[{"data":1,"prerenderedAt":109054},["ShallowReactive",2],{"sidebar-courses-with-stats":3,"wiki-narodni-duchod":1626,"course-stats-imek":11667,"course-topics-imek":11671,"backlinks-narodni-duchod":109029,"related-narodni-duchod":109047},{"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":11666},{"id":1628,"title":936,"body":1629,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":11653,"navigation":664,"path":11654,"seo":11655,"sources":11656,"stem":11657,"tags":11658,"type":11664,"updated":677,"__hash__":11665},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":9,"value":1630,"toc":11614},[1631,1634,1638,1784,1927,1931,1934,2056,2060,2089,2138,2141,2207,2252,2255,2282,2314,2318,2322,2367,2411,2475,2530,2533,2537,2540,2588,2692,2798,2804,2881,2910,3050,3054,3084,3134,3283,3373,3377,3403,3443,3470,3508,3570,3648,3726,3785,3853,3897,3901,3961,4010,4055,4272,4393,4399,4403,4427,4431,4440,4444,4475,4510,4514,4565,4653,4696,4717,4780,4840,4844,4916,4984,5056,5174,5222,5226,5229,5270,5309,5333,5448,5615,5623,5650,5680,5683,5760,5913,5998,6338,6342,6470,6606,6743,6799,6802,7052,7133,7137,7140,7198,7230,7233,7282,7285,7356,7552,7556,7708,7942,7980,8034,8080,8083,8139,8189,8394,8484,8488,8504,8511,8681,8685,8756,8838,8919,8998,9144,9232,9236,9424,9562,9610,9710,9714,10458,10462,11521,11525],[12,1632,936],{"id":1633},"národní-důchod",[115,1635,1637],{"id":1636},"tldr","TL;DR",[724,1639,1640,1641,1647,1648,1651,1652,1647,1655,1669,1670,1673,1674,1677,1678,1681,1682,1685,1686,1647,1689,1709,1710,1727,1728,1731,1732,1783],{},"Kapitola 7 ",[207,1642,1646],{"className":1643,"dataFsResolvedFilePath":1644,"href":1645},[210],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematické ekonomie"," ",[38,1649,1650],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[38,1653,1654],{},"národním důchodem",[883,1656,1658],{"className":1657},[886],[888,1659,1660],{"xmlns":890},[892,1661,1662,1667],{},[895,1663,1664],{},[898,1665,1666],{},"Y",[902,1668,1666],{"encoding":904},". Budují se postupně bohatší modely — ",[38,1671,1672],{},"C-I"," (jen spotřeba a investice) → ",[38,1675,1676],{},"C-I-G"," (přidá vládu a zdanění) → ",[38,1679,1680],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[38,1683,1684],{},"IS-LM"," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[38,1687,1688],{},"rovnovážný důchod",[883,1690,1692],{"className":1691},[886],[888,1693,1694],{"xmlns":890},[892,1695,1696,1706],{},[895,1697,1698],{},[1699,1700,1701,1703],"msup",{},[898,1702,1666],{},[898,1704,1705],{},"E",[902,1707,1708],{"encoding":904},"Y^E"," jako řešení soustavy lineárních rovnic; citlivost ",[883,1711,1713],{"className":1712},[886],[888,1714,1715],{"xmlns":890},[892,1716,1717,1725],{},[895,1718,1719],{},[1699,1720,1721,1723],{},[898,1722,1666],{},[898,1724,1705],{},[902,1726,1708],{"encoding":904}," na exogenní veličiny popisují ",[38,1729,1730],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[883,1733,1735],{"className":1734},[886],[888,1736,1737],{"xmlns":890},[892,1738,1739,1780],{},[895,1740,1741,1745,1749,1754,1756,1759,1761,1764,1767,1769,1771,1774,1777],{},[1742,1743,1744],"mn",{},"1",[898,1746,1748],{"mathvariant":1747},"normal","\u002F",[1750,1751,1753],"mo",{"stretchy":1752},"false","(",[1742,1755,1744],{},[1750,1757,1758],{},"−",[898,1760,207],{},[1750,1762,1763],{"stretchy":1752},")",[1750,1765,1766],{},"=",[1742,1768,1744],{},[898,1770,1748],{"mathvariant":1747},[898,1772,1773],{},"M",[898,1775,1776],{},"P",[898,1778,1779],{},"S",[902,1781,1782],{"encoding":904},"1\u002F(1-a) = 1\u002FMPS",").",[1785,1786,1787],"blockquote",{},[724,1788,1789,1792,1793,1796,1797,1816,1817,1847,1848,1897,1898,1900,1901,1926],{},[883,1790,1791],{},"!info"," Intuice\n",[38,1794,1795],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[883,1798,1800],{"className":1799},[886],[888,1801,1802],{"xmlns":890},[892,1803,1804,1813],{},[895,1805,1806,1808,1810],{},[898,1807,1773],{},[898,1809,1776],{},[898,1811,1812],{},"C",[902,1814,1815],{"encoding":904},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[883,1818,1820],{"className":1819},[886],[888,1821,1822],{"xmlns":890},[892,1823,1824,1844],{},[895,1825,1826,1828,1830,1832,1834,1836,1838,1840,1842],{},[898,1827,1773],{},[898,1829,1776],{},[898,1831,1779],{},[1750,1833,1766],{},[1742,1835,1744],{},[1750,1837,1758],{},[898,1839,1773],{},[898,1841,1776],{},[898,1843,1812],{},[902,1845,1846],{"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 ",[883,1849,1851],{"className":1850},[886],[888,1852,1853],{"xmlns":890},[892,1854,1855,1894],{},[895,1856,1857,1859,1862,1864,1866,1873,1875,1878,1880,1882,1884,1886,1888,1890,1892],{},[1742,1858,1744],{},[1750,1860,1861],{},"+",[898,1863,207],{},[1750,1865,1861],{},[1699,1867,1868,1870],{},[898,1869,207],{},[1742,1871,1872],{},"2",[1750,1874,1861],{},[1750,1876,1877],{},"⋯",[1750,1879,1766],{},[1742,1881,1744],{},[898,1883,1748],{"mathvariant":1747},[1750,1885,1753],{"stretchy":1752},[1742,1887,1744],{},[1750,1889,1758],{},[898,1891,207],{},[1750,1893,1763],{"stretchy":1752},[902,1895,1896],{"encoding":904},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[38,1899,1684],{}," 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 ",[883,1902,1904],{"className":1903},[886],[888,1905,1906],{"xmlns":890},[892,1907,1908,1923],{},[895,1909,1910,1912,1914,1918,1921],{},[1750,1911,1753],{"stretchy":1752},[898,1913,1666],{},[1750,1915,1917],{"separator":1916},"true",",",[898,1919,1920],{},"r",[1750,1922,1763],{"stretchy":1752},[902,1924,1925],{"encoding":904},"(Y, r)"," jsou oba trhy v rovnováze současně.",[115,1928,1930],{"id":1929},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[724,1932,1933],{},"Po prostudování kapitoly by čtenář měl umět:",[120,1935,1936,1939,1942,1945,1948,1951,1954,2053],{},[123,1937,1938],{},"popsat zjednodušený model národní ekonomiky,",[123,1940,1941],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[123,1943,1944],{},"popsat lineární model spotřeby a úspor,",[123,1946,1947],{},"stanovit mezní sklony ke spotřebě a úsporám,",[123,1949,1950],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[123,1952,1953],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[123,1955,1956,1957,1343,1978,1343,2001,2028,2029,2052],{},"popsat modely ",[883,1958,1960],{"className":1959},[886],[888,1961,1962],{"xmlns":890},[892,1963,1964,1975],{},[895,1965,1966,1968,1972],{},[898,1967,1812],{},[1969,1970,1971],"mtext",{},"-",[898,1973,1974],{},"I",[902,1976,1977],{"encoding":904},"C\\text{-}I",[883,1979,1981],{"className":1980},[886],[888,1982,1983],{"xmlns":890},[892,1984,1985,1998],{},[895,1986,1987,1989,1991,1993,1995],{},[898,1988,1812],{},[1969,1990,1971],{},[898,1992,1974],{},[1969,1994,1971],{},[898,1996,1997],{},"G",[902,1999,2000],{"encoding":904},"C\\text{-}I\\text{-}G",[883,2002,2004],{"className":2003},[886],[888,2005,2006],{"xmlns":890},[892,2007,2008,2025],{},[895,2009,2010,2012,2014,2016,2018,2020,2022],{},[898,2011,1812],{},[1969,2013,1971],{},[898,2015,1974],{},[1969,2017,1971],{},[898,2019,1997],{},[1969,2021,1971],{},[898,2023,2024],{},"X",[902,2026,2027],{"encoding":904},"C\\text{-}I\\text{-}G\\text{-}X"," a ",[883,2030,2032],{"className":2031},[886],[888,2033,2034],{"xmlns":890},[892,2035,2036,2049],{},[895,2037,2038,2040,2042,2044,2047],{},[898,2039,1974],{},[898,2041,1779],{},[1969,2043,1971],{},[898,2045,2046],{},"L",[898,2048,1773],{},[902,2050,2051],{"encoding":904},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[123,2054,2055],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[115,2057,2059],{"id":2058},"gnp-a-národní-důchod","GNP a národní důchod",[724,2061,2062,1647,2065,2084,2085,2088],{},[38,2063,2064],{},"Hrubý národní produkt",[883,2066,2068],{"className":2067},[886],[888,2069,2070],{"xmlns":890},[892,2071,2072,2081],{},[895,2073,2074,2076,2079],{},[898,2075,1997],{},[898,2077,2078],{},"N",[898,2080,1776],{},[902,2082,2083],{"encoding":904},"GNP"," (",[614,2086,2087],{},"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:",[724,2090,2091],{},[883,2092,2094],{"className":2093},[886],[888,2095,2096],{"xmlns":890},[892,2097,2098,2135],{},[895,2099,2100,2102,2104,2106,2108,2110,2112,2114,2116,2118,2120,2122,2124,2128,2130,2133],{},[898,2101,1997],{},[898,2103,2078],{},[898,2105,1776],{},[1750,2107,1766],{},[898,2109,1812],{},[1750,2111,1861],{},[898,2113,1974],{},[1750,2115,1861],{},[898,2117,1997],{},[1750,2119,1861],{},[898,2121,2024],{},[1750,2123,1917],{"separator":1916},[2125,2126],"mspace",{"width":2127},"2em",[1750,2129,1753],{"stretchy":1752},[1742,2131,2132],{},"7.1",[1750,2134,1763],{"stretchy":1752},[902,2136,2137],{"encoding":904},"GNP = C + I + G + X, \\qquad (7.1)",[724,2139,2140],{},"kde",[120,2142,2143,2159,2175,2191],{},[123,2144,2145,2158],{},[883,2146,2148],{"className":2147},[886],[888,2149,2150],{"xmlns":890},[892,2151,2152,2156],{},[895,2153,2154],{},[898,2155,1812],{},[902,2157,1812],{"encoding":904}," — výdaje domácností na spotřebu,",[123,2160,2161,2174],{},[883,2162,2164],{"className":2163},[886],[888,2165,2166],{"xmlns":890},[892,2167,2168,2172],{},[895,2169,2170],{},[898,2171,1974],{},[902,2173,1974],{"encoding":904}," — hrubé domácí investice,",[123,2176,2177,2190],{},[883,2178,2180],{"className":2179},[886],[888,2181,2182],{"xmlns":890},[892,2183,2184,2188],{},[895,2185,2186],{},[898,2187,1997],{},[902,2189,1997],{"encoding":904}," — vládní výdaje,",[123,2192,2193,2206],{},[883,2194,2196],{"className":2195},[886],[888,2197,2198],{"xmlns":890},[892,2199,2200,2204],{},[895,2201,2202],{},[898,2203,2024],{},[902,2205,2024],{"encoding":904}," — čistý export.",[724,2208,2209,2210,2227,2228,2231,2232,1647,2235,2084,2248,2251],{},"K měření ",[883,2211,2213],{"className":2212},[886],[888,2214,2215],{"xmlns":890},[892,2216,2217,2225],{},[895,2218,2219,2221,2223],{},[898,2220,1997],{},[898,2222,2078],{},[898,2224,1776],{},[902,2226,2083],{"encoding":904}," se užívá ",[38,2229,2230],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[38,2233,2234],{},"národní důchod",[883,2236,2238],{"className":2237},[886],[888,2239,2240],{"xmlns":890},[892,2241,2242,2246],{},[895,2243,2244],{},[898,2245,1666],{},[902,2247,1666],{"encoding":904},[614,2249,2250],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[724,2253,2254],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[724,2256,2257],{},[883,2258,2260],{"className":2259},[886],[888,2261,2262],{"xmlns":890},[892,2263,2264,2279],{},[895,2265,2266,2268,2270,2272,2275,2277],{},[898,2267,1997],{},[898,2269,2078],{},[898,2271,1776],{},[1750,2273,2274],{},"≈",[898,2276,1666],{},[1750,2278,1917],{"separator":1916},[902,2280,2281],{"encoding":904},"GNP \\approx Y,",[724,2283,2284,2285,2084,2288,2291,2292,2305,2306,2309,2310,2313],{},"a užívá se společného názvu ",[38,2286,2287],{},"důchod",[614,2289,2290],{},"income",") s označením ",[883,2293,2295],{"className":2294},[886],[888,2296,2297],{"xmlns":890},[892,2298,2299,2303],{},[895,2300,2301],{},[898,2302,1666],{},[902,2304,1666],{"encoding":904},". Domácnosti důchod použijí ke ",[38,2307,2308],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[38,2311,2312],{},"úspor",".",[115,2315,2317],{"id":2316},"spotřeba-a-úspory","Spotřeba a úspory",[198,2319,2321],{"id":2320},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[724,2323,2324,2325,2338,2339,2352,2353,2366],{},"Jak spotřeba ",[883,2326,2328],{"className":2327},[886],[888,2329,2330],{"xmlns":890},[892,2331,2332,2336],{},[895,2333,2334],{},[898,2335,1812],{},[902,2337,1812],{"encoding":904},", tak úspory ",[883,2340,2342],{"className":2341},[886],[888,2343,2344],{"xmlns":890},[892,2345,2346,2350],{},[895,2347,2348],{},[898,2349,1779],{},[902,2351,1779],{"encoding":904}," závisejí na důchodu ",[883,2354,2356],{"className":2355},[886],[888,2357,2358],{"xmlns":890},[892,2359,2360,2364],{},[895,2361,2362],{},[898,2363,1666],{},[902,2365,1666],{"encoding":904},":",[724,2368,2369],{},[883,2370,2372],{"className":2371},[886],[888,2373,2374],{"xmlns":890},[892,2375,2376,2408],{},[895,2377,2378,2380,2382,2384,2386,2388,2390,2392,2394,2396,2398,2400,2402,2404,2406],{},[898,2379,1812],{},[1750,2381,1766],{},[898,2383,1812],{},[1750,2385,1753],{"stretchy":1752},[898,2387,1666],{},[1750,2389,1763],{"stretchy":1752},[1750,2391,1917],{"separator":1916},[2125,2393],{"width":2127},[898,2395,1779],{},[1750,2397,1766],{},[898,2399,1779],{},[1750,2401,1753],{"stretchy":1752},[898,2403,1666],{},[1750,2405,1763],{"stretchy":1752},[898,2407,2313],{"mathvariant":1747},[902,2409,2410],{"encoding":904},"C = C(Y), \\qquad S = S(Y).",[724,2412,2413,2433,2434,2084,2437,2440,2441,2433,2461,2084,2464,2467,2468,2028,2471,2474],{},[883,2414,2416],{"className":2415},[886],[888,2417,2418],{"xmlns":890},[892,2419,2420,2430],{},[895,2421,2422,2424,2426,2428],{},[898,2423,1812],{},[1750,2425,1753],{"stretchy":1752},[898,2427,1666],{},[1750,2429,1763],{"stretchy":1752},[902,2431,2432],{"encoding":904},"C(Y)"," je ",[38,2435,2436],{},"funkce spotřeby",[614,2438,2439],{},"consumption function","), ",[883,2442,2444],{"className":2443},[886],[888,2445,2446],{"xmlns":890},[892,2447,2448,2458],{},[895,2449,2450,2452,2454,2456],{},[898,2451,1779],{},[1750,2453,1753],{"stretchy":1752},[898,2455,1666],{},[1750,2457,1763],{"stretchy":1752},[902,2459,2460],{"encoding":904},"S(Y)",[38,2462,2463],{},"funkce úspor",[614,2465,2466],{},"savings function","); jejich grafy se nazývají ",[38,2469,2470],{},"křivka spotřeby",[38,2472,2473],{},"křivka úspor",". Platí základní identita",[724,2476,2477],{},[883,2478,2480],{"className":2479},[886],[888,2481,2482],{"xmlns":890},[892,2483,2484,2527],{},[895,2485,2486,2488,2490,2492,2494,2496,2498,2500,2502,2504,2506,2508,2510,2512,2514,2516,2518,2520,2522,2525],{},[898,2487,1666],{},[1750,2489,1766],{},[898,2491,1812],{},[1750,2493,1861],{},[898,2495,1779],{},[1750,2497,1766],{},[898,2499,1812],{},[1750,2501,1753],{"stretchy":1752},[898,2503,1666],{},[1750,2505,1763],{"stretchy":1752},[1750,2507,1861],{},[898,2509,1779],{},[1750,2511,1753],{"stretchy":1752},[898,2513,1666],{},[1750,2515,1763],{"stretchy":1752},[898,2517,2313],{"mathvariant":1747},[2125,2519],{"width":2127},[1750,2521,1753],{"stretchy":1752},[1742,2523,2524],{},"7.2",[1750,2526,1763],{"stretchy":1752},[902,2528,2529],{"encoding":904},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[724,2531,2532],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[198,2534,2536],{"id":2535},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[724,2538,2539],{},"Nejjednodušší model předpokládá lineární tvar",[724,2541,2542],{},[883,2543,2545],{"className":2544},[886],[888,2546,2547],{"xmlns":890},[892,2548,2549,2585],{},[895,2550,2551,2553,2555,2557,2559,2561,2563,2565,2567,2569,2571,2574,2576,2578,2580,2583],{},[898,2552,1812],{},[1750,2554,1766],{},[898,2556,1812],{},[1750,2558,1753],{"stretchy":1752},[898,2560,1666],{},[1750,2562,1763],{"stretchy":1752},[1750,2564,1766],{},[898,2566,207],{},[898,2568,1666],{},[1750,2570,1861],{},[898,2572,2573],{},"b",[1750,2575,1917],{"separator":1916},[2125,2577],{"width":2127},[1750,2579,1753],{"stretchy":1752},[1742,2581,2582],{},"7.3",[1750,2584,1763],{"stretchy":1752},[902,2586,2587],{"encoding":904},"C = C(Y) = aY + b, \\qquad (7.3)",[724,2589,2590,2591,2028,2611,2634,2635,2678,2679,2313],{},"kde ",[883,2592,2594],{"className":2593},[886],[888,2595,2596],{"xmlns":890},[892,2597,2598,2608],{},[895,2599,2600,2602,2605],{},[898,2601,2573],{},[1750,2603,2604],{},">",[1742,2606,2607],{},"0",[902,2609,2610],{"encoding":904},"b > 0",[883,2612,2614],{"className":2613},[886],[888,2615,2616],{"xmlns":890},[892,2617,2618,2631],{},[895,2619,2620,2622,2625,2627,2629],{},[1742,2621,2607],{},[1750,2623,2624],{},"\u003C",[898,2626,207],{},[1750,2628,2624],{},[1742,2630,1744],{},[902,2632,2633],{"encoding":904},"0 \u003C a \u003C 1",". Směrnice ",[883,2636,2638],{"className":2637},[886],[888,2639,2640],{"xmlns":890},[892,2641,2642,2675],{},[895,2643,2644,2646,2648,2656,2659,2662,2664,2667,2669,2671,2673],{},[898,2645,207],{},[1750,2647,1766],{},[895,2649,2650,2653],{},[898,2651,2652],{"mathvariant":1747},"t",[898,2654,2655],{"mathvariant":1747},"g",[1969,2657,2658],{}," ",[898,2660,2661],{},"α",[1750,2663,1766],{},[898,2665,2666],{"mathvariant":1747},"Δ",[898,2668,1812],{},[898,2670,1748],{"mathvariant":1747},[898,2672,2666],{"mathvariant":1747},[898,2674,1666],{},[902,2676,2677],{"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 ",[883,2680,2682],{"className":2681},[886],[888,2683,2684],{"xmlns":890},[892,2685,2686,2690],{},[895,2687,2688],{},[898,2689,1666],{},[902,2691,1666],{"encoding":904},[724,2693,2694],{},[614,2695,2696,2697,2721,2722,2760,2761,2777,2778,2313],{},"Obrázek 7.1 — Přímka spotřeby ",[883,2698,2700],{"className":2699},[886],[888,2701,2702],{"xmlns":890},[892,2703,2704,2718],{},[895,2705,2706,2708,2710,2712,2714,2716],{},[898,2707,1812],{},[1750,2709,1766],{},[898,2711,207],{},[898,2713,1666],{},[1750,2715,1861],{},[898,2717,2573],{},[902,2719,2720],{"encoding":904},"C = aY + b"," se směrnicí ",[883,2723,2725],{"className":2724},[886],[888,2726,2727],{"xmlns":890},[892,2728,2729,2757],{},[895,2730,2731,2733,2735,2741,2743,2745,2747,2749,2751,2753,2755],{},[898,2732,207],{},[1750,2734,1766],{},[895,2736,2737,2739],{},[898,2738,2652],{"mathvariant":1747},[898,2740,2655],{"mathvariant":1747},[1969,2742,2658],{},[898,2744,2661],{},[1750,2746,1766],{},[898,2748,2666],{"mathvariant":1747},[898,2750,1812],{},[898,2752,1748],{"mathvariant":1747},[898,2754,2666],{"mathvariant":1747},[898,2756,1666],{},[902,2758,2759],{"encoding":904},"a = \\mathrm{tg}\\,\\alpha = \\Delta C\u002F\\Delta Y","; znázornění ",[883,2762,2764],{"className":2763},[886],[888,2765,2766],{"xmlns":890},[892,2767,2768,2774],{},[895,2769,2770,2772],{},[898,2771,2666],{"mathvariant":1747},[898,2773,1812],{},[902,2775,2776],{"encoding":904},"\\Delta C"," při jednotkovém přírůstku ",[883,2779,2781],{"className":2780},[886],[888,2782,2783],{"xmlns":890},[892,2784,2785,2795],{},[895,2786,2787,2789,2791,2793],{},[898,2788,2666],{"mathvariant":1747},[898,2790,1666],{},[1750,2792,1766],{},[1742,2794,1744],{},[902,2796,2797],{"encoding":904},"\\Delta Y = 1",[724,2799,2800,2801,2366],{},"Dosazením do (7.2) plyne ",[38,2802,2803],{},"lineární model úspor",[724,2805,2806],{},[883,2807,2809],{"className":2808},[886],[888,2810,2811],{"xmlns":890},[892,2812,2813,2878],{},[895,2814,2815,2817,2819,2821,2823,2825,2827,2829,2831,2833,2835,2837,2839,2841,2843,2845,2847,2849,2851,2853,2855,2857,2859,2861,2863,2865,2867,2869,2871,2873,2876],{},[898,2816,1779],{},[1750,2818,1766],{},[898,2820,1666],{},[1750,2822,1758],{},[898,2824,1812],{},[1750,2826,1753],{"stretchy":1752},[898,2828,1666],{},[1750,2830,1763],{"stretchy":1752},[1750,2832,1766],{},[898,2834,1666],{},[1750,2836,1758],{},[1750,2838,1753],{"stretchy":1752},[898,2840,207],{},[898,2842,1666],{},[1750,2844,1861],{},[898,2846,2573],{},[1750,2848,1763],{"stretchy":1752},[1750,2850,1766],{},[1750,2852,1753],{"stretchy":1752},[1742,2854,1744],{},[1750,2856,1758],{},[898,2858,207],{},[1750,2860,1763],{"stretchy":1752},[898,2862,1666],{},[1750,2864,1758],{},[898,2866,2573],{},[898,2868,2313],{"mathvariant":1747},[2125,2870],{"width":2127},[1750,2872,1753],{"stretchy":1752},[1742,2874,2875],{},"7.4",[1750,2877,1763],{"stretchy":1752},[902,2879,2880],{"encoding":904},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[724,2882,2883,2884,1783],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[883,2885,2887],{"className":2886},[886],[888,2888,2889],{"xmlns":890},[892,2890,2891,2907],{},[895,2892,2893,2895,2897,2899,2901,2903,2905],{},[1742,2894,2607],{},[1750,2896,2624],{},[1742,2898,1744],{},[1750,2900,1758],{},[898,2902,207],{},[1750,2904,2624],{},[1742,2906,1744],{},[902,2908,2909],{"encoding":904},"0 \u003C 1 - a \u003C 1",[724,2911,2912],{},[614,2913,2914,2915,2028,2938,2970,2971,2984,2985,3015,3016,2984,3034,2313],{},"Obrázek 7.2 — Přímky ",[883,2916,2918],{"className":2917},[886],[888,2919,2920],{"xmlns":890},[892,2921,2922,2936],{},[895,2923,2924,2926,2928,2930,2932,2934],{},[898,2925,1812],{},[1750,2927,1766],{},[898,2929,207],{},[898,2931,1666],{},[1750,2933,1861],{},[898,2935,2573],{},[902,2937,2720],{"encoding":904},[883,2939,2941],{"className":2940},[886],[888,2942,2943],{"xmlns":890},[892,2944,2945,2967],{},[895,2946,2947,2949,2951,2953,2955,2957,2959,2961,2963,2965],{},[898,2948,1779],{},[1750,2950,1766],{},[1750,2952,1753],{"stretchy":1752},[1742,2954,1744],{},[1750,2956,1758],{},[898,2958,207],{},[1750,2960,1763],{"stretchy":1752},[898,2962,1666],{},[1750,2964,1758],{},[898,2966,2573],{},[902,2968,2969],{"encoding":904},"S = (1-a)Y - b",". Přímka úspor protíná osu ",[883,2972,2974],{"className":2973},[886],[888,2975,2976],{"xmlns":890},[892,2977,2978,2982],{},[895,2979,2980],{},[898,2981,1666],{},[902,2983,1666],{"encoding":904}," v bodě ",[883,2986,2988],{"className":2987},[886],[888,2989,2990],{"xmlns":890},[892,2991,2992,3012],{},[895,2993,2994,2996,2998,3000,3002,3004,3006,3008,3010],{},[898,2995,1666],{},[1750,2997,1766],{},[898,2999,2573],{},[898,3001,1748],{"mathvariant":1747},[1750,3003,1753],{"stretchy":1752},[1742,3005,1744],{},[1750,3007,1758],{},[898,3009,207],{},[1750,3011,1763],{"stretchy":1752},[902,3013,3014],{"encoding":904},"Y = b\u002F(1-a)"," a osu ",[883,3017,3019],{"className":3018},[886],[888,3020,3021],{"xmlns":890},[892,3022,3023,3031],{},[895,3024,3025,3027,3029],{},[898,3026,1812],{},[1750,3028,1917],{"separator":1916},[898,3030,1779],{},[902,3032,3033],{"encoding":904},"C, S",[883,3035,3037],{"className":3036},[886],[888,3038,3039],{"xmlns":890},[892,3040,3041,3047],{},[895,3042,3043,3045],{},[1750,3044,1758],{},[898,3046,2573],{},[902,3048,3049],{"encoding":904},"-b",[198,3051,3053],{"id":3052},"příklad-71","Příklad 7.1",[724,3055,3056,3057,3083],{},"Pro spotřebu ",[883,3058,3060],{"className":3059},[886],[888,3061,3062],{"xmlns":890},[892,3063,3064,3080],{},[895,3065,3066,3068,3070,3073,3075,3077],{},[898,3067,1812],{},[1750,3069,1766],{},[1742,3071,3072],{},"0,4",[898,3074,1666],{},[1750,3076,1861],{},[1742,3078,3079],{},"10",[902,3081,3082],{"encoding":904},"C = 0{,}4Y + 10"," jsou úspory",[724,3085,3086],{},[883,3087,3089],{"className":3088},[886],[888,3090,3091],{"xmlns":890},[892,3092,3093,3131],{},[895,3094,3095,3097,3099,3101,3103,3105,3107,3109,3111,3113,3115,3117,3119,3121,3124,3126,3128],{},[898,3096,1779],{},[1750,3098,1766],{},[898,3100,1666],{},[1750,3102,1758],{},[898,3104,1812],{},[1750,3106,1766],{},[898,3108,1666],{},[1750,3110,1758],{},[1742,3112,3072],{},[898,3114,1666],{},[1750,3116,1758],{},[1742,3118,3079],{},[1750,3120,1766],{},[1742,3122,3123],{},"0,6",[898,3125,1666],{},[1750,3127,1758],{},[1742,3129,3130],{},"10.",[902,3132,3133],{"encoding":904},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[724,3135,3136],{},[614,3137,3138,3139,2028,3162,3186,3187,2433,3200,3226,3227,2433,3244,3260,3261,2313],{},"Obrázek 7.3 — Přímky ",[883,3140,3142],{"className":3141},[886],[888,3143,3144],{"xmlns":890},[892,3145,3146,3160],{},[895,3147,3148,3150,3152,3154,3156,3158],{},[898,3149,1812],{},[1750,3151,1766],{},[1742,3153,3072],{},[898,3155,1666],{},[1750,3157,1861],{},[1742,3159,3079],{},[902,3161,3082],{"encoding":904},[883,3163,3165],{"className":3164},[886],[888,3166,3167],{"xmlns":890},[892,3168,3169,3183],{},[895,3170,3171,3173,3175,3177,3179,3181],{},[898,3172,1779],{},[1750,3174,1766],{},[1742,3176,3123],{},[898,3178,1666],{},[1750,3180,1758],{},[1742,3182,3079],{},[902,3184,3185],{"encoding":904},"S = 0{,}6Y - 10","; průsečík přímky úspor s osou ",[883,3188,3190],{"className":3189},[886],[888,3191,3192],{"xmlns":890},[892,3193,3194,3198],{},[895,3195,3196],{},[898,3197,1666],{},[902,3199,1666],{"encoding":904},[883,3201,3203],{"className":3202},[886],[888,3204,3205],{"xmlns":890},[892,3206,3207,3223],{},[895,3208,3209,3211,3214],{},[1750,3210,2274],{},[1742,3212,3213],{},"16,",[3215,3216,3217,3220],"mover",{"accent":1916},[1742,3218,3219],{},"6",[1750,3221,3222],{},"ˉ",[902,3224,3225],{"encoding":904},"\\approx 16{,}\\bar{6}",", s osou ",[883,3228,3230],{"className":3229},[886],[888,3231,3232],{"xmlns":890},[892,3233,3234,3242],{},[895,3235,3236,3238,3240],{},[898,3237,1812],{},[1750,3239,1917],{"separator":1916},[898,3241,1779],{},[902,3243,3033],{"encoding":904},[883,3245,3247],{"className":3246},[886],[888,3248,3249],{"xmlns":890},[892,3250,3251,3257],{},[895,3252,3253,3255],{},[1750,3254,1758],{},[1742,3256,3079],{},[902,3258,3259],{"encoding":904},"-10","; přímka spotřeby prochází bodem ",[883,3262,3264],{"className":3263},[886],[888,3265,3266],{"xmlns":890},[892,3267,3268,3280],{},[895,3269,3270,3272,3274,3276,3278],{},[1750,3271,1753],{"stretchy":1752},[1742,3273,2607],{},[1750,3275,1917],{"separator":1916},[1742,3277,3079],{},[1750,3279,1763],{"stretchy":1752},[902,3281,3282],{"encoding":904},"(0, 10)",[724,3284,3285,3286,2433,3304,3334,3335,2084,3338,3341,3342,2433,3366,2084,3369,3372],{},"Funkce úspor může nabývat záporných hodnot — pro ",[883,3287,3289],{"className":3288},[886],[888,3290,3291],{"xmlns":890},[892,3292,3293,3301],{},[895,3294,3295,3297,3299],{},[898,3296,1666],{},[1750,3298,1766],{},[1742,3300,2607],{},[902,3302,3303],{"encoding":904},"Y = 0",[883,3305,3307],{"className":3306},[886],[888,3308,3309],{"xmlns":890},[892,3310,3311,3331],{},[895,3312,3313,3315,3317,3319,3321,3323,3325,3327,3329],{},[898,3314,1779],{},[1750,3316,1753],{"stretchy":1752},[1742,3318,2607],{},[1750,3320,1763],{"stretchy":1752},[1750,3322,1766],{},[1750,3324,1758],{},[898,3326,2573],{},[1750,3328,2624],{},[1742,3330,2607],{},[902,3332,3333],{"encoding":904},"S(0) = -b \u003C 0","; hovoří se o ",[38,3336,3337],{},"autonomních úsporách",[614,3339,3340],{},"autonomous savings","). Analogicky ",[883,3343,3345],{"className":3344},[886],[888,3346,3347],{"xmlns":890},[892,3348,3349,3363],{},[895,3350,3351,3353,3355,3357,3359,3361],{},[898,3352,1812],{},[1750,3354,1753],{"stretchy":1752},[1742,3356,2607],{},[1750,3358,1763],{"stretchy":1752},[1750,3360,1766],{},[898,3362,2573],{},[902,3364,3365],{"encoding":904},"C(0) = b",[38,3367,3368],{},"autonomní spotřeba",[614,3370,3371],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[115,3374,3376],{"id":3375},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[724,3378,3379,1647,3382,2084,3399,3402],{},[38,3380,3381],{},"Mezní sklon ke spotřebě",[883,3383,3385],{"className":3384},[886],[888,3386,3387],{"xmlns":890},[892,3388,3389,3397],{},[895,3390,3391,3393,3395],{},[898,3392,1773],{},[898,3394,1776],{},[898,3396,1812],{},[902,3398,1815],{"encoding":904},[614,3400,3401],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[724,3404,3405],{},[883,3406,3408],{"className":3407},[886],[888,3409,3410],{"xmlns":890},[892,3411,3412,3440],{},[895,3413,3414,3416,3418,3420,3422,3438],{},[898,3415,1773],{},[898,3417,1776],{},[898,3419,1812],{},[1750,3421,1766],{},[3423,3424,3425,3432],"mfrac",{},[895,3426,3427,3430],{},[898,3428,3429],{"mathvariant":1747},"d",[898,3431,1812],{},[895,3433,3434,3436],{},[898,3435,3429],{"mathvariant":1747},[898,3437,1666],{},[898,3439,2313],{"mathvariant":1747},[902,3441,3442],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[724,3444,3445,1647,3448,2084,3466,3469],{},[38,3446,3447],{},"Mezní sklon k úsporám",[883,3449,3451],{"className":3450},[886],[888,3452,3453],{"xmlns":890},[892,3454,3455,3463],{},[895,3456,3457,3459,3461],{},[898,3458,1773],{},[898,3460,1776],{},[898,3462,1779],{},[902,3464,3465],{"encoding":904},"MPS",[614,3467,3468],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[724,3471,3472],{},[883,3473,3475],{"className":3474},[886],[888,3476,3477],{"xmlns":890},[892,3478,3479,3505],{},[895,3480,3481,3483,3485,3487,3489,3503],{},[898,3482,1773],{},[898,3484,1776],{},[898,3486,1779],{},[1750,3488,1766],{},[3423,3490,3491,3497],{},[895,3492,3493,3495],{},[898,3494,3429],{"mathvariant":1747},[898,3496,1779],{},[895,3498,3499,3501],{},[898,3500,3429],{"mathvariant":1747},[898,3502,1666],{},[898,3504,2313],{"mathvariant":1747},[902,3506,3507],{"encoding":904},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[724,3509,3510,3511,3569],{},"Z (7.2) plyne ",[883,3512,3514],{"className":3513},[886],[888,3515,3516],{"xmlns":890},[892,3517,3518,3566],{},[895,3519,3520,3534,3536,3550,3552],{},[3423,3521,3522,3528],{},[895,3523,3524,3526],{},[898,3525,3429],{"mathvariant":1747},[898,3527,1666],{},[895,3529,3530,3532],{},[898,3531,3429],{"mathvariant":1747},[898,3533,1666],{},[1750,3535,1766],{},[3423,3537,3538,3544],{},[895,3539,3540,3542],{},[898,3541,3429],{"mathvariant":1747},[898,3543,1812],{},[895,3545,3546,3548],{},[898,3547,3429],{"mathvariant":1747},[898,3549,1666],{},[1750,3551,1861],{},[3423,3553,3554,3560],{},[895,3555,3556,3558],{},[898,3557,3429],{"mathvariant":1747},[898,3559,1779],{},[895,3561,3562,3564],{},[898,3563,3429],{"mathvariant":1747},[898,3565,1666],{},[902,3567,3568],{"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",[724,3571,3572],{},[883,3573,3575],{"className":3574},[886],[888,3576,3577],{"xmlns":890},[892,3578,3579,3645],{},[895,3580,3581,3636,3638,3640,3643],{},[3582,3583,3585],"menclose",{"notation":3584},"box",[3586,3587,3588],"mstyle",{"scriptlevel":2607,"displaystyle":1752},[3586,3589,3590],{"scriptlevel":2607,"displaystyle":1752},[3586,3591,3592],{"scriptlevel":2607,"displaystyle":1916},[895,3593,3594,3596,3598,3600,3602,3604,3606,3608,3610,3612,3614,3616,3618,3620,3622,3624,3626,3628,3630,3632,3634],{},[898,3595,1773],{},[898,3597,1776],{},[898,3599,1812],{},[1750,3601,1861],{},[898,3603,1773],{},[898,3605,1776],{},[898,3607,1779],{},[1750,3609,1766],{},[1742,3611,1744],{},[1750,3613,1917],{"separator":1916},[2125,3615],{"width":2127},[898,3617,1773],{},[898,3619,1776],{},[898,3621,1779],{},[1750,3623,1766],{},[1742,3625,1744],{},[1750,3627,1758],{},[898,3629,1773],{},[898,3631,1776],{},[898,3633,1812],{},[898,3635,2313],{"mathvariant":1747},[2125,3637],{"width":2127},[1750,3639,1753],{"stretchy":1752},[1742,3641,3642],{},"7.5",[1750,3644,1763],{"stretchy":1752},[902,3646,3647],{"encoding":904},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[724,3649,3650,1647,3653,3676,3677,2028,3699,3725],{},[38,3651,3652],{},"Pro lineární model",[883,3654,3656],{"className":3655},[886],[888,3657,3658],{"xmlns":890},[892,3659,3660,3674],{},[895,3661,3662,3664,3666,3668,3670,3672],{},[898,3663,1812],{},[1750,3665,1766],{},[898,3667,207],{},[898,3669,1666],{},[1750,3671,1861],{},[898,3673,2573],{},[902,3675,2720],{"encoding":904}," vychází ",[883,3678,3680],{"className":3679},[886],[888,3681,3682],{"xmlns":890},[892,3683,3684,3696],{},[895,3685,3686,3688,3690,3692,3694],{},[898,3687,1773],{},[898,3689,1776],{},[898,3691,1812],{},[1750,3693,1766],{},[898,3695,207],{},[902,3697,3698],{"encoding":904},"MPC = a",[883,3700,3702],{"className":3701},[886],[888,3703,3704],{"xmlns":890},[892,3705,3706,3722],{},[895,3707,3708,3710,3712,3714,3716,3718,3720],{},[898,3709,1773],{},[898,3711,1776],{},[898,3713,1779],{},[1750,3715,1766],{},[1742,3717,1744],{},[1750,3719,1758],{},[898,3721,207],{},[902,3723,3724],{"encoding":904},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[724,3727,3728,3731,3732,3755,3756,3784],{},[38,3729,3730],{},"Interpretace diferenciálem."," Pro pevné ",[883,3733,3735],{"className":3734},[886],[888,3736,3737],{"xmlns":890},[892,3738,3739,3752],{},[895,3740,3741,3743,3745],{},[898,3742,1666],{},[1750,3744,1766],{},[1699,3746,3747,3749],{},[898,3748,1666],{},[1750,3750,3751],{},"∗",[902,3753,3754],{"encoding":904},"Y = Y^*"," udává ",[883,3757,3759],{"className":3758},[886],[888,3760,3761],{"xmlns":890},[892,3762,3763,3781],{},[895,3764,3765,3767,3769,3771,3773,3779],{},[898,3766,1773],{},[898,3768,1776],{},[898,3770,1812],{},[1750,3772,1753],{"stretchy":1752},[1699,3774,3775,3777],{},[898,3776,1666],{},[1750,3778,3751],{},[1750,3780,1763],{"stretchy":1752},[902,3782,3783],{"encoding":904},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[724,3786,3787],{},[883,3788,3790],{"className":3789},[886],[888,3791,3792],{"xmlns":890},[892,3793,3794,3850],{},[895,3795,3796,3798,3800,3802,3804,3806,3808,3816,3818,3820,3822,3824,3826,3828,3830,3832,3834,3836,3838,3840,3842,3844,3846,3848],{},[898,3797,2666],{"mathvariant":1747},[898,3799,1812],{},[1750,3801,2274],{},[898,3803,3429],{"mathvariant":1747},[898,3805,1812],{},[1750,3807,1766],{},[1699,3809,3810,3812],{},[898,3811,1812],{},[1750,3813,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},"0em","′",[1750,3817,1753],{"stretchy":1752},[898,3819,1666],{},[1750,3821,1763],{"stretchy":1752},[1969,3823,2658],{},[898,3825,3429],{"mathvariant":1747},[898,3827,1666],{},[1750,3829,1766],{},[898,3831,1773],{},[898,3833,1776],{},[898,3835,1812],{},[1750,3837,1753],{"stretchy":1752},[898,3839,1666],{},[1750,3841,1763],{"stretchy":1752},[1969,3843,2658],{},[898,3845,3429],{"mathvariant":1747},[898,3847,1666],{},[898,3849,2313],{"mathvariant":1747},[902,3851,3852],{"encoding":904},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[724,3854,3855,3856,3892,3893,3896],{},"Analogicky ",[883,3857,3859],{"className":3858},[886],[888,3860,3861],{"xmlns":890},[892,3862,3863,3889],{},[895,3864,3865,3867,3869,3871,3873,3875,3877,3879,3881,3883,3885,3887],{},[898,3866,2666],{"mathvariant":1747},[898,3868,1779],{},[1750,3870,2274],{},[898,3872,1773],{},[898,3874,1776],{},[898,3876,1779],{},[1750,3878,1753],{"stretchy":1752},[898,3880,1666],{},[1750,3882,1763],{"stretchy":1752},[1969,3884,2658],{},[898,3886,3429],{"mathvariant":1747},[898,3888,1666],{},[902,3890,3891],{"encoding":904},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",". Viz ",[207,3894,1145],{"className":3895,"dataFsResolvedFilePath":764,"href":765},[210]," a její ekonomická interpretace.",[198,3898,3900],{"id":3899},"příklad-72","Příklad 7.2",[724,3902,3056,3903,3940,3941,3960],{},[883,3904,3906],{"className":3905},[886],[888,3907,3908],{"xmlns":890},[892,3909,3910,3937],{},[895,3911,3912,3914,3916,3919,3925,3927,3930,3932,3934],{},[898,3913,1812],{},[1750,3915,1766],{},[1742,3917,3918],{},"0,001",[1699,3920,3921,3923],{},[898,3922,1666],{},[1742,3924,1872],{},[1750,3926,1861],{},[1742,3928,3929],{},"0,2",[898,3931,1666],{},[1750,3933,1861],{},[1742,3935,3936],{},"50",[902,3938,3939],{"encoding":904},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[883,3942,3944],{"className":3943},[886],[888,3945,3946],{"xmlns":890},[892,3947,3948,3957],{},[895,3949,3950,3952,3954],{},[898,3951,1666],{},[1750,3953,2624],{},[1742,3955,3956],{},"400",[902,3958,3959],{"encoding":904},"Y \u003C 400",") platí",[724,3962,3963],{},[883,3964,3966],{"className":3965},[886],[888,3967,3968],{"xmlns":890},[892,3969,3970,4007],{},[895,3971,3972,3974,3976,3978,3980,3994,3996,3999,4001,4003,4005],{},[898,3973,1773],{},[898,3975,1776],{},[898,3977,1812],{},[1750,3979,1766],{},[3423,3981,3982,3988],{},[895,3983,3984,3986],{},[898,3985,3429],{"mathvariant":1747},[898,3987,1812],{},[895,3989,3990,3992],{},[898,3991,3429],{"mathvariant":1747},[898,3993,1666],{},[1750,3995,1766],{},[1742,3997,3998],{},"0,002",[898,4000,1666],{},[1750,4002,1861],{},[1742,4004,3929],{},[1750,4006,1917],{"separator":1916},[902,4008,4009],{"encoding":904},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[724,4011,4012],{},[883,4013,4015],{"className":4014},[886],[888,4016,4017],{"xmlns":890},[892,4018,4019,4052],{},[895,4020,4021,4023,4025,4027,4029,4031,4033,4035,4037,4039,4041,4043,4045,4047,4049],{},[898,4022,1773],{},[898,4024,1776],{},[898,4026,1779],{},[1750,4028,1766],{},[1742,4030,1744],{},[1750,4032,1758],{},[898,4034,1773],{},[898,4036,1776],{},[898,4038,1812],{},[1750,4040,1766],{},[1750,4042,1758],{},[1742,4044,3998],{},[898,4046,1666],{},[1750,4048,1861],{},[1742,4050,4051],{},"0,8.",[902,4053,4054],{"encoding":904},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[120,4056,4057,4138,4218],{},[123,4058,4059,1343,4088,4116,4117,2433,4135,2313],{},[883,4060,4062],{"className":4061},[886],[888,4063,4064],{"xmlns":890},[892,4065,4066,4085],{},[895,4067,4068,4070,4072,4074,4076,4079,4081,4083],{},[898,4069,1773],{},[898,4071,1776],{},[898,4073,1812],{},[1750,4075,1753],{"stretchy":1752},[1742,4077,4078],{},"100",[1750,4080,1763],{"stretchy":1752},[1750,4082,1766],{},[1742,4084,3072],{},[902,4086,4087],{"encoding":904},"MPC(100) = 0{,}4",[883,4089,4091],{"className":4090},[886],[888,4092,4093],{"xmlns":890},[892,4094,4095,4113],{},[895,4096,4097,4099,4101,4103,4105,4107,4109,4111],{},[898,4098,1773],{},[898,4100,1776],{},[898,4102,1779],{},[1750,4104,1753],{"stretchy":1752},[1742,4106,4078],{},[1750,4108,1763],{"stretchy":1752},[1750,4110,1766],{},[1742,4112,3123],{},[902,4114,4115],{"encoding":904},"MPS(100) = 0{,}6"," — při ",[883,4118,4120],{"className":4119},[886],[888,4121,4122],{"xmlns":890},[892,4123,4124,4132],{},[895,4125,4126,4128,4130],{},[898,4127,1666],{},[1750,4129,1766],{},[1742,4131,4078],{},[902,4133,4134],{"encoding":904},"Y = 100",[38,4136,4137],{},"větší sklon k úsporám",[123,4139,4140,1343,4169,4116,4197,2433,4215,2313],{},[883,4141,4143],{"className":4142},[886],[888,4144,4145],{"xmlns":890},[892,4146,4147,4166],{},[895,4148,4149,4151,4153,4155,4157,4160,4162,4164],{},[898,4150,1773],{},[898,4152,1776],{},[898,4154,1812],{},[1750,4156,1753],{"stretchy":1752},[1742,4158,4159],{},"200",[1750,4161,1763],{"stretchy":1752},[1750,4163,1766],{},[1742,4165,3123],{},[902,4167,4168],{"encoding":904},"MPC(200) = 0{,}6",[883,4170,4172],{"className":4171},[886],[888,4173,4174],{"xmlns":890},[892,4175,4176,4194],{},[895,4177,4178,4180,4182,4184,4186,4188,4190,4192],{},[898,4179,1773],{},[898,4181,1776],{},[898,4183,1779],{},[1750,4185,1753],{"stretchy":1752},[1742,4187,4159],{},[1750,4189,1763],{"stretchy":1752},[1750,4191,1766],{},[1742,4193,3072],{},[902,4195,4196],{"encoding":904},"MPS(200) = 0{,}4",[883,4198,4200],{"className":4199},[886],[888,4201,4202],{"xmlns":890},[892,4203,4204,4212],{},[895,4205,4206,4208,4210],{},[898,4207,1666],{},[1750,4209,1766],{},[1742,4211,4159],{},[902,4213,4214],{"encoding":904},"Y = 200",[38,4216,4217],{},"větší sklon ke spotřebě",[123,4219,4220,4221,4240,4241,1783],{},"Přesně při ",[883,4222,4224],{"className":4223},[886],[888,4225,4226],{"xmlns":890},[892,4227,4228,4237],{},[895,4229,4230,4232,4234],{},[898,4231,1666],{},[1750,4233,1766],{},[1742,4235,4236],{},"150",[902,4238,4239],{"encoding":904},"Y = 150"," se oba sklony rovnají (",[883,4242,4244],{"className":4243},[886],[888,4245,4246],{"xmlns":890},[892,4247,4248,4269],{},[895,4249,4250,4252,4254,4256,4258,4260,4262,4264,4266],{},[898,4251,1773],{},[898,4253,1776],{},[898,4255,1812],{},[1750,4257,1766],{},[898,4259,1773],{},[898,4261,1776],{},[898,4263,1779],{},[1750,4265,1766],{},[1742,4267,4268],{},"0,5",[902,4270,4271],{"encoding":904},"MPC = MPS = 0{,}5",[724,4273,4274,4275,4292,4293,4307,4308,4321,4322,4336,4337,4350,4351,4392],{},"Interpretace: při ",[883,4276,4278],{"className":4277},[886],[888,4279,4280],{"xmlns":890},[892,4281,4282,4290],{},[895,4283,4284,4286,4288],{},[898,4285,1666],{},[1750,4287,1766],{},[1742,4289,4078],{},[902,4291,4134],{"encoding":904}," se spotřeba mění ",[883,4294,4296],{"className":4295},[886],[888,4297,4298],{"xmlns":890},[892,4299,4300,4304],{},[895,4301,4302],{},[1742,4303,3072],{},[902,4305,4306],{"encoding":904},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[883,4309,4311],{"className":4310},[886],[888,4312,4313],{"xmlns":890},[892,4314,4315,4319],{},[895,4316,4317],{},[1742,4318,4078],{},[902,4320,4078],{"encoding":904}," na ",[883,4323,4325],{"className":4324},[886],[888,4326,4327],{"xmlns":890},[892,4328,4329,4334],{},[895,4330,4331],{},[1742,4332,4333],{},"101",[902,4335,4333],{"encoding":904},", změní se spotřeba přibližně o ",[883,4338,4340],{"className":4339},[886],[888,4341,4342],{"xmlns":890},[892,4343,4344,4348],{},[895,4345,4346],{},[1742,4347,3072],{},[902,4349,4306],{"encoding":904},". Skutečná změna ",[883,4352,4354],{"className":4353},[886],[888,4355,4356],{"xmlns":890},[892,4357,4358,4389],{},[895,4359,4360,4362,4364,4366,4368,4370,4372,4374,4376,4378,4380,4382,4384,4386],{},[898,4361,2666],{"mathvariant":1747},[898,4363,1812],{},[1750,4365,1766],{},[898,4367,1812],{},[1750,4369,1753],{"stretchy":1752},[1742,4371,4333],{},[1750,4373,1763],{"stretchy":1752},[1750,4375,1758],{},[898,4377,1812],{},[1750,4379,1753],{"stretchy":1752},[1742,4381,4078],{},[1750,4383,1763],{"stretchy":1752},[1750,4385,1766],{},[1742,4387,4388],{},"0,401",[902,4390,4391],{"encoding":904},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[724,4394,4395,4396],{},"Obecný trend: ",[38,4397,4398],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[115,4400,4402],{"id":4401},"makroekonomická-rovnováha","Makroekonomická rovnováha",[724,4404,4405,4406,2084,4409,4412,4413,2084,4416,4419,4420,2084,4423,4426],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[38,4407,4408],{},"makroekonomická rovnováha",[614,4410,4411],{},"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 ",[38,4414,4415],{},"agregátní poptávky",[614,4417,4418],{},"aggregate demand",") a ",[38,4421,4422],{},"agregátní nabídky",[614,4424,4425],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[115,4428,4430],{"id":4429},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[724,4432,4433],{},[4434,4435],"img",{"alt":4436,"className":4437,"src":4439},"imek-keynesian-kriz",[210,4438],"wikilink-broken","\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[198,4441,4443],{"id":4442},"zadání-modelu","Zadání modelu",[724,4445,4446,4447,4460,4461,4474],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[883,4448,4450],{"className":4449},[886],[888,4451,4452],{"xmlns":890},[892,4453,4454,4458],{},[895,4455,4456],{},[898,4457,1812],{},[902,4459,1812],{"encoding":904}," a investice ",[883,4462,4464],{"className":4463},[886],[888,4465,4466],{"xmlns":890},[892,4467,4468,4472],{},[895,4469,4470],{},[898,4471,1974],{},[902,4473,1974],{"encoding":904},". Podmínka rovnováhy:",[724,4476,4477],{},[883,4478,4480],{"className":4479},[886],[888,4481,4482],{"xmlns":890},[892,4483,4484,4507],{},[895,4485,4486,4488,4490,4492,4494,4496,4498,4500,4502,4505],{},[898,4487,1666],{},[1750,4489,1766],{},[898,4491,1812],{},[1750,4493,1861],{},[898,4495,1974],{},[898,4497,2313],{"mathvariant":1747},[2125,4499],{"width":2127},[1750,4501,1753],{"stretchy":1752},[1742,4503,4504],{},"7.6",[1750,4506,1763],{"stretchy":1752},[902,4508,4509],{"encoding":904},"Y = C + I. \\qquad (7.6)",[198,4511,4513],{"id":4512},"soustava-rovnic","Soustava rovnic",[724,4515,4516,4517,4539,4540,4564],{},"Pro pevně zadané (plánované) investice ",[883,4518,4520],{"className":4519},[886],[888,4521,4522],{"xmlns":890},[892,4523,4524,4536],{},[895,4525,4526,4528,4530],{},[898,4527,1974],{},[1750,4529,1766],{},[1699,4531,4532,4534],{},[898,4533,1974],{},[1750,4535,3751],{},[902,4537,4538],{"encoding":904},"I = I^*"," a funkci spotřeby ",[883,4541,4543],{"className":4542},[886],[888,4544,4545],{"xmlns":890},[892,4546,4547,4561],{},[895,4548,4549,4551,4553,4555,4557,4559],{},[898,4550,1812],{},[1750,4552,1766],{},[898,4554,1812],{},[1750,4556,1753],{"stretchy":1752},[898,4558,1666],{},[1750,4560,1763],{"stretchy":1752},[902,4562,4563],{"encoding":904},"C = C(Y)"," dostáváme soustavu",[724,4566,4567],{},[883,4568,4570],{"className":4569},[886],[888,4571,4572],{"xmlns":890},[892,4573,4574,4650],{},[895,4575,4576,4641,4643,4645,4648],{},[4577,4578,4581,4613],"mtable",{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},"0.25em","right left",[4582,4583,4584,4591],"mtr",{},[4585,4586,4587],"mtd",{},[3586,4588,4589],{"scriptlevel":2607,"displaystyle":1916},[898,4590,1666],{},[4585,4592,4593],{},[3586,4594,4595],{"scriptlevel":2607,"displaystyle":1916},[895,4596,4597,4599,4601,4603,4605,4611],{},[895,4598],{},[1750,4600,1766],{},[898,4602,1812],{},[1750,4604,1861],{},[1699,4606,4607,4609],{},[898,4608,1974],{},[1750,4610,3751],{},[1750,4612,1917],{"separator":1916},[4582,4614,4615,4621],{},[4585,4616,4617],{},[3586,4618,4619],{"scriptlevel":2607,"displaystyle":1916},[898,4620,1812],{},[4585,4622,4623],{},[3586,4624,4625],{"scriptlevel":2607,"displaystyle":1916},[895,4626,4627,4629,4631,4633,4635,4637,4639],{},[895,4628],{},[1750,4630,1766],{},[898,4632,1812],{},[1750,4634,1753],{"stretchy":1752},[898,4636,1666],{},[1750,4638,1763],{"stretchy":1752},[1750,4640,1917],{"separator":1916},[2125,4642],{"width":2127},[1750,4644,1753],{"stretchy":1752},[1742,4646,4647],{},"7.7",[1750,4649,1763],{"stretchy":1752},[902,4651,4652],{"encoding":904},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[724,4654,4655,4656,1647,4658,2028,4675,1647,4678,2313],{},"jejímž řešením jsou ",[38,4657,1688],{},[883,4659,4661],{"className":4660},[886],[888,4662,4663],{"xmlns":890},[892,4664,4665,4673],{},[895,4666,4667],{},[1699,4668,4669,4671],{},[898,4670,1666],{},[898,4672,1705],{},[902,4674,1708],{"encoding":904},[38,4676,4677],{},"rovnovážná spotřeba",[883,4679,4681],{"className":4680},[886],[888,4682,4683],{"xmlns":890},[892,4684,4685,4693],{},[895,4686,4687],{},[1699,4688,4689,4691],{},[898,4690,1812],{},[898,4692,1705],{},[902,4694,4695],{"encoding":904},"C^E",[198,4697,4699,4700],{"id":4698},"výpočet-yeye","Výpočet ",[883,4701,4703],{"className":4702},[886],[888,4704,4705],{"xmlns":890},[892,4706,4707,4715],{},[895,4708,4709],{},[1699,4710,4711,4713],{},[898,4712,1666],{},[898,4714,1705],{},[902,4716,1708],{"encoding":904},[724,4718,4719,4720,4743,4744,4776,4777],{},"Pro lineární spotřebu ",[883,4721,4723],{"className":4722},[886],[888,4724,4725],{"xmlns":890},[892,4726,4727,4741],{},[895,4728,4729,4731,4733,4735,4737,4739],{},[898,4730,1812],{},[1750,4732,1766],{},[898,4734,207],{},[898,4736,1666],{},[1750,4738,1861],{},[898,4740,2573],{},[902,4742,2720],{"encoding":904}," plyne z (7.7) rovnice ",[883,4745,4747],{"className":4746},[886],[888,4748,4749],{"xmlns":890},[892,4750,4751,4773],{},[895,4752,4753,4755,4757,4759,4761,4763,4765,4767],{},[898,4754,1666],{},[1750,4756,1766],{},[898,4758,207],{},[898,4760,1666],{},[1750,4762,1861],{},[898,4764,2573],{},[1750,4766,1861],{},[1699,4768,4769,4771],{},[898,4770,1974],{},[1750,4772,3751],{},[902,4774,4775],{"encoding":904},"Y = aY + b + I^*",", odkud ",[38,4778,4779],{},"redukovaný tvar",[724,4781,4782],{},[883,4783,4785],{"className":4784},[886],[888,4786,4787],{"xmlns":890},[892,4788,4789,4837],{},[895,4790,4791],{},[3582,4792,4793],{"notation":3584},[3586,4794,4795],{"scriptlevel":2607,"displaystyle":1752},[3586,4796,4797],{"scriptlevel":2607,"displaystyle":1752},[3586,4798,4799],{"scriptlevel":2607,"displaystyle":1916},[895,4800,4801,4803,4809,4811,4833,4835],{},[1969,4802,2658],{},[1699,4804,4805,4807],{},[898,4806,1666],{},[898,4808,1705],{},[1750,4810,1766],{},[3423,4812,4813,4825],{},[895,4814,4815,4817,4819],{},[898,4816,2573],{},[1750,4818,1861],{},[1699,4820,4821,4823],{},[898,4822,1974],{},[1750,4824,3751],{},[895,4826,4827,4829,4831],{},[1742,4828,1744],{},[1750,4830,1758],{},[898,4832,207],{},[898,4834,2313],{"mathvariant":1747},[1969,4836,2658],{},[902,4838,4839],{"encoding":904},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[198,4841,4843],{"id":4842},"příklad-73","Příklad 7.3",[724,4845,4846,4847,2433,4864,2028,4888,4915],{},"V modelu ",[883,4848,4850],{"className":4849},[886],[888,4851,4852],{"xmlns":890},[892,4853,4854,4862],{},[895,4855,4856,4858,4860],{},[898,4857,1812],{},[1969,4859,1971],{},[898,4861,1974],{},[902,4863,1977],{"encoding":904},[883,4865,4867],{"className":4866},[886],[888,4868,4869],{"xmlns":890},[892,4870,4871,4885],{},[895,4872,4873,4875,4877,4879,4881,4883],{},[898,4874,1812],{},[1750,4876,1766],{},[1742,4878,3123],{},[898,4880,1666],{},[1750,4882,1861],{},[1742,4884,3079],{},[902,4886,4887],{"encoding":904},"C = 0{,}6Y + 10",[883,4889,4891],{"className":4890},[886],[888,4892,4893],{"xmlns":890},[892,4894,4895,4912],{},[895,4896,4897,4899,4901,4904,4906],{},[898,4898,1974],{},[1750,4900,1766],{},[1742,4902,4903],{},"12",[1750,4905,1766],{},[1699,4907,4908,4910],{},[898,4909,1974],{},[1750,4911,3751],{},[902,4913,4914],{"encoding":904},"I = 12 = I^*",". Soustava",[724,4917,4918],{},[883,4919,4921],{"className":4920},[886],[888,4922,4923],{"xmlns":890},[892,4924,4925,4981],{},[4577,4926,4927,4953],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,4928,4929,4935],{},[4585,4930,4931],{},[3586,4932,4933],{"scriptlevel":2607,"displaystyle":1916},[898,4934,1666],{},[4585,4936,4937],{},[3586,4938,4939],{"scriptlevel":2607,"displaystyle":1916},[895,4940,4941,4943,4945,4947,4949,4951],{},[895,4942],{},[1750,4944,1766],{},[898,4946,1812],{},[1750,4948,1861],{},[1742,4950,4903],{},[1750,4952,1917],{"separator":1916},[4582,4954,4955,4961],{},[4585,4956,4957],{},[3586,4958,4959],{"scriptlevel":2607,"displaystyle":1916},[898,4960,1812],{},[4585,4962,4963],{},[3586,4964,4965],{"scriptlevel":2607,"displaystyle":1916},[895,4966,4967,4969,4971,4973,4975,4977,4979],{},[895,4968],{},[1750,4970,1766],{},[1742,4972,3123],{},[898,4974,1666],{},[1750,4976,1861],{},[1742,4978,3079],{},[1750,4980,1917],{"separator":1916},[902,4982,4983],{"encoding":904},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[724,4985,4986,4987,1343,5010,5033,5034,1783],{},"má řešení ",[883,4988,4990],{"className":4989},[886],[888,4991,4992],{"xmlns":890},[892,4993,4994,5007],{},[895,4995,4996,5002,5004],{},[1699,4997,4998,5000],{},[898,4999,1666],{},[898,5001,1705],{},[1750,5003,1766],{},[1742,5005,5006],{},"55",[902,5008,5009],{"encoding":904},"Y^E = 55",[883,5011,5013],{"className":5012},[886],[888,5014,5015],{"xmlns":890},[892,5016,5017,5030],{},[895,5018,5019,5025,5027],{},[1699,5020,5021,5023],{},[898,5022,1812],{},[898,5024,1705],{},[1750,5026,1766],{},[1742,5028,5029],{},"43",[902,5031,5032],{"encoding":904},"C^E = 43"," (a ",[883,5035,5037],{"className":5036},[886],[888,5038,5039],{"xmlns":890},[892,5040,5041,5053],{},[895,5042,5043,5049,5051],{},[1699,5044,5045,5047],{},[898,5046,1779],{},[898,5048,1705],{},[1750,5050,1766],{},[1742,5052,4903],{},[902,5054,5055],{"encoding":904},"S^E = 12",[724,5057,5058],{},[614,5059,5060,5061,5083,5084,4419,5106,5129,5130,2313],{},"Obrázek 7.5 — Přímky ",[883,5062,5064],{"className":5063},[886],[888,5065,5066],{"xmlns":890},[892,5067,5068,5080],{},[895,5069,5070,5072,5074,5076,5078],{},[898,5071,1812],{},[1750,5073,1766],{},[898,5075,1666],{},[1750,5077,1758],{},[1742,5079,4903],{},[902,5081,5082],{"encoding":904},"C = Y - 12"," (rovnováha ",[883,5085,5087],{"className":5086},[886],[888,5088,5089],{"xmlns":890},[892,5090,5091,5103],{},[895,5092,5093,5095,5097,5099,5101],{},[898,5094,1666],{},[1750,5096,1766],{},[898,5098,1812],{},[1750,5100,1861],{},[898,5102,1974],{},[902,5104,5105],{"encoding":904},"Y = C + I",[883,5107,5109],{"className":5108},[886],[888,5110,5111],{"xmlns":890},[892,5112,5113,5127],{},[895,5114,5115,5117,5119,5121,5123,5125],{},[898,5116,1812],{},[1750,5118,1766],{},[1742,5120,3123],{},[898,5122,1666],{},[1750,5124,1861],{},[1742,5126,3079],{},[902,5128,4887],{"encoding":904}," (funkce spotřeby) se protínají v bodě ",[883,5131,5133],{"className":5132},[886],[888,5134,5135],{"xmlns":890},[892,5136,5137,5171],{},[895,5138,5139,5142,5148,5150,5156,5159,5161,5163,5165,5167,5169],{},[1750,5140,5141],{"stretchy":1752},"[",[1699,5143,5144,5146],{},[898,5145,1666],{},[898,5147,1705],{},[1750,5149,1917],{"separator":1916},[1699,5151,5152,5154],{},[898,5153,1812],{},[898,5155,1705],{},[1750,5157,5158],{"stretchy":1752},"]",[1750,5160,1766],{},[1750,5162,5141],{"stretchy":1752},[1742,5164,5006],{},[1750,5166,1917],{"separator":1916},[1742,5168,5029],{},[1750,5170,5158],{"stretchy":1752},[902,5172,5173],{"encoding":904},"[Y^E, C^E] = [55, 43]",[724,5175,5176,5179,5180,5197,5198,2313],{},[38,5177,5178],{},"Komentář k přechodu."," Model ",[883,5181,5183],{"className":5182},[886],[888,5184,5185],{"xmlns":890},[892,5186,5187,5195],{},[895,5188,5189,5191,5193],{},[898,5190,1812],{},[1969,5192,1971],{},[898,5194,1974],{},[902,5196,1977],{"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 ",[38,5199,5200,5201],{},"model ",[883,5202,5204],{"className":5203},[886],[888,5205,5206],{"xmlns":890},[892,5207,5208,5220],{},[895,5209,5210,5212,5214,5216,5218],{},[898,5211,1812],{},[1969,5213,1971],{},[898,5215,1974],{},[1969,5217,1971],{},[898,5219,1997],{},[902,5221,2000],{"encoding":904},[115,5223,5225],{"id":5224},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[198,5227,4443],{"id":5228},"zadání-modelu-1",[724,5230,5231,5232,5249,5250,1647,5253,2084,5266,5269],{},"Rozšíření modelu ",[883,5233,5235],{"className":5234},[886],[888,5236,5237],{"xmlns":890},[892,5238,5239,5247],{},[895,5240,5241,5243,5245],{},[898,5242,1812],{},[1969,5244,1971],{},[898,5246,1974],{},[902,5248,1977],{"encoding":904}," o ",[38,5251,5252],{},"vládní výdaje",[883,5254,5256],{"className":5255},[886],[888,5257,5258],{"xmlns":890},[892,5259,5260,5264],{},[895,5261,5262],{},[898,5263,1997],{},[902,5265,1997],{"encoding":904},[614,5267,5268],{},"government expenditure","). Podmínka rovnováhy:",[724,5271,5272],{},[883,5273,5275],{"className":5274},[886],[888,5276,5277],{"xmlns":890},[892,5278,5279,5306],{},[895,5280,5281,5283,5285,5287,5289,5291,5293,5295,5297,5299,5301,5304],{},[898,5282,1666],{},[1750,5284,1766],{},[898,5286,1812],{},[1750,5288,1861],{},[898,5290,1974],{},[1750,5292,1861],{},[898,5294,1997],{},[898,5296,2313],{"mathvariant":1747},[2125,5298],{"width":2127},[1750,5300,1753],{"stretchy":1752},[1742,5302,5303],{},"7.8",[1750,5305,1763],{"stretchy":1752},[902,5307,5308],{"encoding":904},"Y = C + I + G. \\qquad (7.8)",[724,5310,5311,5312,1647,5315,2084,5329,5332],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[38,5313,5314],{},"zdaněním domácností",[883,5316,5318],{"className":5317},[886],[888,5319,5320],{"xmlns":890},[892,5321,5322,5327],{},[895,5323,5324],{},[898,5325,5326],{},"T",[902,5328,5326],{"encoding":904},[614,5330,5331],{},"taxation","). Zdanění bývá:",[120,5334,5335,5368,5393],{},[123,5336,5337,5338,1917],{},"úměrné důchodu: ",[883,5339,5341],{"className":5340},[886],[888,5342,5343],{"xmlns":890},[892,5344,5345,5365],{},[895,5346,5347,5349,5351,5353,5355,5357,5359,5361,5363],{},[898,5348,5326],{},[1750,5350,1766],{},[898,5352,5326],{},[1750,5354,1753],{"stretchy":1752},[898,5356,1666],{},[1750,5358,1763],{"stretchy":1752},[1750,5360,1766],{},[898,5362,2652],{},[898,5364,1666],{},[902,5366,5367],{"encoding":904},"T = T(Y) = tY",[123,5369,5370,5371,1917],{},"fixní: ",[883,5372,5374],{"className":5373},[886],[888,5375,5376],{"xmlns":890},[892,5377,5378,5390],{},[895,5379,5380,5382,5384],{},[898,5381,5326],{},[1750,5383,1766],{},[1699,5385,5386,5388],{},[898,5387,5326],{},[1750,5389,3751],{},[902,5391,5392],{"encoding":904},"T = T^*",[123,5394,5395,5396,5424,5425,2313],{},"kombinované: ",[883,5397,5399],{"className":5398},[886],[888,5400,5401],{"xmlns":890},[892,5402,5403,5421],{},[895,5404,5405,5407,5409,5415,5417,5419],{},[898,5406,5326],{},[1750,5408,1766],{},[1699,5410,5411,5413],{},[898,5412,5326],{},[1750,5414,3751],{},[1750,5416,1861],{},[898,5418,2652],{},[898,5420,1666],{},[902,5422,5423],{"encoding":904},"T = T^* + tY",", kde ",[883,5426,5428],{"className":5427},[886],[888,5429,5430],{"xmlns":890},[892,5431,5432,5445],{},[895,5433,5434,5436,5439,5441,5443],{},[1742,5435,2607],{},[1750,5437,5438],{},"≤",[898,5440,2652],{},[1750,5442,2624],{},[1742,5444,1744],{},[902,5446,5447],{"encoding":904},"0 \\le t \u003C 1",[1785,5449,5450],{},[724,5451,5452,5455,5456,5477,5478,5481,5482,5495,5496,4419,5522,1647,5525,5553,5554,5582,5583,2028,5596,5614],{},[883,5453,5454],{},"!warning"," Pozor na disponibilní důchod\nV modelu ",[883,5457,5459],{"className":5458},[886],[888,5460,5461],{"xmlns":890},[892,5462,5463,5475],{},[895,5464,5465,5467,5469,5471,5473],{},[898,5466,1812],{},[1969,5468,1971],{},[898,5470,1974],{},[1969,5472,1971],{},[898,5474,1997],{},[902,5476,2000],{"encoding":904}," je nutné ",[38,5479,5480],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[883,5483,5485],{"className":5484},[886],[888,5486,5487],{"xmlns":890},[892,5488,5489,5493],{},[895,5490,5491],{},[898,5492,1666],{},[902,5494,1666],{"encoding":904}," (vstupuje do podmínky rovnováhy ",[883,5497,5499],{"className":5498},[886],[888,5500,5501],{"xmlns":890},[892,5502,5503,5519],{},[895,5504,5505,5507,5509,5511,5513,5515,5517],{},[898,5506,1666],{},[1750,5508,1766],{},[898,5510,1812],{},[1750,5512,1861],{},[898,5514,1974],{},[1750,5516,1861],{},[898,5518,1997],{},[902,5520,5521],{"encoding":904},"Y = C + I + G",[38,5523,5524],{},"disponibilní důchod",[883,5526,5528],{"className":5527},[886],[888,5529,5530],{"xmlns":890},[892,5531,5532,5550],{},[895,5533,5534,5542,5544,5546,5548],{},[5535,5536,5537,5539],"msub",{},[898,5538,1666],{},[898,5540,5541],{},"D",[1750,5543,1766],{},[898,5545,1666],{},[1750,5547,1758],{},[898,5549,5326],{},[902,5551,5552],{"encoding":904},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[883,5555,5557],{"className":5556},[886],[888,5558,5559],{"xmlns":890},[892,5560,5561,5579],{},[895,5562,5563,5565,5567,5569,5571,5577],{},[898,5564,1812],{},[1750,5566,1766],{},[898,5568,1812],{},[1750,5570,1753],{"stretchy":1752},[5535,5572,5573,5575],{},[898,5574,1666],{},[898,5576,5541],{},[1750,5578,1763],{"stretchy":1752},[902,5580,5581],{"encoding":904},"C = C(Y_D)","). Záměna ",[883,5584,5586],{"className":5585},[886],[888,5587,5588],{"xmlns":890},[892,5589,5590,5594],{},[895,5591,5592],{},[898,5593,1666],{},[902,5595,1666],{"encoding":904},[883,5597,5599],{"className":5598},[886],[888,5600,5601],{"xmlns":890},[892,5602,5603,5611],{},[895,5604,5605],{},[5535,5606,5607,5609],{},[898,5608,1666],{},[898,5610,5541],{},[902,5612,5613],{"encoding":904},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[724,5616,5617,2084,5620,1763],{},[38,5618,5619],{},"Disponibilní důchod",[614,5621,5622],{},"disposable income",[724,5624,5625],{},[883,5626,5628],{"className":5627},[886],[888,5629,5630],{"xmlns":890},[892,5631,5632,5648],{},[895,5633,5634,5640,5642,5644,5646],{},[5535,5635,5636,5638],{},[898,5637,1666],{},[898,5639,5541],{},[1750,5641,1766],{},[898,5643,1666],{},[1750,5645,1758],{},[898,5647,5326],{},[902,5649,5552],{"encoding":904},[724,5651,5652,5653,2313],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[883,5654,5656],{"className":5655},[886],[888,5657,5658],{"xmlns":890},[892,5659,5660,5678],{},[895,5661,5662,5664,5666,5668,5670,5676],{},[898,5663,1812],{},[1750,5665,1766],{},[898,5667,1812],{},[1750,5669,1753],{"stretchy":1752},[5535,5671,5672,5674],{},[898,5673,1666],{},[898,5675,5541],{},[1750,5677,1763],{"stretchy":1752},[902,5679,5581],{"encoding":904},[198,5681,4513],{"id":5682},"soustava-rovnic-1",[724,5684,5685,5686,1343,5707,5729,5730,2366],{},"Pro pevně zadané ",[883,5687,5689],{"className":5688},[886],[888,5690,5691],{"xmlns":890},[892,5692,5693,5705],{},[895,5694,5695,5697,5699],{},[898,5696,1974],{},[1750,5698,1766],{},[1699,5700,5701,5703],{},[898,5702,1974],{},[1750,5704,3751],{},[902,5706,4538],{"encoding":904},[883,5708,5710],{"className":5709},[886],[888,5711,5712],{"xmlns":890},[892,5713,5714,5726],{},[895,5715,5716,5718,5720],{},[898,5717,1997],{},[1750,5719,1766],{},[1699,5721,5722,5724],{},[898,5723,1997],{},[1750,5725,3751],{},[902,5727,5728],{"encoding":904},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[883,5731,5733],{"className":5732},[886],[888,5734,5735],{"xmlns":890},[892,5736,5737,5757],{},[895,5738,5739,5741,5743,5745,5747,5753,5755],{},[898,5740,1666],{},[1750,5742,1917],{"separator":1916},[898,5744,1812],{},[1750,5746,1917],{"separator":1916},[5535,5748,5749,5751],{},[898,5750,1666],{},[898,5752,5541],{},[1750,5754,1917],{"separator":1916},[898,5756,5326],{},[902,5758,5759],{"encoding":904},"Y, C, Y_D, T",[724,5761,5762],{},[883,5763,5765],{"className":5764},[886],[888,5766,5767],{"xmlns":890},[892,5768,5769,5910],{},[895,5770,5771,5901,5903,5905,5908],{},[4577,5772,5773,5811,5839,5871],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,5774,5775,5781],{},[4585,5776,5777],{},[3586,5778,5779],{"scriptlevel":2607,"displaystyle":1916},[898,5780,1666],{},[4585,5782,5783],{},[3586,5784,5785],{"scriptlevel":2607,"displaystyle":1916},[895,5786,5787,5789,5791,5793,5795,5801,5803,5809],{},[895,5788],{},[1750,5790,1766],{},[898,5792,1812],{},[1750,5794,1861],{},[1699,5796,5797,5799],{},[898,5798,1974],{},[1750,5800,3751],{},[1750,5802,1861],{},[1699,5804,5805,5807],{},[898,5806,1997],{},[1750,5808,3751],{},[1750,5810,1917],{"separator":1916},[4582,5812,5813,5819],{},[4585,5814,5815],{},[3586,5816,5817],{"scriptlevel":2607,"displaystyle":1916},[898,5818,5326],{},[4585,5820,5821],{},[3586,5822,5823],{"scriptlevel":2607,"displaystyle":1916},[895,5824,5825,5827,5829,5831,5833,5835,5837],{},[895,5826],{},[1750,5828,1766],{},[898,5830,5326],{},[1750,5832,1753],{"stretchy":1752},[898,5834,1666],{},[1750,5836,1763],{"stretchy":1752},[1750,5838,1917],{"separator":1916},[4582,5840,5841,5847],{},[4585,5842,5843],{},[3586,5844,5845],{"scriptlevel":2607,"displaystyle":1916},[898,5846,1812],{},[4585,5848,5849],{},[3586,5850,5851],{"scriptlevel":2607,"displaystyle":1916},[895,5852,5853,5855,5857,5859,5861,5867,5869],{},[895,5854],{},[1750,5856,1766],{},[898,5858,1812],{},[1750,5860,1753],{"stretchy":1752},[5535,5862,5863,5865],{},[898,5864,1666],{},[898,5866,5541],{},[1750,5868,1763],{"stretchy":1752},[1750,5870,1917],{"separator":1916},[4582,5872,5873,5883],{},[4585,5874,5875],{},[3586,5876,5877],{"scriptlevel":2607,"displaystyle":1916},[5535,5878,5879,5881],{},[898,5880,1666],{},[898,5882,5541],{},[4585,5884,5885],{},[3586,5886,5887],{"scriptlevel":2607,"displaystyle":1916},[895,5888,5889,5891,5893,5895,5897,5899],{},[895,5890],{},[1750,5892,1766],{},[898,5894,1666],{},[1750,5896,1758],{},[898,5898,5326],{},[1750,5900,1917],{"separator":1916},[2125,5902],{"width":2127},[1750,5904,1753],{"stretchy":1752},[1742,5906,5907],{},"7.9",[1750,5909,1763],{"stretchy":1752},[902,5911,5912],{"encoding":904},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[724,5914,5915,5916,5961,5962,2313],{},"s řešeními ",[883,5917,5919],{"className":5918},[886],[888,5920,5921],{"xmlns":890},[892,5922,5923,5958],{},[895,5924,5925,5931,5933,5939,5941,5947,5949],{},[1699,5926,5927,5929],{},[898,5928,1666],{},[898,5930,1705],{},[1750,5932,1917],{"separator":1916},[1699,5934,5935,5937],{},[898,5936,1812],{},[898,5938,1705],{},[1750,5940,1917],{"separator":1916},[1699,5942,5943,5945],{},[898,5944,5326],{},[898,5946,1705],{},[1750,5948,1917],{"separator":1916},[5950,5951,5952,5954,5956],"msubsup",{},[898,5953,1666],{},[898,5955,5541],{},[898,5957,1705],{},[902,5959,5960],{"encoding":904},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[883,5963,5965],{"className":5964},[886],[888,5966,5967],{"xmlns":890},[892,5968,5969,5995],{},[895,5970,5971,5977,5979,5987,5989],{},[1699,5972,5973,5975],{},[898,5974,1779],{},[898,5976,1705],{},[1750,5978,1766],{},[5950,5980,5981,5983,5985],{},[898,5982,1666],{},[898,5984,5541],{},[898,5986,1705],{},[1750,5988,1758],{},[1699,5990,5991,5993],{},[898,5992,1812],{},[898,5994,1705],{},[902,5996,5997],{"encoding":904},"S^E = Y_D^E - C^E",[1785,5999,6000,6006],{},[724,6001,6002,6005],{},[883,6003,6004],{},"!tip"," Postup — jak sestavit a vyřešit soustavu C-I-G",[152,6007,6008,6031,6114,6169,6259],{},[123,6009,6010,6013,6014,2313],{},[38,6011,6012],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[883,6015,6017],{"className":6016},[886],[888,6018,6019],{"xmlns":890},[892,6020,6021,6029],{},[895,6022,6023],{},[5535,6024,6025,6027],{},[898,6026,1666],{},[898,6028,5541],{},[902,6030,5613],{"encoding":904},[123,6032,6033,6082,6083,6100,6101,2313],{},[38,6034,6035,6036,6056,6057],{},"Dosaď ",[883,6037,6039],{"className":6038},[886],[888,6040,6041],{"xmlns":890},[892,6042,6043,6053],{},[895,6044,6045,6047,6049,6051],{},[898,6046,5326],{},[1750,6048,1753],{"stretchy":1752},[898,6050,1666],{},[1750,6052,1763],{"stretchy":1752},[902,6054,6055],{"encoding":904},"T(Y)"," do ",[883,6058,6060],{"className":6059},[886],[888,6061,6062],{"xmlns":890},[892,6063,6064,6080],{},[895,6065,6066,6072,6074,6076,6078],{},[5535,6067,6068,6070],{},[898,6069,1666],{},[898,6071,5541],{},[1750,6073,1766],{},[898,6075,1666],{},[1750,6077,1758],{},[898,6079,5326],{},[902,6081,5552],{"encoding":904}," — dostaneš ",[883,6084,6086],{"className":6085},[886],[888,6087,6088],{"xmlns":890},[892,6089,6090,6098],{},[895,6091,6092],{},[5535,6093,6094,6096],{},[898,6095,1666],{},[898,6097,5541],{},[902,6099,5613],{"encoding":904}," jako lineární funkci ",[883,6102,6104],{"className":6103},[886],[888,6105,6106],{"xmlns":890},[892,6107,6108,6112],{},[895,6109,6110],{},[898,6111,1666],{},[902,6113,1666],{"encoding":904},[123,6115,6116,6082,6143,6100,6156,2313],{},[38,6117,6035,6118,6142],{},[883,6119,6121],{"className":6120},[886],[888,6122,6123],{"xmlns":890},[892,6124,6125,6139],{},[895,6126,6127,6133,6135,6137],{},[5535,6128,6129,6131],{},[898,6130,1666],{},[898,6132,5541],{},[1750,6134,1753],{"stretchy":1752},[898,6136,1666],{},[1750,6138,1763],{"stretchy":1752},[902,6140,6141],{"encoding":904},"Y_D(Y)"," do funkce spotřeby",[883,6144,6146],{"className":6145},[886],[888,6147,6148],{"xmlns":890},[892,6149,6150,6154],{},[895,6151,6152],{},[898,6153,1812],{},[902,6155,1812],{"encoding":904},[883,6157,6159],{"className":6158},[886],[888,6160,6161],{"xmlns":890},[892,6162,6163,6167],{},[895,6164,6165],{},[898,6166,1666],{},[902,6168,1666],{"encoding":904},[123,6170,6171,1647,6193,6227,6228,6241,6242,2313],{},[38,6172,6035,6173,6192],{},[883,6174,6176],{"className":6175},[886],[888,6177,6178],{"xmlns":890},[892,6179,6180,6190],{},[895,6181,6182,6184,6186,6188],{},[898,6183,1812],{},[1750,6185,1753],{"stretchy":1752},[898,6187,1666],{},[1750,6189,1763],{"stretchy":1752},[902,6191,2432],{"encoding":904}," do podmínky rovnováhy",[883,6194,6196],{"className":6195},[886],[888,6197,6198],{"xmlns":890},[892,6199,6200,6224],{},[895,6201,6202,6204,6206,6208,6210,6216,6218],{},[898,6203,1666],{},[1750,6205,1766],{},[898,6207,1812],{},[1750,6209,1861],{},[1699,6211,6212,6214],{},[898,6213,1974],{},[1750,6215,3751],{},[1750,6217,1861],{},[1699,6219,6220,6222],{},[898,6221,1997],{},[1750,6223,3751],{},[902,6225,6226],{"encoding":904},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[883,6229,6231],{"className":6230},[886],[888,6232,6233],{"xmlns":890},[892,6234,6235,6239],{},[895,6236,6237],{},[898,6238,1666],{},[902,6240,1666],{"encoding":904},", odtud ",[883,6243,6245],{"className":6244},[886],[888,6246,6247],{"xmlns":890},[892,6248,6249,6257],{},[895,6250,6251],{},[1699,6252,6253,6255],{},[898,6254,1666],{},[898,6256,1705],{},[902,6258,1708],{"encoding":904},[123,6260,6261,6264,6265,1343,6283,1343,6303,1343,6320,2313],{},[38,6262,6263],{},"Zpětným dosazením"," dopočítej ",[883,6266,6268],{"className":6267},[886],[888,6269,6270],{"xmlns":890},[892,6271,6272,6280],{},[895,6273,6274],{},[1699,6275,6276,6278],{},[898,6277,5326],{},[898,6279,1705],{},[902,6281,6282],{"encoding":904},"T^E",[883,6284,6286],{"className":6285},[886],[888,6287,6288],{"xmlns":890},[892,6289,6290,6300],{},[895,6291,6292],{},[5950,6293,6294,6296,6298],{},[898,6295,1666],{},[898,6297,5541],{},[898,6299,1705],{},[902,6301,6302],{"encoding":904},"Y_D^E",[883,6304,6306],{"className":6305},[886],[888,6307,6308],{"xmlns":890},[892,6309,6310,6318],{},[895,6311,6312],{},[1699,6313,6314,6316],{},[898,6315,1812],{},[898,6317,1705],{},[902,6319,4695],{"encoding":904},[883,6321,6323],{"className":6322},[886],[888,6324,6325],{"xmlns":890},[892,6326,6327,6335],{},[895,6328,6329],{},[1699,6330,6331,6333],{},[898,6332,1779],{},[898,6334,1705],{},[902,6336,6337],{"encoding":904},"S^E",[198,6339,6341],{"id":6340},"příklad-74","Příklad 7.4",[724,6343,4846,6344,6365,6366,1343,6398,1343,6423,1343,6446,6469],{},[883,6345,6347],{"className":6346},[886],[888,6348,6349],{"xmlns":890},[892,6350,6351,6363],{},[895,6352,6353,6355,6357,6359,6361],{},[898,6354,1812],{},[1969,6356,1971],{},[898,6358,1974],{},[1969,6360,1971],{},[898,6362,1997],{},[902,6364,2000],{"encoding":904}," jsou dány ",[883,6367,6369],{"className":6368},[886],[888,6370,6371],{"xmlns":890},[892,6372,6373,6395],{},[895,6374,6375,6377,6379,6382,6384,6390,6392],{},[898,6376,1812],{},[1750,6378,1766],{},[1742,6380,6381],{},"0,9",[1969,6383,2658],{},[5535,6385,6386,6388],{},[898,6387,1666],{},[898,6389,5541],{},[1750,6391,1861],{},[1742,6393,6394],{},"70",[902,6396,6397],{"encoding":904},"C = 0{,}9\\,Y_D + 70",[883,6399,6401],{"className":6400},[886],[888,6402,6403],{"xmlns":890},[892,6404,6405,6420],{},[895,6406,6407,6409,6411,6413,6415,6417],{},[898,6408,5326],{},[1750,6410,1766],{},[1742,6412,3929],{},[898,6414,1666],{},[1750,6416,1861],{},[1742,6418,6419],{},"25",[902,6421,6422],{"encoding":904},"T = 0{,}2Y + 25",[883,6424,6426],{"className":6425},[886],[888,6427,6428],{"xmlns":890},[892,6429,6430,6443],{},[895,6431,6432,6438,6440],{},[1699,6433,6434,6436],{},[898,6435,1974],{},[1750,6437,3751],{},[1750,6439,1766],{},[1742,6441,6442],{},"35",[902,6444,6445],{"encoding":904},"I^* = 35",[883,6447,6449],{"className":6448},[886],[888,6450,6451],{"xmlns":890},[892,6452,6453,6466],{},[895,6454,6455,6461,6463],{},[1699,6456,6457,6459],{},[898,6458,1997],{},[1750,6460,3751],{},[1750,6462,1766],{},[1742,6464,6465],{},"20",[902,6467,6468],{"encoding":904},"G^* = 20",". Soustava (7.9):",[724,6471,6472],{},[883,6473,6475],{"className":6474},[886],[888,6476,6477],{"xmlns":890},[892,6478,6479,6603],{},[4577,6480,6481,6511,6539,6573],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,6482,6483,6489],{},[4585,6484,6485],{},[3586,6486,6487],{"scriptlevel":2607,"displaystyle":1916},[898,6488,1666],{},[4585,6490,6491],{},[3586,6492,6493],{"scriptlevel":2607,"displaystyle":1916},[895,6494,6495,6497,6499,6501,6503,6505,6507,6509],{},[895,6496],{},[1750,6498,1766],{},[898,6500,1812],{},[1750,6502,1861],{},[1742,6504,6442],{},[1750,6506,1861],{},[1742,6508,6465],{},[1750,6510,1917],{"separator":1916},[4582,6512,6513,6519],{},[4585,6514,6515],{},[3586,6516,6517],{"scriptlevel":2607,"displaystyle":1916},[898,6518,5326],{},[4585,6520,6521],{},[3586,6522,6523],{"scriptlevel":2607,"displaystyle":1916},[895,6524,6525,6527,6529,6531,6533,6535,6537],{},[895,6526],{},[1750,6528,1766],{},[1742,6530,3929],{},[898,6532,1666],{},[1750,6534,1861],{},[1742,6536,6419],{},[1750,6538,1917],{"separator":1916},[4582,6540,6541,6547],{},[4585,6542,6543],{},[3586,6544,6545],{"scriptlevel":2607,"displaystyle":1916},[898,6546,1812],{},[4585,6548,6549],{},[3586,6550,6551],{"scriptlevel":2607,"displaystyle":1916},[895,6552,6553,6555,6557,6559,6561,6567,6569,6571],{},[895,6554],{},[1750,6556,1766],{},[1742,6558,6381],{},[1969,6560,2658],{},[5535,6562,6563,6565],{},[898,6564,1666],{},[898,6566,5541],{},[1750,6568,1861],{},[1742,6570,6394],{},[1750,6572,1917],{"separator":1916},[4582,6574,6575,6585],{},[4585,6576,6577],{},[3586,6578,6579],{"scriptlevel":2607,"displaystyle":1916},[5535,6580,6581,6583],{},[898,6582,1666],{},[898,6584,5541],{},[4585,6586,6587],{},[3586,6588,6589],{"scriptlevel":2607,"displaystyle":1916},[895,6590,6591,6593,6595,6597,6599,6601],{},[895,6592],{},[1750,6594,1766],{},[898,6596,1666],{},[1750,6598,1758],{},[898,6600,5326],{},[898,6602,2313],{"mathvariant":1747},[902,6604,6605],{"encoding":904},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[724,6607,6608,6611,6612,6667,6668,6714,6715,2366],{},[38,6609,6610],{},"Řešení."," Z definice ",[883,6613,6615],{"className":6614},[886],[888,6616,6617],{"xmlns":890},[892,6618,6619,6664],{},[895,6620,6621,6627,6629,6631,6633,6635,6637,6639,6641,6643,6645,6647,6649,6651,6653,6655,6658,6660,6662],{},[5535,6622,6623,6625],{},[898,6624,1666],{},[898,6626,5541],{},[1750,6628,1766],{},[898,6630,1666],{},[1750,6632,1758],{},[898,6634,5326],{},[1750,6636,1766],{},[898,6638,1666],{},[1750,6640,1758],{},[1750,6642,1753],{"stretchy":1752},[1742,6644,3929],{},[898,6646,1666],{},[1750,6648,1861],{},[1742,6650,6419],{},[1750,6652,1763],{"stretchy":1752},[1750,6654,1766],{},[1742,6656,6657],{},"0,8",[898,6659,1666],{},[1750,6661,1758],{},[1742,6663,6419],{},[902,6665,6666],{"encoding":904},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[883,6669,6671],{"className":6670},[886],[888,6672,6673],{"xmlns":890},[892,6674,6675,6711],{},[895,6676,6677,6679,6681,6683,6685,6687,6689,6691,6693,6695,6697,6699,6701,6704,6706,6708],{},[898,6678,1812],{},[1750,6680,1766],{},[1742,6682,6381],{},[1750,6684,1753],{"stretchy":1752},[1742,6686,6657],{},[898,6688,1666],{},[1750,6690,1758],{},[1742,6692,6419],{},[1750,6694,1763],{"stretchy":1752},[1750,6696,1861],{},[1742,6698,6394],{},[1750,6700,1766],{},[1742,6702,6703],{},"0,72",[898,6705,1666],{},[1750,6707,1861],{},[1742,6709,6710],{},"47,5",[902,6712,6713],{"encoding":904},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[883,6716,6718],{"className":6717},[886],[888,6719,6720],{"xmlns":890},[892,6721,6722,6740],{},[895,6723,6724,6726,6728,6730,6732,6734,6736,6738],{},[898,6725,1666],{},[1750,6727,1766],{},[1742,6729,6703],{},[898,6731,1666],{},[1750,6733,1861],{},[1742,6735,6710],{},[1750,6737,1861],{},[1742,6739,5006],{},[902,6741,6742],{"encoding":904},"Y = 0{,}72Y + 47{,}5 + 55",[724,6744,6745],{},[883,6746,6748],{"className":6747},[886],[888,6749,6750],{"xmlns":890},[892,6751,6752,6796],{},[895,6753,6754,6757,6759,6761,6764,6767,6770,6772,6778,6780,6790,6793],{},[1742,6755,6756],{},"0,28",[898,6758,1666],{},[1750,6760,1766],{},[1742,6762,6763],{},"102,5",[1969,6765,6766],{},"  ",[1750,6768,6769],{},"⟹",[1969,6771,6766],{},[1699,6773,6774,6776],{},[898,6775,1666],{},[898,6777,1705],{},[1750,6779,1766],{},[3586,6781,6782],{"scriptlevel":2607,"displaystyle":1752},[3423,6783,6784,6787],{},[1742,6785,6786],{},"5125",[1742,6788,6789],{},"14",[1750,6791,6792],{},"≐",[1742,6794,6795],{},"366,071.",[902,6797,6798],{"encoding":904},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[724,6800,6801],{},"Rovnovážné veličiny:",[120,6803,6804,6839,6891,6945,6993],{},[123,6805,6806,1917],{},[883,6807,6809],{"className":6808},[886],[888,6810,6811],{"xmlns":890},[892,6812,6813,6836],{},[895,6814,6815,6821,6823,6831,6833],{},[1699,6816,6817,6819],{},[898,6818,1666],{},[898,6820,1705],{},[1750,6822,1766],{},[3586,6824,6825],{"scriptlevel":2607,"displaystyle":1752},[3423,6826,6827,6829],{},[1742,6828,6786],{},[1742,6830,6789],{},[1750,6832,6792],{},[1742,6834,6835],{},"366,071",[902,6837,6838],{"encoding":904},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[123,6840,6841,1917],{},[883,6842,6844],{"className":6843},[886],[888,6845,6846],{"xmlns":890},[892,6847,6848,6888],{},[895,6849,6850,6856,6858,6860,6862,6868,6870,6872,6874,6883,6885],{},[1699,6851,6852,6854],{},[898,6853,5326],{},[898,6855,1705],{},[1750,6857,1766],{},[1742,6859,3929],{},[1969,6861,2658],{},[1699,6863,6864,6866],{},[898,6865,1666],{},[898,6867,1705],{},[1750,6869,1861],{},[1742,6871,6419],{},[1750,6873,1766],{},[3586,6875,6876],{"scriptlevel":2607,"displaystyle":1752},[3423,6877,6878,6881],{},[1742,6879,6880],{},"1375",[1742,6882,6789],{},[1750,6884,6792],{},[1742,6886,6887],{},"98,214",[902,6889,6890],{"encoding":904},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[123,6892,6893,1917],{},[883,6894,6896],{"className":6895},[886],[888,6897,6898],{"xmlns":890},[892,6899,6900,6942],{},[895,6901,6902,6910,6912,6918,6920,6926,6928,6937,6939],{},[5950,6903,6904,6906,6908],{},[898,6905,1666],{},[898,6907,5541],{},[898,6909,1705],{},[1750,6911,1766],{},[1699,6913,6914,6916],{},[898,6915,1666],{},[898,6917,1705],{},[1750,6919,1758],{},[1699,6921,6922,6924],{},[898,6923,5326],{},[898,6925,1705],{},[1750,6927,1766],{},[3586,6929,6930],{"scriptlevel":2607,"displaystyle":1752},[3423,6931,6932,6935],{},[1742,6933,6934],{},"3750",[1742,6936,6789],{},[1750,6938,6792],{},[1742,6940,6941],{},"267,857",[902,6943,6944],{"encoding":904},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[123,6946,6947,1917],{},[883,6948,6950],{"className":6949},[886],[888,6951,6952],{"xmlns":890},[892,6953,6954,6990],{},[895,6955,6956,6962,6964,6970,6972,6974,6976,6985,6987],{},[1699,6957,6958,6960],{},[898,6959,1812],{},[898,6961,1705],{},[1750,6963,1766],{},[1699,6965,6966,6968],{},[898,6967,1666],{},[898,6969,1705],{},[1750,6971,1758],{},[1742,6973,5006],{},[1750,6975,1766],{},[3586,6977,6978],{"scriptlevel":2607,"displaystyle":1752},[3423,6979,6980,6983],{},[1742,6981,6982],{},"4355",[1742,6984,6789],{},[1750,6986,6792],{},[1742,6988,6989],{},"311,071",[902,6991,6992],{"encoding":904},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[123,6994,6995,7051],{},[883,6996,6998],{"className":6997},[886],[888,6999,7000],{"xmlns":890},[892,7001,7002,7048],{},[895,7003,7004,7010,7012,7020,7022,7028,7030,7032,7041,7043,7045],{},[1699,7005,7006,7008],{},[898,7007,1779],{},[898,7009,1705],{},[1750,7011,1766],{},[5950,7013,7014,7016,7018],{},[898,7015,1666],{},[898,7017,5541],{},[898,7019,1705],{},[1750,7021,1758],{},[1699,7023,7024,7026],{},[898,7025,1812],{},[898,7027,1705],{},[1750,7029,1766],{},[1750,7031,1758],{},[3586,7033,7034],{"scriptlevel":2607,"displaystyle":1752},[3423,7035,7036,7039],{},[1742,7037,7038],{},"605",[1742,7040,6789],{},[1750,7042,6792],{},[1750,7044,1758],{},[1742,7046,7047],{},"43,214",[902,7049,7050],{"encoding":904},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[724,7053,7054,5179,7056,7077,7078,7081,7082,7105,7106,2313],{},[38,7055,5178],{},[883,7057,7059],{"className":7058},[886],[888,7060,7061],{"xmlns":890},[892,7062,7063,7075],{},[895,7064,7065,7067,7069,7071,7073],{},[898,7066,1812],{},[1969,7068,1971],{},[898,7070,1974],{},[1969,7072,1971],{},[898,7074,1997],{},[902,7076,2000],{"encoding":904}," stále uvažuje ",[38,7079,7080],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[883,7083,7085],{"className":7084},[886],[888,7086,7087],{"xmlns":890},[892,7088,7089,7102],{},[895,7090,7091,7093,7095,7098,7100],{},[898,7092,2024],{},[1750,7094,1766],{},[898,7096,7097],{},"B",[1750,7099,1758],{},[898,7101,1773],{},[902,7103,7104],{"encoding":904},"X = B - M"," dává ",[38,7107,5200,7108],{},[883,7109,7111],{"className":7110},[886],[888,7112,7113],{"xmlns":890},[892,7114,7115,7131],{},[895,7116,7117,7119,7121,7123,7125,7127,7129],{},[898,7118,1812],{},[1969,7120,1971],{},[898,7122,1974],{},[1969,7124,1971],{},[898,7126,1997],{},[1969,7128,1971],{},[898,7130,2024],{},[902,7132,2027],{"encoding":904},[115,7134,7136],{"id":7135},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[198,7138,4443],{"id":7139},"zadání-modelu-2",[724,7141,7142,7143,1647,7146,5424,7167,7180,7181,4419,7184,7197],{},"Rozšíření o ",[38,7144,7145],{},"čistý export",[883,7147,7149],{"className":7148},[886],[888,7150,7151],{"xmlns":890},[892,7152,7153,7165],{},[895,7154,7155,7157,7159,7161,7163],{},[898,7156,2024],{},[1750,7158,1766],{},[898,7160,7097],{},[1750,7162,1758],{},[898,7164,1773],{},[902,7166,7104],{"encoding":904},[883,7168,7170],{"className":7169},[886],[888,7171,7172],{"xmlns":890},[892,7173,7174,7178],{},[895,7175,7176],{},[898,7177,7097],{},[902,7179,7097],{"encoding":904}," je hrubý export (",[614,7182,7183],{},"brutto export",[883,7185,7187],{"className":7186},[886],[888,7188,7189],{"xmlns":890},[892,7190,7191,7195],{},[895,7192,7193],{},[898,7194,1773],{},[902,7196,1773],{"encoding":904}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[724,7199,7200],{},[883,7201,7203],{"className":7202},[886],[888,7204,7205],{"xmlns":890},[892,7206,7207,7227],{},[895,7208,7209,7211,7213,7215,7217,7223,7225],{},[898,7210,1773],{},[1750,7212,1766],{},[898,7214,1773],{},[1750,7216,1753],{"stretchy":1752},[5535,7218,7219,7221],{},[898,7220,1666],{},[898,7222,5541],{},[1750,7224,1763],{"stretchy":1752},[898,7226,2313],{"mathvariant":1747},[902,7228,7229],{"encoding":904},"M = M(Y_D).",[724,7231,7232],{},"Podmínka rovnováhy:",[724,7234,7235],{},[883,7236,7238],{"className":7237},[886],[888,7239,7240],{"xmlns":890},[892,7241,7242,7279],{},[895,7243,7244,7246,7248,7250,7252,7254,7256,7258,7260,7262,7264,7266,7268,7270,7272,7275,7277],{},[898,7245,1666],{},[1750,7247,1766],{},[898,7249,1812],{},[1750,7251,1861],{},[898,7253,1974],{},[1750,7255,1861],{},[898,7257,1997],{},[1750,7259,1861],{},[898,7261,7097],{},[1750,7263,1758],{},[898,7265,1773],{},[898,7267,2313],{"mathvariant":1747},[2125,7269],{"width":2127},[1750,7271,1753],{"stretchy":1752},[1742,7273,7274],{},"7.10",[1969,7276,207],{},[1750,7278,1763],{"stretchy":1752},[902,7280,7281],{"encoding":904},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[198,7283,4513],{"id":7284},"soustava-rovnic-2",[724,7286,5685,7287,7321,7322,2366],{},[883,7288,7290],{"className":7289},[886],[888,7291,7292],{"xmlns":890},[892,7293,7294,7318],{},[895,7295,7296,7302,7304,7310,7312],{},[1699,7297,7298,7300],{},[898,7299,1974],{},[1750,7301,3751],{},[1750,7303,1917],{"separator":1916},[1699,7305,7306,7308],{},[898,7307,1997],{},[1750,7309,3751],{},[1750,7311,1917],{"separator":1916},[1699,7313,7314,7316],{},[898,7315,7097],{},[1750,7317,3751],{},[902,7319,7320],{"encoding":904},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[883,7323,7325],{"className":7324},[886],[888,7326,7327],{"xmlns":890},[892,7328,7329,7353],{},[895,7330,7331,7333,7335,7337,7339,7341,7343,7349,7351],{},[898,7332,1666],{},[1750,7334,1917],{"separator":1916},[898,7336,1812],{},[1750,7338,1917],{"separator":1916},[898,7340,5326],{},[1750,7342,1917],{"separator":1916},[5535,7344,7345,7347],{},[898,7346,1666],{},[898,7348,5541],{},[1750,7350,1917],{"separator":1916},[898,7352,1773],{},[902,7354,7355],{"encoding":904},"Y, C, T, Y_D, M",[724,7357,7358],{},[883,7359,7361],{"className":7360},[886],[888,7362,7363],{"xmlns":890},[892,7364,7365,7549],{},[895,7366,7367,7541,7543,7545,7547],{},[4577,7368,7369,7401,7431,7459,7491],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,7370,7371,7377],{},[4585,7372,7373],{},[3586,7374,7375],{"scriptlevel":2607,"displaystyle":1916},[898,7376,1812],{},[4585,7378,7379],{},[3586,7380,7381],{"scriptlevel":2607,"displaystyle":1916},[895,7382,7383,7385,7387,7389,7391,7397,7399],{},[895,7384],{},[1750,7386,1766],{},[898,7388,1812],{},[1750,7390,1753],{"stretchy":1752},[5535,7392,7393,7395],{},[898,7394,1666],{},[898,7396,5541],{},[1750,7398,1763],{"stretchy":1752},[1750,7400,1917],{"separator":1916},[4582,7402,7403,7413],{},[4585,7404,7405],{},[3586,7406,7407],{"scriptlevel":2607,"displaystyle":1916},[5535,7408,7409,7411],{},[898,7410,1666],{},[898,7412,5541],{},[4585,7414,7415],{},[3586,7416,7417],{"scriptlevel":2607,"displaystyle":1916},[895,7418,7419,7421,7423,7425,7427,7429],{},[895,7420],{},[1750,7422,1766],{},[898,7424,1666],{},[1750,7426,1758],{},[898,7428,5326],{},[1750,7430,1917],{"separator":1916},[4582,7432,7433,7439],{},[4585,7434,7435],{},[3586,7436,7437],{"scriptlevel":2607,"displaystyle":1916},[898,7438,5326],{},[4585,7440,7441],{},[3586,7442,7443],{"scriptlevel":2607,"displaystyle":1916},[895,7444,7445,7447,7449,7451,7453,7455,7457],{},[895,7446],{},[1750,7448,1766],{},[898,7450,5326],{},[1750,7452,1753],{"stretchy":1752},[898,7454,1666],{},[1750,7456,1763],{"stretchy":1752},[1750,7458,1917],{"separator":1916},[4582,7460,7461,7467],{},[4585,7462,7463],{},[3586,7464,7465],{"scriptlevel":2607,"displaystyle":1916},[898,7466,1773],{},[4585,7468,7469],{},[3586,7470,7471],{"scriptlevel":2607,"displaystyle":1916},[895,7472,7473,7475,7477,7479,7481,7487,7489],{},[895,7474],{},[1750,7476,1766],{},[898,7478,1773],{},[1750,7480,1753],{"stretchy":1752},[5535,7482,7483,7485],{},[898,7484,1666],{},[898,7486,5541],{},[1750,7488,1763],{"stretchy":1752},[1750,7490,1917],{"separator":1916},[4582,7492,7493,7499],{},[4585,7494,7495],{},[3586,7496,7497],{"scriptlevel":2607,"displaystyle":1916},[898,7498,1666],{},[4585,7500,7501],{},[3586,7502,7503],{"scriptlevel":2607,"displaystyle":1916},[895,7504,7505,7507,7509,7511,7513,7519,7521,7527,7529,7535,7537,7539],{},[895,7506],{},[1750,7508,1766],{},[898,7510,1812],{},[1750,7512,1861],{},[1699,7514,7515,7517],{},[898,7516,1974],{},[1750,7518,3751],{},[1750,7520,1861],{},[1699,7522,7523,7525],{},[898,7524,1997],{},[1750,7526,3751],{},[1750,7528,1861],{},[1699,7530,7531,7533],{},[898,7532,7097],{},[1750,7534,3751],{},[1750,7536,1758],{},[898,7538,1773],{},[898,7540,2313],{"mathvariant":1747},[2125,7542],{"width":2127},[1750,7544,1753],{"stretchy":1752},[1742,7546,7274],{},[1750,7548,1763],{"stretchy":1752},[902,7550,7551],{"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)",[198,7553,7555],{"id":7554},"příklad-75","Příklad 7.5",[724,7557,7558,7559,1343,7591,1343,7618,1343,7639,1343,7662,1343,7684,7707],{},"Dáno: ",[883,7560,7562],{"className":7561},[886],[888,7563,7564],{"xmlns":890},[892,7565,7566,7588],{},[895,7567,7568,7570,7572,7575,7577,7583,7585],{},[898,7569,1812],{},[1750,7571,1766],{},[1742,7573,7574],{},"0,75",[1969,7576,2658],{},[5535,7578,7579,7581],{},[898,7580,1666],{},[898,7582,5541],{},[1750,7584,1861],{},[1742,7586,7587],{},"750",[902,7589,7590],{"encoding":904},"C = 0{,}75\\,Y_D + 750",[883,7592,7594],{"className":7593},[886],[888,7595,7596],{"xmlns":890},[892,7597,7598,7615],{},[895,7599,7600,7602,7604,7607,7609],{},[898,7601,1773],{},[1750,7603,1766],{},[1742,7605,7606],{},"0,15",[1969,7608,2658],{},[5535,7610,7611,7613],{},[898,7612,1666],{},[898,7614,5541],{},[902,7616,7617],{"encoding":904},"M = 0{,}15\\,Y_D",[883,7619,7621],{"className":7620},[886],[888,7622,7623],{"xmlns":890},[892,7624,7625,7636],{},[895,7626,7627,7629,7631,7634],{},[898,7628,5326],{},[1750,7630,1766],{},[1742,7632,7633],{},"0,25",[898,7635,1666],{},[902,7637,7638],{"encoding":904},"T = 0{,}25Y",[883,7640,7642],{"className":7641},[886],[888,7643,7644],{"xmlns":890},[892,7645,7646,7659],{},[895,7647,7648,7654,7656],{},[1699,7649,7650,7652],{},[898,7651,1974],{},[1750,7653,3751],{},[1750,7655,1766],{},[1742,7657,7658],{},"500",[902,7660,7661],{"encoding":904},"I^* = 500",[883,7663,7665],{"className":7664},[886],[888,7666,7667],{"xmlns":890},[892,7668,7669,7681],{},[895,7670,7671,7677,7679],{},[1699,7672,7673,7675],{},[898,7674,1997],{},[1750,7676,3751],{},[1750,7678,1766],{},[1742,7680,4236],{},[902,7682,7683],{"encoding":904},"G^* = 150",[883,7685,7687],{"className":7686},[886],[888,7688,7689],{"xmlns":890},[892,7690,7691,7704],{},[895,7692,7693,7699,7701],{},[1699,7694,7695,7697],{},[898,7696,7097],{},[1750,7698,3751],{},[1750,7700,1766],{},[1742,7702,7703],{},"800",[902,7705,7706],{"encoding":904},"B^* = 800",". Soustava:",[724,7709,7710],{},[883,7711,7713],{"className":7712},[886],[888,7714,7715],{"xmlns":890},[892,7716,7717,7939],{},[4577,7718,7719,7766,7808,7845,7888],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,7720,7721,7738],{},[4585,7722,7723],{},[3586,7724,7725],{"scriptlevel":2607,"displaystyle":1916},[895,7726,7727,7729,7731,7733,7735],{},[1750,7728,1753],{"stretchy":1752},[898,7730,1920],{},[1742,7732,1744],{},[1750,7734,1763],{"stretchy":1752},[1969,7736,7737],{}," ",[4585,7739,7740],{},[3586,7741,7742],{"scriptlevel":2607,"displaystyle":1916},[895,7743,7744,7746,7748,7750,7752,7754,7760,7762,7764],{},[895,7745],{},[898,7747,1812],{},[1750,7749,1766],{},[1742,7751,7574],{},[1969,7753,2658],{},[5535,7755,7756,7758],{},[898,7757,1666],{},[898,7759,5541],{},[1750,7761,1861],{},[1742,7763,7587],{},[1750,7765,1917],{"separator":1916},[4582,7767,7768,7784],{},[4585,7769,7770],{},[3586,7771,7772],{"scriptlevel":2607,"displaystyle":1916},[895,7773,7774,7776,7778,7780,7782],{},[1750,7775,1753],{"stretchy":1752},[898,7777,1920],{},[1742,7779,1872],{},[1750,7781,1763],{"stretchy":1752},[1969,7783,7737],{},[4585,7785,7786],{},[3586,7787,7788],{"scriptlevel":2607,"displaystyle":1916},[895,7789,7790,7792,7798,7800,7802,7804,7806],{},[895,7791],{},[5535,7793,7794,7796],{},[898,7795,1666],{},[898,7797,5541],{},[1750,7799,1766],{},[898,7801,1666],{},[1750,7803,1758],{},[898,7805,5326],{},[1750,7807,1917],{"separator":1916},[4582,7809,7810,7827],{},[4585,7811,7812],{},[3586,7813,7814],{"scriptlevel":2607,"displaystyle":1916},[895,7815,7816,7818,7820,7823,7825],{},[1750,7817,1753],{"stretchy":1752},[898,7819,1920],{},[1742,7821,7822],{},"3",[1750,7824,1763],{"stretchy":1752},[1969,7826,7737],{},[4585,7828,7829],{},[3586,7830,7831],{"scriptlevel":2607,"displaystyle":1916},[895,7832,7833,7835,7837,7839,7841,7843],{},[895,7834],{},[898,7836,5326],{},[1750,7838,1766],{},[1742,7840,7633],{},[898,7842,1666],{},[1750,7844,1917],{"separator":1916},[4582,7846,7847,7864],{},[4585,7848,7849],{},[3586,7850,7851],{"scriptlevel":2607,"displaystyle":1916},[895,7852,7853,7855,7857,7860,7862],{},[1750,7854,1753],{"stretchy":1752},[898,7856,1920],{},[1742,7858,7859],{},"4",[1750,7861,1763],{"stretchy":1752},[1969,7863,7737],{},[4585,7865,7866],{},[3586,7867,7868],{"scriptlevel":2607,"displaystyle":1916},[895,7869,7870,7872,7874,7876,7878,7880,7886],{},[895,7871],{},[898,7873,1773],{},[1750,7875,1766],{},[1742,7877,7606],{},[1969,7879,2658],{},[5535,7881,7882,7884],{},[898,7883,1666],{},[898,7885,5541],{},[1750,7887,1917],{"separator":1916},[4582,7889,7890,7907],{},[4585,7891,7892],{},[3586,7893,7894],{"scriptlevel":2607,"displaystyle":1916},[895,7895,7896,7898,7900,7903,7905],{},[1750,7897,1753],{"stretchy":1752},[898,7899,1920],{},[1742,7901,7902],{},"5",[1750,7904,1763],{"stretchy":1752},[1969,7906,7737],{},[4585,7908,7909],{},[3586,7910,7911],{"scriptlevel":2607,"displaystyle":1916},[895,7912,7913,7915,7917,7919,7921,7923,7925,7927,7929,7931,7933,7935,7937],{},[895,7914],{},[898,7916,1666],{},[1750,7918,1766],{},[898,7920,1812],{},[1750,7922,1861],{},[1742,7924,7658],{},[1750,7926,1861],{},[1742,7928,4236],{},[1750,7930,1861],{},[1742,7932,7703],{},[1750,7934,1758],{},[898,7936,1773],{},[898,7938,2313],{"mathvariant":1747},[902,7940,7941],{"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}",[724,7943,7944,7945,7979],{},"Postupná substituce — z (r3) do (r2): ",[883,7946,7948],{"className":7947},[886],[888,7949,7950],{"xmlns":890},[892,7951,7952,7976],{},[895,7953,7954,7960,7962,7964,7966,7968,7970,7972,7974],{},[5535,7955,7956,7958],{},[898,7957,1666],{},[898,7959,5541],{},[1750,7961,1766],{},[898,7963,1666],{},[1750,7965,1758],{},[1742,7967,7633],{},[898,7969,1666],{},[1750,7971,1766],{},[1742,7973,7574],{},[898,7975,1666],{},[902,7977,7978],{"encoding":904},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[724,7981,7982],{},[883,7983,7985],{"className":7984},[886],[888,7986,7987],{"xmlns":890},[892,7988,7989,8031],{},[895,7990,7991,7993,7995,7997,7999,8001,8003,8005,8007,8010,8012,8014,8016,8018,8020,8023,8025,8027,8029],{},[1750,7992,1753],{"stretchy":1752},[898,7994,1920],{},[1742,7996,3219],{},[1750,7998,1763],{"stretchy":1752},[1969,8000,7737],{},[898,8002,1812],{},[1750,8004,1766],{},[1742,8006,7574],{},[1750,8008,8009],{},"⋅",[1742,8011,7574],{},[898,8013,1666],{},[1750,8015,1861],{},[1742,8017,7587],{},[1750,8019,1766],{},[1742,8021,8022],{},"0,5625",[898,8024,1666],{},[1750,8026,1861],{},[1742,8028,7587],{},[1750,8030,1917],{"separator":1916},[902,8032,8033],{"encoding":904},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[724,8035,8036],{},[883,8037,8039],{"className":8038},[886],[888,8040,8041],{"xmlns":890},[892,8042,8043,8077],{},[895,8044,8045,8047,8049,8052,8054,8056,8058,8060,8062,8064,8066,8068,8070,8073,8075],{},[1750,8046,1753],{"stretchy":1752},[898,8048,1920],{},[1742,8050,8051],{},"7",[1750,8053,1763],{"stretchy":1752},[1969,8055,7737],{},[898,8057,1773],{},[1750,8059,1766],{},[1742,8061,7606],{},[1750,8063,8009],{},[1742,8065,7574],{},[898,8067,1666],{},[1750,8069,1766],{},[1742,8071,8072],{},"0,1125",[898,8074,1666],{},[898,8076,2313],{"mathvariant":1747},[902,8078,8079],{"encoding":904},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[724,8081,8082],{},"Dosazením do (r5):",[724,8084,8085],{},[883,8086,8088],{"className":8087},[886],[888,8089,8090],{"xmlns":890},[892,8091,8092,8136],{},[895,8093,8094,8096,8098,8100,8102,8104,8106,8108,8110,8112,8114,8116,8118,8120,8122,8124,8126,8129,8131,8133],{},[898,8095,1666],{},[1750,8097,1766],{},[1742,8099,8022],{},[898,8101,1666],{},[1750,8103,1861],{},[1742,8105,7587],{},[1750,8107,1861],{},[1742,8109,7658],{},[1750,8111,1861],{},[1742,8113,4236],{},[1750,8115,1861],{},[1742,8117,7703],{},[1750,8119,1758],{},[1742,8121,8072],{},[898,8123,1666],{},[1750,8125,1766],{},[1742,8127,8128],{},"0,45",[898,8130,1666],{},[1750,8132,1861],{},[1742,8134,8135],{},"2200.",[902,8137,8138],{"encoding":904},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[724,8140,8141,8142,8164,8165,8188],{},"Odtud ",[883,8143,8145],{"className":8144},[886],[888,8146,8147],{"xmlns":890},[892,8148,8149,8161],{},[895,8150,8151,8154,8156,8158],{},[1742,8152,8153],{},"0,55",[898,8155,1666],{},[1750,8157,1766],{},[1742,8159,8160],{},"2200",[902,8162,8163],{"encoding":904},"0{,}55Y = 2200",", tedy ",[883,8166,8168],{"className":8167},[886],[888,8169,8170],{"xmlns":890},[892,8171,8172,8185],{},[895,8173,8174,8180,8182],{},[1699,8175,8176,8178],{},[898,8177,1666],{},[898,8179,1705],{},[1750,8181,1766],{},[1742,8183,8184],{},"4000",[902,8186,8187],{"encoding":904},"Y^E = 4000",". Rovnovážné veličiny:",[120,8190,8191,8214,8247,8282,8315,8351],{},[123,8192,8193,1917],{},[883,8194,8196],{"className":8195},[886],[888,8197,8198],{"xmlns":890},[892,8199,8200,8212],{},[895,8201,8202,8208,8210],{},[1699,8203,8204,8206],{},[898,8205,1666],{},[898,8207,1705],{},[1750,8209,1766],{},[1742,8211,8184],{},[902,8213,8187],{"encoding":904},[123,8215,8216,1917],{},[883,8217,8219],{"className":8218},[886],[888,8220,8221],{"xmlns":890},[892,8222,8223,8244],{},[895,8224,8225,8231,8233,8235,8237,8239,8241],{},[1699,8226,8227,8229],{},[898,8228,5326],{},[898,8230,1705],{},[1750,8232,1766],{},[1742,8234,7633],{},[1750,8236,8009],{},[1742,8238,8184],{},[1750,8240,1766],{},[1742,8242,8243],{},"1000",[902,8245,8246],{"encoding":904},"T^E = 0{,}25 \\cdot 4000 = 1000",[123,8248,8249,1917],{},[883,8250,8252],{"className":8251},[886],[888,8253,8254],{"xmlns":890},[892,8255,8256,8279],{},[895,8257,8258,8266,8268,8270,8272,8274,8276],{},[5950,8259,8260,8262,8264],{},[898,8261,1666],{},[898,8263,5541],{},[898,8265,1705],{},[1750,8267,1766],{},[1742,8269,7574],{},[1750,8271,8009],{},[1742,8273,8184],{},[1750,8275,1766],{},[1742,8277,8278],{},"3000",[902,8280,8281],{"encoding":904},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[123,8283,8284,1917],{},[883,8285,8287],{"className":8286},[886],[888,8288,8289],{"xmlns":890},[892,8290,8291,8312],{},[895,8292,8293,8299,8301,8303,8305,8307,8309],{},[1699,8294,8295,8297],{},[898,8296,1773],{},[898,8298,1705],{},[1750,8300,1766],{},[1742,8302,7606],{},[1750,8304,8009],{},[1742,8306,8278],{},[1750,8308,1766],{},[1742,8310,8311],{},"450",[902,8313,8314],{"encoding":904},"M^E = 0{,}15 \\cdot 3000 = 450",[123,8316,8317,1917],{},[883,8318,8320],{"className":8319},[886],[888,8321,8322],{"xmlns":890},[892,8323,8324,8348],{},[895,8325,8326,8332,8334,8336,8338,8340,8342,8344,8346],{},[1699,8327,8328,8330],{},[898,8329,1812],{},[898,8331,1705],{},[1750,8333,1766],{},[1742,8335,7574],{},[1750,8337,8009],{},[1742,8339,8278],{},[1750,8341,1861],{},[1742,8343,7587],{},[1750,8345,1766],{},[1742,8347,8278],{},[902,8349,8350],{"encoding":904},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[123,8352,8353,8393],{},[883,8354,8356],{"className":8355},[886],[888,8357,8358],{"xmlns":890},[892,8359,8360,8390],{},[895,8361,8362,8368,8370,8378,8380,8386,8388],{},[1699,8363,8364,8366],{},[898,8365,1779],{},[898,8367,1705],{},[1750,8369,1766],{},[5950,8371,8372,8374,8376],{},[898,8373,1666],{},[898,8375,5541],{},[898,8377,1705],{},[1750,8379,1758],{},[1699,8381,8382,8384],{},[898,8383,1812],{},[898,8385,1705],{},[1750,8387,1766],{},[1742,8389,2607],{},[902,8391,8392],{"encoding":904},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[724,8395,8396,8398,8399,1343,8416,2028,8437,8462,8463,8466,8467,8480,8481,2313],{},[38,8397,5178],{}," Modely ",[883,8400,8402],{"className":8401},[886],[888,8403,8404],{"xmlns":890},[892,8405,8406,8414],{},[895,8407,8408,8410,8412],{},[898,8409,1812],{},[1969,8411,1971],{},[898,8413,1974],{},[902,8415,1977],{"encoding":904},[883,8417,8419],{"className":8418},[886],[888,8420,8421],{"xmlns":890},[892,8422,8423,8435],{},[895,8424,8425,8427,8429,8431,8433],{},[898,8426,1812],{},[1969,8428,1971],{},[898,8430,1974],{},[1969,8432,1971],{},[898,8434,1997],{},[902,8436,2000],{"encoding":904},[883,8438,8440],{"className":8439},[886],[888,8441,8442],{"xmlns":890},[892,8443,8444,8460],{},[895,8445,8446,8448,8450,8452,8454,8456,8458],{},[898,8447,1812],{},[1969,8449,1971],{},[898,8451,1974],{},[1969,8453,1971],{},[898,8455,1997],{},[1969,8457,1971],{},[898,8459,2024],{},[902,8461,2027],{"encoding":904}," pokládají investice za ",[38,8464,8465],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[883,8468,8470],{"className":8469},[886],[888,8471,8472],{"xmlns":890},[892,8473,8474,8478],{},[895,8475,8476],{},[898,8477,1920],{},[902,8479,1920],{"encoding":904},". Přidáním trhu peněz a úrokové míry vzniká ",[38,8482,8483],{},"model IS-LM",[115,8485,8487],{"id":8486},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[724,8489,8490,8491,8495,8496,8499,8500,8503],{},"V článku ",[207,8492,8494],{"className":8493,"dataFsResolvedFilePath":827,"href":828},[210],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[38,8497,8498],{},"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 ",[38,8501,8502],{},"výraznější"," než v mikroekonomických modelech.",[724,8505,8506],{},[4434,8507],{"alt":8508,"className":8509,"src":8510},"imek-multiplikatorovy-efekt-chain",[210,4438],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[724,8512,8513,8514,1343,8531,1343,8552,8577,8578,8581,8582,8600,8601,8619,8620,8638,8639,8642,8643,1343,8660,8677,8678,8680],{},"V modelech ",[883,8515,8517],{"className":8516},[886],[888,8518,8519],{"xmlns":890},[892,8520,8521,8529],{},[895,8522,8523,8525,8527],{},[898,8524,1812],{},[1969,8526,1971],{},[898,8528,1974],{},[902,8530,1977],{"encoding":904},[883,8532,8534],{"className":8533},[886],[888,8535,8536],{"xmlns":890},[892,8537,8538,8550],{},[895,8539,8540,8542,8544,8546,8548],{},[898,8541,1812],{},[1969,8543,1971],{},[898,8545,1974],{},[1969,8547,1971],{},[898,8549,1997],{},[902,8551,2000],{"encoding":904},[883,8553,8555],{"className":8554},[886],[888,8556,8557],{"xmlns":890},[892,8558,8559,8575],{},[895,8560,8561,8563,8565,8567,8569,8571,8573],{},[898,8562,1812],{},[1969,8564,1971],{},[898,8566,1974],{},[1969,8568,1971],{},[898,8570,1997],{},[1969,8572,1971],{},[898,8574,2024],{},[902,8576,2027],{"encoding":904}," se vyšetřuje vliv změn ",[38,8579,8580],{},"exogenních"," veličin (plánovaných investic ",[883,8583,8585],{"className":8584},[886],[888,8586,8587],{"xmlns":890},[892,8588,8589,8597],{},[895,8590,8591],{},[1699,8592,8593,8595],{},[898,8594,1974],{},[1750,8596,3751],{},[902,8598,8599],{"encoding":904},"I^*",", vládních výdajů ",[883,8602,8604],{"className":8603},[886],[888,8605,8606],{"xmlns":890},[892,8607,8608,8616],{},[895,8609,8610],{},[1699,8611,8612,8614],{},[898,8613,1997],{},[1750,8615,3751],{},[902,8617,8618],{"encoding":904},"G^*",", exportu ",[883,8621,8623],{"className":8622},[886],[888,8624,8625],{"xmlns":890},[892,8626,8627,8635],{},[895,8628,8629],{},[1699,8630,8631,8633],{},[898,8632,7097],{},[1750,8634,3751],{},[902,8636,8637],{"encoding":904},"B^*",") na změny ",[38,8640,8641],{},"endogenních"," rovnovážných veličin (",[883,8644,8646],{"className":8645},[886],[888,8647,8648],{"xmlns":890},[892,8649,8650,8658],{},[895,8651,8652],{},[1699,8653,8654,8656],{},[898,8655,1666],{},[898,8657,1705],{},[902,8659,1708],{"encoding":904},[883,8661,8663],{"className":8662},[886],[888,8664,8665],{"xmlns":890},[892,8666,8667,8675],{},[895,8668,8669],{},[1699,8670,8671,8673],{},[898,8672,1812],{},[898,8674,1705],{},[902,8676,4695],{"encoding":904}," atd.). Tyto citlivosti se vyjadřují ",[38,8679,1730],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[198,8682,8684],{"id":8683},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[724,8686,4719,8687,8710,8711,8755],{},[883,8688,8690],{"className":8689},[886],[888,8691,8692],{"xmlns":890},[892,8693,8694,8708],{},[895,8695,8696,8698,8700,8702,8704,8706],{},[898,8697,1812],{},[1750,8699,1766],{},[898,8701,207],{},[898,8703,1666],{},[1750,8705,1861],{},[898,8707,2573],{},[902,8709,2720],{"encoding":904}," dává (7.7) redukovaný tvar ",[883,8712,8714],{"className":8713},[886],[888,8715,8716],{"xmlns":890},[892,8717,8718,8752],{},[895,8719,8720,8726,8728],{},[1699,8721,8722,8724],{},[898,8723,1666],{},[898,8725,1705],{},[1750,8727,1766],{},[3586,8729,8730],{"scriptlevel":2607,"displaystyle":1916},[3423,8731,8732,8744],{},[895,8733,8734,8736,8738],{},[898,8735,2573],{},[1750,8737,1861],{},[1699,8739,8740,8742],{},[898,8741,1974],{},[1750,8743,3751],{},[895,8745,8746,8748,8750],{},[1742,8747,1744],{},[1750,8749,1758],{},[898,8751,207],{},[902,8753,8754],{"encoding":904},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[724,8757,8758],{},[883,8759,8761],{"className":8760},[886],[888,8762,8763],{"xmlns":890},[892,8764,8765,8835],{},[895,8766,8767,8786,8788,8818,8820],{},[3423,8768,8769,8780],{},[895,8770,8771,8774],{},[898,8772,8773],{"mathvariant":1747},"∂",[1699,8775,8776,8778],{},[898,8777,1666],{},[898,8779,1705],{},[895,8781,8782,8784],{},[898,8783,8773],{"mathvariant":1747},[898,8785,207],{},[1750,8787,1766],{},[3423,8789,8790,8802],{},[895,8791,8792,8794,8796],{},[898,8793,2573],{},[1750,8795,1861],{},[1699,8797,8798,8800],{},[898,8799,1974],{},[1750,8801,3751],{},[895,8803,8804,8806,8808,8810,8812],{},[1750,8805,1753],{"stretchy":1752},[1742,8807,1744],{},[1750,8809,1758],{},[898,8811,207],{},[1699,8813,8814,8816],{},[1750,8815,1763],{"stretchy":1752},[1742,8817,1872],{},[2125,8819],{"width":2127},[895,8821,8822,8825,8832],{},[1969,8823,8824],{},"(multiplik",[3215,8826,8827,8829],{"accent":1916},[1969,8828,207],{},[1750,8830,8831],{},"ˊ",[1969,8833,8834],{},"tor MPC)",[902,8836,8837],{"encoding":904},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[724,8839,8840],{},[883,8841,8843],{"className":8842},[886],[888,8844,8845],{"xmlns":890},[892,8846,8847,8916],{},[895,8848,8849,8867,8869,8881,8883],{},[3423,8850,8851,8861],{},[895,8852,8853,8855],{},[898,8854,8773],{"mathvariant":1747},[1699,8856,8857,8859],{},[898,8858,1666],{},[898,8860,1705],{},[895,8862,8863,8865],{},[898,8864,8773],{"mathvariant":1747},[898,8866,2573],{},[1750,8868,1766],{},[3423,8870,8871,8873],{},[1742,8872,1744],{},[895,8874,8875,8877,8879],{},[1742,8876,1744],{},[1750,8878,1758],{},[898,8880,207],{},[2125,8882],{"width":2127},[895,8884,8885,8887,8893,8896,8903,8906,8913],{},[1969,8886,8824],{},[3215,8888,8889,8891],{"accent":1916},[1969,8890,207],{},[1750,8892,8831],{},[1969,8894,8895],{},"tor autonomn",[3215,8897,8898,8901],{"accent":1916},[1969,8899,8900],{},"ı",[1750,8902,8831],{},[1969,8904,8905],{}," spot",[3215,8907,8908,8910],{"accent":1916},[1969,8909,1920],{},[1750,8911,8912],{},"ˇ",[1969,8914,8915],{},"eby)",[902,8917,8918],{"encoding":904},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[724,8920,8921],{},[883,8922,8924],{"className":8923},[886],[888,8925,8926],{"xmlns":890},[892,8927,8928,8995],{},[895,8929,8930,8952,8954,8966,8968,8980,8982],{},[3423,8931,8932,8942],{},[895,8933,8934,8936],{},[898,8935,8773],{"mathvariant":1747},[1699,8937,8938,8940],{},[898,8939,1666],{},[898,8941,1705],{},[895,8943,8944,8946],{},[898,8945,8773],{"mathvariant":1747},[1699,8947,8948,8950],{},[898,8949,1974],{},[1750,8951,3751],{},[1750,8953,1766],{},[3423,8955,8956,8958],{},[1742,8957,1744],{},[895,8959,8960,8962,8964],{},[1742,8961,1744],{},[1750,8963,1758],{},[898,8965,207],{},[1750,8967,1766],{},[3423,8969,8970,8972],{},[1742,8971,1744],{},[895,8973,8974,8976,8978],{},[898,8975,1773],{},[898,8977,1776],{},[898,8979,1779],{},[2125,8981],{"width":2127},[895,8983,8984,8986,8992],{},[1969,8985,8824],{},[3215,8987,8988,8990],{"accent":1916},[1969,8989,207],{},[1750,8991,8831],{},[1969,8993,8994],{},"tor investic)",[902,8996,8997],{"encoding":904},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1785,8999,9000],{},[724,9001,9002,9004,9005,9008,9009,9022,9023,9040,9041,9059,9060,9104,9105,5249,9122,9125,9126,9143],{},[883,9003,1791],{}," Intuice — proč Keynesův multiplikátor funguje\nInvestice o 1 Kč se stanou něčím ",[38,9006,9007],{},"důchodem","; z něj se utratí ",[883,9010,9012],{"className":9011},[886],[888,9013,9014],{"xmlns":890},[892,9015,9016,9020],{},[895,9017,9018],{},[898,9019,207],{},[902,9021,207],{"encoding":904}," Kč (= ",[883,9024,9026],{"className":9025},[886],[888,9027,9028],{"xmlns":890},[892,9029,9030,9038],{},[895,9031,9032,9034,9036],{},[898,9033,1773],{},[898,9035,1776],{},[898,9037,1812],{},[902,9039,1815],{"encoding":904},"), to je zase něčí důchod, z něj ",[883,9042,9044],{"className":9043},[886],[888,9045,9046],{"xmlns":890},[892,9047,9048,9056],{},[895,9049,9050],{},[1699,9051,9052,9054],{},[898,9053,207],{},[1742,9055,1872],{},[902,9057,9058],{"encoding":904},"a^2"," Kč… Součet geometrické řady ",[883,9061,9063],{"className":9062},[886],[888,9064,9065],{"xmlns":890},[892,9066,9067,9101],{},[895,9068,9069,9071,9073,9075,9077,9083,9085,9087,9089],{},[1742,9070,1744],{},[1750,9072,1861],{},[898,9074,207],{},[1750,9076,1861],{},[1699,9078,9079,9081],{},[898,9080,207],{},[1742,9082,1872],{},[1750,9084,1861],{},[1750,9086,1877],{},[1750,9088,1766],{},[3423,9090,9091,9093],{},[1742,9092,1744],{},[895,9094,9095,9097,9099],{},[1742,9096,1744],{},[1750,9098,1758],{},[898,9100,207],{},[902,9102,9103],{"encoding":904},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[883,9106,9108],{"className":9107},[886],[888,9109,9110],{"xmlns":890},[892,9111,9112,9120],{},[895,9113,9114],{},[1699,9115,9116,9118],{},[898,9117,1666],{},[898,9119,1705],{},[902,9121,1708],{"encoding":904},[38,9123,9124],{},"více"," než korunu — čím vyšší ",[883,9127,9129],{"className":9128},[886],[888,9130,9131],{"xmlns":890},[892,9132,9133,9141],{},[895,9134,9135,9137,9139],{},[898,9136,1773],{},[898,9138,1776],{},[898,9140,1812],{},[902,9142,1815],{"encoding":904},", tím silnější multiplikační efekt.",[724,9145,9146,9149,9150,9176,9177,9180,9181,2028,9202,9227,9228,2313],{},[38,9147,9148],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[883,9151,9153],{"className":9152},[886],[888,9154,9155],{"xmlns":890},[892,9156,9157,9173],{},[895,9158,9159],{},[3586,9160,9161],{"scriptlevel":2607,"displaystyle":1752},[3423,9162,9163,9165],{},[1742,9164,1744],{},[895,9166,9167,9169,9171],{},[1742,9168,1744],{},[1750,9170,1758],{},[898,9172,207],{},[902,9174,9175],{"encoding":904},"\\tfrac{1}{1-a}",", což je standardní ",[38,9178,9179],{},"Keynesův multiplikátor",". Analogicky se v modelech ",[883,9182,9184],{"className":9183},[886],[888,9185,9186],{"xmlns":890},[892,9187,9188,9200],{},[895,9189,9190,9192,9194,9196,9198],{},[898,9191,1812],{},[1969,9193,1971],{},[898,9195,1974],{},[1969,9197,1971],{},[898,9199,1997],{},[902,9201,2000],{"encoding":904},[883,9203,9205],{"className":9204},[886],[888,9206,9207],{"xmlns":890},[892,9208,9209,9225],{},[895,9210,9211,9213,9215,9217,9219,9221,9223],{},[898,9212,1812],{},[1969,9214,1971],{},[898,9216,1974],{},[1969,9218,1971],{},[898,9220,1997],{},[1969,9222,1971],{},[898,9224,2024],{},[902,9226,2027],{"encoding":904}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[207,9229,9231],{"className":9230,"dataFsResolvedFilePath":800,"href":801},[210],"poptávka a nabídka",[115,9233,9235],{"id":9234},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[724,9237,8513,9238,1343,9255,2028,9276,9301,9302,2084,9305,9326,9327,1647,9330,9343,9344,9375,9376,9394,9395,9398,9399,9401,9402,9423],{},[883,9239,9241],{"className":9240},[886],[888,9242,9243],{"xmlns":890},[892,9244,9245,9253],{},[895,9246,9247,9249,9251],{},[898,9248,1812],{},[1969,9250,1971],{},[898,9252,1974],{},[902,9254,1977],{"encoding":904},[883,9256,9258],{"className":9257},[886],[888,9259,9260],{"xmlns":890},[892,9261,9262,9274],{},[895,9263,9264,9266,9268,9270,9272],{},[898,9265,1812],{},[1969,9267,1971],{},[898,9269,1974],{},[1969,9271,1971],{},[898,9273,1997],{},[902,9275,2000],{"encoding":904},[883,9277,9279],{"className":9278},[886],[888,9280,9281],{"xmlns":890},[892,9282,9283,9299],{},[895,9284,9285,9287,9289,9291,9293,9295,9297],{},[898,9286,1812],{},[1969,9288,1971],{},[898,9290,1974],{},[1969,9292,1971],{},[898,9294,1997],{},[1969,9296,1971],{},[898,9298,2024],{},[902,9300,2027],{"encoding":904}," byly ",[38,9303,9304],{},"investice konstantní",[883,9306,9308],{"className":9307},[886],[888,9309,9310],{"xmlns":890},[892,9311,9312,9324],{},[895,9313,9314,9316,9318],{},[898,9315,1974],{},[1750,9317,1766],{},[1699,9319,9320,9322],{},[898,9321,1974],{},[1750,9323,3751],{},[902,9325,4538],{"encoding":904},"). Reálnější je předpoklad, že ",[38,9328,9329],{},"investice závisejí na úrokové míře",[883,9331,9333],{"className":9332},[886],[888,9334,9335],{"xmlns":890},[892,9336,9337,9341],{},[895,9338,9339],{},[898,9340,1920],{},[902,9342,1920],{"encoding":904}," — klesající funkce ",[883,9345,9347],{"className":9346},[886],[888,9348,9349],{"xmlns":890},[892,9350,9351,9372],{},[895,9352,9353,9355,9357,9359,9361,9363,9366,9368,9370],{},[898,9354,1974],{},[1750,9356,1753],{"stretchy":1752},[898,9358,1920],{},[1750,9360,1763],{"stretchy":1752},[1750,9362,1766],{},[898,9364,9365],{},"c",[898,9367,1920],{},[1750,9369,1861],{},[898,9371,3429],{},[902,9373,9374],{"encoding":904},"I(r) = cr + d"," s ",[883,9377,9379],{"className":9378},[886],[888,9380,9381],{"xmlns":890},[892,9382,9383,9391],{},[895,9384,9385,9387,9389],{},[898,9386,9365],{},[1750,9388,2624],{},[1742,9390,2607],{},[902,9392,9393],{"encoding":904},"c \u003C 0",". Přidáním ",[38,9396,9397],{},"trhu peněz"," k trhu zboží vzniká model ",[38,9400,1684],{}," se dvěma neznámými ",[883,9403,9405],{"className":9404},[886],[888,9406,9407],{"xmlns":890},[892,9408,9409,9421],{},[895,9410,9411,9413,9415,9417,9419],{},[1750,9412,1753],{"stretchy":1752},[898,9414,1666],{},[1750,9416,1917],{"separator":1916},[898,9418,1920],{},[1750,9420,1763],{"stretchy":1752},[902,9422,1925],{"encoding":904}," a dvěma rovnicemi:",[120,9425,9426,9479],{},[123,9427,9428,2084,9431,9434,9435,9457,9458,2313],{},[38,9429,9430],{},"Křivka IS",[614,9432,9433],{},"Investment = Savings",") — klesající přímka v rovině ",[883,9436,9438],{"className":9437},[886],[888,9439,9440],{"xmlns":890},[892,9441,9442,9454],{},[895,9443,9444,9446,9448,9450,9452],{},[1750,9445,1753],{"stretchy":1752},[898,9447,1920],{},[1750,9449,1917],{"separator":1916},[898,9451,1666],{},[1750,9453,1763],{"stretchy":1752},[902,9455,9456],{"encoding":904},"(r, Y)",", odvozená z rovnováhy trhu zboží ",[883,9459,9461],{"className":9460},[886],[888,9462,9463],{"xmlns":890},[892,9464,9465,9477],{},[895,9466,9467,9469,9471,9473,9475],{},[898,9468,1666],{},[1750,9470,1766],{},[898,9472,1812],{},[1750,9474,1861],{},[898,9476,1974],{},[902,9478,5105],{"encoding":904},[123,9480,9481,2084,9484,9487,9488,5424,9514,9561],{},[38,9482,9483],{},"Křivka LM",[614,9485,9486],{},"Liquidity of Money",") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[883,9489,9491],{"className":9490},[886],[888,9492,9493],{"xmlns":890},[892,9494,9495,9511],{},[895,9496,9497,9503,9505],{},[1699,9498,9499,9501],{},[898,9500,1773],{},[898,9502,5541],{},[1750,9504,1766],{},[1699,9506,9507,9509],{},[898,9508,1773],{},[1750,9510,3751],{},[902,9512,9513],{"encoding":904},"M^D = M^*",[883,9515,9517],{"className":9516},[886],[888,9518,9519],{"xmlns":890},[892,9520,9521,9558],{},[895,9522,9523,9529,9531,9538,9540,9542,9548,9550,9552],{},[1699,9524,9525,9527],{},[898,9526,1773],{},[898,9528,5541],{},[1750,9530,1766],{},[5535,9532,9533,9536],{},[898,9534,9535],{},"k",[1742,9537,1744],{},[898,9539,1666],{},[1750,9541,1861],{},[5535,9543,9544,9546],{},[898,9545,9535],{},[1742,9547,1872],{},[898,9549,1920],{},[1750,9551,1861],{},[5535,9553,9554,9556],{},[898,9555,9535],{},[1742,9557,7822],{},[902,9559,9560],{"encoding":904},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[724,9563,9564,1647,9567,9601,9602,9605,9606,9609],{},[38,9565,9566],{},"Simultánní rovnovážný bod",[883,9568,9570],{"className":9569},[886],[888,9571,9572],{"xmlns":890},[892,9573,9574,9598],{},[895,9575,9576,9578,9580,9582,9588,9590,9596],{},[898,9577,1705],{},[1750,9579,1766],{},[1750,9581,1753],{"stretchy":1752},[1699,9583,9584,9586],{},[898,9585,1920],{},[898,9587,1705],{},[1750,9589,1917],{"separator":1916},[1699,9591,9592,9594],{},[898,9593,1666],{},[898,9595,1705],{},[1750,9597,1763],{"stretchy":1752},[902,9599,9600],{"encoding":904},"E = (r^E, Y^E)"," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[38,9603,9604],{},"fiskální politiky"," (posun IS) a ",[38,9607,9608],{},"monetární politiky"," (posun LM).",[724,9611,9612],{},[38,9613,9614,9615,1343,9638,1343,9660,1343,9683,9706,9707,2313],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[883,9616,9618],{"className":9617},[886],[888,9619,9620],{"xmlns":890},[892,9621,9622,9635],{},[895,9623,9624,9630,9632],{},[1699,9625,9626,9628],{},[898,9627,1666],{},[898,9629,1705],{},[1750,9631,1766],{},[1742,9633,9634],{},"5000",[902,9636,9637],{"encoding":904},"Y^E = 5000",[883,9639,9641],{"className":9640},[886],[888,9642,9643],{"xmlns":890},[892,9644,9645,9657],{},[895,9646,9647,9653,9655],{},[1699,9648,9649,9651],{},[898,9650,1920],{},[898,9652,1705],{},[1750,9654,1766],{},[1742,9656,7902],{},[902,9658,9659],{"encoding":904},"r^E = 5",[883,9661,9663],{"className":9662},[886],[888,9664,9665],{"xmlns":890},[892,9666,9667,9680],{},[895,9668,9669,9675,9677],{},[1699,9670,9671,9673],{},[898,9672,1812],{},[898,9674,1705],{},[1750,9676,1766],{},[1742,9678,9679],{},"4100",[902,9681,9682],{"encoding":904},"C^E = 4100",[883,9684,9686],{"className":9685},[886],[888,9687,9688],{"xmlns":890},[892,9689,9690,9703],{},[895,9691,9692,9698,9700],{},[1699,9693,9694,9696],{},[898,9695,1974],{},[898,9697,1705],{},[1750,9699,1766],{},[1742,9701,9702],{},"900",[902,9704,9705],{"encoding":904},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[207,9708,945],{"className":9709,"dataFsResolvedFilePath":943,"href":944},[210],[115,9711,9713],{"id":9712},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[152,9715,9716,9780,9892,10035,10277,10345],{},[123,9717,9718,9721,9722,9744,9745,9779],{},[38,9719,9720],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[883,9723,9725],{"className":9724},[886],[888,9726,9727],{"xmlns":890},[892,9728,9729,9741],{},[895,9730,9731,9733,9735,9737,9739],{},[898,9732,1997],{},[898,9734,2078],{},[898,9736,1776],{},[1750,9738,2274],{},[898,9740,1666],{},[902,9742,9743],{"encoding":904},"GNP \\approx Y"," (národní důchod). Základ: ",[883,9746,9748],{"className":9747},[886],[888,9749,9750],{"xmlns":890},[892,9751,9752,9776],{},[895,9753,9754,9756,9758,9760,9762,9764,9766,9768,9770,9772,9774],{},[898,9755,1997],{},[898,9757,2078],{},[898,9759,1776],{},[1750,9761,1766],{},[898,9763,1812],{},[1750,9765,1861],{},[898,9767,1974],{},[1750,9769,1861],{},[898,9771,1997],{},[1750,9773,1861],{},[898,9775,2024],{},[902,9777,9778],{"encoding":904},"GNP = C + I + G + X"," (7.1).",[123,9781,9782,9784,9785,9807,9808,1343,9831,9862,9863,9876,9877,2313],{},[38,9783,2317],{}," splňují ",[883,9786,9788],{"className":9787},[886],[888,9789,9790],{"xmlns":890},[892,9791,9792,9804],{},[895,9793,9794,9796,9798,9800,9802],{},[898,9795,1666],{},[1750,9797,1766],{},[898,9799,1812],{},[1750,9801,1861],{},[898,9803,1779],{},[902,9805,9806],{"encoding":904},"Y = C + S"," (7.2); lineární model ",[883,9809,9811],{"className":9810},[886],[888,9812,9813],{"xmlns":890},[892,9814,9815,9829],{},[895,9816,9817,9819,9821,9823,9825,9827],{},[898,9818,1812],{},[1750,9820,1766],{},[898,9822,207],{},[898,9824,1666],{},[1750,9826,1861],{},[898,9828,2573],{},[902,9830,2720],{"encoding":904},[883,9832,9834],{"className":9833},[886],[888,9835,9836],{"xmlns":890},[892,9837,9838,9860],{},[895,9839,9840,9842,9844,9846,9848,9850,9852,9854,9856,9858],{},[898,9841,1779],{},[1750,9843,1766],{},[1750,9845,1753],{"stretchy":1752},[1742,9847,1744],{},[1750,9849,1758],{},[898,9851,207],{},[1750,9853,1763],{"stretchy":1752},[898,9855,1666],{},[1750,9857,1758],{},[898,9859,2573],{},[902,9861,2969],{"encoding":904}," s autonomní spotřebou ",[883,9864,9866],{"className":9865},[886],[888,9867,9868],{"xmlns":890},[892,9869,9870,9874],{},[895,9871,9872],{},[898,9873,2573],{},[902,9875,2573],{"encoding":904}," a autonomními úsporami ",[883,9878,9880],{"className":9879},[886],[888,9881,9882],{"xmlns":890},[892,9883,9884,9890],{},[895,9885,9886,9888],{},[1750,9887,1758],{},[898,9889,2573],{},[902,9891,3049],{"encoding":904},[123,9893,9894,1647,9897,1343,9927,9957,9958,9988,9989,1343,10010,2313],{},[38,9895,9896],{},"Mezní sklony",[883,9898,9900],{"className":9899},[886],[888,9901,9902],{"xmlns":890},[892,9903,9904,9924],{},[895,9905,9906,9908,9910,9912,9914,9916,9918,9920,9922],{},[898,9907,1773],{},[898,9909,1776],{},[898,9911,1812],{},[1750,9913,1766],{},[898,9915,3429],{"mathvariant":1747},[898,9917,1812],{},[898,9919,1748],{"mathvariant":1747},[898,9921,3429],{"mathvariant":1747},[898,9923,1666],{},[902,9925,9926],{"encoding":904},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[883,9928,9930],{"className":9929},[886],[888,9931,9932],{"xmlns":890},[892,9933,9934,9954],{},[895,9935,9936,9938,9940,9942,9944,9946,9948,9950,9952],{},[898,9937,1773],{},[898,9939,1776],{},[898,9941,1779],{},[1750,9943,1766],{},[898,9945,3429],{"mathvariant":1747},[898,9947,1779],{},[898,9949,1748],{"mathvariant":1747},[898,9951,3429],{"mathvariant":1747},[898,9953,1666],{},[902,9955,9956],{"encoding":904},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[883,9959,9961],{"className":9960},[886],[888,9962,9963],{"xmlns":890},[892,9964,9965,9985],{},[895,9966,9967,9969,9971,9973,9975,9977,9979,9981,9983],{},[898,9968,1773],{},[898,9970,1776],{},[898,9972,1812],{},[1750,9974,1861],{},[898,9976,1773],{},[898,9978,1776],{},[898,9980,1779],{},[1750,9982,1766],{},[1742,9984,1744],{},[902,9986,9987],{"encoding":904},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[883,9990,9992],{"className":9991},[886],[888,9993,9994],{"xmlns":890},[892,9995,9996,10008],{},[895,9997,9998,10000,10002,10004,10006],{},[898,9999,1773],{},[898,10001,1776],{},[898,10003,1812],{},[1750,10005,1766],{},[898,10007,207],{},[902,10009,3698],{"encoding":904},[883,10011,10013],{"className":10012},[886],[888,10014,10015],{"xmlns":890},[892,10016,10017,10033],{},[895,10018,10019,10021,10023,10025,10027,10029,10031],{},[898,10020,1773],{},[898,10022,1776],{},[898,10024,1779],{},[1750,10026,1766],{},[1742,10028,1744],{},[1750,10030,1758],{},[898,10032,207],{},[902,10034,3724],{"encoding":904},[123,10036,10037,10040,10041],{},[38,10038,10039],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[120,10042,10043,10131,10200],{},[123,10044,10045,10062,10063,10084,10085,1917],{},[883,10046,10048],{"className":10047},[886],[888,10049,10050],{"xmlns":890},[892,10051,10052,10060],{},[895,10053,10054,10056,10058],{},[898,10055,1812],{},[1969,10057,1971],{},[898,10059,1974],{},[902,10061,1977],{"encoding":904},": ",[883,10064,10066],{"className":10065},[886],[888,10067,10068],{"xmlns":890},[892,10069,10070,10082],{},[895,10071,10072,10074,10076,10078,10080],{},[898,10073,1666],{},[1750,10075,1766],{},[898,10077,1812],{},[1750,10079,1861],{},[898,10081,1974],{},[902,10083,5105],{"encoding":904}," (uzavřená ekonomika bez vlády), ",[883,10086,10088],{"className":10087},[886],[888,10089,10090],{"xmlns":890},[892,10091,10092,10128],{},[895,10093,10094,10100,10102,10104,10106,10108,10114,10116,10118,10120,10122,10124,10126],{},[1699,10095,10096,10098],{},[898,10097,1666],{},[898,10099,1705],{},[1750,10101,1766],{},[1750,10103,1753],{"stretchy":1752},[898,10105,2573],{},[1750,10107,1861],{},[1699,10109,10110,10112],{},[898,10111,1974],{},[1750,10113,3751],{},[1750,10115,1763],{"stretchy":1752},[898,10117,1748],{"mathvariant":1747},[1750,10119,1753],{"stretchy":1752},[1742,10121,1744],{},[1750,10123,1758],{},[898,10125,207],{},[1750,10127,1763],{"stretchy":1752},[902,10129,10130],{"encoding":904},"Y^E = (b + I^*)\u002F(1-a)",[123,10132,10133,10154,10155,10174,10175,1917],{},[883,10134,10136],{"className":10135},[886],[888,10137,10138],{"xmlns":890},[892,10139,10140,10152],{},[895,10141,10142,10144,10146,10148,10150],{},[898,10143,1812],{},[1969,10145,1971],{},[898,10147,1974],{},[1969,10149,1971],{},[898,10151,1997],{},[902,10153,2000],{"encoding":904},": přidává vládu, zdanění ",[883,10156,10158],{"className":10157},[886],[888,10159,10160],{"xmlns":890},[892,10161,10162,10172],{},[895,10163,10164,10166,10168,10170],{},[898,10165,5326],{},[1750,10167,1753],{"stretchy":1752},[898,10169,1666],{},[1750,10171,1763],{"stretchy":1752},[902,10173,6055],{"encoding":904}," a disponibilní důchod ",[883,10176,10178],{"className":10177},[886],[888,10179,10180],{"xmlns":890},[892,10181,10182,10198],{},[895,10183,10184,10190,10192,10194,10196],{},[5535,10185,10186,10188],{},[898,10187,1666],{},[898,10189,5541],{},[1750,10191,1766],{},[898,10193,1666],{},[1750,10195,1758],{},[898,10197,5326],{},[902,10199,5552],{"encoding":904},[123,10201,10202,10227,10228,5424,10249,2313],{},[883,10203,10205],{"className":10204},[886],[888,10206,10207],{"xmlns":890},[892,10208,10209,10225],{},[895,10210,10211,10213,10215,10217,10219,10221,10223],{},[898,10212,1812],{},[1969,10214,1971],{},[898,10216,1974],{},[1969,10218,1971],{},[898,10220,1997],{},[1969,10222,1971],{},[898,10224,2024],{},[902,10226,2027],{"encoding":904},": otevírá ekonomiku čistým exportem ",[883,10229,10231],{"className":10230},[886],[888,10232,10233],{"xmlns":890},[892,10234,10235,10247],{},[895,10236,10237,10239,10241,10243,10245],{},[898,10238,2024],{},[1750,10240,1766],{},[898,10242,7097],{},[1750,10244,1758],{},[898,10246,1773],{},[902,10248,7104],{"encoding":904},[883,10250,10252],{"className":10251},[886],[888,10253,10254],{"xmlns":890},[892,10255,10256,10274],{},[895,10257,10258,10260,10262,10264,10266,10272],{},[898,10259,1773],{},[1750,10261,1766],{},[898,10263,1773],{},[1750,10265,1753],{"stretchy":1752},[5535,10267,10268,10270],{},[898,10269,1666],{},[898,10271,5541],{},[1750,10273,1763],{"stretchy":1752},[902,10275,10276],{"encoding":904},"M = M(Y_D)",[123,10278,10279,10282,10283,1647,10286,10344],{},[38,10280,10281],{},"Multiplikátory"," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[38,10284,10285],{},"multiplikátor investic",[883,10287,10289],{"className":10288},[886],[888,10290,10291],{"xmlns":890},[892,10292,10293,10341],{},[895,10294,10295,10297,10303,10305,10307,10313,10315,10317,10319,10321,10323,10325,10327,10329,10331,10333,10335,10337,10339],{},[898,10296,8773],{"mathvariant":1747},[1699,10298,10299,10301],{},[898,10300,1666],{},[898,10302,1705],{},[898,10304,1748],{"mathvariant":1747},[898,10306,8773],{"mathvariant":1747},[1699,10308,10309,10311],{},[898,10310,1974],{},[1750,10312,3751],{},[1750,10314,1766],{},[1742,10316,1744],{},[898,10318,1748],{"mathvariant":1747},[1750,10320,1753],{"stretchy":1752},[1742,10322,1744],{},[1750,10324,1758],{},[898,10326,207],{},[1750,10328,1763],{"stretchy":1752},[1750,10330,1766],{},[1742,10332,1744],{},[898,10334,1748],{"mathvariant":1747},[898,10336,1773],{},[898,10338,1776],{},[898,10340,1779],{},[902,10342,10343],{"encoding":904},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[123,10346,10347,10349,10350,10366,10367,2440,10385,10401,10402,10427,10428,2313],{},[38,10348,945],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[883,10351,10353],{"className":10352},[886],[888,10354,10355],{"xmlns":890},[892,10356,10357,10363],{},[895,10358,10359,10361],{},[898,10360,1974],{},[898,10362,1779],{},[902,10364,10365],{"encoding":904},"IS"," popisuje rovnováhu trhu zboží (",[883,10368,10370],{"className":10369},[886],[888,10371,10372],{"xmlns":890},[892,10373,10374,10382],{},[895,10375,10376,10378,10380],{},[898,10377,1974],{},[1750,10379,1766],{},[898,10381,1779],{},[902,10383,10384],{"encoding":904},"I = S",[883,10386,10388],{"className":10387},[886],[888,10389,10390],{"xmlns":890},[892,10391,10392,10398],{},[895,10393,10394,10396],{},[898,10395,2046],{},[898,10397,1773],{},[902,10399,10400],{"encoding":904},"LM"," rovnováhu trhu peněz (",[883,10403,10405],{"className":10404},[886],[888,10406,10407],{"xmlns":890},[892,10408,10409,10425],{},[895,10410,10411,10417,10419],{},[1699,10412,10413,10415],{},[898,10414,1773],{},[898,10416,5541],{},[1750,10418,1766],{},[1699,10420,10421,10423],{},[898,10422,1773],{},[1750,10424,3751],{},[902,10426,9513],{"encoding":904},"); průsečík dává ",[883,10429,10431],{"className":10430},[886],[888,10432,10433],{"xmlns":890},[892,10434,10435,10455],{},[895,10436,10437,10439,10445,10447,10453],{},[1750,10438,1753],{"stretchy":1752},[1699,10440,10441,10443],{},[898,10442,1666],{},[898,10444,1705],{},[1750,10446,1917],{"separator":1916},[1699,10448,10449,10451],{},[898,10450,1920],{},[898,10452,1705],{},[1750,10454,1763],{"stretchy":1752},[902,10456,10457],{"encoding":904},"(Y^E, r^E)",[115,10459,10461],{"id":10460},"klíčové-pojmy","Klíčové pojmy",[120,10463,10464,10503,10543,10633,10715,10769,10825,10884,10919,10924,10997,11072,11158,11220,11290,11349,11403,11442],{},[123,10465,10466,10469,10470,9779],{},[38,10467,10468],{},"Hrubý národní produkt (GNP)"," — ",[883,10471,10473],{"className":10472},[886],[888,10474,10475],{"xmlns":890},[892,10476,10477,10501],{},[895,10478,10479,10481,10483,10485,10487,10489,10491,10493,10495,10497,10499],{},[898,10480,1997],{},[898,10482,2078],{},[898,10484,1776],{},[1750,10486,1766],{},[898,10488,1812],{},[1750,10490,1861],{},[898,10492,1974],{},[1750,10494,1861],{},[898,10496,1997],{},[1750,10498,1861],{},[898,10500,2024],{},[902,10502,9778],{"encoding":904},[123,10504,10505,10521,10522,2313],{},[38,10506,10507,10508],{},"Národní důchod ",[883,10509,10511],{"className":10510},[886],[888,10512,10513],{"xmlns":890},[892,10514,10515,10519],{},[895,10516,10517],{},[898,10518,1666],{},[902,10520,1666],{"encoding":904}," — součet důchodů domácností; v modelech ",[883,10523,10525],{"className":10524},[886],[888,10526,10527],{"xmlns":890},[892,10528,10529,10541],{},[895,10530,10531,10533,10535,10537,10539],{},[898,10532,1997],{},[898,10534,2078],{},[898,10536,1776],{},[1750,10538,2274],{},[898,10540,1666],{},[902,10542,9743],{"encoding":904},[123,10544,10545,10571,10572,1343,10595,1343,10616,2313],{},[38,10546,10547,10548],{},"Funkce spotřeby ",[883,10549,10551],{"className":10550},[886],[888,10552,10553],{"xmlns":890},[892,10554,10555,10569],{},[895,10556,10557,10559,10561,10563,10565,10567],{},[898,10558,1812],{},[1750,10560,1766],{},[898,10562,1812],{},[1750,10564,1753],{"stretchy":1752},[898,10566,1666],{},[1750,10568,1763],{"stretchy":1752},[902,10570,4563],{"encoding":904}," — lineární model ",[883,10573,10575],{"className":10574},[886],[888,10576,10577],{"xmlns":890},[892,10578,10579,10593],{},[895,10580,10581,10583,10585,10587,10589,10591],{},[898,10582,1812],{},[1750,10584,1766],{},[898,10586,207],{},[898,10588,1666],{},[1750,10590,1861],{},[898,10592,2573],{},[902,10594,2720],{"encoding":904},[883,10596,10598],{"className":10597},[886],[888,10599,10600],{"xmlns":890},[892,10601,10602,10614],{},[895,10603,10604,10606,10608,10610,10612],{},[1742,10605,2607],{},[1750,10607,2624],{},[898,10609,207],{},[1750,10611,2624],{},[1742,10613,1744],{},[902,10615,2633],{"encoding":904},[883,10617,10619],{"className":10618},[886],[888,10620,10621],{"xmlns":890},[892,10622,10623,10631],{},[895,10624,10625,10627,10629],{},[898,10626,2573],{},[1750,10628,2604],{},[1742,10630,2607],{},[902,10632,2610],{"encoding":904},[123,10634,10635,10469,10662,10683,10684,2313],{},[38,10636,10637,10638],{},"Funkce úspor ",[883,10639,10641],{"className":10640},[886],[888,10642,10643],{"xmlns":890},[892,10644,10645,10659],{},[895,10646,10647,10649,10651,10653,10655,10657],{},[898,10648,1779],{},[1750,10650,1766],{},[898,10652,1779],{},[1750,10654,1753],{"stretchy":1752},[898,10656,1666],{},[1750,10658,1763],{"stretchy":1752},[902,10660,10661],{"encoding":904},"S = S(Y)",[883,10663,10665],{"className":10664},[886],[888,10666,10667],{"xmlns":890},[892,10668,10669,10681],{},[895,10670,10671,10673,10675,10677,10679],{},[898,10672,1666],{},[1750,10674,1766],{},[898,10676,1812],{},[1750,10678,1861],{},[898,10680,1779],{},[902,10682,9806],{"encoding":904},"; lineární ",[883,10685,10687],{"className":10686},[886],[888,10688,10689],{"xmlns":890},[892,10690,10691,10713],{},[895,10692,10693,10695,10697,10699,10701,10703,10705,10707,10709,10711],{},[898,10694,1779],{},[1750,10696,1766],{},[1750,10698,1753],{"stretchy":1752},[1742,10700,1744],{},[1750,10702,1758],{},[898,10704,207],{},[1750,10706,1763],{"stretchy":1752},[898,10708,1666],{},[1750,10710,1758],{},[898,10712,2573],{},[902,10714,2969],{"encoding":904},[123,10716,10717,10469,10720,1343,10743,2313],{},[38,10718,10719],{},"Autonomní spotřeba\u002Fúspory",[883,10721,10723],{"className":10722},[886],[888,10724,10725],{"xmlns":890},[892,10726,10727,10741],{},[895,10728,10729,10731,10733,10735,10737,10739],{},[898,10730,1812],{},[1750,10732,1753],{"stretchy":1752},[1742,10734,2607],{},[1750,10736,1763],{"stretchy":1752},[1750,10738,1766],{},[898,10740,2573],{},[902,10742,3365],{"encoding":904},[883,10744,10746],{"className":10745},[886],[888,10747,10748],{"xmlns":890},[892,10749,10750,10766],{},[895,10751,10752,10754,10756,10758,10760,10762,10764],{},[898,10753,1779],{},[1750,10755,1753],{"stretchy":1752},[1742,10757,2607],{},[1750,10759,1763],{"stretchy":1752},[1750,10761,1766],{},[1750,10763,1758],{},[898,10765,2573],{},[902,10767,10768],{"encoding":904},"S(0) = -b",[123,10770,10771,10803,10804,1783],{},[38,10772,10773,10774],{},"Mezní sklon ke spotřebě ",[883,10775,10777],{"className":10776},[886],[888,10778,10779],{"xmlns":890},[892,10780,10781,10801],{},[895,10782,10783,10785,10787,10789,10791,10793,10795,10797,10799],{},[898,10784,1773],{},[898,10786,1776],{},[898,10788,1812],{},[1750,10790,1766],{},[898,10792,3429],{"mathvariant":1747},[898,10794,1812],{},[898,10796,1748],{"mathvariant":1747},[898,10798,3429],{"mathvariant":1747},[898,10800,1666],{},[902,10802,9926],{"encoding":904}," (v lineárním modelu ",[883,10805,10807],{"className":10806},[886],[888,10808,10809],{"xmlns":890},[892,10810,10811,10823],{},[895,10812,10813,10815,10817,10819,10821],{},[898,10814,1773],{},[898,10816,1776],{},[898,10818,1812],{},[1750,10820,1766],{},[898,10822,207],{},[902,10824,3698],{"encoding":904},[123,10826,10827,10803,10859,1783],{},[38,10828,10829,10830],{},"Mezní sklon k úsporám ",[883,10831,10833],{"className":10832},[886],[888,10834,10835],{"xmlns":890},[892,10836,10837,10857],{},[895,10838,10839,10841,10843,10845,10847,10849,10851,10853,10855],{},[898,10840,1773],{},[898,10842,1776],{},[898,10844,1779],{},[1750,10846,1766],{},[898,10848,3429],{"mathvariant":1747},[898,10850,1779],{},[898,10852,1748],{"mathvariant":1747},[898,10854,3429],{"mathvariant":1747},[898,10856,1666],{},[902,10858,9956],{"encoding":904},[883,10860,10862],{"className":10861},[886],[888,10863,10864],{"xmlns":890},[892,10865,10866,10882],{},[895,10867,10868,10870,10872,10874,10876,10878,10880],{},[898,10869,1773],{},[898,10871,1776],{},[898,10873,1779],{},[1750,10875,1766],{},[1742,10877,1744],{},[1750,10879,1758],{},[898,10881,207],{},[902,10883,3724],{"encoding":904},[123,10885,10886,1647,10889,10918],{},[38,10887,10888],{},"Vztah",[883,10890,10892],{"className":10891},[886],[888,10893,10894],{"xmlns":890},[892,10895,10896,10916],{},[895,10897,10898,10900,10902,10904,10906,10908,10910,10912,10914],{},[898,10899,1773],{},[898,10901,1776],{},[898,10903,1812],{},[1750,10905,1861],{},[898,10907,1773],{},[898,10909,1776],{},[898,10911,1779],{},[1750,10913,1766],{},[1742,10915,1744],{},[902,10917,9987],{"encoding":904}," (7.5).",[123,10920,10921,10923],{},[38,10922,4402],{}," — rovnováha agregátní poptávky a nabídky.",[123,10925,10926,10929,10930,10951,10952,2313],{},[38,10927,10928],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[883,10931,10933],{"className":10932},[886],[888,10934,10935],{"xmlns":890},[892,10936,10937,10949],{},[895,10938,10939,10941,10943,10945,10947],{},[898,10940,1666],{},[1750,10942,1766],{},[898,10944,1812],{},[1750,10946,1861],{},[898,10948,1974],{},[902,10950,5105],{"encoding":904},"; ",[883,10953,10955],{"className":10954},[886],[888,10956,10957],{"xmlns":890},[892,10958,10959,10995],{},[895,10960,10961,10967,10969,10971,10973,10975,10981,10983,10985,10987,10989,10991,10993],{},[1699,10962,10963,10965],{},[898,10964,1666],{},[898,10966,1705],{},[1750,10968,1766],{},[1750,10970,1753],{"stretchy":1752},[898,10972,2573],{},[1750,10974,1861],{},[1699,10976,10977,10979],{},[898,10978,1974],{},[1750,10980,3751],{},[1750,10982,1763],{"stretchy":1752},[898,10984,1748],{"mathvariant":1747},[1750,10986,1753],{"stretchy":1752},[1742,10988,1744],{},[1750,10990,1758],{},[898,10992,207],{},[1750,10994,1763],{"stretchy":1752},[902,10996,10130],{"encoding":904},[123,10998,10999,11002,11003,1343,11022,10951,11047,2313],{},[38,11000,11001],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[883,11004,11006],{"className":11005},[886],[888,11007,11008],{"xmlns":890},[892,11009,11010,11020],{},[895,11011,11012,11014,11016,11018],{},[898,11013,5326],{},[1750,11015,1753],{"stretchy":1752},[898,11017,1666],{},[1750,11019,1763],{"stretchy":1752},[902,11021,6055],{"encoding":904},[883,11023,11025],{"className":11024},[886],[888,11026,11027],{"xmlns":890},[892,11028,11029,11045],{},[895,11030,11031,11037,11039,11041,11043],{},[5535,11032,11033,11035],{},[898,11034,1666],{},[898,11036,5541],{},[1750,11038,1766],{},[898,11040,1666],{},[1750,11042,1758],{},[898,11044,5326],{},[902,11046,5552],{"encoding":904},[883,11048,11050],{"className":11049},[886],[888,11051,11052],{"xmlns":890},[892,11053,11054,11070],{},[895,11055,11056,11058,11060,11062,11064,11066,11068],{},[898,11057,1666],{},[1750,11059,1766],{},[898,11061,1812],{},[1750,11063,1861],{},[898,11065,1974],{},[1750,11067,1861],{},[898,11069,1997],{},[902,11071,5521],{"encoding":904},[123,11073,11074,11077,11078,11099,11100,10951,11124,2313],{},[38,11075,11076],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[883,11079,11081],{"className":11080},[886],[888,11082,11083],{"xmlns":890},[892,11084,11085,11097],{},[895,11086,11087,11089,11091,11093,11095],{},[898,11088,2024],{},[1750,11090,1766],{},[898,11092,7097],{},[1750,11094,1758],{},[898,11096,1773],{},[902,11098,7104],{"encoding":904},", importem ",[883,11101,11103],{"className":11102},[886],[888,11104,11105],{"xmlns":890},[892,11106,11107,11121],{},[895,11108,11109,11111,11113,11119],{},[898,11110,1773],{},[1750,11112,1753],{"stretchy":1752},[5535,11114,11115,11117],{},[898,11116,1666],{},[898,11118,5541],{},[1750,11120,1763],{"stretchy":1752},[902,11122,11123],{"encoding":904},"M(Y_D)",[883,11125,11127],{"className":11126},[886],[888,11128,11129],{"xmlns":890},[892,11130,11131,11155],{},[895,11132,11133,11135,11137,11139,11141,11143,11145,11147,11149,11151,11153],{},[898,11134,1666],{},[1750,11136,1766],{},[898,11138,1812],{},[1750,11140,1861],{},[898,11142,1974],{},[1750,11144,1861],{},[898,11146,1997],{},[1750,11148,1861],{},[898,11150,7097],{},[1750,11152,1758],{},[898,11154,1773],{},[902,11156,11157],{"encoding":904},"Y = C + I + G + B - M",[123,11159,11160,10469,11163,10344],{},[38,11161,11162],{},"Multiplikátor investic",[883,11164,11166],{"className":11165},[886],[888,11167,11168],{"xmlns":890},[892,11169,11170,11218],{},[895,11171,11172,11174,11180,11182,11184,11190,11192,11194,11196,11198,11200,11202,11204,11206,11208,11210,11212,11214,11216],{},[898,11173,8773],{"mathvariant":1747},[1699,11175,11176,11178],{},[898,11177,1666],{},[898,11179,1705],{},[898,11181,1748],{"mathvariant":1747},[898,11183,8773],{"mathvariant":1747},[1699,11185,11186,11188],{},[898,11187,1974],{},[1750,11189,3751],{},[1750,11191,1766],{},[1742,11193,1744],{},[898,11195,1748],{"mathvariant":1747},[1750,11197,1753],{"stretchy":1752},[1742,11199,1744],{},[1750,11201,1758],{},[898,11203,207],{},[1750,11205,1763],{"stretchy":1752},[1750,11207,1766],{},[1742,11209,1744],{},[898,11211,1748],{"mathvariant":1747},[898,11213,1773],{},[898,11215,1776],{},[898,11217,1779],{},[902,11219,10343],{"encoding":904},[123,11221,11222,10469,11254,1343,11271,11289],{},[38,11223,11224,11225],{},"Funkce investic ",[883,11226,11228],{"className":11227},[886],[888,11229,11230],{"xmlns":890},[892,11231,11232,11252],{},[895,11233,11234,11236,11238,11240,11242,11244,11246,11248,11250],{},[898,11235,1974],{},[1750,11237,1753],{"stretchy":1752},[898,11239,1920],{},[1750,11241,1763],{"stretchy":1752},[1750,11243,1766],{},[898,11245,9365],{},[898,11247,1920],{},[1750,11249,1861],{},[898,11251,3429],{},[902,11253,9374],{"encoding":904},[883,11255,11257],{"className":11256},[886],[888,11258,11259],{"xmlns":890},[892,11260,11261,11269],{},[895,11262,11263,11265,11267],{},[898,11264,9365],{},[1750,11266,2624],{},[1742,11268,2607],{},[902,11270,9393],{"encoding":904},[883,11272,11274],{"className":11273},[886],[888,11275,11276],{"xmlns":890},[892,11277,11278,11286],{},[895,11279,11280,11282,11284],{},[898,11281,3429],{},[1750,11283,2604],{},[1742,11285,2607],{},[902,11287,11288],{"encoding":904},"d > 0","; klesající.",[123,11291,11292,11294,11295,11297,11298,11348],{},[38,11293,9430],{}," — rovnováha na trhu zboží (",[614,11296,9433],{},"); ",[883,11299,11301],{"className":11300},[886],[888,11302,11303],{"xmlns":890},[892,11304,11305,11345],{},[895,11306,11307,11309,11311,11323,11325,11327],{},[898,11308,1666],{},[1750,11310,1766],{},[3423,11312,11313,11315],{},[898,11314,9365],{},[895,11316,11317,11319,11321],{},[1742,11318,1744],{},[1750,11320,1758],{},[898,11322,207],{},[898,11324,1920],{},[1750,11326,1861],{},[3423,11328,11329,11337],{},[895,11330,11331,11333,11335],{},[898,11332,2573],{},[1750,11334,1861],{},[898,11336,3429],{},[895,11338,11339,11341,11343],{},[1742,11340,1744],{},[1750,11342,1758],{},[898,11344,207],{},[902,11346,11347],{"encoding":904},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); klesající.",[123,11350,11351,11353,11354,11297,11356,11402],{},[38,11352,9483],{}," — rovnováha na trhu peněz (",[614,11355,9486],{},[883,11357,11359],{"className":11358},[886],[888,11360,11361],{"xmlns":890},[892,11362,11363,11399],{},[895,11364,11365,11371,11373,11379,11381,11383,11389,11391,11393],{},[1699,11366,11367,11369],{},[898,11368,1773],{},[1750,11370,3751],{},[1750,11372,1766],{},[5535,11374,11375,11377],{},[898,11376,9535],{},[1742,11378,1744],{},[898,11380,1666],{},[1750,11382,1861],{},[5535,11384,11385,11387],{},[898,11386,9535],{},[1742,11388,1872],{},[898,11390,1920],{},[1750,11392,1861],{},[5535,11394,11395,11397],{},[898,11396,9535],{},[1742,11398,7822],{},[902,11400,11401],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3"," (7.15); rostoucí.",[123,11404,11405,10469,11408,2313],{},[38,11406,11407],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[883,11409,11411],{"className":11410},[886],[888,11412,11413],{"xmlns":890},[892,11414,11415,11439],{},[895,11416,11417,11423,11425,11431,11433],{},[1699,11418,11419,11421],{},[898,11420,1773],{},[898,11422,5541],{},[1750,11424,1766],{},[5535,11426,11427,11429],{},[898,11428,2046],{},[1742,11430,1744],{},[1750,11432,1861],{},[5535,11434,11435,11437],{},[898,11436,2046],{},[1742,11438,1872],{},[902,11440,11441],{"encoding":904},"M^D = L_1 + L_2",[123,11443,11444,11446,11447,11460,11461,2028,11476,11491,11492,2313],{},[38,11445,945],{}," — průsečík ",[883,11448,11450],{"className":11449},[886],[888,11451,11452],{"xmlns":890},[892,11453,11454,11458],{},[895,11455,11456],{},[898,11457,1705],{},[902,11459,1705],{"encoding":904}," křivek ",[883,11462,11464],{"className":11463},[886],[888,11465,11466],{"xmlns":890},[892,11467,11468,11474],{},[895,11469,11470,11472],{},[898,11471,1974],{},[898,11473,1779],{},[902,11475,10365],{"encoding":904},[883,11477,11479],{"className":11478},[886],[888,11480,11481],{"xmlns":890},[892,11482,11483,11489],{},[895,11484,11485,11487],{},[898,11486,2046],{},[898,11488,1773],{},[902,11490,10400],{"encoding":904}," určuje ",[883,11493,11495],{"className":11494},[886],[888,11496,11497],{"xmlns":890},[892,11498,11499,11519],{},[895,11500,11501,11503,11509,11511,11517],{},[1750,11502,1753],{"stretchy":1752},[1699,11504,11505,11507],{},[898,11506,1666],{},[898,11508,1705],{},[1750,11510,1917],{"separator":1916},[1699,11512,11513,11515],{},[898,11514,1920],{},[898,11516,1705],{},[1750,11518,1763],{"stretchy":1752},[902,11520,10457],{"encoding":904},[115,11522,11524],{"id":11523},"navigace","Navigace",[120,11526,11527,11536,11545],{},[123,11528,11529,1647,11532],{},[38,11530,11531],{},"Kurz:",[207,11533,11535],{"className":11534,"dataFsResolvedFilePath":1644,"href":1645},[210],"Matematická ekonomie",[123,11537,11538,1647,11541],{},[38,11539,11540],{},"Přednáška:",[207,11542,11544],{"className":11543,"dataFsResolvedFilePath":868,"href":869},[210],"imek-blok-03",[123,11546,11547,11550],{},[38,11548,11549],{},"Související:",[120,11551,11552,11559,11566,11573],{},[123,11553,11554,11558],{},[207,11555,11557],{"className":11556,"dataFsResolvedFilePath":943,"href":944},[210],"is-lm"," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[123,11560,11561,11565],{},[207,11562,11564],{"className":11563,"dataFsResolvedFilePath":800,"href":801},[210],"poptavka-nabidka"," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[123,11567,11568,11572],{},[207,11569,11571],{"className":11570,"dataFsResolvedFilePath":827,"href":828},[210],"prijem-naklady-zisk"," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[123,11574,11575,11578,11579,1343,11596,11613],{},[207,11576,1145],{"className":11577,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro ",[883,11580,11582],{"className":11581},[886],[888,11583,11584],{"xmlns":890},[892,11585,11586,11594],{},[895,11587,11588,11590,11592],{},[898,11589,1773],{},[898,11591,1776],{},[898,11593,1812],{},[902,11595,1815],{"encoding":904},[883,11597,11599],{"className":11598},[886],[888,11600,11601],{"xmlns":890},[892,11602,11603,11611],{},[895,11604,11605,11607,11609],{},[898,11606,1773],{},[898,11608,1776],{},[898,11610,1779],{},[902,11612,3465],{"encoding":904}," a interpretaci změn diferenciálem",{"title":641,"searchDepth":642,"depth":642,"links":11615},[11616,11617,11618,11619,11624,11627,11628,11635,11640,11645,11648,11649,11650,11651],{"id":1636,"depth":642,"text":1637},{"id":1929,"depth":642,"text":1930},{"id":2058,"depth":642,"text":2059},{"id":2316,"depth":642,"text":2317,"children":11620},[11621,11622,11623],{"id":2320,"depth":649,"text":2321},{"id":2535,"depth":649,"text":2536},{"id":3052,"depth":649,"text":3053},{"id":3375,"depth":642,"text":3376,"children":11625},[11626],{"id":3899,"depth":649,"text":3900},{"id":4401,"depth":642,"text":4402},{"id":4429,"depth":642,"text":4430,"children":11629},[11630,11631,11632,11634],{"id":4442,"depth":649,"text":4443},{"id":4512,"depth":649,"text":4513},{"id":4698,"depth":649,"text":11633},"Výpočet YEY^E",{"id":4842,"depth":649,"text":4843},{"id":5224,"depth":642,"text":5225,"children":11636},[11637,11638,11639],{"id":5228,"depth":649,"text":4443},{"id":5682,"depth":649,"text":4513},{"id":6340,"depth":649,"text":6341},{"id":7135,"depth":642,"text":7136,"children":11641},[11642,11643,11644],{"id":7139,"depth":649,"text":4443},{"id":7284,"depth":649,"text":4513},{"id":7554,"depth":649,"text":7555},{"id":8486,"depth":642,"text":8487,"children":11646},[11647],{"id":8683,"depth":649,"text":8684},{"id":9234,"depth":642,"text":9235},{"id":9712,"depth":642,"text":9713},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},"2026-04-22",{},"\u002Ftopics\u002Fnarodni-duchod",{"title":936,"description":641},[1138,1137],"topics\u002Fnarodni-duchod",[1128,11659,1143,11660,11661,11662,11557,11663],"narodni-duchod","gnp","mpc","mps","multiplikator","topic","BMicmr68yKQbb8qpoE9KfzU5NFshq3Inq6w0tL8-GjU","topics",{"zapisku":1625,"topics":11668,"summaries":11669,"outputs":11670},15,5,1,[11672,13526,19204,20757,21629,25851,27457,36688,45682,59749,64041,83385,95497,104456,104744],{"id":11673,"title":11674,"body":11675,"course":1128,"courses":659,"created":1129,"description":13515,"extension":661,"meta":13516,"navigation":664,"path":13517,"seo":13518,"sources":13519,"stem":13520,"tags":13521,"type":11664,"updated":677,"__hash__":13525},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":9,"value":11676,"toc":13498},[11677,11680,11699,11703,11782,11785,11908,12051,12054,12134,12138,12197,12247,12254,12258,12391,12441,12445,12486,12552,12622,12629,12633,12671,12743,12747,12826,12874,12918,12922,12926,12996,13000,13050,13127,13134,13137,13189,13459,13461],[12,11678,11674],{"id":11679},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[724,11681,11682,11683,11687,11688,11691,11692,11695,11696,2313],{},"Matematický aparát kurzu ",[207,11684,11686],{"className":11685,"dataFsResolvedFilePath":1644,"href":1645},[210],"ImeK",". Bez derivace se neobejdou ",[38,11689,11690],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[38,11693,11694],{},"maximalizace zisku"," ani ",[38,11697,11698],{},"minimalizace nákladů",[115,11700,11702],{"id":11701},"funkce-a-polynomy","Funkce a polynomy",[724,11704,11705,11706,11733,11734,11747,11748,11761,11762,2313],{},"Funkce jedné proměnné ",[883,11707,11709],{"className":11708},[886],[888,11710,11711],{"xmlns":890},[892,11712,11713,11730],{},[895,11714,11715,11718,11720,11723,11725,11728],{},[898,11716,11717],{},"y",[1750,11719,1766],{},[898,11721,11722],{},"f",[1750,11724,1753],{"stretchy":1752},[898,11726,11727],{},"x",[1750,11729,1763],{"stretchy":1752},[902,11731,11732],{"encoding":904},"y = f(x)"," — předpis závislosti ",[883,11735,11737],{"className":11736},[886],[888,11738,11739],{"xmlns":890},[892,11740,11741,11745],{},[895,11742,11743],{},[898,11744,11727],{},[902,11746,11727],{"encoding":904}," (nezávislá) → ",[883,11749,11751],{"className":11750},[886],[888,11752,11753],{"xmlns":890},[892,11754,11755,11759],{},[895,11756,11757],{},[898,11758,11717],{},[902,11760,11717],{"encoding":904}," (závislá). Hodnota v bodě: ",[883,11763,11765],{"className":11764},[886],[888,11766,11767],{"xmlns":890},[892,11768,11769,11779],{},[895,11770,11771,11773,11775,11777],{},[898,11772,11722],{},[1750,11774,1753],{"stretchy":1752},[898,11776,207],{},[1750,11778,1763],{"stretchy":1752},[902,11780,11781],{"encoding":904},"f(a)",[724,11783,11784],{},"Polynomy:",[120,11786,11787,11818,11858],{},[123,11788,11789],{},[152,11790,11791],{},[123,11792,11793,11794],{},"stupně: ",[883,11795,11797],{"className":11796},[886],[888,11798,11799],{"xmlns":890},[892,11800,11801,11815],{},[895,11802,11803,11805,11807,11809,11811,11813],{},[898,11804,11717],{},[1750,11806,1766],{},[898,11808,207],{},[898,11810,11727],{},[1750,11812,1861],{},[898,11814,2573],{},[902,11816,11817],{"encoding":904},"y = ax + b",[123,11819,11820],{},[152,11821,11822],{"start":642},[123,11823,11793,11824],{},[883,11825,11827],{"className":11826},[886],[888,11828,11829],{"xmlns":890},[892,11830,11831,11855],{},[895,11832,11833,11835,11837,11839,11845,11847,11849,11851,11853],{},[898,11834,11717],{},[1750,11836,1766],{},[898,11838,207],{},[1699,11840,11841,11843],{},[898,11842,11727],{},[1742,11844,1872],{},[1750,11846,1861],{},[898,11848,2573],{},[898,11850,11727],{},[1750,11852,1861],{},[898,11854,9365],{},[902,11856,11857],{"encoding":904},"y = ax^2 + bx + c",[123,11859,11860],{},[152,11861,11862],{"start":649},[123,11863,11793,11864],{},[883,11865,11867],{"className":11866},[886],[888,11868,11869],{"xmlns":890},[892,11870,11871,11905],{},[895,11872,11873,11875,11877,11879,11885,11887,11889,11895,11897,11899,11901,11903],{},[898,11874,11717],{},[1750,11876,1766],{},[898,11878,207],{},[1699,11880,11881,11883],{},[898,11882,11727],{},[1742,11884,7822],{},[1750,11886,1861],{},[898,11888,2573],{},[1699,11890,11891,11893],{},[898,11892,11727],{},[1742,11894,1872],{},[1750,11896,1861],{},[898,11898,9365],{},[898,11900,11727],{},[1750,11902,1861],{},[898,11904,3429],{},[902,11906,11907],{"encoding":904},"y = ax^3 + bx^2 + cx + d",[724,11909,11910,1647,11913,11967,11968,12004,12005,2313],{},[38,11911,11912],{},"Příklad rozkladu:",[883,11914,11916],{"className":11915},[886],[888,11917,11918],{"xmlns":890},[892,11919,11920,11964],{},[895,11921,11922,11924,11926,11932,11934,11936,11938,11940,11942,11944,11946,11948,11950,11952,11954,11956,11958,11960,11962],{},[898,11923,11717],{},[1750,11925,1766],{},[1699,11927,11928,11930],{},[898,11929,11727],{},[1742,11931,1872],{},[1750,11933,1758],{},[1742,11935,7902],{},[898,11937,11727],{},[1750,11939,1861],{},[1742,11941,3219],{},[1750,11943,1766],{},[1750,11945,1753],{"stretchy":1752},[898,11947,11727],{},[1750,11949,1758],{},[1742,11951,1872],{},[1750,11953,1763],{"stretchy":1752},[1750,11955,1753],{"stretchy":1752},[898,11957,11727],{},[1750,11959,1758],{},[1742,11961,7822],{},[1750,11963,1763],{"stretchy":1752},[902,11965,11966],{"encoding":904},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[883,11969,11971],{"className":11970},[886],[888,11972,11973],{"xmlns":890},[892,11974,11975,12001],{},[895,11976,11977,11983,11985,11987,11989,11991,11997,11999],{},[5535,11978,11979,11981],{},[898,11980,11727],{},[1742,11982,1744],{},[1750,11984,1766],{},[1742,11986,1872],{},[1750,11988,1917],{"separator":1916},[1969,11990,7737],{},[5535,11992,11993,11995],{},[898,11994,11727],{},[1742,11996,1872],{},[1750,11998,1766],{},[1742,12000,7822],{},[902,12002,12003],{"encoding":904},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[883,12006,12008],{"className":12007},[886],[888,12009,12010],{"xmlns":890},[892,12011,12012,12048],{},[895,12013,12014,12016,12018,12020,12022,12024,12032,12038,12040],{},[898,12015,11717],{},[1750,12017,1766],{},[1750,12019,1753],{"stretchy":1752},[898,12021,11727],{},[1750,12023,1758],{},[3586,12025,12026],{"scriptlevel":2607,"displaystyle":1752},[3423,12027,12028,12030],{},[1742,12029,7902],{},[1742,12031,1872],{},[1699,12033,12034,12036],{},[1750,12035,1763],{"stretchy":1752},[1742,12037,1872],{},[1750,12039,1758],{},[3586,12041,12042],{"scriptlevel":2607,"displaystyle":1752},[3423,12043,12044,12046],{},[1742,12045,1744],{},[1742,12047,7859],{},[902,12049,12050],{"encoding":904},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[115,12052,12053],{"id":1145},"Derivace",[724,12055,12056,12057,1348,12081,12109,12110,2313],{},"Označení ",[883,12058,12060],{"className":12059},[886],[888,12061,12062],{"xmlns":890},[892,12063,12064,12078],{},[895,12065,12066,12072,12074,12076],{},[1699,12067,12068,12070],{},[898,12069,11722],{},[1750,12071,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12073,1753],{"stretchy":1752},[898,12075,11727],{},[1750,12077,1763],{"stretchy":1752},[902,12079,12080],{"encoding":904},"f'(x)",[883,12082,12084],{"className":12083},[886],[888,12085,12086],{"xmlns":890},[892,12087,12088,12106],{},[895,12089,12090],{},[3586,12091,12092],{"scriptlevel":2607,"displaystyle":1916},[3423,12093,12094,12100],{},[895,12095,12096,12098],{},[898,12097,3429],{},[898,12099,11717],{},[895,12101,12102,12104],{},[898,12103,3429],{},[898,12105,11727],{},[902,12107,12108],{"encoding":904},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[883,12111,12113],{"className":12112},[886],[888,12114,12115],{"xmlns":890},[892,12116,12117,12131],{},[895,12118,12119,12125,12127,12129],{},[1699,12120,12121,12123],{},[898,12122,11722],{},[1750,12124,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12126,1753],{"stretchy":1752},[898,12128,207],{},[1750,12130,1763],{"stretchy":1752},[902,12132,12133],{"encoding":904},"f'(a)",[198,12135,12137],{"id":12136},"geometrická-interpretace","Geometrická interpretace",[724,12139,12140,12163,12164,12167,12168,12196],{},[883,12141,12143],{"className":12142},[886],[888,12144,12145],{"xmlns":890},[892,12146,12147,12161],{},[895,12148,12149,12155,12157,12159],{},[1699,12150,12151,12153],{},[898,12152,11722],{},[1750,12154,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12156,1753],{"stretchy":1752},[898,12158,207],{},[1750,12160,1763],{"stretchy":1752},[902,12162,12133],{"encoding":904}," = ",[38,12165,12166],{},"sklon tečny"," ke grafu funkce v bodě ",[883,12169,12171],{"className":12170},[886],[888,12172,12173],{"xmlns":890},[892,12174,12175,12193],{},[895,12176,12177,12179,12181,12183,12185,12187,12189,12191],{},[1750,12178,5141],{"stretchy":1752},[898,12180,207],{},[1750,12182,1917],{"separator":1916},[898,12184,11722],{},[1750,12186,1753],{"stretchy":1752},[898,12188,207],{},[1750,12190,1763],{"stretchy":1752},[1750,12192,5158],{"stretchy":1752},[902,12194,12195],{"encoding":904},"[a, f(a)]",". Rovnice tečny:",[724,12198,12199],{},[883,12200,12202],{"className":12201},[886],[888,12203,12204],{"xmlns":890},[892,12205,12206,12244],{},[895,12207,12208,12210,12212,12214,12216,12218,12220,12222,12228,12230,12232,12234,12236,12238,12240,12242],{},[898,12209,11717],{},[1750,12211,1758],{},[898,12213,11722],{},[1750,12215,1753],{"stretchy":1752},[898,12217,207],{},[1750,12219,1763],{"stretchy":1752},[1750,12221,1766],{},[1699,12223,12224,12226],{},[898,12225,11722],{},[1750,12227,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12229,1753],{"stretchy":1752},[898,12231,207],{},[1750,12233,1763],{"stretchy":1752},[1750,12235,1753],{"stretchy":1752},[898,12237,11727],{},[1750,12239,1758],{},[898,12241,207],{},[1750,12243,1763],{"stretchy":1752},[902,12245,12246],{"encoding":904},"y - f(a) = f'(a)(x - a)",[724,12248,12249],{},[4434,12250],{"alt":12251,"className":12252,"src":12253},"imek-derivace-tecna",[210,4438],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[198,12255,12257],{"id":12256},"inženýrská-interpretace","Inženýrská interpretace",[724,12259,12260,12163,12283,1647,12286,12299,12300,2984,12313,12331,12332,12345,12346,12359,12360,4321,12373,2366],{},[883,12261,12263],{"className":12262},[886],[888,12264,12265],{"xmlns":890},[892,12266,12267,12281],{},[895,12268,12269,12275,12277,12279],{},[1699,12270,12271,12273],{},[898,12272,11722],{},[1750,12274,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12276,1753],{"stretchy":1752},[898,12278,207],{},[1750,12280,1763],{"stretchy":1752},[902,12282,12133],{"encoding":904},[38,12284,12285],{},"rychlost změny",[883,12287,12289],{"className":12288},[886],[888,12290,12291],{"xmlns":890},[892,12292,12293,12297],{},[895,12294,12295],{},[898,12296,11717],{},[902,12298,11717],{"encoding":904}," vzhledem k ",[883,12301,12303],{"className":12302},[886],[888,12304,12305],{"xmlns":890},[892,12306,12307,12311],{},[895,12308,12309],{},[898,12310,11727],{},[902,12312,11727],{"encoding":904},[883,12314,12316],{"className":12315},[886],[888,12317,12318],{"xmlns":890},[892,12319,12320,12328],{},[895,12321,12322,12324,12326],{},[898,12323,11727],{},[1750,12325,1766],{},[898,12327,207],{},[902,12329,12330],{"encoding":904},"x = a","; přibližná změna ",[883,12333,12335],{"className":12334},[886],[888,12336,12337],{"xmlns":890},[892,12338,12339,12343],{},[895,12340,12341],{},[898,12342,11717],{},[902,12344,11717],{"encoding":904}," při změně ",[883,12347,12349],{"className":12348},[886],[888,12350,12351],{"xmlns":890},[892,12352,12353,12357],{},[895,12354,12355],{},[898,12356,11727],{},[902,12358,11727],{"encoding":904}," z ",[883,12361,12363],{"className":12362},[886],[888,12364,12365],{"xmlns":890},[892,12366,12367,12371],{},[895,12368,12369],{},[898,12370,207],{},[902,12372,207],{"encoding":904},[883,12374,12376],{"className":12375},[886],[888,12377,12378],{"xmlns":890},[892,12379,12380,12388],{},[895,12381,12382,12384,12386],{},[898,12383,207],{},[1750,12385,1861],{},[1742,12387,1744],{},[902,12389,12390],{"encoding":904},"a+1",[724,12392,12393],{},[883,12394,12396],{"className":12395},[886],[888,12397,12398],{"xmlns":890},[892,12399,12400,12438],{},[895,12401,12402,12404,12406,12408,12410,12412,12414,12416,12418,12420,12422,12424,12426,12432,12434,12436],{},[898,12403,11722],{},[1750,12405,1753],{"stretchy":1752},[898,12407,207],{},[1750,12409,1861],{},[1742,12411,1744],{},[1750,12413,1763],{"stretchy":1752},[1750,12415,2274],{},[898,12417,11722],{},[1750,12419,1753],{"stretchy":1752},[898,12421,207],{},[1750,12423,1763],{"stretchy":1752},[1750,12425,1861],{},[1699,12427,12428,12430],{},[898,12429,11722],{},[1750,12431,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12433,1753],{"stretchy":1752},[898,12435,207],{},[1750,12437,1763],{"stretchy":1752},[902,12439,12440],{"encoding":904},"f(a+1) \\approx