",[902,90872,90873],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,90875,18149,90876,90898,90899,90901,90902,1853],{},[883,90877,90879],{"className":90878},[886],[888,90880,90881],{"xmlns":890},[892,90882,90883,90895],{},[895,90884,90885,90887,90889,90891,90893],{},[898,90886,10871],{},[1716,90888,1719],{"separator":1718},[898,90890,207],{},[1716,90892,1719],{"separator":1718},[898,90894,1952],{},[902,90896,90897],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,90900,87453],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,90903,90905],{"className":90904},[886],[888,90906,90907],{"xmlns":890},[892,90908,90909,90921],{},[895,90910,90911,90913,90915,90917,90919],{},[898,90912,207],{},[1716,90914,1719],{"separator":1718},[898,90916,1952],{},[1716,90918,2704],{},[1712,90920,1714],{},[902,90922,90923],{"encoding":904},"a, b \u003C 1",[724,90925,90926],{},[3682,90927],{"alt":90928,"className":90929,"src":90930},"imek-vynosy-z-rozsahu-3typy",[210,3686],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,90932,90933,90934,90937,90938,3942,90951,90967,90968,3942,90981,2291],{},"Reflektují ekonomickou zákonitost, že ",[38,90935,90936],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,90939,90941],{"className":90940},[886],[888,90942,90943],{"xmlns":890},[892,90944,90945,90949],{},[895,90946,90947],{},[898,90948,1775],{},[902,90950,1775],{"encoding":904},[883,90952,90954],{"className":90953},[886],[888,90955,90956],{"xmlns":890},[892,90957,90958,90964],{},[895,90959,90960,90962],{},[898,90961,2098],{},[898,90963,1775],{},[902,90965,90966],{"encoding":904},"rL"," a kapitál z ",[883,90969,90971],{"className":90970},[886],[888,90972,90973],{"xmlns":890},[892,90974,90975,90979],{},[895,90976,90977],{},[898,90978,1790],{},[902,90980,1790],{"encoding":904},[883,90982,90984],{"className":90983},[886],[888,90985,90986],{"xmlns":890},[892,90987,90988,90994],{},[895,90989,90990,90992],{},[898,90991,2098],{},[898,90993,1790],{},[902,90995,90996],{"encoding":904},"rK",[883,90998,91000],{"className":90999},[886],[888,91001,91002],{"xmlns":890,"display":2004},[892,91003,91004,91127],{},[2008,91005,91006],{"width":2010},[2012,91007,91008,91010,91120,91122],{},[2015,91009],{"width":2017},[2015,91011,91012],{},[895,91013,91014,91016,91018,91020,91022,91024,91026,91028,91030,91032,91034,91036,91038,91040,91046,91048,91050,91052,91058,91060,91062,91064,91076,91078,91084,91090,91092,91104,91106,91108,91110,91112,91114,91116,91118],{},[898,91015,1878],{},[1716,91017,1920],{"stretchy":1919},[898,91019,2098],{},[898,91021,1775],{},[1716,91023,1719],{"separator":1718},[898,91025,2098],{},[898,91027,1790],{},[1716,91029,1925],{"stretchy":1919},[1716,91031,1913],{},[898,91033,10871],{},[1716,91035,1920],{"stretchy":1919},[898,91037,2098],{},[898,91039,1775],{},[3074,91041,91042,91044],{},[1716,91043,1925],{"stretchy":1919},[898,91045,207],{},[1716,91047,1920],{"stretchy":1919},[898,91049,2098],{},[898,91051,1790],{},[3074,91053,91054,91056],{},[1716,91055,1925],{"stretchy":1919},[898,91057,1952],{},[1716,91059,1913],{},[898,91061,10871],{},[2074,91063,8508],{},[3074,91065,91066,91068],{},[898,91067,2098],{},[895,91069,91070,91072,91074],{},[898,91071,207],{},[1716,91073,1949],{},[898,91075,1952],{},[2074,91077,8508],{},[3074,91079,91080,91082],{},[898,91081,1775],{},[898,91083,207],{},[3074,91085,91086,91088],{},[898,91087,1790],{},[898,91089,1952],{},[1716,91091,1913],{},[3074,91093,91094,91096],{},[898,91095,2098],{},[895,91097,91098,91100,91102],{},[898,91099,207],{},[1716,91101,1949],{},[898,91103,1952],{},[2074,91105,8508],{},[898,91107,1878],{},[1716,91109,1920],{"stretchy":1919},[898,91111,1775],{},[1716,91113,1719],{"separator":1718},[898,91115,1790],{},[1716,91117,1925],{"stretchy":1919},[898,91119,1853],{"mathvariant":2068},[2015,91121],{"width":2017},[2015,91123,91124],{},[2074,91125,91126],{},"(5.8)",[902,91128,91129],{"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}",[724,91131,91132,91133],{},"Volně: ",[38,91134,91135,91136,91149,91150,91174],{},"změní-li se vstupy ",[883,91137,91139],{"className":91138},[886],[888,91140,91141],{"xmlns":890},[892,91142,91143,91147],{},[895,91144,91145],{},[898,91146,2098],{},[902,91148,2098],{"encoding":904},"-krát, změní se výstup ",[883,91151,91153],{"className":91152},[886],[888,91154,91155],{"xmlns":890},[892,91156,91157,91171],{},[895,91158,91159],{},[3074,91160,91161,91163],{},[898,91162,2098],{},[895,91164,91165,91167,91169],{},[898,91166,207],{},[1716,91168,1949],{},[898,91170,1952],{},[902,91172,91173],{"encoding":904},"r^{a+b}","-krát.",[198,91176,91178],{"id":91177},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,91180,91181,91182,91199],{},"Součet exponentů ",[883,91183,91185],{"className":91184},[886],[888,91186,91187],{"xmlns":890},[892,91188,91189,91197],{},[895,91190,91191,91193,91195],{},[898,91192,207],{},[1716,91194,1949],{},[898,91196,1952],{},[902,91198,87578],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,91201,91202,91231],{},[19,91203,91204],{},[22,91205,91206,91209,91212,91229],{},[25,91207,91208],{},"Typ",[25,91210,91211],{},"Podmínka",[25,91213,91214,91215,91228],{},"Chování produkce při ",[883,91216,91218],{"className":91217},[886],[888,91219,91220],{"xmlns":890},[892,91221,91222,91226],{},[895,91223,91224],{},[898,91225,2098],{},[902,91227,2098],{"encoding":904},"-násobném zvýšení vstupů",[25,91230,16935],{},[30,91232,91233,91344,91459],{},[22,91234,91235,91243,91267,91300],{},[35,91236,88291,91237,1994,91240,1925],{},[38,91238,91239],{},"Konstantní",[614,91241,91242],{},"constant returns",[35,91244,91245],{},[883,91246,91248],{"className":91247},[886],[888,91249,91250],{"xmlns":890},[892,91251,91252,91264],{},[895,91253,91254,91256,91258,91260,91262],{},[898,91255,207],{},[1716,91257,1949],{},[898,91259,1952],{},[1716,91261,1913],{},[1712,91263,1714],{},[902,91265,91266],{"encoding":904},"a+b = 1",[35,91268,91269,91282,91283,3495,91286,91299],{},[883,91270,91272],{"className":91271},[886],[888,91273,91274],{"xmlns":890},[892,91275,91276,91280],{},[895,91277,91278],{},[898,91279,1878],{},[902,91281,1878],{"encoding":904}," vzroste ",[38,91284,91285],{},"přesně",[883,91287,91289],{"className":91288},[886],[888,91290,91291],{"xmlns":890},[892,91292,91293,91297],{},[895,91294,91295],{},[898,91296,2098],{},[902,91298,2098],{"encoding":904},"-krát",[35,91301,91302],{},[883,91303,91305],{"className":91304},[886],[888,91306,91307],{"xmlns":890},[892,91308,91309,91341],{},[895,91310,91311,91313,91315,91317,91329],{},[898,91312,1878],{},[1716,91314,1913],{},[1712,91316,1726],{},[3074,91318,91319,91321],{},[898,91320,1775],{},[895,91322,91323,91325,91327],{},[1712,91324,1714],{},[898,91326,3045],{"mathvariant":2068},[1712,91328,6849],{},[3074,91330,91331,91333],{},[898,91332,1790],{},[895,91334,91335,91337,91339],{},[1712,91336,7072],{},[898,91338,3045],{"mathvariant":2068},[1712,91340,6849],{},[902,91342,91343],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,91345,91346,91355,91379,91409],{},[35,91347,91348,91349,1994,91352,1925],{},"2° ",[38,91350,91351],{},"Rostoucí",[614,91353,91354],{},"increasing returns",[35,91356,91357],{},[883,91358,91360],{"className":91359},[886],[888,91361,91362],{"xmlns":890},[892,91363,91364,91376],{},[895,91365,91366,91368,91370,91372,91374],{},[898,91367,207],{},[1716,91369,1949],{},[898,91371,1952],{},[1716,91373,2716],{},[1712,91375,1714],{},[902,91377,91378],{"encoding":904},"a+b > 1",[35,91380,91381,91282,91394,63985,91396,91299],{},[883,91382,91384],{"className":91383},[886],[888,91385,91386],{"xmlns":890},[892,91387,91388,91392],{},[895,91389,91390],{},[898,91391,1878],{},[902,91393,1878],{"encoding":904},[38,91395,39040],{},[883,91397,91399],{"className":91398},[886],[888,91400,91401],{"xmlns":890},[892,91402,91403,91407],{},[895,91404,91405],{},[898,91406,2098],{},[902,91408,2098],{"encoding":904},[35,91410,91411,1994,91437,1925],{},[883,91412,91414],{"className":91413},[886],[888,91415,91416],{"xmlns":890},[892,91417,91418,91434],{},[895,91419,91420,91422,91424,91426,91428],{},[898,91421,1878],{},[1716,91423,1913],{},[1712,91425,7109],{},[898,91427,1775],{},[3074,91429,91430,91432],{},[898,91431,1790],{},[1712,91433,1726],{},[902,91435,91436],{"encoding":904},"Q = 7LK^2",[883,91438,91440],{"className":91439},[886],[888,91441,91442],{"xmlns":890},[892,91443,91444,91456],{},[895,91445,91446,91448,91450,91452,91454],{},[898,91447,207],{},[1716,91449,1949],{},[898,91451,1952],{},[1716,91453,1913],{},[1712,91455,7072],{},[902,91457,91458],{"encoding":904},"a+b = 3",[22,91460,91461,91470,91494,91525],{},[35,91462,91463,91464,1994,91467,1925],{},"3° ",[38,91465,91466],{},"Klesající",[614,91468,91469],{},"decreasing returns",[35,91471,91472],{},[883,91473,91475],{"className":91474},[886],[888,91476,91477],{"xmlns":890},[892,91478,91479,91491],{},[895,91480,91481,91483,91485,91487,91489],{},[898,91482,207],{},[1716,91484,1949],{},[898,91486,1952],{},[1716,91488,2704],{},[1712,91490,1714],{},[902,91492,91493],{"encoding":904},"a+b \u003C 1",[35,91495,91496,91282,91509,63985,91512,91299],{},[883,91497,91499],{"className":91498},[886],[888,91500,91501],{"xmlns":890},[892,91502,91503,91507],{},[895,91504,91505],{},[898,91506,1878],{},[902,91508,1878],{"encoding":904},[38,91510,91511],{},"méně",[883,91513,91515],{"className":91514},[886],[888,91516,91517],{"xmlns":890},[892,91518,91519,91523],{},[895,91520,91521],{},[898,91522,2098],{},[902,91524,2098],{"encoding":904},[35,91526,91527,1994,91557,1925],{},[883,91528,91530],{"className":91529},[886],[888,91531,91532],{"xmlns":890},[892,91533,91534,91554],{},[895,91535,91536,91538,91540,91542,91548],{},[898,91537,1878],{},[1716,91539,1913],{},[1712,91541,2998],{},[3074,91543,91544,91546],{},[898,91545,1775],{},[1712,91547,80965],{},[3074,91549,91550,91552],{},[898,91551,1790],{},[1712,91553,5771],{},[902,91555,91556],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,91558,91560],{"className":91559},[886],[888,91561,91562],{"xmlns":890},[892,91563,91564,91576],{},[895,91565,91566,91568,91570,91572,91574],{},[898,91567,207],{},[1716,91569,1949],{},[898,91571,1952],{},[1716,91573,1913],{},[1712,91575,13254],{},[902,91577,91578],{"encoding":904},"a+b = 0{,}8",[1635,91580,91581],{},[724,91582,91583,91585,91586,91603,91604,91607,91608,3495,91611,91647,91648,91670,91671,1853],{},[883,91584,2233],{}," Pozor\nSoučet ",[883,91587,91589],{"className":91588},[886],[888,91590,91591],{"xmlns":890},[892,91592,91593,91601],{},[895,91594,91595,91597,91599],{},[898,91596,207],{},[1716,91598,1949],{},[898,91600,1952],{},[902,91602,87578],{"encoding":904}," neudává velikost produkce, ale ",[38,91605,91606],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,91609,91610],{},"ryzí Cobb-Douglas",[883,91612,91614],{"className":91613},[886],[888,91615,91616],{"xmlns":890},[892,91617,91618,91644],{},[895,91619,91620,91622,91624,91626,91632],{},[898,91621,1878],{},[1716,91623,1913],{},[898,91625,10871],{},[3074,91627,91628,91630],{},[898,91629,1775],{},[898,91631,207],{},[3074,91633,91634,91636],{},[898,91635,1790],{},[895,91637,91638,91640,91642],{},[1712,91639,1714],{},[1716,91641,2760],{},[898,91643,207],{},[902,91645,91646],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,91649,91651],{"className":91650},[886],[888,91652,91653],{"xmlns":890},[892,91654,91655,91667],{},[895,91656,91657,91659,91661,91663,91665],{},[898,91658,1952],{},[1716,91660,1913],{},[1712,91662,1714],{},[1716,91664,2760],{},[898,91666,207],{},[902,91668,91669],{"encoding":904},"b = 1-a",", tedy vždy ",[38,91672,91673],{},"konstantní výnosy z rozsahu",[198,91675,91677,91678],{"id":91676},"parametr-efektivity-aa","Parametr efektivity ",[883,91679,91681],{"className":91680},[886],[888,91682,91683],{"xmlns":890},[892,91684,91685,91689],{},[895,91686,91687],{},[898,91688,10871],{},[902,91690,10871],{"encoding":904},[724,91692,91693,91694,91707,91708,91721,91722,91740,91741,91744],{},"Konstanta ",[883,91695,91697],{"className":91696},[886],[888,91698,91699],{"xmlns":890},[892,91700,91701,91705],{},[895,91702,91703],{},[898,91704,10871],{},[902,91706,10871],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,91709,91711],{"className":91710},[886],[888,91712,91713],{"xmlns":890},[892,91714,91715,91719],{},[895,91716,91717],{},[898,91718,1878],{},[902,91720,1878],{"encoding":904}," při pevně zadaných ",[883,91723,91725],{"className":91724},[886],[888,91726,91727],{"xmlns":890},[892,91728,91729,91737],{},[895,91730,91731,91733,91735],{},[898,91732,1775],{},[1716,91734,1719],{"separator":1718},[898,91736,1790],{},[902,91738,91739],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,91742,91743],{},"parametr efektivity"," — indikátor stavu technologie.",[198,91746,91748],{"id":91747},"příklad-53","Příklad 5.3",[724,91750,91751,91752,91647,91794,91796,91797,1853],{},"Produkční funkce ",[883,91753,91755],{"className":91754},[886],[888,91756,91757],{"xmlns":890},[892,91758,91759,91791],{},[895,91760,91761,91763,91765,91767,91779],{},[898,91762,1878],{},[1716,91764,1913],{},[1712,91766,1726],{},[3074,91768,91769,91771],{},[898,91770,1775],{},[895,91772,91773,91775,91777],{},[1712,91774,1714],{},[898,91776,3045],{"mathvariant":2068},[1712,91778,6849],{},[3074,91780,91781,91783],{},[898,91782,1790],{},[895,91784,91785,91787,91789],{},[1712,91786,7072],{},[898,91788,3045],{"mathvariant":2068},[1712,91790,6849],{},[902,91792,91793],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,91795,38384],{}," výnosy z rozsahu, neboť ",[883,91798,91800],{"className":91799},[886],[888,91801,91802],{"xmlns":890},[892,91803,91804,91828],{},[895,91805,91806,91814,91816,91824,91826],{},[2747,91807,91808],{"scriptlevel":2505,"displaystyle":1919},[2750,91809,91810,91812],{},[1712,91811,1714],{},[1712,91813,6849],{},[1716,91815,1949],{},[2747,91817,91818],{"scriptlevel":2505,"displaystyle":1919},[2750,91819,91820,91822],{},[1712,91821,7072],{},[1712,91823,6849],{},[1716,91825,1913],{},[1712,91827,1714],{},[902,91829,91830],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,91832,91833,91834,7364,91847,91860,91861,3495,91874,91914],{},"Změní-li se ",[883,91835,91837],{"className":91836},[886],[888,91838,91839],{"xmlns":890},[892,91840,91841,91845],{},[895,91842,91843],{},[898,91844,1775],{},[902,91846,1775],{"encoding":904},[883,91848,91850],{"className":91849},[886],[888,91851,91852],{"xmlns":890},[892,91853,91854,91858],{},[895,91855,91856],{},[898,91857,1790],{},[902,91859,1790],{"encoding":904}," čtyřnásobně, změní se ",[883,91862,91864],{"className":91863},[886],[888,91865,91866],{"xmlns":890},[892,91867,91868,91872],{},[895,91869,91870],{},[898,91871,1878],{},[902,91873,1878],{"encoding":904},[883,91875,91877],{"className":91876},[886],[888,91878,91879],{"xmlns":890},[892,91880,91881,91911],{},[895,91882,91883,91903,91905],{},[3074,91884,91885,91887],{},[1712,91886,6849],{},[895,91888,91889,91891,91893,91895,91897,91899,91901],{},[1712,91890,1714],{},[898,91892,3045],{"mathvariant":2068},[1712,91894,6849],{},[1716,91896,1949],{},[1712,91898,7072],{},[898,91900,3045],{"mathvariant":2068},[1712,91902,6849],{},[1716,91904,1913],{},[3074,91906,91907,91909],{},[1712,91908,6849],{},[1712,91910,1714],{},[902,91912,91913],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,91916,91918],{"className":91917},[886],[888,91919,91920],{"xmlns":890,"display":2004},[892,91921,91922,92082],{},[895,91923,91924,91926,91928,91930,91932,91934,91936,91938,91940,91942,91944,91946,91948,91950,91962,91964,91966,91968,91980,91982,91984,91986,92006,92018,92030,92032,92034,92036,92038,92050,92062,92064,92066,92068,92070,92072,92074,92076,92078,92080],{},[898,91925,1878],{},[1716,91927,1920],{"stretchy":1919},[1712,91929,6849],{},[898,91931,1775],{},[1716,91933,1719],{"separator":1718},[1712,91935,6849],{},[898,91937,1790],{},[1716,91939,1925],{"stretchy":1919},[1716,91941,1913],{},[1712,91943,1726],{},[1716,91945,1920],{"stretchy":1919},[1712,91947,6849],{},[898,91949,1775],{},[3074,91951,91952,91954],{},[1716,91953,1925],{"stretchy":1919},[895,91955,91956,91958,91960],{},[1712,91957,1714],{},[898,91959,3045],{"mathvariant":2068},[1712,91961,6849],{},[1716,91963,1920],{"stretchy":1919},[1712,91965,6849],{},[898,91967,1790],{},[3074,91969,91970,91972],{},[1716,91971,1925],{"stretchy":1919},[895,91973,91974,91976,91978],{},[1712,91975,7072],{},[898,91977,3045],{"mathvariant":2068},[1712,91979,6849],{},[1716,91981,1913],{},[1712,91983,1726],{},[1716,91985,9532],{},[3074,91987,91988,91990],{},[1712,91989,6849],{},[895,91991,91992,91994,91996,91998,92000,92002,92004],{},[1712,91993,1714],{},[898,91995,3045],{"mathvariant":2068},[1712,91997,6849],{},[1716,91999,1949],{},[1712,92001,7072],{},[898,92003,3045],{"mathvariant":2068},[1712,92005,6849],{},[3074,92007,92008,92010],{},[898,92009,1775],{},[895,92011,92012,92014,92016],{},[1712,92013,1714],{},[898,92015,3045],{"mathvariant":2068},[1712,92017,6849],{},[3074,92019,92020,92022],{},[898,92021,1790],{},[895,92023,92024,92026,92028],{},[1712,92025,7072],{},[898,92027,3045],{"mathvariant":2068},[1712,92029,6849],{},[1716,92031,1913],{},[1712,92033,6849],{},[1716,92035,9532],{},[1712,92037,1726],{},[3074,92039,92040,92042],{},[898,92041,1775],{},[895,92043,92044,92046,92048],{},[1712,92045,1714],{},[898,92047,3045],{"mathvariant":2068},[1712,92049,6849],{},[3074,92051,92052,92054],{},[898,92053,1790],{},[895,92055,92056,92058,92060],{},[1712,92057,7072],{},[898,92059,3045],{"mathvariant":2068},[1712,92061,6849],{},[1716,92063,1913],{},[1712,92065,6849],{},[2074,92067,8508],{},[898,92069,1878],{},[1716,92071,1920],{"stretchy":1919},[898,92073,1775],{},[1716,92075,1719],{"separator":1718},[898,92077,1790],{},[1716,92079,1925],{"stretchy":1919},[898,92081,1853],{"mathvariant":2068},[902,92083,92084],{"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).",[198,92086,92087],{"id":2085},"Homogenita",[724,92089,92090,92091,2574,92114,92130],{},"Funkce ",[883,92092,92094],{"className":92093},[886],[888,92095,92096],{"xmlns":890},[892,92097,92098,92112],{},[895,92099,92100,92102,92104,92106,92108,92110],{},[898,92101,1878],{},[1716,92103,1920],{"stretchy":1919},[898,92105,1775],{},[1716,92107,1719],{"separator":1718},[898,92109,1790],{},[1716,92111,1925],{"stretchy":1919},[902,92113,23802],{"encoding":904},[38,92115,92116,92117],{},"homogenní stupně ",[883,92118,92120],{"className":92119},[886],[888,92121,92122],{"xmlns":890},[892,92123,92124,92128],{},[895,92125,92126],{},[898,92127,1740],{},[902,92129,1740],{"encoding":904},", jestliže",[883,92132,92134],{"className":92133},[886],[888,92135,92136],{"xmlns":890,"display":2004},[892,92137,92138,92195],{},[2008,92139,92140],{"width":2010},[2012,92141,92142,92144,92188,92190],{},[2015,92143],{"width":2017},[2015,92145,92146],{},[895,92147,92148,92150,92152,92154,92156,92158,92160,92162,92164,92166,92172,92174,92176,92178,92180,92182,92184,92186],{},[898,92149,1878],{},[1716,92151,1920],{"stretchy":1919},[898,92153,2098],{},[898,92155,1775],{},[1716,92157,1719],{"separator":1718},[898,92159,2098],{},[898,92161,1790],{},[1716,92163,1925],{"stretchy":1919},[1716,92165,1913],{},[3074,92167,92168,92170],{},[898,92169,2098],{},[898,92171,1740],{},[2074,92173,8508],{},[898,92175,1878],{},[1716,92177,1920],{"stretchy":1919},[898,92179,1775],{},[1716,92181,1719],{"separator":1718},[898,92183,1790],{},[1716,92185,1925],{"stretchy":1919},[1716,92187,1719],{"separator":1718},[2015,92189],{"width":2017},[2015,92191,92192],{},[2074,92193,92194],{},"(5.10)",[902,92196,92197],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,92199,18149,92200,92218,92219,92237,92238,8626,92251,92254,92255,1853],{},[883,92201,92203],{"className":92202},[886],[888,92204,92205],{"xmlns":890},[892,92206,92207,92215],{},[895,92208,92209,92211,92213],{},[898,92210,1740],{},[1716,92212,18320],{},[1712,92214,2505],{},[902,92216,92217],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,92220,92222],{"className":92221},[886],[888,92223,92224],{"xmlns":890},[892,92225,92226,92234],{},[895,92227,92228,92230,92232],{},[898,92229,2098],{},[1716,92231,2716],{},[1712,92233,2505],{},[902,92235,92236],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,92239,92241],{"className":92240},[886],[888,92242,92243],{"xmlns":890},[892,92244,92245,92249],{},[895,92246,92247],{},[1712,92248,1714],{},[902,92250,1714],{"encoding":904},[38,92252,92253],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,92256,92258],{"className":92257},[886],[888,92259,92260],{"xmlns":890},[892,92261,92262,92270],{},[895,92263,92264,92266,92268],{},[898,92265,207],{},[1716,92267,1949],{},[898,92269,1952],{},[902,92271,87578],{"encoding":904},[115,92273,92275],{"id":92274},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,92277,92278],{},[38,92279,92280],{},"Ryzí Cobb-Douglasovy funkce:",[883,92282,92284],{"className":92283},[886],[888,92285,92286],{"xmlns":890,"display":2004},[892,92287,92288,92347],{},[2008,92289,92290],{"width":2010},[2012,92291,92292,92294,92340,92342],{},[2015,92293],{"width":2017},[2015,92295,92296],{},[895,92297,92298,92300,92302,92304,92306,92312,92314,92326,92328,92330,92332,92334,92336,92338],{},[898,92299,1878],{},[1716,92301,1913],{},[898,92303,10871],{},[2074,92305,8508],{},[3074,92307,92308,92310],{},[898,92309,1775],{},[898,92311,207],{},[2074,92313,8508],{},[3074,92315,92316,92318],{},[898,92317,1790],{},[895,92319,92320,92322,92324],{},[1712,92321,1714],{},[1716,92323,2760],{},[898,92325,207],{},[1716,92327,1719],{"separator":1718},[2324,92329],{"width":8689},[1712,92331,2505],{},[1716,92333,2704],{},[898,92335,207],{},[1716,92337,2704],{},[1712,92339,27058],{},[2015,92341],{"width":2017},[2015,92343,92344],{},[2074,92345,92346],{},"(5.9)",[902,92348,92349],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,92351,92352,92353,92355,92356,1853],{},"Mají vždy ",[38,92354,91673],{}," a jsou ",[38,92357,92253],{},[724,92359,92360,1994,92363,92366],{},[38,92361,92362],{},"CES produkční funkce",[614,92364,92365],{},"Constant Elasticity of Substitution",", 1961):",[883,92368,92370],{"className":92369},[886],[888,92371,92372],{"xmlns":890,"display":2004},[892,92373,92374,92442],{},[895,92375,92376,92378,92380,92382,92440],{},[898,92377,1878],{},[1716,92379,1913],{},[898,92381,10871],{},[3074,92383,92384,92428],{},[895,92385,92386,92388,92390,92392,92394,92396,92398,92400,92410,92412,92414,92416,92426],{},[1716,92387,2502],{"fence":1718},[1716,92389,1920],{"stretchy":1919},[1712,92391,1714],{},[1716,92393,2760],{},[898,92395,207],{},[1716,92397,1925],{"stretchy":1919},[2074,92399,8508],{},[3074,92401,92402,92404],{},[898,92403,1775],{},[895,92405,92406,92408],{},[1716,92407,2760],{},[898,92409,1952],{},[1716,92411,1949],{},[898,92413,207],{},[2074,92415,8508],{},[3074,92417,92418,92420],{},[898,92419,1790],{},[895,92421,92422,92424],{},[1716,92423,2760],{},[898,92425,1952],{},[1716,92427,2516],{"fence":1718},[895,92429,92430,92432],{},[1716,92431,2760],{},[2747,92433,92434],{"scriptlevel":2505,"displaystyle":1919},[2750,92435,92436,92438],{},[1712,92437,1714],{},[898,92439,1952],{},[1716,92441,1719],{"separator":1718},[902,92443,92444],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,92446,18149,92447,1343,92465,1343,92486,92510],{},[883,92448,92450],{"className":92449},[886],[888,92451,92452],{"xmlns":890},[892,92453,92454,92462],{},[895,92455,92456,92458,92460],{},[898,92457,10871],{},[1716,92459,2716],{},[1712,92461,2505],{},[902,92463,92464],{"encoding":904},"A > 0",[883,92466,92468],{"className":92467},[886],[888,92469,92470],{"xmlns":890},[892,92471,92472,92484],{},[895,92473,92474,92476,92478,92480,92482],{},[1712,92475,2505],{},[1716,92477,2704],{},[898,92479,207],{},[1716,92481,2704],{},[1712,92483,1714],{},[902,92485,32621],{"encoding":904},[883,92487,92489],{"className":92488},[886],[888,92490,92491],{"xmlns":890},[892,92492,92493,92507],{},[895,92494,92495,92497,92499,92501,92503,92505],{},[1716,92496,2760],{},[1712,92498,1714],{},[1716,92500,2704],{},[898,92502,1952],{},[1716,92504,17231],{"mathvariant":2068},[1712,92506,2505],{},[902,92508,92509],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,92512,92513],{},[38,92514,92515],{},"Další typy:",[120,92517,92518,92560],{},[123,92519,92520,3495,92523,92559],{},[38,92521,92522],{},"Lineární:",[883,92524,92526],{"className":92525},[886],[888,92527,92528],{"xmlns":890},[892,92529,92530,92556],{},[895,92531,92532,92534,92536,92538,92540,92542,92544,92546,92548,92550,92552,92554],{},[898,92533,1878],{},[1716,92535,1920],{"stretchy":1919},[898,92537,1775],{},[1716,92539,1719],{"separator":1718},[898,92541,1790],{},[1716,92543,1925],{"stretchy":1919},[1716,92545,1913],{},[898,92547,207],{},[898,92549,1775],{},[1716,92551,1949],{},[898,92553,1952],{},[898,92555,1790],{},[902,92557,92558],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,92561,92562,3495,92565,92610],{},[38,92563,92564],{},"Leontiefova:",[883,92566,92568],{"className":92567},[886],[888,92569,92570],{"xmlns":890},[892,92571,92572,92607],{},[895,92573,92574,92576,92578,92580,92582,92584,92586,92588,92591,92593,92595,92597,92599,92601,92603,92605],{},[898,92575,1878],{},[1716,92577,1920],{"stretchy":1919},[898,92579,1775],{},[1716,92581,1719],{"separator":1718},[898,92583,1790],{},[1716,92585,1925],{"stretchy":1919},[1716,92587,1913],{},[898,92589,92590],{},"min",[1716,92592,68954],{},[1716,92594,1920],{"stretchy":1919},[898,92596,207],{},[898,92598,1775],{},[1716,92600,1719],{"separator":1718},[898,92602,1952],{},[898,92604,1790],{},[1716,92606,1925],{"stretchy":1919},[902,92608,92609],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,92612,92614,92615,1343,92634,92653],{"id":92613},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,92616,92618],{"className":92617},[886],[888,92619,92620],{"xmlns":890},[892,92621,92622,92632],{},[895,92623,92624,92626],{},[898,92625,16690],{},[1707,92627,92628,92630],{},[898,92629,1690],{},[898,92631,1775],{},[902,92633,23849],{"encoding":904},[883,92635,92637],{"className":92636},[886],[888,92638,92639],{"xmlns":890},[892,92640,92641,92651],{},[895,92642,92643,92645],{},[898,92644,16690],{},[1707,92646,92647,92649],{},[898,92648,1690],{},[898,92650,1790],{},[902,92652,23894],{"encoding":904}," a totální diferenciál",[724,92655,92656],{},[38,92657,92658],{},"Mezní produkt práce:",[883,92660,92662],{"className":92661},[886],[888,92663,92664],{"xmlns":890,"display":2004},[892,92665,92666,92704],{},[895,92667,92668,92670,92676,92678,92686,92688,92702],{},[898,92669,16690],{},[1707,92671,92672,92674],{},[898,92673,1690],{},[898,92675,1775],{},[1716,92677,1913],{},[7204,92679,92680,92682,92684],{},[898,92681,1878],{},[898,92683,1775],{},[1716,92685,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,92687,1913],{},[2750,92689,92690,92696],{},[895,92691,92692,92694],{},[898,92693,23677],{"mathvariant":2068},[898,92695,1878],{},[895,92697,92698,92700],{},[898,92699,23677],{"mathvariant":2068},[898,92701,1775],{},[898,92703,1853],{"mathvariant":2068},[902,92705,92706],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,92708,92709],{},[38,92710,92711],{},"Mezní produkt kapitálu:",[883,92713,92715],{"className":92714},[886],[888,92716,92717],{"xmlns":890,"display":2004},[892,92718,92719,92757],{},[895,92720,92721,92723,92729,92731,92739,92741,92755],{},[898,92722,16690],{},[1707,92724,92725,92727],{},[898,92726,1690],{},[898,92728,1790],{},[1716,92730,1913],{},[7204,92732,92733,92735,92737],{},[898,92734,1878],{},[898,92736,1790],{},[1716,92738,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,92740,1913],{},[2750,92742,92743,92749],{},[895,92744,92745,92747],{},[898,92746,23677],{"mathvariant":2068},[898,92748,1878],{},[895,92750,92751,92753],{},[898,92752,23677],{"mathvariant":2068},[898,92754,1790],{},[898,92756,1853],{"mathvariant":2068},[902,92758,92759],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,92761,92762,92792,92793,92814,92815,92833,92834,92847,92848,1853],{},[883,92763,92765],{"className":92764},[886],[888,92766,92767],{"xmlns":890},[892,92768,92769,92789],{},[895,92770,92771,92773,92779,92781,92783,92785,92787],{},[898,92772,16690],{},[1707,92774,92775,92777],{},[898,92776,1690],{},[898,92778,1775],{},[1716,92780,1920],{"stretchy":1919},[898,92782,207],{},[1716,92784,1719],{"separator":1718},[898,92786,1952],{},[1716,92788,1925],{"stretchy":1919},[902,92790,92791],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,92794,92796],{"className":92795},[886],[888,92797,92798],{"xmlns":890},[892,92799,92800,92812],{},[895,92801,92802,92804,92806,92808,92810],{},[1716,92803,2502],{"stretchy":1919},[898,92805,207],{},[1716,92807,1719],{"separator":1718},[898,92809,1952],{},[1716,92811,2516],{"stretchy":1919},[902,92813,24628],{"encoding":904}," (na hladině ",[883,92816,92818],{"className":92817},[886],[888,92819,92820],{"xmlns":890},[892,92821,92822,92830],{},[895,92823,92824,92826,92828],{},[898,92825,1790],{},[1716,92827,1913],{},[898,92829,1952],{},[902,92831,92832],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,92835,92837],{"className":92836},[886],[888,92838,92839],{"xmlns":890},[892,92840,92841,92845],{},[895,92842,92843],{},[898,92844,1775],{},[902,92846,1775],{"encoding":904},". Analogicky ",[883,92849,92851],{"className":92850},[886],[888,92852,92853],{"xmlns":890},[892,92854,92855,92875],{},[895,92856,92857,92859,92865,92867,92869,92871,92873],{},[898,92858,16690],{},[1707,92860,92861,92863],{},[898,92862,1690],{},[898,92864,1790],{},[1716,92866,1920],{"stretchy":1919},[898,92868,207],{},[1716,92870,1719],{"separator":1718},[898,92872,1952],{},[1716,92874,1925],{"stretchy":1919},[902,92876,92877],{"encoding":904},"MP_K(a, b)",[1635,92879,92880,92884],{},[724,92881,92882,63973],{},[883,92883,1641],{},[120,92885,92886,92924],{},[123,92887,92888,39959,92907],{},[883,92889,92891],{"className":92890},[886],[888,92892,92893],{"xmlns":890},[892,92894,92895,92905],{},[895,92896,92897,92899],{},[898,92898,16690],{},[1707,92900,92901,92903],{},[898,92902,1690],{},[898,92904,1775],{},[902,92906,23849],{"encoding":904},[614,92908,92909,92910,92923],{},"„o kolik vzroste ",[883,92911,92913],{"className":92912},[886],[888,92914,92915],{"xmlns":890},[892,92916,92917,92921],{},[895,92918,92919],{},[898,92920,1878],{},[902,92922,1878],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,92925,92926,39959,92945],{},[883,92927,92929],{"className":92928},[886],[888,92930,92931],{"xmlns":890},[892,92932,92933,92943],{},[895,92934,92935,92937],{},[898,92936,16690],{},[1707,92938,92939,92941],{},[898,92940,1690],{},[898,92942,1790],{},[902,92944,23894],{"encoding":904},[614,92946,92909,92947,92960],{},[883,92948,92950],{"className":92949},[886],[888,92951,92952],{"xmlns":890},[892,92953,92954,92958],{},[895,92955,92956],{},[898,92957,1878],{},[902,92959,1878],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,92962,92963,92966,92967,92982,92983,2291],{},[38,92964,92965],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,92968,92970],{"className":92969},[886],[888,92971,92972],{"xmlns":890},[892,92973,92974,92980],{},[895,92975,92976,92978],{},[898,92977,5198],{},[898,92979,1775],{},[902,92981,88110],{"encoding":904}," a kapitálu o ",[883,92984,92986],{"className":92985},[886],[888,92987,92988],{"xmlns":890},[892,92989,92990,92996],{},[895,92991,92992,92994],{},[898,92993,5198],{},[898,92995,1790],{},[902,92997,92998],{"encoding":904},"dK",[883,93000,93002],{"className":93001},[886],[888,93003,93004],{"xmlns":890,"display":2004},[892,93005,93006,93099],{},[2008,93007,93008],{"width":2010},[2012,93009,93010,93012,93092,93094],{},[2015,93011],{"width":2017},[2015,93013,93014],{},[895,93015,93016,93018,93020,93022,93024,93026,93028,93036,93038,93040,93042,93044,93052,93054,93056,93058,93060,93062,93068,93070,93072,93074,93076,93078,93084,93086,93088,93090],{},[898,93017,8485],{"mathvariant":2068},[898,93019,1878],{},[1716,93021,8490],{},[898,93023,5198],{},[898,93025,1878],{},[1716,93027,1913],{},[7204,93029,93030,93032,93034],{},[898,93031,1878],{},[898,93033,1775],{},[1716,93035,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,93037,8508],{},[898,93039,5198],{},[898,93041,1775],{},[1716,93043,1949],{},[7204,93045,93046,93048,93050],{},[898,93047,1878],{},[898,93049,1790],{},[1716,93051,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[2074,93053,8508],{},[898,93055,5198],{},[898,93057,1790],{},[1716,93059,1913],{},[898,93061,16690],{},[1707,93063,93064,93066],{},[898,93065,1690],{},[898,93067,1775],{},[2074,93069,8508],{},[898,93071,5198],{},[898,93073,1775],{},[1716,93075,1949],{},[898,93077,16690],{},[1707,93079,93080,93082],{},[898,93081,1690],{},[898,93083,1790],{},[2074,93085,8508],{},[898,93087,5198],{},[898,93089,1790],{},[898,93091,1853],{"mathvariant":2068},[2015,93093],{"width":2017},[2015,93095,93096],{},[2074,93097,93098],{},"(5.11)",[902,93100,93101],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,93103,93104,93105,1853],{},"Skutečná změna: ",[883,93106,93108],{"className":93107},[886],[888,93109,93110],{"xmlns":890},[892,93111,93112,93158],{},[895,93113,93114,93116,93118,93120,93122,93124,93126,93128,93130,93132,93134,93136,93138,93140,93142,93144,93146,93148,93150,93152,93154,93156],{},[898,93115,8485],{"mathvariant":2068},[898,93117,1878],{},[1716,93119,1913],{},[898,93121,1878],{},[1716,93123,1920],{"stretchy":1919},[898,93125,1775],{},[1716,93127,1949],{},[898,93129,5198],{},[898,93131,1775],{},[1716,93133,1719],{"separator":1718},[898,93135,1790],{},[1716,93137,1949],{},[898,93139,5198],{},[898,93141,1790],{},[1716,93143,1925],{"stretchy":1919},[1716,93145,2760],{},[898,93147,1878],{},[1716,93149,1920],{"stretchy":1919},[898,93151,1775],{},[1716,93153,1719],{"separator":1718},[898,93155,1790],{},[1716,93157,1925],{"stretchy":1919},[902,93159,93160],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,93162,93163,93165,93166,93184,93185,93198,93199,93218,93219,93251,93252,93284,93285,1853],{},[38,93164,88274],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,93167,93169],{"className":93168},[886],[888,93170,93171],{"xmlns":890},[892,93172,93173,93181],{},[895,93174,93175],{},[1707,93176,93177,93179],{},[898,93178,1790],{},[1712,93180,2505],{},[902,93182,93183],{"encoding":904},"K_0"," se od jistého ",[883,93186,93188],{"className":93187},[886],[888,93189,93190],{"xmlns":890},[892,93191,93192,93196],{},[895,93193,93194],{},[898,93195,1775],{},[902,93197,1775],{"encoding":904}," stane ",[883,93200,93202],{"className":93201},[886],[888,93203,93204],{"xmlns":890},[892,93205,93206,93216],{},[895,93207,93208,93210],{},[898,93209,16690],{},[1707,93211,93212,93214],{},[898,93213,1690],{},[898,93215,1775],{},[902,93217,23849],{"encoding":904}," klesající (",[883,93220,93222],{"className":93221},[886],[888,93223,93224],{"xmlns":890},[892,93225,93226,93248],{},[895,93227,93228,93244,93246],{},[7204,93229,93230,93232,93238],{},[898,93231,1878],{},[895,93233,93234,93236],{},[898,93235,1775],{},[898,93237,1775],{},[895,93239,93240,93242],{},[1716,93241,8505],{"mathvariant":2068},[1716,93243,8505],{"mathvariant":2068},[1716,93245,2704],{},[1712,93247,2505],{},[902,93249,93250],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,93253,93255],{"className":93254},[886],[888,93256,93257],{"xmlns":890},[892,93258,93259,93281],{},[895,93260,93261,93277,93279],{},[7204,93262,93263,93265,93271],{},[898,93264,1878],{},[895,93266,93267,93269],{},[898,93268,1790],{},[898,93270,1790],{},[895,93272,93273,93275],{},[1716,93274,8505],{"mathvariant":2068},[1716,93276,8505],{"mathvariant":2068},[1716,93278,2704],{},[1712,93280,2505],{},[902,93282,93283],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,93286,93288],{"className":93287},[886],[888,93289,93290],{"xmlns":890},[892,93291,93292,93300],{},[895,93293,93294],{},[1707,93295,93296,93298],{},[898,93297,1775],{},[1712,93299,2505],{},[902,93301,88312],{"encoding":904},[115,93303,93305],{"id":93304},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,93307,93308,93311,93312,93335,93336,43707],{},[38,93309,93310],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,93313,93315],{"className":93314},[886],[888,93316,93317],{"xmlns":890},[892,93318,93319,93333],{},[895,93320,93321,93323,93325,93327,93329,93331],{},[898,93322,1878],{},[1716,93324,1920],{"stretchy":1919},[898,93326,1775],{},[1716,93328,1719],{"separator":1718},[898,93330,1790],{},[1716,93332,1925],{"stretchy":1919},[902,93334,23802],{"encoding":904}," stupně ",[883,93337,93339],{"className":93338},[886],[888,93340,93341],{"xmlns":890},[892,93342,93343,93347],{},[895,93344,93345],{},[898,93346,1740],{},[902,93348,1740],{"encoding":904},[883,93350,93352],{"className":93351},[886],[888,93353,93354],{"xmlns":890,"display":2004},[892,93355,93356,93419],{},[2008,93357,93358],{"width":2010},[2012,93359,93360,93362,93412,93414],{},[2015,93361],{"width":2017},[2015,93363,93364],{},[895,93365,93366,93368,93370,93378,93380,93382,93384,93392,93394,93396,93398,93400,93402,93404,93406,93408,93410],{},[898,93367,1775],{},[2074,93369,8508],{},[7204,93371,93372,93374,93376],{},[898,93373,1878],{},[898,93375,1775],{},[1716,93377,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,93379,1949],{},[898,93381,1790],{},[2074,93383,8508],{},[7204,93385,93386,93388,93390],{},[898,93387,1878],{},[898,93389,1790],{},[1716,93391,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,93393,1913],{},[898,93395,1740],{},[2074,93397,8508],{},[898,93399,1878],{},[1716,93401,1920],{"stretchy":1919},[898,93403,1775],{},[1716,93405,1719],{"separator":1718},[898,93407,1790],{},[1716,93409,1925],{"stretchy":1919},[898,93411,1853],{"mathvariant":2068},[2015,93413],{"width":2017},[2015,93415,93416],{},[2074,93417,93418],{},"(5.12)",[902,93420,93421],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,93423,93424,93445],{},[38,93425,93426,93427],{},"Speciální případ ",[883,93428,93430],{"className":93429},[886],[888,93431,93432],{"xmlns":890},[892,93433,93434,93442],{},[895,93435,93436,93438,93440],{},[898,93437,1740],{},[1716,93439,1913],{},[1712,93441,1714],{},[902,93443,93444],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,93447,93449],{"className":93448},[886],[888,93450,93451],{"xmlns":890,"display":2004},[892,93452,93453,93497],{},[895,93454,93455,93457,93459,93461,93467,93469,93471,93473,93475,93481,93483,93485,93487,93489,93491,93493,93495],{},[898,93456,1775],{},[1716,93458,9532],{},[898,93460,16690],{},[1707,93462,93463,93465],{},[898,93464,1690],{},[898,93466,1775],{},[1716,93468,1949],{},[898,93470,1790],{},[1716,93472,9532],{},[898,93474,16690],{},[1707,93476,93477,93479],{},[898,93478,1690],{},[898,93480,1790],{},[1716,93482,1913],{},[898,93484,1878],{},[1716,93486,1920],{"stretchy":1919},[898,93488,1775],{},[1716,93490,1719],{"separator":1718},[898,93492,1790],{},[1716,93494,1925],{"stretchy":1919},[898,93496,1853],{"mathvariant":2068},[902,93498,93499],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,93501,93502,93503,93506],{},"Slovně — ",[38,93504,93505],{},"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).",[115,93508,23585],{"id":87648},[724,93510,93511,1994,93513,93516,93517,93539,93540,2291],{},[38,93512,23585],{},[614,93514,93515],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,93518,93520],{"className":93519},[886],[888,93521,93522],{"xmlns":890},[892,93523,93524,93536],{},[895,93525,93526,93528,93530,93532,93534],{},[1716,93527,2502],{"stretchy":1919},[898,93529,1775],{},[1716,93531,1719],{"separator":1718},[898,93533,1790],{},[1716,93535,2516],{"stretchy":1919},[902,93537,93538],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,93541,93543],{"className":93542},[886],[888,93544,93545],{"xmlns":890},[892,93546,93547,93552],{},[895,93548,93549],{},[898,93550,93551],{},"q",[902,93553,93551],{"encoding":904},[883,93555,93557],{"className":93556},[886],[888,93558,93559],{"xmlns":890,"display":2004},[892,93560,93561,93596],{},[2008,93562,93563],{"width":2010},[2012,93564,93565,93567,93589,93591],{},[2015,93566],{"width":2017},[2015,93568,93569],{},[895,93570,93571,93573,93575,93577,93579,93581,93583,93585,93587],{},[898,93572,1878],{},[1716,93574,1920],{"stretchy":1919},[898,93576,1775],{},[1716,93578,1719],{"separator":1718},[898,93580,1790],{},[1716,93582,1925],{"stretchy":1919},[1716,93584,1913],{},[898,93586,93551],{},[898,93588,1853],{"mathvariant":2068},[2015,93590],{"width":2017},[2015,93592,93593],{},[2074,93594,93595],{},"(5.13)",[902,93597,93598],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,93600,93601,93602,93605,93606,2365],{},"Jsou to ",[38,93603,93604],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,93607,93609],{"className":93608,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,93611,93612],{},[38,93613,93614],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,93616,93617,93622,93627,93632],{},[123,93618,93619,93621],{},[38,93620,26319],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,93623,93624,93626],{},[38,93625,2581],{}," (úloha 5.14);",[123,93628,93629,22241],{},[38,93630,93631],{},"neprotínají se",[123,93633,93634,93635,18195,93648,1853],{},"s rostoucím ",[883,93636,93638],{"className":93637},[886],[888,93639,93640],{"xmlns":890},[892,93641,93642,93646],{},[895,93643,93644],{},[898,93645,93551],{},[902,93647,93551],{"encoding":904},[38,93649,93650],{},"vzdalují od počátku",[724,93652,93653],{},[614,93654,93655,93656,93678,93679,1853],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,93657,93659],{"className":93658},[886],[888,93660,93661],{"xmlns":890},[892,93662,93663,93675],{},[895,93664,93665,93667,93669,93671,93673],{},[1716,93666,1920],{"stretchy":1919},[898,93668,1775],{},[1716,93670,1719],{"separator":1718},[898,93672,1790],{},[1716,93674,1925],{"stretchy":1919},[902,93676,93677],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,93680,93682],{"className":93681},[886],[888,93683,93684],{"xmlns":890},[892,93685,93686,93710],{},[895,93687,93688,93694,93696,93702,93704],{},[1707,93689,93690,93692],{},[898,93691,93551],{},[1712,93693,1714],{},[1716,93695,2704],{},[1707,93697,93698,93700],{},[898,93699,93551],{},[1712,93701,2505],{},[1716,93703,2704],{},[1707,93705,93706,93708],{},[898,93707,93551],{},[1712,93709,1726],{},[902,93711,93712],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,93714,93716,93717,1925],{"id":93715},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,93718,93720],{"className":93719},[886],[888,93721,93722],{"xmlns":890},[892,93723,93724,93734],{},[895,93725,93726,93728,93730,93732],{},[898,93727,16690],{},[898,93729,17840],{},[898,93731,4164],{},[898,93733,5352],{},[902,93735,24403],{"encoding":904},[724,93737,93738,1994,93741,93744],{},[38,93739,93740],{},"Mezní míra technické substituce",[614,93742,93743],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,93746,93748],{"className":93747},[886],[888,93749,93750],{"xmlns":890,"display":2004},[892,93751,93752,93843],{},[2008,93753,93754],{"width":2010},[2012,93755,93756,93758,93836,93838],{},[2015,93757],{"width":2017},[2015,93759,93760],{},[895,93761,93762,93764,93766,93768,93770,93772,93774,93776,93778,93780,93782,93784,93786,93788,93790,93792,93814,93816,93834],{},[898,93763,16690],{},[898,93765,17840],{},[898,93767,4164],{},[898,93769,5352],{},[1716,93771,1913],{},[898,93773,16690],{},[898,93775,17840],{},[898,93777,4164],{},[898,93779,5352],{},[1716,93781,1920],{"stretchy":1919},[898,93783,1775],{},[1716,93785,1719],{"separator":1718},[898,93787,1790],{},[1716,93789,1925],{"stretchy":1919},[1716,93791,1913],{},[2750,93793,93794,93804],{},[895,93795,93796,93798],{},[898,93797,16690],{},[1707,93799,93800,93802],{},[898,93801,1690],{},[898,93803,1775],{},[895,93805,93806,93808],{},[898,93807,16690],{},[1707,93809,93810,93812],{},[898,93811,1690],{},[898,93813,1790],{},[1716,93815,1913],{},[2750,93817,93818,93826],{},[7204,93819,93820,93822,93824],{},[898,93821,1878],{},[898,93823,1775],{},[1716,93825,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,93827,93828,93830,93832],{},[898,93829,1878],{},[898,93831,1790],{},[1716,93833,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[898,93835,1853],{"mathvariant":2068},[2015,93837],{"width":2017},[2015,93839,93840],{},[2074,93841,93842],{},"(5.14)",[902,93844,93845],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,93847,93848,3495,93850,93880,93881,93912],{},[38,93849,23026],{},[883,93851,93853],{"className":93852},[886],[888,93854,93855],{"xmlns":890},[892,93856,93857,93877],{},[895,93858,93859,93861,93863,93865,93867,93869,93871,93873,93875],{},[898,93860,16690],{},[898,93862,17840],{},[898,93864,4164],{},[898,93866,5352],{},[1716,93868,1920],{"stretchy":1919},[898,93870,1775],{},[1716,93872,1719],{"separator":1718},[898,93874,1790],{},[1716,93876,1925],{"stretchy":1919},[902,93878,93879],{"encoding":904},"MRTS(L, K)"," udává, ",[38,93882,93883,93884,93897,93898,93911],{},"o kolik se musí přibližně změnit kapitál ",[883,93885,93887],{"className":93886},[886],[888,93888,93889],{"xmlns":890},[892,93890,93891,93895],{},[895,93892,93893],{},[898,93894,1790],{},[902,93896,1790],{"encoding":904},", jestliže se práce ",[883,93899,93901],{"className":93900},[886],[888,93902,93903],{"xmlns":890},[892,93904,93905,93909],{},[895,93906,93907],{},[898,93908,1775],{},[902,93910,1775],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1635,93914,93915],{},[724,93916,93917,31810,93919,93938,93939,93976,93977,93980,93981,93985],{},[883,93918,1641],{},[883,93920,93922],{"className":93921},[886],[888,93923,93924],{"xmlns":890},[892,93925,93926,93936],{},[895,93927,93928,93930,93932,93934],{},[898,93929,16690],{},[898,93931,17840],{},[898,93933,4164],{},[898,93935,5352],{},[902,93937,24403],{"encoding":904}," říká: ",[614,93940,93941,93942,93961,93962,93975],{},"„jednu jednotku práce musím nahradit přibližně ",[883,93943,93945],{"className":93944},[886],[888,93946,93947],{"xmlns":890},[892,93948,93949,93959],{},[895,93950,93951,93953,93955,93957],{},[898,93952,16690],{},[898,93954,17840],{},[898,93956,4164],{},[898,93958,5352],{},[902,93960,24403],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,93963,93965],{"className":93964},[886],[888,93966,93967],{"xmlns":890},[892,93968,93969,93973],{},[895,93970,93971],{},[898,93972,1878],{},[902,93974,1878],{"encoding":904}," zůstala stejná.