f(a) + f'(a)",[198,12442,12444],{"id":12443},"příklad-mezní-náklady","Příklad — mezní náklady",[724,12446,12447,12448,2313],{},"Celkové náklady ",[883,12449,12451],{"className":12450},[886],[888,12452,12453],{"xmlns":890},[892,12454,12455,12483],{},[895,12456,12457,12459,12461,12463,12465,12467,12469,12472,12474,12477],{},[898,12458,5326],{},[898,12460,1812],{},[1750,12462,1766],{},[1742,12464,8243],{},[1750,12466,1861],{},[1742,12468,1872],{},[898,12470,12471],{},"Q",[1750,12473,1861],{},[1742,12475,12476],{},"0,1",[1699,12478,12479,12481],{},[898,12480,12471],{},[1742,12482,1872],{},[902,12484,12485],{"encoding":904},"TC = 1000 + 2Q + 0{,}1 Q^2",[724,12487,12488,12489,12525,12526,2313],{},"Mezní náklady: ",[883,12490,12492],{"className":12491},[886],[888,12493,12494],{"xmlns":890},[892,12495,12496,12522],{},[895,12497,12498,12500,12502,12504,12506,12512,12514,12516,12518,12520],{},[898,12499,1773],{},[898,12501,1812],{},[1750,12503,1766],{},[898,12505,5326],{},[1699,12507,12508,12510],{},[898,12509,1812],{},[1750,12511,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12513,1766],{},[1742,12515,1872],{},[1750,12517,1861],{},[1742,12519,3929],{},[898,12521,12471],{},[902,12523,12524],{"encoding":904},"MC = TC' = 2 + 0{,}2 Q",", takže ",[883,12527,12529],{"className":12528},[886],[888,12530,12531],{"xmlns":890},[892,12532,12533,12549],{},[895,12534,12535,12537,12539,12541,12543,12545,12547],{},[898,12536,1773],{},[898,12538,1812],{},[1750,12540,1753],{"stretchy":1752},[1742,12542,3079],{},[1750,12544,1763],{"stretchy":1752},[1750,12546,1766],{},[1742,12548,7859],{},[902,12550,12551],{"encoding":904},"MC(10) = 4",[724,12553,12554,1647,12557,12605,12606,1647,12609,2313],{},[38,12555,12556],{},"Skutečný přírůstek:",[883,12558,12560],{"className":12559},[886],[888,12561,12562],{"xmlns":890},[892,12563,12564,12602],{},[895,12565,12566,12568,12570,12572,12574,12576,12578,12580,12583,12585,12587,12589,12591,12593,12595,12597,12599],{},[898,12567,2666],{"mathvariant":1747},[898,12569,5326],{},[898,12571,1812],{},[1750,12573,1766],{},[898,12575,5326],{},[898,12577,1812],{},[1750,12579,1753],{"stretchy":1752},[1742,12581,12582],{},"11",[1750,12584,1763],{"stretchy":1752},[1750,12586,1758],{},[898,12588,5326],{},[898,12590,1812],{},[1750,12592,1753],{"stretchy":1752},[1742,12594,3079],{},[1750,12596,1763],{"stretchy":1752},[1750,12598,1766],{},[1742,12600,12601],{},"4,2",[902,12603,12604],{"encoding":904},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[38,12607,12608],{},"Přibližný (lineární):",[883,12610,12612],{"className":12611},[886],[888,12613,12614],{"xmlns":890},[892,12615,12616,12620],{},[895,12617,12618],{},[1742,12619,7859],{},[902,12621,7859],{"encoding":904},[724,12623,12624,12625,12628],{},"(Viz aplikace v ",[207,12626,11571],{"className":12627,"dataFsResolvedFilePath":827,"href":828},[210],".)",[115,12630,12632],{"id":12631},"diferenciál","Diferenciál",[724,12634,12635],{},[883,12636,12638],{"className":12637},[886],[888,12639,12640],{"xmlns":890},[892,12641,12642,12668],{},[895,12643,12644,12646,12648,12650,12656,12658,12660,12662,12664,12666],{},[898,12645,3429],{},[898,12647,11722],{},[1750,12649,1766],{},[1699,12651,12652,12654],{},[898,12653,11722],{},[1750,12655,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12657,1753],{"stretchy":1752},[898,12659,11727],{},[1750,12661,1763],{"stretchy":1752},[1969,12663,2658],{},[898,12665,3429],{},[898,12667,11727],{},[902,12669,12670],{"encoding":904},"df = f'(x)\\, dx",[724,12672,12673,12674,12690,12691,12739,12740,2313],{},"Pro malá ",[883,12675,12677],{"className":12676},[886],[888,12678,12679],{"xmlns":890},[892,12680,12681,12687],{},[895,12682,12683,12685],{},[898,12684,3429],{},[898,12686,11727],{},[902,12688,12689],{"encoding":904},"dx"," platí: ",[883,12692,12694],{"className":12693},[886],[888,12695,12696],{"xmlns":890},[892,12697,12698,12736],{},[895,12699,12700,12702,12704,12706,12708,12710,12712,12714,12716,12718,12720,12722,12724,12726,12728,12730,12732,12734],{},[898,12701,2666],{"mathvariant":1747},[898,12703,11722],{},[1750,12705,1766],{},[898,12707,11722],{},[1750,12709,1753],{"stretchy":1752},[898,12711,11727],{},[1750,12713,1861],{},[898,12715,3429],{},[898,12717,11727],{},[1750,12719,1763],{"stretchy":1752},[1750,12721,1758],{},[898,12723,11722],{},[1750,12725,1753],{"stretchy":1752},[898,12727,11727],{},[1750,12729,1763],{"stretchy":1752},[1750,12731,2274],{},[898,12733,3429],{},[898,12735,11722],{},[902,12737,12738],{"encoding":904},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[38,12741,12742],{},"lineární odhad přírůstku",[198,12744,12746],{"id":12745},"příklad","Příklad",[724,12748,12749,12779,12780,12804,12805,12825],{},[883,12750,12752],{"className":12751},[886],[888,12753,12754],{"xmlns":890},[892,12755,12756,12776],{},[895,12757,12758,12760,12762,12764,12766,12768,12770],{},[898,12759,5326],{},[898,12761,1812],{},[1750,12763,1766],{},[1742,12765,4078],{},[1750,12767,1861],{},[1742,12769,12476],{},[1699,12771,12772,12774],{},[898,12773,12471],{},[1742,12775,1872],{},[902,12777,12778],{"encoding":904},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[883,12781,12783],{"className":12782},[886],[888,12784,12785],{"xmlns":890},[892,12786,12787,12801],{},[895,12788,12789,12791,12793,12795,12798],{},[898,12790,12471],{},[1750,12792,2366],{},[1742,12794,3936],{},[1750,12796,12797],{},"→",[1742,12799,12800],{},"60",[902,12802,12803],{"encoding":904},"Q: 50 \\to 60"," (tj. ",[883,12806,12808],{"className":12807},[886],[888,12809,12810],{"xmlns":890},[892,12811,12812,12822],{},[895,12813,12814,12816,12818,12820],{},[898,12815,3429],{},[898,12817,12471],{},[1750,12819,1766],{},[1742,12821,3079],{},[902,12823,12824],{"encoding":904},"dQ = 10","):",[724,12827,12828],{},[883,12829,12831],{"className":12830},[886],[888,12832,12833],{"xmlns":890},[892,12834,12835,12871],{},[895,12836,12837,12839,12841,12843,12845,12847,12849,12851,12853,12855,12857,12859,12861,12863,12865,12867,12869],{},[898,12838,3429],{},[898,12840,5326],{},[898,12842,1812],{},[1750,12844,1766],{},[1742,12846,3929],{},[898,12848,12471],{},[1750,12850,8009],{},[898,12852,3429],{},[898,12854,12471],{},[1750,12856,1766],{},[1742,12858,3929],{},[1750,12860,8009],{},[1742,12862,3936],{},[1750,12864,8009],{},[1742,12866,3079],{},[1750,12868,1766],{},[1742,12870,4078],{},[902,12872,12873],{"encoding":904},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[724,12875,12876,12877,12900,12901,12917],{},"Přesná změna: ",[883,12878,12880],{"className":12879},[886],[888,12881,12882],{"xmlns":890},[892,12883,12884,12897],{},[895,12885,12886,12888,12890,12892,12894],{},[898,12887,2666],{"mathvariant":1747},[898,12889,5326],{},[898,12891,1812],{},[1750,12893,1766],{},[1742,12895,12896],{},"110",[902,12898,12899],{"encoding":904},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[883,12902,12904],{"className":12903},[886],[888,12905,12906],{"xmlns":890},[892,12907,12908,12914],{},[895,12909,12910,12912],{},[898,12911,5326],{},[898,12913,1812],{},[902,12915,12916],{"encoding":904},"TC"," je konvexní.",[115,12919,12921],{"id":12920},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[198,12923,12925],{"id":12924},"nutná-podmínka","Nutná podmínka",[724,12927,12928,12929,2984,12949,12962,12963,12991,12992,12995],{},"Má-li ",[883,12930,12932],{"className":12931},[886],[888,12933,12934],{"xmlns":890},[892,12935,12936,12946],{},[895,12937,12938,12940,12942,12944],{},[898,12939,11722],{},[1750,12941,1753],{"stretchy":1752},[898,12943,11727],{},[1750,12945,1763],{"stretchy":1752},[902,12947,12948],{"encoding":904},"f(x)",[883,12950,12952],{"className":12951},[886],[888,12953,12954],{"xmlns":890},[892,12955,12956,12960],{},[895,12957,12958],{},[898,12959,207],{},[902,12961,207],{"encoding":904}," extrém, pak ",[883,12964,12966],{"className":12965},[886],[888,12967,12968],{"xmlns":890},[892,12969,12970,12988],{},[895,12971,12972,12978,12980,12982,12984,12986],{},[1699,12973,12974,12976],{},[898,12975,11722],{},[1750,12977,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,12979,1753],{"stretchy":1752},[898,12981,207],{},[1750,12983,1763],{"stretchy":1752},[1750,12985,1766],{},[1742,12987,2607],{},[902,12989,12990],{"encoding":904},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[38,12993,12994],{},"stacionární"," (podezřelé) body.",[198,12997,12999],{"id":12998},"postačující-podmínka","Postačující podmínka",[724,13001,13002,13003,13016,13017,2366],{},"Pro stacionární bod ",[883,13004,13006],{"className":13005},[886],[888,13007,13008],{"xmlns":890},[892,13009,13010,13014],{},[895,13011,13012],{},[898,13013,207],{},[902,13015,207],{"encoding":904},", je-li ",[883,13018,13020],{"className":13019},[886],[888,13021,13022],{"xmlns":890},[892,13023,13024,13047],{},[895,13025,13026,13036,13038,13040,13042,13045],{},[1699,13027,13028,13030],{},[898,13029,11722],{},[895,13031,13032,13034],{},[1750,13033,3815],{"mathvariant":1747},[1750,13035,3815],{"mathvariant":1747},[1750,13037,1753],{"stretchy":1752},[898,13039,207],{},[1750,13041,1763],{"stretchy":1752},[1750,13043,13044],{"mathvariant":1747},"≠",[1742,13046,2607],{},[902,13048,13049],{"encoding":904},"f''(a) \\neq 0",[120,13051,13052,13090],{},[123,13053,13054,13086,13087],{},[883,13055,13057],{"className":13056},[886],[888,13058,13059],{"xmlns":890},[892,13060,13061,13083],{},[895,13062,13063,13073,13075,13077,13079,13081],{},[1699,13064,13065,13067],{},[898,13066,11722],{},[895,13068,13069,13071],{},[1750,13070,3815],{"mathvariant":1747},[1750,13072,3815],{"mathvariant":1747},[1750,13074,1753],{"stretchy":1752},[898,13076,207],{},[1750,13078,1763],{"stretchy":1752},[1750,13080,2604],{},[1742,13082,2607],{},[902,13084,13085],{"encoding":904},"f''(a) > 0"," ⇒ ",[38,13088,13089],{},"lokální minimum",[123,13091,13092,13086,13124],{},[883,13093,13095],{"className":13094},[886],[888,13096,13097],{"xmlns":890},[892,13098,13099,13121],{},[895,13100,13101,13111,13113,13115,13117,13119],{},[1699,13102,13103,13105],{},[898,13104,11722],{},[895,13106,13107,13109],{},[1750,13108,3815],{"mathvariant":1747},[1750,13110,3815],{"mathvariant":1747},[1750,13112,1753],{"stretchy":1752},[898,13114,207],{},[1750,13116,1763],{"stretchy":1752},[1750,13118,2624],{},[1742,13120,2607],{},[902,13122,13123],{"encoding":904},"f''(a) \u003C 0",[38,13125,13126],{},"lokální maximum",[724,13128,13129],{},[4434,13130],{"alt":13131,"className":13132,"src":13133},"imek-extremy-1d",[210,4438],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[198,13135,12746],{"id":13136},"příklad-1",[724,13138,13139],{},[883,13140,13142],{"className":13141},[886],[888,13143,13144],{"xmlns":890},[892,13145,13146,13186],{},[895,13147,13148,13150,13152,13154,13156,13158,13160,13166,13168,13170,13176,13178,13180,13182,13184],{},[898,13149,11722],{},[1750,13151,1753],{"stretchy":1752},[898,13153,11727],{},[1750,13155,1763],{"stretchy":1752},[1750,13157,1766],{},[1742,13159,1872],{},[1699,13161,13162,13164],{},[898,13163,11727],{},[1742,13165,7822],{},[1750,13167,1758],{},[1742,13169,7822],{},[1699,13171,13172,13174],{},[898,13173,11727],{},[1742,13175,1872],{},[1750,13177,1758],{},[1742,13179,4903],{},[898,13181,11727],{},[1750,13183,1861],{},[1742,13185,7822],{},[902,13187,13188],{"encoding":904},"f(x) = 2x^3 - 3x^2 - 12x + 3",[120,13190,13191,13302,13342,13405],{},[123,13192,13193,13265,13266],{},[883,13194,13196],{"className":13195},[886],[888,13197,13198],{"xmlns":890},[892,13199,13200,13262],{},[895,13201,13202,13208,13210,13212,13214,13216,13218,13224,13226,13228,13230,13232,13234,13236,13238,13240,13242,13244,13246,13248,13250,13252,13254,13256,13258,13260],{},[1699,13203,13204,13206],{},[898,13205,11722],{},[1750,13207,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,13209,1753],{"stretchy":1752},[898,13211,11727],{},[1750,13213,1763],{"stretchy":1752},[1750,13215,1766],{},[1742,13217,3219],{},[1699,13219,13220,13222],{},[898,13221,11727],{},[1742,13223,1872],{},[1750,13225,1758],{},[1742,13227,3219],{},[898,13229,11727],{},[1750,13231,1758],{},[1742,13233,4903],{},[1750,13235,1766],{},[1742,13237,3219],{},[1750,13239,1753],{"stretchy":1752},[898,13241,11727],{},[1750,13243,1861],{},[1742,13245,1744],{},[1750,13247,1763],{"stretchy":1752},[1750,13249,1753],{"stretchy":1752},[898,13251,11727],{},[1750,13253,1758],{},[1742,13255,1872],{},[1750,13257,1763],{"stretchy":1752},[1750,13259,1766],{},[1742,13261,2607],{},[902,13263,13264],{"encoding":904},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[883,13267,13269],{"className":13268},[886],[888,13270,13271],{"xmlns":890},[892,13272,13273,13299],{},[895,13274,13275,13281,13283,13285,13287,13289,13295,13297],{},[5535,13276,13277,13279],{},[898,13278,11727],{},[1742,13280,1744],{},[1750,13282,1766],{},[1750,13284,1758],{},[1742,13286,1744],{},[1750,13288,1917],{"separator":1916},[5535,13290,13291,13293],{},[898,13292,11727],{},[1742,13294,1872],{},[1750,13296,1766],{},[1742,13298,1872],{},[902,13300,13301],{"encoding":904},"x_1 = -1, x_2 = 2",[123,13303,13304],{},[883,13305,13307],{"className":13306},[886],[888,13308,13309],{"xmlns":890},[892,13310,13311,13339],{},[895,13312,13313,13323,13325,13327,13329,13331,13333,13335,13337],{},[1699,13314,13315,13317],{},[898,13316,11722],{},[895,13318,13319,13321],{},[1750,13320,3815],{"mathvariant":1747},[1750,13322,3815],{"mathvariant":1747},[1750,13324,1753],{"stretchy":1752},[898,13326,11727],{},[1750,13328,1763],{"stretchy":1752},[1750,13330,1766],{},[1742,13332,4903],{},[898,13334,11727],{},[1750,13336,1758],{},[1742,13338,3219],{},[902,13340,13341],{"encoding":904},"f''(x) = 12x - 6",[123,13343,13344,13086,13385,13388,13389],{},[883,13345,13347],{"className":13346},[886],[888,13348,13349],{"xmlns":890},[892,13350,13351,13382],{},[895,13352,13353,13363,13365,13367,13369,13371,13373,13375,13378,13380],{},[1699,13354,13355,13357],{},[898,13356,11722],{},[895,13358,13359,13361],{},[1750,13360,3815],{"mathvariant":1747},[1750,13362,3815],{"mathvariant":1747},[1750,13364,1753],{"stretchy":1752},[1750,13366,1758],{},[1742,13368,1744],{},[1750,13370,1763],{"stretchy":1752},[1750,13372,1766],{},[1750,13374,1758],{},[1742,13376,13377],{},"18",[1750,13379,2624],{},[1742,13381,2607],{},[902,13383,13384],{"encoding":904},"f''(-1) = -18 \u003C 0",[38,13386,13387],{},"maximum"," v ",[883,13390,13392],{"className":13391},[886],[888,13393,13394],{"xmlns":890},[892,13395,13396,13402],{},[895,13397,13398,13400],{},[1750,13399,1758],{},[1742,13401,1744],{},[902,13403,13404],{"encoding":904},"-1",[123,13406,13407,13086,13443,13388,13446],{},[883,13408,13410],{"className":13409},[886],[888,13411,13412],{"xmlns":890},[892,13413,13414,13440],{},[895,13415,13416,13426,13428,13430,13432,13434,13436,13438],{},[1699,13417,13418,13420],{},[898,13419,11722],{},[895,13421,13422,13424],{},[1750,13423,3815],{"mathvariant":1747},[1750,13425,3815],{"mathvariant":1747},[1750,13427,1753],{"stretchy":1752},[1742,13429,1872],{},[1750,13431,1763],{"stretchy":1752},[1750,13433,1766],{},[1742,13435,13377],{},[1750,13437,2604],{},[1742,13439,2607],{},[902,13441,13442],{"encoding":904},"f''(2) = 18 > 0",[38,13444,13445],{},"minimum",[883,13447,13449],{"className":13448},[886],[888,13450,13451],{"xmlns":890},[892,13452,13453,13457],{},[895,13454,13455],{},[1742,13456,1872],{},[902,13458,1872],{"encoding":904},[115,13460,11524],{"id":11523},[120,13462,13463,13471,13479],{},[123,13464,13465,1647,13468],{},[38,13466,13467],{},"Předchozí:",[207,13469,757],{"className":13470,"dataFsResolvedFilePath":755,"href":756},[210],[123,13472,13473,1647,13476],{},[38,13474,13475],{},"Navazující:",[207,13477,775],{"className":13478,"dataFsResolvedFilePath":773,"href":774},[210],[123,13480,13481,1647,13484,13487,13488,13492,13493,13497],{},[38,13482,13483],{},"Souvislosti:",[207,13485,784],{"className":13486,"dataFsResolvedFilePath":782,"href":783},[210]," (rozšíření na 2D), ",[207,13489,13491],{"className":13490,"dataFsResolvedFilePath":827,"href":828},[210],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[207,13494,13496],{"className":13495,"dataFsResolvedFilePath":848,"href":849},[210],"Elasticita"," (procentní citlivost přes derivaci)",{"title":641,"searchDepth":642,"depth":642,"links":13499},[13500,13501,13506,13509,13514],{"id":11701,"depth":642,"text":11702},{"id":1145,"depth":642,"text":12053,"children":13502},[13503,13504,13505],{"id":12136,"depth":649,"text":12137},{"id":12256,"depth":649,"text":12257},{"id":12443,"depth":649,"text":12444},{"id":12631,"depth":642,"text":12632,"children":13507},[13508],{"id":12745,"depth":649,"text":12746},{"id":12920,"depth":642,"text":12921,"children":13510},[13511,13512,13513],{"id":12924,"depth":649,"text":12925},{"id":12998,"depth":649,"text":12999},{"id":13136,"depth":649,"text":12746},{"id":11523,"depth":642,"text":11524},"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":11674,"description":13515},[1135],"topics\u002Fderivace",[1128,1145,13522,13523,13524],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":13527,"title":13528,"body":13529,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":19193,"navigation":664,"path":19194,"seo":19195,"sources":19196,"stem":19197,"tags":19198,"type":11664,"updated":677,"__hash__":19203},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":9,"value":13530,"toc":19166},[13531,13534,13555,13559,13585,13589,13630,13720,13764,13768,13792,13799,13803,13813,13824,13828,13856,13865,13921,13927,13930,13936,13963,13969,14065,14224,14513,14517,14597,14603,14607,14703,14769,14937,14941,15019,15050,15077,15083,15115,15193,15279,15283,15345,15351,15354,15360,15474,15555,15599,15603,15649,15656,15973,15978,16002,16031,16098,16195,16199,16206,16213,16284,16404,16488,16491,16497,16823,16827,16990,16998,17134,17142,17378,17386,17389,17394,17650,17654,17827,17961,17998,18040,18043,18173,18263,18281,18285,18292,18298,18358,18361,18385,18388,18394,18397,18403,18406,18410,18447,18505,18693,18697,18769,18775,18782,18786,18792,18933,18937,18943,18979,18984,19161],[12,13532,13528],{"id":13533},"elasticita-poptávky-a-nabídky",[1785,13535,13536],{},[724,13537,13538,13541,13542,13544,13545,13548,13549,2028,13552,2313],{},[883,13539,13540],{},"!abstract"," TL;DR\n",[38,13543,13496],{}," 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: ",[38,13546,13547],{},"cenovou elasticitu poptávky"," (a nabídky), ",[38,13550,13551],{},"křížově-cenovou elasticitu",[38,13553,13554],{},"důchodovou elasticitu",[115,13556,13558],{"id":13557},"úvod-motivace","Úvod — motivace",[724,13560,13561,13562,13565,13566,13569,13570,13573,13574,13577,13578,13581,13582,1783],{},"Termín ",[614,13563,13564],{},"elasticita"," (alternativně ",[614,13567,13568],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[38,13571,13572],{},"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 ",[614,13575,13576],{},"cenové elasticity poptávky"," (resp. ",[614,13579,13580],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[207,13583,12053],{"className":13584,"dataFsResolvedFilePath":764,"href":765},[210],[198,13586,13588],{"id":13587},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[724,13590,13591,13592,13610,13611,13629],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[883,13593,13595],{"className":13594},[886],[888,13596,13597],{"xmlns":890},[892,13598,13599,13607],{},[895,13600,13601,13603,13605],{},[898,13602,1776],{},[1750,13604,1766],{},[1742,13606,3079],{},[902,13608,13609],{"encoding":904},"P=10"," a při této ceně se prodá ",[883,13612,13614],{"className":13613},[886],[888,13615,13616],{"xmlns":890},[892,13617,13618,13626],{},[895,13619,13620,13622,13624],{},[898,13621,12471],{},[1750,13623,1766],{},[1742,13625,4078],{},[902,13627,13628],{"encoding":904},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[120,13631,13632,13677],{},[123,13633,13634,13637,13638,13676],{},[38,13635,13636],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[883,13639,13641],{"className":13640},[886],[888,13642,13643],{"xmlns":890},[892,13644,13645,13673],{},[895,13646,13647,13649,13652,13654,13656,13659,13661,13664,13666,13668,13670],{},[1969,13648,6766],{},[1750,13650,13651],{},"⇒",[1969,13653,6766],{},[898,13655,5326],{},[898,13657,13658],{},"R",[1750,13660,1766],{},[1742,13662,13663],{},"9",[1750,13665,8009],{},[1742,13667,12896],{},[1750,13669,1766],{},[1742,13671,13672],{},"990",[902,13674,13675],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[123,13678,13679,13682,13683,13719],{},[38,13680,13681],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[883,13684,13686],{"className":13685},[886],[888,13687,13688],{"xmlns":890},[892,13689,13690,13716],{},[895,13691,13692,13694,13696,13698,13700,13702,13704,13706,13708,13711,13713],{},[1969,13693,6766],{},[1750,13695,13651],{},[1969,13697,6766],{},[898,13699,5326],{},[898,13701,13658],{},[1750,13703,1766],{},[1742,13705,13663],{},[1750,13707,8009],{},[1742,13709,13710],{},"120",[1750,13712,1766],{},[1742,13714,13715],{},"1080",[902,13717,13718],{"encoding":904},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[724,13721,13722,13723,13726,13727,13730,13731,13734,13735,13738,13739,13742,13743,13759,13760,13763],{},"Závěr: snížení ceny bylo na Trhu 1 ",[38,13724,13725],{},"nerozumné",", na Trhu 2 ",[38,13728,13729],{},"rozumné",". Trh 2 je ",[38,13732,13733],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[614,13736,13737],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[614,13740,13741],{},"neelastická"," a vyššího ",[883,13744,13746],{"className":13745},[886],[888,13747,13748],{"xmlns":890},[892,13749,13750,13756],{},[895,13751,13752,13754],{},[898,13753,5326],{},[898,13755,13658],{},[902,13757,13758],{"encoding":904},"TR"," lze naopak dosáhnout ",[614,13761,13762],{},"zvýšením"," ceny.",[198,13765,13767],{"id":13766},"hypotéza-41","Hypotéza 4.1",[1785,13769,13770],{},[724,13771,13772,13773],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[883,13774,13776],{"className":13775},[886],[888,13777,13778],{"xmlns":890},[892,13779,13780,13789],{},[895,13781,13782,13784,13787],{},[1750,13783,1753],{"stretchy":1752},[1742,13785,13786],{},"4.1",[1750,13788,1763],{"stretchy":1752},[902,13790,13791],{"encoding":904},"(4.1)",[724,13793,13794,13795,13798],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[38,13796,13797],{},"procentní změny"," obou faktorů.",[115,13800,13802],{"id":13801},"pojem-elasticity","Pojem elasticity",[724,13804,13805,13806,13808,13809,13812],{},"Obecně ",[38,13807,13564],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[38,13810,13811],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[1785,13814,13815],{},[724,13816,13817,13819,13820,13823],{},[883,13818,1791],{}," Intuice\nElasticitu lze číst jako ",[38,13821,13822],{},"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.",[115,13825,13827],{"id":13826},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[724,13829,13830,13831,13855],{},"Nechť ",[883,13832,13834],{"className":13833},[886],[888,13835,13836],{"xmlns":890},[892,13837,13838,13852],{},[895,13839,13840,13842,13844,13846,13848,13850],{},[898,13841,12471],{},[1750,13843,1766],{},[898,13845,5541],{},[1750,13847,1753],{"stretchy":1752},[898,13849,1776],{},[1750,13851,1763],{"stretchy":1752},[902,13853,13854],{"encoding":904},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[724,13857,13858],{},[883,13859,13864],{"className":13860,"title":13862,"style":13863},[13861],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[724,13866,13867,13868,2028,13884,13900,13901,13920],{},"Znaménko minus je korekce: změny ",[883,13869,13871],{"className":13870},[886],[888,13872,13873],{"xmlns":890},[892,13874,13875,13881],{},[895,13876,13877,13879],{},[898,13878,2666],{"mathvariant":1747},[898,13880,12471],{},[902,13882,13883],{"encoding":904},"\\Delta Q",[883,13885,13887],{"className":13886},[886],[888,13888,13889],{"xmlns":890},[892,13890,13891,13897],{},[895,13892,13893,13895],{},[898,13894,2666],{"mathvariant":1747},[898,13896,1776],{},[902,13898,13899],{"encoding":904},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[883,13902,13904],{"className":13903},[886],[888,13905,13906],{"xmlns":890},[892,13907,13908,13917],{},[895,13909,13910],{},[1699,13911,13912,13914],{},[898,13913,1705],{},[898,13915,13916],{},"A",[902,13918,13919],{"encoding":904},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[724,13922,13923],{},[883,13924,13926],{"className":13925,"title":13862,"style":13863},[13861],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[724,13928,13929],{},"Po dosazení:",[724,13931,13932],{},[883,13933,13935],{"className":13934,"title":13862,"style":13863},[13861],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[724,13937,13938,13939,13959,13960,13962],{},"Limitním přechodem ",[883,13940,13942],{"className":13941},[886],[888,13943,13944],{"xmlns":890},[892,13945,13946,13956],{},[895,13947,13948,13950,13952,13954],{},[898,13949,2666],{"mathvariant":1747},[898,13951,1776],{},[1750,13953,12797],{},[1742,13955,2607],{},[902,13957,13958],{"encoding":904},"\\Delta P \\to 0"," získáme definici ",[38,13961,13576],{}," (price elasticity of demand):",[724,13964,13965],{},[883,13966,13968],{"className":13967,"title":13862,"style":13863},[13861],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[724,13970,2590,13971,13994,13995,14017,14018,14042,14043,14064],{},[883,13972,13974],{"className":13973},[886],[888,13975,13976],{"xmlns":890},[892,13977,13978,13992],{},[895,13979,13980,13982,13984,13986,13988,13990],{},[898,13981,12471],{},[1750,13983,1766],{},[898,13985,5541],{},[1750,13987,1753],{"stretchy":1752},[898,13989,1776],{},[1750,13991,1763],{"stretchy":1752},[902,13993,13854],{"encoding":904},". Pro pevnou cenu ",[883,13996,13998],{"className":13997},[886],[888,13999,14000],{"xmlns":890},[892,14001,14002,14014],{},[895,14003,14004,14006,14008],{},[898,14005,1776],{},[1750,14007,1766],{},[1699,14009,14010,14012],{},[898,14011,1776],{},[1750,14013,3751],{},[902,14015,14016],{"encoding":904},"P = P^*"," se ",[883,14019,14021],{"className":14020},[886],[888,14022,14023],{"xmlns":890},[892,14024,14025,14039],{},[895,14026,14027,14029,14031,14037],{},[898,14028,1705],{},[1750,14030,1753],{"stretchy":1752},[1699,14032,14033,14035],{},[898,14034,1776],{},[1750,14036,3751],{},[1750,14038,1763],{"stretchy":1752},[902,14040,14041],{"encoding":904},"E(P^*)"," nazývá ",[614,14044,14045,14046],{},"elasticita poptávky při ceně ",[883,14047,14049],{"className":14048},[886],[888,14050,14051],{"xmlns":890},[892,14052,14053,14061],{},[895,14054,14055],{},[1699,14056,14057,14059],{},[898,14058,1776],{},[1750,14060,3751],{},[902,14062,14063],{"encoding":904},"P^*"," a je to vždy nezáporné číslo.",[1785,14066,14067],{},[724,14068,14069,14071,14072,14090,14091,14119,14120,14149,14150,1343,14168,1343,14186,14204,14205,14220,14221,2313],{},[883,14070,5454],{}," Pozor na znaménko\nV (4.5) je ",[38,14073,14074,14075],{},"explicitní ",[883,14076,14078],{"className":14077},[886],[888,14079,14080],{"xmlns":890},[892,14081,14082,14088],{},[895,14083,14084,14086],{},[1750,14085,1758],{},[1742,14087,1744],{},[902,14089,13404],{"encoding":904}," právě proto, že ",[883,14092,14094],{"className":14093},[886],[888,14095,14096],{"xmlns":890},[892,14097,14098,14116],{},[895,14099,14100,14106,14108,14110,14112,14114],{},[1699,14101,14102,14104],{},[898,14103,12471],{},[1750,14105,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,14107,1753],{"stretchy":1752},[898,14109,1776],{},[1750,14111,1763],{"stretchy":1752},[1750,14113,2624],{},[1742,14115,2607],{},[902,14117,14118],{"encoding":904},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[883,14121,14123],{"className":14122},[886],[888,14124,14125],{"xmlns":890},[892,14126,14127,14146],{},[895,14128,14129,14131,14133,14139,14141,14144],{},[898,14130,1705],{},[1750,14132,1753],{"stretchy":1752},[1699,14134,14135,14137],{},[898,14136,1776],{},[1750,14138,3751],{},[1750,14140,1763],{"stretchy":1752},[1750,14142,14143],{},"≥",[1742,14145,2607],{},[902,14147,14148],{"encoding":904},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[883,14151,14153],{"className":14152},[886],[888,14154,14155],{"xmlns":890},[892,14156,14157,14165],{},[895,14158,14159,14161,14163],{},[898,14160,1705],{},[1750,14162,2604],{},[1742,14164,1744],{},[902,14166,14167],{"encoding":904},"E > 1",[883,14169,14171],{"className":14170},[886],[888,14172,14173],{"xmlns":890},[892,14174,14175,14183],{},[895,14176,14177,14179,14181],{},[898,14178,1705],{},[1750,14180,2624],{},[1742,14182,1744],{},[902,14184,14185],{"encoding":904},"E \u003C 1",[883,14187,14189],{"className":14188},[886],[888,14190,14191],{"xmlns":890},[892,14192,14193,14201],{},[895,14194,14195,14197,14199],{},[898,14196,1705],{},[1750,14198,1766],{},[1742,14200,1744],{},[902,14202,14203],{"encoding":904},"E = 1",". V některých starších pramenech se ",[883,14206,14208],{"className":14207},[886],[888,14209,14210],{"xmlns":890},[892,14211,14212,14218],{},[895,14213,14214,14216],{},[1750,14215,1758],{},[1742,14217,1744],{},[902,14219,13404],{"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 ",[38,14222,14223],{},"absolutní hodnotou",[1785,14225,14226,14245],{},[724,14227,14228,14230,14231,14244],{},[883,14229,6004],{}," Postup: jak spočítat ",[883,14232,14234],{"className":14233},[886],[888,14235,14236],{"xmlns":890},[892,14237,14238,14242],{},[895,14239,14240],{},[898,14241,1705],{},[902,14243,1705],{"encoding":904}," v bodě",[152,14246,14247,14299,14338,14391,14456],{},[123,14248,14249,14250,14273,14274,14298],{},"Zapište ",[883,14251,14253],{"className":14252},[886],[888,14254,14255],{"xmlns":890},[892,14256,14257,14271],{},[895,14258,14259,14261,14263,14265,14267,14269],{},[898,14260,12471],{},[1750,14262,1766],{},[898,14264,5541],{},[1750,14266,1753],{"stretchy":1752},[898,14268,1776],{},[1750,14270,1763],{"stretchy":1752},[902,14272,13854],{"encoding":904},". Pokud je poptávka zadaná jako ",[883,14275,14277],{"className":14276},[886],[888,14278,14279],{"xmlns":890},[892,14280,14281,14295],{},[895,14282,14283,14285,14287,14289,14291,14293],{},[898,14284,1776],{},[1750,14286,1766],{},[898,14288,5541],{},[1750,14290,1753],{"stretchy":1752},[898,14292,12471],{},[1750,14294,1763],{"stretchy":1752},[902,14296,14297],{"encoding":904},"P = D(Q)",", použijte vztah (4.9).",[123,14300,14301,14302,2313],{},"Spočítejte derivaci ",[883,14303,14305],{"className":14304},[886],[888,14306,14307],{"xmlns":890},[892,14308,14309,14335],{},[895,14310,14311,14317,14319,14321,14323,14325,14327,14329,14331,14333],{},[1699,14312,14313,14315],{},[898,14314,12471],{},[1750,14316,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,14318,1753],{"stretchy":1752},[898,14320,1776],{},[1750,14322,1763],{"stretchy":1752},[1750,14324,1766],{},[898,14326,3429],{"mathvariant":1747},[898,14328,12471],{},[898,14330,1748],{"mathvariant":1747},[898,14332,3429],{"mathvariant":1747},[898,14334,1776],{},[902,14336,14337],{"encoding":904},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[123,14339,14340,14341,14358,14359,2313],{},"Dosaďte zadanou cenu ",[883,14342,14344],{"className":14343},[886],[888,14345,14346],{"xmlns":890},[892,14347,14348,14356],{},[895,14349,14350],{},[1699,14351,14352,14354],{},[898,14353,1776],{},[1750,14355,3751],{},[902,14357,14063],{"encoding":904}," a dopočítejte odpovídající ",[883,14360,14362],{"className":14361},[886],[888,14363,14364],{"xmlns":890},[892,14365,14366,14388],{},[895,14367,14368,14374,14376,14378,14380,14386],{},[1699,14369,14370,14372],{},[898,14371,12471],{},[1750,14373,3751],{},[1750,14375,1766],{},[898,14377,5541],{},[1750,14379,1753],{"stretchy":1752},[1699,14381,14382,14384],{},[898,14383,1776],{},[1750,14385,3751],{},[1750,14387,1763],{"stretchy":1752},[902,14389,14390],{"encoding":904},"Q^* = D(P^*)",[123,14392,14393,14394,2313],{},"Dosaďte do (4.5): ",[883,14395,14397],{"className":14396},[886],[888,14398,14399],{"xmlns":890},[892,14400,14401,14453],{},[895,14402,14403,14405,14407,14413,14415,14417,14419,14435,14437,14443,14445,14451],{},[898,14404,1705],{},[1750,14406,1753],{"stretchy":1752},[1699,14408,14409,14411],{},[898,14410,1776],{},[1750,14412,3751],{},[1750,14414,1763],{"stretchy":1752},[1750,14416,1766],{},[1750,14418,1758],{},[3586,14420,14421],{"scriptlevel":2607,"displaystyle":1916},[3423,14422,14423,14429],{},[1699,14424,14425,14427],{},[898,14426,1776],{},[1750,14428,3751],{},[1699,14430,14431,14433],{},[898,14432,12471],{},[1750,14434,3751],{},[1969,14436,2658],{},[1699,14438,14439,14441],{},[898,14440,12471],{},[1750,14442,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,14444,1753],{"stretchy":1752},[1699,14446,14447,14449],{},[898,14448,1776],{},[1750,14450,3751],{},[1750,14452,1763],{"stretchy":1752},[902,14454,14455],{"encoding":904},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[123,14457,14458,14459,14476,14477,14494,14495,14512],{},"Klasifikujte: ",[883,14460,14462],{"className":14461},[886],[888,14463,14464],{"xmlns":890},[892,14465,14466,14474],{},[895,14467,14468,14470,14472],{},[898,14469,1705],{},[1750,14471,2604],{},[1742,14473,1744],{},[902,14475,14167],{"encoding":904}," elastická, ",[883,14478,14480],{"className":14479},[886],[888,14481,14482],{"xmlns":890},[892,14483,14484,14492],{},[895,14485,14486,14488,14490],{},[898,14487,1705],{},[1750,14489,1766],{},[1742,14491,1744],{},[902,14493,14203],{"encoding":904}," jednotková, ",[883,14496,14498],{"className":14497},[886],[888,14499,14500],{"xmlns":890},[892,14501,14502,14510],{},[895,14503,14504,14506,14508],{},[898,14505,1705],{},[1750,14507,2624],{},[1742,14509,1744],{},[902,14511,14185],{"encoding":904}," neelastická.",[198,14514,14516],{"id":14515},"interpretace-46","Interpretace (4.6)",[1785,14518,14519],{},[724,14520,14521,14522,14545,14546,14559,14560,14577,14578],{},"Číslo ",[883,14523,14525],{"className":14524},[886],[888,14526,14527],{"xmlns":890},[892,14528,14529,14543],{},[895,14530,14531,14533,14535,14541],{},[898,14532,1705],{},[1750,14534,1753],{"stretchy":1752},[1699,14536,14537,14539],{},[898,14538,1776],{},[1750,14540,3751],{},[1750,14542,1763],{"stretchy":1752},[902,14544,14041],{"encoding":904}," udává, o kolik % se přibližně změní poptávané množství ",[883,14547,14549],{"className":14548},[886],[888,14550,14551],{"xmlns":890},[892,14552,14553,14557],{},[895,14554,14555],{},[898,14556,12471],{},[902,14558,12471],{"encoding":904},", jestliže se cena ",[883,14561,14563],{"className":14562},[886],[888,14564,14565],{"xmlns":890},[892,14566,14567,14575],{},[895,14568,14569],{},[1699,14570,14571,14573],{},[898,14572,1776],{},[1750,14574,3751],{},[902,14576,14063],{"encoding":904}," změní o 1 %. ",[883,14579,14581],{"className":14580},[886],[888,14582,14583],{"xmlns":890},[892,14584,14585,14594],{},[895,14586,14587,14589,14592],{},[1750,14588,1753],{"stretchy":1752},[1742,14590,14591],{},"4.6",[1750,14593,1763],{"stretchy":1752},[902,14595,14596],{"encoding":904},"(4.6)",[724,14598,14599,14602],{},[38,14600,14601],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[198,14604,14606],{"id":14605},"příklad-41","Příklad 4.1",[724,14608,14609,14610,14644,14645,1343,14669,2366],{},"Poptávka ",[883,14611,14613],{"className":14612},[886],[888,14614,14615],{"xmlns":890},[892,14616,14617,14641],{},[895,14618,14619,14621,14623,14625,14627,14629,14631,14633,14635,14637,14639],{},[898,14620,1776],{},[1750,14622,1766],{},[898,14624,5541],{},[1750,14626,1753],{"stretchy":1752},[898,14628,12471],{},[1750,14630,1763],{"stretchy":1752},[1750,14632,1766],{},[1742,14634,3936],{},[1750,14636,1758],{},[1742,14638,1872],{},[898,14640,12471],{},[902,14642,14643],{"encoding":904},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[883,14646,14648],{"className":14647},[886],[888,14649,14650],{"xmlns":890},[892,14651,14652,14666],{},[895,14653,14654,14656,14658,14660,14662,14664],{},[898,14655,12471],{},[1750,14657,1766],{},[1742,14659,6419],{},[1750,14661,1758],{},[1742,14663,4268],{},[898,14665,1776],{},[902,14667,14668],{"encoding":904},"Q = 25 - 0{,}5P",[883,14670,14672],{"className":14671},[886],[888,14673,14674],{"xmlns":890},[892,14675,14676,14700],{},[895,14677,14678,14694,14696,14698],{},[3586,14679,14680],{"scriptlevel":2607,"displaystyle":1916},[3423,14681,14682,14688],{},[895,14683,14684,14686],{},[898,14685,3429],{"mathvariant":1747},[898,14687,12471],{},[895,14689,14690,14692],{},[898,14691,3429],{"mathvariant":1747},[898,14693,1776],{},[1750,14695,1766],{},[1750,14697,1758],{},[1742,14699,4268],{},[902,14701,14702],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[724,14704,14705],{},[883,14706,14708],{"className":14707},[886],[888,14709,14710],{"xmlns":890},[892,14711,14712,14766],{},[895,14713,14714,14716,14718,14720,14734,14736,14738,14740,14742,14744,14746,14764],{},[898,14715,1705],{},[1750,14717,1766],{},[1750,14719,1758],{},[3423,14721,14722,14724],{},[898,14723,1776],{},[895,14725,14726,14728,14730,14732],{},[1742,14727,6419],{},[1750,14729,1758],{},[1742,14731,4268],{},[898,14733,1776],{},[1750,14735,8009],{},[1750,14737,1753],{"stretchy":1752},[1750,14739,1758],{},[1742,14741,4268],{},[1750,14743,1763],{"stretchy":1752},[1750,14745,1766],{},[3423,14747,14748,14754],{},[895,14749,14750,14752],{},[1742,14751,4268],{},[898,14753,1776],{},[895,14755,14756,14758,14760,14762],{},[1742,14757,6419],{},[1750,14759,1758],{},[1742,14761,4268],{},[898,14763,1776],{},[898,14765,2313],{"mathvariant":1747},[902,14767,14768],{"encoding":904},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[724,14770,14771,14772,1343,14796,1343,14826,1343,14850,14875,14876,14899,14900,4321,14918,1783],{},"Potom ",[883,14773,14775],{"className":14774},[886],[888,14776,14777],{"xmlns":890},[892,14778,14779,14793],{},[895,14780,14781,14783,14785,14787,14789,14791],{},[898,14782,1705],{},[1750,14784,1753],{"stretchy":1752},[1742,14786,2607],{},[1750,14788,1763],{"stretchy":1752},[1750,14790,1766],{},[1742,14792,2607],{},[902,14794,14795],{"encoding":904},"E(0)=0",[883,14797,14799],{"className":14798},[886],[888,14800,14801],{"xmlns":890},[892,14802,14803,14823],{},[895,14804,14805,14807,14809,14811,14813,14815],{},[898,14806,1705],{},[1750,14808,1753],{"stretchy":1752},[1742,14810,3079],{},[1750,14812,1763],{"stretchy":1752},[1750,14814,1766],{},[3586,14816,14817],{"scriptlevel":2607,"displaystyle":1752},[3423,14818,14819,14821],{},[1742,14820,1744],{},[1742,14822,7859],{},[902,14824,14825],{"encoding":904},"E(10)=\\tfrac{1}{4}",[883,14827,14829],{"className":14828},[886],[888,14830,14831],{"xmlns":890},[892,14832,14833,14847],{},[895,14834,14835,14837,14839,14841,14843,14845],{},[898,14836,1705],{},[1750,14838,1753],{"stretchy":1752},[1742,14840,6419],{},[1750,14842,1763],{"stretchy":1752},[1750,14844,1766],{},[1742,14846,1744],{},[902,14848,14849],{"encoding":904},"E(25)=1",[883,14851,14853],{"className":14852},[886],[888,14854,14855],{"xmlns":890},[892,14856,14857,14872],{},[895,14858,14859,14861,14863,14866,14868,14870],{},[898,14860,1705],{},[1750,14862,1753],{"stretchy":1752},[1742,14864,14865],{},"40",[1750,14867,1763],{"stretchy":1752},[1750,14869,1766],{},[1742,14871,7859],{},[902,14873,14874],{"encoding":904},"E(40)=4",". Např. ",[883,14877,14879],{"className":14878},[886],[888,14880,14881],{"xmlns":890},[892,14882,14883,14897],{},[895,14884,14885,14887,14889,14891,14893,14895],{},[898,14886,1705],{},[1750,14888,1753],{"stretchy":1752},[1742,14890,14865],{},[1750,14892,1763],{"stretchy":1752},[1750,14894,1766],{},[1742,14896,7859],{},[902,14898,14874],{"encoding":904}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[883,14901,14903],{"className":14902},[886],[888,14904,14905],{"xmlns":890},[892,14906,14907,14915],{},[895,14908,14909,14911,14913],{},[898,14910,12471],{},[1750,14912,1766],{},[1742,14914,7902],{},[902,14916,14917],{"encoding":904},"Q=5",[883,14919,14921],{"className":14920},[886],[888,14922,14923],{"xmlns":890},[892,14924,14925,14934],{},[895,14926,14927,14929,14931],{},[898,14928,12471],{},[1750,14930,1766],{},[1742,14932,14933],{},"4,8",[902,14935,14936],{"encoding":904},"Q=4{,}8",[198,14938,14940],{"id":14939},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[120,14942,14943,14999],{},[123,14944,14945,14948,14949,14966,14967,2313],{},[38,14946,14947],{},"Oblouková"," (průměrná) elasticita: výraz ",[883,14950,14952],{"className":14951},[886],[888,14953,14954],{"xmlns":890},[892,14955,14956,14964],{},[895,14957,14958],{},[1699,14959,14960,14962],{},[898,14961,1705],{},[898,14963,13916],{},[902,14965,13919],{"encoding":904}," ze (4.4) vztažený k intervalu ",[883,14968,14970],{"className":14969},[886],[888,14971,14972],{"xmlns":890},[892,14973,14974,14996],{},[895,14975,14976,14979,14981,14983,14985,14987,14989,14991,14993],{},[1750,14977,14978],{"stretchy":1752},"⟨",[898,14980,1776],{},[1750,14982,1917],{"separator":1916},[1969,14984,2658],{},[898,14986,1776],{},[1750,14988,1861],{},[898,14990,2666],{"mathvariant":1747},[898,14992,1776],{},[1750,14994,14995],{"stretchy":1752},"⟩",[902,14997,14998],{"encoding":904},"\\langle P,\\, P+\\Delta P\\rangle",[123,15000,15001,15004,15005,15018],{},[38,15002,15003],{},"Bodová"," (okamžitá) elasticita: ",[883,15006,15008],{"className":15007},[886],[888,15009,15010],{"xmlns":890},[892,15011,15012,15016],{},[895,15013,15014],{},[898,15015,1705],{},[902,15017,1705],{"encoding":904}," dle (4.5) — výchozí pojem dále v textu.",[198,15020,15022,15023,15036,15037],{"id":15021},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[883,15024,15026],{"className":15025},[886],[888,15027,15028],{"xmlns":890},[892,15029,15030,15034],{},[895,15031,15032],{},[898,15033,1776],{},[902,15035,1776],{"encoding":904}," jako funkce ",[883,15038,15040],{"className":15039},[886],[888,15041,15042],{"xmlns":890},[892,15043,15044,15048],{},[895,15045,15046],{},[898,15047,12471],{},[902,15049,12471],{"encoding":904},[724,15051,15052,15053,15076],{},"Pokud je poptávka zadaná ve tvaru ",[883,15054,15056],{"className":15055},[886],[888,15057,15058],{"xmlns":890},[892,15059,15060,15074],{},[895,15061,15062,15064,15066,15068,15070,15072],{},[898,15063,1776],{},[1750,15065,1766],{},[898,15067,5541],{},[1750,15069,1753],{"stretchy":1752},[898,15071,12471],{},[1750,15073,1763],{"stretchy":1752},[902,15075,14297],{"encoding":904},", využijeme vztah pro derivaci inverzní funkce",[724,15078,15079],{},[883,15080,15082],{"className":15081,"title":13862,"style":13863},[13861],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[724,15084,15085,1647,15088,15114],{},[38,15086,15087],{},"Příklad 4.3.",[883,15089,15091],{"className":15090},[886],[888,15092,15093],{"xmlns":890},[892,15094,15095,15111],{},[895,15096,15097,15099,15101,15103,15105],{},[898,15098,1776],{},[1750,15100,1766],{},[1742,15102,4078],{},[1750,15104,1758],{},[1699,15106,15107,15109],{},[898,15108,12471],{},[1742,15110,1872],{},[902,15112,15113],{"encoding":904},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[724,15116,15117],{},[883,15118,15120],{"className":15119},[886],[888,15121,15122],{"xmlns":890},[892,15123,15124,15190],{},[895,15125,15126,15128,15130,15132,15148,15150,15162,15164,15188],{},[898,15127,1705],{},[1750,15129,1766],{},[1750,15131,1758],{},[3423,15133,15134,15146],{},[895,15135,15136,15138,15140],{},[1742,15137,4078],{},[1750,15139,1758],{},[1699,15141,15142,15144],{},[898,15143,12471],{},[1742,15145,1872],{},[898,15147,12471],{},[1750,15149,8009],{},[3423,15151,15152,15154],{},[1742,15153,1744],{},[895,15155,15156,15158,15160],{},[1750,15157,1758],{},[1742,15159,1872],{},[898,15161,12471],{},[1750,15163,1766],{},[3423,15165,15166,15178],{},[895,15167,15168,15170,15172],{},[1742,15169,4078],{},[1750,15171,1758],{},[1699,15173,15174,15176],{},[898,15175,12471],{},[1742,15177,1872],{},[895,15179,15180,15182],{},[1742,15181,1872],{},[1699,15183,15184,15186],{},[898,15185,12471],{},[1742,15187,1872],{},[898,15189,2313],{"mathvariant":1747},[902,15191,15192],{"encoding":904},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[724,15194,15195,15196,15223,15224,8164,15243,2313],{},"Z rovnice ",[883,15197,15199],{"className":15198},[886],[888,15200,15201],{"xmlns":890},[892,15202,15203,15220],{},[895,15204,15205,15207,15209,15215,15217],{},[1742,15206,4078],{},[1750,15208,1758],{},[1699,15210,15211,15213],{},[898,15212,12471],{},[1742,15214,1872],{},[1750,15216,1766],{},[1742,15218,15219],{},"36",[902,15221,15222],{"encoding":904},"100 - Q^2 = 36"," plyne ",[883,15225,15227],{"className":15226},[886],[888,15228,15229],{"xmlns":890},[892,15230,15231,15240],{},[895,15232,15233,15235,15237],{},[898,15234,12471],{},[1750,15236,1766],{},[1742,15238,15239],{},"8",[902,15241,15242],{"encoding":904},"Q = 8",[883,15244,15246],{"className":15245},[886],[888,15247,15248],{"xmlns":890},[892,15249,15250,15276],{},[895,15251,15252,15254,15256,15258,15260,15262,15271,15273],{},[898,15253,1705],{},[1750,15255,1753],{"stretchy":1752},[1742,15257,15239],{},[1750,15259,1763],{"stretchy":1752},[1750,15261,1766],{},[3586,15263,15264],{"scriptlevel":2607,"displaystyle":1752},[3423,15265,15266,15268],{},[1742,15267,15219],{},[1742,15269,15270],{},"128",[1750,15272,1766],{},[1742,15274,15275],{},"0,281",[902,15277,15278],{"encoding":904},"E(8) = \\tfrac{36}{128} = 0{,}281",[198,15280,15282],{"id":15281},"přibližné-změny","Přibližné změny",[724,15284,15285,15286,9375,15322,15344],{},"Diferenciál ",[883,15287,15289],{"className":15288},[886],[888,15290,15291],{"xmlns":890},[892,15292,15293,15319],{},[895,15294,15295,15297,15299,15301,15307,15309,15311,15313,15315,15317],{},[898,15296,3429],{"mathvariant":1747},[898,15298,12471],{},[1750,15300,1766],{},[1699,15302,15303,15305],{},[898,15304,12471],{},[1750,15306,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,15308,1753],{"stretchy":1752},[898,15310,1776],{},[1750,15312,1763],{"stretchy":1752},[1969,15314,2658],{},[898,15316,3429],{"mathvariant":1747},[898,15318,1776],{},[902,15320,15321],{"encoding":904},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P",[883,15323,15325],{"className":15324},[886],[888,15326,15327],{"xmlns":890},[892,15328,15329,15341],{},[895,15330,15331,15333,15335,15337,15339],{},[898,15332,3429],{"mathvariant":1747},[898,15334,1776],{},[1750,15336,1766],{},[898,15338,2666],{"mathvariant":1747},[898,15340,1776],{},[902,15342,15343],{"encoding":904},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[724,15346,15347],{},[883,15348,15350],{"className":15349,"title":13862,"style":13863},[13861],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[724,15352,15353],{},"Po přechodu na procentní změny (vztah (4.3)):",[724,15355,15356],{},[883,15357,15359],{"className":15358,"title":13862,"style":13863},[13861],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[724,15361,15362,1647,15365,15400,15401,15420,15421,15455,15456,15473],{},[38,15363,15364],{},"Příklad 4.5.",[883,15366,15368],{"className":15367},[886],[888,15369,15370],{"xmlns":890},[892,15371,15372,15397],{},[895,15373,15374,15376,15378,15380,15386,15388,15390,15392,15394],{},[898,15375,1776],{},[1750,15377,1766],{},[1750,15379,1758],{},[1699,15381,15382,15384],{},[898,15383,12471],{},[1742,15385,1872],{},[1750,15387,1758],{},[1742,15389,7859],{},[898,15391,12471],{},[1750,15393,1861],{},[1742,15395,15396],{},"96",[902,15398,15399],{"encoding":904},"P = -Q^2 - 4Q + 96",", cena ",[883,15402,15404],{"className":15403},[886],[888,15405,15406],{"xmlns":890},[892,15407,15408,15417],{},[895,15409,15410,15412,15414],{},[898,15411,1776],{},[1750,15413,1766],{},[1742,15415,15416],{},"51",[902,15418,15419],{"encoding":904},"P=51",". Z rovnice ",[883,15422,15424],{"className":15423},[886],[888,15425,15426],{"xmlns":890},[892,15427,15428,15452],{},[895,15429,15430,15432,15434,15436,15442,15444,15446,15448,15450],{},[1742,15431,15416],{},[1750,15433,1766],{},[1750,15435,1758],{},[1699,15437,15438,15440],{},[898,15439,12471],{},[1742,15441,1872],{},[1750,15443,1758],{},[1742,15445,7859],{},[898,15447,12471],{},[1750,15449,1861],{},[1742,15451,15396],{},[902,15453,15454],{"encoding":904},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[883,15457,15459],{"className":15458},[886],[888,15460,15461],{"xmlns":890},[892,15462,15463,15471],{},[895,15464,15465,15467,15469],{},[898,15466,12471],{},[1750,15468,1766],{},[1742,15470,7902],{},[902,15472,14917],{"encoding":904},". Elasticita:",[724,15475,15476],{},[883,15477,15479],{"className":15478},[886],[888,15480,15481],{"xmlns":890},[892,15482,15483,15552],{},[895,15484,15485,15487,15489,15527,15529,15531,15533,15535,15537,15539,15541,15547,15549],{},[898,15486,1705],{},[1750,15488,1766],{},[3423,15490,15491,15511],{},[895,15492,15493,15495,15501,15503,15505,15507,15509],{},[1750,15494,1758],{},[1699,15496,15497,15499],{},[898,15498,12471],{},[1742,15500,1872],{},[1750,15502,1758],{},[1742,15504,7859],{},[898,15506,12471],{},[1750,15508,1861],{},[1742,15510,15396],{},[895,15512,15513,15515,15517,15519,15521,15523,15525],{},[898,15514,12471],{},[1750,15516,1753],{"stretchy":1752},[1742,15518,1872],{},[898,15520,12471],{},[1750,15522,1861],{},[1742,15524,7859],{},[1750,15526,1763],{"stretchy":1752},[1750,15528,1917],{"separator":1916},[2125,15530],{"width":2127},[898,15532,1705],{},[1750,15534,1753],{"stretchy":1752},[1742,15536,7902],{},[1750,15538,1763],{"stretchy":1752},[1750,15540,1766],{},[3423,15542,15543,15545],{},[1742,15544,15416],{},[1742,15546,6394],{},[1750,15548,6792],{},[1742,15550,15551],{},"0,728.",[902,15553,15554],{"encoding":904},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[724,15556,15557,15558,2313],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[883,15559,15561],{"className":15560},[886],[888,15562,15563],{"xmlns":890},[892,15564,15565,15596],{},[895,15566,15567,15569,15571,15574,15576,15578,15581,15583,15585,15587,15589,15592,15594],{},[898,15568,2666],{"mathvariant":1747},[898,15570,12471],{},[898,15572,15573],{"mathvariant":1747},"%",[1750,15575,2274],{},[1750,15577,1758],{},[1742,15579,15580],{},"0,728",[1750,15582,8009],{},[1742,15584,1872],{},[1750,15586,1766],{},[1750,15588,1758],{},[1742,15590,15591],{},"1,456",[1969,15593,2658],{},[898,15595,15573],{"mathvariant":1747},[902,15597,15598],{"encoding":904},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[115,15600,15602],{"id":15601},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[724,15604,15605,15606,15629,15630,2366],{},"V závislosti na hodnotě ",[883,15607,15609],{"className":15608},[886],[888,15610,15611],{"xmlns":890},[892,15612,15613,15627],{},[895,15614,15615,15617,15619,15625],{},[898,15616,1705],{},[1750,15618,1753],{"stretchy":1752},[1699,15620,15621,15623],{},[898,15622,1776],{},[1750,15624,3751],{},[1750,15626,1763],{"stretchy":1752},[902,15628,14041],{"encoding":904}," mluvíme o poptávce podle následující tabulky ",[883,15631,15633],{"className":15632},[886],[888,15634,15635],{"xmlns":890},[892,15636,15637,15646],{},[895,15638,15639,15641,15644],{},[1750,15640,1753],{"stretchy":1752},[1742,15642,15643],{},"4.7",[1750,15645,1763],{"stretchy":1752},[902,15647,15648],{"encoding":904},"(4.7)",[724,15650,15651],{},[4434,15652],{"alt":15653,"className":15654,"src":15655},"imek-typy-elasticity-5panelu",[210,4438],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[16,15657,15658,15697],{},[19,15659,15660],{},[22,15661,15662,15688,15691,15694],{},[25,15663,15664,15665],{},"Hodnota ",[883,15666,15668],{"className":15667},[886],[888,15669,15670],{"xmlns":890},[892,15671,15672,15686],{},[895,15673,15674,15676,15678,15684],{},[898,15675,1705],{},[1750,15677,1753],{"stretchy":1752},[1699,15679,15680,15682],{},[898,15681,1776],{},[1750,15683,3751],{},[1750,15685,1763],{"stretchy":1752},[902,15687,14041],{"encoding":904},[25,15689,15690],{},"Typ poptávky",[25,15692,15693],{},"Termín",[25,15695,15696],{},"Význam",[30,15698,15699,15732,15794,15869,15926],{},[22,15700,15701,15721,15726,15729],{},[35,15702,15703],{},[883,15704,15706],{"className":15705},[886],[888,15707,15708],{"xmlns":890},[892,15709,15710,15718],{},[895,15711,15712,15714,15716],{},[898,15713,1705],{},[1750,15715,1766],{},[1742,15717,2607],{},[902,15719,15720],{"encoding":904},"E = 0",[35,15722,15723],{},[38,15724,15725],{},"dokonale neelastická",[35,15727,15728],{},"perfectly inelastic",[35,15730,15731],{},"množství se nemění bez ohledu na cenu",[22,15733,15734,15758,15762,15765],{},[35,15735,15736],{},[883,15737,15739],{"className":15738},[886],[888,15740,15741],{"xmlns":890},[892,15742,15743,15755],{},[895,15744,15745,15747,15749,15751,15753],{},[1742,15746,2607],{},[1750,15748,2624],{},[898,15750,1705],{},[1750,15752,2624],{},[1742,15754,1744],{},[902,15756,15757],{"encoding":904},"0 \u003C E \u003C 1",[35,15759,15760],{},[38,15761,13741],{},[35,15763,15764],{},"inelastic",[35,15766,15767,15780,15781],{},[883,15768,15770],{"className":15769},[886],[888,15771,15772],{"xmlns":890},[892,15773,15774,15778],{},[895,15775,15776],{},[898,15777,12471],{},[902,15779,12471],{"encoding":904}," se mění pomaleji než ",[883,15782,15784],{"className":15783},[886],[888,15785,15786],{"xmlns":890},[892,15787,15788,15792],{},[895,15789,15790],{},[898,15791,1776],{},[902,15793,1776],{"encoding":904},[22,15795,15796,15815,15820,15823],{},[35,15797,15798],{},[883,15799,15801],{"className":15800},[886],[888,15802,15803],{"xmlns":890},[892,15804,15805,15813],{},[895,15806,15807,15809,15811],{},[898,15808,1705],{},[1750,15810,1766],{},[1742,15812,1744],{},[902,15814,14203],{"encoding":904},[35,15816,15817],{},[38,15818,15819],{},"jednotkově elastická",[35,15821,15822],{},"unit elastic",[35,15824,15825,15838,15839,15852,15853,15868],{},[883,15826,15828],{"className":15827},[886],[888,15829,15830],{"xmlns":890},[892,15831,15832,15836],{},[895,15833,15834],{},[898,15835,12471],{},[902,15837,12471],{"encoding":904}," i ",[883,15840,15842],{"className":15841},[886],[888,15843,15844],{"xmlns":890},[892,15845,15846,15850],{},[895,15847,15848],{},[898,15849,1776],{},[902,15851,1776],{"encoding":904}," se mění stejně rychle; ",[883,15854,15856],{"className":15855},[886],[888,15857,15858],{"xmlns":890},[892,15859,15860,15866],{},[895,15861,15862,15864],{},[898,15863,5326],{},[898,15865,13658],{},[902,15867,13758],{"encoding":904}," má maximum",[22,15870,15871,15890,15894,15897],{},[35,15872,15873],{},[883,15874,15876],{"className":15875},[886],[888,15877,15878],{"xmlns":890},[892,15879,15880,15888],{},[895,15881,15882,15884,15886],{},[898,15883,1705],{},[1750,15885,2604],{},[1742,15887,1744],{},[902,15889,14167],{"encoding":904},[35,15891,15892],{},[38,15893,13737],{},[35,15895,15896],{},"elastic",[35,15898,15899,15912,15913],{},[883,15900,15902],{"className":15901},[886],[888,15903,15904],{"xmlns":890},[892,15905,15906,15910],{},[895,15907,15908],{},[898,15909,12471],{},[902,15911,12471],{"encoding":904}," se mění rychleji než ",[883,15914,15916],{"className":15915},[886],[888,15917,15918],{"xmlns":890},[892,15919,15920,15924],{},[895,15921,15922],{},[898,15923,1776],{},[902,15925,1776],{"encoding":904},[22,15927,15928,15949,15954,15957],{},[35,15929,15930],{},[883,15931,15933],{"className":15932},[886],[888,15934,15935],{"xmlns":890},[892,15936,15937,15946],{},[895,15938,15939,15941,15943],{},[898,15940,1705],{},[1750,15942,12797],{},[898,15944,15945],{"mathvariant":1747},"∞",[902,15947,15948],{"encoding":904},"E \\to \\infty",[35,15950,15951],{},[38,15952,15953],{},"dokonale elastická",[35,15955,15956],{},"perfectly elastic",[35,15958,15959,15960],{},"sebemenší změna ceny úplně mění ",[883,15961,15963],{"className":15962},[886],[888,15964,15965],{"xmlns":890},[892,15966,15967,15971],{},[895,15968,15969],{},[898,15970,12471],{},[902,15972,12471],{"encoding":904},[724,15974,15975],{},[38,15976,15977],{},"Pravidlo růstu elasticity s cenou:",[1785,15979,15980],{},[724,15981,15982,15983],{},"S rostoucí cenou elasticita poptávky roste. ",[883,15984,15986],{"className":15985},[886],[888,15987,15988],{"xmlns":890},[892,15989,15990,15999],{},[895,15991,15992,15994,15997],{},[1750,15993,1753],{"stretchy":1752},[1742,15995,15996],{},"4.8",[1750,15998,1763],{"stretchy":1752},[902,16000,16001],{"encoding":904},"(4.8)",[724,16003,16004,16005,16008,16009,16012,16013,16030],{},"Z toho plyne, že při ",[614,16006,16007],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[614,16010,16011],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[883,16014,16016],{"className":16015},[886],[888,16017,16018],{"xmlns":890},[892,16019,16020,16028],{},[895,16021,16022],{},[1699,16023,16024,16026],{},[898,16025,1776],{},[1750,16027,3751],{},[902,16029,14063],{"encoding":904},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1785,16032,16033,16038],{},[724,16034,16035,16037],{},[883,16036,6004],{}," Postup: jak klasifikovat poptávku",[152,16039,16040,16067,16070],{},[123,16041,16042,16043,16066],{},"Spočítejte ",[883,16044,16046],{"className":16045},[886],[888,16047,16048],{"xmlns":890},[892,16049,16050,16064],{},[895,16051,16052,16054,16056,16062],{},[898,16053,1705],{},[1750,16055,1753],{"stretchy":1752},[1699,16057,16058,16060],{},[898,16059,1776],{},[1750,16061,3751],{},[1750,16063,1763],{"stretchy":1752},[902,16065,14041],{"encoding":904}," dle (4.5).",[123,16068,16069],{},"Porovnejte s jedničkou (viz tabulka výše).",[123,16071,16072,16073,16097],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[883,16074,16076],{"className":16075},[886],[888,16077,16078],{"xmlns":890},[892,16079,16080,16094],{},[895,16081,16082,16084,16086,16088,16090,16092],{},[898,16083,1705],{},[1750,16085,1753],{"stretchy":1752},[898,16087,1776],{},[1750,16089,1763],{"stretchy":1752},[1750,16091,1766],{},[1742,16093,1744],{},[902,16095,16096],{"encoding":904},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[724,16099,16100,16103,16104,16121,16122,16140,16141,16168,16169,2313],{},[38,16101,16102],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[883,16105,16107],{"className":16106},[886],[888,16108,16109],{"xmlns":890},[892,16110,16111,16119],{},[895,16112,16113,16115,16117],{},[898,16114,1705],{},[1750,16116,1766],{},[1742,16118,1744],{},[902,16120,14203],{"encoding":904}," pro ",[883,16123,16125],{"className":16124},[886],[888,16126,16127],{"xmlns":890},[892,16128,16129,16137],{},[895,16130,16131,16133,16135],{},[898,16132,1776],{},[1750,16134,1766],{},[1742,16136,6419],{},[902,16138,16139],{"encoding":904},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[883,16142,16144],{"className":16143},[886],[888,16145,16146],{"xmlns":890},[892,16147,16148,16165],{},[895,16149,16150,16152,16155,16157,16159,16161,16163],{},[898,16151,1776],{},[1750,16153,16154],{},"∈",[1750,16156,14978],{"stretchy":1752},[1742,16158,2607],{},[1750,16160,1917],{"separator":1916},[1742,16162,6419],{},[1750,16164,1763],{"stretchy":1752},[902,16166,16167],{"encoding":904},"P \\in \\langle 0, 25)"," a elastická pro ",[883,16170,16172],{"className":16171},[886],[888,16173,16174],{"xmlns":890},[892,16175,16176,16192],{},[895,16177,16178,16180,16182,16184,16186,16188,16190],{},[898,16179,1776],{},[1750,16181,16154],{},[1750,16183,1753],{"stretchy":1752},[1742,16185,6419],{},[1750,16187,1917],{"separator":1916},[1742,16189,3936],{},[1750,16191,14995],{"stretchy":1752},[902,16193,16194],{"encoding":904},"P \\in (25, 50\\rangle",[115,16196,16198],{"id":16197},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[724,16200,16201],{},[4434,16202],{"alt":16203,"className":16204,"src":16205},"imek-elasticita-tr",[210,4438],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[724,16207,16208],{},[4434,16209],{"alt":16210,"className":16211,"src":16212},"imek-elasticita-podel-linearni-poptavky",[210,4438],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[724,16214,16215,16216,16266,16267,16283],{},"Pro celkový příjem platí ",[883,16217,16219],{"className":16218},[886],[888,16220,16221],{"xmlns":890},[892,16222,16223,16263],{},[895,16224,16225,16227,16229,16231,16233,16235,16237,16239,16241,16243,16245,16247,16249,16251,16253,16255,16257,16259,16261],{},[898,16226,5326],{},[898,16228,13658],{},[1750,16230,1766],{},[898,16232,5326],{},[898,16234,13658],{},[1750,16236,1753],{"stretchy":1752},[898,16238,12471],{},[1750,16240,1763],{"stretchy":1752},[1750,16242,1766],{},[898,16244,1776],{},[1750,16246,8009],{},[898,16248,12471],{},[1750,16250,1766],{},[898,16252,12471],{},[1750,16254,8009],{},[898,16256,5541],{},[1750,16258,1753],{"stretchy":1752},[898,16260,12471],{},[1750,16262,1763],{"stretchy":1752},[902,16264,16265],{"encoding":904},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[883,16268,16270],{"className":16269},[886],[888,16271,16272],{"xmlns":890},[892,16273,16274,16280],{},[895,16275,16276,16278],{},[898,16277,1773],{},[898,16279,13658],{},[902,16281,16282],{"encoding":904},"MR"," odvodíme:",[724,16285,16286],{},[883,16287,16289],{"className":16288},[886],[888,16290,16291],{"xmlns":890},[892,16292,16293,16401],{},[895,16294,16295,16297,16299,16301,16303,16309,16311,16313,16315,16317,16319,16321,16323,16325,16327,16329,16331,16337,16339,16341,16343,16345,16347,16349,16351,16365,16367,16369],{},[898,16296,1773],{},[898,16298,13658],{},[1750,16300,1766],{},[898,16302,5326],{},[1699,16304,16305,16307],{},[898,16306,13658],{},[1750,16308,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,16310,1753],{"stretchy":1752},[898,16312,12471],{},[1750,16314,1763],{"stretchy":1752},[1750,16316,1766],{},[898,16318,5541],{},[1750,16320,1753],{"stretchy":1752},[898,16322,12471],{},[1750,16324,1763],{"stretchy":1752},[1750,16326,1861],{},[898,16328,12471],{},[1969,16330,2658],{},[1699,16332,16333,16335],{},[898,16334,5541],{},[1750,16336,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,16338,1753],{"stretchy":1752},[898,16340,12471],{},[1750,16342,1763],{"stretchy":1752},[1750,16344,1766],{},[898,16346,1776],{},[1750,16348,1861],{},[898,16350,12471],{},[3423,16352,16353,16359],{},[895,16354,16355,16357],{},[898,16356,3429],{"mathvariant":1747},[898,16358,1776],{},[895,16360,16361,16363],{},[898,16362,3429],{"mathvariant":1747},[898,16364,12471],{},[1750,16366,1766],{},[898,16368,1776],{},[895,16370,16371,16373,16375,16377,16383,16385,16399],{},[1750,16372,1753],{"fence":1916},[1742,16374,1744],{},[1750,16376,1861],{},[3423,16378,16379,16381],{},[898,16380,12471],{},[898,16382,1776],{},[1750,16384,8009],{},[3423,16386,16387,16393],{},[895,16388,16389,16391],{},[898,16390,3429],{"mathvariant":1747},[898,16392,1776],{},[895,16394,16395,16397],{},[898,16396,3429],{"mathvariant":1747},[898,16398,12471],{},[1750,16400,1763],{"fence":1916},[902,16402,16403],{"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)",[724,16405,16406],{},[883,16407,16409],{"className":16408},[886],[888,16410,16411],{"xmlns":890},[892,16412,16413,16485],{},[895,16414,16415,16417,16419,16461,16463,16465],{},[1750,16416,1766],{},[898,16418,1776],{},[895,16420,16421,16423,16425,16427,16459],{},[1750,16422,1753],{"fence":1916},[1742,16424,1744],{},[1750,16426,1861],{},[3423,16428,16429,16431],{},[1742,16430,1744],{},[895,16432,16433,16441,16443],{},[3586,16434,16435],{"scriptlevel":2607,"displaystyle":1752},[3423,16436,16437,16439],{},[898,16438,1776],{},[898,16440,12471],{},[1750,16442,8009],{},[3586,16444,16445],{"scriptlevel":2607,"displaystyle":1752},[3423,16446,16447,16453],{},[895,16448,16449,16451],{},[898,16450,3429],{"mathvariant":1747},[898,16452,12471],{},[895,16454,16455,16457],{},[898,16456,3429],{"mathvariant":1747},[898,16458,1776],{},[1750,16460,1763],{"fence":1916},[1750,16462,1766],{},[898,16464,1776],{},[895,16466,16467,16469,16471,16473,16483],{},[1750,16468,1753],{"fence":1916},[1742,16470,1744],{},[1750,16472,1861],{},[3423,16474,16475,16477],{},[1742,16476,1744],{},[895,16478,16479,16481],{},[1750,16480,1758],{},[898,16482,1705],{},[1750,16484,1763],{"fence":1916},[902,16486,16487],{"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)",[724,16489,16490],{},"a tedy",[724,16492,16493],{},[883,16494,16496],{"className":16495,"title":13862,"style":13863},[13861],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1785,16498,16499,16568,16817],{},[724,16500,16501,16503,16504,16538,16539,16554,16555,2366],{},[883,16502,1791],{}," Intuice: vztah ",[883,16505,16507],{"className":16506},[886],[888,16508,16509],{"xmlns":890},[892,16510,16511,16535],{},[895,16512,16513,16515,16517,16519,16521,16523,16525,16527,16529,16531,16533],{},[898,16514,1773],{},[898,16516,13658],{},[1750,16518,1766],{},[898,16520,1776],{},[1750,16522,1753],{"stretchy":1752},[1742,16524,1744],{},[1750,16526,1758],{},[1742,16528,1744],{},[898,16530,1748],{"mathvariant":1747},[898,16532,1705],{},[1750,16534,1763],{"stretchy":1752},[902,16536,16537],{"encoding":904},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[883,16540,16542],{"className":16541},[886],[888,16543,16544],{"xmlns":890},[892,16545,16546,16552],{},[895,16547,16548,16550],{},[898,16549,1773],{},[898,16551,13658],{},[902,16553,16282],{"encoding":904}," jednoznačně určuje hodnota ",[883,16556,16558],{"className":16557},[886],[888,16559,16560],{"xmlns":890},[892,16561,16562,16566],{},[895,16563,16564],{},[898,16565,1705],{},[902,16567,1705],{"encoding":904},[120,16569,16570,16679,16748],{},[123,16571,16572,16589,16590,1647,16604,1647,16630,1647,16643,10469,16663,16678],{},[883,16573,16575],{"className":16574},[886],[888,16576,16577],{"xmlns":890},[892,16578,16579,16587],{},[895,16580,16581,16583,16585],{},[898,16582,1705],{},[1750,16584,2604],{},[1742,16586,1744],{},[902,16588,14167],{"encoding":904}," (elastická) ",[883,16591,16593],{"className":16592},[886],[888,16594,16595],{"xmlns":890},[892,16596,16597,16601],{},[895,16598,16599],{},[1750,16600,13651],{},[902,16602,16603],{"encoding":904},"\\Rightarrow",[883,16605,16607],{"className":16606},[886],[888,16608,16609],{"xmlns":890},[892,16610,16611,16627],{},[895,16612,16613,16615,16617,16619,16621,16623,16625],{},[1742,16614,1744],{},[1750,16616,1758],{},[1742,16618,1744],{},[898,16620,1748],{"mathvariant":1747},[898,16622,1705],{},[1750,16624,2604],{},[1742,16626,2607],{},[902,16628,16629],{"encoding":904},"1 - 1\u002FE > 0",[883,16631,16633],{"className":16632},[886],[888,16634,16635],{"xmlns":890},[892,16636,16637,16641],{},[895,16638,16639],{},[1750,16640,13651],{},[902,16642,16603],{"encoding":904},[883,16644,16646],{"className":16645},[886],[888,16647,16648],{"xmlns":890},[892,16649,16650,16660],{},[895,16651,16652,16654,16656,16658],{},[898,16653,1773],{},[898,16655,13658],{},[1750,16657,2604],{},[1742,16659,2607],{},[902,16661,16662],{"encoding":904},"MR > 0",[883,16664,16666],{"className":16665},[886],[888,16667,16668],{"xmlns":890},[892,16669,16670,16676],{},[895,16671,16672,16674],{},[898,16673,5326],{},[898,16675,13658],{},[902,16677,13758],{"encoding":904}," roste s množstvím, tj. klesá s cenou.",[123,16680,16681,16698,16699,1647,16712,10469,16732,16747],{},[883,16682,16684],{"className":16683},[886],[888,16685,16686],{"xmlns":890},[892,16687,16688,16696],{},[895,16689,16690,16692,16694],{},[898,16691,1705],{},[1750,16693,1766],{},[1742,16695,1744],{},[902,16697,14203],{"encoding":904}," (jednotková) ",[883,16700,16702],{"className":16701},[886],[888,16703,16704],{"xmlns":890},[892,16705,16706,16710],{},[895,16707,16708],{},[1750,16709,13651],{},[902,16711,16603],{"encoding":904},[883,16713,16715],{"className":16714},[886],[888,16716,16717],{"xmlns":890},[892,16718,16719,16729],{},[895,16720,16721,16723,16725,16727],{},[898,16722,1773],{},[898,16724,13658],{},[1750,16726,1766],{},[1742,16728,2607],{},[902,16730,16731],{"encoding":904},"MR = 0",[883,16733,16735],{"className":16734},[886],[888,16736,16737],{"xmlns":890},[892,16738,16739,16745],{},[895,16740,16741,16743],{},[898,16742,5326],{},[898,16744,13658],{},[902,16746,13758],{"encoding":904}," je extrém (maximum).",[123,16749,16750,16767,16768,1647,16781,10469,16801,16816],{},[883,16751,16753],{"className":16752},[886],[888,16754,16755],{"xmlns":890},[892,16756,16757,16765],{},[895,16758,16759,16761,16763],{},[898,16760,1705],{},[1750,16762,2624],{},[1742,16764,1744],{},[902,16766,14185],{"encoding":904}," (neelastická) ",[883,16769,16771],{"className":16770},[886],[888,16772,16773],{"xmlns":890},[892,16774,16775,16779],{},[895,16776,16777],{},[1750,16778,13651],{},[902,16780,16603],{"encoding":904},[883,16782,16784],{"className":16783},[886],[888,16785,16786],{"xmlns":890},[892,16787,16788,16798],{},[895,16789,16790,16792,16794,16796],{},[898,16791,1773],{},[898,16793,13658],{},[1750,16795,2624],{},[1742,16797,2607],{},[902,16799,16800],{"encoding":904},"MR \u003C 0",[883,16802,16804],{"className":16803},[886],[888,16805,16806],{"xmlns":890},[892,16807,16808,16814],{},[895,16809,16810,16812],{},[898,16811,5326],{},[898,16813,13658],{},[902,16815,13758],{"encoding":904}," klesá s množstvím, tj. roste s cenou.",[724,16818,16819,16820,2313],{},"Viz také ",[207,16821,13491],{"className":16822,"dataFsResolvedFilePath":827,"href":828},[210],[198,16824,16826],{"id":16825},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[724,16828,16829,16849,16850,16876,16877,16892,16893,16906,16907,16920,16921,16934,16935,16951,16952,1647,16967,16970,16971,16951,16987,2313],{},[38,16830,16831,16832,1783],{},"(a) Poptávka elastická (",[883,16833,16835],{"className":16834},[886],[888,16836,16837],{"xmlns":890},[892,16838,16839,16847],{},[895,16840,16841,16843,16845],{},[898,16842,1705],{},[1750,16844,2604],{},[1742,16846,1744],{},[902,16848,14167],{"encoding":904}," Z (4.12) plyne ",[883,16851,16853],{"className":16852},[886],[888,16854,16855],{"xmlns":890},[892,16856,16857,16873],{},[895,16858,16859,16861,16863,16865,16867,16869,16871],{},[898,16860,1773],{},[898,16862,13658],{},[1750,16864,1753],{"stretchy":1752},[898,16866,12471],{},[1750,16868,1763],{"stretchy":1752},[1750,16870,2604],{},[1742,16872,2607],{},[902,16874,16875],{"encoding":904},"MR(Q) > 0",", a tedy celkový příjem ",[883,16878,16880],{"className":16879},[886],[888,16881,16882],{"xmlns":890},[892,16883,16884,16890],{},[895,16885,16886,16888],{},[898,16887,5326],{},[898,16889,13658],{},[902,16891,13758],{"encoding":904}," je rostoucí funkcí ",[883,16894,16896],{"className":16895},[886],[888,16897,16898],{"xmlns":890},[892,16899,16900,16904],{},[895,16901,16902],{},[898,16903,12471],{},[902,16905,12471],{"encoding":904},". Avšak růst ",[883,16908,16910],{"className":16909},[886],[888,16911,16912],{"xmlns":890},[892,16913,16914,16918],{},[895,16915,16916],{},[898,16917,12471],{},[902,16919,12471],{"encoding":904}," je odezvou na pokles ceny ",[883,16922,16924],{"className":16923},[886],[888,16925,16926],{"xmlns":890},[892,16927,16928,16932],{},[895,16929,16930],{},[898,16931,1776],{},[902,16933,1776],{"encoding":904},". Tudíž s ",[614,16936,16937,16938],{},"poklesem ceny ",[883,16939,16941],{"className":16940},[886],[888,16942,16943],{"xmlns":890},[892,16944,16945,16949],{},[895,16946,16947],{},[898,16948,1776],{},[902,16950,1776],{"encoding":904}," celkový příjem ",[883,16953,16955],{"className":16954},[886],[888,16956,16957],{"xmlns":890},[892,16958,16959,16965],{},[895,16960,16961,16963],{},[898,16962,5326],{},[898,16964,13658],{},[902,16966,13758],{"encoding":904},[614,16968,16969],{},"roste"," a s ",[614,16972,16973,16974],{},"růstem ceny ",[883,16975,16977],{"className":16976},[886],[888,16978,16979],{"xmlns":890},[892,16980,16981,16985],{},[895,16982,16983],{},[898,16984,1776],{},[902,16986,1776],{"encoding":904},[614,16988,16989],{},"klesá",[1785,16991,16992],{},[724,16993,16994,16997],{},[38,16995,16996],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[724,16999,17000,16849,17020,1343,17046,17061,17062,17075,17076,17089,17090,17103,17104,16951,17117,1647,17132,2313],{},[38,17001,17002,17003,1783],{},"(b) Poptávka neelastická (",[883,17004,17006],{"className":17005},[886],[888,17007,17008],{"xmlns":890},[892,17009,17010,17018],{},[895,17011,17012,17014,17016],{},[898,17013,1705],{},[1750,17015,2624],{},[1742,17017,1744],{},[902,17019,14185],{"encoding":904},[883,17021,17023],{"className":17022},[886],[888,17024,17025],{"xmlns":890},[892,17026,17027,17043],{},[895,17028,17029,17031,17033,17035,17037,17039,17041],{},[898,17030,1773],{},[898,17032,13658],{},[1750,17034,1753],{"stretchy":1752},[898,17036,12471],{},[1750,17038,1763],{"stretchy":1752},[1750,17040,2624],{},[1742,17042,2607],{},[902,17044,17045],{"encoding":904},"MR(Q) \u003C 0",[883,17047,17049],{"className":17048},[886],[888,17050,17051],{"xmlns":890},[892,17052,17053,17059],{},[895,17054,17055,17057],{},[898,17056,5326],{},[898,17058,13658],{},[902,17060,13758],{"encoding":904}," je klesající funkce ",[883,17063,17065],{"className":17064},[886],[888,17066,17067],{"xmlns":890},[892,17068,17069,17073],{},[895,17070,17071],{},[898,17072,12471],{},[902,17074,12471],{"encoding":904},", tj. s růstem ",[883,17077,17079],{"className":17078},[886],[888,17080,17081],{"xmlns":890},[892,17082,17083,17087],{},[895,17084,17085],{},[898,17086,12471],{},[902,17088,12471],{"encoding":904}," (s poklesem ceny ",[883,17091,17093],{"className":17092},[886],[888,17094,17095],{"xmlns":890},[892,17096,17097,17101],{},[895,17098,17099],{},[898,17100,1776],{},[902,17102,1776],{"encoding":904},") celkový příjem klesá. S růstem ceny ",[883,17105,17107],{"className":17106},[886],[888,17108,17109],{"xmlns":890},[892,17110,17111,17115],{},[895,17112,17113],{},[898,17114,1776],{},[902,17116,1776],{"encoding":904},[883,17118,17120],{"className":17119},[886],[888,17121,17122],{"xmlns":890},[892,17123,17124,17130],{},[895,17125,17126,17128],{},[898,17127,5326],{},[898,17129,13658],{},[902,17131,13758],{"encoding":904},[614,17133,16969],{},[1785,17135,17136],{},[724,17137,17138,17141],{},[38,17139,17140],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[724,17143,17144,16849,17164,17183,17184,17199,17200,17270,17271,2028,17299,4776,17331,8164,17359,17374,17375,2313],{},[38,17145,17146,17147,1783],{},"(c) Jednotková elasticita (",[883,17148,17150],{"className":17149},[886],[888,17151,17152],{"xmlns":890},[892,17153,17154,17162],{},[895,17155,17156,17158,17160],{},[898,17157,1705],{},[1750,17159,1766],{},[1742,17161,1744],{},[902,17163,14203],{"encoding":904},[883,17165,17167],{"className":17166},[886],[888,17168,17169],{"xmlns":890},[892,17170,17171,17181],{},[895,17172,17173,17175,17177,17179],{},[898,17174,1773],{},[898,17176,13658],{},[1750,17178,1766],{},[1742,17180,2607],{},[902,17182,16731],{"encoding":904}," — nutná podmínka extrému ",[883,17185,17187],{"className":17186},[886],[888,17188,17189],{"xmlns":890},[892,17190,17191,17197],{},[895,17192,17193,17195],{},[898,17194,5326],{},[898,17196,13658],{},[902,17198,13758],{"encoding":904},". Dále ",[883,17201,17203],{"className":17202},[886],[888,17204,17205],{"xmlns":890},[892,17206,17207,17267],{},[895,17208,17209,17211,17221,17223,17225,17231,17233,17239,17241,17243,17245,17247,17249,17251,17261,17263,17265],{},[898,17210,5326],{},[1699,17212,17213,17215],{},[898,17214,13658],{},[895,17216,17217,17219],{},[1750,17218,3815],{"mathvariant":1747},[1750,17220,3815],{"mathvariant":1747},[1750,17222,1766],{},[898,17224,1773],{},[1699,17226,17227,17229],{},[898,17228,13658],{},[1750,17230,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,17232,1766],{},[1699,17234,17235,17237],{},[898,17236,5541],{},[1750,17238,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,17240,1753],{"stretchy":1752},[898,17242,12471],{},[1750,17244,1763],{"stretchy":1752},[1750,17246,1861],{},[898,17248,12471],{},[1969,17250,2658],{},[1699,17252,17253,17255],{},[898,17254,5541],{},[895,17256,17257,17259],{},[1750,17258,3815],{"mathvariant":1747},[1750,17260,3815],{"mathvariant":1747},[1750,17262,1753],{"stretchy":1752},[898,17264,12471],{},[1750,17266,1763],{"stretchy":1752},[902,17268,17269],{"encoding":904},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[883,17272,17274],{"className":17273},[886],[888,17275,17276],{"xmlns":890},[892,17277,17278,17296],{},[895,17279,17280,17286,17288,17290,17292,17294],{},[1699,17281,17282,17284],{},[898,17283,5541],{},[1750,17285,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,17287,1753],{"stretchy":1752},[898,17289,12471],{},[1750,17291,1763],{"stretchy":1752},[1750,17293,2624],{},[1742,17295,2607],{},[902,17297,17298],{"encoding":904},"D'(Q) \u003C 0",[883,17300,17302],{"className":17301},[886],[888,17303,17304],{"xmlns":890},[892,17305,17306,17328],{},[895,17307,17308,17318,17320,17322,17324,17326],{},[1699,17309,17310,17312],{},[898,17311,5541],{},[895,17313,17314,17316],{},[1750,17315,3815],{"mathvariant":1747},[1750,17317,3815],{"mathvariant":1747},[1750,17319,1753],{"stretchy":1752},[898,17321,12471],{},[1750,17323,1763],{"stretchy":1752},[1750,17325,5438],{},[1742,17327,2607],{},[902,17329,17330],{"encoding":904},"D''(Q) \\le 0",[883,17332,17334],{"className":17333},[886],[888,17335,17336],{"xmlns":890},[892,17337,17338,17356],{},[895,17339,17340,17342,17352,17354],{},[898,17341,5326],{},[1699,17343,17344,17346],{},[898,17345,13658],{},[895,17347,17348,17350],{},[1750,17349,3815],{"mathvariant":1747},[1750,17351,3815],{"mathvariant":1747},[1750,17353,2624],{},[1742,17355,2607],{},[902,17357,17358],{"encoding":904},"TR'' \u003C 0",[883,17360,17362],{"className":17361},[886],[888,17363,17364],{"xmlns":890},[892,17365,17366,17372],{},[895,17367,17368,17370],{},[898,17369,5326],{},[898,17371,13658],{},[902,17373,13758],{"encoding":904}," nabývá ",[38,17376,17377],{},"maxima",[1785,17379,17380],{},[724,17381,17382,17385],{},[38,17383,17384],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[724,17387,17388],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[724,17390,17391],{},[38,17392,17393],{},"Souhrnná tabulka Pravidel 1–3:",[16,17395,17396,17500],{},[19,17397,17398],{},[22,17399,17400,17403,17418,17435,17466,17497],{},[25,17401,17402],{},"Charakter