\""," Je to ",[38,93978,93979],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,93982,93984],{"className":93983,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,93987,93988],{},[3682,93989],{"alt":93990,"className":93991,"src":93992},"imek-izokvanty-mrts",[210,3686],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,93994,93995,93998,93999,2574,94029,94051,94052,1998],{},[38,93996,93997],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,94000,94002],{"className":94001},[886],[888,94003,94004],{"xmlns":890},[892,94005,94006,94026],{},[895,94007,94008,94010,94016,94018,94024],{},[1716,94009,2502],{"stretchy":1919},[1707,94011,94012,94014],{},[898,94013,1775],{},[1712,94015,2505],{},[1716,94017,1719],{"separator":1718},[1707,94019,94020,94022],{},[898,94021,1790],{},[1712,94023,2505],{},[1716,94025,2516],{"stretchy":1919},[902,94027,94028],{"encoding":904},"[L_0, K_0]",[883,94030,94032],{"className":94031},[886],[888,94033,94034],{"xmlns":890},[892,94035,94036,94048],{},[895,94037,94038,94040,94042,94044,94046],{},[1716,94039,2760],{},[898,94041,16690],{},[898,94043,17840],{},[898,94045,4164],{},[898,94047,5352],{},[902,94049,94050],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,94053,94055],{"className":94054},[886],[888,94056,94057],{"xmlns":890},[892,94058,94059,94081],{},[895,94060,94061,94063,94065,94067,94069,94071,94073,94075],{},[898,94062,1878],{},[1716,94064,1920],{"stretchy":1919},[898,94066,1775],{},[1716,94068,1719],{"separator":1718},[898,94070,1790],{},[1716,94072,1925],{"stretchy":1919},[1716,94074,1913],{},[1707,94076,94077,94079],{},[898,94078,93551],{},[1712,94080,2505],{},[902,94082,94083],{"encoding":904},"Q(L,K) = q_0",[883,94085,94087],{"className":94086},[886],[888,94088,94089],{"xmlns":890,"display":2004},[892,94090,94091,94143],{},[895,94092,94093,94107,94109,94111,94129,94131,94133,94135,94137,94139,94141],{},[2750,94094,94095,94101],{},[895,94096,94097,94099],{},[898,94098,5198],{},[898,94100,1790],{},[895,94102,94103,94105],{},[898,94104,5198],{},[898,94106,1775],{},[1716,94108,1913],{},[1716,94110,2760],{},[2750,94112,94113,94121],{},[7204,94114,94115,94117,94119],{},[898,94116,1878],{},[898,94118,1775],{},[1716,94120,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,94122,94123,94125,94127],{},[898,94124,1878],{},[898,94126,1790],{},[1716,94128,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,94130,1913],{},[1716,94132,2760],{},[898,94134,16690],{},[898,94136,17840],{},[898,94138,4164],{},[898,94140,5352],{},[898,94142,1853],{"mathvariant":2068},[902,94144,94145],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,94147,94148,94149,94164,94165,94181],{},"Změní-li se práce o ",[883,94150,94152],{"className":94151},[886],[888,94153,94154],{"xmlns":890},[892,94155,94156,94162],{},[895,94157,94158,94160],{},[898,94159,5198],{},[898,94161,1775],{},[902,94163,88110],{"encoding":904},", lze pro odhad změny kapitálu ",[883,94166,94168],{"className":94167},[886],[888,94169,94170],{"xmlns":890},[892,94171,94172,94178],{},[895,94173,94174,94176],{},[898,94175,8485],{"mathvariant":2068},[898,94177,1790],{},[902,94179,94180],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,94183,94185],{"className":94184},[886],[888,94186,94187],{"xmlns":890,"display":2004},[892,94188,94189,94236],{},[2008,94190,94191],{"width":2010},[2012,94192,94193,94195,94229,94231],{},[2015,94194],{"width":2017},[2015,94196,94197],{},[895,94198,94199,94201,94203,94205,94207,94209,94211,94213,94215,94217,94219,94221,94223,94225,94227],{},[898,94200,8485],{"mathvariant":2068},[898,94202,1790],{},[1716,94204,8490],{},[898,94206,5198],{},[898,94208,1790],{},[1716,94210,1913],{},[1716,94212,2760],{},[898,94214,16690],{},[898,94216,17840],{},[898,94218,4164],{},[898,94220,5352],{},[2074,94222,8508],{},[898,94224,5198],{},[898,94226,1775],{},[1716,94228,1719],{"separator":1718},[2015,94230],{"width":2017},[2015,94232,94233],{},[2074,94234,94235],{},"(5.15)",[902,94237,94238],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,94240,94242],{"className":94241},[886],[888,94243,94244],{"xmlns":890,"display":2004},[892,94245,94246,94295],{},[2008,94247,94248],{"width":2010},[2012,94249,94250,94252,94288,94290],{},[2015,94251],{"width":2017},[2015,94253,94254],{},[895,94255,94256,94258,94260,94262,94280,94282,94284,94286],{},[898,94257,5198],{},[898,94259,1775],{},[1716,94261,1913],{},[2750,94263,94264,94270],{},[895,94265,94266,94268],{},[1716,94267,2760],{},[1712,94269,1714],{},[895,94271,94272,94274,94276,94278],{},[898,94273,16690],{},[898,94275,17840],{},[898,94277,4164],{},[898,94279,5352],{},[2074,94281,8508],{},[898,94283,5198],{},[898,94285,1790],{},[898,94287,1853],{"mathvariant":2068},[2015,94289],{"width":2017},[2015,94291,94292],{},[2074,94293,94294],{},"(5.16)",[902,94296,94297],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1635,94299,94300,94324],{},[724,94301,94302,94304,94305],{},[883,94303,3776],{}," Postup — jak spočítat ",[883,94306,94308],{"className":94307},[886],[888,94309,94310],{"xmlns":890},[892,94311,94312,94322],{},[895,94313,94314,94316,94318,94320],{},[898,94315,16690],{},[898,94317,17840],{},[898,94319,4164],{},[898,94321,5352],{},[902,94323,24403],{"encoding":904},[152,94325,94326,94367,94410,94442],{},[123,94327,94328,94329,2247,94348,1853],{},"Vypočtěte parciální derivace ",[883,94330,94332],{"className":94331},[886],[888,94333,94334],{"xmlns":890},[892,94335,94336,94346],{},[895,94337,94338],{},[7204,94339,94340,94342,94344],{},[898,94341,1878],{},[898,94343,1775],{},[1716,94345,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,94347,23826],{"encoding":904},[883,94349,94351],{"className":94350},[886],[888,94352,94353],{"xmlns":890},[892,94354,94355,94365],{},[895,94356,94357],{},[7204,94358,94359,94361,94363],{},[898,94360,1878],{},[898,94362,1790],{},[1716,94364,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,94366,23871],{"encoding":904},[123,94368,78595,94369,94409],{},[883,94370,94372],{"className":94371},[886],[888,94373,94374],{"xmlns":890},[892,94375,94376,94406],{},[895,94377,94378,94380,94382,94384,94386,94388,94396,94398],{},[898,94379,16690],{},[898,94381,17840],{},[898,94383,4164],{},[898,94385,5352],{},[1716,94387,1913],{},[7204,94389,94390,94392,94394],{},[898,94391,1878],{},[898,94393,1775],{},[1716,94395,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[898,94397,3045],{"mathvariant":2068},[7204,94399,94400,94402,94404],{},[898,94401,1878],{},[898,94403,1790],{},[1716,94405,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,94407,94408],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,94411,94412,94413,1853],{},"Případně dosaďte konkrétní ",[883,94414,94416],{"className":94415},[886],[888,94417,94418],{"xmlns":890},[892,94419,94420,94440],{},[895,94421,94422,94424,94430,94432,94438],{},[1716,94423,2502],{"stretchy":1919},[1707,94425,94426,94428],{},[898,94427,1775],{},[1712,94429,2505],{},[1716,94431,1719],{"separator":1718},[1707,94433,94434,94436],{},[898,94435,1790],{},[1712,94437,2505],{},[1716,94439,2516],{"stretchy":1919},[902,94441,94028],{"encoding":904},[123,94443,94444,94445,94479,94480,94482],{},"Pro odhad substituce použijte ",[883,94446,94448],{"className":94447},[886],[888,94449,94450],{"xmlns":890},[892,94451,94452,94476],{},[895,94453,94454,94456,94458,94460,94462,94464,94466,94468,94470,94472,94474],{},[898,94455,8485],{"mathvariant":2068},[898,94457,1790],{},[1716,94459,8490],{},[1716,94461,2760],{},[898,94463,16690],{},[898,94465,17840],{},[898,94467,4164],{},[898,94469,5352],{},[1716,94471,9532],{},[898,94473,8485],{"mathvariant":2068},[898,94475,1775],{},[902,94477,94478],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,94481,65360],{}," — substituce, ne doplnění).",[724,94484,94485],{},[614,94486,94487,94488,94520,94521,16504,94534,29583,94563,94578],{},"Obrázek 5.7 — izokvanta ",[883,94489,94491],{"className":94490},[886],[888,94492,94493],{"xmlns":890},[892,94494,94495,94517],{},[895,94496,94497,94503,94505,94507,94509,94511,94513,94515],{},[1707,94498,94499,94501],{},[898,94500,93551],{},[1712,94502,2505],{},[1716,94504,1913],{},[898,94506,1878],{},[1716,94508,1920],{"stretchy":1919},[898,94510,1775],{},[1716,94512,1719],{"separator":1718},[898,94514,1790],{},[1716,94516,1925],{"stretchy":1919},[902,94518,94519],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,94522,94524],{"className":94523},[886],[888,94525,94526],{"xmlns":890},[892,94527,94528,94532],{},[895,94529,94530],{},[898,94531,32640],{},[902,94533,32640],{"encoding":904},[883,94535,94537],{"className":94536},[886],[888,94538,94539],{"xmlns":890},[892,94540,94541,94561],{},[895,94542,94543,94545,94551,94553,94559],{},[1716,94544,2502],{"stretchy":1919},[1707,94546,94547,94549],{},[898,94548,1775],{},[1712,94550,2505],{},[1716,94552,1719],{"separator":1718},[1707,94554,94555,94557],{},[898,94556,1790],{},[1712,94558,2505],{},[1716,94560,2516],{"stretchy":1919},[902,94562,94028],{"encoding":904},[883,94564,94566],{"className":94565},[886],[888,94567,94568],{"xmlns":890},[892,94569,94570,94576],{},[895,94571,94572,94574],{},[898,94573,8485],{"mathvariant":2068},[898,94575,1790],{},[902,94577,94180],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,94580,94582],{"id":94581},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,94584,94586],{"id":94585},"příklad-54","Příklad 5.4",[724,94588,89427,94589,1343,94631,1343,94648,1853],{},[883,94590,94592],{"className":94591},[886],[888,94593,94594],{"xmlns":890},[892,94595,94596,94628],{},[895,94597,94598,94600,94602,94604,94616],{},[898,94599,1878],{},[1716,94601,1913],{},[1712,94603,3221],{},[3074,94605,94606,94608],{},[898,94607,1775],{},[895,94609,94610,94612,94614],{},[1712,94611,1714],{},[898,94613,3045],{"mathvariant":2068},[1712,94615,1726],{},[3074,94617,94618,94620],{},[898,94619,1790],{},[895,94621,94622,94624,94626],{},[1712,94623,1714],{},[898,94625,3045],{"mathvariant":2068},[1712,94627,7072],{},[902,94629,94630],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,94632,94634],{"className":94633},[886],[888,94635,94636],{"xmlns":890},[892,94637,94638,94646],{},[895,94639,94640,94642,94644],{},[898,94641,1775],{},[1716,94643,1913],{},[1712,94645,2976],{},[902,94647,89801],{"encoding":904},[883,94649,94651],{"className":94650},[886],[888,94652,94653],{"xmlns":890},[892,94654,94655,94663],{},[895,94656,94657,94659,94661],{},[898,94658,1790],{},[1716,94660,1913],{},[1712,94662,12151],{},[902,94664,94665],{"encoding":904},"K = 100",[724,94667,94668],{},[38,94669,94670],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,94672,94674],{"className":94673},[886],[888,94675,94676],{"xmlns":890,"display":2004},[892,94677,94678,94792],{},[895,94679,94680,94682,94688,94690,94698,94700,94708,94722,94734,94736,94738,94740,94746,94748,94750,94752,94754,94756,94758,94766,94768,94778,94780,94787,94789],{},[898,94681,16690],{},[1707,94683,94684,94686],{},[898,94685,1690],{},[898,94687,1775],{},[1716,94689,1913],{},[7204,94691,94692,94694,94696],{},[898,94693,1878],{},[898,94695,1775],{},[1716,94697,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,94699,1913],{},[2747,94701,94702],{"scriptlevel":2505,"displaystyle":1919},[2750,94703,94704,94706],{},[1712,94705,3221],{},[1712,94707,1726],{},[3074,94709,94710,94712],{},[898,94711,1775],{},[895,94713,94714,94716,94718,94720],{},[1716,94715,2760],{},[1712,94717,1714],{},[898,94719,3045],{"mathvariant":2068},[1712,94721,1726],{},[3074,94723,94724,94726],{},[898,94725,1790],{},[895,94727,94728,94730,94732],{},[1712,94729,1714],{},[898,94731,3045],{"mathvariant":2068},[1712,94733,7072],{},[1716,94735,1719],{"separator":1718},[2324,94737],{"width":8689},[898,94739,16690],{},[1707,94741,94742,94744],{},[898,94743,1690],{},[898,94745,1775],{},[1716,94747,1920],{"stretchy":1919},[1712,94749,2976],{},[1716,94751,1719],{"separator":1718},[1712,94753,12151],{},[1716,94755,1925],{"stretchy":1919},[1716,94757,1913],{},[2747,94759,94760],{"scriptlevel":2505,"displaystyle":1919},[2750,94761,94762,94764],{},[1712,94763,3221],{},[1712,94765,1726],{},[1716,94767,9532],{},[2747,94769,94770],{"scriptlevel":2505,"displaystyle":1919},[2750,94771,94772,94774],{},[1712,94773,1714],{},[10595,94775,94776],{},[1712,94777,2976],{},[1716,94779,9532],{},[94781,94782,94783,94785],"mroot",{},[1712,94784,12151],{},[1712,94786,7072],{},[1716,94788,8490],{},[1712,94790,94791],{},"7,153.",[902,94793,94794],{"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.",[724,94796,94797,94798,9152,94820,24037,94837,94858,94859,94880],{},"Přibližná změna při ",[883,94799,94801],{"className":94800},[886],[888,94802,94803],{"xmlns":890},[892,94804,94805,94817],{},[895,94806,94807,94809,94811,94813,94815],{},[898,94808,1775],{},[1716,94810,2291],{},[1712,94812,2976],{},[1716,94814,16986],{},[1712,94816,3283],{},[902,94818,94819],{"encoding":904},"L: 20 \\to 21",[883,94821,94823],{"className":94822},[886],[888,94824,94825],{"xmlns":890},[892,94826,94827,94835],{},[895,94828,94829,94831,94833],{},[898,94830,1790],{},[1716,94832,1913],{},[1712,94834,12151],{},[902,94836,94665],{"encoding":904},[883,94838,94840],{"className":94839},[886],[888,94841,94842],{"xmlns":890},[892,94843,94844,94855],{},[895,94845,94846,94848,94850,94852],{},[898,94847,8485],{"mathvariant":2068},[898,94849,1878],{},[1716,94851,8490],{},[1712,94853,94854],{},"7,153",[902,94856,94857],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,94860,94862],{"className":94861},[886],[888,94863,94864],{"xmlns":890},[892,94865,94866,94877],{},[895,94867,94868,94870,94872,94874],{},[898,94869,8485],{"mathvariant":2068},[898,94871,1878],{},[1716,94873,8490],{},[1712,94875,94876],{},"26,888",[902,94878,94879],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,94882,94883,94886],{},[38,94884,94885],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,94888,94890],{"className":94889},[886],[888,94891,94892],{"xmlns":890,"display":2004},[892,94893,94894,94994],{},[895,94895,94896,94898,94904,94906,94914,94916,94918,94930,94944,94946,94948,94950,94956,94958,94960,94962,94964,94966,94968,94970,94974,94976,94989,94991],{},[898,94897,16690],{},[1707,94899,94900,94902],{},[898,94901,1690],{},[898,94903,1790],{},[1716,94905,1913],{},[7204,94907,94908,94910,94912],{},[898,94909,1878],{},[898,94911,1790],{},[1716,94913,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,94915,1913],{},[1712,94917,6985],{},[3074,94919,94920,94922],{},[898,94921,1775],{},[895,94923,94924,94926,94928],{},[1712,94925,1714],{},[898,94927,3045],{"mathvariant":2068},[1712,94929,1726],{},[3074,94931,94932,94934],{},[898,94933,1790],{},[895,94935,94936,94938,94940,94942],{},[1716,94937,2760],{},[1712,94939,1726],{},[898,94941,3045],{"mathvariant":2068},[1712,94943,7072],{},[1716,94945,1719],{"separator":1718},[2324,94947],{"width":8689},[898,94949,16690],{},[1707,94951,94952,94954],{},[898,94953,1690],{},[898,94955,1790],{},[1716,94957,1920],{"stretchy":1919},[1712,94959,2976],{},[1716,94961,1719],{"separator":1718},[1712,94963,12151],{},[1716,94965,1925],{"stretchy":1919},[1716,94967,1913],{},[1712,94969,6985],{},[10595,94971,94972],{},[1712,94973,2976],{},[1716,94975,9532],{},[2747,94977,94978],{"scriptlevel":2505,"displaystyle":1919},[2750,94979,94980,94982],{},[1712,94981,1714],{},[94781,94983,94984,94987],{},[1712,94985,94986],{},"10000",[1712,94988,7072],{},[1716,94990,8490],{},[1712,94992,94993],{},"4,525.",[902,94995,94996],{"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.",[724,94998,94999,95000,3942,95017,2365],{},"Produkce poklesne přibližně o 4,525 (z ",[883,95001,95003],{"className":95002},[886],[888,95004,95005],{"xmlns":890},[892,95006,95007,95014],{},[895,95008,95009,95011],{},[1716,95010,8490],{},[1712,95012,95013],{},"905,126",[902,95015,95016],{"encoding":904},"\\approx 905{,}126",[883,95018,95020],{"className":95019},[886],[888,95021,95022],{"xmlns":890},[892,95023,95024,95031],{},[895,95025,95026,95028],{},[1716,95027,8490],{},[1712,95029,95030],{},"900,601",[902,95032,95033],{"encoding":904},"\\approx 900{,}601",[724,95035,95036,16992,95083,1343,95105,2365],{},[38,95037,95038,95039,2247,95061],{},"(c) Změna ",[883,95040,95042],{"className":95041},[886],[888,95043,95044],{"xmlns":890},[892,95045,95046,95058],{},[895,95047,95048,95050,95052,95054,95056],{},[898,95049,1775],{},[1716,95051,2291],{},[1712,95053,2976],{},[1716,95055,16986],{},[1712,95057,3221],{},[902,95059,95060],{"encoding":904},"L: 20 \\to 15",[883,95062,95064],{"className":95063},[886],[888,95065,95066],{"xmlns":890},[892,95067,95068,95080],{},[895,95069,95070,95072,95074,95076,95078],{},[898,95071,1790],{},[1716,95073,2291],{},[1712,95075,12151],{},[1716,95077,16986],{},[1712,95079,6653],{},[902,95081,95082],{"encoding":904},"K: 100 \\to 150",[883,95084,95086],{"className":95085},[886],[888,95087,95088],{"xmlns":890},[892,95089,95090,95102],{},[895,95091,95092,95094,95096,95098,95100],{},[898,95093,5198],{},[898,95095,1775],{},[1716,95097,1913],{},[1716,95099,2760],{},[1712,95101,6985],{},[902,95103,95104],{"encoding":904},"dL = -5",[883,95106,95108],{"className":95107},[886],[888,95109,95110],{"xmlns":890},[892,95111,95112,95122],{},[895,95113,95114,95116,95118,95120],{},[898,95115,5198],{},[898,95117,1790],{},[1716,95119,1913],{},[1712,95121,5808],{},[902,95123,95124],{"encoding":904},"dK = 50",[883,95126,95128],{"className":95127},[886],[888,95129,95130],{"xmlns":890,"display":2004},[892,95131,95132,95220],{},[895,95133,95134,95136,95138,95140,95142,95148,95150,95152,95154,95156,95158,95160,95162,95164,95166,95168,95170,95172,95178,95180,95182,95184,95186,95188,95190,95192,95194,95196,95198,95200,95202,95204,95206,95208,95211,95213,95215,95217],{},[898,95135,5198],{},[898,95137,1878],{},[1716,95139,1913],{},[898,95141,16690],{},[1707,95143,95144,95146],{},[898,95145,1690],{},[898,95147,1775],{},[1716,95149,1920],{"stretchy":1919},[1712,95151,2976],{},[1716,95153,1719],{"separator":1718},[1712,95155,12151],{},[1716,95157,1925],{"stretchy":1919},[1716,95159,9532],{},[1716,95161,1920],{"stretchy":1919},[1716,95163,2760],{},[1712,95165,6985],{},[1716,95167,1925],{"stretchy":1919},[1716,95169,1949],{},[898,95171,16690],{},[1707,95173,95174,95176],{},[898,95175,1690],{},[898,95177,1790],{},[1716,95179,1920],{"stretchy":1919},[1712,95181,2976],{},[1716,95183,1719],{"separator":1718},[1712,95185,12151],{},[1716,95187,1925],{"stretchy":1919},[1716,95189,9532],{},[1712,95191,5808],{},[1716,95193,1913],{},[1712,95195,94854],{},[1716,95197,9532],{},[1716,95199,1920],{"stretchy":1919},[1716,95201,2760],{},[1712,95203,6985],{},[1716,95205,1925],{"stretchy":1919},[1716,95207,1949],{},[1712,95209,95210],{},"4,525",[1716,95212,9532],{},[1712,95214,5808],{},[1716,95216,8490],{},[1712,95218,95219],{},"190,485.",[902,95221,95222],{"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.",[724,95224,95225],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,95227,95229],{"id":95228},"příklad-55","Příklad 5.5",[724,95231,95232,95233,95269,95270,1853],{},"Pro produkci ",[883,95234,95236],{"className":95235},[886],[888,95237,95238],{"xmlns":890},[892,95239,95240,95266],{},[895,95241,95242,95244,95246,95248,95250,95252,95254,95256,95262],{},[898,95243,1878],{},[1716,95245,1920],{"stretchy":1919},[898,95247,1775],{},[1716,95249,1719],{"separator":1718},[898,95251,1790],{},[1716,95253,1925],{"stretchy":1919},[1716,95255,1913],{},[94781,95257,95258,95260],{},[898,95259,1775],{},[1712,95261,7072],{},[10595,95263,95264],{},[898,95265,1790],{},[902,95267,95268],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,95271,95273],{"className":95272},[886],[888,95274,95275],{"xmlns":890},[892,95276,95277,95293],{},[895,95278,95279,95285,95289,95291],{},[94781,95280,95281,95283],{},[898,95282,1775],{},[1712,95284,7072],{},[10595,95286,95287],{},[898,95288,1790],{},[1716,95290,1913],{},[898,95292,93551],{},[902,95294,95295],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,95297,95298,95299,1853],{},"Umocněním na druhou: ",[883,95300,95302],{"className":95301},[886],[888,95303,95304],{"xmlns":890},[892,95305,95306,95330],{},[895,95307,95308,95310,95312,95318,95320],{},[898,95309,1790],{},[1716,95311,1913],{},[3074,95313,95314,95316],{},[898,95315,93551],{},[1712,95317,1726],{},[898,95319,3045],{"mathvariant":2068},[94781,95321,95322,95328],{},[3074,95323,95324,95326],{},[898,95325,1775],{},[1712,95327,1726],{},[1712,95329,7072],{},[902,95331,95332],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,95334,95335,95375,95415],{},[123,95336,95337],{},[883,95338,95340],{"className":95339},[886],[888,95341,95342],{"xmlns":890},[892,95343,95344,95372],{},[895,95345,95346,95348,95350,95352,95354,95356,95358,95360,95362],{},[898,95347,93551],{},[1716,95349,1913],{},[1712,95351,1714],{},[1716,95353,17833],{},[898,95355,1790],{},[1716,95357,1913],{},[1712,95359,1714],{},[898,95361,3045],{"mathvariant":2068},[94781,95363,95364,95370],{},[3074,95365,95366,95368],{},[898,95367,1775],{},[1712,95369,1726],{},[1712,95371,7072],{},[902,95373,95374],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,95376,95377],{},[883,95378,95380],{"className":95379},[886],[888,95381,95382],{"xmlns":890},[892,95383,95384,95412],{},[895,95385,95386,95388,95390,95392,95394,95396,95398,95400,95402],{},[898,95387,93551],{},[1716,95389,1913],{},[1712,95391,1726],{},[1716,95393,17833],{},[898,95395,1790],{},[1716,95397,1913],{},[1712,95399,6849],{},[898,95401,3045],{"mathvariant":2068},[94781,95403,95404,95410],{},[3074,95405,95406,95408],{},[898,95407,1775],{},[1712,95409,1726],{},[1712,95411,7072],{},[902,95413,95414],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,95416,95417],{},[883,95418,95420],{"className":95419},[886],[888,95421,95422],{"xmlns":890},[892,95423,95424,95452],{},[895,95425,95426,95428,95430,95432,95434,95436,95438,95440,95442],{},[898,95427,93551],{},[1716,95429,1913],{},[1712,95431,7072],{},[1716,95433,17833],{},[898,95435,1790],{},[1716,95437,1913],{},[1712,95439,7141],{},[898,95441,3045],{"mathvariant":2068},[94781,95443,95444,95450],{},[3074,95445,95446,95448],{},[898,95447,1775],{},[1712,95449,1726],{},[1712,95451,7072],{},[902,95453,95454],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,95456,95457],{},[614,95458,95459,95460,20296,95481,1853],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,95461,95463],{"className":95462},[886],[888,95464,95465],{"xmlns":890},[892,95466,95467,95479],{},[895,95468,95469,95471,95473,95475,95477],{},[1716,95470,1920],{"stretchy":1919},[898,95472,1775],{},[1716,95474,1719],{"separator":1718},[898,95476,1790],{},[1716,95478,1925],{"stretchy":1919},[902,95480,93677],{"encoding":904},[883,95482,95484],{"className":95483},[886],[888,95485,95486],{"xmlns":890},[892,95487,95488,95504],{},[895,95489,95490,95492,95494,95496,95498,95500,95502],{},[898,95491,93551],{},[1716,95493,1913],{},[1712,95495,1714],{},[1716,95497,1719],{"separator":1718},[1712,95499,1726],{},[1716,95501,1719],{"separator":1718},[1712,95503,7072],{},[902,95505,95506],{"encoding":904},"q = 1, 2, 3",[198,95508,95510],{"id":95509},"příklad-56","Příklad 5.6",[724,95512,89427,95513,1853],{},[883,95514,95516],{"className":95515},[886],[888,95517,95518],{"xmlns":890},[892,95519,95520,95536],{},[895,95521,95522,95524,95526,95528,95530,95532],{},[898,95523,1878],{},[1716,95525,1913],{},[1712,95527,1726],{},[898,95529,1775],{},[1716,95531,1949],{},[10595,95533,95534],{},[898,95535,1790],{},[902,95537,95538],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,95540,95542],{"className":95541},[886],[888,95543,95544],{"xmlns":890,"display":2004},[892,95545,95546,95588],{},[895,95547,95548,95550,95556,95558,95560,95562,95564,95566,95572,95574,95586],{},[898,95549,16690],{},[1707,95551,95552,95554],{},[898,95553,1690],{},[898,95555,1775],{},[1716,95557,1913],{},[1712,95559,1726],{},[1716,95561,1719],{"separator":1718},[2324,95563],{"width":2326},[898,95565,16690],{},[1707,95567,95568,95570],{},[898,95569,1690],{},[898,95571,1790],{},[1716,95573,1913],{},[2750,95575,95576,95578],{},[1712,95577,1714],{},[895,95579,95580,95582],{},[1712,95581,1726],{},[10595,95583,95584],{},[898,95585,1790],{},[898,95587,1853],{"mathvariant":2068},[902,95589,95590],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,95592,95594],{"className":95593},[886],[888,95595,95596],{"xmlns":890,"display":2004},[892,95597,95598,95662],{},[895,95599,95600,95602,95604,95606,95608,95610,95632,95634,95652,95654,95656,95660],{},[898,95601,16690],{},[898,95603,17840],{},[898,95605,4164],{},[898,95607,5352],{},[1716,95609,1913],{},[2750,95611,95612,95622],{},[895,95613,95614,95616],{},[898,95615,16690],{},[1707,95617,95618,95620],{},[898,95619,1690],{},[898,95621,1775],{},[895,95623,95624,95626],{},[898,95625,16690],{},[1707,95627,95628,95630],{},[898,95629,1690],{},[898,95631,1790],{},[1716,95633,1913],{},[2750,95635,95636,95638],{},[1712,95637,1726],{},[2747,95639,95640],{"scriptlevel":2505,"displaystyle":1919},[2750,95641,95642,95644],{},[1712,95643,1714],{},[895,95645,95646,95648],{},[1712,95647,1726],{},[10595,95649,95650],{},[898,95651,1790],{},[1716,95653,1913],{},[1712,95655,6849],{},[10595,95657,95658],{},[898,95659,1790],{},[898,95661,1853],{"mathvariant":2068},[902,95663,95664],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,95666,95667,95668,95711,95712,95751,95752,1853],{},"Například ",[883,95669,95671],{"className":95670},[886],[888,95672,95673],{"xmlns":890},[892,95674,95675,95708],{},[895,95676,95677,95679,95681,95683,95685,95687,95689,95691,95693,95695,95697,95699,95703,95705],{},[898,95678,16690],{},[898,95680,17840],{},[898,95682,4164],{},[898,95684,5352],{},[1716,95686,1920],{"stretchy":1919},[1712,95688,6849],{},[1716,95690,1719],{"separator":1718},[1712,95692,7109],{},[1716,95694,1925],{"stretchy":1919},[1716,95696,1913],{},[1712,95698,6849],{},[10595,95700,95701],{},[1712,95702,7109],{},[1716,95704,8490],{},[1712,95706,95707],{},"10,58",[902,95709,95710],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,95713,95715],{"className":95714},[886],[888,95716,95717],{"xmlns":890},[892,95718,95719,95748],{},[895,95720,95721,95723,95725,95727,95729,95731,95733,95735,95737,95739,95743,95745],{},[898,95722,1878],{},[1716,95724,1920],{"stretchy":1919},[1712,95726,6849],{},[1716,95728,1719],{"separator":1718},[1712,95730,7109],{},[1716,95732,1925],{"stretchy":1919},[1716,95734,1913],{},[1712,95736,12398],{},[1716,95738,1949],{},[10595,95740,95741],{},[1712,95742,7109],{},[1716,95744,8490],{},[1712,95746,95747],{},"10,646",[902,95749,95750],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,95753,95755],{"className":95754},[886],[888,95756,95757],{"xmlns":890},[892,95758,95759,95767],{},[895,95760,95761,95763],{},[1712,95762,6849],{},[10595,95764,95765],{},[1712,95766,7109],{},[902,95768,95769],{"encoding":904},"4\\sqrt{7}",[724,95771,95772,95773,95793],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,95774,95776],{"className":95775},[886],[888,95777,95778],{"xmlns":890},[892,95779,95780,95790],{},[895,95781,95782,95784,95786,95788],{},[898,95783,5198],{},[898,95785,1775],{},[1716,95787,1913],{},[1712,95789,1726],{},[902,95791,95792],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,95795,95797],{"className":95796},[886],[888,95798,95799],{"xmlns":890,"display":2004},[892,95800,95801,95850],{},[895,95802,95803,95805,95807,95809,95811,95813,95815,95817,95819,95821,95823,95825,95827,95829,95831,95833,95835,95837,95839,95843,95845,95847],{},[898,95804,5198],{},[898,95806,1790],{},[1716,95808,1913],{},[1716,95810,2760],{},[898,95812,16690],{},[898,95814,17840],{},[898,95816,4164],{},[898,95818,5352],{},[1716,95820,1920],{"stretchy":1919},[1712,95822,6849],{},[1716,95824,1719],{"separator":1718},[1712,95826,7109],{},[1716,95828,1925],{"stretchy":1919},[1716,95830,9532],{},[1712,95832,1726],{},[1716,95834,1913],{},[1716,95836,2760],{},[1712,95838,12398],{},[10595,95840,95841],{},[1712,95842,7109],{},[1716,95844,8490],{},[1716,95846,2760],{},[1712,95848,95849],{},"21,17.",[902,95851,95852],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,95854,95856],{"id":95855},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,95858,95859,95860,1343,95862,2247,95864,95866,95867,95870,95871,95874],{},"Hlavními faktory produkce jsou ",[38,95861,87668],{},[38,95863,87684],{},[38,95865,87700],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,95868,95869],{},"jednofaktorový"," (pouze práce) a ",[38,95872,95873],{},"dvoufaktorový"," (práce + kapitál) model.",[724,95876,95877,95878,95881,95882,95884,95885,95887,95888,39959,95891,95910,95911,95928,95929,95946,95947,95969,95970,18195,95989,1853],{},"V ",[38,95879,95880],{},"1F modelu"," se definuje ",[38,95883,23829],{}," (derivace produkce podle práce) a ",[38,95886,87603],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,95889,95890],{},"zákonu klesajících výnosů",[883,95892,95894],{"className":95893},[886],[888,95895,95896],{"xmlns":890},[892,95897,95898,95908],{},[895,95899,95900,95902],{},[898,95901,16690],{},[1707,95903,95904,95906],{},[898,95905,1690],{},[898,95907,1775],{},[902,95909,23849],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,95912,95914],{"className":95913},[886],[888,95915,95916],{"xmlns":890},[892,95917,95918,95926],{},[895,95919,95920],{},[1707,95921,95922,95924],{},[898,95923,1775],{},[1712,95925,2505],{},[902,95927,88312],{"encoding":904}," klesá a v bodě ",[883,95930,95932],{"className":95931},[886],[888,95933,95934],{"xmlns":890},[892,95935,95936,95944],{},[895,95937,95938],{},[1707,95939,95940,95942],{},[898,95941,1775],{},[1712,95943,1714],{},[902,95945,27010],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,95948,95949,95950],{},"princip maximalizace ",[883,95951,95953],{"className":95952},[886],[888,95954,95955],{"xmlns":890},[892,95956,95957,95967],{},[895,95958,95959,95961],{},[898,95960,10871],{},[1707,95962,95963,95965],{},[898,95964,1690],{},[898,95966,1775],{},[902,95968,87387],{"encoding":904},": v bodě maxima ",[883,95971,95973],{"className":95972},[886],[888,95974,95975],{"xmlns":890},[892,95976,95977,95987],{},[895,95978,95979,95981],{},[898,95980,10871],{},[1707,95982,95983,95985],{},[898,95984,1690],{},[898,95986,1775],{},[902,95988,87387],{"encoding":904},[883,95990,95992],{"className":95991},[886],[888,95993,95994],{"xmlns":890},[892,95995,95996,96016],{},[895,95997,95998,96000,96006,96008,96010],{},[898,95999,16690],{},[1707,96001,96002,96004],{},[898,96003,1690],{},[898,96005,1775],{},[1716,96007,1913],{},[898,96009,10871],{},[1707,96011,96012,96014],{},[898,96013,1690],{},[898,96015,1775],{},[902,96017,87417],{"encoding":904},[724,96019,96020,96021,96024,96025,3495,96028,96057,96058,96075,96076,96079,96080,96109,96110,96112,96113,2574,96143,96165],{},"Ve ",[38,96022,96023],{},"2F modelu"," se obvykle používají ",[38,96026,96027],{},"Cobb-Douglasovy funkce",[883,96029,96031],{"className":96030},[886],[888,96032,96033],{"xmlns":890},[892,96034,96035,96055],{},[895,96036,96037,96039,96041,96043,96049],{},[898,96038,1878],{},[1716,96040,1913],{},[898,96042,10871],{},[3074,96044,96045,96047],{},[898,96046,1775],{},[898,96048,207],{},[3074,96050,96051,96053],{},[898,96052,1790],{},[898,96054,1952],{},[902,96056,87484],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,96059,96061],{"className":96060},[886],[888,96062,96063],{"xmlns":890},[892,96064,96065,96073],{},[895,96066,96067,96069,96071],{},[898,96068,207],{},[1716,96070,1949],{},[898,96072,1952],{},[902,96074,87578],{"encoding":904}," rozlišujeme ",[38,96077,96078],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,96081,96083],{"className":96082},[886],[888,96084,96085],{"xmlns":890},[892,96086,96087,96107],{},[895,96088,96089,96091,96097,96099,96101],{},[898,96090,16690],{},[1707,96092,96093,96095],{},[898,96094,1690],{},[898,96096,1775],{},[1716,96098,1719],{"separator":1718},[898,96100,16690],{},[1707,96102,96103,96105],{},[898,96104,1690],{},[898,96106,1790],{},[902,96108,87515],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,96111,23585],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,96114,96116],{"className":96115},[886],[888,96117,96118],{"xmlns":890},[892,96119,96120,96140],{},[895,96121,96122,96124,96130,96132,96134],{},[898,96123,16690],{},[1707,96125,96126,96128],{},[898,96127,1690],{},[898,96129,1775],{},[898,96131,3045],{"mathvariant":2068},[898,96133,16690],{},[1707,96135,96136,96138],{},[898,96137,1690],{},[898,96139,1790],{},[902,96141,96142],{"encoding":904},"MP_L\u002FMP_K",[38,96144,96145,96146,1925],{},"mezní míra technické substituce (",[883,96147,96149],{"className":96148},[886],[888,96150,96151],{"xmlns":890},[892,96152,96153,96163],{},[895,96154,96155,96157,96159,96161],{},[898,96156,16690],{},[898,96158,17840],{},[898,96160,4164],{},[898,96162,5352],{},[902,96164,24403],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,96167,14897],{"id":14896},[152,96169,96170,96173,96176,96179,96182,96185,96188,96191,96194,96197,96200],{},[123,96171,96172],{},"Jaké jsou faktory produkce?",[123,96174,96175],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,96177,96178],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,96180,96181],{},"Co udává mezní produkt práce?",[123,96183,96184],{},"Co musí respektovat průběh křivky produkce?",[123,96186,96187],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,96189,96190],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,96192,96193],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,96195,96196],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,96198,96199],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,96201,96202],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,96204,96206],{"id":96205},"úlohy-51517","Úlohy 5.1–5.17",[198,96208,5411],{"id":5410},[724,96210,96211,96214,96215,96237,96238,1343,96258,1343,96278,96298],{},[38,96212,96213],{},"5.1"," Je dána produkce ",[883,96216,96218],{"className":96217},[886],[888,96219,96220],{"xmlns":890},[892,96221,96222,96234],{},[895,96223,96224,96226,96228,96230],{},[898,96225,1878],{},[1716,96227,1913],{},[1712,96229,2998],{},[10595,96231,96232],{},[898,96233,1775],{},[902,96235,96236],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,96239,96241],{"className":96240},[886],[888,96242,96243],{"xmlns":890},[892,96244,96245,96255],{},[895,96246,96247,96249,96251,96253],{},[898,96248,1878],{},[1716,96250,1920],{"stretchy":1919},[1712,96252,1714],{},[1716,96254,1925],{"stretchy":1919},[902,96256,96257],{"encoding":904},"Q(1)",[883,96259,96261],{"className":96260},[886],[888,96262,96263],{"xmlns":890},[892,96264,96265,96275],{},[895,96266,96267,96269,96271,96273],{},[898,96268,1878],{},[1716,96270,1920],{"stretchy":1919},[1712,96272,6849],{},[1716,96274,1925],{"stretchy":1919},[902,96276,96277],{"encoding":904},"Q(4)",[883,96279,96281],{"className":96280},[886],[888,96282,96283],{"xmlns":890},[892,96284,96285,96295],{},[895,96286,96287,96289,96291,96293],{},[898,96288,1878],{},[1716,96290,1920],{"stretchy":1919},[1712,96292,7141],{},[1716,96294,1925],{"stretchy":1919},[902,96296,96297],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,96300,96301,96214,96304,96340,96341,96354,96355,96374,96375,96401,96402,3942,96415,96428],{},[38,96302,96303],{},"5.2",[883,96305,96307],{"className":96306},[886],[888,96308,96309],{"xmlns":890},[892,96310,96311,96337],{},[895,96312,96313,96315,96317,96319,96321,96327,96329,96331],{},[898,96314,1878],{},[1716,96316,1913],{},[1716,96318,2760],{},[1712,96320,9535],{},[3074,96322,96323,96325],{},[898,96324,1775],{},[1712,96326,7072],{},[1716,96328,1949],{},[1712,96330,7141],{},[3074,96332,96333,96335],{},[898,96334,1775],{},[1712,96336,1726],{},[902,96338,96339],{"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 ",[883,96342,96344],{"className":96343},[886],[888,96345,96346],{"xmlns":890},[892,96347,96348,96352],{},[895,96349,96350],{},[898,96351,1775],{},[902,96353,1775],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,96356,96358],{"className":96357},[886],[888,96359,96360],{"xmlns":890},[892,96361,96362,96372],{},[895,96363,96364,96366],{},[898,96365,16690],{},[1707,96367,96368,96370],{},[898,96369,1690],{},[898,96371,1775],{},[902,96373,23849],{"encoding":904},". (f) Vypočtěte ",[883,96376,96378],{"className":96377},[886],[888,96379,96380],{"xmlns":890},[892,96381,96382,96398],{},[895,96383,96384,96386,96392,96394,96396],{},[898,96385,16690],{},[1707,96387,96388,96390],{},[898,96389,1690],{},[898,96391,1775],{},[1716,96393,1920],{"stretchy":1919},[1712,96395,2998],{},[1716,96397,1925],{"stretchy":1919},[902,96399,96400],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,96403,96405],{"className":96404},[886],[888,96406,96407],{"xmlns":890},[892,96408,96409,96413],{},[895,96410,96411],{},[1712,96412,2998],{},[902,96414,2998],{"encoding":904},[883,96416,96418],{"className":96417},[886],[888,96419,96420],{"xmlns":890},[892,96421,96422,96426],{},[895,96423,96424],{},[1712,96425,7265],{},[902,96427,7265],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,96430,96431,96434,96435,96457,96458,96486,96487,96518,96519,1853],{},[38,96432,96433],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,96436,96438],{"className":96437},[886],[888,96439,96440],{"xmlns":890},[892,96441,96442,96454],{},[895,96443,96444,96446,96448,96450],{},[898,96445,1878],{},[1716,96447,1913],{},[1712,96449,28904],{},[10595,96451,96452],{},[898,96453,1775],{},[902,96455,96456],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,96459,96461],{"className":96460},[886],[888,96462,96463],{"xmlns":890},[892,96464,96465,96483],{},[895,96466,96467,96469,96471,96473,96477,96479,96481],{},[898,96468,1878],{},[1716,96470,1913],{},[1712,96472,43843],{},[10595,96474,96475],{},[898,96476,1775],{},[1716,96478,2760],{},[1712,96480,6849],{},[898,96482,1775],{},[902,96484,96485],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,96488,96490],{"className":96489},[886],[888,96491,96492],{"xmlns":890},[892,96493,96494,96515],{},[895,96495,96496,96498,96500,96502,96504,96506,96509],{},[898,96497,1878],{},[1716,96499,1913],{},[1712,96501,5808],{},[898,96503,1775],{},[1716,96505,2760],{},[1712,96507,96508],{},"0,01",[3074,96510,96511,96513],{},[898,96512,1775],{},[1712,96514,1726],{},[902,96516,96517],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,96520,96522],{"className":96521},[886],[888,96523,96524],{"xmlns":890},[892,96525,96526,96552],{},[895,96527,96528,96530,96532,96534,96536,96542,96544,96546],{},[898,96529,1878],{},[1716,96531,1913],{},[1716,96533,2760],{},[1712,96535,80965],{},[3074,96537,96538,96540],{},[898,96539,1775],{},[1712,96541,7072],{},[1716,96543,1949],{},[1712,96545,7141],{},[3074,96547,96548,96550],{},[898,96549,1775],{},[1712,96551,1726],{},[902,96553,96554],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,96556,96557,96560,96561,16504,96580,84952,96597,1853],{},[38,96558,96559],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,96562,96564],{"className":96563},[886],[888,96565,96566],{"xmlns":890},[892,96567,96568,96578],{},[895,96569,96570,96572],{},[898,96571,10871],{},[1707,96573,96574,96576],{},[898,96575,1690],{},[898,96577,1775],{},[902,96579,87387],{"encoding":904},[883,96581,96583],{"className":96582},[886],[888,96584,96585],{"xmlns":890},[892,96586,96587,96595],{},[895,96588,96589],{},[1707,96590,96591,96593],{},[898,96592,1775],{},[1712,96594,2505],{},[902,96596,88312],{"encoding":904},[883,96598,96600],{"className":96599},[886],[888,96601,96602],{"xmlns":890},[892,96603,96604,96644],{},[895,96605,96606,96608,96614,96616,96622,96624,96626,96628,96634,96636,96642],{},[898,96607,10871],{},[1707,96609,96610,96612],{},[898,96611,1690],{},[898,96613,1775],{},[1716,96615,1920],{"stretchy":1919},[1707,96617,96618,96620],{},[898,96619,1775],{},[1712,96621,2505],{},[1716,96623,1925],{"stretchy":1919},[1716,96625,1913],{},[898,96627,16690],{},[1707,96629,96630,96632],{},[898,96631,1690],{},[898,96633,1775],{},[1716,96635,1920],{"stretchy":1919},[1707,96637,96638,96640],{},[898,96639,1775],{},[1712,96641,2505],{},[1716,96643,1925],{"stretchy":1919},[902,96645,96646],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,96648,96649,96214,96652,2772,96688,96701,96702,96721],{},[38,96650,96651],{},"5.5",[883,96653,96655],{"className":96654},[886],[888,96656,96657],{"xmlns":890},[892,96658,96659,96685],{},[895,96660,96661,96663,96665,96667,96669,96675,96677,96679],{},[898,96662,1878],{},[1716,96664,1913],{},[1716,96666,2760],{},[1712,96668,11302],{},[3074,96670,96671,96673],{},[898,96672,1775],{},[1712,96674,7072],{},[1716,96676,1949],{},[1712,96678,6804],{},[3074,96680,96681,96683],{},[898,96682,1775],{},[1712,96684,1726],{},[902,96686,96687],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,96689,96691],{"className":96690},[886],[888,96692,96693],{"xmlns":890},[892,96694,96695,96699],{},[895,96696,96697],{},[898,96698,1775],{},[902,96700,1775],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,96703,96705],{"className":96704},[886],[888,96706,96707],{"xmlns":890},[892,96708,96709,96719],{},[895,96710,96711,96713],{},[898,96712,10871],{},[1707,96714,96715,96717],{},[898,96716,1690],{},[898,96718,1775],{},[902,96720,87387],{"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.",[198,96723,96725],{"id":96724},"dvoufaktorový-model","Dvoufaktorový