poptávky",[25,17404,17405],{},[883,17406,17408],{"className":17407},[886],[888,17409,17410],{"xmlns":890},[892,17411,17412,17416],{},[895,17413,17414],{},[898,17415,1705],{},[902,17417,1705],{"encoding":904},[25,17419,17420],{},[883,17421,17423],{"className":17422},[886],[888,17424,17425],{"xmlns":890},[892,17426,17427,17433],{},[895,17428,17429,17431],{},[898,17430,1773],{},[898,17432,13658],{},[902,17434,16282],{"encoding":904},[25,17436,17437,17438,1647,17451],{},"Pokles ceny ",[883,17439,17441],{"className":17440},[886],[888,17442,17443],{"xmlns":890},[892,17444,17445,17449],{},[895,17446,17447],{},[1750,17448,13651],{},[902,17450,16603],{"encoding":904},[883,17452,17454],{"className":17453},[886],[888,17455,17456],{"xmlns":890},[892,17457,17458,17464],{},[895,17459,17460,17462],{},[898,17461,5326],{},[898,17463,13658],{},[902,17465,13758],{"encoding":904},[25,17467,17468,17469,1647,17482],{},"Růst ceny ",[883,17470,17472],{"className":17471},[886],[888,17473,17474],{"xmlns":890},[892,17475,17476,17480],{},[895,17477,17478],{},[1750,17479,13651],{},[902,17481,16603],{"encoding":904},[883,17483,17485],{"className":17484},[886],[888,17486,17487],{"xmlns":890},[892,17488,17489,17495],{},[895,17490,17491,17493],{},[898,17492,5326],{},[898,17494,13658],{},[902,17496,13758],{"encoding":904},[25,17498,17499],{},"Doporučení",[30,17501,17502,17551,17601],{},[22,17503,17504,17506,17524,17542,17544,17546],{},[35,17505,13737],{},[35,17507,17508],{},[883,17509,17511],{"className":17510},[886],[888,17512,17513],{"xmlns":890},[892,17514,17515,17521],{},[895,17516,17517,17519],{},[1750,17518,2604],{},[1742,17520,1744],{},[902,17522,17523],{"encoding":904},"> 1",[35,17525,17526],{},[883,17527,17529],{"className":17528},[886],[888,17530,17531],{"xmlns":890},[892,17532,17533,17539],{},[895,17534,17535,17537],{},[1750,17536,2604],{},[1742,17538,2607],{},[902,17540,17541],{"encoding":904},"> 0",[35,17543,16969],{},[35,17545,16989],{},[35,17547,17548],{},[38,17549,17550],{},"snížit cenu",[22,17552,17553,17556,17574,17592,17594,17596],{},[35,17554,17555],{},"jednotková",[35,17557,17558],{},[883,17559,17561],{"className":17560},[886],[888,17562,17563],{"xmlns":890},[892,17564,17565,17571],{},[895,17566,17567,17569],{},[1750,17568,1766],{},[1742,17570,1744],{},[902,17572,17573],{"encoding":904},"= 1",[35,17575,17576],{},[883,17577,17579],{"className":17578},[886],[888,17580,17581],{"xmlns":890},[892,17582,17583,17589],{},[895,17584,17585,17587],{},[1750,17586,1766],{},[1742,17588,2607],{},[902,17590,17591],{"encoding":904},"= 0",[35,17593,13387],{},[35,17595,13387],{},[35,17597,17598],{},[38,17599,17600],{},"držet cenu",[22,17602,17603,17605,17623,17641,17643,17645],{},[35,17604,13741],{},[35,17606,17607],{},[883,17608,17610],{"className":17609},[886],[888,17611,17612],{"xmlns":890},[892,17613,17614,17620],{},[895,17615,17616,17618],{},[1750,17617,2624],{},[1742,17619,1744],{},[902,17621,17622],{"encoding":904},"\u003C 1",[35,17624,17625],{},[883,17626,17628],{"className":17627},[886],[888,17629,17630],{"xmlns":890},[892,17631,17632,17638],{},[895,17633,17634,17636],{},[1750,17635,2624],{},[1742,17637,2607],{},[902,17639,17640],{"encoding":904},"\u003C 0",[35,17642,16989],{},[35,17644,16969],{},[35,17646,17647],{},[38,17648,17649],{},"zvýšit cenu",[198,17651,17653],{"id":17652},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[724,17655,17656,17657,17682,17683,17705,17706,17719,17720,17733,17734,2433,17747,8164,17774,17826],{},"Aplikujme pravidla 1–3 pro poptávku ",[883,17658,17660],{"className":17659},[886],[888,17661,17662],{"xmlns":890},[892,17663,17664,17680],{},[895,17665,17666,17668,17670,17672,17674],{},[898,17667,1776],{},[1750,17669,1766],{},[1742,17671,4078],{},[1750,17673,1758],{},[1699,17675,17676,17678],{},[898,17677,12471],{},[1742,17679,1872],{},[902,17681,15113],{"encoding":904},". Reálné cenové rozpětí je ",[883,17684,17686],{"className":17685},[886],[888,17687,17688],{"xmlns":890},[892,17689,17690,17702],{},[895,17691,17692,17694,17696,17698,17700],{},[1750,17693,14978],{"stretchy":1752},[1742,17695,1744],{},[1750,17697,1917],{"separator":1916},[1742,17699,4078],{},[1750,17701,14995],{"stretchy":1752},[902,17703,17704],{"encoding":904},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[883,17707,17709],{"className":17708},[886],[888,17710,17711],{"xmlns":890},[892,17712,17713,17717],{},[895,17714,17715],{},[898,17716,12471],{},[902,17718,12471],{"encoding":904}," jako funkci ",[883,17721,17723],{"className":17722},[886],[888,17724,17725],{"xmlns":890},[892,17726,17727,17731],{},[895,17728,17729],{},[898,17730,1776],{},[902,17732,1776],{"encoding":904},"; pro nezáporné ",[883,17735,17737],{"className":17736},[886],[888,17738,17739],{"xmlns":890},[892,17740,17741,17745],{},[895,17742,17743],{},[898,17744,12471],{},[902,17746,12471],{"encoding":904},[883,17748,17750],{"className":17749},[886],[888,17751,17752],{"xmlns":890},[892,17753,17754,17771],{},[895,17755,17756,17758,17760],{},[898,17757,12471],{},[1750,17759,1766],{},[17761,17762,17763],"msqrt",{},[895,17764,17765,17767,17769],{},[1742,17766,4078],{},[1750,17768,1758],{},[898,17770,1776],{},[902,17772,17773],{"encoding":904},"Q = \\sqrt{100 - P}",[883,17775,17777],{"className":17776},[886],[888,17778,17779],{"xmlns":890},[892,17780,17781,17823],{},[895,17782,17783,17799,17801,17803],{},[3586,17784,17785],{"scriptlevel":2607,"displaystyle":1916},[3423,17786,17787,17793],{},[895,17788,17789,17791],{},[898,17790,3429],{"mathvariant":1747},[898,17792,12471],{},[895,17794,17795,17797],{},[898,17796,3429],{"mathvariant":1747},[898,17798,1776],{},[1750,17800,1766],{},[1750,17802,1758],{},[3586,17804,17805],{"scriptlevel":2607,"displaystyle":1916},[3423,17806,17807,17809],{},[1742,17808,1744],{},[895,17810,17811,17813],{},[1742,17812,1872],{},[17761,17814,17815],{},[895,17816,17817,17819,17821],{},[1742,17818,4078],{},[1750,17820,1758],{},[898,17822,1776],{},[902,17824,17825],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[724,17828,17829],{},[883,17830,17832],{"className":17831},[886],[888,17833,17834],{"xmlns":890},[892,17835,17836,17958],{},[895,17837,17838,17840,17842,17844,17846,17848,17850,17856,17858,17872,17874,17876,17890,17892,17918,17920,17938,17940,17956],{},[898,17839,1705],{},[1750,17841,1753],{"stretchy":1752},[898,17843,1776],{},[1750,17845,1763],{"stretchy":1752},[1750,17847,1766],{},[1750,17849,1758],{},[3423,17851,17852,17854],{},[898,17853,1776],{},[898,17855,12471],{},[1750,17857,8009],{},[3423,17859,17860,17866],{},[895,17861,17862,17864],{},[898,17863,3429],{"mathvariant":1747},[898,17865,12471],{},[895,17867,17868,17870],{},[898,17869,3429],{"mathvariant":1747},[898,17871,1776],{},[1750,17873,1766],{},[1750,17875,1758],{},[3423,17877,17878,17880],{},[898,17879,1776],{},[17761,17881,17882],{},[895,17883,17884,17886,17888],{},[1742,17885,4078],{},[1750,17887,1758],{},[898,17889,1776],{},[1750,17891,8009],{},[895,17893,17894,17896,17898,17916],{},[1750,17895,1753],{"fence":1916},[1750,17897,1758],{},[3423,17899,17900,17902],{},[1742,17901,1744],{},[895,17903,17904,17906],{},[1742,17905,1872],{},[17761,17907,17908],{},[895,17909,17910,17912,17914],{},[1742,17911,4078],{},[1750,17913,1758],{},[898,17915,1776],{},[1750,17917,1763],{"fence":1916},[1750,17919,1766],{},[3423,17921,17922,17924],{},[898,17923,1776],{},[895,17925,17926,17928,17930,17932,17934,17936],{},[1742,17927,1872],{},[1750,17929,1753],{"stretchy":1752},[1742,17931,4078],{},[1750,17933,1758],{},[898,17935,1776],{},[1750,17937,1763],{"stretchy":1752},[1750,17939,1766],{},[3423,17941,17942,17948],{},[895,17943,17944,17946],{},[1742,17945,4268],{},[898,17947,1776],{},[895,17949,17950,17952,17954],{},[1742,17951,4078],{},[1750,17953,1758],{},[898,17955,1776],{},[898,17957,2313],{"mathvariant":1747},[902,17959,17960],{"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}.",[724,17962,17963,17964,2366],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[883,17965,17967],{"className":17966},[886],[888,17968,17969],{"xmlns":890},[892,17970,17971,17995],{},[895,17972,17973,17991,17993],{},[3586,17974,17975],{"scriptlevel":2607,"displaystyle":1916},[3423,17976,17977,17983],{},[895,17978,17979,17981],{},[1742,17980,4268],{},[898,17982,1776],{},[895,17984,17985,17987,17989],{},[1742,17986,4078],{},[1750,17988,1758],{},[898,17990,1776],{},[1750,17992,1766],{},[1742,17994,1744],{},[902,17996,17997],{"encoding":904},"\\dfrac{0{,}5P}{100-P} = 1",[724,17999,18000],{},[883,18001,18003],{"className":18002},[886],[888,18004,18005],{"xmlns":890},[892,18006,18007,18037],{},[895,18008,18009,18015,18017,18023,18025,18028,18035],{},[1699,18010,18011,18013],{},[898,18012,1776],{},[1750,18014,3751],{},[1750,18016,1766],{},[3423,18018,18019,18021],{},[1742,18020,4159],{},[1742,18022,7822],{},[1750,18024,6792],{},[1742,18026,18027],{},"66,",[3215,18029,18030,18032],{"accent":1916},[1742,18031,3219],{},[1750,18033,18034],{"stretchy":1916},"‾",[898,18036,2313],{"mathvariant":1747},[902,18038,18039],{"encoding":904},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[724,18041,18042],{},"S využitím vlastnosti (4.8):",[120,18044,18045,18091,18133],{},[123,18046,18047,18048,18083,18084,18086,18087,18090],{},"Při cenách ",[883,18049,18051],{"className":18050},[886],[888,18052,18053],{"xmlns":890},[892,18054,18055,18080],{},[895,18056,18057,18059,18061,18063,18065,18068,18070,18072,18078],{},[898,18058,1776],{},[1750,18060,16154],{},[1750,18062,14978],{"stretchy":1752},[1742,18064,1744],{},[1750,18066,18067],{"separator":1916},";",[1969,18069,2658],{},[1742,18071,18027],{},[3215,18073,18074,18076],{"accent":1916},[1742,18075,3219],{},[1750,18077,18034],{"stretchy":1916},[1750,18079,1763],{"stretchy":1752},[902,18081,18082],{"encoding":904},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[38,18085,13741],{}," — dle ",[614,18088,18089],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[123,18092,18047,18093,18083,18127,18086,18129,18132],{},[883,18094,18096],{"className":18095},[886],[888,18097,18098],{"xmlns":890},[892,18099,18100,18124],{},[895,18101,18102,18104,18106,18108,18110,18116,18118,18120,18122],{},[898,18103,1776],{},[1750,18105,16154],{},[1750,18107,1753],{"stretchy":1752},[1742,18109,18027],{},[3215,18111,18112,18114],{"accent":1916},[1742,18113,3219],{},[1750,18115,18034],{"stretchy":1916},[1750,18117,18067],{"separator":1916},[1969,18119,2658],{},[1742,18121,4078],{},[1750,18123,14995],{"stretchy":1752},[902,18125,18126],{"encoding":904},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[38,18128,13737],{},[614,18130,18131],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[123,18134,18135,18136,18139,18140,18168,18169,18172],{},"Dle ",[614,18137,18138],{},"Pravidla 3"," je při ceně ",[883,18141,18143],{"className":18142},[886],[888,18144,18145],{"xmlns":890},[892,18146,18147,18165],{},[895,18148,18149,18155,18157,18159],{},[1699,18150,18151,18153],{},[898,18152,1776],{},[1750,18154,3751],{},[1750,18156,1766],{},[1742,18158,18027],{},[3215,18160,18161,18163],{"accent":1916},[1742,18162,3219],{},[1750,18164,18034],{"stretchy":1916},[902,18166,18167],{"encoding":904},"P^* = 66{,}\\overline{6}"," dosaženo ",[38,18170,18171],{},"maxima celkového příjmu"," ve výši",[724,18174,18175],{},[883,18176,18178],{"className":18177},[886],[888,18179,18180],{"xmlns":890},[892,18181,18182,18260],{},[895,18183,18184,18186,18188,18190,18196,18198,18200,18206,18208,18222,18224,18230,18232,18240,18242,18255,18257],{},[898,18185,5326],{},[898,18187,13658],{},[1750,18189,1753],{"stretchy":1752},[1699,18191,18192,18194],{},[898,18193,1776],{},[1750,18195,3751],{},[1750,18197,1763],{"stretchy":1752},[1750,18199,1766],{},[1699,18201,18202,18204],{},[898,18203,1776],{},[1750,18205,3751],{},[1750,18207,8009],{},[17761,18209,18210],{},[895,18211,18212,18214,18216],{},[1742,18213,4078],{},[1750,18215,1758],{},[1699,18217,18218,18220],{},[898,18219,1776],{},[1750,18221,3751],{},[1750,18223,1766],{},[3423,18225,18226,18228],{},[1742,18227,4159],{},[1742,18229,7822],{},[1750,18231,8009],{},[17761,18233,18234],{},[3423,18235,18236,18238],{},[1742,18237,4078],{},[1742,18239,7822],{},[1750,18241,1766],{},[3423,18243,18244,18247],{},[1742,18245,18246],{},"2000",[895,18248,18249,18251],{},[1742,18250,7822],{},[17761,18252,18253],{},[1742,18254,7822],{},[1750,18256,6792],{},[1742,18258,18259],{},"384,9.",[902,18261,18262],{"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.",[724,18264,18265,18266,2313],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[883,18267,18269],{"className":18268},[886],[888,18270,18271],{"xmlns":890},[892,18272,18273,18279],{},[895,18274,18275,18277],{},[898,18276,5326],{},[898,18278,13658],{},[902,18280,13758],{"encoding":904},[115,18282,18284],{"id":18283},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[724,18286,18287,18288,18291],{},"Analogicky se definuje ",[38,18289,18290],{},"cenová elasticita nabídky"," (price elasticity of supply):",[724,18293,18294],{},[883,18295,18297],{"className":18296,"title":13862,"style":13863},[13861],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[724,18299,2590,18300,18324,18325,18357],{},[883,18301,18303],{"className":18302},[886],[888,18304,18305],{"xmlns":890},[892,18306,18307,18321],{},[895,18308,18309,18311,18313,18315,18317,18319],{},[898,18310,12471],{},[1750,18312,1766],{},[898,18314,1779],{},[1750,18316,1753],{"stretchy":1752},[898,18318,1776],{},[1750,18320,1763],{"stretchy":1752},[902,18322,18323],{"encoding":904},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[883,18326,18328],{"className":18327},[886],[888,18329,18330],{"xmlns":890},[892,18331,18332,18354],{},[895,18333,18334,18350,18352],{},[3586,18335,18336],{"scriptlevel":2607,"displaystyle":1916},[3423,18337,18338,18344],{},[895,18339,18340,18342],{},[898,18341,3429],{"mathvariant":1747},[898,18343,12471],{},[895,18345,18346,18348],{},[898,18347,3429],{"mathvariant":1747},[898,18349,1776],{},[1750,18351,2604],{},[1742,18353,2607],{},[902,18355,18356],{"encoding":904},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[724,18359,18360],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[1785,18362,18363],{},[724,18364,18365,18366],{},"S rostoucí cenou elasticita nabídky roste. ",[883,18367,18369],{"className":18368},[886],[888,18370,18371],{"xmlns":890},[892,18372,18373,18382],{},[895,18374,18375,18377,18380],{},[1750,18376,1753],{"stretchy":1752},[1742,18378,18379],{},"4.14",[1750,18381,1763],{"stretchy":1752},[902,18383,18384],{"encoding":904},"(4.14)",[724,18386,18387],{},"Pro nominální změny platí",[724,18389,18390],{},[883,18391,18393],{"className":18392,"title":13862,"style":13863},[13861],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[724,18395,18396],{},"a pro procentní změny",[724,18398,18399],{},[883,18400,18402],{"className":18401,"title":13862,"style":13863},[13861],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[724,18404,18405],{},"(bez znaménka minus).",[198,18407,18409],{"id":18408},"příklad-47","Příklad 4.7",[724,18411,18412,18413,2366],{},"Nabídka ",[883,18414,18416],{"className":18415},[886],[888,18417,18418],{"xmlns":890},[892,18419,18420,18444],{},[895,18421,18422,18424,18426,18428,18434,18436,18438,18440,18442],{},[898,18423,12471],{},[1750,18425,1766],{},[1742,18427,12476],{},[1699,18429,18430,18432],{},[898,18431,1776],{},[1742,18433,1872],{},[1750,18435,1861],{},[1742,18437,7902],{},[898,18439,1776],{},[1750,18441,1861],{},[1742,18443,4236],{},[902,18445,18446],{"encoding":904},"Q = 0{,}1P^2 + 5P + 150",[724,18448,18449],{},[883,18450,18452],{"className":18451},[886],[888,18453,18454],{"xmlns":890},[892,18455,18456,18502],{},[895,18457,18458,18460,18462,18486,18488,18490,18492,18494,18496,18498,18500],{},[898,18459,1705],{},[1750,18461,1766],{},[3423,18463,18464,18466],{},[898,18465,1776],{},[895,18467,18468,18470,18476,18478,18480,18482,18484],{},[1742,18469,12476],{},[1699,18471,18472,18474],{},[898,18473,1776],{},[1742,18475,1872],{},[1750,18477,1861],{},[1742,18479,7902],{},[898,18481,1776],{},[1750,18483,1861],{},[1742,18485,4236],{},[1969,18487,2658],{},[1750,18489,1753],{"stretchy":1752},[1742,18491,3929],{},[898,18493,1776],{},[1750,18495,1861],{},[1742,18497,7902],{},[1750,18499,1763],{"stretchy":1752},[898,18501,2313],{"mathvariant":1747},[902,18503,18504],{"encoding":904},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[724,18506,14771,18507,1343,18537,1343,18564,18600,18601,18626,18627,18645,18646,2313],{},[883,18508,18510],{"className":18509},[886],[888,18511,18512],{"xmlns":890},[892,18513,18514,18534],{},[895,18515,18516,18518,18520,18522,18524,18526],{},[898,18517,1705],{},[1750,18519,1753],{"stretchy":1752},[1742,18521,3079],{},[1750,18523,1763],{"stretchy":1752},[1750,18525,1766],{},[3586,18527,18528],{"scriptlevel":2607,"displaystyle":1752},[3423,18529,18530,18532],{},[1742,18531,1744],{},[1742,18533,7822],{},[902,18535,18536],{"encoding":904},"E(10) = \\tfrac{1}{3}",[883,18538,18540],{"className":18539},[886],[888,18541,18542],{"xmlns":890},[892,18543,18544,18561],{},[895,18545,18546,18548,18550,18555,18557,18559],{},[898,18547,1705],{},[1750,18549,1753],{"stretchy":1752},[17761,18551,18552],{},[1742,18553,18554],{},"1500",[1750,18556,1763],{"stretchy":1752},[1750,18558,1766],{},[1742,18560,1744],{},[902,18562,18563],{"encoding":904},"E(\\sqrt{1500}) = 1",[883,18565,18567],{"className":18566},[886],[888,18568,18569],{"xmlns":890},[892,18570,18571,18597],{},[895,18572,18573,18575,18577,18579,18581,18583,18592,18594],{},[898,18574,1705],{},[1750,18576,1753],{"stretchy":1752},[1742,18578,4078],{},[1750,18580,1763],{"stretchy":1752},[1750,18582,1766],{},[3586,18584,18585],{"scriptlevel":2607,"displaystyle":1752},[3423,18586,18587,18589],{},[1742,18588,3936],{},[1742,18590,18591],{},"33",[1750,18593,6792],{},[1742,18595,18596],{},"1,515",[902,18598,18599],{"encoding":904},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[883,18602,18604],{"className":18603},[886],[888,18605,18606],{"xmlns":890},[892,18607,18608,18623],{},[895,18609,18610,18612,18614,18618,18620],{},[898,18611,1776],{},[1750,18613,2604],{},[17761,18615,18616],{},[1742,18617,18554],{},[1750,18619,2274],{},[1742,18621,18622],{},"38,7",[902,18624,18625],{"encoding":904},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[883,18628,18630],{"className":18629},[886],[888,18631,18632],{"xmlns":890},[892,18633,18634,18642],{},[895,18635,18636,18638,18640],{},[898,18637,1776],{},[1750,18639,2624],{},[1742,18641,18622],{},[902,18643,18644],{"encoding":904},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[883,18647,18649],{"className":18648},[886],[888,18650,18651],{"xmlns":890},[892,18652,18653,18690],{},[895,18654,18655,18657,18659,18661,18663,18671,18673,18675,18677,18680,18686,18688],{},[898,18656,2666],{"mathvariant":1747},[898,18658,12471],{},[898,18660,15573],{"mathvariant":1747},[1750,18662,2274],{},[3586,18664,18665],{"scriptlevel":2607,"displaystyle":1752},[3423,18666,18667,18669],{},[1742,18668,1744],{},[1742,18670,7822],{},[1750,18672,8009],{},[1742,18674,6465],{},[1750,18676,1766],{},[1742,18678,18679],{},"6,",[3215,18681,18682,18684],{"accent":1916},[1742,18683,3219],{},[1750,18685,18034],{"stretchy":1916},[1969,18687,2658],{},[898,18689,15573],{"mathvariant":1747},[902,18691,18692],{"encoding":904},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[115,18694,18696],{"id":18695},"vícefaktorový-model","Vícefaktorový model",[724,18698,18699,18700,18713,18714,1647,18717,18730,18731,1647,18734,18752,18753,1647,18756,2366],{},"Předpokládejme, že poptávané množství ",[883,18701,18703],{"className":18702},[886],[888,18704,18705],{"xmlns":890},[892,18706,18707,18711],{},[895,18708,18709],{},[898,18710,12471],{},[902,18712,12471],{"encoding":904}," závisí na ",[38,18715,18716],{},"ceně základního zboží",[883,18718,18720],{"className":18719},[886],[888,18721,18722],{"xmlns":890},[892,18723,18724,18728],{},[895,18725,18726],{},[898,18727,1776],{},[902,18729,1776],{"encoding":904},", na ",[38,18732,18733],{},"ceně alternativního zboží",[883,18735,18737],{"className":18736},[886],[888,18738,18739],{"xmlns":890},[892,18740,18741,18749],{},[895,18742,18743],{},[5535,18744,18745,18747],{},[898,18746,1776],{},[898,18748,13916],{},[902,18750,18751],{"encoding":904},"P_A"," a na ",[38,18754,18755],{},"důchodu",[883,18757,18759],{"className":18758},[886],[888,18760,18761],{"xmlns":890},[892,18762,18763,18767],{},[895,18764,18765],{},[898,18766,1666],{},[902,18768,1666],{"encoding":904},[724,18770,18771],{},[883,18772,18774],{"className":18773,"title":13862,"style":13863},[13861],"Q = D(P, P_A, Y). \\tag{4.17}",[724,18776,18777,18778,18781],{},"V analogii jednofaktorového modelu pracujeme s ",[38,18779,18780],{},"parciálními derivacemi"," funkce poptávky.",[198,18783,18785],{"id":18784},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[724,18787,18788],{},[883,18789,18791],{"className":18790,"title":13862,"style":13863},[13861],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[724,18793,2590,18794,18814,18815,18828,18829,12605,18851,1647,18854,18900,18901,18914,18915,18932],{},[883,18795,18797],{"className":18796},[886],[888,18798,18799],{"xmlns":890},[892,18800,18801,18811],{},[895,18802,18803],{},[5950,18804,18805,18807,18809],{},[898,18806,12471],{},[898,18808,1776],{},[1750,18810,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,18812,18813],{"encoding":904},"Q'_P"," je parciální derivace (4.17) podle ",[883,18816,18818],{"className":18817},[886],[888,18819,18820],{"xmlns":890},[892,18821,18822,18826],{},[895,18823,18824],{},[898,18825,1776],{},[902,18827,1776],{"encoding":904},". Vždy ",[883,18830,18832],{"className":18831},[886],[888,18833,18834],{"xmlns":890},[892,18835,18836,18848],{},[895,18837,18838,18844,18846],{},[5535,18839,18840,18842],{},[898,18841,1705],{},[898,18843,1776],{},[1750,18845,14143],{},[1742,18847,2607],{},[902,18849,18850],{"encoding":904},"E_P \\ge 0",[614,18852,18853],{},"Interpretace:",[883,18855,18857],{"className":18856},[886],[888,18858,18859],{"xmlns":890},[892,18860,18861,18897],{},[895,18862,18863,18869,18871,18877,18879,18887,18889,18895],{},[5535,18864,18865,18867],{},[898,18866,1705],{},[898,18868,1776],{},[1750,18870,1753],{"stretchy":1752},[1699,18872,18873,18875],{},[898,18874,1776],{},[1750,18876,3751],{},[1750,18878,1917],{"separator":1916},[5950,18880,18881,18883,18885],{},[898,18882,1776],{},[898,18884,13916],{},[1750,18886,3751],{},[1750,18888,1917],{"separator":1916},[1699,18890,18891,18893],{},[898,18892,1666],{},[1750,18894,3751],{},[1750,18896,1763],{"stretchy":1752},[902,18898,18899],{"encoding":904},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[883,18902,18904],{"className":18903},[886],[888,18905,18906],{"xmlns":890},[892,18907,18908,18912],{},[895,18909,18910],{},[898,18911,12471],{},[902,18913,12471],{"encoding":904}," při 1% změně ",[883,18916,18918],{"className":18917},[886],[888,18919,18920],{"xmlns":890},[892,18921,18922,18930],{},[895,18923,18924],{},[1699,18925,18926,18928],{},[898,18927,1776],{},[1750,18929,3751],{},[902,18931,14063],{"encoding":904},", ceteris paribus.",[198,18934,18936],{"id":18935},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[724,18938,18939],{},[883,18940,18942],{"className":18941,"title":13862,"style":13863},[13861],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[724,18944,18945,18900,18947,18960,18961,18978],{},[614,18946,18853],{},[883,18948,18950],{"className":18949},[886],[888,18951,18952],{"xmlns":890},[892,18953,18954,18958],{},[895,18955,18956],{},[898,18957,12471],{},[902,18959,12471],{"encoding":904}," základního zboží při 1% změně ceny ",[883,18962,18964],{"className":18963},[886],[888,18965,18966],{"xmlns":890},[892,18967,18968,18976],{},[895,18969,18970],{},[5535,18971,18972,18974],{},[898,18973,1776],{},[898,18975,13916],{},[902,18977,18751],{"encoding":904}," alternativního zboží (ceteris paribus).",[724,18980,18981],{},[38,18982,18983],{},"Znaménko závisí na povaze alternativního zboží:",[120,18985,18986,19074],{},[123,18987,18988,18989,18992,18993,19010,19011,1647,19024,2313],{},"Je-li alternativní zboží ",[38,18990,18991],{},"komplement",", růst ",[883,18994,18996],{"className":18995},[886],[888,18997,18998],{"xmlns":890},[892,18999,19000,19008],{},[895,19001,19002],{},[5535,19003,19004,19006],{},[898,19005,1776],{},[898,19007,13916],{},[902,19009,18751],{"encoding":904}," způsobí zdražení dvojice, pokles ",[883,19012,19014],{"className":19013},[886],[888,19015,19016],{"xmlns":890},[892,19017,19018,19022],{},[895,19019,19020],{},[898,19021,12471],{},[902,19023,12471],{"encoding":904},[883,19025,19027],{"className":19026},[886],[888,19028,19029],{"xmlns":890},[892,19030,19031,19071],{},[895,19032,19033,19035,19037,19049,19051,19053,19055,19057,19067,19069],{},[1750,19034,13651],{},[1969,19036,6766],{},[5950,19038,19039,19041,19047],{},[898,19040,12471],{},[5535,19042,19043,19045],{},[898,19044,1776],{},[898,19046,13916],{},[1750,19048,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19050,2624],{},[1742,19052,2607],{},[1750,19054,1917],{"separator":1916},[1969,19056,6766],{},[5535,19058,19059,19061],{},[898,19060,1705],{},[5535,19062,19063,19065],{},[898,19064,1776],{},[898,19066,13916],{},[1750,19068,2624],{},[1742,19070,2607],{},[902,19072,19073],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[123,19075,18988,19076,18992,19079,19096,19097,19110,19111,2313],{},[38,19077,19078],{},"substitut",[883,19080,19082],{"className":19081},[886],[888,19083,19084],{"xmlns":890},[892,19085,19086,19094],{},[895,19087,19088],{},[5535,19089,19090,19092],{},[898,19091,1776],{},[898,19093,13916],{},[902,19095,18751],{"encoding":904}," učiní základní zboží relativně levnější, zájem se přesune, ",[883,19098,19100],{"className":19099},[886],[888,19101,19102],{"xmlns":890},[892,19103,19104,19108],{},[895,19105,19106],{},[898,19107,12471],{},[902,19109,12471],{"encoding":904}," roste ",[883,19112,19114],{"className":19113},[886],[888,19115,19116],{"xmlns":890},[892,19117,19118,19158],{},[895,19119,19120,19122,19124,19136,19138,19140,19142,19144,19154,19156],{},[1750,19121,13651],{},[1969,19123,6766],{},[5950,19125,19126,19128,19134],{},[898,19127,12471],{},[5535,19129,19130,19132],{},[898,19131,1776],{},[898,19133,13916],{},[1750,19135,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19137,2604],{},[1742,19139,2607],{},[1750,19141,1917],{"separator":1916},[1969,19143,6766],{},[5535,19145,19146,19148],{},[898,19147,1705],{},[5535,19149,19150,19152],{},[898,19151,1776],{},[898,19153,13916],{},[1750,19155,2604],{},[1742,19157,2607],{},[902,19159,19160],{"encoding":904},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[883,19162,19165],{"className":19163,"title":19164,"style":13863},[13861],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":641,"searchDepth":642,"depth":642,"links":19167},[19168,19172,19173,19181,19182,19186,19189],{"id":13557,"depth":642,"text":13558,"children":19169},[19170,19171],{"id":13587,"depth":649,"text":13588},{"id":13766,"depth":649,"text":13767},{"id":13801,"depth":642,"text":13802},{"id":13826,"depth":642,"text":13827,"children":19174},[19175,19176,19177,19178,19180],{"id":14515,"depth":649,"text":14516},{"id":14605,"depth":649,"text":14606},{"id":14939,"depth":649,"text":14940},{"id":15021,"depth":649,"text":19179},"Výpočet, je-li dáno PP jako funkce QQ",{"id":15281,"depth":649,"text":15282},{"id":15601,"depth":642,"text":15602},{"id":16197,"depth":642,"text":16198,"children":19183},[19184,19185],{"id":16825,"depth":649,"text":16826},{"id":17652,"depth":649,"text":17653},{"id":18283,"depth":642,"text":18284,"children":19187},[19188],{"id":18408,"depth":649,"text":18409},{"id":18695,"depth":642,"text":18696,"children":19190},[19191,19192],{"id":18784,"depth":649,"text":18785},{"id":18935,"depth":649,"text":18936},{},"\u002Ftopics\u002Felasticita",{"title":13528,"description":641},[1138,1136],"topics\u002Felasticita",[1128,13564,19199,19200,19201,19202],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"id":19205,"title":19206,"body":19207,"course":1128,"courses":659,"created":1129,"description":20745,"extension":661,"meta":20746,"navigation":664,"path":20747,"seo":20748,"sources":20749,"stem":20750,"tags":20751,"type":11664,"updated":677,"__hash__":20756},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":9,"value":19208,"toc":20730},[19209,19212,19286,19293,19297,19361,19449,19453,19480,19546,19601,19605,19632,19724,19726,19758,19929,19933,20003,20051,20055,20116,20222,20237,20241,20243,20271,20336,20338,20345,20433,20458,20656,20660,20695,20697],[12,19210,19206],{"id":19211},"kalkul-funkcí-více-proměnných",[724,19213,19214,19215,19218,19219,1343,19248,2313],{},"Většina ekonomických veličin závisí na ",[38,19216,19217],{},"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 ",[883,19220,19222],{"className":19221},[886],[888,19223,19224],{"xmlns":890},[892,19225,19226,19245],{},[895,19227,19228,19231,19233,19235,19237,19239,19241,19243],{},[898,19229,19230],{},"z",[1750,19232,1766],{},[898,19234,11722],{},[1750,19236,1753],{"stretchy":1752},[898,19238,11727],{},[1750,19240,1917],{"separator":1916},[898,19242,11717],{},[1750,19244,1763],{"stretchy":1752},[902,19246,19247],{"encoding":904},"z = f(x, y)",[883,19249,19251],{"className":19250},[886],[888,19252,19253],{"xmlns":890},[892,19254,19255,19283],{},[895,19256,19257,19260,19262,19264,19266,19268,19270,19272,19274,19276,19278,19280],{},[898,19258,19259],{},"w",[1750,19261,1766],{},[898,19263,11722],{},[1750,19265,1753],{"stretchy":1752},[898,19267,11727],{},[1750,19269,1917],{"separator":1916},[898,19271,11717],{},[1750,19273,1917],{"separator":1916},[898,19275,19230],{},[1750,19277,1763],{"stretchy":1752},[1750,19279,1917],{"separator":1916},[1750,19281,19282],{},"…",[902,19284,19285],{"encoding":904},"w = f(x, y, z), \\ldots",[724,19287,19288],{},[4434,19289],{"alt":19290,"className":19291,"src":19292},"imek-funkce-2d-vrstevnice",[210,4438],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[115,19294,19296],{"id":19295},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[724,19298,19299,19300,19327,19328,19356,19357,19360],{},"Pro ",[883,19301,19303],{"className":19302},[886],[888,19304,19305],{"xmlns":890},[892,19306,19307,19325],{},[895,19308,19309,19311,19313,19315,19317,19319,19321,19323],{},[898,19310,19230],{},[1750,19312,1766],{},[898,19314,11722],{},[1750,19316,1753],{"stretchy":1752},[898,19318,11727],{},[1750,19320,1917],{"separator":1916},[898,19322,11717],{},[1750,19324,1763],{"stretchy":1752},[902,19326,19247],{"encoding":904}," se křivkou s předpisem ",[883,19329,19331],{"className":19330},[886],[888,19332,19333],{"xmlns":890},[892,19334,19335,19353],{},[895,19336,19337,19339,19341,19343,19345,19347,19349,19351],{},[898,19338,11722],{},[1750,19340,1753],{"stretchy":1752},[898,19342,11727],{},[1750,19344,1917],{"separator":1916},[898,19346,11717],{},[1750,19348,1763],{"stretchy":1752},[1750,19350,1766],{},[898,19352,9365],{},[902,19354,19355],{"encoding":904},"f(x, y) = c"," (konstanta) rozumí ",[38,19358,19359],{},"vrstevnice"," funkce. V ekonomii:",[120,19362,19363,19410],{},[123,19364,19365,19368,19369,19405,19406,2313],{},[38,19366,19367],{},"Indiferenční křivky"," užitečnosti ",[883,19370,19372],{"className":19371},[886],[888,19373,19374],{"xmlns":890},[892,19375,19376,19402],{},[895,19377,19378,19380,19382,19388,19390,19396,19398,19400],{},[898,19379,900],{},[1750,19381,1753],{"stretchy":1752},[5535,19383,19384,19386],{},[898,19385,12471],{},[1742,19387,1744],{},[1750,19389,1917],{"separator":1916},[5535,19391,19392,19394],{},[898,19393,12471],{},[1742,19395,1872],{},[1750,19397,1763],{"stretchy":1752},[1750,19399,1766],{},[898,19401,9365],{},[902,19403,19404],{"encoding":904},"U(Q_1, Q_2) = c"," — viz ",[207,19407,19409],{"className":19408,"dataFsResolvedFilePath":878,"href":879},[210],"uzitecnost",[123,19411,19412,19415,19416,19405,19445,2313],{},[38,19413,19414],{},"Izokvanty"," produkce ",[883,19417,19419],{"className":19418},[886],[888,19420,19421],{"xmlns":890},[892,19422,19423,19442],{},[895,19424,19425,19427,19429,19431,19433,19436,19438,19440],{},[898,19426,12471],{},[1750,19428,1753],{"stretchy":1752},[898,19430,2046],{},[1750,19432,1917],{"separator":1916},[898,19434,19435],{},"K",[1750,19437,1763],{"stretchy":1752},[1750,19439,1766],{},[898,19441,9365],{},[902,19443,19444],{"encoding":904},"Q(L, K) = c",[207,19446,19448],{"className":19447,"dataFsResolvedFilePath":857,"href":858},[210],"produkce",[115,19450,19452],{"id":19451},"parciální-derivace","Parciální derivace",[724,19454,19299,19455,19479],{},[883,19456,19458],{"className":19457},[886],[888,19459,19460],{"xmlns":890},[892,19461,19462,19476],{},[895,19463,19464,19466,19468,19470,19472,19474],{},[898,19465,11722],{},[1750,19467,1753],{"stretchy":1752},[898,19469,11727],{},[1750,19471,1917],{"separator":1916},[898,19473,11717],{},[1750,19475,1763],{"stretchy":1752},[902,19477,19478],{"encoding":904},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[724,19481,19482],{},[883,19483,19485],{"className":19484},[886],[888,19486,19487],{"xmlns":890},[892,19488,19489,19543],{},[895,19490,19491,19499,19501,19515,19517,19519,19527,19529],{},[5950,19492,19493,19495,19497],{},[898,19494,11722],{},[898,19496,11727],{},[1750,19498,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19500,1766],{},[3423,19502,19503,19509],{},[895,19504,19505,19507],{},[898,19506,8773],{"mathvariant":1747},[898,19508,11722],{},[895,19510,19511,19513],{},[898,19512,8773],{"mathvariant":1747},[898,19514,11727],{},[1750,19516,1917],{"separator":1916},[2125,19518],{"width":2127},[5950,19520,19521,19523,19525],{},[898,19522,11722],{},[898,19524,11717],{},[1750,19526,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19528,1766],{},[3423,19530,19531,19537],{},[895,19532,19533,19535],{},[898,19534,8773],{"mathvariant":1747},[898,19536,11722],{},[895,19538,19539,19541],{},[898,19540,8773],{"mathvariant":1747},[898,19542,11717],{},[902,19544,19545],{"encoding":904},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[724,19547,19548,19549,2313],{},"Hodnoty v bodě: ",[883,19550,19552],{"className":19551},[886],[888,19553,19554],{"xmlns":890},[892,19555,19556,19598],{},[895,19557,19558,19566,19568,19570,19572,19574,19576,19578,19580,19588,19590,19592,19594,19596],{},[5950,19559,19560,19562,19564],{},[898,19561,11722],{},[898,19563,11727],{},[1750,19565,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19567,1753],{"stretchy":1752},[898,19569,207],{},[1750,19571,1917],{"separator":1916},[898,19573,2573],{},[1750,19575,1763],{"stretchy":1752},[1750,19577,1917],{"separator":1916},[1969,19579,7737],{},[5950,19581,19582,19584,19586],{},[898,19583,11722],{},[898,19585,11717],{},[1750,19587,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19589,1753],{"stretchy":1752},[898,19591,207],{},[1750,19593,1917],{"separator":1916},[898,19595,2573],{},[1750,19597,1763],{"stretchy":1752},[902,19599,19600],{"encoding":904},"f'_x(a, b),\\ f'_y(a, b)",[198,19602,19604],{"id":19603},"ekonomické-značení","Ekonomické značení",[724,19606,19607,19608,2366],{},"Pro produkční funkci ",[883,19609,19611],{"className":19610},[886],[888,19612,19613],{"xmlns":890},[892,19614,19615,19629],{},[895,19616,19617,19619,19621,19623,19625,19627],{},[898,19618,12471],{},[1750,19620,1753],{"stretchy":1752},[898,19622,2046],{},[1750,19624,1917],{"separator":1916},[898,19626,19435],{},[1750,19628,1763],{"stretchy":1752},[902,19630,19631],{"encoding":904},"Q(L, K)",[120,19633,19634,19679],{},[123,19635,19636,12163,19656,2084,19659,1763],{},[883,19637,19639],{"className":19638},[886],[888,19640,19641],{"xmlns":890},[892,19642,19643,19653],{},[895,19644,19645],{},[5950,19646,19647,19649,19651],{},[898,19648,12471],{},[898,19650,2046],{},[1750,19652,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,19654,19655],{"encoding":904},"Q'_L",[38,19657,19658],{},"mezní produkt práce",[883,19660,19662],{"className":19661},[886],[888,19663,19664],{"xmlns":890},[892,19665,19666,19676],{},[895,19667,19668,19670],{},[898,19669,1773],{},[5535,19671,19672,19674],{},[898,19673,1776],{},[898,19675,2046],{},[902,19677,19678],{"encoding":904},"MP_L",[123,19680,19681,12163,19701,2084,19704,1763],{},[883,19682,19684],{"className":19683},[886],[888,19685,19686],{"xmlns":890},[892,19687,19688,19698],{},[895,19689,19690],{},[5950,19691,19692,19694,19696],{},[898,19693,12471],{},[898,19695,19435],{},[1750,19697,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,19699,19700],{"encoding":904},"Q'_K",[38,19702,19703],{},"mezní produkt kapitálu",[883,19705,19707],{"className":19706},[886],[888,19708,19709],{"xmlns":890},[892,19710,19711,19721],{},[895,19712,19713,19715],{},[898,19714,1773],{},[5535,19716,19717,19719],{},[898,19718,1776],{},[898,19720,19435],{},[902,19722,19723],{"encoding":904},"MP_K",[198,19725,12257],{"id":12256},[724,19727,19728,2366],{},[883,19729,19731],{"className":19730},[886],[888,19732,19733],{"xmlns":890},[892,19734,19735,19755],{},[895,19736,19737,19745,19747,19749,19751,19753],{},[5950,19738,19739,19741,19743],{},[898,19740,11722],{},[898,19742,11727],{},[1750,19744,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19746,1753],{"stretchy":1752},[898,19748,207],{},[1750,19750,1917],{"separator":1916},[898,19752,2573],{},[1750,19754,1763],{"stretchy":1752},[902,19756,19757],{"encoding":904},"f'_x(a, b)",[120,19759,19760,19818],{},[123,19761,19762,19763,19776,19777,19790,19791,19817],{},"rychlost změny ",[883,19764,19766],{"className":19765},[886],[888,19767,19768],{"xmlns":890},[892,19769,19770,19774],{},[895,19771,19772],{},[898,19773,11722],{},[902,19775,11722],{"encoding":904}," vůči ",[883,19778,19780],{"className":19779},[886],[888,19781,19782],{"xmlns":890},[892,19783,19784,19788],{},[895,19785,19786],{},[898,19787,11727],{},[902,19789,11727],{"encoding":904}," při ",[883,19792,19794],{"className":19793},[886],[888,19795,19796],{"xmlns":890},[892,19797,19798,19814],{},[895,19799,19800,19802,19804,19806,19808,19810,19812],{},[898,19801,11727],{},[1750,19803,1766],{},[898,19805,207],{},[1750,19807,1917],{"separator":1916},[898,19809,11717],{},[1750,19811,1766],{},[898,19813,2573],{},[902,19815,19816],{"encoding":904},"x = a, y = b"," (kapitál fixní),",[123,19819,19820,19821,12345,19834,19847,19848,19866,19867,2313],{},"přibližná změna ",[883,19822,19824],{"className":19823},[886],[888,19825,19826],{"xmlns":890},[892,19827,19828,19832],{},[895,19829,19830],{},[898,19831,11722],{},[902,19833,11722],{"encoding":904},[883,19835,19837],{"className":19836},[886],[888,19838,19839],{"xmlns":890},[892,19840,19841,19845],{},[895,19842,19843],{},[898,19844,11727],{},[902,19846,11727],{"encoding":904}," o 1 (a pevném ",[883,19849,19851],{"className":19850},[886],[888,19852,19853],{"xmlns":890},[892,19854,19855,19863],{},[895,19856,19857,19859,19861],{},[898,19858,11717],{},[1750,19860,1766],{},[898,19862,2573],{},[902,19864,19865],{"encoding":904},"y = b","): ",[883,19868,19870],{"className":19869},[886],[888,19871,19872],{"xmlns":890},[892,19873,19874,19926],{},[895,19875,19876,19878,19880,19882,19884,19886,19888,19890,19892,19894,19896,19898,19900,19902,19904,19906,19908,19916,19918,19920,19922,19924],{},[898,19877,11722],{},[1750,19879,1753],{"stretchy":1752},[898,19881,207],{},[1750,19883,1861],{},[1742,19885,1744],{},[1750,19887,1917],{"separator":1916},[898,19889,2573],{},[1750,19891,1763],{"stretchy":1752},[1750,19893,2274],{},[898,19895,11722],{},[1750,19897,1753],{"stretchy":1752},[898,19899,207],{},[1750,19901,1917],{"separator":1916},[898,19903,2573],{},[1750,19905,1763],{"stretchy":1752},[1750,19907,1861],{},[5950,19909,19910,19912,19914],{},[898,19911,11722],{},[898,19913,11727],{},[1750,19915,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19917,1753],{"stretchy":1752},[898,19919,207],{},[1750,19921,1917],{"separator":1916},[898,19923,2573],{},[1750,19925,1763],{"stretchy":1752},[902,19927,19928],{"encoding":904},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[115,19930,19932],{"id":19931},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[724,19934,19935],{},[883,19936,19938],{"className":19937},[886],[888,19939,19940],{"xmlns":890},[892,19941,19942,20000],{},[895,19943,19944,19946,19948,19950,19958,19960,19962,19964,19966,19968,19970,19972,19974,19976,19984,19986,19988,19990,19992,19994,19996,19998],{},[898,19945,3429],{},[898,19947,11722],{},[1750,19949,1766],{},[5950,19951,19952,19954,19956],{},[898,19953,11722],{},[898,19955,11727],{},[1750,19957,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19959,1753],{"stretchy":1752},[898,19961,11727],{},[1750,19963,1917],{"separator":1916},[898,19965,11717],{},[1750,19967,1763],{"stretchy":1752},[1969,19969,2658],{},[898,19971,3429],{},[898,19973,11727],{},[1750,19975,1861],{},[5950,19977,19978,19980,19982],{},[898,19979,11722],{},[898,19981,11717],{},[1750,19983,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,19985,1753],{"stretchy":1752},[898,19987,11727],{},[1750,19989,1917],{"separator":1916},[898,19991,11717],{},[1750,19993,1763],{"stretchy":1752},[1969,19995,2658],{},[898,19997,3429],{},[898,19999,11717],{},[902,20001,20002],{"encoding":904},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[724,20004,12673,20005,20027,20028,20050],{},[883,20006,20008],{"className":20007},[886],[888,20009,20010],{"xmlns":890},[892,20011,20012,20024],{},[895,20013,20014,20016,20018,20020,20022],{},[898,20015,3429],{},[898,20017,11727],{},[1750,20019,1917],{"separator":1916},[898,20021,3429],{},[898,20023,11717],{},[902,20025,20026],{"encoding":904},"dx, dy"," platí ",[883,20029,20031],{"className":20030},[886],[888,20032,20033],{"xmlns":890},[892,20034,20035,20047],{},[895,20036,20037,20039,20041,20043,20045],{},[898,20038,2666],{"mathvariant":1747},[898,20040,11722],{},[1750,20042,2274],{},[898,20044,3429],{},[898,20046,11722],{},[902,20048,20049],{"encoding":904},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[115,20052,20054],{"id":20053},"implicitní-funkce","Implicitní funkce",[724,20056,20057,20058,20087,20088,20101,20102,20115],{},"Je-li vztah dán rovnicí ",[883,20059,20061],{"className":20060},[886],[888,20062,20063],{"xmlns":890},[892,20064,20065,20084],{},[895,20066,20067,20070,20072,20074,20076,20078,20080,20082],{},[898,20068,20069],{},"F",[1750,20071,1753],{"stretchy":1752},[898,20073,11727],{},[1750,20075,1917],{"separator":1916},[898,20077,11717],{},[1750,20079,1763],{"stretchy":1752},[1750,20081,1766],{},[1742,20083,2607],{},[902,20085,20086],{"encoding":904},"F(x, y) = 0"," a chceme derivaci ",[883,20089,20091],{"className":20090},[886],[888,20092,20093],{"xmlns":890},[892,20094,20095,20099],{},[895,20096,20097],{},[898,20098,11717],{},[902,20100,11717],{"encoding":904}," podle ",[883,20103,20105],{"className":20104},[886],[888,20106,20107],{"xmlns":890},[892,20108,20109,20113],{},[895,20110,20111],{},[898,20112,11727],{},[902,20114,11727],{"encoding":904}," (nebo naopak):",[724,20117,20118],{},[883,20119,20121],{"className":20120},[886],[888,20122,20123],{"xmlns":890},[892,20124,20125,20219],{},[895,20126,20127,20133,20135,20149,20151,20153,20171,20173,20175,20181,20183,20197,20199,20201],{},[1699,20128,20129,20131],{},[898,20130,11717],{},[1750,20132,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,20134,1766],{},[3423,20136,20137,20143],{},[895,20138,20139,20141],{},[898,20140,3429],{},[898,20142,11717],{},[895,20144,20145,20147],{},[898,20146,3429],{},[898,20148,11727],{},[1750,20150,1766],{},[1750,20152,1758],{},[3423,20154,20155,20163],{},[5950,20156,20157,20159,20161],{},[898,20158,20069],{},[898,20160,11727],{},[1750,20162,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,20164,20165,20167,20169],{},[898,20166,20069],{},[898,20168,11717],{},[1750,20170,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,20172,1917],{"separator":1916},[2125,20174],{"width":2127},[1699,20176,20177,20179],{},[898,20178,11727],{},[1750,20180,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,20182,1766],{},[3423,20184,20185,20191],{},[895,20186,20187,20189],{},[898,20188,3429],{},[898,20190,11727],{},[895,20192,20193,20195],{},[898,20194,3429],{},[898,20196,11717],{},[1750,20198,1766],{},[1750,20200,1758],{},[3423,20202,20203,20211],{},[5950,20204,20205,20207,20209],{},[898,20206,20069],{},[898,20208,11717],{},[1750,20210,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,20212,20213,20215,20217],{},[898,20214,20069],{},[898,20216,11727],{},[1750,20218,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,20220,20221],{"encoding":904},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[724,20223,20224,20225,20228,20229,2028,20233,2313],{},"Tato vzorec dává ",[38,20226,20227],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[207,20230,20232],{"className":20231,"dataFsResolvedFilePath":857,"href":858},[210],"MRTS",[207,20234,20236],{"className":20235,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS",[115,20238,20240],{"id":20239},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[198,20242,12925],{"id":12924},[724,20244,20245,20246,20270],{},"V bodě extrému ",[883,20247,20249],{"className":20248},[886],[888,20250,20251],{"xmlns":890},[892,20252,20253,20267],{},[895,20254,20255,20257,20259,20261,20263,20265],{},[898,20256,13916],{},[1750,20258,5141],{"stretchy":1752},[898,20260,207],{},[1750,20262,1917],{"separator":1916},[898,20264,2573],{},[1750,20266,5158],{"stretchy":1752},[902,20268,20269],{"encoding":904},"A[a, b]"," musí platit současně:",[724,20272,20273],{},[883,20274,20276],{"className":20275},[886],[888,20277,20278],{"xmlns":890},[892,20279,20280,20333],{},[895,20281,20282,20290,20292,20294,20296,20298,20300,20302,20304,20306,20309,20311,20319,20321,20323,20325,20327,20329,20331],{},[5950,20283,20284,20286,20288],{},[898,20285,11722],{},[898,20287,11727],{},[1750,20289,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,20291,1753],{"stretchy":1752},[898,20293,207],{},[1750,20295,1917],{"separator":1916},[898,20297,2573],{},[1750,20299,1763],{"stretchy":1752},[1750,20301,1766],{},[1742,20303,2607],{},[1969,20305,6766],{},[1750,20307,20308],{},"∧",[1969,20310,6766],{},[5950,20312,20313,20315,20317],{},[898,20314,11722],{},[898,20316,11717],{},[1750,20318,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,20320,1753],{"stretchy":1752},[898,20322,207],{},[1750,20324,1917],{"separator":1916},[898,20326,2573],{},[1750,20328,1763],{"stretchy":1752},[1750,20330,1766],{},[1742,20332,2607],{},[902,20334,20335],{"encoding":904},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[198,20337,12999],{"id":12998},[724,20339,20340,20341,20344],{},"Definujeme ",[38,20342,20343],{},"diskriminant"," (Hessián zjednodušeně):",[724,20346,20347],{},[883,20348,20350],{"className":20349},[886],[888,20351,20352],{"xmlns":890},[892,20353,20354,20430],{},[895,20355,20356,20358,20360,20362,20364,20366,20368,20370,20386,20388,20404,20406,20408,20424],{},[898,20357,5541],{},[1750,20359,1753],{"stretchy":1752},[898,20361,11727],{},[1750,20363,1917],{"separator":1916},[898,20365,11717],{},[1750,20367,1763],{"stretchy":1752},[1750,20369,1766],{},[5950,20371,20372,20374,20380],{},[898,20373,11722],{},[895,20375,20376,20378],{},[898,20377,11727],{},[898,20379,11727],{},[895,20381,20382,20384],{},[1750,20383,3815],{"mathvariant":1747},[1750,20385,3815],{"mathvariant":1747},[1750,20387,8009],{},[5950,20389,20390,20392,20398],{},[898,20391,11722],{},[895,20393,20394,20396],{},[898,20395,11717],{},[898,20397,11717],{},[895,20399,20400,20402],{},[1750,20401,3815],{"mathvariant":1747},[1750,20403,3815],{"mathvariant":1747},[1750,20405,1758],{},[1750,20407,1753],{"stretchy":1752},[5950,20409,20410,20412,20418],{},[898,20411,11722],{},[895,20413,20414,20416],{},[898,20415,11727],{},[898,20417,11717],{},[895,20419,20420,20422],{},[1750,20421,3815],{"mathvariant":1747},[1750,20423,3815],{"mathvariant":1747},[1699,20425,20426,20428],{},[1750,20427,1763],{"stretchy":1752},[1742,20429,1872],{},[902,20431,20432],{"encoding":904},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[724,20434,20435,20436,2366],{},"V podezřelém bodě ",[883,20437,20439],{"className":20438},[886],[888,20440,20441],{"xmlns":890},[892,20442,20443,20455],{},[895,20444,20445,20447,20449,20451,20453],{},[1750,20446,5141],{"stretchy":1752},[898,20448,207],{},[1750,20450,1917],{"separator":1916},[898,20452,2573],{},[1750,20454,5158],{"stretchy":1752},[902,20456,20457],{"encoding":904},"[a, b]",[152,20459,20460,20587,20623],{},[123,20461,20462,20492,20493],{},[38,20463,20464,2366],{},[883,20465,20467],{"className":20466},[886],[888,20468,20469],{"xmlns":890},[892,20470,20471,20489],{},[895,20472,20473,20475,20477,20479,20481,20483,20485,20487],{},[898,20474,5541],{},[1750,20476,1753],{"stretchy":1752},[898,20478,207],{},[1750,20480,1917],{"separator":1916},[898,20482,2573],{},[1750,20484,1763],{"stretchy":1752},[1750,20486,2604],{},[1742,20488,2607],{},[902,20490,20491],{"encoding":904},"D(a, b) > 0"," je to extrém.\n",[120,20494,20495,20541],{},[123,20496,20497,13086,20539],{},[883,20498,20500],{"className":20499},[886],[888,20501,20502],{"xmlns":890},[892,20503,20504,20536],{},[895,20505,20506,20522,20524,20526,20528,20530,20532,20534],{},[5950,20507,20508,20510,20516],{},[898,20509,11722],{},[895,20511,20512,20514],{},[898,20513,11727],{},[898,20515,11727],{},[895,20517,20518,20520],{},[1750,20519,3815],{"mathvariant":1747},[1750,20521,3815],{"mathvariant":1747},[1750,20523,1753],{"stretchy":1752},[898,20525,207],{},[1750,20527,1917],{"separator":1916},[898,20529,2573],{},[1750,20531,1763],{"stretchy":1752},[1750,20533,2604],{},[1742,20535,2607],{},[902,20537,20538],{"encoding":904},"f''_{xx}(a, b) > 0",[38,20540,13445],{},[123,20542,20543,13086,20585],{},[883,20544,20546],{"className":20545},[886],[888,20547,20548],{"xmlns":890},[892,20549,20550,20582],{},[895,20551,20552,20568,20570,20572,20574,20576,20578,20580],{},[5950,20553,20554,20556,20562],{},[898,20555,11722],{},[895,20557,20558,20560],{},[898,20559,11727],{},[898,20561,11727],{},[895,20563,20564,20566],{},[1750,20565,3815],{"mathvariant":1747},[1750,20567,3815],{"mathvariant":1747},[1750,20569,1753],{"stretchy":1752},[898,20571,207],{},[1750,20573,1917],{"separator":1916},[898,20575,2573],{},[1750,20577,1763],{"stretchy":1752},[1750,20579,2624],{},[1742,20581,2607],{},[902,20583,20584],{"encoding":904},"f''_{xx}(a, b) \u003C 0",[38,20586,13387],{},[123,20588,20589,1647,20619,20622],{},[38,20590,20591,2366],{},[883,20592,20594],{"className":20593},[886],[888,20595,20596],{"xmlns":890},[892,20597,20598,20616],{},[895,20599,20600,20602,20604,20606,20608,20610,20612,20614],{},[898,20601,5541],{},[1750,20603,1753],{"stretchy":1752},[898,20605,207],{},[1750,20607,1917],{"separator":1916},[898,20609,2573],{},[1750,20611,1763],{"stretchy":1752},[1750,20613,2624],{},[1742,20615,2607],{},[902,20617,20618],{"encoding":904},"D(a, b) \u003C 0",[38,20620,20621],{},"sedlo"," (v daném bodě extrém není).",[123,20624,20625,20655],{},[38,20626,20627,2366],{},[883,20628,20630],{"className":20629},[886],[888,20631,20632],{"xmlns":890},[892,20633,20634,20652],{},[895,20635,20636,20638,20640,20642,20644,20646,20648,20650],{},[898,20637,5541],{},[1750,20639,1753],{"stretchy":1752},[898,20641,207],{},[1750,20643,1917],{"separator":1916},[898,20645,2573],{},[1750,20647,1763],{"stretchy":1752},[1750,20649,1766],{},[1742,20651,2607],{},[902,20653,20654],{"encoding":904},"D(a, b) = 0"," podmínka nerozhoduje.",[115,20657,20659],{"id":20658},"vázané-extrémy","Vázané extrémy",[724,20661,20662,20663,20691,20692,2313],{},"Pro extrémy s omezující podmínkou ",[883,20664,20666],{"className":20665},[886],[888,20667,20668],{"xmlns":890},[892,20669,20670,20688],{},[895,20671,20672,20674,20676,20678,20680,20682,20684,20686],{},[898,20673,2655],{},[1750,20675,1753],{"stretchy":1752},[898,20677,11727],{},[1750,20679,1917],{"separator":1916},[898,20681,11717],{},[1750,20683,1763],{"stretchy":1752},[1750,20685,1766],{},[1742,20687,2607],{},[902,20689,20690],{"encoding":904},"g(x, y) = 0"," se používá ",[207,20693,793],{"className":20694,"dataFsResolvedFilePath":791,"href":792},[210],[115,20696,11524],{"id":11523},[120,20698,20699,20706,20713],{},[123,20700,20701,1647,20703],{},[38,20702,13467],{},[207,20704,775],{"className":20705,"dataFsResolvedFilePath":773,"href":774},[210],[123,20707,20708,1647,20710],{},[38,20709,13475],{},[207,20711,793],{"className":20712,"dataFsResolvedFilePath":791,"href":792},[210],[123,20714,20715,1647,20717,20721,20722,20725,20726,20729],{},[38,20716,13483],{},[207,20718,20720],{"className":20719,"dataFsResolvedFilePath":857,"href":858},[210],"Produkce"," (parciální derivace = mezní produkty), ",[207,20723,880],{"className":20724,"dataFsResolvedFilePath":878,"href":879},[210]," (parciální derivace = mezní užitečnost), ",[207,20727,13496],{"className":20728,"dataFsResolvedFilePath":848,"href":849},[210]," (vícefaktorový model)",{"title":641,"searchDepth":642,"depth":642,"links":20731},[20732,20733,20737,20738,20739,20743,20744],{"id":19295,"depth":642,"text":19296},{"id":19451,"depth":642,"text":19452,"children":20734},[20735,20736],{"id":19603,"depth":649,"text":19604},{"id":12256,"depth":649,"text":12257},{"id":19931,"depth":642,"text":19932},{"id":20053,"depth":642,"text":20054},{"id":20239,"depth":642,"text":20240,"children":20740},[20741,20742],{"id":12924,"depth":649,"text":12925},{"id":12998,"depth":649,"text":12999},{"id":20658,"depth":642,"text":20659},{"id":11523,"depth":642,"text":11524},"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":19206,"description":20745},[1135],"topics\u002Ffunkce-vice-promennych",[1128,20752,13522,20753,20754,20755],"parcialni-derivace","implicitni-funkce","volne-extremy","indiferencni-krivky","iuWLbpl-7gHnuMDZKTa3RcRM2uCyFhGx9GhXHIN1R_A",{"id":20758,"title":775,"body":20759,"course":1128,"courses":659,"created":1129,"description":21615,"extension":661,"meta":21616,"navigation":664,"path":21617,"seo":21618,"sources":21619,"stem":21620,"tags":21621,"type":11664,"updated":677,"__hash__":21628},"topics\u002Ftopics\u002Fintegral.md",{"type":9,"value":20760,"toc":21605},[20761,20764,20775,20779,20824,20904,20908,20984,21026,21033,21037,21041,21070,21128,21175,21213,21217,21267,21319,21371,21415,21418,21421,21493,21496,21568,21575,21577],[12,20762,775],{"id":20763},"integrál",[724,20765,20766,20767,20770,20771,20774],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[38,20768,20769],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[38,20772,20773],{},"přebytků"," (consumer\u002Fproducer surplus).",[115,20776,20778],{"id":20777},"neurčitý-integrál","Neurčitý integrál",[724,20780,20781],{},[883,20782,20784],{"className":20783},[886],[888,20785,20786],{"xmlns":890},[892,20787,20788,20821],{},[895,20789,20790,20792,20794,20796,20798,20800,20803,20805,20807,20809,20811,20813,20815,20817,20819],{},[898,20791,20069],{},[1750,20793,1753],{"stretchy":1752},[898,20795,11727],{},[1750,20797,1763],{"stretchy":1752},[1750,20799,1766],{},[1750,20801,20802],{},"∫",[898,20804,11722],{},[1750,20806,1753],{"stretchy":1752},[898,20808,11727],{},[1750,20810,1763],{"stretchy":1752},[1969,20812,2658],{},[898,20814,3429],{},[898,20816,11727],{},[1750,20818,1861],{},[898,20820,1812],{},[902,20822,20823],{"encoding":904},"F(x) = \\int f(x)\\, dx + C",[724,20825,2590,20826,12605,20860,2433,20873,20876,20877,1343,20890,20903],{},[883,20827,20829],{"className":20828},[886],[888,20830,20831],{"xmlns":890},[892,20832,20833,20857],{},[895,20834,20835,20841,20843,20845,20847,20849,20851,20853,20855],{},[1699,20836,20837,20839],{},[898,20838,20069],{},[1750,20840,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,20842,1753],{"stretchy":1752},[898,20844,11727],{},[1750,20846,1763],{"stretchy":1752},[1750,20848,1766],{},[898,20850,11722],{},[1750,20852,1753],{"stretchy":1752},[898,20854,11727],{},[1750,20856,1763],{"stretchy":1752},[902,20858,20859],{"encoding":904},"F'(x) = f(x)",[883,20861,20863],{"className":20862},[886],[888,20864,20865],{"xmlns":890},[892,20866,20867,20871],{},[895,20868,20869],{},[898,20870,20069],{},[902,20872,20069],{"encoding":904},[38,20874,20875],{},"primitivní funkce"," k ",[883,20878,20880],{"className":20879},[886],[888,20881,20882],{"xmlns":890},[892,20883,20884,20888],{},[895,20885,20886],{},[898,20887,11722],{},[902,20889,11722],{"encoding":904},[883,20891,20893],{"className":20892},[886],[888,20894,20895],{"xmlns":890},[892,20896,20897,20901],{},[895,20898,20899],{},[898,20900,1812],{},[902,20902,1812],{"encoding":904}," konstanta.",[115,20905,20907],{"id":20906},"určitý-integrál","Určitý integrál",[724,20909,20910],{},[883,20911,20913],{"className":20912},[886],[888,20914,20915],{"xmlns":890},[892,20916,20917,20981],{},[895,20918,20919,20927,20929,20931,20933,20935,20937,20939,20941,20943,20945,20947,20949,20951,20953,20961,20963,20965,20967,20969,20971,20973,20975,20977,20979],{},[5950,20920,20921,20923,20925],{},[1750,20922,20802],{},[898,20924,207],{},[898,20926,2573],{},[898,20928,11722],{},[1750,20930,1753],{"stretchy":1752},[898,20932,11727],{},[1750,20934,1763],{"stretchy":1752},[1969,20936,2658],{},[898,20938,3429],{},[898,20940,11727],{},[1750,20942,1766],{},[1750,20944,5141],{"stretchy":1752},[898,20946,20069],{},[1750,20948,1753],{"stretchy":1752},[898,20950,11727],{},[1750,20952,1763],{"stretchy":1752},[5950,20954,20955,20957,20959],{},[1750,20956,5158],{"stretchy":1752},[898,20958,207],{},[898,20960,2573],{},[1750,20962,1766],{},[898,20964,20069],{},[1750,20966,1753],{"stretchy":1752},[898,20968,2573],{},[1750,20970,1763],{"stretchy":1752},[1750,20972,1758],{},[898,20974,20069],{},[1750,20976,1753],{"stretchy":1752},[898,20978,207],{},[1750,20980,1763],{"stretchy":1752},[902,20982,20983],{"encoding":904},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[724,20985,20986,20987,1647,20990,21003,21004,21025],{},"Geometricky ",[38,20988,20989],{},"plocha pod grafem",[883,20991,20993],{"className":20992},[886],[888,20994,20995],{"xmlns":890},[892,20996,20997,21001],{},[895,20998,20999],{},[898,21000,11722],{},[902,21002,11722],{"encoding":904}," na intervalu ",[883,21005,21007],{"className":21006},[886],[888,21008,21009],{"xmlns":890},[892,21010,21011,21023],{},[895,21012,21013,21015,21017,21019,21021],{},[1750,21014,5141],{"stretchy":1752},[898,21016,207],{},[1750,21018,1917],{"separator":1916},[898,21020,2573],{},[1750,21022,5158],{"stretchy":1752},[902,21024,20457],{"encoding":904}," (orientovaná).",[724,21027,21028],{},[4434,21029],{"alt":21030,"className":21031,"src":21032},"imek-integral-plocha",[210,4438],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[115,21034,21036],{"id":21035},"aplikace-v-ekonomii","Aplikace v ekonomii",[198,21038,21040],{"id":21039},"příklad-tr-z-mr","Příklad — TR z MR",[724,21042,21043,21044,2313],{},"Mezní příjem ",[883,21045,21047],{"className":21046},[886],[888,21048,21049],{"xmlns":890},[892,21050,21051,21067],{},[895,21052,21053,21055,21057,21059,21061,21063,21065],{},[898,21054,1773],{},[898,21056,13658],{},[1750,21058,1766],{},[1742,21060,4078],{},[1750,21062,1758],{},[1742,21064,1872],{},[898,21066,12471],{},[902,21068,21069],{"encoding":904},"MR = 100 - 2Q",[724,21071,21072],{},[883,21073,21075],{"className":21074},[886],[888,21076,21077],{"xmlns":890},[892,21078,21079,21125],{},[895,21080,21081,21083,21085,21087,21089,21091,21093,21095,21097,21099,21101,21103,21105,21107,21109,21111,21113,21115,21121,21123],{},[898,21082,5326],{},[898,21084,13658],{},[1750,21086,1766],{},[1750,21088,20802],{},[1750,21090,1753],{"stretchy":1752},[1742,21092,4078],{},[1750,21094,1758],{},[1742,21096,1872],{},[898,21098,12471],{},[1750,21100,1763],{"stretchy":1752},[1969,21102,2658],{},[898,21104,3429],{},[898,21106,12471],{},[1750,21108,1766],{},[1742,21110,4078],{},[898,21112,12471],{},[1750,21114,1758],{},[1699,21116,21117,21119],{},[898,21118,12471],{},[1742,21120,1872],{},[1750,21122,1861],{},[898,21124,9365],{},[902,21126,21127],{"encoding":904},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[724,21129,21130,21131,13086,21157,2366],{},"Okrajová podmínka ",[883,21132,21134],{"className":21133},[886],[888,21135,21136],{"xmlns":890},[892,21137,21138,21154],{},[895,21139,21140,21142,21144,21146,21148,21150,21152],{},[898,21141,5326],{},[898,21143,13658],{},[1750,21145,1753],{"stretchy":1752},[1742,21147,2607],{},[1750,21149,1763],{"stretchy":1752},[1750,21151,1766],{},[1742,21153,2607],{},[902,21155,21156],{"encoding":904},"TR(0) = 0",[883,21158,21160],{"className":21159},[886],[888,21161,21162],{"xmlns":890},[892,21163,21164,21172],{},[895,21165,21166,21168,21170],{},[898,21167,9365],{},[1750,21169,1766],{},[1742,21171,2607],{},[902,21173,21174],{"encoding":904},"c = 0",[724,21176,21177],{},[883,21178,21180],{"className":21179},[886],[888,21181,21182],{"xmlns":890},[892,21183,21184,21210],{},[895,21185,21186,21188,21190,21192,21194,21196,21198,21200,21202,21204],{},[898,21187,5326],{},[898,21189,13658],{},[1750,21191,1753],{"stretchy":1752},[898,21193,12471],{},[1750,21195,1763],{"stretchy":1752},[1750,21197,1766],{},[1742,21199,4078],{},[898,21201,12471],{},[1750,21203,1758],{},[1699,21205,21206,21208],{},[898,21207,12471],{},[1742,21209,1872],{},[902,21211,21212],{"encoding":904},"TR(Q) = 100Q - Q^2",[198,21214,21216],{"id":21215},"příklad-tc-z-mc","Příklad — TC z MC",[724,21218,21219,21220,21246,21247,2313],{},"Mezní náklady ",[883,21221,21223],{"className":21222},[886],[888,21224,21225],{"xmlns":890},[892,21226,21227,21243],{},[895,21228,21229,21231,21233,21235,21237,21239,21241],{},[898,21230,1773],{},[898,21232,1812],{},[1750,21234,1766],{},[1742,21236,1872],{},[1750,21238,1861],{},[1742,21240,3929],{},[898,21242,12471],{},[902,21244,21245],{"encoding":904},"MC = 2 + 0{,}2 Q",", fixní náklady ",[883,21248,21250],{"className":21249},[886],[888,21251,21252],{"xmlns":890},[892,21253,21254,21264],{},[895,21255,21256,21258,21260,21262],{},[898,21257,20069],{},[898,21259,1812],{},[1750,21261,1766],{},[1742,21263,4078],{},[902,21265,21266],{"encoding":904},"FC = 100",[724,21268,21269],{},[883,21270,21272],{"className":21271},[886],[888,21273,21274],{"xmlns":890},[892,21275,21276,21316],{},[895,21277,21278,21280,21282,21284,21286,21288,21290,21292,21294,21296,21298,21300,21302,21304,21306,21312,21314],{},[898,21279,5326],{},[898,21281,1812],{},[1750,21283,1766],{},[1750,21285,20802],{},[898,21287,1773],{},[898,21289,1812],{},[1969,21291,2658],{},[898,21293,3429],{},[898,21295,12471],{},[1750,21297,1766],{},[1742,21299,1872],{},[898,21301,12471],{},[1750,21303,1861],{},[1742,21305,12476],{},[1699,21307,21308,21310],{},[898,21309,12471],{},[1742,21311,1872],{},[1750,21313,1861],{},[898,21315,9365],{},[902,21317,21318],{"encoding":904},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[724,21320,21130,21321,13086,21353,2366],{},[883,21322,21324],{"className":21323},[886],[888,21325,21326],{"xmlns":890},[892,21327,21328,21350],{},[895,21329,21330,21332,21334,21336,21338,21340,21342,21344,21346,21348],{},[898,21331,5326],{},[898,21333,1812],{},[1750,21335,1753],{"stretchy":1752},[1742,21337,2607],{},[1750,21339,1763],{"stretchy":1752},[1750,21341,1766],{},[898,21343,20069],{},[898,21345,1812],{},[1750,21347,1766],{},[1742,21349,4078],{},[902,21351,21352],{"encoding":904},"TC(0) = FC = 100",[883,21354,21356],{"className":21355},[886],[888,21357,21358],{"xmlns":890},[892,21359,21360,21368],{},[895,21361,21362,21364,21366],{},[898,21363,9365],{},[1750,21365,1766],{},[1742,21367,4078],{},[902,21369,21370],{"encoding":904},"c = 100",[724,21372,21373],{},[883,21374,21376],{"className":21375},[886],[888,21377,21378],{"xmlns":890},[892,21379,21380,21412],{},[895,21381,21382,21384,21386,21388,21390,21392,21394,21396,21398,21400,21402,21404,21406],{},[898,21383,5326],{},[898,21385,1812],{},[1750,21387,1753],{"stretchy":1752},[898,21389,12471],{},[1750,21391,1763],{"stretchy":1752},[1750,21393,1766],{},[1742,21395,4078],{},[1750,21397,1861],{},[1742,21399,1872],{},[898,21401,12471],{},[1750,21403,1861],{},[1742,21405,12476],{},[1699,21407,21408,21410],{},[898,21409,12471],{},[1742,21411,1872],{},[902,21413,21414],{"encoding":904},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[198,21416,820],{"id":21417},"přebytek-spotřebitele-a-výrobce",[724,21419,21420],{},"Přebytek spotřebitele:",[724,21422,21423],{},[883,21424,21426],{"className":21425},[886],[888,21427,21428],{"xmlns":890},[892,21429,21430,21490],{},[895,21431,21432,21434,21436,21438,21444,21446,21448,21460,21462,21464,21466,21468,21470,21472,21474,21476,21482,21484],{},[898,21433,1812],{},[898,21435,1779],{},[1750,21437,1753],{"stretchy":1752},[5535,21439,21440,21442],{},[898,21441,12471],{},[1742,21443,2607],{},[1750,21445,1763],{"stretchy":1752},[1750,21447,1766],{},[5950,21449,21450,21452,21454],{},[1750,21451,20802],{},[1742,21453,2607],{},[5535,21455,21456,21458],{},[898,21457,12471],{},[1742,21459,2607],{},[898,21461,5541],{},[1750,21463,1753],{"stretchy":1752},[898,21465,12471],{},[1750,21467,1763],{"stretchy":1752},[1969,21469,2658],{},[898,21471,3429],{},[898,21473,12471],{},[1750,21475,1758],{},[5535,21477,21478,21480],{},[898,21479,1776],{},[1742,21481,2607],{},[1969,21483,2658],{},[5535,21485,21486,21488],{},[898,21487,12471],{},[1742,21489,2607],{},[902,21491,21492],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[724,21494,21495],{},"Přebytek výrobce:",[724,21497,21498],{},[883,21499,21501],{"className":21500},[886],[888,21502,21503],{"xmlns":890},[892,21504,21505,21565],{},[895,21506,21507,21509,21511,21513,21519,21521,21523,21529,21531,21537,21539,21551,21553,21555,21557,21559,21561,21563],{},[898,21508,1776],{},[898,21510,1779],{},[1750,21512,1753],{"stretchy":1752},[5535,21514,21515,21517],{},[898,21516,12471],{},[1742,21518,2607],{},[1750,21520,1763],{"stretchy":1752},[1750,21522,1766],{},[5535,21524,21525,21527],{},[898,21526,1776],{},[1742,21528,2607],{},[1969,21530,2658],{},[5535,21532,21533,21535],{},[898,21534,12471],{},[1742,21536,2607],{},[1750,21538,1758],{},[5950,21540,21541,21543,21545],{},[1750,21542,20802],{},[1742,21544,2607],{},[5535,21546,21547,21549],{},[898,21548,12471],{},[1742,21550,2607],{},[898,21552,1779],{},[1750,21554,1753],{"stretchy":1752},[898,21556,12471],{},[1750,21558,1763],{"stretchy":1752},[1969,21560,2658],{},[898,21562,3429],{},[898,21564,12471],{},[902,21566,21567],{"encoding":904},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[724,21569,21570,21571,2313],{},"Detailně viz ",[207,21572,21574],{"className":21573,"dataFsResolvedFilePath":800,"href":801},[210],"Poptávka a nabídka",[115,21576,11524],{"id":11523},[120,21578,21579,21586,21593],{},[123,21580,21581,1647,21583],{},[38,21582,13467],{},[207,21584,766],{"className":21585,"dataFsResolvedFilePath":764,"href":765},[210],[123,21587,21588,1647,21590],{},[38,21589,13475],{},[207,21591,784],{"className":21592,"dataFsResolvedFilePath":782,"href":783},[210],[123,21594,21595,1647,21597,21600,21601,21604],{},[38,21596,13483],{},[207,21598,13491],{"className":21599,"dataFsResolvedFilePath":827,"href":828},[210]," (TR\u002FTC), ",[207,21602,21574],{"className":21603,"dataFsResolvedFilePath":800,"href":801},[210]," (přebytky CS\u002FPS)",{"title":641,"searchDepth":642,"depth":642,"links":21606},[21607,21608,21609,21614],{"id":20777,"depth":642,"text":20778},{"id":20906,"depth":642,"text":20907},{"id":21035,"depth":642,"text":21036,"children":21610},[21611,21612,21613],{"id":21039,"depth":649,"text":21040},{"id":21215,"depth":649,"text":21216},{"id":21417,"depth":649,"text":820},{"id":11523,"depth":642,"text":11524},"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":21615},[1135],"topics\u002Fintegral",[1128,21622,21623,21624,21625,21626,21627],"integral","neurcity","urcity","primitivni-funkce","tr-z-mr","tc-z-mc","H1oOmn3Z5yZ_KZm1LLzfN_DVUhYSxx7eveFc7CASwZY",{"id":21630,"title":21631,"body":21632,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":25840,"navigation":664,"path":25841,"seo":25842,"sources":25843,"stem":25844,"tags":25845,"type":11664,"updated":677,"__hash__":25850},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":9,"value":21633,"toc":25828},[21634,21637,21639,21772,21779,21783,21849,21887,21986,21990,22020,22086,22131,22134,22203,22206,22241,22277,22281,22327,22334,22380,22426,22429,22506,22602,22685,22689,22733,22763,22769,22798,22820,22869,22922,22988,22991,23057,23085,23144,23160,23247,23345,23476,23480,23633,23782,24161,24165,24168,24226,24229,24315,24342,24380,24383,24420,24460,24494,24496,24533,24565,24661,24666,24786,24838,24920,25059,25063,25183,25190,25301,25308,25310,25776,25778],[12,21635,21631],{"id":21636},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[115,21638,1637],{"id":1636},[724,21640,21641,21643,21644,2084,21647,21660,21661,21674,21675,21678,21679,1343,21681,21683,21684,1343,21686,21688,21689,1647,21692,21721,21722,21724,21725,1343,21738,4419,21751,21753,21754,1783],{},[38,21642,1684],{}," je makroekonomický model se ",[38,21645,21646],{},"dvěma neznámými",[883,21648,21650],{"className":21649},[886],[888,21651,21652],{"xmlns":890},[892,21653,21654,21658],{},[895,21655,21656],{},[898,21657,1666],{},[902,21659,1666],{"encoding":904}," — národní důchod a ",[883,21662,21664],{"className":21663},[886],[888,21665,21666],{"xmlns":890},[892,21667,21668,21672],{},[895,21669,21670],{},[898,21671,1920],{},[902,21673,1920],{"encoding":904}," — úroková míra) a ",[38,21676,21677],{},"dvěma trhy",": trhem zboží (křivka ",[38,21680,10365],{},[614,21682,9433],{},") a trhem peněz (křivka ",[38,21685,10400],{},[614,21687,9486],{},"). Průsečík obou křivek určuje ",[38,21690,21691],{},"simultánní rovnováhu",[883,21693,21695],{"className":21694},[886],[888,21696,21697],{"xmlns":890},[892,21698,21699,21719],{},[895,21700,21701,21703,21709,21711,21717],{},[1750,21702,1753],{"stretchy":1752},[1699,21704,21705,21707],{},[898,21706,1666],{},[898,21708,1705],{},[1750,21710,1917],{"separator":1916},[1699,21712,21713,21715],{},[898,21714,1920],{},[898,21716,1705],{},[1750,21718,1763],{"stretchy":1752},[902,21720,10457],{"encoding":904},", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[38,21723,9604],{}," (posun IS změnou ",[883,21726,21728],{"className":21727},[886],[888,21729,21730],{"xmlns":890},[892,21731,21732,21736],{},[895,21733,21734],{},[898,21735,1997],{},[902,21737,1997],{"encoding":904},[883,21739,21741],{"className":21740},[886],[888,21742,21743],{"xmlns":890},[892,21744,21745,21749],{},[895,21746,21747],{},[898,21748,5326],{},[902,21750,5326],{"encoding":904},[38,21752,9608],{}," (posun LM změnou nabídky peněz ",[883,21755,21757],{"className":21756},[886],[888,21758,21759],{"xmlns":890},[892,21760,21761,21769],{},[895,21762,21763],{},[1699,21764,21765,21767],{},[898,21766,1773],{},[1750,21768,3751],{},[902,21770,21771],{"encoding":904},"M^*",[724,21773,21774],{},[4434,21775],{"alt":21776,"className":21777,"src":21778},"imek-is-lm-model",[210,4438],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[115,21780,21782],{"id":21781},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[724,21784,8513,21785,9301,21789,2084,21792,21813,21814,21817,21818,21834,21835,21848],{},[207,21786,21788],{"className":21787,"dataFsResolvedFilePath":934,"href":935},[210],"C-I, C-I-G a C-I-G-X",[38,21790,21791],{},"investice pokládány za konstantní",[883,21793,21795],{"className":21794},[886],[888,21796,21797],{"xmlns":890},[892,21798,21799,21811],{},[895,21800,21801,21803,21805],{},[898,21802,1974],{},[1750,21804,1766],{},[1699,21806,21807,21809],{},[898,21808,1974],{},[1750,21810,3751],{},[902,21812,4538],{"encoding":904},"). To není realistické — investice firem závisejí na ",[38,21815,21816],{},"ceně peněz",", tedy na ",[38,21819,21820,21821],{},"úrokové míře ",[883,21822,21824],{"className":21823},[886],[888,21825,21826],{"xmlns":890},[892,21827,21828,21832],{},[895,21829,21830],{},[898,21831,1920],{},[902,21833,1920],{"encoding":904},": čím vyšší ",[883,21836,21838],{"className":21837},[886],[888,21839,21840],{"xmlns":890},[892,21841,21842,21846],{},[895,21843,21844],{},[898,21845,1920],{},[902,21847,1920],{"encoding":904},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[120,21850,21851,21881],{},[123,21852,21853,1647,21856,21880],{},[38,21854,21855],{},"funkci investic",[883,21857,21859],{"className":21858},[886],[888,21860,21861],{"xmlns":890},[892,21862,21863,21877],{},[895,21864,21865,21867,21869,21871,21873,21875],{},[898,21866,1974],{},[1750,21868,1766],{},[898,21870,1974],{},[1750,21872,1753],{"stretchy":1752},[898,21874,1920],{},[1750,21876,1763],{"stretchy":1752},[902,21878,21879],{"encoding":904},"I = I(r)"," jako klesající funkci úrokové míry,",[123,21882,21883,21886],{},[38,21884,21885],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1785,21888,21889],{},[724,21890,21891,21893,21894,21911,21912,21937,21938,21951,21952,21981,21982,21985],{},[883,21892,5454],{}," Pozor — dvě neznámé vyžadují dvě rovnice\nV modelech ",[883,21895,21897],{"className":21896},[886],[888,21898,21899],{"xmlns":890},[892,21900,21901,21909],{},[895,21902,21903,21905,21907],{},[898,21904,1812],{},[1969,21906,1971],{},[898,21908,1974],{},[902,21910,1977],{"encoding":904}," až ",[883,21913,21915],{"className":21914},[886],[888,21916,21917],{"xmlns":890},[892,21918,21919,21935],{},[895,21920,21921,21923,21925,21927,21929,21931,21933],{},[898,21922,1812],{},[1969,21924,1971],{},[898,21926,1974],{},[1969,21928,1971],{},[898,21930,1997],{},[1969,21932,1971],{},[898,21934,2024],{},[902,21936,2027],{"encoding":904}," byla hlavní neznámou jen ",[883,21939,21941],{"className":21940},[886],[888,21942,21943],{"xmlns":890},[892,21944,21945,21949],{},[895,21946,21947],{},[898,21948,1666],{},[902,21950,1666],{"encoding":904},". V IS-LM jsou ",[38,21953,21954,21955,2028,21968],{},"dvě neznámé ",[883,21956,21958],{"className":21957},[886],[888,21959,21960],{"xmlns":890},[892,21961,21962,21966],{},[895,21963,21964],{},[898,21965,1666],{},[902,21967,1666],{"encoding":904},[883,21969,21971],{"className":21970},[886],[888,21972,21973],{"xmlns":890},[892,21974,21975,21979],{},[895,21976,21977],{},[898,21978,1920],{},[902,21980,1920],{"encoding":904},", a proto potřebujeme ",[38,21983,21984],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[115,21987,21989],{"id":21988},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[724,21991,21992,21993,22006,22007,2366],{},"Lineární závislost investic ",[883,21994,21996],{"className":21995},[886],[888,21997,21998],{"xmlns":890},[892,21999,22000,22004],{},[895,22001,22002],{},[898,22003,1974],{},[902,22005,1974],{"encoding":904}," na úrokové míře ",[883,22008,22010],{"className":22009},[886],[888,22011,22012],{"xmlns":890},[892,22013,22014,22018],{},[895,22015,22016],{},[898,22017,1920],{},[902,22019,1920],{"encoding":904},[724,22021,22022],{},[883,22023,22025],{"className":22024},[886],[888,22026,22027],{"xmlns":890},[892,22028,22029,22083],{},[895,22030,22031,22033,22035,22037,22039,22041,22043,22045,22047,22049,22051,22053,22055,22057,22059,22061,22063,22065,22067,22069,22071,22074,22076,22078,22081],{},[898,22032,1974],{},[1750,22034,1766],{},[898,22036,1974],{},[1750,22038,1753],{"stretchy":1752},[898,22040,1920],{},[1750,22042,1763],{"stretchy":1752},[1750,22044,1766],{},[898,22046,9365],{},[898,22048,1920],{},[1750,22050,1861],{},[898,22052,3429],{},[1750,22054,1917],{"separator":1916},[2125,22056],{"width":2127},[898,22058,9365],{},[1750,22060,2624],{},[1742,22062,2607],{},[1750,22064,1917],{"separator":1916},[1969,22066,7737],{},[898,22068,3429],{},[1750,22070,2604],{},[1742,22072,22073],{},"0.",[2125,22075],{"width":2127},[1750,22077,1753],{"stretchy":1752},[1742,22079,22080],{},"7.11",[1750,22082,1763],{"stretchy":1752},[902,22084,22085],{"encoding":904},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[120,22087,22088,22108],{},[123,22089,22090,22107],{},[883,22091,22093],{"className":22092},[886],[888,22094,22095],{"xmlns":890},[892,22096,22097,22105],{},[895,22098,22099,22101,22103],{},[898,22100,3429],{},[1750,22102,2604],{},[1742,22104,2607],{},[902,22106,11288],{"encoding":904}," zřejmé,",[123,22109,22110,22127,22128,2313],{},[883,22111,22113],{"className":22112},[886],[888,22114,22115],{"xmlns":890},[892,22116,22117,22125],{},[895,22118,22119,22121,22123],{},[898,22120,9365],{},[1750,22122,2624],{},[1742,22124,2607],{},[902,22126,9393],{"encoding":904},", protože růst úrokové míry tlumí investice — funkce investic je ",[38,22129,22130],{},"klesající",[724,22132,22133],{},"Spotřeba zůstává lineární funkcí důchodu:",[724,22135,22136],{},[883,22137,22139],{"className":22138},[886],[888,22140,22141],{"xmlns":890},[892,22142,22143,22200],{},[895,22144,22145,22147,22149,22151,22153,22155,22157,22159,22161,22163,22165,22167,22169,22171,22173,22175,22177,22179,22181,22183,22185,22187,22189,22191,22193,22195,22198],{},[898,22146,1812],{},[1750,22148,1766],{},[898,22150,1812],{},[1750,22152,1753],{"stretchy":1752},[898,22154,1666],{},[1750,22156,1763],{"stretchy":1752},[1750,22158,1766],{},[898,22160,207],{},[898,22162,1666],{},[1750,22164,1861],{},[898,22166,2573],{},[1750,22168,1917],{"separator":1916},[2125,22170],{"width":2127},[1742,22172,2607],{},[1750,22174,2624],{},[898,22176,207],{},[1750,22178,2624],{},[1742,22180,1744],{},[1750,22182,1917],{"separator":1916},[1969,22184,7737],{},[898,22186,2573],{},[1750,22188,2604],{},[1742,22190,22073],{},[2125,22192],{"width":2127},[1750,22194,1753],{"stretchy":1752},[1742,22196,22197],{},"7.12",[1750,22199,1763],{"stretchy":1752},[902,22201,22202],{"encoding":904},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[724,22204,22205],{},"Podmínka rovnováhy na trhu zboží:",[724,22207,22208],{},[883,22209,22211],{"className":22210},[886],[888,22212,22213],{"xmlns":890},[892,22214,22215,22238],{},[895,22216,22217,22219,22221,22223,22225,22227,22229,22231,22233,22236],{},[898,22218,1666],{},[1750,22220,1766],{},[898,22222,1812],{},[1750,22224,1861],{},[898,22226,1974],{},[898,22228,2313],{"mathvariant":1747},[2125,22230],{"width":2127},[1750,22232,1753],{"stretchy":1752},[1742,22234,22235],{},"7.13",[1750,22237,1763],{"stretchy":1752},[902,22239,22240],{"encoding":904},"Y = C + I. \\qquad (7.13)",[724,22242,22243,22244,1647,22247,22273,22274,2313],{},"To dává ",[38,22245,22246],{},"tři rovnice o čtyřech neznámých",[883,22248,22250],{"className":22249},[886],[888,22251,22252],{"xmlns":890},[892,22253,22254,22270],{},[895,22255,22256,22258,22260,22262,22264,22266,22268],{},[898,22257,1666],{},[1750,22259,1917],{"separator":1916},[898,22261,1812],{},[1750,22263,1917],{"separator":1916},[898,22265,1974],{},[1750,22267,1917],{"separator":1916},[898,22269,1920],{},[902,22271,22272],{"encoding":904},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[38,22275,22276],{},"rovnováhy na trhu peněz",[115,22278,22280],{"id":22279},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[724,22282,22283,22284,15223,22305,22322,22323,22326],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[883,22285,22287],{"className":22286},[886],[888,22288,22289],{"xmlns":890},[892,22290,22291,22303],{},[895,22292,22293,22295,22297,22299,22301],{},[898,22294,1666],{},[1750,22296,1766],{},[898,22298,1812],{},[1750,22300,1861],{},[898,22302,1779],{},[902,22304,9806],{"encoding":904},[883,22306,22308],{"className":22307},[886],[888,22309,22310],{"xmlns":890},[892,22311,22312,22320],{},[895,22313,22314,22316,22318],{},[898,22315,1974],{},[1750,22317,1766],{},[898,22319,1779],{},[902,22321,10384],{"encoding":904}," (plánované ",[38,22324,22325],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[724,22328,22329],{},[4434,22330],{"alt":22331,"className":22332,"src":22333},"imek-odvozeni-is-4panelu",[210,4438],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[724,22335,22336],{},[883,22337,22339],{"className":22338},[886],[888,22340,22341],{"xmlns":890},[892,22342,22343,22377],{},[895,22344,22345,22347,22349,22351,22353,22355,22357,22359,22361,22363,22365,22367,22369,22371,22373,22375],{},[898,22346,1666],{},[1750,22348,1766],{},[1750,22350,1753],{"stretchy":1752},[898,22352,207],{},[898,22354,1666],{},[1750,22356,1861],{},[898,22358,2573],{},[1750,22360,1763],{"stretchy":1752},[1750,22362,1861],{},[1750,22364,1753],{"stretchy":1752},[898,22366,9365],{},[898,22368,1920],{},[1750,22370,1861],{},[898,22372,3429],{},[1750,22374,1763],{"stretchy":1752},[1750,22376,1917],{"separator":1916},[902,22378,22379],{"encoding":904},"Y = (aY + b) + (cr + d),",[724,22381,22382],{},[883,22383,22385],{"className":22384},[886],[888,22386,22387],{"xmlns":890},[892,22388,22389,22423],{},[895,22390,22391,22393,22395,22397,22399,22401,22403,22405,22407,22409,22411,22413,22415,22417,22419,22421],{},[1750,22392,1753],{"stretchy":1752},[1742,22394,1744],{},[1750,22396,1758],{},[898,22398,207],{},[1750,22400,1763],{"stretchy":1752},[898,22402,1666],{},[1750,22404,1758],{},[898,22406,9365],{},[898,22408,1920],{},[1750,22410,1758],{},[898,22412,2573],{},[1750,22414,1758],{},[898,22416,3429],{},[1750,22418,1766],{},[1742,22420,2607],{},[1750,22422,1917],{"separator":1916},[902,22424,22425],{"encoding":904},"(1 - a)Y - cr - b - d = 0,",[724,22427,22428],{},"odkud",[724,22430,22431],{},[883,22432,22434],{"className":22433},[886],[888,22435,22436],{"xmlns":890},[892,22437,22438,22503],{},[895,22439,22440,22494,22496,22498,22501],{},[3582,22441,22442],{"notation":3584},[3586,22443,22444],{"scriptlevel":2607,"displaystyle":1752},[3586,22445,22446],{"scriptlevel":2607,"displaystyle":1752},[3586,22447,22448],{"scriptlevel":2607,"displaystyle":1916},[895,22449,22450,22452,22454,22456,22468,22470,22472,22474,22492],{},[1969,22451,2658],{},[898,22453,1666],{},[1750,22455,1766],{},[3423,22457,22458,22460],{},[898,22459,9365],{},[895,22461,22462,22464,22466],{},[1742,22463,1744],{},[1750,22465,1758],{},[898,22467,207],{},[1969,22469,2658],{},[898,22471,1920],{},[1750,22473,1861],{},[3423,22475,22476,22484],{},[895,22477,22478,22480,22482],{},[898,22479,2573],{},[1750,22481,1861],{},[898,22483,3429],{},[895,22485,22486,22488,22490],{},[1742,22487,1744],{},[1750,22489,1758],{},[898,22491,207],{},[1969,22493,2658],{},[2125,22495],{"width":2127},[1750,22497,1753],{"stretchy":1752},[1742,22499,22500],{},"7.14",[1750,22502,1763],{"stretchy":1752},[902,22504,22505],{"encoding":904},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[724,22507,22508,22509,2084,22512,22515,22516,22519,22520,22522,22523,22544,22545,22573,22574,22595,22596,22598,22599,22601],{},"Tento vztah se nazývá ",[38,22510,22511],{},"funkce IS",[614,22513,22514],{},"IS schedule",") a její graf ",[38,22517,22518],{},"křivka IS",". Křivka je ",[38,22521,22130],{}," přímka v rovině ",[883,22524,22526],{"className":22525},[886],[888,22527,22528],{"xmlns":890},[892,22529,22530,22542],{},[895,22531,22532,22534,22536,22538,22540],{},[1750,22533,1753],{"stretchy":1752},[898,22535,1920],{},[1750,22537,1917],{"separator":1916},[898,22539,1666],{},[1750,22541,1763],{"stretchy":1752},[902,22543,9456],{"encoding":904},", neboť ",[883,22546,22548],{"className":22547},[886],[888,22549,22550],{"xmlns":890},[892,22551,22552,22570],{},[895,22553,22554,22566,22568],{},[3423,22555,22556,22558],{},[898,22557,9365],{},[895,22559,22560,22562,22564],{},[1742,22561,1744],{},[1750,22563,1758],{},[898,22565,207],{},[1750,22567,2624],{},[1742,22569,2607],{},[902,22571,22572],{"encoding":904},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[883,22575,22577],{"className":22576},[886],[888,22578,22579],{"xmlns":890},[892,22580,22581,22593],{},[895,22582,22583,22585,22587,22589,22591],{},[1750,22584,1753],{"stretchy":1752},[898,22586,1920],{},[1750,22588,1917],{"separator":1916},[898,22590,1666],{},[1750,22592,1763],{"stretchy":1752},[902,22594,9456],{"encoding":904},", pro které plánované ",[38,22597,1974],{},"nvestment = ",[38,22600,1779],{},"avings.",[1785,22603,22604],{},[724,22605,22606,22608,22609,22622,22623,1647,22626,22639,22640,22653,22654,2028,22667,22680,22681,22684],{},[883,22607,1791],{}," Intuice — proč IS klesá\nNižší úroková míra ",[883,22610,22612],{"className":22611},[886],[888,22613,22614],{"xmlns":890},[892,22615,22616,22620],{},[895,22617,22618],{},[898,22619,1920],{},[902,22621,1920],{"encoding":904}," → levnější úvěr → ",[38,22624,22625],{},"více investic",[883,22627,22629],{"className":22628},[886],[888,22630,22631],{"xmlns":890},[892,22632,22633,22637],{},[895,22634,22635],{},[898,22636,1974],{},[902,22638,1974],{"encoding":904}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[883,22641,22643],{"className":22642},[886],[888,22644,22645],{"xmlns":890},[892,22646,22647,22651],{},[895,22648,22649],{},[898,22650,1666],{},[902,22652,1666],{"encoding":904},". Vztah mezi ",[883,22655,22657],{"className":22656},[886],[888,22658,22659],{"xmlns":890},[892,22660,22661,22665],{},[895,22662,22663],{},[898,22664,1920],{},[902,22666,1920],{"encoding":904},[883,22668,22670],{"className":22669},[886],[888,22671,22672],{"xmlns":890},[892,22673,22674,22678],{},[895,22675,22676],{},[898,22677,1666],{},[902,22679,1666],{"encoding":904}," na trhu zboží je proto ",[38,22682,22683],{},"nepřímý"," (klesající křivka).",[115,22686,22688],{"id":22687},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[724,22690,22691,22692,22710,22711,12605,22729,22732],{},"Rovnováha na trhu peněz: poptávka po penězích ",[883,22693,22695],{"className":22694},[886],[888,22696,22697],{"xmlns":890},[892,22698,22699,22707],{},[895,22700,22701],{},[1699,22702,22703,22705],{},[898,22704,1773],{},[898,22706,5541],{},[902,22708,22709],{"encoding":904},"M^D"," se rovná nabídce peněz ",[883,22712,22714],{"className":22713},[886],[888,22715,22716],{"xmlns":890},[892,22717,22718,22726],{},[895,22719,22720],{},[1699,22721,22722,22724],{},[898,22723,1773],{},[898,22725,1779],{},[902,22727,22728],{"encoding":904},"M^S",[38,22730,22731],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[724,22734,22735],{},[883,22736,22738],{"className":22737},[886],[888,22739,22740],{"xmlns":890},[892,22741,22742,22760],{},[895,22743,22744,22750,22752,22758],{},[1699,22745,22746,22748],{},[898,22747,1773],{},[898,22749,1779],{},[1750,22751,1766],{},[1699,22753,22754,22756],{},[898,22755,1773],{},[1750,22757,3751],{},[898,22759,2313],{"mathvariant":1747},[902,22761,22762],{"encoding":904},"M^S = M^*.",[724,22764,22765,22768],{},[38,22766,22767],{},"Poptávka"," po penězích má tři zdroje:",[120,22770,22771,22780,22789],{},[123,22772,22773,2084,22776,22779],{},[38,22774,22775],{},"transakční poptávka",[614,22777,22778],{},"transactions demand",") — peníze pro nákup zboží,",[123,22781,22782,2084,22785,22788],{},[38,22783,22784],{},"opatrnostní poptávka",[614,22786,22787],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[123,22790,22791,2084,22794,22797],{},[38,22792,22793],{},"spekulační poptávka",[614,22795,22796],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[724,22799,22800,22801,22819],{},"Součet transakční a opatrnostní poptávky ",[883,22802,22804],{"className":22803},[886],[888,22805,22806],{"xmlns":890},[892,22807,22808,22816],{},[895,22809,22810],{},[5535,22811,22812,22814],{},[898,22813,2046],{},[1742,22815,1744],{},[902,22817,22818],{"encoding":904},"L_1"," je úměrný důchodu:",[724,22821,22822],{},[883,22823,22825],{"className":22824},[886],[888,22826,22827],{"xmlns":890},[892,22828,22829,22866],{},[895,22830,22831,22837,22839,22845,22847,22849,22851,22853,22855,22861,22863],{},[5535,22832,22833,22835],{},[898,22834,2046],{},[1742,22836,1744],{},[1750,22838,1766],{},[5535,22840,22841,22843],{},[898,22842,9535],{},[1742,22844,1744],{},[898,22846,1666],{},[1750,22848,1917],{"separator":1916},[2125,22850],{"width":2127},[1742,22852,2607],{},[1750,22854,2624],{},[5535,22856,22857,22859],{},[898,22858,9535],{},[1742,22860,1744],{},[1750,22862,2624],{},[1742,22864,22865],{},"1.",[902,22867,22868],{"encoding":904},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[724,22870,22871,22872,22890,22891,1343,22904,22921],{},"Spekulační poptávka ",[883,22873,22875],{"className":22874},[886],[888,22876,22877],{"xmlns":890},[892,22878,22879,22887],{},[895,22880,22881],{},[5535,22882,22883,22885],{},[898,22884,2046],{},[1742,22886,1872],{},[902,22888,22889],{"encoding":904},"L_2"," závisí na úrokové míře (roste-li ",[883,22892,22894],{"className":22893},[886],[888,22895,22896],{"xmlns":890},[892,22897,22898,22902],{},[895,22899,22900],{},[898,22901,1920],{},[902,22903,1920],{"encoding":904},[883,22905,22907],{"className":22906},[886],[888,22908,22909],{"xmlns":890},[892,22910,22911,22919],{},[895,22912,22913],{},[5535,22914,22915,22917],{},[898,22916,2046],{},[1742,22918,1872],{},[902,22920,22889],{"encoding":904}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[724,22923,22924],{},[883,22925,22927],{"className":22926},[886],[888,22928,22929],{"xmlns":890},[892,22930,22931,22985],{},[895,22932,22933,22939,22941,22947,22949,22951,22957,22959,22961,22967,22969,22971,22973,22975,22981,22983],{},[5535,22934,22935,22937],{},[898,22936,2046],{},[1742,22938,1872],{},[1750,22940,1766],{},[5535,22942,22943,22945],{},[898,22944,9535],{},[1742,22946,1872],{},[898,22948,1920],{},[1750,22950,1861],{},[5535,22952,22953,22955],{},[898,22954,9535],{},[1742,22956,7822],{},[1750,22958,1917],{"separator":1916},[2125,22960],{"width":2127},[5535,22962,22963,22965],{},[898,22964,9535],{},[1742,22966,1872],{},[1750,22968,2624],{},[1742,22970,2607],{},[1750,22972,1917],{"separator":1916},[1969,22974,7737],{},[5535,22976,22977,22979],{},[898,22978,9535],{},[1742,22980,7822],{},[1750,22982,2604],{},[1742,22984,22073],{},[902,22986,22987],{"encoding":904},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[724,22989,22990],{},"Celková poptávka po penězích:",[724,22992,22993],{},[883,22994,22996],{"className":22995},[886],[888,22997,22998],{"xmlns":890},[892,22999,23000,23054],{},[895,23001,23002,23008,23010,23016,23018,23024,23026,23032,23034,23036,23042,23044,23046,23052],{},[1699,23003,23004,23006],{},[898,23005,1773],{},[898,23007,5541],{},[1750,23009,1766],{},[5535,23011,23012,23014],{},[898,23013,2046],{},[1742,23015,1744],{},[1750,23017,1861],{},[5535,23019,23020,23022],{},[898,23021,2046],{},[1742,23023,1872],{},[1750,23025,1766],{},[5535,23027,23028,23030],{},[898,23029,9535],{},[1742,23031,1744],{},[898,23033,1666],{},[1750,23035,1861],{},[5535,23037,23038,23040],{},[898,23039,9535],{},[1742,23041,1872],{},[898,23043,1920],{},[1750,23045,1861],{},[5535,23047,23048,23050],{},[898,23049,9535],{},[1742,23051,7822],{},[898,23053,2313],{"mathvariant":1747},[902,23055,23056],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[724,23058,23059,23060,2366],{},"Podmínka rovnováhy na trhu peněz ",[883,23061,23063],{"className":23062},[886],[888,23064,23065],{"xmlns":890},[892,23066,23067,23083],{},[895,23068,23069,23075,23077],{},[1699,23070,23071,23073],{},[898,23072,1773],{},[898,23074,5541],{},[1750,23076,1766],{},[1699,23078,23079,23081],{},[898,23080,1773],{},[1750,23082,3751],{},[902,23084,9513],{"encoding":904},[724,23086,23087],{},[883,23088,23090],{"className":23089},[886],[888,23091,23092],{"xmlns":890},[892,23093,23094,23141],{},[895,23095,23096,23102,23104,23110,23112,23114,23120,23122,23124,23130,23132,23134,23136,23139],{},[1699,23097,23098,23100],{},[898,23099,1773],{},[1750,23101,3751],{},[1750,23103,1766],{},[5535,23105,23106,23108],{},[898,23107,9535],{},[1742,23109,1744],{},[898,23111,1666],{},[1750,23113,1861],{},[5535,23115,23116,23118],{},[898,23117,9535],{},[1742,23119,1872],{},[898,23121,1920],{},[1750,23123,1861],{},[5535,23125,23126,23128],{},[898,23127,9535],{},[1742,23129,7822],{},[1750,23131,1917],{"separator":1916},[2125,23133],{"width":2127},[1750,23135,1753],{"stretchy":1752},[1742,23137,23138],{},"7.15",[1750,23140,1763],{"stretchy":1752},[902,23142,23143],{"encoding":904},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[724,23145,23146,23147,12825],{},"po úpravě (vyjádření ",[883,23148,23150],{"className":23149},[886],[888,23151,23152],{"xmlns":890},[892,23153,23154,23158],{},[895,23155,23156],{},[898,23157,1666],{},[902,23159,1666],{"encoding":904},[724,23161,23162],{},[883,23163,23165],{"className":23164},[886],[888,23166,23167],{"xmlns":890},[892,23168,23169,23244],{},[895,23170,23171,23235,23237,23239,23242],{},[3582,23172,23173],{"notation":3584},[3586,23174,23175],{"scriptlevel":2607,"displaystyle":1752},[3586,23176,23177],{"scriptlevel":2607,"displaystyle":1752},[3586,23178,23179],{"scriptlevel":2607,"displaystyle":1916},[895,23180,23181,23183,23185,23187,23189,23203,23205,23207,23209,23233],{},[1969,23182,2658],{},[898,23184,1666],{},[1750,23186,1766],{},[1750,23188,1758],{},[3423,23190,23191,23197],{},[5535,23192,23193,23195],{},[898,23194,9535],{},[1742,23196,1872],{},[5535,23198,23199,23201],{},[898,23200,9535],{},[1742,23202,1744],{},[1969,23204,2658],{},[898,23206,1920],{},[1750,23208,1861],{},[3423,23210,23211,23227],{},[895,23212,23213,23219,23221],{},[1699,23214,23215,23217],{},[898,23216,1773],{},[1750,23218,3751],{},[1750,23220,1758],{},[5535,23222,23223,23225],{},[898,23224,9535],{},[1742,23226,7822],{},[5535,23228,23229,23231],{},[898,23230,9535],{},[1742,23232,1744],{},[1969,23234,2658],{},[2125,23236],{"width":2127},[1750,23238,1753],{"stretchy":1752},[1742,23240,23241],{},"7.16",[1750,23243,1763],{"stretchy":1752},[902,23245,23246],{"encoding":904},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[724,23248,22508,23249,2084,23252,23255,23256,22519,23259,22522,23262,22544,23283,23315,23316,23338,23339,23341,23342,23344],{},[38,23250,23251],{},"funkce LM",[614,23253,23254],{},"LM schedule","), její graf ",[38,23257,23258],{},"křivka LM",[38,23260,23261],{},"rostoucí",[883,23263,23265],{"className":23264},[886],[888,23266,23267],{"xmlns":890},[892,23268,23269,23281],{},[895,23270,23271,23273,23275,23277,23279],{},[1750,23272,1753],{"stretchy":1752},[898,23274,1920],{},[1750,23276,1917],{"separator":1916},[898,23278,1666],{},[1750,23280,1763],{"stretchy":1752},[902,23282,9456],{"encoding":904},[883,23284,23286],{"className":23285},[886],[888,23287,23288],{"xmlns":890},[892,23289,23290,23312],{},[895,23291,23292,23294,23308,23310],{},[1750,23293,1758],{},[3423,23295,23296,23302],{},[5535,23297,23298,23300],{},[898,23299,9535],{},[1742,23301,1872],{},[5535,23303,23304,23306],{},[898,23305,9535],{},[1742,23307,1744],{},[1750,23309,2604],{},[1742,23311,2607],{},[902,23313,23314],{"encoding":904},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[883,23317,23319],{"className":23318},[886],[888,23320,23321],{"xmlns":890},[892,23322,23323,23335],{},[895,23324,23325,23331,23333],{},[5535,23326,23327,23329],{},[898,23328,9535],{},[1742,23330,1872],{},[1750,23332,2624],{},[1742,23334,2607],{},[902,23336,23337],{"encoding":904},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[38,23340,2046],{},"iquidity of ",[38,23343,1773],{},"oney.",[1785,23346,23347],{},[724,23348,23349,23351,23352,23365,23366,23394,23395,23412,23413,23426,23427,23444,23445,2028,23458,23471,23472,23475],{},[883,23350,1791],{}," Intuice — proč LM roste\nVyšší důchod ",[883,23353,23355],{"className":23354},[886],[888,23356,23357],{"xmlns":890},[892,23358,23359,23363],{},[895,23360,23361],{},[898,23362,1666],{},[902,23364,1666],{"encoding":904}," → větší transakční poptávka po penězích ",[883,23367,23369],{"className":23368},[886],[888,23370,23371],{"xmlns":890},[892,23372,23373,23391],{},[895,23374,23375,23381,23383,23389],{},[5535,23376,23377,23379],{},[898,23378,2046],{},[1742,23380,1744],{},[1750,23382,1766],{},[5535,23384,23385,23387],{},[898,23386,9535],{},[1742,23388,1744],{},[898,23390,1666],{},[902,23392,23393],{"encoding":904},"L_1 = k_1 Y"," → při pevné nabídce ",[883,23396,23398],{"className":23397},[886],[888,23399,23400],{"xmlns":890},[892,23401,23402,23410],{},[895,23403,23404],{},[1699,23405,23406,23408],{},[898,23407,1773],{},[1750,23409,3751],{},[902,23411,21771],{"encoding":904}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[883,23414,23416],{"className":23415},[886],[888,23417,23418],{"xmlns":890},[892,23419,23420,23424],{},[895,23421,23422],{},[898,23423,1920],{},[902,23425,1920],{"encoding":904}," musí vzrůst, aby se spekulační poptávka ",[883,23428,23430],{"className":23429},[886],[888,23431,23432],{"xmlns":890},[892,23433,23434,23442],{},[895,23435,23436],{},[5535,23437,23438,23440],{},[898,23439,2046],{},[1742,23441,1872],{},[902,23443,22889],{"encoding":904}," stlačila a trh se vyrovnal. Vztah mezi ",[883,23446,23448],{"className":23447},[886],[888,23449,23450],{"xmlns":890},[892,23451,23452,23456],{},[895,23453,23454],{},[898,23455,1666],{},[902,23457,1666],{"encoding":904},[883,23459,23461],{"className":23460},[886],[888,23462,23463],{"xmlns":890},[892,23464,23465,23469],{},[895,23466,23467],{},[898,23468,1920],{},[902,23470,1920],{"encoding":904}," na trhu peněz je proto ",[38,23473,23474],{},"přímý"," (rostoucí křivka).",[115,23477,23479],{"id":23478},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[724,23481,23482,23483,23486,23487,1647,23489,2028,23506,1647,23509,23527,23528,23546,23547,23564,23565,11460,23581,2028,23596,23611,23612,2313],{},"Řešením ",[38,23484,23485],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[38,23488,1688],{},[883,23490,23492],{"className":23491},[886],[888,23493,23494],{"xmlns":890},[892,23495,23496,23504],{},[895,23497,23498],{},[1699,23499,23500,23502],{},[898,23501,1666],{},[898,23503,1705],{},[902,23505,1708],{"encoding":904},[38,23507,23508],{},"rovnovážnou úrokovou míru",[883,23510,23512],{"className":23511},[886],[888,23513,23514],{"xmlns":890},[892,23515,23516,23524],{},[895,23517,23518],{},[1699,23519,23520,23522],{},[898,23521,1920],{},[898,23523,1705],{},[902,23525,23526],{"encoding":904},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[883,23529,23531],{"className":23530},[886],[888,23532,23533],{"xmlns":890},[892,23534,23535,23543],{},[895,23536,23537],{},[1699,23538,23539,23541],{},[898,23540,1974],{},[898,23542,1705],{},[902,23544,23545],{"encoding":904},"I^E"," a rovnovážnou spotřebu ",[883,23548,23550],{"className":23549},[886],[888,23551,23552],{"xmlns":890},[892,23553,23554,23562],{},[895,23555,23556],{},[1699,23557,23558,23560],{},[898,23559,1812],{},[898,23561,1705],{},[902,23563,4695],{"encoding":904},". Graficky jde o ",[38,23566,23567,23568],{},"průsečík ",[883,23569,23571],{"className":23570},[886],[888,23572,23573],{"xmlns":890},[892,23574,23575,23579],{},[895,23576,23577],{},[898,23578,1705],{},[902,23580,1705],{"encoding":904},[883,23582,23584],{"className":23583},[886],[888,23585,23586],{"xmlns":890},[892,23587,23588,23594],{},[895,23589,23590,23592],{},[898,23591,1974],{},[898,23593,1779],{},[902,23595,10365],{"encoding":904},[883,23597,23599],{"className":23598},[886],[888,23600,23601],{"xmlns":890},[892,23602,23603,23609],{},[895,23604,23605,23607],{},[898,23606,2046],{},[898,23608,1773],{},[902,23610,10400],{"encoding":904}," v rovině ",[883,23613,23615],{"className":23614},[886],[888,23616,23617],{"xmlns":890},[892,23618,23619,23631],{},[895,23620,23621,23623,23625,23627,23629],{},[1750,23622,1753],{"stretchy":1752},[898,23624,1920],{},[1750,23626,1917],{"separator":1916},[898,23628,1666],{},[1750,23630,1763],{"stretchy":1752},[902,23632,9456],{"encoding":904},[724,23634,23635],{},[614,23636,23637,23638,23659,23660,23675,23676,23691,23692,23705,23706,23723,23724,4419,23737,23723,23754,23767,23768,23781],{},"Obrázek 7.6 — Schematický graf v rovině ",[883,23639,23641],{"className":23640},[886],[888,23642,23643],{"xmlns":890},[892,23644,23645,23657],{},[895,23646,23647,23649,23651,23653,23655],{},[1750,23648,1753],{"stretchy":1752},[898,23650,1920],{},[1750,23652,1917],{"separator":1916},[898,23654,1666],{},[1750,23656,1763],{"stretchy":1752},[902,23658,9456],{"encoding":904},". Rostoucí přímka ",[883,23661,23663],{"className":23662},[886],[888,23664,23665],{"xmlns":890},[892,23666,23667,23673],{},[895,23668,23669,23671],{},[898,23670,2046],{},[898,23672,1773],{},[902,23674,10400],{"encoding":904}," a klesající přímka ",[883,23677,23679],{"className":23678},[886],[888,23680,23681],{"xmlns":890},[892,23682,23683,23689],{},[895,23684,23685,23687],{},[898,23686,1974],{},[898,23688,1779],{},[902,23690,10365],{"encoding":904}," se protínají v bodě ",[883,23693,23695],{"className":23694},[886],[888,23696,23697],{"xmlns":890},[892,23698,23699,23703],{},[895,23700,23701],{},[898,23702,1705],{},[902,23704,1705],{"encoding":904}," se souřadnicemi ",[883,23707,23709],{"className":23708},[886],[888,23710,23711],{"xmlns":890},[892,23712,23713,23721],{},[895,23714,23715],{},[1699,23716,23717,23719],{},[898,23718,1920],{},[898,23720,1705],{},[902,23722,23526],{"encoding":904}," (na ose ",[883,23725,23727],{"className":23726},[886],[888,23728,23729],{"xmlns":890},[892,23730,23731,23735],{},[895,23732,23733],{},[898,23734,1920],{},[902,23736,1920],{"encoding":904},[883,23738,23740],{"className":23739},[886],[888,23741,23742],{"xmlns":890},[892,23743,23744,23752],{},[895,23745,23746],{},[1699,23747,23748,23750],{},[898,23749,1666],{},[898,23751,1705],{},[902,23753,1708],{"encoding":904},[883,23755,23757],{"className":23756},[886],[888,23758,23759],{"xmlns":890},[892,23760,23761,23765],{},[895,23762,23763],{},[898,23764,1666],{},[902,23766,1666],{"encoding":904},"); tečkované čáry z ",[883,23769,23771],{"className":23770},[886],[888,23772,23773],{"xmlns":890},[892,23774,23775,23779],{},[895,23776,23777],{},[898,23778,1705],{},[902,23780,1705],{"encoding":904}," kolmé k osám vyznačují polohu rovnovážné úrokové míry a rovnovážného národního důchodu.",[1785,23783,23784,23789],{},[724,23785,23786,23788],{},[883,23787,6004],{}," Postup — jak najít IS-LM rovnováhu",[152,23790,23791,23866,23934,23992,24065],{},[123,23792,23793,23796,23797,2028,23816,23836,23837,2028,23850,23863,23864,2313],{},[38,23794,23795],{},"Z trhu zboží (7.13)"," dosaď funkce ",[883,23798,23800],{"className":23799},[886],[888,23801,23802],{"xmlns":890},[892,23803,23804,23814],{},[895,23805,23806,23808,23810,23812],{},[898,23807,1812],{},[1750,23809,1753],{"stretchy":1752},[898,23811,1666],{},[1750,23813,1763],{"stretchy":1752},[902,23815,2432],{"encoding":904},[883,23817,23819],{"className":23818},[886],[888,23820,23821],{"xmlns":890},[892,23822,23823,23833],{},[895,23824,23825,23827,23829,23831],{},[898,23826,1974],{},[1750,23828,1753],{"stretchy":1752},[898,23830,1920],{},[1750,23832,1763],{"stretchy":1752},[902,23834,23835],{"encoding":904},"I(r)"," a vyjádři vztah mezi ",[883,23838,23840],{"className":23839},[886],[888,23841,23842],{"xmlns":890},[892,23843,23844,23848],{},[895,23845,23846],{},[898,23847,1666],{},[902,23849,1666],{"encoding":904},[883,23851,23853],{"className":23852},[886],[888,23854,23855],{"xmlns":890},[892,23856,23857,23861],{},[895,23858,23859],{},[898,23860,1920],{},[902,23862,1920],{"encoding":904}," — dostaneš rovnici ",[38,23865,10365],{},[123,23867,23868,23871,23872,2028,23889,23906,23907,23863,23932,2313],{},[38,23869,23870],{},"Z trhu peněz (7.15)"," dosaď ",[883,23873,23875],{"className":23874},[886],[888,23876,23877],{"xmlns":890},[892,23878,23879,23887],{},[895,23880,23881],{},[5535,23882,23883,23885],{},[898,23884,2046],{},[1742,23886,1744],{},[902,23888,22818],{"encoding":904},[883,23890,23892],{"className":23891},[886],[888,23893,23894],{"xmlns":890},[892,23895,23896,23904],{},[895,23897,23898],{},[5535,23899,23900,23902],{},[898,23901,2046],{},[1742,23903,1872],{},[902,23905,22889],{"encoding":904}," a vztah ",[883,23908,23910],{"className":23909},[886],[888,23911,23912],{"xmlns":890},[892,23913,23914,23930],{},[895,23915,23916,23922,23924],{},[1699,23917,23918,23920],{},[898,23919,1773],{},[898,23921,5541],{},[1750,23923,1766],{},[1699,23925,23926,23928],{},[898,23927,1773],{},[1750,23929,3751],{},[902,23931,9513],{"encoding":904},[38,23933,10400],{},[123,23935,23936,23939,23940,2028,23953,23966,23967,23991],{},[38,23937,23938],{},"Vyřeš soustavu"," dvou lineárních rovnic o dvou neznámých ",[883,23941,23943],{"className":23942},[886],[888,23944,23945],{"xmlns":890},[892,23946,23947,23951],{},[895,23948,23949],{},[898,23950,1666],{},[902,23952,1666],{"encoding":904},[883,23954,23956],{"className":23955},[886],[888,23957,23958],{"xmlns":890},[892,23959,23960,23964],{},[895,23961,23962],{},[898,23963,1920],{},[902,23965,1920],{"encoding":904}," — nejsnáze substituční metodou (vyjádři z IS ",[883,23968,23970],{"className":23969},[886],[888,23971,23972],{"xmlns":890},[892,23973,23974,23988],{},[895,23975,23976,23978,23980,23982,23984,23986],{},[898,23977,1666],{},[1750,23979,1766],{},[898,23981,11722],{},[1750,23983,1753],{"stretchy":1752},[898,23985,1920],{},[1750,23987,1763],{"stretchy":1752},[902,23989,23990],{"encoding":904},"Y = f(r)"," a dosaď do LM).",[123,23993,23994,1647,23997,2028,24031,2313],{},[38,23995,23996],{},"Zpětně dopočítej",[883,23998,24000],{"className":23999},[886],[888,24001,24002],{"xmlns":890},[892,24003,24004,24028],{},[895,24005,24006,24012,24014,24016,24018,24024,24026],{},[1699,24007,24008,24010],{},[898,24009,1812],{},[898,24011,1705],{},[1750,24013,1766],{},[898,24015,207],{},[1969,24017,2658],{},[1699,24019,24020,24022],{},[898,24021,1666],{},[898,24023,1705],{},[1750,24025,1861],{},[898,24027,2573],{},[902,24029,24030],{"encoding":904},"C^E = a\\,Y^E + b",[883,24032,24034],{"className":24033},[886],[888,24035,24036],{"xmlns":890},[892,24037,24038,24062],{},[895,24039,24040,24046,24048,24050,24052,24058,24060],{},[1699,24041,24042,24044],{},[898,24043,1974],{},[898,24045,1705],{},[1750,24047,1766],{},[898,24049,9365],{},[1969,24051,2658],{},[1699,24053,24054,24056],{},[898,24055,1920],{},[898,24057,1705],{},[1750,24059,1861],{},[898,24061,3429],{},[902,24063,24064],{"encoding":904},"I^E = c\\,r^E + d",[123,24066,24067,24070,24071,24105,24106,24160],{},[38,24068,24069],{},"Ověř:"," musí platit ",[883,24072,24074],{"className":24073},[886],[888,24075,24076],{"xmlns":890},[892,24077,24078,24102],{},[895,24079,24080,24086,24088,24094,24096],{},[1699,24081,24082,24084],{},[898,24083,1666],{},[898,24085,1705],{},[1750,24087,1766],{},[1699,24089,24090,24092],{},[898,24091,1812],{},[898,24093,1705],{},[1750,24095,1861],{},[1699,24097,24098,24100],{},[898,24099,1974],{},[898,24101,1705],{},[902,24103,24104],{"encoding":904},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[883,24107,24109],{"className":24108},[886],[888,24110,24111],{"xmlns":890},[892,24112,24113,24157],{},[895,24114,24115,24121,24123,24129,24135,24137,24143,24149,24151],{},[1699,24116,24117,24119],{},[898,24118,1773],{},[1750,24120,3751],{},[1750,24122,1766],{},[5535,24124,24125,24127],{},[898,24126,9535],{},[1742,24128,1744],{},[1699,24130,24131,24133],{},[898,24132,1666],{},[898,24134,1705],{},[1750,24136,1861],{},[5535,24138,24139,24141],{},[898,24140,9535],{},[1742,24142,1872],{},[1699,24144,24145,24147],{},[898,24146,1920],{},[898,24148,1705],{},[1750,24150,1861],{},[5535,24152,24153,24155],{},[898,24154,9535],{},[1742,24156,7822],{},[902,24158,24159],{"encoding":904},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[115,24162,24164],{"id":24163},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[724,24166,24167],{},"Pro trh zboží jsou dány:",[120,24169,24170,24197],{},[123,24171,24172,24173,1917],{},"spotřeba ",[883,24174,24176],{"className":24175},[886],[888,24177,24178],{"xmlns":890},[892,24179,24180,24194],{},[895,24181,24182,24184,24186,24188,24190,24192],{},[898,24183,1812],{},[1750,24185,1766],{},[1742,24187,6657],{},[898,24189,1666],{},[1750,24191,1861],{},[1742,24193,4078],{},[902,24195,24196],{"encoding":904},"C = 0{,}8Y + 100",[123,24198,24199,24200,2313],{},"investice ",[883,24201,24203],{"className":24202},[886],[888,24204,24205],{"xmlns":890},[892,24206,24207,24223],{},[895,24208,24209,24211,24213,24215,24217,24219,24221],{},[898,24210,1974],{},[1750,24212,1766],{},[1750,24214,1758],{},[1742,24216,6465],{},[898,24218,1920],{},[1750,24220,1861],{},[1742,24222,8243],{},[902,24224,24225],{"encoding":904},"I = -20r + 1000",[724,24227,24228],{},"Pro trh peněz:",[120,24230,24231,24257,24289],{},[123,24232,24233,1917],{},[883,24234,24236],{"className":24235},[886],[888,24237,24238],{"xmlns":890},[892,24239,24240,24254],{},[895,24241,24242,24248,24250,24252],{},[5535,24243,24244,24246],{},[898,24245,2046],{},[1742,24247,1744],{},[1750,24249,1766],{},[1742,24251,12476],{},[898,24253,1666],{},[902,24255,24256],{"encoding":904},"L_1 = 0{,}1Y",[123,24258,24259,1917],{},[883,24260,24262],{"className":24261},[886],[888,24263,24264],{"xmlns":890},[892,24265,24266,24286],{},[895,24267,24268,24274,24276,24278,24280,24282,24284],{},[5535,24269,24270,24272],{},[898,24271,2046],{},[1742,24273,1872],{},[1750,24275,1766],{},[1750,24277,1758],{},[1742,24279,6419],{},[898,24281,1920],{},[1750,24283,1861],{},[1742,24285,18246],{},[902,24287,24288],{"encoding":904},"L_2 = -25r + 2000",[123,24290,24291,24292,2313],{},"nabídka peněz ",[883,24293,24295],{"className":24294},[886],[888,24296,24297],{"xmlns":890},[892,24298,24299,24312],{},[895,24300,24301,24307,24309],{},[1699,24302,24303,24305],{},[898,24304,1773],{},[1750,24306,3751],{},[1750,24308,1766],{},[1742,24310,24311],{},"2375",[902,24313,24314],{"encoding":904},"M^* = 2375",[724,24316,24317,24320,24321,2366],{},[38,24318,24319],{},"Funkce IS"," — dosazením do (7.13) ",[883,24322,24324],{"className":24323},[886],[888,24325,24326],{"xmlns":890},[892,24327,24328,24340],{},[895,24329,24330,24332,24334,24336,24338],{},[898,24331,1666],{},[1750,24333,1766],{},[898,24335,1812],{},[1750,24337,1861],{},[898,24339,1974],{},[902,24341,5105],{"encoding":904},[724,24343,24344],{},[883,24345,24347],{"className":24346},[886],[888,24348,24349],{"xmlns":890},[892,24350,24351,24377],{},[895,24352,24353,24355,24357,24359,24361,24363,24365,24367,24369,24371,24373,24375],{},[898,24354,1666],{},[1750,24356,1766],{},[1742,24358,6657],{},[898,24360,1666],{},[1750,24362,1861],{},[1742,24364,4078],{},[1750,24366,1758],{},[1742,24368,6465],{},[898,24370,1920],{},[1750,24372,1861],{},[1742,24374,8243],{},[1750,24376,1917],{"separator":1916},[902,24378,24379],{"encoding":904},"Y = 0{,}8Y + 100 - 20r + 1000,",[724,24381,24382],{},"tj.",[724,24384,24385],{},[883,24386,24388],{"className":24387},[886],[888,24389,24390],{"xmlns":890},[892,24391,24392,24417],{},[895,24393,24394,24396,24398,24400,24402,24404,24406,24409,24411,24413,24415],{},[1742,24395,3929],{},[898,24397,1666],{},[1750,24399,1861],{},[1742,24401,6465],{},[898,24403,1920],{},[1750,24405,1766],{},[1742,24407,24408],{},"1100.",[2125,24410],{"width":2127},[1750,24412,1753],{"stretchy":1752},[1969,24414,10365],{},[1750,24416,1763],{"stretchy":1752},[902,24418,24419],{"encoding":904},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[724,24421,24422,24425,24426,2366],{},[38,24423,24424],{},"Funkce LM"," — dosazením do (7.15) ",[883,24427,24429],{"className":24428},[886],[888,24430,24431],{"xmlns":890},[892,24432,24433,24457],{},[895,24434,24435,24441,24443,24449,24451],{},[1699,24436,24437,24439],{},[898,24438,1773],{},[1750,24440,3751],{},[1750,24442,1766],{},[5535,24444,24445,24447],{},[898,24446,2046],{},[1742,24448,1744],{},[1750,24450,1861],{},[5535,24452,24453,24455],{},[898,24454,2046],{},[1742,24456,1872],{},[902,24458,24459],{"encoding":904},"M^* = L_1 + L_2",[724,24461,24462],{},[883,24463,24465],{"className":24464},[886],[888,24466,24467],{"xmlns":890},[892,24468,24469,24491],{},[895,24470,24471,24473,24475,24477,24479,24481,24483,24485,24487,24489],{},[1742,24472,24311],{},[1750,24474,1766],{},[1742,24476,12476],{},[898,24478,1666],{},[1750,24480,1758],{},[1742,24482,6419],{},[898,24484,1920],{},[1750,24486,1861],{},[1742,24488,18246],{},[1750,24490,1917],{"separator":1916},[902,24492,24493],{"encoding":904},"2375 = 0{,}1Y - 25r + 2000,",[724,24495,24382],{},[724,24497,24498],{},[883,24499,24501],{"className":24500},[886],[888,24502,24503],{"xmlns":890},[892,24504,24505,24530],{},[895,24506,24507,24509,24511,24513,24515,24517,24519,24522,24524,24526,24528],{},[1742,24508,12476],{},[898,24510,1666],{},[1750,24512,1758],{},[1742,24514,6419],{},[898,24516,1920],{},[1750,24518,1766],{},[1742,24520,24521],{},"375.",[2125,24523],{"width":2127},[1750,24525,1753],{"stretchy":1752},[1969,24527,10400],{},[1750,24529,1763],{"stretchy":1752},[902,24531,24532],{"encoding":904},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[724,24534,24535,24538,24539,24564],{},[38,24536,24537],{},"Řešení soustavy."," Z (IS) vyjádříme ",[883,24540,24542],{"className":24541},[886],[888,24543,24544],{"xmlns":890},[892,24545,24546,24561],{},[895,24547,24548,24550,24552,24555,24557,24559],{},[898,24549,1666],{},[1750,24551,1766],{},[1742,24553,24554],{},"5500",[1750,24556,1758],{},[1742,24558,4078],{},[898,24560,1920],{},[902,24562,24563],{"encoding":904},"Y = 5500 - 100r"," a dosadíme do (LM):",[724,24566,24567],{},[883,24568,24570],{"className":24569},[886],[888,24571,24572],{"xmlns":890},[892,24573,24574,24658],{},[895,24575,24576,24578,24580,24582,24584,24586,24588,24590,24592,24594,24596,24598,24601,24603,24605,24607,24610,24612,24614,24616,24618,24620,24622,24624,24626,24628,24630,24632,24634,24636,24638,24641,24643,24645,24647,24653,24655],{},[1742,24577,12476],{},[1750,24579,1753],{"stretchy":1752},[1742,24581,24554],{},[1750,24583,1758],{},[1742,24585,4078],{},[898,24587,1920],{},[1750,24589,1763],{"stretchy":1752},[1750,24591,1758],{},[1742,24593,6419],{},[898,24595,1920],{},[1750,24597,1766],{},[1742,24599,24600],{},"375",[1969,24602,6766],{},[1750,24604,6769],{},[1969,24606,6766],{},[1742,24608,24609],{},"550",[1750,24611,1758],{},[1742,24613,3079],{},[898,24615,1920],{},[1750,24617,1758],{},[1742,24619,6419],{},[898,24621,1920],{},[1750,24623,1766],{},[1742,24625,24600],{},[1969,24627,6766],{},[1750,24629,6769],{},[1969,24631,6766],{},[1742,24633,6442],{},[898,24635,1920],{},[1750,24637,1766],{},[1742,24639,24640],{},"175",[1969,24642,6766],{},[1750,24644,6769],{},[1969,24646,6766],{},[1699,24648,24649,24651],{},[898,24650,1920],{},[898,24652,1705],{},[1750,24654,1766],{},[1742,24656,24657],{},"5.",[902,24659,24660],{"encoding":904},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[724,24662,24663],{},[38,24664,24665],{},"Zpětné dosazení:",[120,24667,24668,24712,24748],{},[123,24669,24670,1917],{},[883,24671,24673],{"className":24672},[886],[888,24674,24675],{"xmlns":890},[892,24676,24677,24709],{},[895,24678,24679,24685,24687,24689,24691,24693,24695,24697,24699,24701,24703,24705,24707],{},[1699,24680,24681,24683],{},[898,24682,1666],{},[898,24684,1705],{},[1750,24686,1766],{},[1742,24688,24554],{},[1750,24690,1758],{},[1742,24692,4078],{},[1750,24694,8009],{},[1742,24696,7902],{},[1750,24698,1766],{},[1742,24700,24554],{},[1750,24702,1758],{},[1742,24704,7658],{},[1750,24706,1766],{},[1742,24708,9634],{},[902,24710,24711],{"encoding":904},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[123,24713,24714,1917],{},[883,24715,24717],{"className":24716},[886],[888,24718,24719],{"xmlns":890},[892,24720,24721,24745],{},[895,24722,24723,24729,24731,24733,24735,24737,24739,24741,24743],{},[1699,24724,24725,24727],{},[898,24726,1812],{},[898,24728,1705],{},[1750,24730,1766],{},[1742,24732,6657],{},[1750,24734,8009],{},[1742,24736,9634],{},[1750,24738,1861],{},[1742,24740,4078],{},[1750,24742,1766],{},[1742,24744,9679],{},[902,24746,24747],{"encoding":904},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[123,24749,24750,2313],{},[883,24751,24753],{"className":24752},[886],[888,24754,24755],{"xmlns":890},[892,24756,24757,24783],{},[895,24758,24759,24765,24767,24769,24771,24773,24775,24777,24779,24781],{},[1699,24760,24761,24763],{},[898,24762,1974],{},[898,24764,1705],{},[1750,24766,1766],{},[1750,24768,1758],{},[1742,24770,6465],{},[1750,24772,8009],{},[1742,24774,7902],{},[1750,24776,1861],{},[1742,24778,8243],{},[1750,24780,1766],{},[1742,24782,9702],{},[902,24784,24785],{"encoding":904},"I^E = -20 \\cdot 5 + 1000 = 900",[724,24787,24788,1647,24791,24837],{},[38,24789,24790],{},"Ověření:",[883,24792,24794],{"className":24793},[886],[888,24795,24796],{"xmlns":890},[892,24797,24798,24834],{},[895,24799,24800,24806,24808,24814,24816,24818,24820,24822,24824,24826,24828],{},[1699,24801,24802,24804],{},[898,24803,1812],{},[898,24805,1705],{},[1750,24807,1861],{},[1699,24809,24810,24812],{},[898,24811,1974],{},[898,24813,1705],{},[1750,24815,1766],{},[1742,24817,9679],{},[1750,24819,1861],{},[1742,24821,9702],{},[1750,24823,1766],{},[1742,24825,9634],{},[1750,24827,1766],{},[1699,24829,24830,24832],{},[898,24831,1666],{},[898,24833,1705],{},[902,24835,24836],{"encoding":904},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[724,24839,24840],{},[883,24841,24843],{"className":24842},[886],[888,24844,24845],{"xmlns":890},[892,24846,24847,24917],{},[895,24848,24849],{},[3582,24850,24851],{"notation":3584},[3586,24852,24853],{"scriptlevel":2607,"displaystyle":1752},[3586,24854,24855],{"scriptlevel":2607,"displaystyle":1752},[3586,24856,24857],{"scriptlevel":2607,"displaystyle":1916},[895,24858,24859,24861,24867,24869,24871,24873,24876,24882,24884,24886,24888,24890,24896,24898,24900,24902,24904,24910,24912,24915],{},[1969,24860,2658],{},[1699,24862,24863,24865],{},[898,24864,1666],{},[898,24866,1705],{},[1750,24868,1766],{},[1742,24870,9634],{},[1750,24872,1917],{"separator":1916},[2125,24874],{"width":24875},"1em",[1699,24877,24878,24880],{},[898,24879,1920],{},[898,24881,1705],{},[1750,24883,1766],{},[1742,24885,7902],{},[1750,24887,1917],{"separator":1916},[2125,24889],{"width":24875},[1699,24891,24892,24894],{},[898,24893,1812],{},[898,24895,1705],{},[1750,24897,1766],{},[1742,24899,9679],{},[1750,24901,1917],{"separator":1916},[2125,24903],{"width":24875},[1699,24905,24906,24908],{},[898,24907,1974],{},[898,24909,1705],{},[1750,24911,1766],{},[1742,24913,24914],{},"900.",[1969,24916,2658],{},[902,24918,24919],{"encoding":904},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[724,24921,24922],{},[614,24923,24924,24925,24938,24939,24952,24953,24968,24969,24982,24983,24998,24999,25012,25013,25026,25027,2313],{},"Obrázek 7.7 — Konkrétní numerický příklad IS-LM rovnováhy. Na ose ",[883,24926,24928],{"className":24927},[886],[888,24929,24930],{"xmlns":890},[892,24931,24932,24936],{},[895,24933,24934],{},[898,24935,1666],{},[902,24937,1666],{"encoding":904}," jsou vyznačeny hodnoty 3750, 5000, 5500; na ose ",[883,24940,24942],{"className":24941},[886],[888,24943,24944],{"xmlns":890},[892,24945,24946,24950],{},[895,24947,24948],{},[898,24949,1920],{},[902,24951,1920],{"encoding":904}," hodnoty 5 a 55. Přímka ",[883,24954,24956],{"className":24955},[886],[888,24957,24958],{"xmlns":890},[892,24959,24960,24966],{},[895,24961,24962,24964],{},[898,24963,2046],{},[898,24965,1773],{},[902,24967,10400],{"encoding":904}," stoupá z oblasti nízkých ",[883,24970,24972],{"className":24971},[886],[888,24973,24974],{"xmlns":890},[892,24975,24976,24980],{},[895,24977,24978],{},[898,24979,1920],{},[902,24981,1920],{"encoding":904},", přímka ",[883,24984,24986],{"className":24985},[886],[888,24987,24988],{"xmlns":890},[892,24989,24990,24996],{},[895,24991,24992,24994],{},[898,24993,1974],{},[898,24995,1779],{},[902,24997,10365],{"encoding":904}," klesá a protíná osu ",[883,25000,25002],{"className":25001},[886],[888,25003,25004],{"xmlns":890},[892,25005,25006,25010],{},[895,25007,25008],{},[898,25009,1920],{},[902,25011,1920],{"encoding":904}," kolem hodnoty 55. Průsečík ",[883,25014,25016],{"className":25015},[886],[888,25017,25018],{"xmlns":890},[892,25019,25020,25024],{},[895,25021,25022],{},[898,25023,1705],{},[902,25025,1705],{"encoding":904}," leží v bodě ",[883,25028,25030],{"className":25029},[886],[888,25031,25032],{"xmlns":890},[892,25033,25034,25056],{},[895,25035,25036,25038,25040,25042,25044,25046,25048,25050,25052,25054],{},[1750,25037,5141],{"stretchy":1752},[898,25039,1920],{},[1750,25041,1766],{},[1742,25043,7902],{},[1750,25045,1917],{"separator":1916},[1969,25047,7737],{},[898,25049,1666],{},[1750,25051,1766],{},[1742,25053,9634],{},[1750,25055,5158],{"stretchy":1752},[902,25057,25058],{"encoding":904},"[r = 5,\\ Y = 5000]",[115,25060,25062],{"id":25061},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[724,25064,25065,25068,25069,25082,25083,10469,25096,25099,25100,25118,25119,25136,25137,25154,25155,25168,25169,25182],{},[38,25066,25067],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[883,25070,25072],{"className":25071},[886],[888,25073,25074],{"xmlns":890},[892,25075,25076,25080],{},[895,25077,25078],{},[898,25079,1997],{},[902,25081,1997],{"encoding":904}," nebo snížení daní ",[883,25084,25086],{"className":25085},[886],[888,25087,25088],{"xmlns":890},[892,25089,25090,25094],{},[895,25091,25092],{},[898,25093,5326],{},[902,25095,5326],{"encoding":904},[38,25097,25098],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[883,25101,25103],{"className":25102},[886],[888,25104,25105],{"xmlns":890},[892,25106,25107,25115],{},[895,25108,25109],{},[1699,25110,25111,25113],{},[898,25112,1705],{},[1750,25114,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,25116,25117],{"encoding":904},"E'"," má vyšší ",[883,25120,25122],{"className":25121},[886],[888,25123,25124],{"xmlns":890},[892,25125,25126,25134],{},[895,25127,25128],{},[1699,25129,25130,25132],{},[898,25131,1666],{},[898,25133,1705],{},[902,25135,1708],{"encoding":904}," i vyšší ",[883,25138,25140],{"className":25139},[886],[888,25141,25142],{"xmlns":890},[892,25143,25144,25152],{},[895,25145,25146],{},[1699,25147,25148,25150],{},[898,25149,1920],{},[898,25151,1705],{},[902,25153,23526],{"encoding":904}," (vyšší ",[883,25156,25158],{"className":25157},[886],[888,25159,25160],{"xmlns":890},[892,25161,25162,25166],{},[895,25163,25164],{},[898,25165,1666],{},[902,25167,1666],{"encoding":904}," zvedá poptávku po penězích, což tlačí ",[883,25170,25172],{"className":25171},[886],[888,25173,25174],{"xmlns":890},[892,25175,25176,25180],{},[895,25177,25178],{},[898,25179,1920],{},[902,25181,1920],{"encoding":904}," nahoru).",[724,25184,25185],{},[4434,25186],{"alt":25187,"className":25188,"src":25189},"imek-posun-is-lm-politiky",[210,4438],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[724,25191,25192,25195,25196,25213,25214,25217,25218,25235,25236,25253,25254,25267,25268,25287,25288,1783],{},[38,25193,25194],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[883,25197,25199],{"className":25198},[886],[888,25200,25201],{"xmlns":890},[892,25202,25203,25211],{},[895,25204,25205],{},[1699,25206,25207,25209],{},[898,25208,1773],{},[1750,25210,3751],{},[902,25212,21771],{"encoding":904}," národní bankou — ",[38,25215,25216],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[883,25219,25221],{"className":25220},[886],[888,25222,25223],{"xmlns":890},[892,25224,25225,25233],{},[895,25226,25227],{},[1699,25228,25229,25231],{},[898,25230,1920],{},[898,25232,1705],{},[902,25234,23526],{"encoding":904}," a vyšší ",[883,25237,25239],{"className":25238},[886],[888,25240,25241],{"xmlns":890},[892,25242,25243,25251],{},[895,25244,25245],{},[1699,25246,25247,25249],{},[898,25248,1666],{},[898,25250,1705],{},[902,25252,1708],{"encoding":904}," (nižší ",[883,25255,25257],{"className":25256},[886],[888,25258,25259],{"xmlns":890},[892,25260,25261,25265],{},[895,25262,25263],{},[898,25264,1920],{},[902,25266,1920],{"encoding":904}," povzbuzuje investice ",[883,25269,25271],{"className":25270},[886],[888,25272,25273],{"xmlns":890},[892,25274,25275,25285],{},[895,25276,25277,25279,25281,25283],{},[898,25278,1974],{},[1750,25280,1753],{"stretchy":1752},[898,25282,1920],{},[1750,25284,1763],{"stretchy":1752},[902,25286,23835],{"encoding":904},", ty zvedají ",[883,25289,25291],{"className":25290},[886],[888,25292,25293],{"xmlns":890},[892,25294,25295,25299],{},[895,25296,25297],{},[898,25298,1666],{},[902,25300,1666],{"encoding":904},[724,25302,25303,25304,25307],{},"IS-LM tak dává jednotný rámec pro diskusi ",[38,25305,25306],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[115,25309,10461],{"id":10460},[120,25311,25312,25382,25428,25508,25558,25625,25680,25719,25752],{},[123,25313,25314,10469,25345,1343,25362,10951,25379,25381],{},[38,25315,11224,25316],{},[883,25317,25319],{"className":25318},[886],[888,25320,25321],{"xmlns":890},[892,25322,25323,25343],{},[895,25324,25325,25327,25329,25331,25333,25335,25337,25339,25341],{},[898,25326,1974],{},[1750,25328,1753],{"stretchy":1752},[898,25330,1920],{},[1750,25332,1763],{"stretchy":1752},[1750,25334,1766],{},[898,25336,9365],{},[898,25338,1920],{},[1750,25340,1861],{},[898,25342,3429],{},[902,25344,9374],{"encoding":904},[883,25346,25348],{"className":25347},[886],[888,25349,25350],{"xmlns":890},[892,25351,25352,25360],{},[895,25353,25354,25356,25358],{},[898,25355,9365],{},[1750,25357,2624],{},[1742,25359,2607],{},[902,25361,9393],{"encoding":904},[883,25363,25365],{"className":25364},[886],[888,25366,25367],{"xmlns":890},[892,25368,25369,25377],{},[895,25370,25371,25373,25375],{},[898,25372,3429],{},[1750,25374,2604],{},[1742,25376,2607],{},[902,25378,11288],{"encoding":904},[38,25380,22130],{}," funkce úrokové míry.",[123,25383,25384,25387,25388,25409,25410,25427],{},[38,25385,25386],{},"Trh zboží"," — rovnováha ",[883,25389,25391],{"className":25390},[886],[888,25392,25393],{"xmlns":890},[892,25394,25395,25407],{},[895,25396,25397,25399,25401,25403,25405],{},[898,25398,1666],{},[1750,25400,1766],{},[898,25402,1812],{},[1750,25404,1861],{},[898,25406,1974],{},[902,25408,5105],{"encoding":904},", ekvivalentně ",[883,25411,25413],{"className":25412},[886],[888,25414,25415],{"xmlns":890},[892,25416,25417,25425],{},[895,25418,25419,25421,25423],{},[898,25420,1974],{},[1750,25422,1766],{},[898,25424,1779],{},[902,25426,10384],{"encoding":904}," (investice = úspory).",[123,25429,25430,2084,25432,25434,25435,25484,25485,22522,25487,2313],{},[38,25431,9430],{},[614,25433,9433],{},") — ",[883,25436,25438],{"className":25437},[886],[888,25439,25440],{"xmlns":890},[892,25441,25442,25482],{},[895,25443,25444,25446,25448,25460,25462,25464],{},[898,25445,1666],{},[1750,25447,1766],{},[3423,25449,25450,25452],{},[898,25451,9365],{},[895,25453,25454,25456,25458],{},[1742,25455,1744],{},[1750,25457,1758],{},[898,25459,207],{},[898,25461,1920],{},[1750,25463,1861],{},[3423,25465,25466,25474],{},[895,25467,25468,25470,25472],{},[898,25469,2573],{},[1750,25471,1861],{},[898,25473,3429],{},[895,25475,25476,25478,25480],{},[1742,25477,1744],{},[1750,25479,1758],{},[898,25481,207],{},[902,25483,11347],{"encoding":904}," (7.14); ",[38,25486,22130],{},[883,25488,25490],{"className":25489},[886],[888,25491,25492],{"xmlns":890},[892,25493,25494,25506],{},[895,25495,25496,25498,25500,25502,25504],{},[1750,25497,1753],{"stretchy":1752},[898,25499,1920],{},[1750,25501,1917],{"separator":1916},[898,25503,1666],{},[1750,25505,1763],{"stretchy":1752},[902,25507,9456],{"encoding":904},[123,25509,25510,25387,25513,25539,25540,2313],{},[38,25511,25512],{},"Trh peněz",[883,25514,25516],{"className":25515},[886],[888,25517,25518],{"xmlns":890},[892,25519,25520,25536],{},[895,25521,25522,25528,25530],{},[1699,25523,25524,25526],{},[898,25525,1773],{},[898,25527,5541],{},[1750,25529,1766],{},[1699,25531,25532,25534],{},[898,25533,1773],{},[898,25535,1779],{},[902,25537,25538],{"encoding":904},"M^D = M^S"," při pevné nabídce ",[883,25541,25543],{"className":25542},[886],[888,25544,25545],{"xmlns":890},[892,25546,25547,25555],{},[895,25548,25549],{},[1699,25550,25551,25553],{},[898,25552,1773],{},[1750,25554,3751],{},[902,25556,25557],{"encoding":904},"M^* ",[123,25559,25560,10469,25563,2313],{},[38,25561,25562],{},"Transakční, opatrnostní, spekulační poptávka",[883,25564,25566],{"className":25565},[886],[888,25567,25568],{"xmlns":890},[892,25569,25570,25622],{},[895,25571,25572,25578,25580,25586,25588,25594,25596,25602,25604,25606,25612,25614,25616],{},[1699,25573,25574,25576],{},[898,25575,1773],{},[898,25577,5541],{},[1750,25579,1766],{},[5535,25581,25582,25584],{},[898,25583,2046],{},[1742,25585,1744],{},[1750,25587,1861],{},[5535,25589,25590,25592],{},[898,25591,2046],{},[1742,25593,1872],{},[1750,25595,1766],{},[5535,25597,25598,25600],{},[898,25599,9535],{},[1742,25601,1744],{},[898,25603,1666],{},[1750,25605,1861],{},[5535,25607,25608,25610],{},[898,25609,9535],{},[1742,25611,1872],{},[898,25613,1920],{},[1750,25615,1861],{},[5535,25617,25618,25620],{},[898,25619,9535],{},[1742,25621,7822],{},[902,25623,25624],{"encoding":904},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[123,25626,25627,2084,25629,25434,25631,25676,25677,25679],{},[38,25628,9483],{},[614,25630,9486],{},[883,25632,25634],{"className":25633},[886],[888,25635,25636],{"xmlns":890},[892,25637,25638,25674],{},[895,25639,25640,25646,25648,25654,25656,25658,25664,25666,25668],{},[1699,25641,25642,25644],{},[898,25643,1773],{},[1750,25645,3751],{},[1750,25647,1766],{},[5535,25649,25650,25652],{},[898,25651,9535],{},[1742,25653,1744],{},[898,25655,1666],{},[1750,25657,1861],{},[5535,25659,25660,25662],{},[898,25661,9535],{},[1742,25663,1872],{},[898,25665,1920],{},[1750,25667,1861],{},[5535,25669,25670,25672],{},[898,25671,9535],{},[1742,25673,7822],{},[902,25675,11401],{"encoding":904}," (7.15); ",[38,25678,23261],{}," přímka.",[123,25681,25682,11446,25685,25718],{},[38,25683,25684],{},"Simultánní rovnováha",[883,25686,25688],{"className":25687},[886],[888,25689,25690],{"xmlns":890},[892,25691,25692,25716],{},[895,25693,25694,25696,25698,25700,25706,25708,25714],{},[898,25695,1705],{},[1750,25697,1766],{},[1750,25699,1753],{"stretchy":1752},[1699,25701,25702,25704],{},[898,25703,1920],{},[898,25705,1705],{},[1750,25707,1917],{"separator":1916},[1699,25709,25710,25712],{},[898,25711,1666],{},[898,25713,1705],{},[1750,25715,1763],{"stretchy":1752},[902,25717,9600],{"encoding":904}," křivek IS a LM.",[123,25720,25721,25724,25725,1343,25738,25751],{},[38,25722,25723],{},"Fiskální politika"," — nástroje ",[883,25726,25728],{"className":25727},[886],[888,25729,25730],{"xmlns":890},[892,25731,25732,25736],{},[895,25733,25734],{},[898,25735,1997],{},[902,25737,1997],{"encoding":904},[883,25739,25741],{"className":25740},[886],[888,25742,25743],{"xmlns":890},[892,25744,25745,25749],{},[895,25746,25747],{},[898,25748,5326],{},[902,25750,5326],{"encoding":904}," posouvající křivku IS.",[123,25753,25754,25757,25758,25775],{},[38,25755,25756],{},"Monetární politika"," — nástroj ",[883,25759,25761],{"className":25760},[886],[888,25762,25763],{"xmlns":890},[892,25764,25765,25773],{},[895,25766,25767],{},[1699,25768,25769,25771],{},[898,25770,1773],{},[1750,25772,3751],{},[902,25774,21771],{"encoding":904}," posouvající křivku LM.",[115,25777,11524],{"id":11523},[120,25779,25780,25787,25794,25803],{},[123,25781,25782,1647,25784],{},[38,25783,11531],{},[207,25785,11535],{"className":25786,"dataFsResolvedFilePath":1644,"href":1645},[210],[123,25788,25789,1647,25791],{},[38,25790,11540],{},[207,25792,11544],{"className":25793,"dataFsResolvedFilePath":868,"href":869},[210],[123,25795,25796,1647,25799,25802],{},[38,25797,25798],{},"Nadřazené téma:",[207,25800,11659],{"className":25801,"dataFsResolvedFilePath":934,"href":935},[210]," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[123,25804,25805,25807],{},[38,25806,11549],{},[120,25808,25809,25815,25821],{},[123,25810,25811,25814],{},[207,25812,11564],{"className":25813,"dataFsResolvedFilePath":800,"href":801},[210]," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[123,25816,25817,25820],{},[207,25818,1145],{"className":25819,"dataFsResolvedFilePath":764,"href":765},[210]," — matematický základ pro směrnice IS a LM",[123,25822,25823,25827],{},[207,25824,25826],{"className":25825,"dataFsResolvedFilePath":782,"href":783},[210],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":641,"searchDepth":642,"depth":642,"links":25829},[25830,25831,25832,25833,25834,25835,25836,25837,25838,25839],{"id":1636,"depth":642,"text":1637},{"id":21781,"depth":642,"text":21782},{"id":21988,"depth":642,"text":21989},{"id":22279,"depth":642,"text":22280},{"id":22687,"depth":642,"text":22688},{"id":23478,"depth":642,"text":23479},{"id":24163,"depth":642,"text":24164},{"id":25061,"depth":642,"text":25062},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Fis-lm",{"title":21631,"description":641},[1138,1137],"topics\u002Fis-lm",[1128,11557,1143,25846,25847,25848,25849,11659],"trh-zbozi","trh-penez","urokova-mira","investice","OcXqlUxNqiCsj643lVoQEu_ZWU2vH0D_lWZ_-SxoyHk",{"id":25852,"title":25853,"body":25854,"course":659,"courses":27447,"created":1129,"description":27448,"extension":661,"meta":27449,"navigation":664,"path":27450,"seo":27451,"sources":27452,"stem":27453,"tags":27454,"type":11664,"updated":677,"__hash__":27456},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":9,"value":25855,"toc":27435},[25856,25859,25955,25962,25982,25986,25991,26054,26073,26075,26078,26214,26216,26426,26460,26597,26601,26665,26681,26709,26713,26811,26815,26819,26872,26978,27192,27196,27239,27345,27397,27399],[12,25857,25853],{"id":25858},"lagrangeova-metoda-vázané-extrémy",[724,25860,25861,25862,13577,25885,25917,25918,25921,25922,25949,25950,25954],{},"Hledáme extrém funkce ",[883,25863,25865],{"className":25864},[886],[888,25866,25867],{"xmlns":890},[892,25868,25869,25883],{},[895,25870,25871,25873,25875,25877,25879,25881],{},[898,25872,11722],{},[1750,25874,1753],{"stretchy":1752},[898,25876,11727],{},[1750,25878,1917],{"separator":1916},[898,25880,11717],{},[1750,25882,1763],{"stretchy":1752},[902,25884,19478],{"encoding":904},[883,25886,25888],{"className":25887},[886],[888,25889,25890],{"xmlns":890},[892,25891,25892,25914],{},[895,25893,25894,25896,25898,25904,25906,25912],{},[898,25895,900],{},[1750,25897,1753],{"stretchy":1752},[5535,25899,25900,25902],{},[898,25901,12471],{},[1742,25903,1744],{},[1750,25905,1917],{"separator":1916},[5535,25907,25908,25910],{},[898,25909,12471],{},[1742,25911,1872],{},[1750,25913,1763],{"stretchy":1752},[902,25915,25916],{"encoding":904},"U(Q_1, Q_2)"," apod.) ",[38,25919,25920],{},"podmíněný"," rovnicí ",[883,25923,25925],{"className":25924},[886],[888,25926,25927],{"xmlns":890},[892,25928,25929,25947],{},[895,25930,25931,25933,25935,25937,25939,25941,25943,25945],{},[898,25932,2655],{},[1750,25934,1753],{"stretchy":1752},[898,25936,11727],{},[1750,25938,1917],{"separator":1916},[898,25940,11717],{},[1750,25942,1763],{"stretchy":1752},[1750,25944,1766],{},[1742,25946,2607],{},[902,25948,20690],{"encoding":904},". V ",[207,25951,25953],{"className":25952,"dataFsResolvedFilePath":1644,"href":1645},[210],"matematické ekonomii"," se používá pro:",[724,25956,25957],{},[4434,25958],{"alt":25959,"className":25960,"src":25961},"imek-lagrange-tecnost",[210,4438],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[120,25963,25964,25973,25979],{},[123,25965,25966,25969,25970,1763],{},[38,25967,25968],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[207,25971,19409],{"className":25972,"dataFsResolvedFilePath":878,"href":879},[210],[123,25974,25975,25978],{},[38,25976,25977],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[123,25980,25981],{},"Optimalizaci produkce \u002F nákladů za omezení",[115,25983,25985],{"id":25984},"princip","Princip",[724,25987,20340,25988,2366],{},[38,25989,25990],{},"Lagrangeovu funkci",[724,25992,25993],{},[883,25994,25996],{"className":25995},[886],[888,25997,25998],{"xmlns":890},[892,25999,26000,26051],{},[895,26001,26002,26004,26006,26008,26010,26012,26014,26017,26019,26021,26023,26025,26027,26029,26031,26033,26035,26037,26039,26041,26043,26045,26047,26049],{},[898,26003,2046],{},[1750,26005,1753],{"stretchy":1752},[898,26007,11727],{},[1750,26009,1917],{"separator":1916},[898,26011,11717],{},[1750,26013,1917],{"separator":1916},[898,26015,26016],{},"λ",[1750,26018,1763],{"stretchy":1752},[1750,26020,1766],{},[898,26022,11722],{},[1750,26024,1753],{"stretchy":1752},[898,26026,11727],{},[1750,26028,1917],{"separator":1916},[898,26030,11717],{},[1750,26032,1763],{"stretchy":1752},[1750,26034,1861],{},[898,26036,26016],{},[1969,26038,2658],{},[898,26040,2655],{},[1750,26042,1753],{"stretchy":1752},[898,26044,11727],{},[1750,26046,1917],{"separator":1916},[898,26048,11717],{},[1750,26050,1763],{"stretchy":1752},[902,26052,26053],{"encoding":904},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[724,26055,2590,26056,2433,26070,2313],{},[883,26057,26059],{"className":26058},[886],[888,26060,26061],{"xmlns":890},[892,26062,26063,26067],{},[895,26064,26065],{},[898,26066,26016],{},[902,26068,26069],{"encoding":904},"\\lambda",[38,26071,26072],{},"Lagrangeův multiplikátor",[115,26074,12925],{"id":12924},[724,26076,26077],{},"Řešíme soustavu:",[724,26079,26080,26128,26176],{},[883,26081,26083],{"className":26082},[886],[888,26084,26085],{"xmlns":890},[892,26086,26087,26125],{},[895,26088,26089,26097,26099,26107,26109,26111,26113,26121,26123],{},[5950,26090,26091,26093,26095],{},[898,26092,2046],{},[898,26094,11727],{},[1750,26096,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26098,1766],{},[5950,26100,26101,26103,26105],{},[898,26102,11722],{},[898,26104,11727],{},[1750,26106,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26108,1861],{},[898,26110,26016],{},[1969,26112,2658],{},[5950,26114,26115,26117,26119],{},[898,26116,2655],{},[898,26118,11727],{},[1750,26120,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26122,1766],{},[1742,26124,2607],{},[902,26126,26127],{"encoding":904},"L'_x = f'_x + \\lambda\\, g'_x = 0",[883,26129,26131],{"className":26130},[886],[888,26132,26133],{"xmlns":890},[892,26134,26135,26173],{},[895,26136,26137,26145,26147,26155,26157,26159,26161,26169,26171],{},[5950,26138,26139,26141,26143],{},[898,26140,2046],{},[898,26142,11717],{},[1750,26144,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26146,1766],{},[5950,26148,26149,26151,26153],{},[898,26150,11722],{},[898,26152,11717],{},[1750,26154,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26156,1861],{},[898,26158,26016],{},[1969,26160,2658],{},[5950,26162,26163,26165,26167],{},[898,26164,2655],{},[898,26166,11717],{},[1750,26168,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26170,1766],{},[1742,26172,2607],{},[902,26174,26175],{"encoding":904},"L'_y = f'_y + \\lambda\\, g'_y = 0",[883,26177,26179],{"className":26178},[886],[888,26180,26181],{"xmlns":890},[892,26182,26183,26211],{},[895,26184,26185,26193,26195,26197,26199,26201,26203,26205,26207,26209],{},[5950,26186,26187,26189,26191],{},[898,26188,2046],{},[898,26190,26016],{},[1750,26192,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26194,1766],{},[898,26196,2655],{},[1750,26198,1753],{"stretchy":1752},[898,26200,11727],{},[1750,26202,1917],{"separator":1916},[898,26204,11717],{},[1750,26206,1763],{"stretchy":1752},[1750,26208,1766],{},[1742,26210,2607],{},[902,26212,26213],{"encoding":904},"L'_\\lambda = g(x, y) = 0",[115,26215,12999],{"id":12998},[724,26217,26218],{},[883,26219,26221],{"className":26220},[886],[888,26222,26223],{"xmlns":890},[892,26224,26225,26423],{},[895,26226,26227,26229,26231,26233,26235,26237,26239,26241,26243,26245,26247,26263,26265,26267,26283,26285,26287,26295,26301,26303,26305,26321,26323,26325,26341,26343,26345,26353,26359,26361,26363,26365,26381,26383,26385,26401,26403,26405,26413,26415],{},[898,26228,5541],{},[1750,26230,1753],{"stretchy":1752},[898,26232,11727],{},[1750,26234,1917],{"separator":1916},[898,26236,11717],{},[1750,26238,1917],{"separator":1916},[898,26240,26016],{},[1750,26242,1763],{"stretchy":1752},[1750,26244,1766],{},[1750,26246,1753],{"stretchy":1752},[5950,26248,26249,26251,26257],{},[898,26250,11722],{},[895,26252,26253,26255],{},[898,26254,11727],{},[898,26256,11727],{},[895,26258,26259,26261],{},[1750,26260,3815],{"mathvariant":1747},[1750,26262,3815],{"mathvariant":1747},[1750,26264,1861],{},[898,26266,26016],{},[5950,26268,26269,26271,26277],{},[898,26270,2655],{},[895,26272,26273,26275],{},[898,26274,11727],{},[898,26276,11727],{},[895,26278,26279,26281],{},[1750,26280,3815],{"mathvariant":1747},[1750,26282,3815],{"mathvariant":1747},[1750,26284,1763],{"stretchy":1752},[1750,26286,1753],{"stretchy":1752},[5950,26288,26289,26291,26293],{},[898,26290,2655],{},[898,26292,11717],{},[1750,26294,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1699,26296,26297,26299],{},[1750,26298,1763],{"stretchy":1752},[1742,26300,1872],{},[1750,26302,1861],{},[1750,26304,1753],{"stretchy":1752},[5950,26306,26307,26309,26315],{},[898,26308,11722],{},[895,26310,26311,26313],{},[898,26312,11717],{},[898,26314,11717],{},[895,26316,26317,26319],{},[1750,26318,3815],{"mathvariant":1747},[1750,26320,3815],{"mathvariant":1747},[1750,26322,1861],{},[898,26324,26016],{},[5950,26326,26327,26329,26335],{},[898,26328,2655],{},[895,26330,26331,26333],{},[898,26332,11717],{},[898,26334,11717],{},[895,26336,26337,26339],{},[1750,26338,3815],{"mathvariant":1747},[1750,26340,3815],{"mathvariant":1747},[1750,26342,1763],{"stretchy":1752},[1750,26344,1753],{"stretchy":1752},[5950,26346,26347,26349,26351],{},[898,26348,2655],{},[898,26350,11727],{},[1750,26352,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1699,26354,26355,26357],{},[1750,26356,1763],{"stretchy":1752},[1742,26358,1872],{},[1750,26360,1758],{},[1742,26362,1872],{},[1750,26364,1753],{"stretchy":1752},[5950,26366,26367,26369,26375],{},[898,26368,11722],{},[895,26370,26371,26373],{},[898,26372,11727],{},[898,26374,11717],{},[895,26376,26377,26379],{},[1750,26378,3815],{"mathvariant":1747},[1750,26380,3815],{"mathvariant":1747},[1750,26382,1861],{},[898,26384,26016],{},[5950,26386,26387,26389,26395],{},[898,26388,2655],{},[895,26390,26391,26393],{},[898,26392,11727],{},[898,26394,11717],{},[895,26396,26397,26399],{},[1750,26398,3815],{"mathvariant":1747},[1750,26400,3815],{"mathvariant":1747},[1750,26402,1763],{"stretchy":1752},[1969,26404,2658],{},[5950,26406,26407,26409,26411],{},[898,26408,2655],{},[898,26410,11727],{},[1750,26412,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,26414,2658],{},[5950,26416,26417,26419,26421],{},[898,26418,2655],{},[898,26420,11717],{},[1750,26422,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,26424,26425],{"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",[724,26427,26428,26429,26459],{},"Je-li ",[883,26430,26432],{"className":26431},[886],[888,26433,26434],{"xmlns":890},[892,26435,26436,26456],{},[895,26437,26438,26440,26442,26444,26446,26448,26454],{},[1750,26439,5141],{"stretchy":1752},[898,26441,207],{},[1750,26443,1917],{"separator":1916},[898,26445,2573],{},[1750,26447,1917],{"separator":1916},[5535,26449,26450,26452],{},[898,26451,26016],{},[1742,26453,2607],{},[1750,26455,5158],{"stretchy":1752},[902,26457,26458],{"encoding":904},"[a, b, \\lambda_0]"," podezřelý bod:",[120,26461,26462,26530],{},[123,26463,26464,13086,26500,26502,26503],{},[883,26465,26467],{"className":26466},[886],[888,26468,26469],{"xmlns":890},[892,26470,26471,26497],{},[895,26472,26473,26475,26477,26479,26481,26483,26485,26491,26493,26495],{},[898,26474,5541],{},[1750,26476,1753],{"stretchy":1752},[898,26478,207],{},[1750,26480,1917],{"separator":1916},[898,26482,2573],{},[1750,26484,1917],{"separator":1916},[5535,26486,26487,26489],{},[898,26488,26016],{},[1742,26490,2607],{},[1750,26492,1763],{"stretchy":1752},[1750,26494,2624],{},[1742,26496,2607],{},[902,26498,26499],{"encoding":904},"D(a, b, \\lambda_0) \u003C 0",[38,26501,13387],{}," vázané podmínkou ",[883,26504,26506],{"className":26505},[886],[888,26507,26508],{"xmlns":890},[892,26509,26510,26528],{},[895,26511,26512,26514,26516,26518,26520,26522,26524,26526],{},[898,26513,2655],{},[1750,26515,1753],{"stretchy":1752},[898,26517,11727],{},[1750,26519,1917],{"separator":1916},[898,26521,11717],{},[1750,26523,1763],{"stretchy":1752},[1750,26525,1766],{},[1742,26527,2607],{},[902,26529,20690],{"encoding":904},[123,26531,26532,13086,26568,26502,26570],{},[883,26533,26535],{"className":26534},[886],[888,26536,26537],{"xmlns":890},[892,26538,26539,26565],{},[895,26540,26541,26543,26545,26547,26549,26551,26553,26559,26561,26563],{},[898,26542,5541],{},[1750,26544,1753],{"stretchy":1752},[898,26546,207],{},[1750,26548,1917],{"separator":1916},[898,26550,2573],{},[1750,26552,1917],{"separator":1916},[5535,26554,26555,26557],{},[898,26556,26016],{},[1742,26558,2607],{},[1750,26560,1763],{"stretchy":1752},[1750,26562,2604],{},[1742,26564,2607],{},[902,26566,26567],{"encoding":904},"D(a, b, \\lambda_0) > 0",[38,26569,13445],{},[883,26571,26573],{"className":26572},[886],[888,26574,26575],{"xmlns":890},[892,26576,26577,26595],{},[895,26578,26579,26581,26583,26585,26587,26589,26591,26593],{},[898,26580,2655],{},[1750,26582,1753],{"stretchy":1752},[898,26584,11727],{},[1750,26586,1917],{"separator":1916},[898,26588,11717],{},[1750,26590,1763],{"stretchy":1752},[1750,26592,1766],{},[1742,26594,2607],{},[902,26596,20690],{"encoding":904},[115,26598,26600],{"id":26599},"význam-multiplikátoru","Význam multiplikátoru",[724,26602,26603],{},[883,26604,26606],{"className":26605},[886],[888,26607,26608],{"xmlns":890},[892,26609,26610,26662],{},[895,26611,26612,26614,26616,26638,26640],{},[898,26613,26016],{},[1750,26615,1766],{},[3423,26617,26618,26626],{},[5950,26619,26620,26622,26624],{},[898,26621,11722],{},[898,26623,11727],{},[1750,26625,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[895,26627,26628,26630],{},[1750,26629,1758],{},[5950,26631,26632,26634,26636],{},[898,26633,2655],{},[898,26635,11727],{},[1750,26637,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26639,1766],{},[3423,26641,26642,26650],{},[5950,26643,26644,26646,26648],{},[898,26645,11722],{},[898,26647,11717],{},[1750,26649,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[895,26651,26652,26654],{},[1750,26653,1758],{},[5950,26655,26656,26658,26660],{},[898,26657,2655],{},[898,26659,11717],{},[1750,26661,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,26663,26664],{"encoding":904},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[724,26666,26667,26680],{},[883,26668,26670],{"className":26669},[886],[888,26671,26672],{"xmlns":890},[892,26673,26674,26678],{},[895,26675,26676],{},[898,26677,26016],{},[902,26679,26069],{"encoding":904}," udává:",[120,26682,26683,26689],{},[123,26684,26685,26686],{},"konstantní ",[38,26687,26688],{},"poměr mezi mezním prospěchem a mezním nákladem",[123,26690,26691,26694,26695,26708],{},[38,26692,26693],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[883,26696,26698],{"className":26697},[886],[888,26699,26700],{"xmlns":890},[892,26701,26702,26706],{},[895,26703,26704],{},[898,26705,11722],{},[902,26707,11722],{"encoding":904},", uvolní-li se omezení o jednotku",[115,26710,26712],{"id":26711},"alternativní-postup","Alternativní postup",[724,26714,26715,26716,26743,26744,26768,26769,26793,26794,26807,26808,2313],{},"Lze-li z ",[883,26717,26719],{"className":26718},[886],[888,26720,26721],{"xmlns":890},[892,26722,26723,26741],{},[895,26724,26725,26727,26729,26731,26733,26735,26737,26739],{},[898,26726,2655],{},[1750,26728,1753],{"stretchy":1752},[898,26730,11727],{},[1750,26732,1917],{"separator":1916},[898,26734,11717],{},[1750,26736,1763],{"stretchy":1752},[1750,26738,1766],{},[1742,26740,2607],{},[902,26742,20690],{"encoding":904}," vyjádřit ",[883,26745,26747],{"className":26746},[886],[888,26748,26749],{"xmlns":890},[892,26750,26751,26765],{},[895,26752,26753,26755,26757,26759,26761,26763],{},[898,26754,11717],{},[1750,26756,1766],{},[898,26758,11717],{},[1750,26760,1753],{"stretchy":1752},[898,26762,11727],{},[1750,26764,1763],{"stretchy":1752},[902,26766,26767],{"encoding":904},"y = y(x)"," (nebo ",[883,26770,26772],{"className":26771},[886],[888,26773,26774],{"xmlns":890},[892,26775,26776,26790],{},[895,26777,26778,26780,26782,26784,26786,26788],{},[898,26779,11727],{},[1750,26781,1766],{},[898,26783,11727],{},[1750,26785,1753],{"stretchy":1752},[898,26787,11717],{},[1750,26789,1763],{"stretchy":1752},[902,26791,26792],{"encoding":904},"x = x(y)","), dosadíme do ",[883,26795,26797],{"className":26796},[886],[888,26798,26799],{"xmlns":890},[892,26800,26801,26805],{},[895,26802,26803],{},[898,26804,11722],{},[902,26806,11722],{"encoding":904}," a převedeme na ",[38,26809,26810],{},"extrém funkce jedné proměnné",[115,26812,26814],{"id":26813},"použití-v-imek","Použití v ImeK",[198,26816,26818],{"id":26817},"maximalizace-užitečnosti","Maximalizace užitečnosti",[724,26820,26821,26822,2313],{},"Rozpočtové omezení: ",[883,26823,26825],{"className":26824},[886],[888,26826,26827],{"xmlns":890},[892,26828,26829,26869],{},[895,26830,26831,26837,26839,26847,26853,26855,26863],{},[1699,26832,26833,26835],{},[898,26834,1666],{},[1750,26836,3751],{},[1750,26838,1766],{},[5950,26840,26841,26843,26845],{},[898,26842,1776],{},[1742,26844,1744],{},[1750,26846,3751],{},[5535,26848,26849,26851],{},[898,26850,12471],{},[1742,26852,1744],{},[1750,26854,1861],{},[5950,26856,26857,26859,26861],{},[898,26858,1776],{},[1742,26860,1872],{},[1750,26862,3751],{},[5535,26864,26865,26867],{},[898,26866,12471],{},[1742,26868,1872],{},[902,26870,26871],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2",[724,26873,26874],{},[883,26875,26877],{"className":26876},[886],[888,26878,26879],{"xmlns":890},[892,26880,26881,26975],{},[895,26882,26883,26885,26887,26893,26895,26901,26903,26905,26907,26909,26911,26913,26919,26921,26927,26929,26931,26933,26935,26941,26943,26951,26957,26959,26967,26973],{},[898,26884,2046],{},[1750,26886,1753],{"stretchy":1752},[5535,26888,26889,26891],{},[898,26890,12471],{},[1742,26892,1744],{},[1750,26894,1917],{"separator":1916},[5535,26896,26897,26899],{},[898,26898,12471],{},[1742,26900,1872],{},[1750,26902,1917],{"separator":1916},[898,26904,26016],{},[1750,26906,1763],{"stretchy":1752},[1750,26908,1766],{},[898,26910,900],{},[1750,26912,1753],{"stretchy":1752},[5535,26914,26915,26917],{},[898,26916,12471],{},[1742,26918,1744],{},[1750,26920,1917],{"separator":1916},[5535,26922,26923,26925],{},[898,26924,12471],{},[1742,26926,1872],{},[1750,26928,1763],{"stretchy":1752},[1750,26930,1861],{},[898,26932,26016],{},[1750,26934,1753],{"stretchy":1752},[1699,26936,26937,26939],{},[898,26938,1666],{},[1750,26940,3751],{},[1750,26942,1758],{},[5950,26944,26945,26947,26949],{},[898,26946,1776],{},[1742,26948,1744],{},[1750,26950,3751],{},[5535,26952,26953,26955],{},[898,26954,12471],{},[1742,26956,1744],{},[1750,26958,1758],{},[5950,26960,26961,26963,26965],{},[898,26962,1776],{},[1742,26964,1872],{},[1750,26966,3751],{},[5535,26968,26969,26971],{},[898,26970,12471],{},[1742,26972,1872],{},[1750,26974,1763],{"stretchy":1752},[902,26976,26977],{"encoding":904},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[724,26979,26980,26981,1343,27013,1343,27045,27094,27095,27149,27150,2313],{},"Soustava: ",[883,26982,26984],{"className":26983},[886],[888,26985,26986],{"xmlns":890},[892,26987,26988,27010],{},[895,26989,26990,26998,27000,27002],{},[5950,26991,26992,26994,26996],{},[898,26993,900],{},[1742,26995,1744],{},[1750,26997,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,26999,1766],{},[898,27001,26016],{},[5950,27003,27004,27006,27008],{},[898,27005,1776],{},[1742,27007,1744],{},[1750,27009,3751],{},[902,27011,27012],{"encoding":904},"U'_1 = \\lambda P_1^*",[883,27014,27016],{"className":27015},[886],[888,27017,27018],{"xmlns":890},[892,27019,27020,27042],{},[895,27021,27022,27030,27032,27034],{},[5950,27023,27024,27026,27028],{},[898,27025,900],{},[1742,27027,1872],{},[1750,27029,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,27031,1766],{},[898,27033,26016],{},[5950,27035,27036,27038,27040],{},[898,27037,1776],{},[1742,27039,1872],{},[1750,27041,3751],{},[902,27043,27044],{"encoding":904},"U'_2 = \\lambda P_2^*",[883,27046,27048],{"className":27047},[886],[888,27049,27050],{"xmlns":890},[892,27051,27052,27092],{},[895,27053,27054,27060,27062,27070,27076,27078,27086],{},[1699,27055,27056,27058],{},[898,27057,1666],{},[1750,27059,3751],{},[1750,27061,1766],{},[5950,27063,27064,27066,27068],{},[898,27065,1776],{},[1742,27067,1744],{},[1750,27069,3751],{},[5535,27071,27072,27074],{},[898,27073,12471],{},[1742,27075,1744],{},[1750,27077,1861],{},[5950,27079,27080,27082,27084],{},[898,27081,1776],{},[1742,27083,1872],{},[1750,27085,3751],{},[5535,27087,27088,27090],{},[898,27089,12471],{},[1742,27091,1872],{},[902,27093,26871],{"encoding":904},". Z prvních dvou: ",[883,27096,27098],{"className":27097},[886],[888,27099,27100],{"xmlns":890},[892,27101,27102,27146],{},[895,27103,27104,27124,27126],{},[3586,27105,27106],{"scriptlevel":2607,"displaystyle":1752},[3423,27107,27108,27116],{},[5950,27109,27110,27112,27114],{},[898,27111,900],{},[1742,27113,1744],{},[1750,27115,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,27117,27118,27120,27122],{},[898,27119,900],{},[1742,27121,1872],{},[1750,27123,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,27125,1766],{},[3586,27127,27128],{"scriptlevel":2607,"displaystyle":1752},[3423,27129,27130,27138],{},[5950,27131,27132,27134,27136],{},[898,27133,1776],{},[1742,27135,1744],{},[1750,27137,3751],{},[5950,27139,27140,27142,27144],{},[898,27141,1776],{},[1742,27143,1872],{},[1750,27145,3751],{},[902,27147,27148],{"encoding":904},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[883,27151,27153],{"className":27152},[886],[888,27154,27155],{"xmlns":890},[892,27156,27157,27189],{},[895,27158,27159,27161,27163,27165,27167,27169],{},[898,27160,1773],{},[898,27162,13658],{},[898,27164,1812],{},[898,27166,1779],{},[1750,27168,1766],{},[3586,27170,27171],{"scriptlevel":2607,"displaystyle":1752},[3423,27172,27173,27181],{},[5950,27174,27175,27177,27179],{},[898,27176,1776],{},[1742,27178,1744],{},[1750,27180,3751],{},[5950,27182,27183,27185,27187],{},[898,27184,1776],{},[1742,27186,1872],{},[1750,27188,3751],{},[902,27190,27191],{"encoding":904},"MRCS = \\tfrac{P_1^*}{P_2^*}",[198,27193,27195],{"id":27194},"minimalizace-výdajů","Minimalizace výdajů",[724,27197,27198,27199,2313],{},"Podmínka dané užitečnosti ",[883,27200,27202],{"className":27201},[886],[888,27203,27204],{"xmlns":890},[892,27205,27206,27236],{},[895,27207,27208,27214,27216,27218,27220,27226,27228,27234],{},[1699,27209,27210,27212],{},[898,27211,900],{},[1750,27213,3751],{},[1750,27215,1766],{},[898,27217,900],{},[1750,27219,1753],{"stretchy":1752},[5535,27221,27222,27224],{},[898,27223,12471],{},[1742,27225,1744],{},[1750,27227,1917],{"separator":1916},[5535,27229,27230,27232],{},[898,27231,12471],{},[1742,27233,1872],{},[1750,27235,1763],{"stretchy":1752},[902,27237,27238],{"encoding":904},"U^* = U(Q_1, Q_2)",[724,27240,27241],{},[883,27242,27244],{"className":27243},[886],[888,27245,27246],{"xmlns":890},[892,27247,27248,27342],{},[895,27249,27250,27252,27254,27260,27262,27268,27270,27272,27274,27276,27284,27290,27292,27300,27306,27308,27310,27312,27318,27320,27322,27324,27330,27332,27338,27340],{},[898,27251,2046],{},[1750,27253,1753],{"stretchy":1752},[5535,27255,27256,27258],{},[898,27257,12471],{},[1742,27259,1744],{},[1750,27261,1917],{"separator":1916},[5535,27263,27264,27266],{},[898,27265,12471],{},[1742,27267,1872],{},[1750,27269,1917],{"separator":1916},[898,27271,26016],{},[1750,27273,1763],{"stretchy":1752},[1750,27275,1766],{},[5950,27277,27278,27280,27282],{},[898,27279,1776],{},[1742,27281,1744],{},[1750,27283,3751],{},[5535,27285,27286,27288],{},[898,27287,12471],{},[1742,27289,1744],{},[1750,27291,1861],{},[5950,27293,27294,27296,27298],{},[898,27295,1776],{},[1742,27297,1872],{},[1750,27299,3751],{},[5535,27301,27302,27304],{},[898,27303,12471],{},[1742,27305,1872],{},[1750,27307,1861],{},[898,27309,26016],{},[1750,27311,1753],{"stretchy":1752},[1699,27313,27314,27316],{},[898,27315,900],{},[1750,27317,3751],{},[1750,27319,1758],{},[898,27321,900],{},[1750,27323,1753],{"stretchy":1752},[5535,27325,27326,27328],{},[898,27327,12471],{},[1742,27329,1744],{},[1750,27331,1917],{"separator":1916},[5535,27333,27334,27336],{},[898,27335,12471],{},[1742,27337,1872],{},[1750,27339,1763],{"stretchy":1752},[1750,27341,1763],{"stretchy":1752},[902,27343,27344],{"encoding":904},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[724,27346,27347,27348,2313],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[883,27349,27351],{"className":27350},[886],[888,27352,27353],{"xmlns":890},[892,27354,27355,27394],{},[895,27356,27357,27364,27366,27372,27374,27380,27382,27388,27390,27392],{},[5535,27358,27359,27361],{},[898,27360,12471],{},[898,27362,27363],{},"i",[1750,27365,1766],{},[5535,27367,27368,27370],{},[898,27369,5541],{},[898,27371,27363],{},[1750,27373,1753],{"stretchy":1752},[5535,27375,27376,27378],{},[898,27377,1776],{},[1742,27379,1744],{},[1750,27381,1917],{"separator":1916},[5535,27383,27384,27386],{},[898,27385,1776],{},[1742,27387,1872],{},[1750,27389,1917],{"separator":1916},[898,27391,900],{},[1750,27393,1763],{"stretchy":1752},[902,27395,27396],{"encoding":904},"Q_i = D_i(P_1, P_2, U)",[115,27398,11524],{"id":11523},[120,27400,27401,27408,27415,27424],{},[123,27402,27403,1647,27405],{},[38,27404,13467],{},[207,27406,784],{"className":27407,"dataFsResolvedFilePath":782,"href":783},[210],[123,27409,27410,1647,27412],{},[38,27411,13475],{},[207,27413,21574],{"className":27414,"dataFsResolvedFilePath":800,"href":801},[210],[123,27416,27417,1647,27420,27423],{},[38,27418,27419],{},"Aplikace v kurzu:",[207,27421,880],{"className":27422,"dataFsResolvedFilePath":878,"href":879},[210]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[123,27425,27426,1647,27428,1343,27431,27434],{},[38,27427,13483],{},[207,27429,936],{"className":27430,"dataFsResolvedFilePath":934,"href":935},[210],[207,27432,1400],{"className":27433,"dataFsResolvedFilePath":1398,"href":1399},[210]," (IpmrK)",{"title":641,"searchDepth":642,"depth":642,"links":27436},[27437,27438,27439,27440,27441,27442,27446],{"id":25984,"depth":642,"text":25985},{"id":12924,"depth":642,"text":12925},{"id":12998,"depth":642,"text":12999},{"id":26599,"depth":642,"text":26600},{"id":26711,"depth":642,"text":26712},{"id":26813,"depth":642,"text":26814,"children":27443},[27444,27445],{"id":26817,"depth":649,"text":26818},{"id":27194,"depth":649,"text":27195},{"id":11523,"depth":642,"text":11524},[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":25853,"description":27448},[1135,1137],"topics\u002Flagrangeova-metoda",[1128,1619,27455,11663],"vazane-extremy","PRnK6wpMGySFp-C47ico7wAs4MDBp47Titm-Obyzgow",{"id":1628,"title":936,"body":27458,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":36684,"navigation":664,"path":11654,"seo":36685,"sources":36686,"stem":11657,"tags":36687,"type":11664,"updated":677,"__hash__":11665},{"type":9,"value":27459,"toc":36647},[27460,27462,27464,27569,27691,27693,27695,27797,27799,27822,27867,27869,27931,27969,27971,27996,28019,28021,28023,28064,28107,28159,28212,28214,28216,28218,28263,28353,28451,28455,28530,28557,28689,28691,28716,28763,28900,28979,28981,29004,29041,29064,29101,29160,29233,29306,29358,29423,29463,29465,29517,29564,29607,29807,29917,29921,29923,29937,29939,29944,29946,29974,30007,30009,30055,30136,30176,30195,30253,30312,30314,30381,30448,30513,30623,30667,30669,30671,30707,30744,30763,30869,31020,31026,31053,31082,31084,31157,31308,31388,31708,31710,31827,31962,32089,32136,32138,32373,32448,32450,32452,32505,32536,32538,32585,32587,32655,32850,32852,32990,33219,33254,33305,33348,33350,33403,33445,33641,33725,33727,33736,33741,33897,33899,33967,34044,34119,34196,34330,34410,34412,34586,34712,34753,34844,34846,35551,35553,36569,36571],[12,27461,936],{"id":1633},[115,27463,1637],{"id":1636},[724,27465,1640,27466,1647,27469,1651,27471,1647,27473,1669,27486,1673,27488,1677,27490,1681,27492,1685,27494,1647,27496,1709,27513,1727,27530,1731,27532,1783],{},[207,27467,1646],{"className":27468,"dataFsResolvedFilePath":1644,"href":1645},[210],[38,27470,1650],{},[38,27472,1654],{},[883,27474,27476],{"className":27475},[886],[888,27477,27478],{"xmlns":890},[892,27479,27480,27484],{},[895,27481,27482],{},[898,27483,1666],{},[902,27485,1666],{"encoding":904},[38,27487,1672],{},[38,27489,1676],{},[38,27491,1680],{},[38,27493,1684],{},[38,27495,1688],{},[883,27497,27499],{"className":27498},[886],[888,27500,27501],{"xmlns":890},[892,27502,27503,27511],{},[895,27504,27505],{},[1699,27506,27507,27509],{},[898,27508,1666],{},[898,27510,1705],{},[902,27512,1708],{"encoding":904},[883,27514,27516],{"className":27515},[886],[888,27517,27518],{"xmlns":890},[892,27519,27520,27528],{},[895,27521,27522],{},[1699,27523,27524,27526],{},[898,27525,1666],{},[898,27527,1705],{},[902,27529,1708],{"encoding":904},[38,27531,1730],{},[883,27533,27535],{"className":27534},[886],[888,27536,27537],{"xmlns":890},[892,27538,27539,27567],{},[895,27540,27541,27543,27545,27547,27549,27551,27553,27555,27557,27559,27561,27563,27565],{},[1742,27542,1744],{},[898,27544,1748],{"mathvariant":1747},[1750,27546,1753],{"stretchy":1752},[1742,27548,1744],{},[1750,27550,1758],{},[898,27552,207],{},[1750,27554,1763],{"stretchy":1752},[1750,27556,1766],{},[1742,27558,1744],{},[898,27560,1748],{"mathvariant":1747},[898,27562,1773],{},[898,27564,1776],{},[898,27566,1779],{},[902,27568,1782],{"encoding":904},[1785,27570,27571],{},[724,27572,27573,1792,27575,1796,27577,1816,27594,1847,27623,1897,27668,1900,27670,1926],{},[883,27574,1791],{},[38,27576,1795],{},[883,27578,27580],{"className":27579},[886],[888,27581,27582],{"xmlns":890},[892,27583,27584,27592],{},[895,27585,27586,27588,27590],{},[898,27587,1773],{},[898,27589,1776],{},[898,27591,1812],{},[902,27593,1815],{"encoding":904},[883,27595,27597],{"className":27596},[886],[888,27598,27599],{"xmlns":890},[892,27600,27601,27621],{},[895,27602,27603,27605,27607,27609,27611,27613,27615,27617,27619],{},[898,27604,1773],{},[898,27606,1776],{},[898,27608,1779],{},[1750,27610,1766],{},[1742,27612,1744],{},[1750,27614,1758],{},[898,27616,1773],{},[898,27618,1776],{},[898,27620,1812],{},[902,27622,1846],{"encoding":904},[883,27624,27626],{"className":27625},[886],[888,27627,27628],{"xmlns":890},[892,27629,27630,27666],{},[895,27631,27632,27634,27636,27638,27640,27646,27648,27650,27652,27654,27656,27658,27660,27662,27664],{},[1742,27633,1744],{},[1750,27635,1861],{},[898,27637,207],{},[1750,27639,1861],{},[1699,27641,27642,27644],{},[898,27643,207],{},[1742,27645,1872],{},[1750,27647,1861],{},[1750,27649,1877],{},[1750,27651,1766],{},[1742,27653,1744],{},[898,27655,1748],{"mathvariant":1747},[1750,27657,1753],{"stretchy":1752},[1742,27659,1744],{},[1750,27661,1758],{},[898,27663,207],{},[1750,27665,1763],{"stretchy":1752},[902,27667,1896],{"encoding":904},[38,27669,1684],{},[883,27671,27673],{"className":27672},[886],[888,27674,27675],{"xmlns":890},[892,27676,27677,27689],{},[895,27678,27679,27681,27683,27685,27687],{},[1750,27680,1753],{"stretchy":1752},[898,27682,1666],{},[1750,27684,1917],{"separator":1916},[898,27686,1920],{},[1750,27688,1763],{"stretchy":1752},[902,27690,1925],{"encoding":904},[115,27692,1930],{"id":1929},[724,27694,1933],{},[120,27696,27697,27699,27701,27703,27705,27707,27709,27795],{},[123,27698,1938],{},[123,27700,1941],{},[123,27702,1944],{},[123,27704,1947],{},[123,27706,1950],{},[123,27708,1953],{},[123,27710,1956,27711,1343,27728,1343,27749,2028,27774,2052],{},[883,27712,27714],{"className":27713},[886],[888,27715,27716],{"xmlns":890},[892,27717,27718,27726],{},[895,27719,27720,27722,27724],{},[898,27721,1812],{},[1969,27723,1971],{},[898,27725,1974],{},[902,27727,1977],{"encoding":904},[883,27729,27731],{"className":27730},[886],[888,27732,27733],{"xmlns":890},[892,27734,27735,27747],{},[895,27736,27737,27739,27741,27743,27745],{},[898,27738,1812],{},[1969,27740,1971],{},[898,27742,1974],{},[1969,27744,1971],{},[898,27746,1997],{},[902,27748,2000],{"encoding":904},[883,27750,27752],{"className":27751},[886],[888,27753,27754],{"xmlns":890},[892,27755,27756,27772],{},[895,27757,27758,27760,27762,27764,27766,27768,27770],{},[898,27759,1812],{},[1969,27761,1971],{},[898,27763,1974],{},[1969,27765,1971],{},[898,27767,1997],{},[1969,27769,1971],{},[898,27771,2024],{},[902,27773,2027],{"encoding":904},[883,27775,27777],{"className":27776},[886],[888,27778,27779],{"xmlns":890},[892,27780,27781,27793],{},[895,27782,27783,27785,27787,27789,27791],{},[898,27784,1974],{},[898,27786,1779],{},[1969,27788,1971],{},[898,27790,2046],{},[898,27792,1773],{},[902,27794,2051],{"encoding":904},[123,27796,2055],{},[115,27798,2059],{"id":2058},[724,27800,27801,1647,27803,2084,27820,2088],{},[38,27802,2064],{},[883,27804,27806],{"className":27805},[886],[888,27807,27808],{"xmlns":890},[892,27809,27810,27818],{},[895,27811,27812,27814,27816],{},[898,27813,1997],{},[898,27815,2078],{},[898,27817,1776],{},[902,27819,2083],{"encoding":904},[614,27821,2087],{},[724,27823,27824],{},[883,27825,27827],{"className":27826},[886],[888,27828,27829],{"xmlns":890},[892,27830,27831,27865],{},[895,27832,27833,27835,27837,27839,27841,27843,27845,27847,27849,27851,27853,27855,27857,27859,27861,27863],{},[898,27834,1997],{},[898,27836,2078],{},[898,27838,1776],{},[1750,27840,1766],{},[898,27842,1812],{},[1750,27844,1861],{},[898,27846,1974],{},[1750,27848,1861],{},[898,27850,1997],{},[1750,27852,1861],{},[898,27854,2024],{},[1750,27856,1917],{"separator":1916},[2125,27858],{"width":2127},[1750,27860,1753],{"stretchy":1752},[1742,27862,2132],{},[1750,27864,1763],{"stretchy":1752},[902,27866,2137],{"encoding":904},[724,27868,2140],{},[120,27870,27871,27886,27901,27916],{},[123,27872,27873,2158],{},[883,27874,27876],{"className":27875},[886],[888,27877,27878],{"xmlns":890},[892,27879,27880,27884],{},[895,27881,27882],{},[898,27883,1812],{},[902,27885,1812],{"encoding":904},[123,27887,27888,2174],{},[883,27889,27891],{"className":27890},[886],[888,27892,27893],{"xmlns":890},[892,27894,27895,27899],{},[895,27896,27897],{},[898,27898,1974],{},[902,27900,1974],{"encoding":904},[123,27902,27903,2190],{},[883,27904,27906],{"className":27905},[886],[888,27907,27908],{"xmlns":890},[892,27909,27910,27914],{},[895,27911,27912],{},[898,27913,1997],{},[902,27915,1997],{"encoding":904},[123,27917,27918,2206],{},[883,27919,27921],{"className":27920},[886],[888,27922,27923],{"xmlns":890},[892,27924,27925,27929],{},[895,27926,27927],{},[898,27928,2024],{},[902,27930,2024],{"encoding":904},[724,27932,2209,27933,2227,27950,2231,27952,1647,27954,2084,27967,2251],{},[883,27934,27936],{"className":27935},[886],[888,27937,27938],{"xmlns":890},[892,27939,27940,27948],{},[895,27941,27942,27944,27946],{},[898,27943,1997],{},[898,27945,2078],{},[898,27947,1776],{},[902,27949,2083],{"encoding":904},[38,27951,2230],{},[38,27953,2234],{},[883,27955,27957],{"className":27956},[886],[888,27958,27959],{"xmlns":890},[892,27960,27961,27965],{},[895,27962,27963],{},[898,27964,1666],{},[902,27966,1666],{"encoding":904},[614,27968,2250],{},[724,27970,2254],{},[724,27972,27973],{},[883,27974,27976],{"className":27975},[886],[888,27977,27978],{"xmlns":890},[892,27979,27980,27994],{},[895,27981,27982,27984,27986,27988,27990,27992],{},[898,27983,1997],{},[898,27985,2078],{},[898,27987,1776],{},[1750,27989,2274],{},[898,27991,1666],{},[1750,27993,1917],{"separator":1916},[902,27995,2281],{"encoding":904},[724,27997,2284,27998,2084,28000,2291,28002,2305,28015,2309,28017,2313],{},[38,27999,2287],{},[614,28001,2290],{},[883,28003,28005],{"className":28004},[886],[888,28006,28007],{"xmlns":890},[892,28008,28009,28013],{},[895,28010,28011],{},[898,28012,1666],{},[902,28014,1666],{"encoding":904},[38,28016,2308],{},[38,28018,2312],{},[115,28020,2317],{"id":2316},[198,28022,2321],{"id":2320},[724,28024,2324,28025,2338,28038,2352,28051,2366],{},[883,28026,28028],{"className":28027},[886],[888,28029,28030],{"xmlns":890},[892,28031,28032,28036],{},[895,28033,28034],{},[898,28035,1812],{},[902,28037,1812],{"encoding":904},[883,28039,28041],{"className":28040},[886],[888,28042,28043],{"xmlns":890},[892,28044,28045,28049],{},[895,28046,28047],{},[898,28048,1779],{},[902,28050,1779],{"encoding":904},[883,28052,28054],{"className":28053},[886],[888,28055,28056],{"xmlns":890},[892,28057,28058,28062],{},[895,28059,28060],{},[898,28061,1666],{},[902,28063,1666],{"encoding":904},[724,28065,28066],{},[883,28067,28069],{"className":28068},[886],[888,28070,28071],{"xmlns":890},[892,28072,28073,28105],{},[895,28074,28075,28077,28079,28081,28083,28085,28087,28089,28091,28093,28095,28097,28099,28101,28103],{},[898,28076,1812],{},[1750,28078,1766],{},[898,28080,1812],{},[1750,28082,1753],{"stretchy":1752},[898,28084,1666],{},[1750,28086,1763],{"stretchy":1752},[1750,28088,1917],{"separator":1916},[2125,28090],{"width":2127},[898,28092,1779],{},[1750,28094,1766],{},[898,28096,1779],{},[1750,28098,1753],{"stretchy":1752},[898,28100,1666],{},[1750,28102,1763],{"stretchy":1752},[898,28104,2313],{"mathvariant":1747},[902,28106,2410],{"encoding":904},[724,28108,28109,2433,28128,2084,28130,2440,28132,2433,28151,2084,28153,2467,28155,2028,28157,2474],{},[883,28110,28112],{"className":28111},[886],[888,28113,28114],{"xmlns":890},[892,28115,28116,28126],{},[895,28117,28118,28120,28122,28124],{},[898,28119,1812],{},[1750,28121,1753],{"stretchy":1752},[898,28123,1666],{},[1750,28125,1763],{"stretchy":1752},[902,28127,2432],{"encoding":904},[38,28129,2436],{},[614,28131,2439],{},[883,28133,28135],{"className":28134},[886],[888,28136,28137],{"xmlns":890},[892,28138,28139,28149],{},[895,28140,28141,28143,28145,28147],{},[898,28142,1779],{},[1750,28144,1753],{"stretchy":1752},[898,28146,1666],{},[1750,28148,1763],{"stretchy":1752},[902,28150,2460],{"encoding":904},[38,28152,2463],{},[614,28154,2466],{},[38,28156,2470],{},[38,28158,2473],{},[724,28160,28161],{},[883,28162,28164],{"className":28163},[886],[888,28165,28166],{"xmlns":890},[892,28167,28168,28210],{},[895,28169,28170,28172,28174,28176,28178,28180,28182,28184,28186,28188,28190,28192,28194,28196,28198,28200,28202,28204,28206,28208],{},[898,28171,1666],{},[1750,28173,1766],{},[898,28175,1812],{},[1750,28177,1861],{},[898,28179,1779],{},[1750,28181,1766],{},[898,28183,1812],{},[1750,28185,1753],{"stretchy":1752},[898,28187,1666],{},[1750,28189,1763],{"stretchy":1752},[1750,28191,1861],{},[898,28193,1779],{},[1750,28195,1753],{"stretchy":1752},[898,28197,1666],{},[1750,28199,1763],{"stretchy":1752},[898,28201,2313],{"mathvariant":1747},[2125,28203],{"width":2127},[1750,28205,1753],{"stretchy":1752},[1742,28207,2524],{},[1750,28209,1763],{"stretchy":1752},[902,28211,2529],{"encoding":904},[724,28213,2532],{},[198,28215,2536],{"id":2535},[724,28217,2539],{},[724,28219,28220],{},[883,28221,28223],{"className":28222},[886],[888,28224,28225],{"xmlns":890},[892,28226,28227,28261],{},[895,28228,28229,28231,28233,28235,28237,28239,28241,28243,28245,28247,28249,28251,28253,28255,28257,28259],{},[898,28230,1812],{},[1750,28232,1766],{},[898,28234,1812],{},[1750,28236,1753],{"stretchy":1752},[898,28238,1666],{},[1750,28240,1763],{"stretchy":1752},[1750,28242,1766],{},[898,28244,207],{},[898,28246,1666],{},[1750,28248,1861],{},[898,28250,2573],{},[1750,28252,1917],{"separator":1916},[2125,28254],{"width":2127},[1750,28256,1753],{"stretchy":1752},[1742,28258,2582],{},[1750,28260,1763],{"stretchy":1752},[902,28262,2587],{"encoding":904},[724,28264,2590,28265,2028,28282,2634,28303,2678,28340,2313],{},[883,28266,28268],{"className":28267},[886],[888,28269,28270],{"xmlns":890},[892,28271,28272,28280],{},[895,28273,28274,28276,28278],{},[898,28275,2573],{},[1750,28277,2604],{},[1742,28279,2607],{},[902,28281,2610],{"encoding":904},[883,28283,28285],{"className":28284},[886],[888,28286,28287],{"xmlns":890},[892,28288,28289,28301],{},[895,28290,28291,28293,28295,28297,28299],{},[1742,28292,2607],{},[1750,28294,2624],{},[898,28296,207],{},[1750,28298,2624],{},[1742,28300,1744],{},[902,28302,2633],{"encoding":904},[883,28304,28306],{"className":28305},[886],[888,28307,28308],{"xmlns":890},[892,28309,28310,28338],{},[895,28311,28312,28314,28316,28322,28324,28326,28328,28330,28332,28334,28336],{},[898,28313,207],{},[1750,28315,1766],{},[895,28317,28318,28320],{},[898,28319,2652],{"mathvariant":1747},[898,28321,2655],{"mathvariant":1747},[1969,28323,2658],{},[898,28325,2661],{},[1750,28327,1766],{},[898,28329,2666],{"mathvariant":1747},[898,28331,1812],{},[898,28333,1748],{"mathvariant":1747},[898,28335,2666],{"mathvariant":1747},[898,28337,1666],{},[902,28339,2677],{"encoding":904},[883,28341,28343],{"className":28342},[886],[888,28344,28345],{"xmlns":890},[892,28346,28347,28351],{},[895,28348,28349],{},[898,28350,1666],{},[902,28352,1666],{"encoding":904},[724,28354,28355],{},[614,28356,2696,28357,2721,28380,2760,28417,2777,28432,2313],{},[883,28358,28360],{"className":28359},[886],[888,28361,28362],{"xmlns":890},[892,28363,28364,28378],{},[895,28365,28366,28368,28370,28372,28374,28376],{},[898,28367,1812],{},[1750,28369,1766],{},[898,28371,207],{},[898,28373,1666],{},[1750,28375,1861],{},[898,28377,2573],{},[902,28379,2720],{"encoding":904},[883,28381,28383],{"className":28382},[886],[888,28384,28385],{"xmlns":890},[892,28386,28387,28415],{},[895,28388,28389,28391,28393,28399,28401,28403,28405,28407,28409,28411,28413],{},[898,28390,207],{},[1750,28392,1766],{},[895,28394,28395,28397],{},[898,28396,2652],{"mathvariant":1747},[898,28398,2655],{"mathvariant":1747},[1969,28400,2658],{},[898,28402,2661],{},[1750,28404,1766],{},[898,28406,2666],{"mathvariant":1747},[898,28408,1812],{},[898,28410,1748],{"mathvariant":1747},[898,28412,2666],{"mathvariant":1747},[898,28414,1666],{},[902,28416,2759],{"encoding":904},[883,28418,28420],{"className":28419},[886],[888,28421,28422],{"xmlns":890},[892,28423,28424,28430],{},[895,28425,28426,28428],{},[898,28427,2666],{"mathvariant":1747},[898,28429,1812],{},[902,28431,2776],{"encoding":904},[883,28433,28435],{"className":28434},[886],[888,28436,28437],{"xmlns":890},[892,28438,28439,28449],{},[895,28440,28441,28443,28445,28447],{},[898,28442,2666],{"mathvariant":1747},[898,28444,1666],{},[1750,28446,1766],{},[1742,28448,1744],{},[902,28450,2797],{"encoding":904},[724,28452,2800,28453,2366],{},[38,28454,2803],{},[724,28456,28457],{},[883,28458,28460],{"className":28459},[886],[888,28461,28462],{"xmlns":890},[892,28463,28464,28528],{},[895,28465,28466,28468,28470,28472,28474,28476,28478,28480,28482,28484,28486,28488,28490,28492,28494,28496,28498,28500,28502,28504,28506,28508,28510,28512,28514,28516,28518,28520,28522,28524,28526],{},[898,28467,1779],{},[1750,28469,1766],{},[898,28471,1666],{},[1750,28473,1758],{},[898,28475,1812],{},[1750,28477,1753],{"stretchy":1752},[898,28479,1666],{},[1750,28481,1763],{"stretchy":1752},[1750,28483,1766],{},[898,28485,1666],{},[1750,28487,1758],{},[1750,28489,1753],{"stretchy":1752},[898,28491,207],{},[898,28493,1666],{},[1750,28495,1861],{},[898,28497,2573],{},[1750,28499,1763],{"stretchy":1752},[1750,28501,1766],{},[1750,28503,1753],{"stretchy":1752},[1742,28505,1744],{},[1750,28507,1758],{},[898,28509,207],{},[1750,28511,1763],{"stretchy":1752},[898,28513,1666],{},[1750,28515,1758],{},[898,28517,2573],{},[898,28519,2313],{"mathvariant":1747},[2125,28521],{"width":2127},[1750,28523,1753],{"stretchy":1752},[1742,28525,2875],{},[1750,28527,1763],{"stretchy":1752},[902,28529,2880],{"encoding":904},[724,28531,2883,28532,1783],{},[883,28533,28535],{"className":28534},[886],[888,28536,28537],{"xmlns":890},[892,28538,28539,28555],{},[895,28540,28541,28543,28545,28547,28549,28551,28553],{},[1742,28542,2607],{},[1750,28544,2624],{},[1742,28546,1744],{},[1750,28548,1758],{},[898,28550,207],{},[1750,28552,2624],{},[1742,28554,1744],{},[902,28556,2909],{"encoding":904},[724,28558,28559],{},[614,28560,2914,28561,2028,28584,2970,28615,2984,28628,3015,28657,2984,28674,2313],{},[883,28562,28564],{"className":28563},[886],[888,28565,28566],{"xmlns":890},[892,28567,28568,28582],{},[895,28569,28570,28572,28574,28576,28578,28580],{},[898,28571,1812],{},[1750,28573,1766],{},[898,28575,207],{},[898,28577,1666],{},[1750,28579,1861],{},[898,28581,2573],{},[902,28583,2720],{"encoding":904},[883,28585,28587],{"className":28586},[886],[888,28588,28589],{"xmlns":890},[892,28590,28591,28613],{},[895,28592,28593,28595,28597,28599,28601,28603,28605,28607,28609,28611],{},[898,28594,1779],{},[1750,28596,1766],{},[1750,28598,1753],{"stretchy":1752},[1742,28600,1744],{},[1750,28602,1758],{},[898,28604,207],{},[1750,28606,1763],{"stretchy":1752},[898,28608,1666],{},[1750,28610,1758],{},[898,28612,2573],{},[902,28614,2969],{"encoding":904},[883,28616,28618],{"className":28617},[886],[888,28619,28620],{"xmlns":890},[892,28621,28622,28626],{},[895,28623,28624],{},[898,28625,1666],{},[902,28627,1666],{"encoding":904},[883,28629,28631],{"className":28630},[886],[888,28632,28633],{"xmlns":890},[892,28634,28635,28655],{},[895,28636,28637,28639,28641,28643,28645,28647,28649,28651,28653],{},[898,28638,1666],{},[1750,28640,1766],{},[898,28642,2573],{},[898,28644,1748],{"mathvariant":1747},[1750,28646,1753],{"stretchy":1752},[1742,28648,1744],{},[1750,28650,1758],{},[898,28652,207],{},[1750,28654,1763],{"stretchy":1752},[902,28656,3014],{"encoding":904},[883,28658,28660],{"className":28659},[886],[888,28661,28662],{"xmlns":890},[892,28663,28664,28672],{},[895,28665,28666,28668,28670],{},[898,28667,1812],{},[1750,28669,1917],{"separator":1916},[898,28671,1779],{},[902,28673,3033],{"encoding":904},[883,28675,28677],{"className":28676},[886],[888,28678,28679],{"xmlns":890},[892,28680,28681,28687],{},[895,28682,28683,28685],{},[1750,28684,1758],{},[898,28686,2573],{},[902,28688,3049],{"encoding":904},[198,28690,3053],{"id":3052},[724,28692,3056,28693,3083],{},[883,28694,28696],{"className":28695},[886],[888,28697,28698],{"xmlns":890},[892,28699,28700,28714],{},[895,28701,28702,28704,28706,28708,28710,28712],{},[898,28703,1812],{},[1750,28705,1766],{},[1742,28707,3072],{},[898,28709,1666],{},[1750,28711,1861],{},[1742,28713,3079],{},[902,28715,3082],{"encoding":904},[724,28717,28718],{},[883,28719,28721],{"className":28720},[886],[888,28722,28723],{"xmlns":890},[892,28724,28725,28761],{},[895,28726,28727,28729,28731,28733,28735,28737,28739,28741,28743,28745,28747,28749,28751,28753,28755,28757,28759],{},[898,28728,1779],{},[1750,28730,1766],{},[898,28732,1666],{},[1750,28734,1758],{},[898,28736,1812],{},[1750,28738,1766],{},[898,28740,1666],{},[1750,28742,1758],{},[1742,28744,3072],{},[898,28746,1666],{},[1750,28748,1758],{},[1742,28750,3079],{},[1750,28752,1766],{},[1742,28754,3123],{},[898,28756,1666],{},[1750,28758,1758],{},[1742,28760,3130],{},[902,28762,3133],{"encoding":904},[724,28764,28765],{},[614,28766,3138,28767,2028,28790,3186,28813,2433,28826,3226,28847,2433,28864,3260,28879,2313],{},[883,28768,28770],{"className":28769},[886],[888,28771,28772],{"xmlns":890},[892,28773,28774,28788],{},[895,28775,28776,28778,28780,28782,28784,28786],{},[898,28777,1812],{},[1750,28779,1766],{},[1742,28781,3072],{},[898,28783,1666],{},[1750,28785,1861],{},[1742,28787,3079],{},[902,28789,3082],{"encoding":904},[883,28791,28793],{"className":28792},[886],[888,28794,28795],{"xmlns":890},[892,28796,28797,28811],{},[895,28798,28799,28801,28803,28805,28807,28809],{},[898,28800,1779],{},[1750,28802,1766],{},[1742,28804,3123],{},[898,28806,1666],{},[1750,28808,1758],{},[1742,28810,3079],{},[902,28812,3185],{"encoding":904},[883,28814,28816],{"className":28815},[886],[888,28817,28818],{"xmlns":890},[892,28819,28820,28824],{},[895,28821,28822],{},[898,28823,1666],{},[902,28825,1666],{"encoding":904},[883,28827,28829],{"className":28828},[886],[888,28830,28831],{"xmlns":890},[892,28832,28833,28845],{},[895,28834,28835,28837,28839],{},[1750,28836,2274],{},[1742,28838,3213],{},[3215,28840,28841,28843],{"accent":1916},[1742,28842,3219],{},[1750,28844,3222],{},[902,28846,3225],{"encoding":904},[883,28848,28850],{"className":28849},[886],[888,28851,28852],{"xmlns":890},[892,28853,28854,28862],{},[895,28855,28856,28858,28860],{},[898,28857,1812],{},[1750,28859,1917],{"separator":1916},[898,28861,1779],{},[902,28863,3033],{"encoding":904},[883,28865,28867],{"className":28866},[886],[888,28868,28869],{"xmlns":890},[892,28870,28871,28877],{},[895,28872,28873,28875],{},[1750,28874,1758],{},[1742,28876,3079],{},[902,28878,3259],{"encoding":904},[883,28880,28882],{"className":28881},[886],[888,28883,28884],{"xmlns":890},[892,28885,28886,28898],{},[895,28887,28888,28890,28892,28894,28896],{},[1750,28889,1753],{"stretchy":1752},[1742,28891,2607],{},[1750,28893,1917],{"separator":1916},[1742,28895,3079],{},[1750,28897,1763],{"stretchy":1752},[902,28899,3282],{"encoding":904},[724,28901,3285,28902,2433,28919,3334,28948,2084,28950,3341,28952,2433,28975,2084,28977,3372],{},[883,28903,28905],{"className":28904},[886],[888,28906,28907],{"xmlns":890},[892,28908,28909,28917],{},[895,28910,28911,28913,28915],{},[898,28912,1666],{},[1750,28914,1766],{},[1742,28916,2607],{},[902,28918,3303],{"encoding":904},[883,28920,28922],{"className":28921},[886],[888,28923,28924],{"xmlns":890},[892,28925,28926,28946],{},[895,28927,28928,28930,28932,28934,28936,28938,28940,28942,28944],{},[898,28929,1779],{},[1750,28931,1753],{"stretchy":1752},[1742,28933,2607],{},[1750,28935,1763],{"stretchy":1752},[1750,28937,1766],{},[1750,28939,1758],{},[898,28941,2573],{},[1750,28943,2624],{},[1742,28945,2607],{},[902,28947,3333],{"encoding":904},[38,28949,3337],{},[614,28951,3340],{},[883,28953,28955],{"className":28954},[886],[888,28956,28957],{"xmlns":890},[892,28958,28959,28973],{},[895,28960,28961,28963,28965,28967,28969,28971],{},[898,28962,1812],{},[1750,28964,1753],{"stretchy":1752},[1742,28966,2607],{},[1750,28968,1763],{"stretchy":1752},[1750,28970,1766],{},[898,28972,2573],{},[902,28974,3365],{"encoding":904},[38,28976,3368],{},[614,28978,3371],{},[115,28980,3376],{"id":3375},[724,28982,28983,1647,28985,2084,29002,3402],{},[38,28984,3381],{},[883,28986,28988],{"className":28987},[886],[888,28989,28990],{"xmlns":890},[892,28991,28992,29000],{},[895,28993,28994,28996,28998],{},[898,28995,1773],{},[898,28997,1776],{},[898,28999,1812],{},[902,29001,1815],{"encoding":904},[614,29003,3401],{},[724,29005,29006],{},[883,29007,29009],{"className":29008},[886],[888,29010,29011],{"xmlns":890},[892,29012,29013,29039],{},[895,29014,29015,29017,29019,29021,29023,29037],{},[898,29016,1773],{},[898,29018,1776],{},[898,29020,1812],{},[1750,29022,1766],{},[3423,29024,29025,29031],{},[895,29026,29027,29029],{},[898,29028,3429],{"mathvariant":1747},[898,29030,1812],{},[895,29032,29033,29035],{},[898,29034,3429],{"mathvariant":1747},[898,29036,1666],{},[898,29038,2313],{"mathvariant":1747},[902,29040,3442],{"encoding":904},[724,29042,29043,1647,29045,2084,29062,3469],{},[38,29044,3447],{},[883,29046,29048],{"className":29047},[886],[888,29049,29050],{"xmlns":890},[892,29051,29052,29060],{},[895,29053,29054,29056,29058],{},[898,29055,1773],{},[898,29057,1776],{},[898,29059,1779],{},[902,29061,3465],{"encoding":904},[614,29063,3468],{},[724,29065,29066],{},[883,29067,29069],{"className":29068},[886],[888,29070,29071],{"xmlns":890},[892,29072,29073,29099],{},[895,29074,29075,29077,29079,29081,29083,29097],{},[898,29076,1773],{},[898,29078,1776],{},[898,29080,1779],{},[1750,29082,1766],{},[3423,29084,29085,29091],{},[895,29086,29087,29089],{},[898,29088,3429],{"mathvariant":1747},[898,29090,1779],{},[895,29092,29093,29095],{},[898,29094,3429],{"mathvariant":1747},[898,29096,1666],{},[898,29098,2313],{"mathvariant":1747},[902,29100,3507],{"encoding":904},[724,29102,3510,29103,3569],{},[883,29104,29106],{"className":29105},[886],[888,29107,29108],{"xmlns":890},[892,29109,29110,29158],{},[895,29111,29112,29126,29128,29142,29144],{},[3423,29113,29114,29120],{},[895,29115,29116,29118],{},[898,29117,3429],{"mathvariant":1747},[898,29119,1666],{},[895,29121,29122,29124],{},[898,29123,3429],{"mathvariant":1747},[898,29125,1666],{},[1750,29127,1766],{},[3423,29129,29130,29136],{},[895,29131,29132,29134],{},[898,29133,3429],{"mathvariant":1747},[898,29135,1812],{},[895,29137,29138,29140],{},[898,29139,3429],{"mathvariant":1747},[898,29141,1666],{},[1750,29143,1861],{},[3423,29145,29146,29152],{},[895,29147,29148,29150],{},[898,29149,3429],{"mathvariant":1747},[898,29151,1779],{},[895,29153,29154,29156],{},[898,29155,3429],{"mathvariant":1747},[898,29157,1666],{},[902,29159,3568],{"encoding":904},[724,29161,29162],{},[883,29163,29165],{"className":29164},[886],[888,29166,29167],{"xmlns":890},[892,29168,29169,29231],{},[895,29170,29171,29223,29225,29227,29229],{},[3582,29172,29173],{"notation":3584},[3586,29174,29175],{"scriptlevel":2607,"displaystyle":1752},[3586,29176,29177],{"scriptlevel":2607,"displaystyle":1752},[3586,29178,29179],{"scriptlevel":2607,"displaystyle":1916},[895,29180,29181,29183,29185,29187,29189,29191,29193,29195,29197,29199,29201,29203,29205,29207,29209,29211,29213,29215,29217,29219,29221],{},[898,29182,1773],{},[898,29184,1776],{},[898,29186,1812],{},[1750,29188,1861],{},[898,29190,1773],{},[898,29192,1776],{},[898,29194,1779],{},[1750,29196,1766],{},[1742,29198,1744],{},[1750,29200,1917],{"separator":1916},[2125,29202],{"width":2127},[898,29204,1773],{},[898,29206,1776],{},[898,29208,1779],{},[1750,29210,1766],{},[1742,29212,1744],{},[1750,29214,1758],{},[898,29216,1773],{},[898,29218,1776],{},[898,29220,1812],{},[898,29222,2313],{"mathvariant":1747},[2125,29224],{"width":2127},[1750,29226,1753],{"stretchy":1752},[1742,29228,3642],{},[1750,29230,1763],{"stretchy":1752},[902,29232,3647],{"encoding":904},[724,29234,29235,1647,29237,3676,29260,2028,29281,3725],{},[38,29236,3652],{},[883,29238,29240],{"className":29239},[886],[888,29241,29242],{"xmlns":890},[892,29243,29244,29258],{},[895,29245,29246,29248,29250,29252,29254,29256],{},[898,29247,1812],{},[1750,29249,1766],{},[898,29251,207],{},[898,29253,1666],{},[1750,29255,1861],{},[898,29257,2573],{},[902,29259,2720],{"encoding":904},[883,29261,29263],{"className":29262},[886],[888,29264,29265],{"xmlns":890},[892,29266,29267,29279],{},[895,29268,29269,29271,29273,29275,29277],{},[898,29270,1773],{},[898,29272,1776],{},[898,29274,1812],{},[1750,29276,1766],{},[898,29278,207],{},[902,29280,3698],{"encoding":904},[883,29282,29284],{"className":29283},[886],[888,29285,29286],{"xmlns":890},[892,29287,29288,29304],{},[895,29289,29290,29292,29294,29296,29298,29300,29302],{},[898,29291,1773],{},[898,29293,1776],{},[898,29295,1779],{},[1750,29297,1766],{},[1742,29299,1744],{},[1750,29301,1758],{},[898,29303,207],{},[902,29305,3724],{"encoding":904},[724,29307,29308,3731,29310,3755,29331,3784],{},[38,29309,3730],{},[883,29311,29313],{"className":29312},[886],[888,29314,29315],{"xmlns":890},[892,29316,29317,29329],{},[895,29318,29319,29321,29323],{},[898,29320,1666],{},[1750,29322,1766],{},[1699,29324,29325,29327],{},[898,29326,1666],{},[1750,29328,3751],{},[902,29330,3754],{"encoding":904},[883,29332,29334],{"className":29333},[886],[888,29335,29336],{"xmlns":890},[892,29337,29338,29356],{},[895,29339,29340,29342,29344,29346,29348,29354],{},[898,29341,1773],{},[898,29343,1776],{},[898,29345,1812],{},[1750,29347,1753],{"stretchy":1752},[1699,29349,29350,29352],{},[898,29351,1666],{},[1750,29353,3751],{},[1750,29355,1763],{"stretchy":1752},[902,29357,3783],{"encoding":904},[724,29359,29360],{},[883,29361,29363],{"className":29362},[886],[888,29364,29365],{"xmlns":890},[892,29366,29367,29421],{},[895,29368,29369,29371,29373,29375,29377,29379,29381,29387,29389,29391,29393,29395,29397,29399,29401,29403,29405,29407,29409,29411,29413,29415,29417,29419],{},[898,29370,2666],{"mathvariant":1747},[898,29372,1812],{},[1750,29374,2274],{},[898,29376,3429],{"mathvariant":1747},[898,29378,1812],{},[1750,29380,1766],{},[1699,29382,29383,29385],{},[898,29384,1812],{},[1750,29386,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,29388,1753],{"stretchy":1752},[898,29390,1666],{},[1750,29392,1763],{"stretchy":1752},[1969,29394,2658],{},[898,29396,3429],{"mathvariant":1747},[898,29398,1666],{},[1750,29400,1766],{},[898,29402,1773],{},[898,29404,1776],{},[898,29406,1812],{},[1750,29408,1753],{"stretchy":1752},[898,29410,1666],{},[1750,29412,1763],{"stretchy":1752},[1969,29414,2658],{},[898,29416,3429],{"mathvariant":1747},[898,29418,1666],{},[898,29420,2313],{"mathvariant":1747},[902,29422,3852],{"encoding":904},[724,29424,3855,29425,3892,29460,3896],{},[883,29426,29428],{"className":29427},[886],[888,29429,29430],{"xmlns":890},[892,29431,29432,29458],{},[895,29433,29434,29436,29438,29440,29442,29444,29446,29448,29450,29452,29454,29456],{},[898,29435,2666],{"mathvariant":1747},[898,29437,1779],{},[1750,29439,2274],{},[898,29441,1773],{},[898,29443,1776],{},[898,29445,1779],{},[1750,29447,1753],{"stretchy":1752},[898,29449,1666],{},[1750,29451,1763],{"stretchy":1752},[1969,29453,2658],{},[898,29455,3429],{"mathvariant":1747},[898,29457,1666],{},[902,29459,3891],{"encoding":904},[207,29461,1145],{"className":29462,"dataFsResolvedFilePath":764,"href":765},[210],[198,29464,3900],{"id":3899},[724,29466,3056,29467,3940,29500,3960],{},[883,29468,29470],{"className":29469},[886],[888,29471,29472],{"xmlns":890},[892,29473,29474,29498],{},[895,29475,29476,29478,29480,29482,29488,29490,29492,29494,29496],{},[898,29477,1812],{},[1750,29479,1766],{},[1742,29481,3918],{},[1699,29483,29484,29486],{},[898,29485,1666],{},[1742,29487,1872],{},[1750,29489,1861],{},[1742,29491,3929],{},[898,29493,1666],{},[1750,29495,1861],{},[1742,29497,3936],{},[902,29499,3939],{"encoding":904},[883,29501,29503],{"className":29502},[886],[888,29504,29505],{"xmlns":890},[892,29506,29507,29515],{},[895,29508,29509,29511,29513],{},[898,29510,1666],{},[1750,29512,2624],{},[1742,29514,3956],{},[902,29516,3959],{"encoding":904},[724,29518,29519],{},[883,29520,29522],{"className":29521},[886],[888,29523,29524],{"xmlns":890},[892,29525,29526,29562],{},[895,29527,29528,29530,29532,29534,29536,29550,29552,29554,29556,29558,29560],{},[898,29529,1773],{},[898,29531,1776],{},[898,29533,1812],{},[1750,29535,1766],{},[3423,29537,29538,29544],{},[895,29539,29540,29542],{},[898,29541,3429],{"mathvariant":1747},[898,29543,1812],{},[895,29545,29546,29548],{},[898,29547,3429],{"mathvariant":1747},[898,29549,1666],{},[1750,29551,1766],{},[1742,29553,3998],{},[898,29555,1666],{},[1750,29557,1861],{},[1742,29559,3929],{},[1750,29561,1917],{"separator":1916},[902,29563,4009],{"encoding":904},[724,29565,29566],{},[883,29567,29569],{"className":29568},[886],[888,29570,29571],{"xmlns":890},[892,29572,29573,29605],{},[895,29574,29575,29577,29579,29581,29583,29585,29587,29589,29591,29593,29595,29597,29599,29601,29603],{},[898,29576,1773],{},[898,29578,1776],{},[898,29580,1779],{},[1750,29582,1766],{},[1742,29584,1744],{},[1750,29586,1758],{},[898,29588,1773],{},[898,29590,1776],{},[898,29592,1812],{},[1750,29594,1766],{},[1750,29596,1758],{},[1742,29598,3998],{},[898,29600,1666],{},[1750,29602,1861],{},[1742,29604,4051],{},[902,29606,4054],{"encoding":904},[120,29608,29609,29684,29759],{},[123,29610,29611,1343,29638,4116,29665,2433,29682,2313],{},[883,29612,29614],{"className":29613},[886],[888,29615,29616],{"xmlns":890},[892,29617,29618,29636],{},[895,29619,29620,29622,29624,29626,29628,29630,29632,29634],{},[898,29621,1773],{},[898,29623,1776],{},[898,29625,1812],{},[1750,29627,1753],{"stretchy":1752},[1742,29629,4078],{},[1750,29631,1763],{"stretchy":1752},[1750,29633,1766],{},[1742,29635,3072],{},[902,29637,4087],{"encoding":904},[883,29639,29641],{"className":29640},[886],[888,29642,29643],{"xmlns":890},[892,29644,29645,29663],{},[895,29646,29647,29649,29651,29653,29655,29657,29659,29661],{},[898,29648,1773],{},[898,29650,1776],{},[898,29652,1779],{},[1750,29654,1753],{"stretchy":1752},[1742,29656,4078],{},[1750,29658,1763],{"stretchy":1752},[1750,29660,1766],{},[1742,29662,3123],{},[902,29664,4115],{"encoding":904},[883,29666,29668],{"className":29667},[886],[888,29669,29670],{"xmlns":890},[892,29671,29672,29680],{},[895,29673,29674,29676,29678],{},[898,29675,1666],{},[1750,29677,1766],{},[1742,29679,4078],{},[902,29681,4134],{"encoding":904},[38,29683,4137],{},[123,29685,29686,1343,29713,4116,29740,2433,29757,2313],{},[883,29687,29689],{"className":29688},[886],[888,29690,29691],{"xmlns":890},[892,29692,29693,29711],{},[895,29694,29695,29697,29699,29701,29703,29705,29707,29709],{},[898,29696,1773],{},[898,29698,1776],{},[898,29700,1812],{},[1750,29702,1753],{"stretchy":1752},[1742,29704,4159],{},[1750,29706,1763],{"stretchy":1752},[1750,29708,1766],{},[1742,29710,3123],{},[902,29712,4168],{"encoding":904},[883,29714,29716],{"className":29715},[886],[888,29717,29718],{"xmlns":890},[892,29719,29720,29738],{},[895,29721,29722,29724,29726,29728,29730,29732,29734,29736],{},[898,29723,1773],{},[898,29725,1776],{},[898,29727,1779],{},[1750,29729,1753],{"stretchy":1752},[1742,29731,4159],{},[1750,29733,1763],{"stretchy":1752},[1750,29735,1766],{},[1742,29737,3072],{},[902,29739,4196],{"encoding":904},[883,29741,29743],{"className":29742},[886],[888,29744,29745],{"xmlns":890},[892,29746,29747,29755],{},[895,29748,29749,29751,29753],{},[898,29750,1666],{},[1750,29752,1766],{},[1742,29754,4159],{},[902,29756,4214],{"encoding":904},[38,29758,4217],{},[123,29760,4220,29761,4240,29778,1783],{},[883,29762,29764],{"className":29763},[886],[888,29765,29766],{"xmlns":890},[892,29767,29768,29776],{},[895,29769,29770,29772,29774],{},[898,29771,1666],{},[1750,29773,1766],{},[1742,29775,4236],{},[902,29777,4239],{"encoding":904},[883,29779,29781],{"className":29780},[886],[888,29782,29783],{"xmlns":890},[892,29784,29785,29805],{},[895,29786,29787,29789,29791,29793,29795,29797,29799,29801,29803],{},[898,29788,1773],{},[898,29790,1776],{},[898,29792,1812],{},[1750,29794,1766],{},[898,29796,1773],{},[898,29798,1776],{},[898,29800,1779],{},[1750,29802,1766],{},[1742,29804,4268],{},[902,29806,4271],{"encoding":904},[724,29808,4274,29809,4292,29826,4307,29839,4321,29852,4336,29865,4350,29878,4392],{},[883,29810,29812],{"className":29811},[886],[888,29813,29814],{"xmlns":890},[892,29815,29816,29824],{},[895,29817,29818,29820,29822],{},[898,29819,1666],{},[1750,29821,1766],{},[1742,29823,4078],{},[902,29825,4134],{"encoding":904},[883,29827,29829],{"className":29828},[886],[888,29830,29831],{"xmlns":890},[892,29832,29833,29837],{},[895,29834,29835],{},[1742,29836,3072],{},[902,29838,4306],{"encoding":904},[883,29840,29842],{"className":29841},[886],[888,29843,29844],{"xmlns":890},[892,29845,29846,29850],{},[895,29847,29848],{},[1742,29849,4078],{},[902,29851,4078],{"encoding":904},[883,29853,29855],{"className":29854},[886],[888,29856,29857],{"xmlns":890},[892,29858,29859,29863],{},[895,29860,29861],{},[1742,29862,4333],{},[902,29864,4333],{"encoding":904},[883,29866,29868],{"className":29867},[886],[888,29869,29870],{"xmlns":890},[892,29871,29872,29876],{},[895,29873,29874],{},[1742,29875,3072],{},[902,29877,4306],{"encoding":904},[883,29879,29881],{"className":29880},[886],[888,29882,29883],{"xmlns":890},[892,29884,29885,29915],{},[895,29886,29887,29889,29891,29893,29895,29897,29899,29901,29903,29905,29907,29909,29911,29913],{},[898,29888,2666],{"mathvariant":1747},[898,29890,1812],{},[1750,29892,1766],{},[898,29894,1812],{},[1750,29896,1753],{"stretchy":1752},[1742,29898,4333],{},[1750,29900,1763],{"stretchy":1752},[1750,29902,1758],{},[898,29904,1812],{},[1750,29906,1753],{"stretchy":1752},[1742,29908,4078],{},[1750,29910,1763],{"stretchy":1752},[1750,29912,1766],{},[1742,29914,4388],{},[902,29916,4391],{"encoding":904},[724,29918,4395,29919],{},[38,29920,4398],{},[115,29922,4402],{"id":4401},[724,29924,4405,29925,2084,29927,4412,29929,2084,29931,4419,29933,2084,29935,4426],{},[38,29926,4408],{},[614,29928,4411],{},[38,29930,4415],{},[614,29932,4418],{},[38,29934,4422],{},[614,29936,4425],{},[115,29938,4430],{"id":4429},[724,29940,29941],{},[4434,29942],{"alt":4436,"className":29943,"src":4439},[210,4438],[198,29945,4443],{"id":4442},[724,29947,4446,29948,4460,29961,4474],{},[883,29949,29951],{"className":29950},[886],[888,29952,29953],{"xmlns":890},[892,29954,29955,29959],{},[895,29956,29957],{},[898,29958,1812],{},[902,29960,1812],{"encoding":904},[883,29962,29964],{"className":29963},[886],[888,29965,29966],{"xmlns":890},[892,29967,29968,29972],{},[895,29969,29970],{},[898,29971,1974],{},[902,29973,1974],{"encoding":904},[724,29975,29976],{},[883,29977,29979],{"className":29978},[886],[888,29980,29981],{"xmlns":890},[892,29982,29983,30005],{},[895,29984,29985,29987,29989,29991,29993,29995,29997,29999,30001,30003],{},[898,29986,1666],{},[1750,29988,1766],{},[898,29990,1812],{},[1750,29992,1861],{},[898,29994,1974],{},[898,29996,2313],{"mathvariant":1747},[2125,29998],{"width":2127},[1750,30000,1753],{"stretchy":1752},[1742,30002,4504],{},[1750,30004,1763],{"stretchy":1752},[902,30006,4509],{"encoding":904},[198,30008,4513],{"id":4512},[724,30010,4516,30011,4539,30032,4564],{},[883,30012,30014],{"className":30013},[886],[888,30015,30016],{"xmlns":890},[892,30017,30018,30030],{},[895,30019,30020,30022,30024],{},[898,30021,1974],{},[1750,30023,1766],{},[1699,30025,30026,30028],{},[898,30027,1974],{},[1750,30029,3751],{},[902,30031,4538],{"encoding":904},[883,30033,30035],{"className":30034},[886],[888,30036,30037],{"xmlns":890},[892,30038,30039,30053],{},[895,30040,30041,30043,30045,30047,30049,30051],{},[898,30042,1812],{},[1750,30044,1766],{},[898,30046,1812],{},[1750,30048,1753],{"stretchy":1752},[898,30050,1666],{},[1750,30052,1763],{"stretchy":1752},[902,30054,4563],{"encoding":904},[724,30056,30057],{},[883,30058,30060],{"className":30059},[886],[888,30061,30062],{"xmlns":890},[892,30063,30064,30134],{},[895,30065,30066,30126,30128,30130,30132],{},[4577,30067,30068,30098],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,30069,30070,30076],{},[4585,30071,30072],{},[3586,30073,30074],{"scriptlevel":2607,"displaystyle":1916},[898,30075,1666],{},[4585,30077,30078],{},[3586,30079,30080],{"scriptlevel":2607,"displaystyle":1916},[895,30081,30082,30084,30086,30088,30090,30096],{},[895,30083],{},[1750,30085,1766],{},[898,30087,1812],{},[1750,30089,1861],{},[1699,30091,30092,30094],{},[898,30093,1974],{},[1750,30095,3751],{},[1750,30097,1917],{"separator":1916},[4582,30099,30100,30106],{},[4585,30101,30102],{},[3586,30103,30104],{"scriptlevel":2607,"displaystyle":1916},[898,30105,1812],{},[4585,30107,30108],{},[3586,30109,30110],{"scriptlevel":2607,"displaystyle":1916},[895,30111,30112,30114,30116,30118,30120,30122,30124],{},[895,30113],{},[1750,30115,1766],{},[898,30117,1812],{},[1750,30119,1753],{"stretchy":1752},[898,30121,1666],{},[1750,30123,1763],{"stretchy":1752},[1750,30125,1917],{"separator":1916},[2125,30127],{"width":2127},[1750,30129,1753],{"stretchy":1752},[1742,30131,4647],{},[1750,30133,1763],{"stretchy":1752},[902,30135,4652],{"encoding":904},[724,30137,4655,30138,1647,30140,2028,30157,1647,30159,2313],{},[38,30139,1688],{},[883,30141,30143],{"className":30142},[886],[888,30144,30145],{"xmlns":890},[892,30146,30147,30155],{},[895,30148,30149],{},[1699,30150,30151,30153],{},[898,30152,1666],{},[898,30154,1705],{},[902,30156,1708],{"encoding":904},[38,30158,4677],{},[883,30160,30162],{"className":30161},[886],[888,30163,30164],{"xmlns":890},[892,30165,30166,30174],{},[895,30167,30168],{},[1699,30169,30170,30172],{},[898,30171,1812],{},[898,30173,1705],{},[902,30175,4695],{"encoding":904},[198,30177,4699,30178],{"id":4698},[883,30179,30181],{"className":30180},[886],[888,30182,30183],{"xmlns":890},[892,30184,30185,30193],{},[895,30186,30187],{},[1699,30188,30189,30191],{},[898,30190,1666],{},[898,30192,1705],{},[902,30194,1708],{"encoding":904},[724,30196,4719,30197,4743,30220,4776,30251],{},[883,30198,30200],{"className":30199},[886],[888,30201,30202],{"xmlns":890},[892,30203,30204,30218],{},[895,30205,30206,30208,30210,30212,30214,30216],{},[898,30207,1812],{},[1750,30209,1766],{},[898,30211,207],{},[898,30213,1666],{},[1750,30215,1861],{},[898,30217,2573],{},[902,30219,2720],{"encoding":904},[883,30221,30223],{"className":30222},[886],[888,30224,30225],{"xmlns":890},[892,30226,30227,30249],{},[895,30228,30229,30231,30233,30235,30237,30239,30241,30243],{},[898,30230,1666],{},[1750,30232,1766],{},[898,30234,207],{},[898,30236,1666],{},[1750,30238,1861],{},[898,30240,2573],{},[1750,30242,1861],{},[1699,30244,30245,30247],{},[898,30246,1974],{},[1750,30248,3751],{},[902,30250,4775],{"encoding":904},[38,30252,4779],{},[724,30254,30255],{},[883,30256,30258],{"className":30257},[886],[888,30259,30260],{"xmlns":890},[892,30261,30262,30310],{},[895,30263,30264],{},[3582,30265,30266],{"notation":3584},[3586,30267,30268],{"scriptlevel":2607,"displaystyle":1752},[3586,30269,30270],{"scriptlevel":2607,"displaystyle":1752},[3586,30271,30272],{"scriptlevel":2607,"displaystyle":1916},[895,30273,30274,30276,30282,30284,30306,30308],{},[1969,30275,2658],{},[1699,30277,30278,30280],{},[898,30279,1666],{},[898,30281,1705],{},[1750,30283,1766],{},[3423,30285,30286,30298],{},[895,30287,30288,30290,30292],{},[898,30289,2573],{},[1750,30291,1861],{},[1699,30293,30294,30296],{},[898,30295,1974],{},[1750,30297,3751],{},[895,30299,30300,30302,30304],{},[1742,30301,1744],{},[1750,30303,1758],{},[898,30305,207],{},[898,30307,2313],{"mathvariant":1747},[1969,30309,2658],{},[902,30311,4839],{"encoding":904},[198,30313,4843],{"id":4842},[724,30315,4846,30316,2433,30333,2028,30356,4915],{},[883,30317,30319],{"className":30318},[886],[888,30320,30321],{"xmlns":890},[892,30322,30323,30331],{},[895,30324,30325,30327,30329],{},[898,30326,1812],{},[1969,30328,1971],{},[898,30330,1974],{},[902,30332,1977],{"encoding":904},[883,30334,30336],{"className":30335},[886],[888,30337,30338],{"xmlns":890},[892,30339,30340,30354],{},[895,30341,30342,30344,30346,30348,30350,30352],{},[898,30343,1812],{},[1750,30345,1766],{},[1742,30347,3123],{},[898,30349,1666],{},[1750,30351,1861],{},[1742,30353,3079],{},[902,30355,4887],{"encoding":904},[883,30357,30359],{"className":30358},[886],[888,30360,30361],{"xmlns":890},[892,30362,30363,30379],{},[895,30364,30365,30367,30369,30371,30373],{},[898,30366,1974],{},[1750,30368,1766],{},[1742,30370,4903],{},[1750,30372,1766],{},[1699,30374,30375,30377],{},[898,30376,1974],{},[1750,30378,3751],{},[902,30380,4914],{"encoding":904},[724,30382,30383],{},[883,30384,30386],{"className":30385},[886],[888,30387,30388],{"xmlns":890},[892,30389,30390,30446],{},[4577,30391,30392,30418],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,30393,30394,30400],{},[4585,30395,30396],{},[3586,30397,30398],{"scriptlevel":2607,"displaystyle":1916},[898,30399,1666],{},[4585,30401,30402],{},[3586,30403,30404],{"scriptlevel":2607,"displaystyle":1916},[895,30405,30406,30408,30410,30412,30414,30416],{},[895,30407],{},[1750,30409,1766],{},[898,30411,1812],{},[1750,30413,1861],{},[1742,30415,4903],{},[1750,30417,1917],{"separator":1916},[4582,30419,30420,30426],{},[4585,30421,30422],{},[3586,30423,30424],{"scriptlevel":2607,"displaystyle":1916},[898,30425,1812],{},[4585,30427,30428],{},[3586,30429,30430],{"scriptlevel":2607,"displaystyle":1916},[895,30431,30432,30434,30436,30438,30440,30442,30444],{},[895,30433],{},[1750,30435,1766],{},[1742,30437,3123],{},[898,30439,1666],{},[1750,30441,1861],{},[1742,30443,3079],{},[1750,30445,1917],{"separator":1916},[902,30447,4983],{"encoding":904},[724,30449,4986,30450,1343,30471,5033,30492,1783],{},[883,30451,30453],{"className":30452},[886],[888,30454,30455],{"xmlns":890},[892,30456,30457,30469],{},[895,30458,30459,30465,30467],{},[1699,30460,30461,30463],{},[898,30462,1666],{},[898,30464,1705],{},[1750,30466,1766],{},[1742,30468,5006],{},[902,30470,5009],{"encoding":904},[883,30472,30474],{"className":30473},[886],[888,30475,30476],{"xmlns":890},[892,30477,30478,30490],{},[895,30479,30480,30486,30488],{},[1699,30481,30482,30484],{},[898,30483,1812],{},[898,30485,1705],{},[1750,30487,1766],{},[1742,30489,5029],{},[902,30491,5032],{"encoding":904},[883,30493,30495],{"className":30494},[886],[888,30496,30497],{"xmlns":890},[892,30498,30499,30511],{},[895,30500,30501,30507,30509],{},[1699,30502,30503,30505],{},[898,30504,1779],{},[898,30506,1705],{},[1750,30508,1766],{},[1742,30510,4903],{},[902,30512,5055],{"encoding":904},[724,30514,30515],{},[614,30516,5060,30517,5083,30538,4419,30559,5129,30582,2313],{},[883,30518,30520],{"className":30519},[886],[888,30521,30522],{"xmlns":890},[892,30523,30524,30536],{},[895,30525,30526,30528,30530,30532,30534],{},[898,30527,1812],{},[1750,30529,1766],{},[898,30531,1666],{},[1750,30533,1758],{},[1742,30535,4903],{},[902,30537,5082],{"encoding":904},[883,30539,30541],{"className":30540},[886],[888,30542,30543],{"xmlns":890},[892,30544,30545,30557],{},[895,30546,30547,30549,30551,30553,30555],{},[898,30548,1666],{},[1750,30550,1766],{},[898,30552,1812],{},[1750,30554,1861],{},[898,30556,1974],{},[902,30558,5105],{"encoding":904},[883,30560,30562],{"className":30561},[886],[888,30563,30564],{"xmlns":890},[892,30565,30566,30580],{},[895,30567,30568,30570,30572,30574,30576,30578],{},[898,30569,1812],{},[1750,30571,1766],{},[1742,30573,3123],{},[898,30575,1666],{},[1750,30577,1861],{},[1742,30579,3079],{},[902,30581,4887],{"encoding":904},[883,30583,30585],{"className":30584},[886],[888,30586,30587],{"xmlns":890},[892,30588,30589,30621],{},[895,30590,30591,30593,30599,30601,30607,30609,30611,30613,30615,30617,30619],{},[1750,30592,5141],{"stretchy":1752},[1699,30594,30595,30597],{},[898,30596,1666],{},[898,30598,1705],{},[1750,30600,1917],{"separator":1916},[1699,30602,30603,30605],{},[898,30604,1812],{},[898,30606,1705],{},[1750,30608,5158],{"stretchy":1752},[1750,30610,1766],{},[1750,30612,5141],{"stretchy":1752},[1742,30614,5006],{},[1750,30616,1917],{"separator":1916},[1742,30618,5029],{},[1750,30620,5158],{"stretchy":1752},[902,30622,5173],{"encoding":904},[724,30624,30625,5179,30627,5197,30644,2313],{},[38,30626,5178],{},[883,30628,30630],{"className":30629},[886],[888,30631,30632],{"xmlns":890},[892,30633,30634,30642],{},[895,30635,30636,30638,30640],{},[898,30637,1812],{},[1969,30639,1971],{},[898,30641,1974],{},[902,30643,1977],{"encoding":904},[38,30645,5200,30646],{},[883,30647,30649],{"className":30648},[886],[888,30650,30651],{"xmlns":890},[892,30652,30653,30665],{},[895,30654,30655,30657,30659,30661,30663],{},[898,30656,1812],{},[1969,30658,1971],{},[898,30660,1974],{},[1969,30662,1971],{},[898,30664,1997],{},[902,30666,2000],{"encoding":904},[115,30668,5225],{"id":5224},[198,30670,4443],{"id":5228},[724,30672,5231,30673,5249,30690,1647,30692,2084,30705,5269],{},[883,30674,30676],{"className":30675},[886],[888,30677,30678],{"xmlns":890},[892,30679,30680,30688],{},[895,30681,30682,30684,30686],{},[898,30683,1812],{},[1969,30685,1971],{},[898,30687,1974],{},[902,30689,1977],{"encoding":904},[38,30691,5252],{},[883,30693,30695],{"className":30694},[886],[888,30696,30697],{"xmlns":890},[892,30698,30699,30703],{},[895,30700,30701],{},[898,30702,1997],{},[902,30704,1997],{"encoding":904},[614,30706,5268],{},[724,30708,30709],{},[883,30710,30712],{"className":30711},[886],[888,30713,30714],{"xmlns":890},[892,30715,30716,30742],{},[895,30717,30718,30720,30722,30724,30726,30728,30730,30732,30734,30736,30738,30740],{},[898,30719,1666],{},[1750,30721,1766],{},[898,30723,1812],{},[1750,30725,1861],{},[898,30727,1974],{},[1750,30729,1861],{},[898,30731,1997],{},[898,30733,2313],{"mathvariant":1747},[2125,30735],{"width":2127},[1750,30737,1753],{"stretchy":1752},[1742,30739,5303],{},[1750,30741,1763],{"stretchy":1752},[902,30743,5308],{"encoding":904},[724,30745,5311,30746,1647,30748,2084,30761,5332],{},[38,30747,5314],{},[883,30749,30751],{"className":30750},[886],[888,30752,30753],{"xmlns":890},[892,30754,30755,30759],{},[895,30756,30757],{},[898,30758,5326],{},[902,30760,5326],{"encoding":904},[614,30762,5331],{},[120,30764,30765,30796,30819],{},[123,30766,5337,30767,1917],{},[883,30768,30770],{"className":30769},[886],[888,30771,30772],{"xmlns":890},[892,30773,30774,30794],{},[895,30775,30776,30778,30780,30782,30784,30786,30788,30790,30792],{},[898,30777,5326],{},[1750,30779,1766],{},[898,30781,5326],{},[1750,30783,1753],{"stretchy":1752},[898,30785,1666],{},[1750,30787,1763],{"stretchy":1752},[1750,30789,1766],{},[898,30791,2652],{},[898,30793,1666],{},[902,30795,5367],{"encoding":904},[123,30797,5370,30798,1917],{},[883,30799,30801],{"className":30800},[886],[888,30802,30803],{"xmlns":890},[892,30804,30805,30817],{},[895,30806,30807,30809,30811],{},[898,30808,5326],{},[1750,30810,1766],{},[1699,30812,30813,30815],{},[898,30814,5326],{},[1750,30816,3751],{},[902,30818,5392],{"encoding":904},[123,30820,5395,30821,5424,30848,2313],{},[883,30822,30824],{"className":30823},[886],[888,30825,30826],{"xmlns":890},[892,30827,30828,30846],{},[895,30829,30830,30832,30834,30840,30842,30844],{},[898,30831,5326],{},[1750,30833,1766],{},[1699,30835,30836,30838],{},[898,30837,5326],{},[1750,30839,3751],{},[1750,30841,1861],{},[898,30843,2652],{},[898,30845,1666],{},[902,30847,5423],{"encoding":904},[883,30849,30851],{"className":30850},[886],[888,30852,30853],{"xmlns":890},[892,30854,30855,30867],{},[895,30856,30857,30859,30861,30863,30865],{},[1742,30858,2607],{},[1750,30860,5438],{},[898,30862,2652],{},[1750,30864,2624],{},[1742,30866,1744],{},[902,30868,5447],{"encoding":904},[1785,30870,30871],{},[724,30872,30873,5455,30875,5477,30896,5481,30898,5495,30911,4419,30936,1647,30938,5553,30963,5582,30990,2028,31003,5614],{},[883,30874,5454],{},[883,30876,30878],{"className":30877},[886],[888,30879,30880],{"xmlns":890},[892,30881,30882,30894],{},[895,30883,30884,30886,30888,30890,30892],{},[898,30885,1812],{},[1969,30887,1971],{},[898,30889,1974],{},[1969,30891,1971],{},[898,30893,1997],{},[902,30895,2000],{"encoding":904},[38,30897,5480],{},[883,30899,30901],{"className":30900},[886],[888,30902,30903],{"xmlns":890},[892,30904,30905,30909],{},[895,30906,30907],{},[898,30908,1666],{},[902,30910,1666],{"encoding":904},[883,30912,30914],{"className":30913},[886],[888,30915,30916],{"xmlns":890},[892,30917,30918,30934],{},[895,30919,30920,30922,30924,30926,30928,30930,30932],{},[898,30921,1666],{},[1750,30923,1766],{},[898,30925,1812],{},[1750,30927,1861],{},[898,30929,1974],{},[1750,30931,1861],{},[898,30933,1997],{},[902,30935,5521],{"encoding":904},[38,30937,5524],{},[883,30939,30941],{"className":30940},[886],[888,30942,30943],{"xmlns":890},[892,30944,30945,30961],{},[895,30946,30947,30953,30955,30957,30959],{},[5535,30948,30949,30951],{},[898,30950,1666],{},[898,30952,5541],{},[1750,30954,1766],{},[898,30956,1666],{},[1750,30958,1758],{},[898,30960,5326],{},[902,30962,5552],{"encoding":904},[883,30964,30966],{"className":30965},[886],[888,30967,30968],{"xmlns":890},[892,30969,30970,30988],{},[895,30971,30972,30974,30976,30978,30980,30986],{},[898,30973,1812],{},[1750,30975,1766],{},[898,30977,1812],{},[1750,30979,1753],{"stretchy":1752},[5535,30981,30982,30984],{},[898,30983,1666],{},[898,30985,5541],{},[1750,30987,1763],{"stretchy":1752},[902,30989,5581],{"encoding":904},[883,30991,30993],{"className":30992},[886],[888,30994,30995],{"xmlns":890},[892,30996,30997,31001],{},[895,30998,30999],{},[898,31000,1666],{},[902,31002,1666],{"encoding":904},[883,31004,31006],{"className":31005},[886],[888,31007,31008],{"xmlns":890},[892,31009,31010,31018],{},[895,31011,31012],{},[5535,31013,31014,31016],{},[898,31015,1666],{},[898,31017,5541],{},[902,31019,5613],{"encoding":904},[724,31021,31022,2084,31024,1763],{},[38,31023,5619],{},[614,31025,5622],{},[724,31027,31028],{},[883,31029,31031],{"className":31030},[886],[888,31032,31033],{"xmlns":890},[892,31034,31035,31051],{},[895,31036,31037,31043,31045,31047,31049],{},[5535,31038,31039,31041],{},[898,31040,1666],{},[898,31042,5541],{},[1750,31044,1766],{},[898,31046,1666],{},[1750,31048,1758],{},[898,31050,5326],{},[902,31052,5552],{"encoding":904},[724,31054,5652,31055,2313],{},[883,31056,31058],{"className":31057},[886],[888,31059,31060],{"xmlns":890},[892,31061,31062,31080],{},[895,31063,31064,31066,31068,31070,31072,31078],{},[898,31065,1812],{},[1750,31067,1766],{},[898,31069,1812],{},[1750,31071,1753],{"stretchy":1752},[5535,31073,31074,31076],{},[898,31075,1666],{},[898,31077,5541],{},[1750,31079,1763],{"stretchy":1752},[902,31081,5581],{"encoding":904},[198,31083,4513],{"id":5682},[724,31085,5685,31086,1343,31107,5729,31128,2366],{},[883,31087,31089],{"className":31088},[886],[888,31090,31091],{"xmlns":890},[892,31092,31093,31105],{},[895,31094,31095,31097,31099],{},[898,31096,1974],{},[1750,31098,1766],{},[1699,31100,31101,31103],{},[898,31102,1974],{},[1750,31104,3751],{},[902,31106,4538],{"encoding":904},[883,31108,31110],{"className":31109},[886],[888,31111,31112],{"xmlns":890},[892,31113,31114,31126],{},[895,31115,31116,31118,31120],{},[898,31117,1997],{},[1750,31119,1766],{},[1699,31121,31122,31124],{},[898,31123,1997],{},[1750,31125,3751],{},[902,31127,5728],{"encoding":904},[883,31129,31131],{"className":31130},[886],[888,31132,31133],{"xmlns":890},[892,31134,31135,31155],{},[895,31136,31137,31139,31141,31143,31145,31151,31153],{},[898,31138,1666],{},[1750,31140,1917],{"separator":1916},[898,31142,1812],{},[1750,31144,1917],{"separator":1916},[5535,31146,31147,31149],{},[898,31148,1666],{},[898,31150,5541],{},[1750,31152,1917],{"separator":1916},[898,31154,5326],{},[902,31156,5759],{"encoding":904},[724,31158,31159],{},[883,31160,31162],{"className":31161},[886],[888,31163,31164],{"xmlns":890},[892,31165,31166,31306],{},[895,31167,31168,31298,31300,31302,31304],{},[4577,31169,31170,31208,31236,31268],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,31171,31172,31178],{},[4585,31173,31174],{},[3586,31175,31176],{"scriptlevel":2607,"displaystyle":1916},[898,31177,1666],{},[4585,31179,31180],{},[3586,31181,31182],{"scriptlevel":2607,"displaystyle":1916},[895,31183,31184,31186,31188,31190,31192,31198,31200,31206],{},[895,31185],{},[1750,31187,1766],{},[898,31189,1812],{},[1750,31191,1861],{},[1699,31193,31194,31196],{},[898,31195,1974],{},[1750,31197,3751],{},[1750,31199,1861],{},[1699,31201,31202,31204],{},[898,31203,1997],{},[1750,31205,3751],{},[1750,31207,1917],{"separator":1916},[4582,31209,31210,31216],{},[4585,31211,31212],{},[3586,31213,31214],{"scriptlevel":2607,"displaystyle":1916},[898,31215,5326],{},[4585,31217,31218],{},[3586,31219,31220],{"scriptlevel":2607,"displaystyle":1916},[895,31221,31222,31224,31226,31228,31230,31232,31234],{},[895,31223],{},[1750,31225,1766],{},[898,31227,5326],{},[1750,31229,1753],{"stretchy":1752},[898,31231,1666],{},[1750,31233,1763],{"stretchy":1752},[1750,31235,1917],{"separator":1916},[4582,31237,31238,31244],{},[4585,31239,31240],{},[3586,31241,31242],{"scriptlevel":2607,"displaystyle":1916},[898,31243,1812],{},[4585,31245,31246],{},[3586,31247,31248],{"scriptlevel":2607,"displaystyle":1916},[895,31249,31250,31252,31254,31256,31258,31264,31266],{},[895,31251],{},[1750,31253,1766],{},[898,31255,1812],{},[1750,31257,1753],{"stretchy":1752},[5535,31259,31260,31262],{},[898,31261,1666],{},[898,31263,5541],{},[1750,31265,1763],{"stretchy":1752},[1750,31267,1917],{"separator":1916},[4582,31269,31270,31280],{},[4585,31271,31272],{},[3586,31273,31274],{"scriptlevel":2607,"displaystyle":1916},[5535,31275,31276,31278],{},[898,31277,1666],{},[898,31279,5541],{},[4585,31281,31282],{},[3586,31283,31284],{"scriptlevel":2607,"displaystyle":1916},[895,31285,31286,31288,31290,31292,31294,31296],{},[895,31287],{},[1750,31289,1766],{},[898,31291,1666],{},[1750,31293,1758],{},[898,31295,5326],{},[1750,31297,1917],{"separator":1916},[2125,31299],{"width":2127},[1750,31301,1753],{"stretchy":1752},[1742,31303,5907],{},[1750,31305,1763],{"stretchy":1752},[902,31307,5912],{"encoding":904},[724,31309,5915,31310,5961,31353,2313],{},[883,31311,31313],{"className":31312},[886],[888,31314,31315],{"xmlns":890},[892,31316,31317,31351],{},[895,31318,31319,31325,31327,31333,31335,31341,31343],{},[1699,31320,31321,31323],{},[898,31322,1666],{},[898,31324,1705],{},[1750,31326,1917],{"separator":1916},[1699,31328,31329,31331],{},[898,31330,1812],{},[898,31332,1705],{},[1750,31334,1917],{"separator":1916},[1699,31336,31337,31339],{},[898,31338,5326],{},[898,31340,1705],{},[1750,31342,1917],{"separator":1916},[5950,31344,31345,31347,31349],{},[898,31346,1666],{},[898,31348,5541],{},[898,31350,1705],{},[902,31352,5960],{"encoding":904},[883,31354,31356],{"className":31355},[886],[888,31357,31358],{"xmlns":890},[892,31359,31360,31386],{},[895,31361,31362,31368,31370,31378,31380],{},[1699,31363,31364,31366],{},[898,31365,1779],{},[898,31367,1705],{},[1750,31369,1766],{},[5950,31371,31372,31374,31376],{},[898,31373,1666],{},[898,31375,5541],{},[898,31377,1705],{},[1750,31379,1758],{},[1699,31381,31382,31384],{},[898,31383,1812],{},[898,31385,1705],{},[902,31387,5997],{"encoding":904},[1785,31389,31390,31394],{},[724,31391,31392,6005],{},[883,31393,6004],{},[152,31395,31396,31417,31495,31548,31634],{},[123,31397,31398,6013,31400,2313],{},[38,31399,6012],{},[883,31401,31403],{"className":31402},[886],[888,31404,31405],{"xmlns":890},[892,31406,31407,31415],{},[895,31408,31409],{},[5535,31410,31411,31413],{},[898,31412,1666],{},[898,31414,5541],{},[902,31416,5613],{"encoding":904},[123,31418,31419,6082,31465,6100,31482,2313],{},[38,31420,6035,31421,6056,31440],{},[883,31422,31424],{"className":31423},[886],[888,31425,31426],{"xmlns":890},[892,31427,31428,31438],{},[895,31429,31430,31432,31434,31436],{},[898,31431,5326],{},[1750,31433,1753],{"stretchy":1752},[898,31435,1666],{},[1750,31437,1763],{"stretchy":1752},[902,31439,6055],{"encoding":904},[883,31441,31443],{"className":31442},[886],[888,31444,31445],{"xmlns":890},[892,31446,31447,31463],{},[895,31448,31449,31455,31457,31459,31461],{},[5535,31450,31451,31453],{},[898,31452,1666],{},[898,31454,5541],{},[1750,31456,1766],{},[898,31458,1666],{},[1750,31460,1758],{},[898,31462,5326],{},[902,31464,5552],{"encoding":904},[883,31466,31468],{"className":31467},[886],[888,31469,31470],{"xmlns":890},[892,31471,31472,31480],{},[895,31473,31474],{},[5535,31475,31476,31478],{},[898,31477,1666],{},[898,31479,5541],{},[902,31481,5613],{"encoding":904},[883,31483,31485],{"className":31484},[886],[888,31486,31487],{"xmlns":890},[892,31488,31489,31493],{},[895,31490,31491],{},[898,31492,1666],{},[902,31494,1666],{"encoding":904},[123,31496,31497,6082,31522,6100,31535,2313],{},[38,31498,6035,31499,6142],{},[883,31500,31502],{"className":31501},[886],[888,31503,31504],{"xmlns":890},[892,31505,31506,31520],{},[895,31507,31508,31514,31516,31518],{},[5535,31509,31510,31512],{},[898,31511,1666],{},[898,31513,5541],{},[1750,31515,1753],{"stretchy":1752},[898,31517,1666],{},[1750,31519,1763],{"stretchy":1752},[902,31521,6141],{"encoding":904},[883,31523,31525],{"className":31524},[886],[888,31526,31527],{"xmlns":890},[892,31528,31529,31533],{},[895,31530,31531],{},[898,31532,1812],{},[902,31534,1812],{"encoding":904},[883,31536,31538],{"className":31537},[886],[888,31539,31540],{"xmlns":890},[892,31541,31542,31546],{},[895,31543,31544],{},[898,31545,1666],{},[902,31547,1666],{"encoding":904},[123,31549,31550,1647,31571,6227,31604,6241,31617,2313],{},[38,31551,6035,31552,6192],{},[883,31553,31555],{"className":31554},[886],[888,31556,31557],{"xmlns":890},[892,31558,31559,31569],{},[895,31560,31561,31563,31565,31567],{},[898,31562,1812],{},[1750,31564,1753],{"stretchy":1752},[898,31566,1666],{},[1750,31568,1763],{"stretchy":1752},[902,31570,2432],{"encoding":904},[883,31572,31574],{"className":31573},[886],[888,31575,31576],{"xmlns":890},[892,31577,31578,31602],{},[895,31579,31580,31582,31584,31586,31588,31594,31596],{},[898,31581,1666],{},[1750,31583,1766],{},[898,31585,1812],{},[1750,31587,1861],{},[1699,31589,31590,31592],{},[898,31591,1974],{},[1750,31593,3751],{},[1750,31595,1861],{},[1699,31597,31598,31600],{},[898,31599,1997],{},[1750,31601,3751],{},[902,31603,6226],{"encoding":904},[883,31605,31607],{"className":31606},[886],[888,31608,31609],{"xmlns":890},[892,31610,31611,31615],{},[895,31612,31613],{},[898,31614,1666],{},[902,31616,1666],{"encoding":904},[883,31618,31620],{"className":31619},[886],[888,31621,31622],{"xmlns":890},[892,31623,31624,31632],{},[895,31625,31626],{},[1699,31627,31628,31630],{},[898,31629,1666],{},[898,31631,1705],{},[902,31633,1708],{"encoding":904},[123,31635,31636,6264,31638,1343,31655,1343,31674,1343,31691,2313],{},[38,31637,6263],{},[883,31639,31641],{"className":31640},[886],[888,31642,31643],{"xmlns":890},[892,31644,31645,31653],{},[895,31646,31647],{},[1699,31648,31649,31651],{},[898,31650,5326],{},[898,31652,1705],{},[902,31654,6282],{"encoding":904},[883,31656,31658],{"className":31657},[886],[888,31659,31660],{"xmlns":890},[892,31661,31662,31672],{},[895,31663,31664],{},[5950,31665,31666,31668,31670],{},[898,31667,1666],{},[898,31669,5541],{},[898,31671,1705],{},[902,31673,6302],{"encoding":904},[883,31675,31677],{"className":31676},[886],[888,31678,31679],{"xmlns":890},[892,31680,31681,31689],{},[895,31682,31683],{},[1699,31684,31685,31687],{},[898,31686,1812],{},[898,31688,1705],{},[902,31690,4695],{"encoding":904},[883,31692,31694],{"className":31693},[886],[888,31695,31696],{"xmlns":890},[892,31697,31698,31706],{},[895,31699,31700],{},[1699,31701,31702,31704],{},[898,31703,1779],{},[898,31705,1705],{},[902,31707,6337],{"encoding":904},[198,31709,6341],{"id":6340},[724,31711,4846,31712,6365,31733,1343,31762,1343,31785,1343,31806,6469],{},[883,31713,31715],{"className":31714},[886],[888,31716,31717],{"xmlns":890},[892,31718,31719,31731],{},[895,31720,31721,31723,31725,31727,31729],{},[898,31722,1812],{},[1969,31724,1971],{},[898,31726,1974],{},[1969,31728,1971],{},[898,31730,1997],{},[902,31732,2000],{"encoding":904},[883,31734,31736],{"className":31735},[886],[888,31737,31738],{"xmlns":890},[892,31739,31740,31760],{},[895,31741,31742,31744,31746,31748,31750,31756,31758],{},[898,31743,1812],{},[1750,31745,1766],{},[1742,31747,6381],{},[1969,31749,2658],{},[5535,31751,31752,31754],{},[898,31753,1666],{},[898,31755,5541],{},[1750,31757,1861],{},[1742,31759,6394],{},[902,31761,6397],{"encoding":904},[883,31763,31765],{"className":31764},[886],[888,31766,31767],{"xmlns":890},[892,31768,31769,31783],{},[895,31770,31771,31773,31775,31777,31779,31781],{},[898,31772,5326],{},[1750,31774,1766],{},[1742,31776,3929],{},[898,31778,1666],{},[1750,31780,1861],{},[1742,31782,6419],{},[902,31784,6422],{"encoding":904},[883,31786,31788],{"className":31787},[886],[888,31789,31790],{"xmlns":890},[892,31791,31792,31804],{},[895,31793,31794,31800,31802],{},[1699,31795,31796,31798],{},[898,31797,1974],{},[1750,31799,3751],{},[1750,31801,1766],{},[1742,31803,6442],{},[902,31805,6445],{"encoding":904},[883,31807,31809],{"className":31808},[886],[888,31810,31811],{"xmlns":890},[892,31812,31813,31825],{},[895,31814,31815,31821,31823],{},[1699,31816,31817,31819],{},[898,31818,1997],{},[1750,31820,3751],{},[1750,31822,1766],{},[1742,31824,6465],{},[902,31826,6468],{"encoding":904},[724,31828,31829],{},[883,31830,31832],{"className":31831},[886],[888,31833,31834],{"xmlns":890},[892,31835,31836,31960],{},[4577,31837,31838,31868,31896,31930],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,31839,31840,31846],{},[4585,31841,31842],{},[3586,31843,31844],{"scriptlevel":2607,"displaystyle":1916},[898,31845,1666],{},[4585,31847,31848],{},[3586,31849,31850],{"scriptlevel":2607,"displaystyle":1916},[895,31851,31852,31854,31856,31858,31860,31862,31864,31866],{},[895,31853],{},[1750,31855,1766],{},[898,31857,1812],{},[1750,31859,1861],{},[1742,31861,6442],{},[1750,31863,1861],{},[1742,31865,6465],{},[1750,31867,1917],{"separator":1916},[4582,31869,31870,31876],{},[4585,31871,31872],{},[3586,31873,31874],{"scriptlevel":2607,"displaystyle":1916},[898,31875,5326],{},[4585,31877,31878],{},[3586,31879,31880],{"scriptlevel":2607,"displaystyle":1916},[895,31881,31882,31884,31886,31888,31890,31892,31894],{},[895,31883],{},[1750,31885,1766],{},[1742,31887,3929],{},[898,31889,1666],{},[1750,31891,1861],{},[1742,31893,6419],{},[1750,31895,1917],{"separator":1916},[4582,31897,31898,31904],{},[4585,31899,31900],{},[3586,31901,31902],{"scriptlevel":2607,"displaystyle":1916},[898,31903,1812],{},[4585,31905,31906],{},[3586,31907,31908],{"scriptlevel":2607,"displaystyle":1916},[895,31909,31910,31912,31914,31916,31918,31924,31926,31928],{},[895,31911],{},[1750,31913,1766],{},[1742,31915,6381],{},[1969,31917,2658],{},[5535,31919,31920,31922],{},[898,31921,1666],{},[898,31923,5541],{},[1750,31925,1861],{},[1742,31927,6394],{},[1750,31929,1917],{"separator":1916},[4582,31931,31932,31942],{},[4585,31933,31934],{},[3586,31935,31936],{"scriptlevel":2607,"displaystyle":1916},[5535,31937,31938,31940],{},[898,31939,1666],{},[898,31941,5541],{},[4585,31943,31944],{},[3586,31945,31946],{"scriptlevel":2607,"displaystyle":1916},[895,31947,31948,31950,31952,31954,31956,31958],{},[895,31949],{},[1750,31951,1766],{},[898,31953,1666],{},[1750,31955,1758],{},[898,31957,5326],{},[898,31959,2313],{"mathvariant":1747},[902,31961,6605],{"encoding":904},[724,31963,31964,6611,31966,6667,32019,6714,32062,2366],{},[38,31965,6610],{},[883,31967,31969],{"className":31968},[886],[888,31970,31971],{"xmlns":890},[892,31972,31973,32017],{},[895,31974,31975,31981,31983,31985,31987,31989,31991,31993,31995,31997,31999,32001,32003,32005,32007,32009,32011,32013,32015],{},[5535,31976,31977,31979],{},[898,31978,1666],{},[898,31980,5541],{},[1750,31982,1766],{},[898,31984,1666],{},[1750,31986,1758],{},[898,31988,5326],{},[1750,31990,1766],{},[898,31992,1666],{},[1750,31994,1758],{},[1750,31996,1753],{"stretchy":1752},[1742,31998,3929],{},[898,32000,1666],{},[1750,32002,1861],{},[1742,32004,6419],{},[1750,32006,1763],{"stretchy":1752},[1750,32008,1766],{},[1742,32010,6657],{},[898,32012,1666],{},[1750,32014,1758],{},[1742,32016,6419],{},[902,32018,6666],{"encoding":904},[883,32020,32022],{"className":32021},[886],[888,32023,32024],{"xmlns":890},[892,32025,32026,32060],{},[895,32027,32028,32030,32032,32034,32036,32038,32040,32042,32044,32046,32048,32050,32052,32054,32056,32058],{},[898,32029,1812],{},[1750,32031,1766],{},[1742,32033,6381],{},[1750,32035,1753],{"stretchy":1752},[1742,32037,6657],{},[898,32039,1666],{},[1750,32041,1758],{},[1742,32043,6419],{},[1750,32045,1763],{"stretchy":1752},[1750,32047,1861],{},[1742,32049,6394],{},[1750,32051,1766],{},[1742,32053,6703],{},[898,32055,1666],{},[1750,32057,1861],{},[1742,32059,6710],{},[902,32061,6713],{"encoding":904},[883,32063,32065],{"className":32064},[886],[888,32066,32067],{"xmlns":890},[892,32068,32069,32087],{},[895,32070,32071,32073,32075,32077,32079,32081,32083,32085],{},[898,32072,1666],{},[1750,32074,1766],{},[1742,32076,6703],{},[898,32078,1666],{},[1750,32080,1861],{},[1742,32082,6710],{},[1750,32084,1861],{},[1742,32086,5006],{},[902,32088,6742],{"encoding":904},[724,32090,32091],{},[883,32092,32094],{"className":32093},[886],[888,32095,32096],{"xmlns":890},[892,32097,32098,32134],{},[895,32099,32100,32102,32104,32106,32108,32110,32112,32114,32120,32122,32130,32132],{},[1742,32101,6756],{},[898,32103,1666],{},[1750,32105,1766],{},[1742,32107,6763],{},[1969,32109,6766],{},[1750,32111,6769],{},[1969,32113,6766],{},[1699,32115,32116,32118],{},[898,32117,1666],{},[898,32119,1705],{},[1750,32121,1766],{},[3586,32123,32124],{"scriptlevel":2607,"displaystyle":1752},[3423,32125,32126,32128],{},[1742,32127,6786],{},[1742,32129,6789],{},[1750,32131,6792],{},[1742,32133,6795],{},[902,32135,6798],{"encoding":904},[724,32137,6801],{},[120,32139,32140,32173,32222,32273,32318],{},[123,32141,32142,1917],{},[883,32143,32145],{"className":32144},[886],[888,32146,32147],{"xmlns":890},[892,32148,32149,32171],{},[895,32150,32151,32157,32159,32167,32169],{},[1699,32152,32153,32155],{},[898,32154,1666],{},[898,32156,1705],{},[1750,32158,1766],{},[3586,32160,32161],{"scriptlevel":2607,"displaystyle":1752},[3423,32162,32163,32165],{},[1742,32164,6786],{},[1742,32166,6789],{},[1750,32168,6792],{},[1742,32170,6835],{},[902,32172,6838],{"encoding":904},[123,32174,32175,1917],{},[883,32176,32178],{"className":32177},[886],[888,32179,32180],{"xmlns":890},[892,32181,32182,32220],{},[895,32183,32184,32190,32192,32194,32196,32202,32204,32206,32208,32216,32218],{},[1699,32185,32186,32188],{},[898,32187,5326],{},[898,32189,1705],{},[1750,32191,1766],{},[1742,32193,3929],{},[1969,32195,2658],{},[1699,32197,32198,32200],{},[898,32199,1666],{},[898,32201,1705],{},[1750,32203,1861],{},[1742,32205,6419],{},[1750,32207,1766],{},[3586,32209,32210],{"scriptlevel":2607,"displaystyle":1752},[3423,32211,32212,32214],{},[1742,32213,6880],{},[1742,32215,6789],{},[1750,32217,6792],{},[1742,32219,6887],{},[902,32221,6890],{"encoding":904},[123,32223,32224,1917],{},[883,32225,32227],{"className":32226},[886],[888,32228,32229],{"xmlns":890},[892,32230,32231,32271],{},[895,32232,32233,32241,32243,32249,32251,32257,32259,32267,32269],{},[5950,32234,32235,32237,32239],{},[898,32236,1666],{},[898,32238,5541],{},[898,32240,1705],{},[1750,32242,1766],{},[1699,32244,32245,32247],{},[898,32246,1666],{},[898,32248,1705],{},[1750,32250,1758],{},[1699,32252,32253,32255],{},[898,32254,5326],{},[898,32256,1705],{},[1750,32258,1766],{},[3586,32260,32261],{"scriptlevel":2607,"displaystyle":1752},[3423,32262,32263,32265],{},[1742,32264,6934],{},[1742,32266,6789],{},[1750,32268,6792],{},[1742,32270,6941],{},[902,32272,6944],{"encoding":904},[123,32274,32275,1917],{},[883,32276,32278],{"className":32277},[886],[888,32279,32280],{"xmlns":890},[892,32281,32282,32316],{},[895,32283,32284,32290,32292,32298,32300,32302,32304,32312,32314],{},[1699,32285,32286,32288],{},[898,32287,1812],{},[898,32289,1705],{},[1750,32291,1766],{},[1699,32293,32294,32296],{},[898,32295,1666],{},[898,32297,1705],{},[1750,32299,1758],{},[1742,32301,5006],{},[1750,32303,1766],{},[3586,32305,32306],{"scriptlevel":2607,"displaystyle":1752},[3423,32307,32308,32310],{},[1742,32309,6982],{},[1742,32311,6789],{},[1750,32313,6792],{},[1742,32315,6989],{},[902,32317,6992],{"encoding":904},[123,32319,32320,7051],{},[883,32321,32323],{"className":32322},[886],[888,32324,32325],{"xmlns":890},[892,32326,32327,32371],{},[895,32328,32329,32335,32337,32345,32347,32353,32355,32357,32365,32367,32369],{},[1699,32330,32331,32333],{},[898,32332,1779],{},[898,32334,1705],{},[1750,32336,1766],{},[5950,32338,32339,32341,32343],{},[898,32340,1666],{},[898,32342,5541],{},[898,32344,1705],{},[1750,32346,1758],{},[1699,32348,32349,32351],{},[898,32350,1812],{},[898,32352,1705],{},[1750,32354,1766],{},[1750,32356,1758],{},[3586,32358,32359],{"scriptlevel":2607,"displaystyle":1752},[3423,32360,32361,32363],{},[1742,32362,7038],{},[1742,32364,6789],{},[1750,32366,6792],{},[1750,32368,1758],{},[1742,32370,7047],{},[902,32372,7050],{"encoding":904},[724,32374,32375,5179,32377,7077,32398,7081,32400,7105,32421,2313],{},[38,32376,5178],{},[883,32378,32380],{"className":32379},[886],[888,32381,32382],{"xmlns":890},[892,32383,32384,32396],{},[895,32385,32386,32388,32390,32392,32394],{},[898,32387,1812],{},[1969,32389,1971],{},[898,32391,1974],{},[1969,32393,1971],{},[898,32395,1997],{},[902,32397,2000],{"encoding":904},[38,32399,7080],{},[883,32401,32403],{"className":32402},[886],[888,32404,32405],{"xmlns":890},[892,32406,32407,32419],{},[895,32408,32409,32411,32413,32415,32417],{},[898,32410,2024],{},[1750,32412,1766],{},[898,32414,7097],{},[1750,32416,1758],{},[898,32418,1773],{},[902,32420,7104],{"encoding":904},[38,32422,5200,32423],{},[883,32424,32426],{"className":32425},[886],[888,32427,32428],{"xmlns":890},[892,32429,32430,32446],{},[895,32431,32432,32434,32436,32438,32440,32442,32444],{},[898,32433,1812],{},[1969,32435,1971],{},[898,32437,1974],{},[1969,32439,1971],{},[898,32441,1997],{},[1969,32443,1971],{},[898,32445,2024],{},[902,32447,2027],{"encoding":904},[115,32449,7136],{"id":7135},[198,32451,4443],{"id":7139},[724,32453,7142,32454,1647,32456,5424,32477,7180,32490,4419,32492,7197],{},[38,32455,7145],{},[883,32457,32459],{"className":32458},[886],[888,32460,32461],{"xmlns":890},[892,32462,32463,32475],{},[895,32464,32465,32467,32469,32471,32473],{},[898,32466,2024],{},[1750,32468,1766],{},[898,32470,7097],{},[1750,32472,1758],{},[898,32474,1773],{},[902,32476,7104],{"encoding":904},[883,32478,32480],{"className":32479},[886],[888,32481,32482],{"xmlns":890},[892,32483,32484,32488],{},[895,32485,32486],{},[898,32487,7097],{},[902,32489,7097],{"encoding":904},[614,32491,7183],{},[883,32493,32495],{"className":32494},[886],[888,32496,32497],{"xmlns":890},[892,32498,32499,32503],{},[895,32500,32501],{},[898,32502,1773],{},[902,32504,1773],{"encoding":904},[724,32506,32507],{},[883,32508,32510],{"className":32509},[886],[888,32511,32512],{"xmlns":890},[892,32513,32514,32534],{},[895,32515,32516,32518,32520,32522,32524,32530,32532],{},[898,32517,1773],{},[1750,32519,1766],{},[898,32521,1773],{},[1750,32523,1753],{"stretchy":1752},[5535,32525,32526,32528],{},[898,32527,1666],{},[898,32529,5541],{},[1750,32531,1763],{"stretchy":1752},[898,32533,2313],{"mathvariant":1747},[902,32535,7229],{"encoding":904},[724,32537,7232],{},[724,32539,32540],{},[883,32541,32543],{"className":32542},[886],[888,32544,32545],{"xmlns":890},[892,32546,32547,32583],{},[895,32548,32549,32551,32553,32555,32557,32559,32561,32563,32565,32567,32569,32571,32573,32575,32577,32579,32581],{},[898,32550,1666],{},[1750,32552,1766],{},[898,32554,1812],{},[1750,32556,1861],{},[898,32558,1974],{},[1750,32560,1861],{},[898,32562,1997],{},[1750,32564,1861],{},[898,32566,7097],{},[1750,32568,1758],{},[898,32570,1773],{},[898,32572,2313],{"mathvariant":1747},[2125,32574],{"width":2127},[1750,32576,1753],{"stretchy":1752},[1742,32578,7274],{},[1969,32580,207],{},[1750,32582,1763],{"stretchy":1752},[902,32584,7281],{"encoding":904},[198,32586,4513],{"id":7284},[724,32588,5685,32589,7321,32622,2366],{},[883,32590,32592],{"className":32591},[886],[888,32593,32594],{"xmlns":890},[892,32595,32596,32620],{},[895,32597,32598,32604,32606,32612,32614],{},[1699,32599,32600,32602],{},[898,32601,1974],{},[1750,32603,3751],{},[1750,32605,1917],{"separator":1916},[1699,32607,32608,32610],{},[898,32609,1997],{},[1750,32611,3751],{},[1750,32613,1917],{"separator":1916},[1699,32615,32616,32618],{},[898,32617,7097],{},[1750,32619,3751],{},[902,32621,7320],{"encoding":904},[883,32623,32625],{"className":32624},[886],[888,32626,32627],{"xmlns":890},[892,32628,32629,32653],{},[895,32630,32631,32633,32635,32637,32639,32641,32643,32649,32651],{},[898,32632,1666],{},[1750,32634,1917],{"separator":1916},[898,32636,1812],{},[1750,32638,1917],{"separator":1916},[898,32640,5326],{},[1750,32642,1917],{"separator":1916},[5535,32644,32645,32647],{},[898,32646,1666],{},[898,32648,5541],{},[1750,32650,1917],{"separator":1916},[898,32652,1773],{},[902,32654,7355],{"encoding":904},[724,32656,32657],{},[883,32658,32660],{"className":32659},[886