model",[724,96727,96728,96731,96732,96457,96758,96486,96800,1853],{},[38,96729,96730],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,96733,96735],{"className":96734},[886],[888,96736,96737],{"xmlns":890},[892,96738,96739,96755],{},[895,96740,96741,96743,96745,96747,96749],{},[898,96742,1878],{},[1716,96744,1913],{},[1712,96746,7109],{},[898,96748,1775],{},[3074,96750,96751,96753],{},[898,96752,1790],{},[1712,96754,1726],{},[902,96756,96757],{"encoding":904},"Q = 7 L K^{2}",[883,96759,96761],{"className":96760},[886],[888,96762,96763],{"xmlns":890},[892,96764,96765,96797],{},[895,96766,96767,96769,96771,96773,96785],{},[898,96768,1878],{},[1716,96770,1913],{},[1712,96772,5808],{},[3074,96774,96775,96777],{},[898,96776,1775],{},[895,96778,96779,96781,96783],{},[1712,96780,1726],{},[898,96782,3045],{"mathvariant":2068},[1712,96784,7072],{},[3074,96786,96787,96789],{},[898,96788,1790],{},[895,96790,96791,96793,96795],{},[1712,96792,1714],{},[898,96794,3045],{"mathvariant":2068},[1712,96796,7072],{},[902,96798,96799],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,96801,96803],{"className":96802},[886],[888,96804,96805],{"xmlns":890},[892,96806,96807,96839],{},[895,96808,96809,96811,96813,96815,96827],{},[898,96810,1878],{},[1716,96812,1913],{},[1712,96814,14816],{},[3074,96816,96817,96819],{},[898,96818,1775],{},[895,96820,96821,96823,96825],{},[1712,96822,7072],{},[898,96824,3045],{"mathvariant":2068},[1712,96826,6985],{},[3074,96828,96829,96831],{},[898,96830,1790],{},[895,96832,96833,96835,96837],{},[1712,96834,1726],{},[898,96836,3045],{"mathvariant":2068},[1712,96838,6985],{},[902,96840,96841],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,96843,96844,96214,96847,96889,96890,1343,96908,96927,96928,96945],{},[38,96845,96846],{},"5.7",[883,96848,96850],{"className":96849},[886],[888,96851,96852],{"xmlns":890},[892,96853,96854,96886],{},[895,96855,96856,96858,96860,96862,96874],{},[898,96857,1878],{},[1716,96859,1913],{},[1712,96861,2998],{},[3074,96863,96864,96866],{},[898,96865,1775],{},[895,96867,96868,96870,96872],{},[1712,96869,1714],{},[898,96871,3045],{"mathvariant":2068},[1712,96873,1726],{},[3074,96875,96876,96878],{},[898,96877,1790],{},[895,96879,96880,96882,96884],{},[1712,96881,1714],{},[898,96883,3045],{"mathvariant":2068},[1712,96885,1726],{},[902,96887,96888],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,96891,96893],{"className":96892},[886],[888,96894,96895],{"xmlns":890},[892,96896,96897,96905],{},[895,96898,96899,96901,96903],{},[898,96900,1775],{},[1716,96902,1913],{},[1712,96904,33925],{},[902,96906,96907],{"encoding":904},"L = 400",[883,96909,96911],{"className":96910},[886],[888,96912,96913],{"xmlns":890},[892,96914,96915,96924],{},[895,96916,96917,96919,96921],{},[898,96918,1790],{},[1716,96920,1913],{},[1712,96922,96923],{},"17576",[902,96925,96926],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,96929,96931],{"className":96930},[886],[888,96932,96933],{"xmlns":890},[892,96934,96935,96943],{},[895,96936,96937,96939,96941],{},[898,96938,1775],{},[1716,96940,1719],{"separator":1718},[898,96942,1790],{},[902,96944,91739],{"encoding":904}," zdvojnásobí.",[724,96947,96948,96951,96952,96889,96983,1343,97001,82338,97019,97049,97050,97080,97081,3942,97094,97108,97109,3942,97122,97135],{},[38,96949,96950],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,96953,96955],{"className":96954},[886],[888,96956,96957],{"xmlns":890},[892,96958,96959,96980],{},[895,96960,96961,96963,96965,96968,96974],{},[898,96962,1878],{},[1716,96964,1913],{},[1712,96966,96967],{},"1,01",[3074,96969,96970,96972],{},[898,96971,1775],{},[1712,96973,37502],{},[3074,96975,96976,96978],{},[898,96977,1790],{},[1712,96979,37561],{},[902,96981,96982],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,96984,96986],{"className":96985},[886],[888,96987,96988],{"xmlns":890},[892,96989,96990,96998],{},[895,96991,96992,96994,96996],{},[898,96993,1775],{},[1716,96995,1913],{},[1712,96997,44505],{},[902,96999,97000],{"encoding":904},"L = 250",[883,97002,97004],{"className":97003},[886],[888,97005,97006],{"xmlns":890},[892,97007,97008,97016],{},[895,97009,97010,97012,97014],{},[898,97011,1790],{},[1716,97013,1913],{},[1712,97015,16656],{},[902,97017,97018],{"encoding":904},"K = 1000",[883,97020,97022],{"className":97021},[886],[888,97023,97024],{"xmlns":890},[892,97025,97026,97046],{},[895,97027,97028,97030,97036,97038,97040,97042,97044],{},[898,97029,16690],{},[1707,97031,97032,97034],{},[898,97033,1690],{},[898,97035,1775],{},[1716,97037,1920],{"stretchy":1919},[1712,97039,44505],{},[1716,97041,1719],{"separator":1718},[1712,97043,16656],{},[1716,97045,1925],{"stretchy":1919},[902,97047,97048],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,97051,97053],{"className":97052},[886],[888,97054,97055],{"xmlns":890},[892,97056,97057,97077],{},[895,97058,97059,97061,97067,97069,97071,97073,97075],{},[898,97060,16690],{},[1707,97062,97063,97065],{},[898,97064,1690],{},[898,97066,1790],{},[1716,97068,1920],{"stretchy":1919},[1712,97070,44505],{},[1716,97072,1719],{"separator":1718},[1712,97074,16656],{},[1716,97076,1925],{"stretchy":1919},[902,97078,97079],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,97082,97084],{"className":97083},[886],[888,97085,97086],{"xmlns":890},[892,97087,97088,97092],{},[895,97089,97090],{},[898,97091,1775],{},[902,97093,1775],{"encoding":904},[883,97095,97097],{"className":97096},[886],[888,97098,97099],{"xmlns":890},[892,97100,97101,97106],{},[895,97102,97103],{},[1712,97104,97105],{},"260",[902,97107,97105],{"encoding":904}," a současném poklesu ",[883,97110,97112],{"className":97111},[886],[888,97113,97114],{"xmlns":890},[892,97115,97116,97120],{},[895,97117,97118],{},[898,97119,1790],{},[902,97121,1790],{"encoding":904},[883,97123,97125],{"className":97124},[886],[888,97126,97127],{"xmlns":890},[892,97128,97129,97133],{},[895,97130,97131],{},[1712,97132,28985],{},[902,97134,28985],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,97137,97138,97141,97142,1853],{},[38,97139,97140],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,97143,97145],{"className":97144},[886],[888,97146,97147],{"xmlns":890},[892,97148,97149,97169],{},[895,97150,97151,97153,97155,97157,97163],{},[898,97152,1878],{},[1716,97154,1913],{},[1712,97156,2998],{},[3074,97158,97159,97161],{},[898,97160,1775],{},[1712,97162,80965],{},[3074,97164,97165,97167],{},[898,97166,1790],{},[1712,97168,5771],{},[902,97170,97171],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,97173,97174,97177,97178,93335,97201,24198,97214,1994,97264,2365],{},[38,97175,97176],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,97179,97181],{"className":97180},[886],[888,97182,97183],{"xmlns":890},[892,97184,97185,97199],{},[895,97186,97187,97189,97191,97193,97195,97197],{},[898,97188,1878],{},[1716,97190,1920],{"stretchy":1919},[898,97192,1775],{},[1716,97194,1719],{"separator":1718},[898,97196,1790],{},[1716,97198,1925],{"stretchy":1919},[902,97200,23802],{"encoding":904},[883,97202,97204],{"className":97203},[886],[888,97205,97206],{"xmlns":890},[892,97207,97208,97212],{},[895,97209,97210],{},[898,97211,1740],{},[902,97213,1740],{"encoding":904},[883,97215,97217],{"className":97216},[886],[888,97218,97219],{"xmlns":890},[892,97220,97221,97261],{},[895,97222,97223,97225,97233,97235,97237,97245,97247,97249,97251,97253,97255,97257,97259],{},[898,97224,1775],{},[7204,97226,97227,97229,97231],{},[898,97228,1878],{},[898,97230,1775],{},[1716,97232,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,97234,1949],{},[898,97236,1790],{},[7204,97238,97239,97241,97243],{},[898,97240,1878],{},[898,97242,1790],{},[1716,97244,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,97246,1913],{},[898,97248,1740],{},[898,97250,1878],{},[1716,97252,1920],{"stretchy":1919},[898,97254,1775],{},[1716,97256,1719],{"separator":1718},[898,97258,1790],{},[1716,97260,1925],{"stretchy":1919},[902,97262,97263],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,97265,93310],{},[724,97267,97268,97271],{},[38,97269,97270],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,97273,97274,96214,97277,97317,97318,1343,97340,1343,97362,97384],{},[38,97275,97276],{},"5.12",[883,97278,97280],{"className":97279},[886],[888,97281,97282],{"xmlns":890},[892,97283,97284,97314],{},[895,97285,97286,97288,97290,97302],{},[898,97287,1878],{},[1716,97289,1913],{},[3074,97291,97292,97294],{},[898,97293,1775],{},[895,97295,97296,97298,97300],{},[1712,97297,1714],{},[898,97299,3045],{"mathvariant":2068},[1712,97301,7072],{},[3074,97303,97304,97306],{},[898,97305,1790],{},[895,97307,97308,97310,97312],{},[1712,97309,1714],{},[898,97311,3045],{"mathvariant":2068},[1712,97313,6849],{},[902,97315,97316],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,97319,97321],{"className":97320},[886],[888,97322,97323],{"xmlns":890},[892,97324,97325,97337],{},[895,97326,97327,97333,97335],{},[1707,97328,97329,97331],{},[898,97330,93551],{},[1712,97332,2505],{},[1716,97334,1913],{},[1712,97336,1714],{},[902,97338,97339],{"encoding":904},"q_0 = 1",[883,97341,97343],{"className":97342},[886],[888,97344,97345],{"xmlns":890},[892,97346,97347,97359],{},[895,97348,97349,97355,97357],{},[1707,97350,97351,97353],{},[898,97352,93551],{},[1712,97354,1714],{},[1716,97356,1913],{},[1712,97358,1726],{},[902,97360,97361],{"encoding":904},"q_1 = 2",[883,97363,97365],{"className":97364},[886],[888,97366,97367],{"xmlns":890},[892,97368,97369,97381],{},[895,97370,97371,97377,97379],{},[1707,97372,97373,97375],{},[898,97374,93551],{},[1712,97376,1726],{},[1716,97378,1913],{},[1712,97380,7072],{},[902,97382,97383],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,97386,97387,96214,97390,97430,97431,1343,97459,1343,97487,1343,97515,1343,97544,1343,97573,1343,97602,1343,97631,1343,97660,1853],{},[38,97388,97389],{},"5.13",[883,97391,97393],{"className":97392},[886],[888,97394,97395],{"xmlns":890},[892,97396,97397,97427],{},[895,97398,97399,97401,97403,97415],{},[898,97400,1878],{},[1716,97402,1913],{},[3074,97404,97405,97407],{},[898,97406,1775],{},[895,97408,97409,97411,97413],{},[1712,97410,1714],{},[898,97412,3045],{"mathvariant":2068},[1712,97414,7072],{},[3074,97416,97417,97419],{},[898,97418,1790],{},[895,97420,97421,97423,97425],{},[1712,97422,1714],{},[898,97424,3045],{"mathvariant":2068},[1712,97426,1726],{},[902,97428,97429],{"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): ",[883,97432,97434],{"className":97433},[886],[888,97435,97436],{"xmlns":890},[892,97437,97438,97456],{},[895,97439,97440,97446,97448,97450,97452,97454],{},[1707,97441,97442,97444],{},[898,97443,10871],{},[1712,97445,1714],{},[1716,97447,2502],{"stretchy":1919},[1712,97449,1714],{},[1716,97451,22241],{"separator":1718},[1712,97453,1714],{},[1716,97455,2516],{"stretchy":1919},[902,97457,97458],{"encoding":904},"A_1[1; 1]",[883,97460,97462],{"className":97461},[886],[888,97463,97464],{"xmlns":890},[892,97465,97466,97484],{},[895,97467,97468,97474,97476,97478,97480,97482],{},[1707,97469,97470,97472],{},[898,97471,10871],{},[1712,97473,1726],{},[1716,97475,2502],{"stretchy":1919},[1712,97477,1714],{},[1716,97479,22241],{"separator":1718},[1712,97481,12398],{},[1716,97483,2516],{"stretchy":1919},[902,97485,97486],{"encoding":904},"A_2[1; 8]",[883,97488,97490],{"className":97489},[886],[888,97491,97492],{"xmlns":890},[892,97493,97494,97512],{},[895,97495,97496,97502,97504,97506,97508,97510],{},[1707,97497,97498,97500],{},[898,97499,10871],{},[1712,97501,7072],{},[1716,97503,2502],{"stretchy":1919},[1712,97505,1714],{},[1716,97507,22241],{"separator":1718},[1712,97509,79351],{},[1716,97511,2516],{"stretchy":1919},[902,97513,97514],{"encoding":904},"A_3[1; 27]",[883,97516,97518],{"className":97517},[886],[888,97519,97520],{"xmlns":890},[892,97521,97522,97541],{},[895,97523,97524,97530,97532,97534,97536,97539],{},[1707,97525,97526,97528],{},[898,97527,10871],{},[1712,97529,6849],{},[1716,97531,2502],{"stretchy":1919},[1712,97533,1726],{},[1716,97535,22241],{"separator":1718},[1712,97537,97538],{},"0,353",[1716,97540,2516],{"stretchy":1919},[902,97542,97543],{"encoding":904},"A_4[2; 0{,}353]",[883,97545,97547],{"className":97546},[886],[888,97548,97549],{"xmlns":890},[892,97550,97551,97570],{},[895,97552,97553,97559,97561,97563,97565,97568],{},[1707,97554,97555,97557],{},[898,97556,10871],{},[1712,97558,6985],{},[1716,97560,2502],{"stretchy":1919},[1712,97562,1726],{},[1716,97564,22241],{"separator":1718},[1712,97566,97567],{},"2,828",[1716,97569,2516],{"stretchy":1919},[902,97571,97572],{"encoding":904},"A_5[2; 2{,}828]",[883,97574,97576],{"className":97575},[886],[888,97577,97578],{"xmlns":890},[892,97579,97580,97599],{},[895,97581,97582,97588,97590,97592,97594,97597],{},[1707,97583,97584,97586],{},[898,97585,10871],{},[1712,97587,6231],{},[1716,97589,2502],{"stretchy":1919},[1712,97591,1726],{},[1716,97593,22241],{"separator":1718},[1712,97595,97596],{},"9,545",[1716,97598,2516],{"stretchy":1919},[902,97600,97601],{"encoding":904},"A_6[2; 9{,}545]",[883,97603,97605],{"className":97604},[886],[888,97606,97607],{"xmlns":890},[892,97608,97609,97628],{},[895,97610,97611,97617,97619,97621,97623,97626],{},[1707,97612,97613,97615],{},[898,97614,10871],{},[1712,97616,7109],{},[1716,97618,2502],{"stretchy":1919},[1712,97620,77313],{},[1716,97622,22241],{"separator":1718},[1712,97624,97625],{},"0,544",[1716,97627,2516],{"stretchy":1919},[902,97629,97630],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,97632,97634],{"className":97633},[886],[888,97635,97636],{"xmlns":890},[892,97637,97638,97657],{},[895,97639,97640,97646,97648,97650,97652,97655],{},[1707,97641,97642,97644],{},[898,97643,10871],{},[1712,97645,12398],{},[1716,97647,2502],{"stretchy":1919},[1712,97649,77313],{},[1716,97651,22241],{"separator":1718},[1712,97653,97654],{},"14,696",[1716,97656,2516],{"stretchy":1919},[902,97658,97659],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,97661,97663],{"className":97662},[886],[888,97664,97665],{"xmlns":890},[892,97666,97667,97685],{},[895,97668,97669,97675,97677,97679,97681,97683],{},[1707,97670,97671,97673],{},[898,97672,10871],{},[1712,97674,7141],{},[1716,97676,2502],{"stretchy":1919},[1712,97678,1726],{},[1716,97680,22241],{"separator":1718},[1712,97682,6985],{},[1716,97684,2516],{"stretchy":1919},[902,97686,97687],{"encoding":904},"A_9[2; 5]",[724,97689,97690,97693],{},[38,97691,97692],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,97695,97696,97699,97700,97730,97731,97744,97745,97758,97759,82071,97778,97797,97798,1853],{},[38,97697,97698],{},"5.15"," Produkce firmy je dána vztahem ",[883,97701,97703],{"className":97702},[886],[888,97704,97705],{"xmlns":890},[892,97706,97707,97727],{},[895,97708,97709,97711,97713,97715,97721],{},[898,97710,1878],{},[1716,97712,1913],{},[1712,97714,1726],{},[3074,97716,97717,97719],{},[898,97718,1775],{},[1712,97720,5771],{},[3074,97722,97723,97725],{},[898,97724,1790],{},[1712,97726,37561],{},[902,97728,97729],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,97732,97734],{"className":97733},[886],[888,97735,97736],{"xmlns":890},[892,97737,97738,97742],{},[895,97739,97740],{},[1712,97741,12151],{},[902,97743,12151],{"encoding":904}," pracovníků a disponuje-li ",[883,97746,97748],{"className":97747},[886],[888,97749,97750],{"xmlns":890},[892,97751,97752,97756],{},[895,97753,97754],{},[1712,97755,77189],{},[902,97757,77189],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,97760,97762],{"className":97761},[886],[888,97763,97764],{"xmlns":890},[892,97765,97766,97776],{},[895,97767,97768,97770,97772,97774],{},[898,97769,16690],{},[898,97771,17840],{},[898,97773,4164],{},[898,97775,5352],{},[902,97777,24403],{"encoding":904},[883,97779,97781],{"className":97780},[886],[888,97782,97783],{"xmlns":890},[892,97784,97785,97795],{},[895,97786,97787,97789,97791,97793],{},[898,97788,16690],{},[898,97790,17840],{},[898,97792,4164],{},[898,97794,5352],{},[902,97796,24403],{"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 ",[883,97799,97801],{"className":97800},[886],[888,97802,97803],{"xmlns":890},[892,97804,97805,97810],{},[895,97806,97807],{},[1712,97808,97809],{},"95",[902,97811,97809],{"encoding":904},[724,97813,97814,96214,97817,83745,97849,97868,97869,97882,97883,97896,97897,97910],{},[38,97815,97816],{},"5.16",[883,97818,97820],{"className":97819},[886],[888,97821,97822],{"xmlns":890},[892,97823,97824,97846],{},[895,97825,97826,97828,97830,97836,97838,97840],{},[898,97827,1878],{},[1716,97829,1913],{},[3074,97831,97832,97834],{},[898,97833,1790],{},[1712,97835,1726],{},[1716,97837,1949],{},[1712,97839,1726],{},[3074,97841,97842,97844],{},[898,97843,1775],{},[1712,97845,1726],{},[902,97847,97848],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,97850,97852],{"className":97851},[886],[888,97853,97854],{"xmlns":890},[892,97855,97856,97866],{},[895,97857,97858,97860,97862,97864],{},[898,97859,16690],{},[898,97861,17840],{},[898,97863,4164],{},[898,97865,5352],{},[902,97867,24403],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,97870,97872],{"className":97871},[886],[888,97873,97874],{"xmlns":890},[892,97875,97876,97880],{},[895,97877,97878],{},[1712,97879,5808],{},[902,97881,5808],{"encoding":904}," pracovníky a ",[883,97884,97886],{"className":97885},[886],[888,97887,97888],{"xmlns":890},[892,97889,97890,97894],{},[895,97891,97892],{},[1712,97893,90371],{},[902,97895,90371],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,97898,97900],{"className":97899},[886],[888,97901,97902],{"xmlns":890},[892,97903,97904,97908],{},[895,97905,97906],{},[1712,97907,11710],{},[902,97909,11710],{"encoding":904}," jednotek.",[724,97912,97913,97916,97917,24198,97947,1853],{},[38,97914,97915],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,97918,97920],{"className":97919},[886],[888,97921,97922],{"xmlns":890},[892,97923,97924,97944],{},[895,97925,97926,97928,97930,97932,97938],{},[898,97927,1878],{},[1716,97929,1913],{},[898,97931,10871],{},[3074,97933,97934,97936],{},[898,97935,1775],{},[898,97937,207],{},[3074,97939,97940,97942],{},[898,97941,1790],{},[898,97943,1952],{},[902,97945,97946],{"encoding":904},"Q = A L^{a} K^{b}",[883,97948,97950],{"className":97949},[886],[888,97951,97952],{"xmlns":890},[892,97953,97954,97984],{},[895,97955,97956,97958,97960,97962,97964,97966,97974,97976],{},[898,97957,16690],{},[898,97959,17840],{},[898,97961,4164],{},[898,97963,5352],{},[1716,97965,1913],{},[2747,97967,97968],{"scriptlevel":2505,"displaystyle":1919},[2750,97969,97970,97972],{},[898,97971,207],{},[898,97973,1952],{},[1716,97975,9532],{},[2747,97977,97978],{"scriptlevel":2505,"displaystyle":1919},[2750,97979,97980,97982],{},[898,97981,1790],{},[898,97983,1775],{},[902,97985,97986],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,97988,14947],{"id":14946},[120,97990,97991,98024,98051,98060,98110,98141,98194,98217,98272,98345,98423,98466,98498,98531,98572,98644,98705,98771,98788,98861,98927,98979,99035,99069,99112],{},[123,97992,97993,97996,97997,1778,98010,98023],{},[38,97994,97995],{},"Faktory (vstupy) produkce:"," práce ",[883,97998,98000],{"className":97999},[886],[888,98001,98002],{"xmlns":890},[892,98003,98004,98008],{},[895,98005,98006],{},[898,98007,1775],{},[902,98009,1775],{"encoding":904},[883,98011,98013],{"className":98012},[886],[888,98014,98015],{"xmlns":890},[892,98016,98017,98021],{},[895,98018,98019],{},[898,98020,1790],{},[902,98022,1790],{"encoding":904},", půda.",[123,98025,98026,3369,98028,1853],{},[38,98027,5411],{},[883,98029,98031],{"className":98030},[886],[888,98032,98033],{"xmlns":890},[892,98034,98035,98049],{},[895,98036,98037,98039,98041,98043,98045,98047],{},[898,98038,1878],{},[1716,98040,1913],{},[898,98042,1878],{},[1716,98044,1920],{"stretchy":1919},[898,98046,1775],{},[1716,98048,1925],{"stretchy":1919},[902,98050,87298],{"encoding":904},[123,98052,98053,1994,98055,8086,98058,1853],{},[38,98054,859],{},[614,98056,98057],{},"production function",[38,98059,87801],{},[123,98061,98062,3495,98064,1853],{},[38,98063,87847],{},[883,98065,98067],{"className":98066},[886],[888,98068,98069],{"xmlns":890},[892,98070,98071,98107],{},[895,98072,98073,98075,98081,98083,98085,98087,98089,98091,98093,98095,98101,98103,98105],{},[898,98074,16690],{},[1707,98076,98077,98079],{},[898,98078,1690],{},[898,98080,1775],{},[1716,98082,1913],{},[898,98084,5198],{},[898,98086,1878],{},[898,98088,3045],{"mathvariant":2068},[898,98090,5198],{},[898,98092,1775],{},[1716,98094,1913],{},[3074,98096,98097,98099],{},[898,98098,1878],{},[1716,98100,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,98102,1920],{"stretchy":1919},[898,98104,1775],{},[1716,98106,1925],{"stretchy":1919},[902,98108,98109],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,98111,98112,3495,98114,1853],{},[38,98113,88782],{},[883,98115,98117],{"className":98116},[886],[888,98118,98119],{"xmlns":890},[892,98120,98121,98139],{},[895,98122,98123,98125,98131,98133,98135,98137],{},[898,98124,10871],{},[1707,98126,98127,98129],{},[898,98128,1690],{},[898,98130,1775],{},[1716,98132,1913],{},[898,98134,1878],{},[898,98136,3045],{"mathvariant":2068},[898,98138,1775],{},[902,98140,87366],{"encoding":904},[123,98142,98143,98145,98146,24198,98163,1853],{},[38,98144,88269],{}," — od určitého ",[883,98147,98149],{"className":98148},[886],[888,98150,98151],{"xmlns":890},[892,98152,98153,98161],{},[895,98154,98155],{},[1707,98156,98157,98159],{},[898,98158,1775],{},[1712,98160,2505],{},[902,98162,88312],{"encoding":904},[883,98164,98166],{"className":98165},[886],[888,98167,98168],{"xmlns":890},[892,98169,98170,98192],{},[895,98171,98172,98182,98184,98186,98188,98190],{},[3074,98173,98174,98176],{},[898,98175,1878],{},[895,98177,98178,98180],{},[1716,98179,8505],{"mathvariant":2068},[1716,98181,8505],{"mathvariant":2068},[1716,98183,1920],{"stretchy":1919},[898,98185,1775],{},[1716,98187,1925],{"stretchy":1919},[1716,98189,2704],{},[1712,98191,2505],{},[902,98193,88458],{"encoding":904},[123,98195,98196,3495,98199,98216],{},[38,98197,98198],{},"Inflexní bod",[883,98200,98202],{"className":98201},[886],[888,98203,98204],{"xmlns":890},[892,98205,98206,98214],{},[895,98207,98208],{},[1707,98209,98210,98212],{},[898,98211,1775],{},[1712,98213,2505],{},[902,98215,88312],{"encoding":904}," — přechod z konvexity do konkavity.",[123,98218,98219,3495,98222,3369,98239,1853],{},[38,98220,98221],{},"Bod maxima produkce",[883,98223,98225],{"className":98224},[886],[888,98226,98227],{"xmlns":890},[892,98228,98229,98237],{},[895,98230,98231],{},[1707,98232,98233,98235],{},[898,98234,1775],{},[1712,98236,1714],{},[902,98238,27010],{"encoding":904},[883,98240,98242],{"className":98241},[886],[888,98243,98244],{"xmlns":890},[892,98245,98246,98270],{},[895,98247,98248,98250,98256,98258,98264,98266,98268],{},[898,98249,16690],{},[1707,98251,98252,98254],{},[898,98253,1690],{},[898,98255,1775],{},[1716,98257,1920],{"stretchy":1919},[1707,98259,98260,98262],{},[898,98261,1775],{},[1712,98263,1714],{},[1716,98265,1925],{"stretchy":1919},[1716,98267,1913],{},[1712,98269,2505],{},[902,98271,88531],{"encoding":904},[123,98273,98274,98296,98297,24198,98316,1853],{},[38,98275,98276,98277],{},"Princip maximalizace ",[883,98278,98280],{"className":98279},[886],[888,98281,98282],{"xmlns":890},[892,98283,98284,98294],{},[895,98285,98286,98288],{},[898,98287,10871],{},[1707,98289,98290,98292],{},[898,98291,1690],{},[898,98293,1775],{},[902,98295,87387],{"encoding":904}," — v bodě maxima ",[883,98298,98300],{"className":98299},[886],[888,98301,98302],{"xmlns":890},[892,98303,98304,98314],{},[895,98305,98306,98308],{},[898,98307,10871],{},[1707,98309,98310,98312],{},[898,98311,1690],{},[898,98313,1775],{},[902,98315,87387],{"encoding":904},[883,98317,98319],{"className":98318},[886],[888,98320,98321],{"xmlns":890},[892,98322,98323,98343],{},[895,98324,98325,98327,98333,98335,98337],{},[898,98326,16690],{},[1707,98328,98329,98331],{},[898,98330,1690],{},[898,98332,1775],{},[1716,98334,1913],{},[898,98336,10871],{},[1707,98338,98339,98341],{},[898,98340,1690],{},[898,98342,1775],{},[902,98344,87417],{"encoding":904},[123,98346,98347,3495,98350,1343,98389,1343,98406,1853],{},[38,98348,98349],{},"Polynomiální produkční funkce",[883,98351,98353],{"className":98352},[886],[888,98354,98355],{"xmlns":890},[892,98356,98357,98387],{},[895,98358,98359,98361,98363,98365,98367,98369,98371,98377,98379,98381],{},[898,98360,1878],{},[1716,98362,1920],{"stretchy":1919},[898,98364,1775],{},[1716,98366,1925],{"stretchy":1919},[1716,98368,1913],{},[898,98370,207],{},[3074,98372,98373,98375],{},[898,98374,1775],{},[1712,98376,7072],{},[1716,98378,1949],{},[898,98380,1952],{},[3074,98382,98383,98385],{},[898,98384,1775],{},[1712,98386,1726],{},[902,98388,88649],{"encoding":904},[883,98390,98392],{"className":98391},[886],[888,98393,98394],{"xmlns":890},[892,98395,98396,98404],{},[895,98397,98398,98400,98402],{},[898,98399,207],{},[1716,98401,2704],{},[1712,98403,2505],{},[902,98405,8067],{"encoding":904},[883,98407,98409],{"className":98408},[886],[888,98410,98411],{"xmlns":890},[892,98412,98413,98421],{},[895,98414,98415,98417,98419],{},[898,98416,1952],{},[1716,98418,2716],{},[1712,98420,2505],{},[902,98422,8085],{"encoding":904},[123,98424,98425,3495,98428,1853],{},[38,98426,98427],{},"Diferenciál produkce",[883,98429,98431],{"className":98430},[886],[888,98432,98433],{"xmlns":890},[892,98434,98435,98463],{},[895,98436,98437,98439,98441,98443,98445,98447,98449,98451,98457,98459,98461],{},[898,98438,8485],{"mathvariant":2068},[898,98440,1878],{},[1716,98442,8490],{},[898,98444,5198],{},[898,98446,1878],{},[1716,98448,1913],{},[898,98450,16690],{},[1707,98452,98453,98455],{},[898,98454,1690],{},[898,98456,1775],{},[2074,98458,8508],{},[898,98460,5198],{},[898,98462,1775],{},[902,98464,98465],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,98467,98468,3369,98470,1853],{},[38,98469,96725],{},[883,98471,98473],{"className":98472},[886],[888,98474,98475],{"xmlns":890},[892,98476,98477,98495],{},[895,98478,98479,98481,98483,98485,98487,98489,98491,98493],{},[898,98480,1878],{},[1716,98482,1913],{},[898,98484,1878],{},[1716,98486,1920],{"stretchy":1919},[898,98488,1775],{},[1716,98490,1719],{"separator":1718},[898,98492,1790],{},[1716,98494,1925],{"stretchy":1919},[902,98496,98497],{"encoding":904},"Q = Q(L, K)",[123,98499,98500,3369,98502,1853],{},[38,98501,90819],{},[883,98503,98505],{"className":98504},[886],[888,98506,98507],{"xmlns":890},[892,98508,98509,98529],{},[895,98510,98511,98513,98515,98517,98523],{},[898,98512,1878],{},[1716,98514,1913],{},[898,98516,10871],{},[3074,98518,98519,98521],{},[898,98520,1775],{},[898,98522,207],{},[3074,98524,98525,98527],{},[898,98526,1790],{},[898,98528,1952],{},[902,98530,87484],{"encoding":904},[123,98532,98533,3369,98536,98571],{},[38,98534,98535],{},"Ryzí Cobb-Douglas",[883,98537,98539],{"className":98538},[886],[888,98540,98541],{"xmlns":890},[892,98542,98543,98569],{},[895,98544,98545,98547,98549,98551,98557],{},[898,98546,1878],{},[1716,98548,1913],{},[898,98550,10871],{},[3074,98552,98553,98555],{},[898,98554,1775],{},[898,98556,207],{},[3074,98558,98559,98561],{},[898,98560,1790],{},[895,98562,98563,98565,98567],{},[1712,98564,1714],{},[1716,98566,2760],{},[898,98568,207],{},[902,98570,91646],{"encoding":904}," (konstantní výnosy).",[123,98573,98574,3369,98576,1853],{},[38,98575,92362],{},[883,98577,98579],{"className":98578},[886],[888,98580,98581],{"xmlns":890},[892,98582,98583,98641],{},[895,98584,98585,98587,98589,98591,98593,98595,98597,98599,98601,98603,98613,98615,98617,98627],{},[898,98586,1878],{},[1716,98588,1913],{},[898,98590,10871],{},[1716,98592,2502],{"stretchy":1919},[1716,98594,1920],{"stretchy":1919},[1712,98596,1714],{},[1716,98598,2760],{},[898,98600,207],{},[1716,98602,1925],{"stretchy":1919},[3074,98604,98605,98607],{},[898,98606,1775],{},[895,98608,98609,98611],{},[1716,98610,2760],{},[898,98612,1952],{},[1716,98614,1949],{},[898,98616,207],{},[3074,98618,98619,98621],{},[898,98620,1790],{},[895,98622,98623,98625],{},[1716,98624,2760],{},[898,98626,1952],{},[3074,98628,98629,98631],{},[1716,98630,2516],{"stretchy":1919},[895,98632,98633,98635,98637,98639],{},[1716,98634,2760],{},[1712,98636,1714],{},[898,98638,3045],{"mathvariant":2068},[898,98640,1952],{},[902,98642,98643],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,98645,98646,1994,98649,8086,98671,1994,98674,98704],{},[38,98647,98648],{},"Lineární",[883,98650,98652],{"className":98651},[886],[888,98653,98654],{"xmlns":890},[892,98655,98656,98668],{},[895,98657,98658,98660,98662,98664,98666],{},[898,98659,207],{},[898,98661,1775],{},[1716,98663,1949],{},[898,98665,1952],{},[898,98667,1790],{},[902,98669,98670],{"encoding":904},"aL + bK",[38,98672,98673],{},"Leontiefova",[883,98675,98677],{"className":98676},[886],[888,98678,98679],{"xmlns":890},[892,98680,98681,98701],{},[895,98682,98683,98685,98687,98689,98691,98693,98695,98697,98699],{},[898,98684,92590],{},[1716,98686,68954],{},[1716,98688,1920],{"stretchy":1919},[898,98690,207],{},[898,98692,1775],{},[1716,98694,1719],{"separator":1718},[898,98696,1952],{},[898,98698,1790],{},[1716,98700,1925],{"stretchy":1919},[902,98702,98703],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,98706,98707,3369,98723,1853],{},[38,98708,98709,98710],{},"Homogenita stupně ",[883,98711,98713],{"className":98712},[886],[888,98714,98715],{"xmlns":890},[892,98716,98717,98721],{},[895,98718,98719],{},[898,98720,1740],{},[902,98722,1740],{"encoding":904},[883,98724,98726],{"className":98725},[886],[888,98727,98728],{"xmlns":890},[892,98729,98730,98768],{},[895,98731,98732,98734,98736,98738,98740,98742,98744,98746,98748,98750,98756,98758,98760,98762,98764,98766],{},[898,98733,1878],{},[1716,98735,1920],{"stretchy":1919},[898,98737,2098],{},[898,98739,1775],{},[1716,98741,1719],{"separator":1718},[898,98743,2098],{},[898,98745,1790],{},[1716,98747,1925],{"stretchy":1919},[1716,98749,1913],{},[3074,98751,98752,98754],{},[898,98753,2098],{},[898,98755,1740],{},[898,98757,1878],{},[1716,98759,1920],{"stretchy":1919},[898,98761,1775],{},[1716,98763,1719],{"separator":1718},[898,98765,1790],{},[1716,98767,1925],{"stretchy":1919},[902,98769,98770],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,98772,98773,91744],{},[38,98774,91677,98775],{},[883,98776,98778],{"className":98777},[886],[888,98779,98780],{"xmlns":890},[892,98781,98782,98786],{},[895,98783,98784],{},[898,98785,10871],{},[902,98787,10871],{"encoding":904},[123,98789,98790,98792,98793,98815,98816,98838,98839,2365],{},[38,98791,91178],{}," — konstantní (",[883,98794,98796],{"className":98795},[886],[888,98797,98798],{"xmlns":890},[892,98799,98800,98812],{},[895,98801,98802,98804,98806,98808,98810],{},[898,98803,207],{},[1716,98805,1949],{},[898,98807,1952],{},[1716,98809,1913],{},[1712,98811,1714],{},[902,98813,98814],{"encoding":904},"a+b=1","), rostoucí (",[883,98817,98819],{"className":98818},[886],[888,98820,98821],{"xmlns":890},[892,98822,98823,98835],{},[895,98824,98825,98827,98829,98831,98833],{},[898,98826,207],{},[1716,98828,1949],{},[898,98830,1952],{},[1716,98832,2716],{},[1712,98834,1714],{},[902,98836,98837],{"encoding":904},"a+b>1","), klesající (",[883,98840,98842],{"className":98841},[886],[888,98843,98844],{"xmlns":890},[892,98845,98846,98858],{},[895,98847,98848,98850,98852,98854,98856],{},[898,98849,207],{},[1716,98851,1949],{},[898,98853,1952],{},[1716,98855,2704],{},[1712,98857,1714],{},[902,98859,98860],{"encoding":904},"a+b\u003C1",[123,98862,98863,3495,98865,1343,98895,3495,98897,1853],{},[38,98864,87847],{},[883,98866,98868],{"className":98867},[886],[888,98869,98870],{"xmlns":890},[892,98871,98872,98892],{},[895,98873,98874,98876,98882,98884],{},[898,98875,16690],{},[1707,98877,98878,98880],{},[898,98879,1690],{},[898,98881,1775],{},[1716,98883,1913],{},[7204,98885,98886,98888,98890],{},[898,98887,1878],{},[898,98889,1775],{},[1716,98891,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,98893,98894],{"encoding":904},"MP_L = Q'_L",[38,98896,90751],{},[883,98898,98900],{"className":98899},[886],[888,98901,98902],{"xmlns":890},[892,98903,98904,98924],{},[895,98905,98906,98908,98914,98916],{},[898,98907,16690],{},[1707,98909,98910,98912],{},[898,98911,1690],{},[898,98913,1790],{},[1716,98915,1913],{},[7204,98917,98918,98920,98922],{},[898,98919,1878],{},[898,98921,1790],{},[1716,98923,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,98925,98926],{"encoding":904},"MP_K = Q'_K",[123,98928,98929,3495,98931,1853],{},[38,98930,92965],{},[883,98932,98934],{"className":98933},[886],[888,98935,98936],{"xmlns":890},[892,98937,98938,98976],{},[895,98939,98940,98942,98944,98946,98948,98954,98956,98958,98960,98962,98964,98970,98972,98974],{},[898,98941,5198],{},[898,98943,1878],{},[1716,98945,1913],{},[898,98947,16690],{},[1707,98949,98950,98952],{},[898,98951,1690],{},[898,98953,1775],{},[2074,98955,8508],{},[898,98957,5198],{},[898,98959,1775],{},[1716,98961,1949],{},[898,98963,16690],{},[1707,98965,98966,98968],{},[898,98967,1690],{},[898,98969,1790],{},[2074,98971,8508],{},[898,98973,5198],{},[898,98975,1790],{},[902,98977,98978],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,98980,98981,3369,98983,1853],{},[38,98982,93310],{},[883,98984,98986],{"className":98985},[886],[888,98987,98988],{"xmlns":890},[892,98989,98990,99032],{},[895,98991,98992,98994,99002,99004,99006,99014,99016,99018,99020,99022,99024,99026,99028,99030],{},[898,98993,1775],{},[7204,98995,98996,98998,99000],{},[898,98997,1878],{},[898,98999,1775],{},[1716,99001,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,99003,1949],{},[898,99005,1790],{},[7204,99007,99008,99010,99012],{},[898,99009,1878],{},[898,99011,1790],{},[1716,99013,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,99015,1913],{},[898,99017,1740],{},[2074,99019,8508],{},[898,99021,1878],{},[1716,99023,1920],{"stretchy":1919},[898,99025,1775],{},[1716,99027,1719],{"separator":1718},[898,99029,1790],{},[1716,99031,1925],{"stretchy":1919},[902,99033,99034],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,99036,99037,99040,99041,1853],{},[38,99038,99039],{},"Izokvanta"," — křivka ",[883,99042,99044],{"className":99043},[886],[888,99045,99046],{"xmlns":890},[892,99047,99048,99066],{},[895,99049,99050,99052,99054,99056,99058,99060,99062,99064],{},[898,99051,1878],{},[1716,99053,1920],{"stretchy":1919},[898,99055,1775],{},[1716,99057,1719],{"separator":1718},[898,99059,1790],{},[1716,99061,1925],{"stretchy":1919},[1716,99063,1913],{},[898,99065,93551],{},[902,99067,99068],{"encoding":904},"Q(L, K) = q",[123,99070,99071,3495,99073,1853],{},[38,99072,93740],{},[883,99074,99076],{"className":99075},[886],[888,99077,99078],{"xmlns":890},[892,99079,99080,99110],{},[895,99081,99082,99084,99086,99088,99090,99092,99094,99100,99102,99104],{},[898,99083,16690],{},[898,99085,17840],{},[898,99087,4164],{},[898,99089,5352],{},[1716,99091,1913],{},[898,99093,16690],{},[1707,99095,99096,99098],{},[898,99097,1690],{},[898,99099,1775],{},[898,99101,3045],{"mathvariant":2068},[898,99103,16690],{},[1707,99105,99106,99108],{},[898,99107,1690],{},[898,99109,1790],{},[902,99111,87559],{"encoding":904},[123,99113,99114,3495,99117,1853],{},[38,99115,99116],{},"Substituční vztah",[883,99118,99120],{"className":99119},[886],[888,99121,99122],{"xmlns":890},[892,99123,99124,99148],{},[895,99125,99126,99128,99130,99132,99134,99136,99138,99140,99142,99144,99146],{},[898,99127,8485],{"mathvariant":2068},[898,99129,1790],{},[1716,99131,8490],{},[1716,99133,2760],{},[898,99135,16690],{},[898,99137,17840],{},[898,99139,4164],{},[898,99141,5352],{},[2074,99143,8508],{},[898,99145,5198],{},[898,99147,1775],{},[902,99149,99150],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,99152,15740],{"id":15739},[120,99154,99155,99252,99259,99266],{},[123,99156,99157,3495,99159,99162,99163,1343,99166,99169,99170,99173,99174,99193,99194,8373,99213,99216,99217,99236,99237,2365],{},[38,99158,15747],{},[207,99160,784],{"className":99161,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,99164,15758],{"className":99165,"dataFsResolvedFilePath":764,"href":765},[210],[207,99167,793],{"className":99168,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,99171,880],{"className":99172,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,99175,99177],{"className":99176},[886],[888,99178,99179],{"xmlns":890},[892,99180,99181,99191],{},[895,99182,99183,99185,99187,99189],{},[898,99184,16690],{},[898,99186,17840],{},[898,99188,4164],{},[898,99190,5352],{},[902,99192,24403],{"encoding":904}," ↔ ",[883,99195,99197],{"className":99196},[886],[888,99198,99199],{"xmlns":890},[892,99200,99201,99211],{},[895,99202,99203,99205,99207,99209],{},[898,99204,16690],{},[898,99206,17840],{},[898,99208,9945],{},[898,99210,5352],{},[902,99212,24407],{"encoding":904},[207,99214,15780],{"className":99215,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,99218,99220],{"className":99219},[886],[888,99221,99222],{"xmlns":890},[892,99223,99224,99234],{},[895,99225,99226,99228],{},[898,99227,10871],{},[1707,99229,99230,99232],{},[898,99231,1690],{},[898,99233,1775],{},[902,99235,87387],{"encoding":904}," ↔ min ",[883,99238,99240],{"className":99239},[886],[888,99241,99242],{"xmlns":890},[892,99243,99244,99250],{},[895,99245,99246,99248],{},[898,99247,10871],{},[898,99249,9945],{},[902,99251,68314],{"encoding":904},[123,99253,99254,3495,99256,1853],{},[38,99255,17652],{},[207,99257,15775],{"className":99258,"dataFsResolvedFilePath":848,"href":849},[210],[123,99260,99261,3495,99263,1853],{},[38,99262,30002],{},[207,99264,1094],{"className":99265,"dataFsResolvedFilePath":838,"href":839},[210],[123,99267,99268,3495,99270,1853],{},[38,99269,15794],{},[207,99271,15800],{"className":99272,"dataFsResolvedFilePath":15798,"href":15799},[210],{"title":641,"searchDepth":642,"depth":642,"links":99274},[99275,99276,99277,99281,99283,99288,99289,99296,99297,99299,99300,99301,99303,99308,99309,99310,99314,99315],{"id":87582,"depth":642,"text":87583},{"id":87719,"depth":642,"text":87720},{"id":87822,"depth":642,"text":99278,"children":99279},"Mezní produkt práce (MPLMP_L)",[99280],{"id":88268,"depth":649,"text":88269},{"id":88757,"depth":642,"text":99282},"Průměrný produkt práce (APLAP_L)",{"id":88875,"depth":642,"text":88876,"children":99284},[99285,99286,99287],{"id":89112,"depth":649,"text":78255},{"id":89423,"depth":649,"text":89424},{"id":90143,"depth":649,"text":90144},{"id":90715,"depth":642,"text":90716},{"id":90818,"depth":642,"text":90819,"children":99290},[99291,99292,99294,99295],{"id":91177,"depth":649,"text":91178},{"id":91676,"depth":649,"text":99293},"Parametr efektivity AA",{"id":91747,"depth":649,"text":91748},{"id":2085,"depth":649,"text":92087},{"id":92274,"depth":642,"text":92275},{"id":92613,"depth":642,"text":99298},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":93304,"depth":642,"text":93305},{"id":87648,"depth":642,"text":23585},{"id":93715,"depth":642,"text":99302},"Mezní míra technické substituce (MRTSMRTS)",{"id":94581,"depth":642,"text":94582,"children":99304},[99305,99306,99307],{"id":94585,"depth":649,"text":94586},{"id":95228,"depth":649,"text":95229},{"id":95509,"depth":649,"text":95510},{"id":95855,"depth":642,"text":95856},{"id":14896,"depth":642,"text":14897},{"id":96205,"depth":642,"text":96206,"children":99311},[99312,99313],{"id":5410,"depth":649,"text":5411},{"id":96724,"depth":649,"text":96725},{"id":14946,"depth":642,"text":14947},{"id":15739,"depth":642,"text":15740},{},"\u002Ftopics\u002Fprodukce",{"title":87218,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,23618,99322,99323,99324,87648,99325,99326],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":99329,"title":99330,"body":99331,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":108278,"navigation":664,"path":108279,"seo":108280,"sources":108281,"stem":108282,"tags":108283,"type":15858,"updated":677,"__hash__":108286},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":99332,"toc":108252},[99333,99336,99338,99535,99544,99548,99551,99604,99608,99620,99624,99627,99644,99767,99773,99917,99927,99931,99966,100004,100052,100109,100169,100211,100787,100791,100874,100983,101076,101334,101337,101390,101501,101583,101587,101598,101831,101886,101892,101932,101995,102006,102197,102303,102456,102504,102509,102623,102661,102787,102833,102860,102937,103012,103092,103222,103283,103371,103375,103378,103447,103530,103537,103597,103907,103911,103917,103970,103986,104037,104175,104251,104364,104681,104685,104692,104852,104911,104915,104937,105034,105155,105269,105292,105355,105412,105664,105672,105676,105683,105937,105987,106043,106046,106210,106214,106312,106314,106346,106350,106483,106725,106909,107077,107384,107517,107704,107716,107718,108153,108155],[12,99334,99330],{"id":99335},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,99337,25809],{"id":25808},[724,99339,99340,3495,99342,99373,99374,99377,99378,99408,99409,99427,99428,99468,99469,99472,99473,99486,99487,42018,99490,99503,99504,99517,99518,99531,99532,1853],{},[38,99341,880],{},[883,99343,99345],{"className":99344},[886],[888,99346,99347],{"xmlns":890},[892,99348,99349,99371],{},[895,99350,99351,99353,99355,99361,99363,99369],{},[898,99352,900],{},[1716,99354,1920],{"stretchy":1919},[1707,99356,99357,99359],{},[898,99358,1878],{},[1712,99360,1714],{},[1716,99362,1719],{"separator":1718},[1707,99364,99365,99367],{},[898,99366,1878],{},[1712,99368,1726],{},[1716,99370,1925],{"stretchy":1919},[902,99372,30133],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,99375,99376],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,99379,99381],{"className":99380},[886],[888,99382,99383],{"xmlns":890},[892,99384,99385,99405],{},[895,99386,99387,99389,99395,99397],{},[898,99388,16690],{},[1707,99390,99391,99393],{},[898,99392,900],{},[898,99394,12546],{},[1716,99396,1913],{},[7204,99398,99399,99401,99403],{},[898,99400,900],{},[898,99402,12546],{},[1716,99404,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,99406,99407],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,99410,99412],{"className":99411},[886],[888,99413,99414],{"xmlns":890},[892,99415,99416,99424],{},[895,99417,99418,99420,99422],{},[898,99419,900],{},[1716,99421,1913],{},[898,99423,4478],{},[902,99425,99426],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,99429,99431],{"className":99430},[886],[888,99432,99433],{"xmlns":890},[892,99434,99435,99465],{},[895,99436,99437,99439,99441,99443,99445,99447,99449,99455,99457,99459],{},[898,99438,16690],{},[898,99440,17840],{},[898,99442,9945],{},[898,99444,5352],{},[1716,99446,1913],{},[898,99448,16690],{},[1707,99450,99451,99453],{},[898,99452,900],{},[1712,99454,1714],{},[898,99456,3045],{"mathvariant":2068},[898,99458,16690],{},[1707,99460,99461,99463],{},[898,99462,900],{},[1712,99464,1726],{},[902,99466,99467],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,99470,99471],{},"teorii užitečnosti"," — funkce ",[883,99474,99476],{"className":99475},[886],[888,99477,99478],{"xmlns":890},[892,99479,99480,99484],{},[895,99481,99482],{},[898,99483,900],{},[902,99485,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,99488,99489],{},"Optimalizaci spotřebitele",[883,99491,99493],{"className":99492},[886],[888,99494,99495],{"xmlns":890},[892,99496,99497,99501],{},[895,99498,99499],{},[898,99500,900],{},[902,99502,900],{"encoding":904}," při rozpočtu, min ",[883,99505,99507],{"className":99506},[886],[888,99508,99509],{"xmlns":890},[892,99510,99511,99515],{},[895,99512,99513],{},[898,99514,1805],{},[902,99516,1805],{"encoding":904}," při dané ",[883,99519,99521],{"className":99520},[886],[888,99522,99523],{"xmlns":890},[892,99524,99525,99529],{},[895,99526,99527],{},[898,99528,900],{},[902,99530,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,99533,913],{"className":99534,"dataFsResolvedFilePath":911,"href":912},[210],[724,99536,99537,99538,99540,99541,1853],{},"Kapitola 6 knihy ",[614,99539,15800],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,99542,50513],{"className":99543,"dataFsResolvedFilePath":911,"href":912},[210],[115,99545,99547],{"id":99546},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,99549,99550],{},"Po prostudování této kapitoly byste měli umět:",[120,99552,99553,99559,99568,99573,99576,99582,99588,99591,99597],{},[123,99554,99555,99556,1719],{},"vyložit, co se rozumí termínem ",[38,99557,99558],{},"užitečnost",[123,99560,99561,99562,2247,99565,1719],{},"definovat pojmy ",[38,99563,99564],{},"svazek zboží",[38,99566,99567],{},"funkce užitečnosti",[123,99569,87597,99570,87604],{},[38,99571,99572],{},"mezní užitečnosti",[123,99574,99575],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,99577,87624,99578,99581],{},[38,99579,99580],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,99583,87645,99584,99587],{},[38,99585,99586],{},"křivky užitečnosti"," (indiferenční křivky),",[123,99589,99590],{},"vyjmenovat jejich základní vlastnosti,",[123,99592,87597,99593,99596],{},[38,99594,99595],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,99598,99599,99600,99603],{},"řešit ",[38,99601,99602],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,99605,99607],{"id":99606},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,99609,99610,99611,99615,99616,99619],{},"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 ",[207,99612,99614],{"className":99613,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,99617,99618],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,99621,99623],{"id":99622},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,99625,99626],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,99628,99629,99635],{},[123,99630,99631,99634],{},[38,99632,99633],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,99636,99637,99640,99641,99643],{},[38,99638,99639],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,99642,99376],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1635,99645,99646],{},[724,99647,99648,99650,99651,99654,99655,3495,99668,99671,99672,2247,99685,99704,99705,1343,99731,99758,99759,99762,99763,99766],{},[883,99649,2233],{}," Pozor — ordinalisté užitečnost ",[38,99652,99653],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,99656,99658],{"className":99657},[886],[888,99659,99660],{"xmlns":890},[892,99661,99662,99666],{},[895,99663,99664],{},[898,99665,900],{},[902,99667,900],{"encoding":904},[38,99669,99670],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,99673,99675],{"className":99674},[886],[888,99676,99677],{"xmlns":890},[892,99678,99679,99683],{},[895,99680,99681],{},[898,99682,900],{},[902,99684,900],{"encoding":904},[883,99686,99688],{"className":99687},[886],[888,99689,99690],{"xmlns":890},[892,99691,99692,99701],{},[895,99693,99694],{},[22202,99695,99696,99698],{"accent":1718},[898,99697,900],{},[1716,99699,99700],{},"~",[902,99702,99703],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,99706,99708],{"className":99707},[886],[888,99709,99710],{"xmlns":890},[892,99711,99712,99728],{},[895,99713,99714,99720,99722],{},[22202,99715,99716,99718],{"accent":1718},[898,99717,900],{},[1716,99719,99700],{},[1716,99721,1913],{},[3074,99723,99724,99726],{},[898,99725,900],{},[1712,99727,1726],{},[902,99729,99730],{"encoding":904},"\\tilde U = U^2",[883,99732,99734],{"className":99733},[886],[888,99735,99736],{"xmlns":890},[892,99737,99738,99755],{},[895,99739,99740,99746,99748,99751,99753],{},[22202,99741,99742,99744],{"accent":1718},[898,99743,900],{},[1716,99745,99700],{},[1716,99747,1913],{},[898,99749,99750],{},"ln",[1716,99752,68954],{},[898,99754,900],{},[902,99756,99757],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,99760,99761],{},"porovnání"," mezi svazky a ",[38,99764,99765],{},"poměry"," mezních veličin.",[724,99768,99769,99770,2291],{},"Ordinalistický přístup vychází z ",[38,99771,99772],{},"pěti hlavních předpokladů",[152,99774,99775,99781,99787,99905,99911],{},[123,99776,99777,99780],{},[38,99778,99779],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,99782,99783,99786],{},[38,99784,99785],{},"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.",[123,99788,99789,99792,99793,74495,99806,99819,99820,74495,99833,7636,99846,99849,99850,2247,99869,75324,99887,1853],{},[38,99790,99791],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,99794,99796],{"className":99795},[886],[888,99797,99798],{"xmlns":890},[892,99799,99800,99804],{},[895,99801,99802],{},[898,99803,10871],{},[902,99805,10871],{"encoding":904},[883,99807,99809],{"className":99808},[886],[888,99810,99811],{"xmlns":890},[892,99812,99813,99817],{},[895,99814,99815],{},[898,99816,10856],{},[902,99818,10856],{"encoding":904},", nebude jindy preferovat ",[883,99821,99823],{"className":99822},[886],[888,99824,99825],{"xmlns":890},[892,99826,99827,99831],{},[895,99828,99829],{},[898,99830,10856],{},[902,99832,10856],{"encoding":904},[883,99834,99836],{"className":99835},[886],[888,99837,99838],{"xmlns":890},[892,99839,99840,99844],{},[895,99841,99842],{},[898,99843,10871],{},[902,99845,10871],{"encoding":904},[38,99847,99848],{},"Tranzitivita",": pokud ",[883,99851,99853],{"className":99852},[886],[888,99854,99855],{"xmlns":890},[892,99856,99857,99866],{},[895,99858,99859,99861,99864],{},[898,99860,10871],{},[1716,99862,99863],{},"≻",[898,99865,10856],{},[902,99867,99868],{"encoding":904},"A \\succ B",[883,99870,99872],{"className":99871},[886],[888,99873,99874],{"xmlns":890},[892,99875,99876,99884],{},[895,99877,99878,99880,99882],{},[898,99879,10856],{},[1716,99881,99863],{},[898,99883,9945],{},[902,99885,99886],{"encoding":904},"B \\succ C",[883,99888,99890],{"className":99889},[886],[888,99891,99892],{"xmlns":890},[892,99893,99894,99902],{},[895,99895,99896,99898,99900],{},[898,99897,10871],{},[1716,99899,99863],{},[898,99901,9945],{},[902,99903,99904],{"encoding":904},"A \\succ C",[123,99906,99907,99910],{},[38,99908,99909],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,99912,99913,99916],{},[38,99914,99915],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,99918,99919,99920,99923,99924,1853],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,99921,99922],{},"preference"," a na příbuzné ",[614,99925,99926],{},"funkci užitečnosti",[115,99928,99930],{"id":99929},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,99932,99933,99934,99947,99948,99951,99952,99965],{},"Uvažujme ",[883,99935,99937],{"className":99936},[886],[888,99938,99939],{"xmlns":890},[892,99940,99941,99945],{},[895,99942,99943],{},[898,99944,1740],{},[902,99946,1740],{"encoding":904}," různých zboží. ",[38,99949,99950],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,99953,99955],{"className":99954},[886],[888,99956,99957],{"xmlns":890},[892,99958,99959,99963],{},[895,99960,99961],{},[898,99962,1740],{},[902,99964,1740],{"encoding":904},"-tice",[724,99967,99968],{},[883,99969,99971],{"className":99970},[886],[888,99972,99973],{"xmlns":890},[892,99974,99975,100001],{},[895,99976,99977,99979,99985,99987,99989,99991,99997,99999],{},[1716,99978,1920],{"stretchy":1919},[1707,99980,99981,99983],{},[898,99982,1878],{},[1712,99984,1714],{},[1716,99986,1719],{"separator":1718},[1716,99988,1731],{},[1716,99990,1719],{"separator":1718},[1707,99992,99993,99995],{},[898,99994,1878],{},[898,99996,1740],{},[1716,99998,1925],{"stretchy":1919},[1716,100000,1719],{"separator":1718},[902,100002,100003],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,100005,18149,100006,100023,100024,100037,100038,100041,100042,100045,100046,100049,100050,2291],{},[883,100007,100009],{"className":100008},[886],[888,100010,100011],{"xmlns":890},[892,100012,100013,100021],{},[895,100014,100015],{},[1707,100016,100017,100019],{},[898,100018,1878],{},[898,100020,12546],{},[902,100022,12549],{"encoding":904}," značí množství ",[883,100025,100027],{"className":100026},[886],[888,100028,100029],{"xmlns":890},[892,100030,100031,100035],{},[895,100032,100033],{},[898,100034,12546],{},[902,100036,12546],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,100039,100040],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,100043,100044],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,100047,100048],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,100051,99926],{},[883,100053,100055],{"className":100054},[886],[888,100056,100057],{"xmlns":890,"display":2004},[892,100058,100059,100106],{},[2008,100060,100061],{"width":2010},[2012,100062,100063,100065,100099,100101],{},[2015,100064],{"width":2017},[2015,100066,100067],{},[895,100068,100069,100071,100073,100075,100077,100083,100085,100087,100089,100095,100097],{},[898,100070,900],{},[1716,100072,1913],{},[898,100074,900],{},[1716,100076,1920],{"stretchy":1919},[1707,100078,100079,100081],{},[898,100080,1878],{},[1712,100082,1714],{},[1716,100084,1719],{"separator":1718},[1716,100086,1731],{},[1716,100088,1719],{"separator":1718},[1707,100090,100091,100093],{},[898,100092,1878],{},[898,100094,1740],{},[1716,100096,1925],{"stretchy":1919},[1716,100098,1719],{"separator":1718},[2015,100100],{"width":2017},[2015,100102,100103],{},[2074,100104,100105],{},"(6.1)",[902,100107,100108],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,100110,18149,100111,100141,100142,100164,100165,100168],{},[883,100112,100114],{"className":100113},[886],[888,100115,100116],{"xmlns":890},[892,100117,100118,100138],{},[895,100119,100120,100126,100128,100130,100132],{},[1707,100121,100122,100124],{},[898,100123,1878],{},[1712,100125,1714],{},[1716,100127,1719],{"separator":1718},[1716,100129,1731],{},[1716,100131,1719],{"separator":1718},[1707,100133,100134,100136],{},[898,100135,1878],{},[898,100137,1740],{},[902,100139,100140],{"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 ",[883,100143,100145],{"className":100144},[886],[888,100146,100147],{"xmlns":890},[892,100148,100149,100161],{},[895,100150,100151,100153,100155],{},[898,100152,900],{},[1716,100154,1719],{"separator":1718},[22202,100156,100157,100159],{"accent":1718},[898,100158,900],{},[1716,100160,99700],{},[902,100162,100163],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,100166,100167],{},"monotónní transformace"," zachovávající pořadí.",[724,100170,100171,100172,3369,100175,1853],{},"Dále se omezíme na funkce pro ",[38,100173,100174],{},"dvě zboží",[883,100176,100178],{"className":100177},[886],[888,100179,100180],{"xmlns":890},[892,100181,100182,100208],{},[895,100183,100184,100186,100188,100190,100192,100198,100200,100206],{},[898,100185,900],{},[1716,100187,1913],{},[898,100189,900],{},[1716,100191,1920],{"stretchy":1919},[1707,100193,100194,100196],{},[898,100195,1878],{},[1712,100197,1714],{},[1716,100199,1719],{"separator":1718},[1707,100201,100202,100204],{},[898,100203,1878],{},[1712,100205,1726],{},[1716,100207,1925],{"stretchy":1919},[902,100209,100210],{"encoding":904},"U = U(Q_1, Q_2)",[1635,100212,100213,100288],{},[724,100214,100215,100217,100218,2291],{},[883,100216,65449],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,100219,100221],{"className":100220},[886],[888,100222,100223],{"xmlns":890},[892,100224,100225,100285],{},[895,100226,100227,100229,100231,100233,100235,100241,100243,100249,100251,100257,100259,100261,100263],{},[898,100228,900],{},[1716,100230,1913],{},[898,100232,900],{},[1716,100234,1920],{"stretchy":1919},[1707,100236,100237,100239],{},[898,100238,1878],{},[1712,100240,1714],{},[1716,100242,1719],{"separator":1718},[1707,100244,100245,100247],{},[898,100246,1878],{},[1712,100248,1726],{},[1716,100250,1719],{"separator":1718},[1707,100252,100253,100255],{},[898,100254,1878],{},[1712,100256,7072],{},[1716,100258,1925],{"stretchy":1919},[1716,100260,1913],{},[1712,100262,1726],{},[10595,100264,100265],{},[895,100266,100267,100273,100279],{},[1707,100268,100269,100271],{},[898,100270,1878],{},[1712,100272,1714],{},[1707,100274,100275,100277],{},[898,100276,1878],{},[1712,100278,1726],{},[1707,100280,100281,100283],{},[898,100282,1878],{},[1712,100284,7072],{},[902,100286,100287],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,100289,100290,100483],{},[123,100291,100292,100293,100319,100320,26738,100346,2247,100405,19417,100465,22241],{},"svazek ",[883,100294,100296],{"className":100295},[886],[888,100297,100298],{"xmlns":890},[892,100299,100300,100316],{},[895,100301,100302,100304,100306,100308,100310,100312,100314],{},[1716,100303,1920],{"stretchy":1919},[1712,100305,6833],{},[1716,100307,1719],{"separator":1718},[1712,100309,6849],{},[1716,100311,1719],{"separator":1718},[1712,100313,6811],{},[1716,100315,1925],{"stretchy":1919},[902,100317,100318],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,100321,100323],{"className":100322},[886],[888,100324,100325],{"xmlns":890},[892,100326,100327,100343],{},[895,100328,100329,100331,100333,100335,100337,100339,100341],{},[1716,100330,1920],{"stretchy":1919},[1712,100332,7141],{},[1716,100334,1719],{"separator":1718},[1712,100336,7141],{},[1716,100338,1719],{"separator":1718},[1712,100340,79351],{},[1716,100342,1925],{"stretchy":1919},[902,100344,100345],{"encoding":904},"(9, 9, 27)",[883,100347,100349],{"className":100348},[886],[888,100350,100351],{"xmlns":890},[892,100352,100353,100402],{},[895,100354,100355,100357,100359,100361,100363,100365,100367,100369,100371,100373,100375,100389,100391,100393,100398,100400],{},[898,100356,900],{},[1716,100358,1920],{"stretchy":1919},[1712,100360,6833],{},[1716,100362,1719],{"separator":1718},[1712,100364,6849],{},[1716,100366,1719],{"separator":1718},[1712,100368,6811],{},[1716,100370,1925],{"stretchy":1919},[1716,100372,1913],{},[1712,100374,1726],{},[10595,100376,100377],{},[895,100378,100379,100381,100383,100385,100387],{},[1712,100380,6833],{},[1716,100382,9532],{},[1712,100384,6849],{},[1716,100386,9532],{},[1712,100388,6811],{},[1716,100390,1913],{},[1712,100392,1726],{},[10595,100394,100395],{},[1712,100396,100397],{},"4096",[1716,100399,1913],{},[1712,100401,6776],{},[902,100403,100404],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,100406,100408],{"className":100407},[886],[888,100409,100410],{"xmlns":890},[892,100411,100412,100462],{},[895,100413,100414,100416,100418,100420,100422,100424,100426,100428,100430,100432,100434,100448,100450,100452,100457,100459],{},[898,100415,900],{},[1716,100417,1920],{"stretchy":1919},[1712,100419,7141],{},[1716,100421,1719],{"separator":1718},[1712,100423,7141],{},[1716,100425,1719],{"separator":1718},[1712,100427,79351],{},[1716,100429,1925],{"stretchy":1919},[1716,100431,1913],{},[1712,100433,1726],{},[10595,100435,100436],{},[895,100437,100438,100440,100442,100444,100446],{},[1712,100439,7141],{},[1716,100441,9532],{},[1712,100443,7141],{},[1716,100445,9532],{},[1712,100447,79351],{},[1716,100449,1913],{},[1712,100451,1726],{},[10595,100453,100454],{},[1712,100455,100456],{},"2187",[1716,100458,19724],{},[1712,100460,100461],{},"93,53",[902,100463,100464],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,100466,100468],{"className":100467},[886],[888,100469,100470],{"xmlns":890},[892,100471,100472,100480],{},[895,100473,100474,100476,100478],{},[1712,100475,6776],{},[1716,100477,2716],{},[1712,100479,100461],{},[902,100481,100482],{"encoding":904},"128 > 93{,}53",[123,100484,100485,100486,2247,100512,100538,100539,2247,100579,100620,100621,100667,100668,2247,100694,16716,100720,2247,100738,100756,100757,1853],{},"svazky ",[883,100487,100489],{"className":100488},[886],[888,100490,100491],{"xmlns":890},[892,100492,100493,100509],{},[895,100494,100495,100497,100499,100501,100503,100505,100507],{},[1716,100496,1920],{"stretchy":1919},[1712,100498,6849],{},[1716,100500,1719],{"separator":1718},[1712,100502,12398],{},[1716,100504,1719],{"separator":1718},[1712,100506,1726],{},[1716,100508,1925],{"stretchy":1919},[902,100510,100511],{"encoding":904},"(4, 8, 2)",[883,100513,100515],{"className":100514},[886],[888,100516,100517],{"xmlns":890},[892,100518,100519,100535],{},[895,100520,100521,100523,100525,100527,100529,100531,100533],{},[1716,100522,1920],{"stretchy":1919},[1712,100524,6811],{},[1716,100526,1719],{"separator":1718},[1712,100528,1714],{},[1716,100530,1719],{"separator":1718},[1712,100532,6849],{},[1716,100534,1925],{"stretchy":1919},[902,100536,100537],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,100540,100542],{"className":100541},[886],[888,100543,100544],{"xmlns":890},[892,100545,100546,100576],{},[895,100547,100548,100550,100552,100554,100556,100558,100560,100562,100564,100566,100568,100572,100574],{},[898,100549,900],{},[1716,100551,1920],{"stretchy":1919},[1712,100553,6849],{},[1716,100555,1719],{"separator":1718},[1712,100557,12398],{},[1716,100559,1719],{"separator":1718},[1712,100561,1726],{},[1716,100563,1925],{"stretchy":1919},[1716,100565,1913],{},[1712,100567,1726],{},[10595,100569,100570],{},[1712,100571,6811],{},[1716,100573,1913],{},[1712,100575,6833],{},[902,100577,100578],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,100580,100582],{"className":100581},[886],[888,100583,100584],{"xmlns":890},[892,100585,100586,100617],{},[895,100587,100588,100590,100592,100594,100596,100598,100600,100602,100604,100606,100608,100613,100615],{},[898,100589,900],{},[1716,100591,1920],{"stretchy":1919},[1712,100593,6811],{},[1716,100595,1719],{"separator":1718},[1712,100597,1714],{},[1716,100599,1719],{"separator":1718},[1712,100601,6849],{},[1716,100603,1925],{"stretchy":1919},[1716,100605,1913],{},[1712,100607,1726],{},[10595,100609,100610],{},[1712,100611,100612],{},"256",[1716,100614,1913],{},[1712,100616,85113],{},[902,100618,100619],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,100622,100624],{"className":100623},[886],[888,100625,100626],{"xmlns":890},[892,100627,100628,100664],{},[895,100629,100630,100632,100634,100636,100638,100640,100642,100644,100646,100648,100650,100652,100654,100656,100658,100660,100662],{},[898,100631,900],{},[1716,100633,1920],{"stretchy":1919},[1712,100635,6849],{},[1716,100637,1719],{"separator":1718},[1712,100639,12398],{},[1716,100641,1719],{"separator":1718},[1712,100643,1726],{},[1716,100645,1925],{"stretchy":1919},[1716,100647,1913],{},[898,100649,900],{},[1716,100651,1920],{"stretchy":1919},[1712,100653,6811],{},[1716,100655,1719],{"separator":1718},[1712,100657,1714],{},[1716,100659,1719],{"separator":1718},[1712,100661,6849],{},[1716,100663,1925],{"stretchy":1919},[902,100665,100666],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,100669,100671],{"className":100670},[886],[888,100672,100673],{"xmlns":890},[892,100674,100675,100691],{},[895,100676,100677,100679,100681,100683,100685,100687,100689],{},[1712,100678,6849],{},[1716,100680,9532],{},[1712,100682,12398],{},[1716,100684,9532],{},[1712,100686,1726],{},[1716,100688,1913],{},[1712,100690,6811],{},[902,100692,100693],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,100695,100697],{"className":100696},[886],[888,100698,100699],{"xmlns":890},[892,100700,100701,100717],{},[895,100702,100703,100705,100707,100709,100711,100713,100715],{},[1712,100704,6811],{},[1716,100706,9532],{},[1712,100708,1714],{},[1716,100710,9532],{},[1712,100712,6849],{},[1716,100714,1913],{},[1712,100716,100612],{},[902,100718,100719],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,100721,100723],{"className":100722},[886],[888,100724,100725],{"xmlns":890},[892,100726,100727,100735],{},[895,100728,100729,100731,100733],{},[898,100730,900],{},[1716,100732,1913],{},[1712,100734,6833],{},[902,100736,100737],{"encoding":904},"U = 16",[883,100739,100741],{"className":100740},[886],[888,100742,100743],{"xmlns":890},[892,100744,100745,100753],{},[895,100746,100747,100749,100751],{},[898,100748,900],{},[1716,100750,1913],{},[1712,100752,85113],{},[902,100754,100755],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,100758,100760],{"className":100759},[886],[888,100761,100762],{"xmlns":890},[892,100763,100764,100784],{},[895,100765,100766,100772,100778],{},[1707,100767,100768,100770],{},[898,100769,1878],{},[1712,100771,1714],{},[1707,100773,100774,100776],{},[898,100775,1878],{},[1712,100777,1726],{},[1707,100779,100780,100782],{},[898,100781,1878],{},[1712,100783,7072],{},[902,100785,100786],{"encoding":904},"Q_1 Q_2 Q_3",[115,100788,100790],{"id":100789},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,100792,100793,100794,2574,100829,3495,100832,6784,100849,1994,100866,100869,100870,100873],{},"Pro funkci užitečnosti ",[883,100795,100797],{"className":100796},[886],[888,100798,100799],{"xmlns":890},[892,100800,100801,100827],{},[895,100802,100803,100805,100807,100809,100811,100817,100819,100825],{},[898,100804,900],{},[1716,100806,1913],{},[898,100808,900],{},[1716,100810,1920],{"stretchy":1919},[1707,100812,100813,100815],{},[898,100814,1878],{},[1712,100816,1714],{},[1716,100818,1719],{"separator":1718},[1707,100820,100821,100823],{},[898,100822,1878],{},[1712,100824,1726],{},[1716,100826,1925],{"stretchy":1919},[902,100828,100210],{"encoding":904},[38,100830,100831],{},"mezní užitečnost",[883,100833,100835],{"className":100834},[886],[888,100836,100837],{"xmlns":890},[892,100838,100839,100847],{},[895,100840,100841],{},[1707,100842,100843,100845],{},[898,100844,1878],{},[1712,100846,1714],{},[902,100848,4189],{"encoding":904},[883,100850,100852],{"className":100851},[886],[888,100853,100854],{"xmlns":890},[892,100855,100856,100864],{},[895,100857,100858],{},[1707,100859,100860,100862],{},[898,100861,1878],{},[1712,100863,1726],{},[902,100865,42785],{"encoding":904},[38,100867,100868],{},"marginal utility",") parciální ",[207,100871,1145],{"className":100872,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,100875,100877],{"className":100876},[886],[888,100878,100879],{"xmlns":890,"display":2004},[892,100880,100881,100980],{},[2008,100882,100883],{"width":2010},[2012,100884,100885,100887,100973,100975],{},[2015,100886],{"width":2017},[2015,100888,100889],{},[895,100890,100891,100893,100899,100901,100909,100911,100929,100931,100933,100935,100941,100943,100951,100953,100971],{},[898,100892,16690],{},[1707,100894,100895,100897],{},[898,100896,900],{},[1712,100898,1714],{},[1716,100900,1913],{},[7204,100902,100903,100905,100907],{},[898,100904,900],{},[1712,100906,1714],{},[1716,100908,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,100910,1913],{},[2750,100912,100913,100919],{},[895,100914,100915,100917],{},[898,100916,23677],{"mathvariant":2068},[898,100918,900],{},[895,100920,100921,100923],{},[898,100922,23677],{"mathvariant":2068},[1707,100924,100925,100927],{},[898,100926,1878],{},[1712,100928,1714],{},[1716,100930,1719],{"separator":1718},[2324,100932],{"width":8689},[898,100934,16690],{},[1707,100936,100937,100939],{},[898,100938,900],{},[1712,100940,1726],{},[1716,100942,1913],{},[7204,100944,100945,100947,100949],{},[898,100946,900],{},[1712,100948,1726],{},[1716,100950,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,100952,1913],{},[2750,100954,100955,100961],{},[895,100956,100957,100959],{},[898,100958,23677],{"mathvariant":2068},[898,100960,900],{},[895,100962,100963,100965],{},[898,100964,23677],{"mathvariant":2068},[1707,100966,100967,100969],{},[898,100968,1878],{},[1712,100970,1726],{},[898,100972,1853],{"mathvariant":2068},[2015,100974],{"width":2017},[2015,100976,100977],{},[2074,100978,100979],{},"(6.2)",[902,100981,100982],{"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}",[724,100984,100985,100986,101020,101021,101051,101052,3495,101055,1853],{},"Pro pevné ",[883,100987,100989],{"className":100988},[886],[888,100990,100991],{"xmlns":890},[892,100992,100993,101017],{},[895,100994,100995,101001,101003,101005,101007,101013,101015],{},[1707,100996,100997,100999],{},[898,100998,1878],{},[1712,101000,1714],{},[1716,101002,1913],{},[898,101004,207],{},[1716,101006,1719],{"separator":1718},[1707,101008,101009,101011],{},[898,101010,1878],{},[1712,101012,1726],{},[1716,101014,1913],{},[898,101016,1952],{},[902,101018,101019],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,101022,101024],{"className":101023},[886],[888,101025,101026],{"xmlns":890},[892,101027,101028,101048],{},[895,101029,101030,101032,101038,101040,101042,101044,101046],{},[898,101031,16690],{},[1707,101033,101034,101036],{},[898,101035,900],{},[1712,101037,1714],{},[1716,101039,1920],{"stretchy":1919},[898,101041,207],{},[1716,101043,1719],{"separator":1718},[898,101045,1952],{},[1716,101047,1925],{"stretchy":1919},[902,101049,101050],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,101053,101054],{},"v bodě (na hladině)",[883,101056,101058],{"className":101057},[886],[888,101059,101060],{"xmlns":890},[892,101061,101062,101074],{},[895,101063,101064,101066,101068,101070,101072],{},[1716,101065,2502],{"stretchy":1919},[898,101067,207],{},[1716,101069,1719],{"separator":1718},[898,101071,1952],{},[1716,101073,2516],{"stretchy":1919},[902,101075,24628],{"encoding":904},[1635,101077,101078],{},[724,101079,101080,101082,101083,101113,101142,101143,16490,101156,16504,101173,101194,101195,9425,101212,3942,101225,101242,101243,101265,101266,101295,101296,20296,101316,101333],{},[883,101081,1641],{}," Intuice — co říká ",[883,101084,101086],{"className":101085},[886],[888,101087,101088],{"xmlns":890},[892,101089,101090,101110],{},[895,101091,101092,101094,101100,101102,101104,101106,101108],{},[898,101093,16690],{},[1707,101095,101096,101098],{},[898,101097,900],{},[1712,101099,1714],{},[1716,101101,1920],{"stretchy":1919},[898,101103,207],{},[1716,101105,1719],{"separator":1718},[898,101107,1952],{},[1716,101109,1925],{"stretchy":1919},[902,101111,101112],{"encoding":904},"MU_1(a,b)",[883,101114,101116],{"className":101115},[886],[888,101117,101118],{"xmlns":890},[892,101119,101120,101140],{},[895,101121,101122,101124,101130,101132,101134,101136,101138],{},[898,101123,16690],{},[1707,101125,101126,101128],{},[898,101127,900],{},[1712,101129,1714],{},[1716,101131,1920],{"stretchy":1919},[898,101133,207],{},[1716,101135,1719],{"separator":1718},[898,101137,1952],{},[1716,101139,1925],{"stretchy":1919},[902,101141,101050],{"encoding":904}," je rychlost změny ",[883,101144,101146],{"className":101145},[886],[888,101147,101148],{"xmlns":890},[892,101149,101150,101154],{},[895,101151,101152],{},[898,101153,900],{},[902,101155,900],{"encoding":904},[883,101157,101159],{"className":101158},[886],[888,101160,101161],{"xmlns":890},[892,101162,101163,101171],{},[895,101164,101165],{},[1707,101166,101167,101169],{},[898,101168,1878],{},[1712,101170,1714],{},[902,101172,4189],{"encoding":904},[883,101174,101176],{"className":101175},[886],[888,101177,101178],{"xmlns":890},[892,101179,101180,101192],{},[895,101181,101182,101184,101186,101188,101190],{},[1716,101183,2502],{"stretchy":1919},[898,101185,207],{},[1716,101187,1719],{"separator":1718},[898,101189,1952],{},[1716,101191,2516],{"stretchy":1919},[902,101193,24628],{"encoding":904},". Přibližně: změní-li se ",[883,101196,101198],{"className":101197},[886],[888,101199,101200],{"xmlns":890},[892,101201,101202,101210],{},[895,101203,101204],{},[1707,101205,101206,101208],{},[898,101207,1878],{},[1712,101209,1714],{},[902,101211,4189],{"encoding":904},[883,101213,101215],{"className":101214},[886],[888,101216,101217],{"xmlns":890},[892,101218,101219,101223],{},[895,101220,101221],{},[898,101222,207],{},[902,101224,207],{"encoding":904},[883,101226,101228],{"className":101227},[886],[888,101229,101230],{"xmlns":890},[892,101231,101232,101240],{},[895,101233,101234,101236,101238],{},[898,101235,207],{},[1716,101237,1949],{},[1712,101239,1714],{},[902,101241,16581],{"encoding":904}," při pevném ",[883,101244,101246],{"className":101245},[886],[888,101247,101248],{"xmlns":890},[892,101249,101250,101262],{},[895,101251,101252,101258,101260],{},[1707,101253,101254,101256],{},[898,101255,1878],{},[1712,101257,1726],{},[1716,101259,1913],{},[898,101261,1952],{},[902,101263,101264],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,101267,101269],{"className":101268},[886],[888,101270,101271],{"xmlns":890},[892,101272,101273,101293],{},[895,101274,101275,101277,101283,101285,101287,101289,101291],{},[898,101276,16690],{},[1707,101278,101279,101281],{},[898,101280,900],{},[1712,101282,1714],{},[1716,101284,1920],{"stretchy":1919},[898,101286,207],{},[1716,101288,1719],{"separator":1718},[898,101290,1952],{},[1716,101292,1925],{"stretchy":1919},[902,101294,101050],{"encoding":904},". Stejně tak ",[883,101297,101299],{"className":101298},[886],[888,101300,101301],{"xmlns":890},[892,101302,101303,101313],{},[895,101304,101305,101307],{},[898,101306,16690],{},[1707,101308,101309,101311],{},[898,101310,900],{},[1712,101312,1726],{},[902,101314,101315],{"encoding":904},"MU_2",[883,101317,101319],{"className":101318},[886],[888,101320,101321],{"xmlns":890},[892,101322,101323,101331],{},[895,101324,101325],{},[1707,101326,101327,101329],{},[898,101328,1878],{},[1712,101330,1726],{},[902,101332,42785],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,101335,92965],{"id":101336},"totální-diferenciál",[724,101338,101339,101340,13352,101356,101386,101387,2291],{},"Přibližnou změnu užitečnosti ",[883,101341,101343],{"className":101342},[886],[888,101344,101345],{"xmlns":890},[892,101346,101347,101353],{},[895,101348,101349,101351],{},[898,101350,8485],{"mathvariant":2068},[898,101352,900],{},[902,101354,101355],{"encoding":904},"\\Delta U",[883,101357,101359],{"className":101358},[886],[888,101360,101361],{"xmlns":890},[892,101362,101363,101383],{},[895,101364,101365,101367,101373,101375,101377],{},[898,101366,5198],{"mathvariant":2068},[1707,101368,101369,101371],{},[898,101370,1878],{},[1712,101372,1714],{},[1716,101374,1719],{"separator":1718},[898,101376,5198],{"mathvariant":2068},[1707,101378,101379,101381],{},[898,101380,1878],{},[1712,101382,1726],{},[902,101384,101385],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,101388,101389],{},"totálního diferenciálu",[883,101391,101393],{"className":101392},[886],[888,101394,101395],{"xmlns":890,"display":2004},[892,101396,101397,101498],{},[2008,101398,101399],{"width":2010},[2012,101400,101401,101403,101491,101493],{},[2015,101402],{"width":2017},[2015,101404,101405],{},[895,101406,101407,101409,101411,101413,101415,101417,101419,101427,101429,101435,101437,101445,101447,101453,101455,101457,101463,101465,101471,101473,101475,101481,101483,101489],{},[898,101408,8485],{"mathvariant":2068},[898,101410,900],{},[1716,101412,8490],{},[898,101414,5198],{"mathvariant":2068},[898,101416,900],{},[1716,101418,1913],{},[7204,101420,101421,101423,101425],{},[898,101422,900],{},[1712,101424,1714],{},[1716,101426,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[898,101428,5198],{"mathvariant":2068},[1707,101430,101431,101433],{},[898,101432,1878],{},[1712,101434,1714],{},[1716,101436,1949],{},[7204,101438,101439,101441,101443],{},[898,101440,900],{},[1712,101442,1726],{},[1716,101444,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[898,101446,5198],{"mathvariant":2068},[1707,101448,101449,101451],{},[898,101450,1878],{},[1712,101452,1726],{},[1716,101454,1913],{},[898,101456,16690],{},[1707,101458,101459,101461],{},[898,101460,900],{},[1712,101462,1714],{},[898,101464,5198],{"mathvariant":2068},[1707,101466,101467,101469],{},[898,101468,1878],{},[1712,101470,1714],{},[1716,101472,1949],{},[898,101474,16690],{},[1707,101476,101477,101479],{},[898,101478,900],{},[1712,101480,1726],{},[898,101482,5198],{"mathvariant":2068},[1707,101484,101485,101487],{},[898,101486,1878],{},[1712,101488,1726],{},[898,101490,1853],{"mathvariant":2068},[2015,101492],{"width":2017},[2015,101494,101495],{},[2074,101496,101497],{},"(6.3)",[902,101499,101500],{"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}",[724,101502,88223,101503,1853],{},[883,101504,101506],{"className":101505},[886],[888,101507,101508],{"xmlns":890},[892,101509,101510,101580],{},[895,101511,101512,101514,101516,101518,101520,101522,101528,101530,101532,101538,101540,101546,101548,101550,101556,101558,101560,101562,101564,101570,101572,101578],{},[898,101513,8485],{"mathvariant":2068},[898,101515,900],{},[1716,101517,1913],{},[898,101519,900],{},[1716,101521,1920],{"stretchy":1919},[1707,101523,101524,101526],{},[898,101525,1878],{},[1712,101527,1714],{},[1716,101529,1949],{},[898,101531,5198],{"mathvariant":2068},[1707,101533,101534,101536],{},[898,101535,1878],{},[1712,101537,1714],{},[1716,101539,1719],{"separator":1718},[1707,101541,101542,101544],{},[898,101543,1878],{},[1712,101545,1726],{},[1716,101547,1949],{},[898,101549,5198],{"mathvariant":2068},[1707,101551,101552,101554],{},[898,101553,1878],{},[1712,101555,1726],{},[1716,101557,1925],{"stretchy":1919},[1716,101559,2760],{},[898,101561,900],{},[1716,101563,1920],{"stretchy":1919},[1707,101565,101566,101568],{},[898,101567,1878],{},[1712,101569,1714],{},[1716,101571,1719],{"separator":1718},[1707,101573,101574,101576],{},[898,101575,1878],{},[1712,101577,1726],{},[1716,101579,1925],{"stretchy":1919},[902,101581,101582],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,101584,101586],{"id":101585},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,101588,101589,101590,101593,101594,101597],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,101591,101592],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,101595,101596],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,101599,101600,101603,101604,6784,101630,101656,101657,1343,101689,101721,101722,2247,101776,101830],{},[38,101601,101602],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,101605,101607],{"className":101606},[886],[888,101608,101609],{"xmlns":890},[892,101610,101611,101627],{},[895,101612,101613,101619,101621],{},[1707,101614,101615,101617],{},[898,101616,1878],{},[1712,101618,1726],{},[1716,101620,1913],{},[1707,101622,101623,101625],{},[898,101624,207],{},[1712,101626,2505],{},[902,101628,101629],{"encoding":904},"Q_2 = a_0",[883,101631,101633],{"className":101632},[886],[888,101634,101635],{"xmlns":890},[892,101636,101637,101653],{},[895,101638,101639,101645,101647],{},[1707,101640,101641,101643],{},[898,101642,1878],{},[1712,101644,1714],{},[1716,101646,1913],{},[1707,101648,101649,101651],{},[898,101650,1952],{},[1712,101652,2505],{},[902,101654,101655],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,101658,101660],{"className":101659},[886],[888,101661,101662],{"xmlns":890},[892,101663,101664,101686],{},[895,101665,101666,101668,101670,101676,101678,101684],{},[898,101667,900],{},[1716,101669,1920],{"stretchy":1919},[1707,101671,101672,101674],{},[898,101673,1878],{},[1712,101675,1714],{},[1716,101677,1719],{"separator":1718},[1707,101679,101680,101682],{},[898,101681,207],{},[1712,101683,2505],{},[1716,101685,1925],{"stretchy":1919},[902,101687,101688],{"encoding":904},"U(Q_1, a_0)",[883,101690,101692],{"className":101691},[886],[888,101693,101694],{"xmlns":890},[892,101695,101696,101718],{},[895,101697,101698,101700,101702,101708,101710,101716],{},[898,101699,900],{},[1716,101701,1920],{"stretchy":1919},[1707,101703,101704,101706],{},[898,101705,1952],{},[1712,101707,2505],{},[1716,101709,1719],{"separator":1718},[1707,101711,101712,101714],{},[898,101713,1878],{},[1712,101715,1726],{},[1716,101717,1925],{"stretchy":1919},[902,101719,101720],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,101723,101725],{"className":101724},[886],[888,101726,101727],{"xmlns":890},[892,101728,101729,101773],{},[895,101730,101731,101769,101771],{},[2747,101732,101733],{"scriptlevel":2505,"displaystyle":1718},[2750,101734,101735,101759],{},[895,101736,101737,101739,101741,101743,101749,101751,101757],{},[898,101738,5198],{"mathvariant":2068},[898,101740,900],{},[1716,101742,1920],{"stretchy":1919},[1707,101744,101745,101747],{},[898,101746,1878],{},[1712,101748,1714],{},[1716,101750,1719],{"separator":1718},[1707,101752,101753,101755],{},[898,101754,207],{},[1712,101756,2505],{},[1716,101758,1925],{"stretchy":1919},[895,101760,101761,101763],{},[898,101762,5198],{"mathvariant":2068},[1707,101764,101765,101767],{},[898,101766,1878],{},[1712,101768,1714],{},[1716,101770,2716],{},[1712,101772,2505],{},[902,101774,101775],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,101777,101779],{"className":101778},[886],[888,101780,101781],{"xmlns":890},[892,101782,101783,101827],{},[895,101784,101785,101823,101825],{},[2747,101786,101787],{"scriptlevel":2505,"displaystyle":1718},[2750,101788,101789,101813],{},[895,101790,101791,101793,101795,101797,101803,101805,101811],{},[898,101792,5198],{"mathvariant":2068},[898,101794,900],{},[1716,101796,1920],{"stretchy":1919},[1707,101798,101799,101801],{},[898,101800,1952],{},[1712,101802,2505],{},[1716,101804,1719],{"separator":1718},[1707,101806,101807,101809],{},[898,101808,1878],{},[1712,101810,1726],{},[1716,101812,1925],{"stretchy":1919},[895,101814,101815,101817],{},[898,101816,5198],{"mathvariant":2068},[1707,101818,101819,101821],{},[898,101820,1878],{},[1712,101822,1726],{},[1716,101824,2716],{},[1712,101826,2505],{},[902,101828,101829],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,101832,101834],{"className":101833},[886],[888,101835,101836],{"xmlns":890,"display":2004},[892,101837,101838,101883],{},[2008,101839,101840],{"width":2010},[2012,101841,101842,101844,101876,101878],{},[2015,101843],{"width":2017},[2015,101845,101846],{},[895,101847,101848,101856,101858,101860,101862,101864,101872,101874],{},[7204,101849,101850,101852,101854],{},[898,101851,900],{},[1712,101853,1714],{},[1716,101855,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,101857,2716],{},[1712,101859,2505],{},[1716,101861,1719],{"separator":1718},[2324,101863],{"width":8689},[7204,101865,101866,101868,101870],{},[898,101867,900],{},[1712,101869,1726],{},[1716,101871,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,101873,2716],{},[1712,101875,2719],{},[2015,101877],{"width":2017},[2015,101879,101880],{},[2074,101881,101882],{},"(6.4)",[902,101884,101885],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,101887,101888,101889,101891],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,101890,65431],{}," — užitečnost roste s množstvím každého zboží.",[724,101893,101894,101897,101898,101928,101929,2291],{},[38,101895,101896],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,101899,101901],{"className":101900},[886],[888,101902,101903],{"xmlns":890},[892,101904,101905,101925],{},[895,101906,101907,101915,101917],{},[7204,101908,101909,101911,101913],{},[898,101910,900],{},[1712,101912,1714],{},[1716,101914,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,101916,1719],{"separator":1718},[7204,101918,101919,101921,101923],{},[898,101920,900],{},[1712,101922,1726],{},[1716,101924,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,101926,101927],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,101930,101931],{},"záporné",[883,101933,101935],{"className":101934},[886],[888,101936,101937],{"xmlns":890,"display":2004},[892,101938,101939,101992],{},[2008,101940,101941],{"width":2010},[2012,101942,101943,101945,101985,101987],{},[2015,101944],{"width":2017},[2015,101946,101947],{},[895,101948,101949,101961,101963,101965,101967,101969,101981,101983],{},[7204,101950,101951,101953,101955],{},[898,101952,900],{},[1712,101954,16773],{},[895,101956,101957,101959],{},[1716,101958,8505],{"mathvariant":2068},[1716,101960,8505],{"mathvariant":2068},[1716,101962,2704],{},[1712,101964,2505],{},[1716,101966,1719],{"separator":1718},[2324,101968],{"width":8689},[7204,101970,101971,101973,101975],{},[898,101972,900],{},[1712,101974,6688],{},[895,101976,101977,101979],{},[1716,101978,8505],{"mathvariant":2068},[1716,101980,8505],{"mathvariant":2068},[1716,101982,2704],{},[1712,101984,2719],{},[2015,101986],{"width":2017},[2015,101988,101989],{},[2074,101990,101991],{},"(6.5)",[902,101993,101994],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,101996,101997,101998,102001,102002,1853],{},"Podmínka (6.5) je známa jako ",[38,101999,102000],{},"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 ",[207,102003,102005],{"className":102004,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,102007,102008,102009,2247,102041,102073,102074,2247,102100,102126,102127,102155,102156,2247,102158,102160,102161,102196],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,102010,102012],{"className":102011},[886],[888,102013,102014],{"xmlns":890},[892,102015,102016,102038],{},[895,102017,102018,102020,102022,102028,102030,102036],{},[898,102019,900],{},[1716,102021,1920],{"stretchy":1919},[1707,102023,102024,102026],{},[898,102025,1878],{},[1712,102027,1714],{},[1716,102029,1719],{"separator":1718},[1707,102031,102032,102034],{},[898,102033,1952],{},[1712,102035,2505],{},[1716,102037,1925],{"stretchy":1919},[902,102039,102040],{"encoding":904},"U(Q_1, b_0)",[883,102042,102044],{"className":102043},[886],[888,102045,102046],{"xmlns":890},[892,102047,102048,102070],{},[895,102049,102050,102052,102054,102060,102062,102068],{},[898,102051,900],{},[1716,102053,1920],{"stretchy":1919},[1707,102055,102056,102058],{},[898,102057,207],{},[1712,102059,2505],{},[1716,102061,1719],{"separator":1718},[1707,102063,102064,102066],{},[898,102065,1878],{},[1712,102067,1726],{},[1716,102069,1925],{"stretchy":1919},[902,102071,102072],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,102075,102077],{"className":102076},[886],[888,102078,102079],{"xmlns":890},[892,102080,102081,102097],{},[895,102082,102083,102085,102087,102089,102095],{},[1716,102084,1920],{"stretchy":1919},[898,102086,900],{},[1716,102088,1719],{"separator":1718},[1707,102090,102091,102093],{},[898,102092,1878],{},[1712,102094,1714],{},[1716,102096,1925],{"stretchy":1919},[902,102098,102099],{"encoding":904},"(U, Q_1)",[883,102101,102103],{"className":102102},[886],[888,102104,102105],{"xmlns":890},[892,102106,102107,102123],{},[895,102108,102109,102111,102113,102115,102121],{},[1716,102110,1920],{"stretchy":1919},[898,102112,900],{},[1716,102114,1719],{"separator":1718},[1707,102116,102117,102119],{},[898,102118,1878],{},[1712,102120,1726],{},[1716,102122,1925],{"stretchy":1919},[902,102124,102125],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,102128,102130],{"className":102129},[886],[888,102131,102132],{"xmlns":890},[892,102133,102134,102152],{},[895,102135,102136,102138,102140,102142,102144,102146,102148,102150],{},[898,102137,900],{},[1716,102139,1920],{"stretchy":1919},[1712,102141,2505],{},[1716,102143,1719],{"separator":1718},[1712,102145,2505],{},[1716,102147,1925],{"stretchy":1919},[1716,102149,1913],{},[1712,102151,2505],{},[902,102153,102154],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,102157,3167],{},[38,102159,3426],{},". Typický tvar grafu ",[883,102162,102164],{"className":102163},[886],[888,102165,102166],{"xmlns":890},[892,102167,102168,102194],{},[895,102169,102170,102172,102174,102176,102178,102184,102186,102192],{},[898,102171,900],{},[1716,102173,1913],{},[898,102175,900],{},[1716,102177,1920],{"stretchy":1919},[1707,102179,102180,102182],{},[898,102181,1878],{},[1712,102183,1714],{},[1716,102185,1719],{"separator":1718},[1707,102187,102188,102190],{},[898,102189,1878],{},[1712,102191,1726],{},[1716,102193,1925],{"stretchy":1919},[902,102195,100210],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,102198,102199],{},[614,102200,102201,102202,101242,102230,102251,102252,101242,102280,102302],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,102203,102205],{"className":102204},[886],[888,102206,102207],{"xmlns":890},[892,102208,102209,102227],{},[895,102210,102211,102213,102215,102221,102223,102225],{},[898,102212,900],{},[1716,102214,1920],{"stretchy":1919},[1707,102216,102217,102219],{},[898,102218,1878],{},[1712,102220,1714],{},[1716,102222,1719],{"separator":1718},[898,102224,1952],{},[1716,102226,1925],{"stretchy":1919},[902,102228,102229],{"encoding":904},"U(Q_1, b)",[883,102231,102233],{"className":102232},[886],[888,102234,102235],{"xmlns":890},[892,102236,102237,102249],{},[895,102238,102239,102245,102247],{},[1707,102240,102241,102243],{},[898,102242,1878],{},[1712,102244,1726],{},[1716,102246,1913],{},[898,102248,1952],{},[902,102250,101264],{"encoding":904}," (vlevo) a ",[883,102253,102255],{"className":102254},[886],[888,102256,102257],{"xmlns":890},[892,102258,102259,102277],{},[895,102260,102261,102263,102265,102267,102269,102275],{},[898,102262,900],{},[1716,102264,1920],{"stretchy":1919},[898,102266,207],{},[1716,102268,1719],{"separator":1718},[1707,102270,102271,102273],{},[898,102272,1878],{},[1712,102274,1726],{},[1716,102276,1925],{"stretchy":1919},[902,102278,102279],{"encoding":904},"U(a, Q_2)",[883,102281,102283],{"className":102282},[886],[888,102284,102285],{"xmlns":890},[892,102286,102287,102299],{},[895,102288,102289,102295,102297],{},[1707,102290,102291,102293],{},[898,102292,1878],{},[1712,102294,1714],{},[1716,102296,1913],{},[898,102298,207],{},[902,102300,102301],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,102304,102305],{},[614,102306,102307,102308,102343,102344,102374,102375,2247,102398,102420,102421,1853],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,102309,102311],{"className":102310},[886],[888,102312,102313],{"xmlns":890},[892,102314,102315,102341],{},[895,102316,102317,102319,102321,102323,102325,102331,102333,102339],{},[898,102318,900],{},[1716,102320,1913],{},[898,102322,900],{},[1716,102324,1920],{"stretchy":1919},[1707,102326,102327,102329],{},[898,102328,1878],{},[1712,102330,1714],{},[1716,102332,1719],{"separator":1718},[1707,102334,102335,102337],{},[898,102336,1878],{},[1712,102338,1726],{},[1716,102340,1925],{"stretchy":1919},[902,102342,100210],{"encoding":904}," nad rovinou ",[883,102345,102347],{"className":102346},[886],[888,102348,102349],{"xmlns":890},[892,102350,102351,102371],{},[895,102352,102353,102355,102361,102363,102369],{},[1716,102354,1920],{"stretchy":1919},[1707,102356,102357,102359],{},[898,102358,1878],{},[1712,102360,1714],{},[1716,102362,1719],{"separator":1718},[1707,102364,102365,102367],{},[898,102366,1878],{},[1712,102368,1726],{},[1716,102370,1925],{"stretchy":1919},[902,102372,102373],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,102376,102378],{"className":102377},[886],[888,102379,102380],{"xmlns":890},[892,102381,102382,102395],{},[895,102383,102384,102390,102392],{},[1707,102385,102386,102388],{},[898,102387,1878],{},[1712,102389,1714],{},[1716,102391,1913],{},[2074,102393,102394],{},"const",[902,102396,102397],{"encoding":904},"Q_1 = \\text{const}",[883,102399,102401],{"className":102400},[886],[888,102402,102403],{"xmlns":890},[892,102404,102405,102417],{},[895,102406,102407,102413,102415],{},[1707,102408,102409,102411],{},[898,102410,1878],{},[1712,102412,1726],{},[1716,102414,1913],{},[2074,102416,102394],{},[902,102418,102419],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,102422,102424],{"className":102423},[886],[888,102425,102426],{"xmlns":890},[892,102427,102428,102454],{},[895,102429,102430,102432,102434,102440,102442,102448,102450,102452],{},[898,102431,900],{},[1716,102433,1920],{"stretchy":1919},[1707,102435,102436,102438],{},[898,102437,1878],{},[1712,102439,1714],{},[1716,102441,1719],{"separator":1718},[1707,102443,102444,102446],{},[898,102445,1878],{},[1712,102447,1726],{},[1716,102449,1925],{"stretchy":1919},[1716,102451,1913],{},[898,102453,4478],{},[902,102455,23575],{"encoding":904},[198,102457,102459,102460],{"id":102458},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,102461,102463],{"className":102462},[886],[888,102464,102465],{"xmlns":890},[892,102466,102467,102501],{},[895,102468,102469,102471,102473,102487],{},[898,102470,900],{},[1716,102472,1913],{},[7204,102474,102475,102477,102479],{},[898,102476,1878],{},[1712,102478,1714],{},[895,102480,102481,102483,102485],{},[1712,102482,1714],{},[898,102484,3045],{"mathvariant":2068},[1712,102486,1726],{},[7204,102488,102489,102491,102493],{},[898,102490,1878],{},[1712,102492,1726],{},[895,102494,102495,102497,102499],{},[1712,102496,1714],{},[898,102498,3045],{"mathvariant":2068},[1712,102500,7072],{},[902,102502,102503],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,102505,102506],{},[38,102507,102508],{},"Ověření (6.4) a (6.5).",[883,102510,102512],{"className":102511},[886],[888,102513,102514],{"xmlns":890,"display":2004},[892,102515,102516,102620],{},[895,102517,102518,102526,102528,102536,102552,102566,102568,102570,102578,102580,102588,102602,102618],{},[7204,102519,102520,102522,102524],{},[898,102521,900],{},[1712,102523,1714],{},[1716,102525,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,102527,1913],{},[2747,102529,102530],{"scriptlevel":2505,"displaystyle":1919},[2750,102531,102532,102534],{},[1712,102533,1714],{},[1712,102535,1726],{},[7204,102537,102538,102540,102542],{},[898,102539,1878],{},[1712,102541,1714],{},[895,102543,102544,102546,102548,102550],{},[1716,102545,2760],{},[1712,102547,1714],{},[898,102549,3045],{"mathvariant":2068},[1712,102551,1726],{},[7204,102553,102554,102556,102558],{},[898,102555,1878],{},[1712,102557,1726],{},[895,102559,102560,102562,102564],{},[1712,102561,1714],{},[898,102563,3045],{"mathvariant":2068},[1712,102565,7072],{},[1716,102567,1719],{"separator":1718},[2324,102569],{"width":8689},[7204,102571,102572,102574,102576],{},[898,102573,900],{},[1712,102575,1726],{},[1716,102577,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,102579,1913],{},[2747,102581,102582],{"scriptlevel":2505,"displaystyle":1919},[2750,102583,102584,102586],{},[1712,102585,1714],{},[1712,102587,7072],{},[7204,102589,102590,102592,102594],{},[898,102591,1878],{},[1712,102593,1714],{},[895,102595,102596,102598,102600],{},[1712,102597,1714],{},[898,102599,3045],{"mathvariant":2068},[1712,102601,1726],{},[7204,102603,102604,102606,102608],{},[898,102605,1878],{},[1712,102607,1726],{},[895,102609,102610,102612,102614,102616],{},[1716,102611,2760],{},[1712,102613,1726],{},[898,102615,3045],{"mathvariant":2068},[1712,102617,7072],{},[1716,102619,1719],{"separator":1718},[902,102621,102622],{"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},",[724,102624,102625,102626,102660],{},"zřejmě ",[883,102627,102629],{"className":102628},[886],[888,102630,102631],{"xmlns":890},[892,102632,102633,102657],{},[895,102634,102635,102643,102645,102653,102655],{},[7204,102636,102637,102639,102641],{},[898,102638,900],{},[1712,102640,1714],{},[1716,102642,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,102644,1719],{"separator":1718},[7204,102646,102647,102649,102651],{},[898,102648,900],{},[1712,102650,1726],{},[1716,102652,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,102654,2716],{},[1712,102656,2505],{},[902,102658,102659],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,102662,102664],{"className":102663},[886],[888,102665,102666],{"xmlns":890,"display":2004},[892,102667,102668,102784],{},[895,102669,102670,102682,102684,102686,102694,102710,102724,102726,102728,102740,102742,102744,102752,102766,102782],{},[7204,102671,102672,102674,102676],{},[898,102673,900],{},[1712,102675,16773],{},[895,102677,102678,102680],{},[1716,102679,8505],{"mathvariant":2068},[1716,102681,8505],{"mathvariant":2068},[1716,102683,1913],{},[1716,102685,2760],{},[2747,102687,102688],{"scriptlevel":2505,"displaystyle":1919},[2750,102689,102690,102692],{},[1712,102691,1714],{},[1712,102693,6849],{},[7204,102695,102696,102698,102700],{},[898,102697,1878],{},[1712,102699,1714],{},[895,102701,102702,102704,102706,102708],{},[1716,102703,2760],{},[1712,102705,7072],{},[898,102707,3045],{"mathvariant":2068},[1712,102709,1726],{},[7204,102711,102712,102714,102716],{},[898,102713,1878],{},[1712,102715,1726],{},[895,102717,102718,102720,102722],{},[1712,102719,1714],{},[898,102721,3045],{"mathvariant":2068},[1712,102723,7072],{},[1716,102725,1719],{"separator":1718},[2324,102727],{"width":8689},[7204,102729,102730,102732,102734],{},[898,102731,900],{},[1712,102733,6688],{},[895,102735,102736,102738],{},[1716,102737,8505],{"mathvariant":2068},[1716,102739,8505],{"mathvariant":2068},[1716,102741,1913],{},[1716,102743,2760],{},[2747,102745,102746],{"scriptlevel":2505,"displaystyle":1919},[2750,102747,102748,102750],{},[1712,102749,1726],{},[1712,102751,7141],{},[7204,102753,102754,102756,102758],{},[898,102755,1878],{},[1712,102757,1714],{},[895,102759,102760,102762,102764],{},[1712,102761,1714],{},[898,102763,3045],{"mathvariant":2068},[1712,102765,1726],{},[7204,102767,102768,102770,102772],{},[898,102769,1878],{},[1712,102771,1726],{},[895,102773,102774,102776,102778,102780],{},[1716,102775,2760],{},[1712,102777,6985],{},[898,102779,3045],{"mathvariant":2068},[1712,102781,7072],{},[1716,102783,1719],{"separator":1718},[902,102785,102786],{"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},",[724,102788,102789,102790,102832],{},"opět ",[883,102791,102793],{"className":102792},[886],[888,102794,102795],{"xmlns":890},[892,102796,102797,102829],{},[895,102798,102799,102811,102813,102825,102827],{},[7204,102800,102801,102803,102805],{},[898,102802,900],{},[1712,102804,16773],{},[895,102806,102807,102809],{},[1716,102808,8505],{"mathvariant":2068},[1716,102810,8505],{"mathvariant":2068},[1716,102812,1719],{"separator":1718},[7204,102814,102815,102817,102819],{},[898,102816,900],{},[1712,102818,6688],{},[895,102820,102821,102823],{},[1716,102822,8505],{"mathvariant":2068},[1716,102824,8505],{"mathvariant":2068},[1716,102826,2704],{},[1712,102828,2505],{},[902,102830,102831],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,102834,102835],{},[38,102836,102837,102838,1853],{},"(a) Mezní užitečnosti v bodě ",[883,102839,102841],{"className":102840},[886],[888,102842,102843],{"xmlns":890},[892,102844,102845,102857],{},[895,102846,102847,102849,102851,102853,102855],{},[1716,102848,2502],{"stretchy":1919},[1712,102850,12151],{},[1716,102852,1719],{"separator":1718},[1712,102854,22193],{},[1716,102856,2516],{"stretchy":1919},[902,102858,102859],{"encoding":904},"[100, 200]",[883,102861,102863],{"className":102862},[886],[888,102864,102865],{"xmlns":890,"display":2004},[892,102866,102867,102934],{},[895,102868,102869,102871,102877,102879,102881,102883,102885,102887,102889,102897,102899,102913,102915,102927,102929,102932],{},[898,102870,16690],{},[1707,102872,102873,102875],{},[898,102874,900],{},[1712,102876,1714],{},[1716,102878,1920],{"stretchy":1919},[1712,102880,12151],{},[1716,102882,1719],{"separator":1718},[1712,102884,22193],{},[1716,102886,1925],{"stretchy":1919},[1716,102888,1913],{},[2747,102890,102891],{"scriptlevel":2505,"displaystyle":1919},[2750,102892,102893,102895],{},[1712,102894,1714],{},[1712,102896,1726],{},[1716,102898,9532],{},[3074,102900,102901,102903],{},[1712,102902,12151],{},[895,102904,102905,102907,102909,102911],{},[1716,102906,2760],{},[1712,102908,1714],{},[898,102910,3045],{"mathvariant":2068},[1712,102912,1726],{},[1716,102914,9532],{},[3074,102916,102917,102919],{},[1712,102918,22193],{},[895,102920,102921,102923,102925],{},[1712,102922,1714],{},[898,102924,3045],{"mathvariant":2068},[1712,102926,7072],{},[1716,102928,19724],{},[1712,102930,102931],{},"0,4204",[1716,102933,1719],{"separator":1718},[902,102935,102936],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,102938,102940],{"className":102939},[886],[888,102941,102942],{"xmlns":890,"display":2004},[892,102943,102944,103009],{},[895,102945,102946,102948,102954,102956,102958,102960,102962,102964,102966,102974,102976,102988,102990,103004,103006],{},[898,102947,16690],{},[1707,102949,102950,102952],{},[898,102951,900],{},[1712,102953,1726],{},[1716,102955,1920],{"stretchy":1919},[1712,102957,12151],{},[1716,102959,1719],{"separator":1718},[1712,102961,22193],{},[1716,102963,1925],{"stretchy":1919},[1716,102965,1913],{},[2747,102967,102968],{"scriptlevel":2505,"displaystyle":1919},[2750,102969,102970,102972],{},[1712,102971,1714],{},[1712,102973,7072],{},[1716,102975,9532],{},[3074,102977,102978,102980],{},[1712,102979,12151],{},[895,102981,102982,102984,102986],{},[1712,102983,1714],{},[898,102985,3045],{"mathvariant":2068},[1712,102987,1726],{},[1716,102989,9532],{},[3074,102991,102992,102994],{},[1712,102993,22193],{},[895,102995,102996,102998,103000,103002],{},[1716,102997,2760],{},[1712,102999,1726],{},[898,103001,3045],{"mathvariant":2068},[1712,103003,7072],{},[1716,103005,19724],{},[1712,103007,103008],{},"0,63067.",[902,103010,103011],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,103013,103014,3495,103016,103051,103052,103073,103074,103091],{},[614,103015,23026],{},[883,103017,103019],{"className":103018},[886],[888,103020,103021],{"xmlns":890},[892,103022,103023,103048],{},[895,103024,103025,103027,103033,103035,103037,103039,103041,103043,103045],{},[898,103026,16690],{},[1707,103028,103029,103031],{},[898,103030,900],{},[1712,103032,1726],{},[1716,103034,1920],{"stretchy":1919},[1712,103036,12151],{},[1716,103038,1719],{"separator":1718},[1712,103040,22193],{},[1716,103042,1925],{"stretchy":1919},[1716,103044,19724],{},[1712,103046,103047],{},"0,63067",[902,103049,103050],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,103053,103055],{"className":103054},[886],[888,103056,103057],{"xmlns":890},[892,103058,103059,103071],{},[895,103060,103061,103063,103065,103067,103069],{},[1716,103062,2502],{"stretchy":1919},[1712,103064,12151],{},[1716,103066,1719],{"separator":1718},[1712,103068,22193],{},[1716,103070,2516],{"stretchy":1919},[902,103072,102859],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,103075,103077],{"className":103076},[886],[888,103078,103079],{"xmlns":890},[892,103080,103081,103089],{},[895,103082,103083],{},[1707,103084,103085,103087],{},[898,103086,1878],{},[1712,103088,1726],{},[902,103090,42785],{"encoding":904}," přibližně o 0,63067.",[724,103093,103094,103113,103114,4134,103135,103152,103153,103179,103180,103197,103198,1998],{},[38,103095,103096,103097,103112],{},"(b) Odhad změny ",[883,103098,103100],{"className":103099},[886],[888,103101,103102],{"xmlns":890},[892,103103,103104,103110],{},[895,103105,103106,103108],{},[898,103107,8485],{"mathvariant":2068},[898,103109,900],{},[902,103111,101355],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,103115,103117],{"className":103116},[886],[888,103118,103119],{"xmlns":890},[892,103120,103121,103133],{},[895,103122,103123,103125,103127,103129,103131],{},[1716,103124,2502],{"stretchy":1919},[1712,103126,12151],{},[1716,103128,1719],{"separator":1718},[1712,103130,22193],{},[1716,103132,2516],{"stretchy":1919},[902,103134,102859],{"encoding":904},[883,103136,103138],{"className":103137},[886],[888,103139,103140],{"xmlns":890},[892,103141,103142,103150],{},[895,103143,103144],{},[1707,103145,103146,103148],{},[898,103147,1878],{},[1712,103149,1714],{},[902,103151,4189],{"encoding":904}," na 98 (tj. ",[883,103154,103156],{"className":103155},[886],[888,103157,103158],{"xmlns":890},[892,103159,103160,103176],{},[895,103161,103162,103164,103170,103172,103174],{},[898,103163,5198],{"mathvariant":2068},[1707,103165,103166,103168],{},[898,103167,1878],{},[1712,103169,1714],{},[1716,103171,1913],{},[1716,103173,2760],{},[1712,103175,1726],{},[902,103177,103178],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,103181,103183],{"className":103182},[886],[888,103184,103185],{"xmlns":890},[892,103186,103187,103195],{},[895,103188,103189],{},[1707,103190,103191,103193],{},[898,103192,1878],{},[1712,103194,1726],{},[902,103196,42785],{"encoding":904}," o 3 (tj. ",[883,103199,103201],{"className":103200},[886],[888,103202,103203],{"xmlns":890},[892,103204,103205,103219],{},[895,103206,103207,103209,103215,103217],{},[898,103208,5198],{"mathvariant":2068},[1707,103210,103211,103213],{},[898,103212,1878],{},[1712,103214,1726],{},[1716,103216,1913],{},[1712,103218,7072],{},[902,103220,103221],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,103223,103225],{"className":103224},[886],[888,103226,103227],{"xmlns":890,"display":2004},[892,103228,103229,103280],{},[895,103230,103231,103233,103235,103237,103239,103241,103243,103245,103247,103249,103251,103253,103255,103257,103259,103261,103263,103265,103267,103270,103272,103275,103277],{},[898,103232,8485],{"mathvariant":2068},[898,103234,900],{},[1716,103236,8490],{},[898,103238,5198],{"mathvariant":2068},[898,103240,900],{},[1716,103242,1913],{},[1712,103244,102931],{},[1716,103246,9532],{},[1716,103248,1920],{"stretchy":1919},[1716,103250,2760],{},[1712,103252,1726],{},[1716,103254,1925],{"stretchy":1919},[1716,103256,1949],{},[1712,103258,103047],{},[1716,103260,9532],{},[1712,103262,7072],{},[1716,103264,1913],{},[1716,103266,2760],{},[1712,103268,103269],{},"0,8408",[1716,103271,1949],{},[1712,103273,103274],{},"1,89201",[1716,103276,19724],{},[1712,103278,103279],{},"1,05.",[902,103281,103282],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,103284,103285,103286,103289,103290,103341,103342,1853],{},"Užitečnost se tedy zvýší přibližně o ",[38,103287,103288],{},"1,05",". Skutečná změna je ",[883,103291,103293],{"className":103292},[886],[888,103294,103295],{"xmlns":890},[892,103296,103297,103338],{},[895,103298,103299,103301,103303,103305,103307,103309,103312,103314,103317,103319,103321,103323,103325,103327,103329,103331,103333,103335],{},[898,103300,8485],{"mathvariant":2068},[898,103302,900],{},[1716,103304,1913],{},[898,103306,900],{},[1716,103308,1920],{"stretchy":1919},[1712,103310,103311],{},"98",[1716,103313,1719],{"separator":1718},[1712,103315,103316],{},"203",[1716,103318,1925],{"stretchy":1919},[1716,103320,2760],{},[898,103322,900],{},[1716,103324,1920],{"stretchy":1919},[1712,103326,12151],{},[1716,103328,1719],{"separator":1718},[1712,103330,22193],{},[1716,103332,1925],{"stretchy":1919},[1716,103334,19724],{},[1712,103336,103337],{},"1,031",[902,103339,103340],{"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 ",[883,103343,103345],{"className":103344},[886],[888,103346,103347],{"xmlns":890},[892,103348,103349,103369],{},[895,103350,103351,103353,103359,103361,103363],{},[898,103352,5198],{"mathvariant":2068},[1707,103354,103355,103357],{},[898,103356,1878],{},[1712,103358,1714],{},[1716,103360,1719],{"separator":1718},[898,103362,5198],{"mathvariant":2068},[1707,103364,103365,103367],{},[898,103366,1878],{},[1712,103368,1726],{},[902,103370,101385],{"encoding":904},[115,103372,103374],{"id":103373},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,103376,103377],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,103379,103381],{"className":103380},[886],[888,103382,103383],{"xmlns":890,"display":2004},[892,103384,103385,103444],{},[2008,103386,103387],{"width":2010},[2012,103388,103389,103391,103437,103439],{},[2015,103390],{"width":2017},[2015,103392,103393],{},[895,103394,103395,103397,103399,103405,103407,103413,103415,103417,103425,103427,103435],{},[898,103396,900],{},[1716,103398,1920],{"stretchy":1919},[1707,103400,103401,103403],{},[898,103402,1878],{},[1712,103404,1714],{},[1716,103406,1719],{"separator":1718},[1707,103408,103409,103411],{},[898,103410,1878],{},[1712,103412,1726],{},[1716,103414,1925],{"stretchy":1919},[1716,103416,1913],{},[7204,103418,103419,103421,103423],{},[898,103420,1878],{},[1712,103422,1714],{},[898,103424,207],{},[1716,103426,9532],{},[7204,103428,103429,103431,103433],{},[898,103430,1878],{},[1712,103432,1726],{},[898,103434,1952],{},[1716,103436,1719],{"separator":1718},[2015,103438],{"width":2017},[2015,103440,103441],{},[2074,103442,103443],{},"(6.6)",[902,103445,103446],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,103448,18149,103449,103467,103468,103470,103471,103475,103476,103506,103507,103529],{},[883,103450,103452],{"className":103451},[886],[888,103453,103454],{"xmlns":890},[892,103455,103456,103464],{},[895,103457,103458,103460,103462],{},[898,103459,207],{},[1716,103461,1719],{"separator":1718},[898,103463,1952],{},[902,103465,103466],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,103469,87453],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,103472,103474],{"className":103473,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,103477,103479],{"className":103478},[886],[888,103480,103481],{"xmlns":890},[892,103482,103483,103503],{},[895,103484,103485,103487,103489,103491,103493,103495,103497,103499,103501],{},[898,103486,207],{},[1716,103488,1719],{"separator":1718},[898,103490,1952],{},[1716,103492,3605],{},[1716,103494,1920],{"stretchy":1919},[1712,103496,2505],{},[1716,103498,1719],{"separator":1718},[1712,103500,1714],{},[1716,103502,1925],{"stretchy":1919},[902,103504,103505],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,103508,103510],{"className":103509},[886],[888,103511,103512],{"xmlns":890},[892,103513,103514,103526],{},[895,103515,103516,103518,103520,103522,103524],{},[898,103517,1952],{},[1716,103519,1913],{},[1712,103521,1714],{},[1716,103523,2760],{},[898,103525,207],{},[902,103527,103528],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,103531,103532],{},[3682,103533],{"alt":103534,"className":103535,"src":103536},"imek-cobb-douglas-3d-plus-ic",[210,3686],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,103538,103540],{"className":103539},[886],[888,103541,103542],{"xmlns":890,"display":2004},[892,103543,103544,103594],{},[895,103545,103546,103548,103550,103556,103558,103564,103566,103568,103576,103578,103592],{},[898,103547,900],{},[1716,103549,1920],{"stretchy":1919},[1707,103551,103552,103554],{},[898,103553,1878],{},[1712,103555,1714],{},[1716,103557,1719],{"separator":1718},[1707,103559,103560,103562],{},[898,103561,1878],{},[1712,103563,1726],{},[1716,103565,1925],{"stretchy":1919},[1716,103567,1913],{},[7204,103569,103570,103572,103574],{},[898,103571,1878],{},[1712,103573,1714],{},[898,103575,207],{},[1716,103577,9532],{},[7204,103579,103580,103582,103584],{},[898,103581,1878],{},[1712,103583,1726],{},[895,103585,103586,103588,103590],{},[1712,103587,1714],{},[1716,103589,2760],{},[898,103591,207],{},[898,103593,1853],{"mathvariant":2068},[902,103595,103596],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1635,103598,103599,103648,103770,103904],{},[724,103600,103601,103603,103604],{},[883,103602,65449],{}," Příklad 6.3 — ověření vlastností pro ",[883,103605,103607],{"className":103606},[886],[888,103608,103609],{"xmlns":890},[892,103610,103611,103645],{},[895,103612,103613,103615,103617,103631],{},[898,103614,900],{},[1716,103616,1913],{},[7204,103618,103619,103621,103623],{},[898,103620,1878],{},[1712,103622,1714],{},[895,103624,103625,103627,103629],{},[1712,103626,1714],{},[898,103628,3045],{"mathvariant":2068},[1712,103630,6849],{},[7204,103632,103633,103635,103637],{},[898,103634,1878],{},[1712,103636,1726],{},[895,103638,103639,103641,103643],{},[1712,103640,7072],{},[898,103642,3045],{"mathvariant":2068},[1712,103644,6849],{},[902,103646,103647],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,103649,103651],{"className":103650},[886],[888,103652,103653],{"xmlns":890,"display":2004},[892,103654,103655,103767],{},[895,103656,103657,103665,103667,103675,103691,103705,103707,103709,103711,103713,103721,103723,103731,103745,103761,103763,103765],{},[7204,103658,103659,103661,103663],{},[898,103660,900],{},[1712,103662,1714],{},[1716,103664,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,103666,1913],{},[2747,103668,103669],{"scriptlevel":2505,"displaystyle":1919},[2750,103670,103671,103673],{},[1712,103672,1714],{},[1712,103674,6849],{},[7204,103676,103677,103679,103681],{},[898,103678,1878],{},[1712,103680,1714],{},[895,103682,103683,103685,103687,103689],{},[1716,103684,2760],{},[1712,103686,7072],{},[898,103688,3045],{"mathvariant":2068},[1712,103690,6849],{},[7204,103692,103693,103695,103697],{},[898,103694,1878],{},[1712,103696,1726],{},[895,103698,103699,103701,103703],{},[1712,103700,7072],{},[898,103702,3045],{"mathvariant":2068},[1712,103704,6849],{},[1716,103706,2716],{},[1712,103708,2505],{},[1716,103710,1719],{"separator":1718},[2324,103712],{"width":8689},[7204,103714,103715,103717,103719],{},[898,103716,900],{},[1712,103718,1726],{},[1716,103720,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,103722,1913],{},[2747,103724,103725],{"scriptlevel":2505,"displaystyle":1919},[2750,103726,103727,103729],{},[1712,103728,7072],{},[1712,103730,6849],{},[7204,103732,103733,103735,103737],{},[898,103734,1878],{},[1712,103736,1714],{},[895,103738,103739,103741,103743],{},[1712,103740,1714],{},[898,103742,3045],{"mathvariant":2068},[1712,103744,6849],{},[7204,103746,103747,103749,103751],{},[898,103748,1878],{},[1712,103750,1726],{},[895,103752,103753,103755,103757,103759],{},[1716,103754,2760],{},[1712,103756,1714],{},[898,103758,3045],{"mathvariant":2068},[1712,103760,6849],{},[1716,103762,2716],{},[1712,103764,2505],{},[1716,103766,1719],{"separator":1718},[902,103768,103769],{"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,",[883,103771,103773],{"className":103772},[886],[888,103774,103775],{"xmlns":890,"display":2004},[892,103776,103777,103901],{},[895,103778,103779,103791,103793,103795,103803,103819,103833,103835,103837,103839,103841,103853,103855,103857,103865,103879,103895,103897,103899],{},[7204,103780,103781,103783,103785],{},[898,103782,900],{},[1712,103784,16773],{},[895,103786,103787,103789],{},[1716,103788,8505],{"mathvariant":2068},[1716,103790,8505],{"mathvariant":2068},[1716,103792,1913],{},[1716,103794,2760],{},[2747,103796,103797],{"scriptlevel":2505,"displaystyle":1919},[2750,103798,103799,103801],{},[1712,103800,7072],{},[1712,103802,6833],{},[7204,103804,103805,103807,103809],{},[898,103806,1878],{},[1712,103808,1714],{},[895,103810,103811,103813,103815,103817],{},[1716,103812,2760],{},[1712,103814,7109],{},[898,103816,3045],{"mathvariant":2068},[1712,103818,6849],{},[7204,103820,103821,103823,103825],{},[898,103822,1878],{},[1712,103824,1726],{},[895,103826,103827,103829,103831],{},[1712,103828,7072],{},[898,103830,3045],{"mathvariant":2068},[1712,103832,6849],{},[1716,103834,2704],{},[1712,103836,2505],{},[1716,103838,1719],{"separator":1718},[2324,103840],{"width":8689},[7204,103842,103843,103845,103847],{},[898,103844,900],{},[1712,103846,6688],{},[895,103848,103849,103851],{},[1716,103850,8505],{"mathvariant":2068},[1716,103852,8505],{"mathvariant":2068},[1716,103854,1913],{},[1716,103856,2760],{},[2747,103858,103859],{"scriptlevel":2505,"displaystyle":1919},[2750,103860,103861,103863],{},[1712,103862,7072],{},[1712,103864,6833],{},[7204,103866,103867,103869,103871],{},[898,103868,1878],{},[1712,103870,1714],{},[895,103872,103873,103875,103877],{},[1712,103874,1714],{},[898,103876,3045],{"mathvariant":2068},[1712,103878,6849],{},[7204,103880,103881,103883,103885],{},[898,103882,1878],{},[1712,103884,1726],{},[895,103886,103887,103889,103891,103893],{},[1716,103888,2760],{},[1712,103890,6985],{},[898,103892,3045],{"mathvariant":2068},[1712,103894,6849],{},[1716,103896,2704],{},[1712,103898,2505],{},[1716,103900,1719],{"separator":1718},[902,103902,103903],{"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,",[724,103905,103906],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,103908,103910],{"id":103909},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,103912,103913,103916],{},[38,103914,103915],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,103918,103920],{"className":103919},[886],[888,103921,103922],{"xmlns":890,"display":2004},[892,103923,103924,103967],{},[2008,103925,103926],{"width":2010},[2012,103927,103928,103930,103960,103962],{},[2015,103929],{"width":2017},[2015,103931,103932],{},[895,103933,103934,103936,103938,103944,103946,103952,103954,103956,103958],{},[898,103935,900],{},[1716,103937,1920],{"stretchy":1919},[1707,103939,103940,103942],{},[898,103941,1878],{},[1712,103943,1714],{},[1716,103945,1719],{"separator":1718},[1707,103947,103948,103950],{},[898,103949,1878],{},[1712,103951,1726],{},[1716,103953,1925],{"stretchy":1919},[1716,103955,1913],{},[898,103957,4478],{},[1716,103959,1719],{"separator":1718},[2015,103961],{"width":2017},[2015,103963,103964],{},[2074,103965,103966],{},"(6.7)",[902,103968,103969],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,103971,18149,103972,103985],{},[883,103973,103975],{"className":103974},[886],[888,103976,103977],{"xmlns":890},[892,103978,103979,103983],{},[895,103980,103981],{},[898,103982,4478],{},[902,103984,4478],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,103987,103989],{"className":103988},[886],[888,103990,103991],{"xmlns":890,"display":2004},[892,103992,103993,104034],{},[2008,103994,103995],{"width":2010},[2012,103996,103997,103999,104027,104029],{},[2015,103998],{"width":2017},[2015,104000,104001],{},[895,104002,104003,104011,104013,104021,104023,104025],{},[7204,104004,104005,104007,104009],{},[898,104006,1878],{},[1712,104008,1714],{},[898,104010,207],{},[1716,104012,9532],{},[7204,104014,104015,104017,104019],{},[898,104016,1878],{},[1712,104018,1726],{},[898,104020,1952],{},[1716,104022,1913],{},[898,104024,4478],{},[898,104026,1853],{"mathvariant":2068},[2015,104028],{"width":2017},[2015,104030,104031],{},[2074,104032,104033],{},"(6.8)",[902,104035,104036],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,104038,104039,104040,18195,104070,3495,104073,104086,104087,104122,104123,104140,104141,104170,104171,104174],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,104041,104043],{"className":104042},[886],[888,104044,104045],{"xmlns":890},[892,104046,104047,104067],{},[895,104048,104049,104051,104057,104059,104065],{},[1716,104050,2502],{"stretchy":1919},[1707,104052,104053,104055],{},[898,104054,1878],{},[1712,104056,1714],{},[1716,104058,1719],{"separator":1718},[1707,104060,104061,104063],{},[898,104062,1878],{},[1712,104064,1726],{},[1716,104066,2516],{"stretchy":1919},[902,104068,104069],{"encoding":904},"[Q_1, Q_2]",[38,104071,104072],{},"stejnou úrovní uspokojení",[883,104074,104076],{"className":104075},[886],[888,104077,104078],{"xmlns":890},[892,104079,104080,104084],{},[895,104081,104082],{},[898,104083,4478],{},[902,104085,4478],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,104088,104090],{"className":104089},[886],[888,104091,104092],{"xmlns":890},[892,104093,104094,104120],{},[895,104095,104096,104098,104100,104102,104104,104110,104112,104118],{},[898,104097,900],{},[1716,104099,1913],{},[898,104101,900],{},[1716,104103,1920],{"stretchy":1919},[1707,104105,104106,104108],{},[898,104107,1878],{},[1712,104109,1714],{},[1716,104111,1719],{"separator":1718},[1707,104113,104114,104116],{},[898,104115,1878],{},[1712,104117,1726],{},[1716,104119,1925],{"stretchy":1919},[902,104121,100210],{"encoding":904}," s rovinami ",[883,104124,104126],{"className":104125},[886],[888,104127,104128],{"xmlns":890},[892,104129,104130,104138],{},[895,104131,104132,104134,104136],{},[898,104133,900],{},[1716,104135,1913],{},[898,104137,4478],{},[902,104139,99426],{"encoding":904}," rovnoběžnými s rovinou ",[883,104142,104144],{"className":104143},[886],[888,104145,104146],{"xmlns":890},[892,104147,104148,104168],{},[895,104149,104150,104152,104158,104160,104166],{},[1716,104151,1920],{"stretchy":1919},[1707,104153,104154,104156],{},[898,104155,1878],{},[1712,104157,1714],{},[1716,104159,1719],{"separator":1718},[1707,104161,104162,104164],{},[898,104163,1878],{},[1712,104165,1726],{},[1716,104167,1925],{"stretchy":1919},[902,104169,102373],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,104172,104173],{},"izokvantami"," produkčních funkcí.",[724,104176,104177],{},[614,104178,104179,104180,102251,104198,104216,104217,1853],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,104181,104183],{"className":104182},[886],[888,104184,104185],{"xmlns":890},[892,104186,104187,104195],{},[895,104188,104189,104191,104193],{},[898,104190,207],{},[1716,104192,2704],{},[898,104194,1952],{},[902,104196,104197],{"encoding":904},"a \u003C b",[883,104199,104201],{"className":104200},[886],[888,104202,104203],{"xmlns":890},[892,104204,104205,104213],{},[895,104206,104207,104209,104211],{},[898,104208,207],{},[1716,104210,2716],{},[898,104212,1952],{},[902,104214,104215],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,104218,104220],{"className":104219},[886],[888,104221,104222],{"xmlns":890},[892,104223,104224,104248],{},[895,104225,104226,104232,104234,104240,104242],{},[1707,104227,104228,104230],{},[898,104229,4478],{},[1712,104231,2505],{},[1716,104233,2704],{},[1707,104235,104236,104238],{},[898,104237,4478],{},[1712,104239,1714],{},[1716,104241,2704],{},[1707,104243,104244,104246],{},[898,104245,4478],{},[1712,104247,1726],{},[902,104249,104250],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,104252,104253],{},[614,104254,104255,104256,104285,104286,104344,104345,104363],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,104257,104259],{"className":104258},[886],[888,104260,104261],{"xmlns":890},[892,104262,104263,104283],{},[895,104264,104265,104267,104273,104275,104281],{},[1716,104266,1920],{"stretchy":1919},[1707,104268,104269,104271],{},[898,104270,1878],{},[1712,104272,1714],{},[1716,104274,1719],{"separator":1718},[1707,104276,104277,104279],{},[898,104278,1878],{},[1712,104280,1726],{},[1716,104282,1925],{"stretchy":1919},[902,104284,102373],{"encoding":904},"; body ",[883,104287,104289],{"className":104288},[886],[888,104290,104291],{"xmlns":890},[892,104292,104293,104341],{},[895,104294,104295,104297,104299,104301,104307,104309,104315,104317,104319,104321,104323,104325,104331,104333,104339],{},[898,104296,10871],{},[1716,104298,1913],{},[1716,104300,2502],{"stretchy":1919},[1707,104302,104303,104305],{},[898,104304,207],{},[1712,104306,1714],{},[1716,104308,1719],{"separator":1718},[1707,104310,104311,104313],{},[898,104312,207],{},[1712,104314,1726],{},[1716,104316,2516],{"stretchy":1919},[1716,104318,1719],{"separator":1718},[898,104320,10856],{},[1716,104322,1913],{},[1716,104324,2502],{"stretchy":1919},[1707,104326,104327,104329],{},[898,104328,1952],{},[1712,104330,1714],{},[1716,104332,1719],{"separator":1718},[1707,104334,104335,104337],{},[898,104336,1952],{},[1712,104338,1726],{},[1716,104340,2516],{"stretchy":1919},[902,104342,104343],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,104346,104348],{"className":104347},[886],[888,104349,104350],{"xmlns":890},[892,104351,104352,104360],{},[895,104353,104354,104356,104358],{},[898,104355,9945],{},[1716,104357,1719],{"separator":1718},[898,104359,1916],{},[902,104361,104362],{"encoding":904},"C, D"," na vyšší hladině.",[1635,104365,104366],{},[724,104367,104368,104370,104371,104433,104434,104478,104479,104513,104514,39959,104532,104513,104586,39959,104604,104680],{},[883,104369,65449],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,104372,104374],{"className":104373},[886],[888,104375,104376],{"xmlns":890},[892,104377,104378,104430],{},[895,104379,104380,104382,104384,104390,104392,104398,104400,104402,104416],{},[898,104381,900],{},[1716,104383,1920],{"stretchy":1919},[1707,104385,104386,104388],{},[898,104387,1878],{},[1712,104389,1714],{},[1716,104391,1719],{"separator":1718},[1707,104393,104394,104396],{},[898,104395,1878],{},[1712,104397,1726],{},[1716,104399,1925],{"stretchy":1919},[1716,104401,1913],{},[7204,104403,104404,104406,104408],{},[898,104405,1878],{},[1712,104407,1714],{},[895,104409,104410,104412,104414],{},[1712,104411,1714],{},[898,104413,3045],{"mathvariant":2068},[1712,104415,6849],{},[7204,104417,104418,104420,104422],{},[898,104419,1878],{},[1712,104421,1726],{},[895,104423,104424,104426,104428],{},[1712,104425,7072],{},[898,104427,3045],{"mathvariant":2068},[1712,104429,6849],{},[902,104431,104432],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,104435,104437],{"className":104436},[886],[888,104438,104439],{"xmlns":890},[892,104440,104441,104475],{},[895,104442,104443,104457,104471,104473],{},[7204,104444,104445,104447,104449],{},[898,104446,1878],{},[1712,104448,1714],{},[895,104450,104451,104453,104455],{},[1712,104452,1714],{},[898,104454,3045],{"mathvariant":2068},[1712,104456,6849],{},[7204,104458,104459,104461,104463],{},[898,104460,1878],{},[1712,104462,1726],{},[895,104464,104465,104467,104469],{},[1712,104466,7072],{},[898,104468,3045],{"mathvariant":2068},[1712,104470,6849],{},[1716,104472,1913],{},[898,104474,4478],{},[902,104476,104477],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,104480,104482],{"className":104481},[886],[888,104483,104484],{"xmlns":890},[892,104485,104486,104510],{},[895,104487,104488,104494,104502,104504],{},[1707,104489,104490,104492],{},[898,104491,1878],{},[1712,104493,1714],{},[7204,104495,104496,104498,104500],{},[898,104497,1878],{},[1712,104499,1726],{},[1712,104501,7072],{},[1716,104503,1913],{},[3074,104505,104506,104508],{},[898,104507,4478],{},[1712,104509,6849],{},[902,104511,104512],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,104515,104517],{"className":104516},[886],[888,104518,104519],{"xmlns":890},[892,104520,104521,104529],{},[895,104522,104523,104525,104527],{},[898,104524,4478],{},[1716,104526,1913],{},[1712,104528,1714],{},[902,104530,104531],{"encoding":904},"c = 1",[883,104533,104535],{"className":104534},[886],[888,104536,104537],{"xmlns":890},[892,104538,104539,104583],{},[895,104540,104541,104547,104549,104565,104567],{},[1707,104542,104543,104545],{},[898,104544,1878],{},[1712,104546,1726],{},[1716,104548,1913],{},[7204,104550,104551,104553,104555],{},[898,104552,1878],{},[1712,104554,1714],{},[895,104556,104557,104559,104561,104563],{},[1716,104558,2760],{},[1712,104560,1714],{},[898,104562,3045],{"mathvariant":2068},[1712,104564,7072],{},[1716,104566,1913],{},[2747,104568,104569],{"scriptlevel":2505,"displaystyle":1718},[2750,104570,104571,104573],{},[1712,104572,1714],{},[94781,104574,104575,104581],{},[1707,104576,104577,104579],{},[898,104578,1878],{},[1712,104580,1714],{},[1712,104582,7072],{},[902,104584,104585],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,104587,104589],{"className":104588},[886],[888,104590,104591],{"xmlns":890},[892,104592,104593,104601],{},[895,104594,104595,104597,104599],{},[898,104596,4478],{},[1716,104598,1913],{},[1712,104600,1726],{},[902,104602,104603],{"encoding":904},"c = 2",[883,104605,104607],{"className":104606},[886],[888,104608,104609],{"xmlns":890},[892,104610,104611,104677],{},[895,104612,104613,104619,104621,104633,104635,104651,104653],{},[1707,104614,104615,104617],{},[898,104616,1878],{},[1712,104618,1726],{},[1716,104620,1913],{},[3074,104622,104623,104625],{},[1712,104624,1726],{},[895,104626,104627,104629,104631],{},[1712,104628,6849],{},[898,104630,3045],{"mathvariant":2068},[1712,104632,7072],{},[1716,104634,9532],{},[7204,104636,104637,104639,104641],{},[898,104638,1878],{},[1712,104640,1714],{},[895,104642,104643,104645,104647,104649],{},[1716,104644,2760],{},[1712,104646,1714],{},[898,104648,3045],{"mathvariant":2068},[1712,104650,7072],{},[1716,104652,1913],{},[2747,104654,104655],{"scriptlevel":2505,"displaystyle":1718},[2750,104656,104657,104667],{},[895,104658,104659,104661],{},[1712,104660,1726],{},[94781,104662,104663,104665],{},[1712,104664,1726],{},[1712,104666,7072],{},[94781,104668,104669,104675],{},[1707,104670,104671,104673],{},[898,104672,1878],{},[1712,104674,1714],{},[1712,104676,7072],{},[902,104678,104679],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,104682,104684],{"id":104683},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,104686,104687],{},[3682,104688],{"alt":104689,"className":104690,"src":104691},"imek-ic-4vlastnosti-anotovane",[210,3686],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1635,104693,104694,104703,104750,104794,104800,104806],{},[724,104695,104696,104698,104699,104702],{},[883,104697,2233],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,104700,104701],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,104704,104705],{},[883,104706,104708],{"className":104707},[886],[888,104709,104710],{"xmlns":890},[892,104711,104712,104747],{},[895,104713,104714,104717,104719,104721,104723,104725,104743,104745],{},[898,104715,104716],{"mathvariant":2068},"tg",[1716,104718,68954],{},[898,104720,32647],{},[1716,104722,1913],{},[1716,104724,2760],{},[2750,104726,104727,104735],{},[7204,104728,104729,104731,104733],{},[898,104730,900],{},[1712,104732,1714],{},[1716,104734,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,104736,104737,104739,104741],{},[898,104738,900],{},[1712,104740,1726],{},[1716,104742,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,104744,2704],{},[1712,104746,2505],{},[902,104748,104749],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,104751,104752,104753,104793],{},"(derivace implicitně zadané funkce ",[883,104754,104756],{"className":104755},[886],[888,104757,104758],{"xmlns":890},[892,104759,104760,104790],{},[895,104761,104762,104764,104766,104772,104774,104780,104782,104784,104786,104788],{},[898,104763,900],{},[1716,104765,1920],{"stretchy":1919},[1707,104767,104768,104770],{},[898,104769,1878],{},[1712,104771,1714],{},[1716,104773,1719],{"separator":1718},[1707,104775,104776,104778],{},[898,104777,1878],{},[1712,104779,1726],{},[1716,104781,1925],{"stretchy":1919},[1716,104783,2760],{},[898,104785,4478],{},[1716,104787,1913],{},[1712,104789,2505],{},[902,104791,104792],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,104795,104796,104799],{},[38,104797,104798],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,104801,104802,104805],{},[38,104803,104804],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,104807,104808,104811,104812,104830,104831,104847,104848,104851],{},[38,104809,104810],{},"4° Konvexní."," Pro každé dva body ",[883,104813,104815],{"className":104814},[886],[888,104816,104817],{"xmlns":890},[892,104818,104819,104827],{},[895,104820,104821,104823,104825],{},[898,104822,10871],{},[1716,104824,1719],{"separator":1718},[898,104826,10856],{},[902,104828,104829],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,104832,104834],{"className":104833},[886],[888,104835,104836],{"xmlns":890},[892,104837,104838,104844],{},[895,104839,104840,104842],{},[898,104841,10871],{},[898,104843,10856],{},[902,104845,104846],{"encoding":904},"AB"," ve ",[38,104849,104850],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,104853,104854],{},[614,104855,104856,104857,104892,104893,1853],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,104858,104860],{"className":104859},[886],[888,104861,104862],{"xmlns":890},[892,104863,104864,104890],{},[895,104865,104866,104868,104870,104876,104878,104884,104886,104888],{},[898,104867,900],{},[1716,104869,1920],{"stretchy":1919},[1707,104871,104872,104874],{},[898,104873,1878],{},[1712,104875,1714],{},[1716,104877,1719],{"separator":1718},[1707,104879,104880,104882],{},[898,104881,1878],{},[1712,104883,1726],{},[1716,104885,1925],{"stretchy":1919},[1716,104887,1913],{},[898,104889,4478],{},[902,104891,23575],{"encoding":904}," s tečnou se sklonem ",[883,104894,104896],{"className":104895},[886],[888,104897,104898],{"xmlns":890},[892,104899,104900,104908],{},[895,104901,104902,104904,104906],{},[898,104903,104716],{"mathvariant":2068},[1716,104905,68954],{},[898,104907,32647],{},[902,104909,104910],{"encoding":904},"\\operatorname{tg}\\alpha",[115,104912,104914],{"id":104913},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,104916,104917,3495,104920,1994,104933,104936],{},[38,104918,104919],{},"Mezní míra komoditní substituce",[883,104921,104923],{"className":104922},[886],[888,104924,104925],{"xmlns":890},[892,104926,104927,104931],{},[895,104928,104929],{},[2074,104930,24407],{},[902,104932,42003],{"encoding":904},[38,104934,104935],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,104938,104940],{"className":104939},[886],[888,104941,104942],{"xmlns":890,"display":2004},[892,104943,104944,105031],{},[2008,104945,104946],{"width":2010},[2012,104947,104948,104950,105024,105026],{},[2015,104949],{"width":2017},[2015,104951,104952],{},[895,104953,104954,104956,104958,104960,104962,104968,104970,104976,104978,104980,105002,105004,105022],{},[2074,104955,24407],{},[1716,104957,1913],{},[2074,104959,24407],{},[1716,104961,1920],{"stretchy":1919},[1707,104963,104964,104966],{},[898,104965,1878],{},[1712,104967,1714],{},[1716,104969,1719],{"separator":1718},[1707,104971,104972,104974],{},[898,104973,1878],{},[1712,104975,1726],{},[1716,104977,1925],{"stretchy":1919},[1716,104979,1913],{},[2750,104981,104982,104992],{},[895,104983,104984,104986],{},[898,104985,16690],{},[1707,104987,104988,104990],{},[898,104989,900],{},[1712,104991,1714],{},[895,104993,104994,104996],{},[898,104995,16690],{},[1707,104997,104998,105000],{},[898,104999,900],{},[1712,105001,1726],{},[1716,105003,1913],{},[2750,105005,105006,105014],{},[7204,105007,105008,105010,105012],{},[898,105009,900],{},[1712,105011,1714],{},[1716,105013,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,105015,105016,105018,105020],{},[898,105017,900],{},[1712,105019,1726],{},[1716,105021,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[898,105023,1853],{"mathvariant":2068},[2015,105025],{"width":2017},[2015,105027,105028],{},[2074,105029,105030],{},"(6.9)",[902,105032,105033],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,105035,105036,105037,105071,105072,105104,105105,105140,105141,105154],{},"Geometricky: ",[883,105038,105040],{"className":105039},[886],[888,105041,105042],{"xmlns":890},[892,105043,105044,105068],{},[895,105045,105046,105048],{},[1716,105047,2760],{},[2747,105049,105050],{"scriptlevel":2505,"displaystyle":1919},[2750,105051,105052,105060],{},[7204,105053,105054,105056,105058],{},[898,105055,900],{},[1712,105057,1714],{},[1716,105059,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,105061,105062,105064,105066],{},[898,105063,900],{},[1712,105065,1726],{},[1716,105067,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,105069,105070],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,105073,105075],{"className":105074},[886],[888,105076,105077],{"xmlns":890},[892,105078,105079,105101],{},[895,105080,105081,105087,105089,105091,105093,105099],{},[1707,105082,105083,105085],{},[898,105084,1878],{},[1712,105086,1726],{},[1716,105088,1913],{},[898,105090,15915],{},[1716,105092,1920],{"stretchy":1919},[1707,105094,105095,105097],{},[898,105096,1878],{},[1712,105098,1714],{},[1716,105100,1925],{"stretchy":1919},[902,105102,105103],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,105106,105108],{"className":105107},[886],[888,105109,105110],{"xmlns":890},[892,105111,105112,105138],{},[895,105113,105114,105116,105118,105124,105126,105132,105134,105136],{},[898,105115,900],{},[1716,105117,1920],{"stretchy":1919},[1707,105119,105120,105122],{},[898,105121,1878],{},[1712,105123,1714],{},[1716,105125,1719],{"separator":1718},[1707,105127,105128,105130],{},[898,105129,1878],{},[1712,105131,1726],{},[1716,105133,1925],{"stretchy":1919},[1716,105135,1913],{},[898,105137,4478],{},[902,105139,23575],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,105142,105144],{"className":105143},[886],[888,105145,105146],{"xmlns":890},[892,105147,105148,105152],{},[895,105149,105150],{},[2074,105151,24407],{},[902,105153,42003],{"encoding":904}," chápeme jako velikost kompenzace.",[1635,105156,105157],{},[724,105158,105159,105161,105162,2574,105194,105232,105233,105250,105251,105268],{},[883,105160,1641],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,105163,105165],{"className":105164},[886],[888,105166,105167],{"xmlns":890},[892,105168,105169,105191],{},[895,105170,105171,105173,105175,105181,105183,105189],{},[2074,105172,24407],{},[1716,105174,1920],{"stretchy":1919},[1707,105176,105177,105179],{},[898,105178,1878],{},[1712,105180,1714],{},[1716,105182,1719],{"separator":1718},[1707,105184,105185,105187],{},[898,105186,1878],{},[1712,105188,1726],{},[1716,105190,1925],{"stretchy":1919},[902,105192,105193],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,105195,105196,105197,42767,105214,105231],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,105198,105200],{"className":105199},[886],[888,105201,105202],{"xmlns":890},[892,105203,105204,105212],{},[895,105205,105206],{},[1707,105207,105208,105210],{},[898,105209,1878],{},[1712,105211,1714],{},[902,105213,4189],{"encoding":904},[883,105215,105217],{"className":105216},[886],[888,105218,105219],{"xmlns":890},[892,105220,105221,105229],{},[895,105222,105223],{},[1707,105224,105225,105227],{},[898,105226,1878],{},[1712,105228,1726],{},[902,105230,42785],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,105234,105236],{"className":105235},[886],[888,105237,105238],{"xmlns":890},[892,105239,105240,105248],{},[895,105241,105242],{},[1707,105243,105244,105246],{},[898,105245,1878],{},[1712,105247,1726],{},[902,105249,42785],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,105252,105254],{"className":105253},[886],[888,105255,105256],{"xmlns":890},[892,105257,105258,105266],{},[895,105259,105260],{},[1707,105261,105262,105264],{},[898,105263,1878],{},[1712,105265,1714],{},[902,105267,4189],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,105270,105271,105272,43707],{},"Pro obecnou změnu ",[883,105273,105275],{"className":105274},[886],[888,105276,105277],{"xmlns":890},[892,105278,105279,105289],{},[895,105280,105281,105283],{},[898,105282,5198],{"mathvariant":2068},[1707,105284,105285,105287],{},[898,105286,1878],{},[1712,105288,1714],{},[902,105290,105291],{"encoding":904},"\\mathrm{d} Q_1",[883,105293,105295],{"className":105294},[886],[888,105296,105297],{"xmlns":890,"display":2004},[892,105298,105299,105352],{},[2008,105300,105301],{"width":2010},[2012,105302,105303,105305,105345,105347],{},[2015,105304],{"width":2017},[2015,105306,105307],{},[895,105308,105309,105311,105317,105319,105321,105327,105329,105331,105333,105335,105337,105343],{},[898,105310,8485],{"mathvariant":2068},[1707,105312,105313,105315],{},[898,105314,1878],{},[1712,105316,1726],{},[1716,105318,8490],{},[898,105320,5198],{"mathvariant":2068},[1707,105322,105323,105325],{},[898,105324,1878],{},[1712,105326,1726],{},[1716,105328,1913],{},[1716,105330,2760],{},[2074,105332,24407],{},[1716,105334,9532],{},[898,105336,5198],{"mathvariant":2068},[1707,105338,105339,105341],{},[898,105340,1878],{},[1712,105342,1714],{},[1716,105344,1719],{"separator":1718},[2015,105346],{"width":2017},[2015,105348,105349],{},[2074,105350,105351],{},"(6.10)",[902,105353,105354],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,105356,105358],{"className":105357},[886],[888,105359,105360],{"xmlns":890,"display":2004},[892,105361,105362,105409],{},[2008,105363,105364],{"width":2010},[2012,105365,105366,105368,105402,105404],{},[2015,105367],{"width":2017},[2015,105369,105370],{},[895,105371,105372,105374,105380,105382,105384,105390,105392,105394,105400],{},[898,105373,5198],{"mathvariant":2068},[1707,105375,105376,105378],{},[898,105377,1878],{},[1712,105379,1714],{},[1716,105381,1913],{},[1716,105383,2760],{},[2750,105385,105386,105388],{},[1712,105387,1714],{},[2074,105389,24407],{},[2074,105391,8508],{},[898,105393,5198],{"mathvariant":2068},[1707,105395,105396,105398],{},[898,105397,1878],{},[1712,105399,1726],{},[898,105401,1853],{"mathvariant":2068},[2015,105403],{"width":2017},[2015,105405,105406],{},[2074,105407,105408],{},"(6.11)",[902,105410,105411],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1635,105413,105414,105480,105597],{},[724,105415,105416,105418,105419,43707],{},[883,105417,65449],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,105420,105422],{"className":105421},[886],[888,105423,105424],{"xmlns":890},[892,105425,105426,105478],{},[895,105427,105428,105430,105432,105438,105440,105446,105448,105450,105464],{},[898,105429,900],{},[1716,105431,1920],{"stretchy":1919},[1707,105433,105434,105436],{},[898,105435,1878],{},[1712,105437,1714],{},[1716,105439,1719],{"separator":1718},[1707,105441,105442,105444],{},[898,105443,1878],{},[1712,105445,1726],{},[1716,105447,1925],{"stretchy":1919},[1716,105449,1913],{},[7204,105451,105452,105454,105456],{},[898,105453,1878],{},[1712,105455,1714],{},[895,105457,105458,105460,105462],{},[1712,105459,1714],{},[898,105461,3045],{"mathvariant":2068},[1712,105463,1726],{},[7204,105465,105466,105468,105470],{},[898,105467,1878],{},[1712,105469,1726],{},[895,105471,105472,105474,105476],{},[1712,105473,1714],{},[898,105475,3045],{"mathvariant":2068},[1712,105477,1726],{},[902,105479,43706],{"encoding":904},[724,105481,105482],{},[883,105483,105485],{"className":105484},[886],[888,105486,105487],{"xmlns":890},[892,105488,105489,105595],{},[895,105490,105491,105493,105495,105577,105579,105593],{},[2074,105492,24407],{},[1716,105494,1913],{},[2750,105496,105497,105537],{},[895,105498,105499,105507,105523],{},[2747,105500,105501],{"scriptlevel":2505,"displaystyle":1919},[2750,105502,105503,105505],{},[1712,105504,1714],{},[1712,105506,1726],{},[7204,105508,105509,105511,105513],{},[898,105510,1878],{},[1712,105512,1714],{},[895,105514,105515,105517,105519,105521],{},[1716,105516,2760],{},[1712,105518,1714],{},[898,105520,3045],{"mathvariant":2068},[1712,105522,1726],{},[7204,105524,105525,105527,105529],{},[898,105526,1878],{},[1712,105528,1726],{},[895,105530,105531,105533,105535],{},[1712,105532,1714],{},[898,105534,3045],{"mathvariant":2068},[1712,105536,1726],{},[895,105538,105539,105547,105561],{},[2747,105540,105541],{"scriptlevel":2505,"displaystyle":1919},[2750,105542,105543,105545],{},[1712,105544,1714],{},[1712,105546,1726],{},[7204,105548,105549,105551,105553],{},[898,105550,1878],{},[1712,105552,1714],{},[895,105554,105555,105557,105559],{},[1712,105556,1714],{},[898,105558,3045],{"mathvariant":2068},[1712,105560,1726],{},[7204,105562,105563,105565,105567],{},[898,105564,1878],{},[1712,105566,1726],{},[895,105568,105569,105571,105573,105575],{},[1716,105570,2760],{},[1712,105572,1714],{},[898,105574,3045],{"mathvariant":2068},[1712,105576,1726],{},[1716,105578,1913],{},[2750,105580,105581,105587],{},[1707,105582,105583,105585],{},[898,105584,1878],{},[1712,105586,1726],{},[1707,105588,105589,105591],{},[898,105590,1878],{},[1712,105592,1714],{},[898,105594,1853],{"mathvariant":2068},[902,105596,43825],{"encoding":904},[724,105598,9827,105599,7636,105642,43875,105644,105663],{},[883,105600,105602],{"className":105601},[886],[888,105603,105604],{"xmlns":890},[892,105605,105606,105640],{},[895,105607,105608,105610,105612,105614,105616,105618,105620,105622,105630,105632],{},[2074,105609,24407],{},[1716,105611,1920],{"stretchy":1919},[1712,105613,43843],{},[1716,105615,1719],{"separator":1718},[1712,105617,28904],{},[1716,105619,1925],{"stretchy":1919},[1716,105621,1913],{},[2747,105623,105624],{"scriptlevel":2505,"displaystyle":1919},[2750,105625,105626,105628],{},[1712,105627,28904],{},[1712,105629,43843],{},[1716,105631,1913],{},[2747,105633,105634],{"scriptlevel":2505,"displaystyle":1919},[2750,105635,105636,105638],{},[1712,105637,6985],{},[1712,105639,7072],{},[902,105641,43872],{"encoding":904},[614,105643,23026],{},[883,105645,105647],{"className":105646},[886],[888,105648,105649],{"xmlns":890},[892,105650,105651,105661],{},[895,105652,105653],{},[2747,105654,105655],{"scriptlevel":2505,"displaystyle":1919},[2750,105656,105657,105659],{},[1712,105658,6985],{},[1712,105660,7072],{},[902,105662,43895],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,105665,105666,105667,105671],{},"(Paralelou je ",[207,105668,105670],{"className":105669,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,105673,105675],{"id":105674},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,105677,105678,105679,105682],{},"Rámcově se v kapitole 6 studují ",[38,105680,105681],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,105684,105685,105821],{},[123,105686,105687,105689,105690,23961,105721,3495,105724,105773,105774,1853],{},[38,105688,42017],{}," — maximalizace ",[883,105691,105693],{"className":105692},[886],[888,105694,105695],{"xmlns":890},[892,105696,105697,105719],{},[895,105698,105699,105701,105703,105709,105711,105717],{},[898,105700,900],{},[1716,105702,1920],{"stretchy":1919},[1707,105704,105705,105707],{},[898,105706,1878],{},[1712,105708,1714],{},[1716,105710,1719],{"separator":1718},[1707,105712,105713,105715],{},[898,105714,1878],{},[1712,105716,1726],{},[1716,105718,1925],{"stretchy":1919},[902,105720,30133],{"encoding":904},[38,105722,105723],{},"rozpočtovém omezení",[883,105725,105727],{"className":105726},[886],[888,105728,105729],{"xmlns":890},[892,105730,105731,105771],{},[895,105732,105733,105739,105741,105749,105755,105757,105765],{},[3074,105734,105735,105737],{},[898,105736,1758],{},[1716,105738,3080],{},[1716,105740,1913],{},[7204,105742,105743,105745,105747],{},[898,105744,1690],{},[1712,105746,1714],{},[1716,105748,3080],{},[1707,105750,105751,105753],{},[898,105752,1878],{},[1712,105754,1714],{},[1716,105756,1949],{},[7204,105758,105759,105761,105763],{},[898,105760,1690],{},[1712,105762,1726],{},[1716,105764,3080],{},[1707,105766,105767,105769],{},[898,105768,1878],{},[1712,105770,1726],{},[902,105772,31088],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,105775,105777],{"className":105776},[886],[888,105778,105779],{"xmlns":890},[892,105780,105781,105819],{},[895,105782,105783,105789,105791,105797,105799,105805,105807,105813,105815,105817],{},[1707,105784,105785,105787],{},[898,105786,1878],{},[898,105788,12546],{},[1716,105790,1913],{},[1707,105792,105793,105795],{},[898,105794,1916],{},[898,105796,12546],{},[1716,105798,1920],{"stretchy":1919},[1707,105800,105801,105803],{},[898,105802,1690],{},[1712,105804,1714],{},[1716,105806,1719],{"separator":1718},[1707,105808,105809,105811],{},[898,105810,1690],{},[1712,105812,1726],{},[1716,105814,1719],{"separator":1718},[898,105816,1758],{},[1716,105818,1925],{"stretchy":1919},[902,105820,50214],{"encoding":904},[123,105822,105823,41670,105826,41713,105872,105889,105890,1853],{},[38,105824,105825],{},"Duální úloha",[883,105827,105829],{"className":105828},[886],[888,105830,105831],{"xmlns":890},[892,105832,105833,105869],{},[895,105834,105835,105837,105839,105847,105853,105855,105863],{},[898,105836,1805],{},[1716,105838,1913],{},[7204,105840,105841,105843,105845],{},[898,105842,1690],{},[1712,105844,1714],{},[1716,105846,3080],{},[1707,105848,105849,105851],{},[898,105850,1878],{},[1712,105852,1714],{},[1716,105854,1949],{},[7204,105856,105857,105859,105861],{},[898,105858,1690],{},[1712,105860,1726],{},[1716,105862,3080],{},[1707,105864,105865,105867],{},[898,105866,1878],{},[1712,105868,1726],{},[902,105870,105871],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,105873,105875],{"className":105874},[886],[888,105876,105877],{"xmlns":890},[892,105878,105879,105887],{},[895,105880,105881],{},[3074,105882,105883,105885],{},[898,105884,900],{},[1716,105886,3080],{},[902,105888,41731],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,105891,105893],{"className":105892},[886],[888,105894,105895],{"xmlns":890},[892,105896,105897,105935],{},[895,105898,105899,105905,105907,105913,105915,105921,105923,105929,105931,105933],{},[1707,105900,105901,105903],{},[898,105902,1878],{},[898,105904,12546],{},[1716,105906,1913],{},[1707,105908,105909,105911],{},[898,105910,1916],{},[898,105912,12546],{},[1716,105914,1920],{"stretchy":1919},[1707,105916,105917,105919],{},[898,105918,1690],{},[1712,105920,1714],{},[1716,105922,1719],{"separator":1718},[1707,105924,105925,105927],{},[898,105926,1690],{},[1712,105928,1726],{},[1716,105930,1719],{"separator":1718},[898,105932,900],{},[1716,105934,1925],{"stretchy":1919},[902,105936,31612],{"encoding":904},[724,105938,105939,105940,105943,105944,3495,105947,105986],{},"Obě úlohy se řeší ",[207,105941,41736],{"className":105942,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,105945,105946],{},"tentýž bod dotyku",[883,105948,105950],{"className":105949},[886],[888,105951,105952],{"xmlns":890},[892,105953,105954,105984],{},[895,105955,105956,105962,105964,105972,105974,105982],{},[3074,105957,105958,105960],{},[898,105959,1878],{},[1716,105961,3080],{},[1716,105963,2502],{"stretchy":1919},[7204,105965,105966,105968,105970],{},[898,105967,1878],{},[1712,105969,1714],{},[1716,105971,3080],{},[1716,105973,1719],{"separator":1718},[7204,105975,105976,105978,105980],{},[898,105977,1878],{},[1712,105979,1726],{},[1716,105981,3080],{},[1716,105983,2516],{"stretchy":1919},[902,105985,42092],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,105988,105990],{"className":105989},[886],[888,105991,105992],{"xmlns":890,"display":2004},[892,105993,105994,106040],{},[895,105995,105996,105998,106000,106018,106020,106038],{},[2074,105997,24407],{},[1716,105999,1913],{},[2750,106001,106002,106010],{},[7204,106003,106004,106006,106008],{},[898,106005,900],{},[1712,106007,1714],{},[1716,106009,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[7204,106011,106012,106014,106016],{},[898,106013,900],{},[1712,106015,1726],{},[1716,106017,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,106019,1913],{},[2750,106021,106022,106030],{},[7204,106023,106024,106026,106028],{},[898,106025,1690],{},[1712,106027,1714],{},[1716,106029,3080],{},[7204,106031,106032,106034,106036],{},[898,106033,1690],{},[1712,106035,1726],{},[1716,106037,3080],{},[898,106039,1853],{"mathvariant":2068},[902,106041,106042],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,106044,106045],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1635,106047,106048],{},[724,106049,106050,106052,106053,106056,106057,106060,106061,106088,106089,106123,106124,106158,106159,106202,106203,106206,106207,1853],{},[883,106051,1641],{}," Pro detailní postup viz ",[207,106054,50513],{"className":106055,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,106058,106059],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,106062,106064],{"className":106063},[886],[888,106065,106066],{"xmlns":890},[892,106067,106068,106086],{},[895,106069,106070,106072,106074,106080],{},[898,106071,900],{},[1716,106073,1913],{},[1707,106075,106076,106078],{},[898,106077,1878],{},[1712,106079,1714],{},[1707,106081,106082,106084],{},[898,106083,1878],{},[1712,106085,1726],{},[902,106087,43988],{"encoding":904}," s výsledkem ",[883,106090,106092],{"className":106091},[886],[888,106093,106094],{"xmlns":890},[892,106095,106096,106120],{},[895,106097,106098,106104,106106,106108,106110,106116,106118],{},[1707,106099,106100,106102],{},[898,106101,1878],{},[1712,106103,1714],{},[1716,106105,1913],{},[1712,106107,5778],{},[1716,106109,1719],{"separator":1718},[1707,106111,106112,106114],{},[898,106113,1878],{},[1712,106115,1726],{},[1716,106117,1913],{},[1712,106119,2998],{},[902,106121,106122],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,106125,106127],{"className":106126},[886],[888,106128,106129],{"xmlns":890},[892,106130,106131,106155],{},[895,106132,106133,106139,106141,106143,106145,106151,106153],{},[1707,106134,106135,106137],{},[898,106136,1878],{},[1712,106138,1714],{},[1716,106140,1913],{},[1712,106142,6849],{},[1716,106144,1719],{"separator":1718},[1707,106146,106147,106149],{},[898,106148,1878],{},[1712,106150,1726],{},[1716,106152,1913],{},[1712,106154,1714],{},[902,106156,106157],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,106160,106162],{"className":106161},[886],[888,106163,106164],{"xmlns":890},[892,106165,106166,106200],{},[895,106167,106168,106170,106172,106186],{},[898,106169,900],{},[1716,106171,1913],{},[7204,106173,106174,106176,106178],{},[898,106175,1878],{},[1712,106177,1714],{},[895,106179,106180,106182,106184],{},[1712,106181,1714],{},[898,106183,3045],{"mathvariant":2068},[1712,106185,1726],{},[7204,106187,106188,106190,106192],{},[898,106189,1878],{},[1712,106191,1726],{},[895,106193,106194,106196,106198],{},[1712,106195,1714],{},[898,106197,3045],{"mathvariant":2068},[1712,106199,1726],{},[902,106201,46919],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,106204,106205],{},"6.8–6.13"," jsou na stránce ",[207,106208,41536],{"className":106209,"dataFsResolvedFilePath":911,"href":912},[210],[115,106211,106213],{"id":106212},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,106215,106216,106217,106230,106231,106233,106234,106236,106237,106239,106240,106242,106243,106245,106246,106248,106249,3495,106251,106286,106287,106300,106301,106304,106305,106308,106309,1853],{},"Každá ",[883,106218,106220],{"className":106219},[886],[888,106221,106222],{"xmlns":890},[892,106223,106224,106228],{},[895,106225,106226],{},[898,106227,1740],{},[902,106229,1740],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,106232,99564],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,106235,100048],{}," a současně ",[38,106238,99567],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,106241,99572],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,106244,65431],{}," (6.4) a druhé parciální derivace ",[38,106247,101931],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,106250,23538],{},[883,106252,106254],{"className":106253},[886],[888,106255,106256],{"xmlns":890},[892,106257,106258,106284],{},[895,106259,106260,106262,106264,106270,106272,106278,106280,106282],{},[898,106261,900],{},[1716,106263,1920],{"stretchy":1919},[1707,106265,106266,106268],{},[898,106267,1878],{},[1712,106269,1714],{},[1716,106271,1719],{"separator":1718},[1707,106273,106274,106276],{},[898,106275,1878],{},[1712,106277,1726],{},[1716,106279,1925],{"stretchy":1919},[1716,106281,1913],{},[898,106283,4478],{},[902,106285,23575],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,106288,106290],{"className":106289},[886],[888,106291,106292],{"xmlns":890},[892,106293,106294,106298],{},[895,106295,106296],{},[2074,106297,24407],{},[902,106299,42003],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,106302,106303],{},"maximalizace užitečnosti"," a duální ",[38,106306,106307],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,106310,50513],{"className":106311,"dataFsResolvedFilePath":911,"href":912},[210],[115,106313,14897],{"id":14896},[152,106315,106316,106319,106322,106325,106328,106331,106334,106337,106340,106343],{},[123,106317,106318],{},"Co se zahrnuje pod termín užitečnost?",[123,106320,106321],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,106323,106324],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,106326,106327],{},"Jak se vypočítá mezní užitečnost?",[123,106329,106330],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,106332,106333],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,106335,106336],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,106338,106339],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,106341,106342],{},"Proč mají křivky užitečnosti záporný sklon?",[123,106344,106345],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,106347,106349],{"id":106348},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,106351,106352,106355,106356,96237,106398,1343,106426,1343,106454,106482],{},[38,106353,106354],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,106357,106359],{"className":106358},[886],[888,106360,106361],{"xmlns":890},[892,106362,106363,106395],{},[895,106364,106365,106367,106369,106375,106377,106379,106385,106387,106389],{},[898,106366,900],{},[1716,106368,1913],{},[1707,106370,106371,106373],{},[898,106372,1878],{},[1712,106374,1714],{},[1716,106376,1949],{},[1712,106378,77313],{},[1707,106380,106381,106383],{},[898,106382,1878],{},[1712,106384,1726],{},[1716,106386,1949],{},[1712,106388,1726],{},[1707,106390,106391,106393],{},[898,106392,1878],{},[1712,106394,7072],{},[902,106396,106397],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,106399,106401],{"className":106400},[886],[888,106402,106403],{"xmlns":890},[892,106404,106405,106423],{},[895,106406,106407,106409,106411,106413,106415,106417,106419,106421],{},[898,106408,900],{},[1716,106410,1920],{"stretchy":1919},[1712,106412,6849],{},[1716,106414,1719],{"separator":1718},[1712,106416,1726],{},[1716,106418,1719],{"separator":1718},[1712,106420,1726],{},[1716,106422,1925],{"stretchy":1919},[902,106424,106425],{"encoding":904},"U(4, 2, 2)",[883,106427,106429],{"className":106428},[886],[888,106430,106431],{"xmlns":890},[892,106432,106433,106451],{},[895,106434,106435,106437,106439,106441,106443,106445,106447,106449],{},[898,106436,900],{},[1716,106438,1920],{"stretchy":1919},[1712,106440,1714],{},[1716,106442,1719],{"separator":1718},[1712,106444,6849],{},[1716,106446,1719],{"separator":1718},[1712,106448,1726],{},[1716,106450,1925],{"stretchy":1919},[902,106452,106453],{"encoding":904},"U(1, 4, 2)",[883,106455,106457],{"className":106456},[886],[888,106458,106459],{"xmlns":890},[892,106460,106461,106479],{},[895,106462,106463,106465,106467,106469,106471,106473,106475,106477],{},[898,106464,900],{},[1716,106466,1920],{"stretchy":1919},[1712,106468,1726],{},[1716,106470,1719],{"separator":1718},[1712,106472,7072],{},[1716,106474,1719],{"separator":1718},[1712,106476,1714],{},[1716,106478,1925],{"stretchy":1919},[902,106480,106481],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,106484,106485,106488,106489,106541,106542,1343,106568,1343,106594,1343,106620,1343,106646,1343,106672,1343,106698,106724],{},[38,106486,106487],{},"6.2"," Je dána užitečnost ",[883,106490,106492],{"className":106491},[886],[888,106493,106494],{"xmlns":890},[892,106495,106496,106538],{},[895,106497,106498,106500,106502,106504,106518,106532],{},[898,106499,900],{},[1716,106501,1913],{},[1712,106503,1726],{},[7204,106505,106506,106508,106510],{},[898,106507,1878],{},[1712,106509,1714],{},[895,106511,106512,106514,106516],{},[1712,106513,1714],{},[898,106515,3045],{"mathvariant":2068},[1712,106517,7072],{},[7204,106519,106520,106522,106524],{},[898,106521,1878],{},[1712,106523,1726],{},[895,106525,106526,106528,106530],{},[1712,106527,1714],{},[898,106529,3045],{"mathvariant":2068},[1712,106531,1726],{},[1707,106533,106534,106536],{},[898,106535,1878],{},[1712,106537,7072],{},[902,106539,106540],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,106543,106545],{"className":106544},[886],[888,106546,106547],{"xmlns":890},[892,106548,106549,106565],{},[895,106550,106551,106553,106555,106557,106559,106561,106563],{},[1716,106552,1920],{"stretchy":1919},[1712,106554,19394],{},[1716,106556,1719],{"separator":1718},[1712,106558,79351],{},[1716,106560,1719],{"separator":1718},[1712,106562,2998],{},[1716,106564,1925],{"stretchy":1919},[902,106566,106567],{"encoding":904},"(36, 27, 10)",[883,106569,106571],{"className":106570},[886],[888,106572,106573],{"xmlns":890},[892,106574,106575,106591],{},[895,106576,106577,106579,106581,106583,106585,106587,106589],{},[1716,106578,1920],{"stretchy":1919},[1712,106580,6811],{},[1716,106582,1719],{"separator":1718},[1712,106584,12398],{},[1716,106586,1719],{"separator":1718},[1712,106588,2976],{},[1716,106590,1925],{"stretchy":1919},[902,106592,106593],{"encoding":904},"(64, 8, 20)",[883,106595,106597],{"className":106596},[886],[888,106598,106599],{"xmlns":890},[892,106600,106601,106617],{},[895,106602,106603,106605,106607,106609,106611,106613,106615],{},[1716,106604,1920],{"stretchy":1919},[1712,106606,5778],{},[1716,106608,1719],{"separator":1718},[1712,106610,6811],{},[1716,106612,1719],{"separator":1718},[1712,106614,12398],{},[1716,106616,1925],{"stretchy":1919},[902,106618,106619],{"encoding":904},"(25, 64, 8)",[883,106621,106623],{"className":106622},[886],[888,106624,106625],{"xmlns":890},[892,106626,106627,106643],{},[895,106628,106629,106631,106633,106635,106637,106639,106641],{},[1716,106630,1920],{"stretchy":1919},[1712,106632,6849],{},[1716,106634,1719],{"separator":1718},[1712,106636,85283],{},[1716,106638,1719],{"separator":1718},[1712,106640,6231],{},[1716,106642,1925],{"stretchy":1919},[902,106644,106645],{"encoding":904},"(4, 125, 6)",[883,106647,106649],{"className":106648},[886],[888,106650,106651],{"xmlns":890},[892,106652,106653,106669],{},[895,106654,106655,106657,106659,106661,106663,106665,106667],{},[1716,106656,1920],{"stretchy":1919},[1712,106658,7141],{},[1716,106660,1719],{"separator":1718},[1712,106662,2973],{},[1716,106664,1719],{"separator":1718},[1712,106666,6804],{},[1716,106668,1925],{"stretchy":1919},[902,106670,106671],{"encoding":904},"(9, 40, 12)",[883,106673,106675],{"className":106674},[886],[888,106676,106677],{"xmlns":890},[892,106678,106679,106695],{},[895,106680,106681,106683,106685,106687,106689,106691,106693],{},[1716,106682,1920],{"stretchy":1919},[1712,106684,7141],{},[1716,106686,1719],{"separator":1718},[1712,106688,6811],{},[1716,106690,1719],{"separator":1718},[1712,106692,6985],{},[1716,106694,1925],{"stretchy":1919},[902,106696,106697],{"encoding":904},"(9, 64, 5)",[883,106699,106701],{"className":106700},[886],[888,106702,106703],{"xmlns":890},[892,106704,106705,106721],{},[895,106706,106707,106709,106711,106713,106715,106717,106719],{},[1716,106708,1920],{"stretchy":1919},[1712,106710,6811],{},[1716,106712,1719],{"separator":1718},[1712,106714,12398],{},[1716,106716,1719],{"separator":1718},[1712,106718,2998],{},[1716,106720,1925],{"stretchy":1919},[902,106722,106723],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,106726,106727,106488,106730,106773,106774,106808,106809,20296,106839,106872,106873,106890,106891,106908],{},[38,106728,106729],{},"6.3",[883,106731,106733],{"className":106732},[886],[888,106734,106735],{"xmlns":890},[892,106736,106737,106771],{},[895,106738,106739,106741,106743,106757],{},[898,106740,900],{},[1716,106742,1913],{},[7204,106744,106745,106747,106749],{},[898,106746,1878],{},[1712,106748,1714],{},[895,106750,106751,106753,106755],{},[1712,106752,1714],{},[898,106754,3045],{"mathvariant":2068},[1712,106756,1726],{},[7204,106758,106759,106761,106763],{},[898,106760,1878],{},[1712,106762,1726],{},[895,106764,106765,106767,106769],{},[1712,106766,1714],{},[898,106768,3045],{"mathvariant":2068},[1712,106770,1726],{},[902,106772,46919],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,106775,106777],{"className":106776},[886],[888,106778,106779],{"xmlns":890},[892,106780,106781,106805],{},[895,106782,106783,106789,106791,106793,106795,106801,106803],{},[1707,106784,106785,106787],{},[898,106786,1878],{},[1712,106788,1714],{},[1716,106790,1913],{},[1712,106792,5808],{},[1716,106794,1719],{"separator":1718},[1707,106796,106797,106799],{},[898,106798,1878],{},[1712,106800,1726],{},[1716,106802,1913],{},[1712,106804,11710],{},[902,106806,106807],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,106810,106812],{"className":106811},[886],[888,106813,106814],{"xmlns":890},[892,106815,106816,106836],{},[895,106817,106818,106820,106826,106828,106830],{},[898,106819,16690],{},[1707,106821,106822,106824],{},[898,106823,900],{},[1712,106825,1714],{},[1716,106827,1719],{"separator":1718},[898,106829,16690],{},[1707,106831,106832,106834],{},[898,106833,900],{},[1712,106835,1726],{},[902,106837,106838],{"encoding":904},"MU_1, MU_2",[883,106840,106842],{"className":106841},[886],[888,106843,106844],{"xmlns":890},[892,106845,106846,106870],{},[895,106847,106848,106854,106856,106858,106860,106866,106868],{},[1707,106849,106850,106852],{},[898,106851,1878],{},[1712,106853,1714],{},[1716,106855,1913],{},[1712,106857,5808],{},[1716,106859,1719],{"separator":1718},[1707,106861,106862,106864],{},[898,106863,1878],{},[1712,106865,1726],{},[1716,106867,1913],{},[1712,106869,11710],{},[902,106871,106807],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,106874,106876],{"className":106875},[886],[888,106877,106878],{"xmlns":890},[892,106879,106880,106888],{},[895,106881,106882],{},[1707,106883,106884,106886],{},[898,106885,1878],{},[1712,106887,1714],{},[902,106889,4189],{"encoding":904}," na 60 a poklesu ",[883,106892,106894],{"className":106893},[886],[888,106895,106896],{"xmlns":890},[892,106897,106898,106906],{},[895,106899,106900],{},[1707,106901,106902,106904],{},[898,106903,1878],{},[1712,106905,1726],{},[902,106907,42785],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,106910,106911,106914,106915,106976,106977,1853],{},[38,106912,106913],{},"6.4"," Je dána funkce ",[883,106916,106918],{"className":106917},[886],[888,106919,106920],{"xmlns":890},[892,106921,106922,106974],{},[895,106923,106924,106926,106928,106934,106936,106942,106944,106946,106960],{},[898,106925,900],{},[1716,106927,1920],{"stretchy":1919},[1707,106929,106930,106932],{},[898,106931,1878],{},[1712,106933,1714],{},[1716,106935,1719],{"separator":1718},[1707,106937,106938,106940],{},[898,106939,1878],{},[1712,106941,1726],{},[1716,106943,1925],{"stretchy":1919},[1716,106945,1913],{},[7204,106947,106948,106950,106952],{},[898,106949,1878],{},[1712,106951,1714],{},[895,106953,106954,106956,106958],{},[1712,106955,1714],{},[898,106957,3045],{"mathvariant":2068},[1712,106959,1726],{},[7204,106961,106962,106964,106966],{},[898,106963,1878],{},[1712,106965,1726],{},[895,106967,106968,106970,106972],{},[1712,106969,1714],{},[898,106971,3045],{"mathvariant":2068},[1712,106973,1726],{},[902,106975,43706],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,106978,106980],{"className":106979},[886],[888,106981,106982],{"xmlns":890},[892,106983,106984,107074],{},[895,106985,106986,106988,106990,106996,106998,107000,107002,107004,107006,107008,107014,107016,107018,107020,107022,107024,107026,107028,107030,107036,107038,107040,107042,107044,107046,107048,107054,107056,107058,107060,107062,107064,107066,107072],{},[898,106987,900],{},[1716,106989,1920],{"stretchy":1919},[1707,106991,106992,106994],{},[898,106993,1878],{},[1712,106995,1714],{},[1716,106997,1719],{"separator":1718},[1712,106999,1714],{},[1716,107001,1925],{"stretchy":1919},[1716,107003,1719],{"separator":1718},[898,107005,900],{},[1716,107007,1920],{"stretchy":1919},[1707,107009,107010,107012],{},[898,107011,1878],{},[1712,107013,1714],{},[1716,107015,1719],{"separator":1718},[1712,107017,1726],{},[1716,107019,1925],{"stretchy":1919},[1716,107021,1719],{"separator":1718},[898,107023,900],{},[1716,107025,1920],{"stretchy":1919},[1712,107027,1714],{},[1716,107029,1719],{"separator":1718},[1707,107031,107032,107034],{},[898,107033,1878],{},[1712,107035,1726],{},[1716,107037,1925],{"stretchy":1919},[1716,107039,1719],{"separator":1718},[898,107041,900],{},[1716,107043,1920],{"stretchy":1919},[1712,107045,1726],{},[1716,107047,1719],{"separator":1718},[1707,107049,107050,107052],{},[898,107051,1878],{},[1712,107053,1726],{},[1716,107055,1925],{"stretchy":1919},[1716,107057,1719],{"separator":1718},[898,107059,900],{},[1716,107061,1920],{"stretchy":1919},[1712,107063,7072],{},[1716,107065,1719],{"separator":1718},[1707,107067,107068,107070],{},[898,107069,1878],{},[1712,107071,1726],{},[1716,107073,1925],{"stretchy":1919},[902,107075,107076],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,107078,107079,106488,107082,107126,107127,107235,107236,1343,107261,1343,107286,107328,107329,1343,107358,107383],{},[38,107080,107081],{},"6.5",[883,107083,107085],{"className":107084},[886],[888,107086,107087],{"xmlns":890},[892,107088,107089,107123],{},[895,107090,107091,107093,107095,107109],{},[898,107092,900],{},[1716,107094,1913],{},[7204,107096,107097,107099,107101],{},[898,107098,1878],{},[1712,107100,1714],{},[895,107102,107103,107105,107107],{},[1712,107104,1726],{},[898,107106,3045],{"mathvariant":2068},[1712,107108,7072],{},[7204,107110,107111,107113,107115],{},[898,107112,1878],{},[1712,107114,1726],{},[895,107116,107117,107119,107121],{},[1712,107118,1714],{},[898,107120,3045],{"mathvariant":2068},[1712,107122,7072],{},[902,107124,107125],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,107128,107130],{"className":107129},[886],[888,107131,107132],{"xmlns":890},[892,107133,107134,107232],{},[895,107135,107136,107138,107140,107146,107148,107154,107156,107158,107160,107162,107164,107166,107172,107174,107176,107178,107180,107182,107184,107190,107192,107194,107196,107198,107200,107202,107204,107206,107212,107214,107216,107218,107220,107222,107224,107230],{},[898,107137,900],{},[1716,107139,1920],{"stretchy":1919},[1707,107141,107142,107144],{},[898,107143,1878],{},[1712,107145,1714],{},[1716,107147,1719],{"separator":1718},[1707,107149,107150,107152],{},[898,107151,1878],{},[1712,107153,1726],{},[1716,107155,1925],{"stretchy":1919},[1716,107157,1913],{},[1712,107159,1726],{},[1716,107161,1719],{"separator":1718},[898,107163,900],{},[1716,107165,1920],{"stretchy":1919},[1707,107167,107168,107170],{},[898,107169,1878],{},[1712,107171,1714],{},[1716,107173,1719],{"separator":1718},[1712,107175,7072],{},[1716,107177,1925],{"stretchy":1919},[1716,107179,1719],{"separator":1718},[898,107181,900],{},[1716,107183,1920],{"stretchy":1919},[1707,107185,107186,107188],{},[898,107187,1878],{},[1712,107189,1714],{},[1716,107191,1719],{"separator":1718},[1712,107193,1726],{},[1716,107195,1925],{"stretchy":1919},[1716,107197,1719],{"separator":1718},[898,107199,900],{},[1716,107201,1920],{"stretchy":1919},[1712,107203,1726],{},[1716,107205,1719],{"separator":1718},[1707,107207,107208,107210],{},[898,107209,1878],{},[1712,107211,1726],{},[1716,107213,1925],{"stretchy":1919},[1716,107215,1719],{"separator":1718},[898,107217,900],{},[1716,107219,1920],{"stretchy":1919},[1712,107221,7072],{},[1716,107223,1719],{"separator":1718},[1707,107225,107226,107228],{},[898,107227,1878],{},[1712,107229,1726],{},[1716,107231,1925],{"stretchy":1919},[902,107233,107234],{"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 ",[883,107237,107239],{"className":107238},[886],[888,107240,107241],{"xmlns":890},[892,107242,107243,107258],{},[895,107244,107245,107247,107249,107251,107253,107256],{},[898,107246,10871],{},[1716,107248,2502],{"stretchy":1919},[1712,107250,77313],{},[1716,107252,22241],{"separator":1718},[1712,107254,107255],{},"3,555",[1716,107257,2516],{"stretchy":1919},[902,107259,107260],{"encoding":904},"A[1{,}5; 3{,}555]",[883,107262,107264],{"className":107263},[886],[888,107265,107266],{"xmlns":890},[892,107267,107268,107283],{},[895,107269,107270,107272,107274,107276,107278,107281],{},[898,107271,10856],{},[1716,107273,2502],{"stretchy":1919},[1712,107275,65953],{},[1716,107277,22241],{"separator":1718},[1712,107279,107280],{},"1,28",[1716,107282,2516],{"stretchy":1919},[902,107284,107285],{"encoding":904},"B[2{,}5; 1{,}28]",[883,107287,107289],{"className":107288},[886],[888,107290,107291],{"xmlns":890},[892,107292,107293,107325],{},[895,107294,107295,107297,107299,107301,107303,107305,107307,107313,107315,107317,107319,107321,107323],{},[898,107296,9945],{},[1716,107298,2502],{"stretchy":1919},[1712,107300,1726],{},[1716,107302,22241],{"separator":1718},[898,107304,900],{},[1716,107306,1920],{"stretchy":1919},[1707,107308,107309,107311],{},[898,107310,1878],{},[1712,107312,1714],{},[1716,107314,1719],{"separator":1718},[1712,107316,7072],{},[1716,107318,1925],{"stretchy":1919},[1716,107320,1913],{},[1712,107322,7072],{},[1716,107324,2516],{"stretchy":1919},[902,107326,107327],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,107330,107332],{"className":107331},[886],[888,107333,107334],{"xmlns":890},[892,107335,107336,107355],{},[895,107337,107338,107340,107342,107344,107346,107348,107350,107353],{},[898,107339,1916],{},[1716,107341,2502],{"stretchy":1919},[1712,107343,7072],{},[1716,107345,22241],{"separator":1718},[1712,107347,1714],{},[1716,107349,22241],{"separator":1718},[1712,107351,107352],{},"0,832",[1716,107354,2516],{"stretchy":1919},[902,107356,107357],{"encoding":904},"D[3; 1; 0{,}832]",[883,107359,107361],{"className":107360},[886],[888,107362,107363],{"xmlns":890},[892,107364,107365,107380],{},[895,107366,107367,107369,107371,107373,107375,107378],{},[898,107368,1805],{},[1716,107370,2502],{"stretchy":1919},[1712,107372,65953],{},[1716,107374,22241],{"separator":1718},[1712,107376,107377],{},"4,32",[1716,107379,2516],{"stretchy":1919},[902,107381,107382],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,107385,107386,106488,107389,107432,107433,20296,107446,107480,107481,107498,107499,107516],{},[38,107387,107388],{},"6.6",[883,107390,107392],{"className":107391},[886],[888,107393,107394],{"xmlns":890},[892,107395,107396,107430],{},[895,107397,107398,107400,107402,107416],{},[898,107399,900],{},[1716,107401,1913],{},[7204,107403,107404,107406,107408],{},[898,107405,1878],{},[1712,107407,1714],{},[895,107409,107410,107412,107414],{},[1712,107411,1726],{},[898,107413,3045],{"mathvariant":2068},[1712,107415,7072],{},[7204,107417,107418,107420,107422],{},[898,107419,1878],{},[1712,107421,1726],{},[895,107423,107424,107426,107428],{},[1712,107425,1714],{},[898,107427,3045],{"mathvariant":2068},[1712,107429,7072],{},[902,107431,107125],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,107434,107436],{"className":107435},[886],[888,107437,107438],{"xmlns":890},[892,107439,107440,107444],{},[895,107441,107442],{},[2074,107443,24407],{},[902,107445,42003],{"encoding":904},[883,107447,107449],{"className":107448},[886],[888,107450,107451],{"xmlns":890},[892,107452,107453,107477],{},[895,107454,107455,107461,107463,107465,107467,107473,107475],{},[1707,107456,107457,107459],{},[898,107458,1878],{},[1712,107460,1714],{},[1716,107462,1913],{},[1712,107464,12151],{},[1716,107466,1719],{"separator":1718},[1707,107468,107469,107471],{},[898,107470,1878],{},[1712,107472,1726],{},[1716,107474,1913],{},[1712,107476,22193],{},[902,107478,107479],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,107482,107484],{"className":107483},[886],[888,107485,107486],{"xmlns":890},[892,107487,107488,107496],{},[895,107489,107490],{},[1707,107491,107492,107494],{},[898,107493,1878],{},[1712,107495,1714],{},[902,107497,4189],{"encoding":904},", poklesne-li ",[883,107500,107502],{"className":107501},[886],[888,107503,107504],{"xmlns":890},[892,107505,107506,107514],{},[895,107507,107508],{},[1707,107509,107510,107512],{},[898,107511,1878],{},[1712,107513,1726],{},[902,107515,42785],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,107518,107519,107522,107523,107540,107541,107558,107559,107591,107592,107617,107618,107631,107632,1343,107656,1343,107680,1853],{},[38,107520,107521],{},"6.7"," Míra uspokojení z nákupu množství ",[883,107524,107526],{"className":107525},[886],[888,107527,107528],{"xmlns":890},[892,107529,107530,107538],{},[895,107531,107532],{},[1707,107533,107534,107536],{},[898,107535,1878],{},[1712,107537,1714],{},[902,107539,4189],{"encoding":904}," nealko nápojů a množství ",[883,107542,107544],{"className":107543},[886],[888,107545,107546],{"xmlns":890},[892,107547,107548,107556],{},[895,107549,107550],{},[1707,107551,107552,107554],{},[898,107553,1878],{},[1712,107555,1726],{},[902,107557,42785],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,107560,107562],{"className":107561},[886],[888,107563,107564],{"xmlns":890},[892,107565,107566,107588],{},[895,107567,107568,107570,107572],{},[898,107569,900],{},[1716,107571,1913],{},[10595,107573,107574],{},[895,107575,107576,107582],{},[1707,107577,107578,107580],{},[898,107579,1878],{},[1712,107581,1714],{},[1707,107583,107584,107586],{},[898,107585,1878],{},[1712,107587,1726],{},[902,107589,107590],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,107593,107595],{"className":107594},[886],[888,107596,107597],{"xmlns":890},[892,107598,107599,107615],{},[895,107600,107601,107607,107609],{},[1707,107602,107603,107605],{},[898,107604,1878],{},[1712,107606,1714],{},[1716,107608,1719],{"separator":1718},[1707,107610,107611,107613],{},[898,107612,1878],{},[1712,107614,1726],{},[902,107616,49382],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,107619,107621],{"className":107620},[886],[888,107622,107623],{"xmlns":890},[892,107624,107625,107629],{},[895,107626,107627],{},[2074,107628,24407],{},[902,107630,42003],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,107633,107635],{"className":107634},[886],[888,107636,107637],{"xmlns":890},[892,107638,107639,107653],{},[895,107640,107641,107643,107645,107647,107649,107651],{},[2074,107642,24407],{},[1716,107644,1920],{"stretchy":1919},[1712,107646,6985],{},[1716,107648,1719],{"separator":1718},[1712,107650,2976],{},[1716,107652,1925],{"stretchy":1919},[902,107654,107655],{"encoding":904},"\\text{MRCS}(5, 20)",[883,107657,107659],{"className":107658},[886],[888,107660,107661],{"xmlns":890},[892,107662,107663,107677],{},[895,107664,107665,107667,107669,107671,107673,107675],{},[2074,107666,24407],{},[1716,107668,1920],{"stretchy":1919},[1712,107670,2976],{},[1716,107672,1719],{"separator":1718},[1712,107674,6985],{},[1716,107676,1925],{"stretchy":1919},[902,107678,107679],{"encoding":904},"\\text{MRCS}(20, 5)",[883,107681,107683],{"className":107682},[886],[888,107684,107685],{"xmlns":890},[892,107686,107687,107701],{},[895,107688,107689,107691,107693,107695,107697,107699],{},[2074,107690,24407],{},[1716,107692,1920],{"stretchy":1919},[1712,107694,1726],{},[1716,107696,1719],{"separator":1718},[1712,107698,5808],{},[1716,107700,1925],{"stretchy":1919},[902,107702,107703],{"encoding":904},"\\text{MRCS}(2, 50)",[1635,107705,107706],{},[724,107707,107708,107710,107711,1853],{},[883,107709,3776],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,107712,107715],{"className":107713,"dataFsResolvedFilePath":911,"href":107714},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,107717,14947],{"id":14946},[120,107719,107720,107726,107731,107737,107790,107800,107846,107901,107964,108021,108076,108115],{},[123,107721,107722,107725],{},[38,107723,107724],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,107727,107728,107730],{},[38,107729,99623],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,107732,107733,107736],{},[38,107734,107735],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,107738,107739,107741,107742,107755,107756,1853],{},[38,107740,99950],{}," — uspořádaná ",[883,107743,107745],{"className":107744},[886],[888,107746,107747],{"xmlns":890},[892,107748,107749,107753],{},[895,107750,107751],{},[898,107752,1740],{},[902,107754,1740],{"encoding":904},"-tice ",[883,107757,107759],{"className":107758},[886],[888,107760,107761],{"xmlns":890},[892,107762,107763,107787],{},[895,107764,107765,107767,107773,107775,107777,107779,107785],{},[1716,107766,1920],{"stretchy":1919},[1707,107768,107769,107771],{},[898,107770,1878],{},[1712,107772,1714],{},[1716,107774,1719],{"separator":1718},[1716,107776,1731],{},[1716,107778,1719],{"separator":1718},[1707,107780,107781,107783],{},[898,107782,1878],{},[898,107784,1740],{},[1716,107786,1925],{"stretchy":1919},[902,107788,107789],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,107791,107792,107795,107796,107799],{},[38,107793,107794],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,107797,107798],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,107801,107802,3495,107805,107845],{},[38,107803,107804],{},"Funkce užitečnosti",[883,107806,107808],{"className":107807},[886],[888,107809,107810],{"xmlns":890},[892,107811,107812,107842],{},[895,107813,107814,107816,107818,107820,107822,107828,107830,107832,107834,107840],{},[898,107815,900],{},[1716,107817,1913],{},[898,107819,900],{},[1716,107821,1920],{"stretchy":1919},[1707,107823,107824,107826],{},[898,107825,1878],{},[1712,107827,1714],{},[1716,107829,1719],{"separator":1718},[1716,107831,1731],{},[1716,107833,1719],{"separator":1718},[1707,107835,107836,107838],{},[898,107837,1878],{},[898,107839,1740],{},[1716,107841,1925],{"stretchy":1919},[902,107843,107844],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,107847,107848,3495,107851,107880,107881,3495,107884,107900],{},[38,107849,107850],{},"Mezní užitečnost",[883,107852,107854],{"className":107853},[886],[888,107855,107856],{"xmlns":890},[892,107857,107858,107878],{},[895,107859,107860,107862,107868,107870],{},[898,107861,16690],{},[1707,107863,107864,107866],{},[898,107865,900],{},[898,107867,12546],{},[1716,107869,1913],{},[7204,107871,107872,107874,107876],{},[898,107873,900],{},[898,107875,12546],{},[1716,107877,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[902,107879,99407],{"encoding":904}," — vzorec (6.2); ",[38,107882,107883],{},"totální diferenciál",[883,107885,107887],{"className":107886},[886],[888,107888,107889],{"xmlns":890},[892,107890,107891,107897],{},[895,107892,107893,107895],{},[898,107894,5198],{"mathvariant":2068},[898,107896,900],{},[902,107898,107899],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,107902,107903,107905,107906,107930,107931,107963],{},[38,107904,101586],{}," — (6.4) ",[883,107907,107909],{"className":107908},[886],[888,107910,107911],{"xmlns":890},[892,107912,107913,107927],{},[895,107914,107915,107923,107925],{},[7204,107916,107917,107919,107921],{},[898,107918,900],{},[898,107920,12546],{},[1716,107922,8505],{"mathvariant":2068,"lspace":4403,"rspace":4403},[1716,107924,2716],{},[1712,107926,2505],{},[902,107928,107929],{"encoding":904},"U'_i > 0",", (6.5) ",[883,107932,107934],{"className":107933},[886],[888,107935,107936],{"xmlns":890},[892,107937,107938,107960],{},[895,107939,107940,107956,107958],{},[7204,107941,107942,107944,107950],{},[898,107943,900],{},[895,107945,107946,107948],{},[898,107947,12546],{},[898,107949,12546],{},[895,107951,107952,107954],{},[1716,107953,8505],{"mathvariant":2068},[1716,107955,8505],{"mathvariant":2068},[1716,107957,2704],{},[1712,107959,2505],{},[902,107961,107962],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,107965,107966,3495,107968,107999,108000,1853],{},[38,107967,103374],{},[883,107969,107971],{"className":107970},[886],[888,107972,107973],{"xmlns":890},[892,107974,107975,107997],{},[895,107976,107977,107979,107981,107989],{},[898,107978,900],{},[1716,107980,1913],{},[7204,107982,107983,107985,107987],{},[898,107984,1878],{},[1712,107986,1714],{},[898,107988,207],{},[7204,107990,107991,107993,107995],{},[898,107992,1878],{},[1712,107994,1726],{},[898,107996,1952],{},[902,107998,49563],{"encoding":904}," — (6.6), speciálně ",[883,108001,108003],{"className":108002},[886],[888,108004,108005],{"xmlns":890},[892,108006,108007,108019],{},[895,108008,108009,108011,108013,108015,108017],{},[898,108010,1952],{},[1716,108012,1913],{},[1712,108014,1714],{},[1716,108016,2760],{},[898,108018,207],{},[902,108020,103528],{"encoding":904},[123,108022,108023,3495,108026,108061,108062,108075],{},[38,108024,108025],{},"Křivky užitečnosti (indiferenční)",[883,108027,108029],{"className":108028},[886],[888,108030,108031],{"xmlns":890},[892,108032,108033,108059],{},[895,108034,108035,108037,108039,108045,108047,108053,108055,108057],{},[898,108036,900],{},[1716,108038,1920],{"stretchy":1919},[1707,108040,108041,108043],{},[898,108042,1878],{},[1712,108044,1714],{},[1716,108046,1719],{"separator":1718},[1707,108048,108049,108051],{},[898,108050,1878],{},[1712,108052,1726],{},[1716,108054,1925],{"stretchy":1919},[1716,108056,1913],{},[898,108058,4478],{},[902,108060,23575],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,108063,108065],{"className":108064},[886],[888,108066,108067],{"xmlns":890},[892,108068,108069,108073],{},[895,108070,108071],{},[898,108072,900],{},[902,108074,900],{"encoding":904},", konvexní.",[123,108077,108078,3495,108080,108114],{},[38,108079,104919],{},[883,108081,108083],{"className":108082},[886],[888,108084,108085],{"xmlns":890},[892,108086,108087,108111],{},[895,108088,108089,108091,108093,108095,108101,108103,108105],{},[2074,108090,24407],{},[1716,108092,1913],{},[898,108094,16690],{},[1707,108096,108097,108099],{},[898,108098,900],{},[1712,108100,1714],{},[898,108102,3045],{"mathvariant":2068},[898,108104,16690],{},[1707,108106,108107,108109],{},[898,108108,900],{},[1712,108110,1726],{},[902,108112,108113],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,108116,108117,3495,108120,23576,108149,108152],{},[38,108118,108119],{},"Podmínka optimality",[883,108121,108123],{"className":108122},[886],[888,108124,108125],{"xmlns":890},[892,108126,108127,108147],{},[895,108128,108129,108131,108133,108139,108141],{},[2074,108130,24407],{},[1716,108132,1913],{},[1707,108134,108135,108137],{},[898,108136,1690],{},[1712,108138,1714],{},[898,108140,3045],{"mathvariant":2068},[1707,108142,108143,108145],{},[898,108144,1690],{},[1712,108146,1726],{},[902,108148,41767],{"encoding":904},[207,108150,50513],{"className":108151,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,108154,15740],{"id":15739},[120,108156,108157,108194,108235,108245],{},[123,108158,108159,3495,108162,108165,108166,108179,108180,108193],{},[38,108160,108161],{},"Navazující téma:",[207,108163,913],{"className":108164,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,108167,108169],{"className":108168},[886],[888,108170,108171],{"xmlns":890},[892,108172,108173,108177],{},[895,108174,108175],{},[898,108176,900],{},[902,108178,900],{"encoding":904},", min ",[883,108181,108183],{"className":108182},[886],[888,108184,108185],{"xmlns":890},[892,108186,108187,108191],{},[895,108188,108189],{},[898,108190,1805],{},[902,108192,1805],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,108195,108196,3495,108199,24897,108202,99162,108205,108208,108209,108212,108213,8373,108231,108234],{},[38,108197,108198],{},"Související pojmy:",[207,108200,784],{"className":108201,"dataFsResolvedFilePath":782,"href":783},[210],[207,108203,15758],{"className":108204,"dataFsResolvedFilePath":764,"href":765},[210],[207,108206,24892],{"className":108207,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,108210,25743],{"className":108211,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,108214,108216],{"className":108215},[886],[888,108217,108218],{"xmlns":890},[892,108219,108220,108228],{},[895,108221,108222],{},[1707,108223,108224,108226],{},[898,108225,1916],{},[898,108227,12546],{},[902,108229,108230],{"encoding":904},"D_i",[207,108232,793],{"className":108233,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,108236,108237,3495,108239,1343,108242],{},[38,108238,50462],{},[207,108240,1094],{"className":108241,"dataFsResolvedFilePath":838,"href":839},[210],[207,108243,1101],{"className":108244,"dataFsResolvedFilePath":868,"href":869},[210],[123,108246,108247,3495,108249],{},[38,108248,15794],{},[207,108250,15800],{"className":108251,"dataFsResolvedFilePath":15798,"href":15799},[210],{"title":641,"searchDepth":642,"depth":642,"links":108253},[108254,108255,108256,108259,108260,108263,108267,108268,108271,108272,108273,108274,108275,108276,108277],{"id":25808,"depth":642,"text":25809},{"id":99546,"depth":642,"text":99547},{"id":99606,"depth":642,"text":99607,"children":108257},[108258],{"id":99622,"depth":649,"text":99623},{"id":99929,"depth":642,"text":99930},{"id":100789,"depth":642,"text":100790,"children":108261},[108262],{"id":101336,"depth":649,"text":92965},{"id":101585,"depth":642,"text":101586,"children":108264},[108265],{"id":102458,"depth":649,"text":108266},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":103373,"depth":642,"text":103374},{"id":103909,"depth":642,"text":103910,"children":108269},[108270],{"id":104683,"depth":649,"text":104684},{"id":104913,"depth":642,"text":104914},{"id":105674,"depth":642,"text":105675},{"id":106212,"depth":642,"text":106213},{"id":14896,"depth":642,"text":14897},{"id":106348,"depth":642,"text":106349},{"id":14946,"depth":642,"text":14947},{"id":15739,"depth":642,"text":15740},{},"\u002Ftopics\u002Fuzitecnost",{"title":99330,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,23580,108284,99324,24926,108285],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":108288,"title":757,"body":108289,"course":1128,"courses":659,"created":1129,"description":108562,"extension":661,"meta":108563,"navigation":664,"path":108564,"seo":108565,"sources":108566,"stem":108567,"tags":108568,"type":15858,"updated":677,"__hash__":108574},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":108290,"toc":108554},[108291,108294,108301,108308,108312,108322,108324,108358,108362,108405,108408,108466,108470,108500,108504,108525,108527],[12,108292,757],{"id":108293},"základy-matematické-ekonomie",[724,108295,108296,108297,108300],{},"Úvodní pojmy a princip modelování v ",[207,108298,30170],{"className":108299,"dataFsResolvedFilePath":15798,"href":15799},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,108302,108303],{},[3682,108304],{"alt":108305,"className":108306,"src":108307},"imek-model-promenne",[210,3686],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,108309,108311],{"id":108310},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,108313,108314,108317,108318,108321],{},[38,108315,108316],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,108319,108320],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,108323,14947],{"id":14946},[120,108325,108326,108332,108338,108344,108353],{},[123,108327,108328,108331],{},[38,108329,108330],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,108333,108334,108337],{},[38,108335,108336],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,108339,108340,108343],{},[38,108341,108342],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,108345,108346,3369,108349,108352],{},[38,108347,108348],{},"Ceteris paribus",[614,108350,108351],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,108354,108355,108357],{},[38,108356,15656],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,108359,108361],{"id":108360},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,108363,108364,108404],{},[883,108365,108367],{"className":108366},[886],[888,108368,108369],{"xmlns":890},[892,108370,108371,108401],{},[895,108372,108373,108375,108377,108379,108381,108383,108385,108387,108389,108391,108393,108395,108397,108399],{},[898,108374,1878],{},[1716,108376,1913],{},[898,108378,1916],{},[1716,108380,1920],{"stretchy":1919},[898,108382,1690],{},[1716,108384,1719],{"separator":1718},[898,108386,1758],{},[1716,108388,1719],{"separator":1718},[898,108390,32081],{},[1716,108392,1719],{"separator":1718},[898,108394,900],{},[1716,108396,1719],{"separator":1718},[1716,108398,1731],{},[1716,108400,1925],{"stretchy":1919},[902,108402,108403],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,108406,108407],{},"Zjednodušení:",[120,108409,108410,108438],{},[123,108411,108412,3495,108415],{},[38,108413,108414],{},"Jednofaktorový model:",[883,108416,108418],{"className":108417},[886],[888,108419,108420],{"xmlns":890},[892,108421,108422,108436],{},[895,108423,108424,108426,108428,108430,108432,108434],{},[898,108425,1878],{},[1716,108427,1913],{},[898,108429,1916],{},[1716,108431,1920],{"stretchy":1919},[898,108433,1690],{},[1716,108435,1925],{"stretchy":1919},[902,108437,1928],{"encoding":904},[123,108439,108440,3495,108443],{},[38,108441,108442],{},"Inverzní zápis:",[883,108444,108446],{"className":108445},[886],[888,108447,108448],{"xmlns":890},[892,108449,108450,108464],{},[895,108451,108452,108454,108456,108458,108460,108462],{},[898,108453,1690],{},[1716,108455,1913],{},[898,108457,1916],{},[1716,108459,1920],{"stretchy":1919},[898,108461,1878],{},[1716,108463,1925],{"stretchy":1919},[902,108465,4115],{"encoding":904},[115,108467,108469],{"id":108468},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,108471,108472,108481],{},[123,108473,108474,108477,108478,2365],{},[38,108475,108476],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,108479,30029],{"className":108480,"dataFsResolvedFilePath":800,"href":801},[210],[123,108482,108483,108486,108487,108490,108491,108494,108495,108499],{},[38,108484,108485],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,108488,1145],{"className":108489,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,108492,30042],{"className":108493,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,108496,108498],{"className":108497,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,108501,108503],{"id":108502},"konvence-z-přednášek","Konvence z přednášek",[120,108505,108506,108513,108519],{},[123,108507,108508,108509,108512],{},"Symbol ",[108510,108511,8490],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,108514,108515,108516,1853],{},"Numerické výsledky ",[38,108517,108518],{},"na 3 desetinná místa",[123,108520,17743,108521,108524],{},[614,108522,108523],{},"jednotková změna"," má standardní význam (změna o 1).",[115,108526,15740],{"id":15739},[120,108528,108529,108534,108542],{},[123,108530,108531,108533],{},[38,108532,17652],{}," —",[123,108535,108536,3495,108538],{},[38,108537,17660],{},[207,108539,108541],{"className":108540,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,108543,108544,3495,108546,1343,108550],{},[38,108545,17668],{},[207,108547,108549],{"className":108548,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,108551,108553],{"className":108552,"dataFsResolvedFilePath":15798,"href":15799},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":108555},[108556,108557,108558,108559,108560,108561],{"id":108310,"depth":642,"text":108311},{"id":14946,"depth":642,"text":14947},{"id":108360,"depth":642,"text":108361},{"id":108468,"depth":642,"text":108469},{"id":108502,"depth":642,"text":108503},{"id":15739,"depth":642,"text":15740},"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":108562},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,108569,108570,108571,108572,108573],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":108576,"title":108577,"body":108578,"course":1128,"courses":659,"created":15845,"description":641,"extension":661,"meta":112850,"navigation":664,"path":112851,"seo":112852,"sources":112853,"stem":112854,"tags":112855,"type":15858,"updated":677,"__hash__":112859},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":108579,"toc":112833},[108580,108583,108677,108681,108703,108717,108769,108771,108775,108838,108881,108900,109063,109162,109165,109232,109236,109365,109404,109434,109546,109591,109657,109710,109786,109842,109844,109848,109912,109956,109976,110137,110140,110224,110321,110324,110390,110394,110443,110469,110574,110638,110643,110739,110786,110788,110791,110813,110855,110862,110895,110897,110968,111022,111131,111135,111224,111300,111564,111602,111604,111608,111611,111618,111929,111932,111990,112170,112199,112201,112205,112211,112349,112358,112360,112362,112787,112789,112791],[12,108581,108577],{"id":108582},"zdanění-trhu-dopady-daně-na-rovnováhu",[1635,108584,108585],{},[724,108586,108587,7608,108589,108602,108603,108606,108607,108609,108610,108613,108614,108635,108636,108659,108660,108663,108664,1853],{},[883,108588,1641],{},[883,108590,108592],{"className":108591},[886],[888,108593,108594],{"xmlns":890},[892,108595,108596,108600],{},[895,108597,108598],{},[898,108599,4164],{},[902,108601,4164],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,108604,108605],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,108608,99614],{}," (je-li uložena spotřebiteli). Výsledné ",[38,108611,108612],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,108615,108617],{"className":108616},[886],[888,108618,108619],{"xmlns":890},[892,108620,108621,108633],{},[895,108622,108623],{},[1707,108624,108625,108627],{},[898,108626,4164],{},[895,108628,108629,108631],{},[898,108630,7658],{},[898,108632,724],{},[902,108634,7663],{"encoding":904}," (spotřebitel) a ",[883,108637,108639],{"className":108638},[886],[888,108640,108641],{"xmlns":890},[892,108642,108643,108657],{},[895,108644,108645],{},[1707,108646,108647,108649],{},[898,108648,4164],{},[895,108650,108651,108653,108655],{},[898,108652,7681],{},[898,108654,7684],{},[898,108656,2098],{},[902,108658,7689],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,108661,108662],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,108665,108667],{"className":108666},[886],[888,108668,108669],{"xmlns":890},[892,108670,108671,108675],{},[895,108672,108673],{},[898,108674,4164],{},[902,108676,4164],{"encoding":904},[115,108678,108680],{"id":108679},"dvě-formy-zdanění","Dvě formy zdanění",[724,108682,108683,108684,108702],{},"Uvažujme jednotkovou daň ",[883,108685,108687],{"className":108686},[886],[888,108688,108689],{"xmlns":890},[892,108690,108691,108699],{},[895,108692,108693,108695,108697],{},[898,108694,4164],{},[1716,108696,2716],{},[1712,108698,2505],{},[902,108700,108701],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,108704,108705,108711],{},[123,108706,108707,108710],{},[38,108708,108709],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,108712,108713,108716],{},[38,108714,108715],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,108718,108719,108720,108733,108734,108737,108738,1853],{},"V obou případech dochází k posunu jedné z křivek o ",[883,108721,108723],{"className":108722},[886],[888,108724,108725],{"xmlns":890},[892,108726,108727,108731],{},[895,108728,108729],{},[898,108730,4164],{},[902,108732,4164],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,108735,108736],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,108739,108741],{"className":108740},[886],[888,108742,108743],{"xmlns":890},[892,108744,108745,108767],{},[895,108746,108747,108749,108751,108757,108759,108765],{},[898,108748,1805],{},[1716,108750,2502],{"stretchy":1919},[3074,108752,108753,108755],{},[898,108754,1878],{},[898,108756,1805],{},[1716,108758,1719],{"separator":1718},[3074,108760,108761,108763],{},[898,108762,1690],{},[898,108764,1805],{},[1716,108766,2516],{"stretchy":1919},[902,108768,6333],{"encoding":904},[1855,108770],{},[115,108772,108774],{"id":108773},"daň-uložená-výrobci","Daň uložená výrobci",[724,108776,108777,108778,108791,108792,108809,108810,108837],{},"Je-li daň ",[883,108779,108781],{"className":108780},[886],[888,108782,108783],{"xmlns":890},[892,108784,108785,108789],{},[895,108786,108787],{},[898,108788,4164],{},[902,108790,4164],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,108793,108795],{"className":108794},[886],[888,108796,108797],{"xmlns":890},[892,108798,108799,108807],{},[895,108800,108801,108803,108805],{},[898,108802,1690],{},[1716,108804,2760],{},[898,108806,4164],{},[902,108808,6087],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,108811,108813],{"className":108812},[886],[888,108814,108815],{"xmlns":890},[892,108816,108817,108835],{},[895,108818,108819,108821,108823,108825,108827,108829,108831,108833],{},[898,108820,1690],{},[1716,108822,2760],{},[898,108824,4164],{},[1716,108826,1913],{},[898,108828,5352],{},[1716,108830,1920],{"stretchy":1919},[898,108832,1878],{},[1716,108834,1925],{"stretchy":1919},[902,108836,6116],{"encoding":904}," nová funkce nabídky:",[883,108839,108841],{"className":108840},[886],[888,108842,108843],{"xmlns":890,"display":2004},[892,108844,108845,108879],{},[895,108846,108847,108849,108851,108857,108859,108861,108863,108865,108867,108869,108871,108873,108875,108877],{},[898,108848,1690],{},[1716,108850,1913],{},[1707,108852,108853,108855],{},[898,108854,5352],{},[1712,108856,1714],{},[1716,108858,1920],{"stretchy":1919},[898,108860,1878],{},[1716,108862,1925],{"stretchy":1919},[1716,108864,1913],{},[898,108866,5352],{},[1716,108868,1920],{"stretchy":1919},[898,108870,1878],{},[1716,108872,1925],{"stretchy":1919},[1716,108874,1949],{},[898,108876,4164],{},[898,108878,1853],{"mathvariant":2068},[902,108880,6161],{"encoding":904},[724,108882,108883,108884,3495,108897,108899],{},"Nabídka se tedy posouvá o ",[883,108885,108887],{"className":108886},[886],[888,108888,108889],{"xmlns":890},[892,108890,108891,108895],{},[895,108892,108893],{},[898,108894,4164],{},[902,108896,4164],{"encoding":904},[38,108898,6194],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,108901,108902,108903,108943,108944,2247,108972,109000,109001,109020,109021,109045,109046,2365],{},"Nový rovnovážný bod ",[883,108904,108906],{"className":108905},[886],[888,108907,108908],{"xmlns":890},[892,108909,108910,108940],{},[895,108911,108912,108918,108920,108928,108930,108938],{},[1707,108913,108914,108916],{},[898,108915,1805],{},[1712,108917,1714],{},[1716,108919,2502],{"stretchy":1919},[7204,108921,108922,108924,108926],{},[898,108923,1878],{},[1712,108925,1714],{},[898,108927,1805],{},[1716,108929,1719],{"separator":1718},[7204,108931,108932,108934,108936],{},[898,108933,1690],{},[1712,108935,1714],{},[898,108937,1805],{},[1716,108939,2516],{"stretchy":1919},[902,108941,108942],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,108945,108947],{"className":108946},[886],[888,108948,108949],{"xmlns":890},[892,108950,108951,108969],{},[895,108952,108953,108961,108963],{},[7204,108954,108955,108957,108959],{},[898,108956,1878],{},[1712,108958,1714],{},[898,108960,1805],{},[1716,108962,2704],{},[3074,108964,108965,108967],{},[898,108966,1878],{},[898,108968,1805],{},[902,108970,108971],{"encoding":904},"Q_1^E \u003C Q^E",[883,108973,108975],{"className":108974},[886],[888,108976,108977],{"xmlns":890},[892,108978,108979,108997],{},[895,108980,108981,108989,108991],{},[7204,108982,108983,108985,108987],{},[898,108984,1690],{},[1712,108986,1714],{},[898,108988,1805],{},[1716,108990,2716],{},[3074,108992,108993,108995],{},[898,108994,1690],{},[898,108996,1805],{},[902,108998,108999],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,109002,109004],{"className":109003},[886],[888,109005,109006],{"xmlns":890},[892,109007,109008,109018],{},[895,109009,109010],{},[7204,109011,109012,109014,109016],{},[898,109013,1690],{},[1712,109015,1714],{},[898,109017,1805],{},[902,109019,12868],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,109022,109024],{"className":109023},[886],[888,109025,109026],{"xmlns":890},[892,109027,109028,109042],{},[895,109029,109030,109038,109040],{},[7204,109031,109032,109034,109036],{},[898,109033,1690],{},[1712,109035,1714],{},[898,109037,1805],{},[1716,109039,2760],{},[898,109041,4164],{},[902,109043,109044],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,109047,109049],{"className":109048},[886],[888,109050,109051],{"xmlns":890},[892,109052,109053,109061],{},[895,109054,109055],{},[3074,109056,109057,109059],{},[898,109058,1690],{},[898,109060,1805],{},[902,109062,6432],{"encoding":904},[724,109064,109065],{},[614,109066,109067,109068,109098,109099,109112,109113,3569,109130,109143,109144,1853],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,109069,109071],{"className":109070},[886],[888,109072,109073],{"xmlns":890},[892,109074,109075,109095],{},[895,109076,109077,109079,109081,109087,109089,109091,109093],{},[898,109078,5352],{},[1716,109080,16986],{},[1707,109082,109083,109085],{},[898,109084,5352],{},[1712,109086,1714],{},[1716,109088,1913],{},[898,109090,5352],{},[1716,109092,1949],{},[898,109094,4164],{},[902,109096,109097],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,109100,109102],{"className":109101},[886],[888,109103,109104],{"xmlns":890},[892,109105,109106,109110],{},[895,109107,109108],{},[898,109109,4164],{},[902,109111,4164],{"encoding":904},". Průsečík ",[883,109114,109116],{"className":109115},[886],[888,109117,109118],{"xmlns":890},[892,109119,109120,109128],{},[895,109121,109122],{},[1707,109123,109124,109126],{},[898,109125,5352],{},[1712,109127,1714],{},[902,109129,5962],{"encoding":904},[883,109131,109133],{"className":109132},[886],[888,109134,109135],{"xmlns":890},[892,109136,109137,109141],{},[895,109138,109139],{},[898,109140,1916],{},[902,109142,1916],{"encoding":904}," je nový rovnovážný bod ",[883,109145,109147],{"className":109146},[886],[888,109148,109149],{"xmlns":890},[892,109150,109151,109159],{},[895,109152,109153],{},[1707,109154,109155,109157],{},[898,109156,1805],{},[1712,109158,1714],{},[902,109160,109161],{"encoding":904},"E_1",[198,109163,10304],{"id":109164},"příklad-29",[724,109166,109167,6621,109169,6657,109193,109213,109214,109231],{},[38,109168,2859],{},[883,109170,109172],{"className":109171},[886],[888,109173,109174],{"xmlns":890},[892,109175,109176,109190],{},[895,109177,109178,109180,109182,109184,109186,109188],{},[898,109179,1690],{},[1716,109181,1913],{},[1712,109183,6804],{},[1716,109185,2760],{},[1712,109187,1726],{},[898,109189,1878],{},[902,109191,109192],{"encoding":904},"P = 12 - 2Q",[883,109194,109196],{"className":109195},[886],[888,109197,109198],{"xmlns":890},[892,109199,109200,109210],{},[895,109201,109202,109204,109206,109208],{},[898,109203,1690],{},[1716,109205,1913],{},[1712,109207,6849],{},[898,109209,1878],{},[902,109211,109212],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,109215,109217],{"className":109216},[886],[888,109218,109219],{"xmlns":890},[892,109220,109221,109229],{},[895,109222,109223,109225,109227],{},[898,109224,4164],{},[1716,109226,1913],{},[1712,109228,6231],{},[902,109230,6234],{"encoding":904}," Kč.",[724,109233,109234],{},[38,109235,2892],{},[724,109237,109238,109241,109242,19398,109268,19417,109288,1343,109310,109340,109341,1853],{},[614,109239,109240],{},"Bez daně."," Z rovnosti ",[883,109243,109245],{"className":109244},[886],[888,109246,109247],{"xmlns":890},[892,109248,109249,109265],{},[895,109250,109251,109253,109255,109257,109259,109261,109263],{},[1712,109252,6804],{},[1716,109254,2760],{},[1712,109256,1726],{},[898,109258,1878],{},[1716,109260,1913],{},[1712,109262,6849],{},[898,109264,1878],{},[902,109266,109267],{"encoding":904},"12 - 2Q = 4Q",[883,109269,109271],{"className":109270},[886],[888,109272,109273],{"xmlns":890},[892,109274,109275,109285],{},[895,109276,109277,109279,109281,109283],{},[1712,109278,6231],{},[898,109280,1878],{},[1716,109282,1913],{},[1712,109284,6804],{},[902,109286,109287],{"encoding":904},"6Q = 12",[883,109289,109291],{"className":109290},[886],[888,109292,109293],{"xmlns":890},[892,109294,109295,109307],{},[895,109296,109297,109303,109305],{},[3074,109298,109299,109301],{},[898,109300,1878],{},[898,109302,1805],{},[1716,109304,1913],{},[1712,109306,1726],{},[902,109308,109309],{"encoding":904},"Q^E = 2",[883,109311,109313],{"className":109312},[886],[888,109314,109315],{"xmlns":890},[892,109316,109317,109337],{},[895,109318,109319,109325,109327,109329,109331,109333,109335],{},[3074,109320,109321,109323],{},[898,109322,1690],{},[898,109324,1805],{},[1716,109326,1913],{},[1712,109328,6849],{},[1716,109330,9532],{},[1712,109332,1726],{},[1716,109334,1913],{},[1712,109336,12398],{},[902,109338,109339],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,109342,109344],{"className":109343},[886],[888,109345,109346],{"xmlns":890},[892,109347,109348,109362],{},[895,109349,109350,109352,109354,109356,109358,109360],{},[898,109351,1805],{},[1716,109353,2502],{"stretchy":1919},[1712,109355,1726],{},[1716,109357,1719],{"separator":1718},[1712,109359,12398],{},[1716,109361,2516],{"stretchy":1919},[902,109363,109364],{"encoding":904},"E[2, 8]",[724,109366,109367,109370,109371,109403],{},[614,109368,109369],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,109372,109374],{"className":109373},[886],[888,109375,109376],{"xmlns":890},[892,109377,109378,109400],{},[895,109379,109380,109386,109388,109390,109392,109394,109396,109398],{},[1707,109381,109382,109384],{},[898,109383,5352],{},[1712,109385,1714],{},[1716,109387,2291],{},[898,109389,1690],{},[1716,109391,1913],{},[1712,109393,6849],{},[898,109395,1878],{},[1716,109397,1949],{},[1712,109399,6231],{},[902,109401,109402],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,109405,109407],{"className":109406},[886],[888,109408,109409],{"xmlns":890,"display":2004},[892,109410,109411,109431],{},[895,109412,109413,109415,109417,109419,109421,109423,109425,109427,109429],{},[1712,109414,6804],{},[1716,109416,2760],{},[1712,109418,1726],{},[898,109420,1878],{},[1716,109422,1913],{},[1712,109424,6849],{},[898,109426,1878],{},[1716,109428,1949],{},[1712,109430,6231],{},[902,109432,109433],{"encoding":904},"12 - 2Q = 4Q + 6",[724,109435,109436,109437,19417,109457,1343,109481,109517,109518,1853],{},"plyne ",[883,109438,109440],{"className":109439},[886],[888,109441,109442],{"xmlns":890},[892,109443,109444,109454],{},[895,109445,109446,109448,109450,109452],{},[1712,109447,6231],{},[898,109449,1878],{},[1716,109451,1913],{},[1712,109453,6231],{},[902,109455,109456],{"encoding":904},"6Q = 6",[883,109458,109460],{"className":109459},[886],[888,109461,109462],{"xmlns":890},[892,109463,109464,109478],{},[895,109465,109466,109474,109476],{},[7204,109467,109468,109470,109472],{},[898,109469,1878],{},[1712,109471,1714],{},[898,109473,1805],{},[1716,109475,1913],{},[1712,109477,1714],{},[902,109479,109480],{"encoding":904},"Q_1^E = 1",[883,109482,109484],{"className":109483},[886],[888,109485,109486],{"xmlns":890},[892,109487,109488,109514],{},[895,109489,109490,109498,109500,109502,109504,109506,109508,109510,109512],{},[7204,109491,109492,109494,109496],{},[898,109493,1690],{},[1712,109495,1714],{},[898,109497,1805],{},[1716,109499,1913],{},[1712,109501,6849],{},[1716,109503,9532],{},[1712,109505,1714],{},[1716,109507,1949],{},[1712,109509,6231],{},[1716,109511,1913],{},[1712,109513,2998],{},[902,109515,109516],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,109519,109521],{"className":109520},[886],[888,109522,109523],{"xmlns":890},[892,109524,109525,109543],{},[895,109526,109527,109533,109535,109537,109539,109541],{},[1707,109528,109529,109531],{},[898,109530,1805],{},[1712,109532,1714],{},[1716,109534,2502],{"stretchy":1919},[1712,109536,1714],{},[1716,109538,1719],{"separator":1718},[1712,109540,2998],{},[1716,109542,2516],{"stretchy":1919},[902,109544,109545],{"encoding":904},"E_1[1, 10]",[724,109547,109548,109551,109552,109576,109577,109590],{},[614,109549,109550],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,109553,109555],{"className":109554},[886],[888,109556,109557],{"xmlns":890},[892,109558,109559,109573],{},[895,109560,109561,109569,109571],{},[7204,109562,109563,109565,109567],{},[898,109564,1690],{},[1712,109566,1714],{},[898,109568,1805],{},[1716,109570,1913],{},[1712,109572,2998],{},[902,109574,109575],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,109578,109580],{"className":109579},[886],[888,109581,109582],{"xmlns":890},[892,109583,109584,109588],{},[895,109585,109586],{},[1712,109587,12398],{},[902,109589,12398],{"encoding":904},", navýšení je",[883,109592,109594],{"className":109593},[886],[888,109595,109596],{"xmlns":890,"display":2004},[892,109597,109598,109654],{},[895,109599,109600,109610,109612,109620,109622,109628,109630,109632,109634,109636,109638,109640,109642,109652],{},[1707,109601,109602,109604],{},[898,109603,4164],{},[895,109605,109606,109608],{},[898,109607,7658],{},[898,109609,724],{},[1716,109611,1913],{},[7204,109613,109614,109616,109618],{},[898,109615,1690],{},[1712,109617,1714],{},[898,109619,1805],{},[1716,109621,2760],{},[3074,109623,109624,109626],{},[898,109625,1690],{},[898,109627,1805],{},[1716,109629,1913],{},[1712,109631,2998],{},[1716,109633,2760],{},[1712,109635,12398],{},[1716,109637,1913],{},[1712,109639,1726],{},[2074,109641,2711],{},[895,109643,109644,109646],{},[2074,109645,1790],{},[22202,109647,109648,109650],{"accent":1718},[2074,109649,4478],{},[1716,109651,38828],{},[898,109653,1853],{"mathvariant":2068},[902,109655,109656],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,109658,109659,109660,109576,109696,109709],{},"Výrobci zůstává čistá cena ",[883,109661,109663],{"className":109662},[886],[888,109664,109665],{"xmlns":890},[892,109666,109667,109693],{},[895,109668,109669,109677,109679,109681,109683,109685,109687,109689,109691],{},[7204,109670,109671,109673,109675],{},[898,109672,1690],{},[1712,109674,1714],{},[898,109676,1805],{},[1716,109678,2760],{},[898,109680,4164],{},[1716,109682,1913],{},[1712,109684,2998],{},[1716,109686,2760],{},[1712,109688,6231],{},[1716,109690,1913],{},[1712,109692,6849],{},[902,109694,109695],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,109697,109699],{"className":109698},[886],[888,109700,109701],{"xmlns":890},[892,109702,109703,109707],{},[895,109704,109705],{},[1712,109706,12398],{},[902,109708,12398],{"encoding":904},", pokles je",[883,109711,109713],{"className":109712},[886],[888,109714,109715],{"xmlns":890,"display":2004},[892,109716,109717,109783],{},[895,109718,109719,109731,109733,109739,109741,109743,109751,109753,109755,109757,109759,109761,109763,109765,109767,109769,109771,109781],{},[1707,109720,109721,109723],{},[898,109722,4164],{},[895,109724,109725,109727,109729],{},[898,109726,7681],{},[898,109728,7684],{},[898,109730,2098],{},[1716,109732,1913],{},[3074,109734,109735,109737],{},[898,109736,1690],{},[898,109738,1805],{},[1716,109740,2760],{},[1716,109742,1920],{"stretchy":1919},[7204,109744,109745,109747,109749],{},[898,109746,1690],{},[1712,109748,1714],{},[898,109750,1805],{},[1716,109752,2760],{},[898,109754,4164],{},[1716,109756,1925],{"stretchy":1919},[1716,109758,1913],{},[1712,109760,12398],{},[1716,109762,2760],{},[1712,109764,6849],{},[1716,109766,1913],{},[1712,109768,6849],{},[2074,109770,2711],{},[895,109772,109773,109775],{},[2074,109774,1790],{},[22202,109776,109777,109779],{"accent":1718},[2074,109778,4478],{},[1716,109780,38828],{},[898,109782,1853],{"mathvariant":2068},[902,109784,109785],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,109787,109788,109789,109841],{},"Kontrola: ",[883,109790,109792],{"className":109791},[886],[888,109793,109794],{"xmlns":890},[892,109795,109796,109838],{},[895,109797,109798,109808,109810,109822,109824,109826,109828,109830,109832,109834,109836],{},[1707,109799,109800,109802],{},[898,109801,4164],{},[895,109803,109804,109806],{},[898,109805,7658],{},[898,109807,724],{},[1716,109809,1949],{},[1707,109811,109812,109814],{},[898,109813,4164],{},[895,109815,109816,109818,109820],{},[898,109817,7681],{},[898,109819,7684],{},[898,109821,2098],{},[1716,109823,1913],{},[1712,109825,1726],{},[1716,109827,1949],{},[1712,109829,6849],{},[1716,109831,1913],{},[1712,109833,6231],{},[1716,109835,1913],{},[898,109837,4164],{},[902,109839,109840],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[1855,109843],{},[115,109845,109847],{"id":109846},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,109849,108777,109850,109863,109864,109882,109883,109911],{},[883,109851,109853],{"className":109852},[886],[888,109854,109855],{"xmlns":890},[892,109856,109857,109861],{},[895,109858,109859],{},[898,109860,4164],{},[902,109862,4164],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,109865,109867],{"className":109866},[886],[888,109868,109869],{"xmlns":890},[892,109870,109871,109879],{},[895,109872,109873,109875,109877],{},[898,109874,1690],{},[1716,109876,1949],{},[898,109878,4164],{},[902,109880,109881],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,109884,109886],{"className":109885},[886],[888,109887,109888],{"xmlns":890},[892,109889,109890,109908],{},[895,109891,109892,109894,109896,109898,109900,109902,109904,109906],{},[898,109893,1690],{},[1716,109895,1949],{},[898,109897,4164],{},[1716,109899,1913],{},[898,109901,1916],{},[1716,109903,1920],{"stretchy":1919},[898,109905,1878],{},[1716,109907,1925],{"stretchy":1919},[902,109909,109910],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,109913,109915],{"className":109914},[886],[888,109916,109917],{"xmlns":890,"display":2004},[892,109918,109919,109953],{},[895,109920,109921,109923,109925,109931,109933,109935,109937,109939,109941,109943,109945,109947,109949,109951],{},[898,109922,1690],{},[1716,109924,1913],{},[1707,109926,109927,109929],{},[898,109928,1916],{},[1712,109930,1726],{},[1716,109932,1920],{"stretchy":1919},[898,109934,1878],{},[1716,109936,1925],{"stretchy":1919},[1716,109938,1913],{},[898,109940,1916],{},[1716,109942,1920],{"stretchy":1919},[898,109944,1878],{},[1716,109946,1925],{"stretchy":1919},[1716,109948,2760],{},[898,109950,4164],{},[898,109952,1853],{"mathvariant":2068},[902,109954,109955],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,109957,109958,109959,3495,109972,109975],{},"Poptávka se tedy posouvá o ",[883,109960,109962],{"className":109961},[886],[888,109963,109964],{"xmlns":890},[892,109965,109966,109970],{},[895,109967,109968],{},[898,109969,4164],{},[902,109971,4164],{"encoding":904},[38,109973,109974],{},"svisle dolů",". Nabídka se nemění.",[724,109977,108902,109978,108943,110018,2247,110046,110074,110075,110094,110095,110119,110120,2365],{},[883,109979,109981],{"className":109980},[886],[888,109982,109983],{"xmlns":890},[892,109984,109985,110015],{},[895,109986,109987,109993,109995,110003,110005,110013],{},[1707,109988,109989,109991],{},[898,109990,1805],{},[1712,109992,1726],{},[1716,109994,2502],{"stretchy":1919},[7204,109996,109997,109999,110001],{},[898,109998,1878],{},[1712,110000,1726],{},[898,110002,1805],{},[1716,110004,1719],{"separator":1718},[7204,110006,110007,110009,110011],{},[898,110008,1690],{},[1712,110010,1726],{},[898,110012,1805],{},[1716,110014,2516],{"stretchy":1919},[902,110016,110017],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,110019,110021],{"className":110020},[886],[888,110022,110023],{"xmlns":890},[892,110024,110025,110043],{},[895,110026,110027,110035,110037],{},[7204,110028,110029,110031,110033],{},[898,110030,1878],{},[1712,110032,1726],{},[898,110034,1805],{},[1716,110036,2704],{},[3074,110038,110039,110041],{},[898,110040,1878],{},[898,110042,1805],{},[902,110044,110045],{"encoding":904},"Q_2^E \u003C Q^E",[883,110047,110049],{"className":110048},[886],[888,110050,110051],{"xmlns":890},[892,110052,110053,110071],{},[895,110054,110055,110063,110065],{},[7204,110056,110057,110059,110061],{},[898,110058,1690],{},[1712,110060,1726],{},[898,110062,1805],{},[1716,110064,2704],{},[3074,110066,110067,110069],{},[898,110068,1690],{},[898,110070,1805],{},[902,110072,110073],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,110076,110078],{"className":110077},[886],[888,110079,110080],{"xmlns":890},[892,110081,110082,110092],{},[895,110083,110084],{},[7204,110085,110086,110088,110090],{},[898,110087,1690],{},[1712,110089,1726],{},[898,110091,1805],{},[902,110093,12929],{"encoding":904},", spotřebitel platí celkem ",[883,110096,110098],{"className":110097},[886],[888,110099,110100],{"xmlns":890},[892,110101,110102,110116],{},[895,110103,110104,110112,110114],{},[7204,110105,110106,110108,110110],{},[898,110107,1690],{},[1712,110109,1726],{},[898,110111,1805],{},[1716,110113,1949],{},[898,110115,4164],{},[902,110117,110118],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,110121,110123],{"className":110122},[886],[888,110124,110125],{"xmlns":890},[892,110126,110127,110135],{},[895,110128,110129],{},[3074,110130,110131,110133],{},[898,110132,1690],{},[898,110134,1805],{},[902,110136,6432],{"encoding":904},[724,110138,110139],{},"Daňové břemeno:",[883,110141,110143],{"className":110142},[886],[888,110144,110145],{"xmlns":890,"display":2004},[892,110146,110147,110221],{},[895,110148,110149,110159,110161,110163,110171,110173,110175,110177,110179,110185,110187,110189,110201,110203,110209,110211,110219],{},[1707,110150,110151,110153],{},[898,110152,4164],{},[895,110154,110155,110157],{},[898,110156,7658],{},[898,110158,724],{},[1716,110160,1913],{},[1716,110162,1920],{"stretchy":1919},[7204,110164,110165,110167,110169],{},[898,110166,1690],{},[1712,110168,1726],{},[898,110170,1805],{},[1716,110172,1949],{},[898,110174,4164],{},[1716,110176,1925],{"stretchy":1919},[1716,110178,2760],{},[3074,110180,110181,110183],{},[898,110182,1690],{},[898,110184,1805],{},[1716,110186,1719],{"separator":1718},[2324,110188],{"width":2326},[1707,110190,110191,110193],{},[898,110192,4164],{},[895,110194,110195,110197,110199],{},[898,110196,7681],{},[898,110198,7684],{},[898,110200,2098],{},[1716,110202,1913],{},[3074,110204,110205,110207],{},[898,110206,1690],{},[898,110208,1805],{},[1716,110210,2760],{},[7204,110212,110213,110215,110217],{},[898,110214,1690],{},[1712,110216,1726],{},[898,110218,1805],{},[898,110220,1853],{"mathvariant":2068},[902,110222,110223],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,110225,110226],{},[614,110227,110228,110229,110259,110260,109112,110273,3569,110290,109143,110303,1853],{},"Obrázek 2.19: Posun ",[883,110230,110232],{"className":110231},[886],[888,110233,110234],{"xmlns":890},[892,110235,110236,110256],{},[895,110237,110238,110240,110242,110248,110250,110252,110254],{},[898,110239,1916],{},[1716,110241,16986],{},[1707,110243,110244,110246],{},[898,110245,1916],{},[1712,110247,1726],{},[1716,110249,1913],{},[898,110251,1916],{},[1716,110253,2760],{},[898,110255,4164],{},[902,110257,110258],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,110261,110263],{"className":110262},[886],[888,110264,110265],{"xmlns":890},[892,110266,110267,110271],{},[895,110268,110269],{},[898,110270,4164],{},[902,110272,4164],{"encoding":904},[883,110274,110276],{"className":110275},[886],[888,110277,110278],{"xmlns":890},[892,110279,110280,110288],{},[895,110281,110282],{},[1707,110283,110284,110286],{},[898,110285,1916],{},[1712,110287,1726],{},[902,110289,3264],{"encoding":904},[883,110291,110293],{"className":110292},[886],[888,110294,110295],{"xmlns":890},[892,110296,110297,110301],{},[895,110298,110299],{},[898,110300,5352],{},[902,110302,5352],{"encoding":904},[883,110304,110306],{"className":110305},[886],[888,110307,110308],{"xmlns":890},[892,110309,110310,110318],{},[895,110311,110312],{},[1707,110313,110314,110316],{},[898,110315,1805],{},[1712,110317,1726],{},[902,110319,110320],{"encoding":904},"E_2",[198,110322,10385],{"id":110323},"příklad-210",[724,110325,110326,110328,110329,6657,110352,110371,110372,110389],{},[38,110327,2859],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,110330,110332],{"className":110331},[886],[888,110333,110334],{"xmlns":890},[892,110335,110336,110350],{},[895,110337,110338,110340,110342,110344,110346,110348],{},[898,110339,1690],{},[1716,110341,1913],{},[1712,110343,6804],{},[1716,110345,2760],{},[1712,110347,1726],{},[898,110349,1878],{},[902,110351,109192],{"encoding":904},[883,110353,110355],{"className":110354},[886],[888,110356,110357],{"xmlns":890},[892,110358,110359,110369],{},[895,110360,110361,110363,110365,110367],{},[898,110362,1690],{},[1716,110364,1913],{},[1712,110366,6849],{},[898,110368,1878],{},[902,110370,109212],{"encoding":904},". Daň ",[883,110373,110375],{"className":110374},[886],[888,110376,110377],{"xmlns":890},[892,110378,110379,110387],{},[895,110380,110381,110383,110385],{},[898,110382,4164],{},[1716,110384,1913],{},[1712,110386,6231],{},[902,110388,6234],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,110391,110392],{},[38,110393,2892],{},[724,110395,110396,110397,109403],{},"Nová poptávka je ",[883,110398,110400],{"className":110399},[886],[888,110401,110402],{"xmlns":890},[892,110403,110404,110440],{},[895,110405,110406,110412,110414,110416,110418,110420,110422,110424,110426,110428,110430,110432,110434,110436,110438],{},[1707,110407,110408,110410],{},[898,110409,1916],{},[1712,110411,1726],{},[1716,110413,2291],{},[898,110415,1690],{},[1716,110417,1913],{},[1712,110419,6804],{},[1716,110421,2760],{},[1712,110423,1726],{},[898,110425,1878],{},[1716,110427,2760],{},[1712,110429,6231],{},[1716,110431,1913],{},[1712,110433,6231],{},[1716,110435,2760],{},[1712,110437,1726],{},[898,110439,1878],{},[902,110441,110442],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,110444,110446],{"className":110445},[886],[888,110447,110448],{"xmlns":890,"display":2004},[892,110449,110450,110466],{},[895,110451,110452,110454,110456,110458,110460,110462,110464],{},[1712,110453,6231],{},[1716,110455,2760],{},[1712,110457,1726],{},[898,110459,1878],{},[1716,110461,1913],{},[1712,110463,6849],{},[898,110465,1878],{},[902,110467,110468],{"encoding":904},"6 - 2Q = 4Q",[724,110470,109436,110471,19417,110490,1343,110514,109517,110546,1853],{},[883,110472,110474],{"className":110473},[886],[888,110475,110476],{"xmlns":890},[892,110477,110478,110488],{},[895,110479,110480,110482,110484,110486],{},[1712,110481,6231],{},[898,110483,1878],{},[1716,110485,1913],{},[1712,110487,6231],{},[902,110489,109456],{"encoding":904},[883,110491,110493],{"className":110492},[886],[888,110494,110495],{"xmlns":890},[892,110496,110497,110511],{},[895,110498,110499,110507,110509],{},[7204,110500,110501,110503,110505],{},[898,110502,1878],{},[1712,110504,1726],{},[898,110506,1805],{},[1716,110508,1913],{},[1712,110510,1714],{},[902,110512,110513],{"encoding":904},"Q_2^E = 1",[883,110515,110517],{"className":110516},[886],[888,110518,110519],{"xmlns":890},[892,110520,110521,110543],{},[895,110522,110523,110531,110533,110535,110537,110539,110541],{},[7204,110524,110525,110527,110529],{},[898,110526,1690],{},[1712,110528,1726],{},[898,110530,1805],{},[1716,110532,1913],{},[1712,110534,6849],{},[1716,110536,9532],{},[1712,110538,1714],{},[1716,110540,1913],{},[1712,110542,6849],{},[902,110544,110545],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,110547,110549],{"className":110548},[886],[888,110550,110551],{"xmlns":890},[892,110552,110553,110571],{},[895,110554,110555,110561,110563,110565,110567,110569],{},[1707,110556,110557,110559],{},[898,110558,1805],{},[1712,110560,1726],{},[1716,110562,2502],{"stretchy":1919},[1712,110564,1714],{},[1716,110566,1719],{"separator":1718},[1712,110568,6849],{},[1716,110570,2516],{"stretchy":1919},[902,110572,110573],{"encoding":904},"E_2[1, 4]",[724,110575,110576,110577,110613,110614,109231],{},"Spotřebitel platí celkem ",[883,110578,110580],{"className":110579},[886],[888,110581,110582],{"xmlns":890},[892,110583,110584,110610],{},[895,110585,110586,110594,110596,110598,110600,110602,110604,110606,110608],{},[7204,110587,110588,110590,110592],{},[898,110589,1690],{},[1712,110591,1726],{},[898,110593,1805],{},[1716,110595,1949],{},[898,110597,4164],{},[1716,110599,1913],{},[1712,110601,6849],{},[1716,110603,1949],{},[1712,110605,6231],{},[1716,110607,1913],{},[1712,110609,2998],{},[902,110611,110612],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,110615,110617],{"className":110616},[886],[888,110618,110619],{"xmlns":890},[892,110620,110621,110635],{},[895,110622,110623,110631,110633],{},[7204,110624,110625,110627,110629],{},[898,110626,1690],{},[1712,110628,1726],{},[898,110630,1805],{},[1716,110632,1913],{},[1712,110634,6849],{},[902,110636,110637],{"encoding":904},"P_2^E = 4",[724,110639,110640],{},[614,110641,110642],{},"Rozklad daňového břemene:",[883,110644,110646],{"className":110645},[886],[888,110647,110648],{"xmlns":890,"display":2004},[892,110649,110650,110736],{},[895,110651,110652,110662,110664,110666,110668,110670,110672,110674,110676,110678,110680,110682,110684,110694,110696,110698,110710,110712,110714,110716,110718,110720,110722,110724,110734],{},[1707,110653,110654,110656],{},[898,110655,4164],{},[895,110657,110658,110660],{},[898,110659,7658],{},[898,110661,724],{},[1716,110663,1913],{},[1716,110665,1920],{"stretchy":1919},[1712,110667,6849],{},[1716,110669,1949],{},[1712,110671,6231],{},[1716,110673,1925],{"stretchy":1919},[1716,110675,2760],{},[1712,110677,12398],{},[1716,110679,1913],{},[1712,110681,1726],{},[2074,110683,2711],{},[895,110685,110686,110688],{},[2074,110687,1790],{},[22202,110689,110690,110692],{"accent":1718},[2074,110691,4478],{},[1716,110693,38828],{},[1716,110695,1719],{"separator":1718},[2324,110697],{"width":2326},[1707,110699,110700,110702],{},[898,110701,4164],{},[895,110703,110704,110706,110708],{},[898,110705,7681],{},[898,110707,7684],{},[898,110709,2098],{},[1716,110711,1913],{},[1712,110713,12398],{},[1716,110715,2760],{},[1712,110717,6849],{},[1716,110719,1913],{},[1712,110721,6849],{},[2074,110723,2711],{},[895,110725,110726,110728],{},[2074,110727,1790],{},[22202,110729,110730,110732],{"accent":1718},[2074,110731,4478],{},[1716,110733,38828],{},[898,110735,1853],{"mathvariant":2068},[902,110737,110738],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,110740,110741,110742,1853],{},"Opět ",[883,110743,110745],{"className":110744},[886],[888,110746,110747],{"xmlns":890},[892,110748,110749,110783],{},[895,110750,110751,110761,110763,110775,110777,110779,110781],{},[1707,110752,110753,110755],{},[898,110754,4164],{},[895,110756,110757,110759],{},[898,110758,7658],{},[898,110760,724],{},[1716,110762,1949],{},[1707,110764,110765,110767],{},[898,110766,4164],{},[895,110768,110769,110771,110773],{},[898,110770,7681],{},[898,110772,7684],{},[898,110774,2098],{},[1716,110776,1913],{},[1712,110778,6231],{},[1716,110780,1913],{},[898,110782,4164],{},[902,110784,110785],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[1855,110787],{},[115,110789,7639],{"id":110790},"daňové-břemeno",[724,110792,110793,1994,110795,110798,110799,110812],{},[38,110794,7639],{},[614,110796,110797],{},"tax burden",") je rozdělení zaplacené daně ",[883,110800,110802],{"className":110801},[886],[888,110803,110804],{"xmlns":890},[892,110805,110806,110810],{},[895,110807,110808],{},[898,110809,4164],{},[902,110811,4164],{"encoding":904}," mezi spotřebitele a výrobce:",[883,110814,110816],{"className":110815},[886],[888,110817,110818],{"xmlns":890,"display":2004},[892,110819,110820,110852],{},[895,110821,110822,110824,110826,110836,110838,110850],{},[898,110823,4164],{},[1716,110825,1913],{},[1707,110827,110828,110830],{},[898,110829,4164],{},[895,110831,110832,110834],{},[898,110833,7658],{},[898,110835,724],{},[1716,110837,1949],{},[1707,110839,110840,110842],{},[898,110841,4164],{},[895,110843,110844,110846,110848],{},[898,110845,7681],{},[898,110847,7684],{},[898,110849,2098],{},[898,110851,1853],{"mathvariant":2068},[902,110853,110854],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,110856,110857],{},[3682,110858],{"alt":110859,"className":110860,"src":110861},"imek-dan-rozklad-bremene-sklony",[210,3686],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1635,110863,110864],{},[724,110865,110866,110868,110869,2247,110882,1853],{},[883,110867,1641],{}," 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 ",[883,110870,110872],{"className":110871},[886],[888,110873,110874],{"xmlns":890},[892,110875,110876,110880],{},[895,110877,110878],{},[898,110879,1916],{},[902,110881,1916],{"encoding":904},[883,110883,110885],{"className":110884},[886],[888,110886,110887],{"xmlns":890},[892,110888,110889,110893],{},[895,110890,110891],{},[898,110892,5352],{},[902,110894,5352],{"encoding":904},[198,110896,16328],{"id":16327},[724,110898,110899,110900,110921,110922,110935,110936,110953,110954,110967],{},"V grafu ",[883,110901,110903],{"className":110902},[886],[888,110904,110905],{"xmlns":890},[892,110906,110907,110919],{},[895,110908,110909,110911,110913,110915,110917],{},[1716,110910,1920],{"stretchy":1919},[898,110912,1878],{},[1716,110914,1719],{"separator":1718},[898,110916,1690],{},[1716,110918,1925],{"stretchy":1919},[902,110920,2608],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,110923,110925],{"className":110924},[886],[888,110926,110927],{"xmlns":890},[892,110928,110929,110933],{},[895,110930,110931],{},[898,110932,4164],{},[902,110934,4164],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,110937,110939],{"className":110938},[886],[888,110940,110941],{"xmlns":890},[892,110942,110943,110951],{},[895,110944,110945],{},[3074,110946,110947,110949],{},[898,110948,1690],{},[898,110950,1805],{},[902,110952,6432],{"encoding":904},", rozdělí se úsečka ",[883,110955,110957],{"className":110956},[886],[888,110958,110959],{"xmlns":890},[892,110960,110961,110965],{},[895,110962,110963],{},[898,110964,4164],{},[902,110966,4164],{"encoding":904}," na dvě části:",[120,110969,110970,110995],{},[123,110971,110972,110973,110994],{},"horní část odpovídá ",[883,110974,110976],{"className":110975},[886],[888,110977,110978],{"xmlns":890},[892,110979,110980,110992],{},[895,110981,110982],{},[1707,110983,110984,110986],{},[898,110985,4164],{},[895,110987,110988,110990],{},[898,110989,7658],{},[898,110991,724],{},[902,110993,7663],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,110996,110997,110998,111021],{},"dolní část odpovídá ",[883,110999,111001],{"className":111000},[886],[888,111002,111003],{"xmlns":890},[892,111004,111005,111019],{},[895,111006,111007],{},[1707,111008,111009,111011],{},[898,111010,4164],{},[895,111012,111013,111015,111017],{},[898,111014,7681],{},[898,111016,7684],{},[898,111018,2098],{},[902,111020,7689],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,111023,111024],{},[614,111025,111026,111027,3942,111040,111061,111062,111085,111086,2247,111107,111130],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,111028,111030],{"className":111029},[886],[888,111031,111032],{"xmlns":890},[892,111033,111034,111038],{},[895,111035,111036],{},[898,111037,4164],{},[902,111039,4164],{"encoding":904},[883,111041,111043],{"className":111042},[886],[888,111044,111045],{"xmlns":890},[892,111046,111047,111059],{},[895,111048,111049],{},[1707,111050,111051,111053],{},[898,111052,4164],{},[895,111054,111055,111057],{},[898,111056,7658],{},[898,111058,724],{},[902,111060,7663],{"encoding":904}," (nahoře) a ",[883,111063,111065],{"className":111064},[886],[888,111066,111067],{"xmlns":890},[892,111068,111069,111083],{},[895,111070,111071],{},[1707,111072,111073,111075],{},[898,111074,4164],{},[895,111076,111077,111079,111081],{},[898,111078,7681],{},[898,111080,7684],{},[898,111082,2098],{},[902,111084,7689],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,111087,111089],{"className":111088},[886],[888,111090,111091],{"xmlns":890},[892,111092,111093,111105],{},[895,111094,111095],{},[1707,111096,111097,111099],{},[898,111098,4164],{},[895,111100,111101,111103],{},[898,111102,7658],{},[898,111104,724],{},[902,111106,7663],{"encoding":904},[883,111108,111110],{"className":111109},[886],[888,111111,111112],{"xmlns":890},[892,111113,111114,111128],{},[895,111115,111116],{},[1707,111117,111118,111120],{},[898,111119,4164],{},[895,111121,111122,111124,111126],{},[898,111123,7681],{},[898,111125,7684],{},[898,111127,2098],{},[902,111129,7689],{"encoding":904}," je v obou případech stejná.",[198,111132,111134],{"id":111133},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,111136,111137,111138,111141,111142,1994,111165,111182,111183,1994,111206,111223],{},"Platí obecně: ",[38,111139,111140],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,111143,111145],{"className":111144},[886],[888,111146,111147],{"xmlns":890},[892,111148,111149,111163],{},[895,111150,111151,111153,111155,111157,111159,111161],{},[898,111152,1690],{},[1716,111154,1913],{},[898,111156,207],{},[898,111158,1878],{},[1716,111160,1949],{},[898,111162,1952],{},[902,111164,1955],{"encoding":904},[883,111166,111168],{"className":111167},[886],[888,111169,111170],{"xmlns":890},[892,111171,111172,111180],{},[895,111173,111174,111176,111178],{},[898,111175,207],{},[1716,111177,2704],{},[1712,111179,2505],{},[902,111181,8067],{"encoding":904},") a lineární nabídku ",[883,111184,111186],{"className":111185},[886],[888,111187,111188],{"xmlns":890},[892,111189,111190,111204],{},[895,111191,111192,111194,111196,111198,111200,111202],{},[898,111193,1690],{},[1716,111195,1913],{},[898,111197,4478],{},[898,111199,1878],{},[1716,111201,1949],{},[898,111203,5198],{},[902,111205,5201],{"encoding":904},[883,111207,111209],{"className":111208},[886],[888,111210,111211],{"xmlns":890},[892,111212,111213,111221],{},[895,111214,111215,111217,111219],{},[898,111216,4478],{},[1716,111218,2716],{},[1712,111220,2505],{},[902,111222,5219],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,111225,111227],{"className":111226},[886],[888,111228,111229],{"xmlns":890,"display":2004},[892,111230,111231,111297],{},[895,111232,111233,111257,111259,111269,111271,111295],{},[2750,111234,111235,111245],{},[1707,111236,111237,111239],{},[898,111238,4164],{},[895,111240,111241,111243],{},[898,111242,7658],{},[898,111244,724],{},[1707,111246,111247,111249],{},[898,111248,4164],{},[895,111250,111251,111253,111255],{},[898,111252,7681],{},[898,111254,7684],{},[898,111256,2098],{},[1716,111258,1913],{},[2750,111260,111261,111263],{},[898,111262,4478],{},[895,111264,111265,111267],{},[1716,111266,2760],{},[898,111268,207],{},[1716,111270,1913],{},[2750,111272,111273,111285],{},[895,111274,111275,111278,111281,111283],{},[898,111276,111277],{"mathvariant":2068},"∣",[2074,111279,111280],{},"sklon ",[898,111282,5352],{},[898,111284,111277],{"mathvariant":2068},[895,111286,111287,111289,111291,111293],{},[898,111288,111277],{"mathvariant":2068},[2074,111290,111280],{},[898,111292,1916],{},[898,111294,111277],{"mathvariant":2068},[898,111296,1853],{"mathvariant":2068},[902,111298,111299],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1635,111301,111302,111307],{},[724,111303,111304,111306],{},[883,111305,3776],{}," Postup výpočtu rozkladu",[152,111308,111309,111344,111397,111476],{},[123,111310,111311,111312,111343],{},"Spočti rovnovážný bod ",[883,111313,111315],{"className":111314},[886],[888,111316,111317],{"xmlns":890},[892,111318,111319,111341],{},[895,111320,111321,111323,111325,111331,111333,111339],{},[898,111322,1805],{},[1716,111324,2502],{"stretchy":1919},[3074,111326,111327,111329],{},[898,111328,1878],{},[898,111330,1805],{},[1716,111332,1719],{"separator":1718},[3074,111334,111335,111337],{},[898,111336,1690],{},[898,111338,1805],{},[1716,111340,2516],{"stretchy":1919},[902,111342,6333],{"encoding":904}," bez daně.",[123,111345,111346,111347,1348,111372,2365],{},"Urči posunutou křivku (",[883,111348,111350],{"className":111349},[886],[888,111351,111352],{"xmlns":890},[892,111353,111354,111370],{},[895,111355,111356,111362,111364,111366,111368],{},[1707,111357,111358,111360],{},[898,111359,5352],{},[1712,111361,1714],{},[1716,111363,1913],{},[898,111365,5352],{},[1716,111367,1949],{},[898,111369,4164],{},[902,111371,7736],{"encoding":904},[883,111373,111375],{"className":111374},[886],[888,111376,111377],{"xmlns":890},[892,111378,111379,111395],{},[895,111380,111381,111387,111389,111391,111393],{},[1707,111382,111383,111385],{},[898,111384,1916],{},[1712,111386,1726],{},[1716,111388,1913],{},[898,111390,1916],{},[1716,111392,2760],{},[898,111394,4164],{},[902,111396,7767],{"encoding":904},[123,111398,111399,111400,17758,111419,8086,111438,17758,111457,2365],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,111401,111403],{"className":111402},[886],[888,111404,111405],{"xmlns":890},[892,111406,111407,111417],{},[895,111408,111409],{},[7204,111410,111411,111413,111415],{},[898,111412,1878],{},[1712,111414,1714],{},[898,111416,1805],{},[902,111418,12847],{"encoding":904},[883,111420,111422],{"className":111421},[886],[888,111423,111424],{"xmlns":890},[892,111425,111426,111436],{},[895,111427,111428],{},[7204,111429,111430,111432,111434],{},[898,111431,1878],{},[1712,111433,1726],{},[898,111435,1805],{},[902,111437,12909],{"encoding":904},[883,111439,111441],{"className":111440},[886],[888,111442,111443],{"xmlns":890},[892,111444,111445,111455],{},[895,111446,111447],{},[7204,111448,111449,111451,111453],{},[898,111450,1690],{},[1712,111452,1714],{},[898,111454,1805],{},[902,111456,12868],{"encoding":904},[883,111458,111460],{"className":111459},[886],[888,111461,111462],{"xmlns":890},[892,111463,111464,111474],{},[895,111465,111466],{},[7204,111467,111468,111470,111472],{},[898,111469,1690],{},[1712,111471,1726],{},[898,111473,1805],{},[902,111475,12929],{"encoding":904},[123,111477,111478,111479,2247,111500,111523,111524,1853],{},"Dopočítej ",[883,111480,111482],{"className":111481},[886],[888,111483,111484],{"xmlns":890},[892,111485,111486,111498],{},[895,111487,111488],{},[1707,111489,111490,111492],{},[898,111491,4164],{},[895,111493,111494,111496],{},[898,111495,7658],{},[898,111497,724],{},[902,111499,7663],{"encoding":904},[883,111501,111503],{"className":111502},[886],[888,111504,111505],{"xmlns":890},[892,111506,111507,111521],{},[895,111508,111509],{},[1707,111510,111511,111513],{},[898,111512,4164],{},[895,111514,111515,111517,111519],{},[898,111516,7681],{},[898,111518,7684],{},[898,111520,2098],{},[902,111522,7689],{"encoding":904}," z definice, vždy ověř ",[883,111525,111527],{"className":111526},[886],[888,111528,111529],{"xmlns":890},[892,111530,111531,111561],{},[895,111532,111533,111543,111545,111557,111559],{},[1707,111534,111535,111537],{},[898,111536,4164],{},[895,111538,111539,111541],{},[898,111540,7658],{},[898,111542,724],{},[1716,111544,1949],{},[1707,111546,111547,111549],{},[898,111548,4164],{},[895,111550,111551,111553,111555],{},[898,111552,7681],{},[898,111554,7684],{},[898,111556,2098],{},[1716,111558,1913],{},[898,111560,4164],{},[902,111562,111563],{"encoding":904},"T_{sp} + T_{vyr} = T",[1635,111565,111566],{},[724,111567,111568,111570,111571,111574,111575,2247,111588,111601],{},[883,111569,2233],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,111572,111573],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,111576,111578],{"className":111577},[886],[888,111579,111580],{"xmlns":890},[892,111581,111582,111586],{},[895,111583,111584],{},[898,111585,1916],{},[902,111587,1916],{"encoding":904},[883,111589,111591],{"className":111590},[886],[888,111592,111593],{"xmlns":890},[892,111594,111595,111599],{},[895,111596,111597],{},[898,111598,5352],{},[902,111600,5352],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[1855,111603],{},[115,111605,111607],{"id":111606},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,111609,111610],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,111612,111613],{},[3682,111614],{"alt":111615,"className":111616,"src":111617},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,3686],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,111619,111620,111632],{},[19,111621,111622],{},[22,111623,111624,111626,111629],{},[25,111625,67050],{},[25,111627,111628],{},"(a) daň výrobci",[25,111630,111631],{},"(b) daň spotřebiteli",[30,111633,111634,111689,111756,111816],{},[22,111635,111636,111639,111664],{},[35,111637,111638],{},"Rovnovážné množství",[35,111640,111641],{},[883,111642,111644],{"className":111643},[886],[888,111645,111646],{"xmlns":890},[892,111647,111648,111662],{},[895,111649,111650,111658,111660],{},[7204,111651,111652,111654,111656],{},[898,111653,1878],{},[1712,111655,1714],{},[898,111657,1805],{},[1716,111659,1913],{},[1712,111661,1714],{},[902,111663,109480],{"encoding":904},[35,111665,111666],{},[883,111667,111669],{"className":111668},[886],[888,111670,111671],{"xmlns":890},[892,111672,111673,111687],{},[895,111674,111675,111683,111685],{},[7204,111676,111677,111679,111681],{},[898,111678,1878],{},[1712,111680,1726],{},[898,111682,1805],{},[1716,111684,1913],{},[1712,111686,1714],{},[902,111688,110513],{"encoding":904},[22,111690,111691,111694,111719],{},[35,111692,111693],{},"Cena placená spotřebitelem",[35,111695,111696],{},[883,111697,111699],{"className":111698},[886],[888,111700,111701],{"xmlns":890},[892,111702,111703,111717],{},[895,111704,111705,111713,111715],{},[7204,111706,111707,111709,111711],{},[898,111708,1690],{},[1712,111710,1714],{},[898,111712,1805],{},[1716,111714,1913],{},[1712,111716,2998],{},[902,111718,109575],{"encoding":904},[35,111720,111721],{},[883,111722,111724],{"className":111723},[886],[888,111725,111726],{"xmlns":890},[892,111727,111728,111754],{},[895,111729,111730,111738,111740,111742,111744,111746,111748,111750,111752],{},[7204,111731,111732,111734,111736],{},[898,111733,1690],{},[1712,111735,1726],{},[898,111737,1805],{},[1716,111739,1949],{},[898,111741,4164],{},[1716,111743,1913],{},[1712,111745,6849],{},[1716,111747,1949],{},[1712,111749,6231],{},[1716,111751,1913],{},[1712,111753,2998],{},[902,111755,110612],{"encoding":904},[22,111757,111758,111761,111791],{},[35,111759,111760],{},"Cena přijímaná výrobcem",[35,111762,111763],{},[883,111764,111766],{"className":111765},[886],[888,111767,111768],{"xmlns":890},[892,111769,111770,111788],{},[895,111771,111772,111780,111782,111784,111786],{},[7204,111773,111774,111776,111778],{},[898,111775,1690],{},[1712,111777,1714],{},[898,111779,1805],{},[1716,111781,2760],{},[898,111783,4164],{},[1716,111785,1913],{},[1712,111787,6849],{},[902,111789,111790],{"encoding":904},"P_1^E - T = 4",[35,111792,111793],{},[883,111794,111796],{"className":111795},[886],[888,111797,111798],{"xmlns":890},[892,111799,111800,111814],{},[895,111801,111802,111810,111812],{},[7204,111803,111804,111806,111808],{},[898,111805,1690],{},[1712,111807,1726],{},[898,111809,1805],{},[1716,111811,1913],{},[1712,111813,6849],{},[902,111815,110637],{"encoding":904},[22,111817,111818,111821,111875],{},[35,111819,111820],{},"Rozklad břemene",[35,111822,111823,1343,111848],{},[883,111824,111826],{"className":111825},[886],[888,111827,111828],{"xmlns":890},[892,111829,111830,111846],{},[895,111831,111832,111842,111844],{},[1707,111833,111834,111836],{},[898,111835,4164],{},[895,111837,111838,111840],{},[898,111839,7658],{},[898,111841,724],{},[1716,111843,1913],{},[1712,111845,1726],{},[902,111847,7958],{"encoding":904},[883,111849,111851],{"className":111850},[886],[888,111852,111853],{"xmlns":890},[892,111854,111855,111873],{},[895,111856,111857,111869,111871],{},[1707,111858,111859,111861],{},[898,111860,4164],{},[895,111862,111863,111865,111867],{},[898,111864,7681],{},[898,111866,7684],{},[898,111868,2098],{},[1716,111870,1913],{},[1712,111872,6849],{},[902,111874,7987],{"encoding":904},[35,111876,111877,1343,111902],{},[883,111878,111880],{"className":111879},[886],[888,111881,111882],{"xmlns":890},[892,111883,111884,111900],{},[895,111885,111886,111896,111898],{},[1707,111887,111888,111890],{},[898,111889,4164],{},[895,111891,111892,111894],{},[898,111893,7658],{},[898,111895,724],{},[1716,111897,1913],{},[1712,111899,1726],{},[902,111901,7958],{"encoding":904},[883,111903,111905],{"className":111904},[886],[888,111906,111907],{"xmlns":890},[892,111908,111909,111927],{},[895,111910,111911,111923,111925],{},[1707,111912,111913,111915],{},[898,111914,4164],{},[895,111916,111917,111919,111921],{},[898,111918,7681],{},[898,111920,7684],{},[898,111922,2098],{},[1716,111924,1913],{},[1712,111926,6849],{},[902,111928,7987],{"encoding":904},[724,111930,111931],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,111933,111935],{"className":111934},[886],[888,111936,111937],{"xmlns":890,"display":2004},[892,111938,111939,111987],{},[895,111940,111941,111949,111951,111959,111961,111963,111971,111973,111975,111977,111985],{},[7204,111942,111943,111945,111947],{},[898,111944,1878],{},[1712,111946,1714],{},[898,111948,1805],{},[1716,111950,1913],{},[7204,111952,111953,111955,111957],{},[898,111954,1878],{},[1712,111956,1726],{},[898,111958,1805],{},[1716,111960,1719],{"separator":1718},[2324,111962],{"width":2326},[7204,111964,111965,111967,111969],{},[898,111966,1690],{},[1712,111968,1714],{},[898,111970,1805],{},[1716,111972,2760],{},[898,111974,4164],{},[1716,111976,1913],{},[7204,111978,111979,111981,111983],{},[898,111980,1690],{},[1712,111982,1726],{},[898,111984,1805],{},[898,111986,1853],{"mathvariant":2068},[902,111988,111989],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1635,111991,111992,112011,112165],{},[724,111993,111994,111996,111997,112010],{},[883,111995,3776],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,111998,112000],{"className":111999},[886],[888,112001,112002],{"xmlns":890},[892,112003,112004,112008],{},[895,112005,112006],{},[898,112007,4164],{},[902,112009,4164],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,112012,112013,112045,112081,112118],{},[123,112014,112015,112016,1719],{},"rovnovážná množství obou režimů, ",[883,112017,112019],{"className":112018},[886],[888,112020,112021],{"xmlns":890},[892,112022,112023,112043],{},[895,112024,112025,112033,112035],{},[7204,112026,112027,112029,112031],{},[898,112028,1878],{},[1712,112030,1714],{},[898,112032,1805],{},[1716,112034,1913],{},[7204,112036,112037,112039,112041],{},[898,112038,1878],{},[1712,112040,1726],{},[898,112042,1805],{},[902,112044,7890],{"encoding":904},[123,112046,112047,112048,1719],{},"čistá cena přijímaná výrobcem, ",[883,112049,112051],{"className":112050},[886],[888,112052,112053],{"xmlns":890},[892,112054,112055,112079],{},[895,112056,112057,112065,112067,112069,112071],{},[7204,112058,112059,112061,112063],{},[898,112060,1690],{},[1712,112062,1714],{},[898,112064,1805],{},[1716,112066,2760],{},[898,112068,4164],{},[1716,112070,1913],{},[7204,112072,112073,112075,112077],{},[898,112074,1690],{},[1712,112076,1726],{},[898,112078,1805],{},[902,112080,7924],{"encoding":904},[123,112082,112083,112084,1719],{},"celková cena placená spotřebitelem, ",[883,112085,112087],{"className":112086},[886],[888,112088,112089],{"xmlns":890},[892,112090,112091,112115],{},[895,112092,112093,112101,112103,112111,112113],{},[7204,112094,112095,112097,112099],{},[898,112096,1690],{},[1712,112098,1714],{},[898,112100,1805],{},[1716,112102,1913],{},[7204,112104,112105,112107,112109],{},[898,112106,1690],{},[1712,112108,1726],{},[898,112110,1805],{},[1716,112112,1949],{},[898,112114,4164],{},[902,112116,112117],{"encoding":904},"P_1^E = P_2^E + T",[123,112119,112120,112121,2247,112142,1853],{},"rozklad daňového břemene ",[883,112122,112124],{"className":112123},[886],[888,112125,112126],{"xmlns":890},[892,112127,112128,112140],{},[895,112129,112130],{},[1707,112131,112132,112134],{},[898,112133,4164],{},[895,112135,112136,112138],{},[898,112137,7658],{},[898,112139,724],{},[902,112141,7663],{"encoding":904},[883,112143,112145],{"className":112144},[886],[888,112146,112147],{"xmlns":890},[892,112148,112149,112163],{},[895,112150,112151],{},[1707,112152,112153,112155],{},[898,112154,4164],{},[895,112156,112157,112159,112161],{},[898,112158,7681],{},[898,112160,7684],{},[898,112162,2098],{},[902,112164,7689],{"encoding":904},[724,112166,112167,112168,1853],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,112169,48957],{},[724,112171,112172,112173,2247,112186,2365],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,112174,112176],{"className":112175},[886],[888,112177,112178],{"xmlns":890},[892,112179,112180,112184],{},[895,112181,112182],{},[898,112183,1916],{},[902,112185,1916],{"encoding":904},[883,112187,112189],{"className":112188},[886],[888,112190,112191],{"xmlns":890},[892,112192,112193,112197],{},[895,112194,112195],{},[898,112196,5352],{},[902,112198,5352],{"encoding":904},[1855,112200],{},[115,112202,112204],{"id":112203},"úlohy","Úlohy",[724,112206,112207,112208,1998],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,112209,30029],{"className":112210,"dataFsResolvedFilePath":800,"href":801},[210],[120,112212,112213,112243,112274],{},[123,112214,112215,112218,112219,112242],{},[38,112216,112217],{},"Úloha 2.4"," — Poptávka ",[883,112220,112222],{"className":112221},[886],[888,112223,112224],{"xmlns":890},[892,112225,112226,112240],{},[895,112227,112228,112230,112232,112234,112236,112238],{},[898,112229,1690],{},[1716,112231,1913],{},[1712,112233,6804],{},[1716,112235,2760],{},[1712,112237,1726],{},[898,112239,1878],{},[902,112241,109192],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,112244,112245,112248,112249,112273],{},[38,112246,112247],{},"Úloha 2.9"," — Nabídka ",[883,112250,112252],{"className":112251},[886],[888,112253,112254],{"xmlns":890},[892,112255,112256,112270],{},[895,112257,112258,112260,112262,112264,112266,112268],{},[898,112259,1690],{},[1716,112261,1913],{},[1712,112263,5771],{},[898,112265,1878],{},[1716,112267,1949],{},[1712,112269,3221],{},[902,112271,112272],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,112275,112276,112279,112280,2247,112306,112330,112331,112348],{},[38,112277,112278],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,112281,112283],{"className":112282},[886],[888,112284,112285],{"xmlns":890},[892,112286,112287,112303],{},[895,112288,112289,112291,112293,112295,112297,112299,112301],{},[898,112290,1690],{},[1716,112292,1913],{},[1716,112294,2760],{},[1712,112296,6849],{},[898,112298,1878],{},[1716,112300,1949],{},[1712,112302,11710],{},[902,112304,112305],{"encoding":904},"P = -4Q + 80",[883,112307,112309],{"className":112308},[886],[888,112310,112311],{"xmlns":890},[892,112312,112313,112327],{},[895,112314,112315,112317,112319,112321,112323,112325],{},[898,112316,1690],{},[1716,112318,1913],{},[1712,112320,7072],{},[898,112322,1878],{},[1716,112324,1949],{},[1712,112326,2998],{},[902,112328,112329],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,112332,112334],{"className":112333},[886],[888,112335,112336],{"xmlns":890},[892,112337,112338,112346],{},[895,112339,112340,112342,112344],{},[898,112341,4164],{},[1716,112343,1913],{},[1712,112345,7109],{},[902,112347,12826],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,112350,112351,112352,112354,112355,112357],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,112353,10229],{}," (posun poptávky při zdanění kupujícího) a ",[38,112356,10263],{}," (posun nabídky při zdanění výrobce).",[1855,112359],{},[115,112361,14947],{"id":14946},[120,112363,112364,112383,112441,112498,112581,112627,112670,112715,112781],{},[123,112365,112366,3495,112369,112382],{},[38,112367,112368],{},"Jednotková daň",[883,112370,112372],{"className":112371},[886],[888,112373,112374],{"xmlns":890},[892,112375,112376,112380],{},[895,112377,112378],{},[898,112379,4164],{},[902,112381,4164],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,112384,112385,112387,112388,112426,112427,112440],{},[38,112386,108774],{}," — posun nabídky ",[883,112389,112391],{"className":112390},[886],[888,112392,112393],{"xmlns":890},[892,112394,112395,112423],{},[895,112396,112397,112403,112405,112407,112409,112411,112413,112415,112417,112419,112421],{},[1707,112398,112399,112401],{},[898,112400,5352],{},[1712,112402,1714],{},[1716,112404,1920],{"stretchy":1919},[898,112406,1878],{},[1716,112408,1925],{"stretchy":1919},[1716,112410,1913],{},[898,112412,5352],{},[1716,112414,1920],{"stretchy":1919},[898,112416,1878],{},[1716,112418,1925],{"stretchy":1919},[1716,112420,1949],{},[898,112422,4164],{},[902,112424,112425],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,112428,112430],{"className":112429},[886],[888,112431,112432],{"xmlns":890},[892,112433,112434,112438],{},[895,112435,112436],{},[898,112437,4164],{},[902,112439,4164],{"encoding":904}," svisle nahoru)",[123,112442,112443,112445,112446,112426,112484,112497],{},[38,112444,109847],{}," — posun poptávky ",[883,112447,112449],{"className":112448},[886],[888,112450,112451],{"xmlns":890},[892,112452,112453,112481],{},[895,112454,112455,112461,112463,112465,112467,112469,112471,112473,112475,112477,112479],{},[1707,112456,112457,112459],{},[898,112458,1916],{},[1712,112460,1726],{},[1716,112462,1920],{"stretchy":1919},[898,112464,1878],{},[1716,112466,1925],{"stretchy":1919},[1716,112468,1913],{},[898,112470,1916],{},[1716,112472,1920],{"stretchy":1919},[898,112474,1878],{},[1716,112476,1925],{"stretchy":1919},[1716,112478,2760],{},[898,112480,4164],{},[902,112482,112483],{"encoding":904},"D_2(Q) = D(Q) - T",[883,112485,112487],{"className":112486},[886],[888,112488,112489],{"xmlns":890},[892,112490,112491,112495],{},[895,112492,112493],{},[898,112494,4164],{},[902,112496,4164],{"encoding":904}," svisle dolů)",[123,112499,112500,3369,112503,6784,112542],{},[38,112501,112502],{},"Rovnovážný bod s daní",[883,112504,112506],{"className":112505},[886],[888,112507,112508],{"xmlns":890},[892,112509,112510,112540],{},[895,112511,112512,112518,112520,112528,112530,112538],{},[1707,112513,112514,112516],{},[898,112515,1805],{},[1712,112517,1714],{},[1716,112519,2502],{"stretchy":1919},[7204,112521,112522,112524,112526],{},[898,112523,1878],{},[1712,112525,1714],{},[898,112527,1805],{},[1716,112529,1719],{"separator":1718},[7204,112531,112532,112534,112536],{},[898,112533,1690],{},[1712,112535,1714],{},[898,112537,1805],{},[1716,112539,2516],{"stretchy":1919},[902,112541,108942],{"encoding":904},[883,112543,112545],{"className":112544},[886],[888,112546,112547],{"xmlns":890},[892,112548,112549,112579],{},[895,112550,112551,112557,112559,112567,112569,112577],{},[1707,112552,112553,112555],{},[898,112554,1805],{},[1712,112556,1726],{},[1716,112558,2502],{"stretchy":1919},[7204,112560,112561,112563,112565],{},[898,112562,1878],{},[1712,112564,1726],{},[898,112566,1805],{},[1716,112568,1719],{"separator":1718},[7204,112570,112571,112573,112575],{},[898,112572,1690],{},[1712,112574,1726],{},[898,112576,1805],{},[1716,112578,2516],{"stretchy":1919},[902,112580,110017],{"encoding":904},[123,112582,112583,1994,112585,112587,112588],{},[38,112584,7639],{},[614,112586,110797],{},") — rozklad ",[883,112589,112591],{"className":112590},[886],[888,112592,112593],{"xmlns":890},[892,112594,112595,112625],{},[895,112596,112597,112599,112601,112611,112613],{},[898,112598,4164],{},[1716,112600,1913],{},[1707,112602,112603,112605],{},[898,112604,4164],{},[895,112606,112607,112609],{},[898,112608,7658],{},[898,112610,724],{},[1716,112612,1949],{},[1707,112614,112615,112617],{},[898,112616,4164],{},[895,112618,112619,112621,112623],{},[898,112620,7681],{},[898,112622,7684],{},[898,112624,2098],{},[902,112626,7826],{"encoding":904},[123,112628,112629,112652,112653,1925],{},[38,112630,112631],{},[883,112632,112634],{"className":112633},[886],[888,112635,112636],{"xmlns":890},[892,112637,112638,112650],{},[895,112639,112640],{},[1707,112641,112642,112644],{},[898,112643,4164],{},[895,112645,112646,112648],{},[898,112647,7658],{},[898,112649,724],{},[902,112651,7663],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,112654,112656],{"className":112655},[886],[888,112657,112658],{"xmlns":890},[892,112659,112660,112668],{},[895,112661,112662],{},[3074,112663,112664,112666],{},[898,112665,1690],{},[898,112667,1805],{},[902,112669,6432],{"encoding":904},[123,112671,112672,112697,112698,1925],{},[38,112673,112674],{},[883,112675,112677],{"className":112676},[886],[888,112678,112679],{"xmlns":890},[892,112680,112681,112695],{},[895,112682,112683],{},[1707,112684,112685,112687],{},[898,112686,4164],{},[895,112688,112689,112691,112693],{},[898,112690,7681],{},[898,112692,7684],{},[898,112694,2098],{},[902,112696,7689],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,112699,112701],{"className":112700},[886],[888,112702,112703],{"xmlns":890},[892,112704,112705,112713],{},[895,112706,112707],{},[3074,112708,112709,112711],{},[898,112710,1690],{},[898,112712,1805],{},[902,112714,6432],{"encoding":904},[123,112716,112717,3369,112719,1343,112748],{},[38,112718,15494],{},[883,112720,112722],{"className":112721},[886],[888,112723,112724],{"xmlns":890},[892,112725,112726,112746],{},[895,112727,112728,112736,112738],{},[7204,112729,112730,112732,112734],{},[898,112731,1878],{},[1712,112733,1714],{},[898,112735,1805],{},[1716,112737,1913],{},[7204,112739,112740,112742,112744],{},[898,112741,1878],{},[1712,112743,1726],{},[898,112745,1805],{},[902,112747,7890],{"encoding":904},[883,112749,112751],{"className":112750},[886],[888,112752,112753],{"xmlns":890},[892,112754,112755,112779],{},[895,112756,112757,112765,112767,112769,112771],{},[7204,112758,112759,112761,112763],{},[898,112760,1690],{},[1712,112762,1714],{},[898,112764,1805],{},[1716,112766,2760],{},[898,112768,4164],{},[1716,112770,1913],{},[7204,112772,112773,112775,112777],{},[898,112774,1690],{},[1712,112776,1726],{},[898,112778,1805],{},[902,112780,7924],{"encoding":904},[123,112782,112783,112786],{},[38,112784,112785],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[1855,112788],{},[115,112790,15740],{"id":15739},[120,112792,112793,112801,112819,112826],{},[123,112794,112795,3495,112798],{},[38,112796,112797],{},"Kontext (hub):",[207,112799,802],{"className":112800,"dataFsResolvedFilePath":800,"href":801},[210],[123,112802,112803,3495,112805,112808,112809,8373,112811,112814,112815,112818],{},[38,112804,15747],{},[207,112806,820],{"className":112807,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,112810,67788],{},[207,112812,15758],{"className":112813,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,112816,15775],{"className":112817,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,112820,112821,3495,112823],{},[38,112822,15785],{},[207,112824,15789],{"className":112825,"dataFsResolvedFilePath":745,"href":746},[210],[123,112827,112828,3495,112830],{},[38,112829,15794],{},[207,112831,15800],{"className":112832,"dataFsResolvedFilePath":15798,"href":15799},[210],{"title":641,"searchDepth":642,"depth":642,"links":112834},[112835,112836,112839,112842,112846,112847,112848,112849],{"id":108679,"depth":642,"text":108680},{"id":108773,"depth":642,"text":108774,"children":112837},[112838],{"id":109164,"depth":649,"text":10304},{"id":109846,"depth":642,"text":109847,"children":112840},[112841],{"id":110323,"depth":649,"text":10385},{"id":110790,"depth":642,"text":7639,"children":112843},[112844,112845],{"id":16327,"depth":649,"text":16328},{"id":111133,"depth":649,"text":111134},{"id":111606,"depth":642,"text":111607},{"id":112203,"depth":642,"text":112204},{"id":14946,"depth":642,"text":14947},{"id":15739,"depth":642,"text":15740},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":108577,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,15856,112856,112857,112858,30029],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[112861,112863,112865,112869,112873,112877,112879,112881],{"slug":3533,"path":849,"title":17711,"snippet":112862},"… oru\", tabulku českých příkladů (MHD, privátní značky, Májka…) a kontextovou závislost viz \u003C\u003Cpoptavka-nabidka>>. ### Procentní a nominální odhady změn Pro procentní odhady při změně jedné proměnné (a …",{"slug":1128,"path":15799,"title":681,"snippet":112864},"… a-metoda|Lagrangeova metoda]] — vázané extrémy, multiplikátor jako náklady příležitosti - \u003C\u003Cpoptavka-nabidka>> — modely D a S, rovnováha, multiplikátory - Zdanění trhu — daň výrobci v …",{"slug":112866,"path":746,"title":112867,"snippet":112868},"imek-blok-01","KS 1. blok — Kalkul a mikroekonomie","… -metoda|Lagrangeova metoda]] — vázané extrémy, multiplikátor jako náklady příležitosti 6. \u003C\u003Cpoptavka-nabidka>> — modely D, S, tržní rovnováha, multiplikátory, přebytky, zdanění 7. [[prijem-naklady-zis …",{"slug":112870,"path":1109,"title":112871,"snippet":112872},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… tek spotřebitele a výrobce. Obsahuje **Příklady 2.1–2.13** a **Úlohy 2.1–2.18**. Topiky: \u003C\u003Cpoptavka-nabidka>>, prebytek-spotrebitele-vyrobce. ### Kapitola 3 — Příjem, náklady, zisk, nabídka firm …",{"slug":112874,"path":959,"title":112875,"snippet":112876},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… jdeš úplné odvození, příklady a úlohy. --- ## 1. 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