],[888,32661,32662],{"xmlns":890},[892,32663,32664,32848],{},[895,32665,32666,32840,32842,32844,32846],{},[4577,32667,32668,32700,32730,32758,32790],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,32669,32670,32676],{},[4585,32671,32672],{},[3586,32673,32674],{"scriptlevel":2607,"displaystyle":1916},[898,32675,1812],{},[4585,32677,32678],{},[3586,32679,32680],{"scriptlevel":2607,"displaystyle":1916},[895,32681,32682,32684,32686,32688,32690,32696,32698],{},[895,32683],{},[1750,32685,1766],{},[898,32687,1812],{},[1750,32689,1753],{"stretchy":1752},[5535,32691,32692,32694],{},[898,32693,1666],{},[898,32695,5541],{},[1750,32697,1763],{"stretchy":1752},[1750,32699,1917],{"separator":1916},[4582,32701,32702,32712],{},[4585,32703,32704],{},[3586,32705,32706],{"scriptlevel":2607,"displaystyle":1916},[5535,32707,32708,32710],{},[898,32709,1666],{},[898,32711,5541],{},[4585,32713,32714],{},[3586,32715,32716],{"scriptlevel":2607,"displaystyle":1916},[895,32717,32718,32720,32722,32724,32726,32728],{},[895,32719],{},[1750,32721,1766],{},[898,32723,1666],{},[1750,32725,1758],{},[898,32727,5326],{},[1750,32729,1917],{"separator":1916},[4582,32731,32732,32738],{},[4585,32733,32734],{},[3586,32735,32736],{"scriptlevel":2607,"displaystyle":1916},[898,32737,5326],{},[4585,32739,32740],{},[3586,32741,32742],{"scriptlevel":2607,"displaystyle":1916},[895,32743,32744,32746,32748,32750,32752,32754,32756],{},[895,32745],{},[1750,32747,1766],{},[898,32749,5326],{},[1750,32751,1753],{"stretchy":1752},[898,32753,1666],{},[1750,32755,1763],{"stretchy":1752},[1750,32757,1917],{"separator":1916},[4582,32759,32760,32766],{},[4585,32761,32762],{},[3586,32763,32764],{"scriptlevel":2607,"displaystyle":1916},[898,32765,1773],{},[4585,32767,32768],{},[3586,32769,32770],{"scriptlevel":2607,"displaystyle":1916},[895,32771,32772,32774,32776,32778,32780,32786,32788],{},[895,32773],{},[1750,32775,1766],{},[898,32777,1773],{},[1750,32779,1753],{"stretchy":1752},[5535,32781,32782,32784],{},[898,32783,1666],{},[898,32785,5541],{},[1750,32787,1763],{"stretchy":1752},[1750,32789,1917],{"separator":1916},[4582,32791,32792,32798],{},[4585,32793,32794],{},[3586,32795,32796],{"scriptlevel":2607,"displaystyle":1916},[898,32797,1666],{},[4585,32799,32800],{},[3586,32801,32802],{"scriptlevel":2607,"displaystyle":1916},[895,32803,32804,32806,32808,32810,32812,32818,32820,32826,32828,32834,32836,32838],{},[895,32805],{},[1750,32807,1766],{},[898,32809,1812],{},[1750,32811,1861],{},[1699,32813,32814,32816],{},[898,32815,1974],{},[1750,32817,3751],{},[1750,32819,1861],{},[1699,32821,32822,32824],{},[898,32823,1997],{},[1750,32825,3751],{},[1750,32827,1861],{},[1699,32829,32830,32832],{},[898,32831,7097],{},[1750,32833,3751],{},[1750,32835,1758],{},[898,32837,1773],{},[898,32839,2313],{"mathvariant":1747},[2125,32841],{"width":2127},[1750,32843,1753],{"stretchy":1752},[1742,32845,7274],{},[1750,32847,1763],{"stretchy":1752},[902,32849,7551],{"encoding":904},[198,32851,7555],{"id":7554},[724,32853,7558,32854,1343,32883,1343,32908,1343,32927,1343,32948,1343,32969,7707],{},[883,32855,32857],{"className":32856},[886],[888,32858,32859],{"xmlns":890},[892,32860,32861,32881],{},[895,32862,32863,32865,32867,32869,32871,32877,32879],{},[898,32864,1812],{},[1750,32866,1766],{},[1742,32868,7574],{},[1969,32870,2658],{},[5535,32872,32873,32875],{},[898,32874,1666],{},[898,32876,5541],{},[1750,32878,1861],{},[1742,32880,7587],{},[902,32882,7590],{"encoding":904},[883,32884,32886],{"className":32885},[886],[888,32887,32888],{"xmlns":890},[892,32889,32890,32906],{},[895,32891,32892,32894,32896,32898,32900],{},[898,32893,1773],{},[1750,32895,1766],{},[1742,32897,7606],{},[1969,32899,2658],{},[5535,32901,32902,32904],{},[898,32903,1666],{},[898,32905,5541],{},[902,32907,7617],{"encoding":904},[883,32909,32911],{"className":32910},[886],[888,32912,32913],{"xmlns":890},[892,32914,32915,32925],{},[895,32916,32917,32919,32921,32923],{},[898,32918,5326],{},[1750,32920,1766],{},[1742,32922,7633],{},[898,32924,1666],{},[902,32926,7638],{"encoding":904},[883,32928,32930],{"className":32929},[886],[888,32931,32932],{"xmlns":890},[892,32933,32934,32946],{},[895,32935,32936,32942,32944],{},[1699,32937,32938,32940],{},[898,32939,1974],{},[1750,32941,3751],{},[1750,32943,1766],{},[1742,32945,7658],{},[902,32947,7661],{"encoding":904},[883,32949,32951],{"className":32950},[886],[888,32952,32953],{"xmlns":890},[892,32954,32955,32967],{},[895,32956,32957,32963,32965],{},[1699,32958,32959,32961],{},[898,32960,1997],{},[1750,32962,3751],{},[1750,32964,1766],{},[1742,32966,4236],{},[902,32968,7683],{"encoding":904},[883,32970,32972],{"className":32971},[886],[888,32973,32974],{"xmlns":890},[892,32975,32976,32988],{},[895,32977,32978,32984,32986],{},[1699,32979,32980,32982],{},[898,32981,7097],{},[1750,32983,3751],{},[1750,32985,1766],{},[1742,32987,7703],{},[902,32989,7706],{"encoding":904},[724,32991,32992],{},[883,32993,32995],{"className":32994},[886],[888,32996,32997],{"xmlns":890},[892,32998,32999,33217],{},[4577,33000,33001,33047,33089,33125,33167],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,33002,33003,33019],{},[4585,33004,33005],{},[3586,33006,33007],{"scriptlevel":2607,"displaystyle":1916},[895,33008,33009,33011,33013,33015,33017],{},[1750,33010,1753],{"stretchy":1752},[898,33012,1920],{},[1742,33014,1744],{},[1750,33016,1763],{"stretchy":1752},[1969,33018,7737],{},[4585,33020,33021],{},[3586,33022,33023],{"scriptlevel":2607,"displaystyle":1916},[895,33024,33025,33027,33029,33031,33033,33035,33041,33043,33045],{},[895,33026],{},[898,33028,1812],{},[1750,33030,1766],{},[1742,33032,7574],{},[1969,33034,2658],{},[5535,33036,33037,33039],{},[898,33038,1666],{},[898,33040,5541],{},[1750,33042,1861],{},[1742,33044,7587],{},[1750,33046,1917],{"separator":1916},[4582,33048,33049,33065],{},[4585,33050,33051],{},[3586,33052,33053],{"scriptlevel":2607,"displaystyle":1916},[895,33054,33055,33057,33059,33061,33063],{},[1750,33056,1753],{"stretchy":1752},[898,33058,1920],{},[1742,33060,1872],{},[1750,33062,1763],{"stretchy":1752},[1969,33064,7737],{},[4585,33066,33067],{},[3586,33068,33069],{"scriptlevel":2607,"displaystyle":1916},[895,33070,33071,33073,33079,33081,33083,33085,33087],{},[895,33072],{},[5535,33074,33075,33077],{},[898,33076,1666],{},[898,33078,5541],{},[1750,33080,1766],{},[898,33082,1666],{},[1750,33084,1758],{},[898,33086,5326],{},[1750,33088,1917],{"separator":1916},[4582,33090,33091,33107],{},[4585,33092,33093],{},[3586,33094,33095],{"scriptlevel":2607,"displaystyle":1916},[895,33096,33097,33099,33101,33103,33105],{},[1750,33098,1753],{"stretchy":1752},[898,33100,1920],{},[1742,33102,7822],{},[1750,33104,1763],{"stretchy":1752},[1969,33106,7737],{},[4585,33108,33109],{},[3586,33110,33111],{"scriptlevel":2607,"displaystyle":1916},[895,33112,33113,33115,33117,33119,33121,33123],{},[895,33114],{},[898,33116,5326],{},[1750,33118,1766],{},[1742,33120,7633],{},[898,33122,1666],{},[1750,33124,1917],{"separator":1916},[4582,33126,33127,33143],{},[4585,33128,33129],{},[3586,33130,33131],{"scriptlevel":2607,"displaystyle":1916},[895,33132,33133,33135,33137,33139,33141],{},[1750,33134,1753],{"stretchy":1752},[898,33136,1920],{},[1742,33138,7859],{},[1750,33140,1763],{"stretchy":1752},[1969,33142,7737],{},[4585,33144,33145],{},[3586,33146,33147],{"scriptlevel":2607,"displaystyle":1916},[895,33148,33149,33151,33153,33155,33157,33159,33165],{},[895,33150],{},[898,33152,1773],{},[1750,33154,1766],{},[1742,33156,7606],{},[1969,33158,2658],{},[5535,33160,33161,33163],{},[898,33162,1666],{},[898,33164,5541],{},[1750,33166,1917],{"separator":1916},[4582,33168,33169,33185],{},[4585,33170,33171],{},[3586,33172,33173],{"scriptlevel":2607,"displaystyle":1916},[895,33174,33175,33177,33179,33181,33183],{},[1750,33176,1753],{"stretchy":1752},[898,33178,1920],{},[1742,33180,7902],{},[1750,33182,1763],{"stretchy":1752},[1969,33184,7737],{},[4585,33186,33187],{},[3586,33188,33189],{"scriptlevel":2607,"displaystyle":1916},[895,33190,33191,33193,33195,33197,33199,33201,33203,33205,33207,33209,33211,33213,33215],{},[895,33192],{},[898,33194,1666],{},[1750,33196,1766],{},[898,33198,1812],{},[1750,33200,1861],{},[1742,33202,7658],{},[1750,33204,1861],{},[1742,33206,4236],{},[1750,33208,1861],{},[1742,33210,7703],{},[1750,33212,1758],{},[898,33214,1773],{},[898,33216,2313],{"mathvariant":1747},[902,33218,7941],{"encoding":904},[724,33220,7944,33221,7979],{},[883,33222,33224],{"className":33223},[886],[888,33225,33226],{"xmlns":890},[892,33227,33228,33252],{},[895,33229,33230,33236,33238,33240,33242,33244,33246,33248,33250],{},[5535,33231,33232,33234],{},[898,33233,1666],{},[898,33235,5541],{},[1750,33237,1766],{},[898,33239,1666],{},[1750,33241,1758],{},[1742,33243,7633],{},[898,33245,1666],{},[1750,33247,1766],{},[1742,33249,7574],{},[898,33251,1666],{},[902,33253,7978],{"encoding":904},[724,33255,33256],{},[883,33257,33259],{"className":33258},[886],[888,33260,33261],{"xmlns":890},[892,33262,33263,33303],{},[895,33264,33265,33267,33269,33271,33273,33275,33277,33279,33281,33283,33285,33287,33289,33291,33293,33295,33297,33299,33301],{},[1750,33266,1753],{"stretchy":1752},[898,33268,1920],{},[1742,33270,3219],{},[1750,33272,1763],{"stretchy":1752},[1969,33274,7737],{},[898,33276,1812],{},[1750,33278,1766],{},[1742,33280,7574],{},[1750,33282,8009],{},[1742,33284,7574],{},[898,33286,1666],{},[1750,33288,1861],{},[1742,33290,7587],{},[1750,33292,1766],{},[1742,33294,8022],{},[898,33296,1666],{},[1750,33298,1861],{},[1742,33300,7587],{},[1750,33302,1917],{"separator":1916},[902,33304,8033],{"encoding":904},[724,33306,33307],{},[883,33308,33310],{"className":33309},[886],[888,33311,33312],{"xmlns":890},[892,33313,33314,33346],{},[895,33315,33316,33318,33320,33322,33324,33326,33328,33330,33332,33334,33336,33338,33340,33342,33344],{},[1750,33317,1753],{"stretchy":1752},[898,33319,1920],{},[1742,33321,8051],{},[1750,33323,1763],{"stretchy":1752},[1969,33325,7737],{},[898,33327,1773],{},[1750,33329,1766],{},[1742,33331,7606],{},[1750,33333,8009],{},[1742,33335,7574],{},[898,33337,1666],{},[1750,33339,1766],{},[1742,33341,8072],{},[898,33343,1666],{},[898,33345,2313],{"mathvariant":1747},[902,33347,8079],{"encoding":904},[724,33349,8082],{},[724,33351,33352],{},[883,33353,33355],{"className":33354},[886],[888,33356,33357],{"xmlns":890},[892,33358,33359,33401],{},[895,33360,33361,33363,33365,33367,33369,33371,33373,33375,33377,33379,33381,33383,33385,33387,33389,33391,33393,33395,33397,33399],{},[898,33362,1666],{},[1750,33364,1766],{},[1742,33366,8022],{},[898,33368,1666],{},[1750,33370,1861],{},[1742,33372,7587],{},[1750,33374,1861],{},[1742,33376,7658],{},[1750,33378,1861],{},[1742,33380,4236],{},[1750,33382,1861],{},[1742,33384,7703],{},[1750,33386,1758],{},[1742,33388,8072],{},[898,33390,1666],{},[1750,33392,1766],{},[1742,33394,8128],{},[898,33396,1666],{},[1750,33398,1861],{},[1742,33400,8135],{},[902,33402,8138],{"encoding":904},[724,33404,8141,33405,8164,33424,8188],{},[883,33406,33408],{"className":33407},[886],[888,33409,33410],{"xmlns":890},[892,33411,33412,33422],{},[895,33413,33414,33416,33418,33420],{},[1742,33415,8153],{},[898,33417,1666],{},[1750,33419,1766],{},[1742,33421,8160],{},[902,33423,8163],{"encoding":904},[883,33425,33427],{"className":33426},[886],[888,33428,33429],{"xmlns":890},[892,33430,33431,33443],{},[895,33432,33433,33439,33441],{},[1699,33434,33435,33437],{},[898,33436,1666],{},[898,33438,1705],{},[1750,33440,1766],{},[1742,33442,8184],{},[902,33444,8187],{"encoding":904},[120,33446,33447,33470,33501,33534,33565,33600],{},[123,33448,33449,1917],{},[883,33450,33452],{"className":33451},[886],[888,33453,33454],{"xmlns":890},[892,33455,33456,33468],{},[895,33457,33458,33464,33466],{},[1699,33459,33460,33462],{},[898,33461,1666],{},[898,33463,1705],{},[1750,33465,1766],{},[1742,33467,8184],{},[902,33469,8187],{"encoding":904},[123,33471,33472,1917],{},[883,33473,33475],{"className":33474},[886],[888,33476,33477],{"xmlns":890},[892,33478,33479,33499],{},[895,33480,33481,33487,33489,33491,33493,33495,33497],{},[1699,33482,33483,33485],{},[898,33484,5326],{},[898,33486,1705],{},[1750,33488,1766],{},[1742,33490,7633],{},[1750,33492,8009],{},[1742,33494,8184],{},[1750,33496,1766],{},[1742,33498,8243],{},[902,33500,8246],{"encoding":904},[123,33502,33503,1917],{},[883,33504,33506],{"className":33505},[886],[888,33507,33508],{"xmlns":890},[892,33509,33510,33532],{},[895,33511,33512,33520,33522,33524,33526,33528,33530],{},[5950,33513,33514,33516,33518],{},[898,33515,1666],{},[898,33517,5541],{},[898,33519,1705],{},[1750,33521,1766],{},[1742,33523,7574],{},[1750,33525,8009],{},[1742,33527,8184],{},[1750,33529,1766],{},[1742,33531,8278],{},[902,33533,8281],{"encoding":904},[123,33535,33536,1917],{},[883,33537,33539],{"className":33538},[886],[888,33540,33541],{"xmlns":890},[892,33542,33543,33563],{},[895,33544,33545,33551,33553,33555,33557,33559,33561],{},[1699,33546,33547,33549],{},[898,33548,1773],{},[898,33550,1705],{},[1750,33552,1766],{},[1742,33554,7606],{},[1750,33556,8009],{},[1742,33558,8278],{},[1750,33560,1766],{},[1742,33562,8311],{},[902,33564,8314],{"encoding":904},[123,33566,33567,1917],{},[883,33568,33570],{"className":33569},[886],[888,33571,33572],{"xmlns":890},[892,33573,33574,33598],{},[895,33575,33576,33582,33584,33586,33588,33590,33592,33594,33596],{},[1699,33577,33578,33580],{},[898,33579,1812],{},[898,33581,1705],{},[1750,33583,1766],{},[1742,33585,7574],{},[1750,33587,8009],{},[1742,33589,8278],{},[1750,33591,1861],{},[1742,33593,7587],{},[1750,33595,1766],{},[1742,33597,8278],{},[902,33599,8350],{"encoding":904},[123,33601,33602,8393],{},[883,33603,33605],{"className":33604},[886],[888,33606,33607],{"xmlns":890},[892,33608,33609,33639],{},[895,33610,33611,33617,33619,33627,33629,33635,33637],{},[1699,33612,33613,33615],{},[898,33614,1779],{},[898,33616,1705],{},[1750,33618,1766],{},[5950,33620,33621,33623,33625],{},[898,33622,1666],{},[898,33624,5541],{},[898,33626,1705],{},[1750,33628,1758],{},[1699,33630,33631,33633],{},[898,33632,1812],{},[898,33634,1705],{},[1750,33636,1766],{},[1742,33638,2607],{},[902,33640,8392],{"encoding":904},[724,33642,33643,8398,33645,1343,33662,2028,33683,8462,33708,8466,33710,8480,33723,2313],{},[38,33644,5178],{},[883,33646,33648],{"className":33647},[886],[888,33649,33650],{"xmlns":890},[892,33651,33652,33660],{},[895,33653,33654,33656,33658],{},[898,33655,1812],{},[1969,33657,1971],{},[898,33659,1974],{},[902,33661,1977],{"encoding":904},[883,33663,33665],{"className":33664},[886],[888,33666,33667],{"xmlns":890},[892,33668,33669,33681],{},[895,33670,33671,33673,33675,33677,33679],{},[898,33672,1812],{},[1969,33674,1971],{},[898,33676,1974],{},[1969,33678,1971],{},[898,33680,1997],{},[902,33682,2000],{"encoding":904},[883,33684,33686],{"className":33685},[886],[888,33687,33688],{"xmlns":890},[892,33689,33690,33706],{},[895,33691,33692,33694,33696,33698,33700,33702,33704],{},[898,33693,1812],{},[1969,33695,1971],{},[898,33697,1974],{},[1969,33699,1971],{},[898,33701,1997],{},[1969,33703,1971],{},[898,33705,2024],{},[902,33707,2027],{"encoding":904},[38,33709,8465],{},[883,33711,33713],{"className":33712},[886],[888,33714,33715],{"xmlns":890},[892,33716,33717,33721],{},[895,33718,33719],{},[898,33720,1920],{},[902,33722,1920],{"encoding":904},[38,33724,8483],{},[115,33726,8487],{"id":8486},[724,33728,8490,33729,8495,33732,8499,33734,8503],{},[207,33730,8494],{"className":33731,"dataFsResolvedFilePath":827,"href":828},[210],[38,33733,8498],{},[38,33735,8502],{},[724,33737,33738],{},[4434,33739],{"alt":8508,"className":33740,"src":8510},[210,4438],[724,33742,8513,33743,1343,33760,1343,33781,8577,33806,8581,33808,8600,33825,8619,33842,8638,33859,8642,33861,1343,33878,8677,33895,8680],{},[883,33744,33746],{"className":33745},[886],[888,33747,33748],{"xmlns":890},[892,33749,33750,33758],{},[895,33751,33752,33754,33756],{},[898,33753,1812],{},[1969,33755,1971],{},[898,33757,1974],{},[902,33759,1977],{"encoding":904},[883,33761,33763],{"className":33762},[886],[888,33764,33765],{"xmlns":890},[892,33766,33767,33779],{},[895,33768,33769,33771,33773,33775,33777],{},[898,33770,1812],{},[1969,33772,1971],{},[898,33774,1974],{},[1969,33776,1971],{},[898,33778,1997],{},[902,33780,2000],{"encoding":904},[883,33782,33784],{"className":33783},[886],[888,33785,33786],{"xmlns":890},[892,33787,33788,33804],{},[895,33789,33790,33792,33794,33796,33798,33800,33802],{},[898,33791,1812],{},[1969,33793,1971],{},[898,33795,1974],{},[1969,33797,1971],{},[898,33799,1997],{},[1969,33801,1971],{},[898,33803,2024],{},[902,33805,2027],{"encoding":904},[38,33807,8580],{},[883,33809,33811],{"className":33810},[886],[888,33812,33813],{"xmlns":890},[892,33814,33815,33823],{},[895,33816,33817],{},[1699,33818,33819,33821],{},[898,33820,1974],{},[1750,33822,3751],{},[902,33824,8599],{"encoding":904},[883,33826,33828],{"className":33827},[886],[888,33829,33830],{"xmlns":890},[892,33831,33832,33840],{},[895,33833,33834],{},[1699,33835,33836,33838],{},[898,33837,1997],{},[1750,33839,3751],{},[902,33841,8618],{"encoding":904},[883,33843,33845],{"className":33844},[886],[888,33846,33847],{"xmlns":890},[892,33848,33849,33857],{},[895,33850,33851],{},[1699,33852,33853,33855],{},[898,33854,7097],{},[1750,33856,3751],{},[902,33858,8637],{"encoding":904},[38,33860,8641],{},[883,33862,33864],{"className":33863},[886],[888,33865,33866],{"xmlns":890},[892,33867,33868,33876],{},[895,33869,33870],{},[1699,33871,33872,33874],{},[898,33873,1666],{},[898,33875,1705],{},[902,33877,1708],{"encoding":904},[883,33879,33881],{"className":33880},[886],[888,33882,33883],{"xmlns":890},[892,33884,33885,33893],{},[895,33886,33887],{},[1699,33888,33889,33891],{},[898,33890,1812],{},[898,33892,1705],{},[902,33894,4695],{"encoding":904},[38,33896,1730],{},[198,33898,8684],{"id":8683},[724,33900,4719,33901,8710,33924,8755],{},[883,33902,33904],{"className":33903},[886],[888,33905,33906],{"xmlns":890},[892,33907,33908,33922],{},[895,33909,33910,33912,33914,33916,33918,33920],{},[898,33911,1812],{},[1750,33913,1766],{},[898,33915,207],{},[898,33917,1666],{},[1750,33919,1861],{},[898,33921,2573],{},[902,33923,2720],{"encoding":904},[883,33925,33927],{"className":33926},[886],[888,33928,33929],{"xmlns":890},[892,33930,33931,33965],{},[895,33932,33933,33939,33941],{},[1699,33934,33935,33937],{},[898,33936,1666],{},[898,33938,1705],{},[1750,33940,1766],{},[3586,33942,33943],{"scriptlevel":2607,"displaystyle":1916},[3423,33944,33945,33957],{},[895,33946,33947,33949,33951],{},[898,33948,2573],{},[1750,33950,1861],{},[1699,33952,33953,33955],{},[898,33954,1974],{},[1750,33956,3751],{},[895,33958,33959,33961,33963],{},[1742,33960,1744],{},[1750,33962,1758],{},[898,33964,207],{},[902,33966,8754],{"encoding":904},[724,33968,33969],{},[883,33970,33972],{"className":33971},[886],[888,33973,33974],{"xmlns":890},[892,33975,33976,34042],{},[895,33977,33978,33996,33998,34028,34030],{},[3423,33979,33980,33990],{},[895,33981,33982,33984],{},[898,33983,8773],{"mathvariant":1747},[1699,33985,33986,33988],{},[898,33987,1666],{},[898,33989,1705],{},[895,33991,33992,33994],{},[898,33993,8773],{"mathvariant":1747},[898,33995,207],{},[1750,33997,1766],{},[3423,33999,34000,34012],{},[895,34001,34002,34004,34006],{},[898,34003,2573],{},[1750,34005,1861],{},[1699,34007,34008,34010],{},[898,34009,1974],{},[1750,34011,3751],{},[895,34013,34014,34016,34018,34020,34022],{},[1750,34015,1753],{"stretchy":1752},[1742,34017,1744],{},[1750,34019,1758],{},[898,34021,207],{},[1699,34023,34024,34026],{},[1750,34025,1763],{"stretchy":1752},[1742,34027,1872],{},[2125,34029],{"width":2127},[895,34031,34032,34034,34040],{},[1969,34033,8824],{},[3215,34035,34036,34038],{"accent":1916},[1969,34037,207],{},[1750,34039,8831],{},[1969,34041,8834],{},[902,34043,8837],{"encoding":904},[724,34045,34046],{},[883,34047,34049],{"className":34048},[886],[888,34050,34051],{"xmlns":890},[892,34052,34053,34117],{},[895,34054,34055,34073,34075,34087,34089],{},[3423,34056,34057,34067],{},[895,34058,34059,34061],{},[898,34060,8773],{"mathvariant":1747},[1699,34062,34063,34065],{},[898,34064,1666],{},[898,34066,1705],{},[895,34068,34069,34071],{},[898,34070,8773],{"mathvariant":1747},[898,34072,2573],{},[1750,34074,1766],{},[3423,34076,34077,34079],{},[1742,34078,1744],{},[895,34080,34081,34083,34085],{},[1742,34082,1744],{},[1750,34084,1758],{},[898,34086,207],{},[2125,34088],{"width":2127},[895,34090,34091,34093,34099,34101,34107,34109,34115],{},[1969,34092,8824],{},[3215,34094,34095,34097],{"accent":1916},[1969,34096,207],{},[1750,34098,8831],{},[1969,34100,8895],{},[3215,34102,34103,34105],{"accent":1916},[1969,34104,8900],{},[1750,34106,8831],{},[1969,34108,8905],{},[3215,34110,34111,34113],{"accent":1916},[1969,34112,1920],{},[1750,34114,8912],{},[1969,34116,8915],{},[902,34118,8918],{"encoding":904},[724,34120,34121],{},[883,34122,34124],{"className":34123},[886],[888,34125,34126],{"xmlns":890},[892,34127,34128,34194],{},[895,34129,34130,34152,34154,34166,34168,34180,34182],{},[3423,34131,34132,34142],{},[895,34133,34134,34136],{},[898,34135,8773],{"mathvariant":1747},[1699,34137,34138,34140],{},[898,34139,1666],{},[898,34141,1705],{},[895,34143,34144,34146],{},[898,34145,8773],{"mathvariant":1747},[1699,34147,34148,34150],{},[898,34149,1974],{},[1750,34151,3751],{},[1750,34153,1766],{},[3423,34155,34156,34158],{},[1742,34157,1744],{},[895,34159,34160,34162,34164],{},[1742,34161,1744],{},[1750,34163,1758],{},[898,34165,207],{},[1750,34167,1766],{},[3423,34169,34170,34172],{},[1742,34171,1744],{},[895,34173,34174,34176,34178],{},[898,34175,1773],{},[898,34177,1776],{},[898,34179,1779],{},[2125,34181],{"width":2127},[895,34183,34184,34186,34192],{},[1969,34185,8824],{},[3215,34187,34188,34190],{"accent":1916},[1969,34189,207],{},[1750,34191,8831],{},[1969,34193,8994],{},[902,34195,8997],{"encoding":904},[1785,34197,34198],{},[724,34199,34200,9004,34202,9008,34204,9022,34217,9040,34234,9059,34251,9104,34294,5249,34311,9125,34313,9143],{},[883,34201,1791],{},[38,34203,9007],{},[883,34205,34207],{"className":34206},[886],[888,34208,34209],{"xmlns":890},[892,34210,34211,34215],{},[895,34212,34213],{},[898,34214,207],{},[902,34216,207],{"encoding":904},[883,34218,34220],{"className":34219},[886],[888,34221,34222],{"xmlns":890},[892,34223,34224,34232],{},[895,34225,34226,34228,34230],{},[898,34227,1773],{},[898,34229,1776],{},[898,34231,1812],{},[902,34233,1815],{"encoding":904},[883,34235,34237],{"className":34236},[886],[888,34238,34239],{"xmlns":890},[892,34240,34241,34249],{},[895,34242,34243],{},[1699,34244,34245,34247],{},[898,34246,207],{},[1742,34248,1872],{},[902,34250,9058],{"encoding":904},[883,34252,34254],{"className":34253},[886],[888,34255,34256],{"xmlns":890},[892,34257,34258,34292],{},[895,34259,34260,34262,34264,34266,34268,34274,34276,34278,34280],{},[1742,34261,1744],{},[1750,34263,1861],{},[898,34265,207],{},[1750,34267,1861],{},[1699,34269,34270,34272],{},[898,34271,207],{},[1742,34273,1872],{},[1750,34275,1861],{},[1750,34277,1877],{},[1750,34279,1766],{},[3423,34281,34282,34284],{},[1742,34283,1744],{},[895,34285,34286,34288,34290],{},[1742,34287,1744],{},[1750,34289,1758],{},[898,34291,207],{},[902,34293,9103],{"encoding":904},[883,34295,34297],{"className":34296},[886],[888,34298,34299],{"xmlns":890},[892,34300,34301,34309],{},[895,34302,34303],{},[1699,34304,34305,34307],{},[898,34306,1666],{},[898,34308,1705],{},[902,34310,1708],{"encoding":904},[38,34312,9124],{},[883,34314,34316],{"className":34315},[886],[888,34317,34318],{"xmlns":890},[892,34319,34320,34328],{},[895,34321,34322,34324,34326],{},[898,34323,1773],{},[898,34325,1776],{},[898,34327,1812],{},[902,34329,1815],{"encoding":904},[724,34331,34332,9149,34334,9176,34359,9180,34361,2028,34382,9227,34407,2313],{},[38,34333,9148],{},[883,34335,34337],{"className":34336},[886],[888,34338,34339],{"xmlns":890},[892,34340,34341,34357],{},[895,34342,34343],{},[3586,34344,34345],{"scriptlevel":2607,"displaystyle":1752},[3423,34346,34347,34349],{},[1742,34348,1744],{},[895,34350,34351,34353,34355],{},[1742,34352,1744],{},[1750,34354,1758],{},[898,34356,207],{},[902,34358,9175],{"encoding":904},[38,34360,9179],{},[883,34362,34364],{"className":34363},[886],[888,34365,34366],{"xmlns":890},[892,34367,34368,34380],{},[895,34369,34370,34372,34374,34376,34378],{},[898,34371,1812],{},[1969,34373,1971],{},[898,34375,1974],{},[1969,34377,1971],{},[898,34379,1997],{},[902,34381,2000],{"encoding":904},[883,34383,34385],{"className":34384},[886],[888,34386,34387],{"xmlns":890},[892,34388,34389,34405],{},[895,34390,34391,34393,34395,34397,34399,34401,34403],{},[898,34392,1812],{},[1969,34394,1971],{},[898,34396,1974],{},[1969,34398,1971],{},[898,34400,1997],{},[1969,34402,1971],{},[898,34404,2024],{},[902,34406,2027],{"encoding":904},[207,34408,9231],{"className":34409,"dataFsResolvedFilePath":800,"href":801},[210],[115,34411,9235],{"id":9234},[724,34413,8513,34414,1343,34431,2028,34452,9301,34477,2084,34479,9326,34500,1647,34502,9343,34515,9375,34544,9394,34561,9398,34563,9401,34565,9423],{},[883,34415,34417],{"className":34416},[886],[888,34418,34419],{"xmlns":890},[892,34420,34421,34429],{},[895,34422,34423,34425,34427],{},[898,34424,1812],{},[1969,34426,1971],{},[898,34428,1974],{},[902,34430,1977],{"encoding":904},[883,34432,34434],{"className":34433},[886],[888,34435,34436],{"xmlns":890},[892,34437,34438,34450],{},[895,34439,34440,34442,34444,34446,34448],{},[898,34441,1812],{},[1969,34443,1971],{},[898,34445,1974],{},[1969,34447,1971],{},[898,34449,1997],{},[902,34451,2000],{"encoding":904},[883,34453,34455],{"className":34454},[886],[888,34456,34457],{"xmlns":890},[892,34458,34459,34475],{},[895,34460,34461,34463,34465,34467,34469,34471,34473],{},[898,34462,1812],{},[1969,34464,1971],{},[898,34466,1974],{},[1969,34468,1971],{},[898,34470,1997],{},[1969,34472,1971],{},[898,34474,2024],{},[902,34476,2027],{"encoding":904},[38,34478,9304],{},[883,34480,34482],{"className":34481},[886],[888,34483,34484],{"xmlns":890},[892,34485,34486,34498],{},[895,34487,34488,34490,34492],{},[898,34489,1974],{},[1750,34491,1766],{},[1699,34493,34494,34496],{},[898,34495,1974],{},[1750,34497,3751],{},[902,34499,4538],{"encoding":904},[38,34501,9329],{},[883,34503,34505],{"className":34504},[886],[888,34506,34507],{"xmlns":890},[892,34508,34509,34513],{},[895,34510,34511],{},[898,34512,1920],{},[902,34514,1920],{"encoding":904},[883,34516,34518],{"className":34517},[886],[888,34519,34520],{"xmlns":890},[892,34521,34522,34542],{},[895,34523,34524,34526,34528,34530,34532,34534,34536,34538,34540],{},[898,34525,1974],{},[1750,34527,1753],{"stretchy":1752},[898,34529,1920],{},[1750,34531,1763],{"stretchy":1752},[1750,34533,1766],{},[898,34535,9365],{},[898,34537,1920],{},[1750,34539,1861],{},[898,34541,3429],{},[902,34543,9374],{"encoding":904},[883,34545,34547],{"className":34546},[886],[888,34548,34549],{"xmlns":890},[892,34550,34551,34559],{},[895,34552,34553,34555,34557],{},[898,34554,9365],{},[1750,34556,2624],{},[1742,34558,2607],{},[902,34560,9393],{"encoding":904},[38,34562,9397],{},[38,34564,1684],{},[883,34566,34568],{"className":34567},[886],[888,34569,34570],{"xmlns":890},[892,34571,34572,34584],{},[895,34573,34574,34576,34578,34580,34582],{},[1750,34575,1753],{"stretchy":1752},[898,34577,1666],{},[1750,34579,1917],{"separator":1916},[898,34581,1920],{},[1750,34583,1763],{"stretchy":1752},[902,34585,1925],{"encoding":904},[120,34587,34588,34636],{},[123,34589,34590,2084,34592,9434,34594,9457,34615,2313],{},[38,34591,9430],{},[614,34593,9433],{},[883,34595,34597],{"className":34596},[886],[888,34598,34599],{"xmlns":890},[892,34600,34601,34613],{},[895,34602,34603,34605,34607,34609,34611],{},[1750,34604,1753],{"stretchy":1752},[898,34606,1920],{},[1750,34608,1917],{"separator":1916},[898,34610,1666],{},[1750,34612,1763],{"stretchy":1752},[902,34614,9456],{"encoding":904},[883,34616,34618],{"className":34617},[886],[888,34619,34620],{"xmlns":890},[892,34621,34622,34634],{},[895,34623,34624,34626,34628,34630,34632],{},[898,34625,1666],{},[1750,34627,1766],{},[898,34629,1812],{},[1750,34631,1861],{},[898,34633,1974],{},[902,34635,5105],{"encoding":904},[123,34637,34638,2084,34640,9487,34642,5424,34667,9561],{},[38,34639,9483],{},[614,34641,9486],{},[883,34643,34645],{"className":34644},[886],[888,34646,34647],{"xmlns":890},[892,34648,34649,34665],{},[895,34650,34651,34657,34659],{},[1699,34652,34653,34655],{},[898,34654,1773],{},[898,34656,5541],{},[1750,34658,1766],{},[1699,34660,34661,34663],{},[898,34662,1773],{},[1750,34664,3751],{},[902,34666,9513],{"encoding":904},[883,34668,34670],{"className":34669},[886],[888,34671,34672],{"xmlns":890},[892,34673,34674,34710],{},[895,34675,34676,34682,34684,34690,34692,34694,34700,34702,34704],{},[1699,34677,34678,34680],{},[898,34679,1773],{},[898,34681,5541],{},[1750,34683,1766],{},[5535,34685,34686,34688],{},[898,34687,9535],{},[1742,34689,1744],{},[898,34691,1666],{},[1750,34693,1861],{},[5535,34695,34696,34698],{},[898,34697,9535],{},[1742,34699,1872],{},[898,34701,1920],{},[1750,34703,1861],{},[5535,34705,34706,34708],{},[898,34707,9535],{},[1742,34709,7822],{},[902,34711,9560],{"encoding":904},[724,34713,34714,1647,34716,9601,34749,9605,34751,9609],{},[38,34715,9566],{},[883,34717,34719],{"className":34718},[886],[888,34720,34721],{"xmlns":890},[892,34722,34723,34747],{},[895,34724,34725,34727,34729,34731,34737,34739,34745],{},[898,34726,1705],{},[1750,34728,1766],{},[1750,34730,1753],{"stretchy":1752},[1699,34732,34733,34735],{},[898,34734,1920],{},[898,34736,1705],{},[1750,34738,1917],{"separator":1916},[1699,34740,34741,34743],{},[898,34742,1666],{},[898,34744,1705],{},[1750,34746,1763],{"stretchy":1752},[902,34748,9600],{"encoding":904},[38,34750,9604],{},[38,34752,9608],{},[724,34754,34755],{},[38,34756,9614,34757,1343,34778,1343,34799,1343,34820,9706,34841,2313],{},[883,34758,34760],{"className":34759},[886],[888,34761,34762],{"xmlns":890},[892,34763,34764,34776],{},[895,34765,34766,34772,34774],{},[1699,34767,34768,34770],{},[898,34769,1666],{},[898,34771,1705],{},[1750,34773,1766],{},[1742,34775,9634],{},[902,34777,9637],{"encoding":904},[883,34779,34781],{"className":34780},[886],[888,34782,34783],{"xmlns":890},[892,34784,34785,34797],{},[895,34786,34787,34793,34795],{},[1699,34788,34789,34791],{},[898,34790,1920],{},[898,34792,1705],{},[1750,34794,1766],{},[1742,34796,7902],{},[902,34798,9659],{"encoding":904},[883,34800,34802],{"className":34801},[886],[888,34803,34804],{"xmlns":890},[892,34805,34806,34818],{},[895,34807,34808,34814,34816],{},[1699,34809,34810,34812],{},[898,34811,1812],{},[898,34813,1705],{},[1750,34815,1766],{},[1742,34817,9679],{},[902,34819,9682],{"encoding":904},[883,34821,34823],{"className":34822},[886],[888,34824,34825],{"xmlns":890},[892,34826,34827,34839],{},[895,34828,34829,34835,34837],{},[1699,34830,34831,34833],{},[898,34832,1974],{},[898,34834,1705],{},[1750,34836,1766],{},[1742,34838,9702],{},[902,34840,9705],{"encoding":904},[207,34842,945],{"className":34843,"dataFsResolvedFilePath":943,"href":944},[210],[115,34845,9713],{"id":9712},[152,34847,34848,34906,35013,35150,35383,35446],{},[123,34849,34850,9721,34852,9744,34873,9779],{},[38,34851,9720],{},[883,34853,34855],{"className":34854},[886],[888,34856,34857],{"xmlns":890},[892,34858,34859,34871],{},[895,34860,34861,34863,34865,34867,34869],{},[898,34862,1997],{},[898,34864,2078],{},[898,34866,1776],{},[1750,34868,2274],{},[898,34870,1666],{},[902,34872,9743],{"encoding":904},[883,34874,34876],{"className":34875},[886],[888,34877,34878],{"xmlns":890},[892,34879,34880,34904],{},[895,34881,34882,34884,34886,34888,34890,34892,34894,34896,34898,34900,34902],{},[898,34883,1997],{},[898,34885,2078],{},[898,34887,1776],{},[1750,34889,1766],{},[898,34891,1812],{},[1750,34893,1861],{},[898,34895,1974],{},[1750,34897,1861],{},[898,34899,1997],{},[1750,34901,1861],{},[898,34903,2024],{},[902,34905,9778],{"encoding":904},[123,34907,34908,9784,34910,9807,34931,1343,34954,9862,34985,9876,34998,2313],{},[38,34909,2317],{},[883,34911,34913],{"className":34912},[886],[888,34914,34915],{"xmlns":890},[892,34916,34917,34929],{},[895,34918,34919,34921,34923,34925,34927],{},[898,34920,1666],{},[1750,34922,1766],{},[898,34924,1812],{},[1750,34926,1861],{},[898,34928,1779],{},[902,34930,9806],{"encoding":904},[883,34932,34934],{"className":34933},[886],[888,34935,34936],{"xmlns":890},[892,34937,34938,34952],{},[895,34939,34940,34942,34944,34946,34948,34950],{},[898,34941,1812],{},[1750,34943,1766],{},[898,34945,207],{},[898,34947,1666],{},[1750,34949,1861],{},[898,34951,2573],{},[902,34953,2720],{"encoding":904},[883,34955,34957],{"className":34956},[886],[888,34958,34959],{"xmlns":890},[892,34960,34961,34983],{},[895,34962,34963,34965,34967,34969,34971,34973,34975,34977,34979,34981],{},[898,34964,1779],{},[1750,34966,1766],{},[1750,34968,1753],{"stretchy":1752},[1742,34970,1744],{},[1750,34972,1758],{},[898,34974,207],{},[1750,34976,1763],{"stretchy":1752},[898,34978,1666],{},[1750,34980,1758],{},[898,34982,2573],{},[902,34984,2969],{"encoding":904},[883,34986,34988],{"className":34987},[886],[888,34989,34990],{"xmlns":890},[892,34991,34992,34996],{},[895,34993,34994],{},[898,34995,2573],{},[902,34997,2573],{"encoding":904},[883,34999,35001],{"className":35000},[886],[888,35002,35003],{"xmlns":890},[892,35004,35005,35011],{},[895,35006,35007,35009],{},[1750,35008,1758],{},[898,35010,2573],{},[902,35012,3049],{"encoding":904},[123,35014,35015,1647,35017,1343,35046,9957,35075,9988,35104,1343,35125,2313],{},[38,35016,9896],{},[883,35018,35020],{"className":35019},[886],[888,35021,35022],{"xmlns":890},[892,35023,35024,35044],{},[895,35025,35026,35028,35030,35032,35034,35036,35038,35040,35042],{},[898,35027,1773],{},[898,35029,1776],{},[898,35031,1812],{},[1750,35033,1766],{},[898,35035,3429],{"mathvariant":1747},[898,35037,1812],{},[898,35039,1748],{"mathvariant":1747},[898,35041,3429],{"mathvariant":1747},[898,35043,1666],{},[902,35045,9926],{"encoding":904},[883,35047,35049],{"className":35048},[886],[888,35050,35051],{"xmlns":890},[892,35052,35053,35073],{},[895,35054,35055,35057,35059,35061,35063,35065,35067,35069,35071],{},[898,35056,1773],{},[898,35058,1776],{},[898,35060,1779],{},[1750,35062,1766],{},[898,35064,3429],{"mathvariant":1747},[898,35066,1779],{},[898,35068,1748],{"mathvariant":1747},[898,35070,3429],{"mathvariant":1747},[898,35072,1666],{},[902,35074,9956],{"encoding":904},[883,35076,35078],{"className":35077},[886],[888,35079,35080],{"xmlns":890},[892,35081,35082,35102],{},[895,35083,35084,35086,35088,35090,35092,35094,35096,35098,35100],{},[898,35085,1773],{},[898,35087,1776],{},[898,35089,1812],{},[1750,35091,1861],{},[898,35093,1773],{},[898,35095,1776],{},[898,35097,1779],{},[1750,35099,1766],{},[1742,35101,1744],{},[902,35103,9987],{"encoding":904},[883,35105,35107],{"className":35106},[886],[888,35108,35109],{"xmlns":890},[892,35110,35111,35123],{},[895,35112,35113,35115,35117,35119,35121],{},[898,35114,1773],{},[898,35116,1776],{},[898,35118,1812],{},[1750,35120,1766],{},[898,35122,207],{},[902,35124,3698],{"encoding":904},[883,35126,35128],{"className":35127},[886],[888,35129,35130],{"xmlns":890},[892,35131,35132,35148],{},[895,35133,35134,35136,35138,35140,35142,35144,35146],{},[898,35135,1773],{},[898,35137,1776],{},[898,35139,1779],{},[1750,35141,1766],{},[1742,35143,1744],{},[1750,35145,1758],{},[898,35147,207],{},[902,35149,3724],{"encoding":904},[123,35151,35152,10040,35154],{},[38,35153,10039],{},[120,35155,35156,35241,35308],{},[123,35157,35158,10062,35175,10084,35196,1917],{},[883,35159,35161],{"className":35160},[886],[888,35162,35163],{"xmlns":890},[892,35164,35165,35173],{},[895,35166,35167,35169,35171],{},[898,35168,1812],{},[1969,35170,1971],{},[898,35172,1974],{},[902,35174,1977],{"encoding":904},[883,35176,35178],{"className":35177},[886],[888,35179,35180],{"xmlns":890},[892,35181,35182,35194],{},[895,35183,35184,35186,35188,35190,35192],{},[898,35185,1666],{},[1750,35187,1766],{},[898,35189,1812],{},[1750,35191,1861],{},[898,35193,1974],{},[902,35195,5105],{"encoding":904},[883,35197,35199],{"className":35198},[886],[888,35200,35201],{"xmlns":890},[892,35202,35203,35239],{},[895,35204,35205,35211,35213,35215,35217,35219,35225,35227,35229,35231,35233,35235,35237],{},[1699,35206,35207,35209],{},[898,35208,1666],{},[898,35210,1705],{},[1750,35212,1766],{},[1750,35214,1753],{"stretchy":1752},[898,35216,2573],{},[1750,35218,1861],{},[1699,35220,35221,35223],{},[898,35222,1974],{},[1750,35224,3751],{},[1750,35226,1763],{"stretchy":1752},[898,35228,1748],{"mathvariant":1747},[1750,35230,1753],{"stretchy":1752},[1742,35232,1744],{},[1750,35234,1758],{},[898,35236,207],{},[1750,35238,1763],{"stretchy":1752},[902,35240,10130],{"encoding":904},[123,35242,35243,10154,35264,10174,35283,1917],{},[883,35244,35246],{"className":35245},[886],[888,35247,35248],{"xmlns":890},[892,35249,35250,35262],{},[895,35251,35252,35254,35256,35258,35260],{},[898,35253,1812],{},[1969,35255,1971],{},[898,35257,1974],{},[1969,35259,1971],{},[898,35261,1997],{},[902,35263,2000],{"encoding":904},[883,35265,35267],{"className":35266},[886],[888,35268,35269],{"xmlns":890},[892,35270,35271,35281],{},[895,35272,35273,35275,35277,35279],{},[898,35274,5326],{},[1750,35276,1753],{"stretchy":1752},[898,35278,1666],{},[1750,35280,1763],{"stretchy":1752},[902,35282,6055],{"encoding":904},[883,35284,35286],{"className":35285},[886],[888,35287,35288],{"xmlns":890},[892,35289,35290,35306],{},[895,35291,35292,35298,35300,35302,35304],{},[5535,35293,35294,35296],{},[898,35295,1666],{},[898,35297,5541],{},[1750,35299,1766],{},[898,35301,1666],{},[1750,35303,1758],{},[898,35305,5326],{},[902,35307,5552],{"encoding":904},[123,35309,35310,10227,35335,5424,35356,2313],{},[883,35311,35313],{"className":35312},[886],[888,35314,35315],{"xmlns":890},[892,35316,35317,35333],{},[895,35318,35319,35321,35323,35325,35327,35329,35331],{},[898,35320,1812],{},[1969,35322,1971],{},[898,35324,1974],{},[1969,35326,1971],{},[898,35328,1997],{},[1969,35330,1971],{},[898,35332,2024],{},[902,35334,2027],{"encoding":904},[883,35336,35338],{"className":35337},[886],[888,35339,35340],{"xmlns":890},[892,35341,35342,35354],{},[895,35343,35344,35346,35348,35350,35352],{},[898,35345,2024],{},[1750,35347,1766],{},[898,35349,7097],{},[1750,35351,1758],{},[898,35353,1773],{},[902,35355,7104],{"encoding":904},[883,35357,35359],{"className":35358},[886],[888,35360,35361],{"xmlns":890},[892,35362,35363,35381],{},[895,35364,35365,35367,35369,35371,35373,35379],{},[898,35366,1773],{},[1750,35368,1766],{},[898,35370,1773],{},[1750,35372,1753],{"stretchy":1752},[5535,35374,35375,35377],{},[898,35376,1666],{},[898,35378,5541],{},[1750,35380,1763],{"stretchy":1752},[902,35382,10276],{"encoding":904},[123,35384,35385,10282,35387,1647,35389,10344],{},[38,35386,10281],{},[38,35388,10285],{},[883,35390,35392],{"className":35391},[886],[888,35393,35394],{"xmlns":890},[892,35395,35396,35444],{},[895,35397,35398,35400,35406,35408,35410,35416,35418,35420,35422,35424,35426,35428,35430,35432,35434,35436,35438,35440,35442],{},[898,35399,8773],{"mathvariant":1747},[1699,35401,35402,35404],{},[898,35403,1666],{},[898,35405,1705],{},[898,35407,1748],{"mathvariant":1747},[898,35409,8773],{"mathvariant":1747},[1699,35411,35412,35414],{},[898,35413,1974],{},[1750,35415,3751],{},[1750,35417,1766],{},[1742,35419,1744],{},[898,35421,1748],{"mathvariant":1747},[1750,35423,1753],{"stretchy":1752},[1742,35425,1744],{},[1750,35427,1758],{},[898,35429,207],{},[1750,35431,1763],{"stretchy":1752},[1750,35433,1766],{},[1742,35435,1744],{},[898,35437,1748],{"mathvariant":1747},[898,35439,1773],{},[898,35441,1776],{},[898,35443,1779],{},[902,35445,10343],{"encoding":904},[123,35447,35448,10349,35450,10366,35465,2440,35482,10401,35497,10427,35522,2313],{},[38,35449,945],{},[883,35451,35453],{"className":35452},[886],[888,35454,35455],{"xmlns":890},[892,35456,35457,35463],{},[895,35458,35459,35461],{},[898,35460,1974],{},[898,35462,1779],{},[902,35464,10365],{"encoding":904},[883,35466,35468],{"className":35467},[886],[888,35469,35470],{"xmlns":890},[892,35471,35472,35480],{},[895,35473,35474,35476,35478],{},[898,35475,1974],{},[1750,35477,1766],{},[898,35479,1779],{},[902,35481,10384],{"encoding":904},[883,35483,35485],{"className":35484},[886],[888,35486,35487],{"xmlns":890},[892,35488,35489,35495],{},[895,35490,35491,35493],{},[898,35492,2046],{},[898,35494,1773],{},[902,35496,10400],{"encoding":904},[883,35498,35500],{"className":35499},[886],[888,35501,35502],{"xmlns":890},[892,35503,35504,35520],{},[895,35505,35506,35512,35514],{},[1699,35507,35508,35510],{},[898,35509,1773],{},[898,35511,5541],{},[1750,35513,1766],{},[1699,35515,35516,35518],{},[898,35517,1773],{},[1750,35519,3751],{},[902,35521,9513],{"encoding":904},[883,35523,35525],{"className":35524},[886],[888,35526,35527],{"xmlns":890},[892,35528,35529,35549],{},[895,35530,35531,35533,35539,35541,35547],{},[1750,35532,1753],{"stretchy":1752},[1699,35534,35535,35537],{},[898,35536,1666],{},[898,35538,1705],{},[1750,35540,1917],{"separator":1916},[1699,35542,35543,35545],{},[898,35544,1920],{},[898,35546,1705],{},[1750,35548,1763],{"stretchy":1752},[902,35550,10457],{"encoding":904},[115,35552,10461],{"id":10460},[120,35554,35555,35592,35630,35718,35797,35849,35903,35961,35994,35998,36068,36141,36222,36283,36350,36405,36456,36493],{},[123,35556,35557,10469,35559,9779],{},[38,35558,10468],{},[883,35560,35562],{"className":35561},[886],[888,35563,35564],{"xmlns":890},[892,35565,35566,35590],{},[895,35567,35568,35570,35572,35574,35576,35578,35580,35582,35584,35586,35588],{},[898,35569,1997],{},[898,35571,2078],{},[898,35573,1776],{},[1750,35575,1766],{},[898,35577,1812],{},[1750,35579,1861],{},[898,35581,1974],{},[1750,35583,1861],{},[898,35585,1997],{},[1750,35587,1861],{},[898,35589,2024],{},[902,35591,9778],{"encoding":904},[123,35593,35594,10521,35609,2313],{},[38,35595,10507,35596],{},[883,35597,35599],{"className":35598},[886],[888,35600,35601],{"xmlns":890},[892,35602,35603,35607],{},[895,35604,35605],{},[898,35606,1666],{},[902,35608,1666],{"encoding":904},[883,35610,35612],{"className":35611},[886],[888,35613,35614],{"xmlns":890},[892,35615,35616,35628],{},[895,35617,35618,35620,35622,35624,35626],{},[898,35619,1997],{},[898,35621,2078],{},[898,35623,1776],{},[1750,35625,2274],{},[898,35627,1666],{},[902,35629,9743],{"encoding":904},[123,35631,35632,10571,35657,1343,35680,1343,35701,2313],{},[38,35633,10547,35634],{},[883,35635,35637],{"className":35636},[886],[888,35638,35639],{"xmlns":890},[892,35640,35641,35655],{},[895,35642,35643,35645,35647,35649,35651,35653],{},[898,35644,1812],{},[1750,35646,1766],{},[898,35648,1812],{},[1750,35650,1753],{"stretchy":1752},[898,35652,1666],{},[1750,35654,1763],{"stretchy":1752},[902,35656,4563],{"encoding":904},[883,35658,35660],{"className":35659},[886],[888,35661,35662],{"xmlns":890},[892,35663,35664,35678],{},[895,35665,35666,35668,35670,35672,35674,35676],{},[898,35667,1812],{},[1750,35669,1766],{},[898,35671,207],{},[898,35673,1666],{},[1750,35675,1861],{},[898,35677,2573],{},[902,35679,2720],{"encoding":904},[883,35681,35683],{"className":35682},[886],[888,35684,35685],{"xmlns":890},[892,35686,35687,35699],{},[895,35688,35689,35691,35693,35695,35697],{},[1742,35690,2607],{},[1750,35692,2624],{},[898,35694,207],{},[1750,35696,2624],{},[1742,35698,1744],{},[902,35700,2633],{"encoding":904},[883,35702,35704],{"className":35703},[886],[888,35705,35706],{"xmlns":890},[892,35707,35708,35716],{},[895,35709,35710,35712,35714],{},[898,35711,2573],{},[1750,35713,2604],{},[1742,35715,2607],{},[902,35717,2610],{"encoding":904},[123,35719,35720,10469,35745,10683,35766,2313],{},[38,35721,10637,35722],{},[883,35723,35725],{"className":35724},[886],[888,35726,35727],{"xmlns":890},[892,35728,35729,35743],{},[895,35730,35731,35733,35735,35737,35739,35741],{},[898,35732,1779],{},[1750,35734,1766],{},[898,35736,1779],{},[1750,35738,1753],{"stretchy":1752},[898,35740,1666],{},[1750,35742,1763],{"stretchy":1752},[902,35744,10661],{"encoding":904},[883,35746,35748],{"className":35747},[886],[888,35749,35750],{"xmlns":890},[892,35751,35752,35764],{},[895,35753,35754,35756,35758,35760,35762],{},[898,35755,1666],{},[1750,35757,1766],{},[898,35759,1812],{},[1750,35761,1861],{},[898,35763,1779],{},[902,35765,9806],{"encoding":904},[883,35767,35769],{"className":35768},[886],[888,35770,35771],{"xmlns":890},[892,35772,35773,35795],{},[895,35774,35775,35777,35779,35781,35783,35785,35787,35789,35791,35793],{},[898,35776,1779],{},[1750,35778,1766],{},[1750,35780,1753],{"stretchy":1752},[1742,35782,1744],{},[1750,35784,1758],{},[898,35786,207],{},[1750,35788,1763],{"stretchy":1752},[898,35790,1666],{},[1750,35792,1758],{},[898,35794,2573],{},[902,35796,2969],{"encoding":904},[123,35798,35799,10469,35801,1343,35824,2313],{},[38,35800,10719],{},[883,35802,35804],{"className":35803},[886],[888,35805,35806],{"xmlns":890},[892,35807,35808,35822],{},[895,35809,35810,35812,35814,35816,35818,35820],{},[898,35811,1812],{},[1750,35813,1753],{"stretchy":1752},[1742,35815,2607],{},[1750,35817,1763],{"stretchy":1752},[1750,35819,1766],{},[898,35821,2573],{},[902,35823,3365],{"encoding":904},[883,35825,35827],{"className":35826},[886],[888,35828,35829],{"xmlns":890},[892,35830,35831,35847],{},[895,35832,35833,35835,35837,35839,35841,35843,35845],{},[898,35834,1779],{},[1750,35836,1753],{"stretchy":1752},[1742,35838,2607],{},[1750,35840,1763],{"stretchy":1752},[1750,35842,1766],{},[1750,35844,1758],{},[898,35846,2573],{},[902,35848,10768],{"encoding":904},[123,35850,35851,10803,35882,1783],{},[38,35852,10773,35853],{},[883,35854,35856],{"className":35855},[886],[888,35857,35858],{"xmlns":890},[892,35859,35860,35880],{},[895,35861,35862,35864,35866,35868,35870,35872,35874,35876,35878],{},[898,35863,1773],{},[898,35865,1776],{},[898,35867,1812],{},[1750,35869,1766],{},[898,35871,3429],{"mathvariant":1747},[898,35873,1812],{},[898,35875,1748],{"mathvariant":1747},[898,35877,3429],{"mathvariant":1747},[898,35879,1666],{},[902,35881,9926],{"encoding":904},[883,35883,35885],{"className":35884},[886],[888,35886,35887],{"xmlns":890},[892,35888,35889,35901],{},[895,35890,35891,35893,35895,35897,35899],{},[898,35892,1773],{},[898,35894,1776],{},[898,35896,1812],{},[1750,35898,1766],{},[898,35900,207],{},[902,35902,3698],{"encoding":904},[123,35904,35905,10803,35936,1783],{},[38,35906,10829,35907],{},[883,35908,35910],{"className":35909},[886],[888,35911,35912],{"xmlns":890},[892,35913,35914,35934],{},[895,35915,35916,35918,35920,35922,35924,35926,35928,35930,35932],{},[898,35917,1773],{},[898,35919,1776],{},[898,35921,1779],{},[1750,35923,1766],{},[898,35925,3429],{"mathvariant":1747},[898,35927,1779],{},[898,35929,1748],{"mathvariant":1747},[898,35931,3429],{"mathvariant":1747},[898,35933,1666],{},[902,35935,9956],{"encoding":904},[883,35937,35939],{"className":35938},[886],[888,35940,35941],{"xmlns":890},[892,35942,35943,35959],{},[895,35944,35945,35947,35949,35951,35953,35955,35957],{},[898,35946,1773],{},[898,35948,1776],{},[898,35950,1779],{},[1750,35952,1766],{},[1742,35954,1744],{},[1750,35956,1758],{},[898,35958,207],{},[902,35960,3724],{"encoding":904},[123,35962,35963,1647,35965,10918],{},[38,35964,10888],{},[883,35966,35968],{"className":35967},[886],[888,35969,35970],{"xmlns":890},[892,35971,35972,35992],{},[895,35973,35974,35976,35978,35980,35982,35984,35986,35988,35990],{},[898,35975,1773],{},[898,35977,1776],{},[898,35979,1812],{},[1750,35981,1861],{},[898,35983,1773],{},[898,35985,1776],{},[898,35987,1779],{},[1750,35989,1766],{},[1742,35991,1744],{},[902,35993,9987],{"encoding":904},[123,35995,35996,10923],{},[38,35997,4402],{},[123,35999,36000,10929,36002,10951,36023,2313],{},[38,36001,10928],{},[883,36003,36005],{"className":36004},[886],[888,36006,36007],{"xmlns":890},[892,36008,36009,36021],{},[895,36010,36011,36013,36015,36017,36019],{},[898,36012,1666],{},[1750,36014,1766],{},[898,36016,1812],{},[1750,36018,1861],{},[898,36020,1974],{},[902,36022,5105],{"encoding":904},[883,36024,36026],{"className":36025},[886],[888,36027,36028],{"xmlns":890},[892,36029,36030,36066],{},[895,36031,36032,36038,36040,36042,36044,36046,36052,36054,36056,36058,36060,36062,36064],{},[1699,36033,36034,36036],{},[898,36035,1666],{},[898,36037,1705],{},[1750,36039,1766],{},[1750,36041,1753],{"stretchy":1752},[898,36043,2573],{},[1750,36045,1861],{},[1699,36047,36048,36050],{},[898,36049,1974],{},[1750,36051,3751],{},[1750,36053,1763],{"stretchy":1752},[898,36055,1748],{"mathvariant":1747},[1750,36057,1753],{"stretchy":1752},[1742,36059,1744],{},[1750,36061,1758],{},[898,36063,207],{},[1750,36065,1763],{"stretchy":1752},[902,36067,10130],{"encoding":904},[123,36069,36070,11002,36072,1343,36091,10951,36116,2313],{},[38,36071,11001],{},[883,36073,36075],{"className":36074},[886],[888,36076,36077],{"xmlns":890},[892,36078,36079,36089],{},[895,36080,36081,36083,36085,36087],{},[898,36082,5326],{},[1750,36084,1753],{"stretchy":1752},[898,36086,1666],{},[1750,36088,1763],{"stretchy":1752},[902,36090,6055],{"encoding":904},[883,36092,36094],{"className":36093},[886],[888,36095,36096],{"xmlns":890},[892,36097,36098,36114],{},[895,36099,36100,36106,36108,36110,36112],{},[5535,36101,36102,36104],{},[898,36103,1666],{},[898,36105,5541],{},[1750,36107,1766],{},[898,36109,1666],{},[1750,36111,1758],{},[898,36113,5326],{},[902,36115,5552],{"encoding":904},[883,36117,36119],{"className":36118},[886],[888,36120,36121],{"xmlns":890},[892,36122,36123,36139],{},[895,36124,36125,36127,36129,36131,36133,36135,36137],{},[898,36126,1666],{},[1750,36128,1766],{},[898,36130,1812],{},[1750,36132,1861],{},[898,36134,1974],{},[1750,36136,1861],{},[898,36138,1997],{},[902,36140,5521],{"encoding":904},[123,36142,36143,11077,36145,11099,36166,10951,36189,2313],{},[38,36144,11076],{},[883,36146,36148],{"className":36147},[886],[888,36149,36150],{"xmlns":890},[892,36151,36152,36164],{},[895,36153,36154,36156,36158,36160,36162],{},[898,36155,2024],{},[1750,36157,1766],{},[898,36159,7097],{},[1750,36161,1758],{},[898,36163,1773],{},[902,36165,7104],{"encoding":904},[883,36167,36169],{"className":36168},[886],[888,36170,36171],{"xmlns":890},[892,36172,36173,36187],{},[895,36174,36175,36177,36179,36185],{},[898,36176,1773],{},[1750,36178,1753],{"stretchy":1752},[5535,36180,36181,36183],{},[898,36182,1666],{},[898,36184,5541],{},[1750,36186,1763],{"stretchy":1752},[902,36188,11123],{"encoding":904},[883,36190,36192],{"className":36191},[886],[888,36193,36194],{"xmlns":890},[892,36195,36196,36220],{},[895,36197,36198,36200,36202,36204,36206,36208,36210,36212,36214,36216,36218],{},[898,36199,1666],{},[1750,36201,1766],{},[898,36203,1812],{},[1750,36205,1861],{},[898,36207,1974],{},[1750,36209,1861],{},[898,36211,1997],{},[1750,36213,1861],{},[898,36215,7097],{},[1750,36217,1758],{},[898,36219,1773],{},[902,36221,11157],{"encoding":904},[123,36223,36224,10469,36226,10344],{},[38,36225,11162],{},[883,36227,36229],{"className":36228},[886],[888,36230,36231],{"xmlns":890},[892,36232,36233,36281],{},[895,36234,36235,36237,36243,36245,36247,36253,36255,36257,36259,36261,36263,36265,36267,36269,36271,36273,36275,36277,36279],{},[898,36236,8773],{"mathvariant":1747},[1699,36238,36239,36241],{},[898,36240,1666],{},[898,36242,1705],{},[898,36244,1748],{"mathvariant":1747},[898,36246,8773],{"mathvariant":1747},[1699,36248,36249,36251],{},[898,36250,1974],{},[1750,36252,3751],{},[1750,36254,1766],{},[1742,36256,1744],{},[898,36258,1748],{"mathvariant":1747},[1750,36260,1753],{"stretchy":1752},[1742,36262,1744],{},[1750,36264,1758],{},[898,36266,207],{},[1750,36268,1763],{"stretchy":1752},[1750,36270,1766],{},[1742,36272,1744],{},[898,36274,1748],{"mathvariant":1747},[898,36276,1773],{},[898,36278,1776],{},[898,36280,1779],{},[902,36282,10343],{"encoding":904},[123,36284,36285,10469,36316,1343,36333,11289],{},[38,36286,11224,36287],{},[883,36288,36290],{"className":36289},[886],[888,36291,36292],{"xmlns":890},[892,36293,36294,36314],{},[895,36295,36296,36298,36300,36302,36304,36306,36308,36310,36312],{},[898,36297,1974],{},[1750,36299,1753],{"stretchy":1752},[898,36301,1920],{},[1750,36303,1763],{"stretchy":1752},[1750,36305,1766],{},[898,36307,9365],{},[898,36309,1920],{},[1750,36311,1861],{},[898,36313,3429],{},[902,36315,9374],{"encoding":904},[883,36317,36319],{"className":36318},[886],[888,36320,36321],{"xmlns":890},[892,36322,36323,36331],{},[895,36324,36325,36327,36329],{},[898,36326,9365],{},[1750,36328,2624],{},[1742,36330,2607],{},[902,36332,9393],{"encoding":904},[883,36334,36336],{"className":36335},[886],[888,36337,36338],{"xmlns":890},[892,36339,36340,36348],{},[895,36341,36342,36344,36346],{},[898,36343,3429],{},[1750,36345,2604],{},[1742,36347,2607],{},[902,36349,11288],{"encoding":904},[123,36351,36352,11294,36354,11297,36356,11348],{},[38,36353,9430],{},[614,36355,9433],{},[883,36357,36359],{"className":36358},[886],[888,36360,36361],{"xmlns":890},[892,36362,36363,36403],{},[895,36364,36365,36367,36369,36381,36383,36385],{},[898,36366,1666],{},[1750,36368,1766],{},[3423,36370,36371,36373],{},[898,36372,9365],{},[895,36374,36375,36377,36379],{},[1742,36376,1744],{},[1750,36378,1758],{},[898,36380,207],{},[898,36382,1920],{},[1750,36384,1861],{},[3423,36386,36387,36395],{},[895,36388,36389,36391,36393],{},[898,36390,2573],{},[1750,36392,1861],{},[898,36394,3429],{},[895,36396,36397,36399,36401],{},[1742,36398,1744],{},[1750,36400,1758],{},[898,36402,207],{},[902,36404,11347],{"encoding":904},[123,36406,36407,11353,36409,11297,36411,11402],{},[38,36408,9483],{},[614,36410,9486],{},[883,36412,36414],{"className":36413},[886],[888,36415,36416],{"xmlns":890},[892,36417,36418,36454],{},[895,36419,36420,36426,36428,36434,36436,36438,36444,36446,36448],{},[1699,36421,36422,36424],{},[898,36423,1773],{},[1750,36425,3751],{},[1750,36427,1766],{},[5535,36429,36430,36432],{},[898,36431,9535],{},[1742,36433,1744],{},[898,36435,1666],{},[1750,36437,1861],{},[5535,36439,36440,36442],{},[898,36441,9535],{},[1742,36443,1872],{},[898,36445,1920],{},[1750,36447,1861],{},[5535,36449,36450,36452],{},[898,36451,9535],{},[1742,36453,7822],{},[902,36455,11401],{"encoding":904},[123,36457,36458,10469,36460,2313],{},[38,36459,11407],{},[883,36461,36463],{"className":36462},[886],[888,36464,36465],{"xmlns":890},[892,36466,36467,36491],{},[895,36468,36469,36475,36477,36483,36485],{},[1699,36470,36471,36473],{},[898,36472,1773],{},[898,36474,5541],{},[1750,36476,1766],{},[5535,36478,36479,36481],{},[898,36480,2046],{},[1742,36482,1744],{},[1750,36484,1861],{},[5535,36486,36487,36489],{},[898,36488,2046],{},[1742,36490,1872],{},[902,36492,11441],{"encoding":904},[123,36494,36495,11446,36497,11460,36510,2028,36525,11491,36540,2313],{},[38,36496,945],{},[883,36498,36500],{"className":36499},[886],[888,36501,36502],{"xmlns":890},[892,36503,36504,36508],{},[895,36505,36506],{},[898,36507,1705],{},[902,36509,1705],{"encoding":904},[883,36511,36513],{"className":36512},[886],[888,36514,36515],{"xmlns":890},[892,36516,36517,36523],{},[895,36518,36519,36521],{},[898,36520,1974],{},[898,36522,1779],{},[902,36524,10365],{"encoding":904},[883,36526,36528],{"className":36527},[886],[888,36529,36530],{"xmlns":890},[892,36531,36532,36538],{},[895,36533,36534,36536],{},[898,36535,2046],{},[898,36537,1773],{},[902,36539,10400],{"encoding":904},[883,36541,36543],{"className":36542},[886],[888,36544,36545],{"xmlns":890},[892,36546,36547,36567],{},[895,36548,36549,36551,36557,36559,36565],{},[1750,36550,1753],{"stretchy":1752},[1699,36552,36553,36555],{},[898,36554,1666],{},[898,36556,1705],{},[1750,36558,1917],{"separator":1916},[1699,36560,36561,36563],{},[898,36562,1920],{},[898,36564,1705],{},[1750,36566,1763],{"stretchy":1752},[902,36568,10457],{"encoding":904},[115,36570,11524],{"id":11523},[120,36572,36573,36580,36587],{},[123,36574,36575,1647,36577],{},[38,36576,11531],{},[207,36578,11535],{"className":36579,"dataFsResolvedFilePath":1644,"href":1645},[210],[123,36581,36582,1647,36584],{},[38,36583,11540],{},[207,36585,11544],{"className":36586,"dataFsResolvedFilePath":868,"href":869},[210],[123,36588,36589,36591],{},[38,36590,11549],{},[120,36592,36593,36598,36603,36608],{},[123,36594,36595,11558],{},[207,36596,11557],{"className":36597,"dataFsResolvedFilePath":943,"href":944},[210],[123,36599,36600,11565],{},[207,36601,11564],{"className":36602,"dataFsResolvedFilePath":800,"href":801},[210],[123,36604,36605,11572],{},[207,36606,11571],{"className":36607,"dataFsResolvedFilePath":827,"href":828},[210],[123,36609,36610,11578,36613,1343,36630,11613],{},[207,36611,1145],{"className":36612,"dataFsResolvedFilePath":764,"href":765},[210],[883,36614,36616],{"className":36615},[886],[888,36617,36618],{"xmlns":890},[892,36619,36620,36628],{},[895,36621,36622,36624,36626],{},[898,36623,1773],{},[898,36625,1776],{},[898,36627,1812],{},[902,36629,1815],{"encoding":904},[883,36631,36633],{"className":36632},[886],[888,36634,36635],{"xmlns":890},[892,36636,36637,36645],{},[895,36638,36639,36641,36643],{},[898,36640,1773],{},[898,36642,1776],{},[898,36644,1779],{},[902,36646,3465],{"encoding":904},{"title":641,"searchDepth":642,"depth":642,"links":36648},[36649,36650,36651,36652,36657,36660,36661,36667,36672,36677,36680,36681,36682,36683],{"id":1636,"depth":642,"text":1637},{"id":1929,"depth":642,"text":1930},{"id":2058,"depth":642,"text":2059},{"id":2316,"depth":642,"text":2317,"children":36653},[36654,36655,36656],{"id":2320,"depth":649,"text":2321},{"id":2535,"depth":649,"text":2536},{"id":3052,"depth":649,"text":3053},{"id":3375,"depth":642,"text":3376,"children":36658},[36659],{"id":3899,"depth":649,"text":3900},{"id":4401,"depth":642,"text":4402},{"id":4429,"depth":642,"text":4430,"children":36662},[36663,36664,36665,36666],{"id":4442,"depth":649,"text":4443},{"id":4512,"depth":649,"text":4513},{"id":4698,"depth":649,"text":11633},{"id":4842,"depth":649,"text":4843},{"id":5224,"depth":642,"text":5225,"children":36668},[36669,36670,36671],{"id":5228,"depth":649,"text":4443},{"id":5682,"depth":649,"text":4513},{"id":6340,"depth":649,"text":6341},{"id":7135,"depth":642,"text":7136,"children":36673},[36674,36675,36676],{"id":7139,"depth":649,"text":4443},{"id":7284,"depth":649,"text":4513},{"id":7554,"depth":649,"text":7555},{"id":8486,"depth":642,"text":8487,"children":36678},[36679],{"id":8683,"depth":649,"text":8684},{"id":9234,"depth":642,"text":9235},{"id":9712,"depth":642,"text":9713},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},{"title":936,"description":641},[1138,1137],[1128,11659,1143,11660,11661,11662,11557,11663],{"id":36689,"title":36690,"body":36691,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":45671,"navigation":664,"path":45672,"seo":45673,"sources":45674,"stem":45675,"tags":45676,"type":11664,"updated":677,"__hash__":45681},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":9,"value":36692,"toc":45640},[36693,36696,36698,36927,36931,36984,37054,37166,37325,37329,37445,37449,37452,37574,37577,37770,37794,37862,38026,38044,38110,38488,38492,38499,38743,38799,38803,38868,38986,39118,39150,39270,39352,39355,39477,39670,39891,39895,39935,40040,40097,40197,40374,40504,40557,40560,40647,40651,40827,40831,40834,40919,40922,40979,41084,41088,41209,41212,41395,41398,41506,41715,42035,42083,42156,42230,42232,42456,42691,42959,42963,42966,43071,43128,43162,43209,43242,43326,43328,43560,43693,43770,43892,44047,44051,44192,44199,44423,44434,44438,44442,44547,44689,44799,44898,44902,45061,45171,45173,45566,45568],[12,36694,36690],{"id":36695},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[115,36697,1637],{"id":1636},[724,36699,36700,36702,36703,36737,36738,36741,36742,36773,36774,36820,36821,36824,36825,36867,36868,36886,36887,36891,36892,36922,36923,36926],{},[38,36701,913],{}," řeší, jaký svazek zboží ",[883,36704,36706],{"className":36705},[886],[888,36707,36708],{"xmlns":890},[892,36709,36710,36734],{},[895,36711,36712,36714,36722,36724,36732],{},[1750,36713,5141],{"stretchy":1752},[5950,36715,36716,36718,36720],{},[898,36717,12471],{},[1742,36719,1744],{},[1750,36721,3751],{},[1750,36723,1917],{"separator":1916},[5950,36725,36726,36728,36730],{},[898,36727,12471],{},[1742,36729,1872],{},[1750,36731,3751],{},[1750,36733,5158],{"stretchy":1752},[902,36735,36736],{"encoding":904},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[38,36739,36740],{},"primární úloha"," — maximalizace užitečnosti ",[883,36743,36745],{"className":36744},[886],[888,36746,36747],{"xmlns":890},[892,36748,36749,36771],{},[895,36750,36751,36753,36755,36761,36763,36769],{},[898,36752,900],{},[1750,36754,1753],{"stretchy":1752},[5535,36756,36757,36759],{},[898,36758,12471],{},[1742,36760,1744],{},[1750,36762,1917],{"separator":1916},[5535,36764,36765,36767],{},[898,36766,12471],{},[1742,36768,1872],{},[1750,36770,1763],{"stretchy":1752},[902,36772,25916],{"encoding":904}," při rozpočtovém omezení ",[883,36775,36777],{"className":36776},[886],[888,36778,36779],{"xmlns":890},[892,36780,36781,36817],{},[895,36782,36783,36789,36791,36797,36803,36805,36811],{},[1699,36784,36785,36787],{},[898,36786,1666],{},[1750,36788,3751],{},[1750,36790,1766],{},[5535,36792,36793,36795],{},[898,36794,1776],{},[1742,36796,1744],{},[5535,36798,36799,36801],{},[898,36800,12471],{},[1742,36802,1744],{},[1750,36804,1861],{},[5535,36806,36807,36809],{},[898,36808,1776],{},[1742,36810,1872],{},[5535,36812,36813,36815],{},[898,36814,12471],{},[1742,36816,1872],{},[902,36818,36819],{"encoding":904},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[38,36822,36823],{},"duální úloha"," — minimalizace výdajů ",[883,36826,36828],{"className":36827},[886],[888,36829,36830],{"xmlns":890},[892,36831,36832,36864],{},[895,36833,36834,36836,36838,36844,36850,36852,36858],{},[898,36835,1705],{},[1750,36837,1766],{},[5535,36839,36840,36842],{},[898,36841,1776],{},[1742,36843,1744],{},[5535,36845,36846,36848],{},[898,36847,12471],{},[1742,36849,1744],{},[1750,36851,1861],{},[5535,36853,36854,36856],{},[898,36855,1776],{},[1742,36857,1872],{},[5535,36859,36860,36862],{},[898,36861,12471],{},[1742,36863,1872],{},[902,36865,36866],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2"," při zadané hladině užitečnosti ",[883,36869,36871],{"className":36870},[886],[888,36872,36873],{"xmlns":890},[892,36874,36875,36883],{},[895,36876,36877],{},[1699,36878,36879,36881],{},[898,36880,900],{},[1750,36882,3751],{},[902,36884,36885],{"encoding":904},"U^*",". Obě úlohy se řeší ",[207,36888,36890],{"className":36889,"dataFsResolvedFilePath":791,"href":792},[210],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[883,36893,36895],{"className":36894},[886],[888,36896,36897],{"xmlns":890},[892,36898,36899,36919],{},[895,36900,36901,36903,36905,36911,36913],{},[1969,36902,20236],{},[1750,36904,1766],{},[5535,36906,36907,36909],{},[898,36908,1776],{},[1742,36910,1744],{},[898,36912,1748],{"mathvariant":1747},[5535,36914,36915,36917],{},[898,36916,1776],{},[1742,36918,1872],{},[902,36920,36921],{"encoding":904},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[38,36924,36925],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[115,36928,36930],{"id":36929},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[724,36932,36933,36934,36952,36953,36983],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[883,36935,36937],{"className":36936},[886],[888,36938,36939],{"xmlns":890},[892,36940,36941,36949],{},[895,36942,36943],{},[1699,36944,36945,36947],{},[898,36946,1666],{},[1750,36948,3751],{},[902,36950,36951],{"encoding":904},"Y^*"," a ceny ",[883,36954,36956],{"className":36955},[886],[888,36957,36958],{"xmlns":890},[892,36959,36960,36980],{},[895,36961,36962,36970,36972],{},[5950,36963,36964,36966,36968],{},[898,36965,1776],{},[1742,36967,1744],{},[1750,36969,3751],{},[1750,36971,1917],{"separator":1916},[5950,36973,36974,36976,36978],{},[898,36975,1776],{},[1742,36977,1872],{},[1750,36979,3751],{},[902,36981,36982],{"encoding":904},"P_1^*, P_2^*",", rozpočtové omezení má tvar",[883,36985,36987],{"className":36986},[886],[888,36988,36990],{"xmlns":890,"display":36989},"block",[892,36991,36992,37051],{},[4577,36993,36995],{"width":36994},"100%",[4582,36996,36997,37000,37044,37046],{},[4585,36998],{"width":36999},"50%",[4585,37001,37002],{},[895,37003,37004,37010,37012,37020,37026,37028,37036,37042],{},[1699,37005,37006,37008],{},[898,37007,1666],{},[1750,37009,3751],{},[1750,37011,1766],{},[5950,37013,37014,37016,37018],{},[898,37015,1776],{},[1742,37017,1744],{},[1750,37019,3751],{},[5535,37021,37022,37024],{},[898,37023,12471],{},[1742,37025,1744],{},[1750,37027,1861],{},[5950,37029,37030,37032,37034],{},[898,37031,1776],{},[1742,37033,1872],{},[1750,37035,3751],{},[5535,37037,37038,37040],{},[898,37039,12471],{},[1742,37041,1872],{},[1750,37043,1917],{"separator":1916},[4585,37045],{"width":36999},[4585,37047,37048],{},[1969,37049,37050],{},"(6.12)",[902,37052,37053],{"encoding":904},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[724,37055,37056,37057,37060,37061,2028,37097,37133,37134,37147,37148,37162,37163,2313],{},"geometricky ",[38,37058,37059],{},"rozpočtová přímka (budget line)"," procházející body ",[883,37062,37064],{"className":37063},[886],[888,37065,37066],{"xmlns":890},[892,37067,37068,37094],{},[895,37069,37070,37072,37078,37080,37088,37090,37092],{},[1750,37071,5141],{"stretchy":1752},[1699,37073,37074,37076],{},[898,37075,1666],{},[1750,37077,3751],{},[898,37079,1748],{"mathvariant":1747},[5950,37081,37082,37084,37086],{},[898,37083,1776],{},[1742,37085,1744],{},[1750,37087,3751],{},[1750,37089,1917],{"separator":1916},[1742,37091,2607],{},[1750,37093,5158],{"stretchy":1752},[902,37095,37096],{"encoding":904},"[Y^*\u002FP_1^*, 0]",[883,37098,37100],{"className":37099},[886],[888,37101,37102],{"xmlns":890},[892,37103,37104,37130],{},[895,37105,37106,37108,37110,37112,37118,37120,37128],{},[1750,37107,5141],{"stretchy":1752},[1742,37109,2607],{},[1750,37111,1917],{"separator":1916},[1699,37113,37114,37116],{},[898,37115,1666],{},[1750,37117,3751],{},[898,37119,1748],{"mathvariant":1747},[5950,37121,37122,37124,37126],{},[898,37123,1776],{},[1742,37125,1872],{},[1750,37127,3751],{},[1750,37129,5158],{"stretchy":1752},[902,37131,37132],{"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 ",[883,37135,37137],{"className":37136},[886],[888,37138,37139],{"xmlns":890},[892,37140,37141,37145],{},[895,37142,37143],{},[898,37144,900],{},[902,37146,900],{"encoding":904},", indiferenční křivky a ",[883,37149,37151],{"className":37150},[886],[888,37152,37153],{"xmlns":890},[892,37154,37155,37159],{},[895,37156,37157],{},[1969,37158,20236],{},[902,37160,37161],{"encoding":904},"\\text{MRCS}"," — je shrnuta v ",[207,37164,880],{"className":37165,"dataFsResolvedFilePath":878,"href":879},[210],[1785,37167,37168],{},[724,37169,37170,37172,37173,37176,37177,37190,37191,37193,37194,37207,37208,1647,37211,37251,37252,37269,37270,37287,37288,37305,37306,37324],{},[883,37171,5454],{}," Pozor — dvě úlohy, totéž řešení\n",[38,37174,37175],{},"Primární úloha"," (max ",[883,37178,37180],{"className":37179},[886],[888,37181,37182],{"xmlns":890},[892,37183,37184,37188],{},[895,37185,37186],{},[898,37187,900],{},[902,37189,900],{"encoding":904}," při pevném rozpočtu) a ",[38,37192,36823],{}," (min ",[883,37195,37197],{"className":37196},[886],[888,37198,37199],{"xmlns":890},[892,37200,37201,37205],{},[895,37202,37203],{},[898,37204,1705],{},[902,37206,1705],{"encoding":904}," při pevné užitečnosti) vedou na ",[38,37209,37210],{},"tentýž bod",[883,37212,37214],{"className":37213},[886],[888,37215,37216],{"xmlns":890},[892,37217,37218,37248],{},[895,37219,37220,37226,37228,37236,37238,37246],{},[1699,37221,37222,37224],{},[898,37223,12471],{},[1750,37225,3751],{},[1750,37227,5141],{"stretchy":1752},[5950,37229,37230,37232,37234],{},[898,37231,12471],{},[1742,37233,1744],{},[1750,37235,3751],{},[1750,37237,1917],{"separator":1916},[5950,37239,37240,37242,37244],{},[898,37241,12471],{},[1742,37243,1872],{},[1750,37245,3751],{},[1750,37247,5158],{"stretchy":1752},[902,37249,37250],{"encoding":904},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[883,37253,37255],{"className":37254},[886],[888,37256,37257],{"xmlns":890},[892,37258,37259,37267],{},[895,37260,37261],{},[1699,37262,37263,37265],{},[898,37264,1666],{},[1750,37266,3751],{},[902,37268,36951],{"encoding":904}," a hledáme maximální ",[883,37271,37273],{"className":37272},[886],[888,37274,37275],{"xmlns":890},[892,37276,37277,37285],{},[895,37278,37279],{},[1699,37280,37281,37283],{},[898,37282,900],{},[1750,37284,3751],{},[902,37286,36885],{"encoding":904},"; u duální úlohy je zadána hladina ",[883,37289,37291],{"className":37290},[886],[888,37292,37293],{"xmlns":890},[892,37294,37295,37303],{},[895,37296,37297],{},[1699,37298,37299,37301],{},[898,37300,900],{},[1750,37302,3751],{},[902,37304,36885],{"encoding":904}," a hledáme minimální ",[883,37307,37309],{"className":37308},[886],[888,37310,37311],{"xmlns":890},[892,37312,37313,37321],{},[895,37314,37315],{},[1699,37316,37317,37319],{},[898,37318,1705],{},[1750,37320,3751],{},[902,37322,37323],{"encoding":904},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[115,37326,37328],{"id":37327},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[724,37330,37331,37332,37363,37364,37440,37441,2313],{},"Úlohou je najít maximum ",[883,37333,37335],{"className":37334},[886],[888,37336,37337],{"xmlns":890},[892,37338,37339,37361],{},[895,37340,37341,37343,37345,37351,37353,37359],{},[898,37342,900],{},[1750,37344,1753],{"stretchy":1752},[5535,37346,37347,37349],{},[898,37348,12471],{},[1742,37350,1744],{},[1750,37352,1917],{"separator":1916},[5535,37354,37355,37357],{},[898,37356,12471],{},[1742,37358,1872],{},[1750,37360,1763],{"stretchy":1752},[902,37362,25916],{"encoding":904}," vázané podmínkou (6.12) ve tvaru ",[883,37365,37367],{"className":37366},[886],[888,37368,37369],{"xmlns":890},[892,37370,37371,37437],{},[895,37372,37373,37375,37377,37383,37385,37391,37393,37395,37401,37403,37411,37417,37419,37427,37433,37435],{},[898,37374,2655],{},[1750,37376,1753],{"stretchy":1752},[5535,37378,37379,37381],{},[898,37380,12471],{},[1742,37382,1744],{},[1750,37384,1917],{"separator":1916},[5535,37386,37387,37389],{},[898,37388,12471],{},[1742,37390,1872],{},[1750,37392,1763],{"stretchy":1752},[1750,37394,1766],{},[1699,37396,37397,37399],{},[898,37398,1666],{},[1750,37400,3751],{},[1750,37402,1758],{},[5950,37404,37405,37407,37409],{},[898,37406,1776],{},[1742,37408,1744],{},[1750,37410,3751],{},[5535,37412,37413,37415],{},[898,37414,12471],{},[1742,37416,1744],{},[1750,37418,1758],{},[5950,37420,37421,37423,37425],{},[898,37422,1776],{},[1742,37424,1872],{},[1750,37426,3751],{},[5535,37428,37429,37431],{},[898,37430,12471],{},[1742,37432,1872],{},[1750,37434,1766],{},[1742,37436,2607],{},[902,37438,37439],{"encoding":904},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[207,37442,37444],{"className":37443,"dataFsResolvedFilePath":791,"href":792},[210],"metodu Lagrangeových multiplikátorů",[198,37446,37448],{"id":37447},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[724,37450,37451],{},"Sestavíme",[883,37453,37455],{"className":37454},[886],[888,37456,37457],{"xmlns":890,"display":36989},[892,37458,37459,37571],{},[4577,37460,37461],{"width":36994},[4582,37462,37463,37465,37564,37566],{},[4585,37464],{"width":36999},[4585,37466,37467],{},[895,37468,37469,37472,37474,37480,37482,37488,37490,37492,37494,37496,37498,37500,37506,37508,37514,37516,37518,37520,37522,37528,37530,37538,37544,37546,37554,37560,37562],{},[898,37470,2046],{"mathvariant":37471},"script",[1750,37473,1753],{"stretchy":1752},[5535,37475,37476,37478],{},[898,37477,12471],{},[1742,37479,1744],{},[1750,37481,1917],{"separator":1916},[5535,37483,37484,37486],{},[898,37485,12471],{},[1742,37487,1872],{},[1750,37489,1917],{"separator":1916},[898,37491,26016],{},[1750,37493,1763],{"stretchy":1752},[1750,37495,1766],{},[898,37497,900],{},[1750,37499,1753],{"stretchy":1752},[5535,37501,37502,37504],{},[898,37503,12471],{},[1742,37505,1744],{},[1750,37507,1917],{"separator":1916},[5535,37509,37510,37512],{},[898,37511,12471],{},[1742,37513,1872],{},[1750,37515,1763],{"stretchy":1752},[1750,37517,1861],{},[898,37519,26016],{},[1750,37521,1753],{"stretchy":1752},[1699,37523,37524,37526],{},[898,37525,1666],{},[1750,37527,3751],{},[1750,37529,1758],{},[5950,37531,37532,37534,37536],{},[898,37533,1776],{},[1742,37535,1744],{},[1750,37537,3751],{},[5535,37539,37540,37542],{},[898,37541,12471],{},[1742,37543,1744],{},[1750,37545,1758],{},[5950,37547,37548,37550,37552],{},[898,37549,1776],{},[1742,37551,1872],{},[1750,37553,3751],{},[5535,37555,37556,37558],{},[898,37557,12471],{},[1742,37559,1872],{},[1750,37561,1763],{"stretchy":1752},[898,37563,2313],{"mathvariant":1747},[4585,37565],{"width":36999},[4585,37567,37568],{},[1969,37569,37570],{},"(6.13)",[902,37572,37573],{"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}",[724,37575,37576],{},"Soustava prvního řádu:",[883,37578,37580],{"className":37579},[886],[888,37581,37582],{"xmlns":890,"display":36989},[892,37583,37584,37767],{},[4577,37585,37586],{"width":36994},[4582,37587,37588,37590,37760,37762],{},[4585,37589],{"width":36999},[4585,37591,37592],{},[4577,37593,37594,37644,37694],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,37595,37596,37608],{},[4585,37597,37598],{},[3586,37599,37600],{"scriptlevel":2607,"displaystyle":1916},[5950,37601,37602,37604,37606],{},[898,37603,2046],{"mathvariant":37471},[1742,37605,1744],{},[1750,37607,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,37609,37610],{},[3586,37611,37612],{"scriptlevel":2607,"displaystyle":1916},[895,37613,37614,37616,37618,37626,37628,37630,37638,37640,37642],{},[895,37615],{},[1750,37617,1766],{},[5950,37619,37620,37622,37624],{},[898,37621,900],{},[1742,37623,1744],{},[1750,37625,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,37627,1758],{},[898,37629,26016],{},[5950,37631,37632,37634,37636],{},[898,37633,1776],{},[1742,37635,1744],{},[1750,37637,3751],{},[1750,37639,1766],{},[1742,37641,2607],{},[1750,37643,1917],{"separator":1916},[4582,37645,37646,37658],{},[4585,37647,37648],{},[3586,37649,37650],{"scriptlevel":2607,"displaystyle":1916},[5950,37651,37652,37654,37656],{},[898,37653,2046],{"mathvariant":37471},[1742,37655,1872],{},[1750,37657,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,37659,37660],{},[3586,37661,37662],{"scriptlevel":2607,"displaystyle":1916},[895,37663,37664,37666,37668,37676,37678,37680,37688,37690,37692],{},[895,37665],{},[1750,37667,1766],{},[5950,37669,37670,37672,37674],{},[898,37671,900],{},[1742,37673,1872],{},[1750,37675,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,37677,1758],{},[898,37679,26016],{},[5950,37681,37682,37684,37686],{},[898,37683,1776],{},[1742,37685,1872],{},[1750,37687,3751],{},[1750,37689,1766],{},[1742,37691,2607],{},[1750,37693,1917],{"separator":1916},[4582,37695,37696,37708],{},[4585,37697,37698],{},[3586,37699,37700],{"scriptlevel":2607,"displaystyle":1916},[5950,37701,37702,37704,37706],{},[898,37703,2046],{"mathvariant":37471},[898,37705,26016],{},[1750,37707,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,37709,37710],{},[3586,37711,37712],{"scriptlevel":2607,"displaystyle":1916},[895,37713,37714,37716,37718,37724,37726,37734,37740,37742,37750,37756,37758],{},[895,37715],{},[1750,37717,1766],{},[1699,37719,37720,37722],{},[898,37721,1666],{},[1750,37723,3751],{},[1750,37725,1758],{},[5950,37727,37728,37730,37732],{},[898,37729,1776],{},[1742,37731,1744],{},[1750,37733,3751],{},[5535,37735,37736,37738],{},[898,37737,12471],{},[1742,37739,1744],{},[1750,37741,1758],{},[5950,37743,37744,37746,37748],{},[898,37745,1776],{},[1742,37747,1872],{},[1750,37749,3751],{},[5535,37751,37752,37754],{},[898,37753,12471],{},[1742,37755,1872],{},[1750,37757,1766],{},[1742,37759,22073],{},[4585,37761],{"width":36999},[4585,37763,37764],{},[1969,37765,37766],{},"(6.14)",[902,37768,37769],{"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}",[724,37771,37772,37773,37776,37777,37790,37791,2366],{},"Díky konvexitě indiferenčních křivek je řešení ",[38,37774,37775],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[883,37778,37780],{"className":37779},[886],[888,37781,37782],{"xmlns":890},[892,37783,37784,37788],{},[895,37785,37786],{},[898,37787,26016],{},[902,37789,26069],{"encoding":904}," dostáváme ",[38,37792,37793],{},"podmínku optimality",[883,37795,37797],{"className":37796},[886],[888,37798,37799],{"xmlns":890,"display":36989},[892,37800,37801,37859],{},[895,37802,37803],{},[3582,37804,37805],{"notation":3584},[3586,37806,37807],{"scriptlevel":2607,"displaystyle":1752},[3586,37808,37809],{"scriptlevel":2607,"displaystyle":1752},[3586,37810,37811],{"scriptlevel":2607,"displaystyle":1916},[895,37812,37813,37815,37817,37819,37837,37839,37857],{},[1969,37814,6766],{},[1969,37816,20236],{},[1750,37818,1766],{},[3423,37820,37821,37829],{},[5950,37822,37823,37825,37827],{},[898,37824,900],{},[1742,37826,1744],{},[1750,37828,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,37830,37831,37833,37835],{},[898,37832,900],{},[1742,37834,1872],{},[1750,37836,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,37838,1766],{},[3423,37840,37841,37849],{},[5950,37842,37843,37845,37847],{},[898,37844,1776],{},[1742,37846,1744],{},[1750,37848,3751],{},[5950,37850,37851,37853,37855],{},[898,37852,1776],{},[1742,37854,1872],{},[1750,37856,3751],{},[1969,37858,6766],{},[902,37860,37861],{"encoding":904},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1785,37863,37864],{},[724,37865,37866,37868,37869,37903,37904,37907,37908,37926,37927,37945,37946,37976,37977,37994,37995,38025],{},[883,37867,1791],{}," Intuice — mezní poměr užitečnosti = mezní poměr cen\nPodmínka ",[883,37870,37872],{"className":37871},[886],[888,37873,37874],{"xmlns":890},[892,37875,37876,37900],{},[895,37877,37878,37880,37882,37890,37892],{},[1969,37879,20236],{},[1750,37881,1766],{},[5950,37883,37884,37886,37888],{},[898,37885,1776],{},[1742,37887,1744],{},[1750,37889,3751],{},[898,37891,1748],{"mathvariant":1747},[5950,37893,37894,37896,37898],{},[898,37895,1776],{},[1742,37897,1872],{},[1750,37899,3751],{},[902,37901,37902],{"encoding":904},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[38,37905,37906],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[883,37909,37911],{"className":37910},[886],[888,37912,37913],{"xmlns":890},[892,37914,37915,37923],{},[895,37916,37917],{},[5535,37918,37919,37921],{},[898,37920,12471],{},[1742,37922,1744],{},[902,37924,37925],{"encoding":904},"Q_1"," za ",[883,37928,37930],{"className":37929},[886],[888,37931,37932],{"xmlns":890},[892,37933,37934,37942],{},[895,37935,37936],{},[5535,37937,37938,37940],{},[898,37939,12471],{},[1742,37941,1872],{},[902,37943,37944],{"encoding":904},"Q_2"," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[883,37947,37949],{"className":37948},[886],[888,37950,37951],{"xmlns":890},[892,37952,37953,37973],{},[895,37954,37955,37957,37959,37965,37967],{},[1969,37956,20236],{},[1750,37958,2604],{},[5535,37960,37961,37963],{},[898,37962,1776],{},[1742,37964,1744],{},[898,37966,1748],{"mathvariant":1747},[5535,37968,37969,37971],{},[898,37970,1776],{},[1742,37972,1872],{},[902,37974,37975],{"encoding":904},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[883,37978,37980],{"className":37979},[886],[888,37981,37982],{"xmlns":890},[892,37983,37984,37992],{},[895,37985,37986],{},[5535,37987,37988,37990],{},[898,37989,12471],{},[1742,37991,1744],{},[902,37993,37925],{"encoding":904}," (subjektivní ocenění převažuje nad tržním); kdyby ",[883,37996,37998],{"className":37997},[886],[888,37999,38000],{"xmlns":890},[892,38001,38002,38022],{},[895,38003,38004,38006,38008,38014,38016],{},[1969,38005,20236],{},[1750,38007,2624],{},[5535,38009,38010,38012],{},[898,38011,1776],{},[1742,38013,1744],{},[898,38015,1748],{"mathvariant":1747},[5535,38017,38018,38020],{},[898,38019,1776],{},[1742,38021,1872],{},[902,38023,38024],{"encoding":904},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[198,38027,38029,38030,38043],{"id":38028},"interpretace-λlambda-mezní-užitečnost-důchodu","Interpretace ",[883,38031,38033],{"className":38032},[886],[888,38034,38035],{"xmlns":890},[892,38036,38037,38041],{},[895,38038,38039],{},[898,38040,26016],{},[902,38042,26069],{"encoding":904}," — mezní užitečnost důchodu",[724,38045,38046,38047,38065,38066,38069,38070,38087,38088,38105,38106,38109],{},"Lagrangeův multiplikátor ",[883,38048,38050],{"className":38049},[886],[888,38051,38052],{"xmlns":890},[892,38053,38054,38062],{},[895,38055,38056],{},[1699,38057,38058,38060],{},[898,38059,26016],{},[1750,38061,3751],{},[902,38063,38064],{"encoding":904},"\\lambda^*"," představuje ",[38,38067,38068],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[883,38071,38073],{"className":38072},[886],[888,38074,38075],{"xmlns":890},[892,38076,38077,38085],{},[895,38078,38079],{},[1699,38080,38081,38083],{},[898,38082,900],{},[1750,38084,3751],{},[902,38086,36885],{"encoding":904}," při jednotkové změně důchodu ",[883,38089,38091],{"className":38090},[886],[888,38092,38093],{"xmlns":890},[892,38094,38095,38103],{},[895,38096,38097],{},[1699,38098,38099,38101],{},[898,38100,1666],{},[1750,38102,3751],{},[902,38104,36951],{"encoding":904},". Je to ",[38,38107,38108],{},"stínová cena"," rozpočtového omezení.",[1785,38111,38112,38117],{},[724,38113,38114,38116],{},[883,38115,6004],{}," Postup — maximalizace užitečnosti Lagrangeovou metodou",[152,38118,38119,38179,38266,38302,38389],{},[123,38120,38121,38124,38125,2313],{},[38,38122,38123],{},"Zapiš rozpočtové omezení"," ve tvaru ",[883,38126,38128],{"className":38127},[886],[888,38129,38130],{"xmlns":890},[892,38131,38132,38176],{},[895,38133,38134,38140,38142,38150,38156,38158,38166,38172,38174],{},[1699,38135,38136,38138],{},[898,38137,1666],{},[1750,38139,3751],{},[1750,38141,1758],{},[5950,38143,38144,38146,38148],{},[898,38145,1776],{},[1742,38147,1744],{},[1750,38149,3751],{},[5535,38151,38152,38154],{},[898,38153,12471],{},[1742,38155,1744],{},[1750,38157,1758],{},[5950,38159,38160,38162,38164],{},[898,38161,1776],{},[1742,38163,1872],{},[1750,38165,3751],{},[5535,38167,38168,38170],{},[898,38169,12471],{},[1742,38171,1872],{},[1750,38173,1766],{},[1742,38175,2607],{},[902,38177,38178],{"encoding":904},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[123,38180,38181,1647,38184,2313],{},[38,38182,38183],{},"Sestav Lagrangeovu funkci",[883,38185,38187],{"className":38186},[886],[888,38188,38189],{"xmlns":890},[892,38190,38191,38263],{},[895,38192,38193,38195,38197,38199,38201,38207,38209,38215,38217,38219,38221,38223,38229,38231,38239,38245,38247,38255,38261],{},[898,38194,2046],{"mathvariant":37471},[1750,38196,1766],{},[898,38198,900],{},[1750,38200,1753],{"stretchy":1752},[5535,38202,38203,38205],{},[898,38204,12471],{},[1742,38206,1744],{},[1750,38208,1917],{"separator":1916},[5535,38210,38211,38213],{},[898,38212,12471],{},[1742,38214,1872],{},[1750,38216,1763],{"stretchy":1752},[1750,38218,1861],{},[898,38220,26016],{},[1750,38222,1753],{"stretchy":1752},[1699,38224,38225,38227],{},[898,38226,1666],{},[1750,38228,3751],{},[1750,38230,1758],{},[5950,38232,38233,38235,38237],{},[898,38234,1776],{},[1742,38236,1744],{},[1750,38238,3751],{},[5535,38240,38241,38243],{},[898,38242,12471],{},[1742,38244,1744],{},[1750,38246,1758],{},[5950,38248,38249,38251,38253],{},[898,38250,1776],{},[1742,38252,1872],{},[1750,38254,3751],{},[5535,38256,38257,38259],{},[898,38258,12471],{},[1742,38260,1872],{},[1750,38262,1763],{"stretchy":1752},[902,38264,38265],{"encoding":904},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[123,38267,38268,20101,38271,38301],{},[38,38269,38270],{},"Spočítej parciální derivace",[883,38272,38274],{"className":38273},[886],[888,38275,38276],{"xmlns":890},[892,38277,38278,38298],{},[895,38279,38280,38286,38288,38294,38296],{},[5535,38281,38282,38284],{},[898,38283,12471],{},[1742,38285,1744],{},[1750,38287,1917],{"separator":1916},[5535,38289,38290,38292],{},[898,38291,12471],{},[1742,38293,1872],{},[1750,38295,1917],{"separator":1916},[898,38297,26016],{},[902,38299,38300],{"encoding":904},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[123,38303,38304,38320,38321,38354,38355,2028,38372,2313],{},[38,38305,38306,38307],{},"Vyluč ",[883,38308,38310],{"className":38309},[886],[888,38311,38312],{"xmlns":890},[892,38313,38314,38318],{},[895,38315,38316],{},[898,38317,26016],{},[902,38319,26069],{"encoding":904}," dělením prvních dvou rovnic — dostaneš podmínku ",[883,38322,38324],{"className":38323},[886],[888,38325,38326],{"xmlns":890},[892,38327,38328,38352],{},[895,38329,38330,38332,38334,38342,38344],{},[1969,38331,20236],{},[1750,38333,1766],{},[5950,38335,38336,38338,38340],{},[898,38337,1776],{},[1742,38339,1744],{},[1750,38341,3751],{},[898,38343,1748],{"mathvariant":1747},[5950,38345,38346,38348,38350],{},[898,38347,1776],{},[1742,38349,1872],{},[1750,38351,3751],{},[902,38353,37902],{"encoding":904},", která dá vztah mezi ",[883,38356,38358],{"className":38357},[886],[888,38359,38360],{"xmlns":890},[892,38361,38362,38370],{},[895,38363,38364],{},[5535,38365,38366,38368],{},[898,38367,12471],{},[1742,38369,1744],{},[902,38371,37925],{"encoding":904},[883,38373,38375],{"className":38374},[886],[888,38376,38377],{"xmlns":890},[892,38378,38379,38387],{},[895,38380,38381],{},[5535,38382,38383,38385],{},[898,38384,12471],{},[1742,38386,1872],{},[902,38388,37944],{"encoding":904},[123,38390,38391,38394,38395,38425,38426,38443,38444,2313],{},[38,38392,38393],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[883,38396,38398],{"className":38397},[886],[888,38399,38400],{"xmlns":890},[892,38401,38402,38422],{},[895,38403,38404,38412,38414],{},[5950,38405,38406,38408,38410],{},[898,38407,12471],{},[1742,38409,1744],{},[1750,38411,3751],{},[1750,38413,1917],{"separator":1916},[5950,38415,38416,38418,38420],{},[898,38417,12471],{},[1742,38419,1872],{},[1750,38421,3751],{},[902,38423,38424],{"encoding":904},"Q_1^*, Q_2^*",", případně ",[883,38427,38429],{"className":38428},[886],[888,38430,38431],{"xmlns":890},[892,38432,38433,38441],{},[895,38434,38435],{},[1699,38436,38437,38439],{},[898,38438,26016],{},[1750,38440,3751],{},[902,38442,38064],{"encoding":904}," a maximální užitečnost ",[883,38445,38447],{"className":38446},[886],[888,38448,38449],{"xmlns":890},[892,38450,38451,38485],{},[895,38452,38453,38459,38461,38463,38465,38473,38475,38483],{},[1699,38454,38455,38457],{},[898,38456,900],{},[1750,38458,3751],{},[1750,38460,1766],{},[898,38462,900],{},[1750,38464,1753],{"stretchy":1752},[5950,38466,38467,38469,38471],{},[898,38468,12471],{},[1742,38470,1744],{},[1750,38472,3751],{},[1750,38474,1917],{"separator":1916},[5950,38476,38477,38479,38481],{},[898,38478,12471],{},[1742,38480,1872],{},[1750,38482,3751],{},[1750,38484,1763],{"stretchy":1752},[902,38486,38487],{"encoding":904},"U^* = U(Q_1^*, Q_2^*)",[115,38489,38491],{"id":38490},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[724,38493,38494],{},[4434,38495],{"alt":38496,"className":38497,"src":38498},"imek-uzitecnost-optimum",[210,4438],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[724,38500,38501],{},[614,38502,38503,38504,38553,38554,2028,38582,38610,38611,38645,38646,38685,38686,38704,38705,38723,38724,38742],{},"Obrázek 6.7 — Rozpočtová přímka ",[883,38505,38507],{"className":38506},[886],[888,38508,38509],{"xmlns":890},[892,38510,38511,38551],{},[895,38512,38513,38519,38521,38529,38535,38537,38545],{},[1699,38514,38515,38517],{},[898,38516,1666],{},[1750,38518,3751],{},[1750,38520,1766],{},[5950,38522,38523,38525,38527],{},[898,38524,1776],{},[1742,38526,1744],{},[1750,38528,3751],{},[5535,38530,38531,38533],{},[898,38532,12471],{},[1742,38534,1744],{},[1750,38536,1861],{},[5950,38538,38539,38541,38543],{},[898,38540,1776],{},[1742,38542,1872],{},[1750,38544,3751],{},[5535,38546,38547,38549],{},[898,38548,12471],{},[1742,38550,1872],{},[902,38552,26871],{"encoding":904}," protíná osy v ",[883,38555,38557],{"className":38556},[886],[888,38558,38559],{"xmlns":890},[892,38560,38561,38579],{},[895,38562,38563,38569,38571],{},[1699,38564,38565,38567],{},[898,38566,1666],{},[1750,38568,3751],{},[898,38570,1748],{"mathvariant":1747},[5950,38572,38573,38575,38577],{},[898,38574,1776],{},[1742,38576,1744],{},[1750,38578,3751],{},[902,38580,38581],{"encoding":904},"Y^*\u002FP_1^*",[883,38583,38585],{"className":38584},[886],[888,38586,38587],{"xmlns":890},[892,38588,38589,38607],{},[895,38590,38591,38597,38599],{},[1699,38592,38593,38595],{},[898,38594,1666],{},[1750,38596,3751],{},[898,38598,1748],{"mathvariant":1747},[5950,38600,38601,38603,38605],{},[898,38602,1776],{},[1742,38604,1872],{},[1750,38606,3751],{},[902,38608,38609],{"encoding":904},"Y^*\u002FP_2^*",". Tři indiferenční křivky ",[883,38612,38614],{"className":38613},[886],[888,38615,38616],{"xmlns":890},[892,38617,38618,38642],{},[895,38619,38620,38626,38628,38634,38636],{},[5535,38621,38622,38624],{},[898,38623,9365],{},[1742,38625,1744],{},[1750,38627,2624],{},[1699,38629,38630,38632],{},[898,38631,9365],{},[1750,38633,3751],{},[1750,38635,2624],{},[5535,38637,38638,38640],{},[898,38639,9365],{},[1742,38641,1872],{},[902,38643,38644],{"encoding":904},"c_1 \u003C c^* \u003C c_2",". Optimum ",[883,38647,38649],{"className":38648},[886],[888,38650,38651],{"xmlns":890},[892,38652,38653,38683],{},[895,38654,38655,38661,38663,38671,38673,38681],{},[1699,38656,38657,38659],{},[898,38658,12471],{},[1750,38660,3751],{},[1750,38662,5141],{"stretchy":1752},[5950,38664,38665,38667,38669],{},[898,38666,12471],{},[1742,38668,1744],{},[1750,38670,3751],{},[1750,38672,1917],{"separator":1916},[5950,38674,38675,38677,38679],{},[898,38676,12471],{},[1742,38678,1872],{},[1750,38680,3751],{},[1750,38682,5158],{"stretchy":1752},[902,38684,37250],{"encoding":904}," je bod dotyku rozpočtové přímky s křivkou ",[883,38687,38689],{"className":38688},[886],[888,38690,38691],{"xmlns":890},[892,38692,38693,38701],{},[895,38694,38695],{},[1699,38696,38697,38699],{},[898,38698,9365],{},[1750,38700,3751],{},[902,38702,38703],{"encoding":904},"c^*",". Křivka ",[883,38706,38708],{"className":38707},[886],[888,38709,38710],{"xmlns":890},[892,38711,38712,38720],{},[895,38713,38714],{},[5535,38715,38716,38718],{},[898,38717,9365],{},[1742,38719,1744],{},[902,38721,38722],{"encoding":904},"c_1"," je dosažitelná, ale nemaximalizuje užitečnost; křivka ",[883,38725,38727],{"className":38726},[886],[888,38728,38729],{"xmlns":890},[892,38730,38731,38739],{},[895,38732,38733],{},[5535,38734,38735,38737],{},[898,38736,9365],{},[1742,38738,1872],{},[902,38740,38741],{"encoding":904},"c_2"," není při daném důchodu dosažitelná.",[724,38744,38745,38746,38749,38750,38768,38769,38798],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[38,38747,38748],{},"dotýkají",", tj. mají v bodě ",[883,38751,38753],{"className":38752},[886],[888,38754,38755],{"xmlns":890},[892,38756,38757,38765],{},[895,38758,38759],{},[1699,38760,38761,38763],{},[898,38762,12471],{},[1750,38764,3751],{},[902,38766,38767],{"encoding":904},"Q^*"," společnou tečnu. To přímo převádí podmínku ",[883,38770,38772],{"className":38771},[886],[888,38773,38774],{"xmlns":890},[892,38775,38776,38796],{},[895,38777,38778,38780,38782,38788,38790],{},[1969,38779,20236],{},[1750,38781,1766],{},[5535,38783,38784,38786],{},[898,38785,1776],{},[1742,38787,1744],{},[898,38789,1748],{"mathvariant":1747},[5535,38791,38792,38794],{},[898,38793,1776],{},[1742,38795,1872],{},[902,38797,36921],{"encoding":904}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[115,38800,38802],{"id":38801},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[724,38804,19299,38805,38867],{},[883,38806,38808],{"className":38807},[886],[888,38809,38810],{"xmlns":890},[892,38811,38812,38864],{},[895,38813,38814,38816,38818,38824,38826,38832,38834,38836,38850],{},[898,38815,900],{},[1750,38817,1753],{"stretchy":1752},[5535,38819,38820,38822],{},[898,38821,12471],{},[1742,38823,1744],{},[1750,38825,1917],{"separator":1916},[5535,38827,38828,38830],{},[898,38829,12471],{},[1742,38831,1872],{},[1750,38833,1763],{"stretchy":1752},[1750,38835,1766],{},[5950,38837,38838,38840,38842],{},[898,38839,12471],{},[1742,38841,1744],{},[895,38843,38844,38846,38848],{},[1742,38845,1744],{},[898,38847,1748],{"mathvariant":1747},[1742,38849,1872],{},[5950,38851,38852,38854,38856],{},[898,38853,12471],{},[1742,38855,1872],{},[895,38857,38858,38860,38862],{},[1742,38859,1744],{},[898,38861,1748],{"mathvariant":1747},[1742,38863,1872],{},[902,38865,38866],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[724,38869,38870],{},[883,38871,38873],{"className":38872},[886],[888,38874,38875],{"xmlns":890},[892,38876,38877,38983],{},[895,38878,38879,38881,38883,38965,38967,38981],{},[1969,38880,20236],{},[1750,38882,1766],{},[3423,38884,38885,38925],{},[895,38886,38887,38895,38911],{},[3586,38888,38889],{"scriptlevel":2607,"displaystyle":1752},[3423,38890,38891,38893],{},[1742,38892,1744],{},[1742,38894,1872],{},[5950,38896,38897,38899,38901],{},[898,38898,12471],{},[1742,38900,1744],{},[895,38902,38903,38905,38907,38909],{},[1750,38904,1758],{},[1742,38906,1744],{},[898,38908,1748],{"mathvariant":1747},[1742,38910,1872],{},[5950,38912,38913,38915,38917],{},[898,38914,12471],{},[1742,38916,1872],{},[895,38918,38919,38921,38923],{},[1742,38920,1744],{},[898,38922,1748],{"mathvariant":1747},[1742,38924,1872],{},[895,38926,38927,38935,38949],{},[3586,38928,38929],{"scriptlevel":2607,"displaystyle":1752},[3423,38930,38931,38933],{},[1742,38932,1744],{},[1742,38934,1872],{},[5950,38936,38937,38939,38941],{},[898,38938,12471],{},[1742,38940,1744],{},[895,38942,38943,38945,38947],{},[1742,38944,1744],{},[898,38946,1748],{"mathvariant":1747},[1742,38948,1872],{},[5950,38950,38951,38953,38955],{},[898,38952,12471],{},[1742,38954,1872],{},[895,38956,38957,38959,38961,38963],{},[1750,38958,1758],{},[1742,38960,1744],{},[898,38962,1748],{"mathvariant":1747},[1742,38964,1872],{},[1750,38966,1766],{},[3423,38968,38969,38975],{},[5535,38970,38971,38973],{},[898,38972,12471],{},[1742,38974,1872],{},[5535,38976,38977,38979],{},[898,38978,12471],{},[1742,38980,1744],{},[898,38982,2313],{"mathvariant":1747},[902,38984,38985],{"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}.",[724,38987,38988,38989,12605,39034,39036,39037,39057,39058,39088,39089,2313],{},"Tedy ",[883,38990,38992],{"className":38991},[886],[888,38993,38994],{"xmlns":890},[892,38995,38996,39031],{},[895,38997,38998,39000,39002,39005,39007,39009,39011,39013,39021,39023],{},[1969,38999,20236],{},[1750,39001,1753],{"stretchy":1752},[1742,39003,39004],{},"300",[1750,39006,1917],{"separator":1916},[1742,39008,7658],{},[1750,39010,1763],{"stretchy":1752},[1750,39012,1766],{},[3586,39014,39015],{"scriptlevel":2607,"displaystyle":1752},[3423,39016,39017,39019],{},[1742,39018,7658],{},[1742,39020,39004],{},[1750,39022,1766],{},[3586,39024,39025],{"scriptlevel":2607,"displaystyle":1752},[3423,39026,39027,39029],{},[1742,39028,7902],{},[1742,39030,7822],{},[902,39032,39033],{"encoding":904},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[614,39035,18853],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[883,39038,39040],{"className":39039},[886],[888,39041,39042],{"xmlns":890},[892,39043,39044,39054],{},[895,39045,39046],{},[3586,39047,39048],{"scriptlevel":2607,"displaystyle":1752},[3423,39049,39050,39052],{},[1742,39051,7902],{},[1742,39053,7822],{},[902,39055,39056],{"encoding":904},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[883,39059,39061],{"className":39060},[886],[888,39062,39063],{"xmlns":890},[892,39064,39065,39085],{},[895,39066,39067,39069,39071,39077,39079],{},[1969,39068,20236],{},[1750,39070,1766],{},[5535,39072,39073,39075],{},[898,39074,12471],{},[1742,39076,1872],{},[898,39078,1748],{"mathvariant":1747},[5535,39080,39081,39083],{},[898,39082,12471],{},[1742,39084,1744],{},[902,39086,39087],{"encoding":904},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[883,39090,39092],{"className":39091},[886],[888,39093,39094],{"xmlns":890},[892,39095,39096,39116],{},[895,39097,39098,39100,39102,39108,39110],{},[1969,39099,20236],{},[1750,39101,1766],{},[5535,39103,39104,39106],{},[898,39105,1776],{},[1742,39107,1744],{},[898,39109,1748],{"mathvariant":1747},[5535,39111,39112,39114],{},[898,39113,1776],{},[1742,39115,1872],{},[902,39117,36921],{"encoding":904},[115,39119,39121,39122],{"id":39120},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[883,39123,39125],{"className":39124},[886],[888,39126,39127],{"xmlns":890},[892,39128,39129,39147],{},[895,39130,39131,39133,39135,39141],{},[898,39132,900],{},[1750,39134,1766],{},[5535,39136,39137,39139],{},[898,39138,12471],{},[1742,39140,1744],{},[5535,39142,39143,39145],{},[898,39144,12471],{},[1742,39146,1872],{},[902,39148,39149],{"encoding":904},"U = Q_1 Q_2",[724,39151,39152,39153,1343,39199,1343,39223,1343,39247,39269],{},"Je dána ",[883,39154,39156],{"className":39155},[886],[888,39157,39158],{"xmlns":890},[892,39159,39160,39196],{},[895,39161,39162,39164,39166,39172,39174,39180,39182,39184,39190],{},[898,39163,900],{},[1750,39165,1753],{"stretchy":1752},[5535,39167,39168,39170],{},[898,39169,12471],{},[1742,39171,1744],{},[1750,39173,1917],{"separator":1916},[5535,39175,39176,39178],{},[898,39177,12471],{},[1742,39179,1872],{},[1750,39181,1763],{"stretchy":1752},[1750,39183,1766],{},[5535,39185,39186,39188],{},[898,39187,12471],{},[1742,39189,1744],{},[5535,39191,39192,39194],{},[898,39193,12471],{},[1742,39195,1872],{},[902,39197,39198],{"encoding":904},"U(Q_1, Q_2) = Q_1 Q_2",[883,39200,39202],{"className":39201},[886],[888,39203,39204],{"xmlns":890},[892,39205,39206,39220],{},[895,39207,39208,39216,39218],{},[5950,39209,39210,39212,39214],{},[898,39211,1776],{},[1742,39213,1744],{},[1750,39215,3751],{},[1750,39217,1766],{},[1742,39219,1872],{},[902,39221,39222],{"encoding":904},"P_1^* = 2",[883,39224,39226],{"className":39225},[886],[888,39227,39228],{"xmlns":890},[892,39229,39230,39244],{},[895,39231,39232,39240,39242],{},[5950,39233,39234,39236,39238],{},[898,39235,1776],{},[1742,39237,1872],{},[1750,39239,3751],{},[1750,39241,1766],{},[1742,39243,7902],{},[902,39245,39246],{"encoding":904},"P_2^* = 5",[883,39248,39250],{"className":39249},[886],[888,39251,39252],{"xmlns":890},[892,39253,39254,39266],{},[895,39255,39256,39262,39264],{},[1699,39257,39258,39260],{},[898,39259,1666],{},[1750,39261,3751],{},[1750,39263,1766],{},[1742,39265,4078],{},[902,39267,39268],{"encoding":904},"Y^* = 100",". Lagrangeova funkce:",[883,39271,39273],{"className":39272},[886],[888,39274,39275],{"xmlns":890,"display":36989},[892,39276,39277,39349],{},[895,39278,39279,39281,39283,39289,39291,39297,39299,39301,39303,39305,39311,39317,39319,39321,39323,39325,39327,39329,39335,39337,39339,39345,39347],{},[898,39280,2046],{"mathvariant":37471},[1750,39282,1753],{"stretchy":1752},[5535,39284,39285,39287],{},[898,39286,12471],{},[1742,39288,1744],{},[1750,39290,1917],{"separator":1916},[5535,39292,39293,39295],{},[898,39294,12471],{},[1742,39296,1872],{},[1750,39298,1917],{"separator":1916},[898,39300,26016],{},[1750,39302,1763],{"stretchy":1752},[1750,39304,1766],{},[5535,39306,39307,39309],{},[898,39308,12471],{},[1742,39310,1744],{},[5535,39312,39313,39315],{},[898,39314,12471],{},[1742,39316,1872],{},[1750,39318,1861],{},[898,39320,26016],{},[1750,39322,1753],{"stretchy":1752},[1742,39324,4078],{},[1750,39326,1758],{},[1742,39328,1872],{},[5535,39330,39331,39333],{},[898,39332,12471],{},[1742,39334,1744],{},[1750,39336,1758],{},[1742,39338,7902],{},[5535,39340,39341,39343],{},[898,39342,12471],{},[1742,39344,1872],{},[1750,39346,1763],{"stretchy":1752},[898,39348,2313],{"mathvariant":1747},[902,39350,39351],{"encoding":904},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[724,39353,39354],{},"Soustava:",[883,39356,39358],{"className":39357},[886],[888,39359,39360],{"xmlns":890,"display":36989},[892,39361,39362,39474],{},[4577,39363,39364,39398,39432],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,39365,39366,39384],{},[4585,39367,39368],{},[3586,39369,39370],{"scriptlevel":2607,"displaystyle":1916},[895,39371,39372,39378,39380,39382],{},[5535,39373,39374,39376],{},[898,39375,12471],{},[1742,39377,1872],{},[1750,39379,1758],{},[1742,39381,1872],{},[898,39383,26016],{},[4585,39385,39386],{},[3586,39387,39388],{"scriptlevel":2607,"displaystyle":1916},[895,39389,39390,39392,39394,39396],{},[895,39391],{},[1750,39393,1766],{},[1742,39395,2607],{},[1750,39397,1917],{"separator":1916},[4582,39399,39400,39418],{},[4585,39401,39402],{},[3586,39403,39404],{"scriptlevel":2607,"displaystyle":1916},[895,39405,39406,39412,39414,39416],{},[5535,39407,39408,39410],{},[898,39409,12471],{},[1742,39411,1744],{},[1750,39413,1758],{},[1742,39415,7902],{},[898,39417,26016],{},[4585,39419,39420],{},[3586,39421,39422],{"scriptlevel":2607,"displaystyle":1916},[895,39423,39424,39426,39428,39430],{},[895,39425],{},[1750,39427,1766],{},[1742,39429,2607],{},[1750,39431,1917],{"separator":1916},[4582,39433,39434,39462],{},[4585,39435,39436],{},[3586,39437,39438],{"scriptlevel":2607,"displaystyle":1916},[895,39439,39440,39442,39444,39446,39452,39454,39456],{},[1742,39441,4078],{},[1750,39443,1758],{},[1742,39445,1872],{},[5535,39447,39448,39450],{},[898,39449,12471],{},[1742,39451,1744],{},[1750,39453,1758],{},[1742,39455,7902],{},[5535,39457,39458,39460],{},[898,39459,12471],{},[1742,39461,1872],{},[4585,39463,39464],{},[3586,39465,39466],{"scriptlevel":2607,"displaystyle":1916},[895,39467,39468,39470,39472],{},[895,39469],{},[1750,39471,1766],{},[1742,39473,22073],{},[902,39475,39476],{"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}",[724,39478,39479,39480,1343,39504,39528,39529,8164,39569,39587,39588,39638,39639,2313],{},"Z prvních dvou rovnic ",[883,39481,39483],{"className":39482},[886],[888,39484,39485],{"xmlns":890},[892,39486,39487,39501],{},[895,39488,39489,39495,39497,39499],{},[5535,39490,39491,39493],{},[898,39492,12471],{},[1742,39494,1872],{},[1750,39496,1766],{},[1742,39498,1872],{},[898,39500,26016],{},[902,39502,39503],{"encoding":904},"Q_2 = 2\\lambda",[883,39505,39507],{"className":39506},[886],[888,39508,39509],{"xmlns":890},[892,39510,39511,39525],{},[895,39512,39513,39519,39521,39523],{},[5535,39514,39515,39517],{},[898,39516,12471],{},[1742,39518,1744],{},[1750,39520,1766],{},[1742,39522,7902],{},[898,39524,26016],{},[902,39526,39527],{"encoding":904},"Q_1 = 5\\lambda","; dosazením do třetí ",[883,39530,39532],{"className":39531},[886],[888,39533,39534],{"xmlns":890},[892,39535,39536,39566],{},[895,39537,39538,39540,39542,39544,39546,39548,39550,39552,39554,39556,39558,39560,39562,39564],{},[1742,39539,4078],{},[1750,39541,1766],{},[1742,39543,1872],{},[1750,39545,8009],{},[1742,39547,7902],{},[898,39549,26016],{},[1750,39551,1861],{},[1742,39553,7902],{},[1750,39555,8009],{},[1742,39557,1872],{},[898,39559,26016],{},[1750,39561,1766],{},[1742,39563,6465],{},[898,39565,26016],{},[902,39567,39568],{"encoding":904},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[883,39570,39572],{"className":39571},[886],[888,39573,39574],{"xmlns":890},[892,39575,39576,39584],{},[895,39577,39578,39580,39582],{},[898,39579,26016],{},[1750,39581,1766],{},[1742,39583,7902],{},[902,39585,39586],{"encoding":904},"\\lambda = 5",". Odtud ",[38,39589,39590,1343,39614],{},[883,39591,39593],{"className":39592},[886],[888,39594,39595],{"xmlns":890},[892,39596,39597,39611],{},[895,39598,39599,39607,39609],{},[5950,39600,39601,39603,39605],{},[898,39602,12471],{},[1742,39604,1744],{},[1750,39606,3751],{},[1750,39608,1766],{},[1742,39610,6419],{},[902,39612,39613],{"encoding":904},"Q_1^* = 25",[883,39615,39617],{"className":39616},[886],[888,39618,39619],{"xmlns":890},[892,39620,39621,39635],{},[895,39622,39623,39631,39633],{},[5950,39624,39625,39627,39629],{},[898,39626,12471],{},[1742,39628,1872],{},[1750,39630,3751],{},[1750,39632,1766],{},[1742,39634,3079],{},[902,39636,39637],{"encoding":904},"Q_2^* = 10",", maximální užitečnost ",[883,39640,39642],{"className":39641},[886],[888,39643,39644],{"xmlns":890},[892,39645,39646,39667],{},[895,39647,39648,39654,39656,39658,39660,39662,39664],{},[1699,39649,39650,39652],{},[898,39651,900],{},[1750,39653,3751],{},[1750,39655,1766],{},[1742,39657,6419],{},[1750,39659,8009],{},[1742,39661,3079],{},[1750,39663,1766],{},[1742,39665,39666],{},"250",[902,39668,39669],{"encoding":904},"U^* = 25 \\cdot 10 = 250",[724,39671,39672],{},[614,39673,39674,39675,37060,39713,2028,39737,39761,39762,39792,39793,39817,39818,39840,39841,2313],{},"Obrázek 6.8 — Rozpočtová přímka ",[883,39676,39678],{"className":39677},[886],[888,39679,39680],{"xmlns":890},[892,39681,39682,39710],{},[895,39683,39684,39686,39688,39690,39696,39698,39700,39706,39708],{},[1742,39685,4078],{},[1750,39687,1758],{},[1742,39689,1872],{},[5535,39691,39692,39694],{},[898,39693,12471],{},[1742,39695,1744],{},[1750,39697,1758],{},[1742,39699,7902],{},[5535,39701,39702,39704],{},[898,39703,12471],{},[1742,39705,1872],{},[1750,39707,1766],{},[1742,39709,2607],{},[902,39711,39712],{"encoding":904},"100 - 2 Q_1 - 5 Q_2 = 0",[883,39714,39716],{"className":39715},[886],[888,39717,39718],{"xmlns":890},[892,39719,39720,39734],{},[895,39721,39722,39724,39726,39728,39730,39732],{},[898,39723,13916],{},[1750,39725,5141],{"stretchy":1752},[1742,39727,2607],{},[1750,39729,1917],{"separator":1916},[1742,39731,6465],{},[1750,39733,5158],{"stretchy":1752},[902,39735,39736],{"encoding":904},"A[0, 20]",[883,39738,39740],{"className":39739},[886],[888,39741,39742],{"xmlns":890},[892,39743,39744,39758],{},[895,39745,39746,39748,39750,39752,39754,39756],{},[898,39747,7097],{},[1750,39749,5141],{"stretchy":1752},[1742,39751,3936],{},[1750,39753,1917],{"separator":1916},[1742,39755,2607],{},[1750,39757,5158],{"stretchy":1752},[902,39759,39760],{"encoding":904},"B[50, 0]","; hyperbolická indiferenční křivka ",[883,39763,39765],{"className":39764},[886],[888,39766,39767],{"xmlns":890},[892,39768,39769,39789],{},[895,39770,39771,39777,39779,39781,39783],{},[5535,39772,39773,39775],{},[898,39774,12471],{},[1742,39776,1872],{},[1750,39778,1766],{},[1742,39780,39666],{},[898,39782,1748],{"mathvariant":1747},[5535,39784,39785,39787],{},[898,39786,12471],{},[1742,39788,1744],{},[902,39790,39791],{"encoding":904},"Q_2 = 250\u002FQ_1"," se dotýká rozpočtové přímky v bodě ",[883,39794,39796],{"className":39795},[886],[888,39797,39798],{"xmlns":890},[892,39799,39800,39814],{},[895,39801,39802,39804,39806,39808,39810,39812],{},[898,39803,1705],{},[1750,39805,5141],{"stretchy":1752},[1742,39807,6419],{},[1750,39809,1917],{"separator":1916},[1742,39811,3079],{},[1750,39813,5158],{"stretchy":1752},[902,39815,39816],{"encoding":904},"E[25, 10]",". Sklon přímky ",[883,39819,39821],{"className":39820},[886],[888,39822,39823],{"xmlns":890},[892,39824,39825,39837],{},[895,39826,39827,39829],{},[1750,39828,1758],{},[3586,39830,39831],{"scriptlevel":2607,"displaystyle":1752},[3423,39832,39833,39835],{},[1742,39834,1872],{},[1742,39836,7902],{},[902,39838,39839],{"encoding":904},"-\\tfrac{2}{5}"," odpovídá ",[883,39842,39844],{"className":39843},[886],[888,39845,39846],{"xmlns":890},[892,39847,39848,39888],{},[895,39849,39850,39852,39854,39856,39858,39860,39862,39864,39866,39868,39876,39878,39880],{},[1750,39851,1758],{},[1969,39853,20236],{},[1750,39855,1753],{"stretchy":1752},[1742,39857,6419],{},[1750,39859,1917],{"separator":1916},[1742,39861,3079],{},[1750,39863,1763],{"stretchy":1752},[1750,39865,1766],{},[1750,39867,1758],{},[3586,39869,39870],{"scriptlevel":2607,"displaystyle":1752},[3423,39871,39872,39874],{},[1742,39873,3079],{},[1742,39875,6419],{},[1750,39877,1766],{},[1750,39879,1758],{},[3586,39881,39882],{"scriptlevel":2607,"displaystyle":1752},[3423,39883,39884,39886],{},[1742,39885,1872],{},[1742,39887,7902],{},[902,39889,39890],{"encoding":904},"-\\text{MRCS}(25, 10) = -\\tfrac{10}{25} = -\\tfrac{2}{5}",[115,39892,39894],{"id":39893},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[724,39896,39897,39898,37926,39928,39931,39932,2366],{},"Považujeme-li v úloze ",[883,39899,39901],{"className":39900},[886],[888,39902,39903],{"xmlns":890},[892,39904,39905,39925],{},[895,39906,39907,39913,39915,39921,39923],{},[5535,39908,39909,39911],{},[898,39910,1776],{},[1742,39912,1744],{},[1750,39914,1917],{"separator":1916},[5535,39916,39917,39919],{},[898,39918,1776],{},[1742,39920,1872],{},[1750,39922,1917],{"separator":1916},[898,39924,1666],{},[902,39926,39927],{"encoding":904},"P_1, P_2, Y",[38,39929,39930],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[38,39933,39934],{},"Marshallovy poptávkové funkce",[883,39936,39938],{"className":39937},[886],[888,39939,39940],{"xmlns":890,"display":36989},[892,39941,39942,40037],{},[4577,39943,39944],{"width":36994},[4582,39945,39946,39948,40030,40032],{},[4585,39947],{"width":36999},[4585,39949,39950],{},[895,39951,39952,39958,39960,39966,39968,39974,39976,39982,39984,39986,39988,39990,39992,39998,40000,40006,40008,40014,40016,40022,40024,40026,40028],{},[5535,39953,39954,39956],{},[898,39955,12471],{},[1742,39957,1744],{},[1750,39959,1766],{},[5535,39961,39962,39964],{},[898,39963,5541],{},[1742,39965,1744],{},[1750,39967,1753],{"stretchy":1752},[5535,39969,39970,39972],{},[898,39971,1776],{},[1742,39973,1744],{},[1750,39975,1917],{"separator":1916},[5535,39977,39978,39980],{},[898,39979,1776],{},[1742,39981,1872],{},[1750,39983,1917],{"separator":1916},[898,39985,1666],{},[1750,39987,1763],{"stretchy":1752},[1750,39989,1917],{"separator":1916},[2125,39991],{"width":24875},[5535,39993,39994,39996],{},[898,39995,12471],{},[1742,39997,1872],{},[1750,39999,1766],{},[5535,40001,40002,40004],{},[898,40003,5541],{},[1742,40005,1872],{},[1750,40007,1753],{"stretchy":1752},[5535,40009,40010,40012],{},[898,40011,1776],{},[1742,40013,1744],{},[1750,40015,1917],{"separator":1916},[5535,40017,40018,40020],{},[898,40019,1776],{},[1742,40021,1872],{},[1750,40023,1917],{"separator":1916},[898,40025,1666],{},[1750,40027,1763],{"stretchy":1752},[1750,40029,1917],{"separator":1916},[4585,40031],{"width":36999},[4585,40033,40034],{},[1969,40035,40036],{},"(6.15)",[902,40038,40039],{"encoding":904},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[883,40041,40043],{"className":40042},[886],[888,40044,40045],{"xmlns":890,"display":36989},[892,40046,40047,40094],{},[4577,40048,40049],{"width":36994},[4582,40050,40051,40053,40087,40089],{},[4585,40052],{"width":36999},[4585,40054,40055],{},[895,40056,40057,40059,40061,40063,40065,40071,40073,40079,40081,40083,40085],{},[898,40058,26016],{},[1750,40060,1766],{},[898,40062,26016],{},[1750,40064,1753],{"stretchy":1752},[5535,40066,40067,40069],{},[898,40068,1776],{},[1742,40070,1744],{},[1750,40072,1917],{"separator":1916},[5535,40074,40075,40077],{},[898,40076,1776],{},[1742,40078,1872],{},[1750,40080,1917],{"separator":1916},[898,40082,1666],{},[1750,40084,1763],{"stretchy":1752},[898,40086,2313],{"mathvariant":1747},[4585,40088],{"width":36999},[4585,40090,40091],{},[1969,40092,40093],{},"(6.16)",[902,40095,40096],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[724,40098,40099,40129,40130,40196],{},[38,40100,40101,40102,2313],{},"Odvození pro ",[883,40103,40105],{"className":40104},[886],[888,40106,40107],{"xmlns":890},[892,40108,40109,40127],{},[895,40110,40111,40113,40115,40121],{},[898,40112,900],{},[1750,40114,1766],{},[5535,40116,40117,40119],{},[898,40118,12471],{},[1742,40120,1744],{},[5535,40122,40123,40125],{},[898,40124,12471],{},[1742,40126,1872],{},[902,40128,39149],{"encoding":904}," Lagrangeova funkce ",[883,40131,40133],{"className":40132},[886],[888,40134,40135],{"xmlns":890},[892,40136,40137,40193],{},[895,40138,40139,40141,40143,40149,40155,40157,40159,40161,40163,40165,40171,40177,40179,40185,40191],{},[898,40140,2046],{"mathvariant":37471},[1750,40142,1766],{},[5535,40144,40145,40147],{},[898,40146,12471],{},[1742,40148,1744],{},[5535,40150,40151,40153],{},[898,40152,12471],{},[1742,40154,1872],{},[1750,40156,1861],{},[898,40158,26016],{},[1750,40160,1753],{"stretchy":1752},[898,40162,1666],{},[1750,40164,1758],{},[5535,40166,40167,40169],{},[898,40168,1776],{},[1742,40170,1744],{},[5535,40172,40173,40175],{},[898,40174,12471],{},[1742,40176,1744],{},[1750,40178,1758],{},[5535,40180,40181,40183],{},[898,40182,1776],{},[1742,40184,1872],{},[5535,40186,40187,40189],{},[898,40188,12471],{},[1742,40190,1872],{},[1750,40192,1763],{"stretchy":1752},[902,40194,40195],{"encoding":904},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[883,40198,40200],{"className":40199},[886],[888,40201,40202],{"xmlns":890,"display":36989},[892,40203,40204,40371],{},[4577,40205,40206],{"width":36994},[4582,40207,40208,40210,40364,40366],{},[4585,40209],{"width":36999},[4585,40211,40212],{},[4577,40213,40214,40260,40306],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,40215,40216,40228],{},[4585,40217,40218],{},[3586,40219,40220],{"scriptlevel":2607,"displaystyle":1916},[5950,40221,40222,40224,40226],{},[898,40223,2046],{"mathvariant":37471},[1742,40225,1744],{},[1750,40227,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,40229,40230],{},[3586,40231,40232],{"scriptlevel":2607,"displaystyle":1916},[895,40233,40234,40236,40238,40244,40246,40248,40254,40256,40258],{},[895,40235],{},[1750,40237,1766],{},[5535,40239,40240,40242],{},[898,40241,12471],{},[1742,40243,1872],{},[1750,40245,1758],{},[898,40247,26016],{},[5535,40249,40250,40252],{},[898,40251,1776],{},[1742,40253,1744],{},[1750,40255,1766],{},[1742,40257,2607],{},[1750,40259,1917],{"separator":1916},[4582,40261,40262,40274],{},[4585,40263,40264],{},[3586,40265,40266],{"scriptlevel":2607,"displaystyle":1916},[5950,40267,40268,40270,40272],{},[898,40269,2046],{"mathvariant":37471},[1742,40271,1872],{},[1750,40273,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,40275,40276],{},[3586,40277,40278],{"scriptlevel":2607,"displaystyle":1916},[895,40279,40280,40282,40284,40290,40292,40294,40300,40302,40304],{},[895,40281],{},[1750,40283,1766],{},[5535,40285,40286,40288],{},[898,40287,12471],{},[1742,40289,1744],{},[1750,40291,1758],{},[898,40293,26016],{},[5535,40295,40296,40298],{},[898,40297,1776],{},[1742,40299,1872],{},[1750,40301,1766],{},[1742,40303,2607],{},[1750,40305,1917],{"separator":1916},[4582,40307,40308,40320],{},[4585,40309,40310],{},[3586,40311,40312],{"scriptlevel":2607,"displaystyle":1916},[5950,40313,40314,40316,40318],{},[898,40315,2046],{"mathvariant":37471},[898,40317,26016],{},[1750,40319,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,40321,40322],{},[3586,40323,40324],{"scriptlevel":2607,"displaystyle":1916},[895,40325,40326,40328,40330,40332,40334,40340,40346,40348,40354,40360,40362],{},[895,40327],{},[1750,40329,1766],{},[898,40331,1666],{},[1750,40333,1758],{},[5535,40335,40336,40338],{},[898,40337,1776],{},[1742,40339,1744],{},[5535,40341,40342,40344],{},[898,40343,12471],{},[1742,40345,1744],{},[1750,40347,1758],{},[5535,40349,40350,40352],{},[898,40351,1776],{},[1742,40353,1872],{},[5535,40355,40356,40358],{},[898,40357,12471],{},[1742,40359,1872],{},[1750,40361,1766],{},[1742,40363,22073],{},[4585,40365],{"width":36999},[4585,40367,40368],{},[1969,40369,40370],{},"(6.17)",[902,40372,40373],{"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}",[724,40375,40376,40377,40405,40406,40434,40435,40503],{},"Z prvních dvou: ",[883,40378,40380],{"className":40379},[886],[888,40381,40382],{"xmlns":890},[892,40383,40384,40402],{},[895,40385,40386,40392,40394,40400],{},[5535,40387,40388,40390],{},[898,40389,12471],{},[1742,40391,1872],{},[1750,40393,1766],{},[5535,40395,40396,40398],{},[898,40397,1776],{},[1742,40399,1744],{},[898,40401,26016],{},[902,40403,40404],{"encoding":904},"Q_2 = P_1 \\lambda"," (6.18), ",[883,40407,40409],{"className":40408},[886],[888,40410,40411],{"xmlns":890},[892,40412,40413,40431],{},[895,40414,40415,40421,40423,40429],{},[5535,40416,40417,40419],{},[898,40418,12471],{},[1742,40420,1744],{},[1750,40422,1766],{},[5535,40424,40425,40427],{},[898,40426,1776],{},[1742,40428,1872],{},[898,40430,26016],{},[902,40432,40433],{"encoding":904},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[883,40436,40438],{"className":40437},[886],[888,40439,40440],{"xmlns":890},[892,40441,40442,40500],{},[895,40443,40444,40446,40448,40454,40456,40462,40464,40466,40472,40474,40480,40482,40484,40486,40492,40498],{},[898,40445,1666],{},[1750,40447,1766],{},[5535,40449,40450,40452],{},[898,40451,1776],{},[1742,40453,1744],{},[1750,40455,8009],{},[5535,40457,40458,40460],{},[898,40459,1776],{},[1742,40461,1872],{},[898,40463,26016],{},[1750,40465,1861],{},[5535,40467,40468,40470],{},[898,40469,1776],{},[1742,40471,1872],{},[1750,40473,8009],{},[5535,40475,40476,40478],{},[898,40477,1776],{},[1742,40479,1744],{},[898,40481,26016],{},[1750,40483,1766],{},[1742,40485,1872],{},[5535,40487,40488,40490],{},[898,40489,1776],{},[1742,40491,1744],{},[5535,40493,40494,40496],{},[898,40495,1776],{},[1742,40497,1872],{},[898,40499,26016],{},[902,40501,40502],{"encoding":904},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[883,40505,40507],{"className":40506},[886],[888,40508,40509],{"xmlns":890,"display":36989},[892,40510,40511,40554],{},[4577,40512,40513],{"width":36994},[4582,40514,40515,40517,40547,40549],{},[4585,40516],{"width":36999},[4585,40518,40519],{},[895,40520,40521,40523,40525,40545],{},[898,40522,26016],{},[1750,40524,1766],{},[3423,40526,40527,40529],{},[898,40528,1666],{},[895,40530,40531,40533,40539],{},[1742,40532,1872],{},[5535,40534,40535,40537],{},[898,40536,1776],{},[1742,40538,1744],{},[5535,40540,40541,40543],{},[898,40542,1776],{},[1742,40544,1872],{},[898,40546,2313],{"mathvariant":1747},[4585,40548],{"width":36999},[4585,40550,40551],{},[1969,40552,40553],{},"(6.20)",[902,40555,40556],{"encoding":904},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[724,40558,40559],{},"Zpětně:",[883,40561,40563],{"className":40562},[886],[888,40564,40565],{"xmlns":890,"display":36989},[892,40566,40567,40644],{},[4577,40568,40569],{"width":36994},[4582,40570,40571,40573,40637,40639],{},[4585,40572],{"width":36999},[4585,40574,40575],{},[3582,40576,40577],{"notation":3584},[3586,40578,40579],{"scriptlevel":2607,"displaystyle":1752},[3586,40580,40581],{"scriptlevel":2607,"displaystyle":1752},[3586,40582,40583],{"scriptlevel":2607,"displaystyle":1916},[895,40584,40585,40587,40593,40595,40609,40611,40613,40619,40621,40635],{},[1969,40586,6766],{},[5535,40588,40589,40591],{},[898,40590,12471],{},[1742,40592,1744],{},[1750,40594,1766],{},[3423,40596,40597,40599],{},[898,40598,1666],{},[895,40600,40601,40603],{},[1742,40602,1872],{},[5535,40604,40605,40607],{},[898,40606,1776],{},[1742,40608,1744],{},[1750,40610,1917],{"separator":1916},[2125,40612],{"width":24875},[5535,40614,40615,40617],{},[898,40616,12471],{},[1742,40618,1872],{},[1750,40620,1766],{},[3423,40622,40623,40625],{},[898,40624,1666],{},[895,40626,40627,40629],{},[1742,40628,1872],{},[5535,40630,40631,40633],{},[898,40632,1776],{},[1742,40634,1872],{},[1969,40636,6766],{},[4585,40638],{"width":36999},[4585,40640,40641],{},[1969,40642,40643],{},"(6.21)",[902,40645,40646],{"encoding":904},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[198,40648,40650],{"id":40649},"engelova-funkce","Engelova funkce",[724,40652,19299,40653,40656,40657,40660,40661,3676,40678,1343,40708,40738,40739,40773,40774,1343,40800,40826],{},[38,40654,40655],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[38,40658,40659],{},"Engelovou funkcí",": pro ",[883,40662,40664],{"className":40663},[886],[888,40665,40666],{"xmlns":890},[892,40667,40668,40676],{},[895,40669,40670,40672,40674],{},[898,40671,1666],{},[1750,40673,1766],{},[1742,40675,4078],{},[902,40677,4134],{"encoding":904},[883,40679,40681],{"className":40680},[886],[888,40682,40683],{"xmlns":890},[892,40684,40685,40705],{},[895,40686,40687,40693,40695,40697,40699],{},[5535,40688,40689,40691],{},[898,40690,12471],{},[1742,40692,1744],{},[1750,40694,1766],{},[1742,40696,3936],{},[898,40698,1748],{"mathvariant":1747},[5535,40700,40701,40703],{},[898,40702,1776],{},[1742,40704,1744],{},[902,40706,40707],{"encoding":904},"Q_1 = 50\u002FP_1",[883,40709,40711],{"className":40710},[886],[888,40712,40713],{"xmlns":890},[892,40714,40715,40735],{},[895,40716,40717,40723,40725,40727,40729],{},[5535,40718,40719,40721],{},[898,40720,12471],{},[1742,40722,1872],{},[1750,40724,1766],{},[1742,40726,3936],{},[898,40728,1748],{"mathvariant":1747},[5535,40730,40731,40733],{},[898,40732,1776],{},[1742,40734,1872],{},[902,40736,40737],{"encoding":904},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[883,40740,40742],{"className":40741},[886],[888,40743,40744],{"xmlns":890},[892,40745,40746,40770],{},[895,40747,40748,40754,40756,40758,40760,40766,40768],{},[5535,40749,40750,40752],{},[898,40751,1776],{},[1742,40753,1744],{},[1750,40755,1766],{},[1742,40757,3079],{},[1750,40759,1917],{"separator":1916},[5535,40761,40762,40764],{},[898,40763,1776],{},[1742,40765,1872],{},[1750,40767,1766],{},[1742,40769,6465],{},[902,40771,40772],{"encoding":904},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[883,40775,40777],{"className":40776},[886],[888,40778,40779],{"xmlns":890},[892,40780,40781,40797],{},[895,40782,40783,40789,40791,40793,40795],{},[5535,40784,40785,40787],{},[898,40786,12471],{},[1742,40788,1744],{},[1750,40790,1766],{},[898,40792,1666],{},[898,40794,1748],{"mathvariant":1747},[1742,40796,6465],{},[902,40798,40799],{"encoding":904},"Q_1 = Y\u002F20",[883,40801,40803],{"className":40802},[886],[888,40804,40805],{"xmlns":890},[892,40806,40807,40823],{},[895,40808,40809,40815,40817,40819,40821],{},[5535,40810,40811,40813],{},[898,40812,12471],{},[1742,40814,1872],{},[1750,40816,1766],{},[898,40818,1666],{},[898,40820,1748],{"mathvariant":1747},[1742,40822,14865],{},[902,40824,40825],{"encoding":904},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[115,40828,40830],{"id":40829},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[724,40832,40833],{},"Výdaje spotřebitele jsou",[883,40835,40837],{"className":40836},[886],[888,40838,40839],{"xmlns":890,"display":36989},[892,40840,40841,40916],{},[4577,40842,40843],{"width":36994},[4582,40844,40845,40847,40909,40911],{},[4585,40846],{"width":36999},[4585,40848,40849],{},[895,40850,40851,40853,40855,40857,40859,40865,40867,40873,40875,40877,40885,40891,40893,40901,40907],{},[898,40852,1705],{},[1750,40854,1766],{},[898,40856,1705],{},[1750,40858,1753],{"stretchy":1752},[5535,40860,40861,40863],{},[898,40862,12471],{},[1742,40864,1744],{},[1750,40866,1917],{"separator":1916},[5535,40868,40869,40871],{},[898,40870,12471],{},[1742,40872,1872],{},[1750,40874,1763],{"stretchy":1752},[1750,40876,1766],{},[5950,40878,40879,40881,40883],{},[898,40880,1776],{},[1742,40882,1744],{},[1750,40884,3751],{},[5535,40886,40887,40889],{},[898,40888,12471],{},[1742,40890,1744],{},[1750,40892,1861],{},[5950,40894,40895,40897,40899],{},[898,40896,1776],{},[1742,40898,1872],{},[1750,40900,3751],{},[5535,40902,40903,40905],{},[898,40904,12471],{},[1742,40906,1872],{},[1750,40908,1917],{"separator":1916},[4585,40910],{"width":36999},[4585,40912,40913],{},[1969,40914,40915],{},"(6.22)",[902,40917,40918],{"encoding":904},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[724,40920,40921],{},"a je pevně zadána hladina užitečnosti",[883,40923,40925],{"className":40924},[886],[888,40926,40927],{"xmlns":890,"display":36989},[892,40928,40929,40976],{},[4577,40930,40931],{"width":36994},[4582,40932,40933,40935,40969,40971],{},[4585,40934],{"width":36999},[4585,40936,40937],{},[895,40938,40939,40945,40947,40949,40951,40957,40959,40965,40967],{},[1699,40940,40941,40943],{},[898,40942,900],{},[1750,40944,3751],{},[1750,40946,1766],{},[898,40948,900],{},[1750,40950,1753],{"stretchy":1752},[5535,40952,40953,40955],{},[898,40954,12471],{},[1742,40956,1744],{},[1750,40958,1917],{"separator":1916},[5535,40960,40961,40963],{},[898,40962,12471],{},[1742,40964,1872],{},[1750,40966,1763],{"stretchy":1752},[898,40968,2313],{"mathvariant":1747},[4585,40970],{"width":36999},[4585,40972,40973],{},[1969,40974,40975],{},"(6.23)",[902,40977,40978],{"encoding":904},"U^* = U(Q_1, Q_2). \\tag{6.23}",[724,40980,40981,40984,40985,41017,41018,2313],{},[38,40982,40983],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[883,40986,40988],{"className":40987},[886],[888,40989,40990],{"xmlns":890},[892,40991,40992,41014],{},[895,40993,40994,40996,40998,41004,41006,41012],{},[898,40995,1705],{},[1750,40997,1753],{"stretchy":1752},[5535,40999,41000,41002],{},[898,41001,12471],{},[1742,41003,1744],{},[1750,41005,1917],{"separator":1916},[5535,41007,41008,41010],{},[898,41009,12471],{},[1742,41011,1872],{},[1750,41013,1763],{"stretchy":1752},[902,41015,41016],{"encoding":904},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[883,41019,41021],{"className":41020},[886],[888,41022,41023],{"xmlns":890},[892,41024,41025,41081],{},[895,41026,41027,41029,41031,41037,41039,41045,41047,41049,41055,41057,41059,41061,41067,41069,41075,41077,41079],{},[898,41028,2655],{},[1750,41030,1753],{"stretchy":1752},[5535,41032,41033,41035],{},[898,41034,12471],{},[1742,41036,1744],{},[1750,41038,1917],{"separator":1916},[5535,41040,41041,41043],{},[898,41042,12471],{},[1742,41044,1872],{},[1750,41046,1763],{"stretchy":1752},[1750,41048,1766],{},[1699,41050,41051,41053],{},[898,41052,900],{},[1750,41054,3751],{},[1750,41056,1758],{},[898,41058,900],{},[1750,41060,1753],{"stretchy":1752},[5535,41062,41063,41065],{},[898,41064,12471],{},[1742,41066,1744],{},[1750,41068,1917],{"separator":1916},[5535,41070,41071,41073],{},[898,41072,12471],{},[1742,41074,1872],{},[1750,41076,1763],{"stretchy":1752},[1750,41078,1766],{},[1742,41080,2607],{},[902,41082,41083],{"encoding":904},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[198,41085,41087],{"id":41086},"lagrangeova-funkce","Lagrangeova funkce",[883,41089,41091],{"className":41090},[886],[888,41092,41093],{"xmlns":890,"display":36989},[892,41094,41095,41206],{},[4577,41096,41097],{"width":36994},[4582,41098,41099,41101,41199,41201],{},[4585,41100],{"width":36999},[4585,41102,41103],{},[895,41104,41105,41107,41109,41115,41117,41123,41125,41127,41129,41131,41139,41145,41147,41155,41161,41163,41165,41167,41173,41175,41177,41179,41185,41187,41193,41195,41197],{},[898,41106,2046],{"mathvariant":37471},[1750,41108,1753],{"stretchy":1752},[5535,41110,41111,41113],{},[898,41112,12471],{},[1742,41114,1744],{},[1750,41116,1917],{"separator":1916},[5535,41118,41119,41121],{},[898,41120,12471],{},[1742,41122,1872],{},[1750,41124,1917],{"separator":1916},[898,41126,26016],{},[1750,41128,1763],{"stretchy":1752},[1750,41130,1766],{},[5950,41132,41133,41135,41137],{},[898,41134,1776],{},[1742,41136,1744],{},[1750,41138,3751],{},[5535,41140,41141,41143],{},[898,41142,12471],{},[1742,41144,1744],{},[1750,41146,1861],{},[5950,41148,41149,41151,41153],{},[898,41150,1776],{},[1742,41152,1872],{},[1750,41154,3751],{},[5535,41156,41157,41159],{},[898,41158,12471],{},[1742,41160,1872],{},[1750,41162,1861],{},[898,41164,26016],{},[1750,41166,1753],{"stretchy":1752},[1699,41168,41169,41171],{},[898,41170,900],{},[1750,41172,3751],{},[1750,41174,1758],{},[898,41176,900],{},[1750,41178,1753],{"stretchy":1752},[5535,41180,41181,41183],{},[898,41182,12471],{},[1742,41184,1744],{},[1750,41186,1917],{"separator":1916},[5535,41188,41189,41191],{},[898,41190,12471],{},[1742,41192,1872],{},[1750,41194,1763],{"stretchy":1752},[1750,41196,1763],{"stretchy":1752},[898,41198,2313],{"mathvariant":1747},[4585,41200],{"width":36999},[4585,41202,41203],{},[1969,41204,41205],{},"(6.24)",[902,41207,41208],{"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}",[724,41210,41211],{},"Soustava podmínek prvního řádu:",[883,41213,41215],{"className":41214},[886],[888,41216,41217],{"xmlns":890,"display":36989},[892,41218,41219,41392],{},[4577,41220,41221],{"width":36994},[4582,41222,41223,41225,41385,41387],{},[4585,41224],{"width":36999},[4585,41226,41227],{},[4577,41228,41229,41279,41329],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,41230,41231,41243],{},[4585,41232,41233],{},[3586,41234,41235],{"scriptlevel":2607,"displaystyle":1916},[5950,41236,41237,41239,41241],{},[898,41238,2046],{"mathvariant":37471},[1742,41240,1744],{},[1750,41242,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,41244,41245],{},[3586,41246,41247],{"scriptlevel":2607,"displaystyle":1916},[895,41248,41249,41251,41253,41261,41263,41265,41273,41275,41277],{},[895,41250],{},[1750,41252,1766],{},[5950,41254,41255,41257,41259],{},[898,41256,1776],{},[1742,41258,1744],{},[1750,41260,3751],{},[1750,41262,1758],{},[898,41264,26016],{},[5950,41266,41267,41269,41271],{},[898,41268,900],{},[1742,41270,1744],{},[1750,41272,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,41274,1766],{},[1742,41276,2607],{},[1750,41278,1917],{"separator":1916},[4582,41280,41281,41293],{},[4585,41282,41283],{},[3586,41284,41285],{"scriptlevel":2607,"displaystyle":1916},[5950,41286,41287,41289,41291],{},[898,41288,2046],{"mathvariant":37471},[1742,41290,1872],{},[1750,41292,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,41294,41295],{},[3586,41296,41297],{"scriptlevel":2607,"displaystyle":1916},[895,41298,41299,41301,41303,41311,41313,41315,41323,41325,41327],{},[895,41300],{},[1750,41302,1766],{},[5950,41304,41305,41307,41309],{},[898,41306,1776],{},[1742,41308,1872],{},[1750,41310,3751],{},[1750,41312,1758],{},[898,41314,26016],{},[5950,41316,41317,41319,41321],{},[898,41318,900],{},[1742,41320,1872],{},[1750,41322,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,41324,1766],{},[1742,41326,2607],{},[1750,41328,1917],{"separator":1916},[4582,41330,41331,41343],{},[4585,41332,41333],{},[3586,41334,41335],{"scriptlevel":2607,"displaystyle":1916},[5950,41336,41337,41339,41341],{},[898,41338,2046],{"mathvariant":37471},[898,41340,26016],{},[1750,41342,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,41344,41345],{},[3586,41346,41347],{"scriptlevel":2607,"displaystyle":1916},[895,41348,41349,41351,41353,41359,41361,41363,41365,41371,41373,41379,41381,41383],{},[895,41350],{},[1750,41352,1766],{},[1699,41354,41355,41357],{},[898,41356,900],{},[1750,41358,3751],{},[1750,41360,1758],{},[898,41362,900],{},[1750,41364,1753],{"stretchy":1752},[5535,41366,41367,41369],{},[898,41368,12471],{},[1742,41370,1744],{},[1750,41372,1917],{"separator":1916},[5535,41374,41375,41377],{},[898,41376,12471],{},[1742,41378,1872],{},[1750,41380,1763],{"stretchy":1752},[1750,41382,1766],{},[1742,41384,22073],{},[4585,41386],{"width":36999},[4585,41388,41389],{},[1969,41390,41391],{},"(6.25)",[902,41393,41394],{"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}",[724,41396,41397],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[883,41399,41401],{"className":41400},[886],[888,41402,41403],{"xmlns":890,"display":36989},[892,41404,41405,41503],{},[4577,41406,41407],{"width":36994},[4582,41408,41409,41411,41496,41498],{},[4585,41410],{"width":36999},[4585,41412,41413],{},[895,41414,41415,41417,41419,41425,41427,41433,41435,41437,41439,41441,41443,41445,41494],{},[898,41416,5541],{},[1750,41418,1753],{"stretchy":1752},[5535,41420,41421,41423],{},[898,41422,12471],{},[1742,41424,1744],{},[1750,41426,1917],{"separator":1916},[5535,41428,41429,41431],{},[898,41430,12471],{},[1742,41432,1872],{},[1750,41434,1917],{"separator":1916},[898,41436,26016],{},[1750,41438,1763],{"stretchy":1752},[1750,41440,1766],{},[1750,41442,1758],{},[898,41444,26016],{},[895,41446,41447,41449,41461,41463,41476,41478,41480,41492],{},[1750,41448,1753],{"fence":1916},[5950,41450,41451,41453,41455],{},[898,41452,900],{},[1742,41454,12582],{},[895,41456,41457,41459],{},[1750,41458,3815],{"mathvariant":1747},[1750,41460,3815],{"mathvariant":1747},[1750,41462,1861],{},[5950,41464,41465,41467,41470],{},[898,41466,900],{},[1742,41468,41469],{},"22",[895,41471,41472,41474],{},[1750,41473,3815],{"mathvariant":1747},[1750,41475,3815],{"mathvariant":1747},[1750,41477,1861],{},[1742,41479,1872],{},[5950,41481,41482,41484,41486],{},[898,41483,900],{},[1742,41485,4903],{},[895,41487,41488,41490],{},[1750,41489,3815],{"mathvariant":1747},[1750,41491,3815],{"mathvariant":1747},[1750,41493,1763],{"fence":1916},[898,41495,2313],{"mathvariant":1747},[4585,41497],{"width":36999},[4585,41499,41500],{},[1969,41501,41502],{},"(6.26)",[902,41504,41505],{"encoding":904},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[724,41507,41508,41511,41512,41551,41552,41591,41592,41642,41643,41669,41670,41687,41688,41714],{},[38,41509,41510],{},"Geometrie (obrázek 6.9)."," Řešením je bod ",[883,41513,41515],{"className":41514},[886],[888,41516,41517],{"xmlns":890},[892,41518,41519,41549],{},[895,41520,41521,41527,41529,41537,41539,41547],{},[1699,41522,41523,41525],{},[898,41524,12471],{},[1750,41526,3751],{},[1750,41528,5141],{"stretchy":1752},[5950,41530,41531,41533,41535],{},[898,41532,12471],{},[1742,41534,1744],{},[1750,41536,3751],{},[1750,41538,1917],{"separator":1916},[5950,41540,41541,41543,41545],{},[898,41542,12471],{},[1742,41544,1872],{},[1750,41546,3751],{},[1750,41548,5158],{"stretchy":1752},[902,41550,37250],{"encoding":904}," dotyku křivky užitečnosti ",[883,41553,41555],{"className":41554},[886],[888,41556,41557],{"xmlns":890},[892,41558,41559,41589],{},[895,41560,41561,41567,41569,41571,41573,41579,41581,41587],{},[1699,41562,41563,41565],{},[898,41564,900],{},[1750,41566,3751],{},[1750,41568,1766],{},[898,41570,900],{},[1750,41572,1753],{"stretchy":1752},[5535,41574,41575,41577],{},[898,41576,12471],{},[1742,41578,1744],{},[1750,41580,1917],{"separator":1916},[5535,41582,41583,41585],{},[898,41584,12471],{},[1742,41586,1872],{},[1750,41588,1763],{"stretchy":1752},[902,41590,27238],{"encoding":904}," s přímkou výdajů ",[883,41593,41595],{"className":41594},[886],[888,41596,41597],{"xmlns":890},[892,41598,41599,41639],{},[895,41600,41601,41607,41609,41617,41623,41625,41633],{},[1699,41602,41603,41605],{},[898,41604,1705],{},[1750,41606,3751],{},[1750,41608,1766],{},[5950,41610,41611,41613,41615],{},[898,41612,1776],{},[1742,41614,1744],{},[1750,41616,3751],{},[5535,41618,41619,41621],{},[898,41620,12471],{},[1742,41622,1744],{},[1750,41624,1861],{},[5950,41626,41627,41629,41631],{},[898,41628,1776],{},[1742,41630,1872],{},[1750,41632,3751],{},[5535,41634,41635,41637],{},[898,41636,12471],{},[1742,41638,1872],{},[902,41640,41641],{"encoding":904},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[883,41644,41646],{"className":41645},[886],[888,41647,41648],{"xmlns":890},[892,41649,41650,41666],{},[895,41651,41652,41658,41660],{},[5535,41653,41654,41656],{},[898,41655,1705],{},[1742,41657,2607],{},[1750,41659,2624],{},[1699,41661,41662,41664],{},[898,41663,1705],{},[1750,41665,3751],{},[902,41667,41668],{"encoding":904},"E_0 \u003C E^*"," nestačí k dosažení ",[883,41671,41673],{"className":41672},[886],[888,41674,41675],{"xmlns":890},[892,41676,41677,41685],{},[895,41678,41679],{},[1699,41680,41681,41683],{},[898,41682,900],{},[1750,41684,3751],{},[902,41686,36885],{"encoding":904},", hladina ",[883,41689,41691],{"className":41690},[886],[888,41692,41693],{"xmlns":890},[892,41694,41695,41711],{},[895,41696,41697,41703,41705],{},[5535,41698,41699,41701],{},[898,41700,1705],{},[1742,41702,1744],{},[1750,41704,2604],{},[1699,41706,41707,41709],{},[898,41708,1705],{},[1750,41710,3751],{},[902,41712,41713],{"encoding":904},"E_1 > E^*"," je nadbytečná.",[1785,41716,41717,41722],{},[724,41718,41719,41721],{},[883,41720,6004],{}," Postup — duální úloha (minimalizace výdajů)",[152,41723,41724,41774,41860,41900,41975],{},[123,41725,41726,1647,41729,41773],{},[38,41727,41728],{},"Zapiš vazbu",[883,41730,41732],{"className":41731},[886],[888,41733,41734],{"xmlns":890},[892,41735,41736,41770],{},[895,41737,41738,41744,41746,41748,41750,41756,41758,41764,41766,41768],{},[1699,41739,41740,41742],{},[898,41741,900],{},[1750,41743,3751],{},[1750,41745,1758],{},[898,41747,900],{},[1750,41749,1753],{"stretchy":1752},[5535,41751,41752,41754],{},[898,41753,12471],{},[1742,41755,1744],{},[1750,41757,1917],{"separator":1916},[5535,41759,41760,41762],{},[898,41761,12471],{},[1742,41763,1872],{},[1750,41765,1763],{"stretchy":1752},[1750,41767,1766],{},[1742,41769,2607],{},[902,41771,41772],{"encoding":904},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[123,41775,41776,1647,41778,2313],{},[38,41777,38183],{},[883,41779,41781],{"className":41780},[886],[888,41782,41783],{"xmlns":890},[892,41784,41785,41857],{},[895,41786,41787,41789,41791,41799,41805,41807,41815,41821,41823,41825,41827,41833,41835,41837,41839,41845,41847,41853,41855],{},[898,41788,2046],{"mathvariant":37471},[1750,41790,1766],{},[5950,41792,41793,41795,41797],{},[898,41794,1776],{},[1742,41796,1744],{},[1750,41798,3751],{},[5535,41800,41801,41803],{},[898,41802,12471],{},[1742,41804,1744],{},[1750,41806,1861],{},[5950,41808,41809,41811,41813],{},[898,41810,1776],{},[1742,41812,1872],{},[1750,41814,3751],{},[5535,41816,41817,41819],{},[898,41818,12471],{},[1742,41820,1872],{},[1750,41822,1861],{},[898,41824,26016],{},[1750,41826,1753],{"stretchy":1752},[1699,41828,41829,41831],{},[898,41830,900],{},[1750,41832,3751],{},[1750,41834,1758],{},[898,41836,900],{},[1750,41838,1753],{"stretchy":1752},[5535,41840,41841,41843],{},[898,41842,12471],{},[1742,41844,1744],{},[1750,41846,1917],{"separator":1916},[5535,41848,41849,41851],{},[898,41850,12471],{},[1742,41852,1872],{},[1750,41854,1763],{"stretchy":1752},[1750,41856,1763],{"stretchy":1752},[902,41858,41859],{"encoding":904},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[123,41861,41862,41865,41866,41899],{},[38,41863,41864],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[883,41867,41869],{"className":41868},[886],[888,41870,41871],{"xmlns":890},[892,41872,41873,41897],{},[895,41874,41875,41877,41879,41887,41889],{},[1969,41876,20236],{},[1750,41878,1766],{},[5950,41880,41881,41883,41885],{},[898,41882,1776],{},[1742,41884,1744],{},[1750,41886,3751],{},[898,41888,1748],{"mathvariant":1747},[5950,41890,41891,41893,41895],{},[898,41892,1776],{},[1742,41894,1872],{},[1750,41896,3751],{},[902,41898,37902],{"encoding":904}," (stejná jako u maximalizace!).",[123,41901,41902,1647,41905,41945,41946,2313],{},[38,41903,41904],{},"Dosaď do vazby",[883,41906,41908],{"className":41907},[886],[888,41909,41910],{"xmlns":890},[892,41911,41912,41942],{},[895,41913,41914,41916,41918,41924,41926,41932,41934,41936],{},[898,41915,900],{},[1750,41917,1753],{"stretchy":1752},[5535,41919,41920,41922],{},[898,41921,12471],{},[1742,41923,1744],{},[1750,41925,1917],{"separator":1916},[5535,41927,41928,41930],{},[898,41929,12471],{},[1742,41931,1872],{},[1750,41933,1763],{"stretchy":1752},[1750,41935,1766],{},[1699,41937,41938,41940],{},[898,41939,900],{},[1750,41941,3751],{},[902,41943,41944],{"encoding":904},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[883,41947,41949],{"className":41948},[886],[888,41950,41951],{"xmlns":890},[892,41952,41953,41973],{},[895,41954,41955,41963,41965],{},[5950,41956,41957,41959,41961],{},[898,41958,12471],{},[1742,41960,1744],{},[1750,41962,3751],{},[1750,41964,1917],{"separator":1916},[5950,41966,41967,41969,41971],{},[898,41968,12471],{},[1742,41970,1872],{},[1750,41972,3751],{},[902,41974,38424],{"encoding":904},[123,41976,41977,1647,41980,42034],{},[38,41978,41979],{},"Vypočítej minimální výdaje",[883,41981,41983],{"className":41982},[886],[888,41984,41985],{"xmlns":890},[892,41986,41987,42031],{},[895,41988,41989,41995,41997,42005,42013,42015,42023],{},[1699,41990,41991,41993],{},[898,41992,1705],{},[1750,41994,3751],{},[1750,41996,1766],{},[5950,41998,41999,42001,42003],{},[898,42000,1776],{},[1742,42002,1744],{},[1750,42004,3751],{},[5950,42006,42007,42009,42011],{},[898,42008,12471],{},[1742,42010,1744],{},[1750,42012,3751],{},[1750,42014,1861],{},[5950,42016,42017,42019,42021],{},[898,42018,1776],{},[1742,42020,1872],{},[1750,42022,3751],{},[5950,42024,42025,42027,42029],{},[898,42026,12471],{},[1742,42028,1872],{},[1750,42030,3751],{},[902,42032,42033],{"encoding":904},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[115,42036,42038,42039],{"id":42037},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[883,42040,42042],{"className":42041},[886],[888,42043,42044],{"xmlns":890},[892,42045,42046,42080],{},[895,42047,42048,42050,42052,42066],{},[898,42049,900],{},[1750,42051,1766],{},[5950,42053,42054,42056,42058],{},[898,42055,12471],{},[1742,42057,1744],{},[895,42059,42060,42062,42064],{},[1742,42061,1744],{},[898,42063,1748],{"mathvariant":1747},[1742,42065,1872],{},[5950,42067,42068,42070,42072],{},[898,42069,12471],{},[1742,42071,1872],{},[895,42073,42074,42076,42078],{},[1742,42075,1744],{},[898,42077,1748],{"mathvariant":1747},[1742,42079,1872],{},[902,42081,42082],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}",[724,42084,42085,42086,1343,42108,1343,42132,39269],{},"Dáno ",[883,42087,42089],{"className":42088},[886],[888,42090,42091],{"xmlns":890},[892,42092,42093,42105],{},[895,42094,42095,42101,42103],{},[1699,42096,42097,42099],{},[898,42098,900],{},[1750,42100,3751],{},[1750,42102,1766],{},[1742,42104,1872],{},[902,42106,42107],{"encoding":904},"U^* = 2",[883,42109,42111],{"className":42110},[886],[888,42112,42113],{"xmlns":890},[892,42114,42115,42129],{},[895,42116,42117,42125,42127],{},[5950,42118,42119,42121,42123],{},[898,42120,1776],{},[1742,42122,1744],{},[1750,42124,3751],{},[1750,42126,1766],{},[1742,42128,7633],{},[902,42130,42131],{"encoding":904},"P_1^* = 0{,}25",[883,42133,42135],{"className":42134},[886],[888,42136,42137],{"xmlns":890},[892,42138,42139,42153],{},[895,42140,42141,42149,42151],{},[5950,42142,42143,42145,42147],{},[898,42144,1776],{},[1742,42146,1872],{},[1750,42148,3751],{},[1750,42150,1766],{},[1742,42152,1744],{},[902,42154,42155],{"encoding":904},"P_2^* = 1",[883,42157,42159],{"className":42158},[886],[888,42160,42161],{"xmlns":890,"display":36989},[892,42162,42163,42227],{},[895,42164,42165,42167,42169,42171,42177,42179,42185,42187,42189,42191,42193,42195,42209,42223,42225],{},[898,42166,2046],{"mathvariant":37471},[1750,42168,1766],{},[1742,42170,7633],{},[5535,42172,42173,42175],{},[898,42174,12471],{},[1742,42176,1744],{},[1750,42178,1861],{},[5535,42180,42181,42183],{},[898,42182,12471],{},[1742,42184,1872],{},[1750,42186,1861],{},[898,42188,26016],{},[1750,42190,1753],{"stretchy":1752},[1742,42192,1872],{},[1750,42194,1758],{},[5950,42196,42197,42199,42201],{},[898,42198,12471],{},[1742,42200,1744],{},[895,42202,42203,42205,42207],{},[1742,42204,1744],{},[898,42206,1748],{"mathvariant":1747},[1742,42208,1872],{},[5950,42210,42211,42213,42215],{},[898,42212,12471],{},[1742,42214,1872],{},[895,42216,42217,42219,42221],{},[1742,42218,1744],{},[898,42220,1748],{"mathvariant":1747},[1742,42222,1872],{},[1750,42224,1763],{"stretchy":1752},[898,42226,2313],{"mathvariant":1747},[902,42228,42229],{"encoding":904},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,42231,39354],{},[883,42233,42235],{"className":42234},[886],[888,42236,42237],{"xmlns":890,"display":36989},[892,42238,42239,42453],{},[4577,42240,42241,42317,42393],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,42242,42243,42255],{},[4585,42244,42245],{},[3586,42246,42247],{"scriptlevel":2607,"displaystyle":1916},[5950,42248,42249,42251,42253],{},[898,42250,2046],{"mathvariant":37471},[1742,42252,1744],{},[1750,42254,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,42256,42257],{},[3586,42258,42259],{"scriptlevel":2607,"displaystyle":1916},[895,42260,42261,42263,42265,42267,42269,42271,42273,42281,42297,42311,42313,42315],{},[895,42262],{},[1750,42264,1766],{},[1742,42266,7633],{},[1750,42268,1758],{},[898,42270,26016],{},[1750,42272,8009],{},[3586,42274,42275],{"scriptlevel":2607,"displaystyle":1752},[3423,42276,42277,42279],{},[1742,42278,1744],{},[1742,42280,1872],{},[5950,42282,42283,42285,42287],{},[898,42284,12471],{},[1742,42286,1744],{},[895,42288,42289,42291,42293,42295],{},[1750,42290,1758],{},[1742,42292,1744],{},[898,42294,1748],{"mathvariant":1747},[1742,42296,1872],{},[5950,42298,42299,42301,42303],{},[898,42300,12471],{},[1742,42302,1872],{},[895,42304,42305,42307,42309],{},[1742,42306,1744],{},[898,42308,1748],{"mathvariant":1747},[1742,42310,1872],{},[1750,42312,1766],{},[1742,42314,2607],{},[1750,42316,1917],{"separator":1916},[4582,42318,42319,42331],{},[4585,42320,42321],{},[3586,42322,42323],{"scriptlevel":2607,"displaystyle":1916},[5950,42324,42325,42327,42329],{},[898,42326,2046],{"mathvariant":37471},[1742,42328,1872],{},[1750,42330,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,42332,42333],{},[3586,42334,42335],{"scriptlevel":2607,"displaystyle":1916},[895,42336,42337,42339,42341,42343,42345,42347,42349,42357,42371,42387,42389,42391],{},[895,42338],{},[1750,42340,1766],{},[1742,42342,1744],{},[1750,42344,1758],{},[898,42346,26016],{},[1750,42348,8009],{},[3586,42350,42351],{"scriptlevel":2607,"displaystyle":1752},[3423,42352,42353,42355],{},[1742,42354,1744],{},[1742,42356,1872],{},[5950,42358,42359,42361,42363],{},[898,42360,12471],{},[1742,42362,1744],{},[895,42364,42365,42367,42369],{},[1742,42366,1744],{},[898,42368,1748],{"mathvariant":1747},[1742,42370,1872],{},[5950,42372,42373,42375,42377],{},[898,42374,12471],{},[1742,42376,1872],{},[895,42378,42379,42381,42383,42385],{},[1750,42380,1758],{},[1742,42382,1744],{},[898,42384,1748],{"mathvariant":1747},[1742,42386,1872],{},[1750,42388,1766],{},[1742,42390,2607],{},[1750,42392,1917],{"separator":1916},[4582,42394,42395,42407],{},[4585,42396,42397],{},[3586,42398,42399],{"scriptlevel":2607,"displaystyle":1916},[5950,42400,42401,42403,42405],{},[898,42402,2046],{"mathvariant":37471},[898,42404,26016],{},[1750,42406,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,42408,42409],{},[3586,42410,42411],{"scriptlevel":2607,"displaystyle":1916},[895,42412,42413,42415,42417,42419,42421,42435,42449,42451],{},[895,42414],{},[1750,42416,1766],{},[1742,42418,1872],{},[1750,42420,1758],{},[5950,42422,42423,42425,42427],{},[898,42424,12471],{},[1742,42426,1744],{},[895,42428,42429,42431,42433],{},[1742,42430,1744],{},[898,42432,1748],{"mathvariant":1747},[1742,42434,1872],{},[5950,42436,42437,42439,42441],{},[898,42438,12471],{},[1742,42440,1872],{},[895,42442,42443,42445,42447],{},[1742,42444,1744],{},[898,42446,1748],{"mathvariant":1747},[1742,42448,1872],{},[1750,42450,1766],{},[1742,42452,22073],{},[902,42454,42455],{"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}",[724,42457,42458,42459,27149,42489,42517,42518,8164,42580,1343,42630,42652,42653,2313],{},"Podílem prvních dvou rovnic: ",[883,42460,42462],{"className":42461},[886],[888,42463,42464],{"xmlns":890},[892,42465,42466,42486],{},[895,42467,42468,42470,42472,42478,42480],{},[1742,42469,7633],{},[1750,42471,1766],{},[5535,42473,42474,42476],{},[898,42475,12471],{},[1742,42477,1872],{},[898,42479,1748],{"mathvariant":1747},[5535,42481,42482,42484],{},[898,42483,12471],{},[1742,42485,1744],{},[902,42487,42488],{"encoding":904},"0{,}25 = Q_2 \u002F Q_1",[883,42490,42492],{"className":42491},[886],[888,42493,42494],{"xmlns":890},[892,42495,42496,42514],{},[895,42497,42498,42504,42506,42508],{},[5535,42499,42500,42502],{},[898,42501,12471],{},[1742,42503,1872],{},[1750,42505,1766],{},[1742,42507,7633],{},[5535,42509,42510,42512],{},[898,42511,12471],{},[1742,42513,1744],{},[902,42515,42516],{"encoding":904},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[883,42519,42521],{"className":42520},[886],[888,42522,42523],{"xmlns":890},[892,42524,42525,42577],{},[895,42526,42527,42541,42543,42545,42551,42563,42565,42567,42573,42575],{},[5950,42528,42529,42531,42533],{},[898,42530,12471],{},[1742,42532,1744],{},[895,42534,42535,42537,42539],{},[1742,42536,1744],{},[898,42538,1748],{"mathvariant":1747},[1742,42540,1872],{},[1750,42542,1753],{"stretchy":1752},[1742,42544,7633],{},[5535,42546,42547,42549],{},[898,42548,12471],{},[1742,42550,1744],{},[1699,42552,42553,42555],{},[1750,42554,1763],{"stretchy":1752},[895,42556,42557,42559,42561],{},[1742,42558,1744],{},[898,42560,1748],{"mathvariant":1747},[1742,42562,1872],{},[1750,42564,1766],{},[1742,42566,4268],{},[5535,42568,42569,42571],{},[898,42570,12471],{},[1742,42572,1744],{},[1750,42574,1766],{},[1742,42576,1872],{},[902,42578,42579],{"encoding":904},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[38,42581,42582,1343,42606],{},[883,42583,42585],{"className":42584},[886],[888,42586,42587],{"xmlns":890},[892,42588,42589,42603],{},[895,42590,42591,42599,42601],{},[5950,42592,42593,42595,42597],{},[898,42594,12471],{},[1742,42596,1744],{},[1750,42598,3751],{},[1750,42600,1766],{},[1742,42602,7859],{},[902,42604,42605],{"encoding":904},"Q_1^* = 4",[883,42607,42609],{"className":42608},[886],[888,42610,42611],{"xmlns":890},[892,42612,42613,42627],{},[895,42614,42615,42623,42625],{},[5950,42616,42617,42619,42621],{},[898,42618,12471],{},[1742,42620,1872],{},[1750,42622,3751],{},[1750,42624,1766],{},[1742,42626,1744],{},[902,42628,42629],{"encoding":904},"Q_2^* = 1",[883,42631,42633],{"className":42632},[886],[888,42634,42635],{"xmlns":890},[892,42636,42637,42649],{},[895,42638,42639,42645,42647],{},[1699,42640,42641,42643],{},[898,42642,26016],{},[1750,42644,3751],{},[1750,42646,1766],{},[1742,42648,1744],{},[902,42650,42651],{"encoding":904},"\\lambda^* = 1",". Minimální výdaje: ",[883,42654,42656],{"className":42655},[886],[888,42657,42658],{"xmlns":890},[892,42659,42660,42688],{},[895,42661,42662,42668,42670,42672,42674,42676,42678,42680,42682,42684,42686],{},[1699,42663,42664,42666],{},[898,42665,1705],{},[1750,42667,3751],{},[1750,42669,1766],{},[1742,42671,7633],{},[1750,42673,8009],{},[1742,42675,7859],{},[1750,42677,1861],{},[1742,42679,1744],{},[1750,42681,8009],{},[1742,42683,1744],{},[1750,42685,1766],{},[1742,42687,1872],{},[902,42689,42690],{"encoding":904},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[724,42692,42693,42696,42697,1343,42763,1343,42829,42895,42896,42933,42934,42956,42957,2313],{},[614,42694,42695],{},"Ověření postačující podmínky"," (6.26): ",[883,42698,42700],{"className":42699},[886],[888,42701,42702],{"xmlns":890},[892,42703,42704,42760],{},[895,42705,42706,42718,42720,42722,42730,42746],{},[5950,42707,42708,42710,42712],{},[898,42709,900],{},[1742,42711,12582],{},[895,42713,42714,42716],{},[1750,42715,3815],{"mathvariant":1747},[1750,42717,3815],{"mathvariant":1747},[1750,42719,1766],{},[1750,42721,1758],{},[3586,42723,42724],{"scriptlevel":2607,"displaystyle":1752},[3423,42725,42726,42728],{},[1742,42727,1744],{},[1742,42729,7859],{},[5950,42731,42732,42734,42736],{},[898,42733,12471],{},[1742,42735,1744],{},[895,42737,42738,42740,42742,42744],{},[1750,42739,1758],{},[1742,42741,7822],{},[898,42743,1748],{"mathvariant":1747},[1742,42745,1872],{},[5950,42747,42748,42750,42752],{},[898,42749,12471],{},[1742,42751,1872],{},[895,42753,42754,42756,42758],{},[1742,42755,1744],{},[898,42757,1748],{"mathvariant":1747},[1742,42759,1872],{},[902,42761,42762],{"encoding":904},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[883,42764,42766],{"className":42765},[886],[888,42767,42768],{"xmlns":890},[892,42769,42770,42826],{},[895,42771,42772,42784,42786,42788,42796,42810],{},[5950,42773,42774,42776,42778],{},[898,42775,900],{},[1742,42777,41469],{},[895,42779,42780,42782],{},[1750,42781,3815],{"mathvariant":1747},[1750,42783,3815],{"mathvariant":1747},[1750,42785,1766],{},[1750,42787,1758],{},[3586,42789,42790],{"scriptlevel":2607,"displaystyle":1752},[3423,42791,42792,42794],{},[1742,42793,1744],{},[1742,42795,7859],{},[5950,42797,42798,42800,42802],{},[898,42799,12471],{},[1742,42801,1744],{},[895,42803,42804,42806,42808],{},[1742,42805,1744],{},[898,42807,1748],{"mathvariant":1747},[1742,42809,1872],{},[5950,42811,42812,42814,42816],{},[898,42813,12471],{},[1742,42815,1872],{},[895,42817,42818,42820,42822,42824],{},[1750,42819,1758],{},[1742,42821,7822],{},[898,42823,1748],{"mathvariant":1747},[1742,42825,1872],{},[902,42827,42828],{"encoding":904},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[883,42830,42832],{"className":42831},[886],[888,42833,42834],{"xmlns":890},[892,42835,42836,42892],{},[895,42837,42838,42850,42852,42860,42876],{},[5950,42839,42840,42842,42844],{},[898,42841,900],{},[1742,42843,4903],{},[895,42845,42846,42848],{},[1750,42847,3815],{"mathvariant":1747},[1750,42849,3815],{"mathvariant":1747},[1750,42851,1766],{},[3586,42853,42854],{"scriptlevel":2607,"displaystyle":1752},[3423,42855,42856,42858],{},[1742,42857,1744],{},[1742,42859,7859],{},[5950,42861,42862,42864,42866],{},[898,42863,12471],{},[1742,42865,1744],{},[895,42867,42868,42870,42872,42874],{},[1750,42869,1758],{},[1742,42871,1744],{},[898,42873,1748],{"mathvariant":1747},[1742,42875,1872],{},[5950,42877,42878,42880,42882],{},[898,42879,12471],{},[1742,42881,1872],{},[895,42883,42884,42886,42888,42890],{},[1750,42885,1758],{},[1742,42887,1744],{},[898,42889,1748],{"mathvariant":1747},[1742,42891,1872],{},[902,42893,42894],{"encoding":904},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[883,42897,42899],{"className":42898},[886],[888,42900,42901],{"xmlns":890},[892,42902,42903,42930],{},[895,42904,42905,42907,42909,42911,42913,42915,42917,42919,42921,42923,42926,42928],{},[898,42906,5541],{},[1750,42908,1753],{"stretchy":1752},[1742,42910,7859],{},[1750,42912,1917],{"separator":1916},[1742,42914,1744],{},[1750,42916,1917],{"separator":1916},[1742,42918,1744],{},[1750,42920,1763],{"stretchy":1752},[1750,42922,1766],{},[1742,42924,42925],{},"0,28125",[1750,42927,2604],{},[1742,42929,2607],{},[902,42931,42932],{"encoding":904},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[883,42935,42937],{"className":42936},[886],[888,42938,42939],{"xmlns":890},[892,42940,42941,42953],{},[895,42942,42943,42945,42947,42949,42951],{},[1750,42944,5141],{"stretchy":1752},[1742,42946,7859],{},[1750,42948,1917],{"separator":1916},[1742,42950,1744],{},[1750,42952,5158],{"stretchy":1752},[902,42954,42955],{"encoding":904},"[4, 1]"," je vázané ",[38,42958,13445],{},[115,42960,42962],{"id":42961},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[724,42964,42965],{},"Obecně:",[883,42967,42969],{"className":42968},[886],[888,42970,42971],{"xmlns":890,"display":36989},[892,42972,42973,43068],{},[4577,42974,42975],{"width":36994},[4582,42976,42977,42979,43061,43063],{},[4585,42978],{"width":36999},[4585,42980,42981],{},[895,42982,42983,42989,42991,42997,42999,43005,43007,43013,43015,43017,43019,43021,43023,43029,43031,43037,43039,43045,43047,43053,43055,43057,43059],{},[5535,42984,42985,42987],{},[898,42986,12471],{},[1742,42988,1744],{},[1750,42990,1766],{},[5535,42992,42993,42995],{},[898,42994,5541],{},[1742,42996,1744],{},[1750,42998,1753],{"stretchy":1752},[5535,43000,43001,43003],{},[898,43002,1776],{},[1742,43004,1744],{},[1750,43006,1917],{"separator":1916},[5535,43008,43009,43011],{},[898,43010,1776],{},[1742,43012,1872],{},[1750,43014,1917],{"separator":1916},[898,43016,900],{},[1750,43018,1763],{"stretchy":1752},[1750,43020,1917],{"separator":1916},[2125,43022],{"width":24875},[5535,43024,43025,43027],{},[898,43026,12471],{},[1742,43028,1872],{},[1750,43030,1766],{},[5535,43032,43033,43035],{},[898,43034,5541],{},[1742,43036,1872],{},[1750,43038,1753],{"stretchy":1752},[5535,43040,43041,43043],{},[898,43042,1776],{},[1742,43044,1744],{},[1750,43046,1917],{"separator":1916},[5535,43048,43049,43051],{},[898,43050,1776],{},[1742,43052,1872],{},[1750,43054,1917],{"separator":1916},[898,43056,900],{},[1750,43058,1763],{"stretchy":1752},[1750,43060,1917],{"separator":1916},[4585,43062],{"width":36999},[4585,43064,43065],{},[1969,43066,43067],{},"(6.27)",[902,43069,43070],{"encoding":904},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[883,43072,43074],{"className":43073},[886],[888,43075,43076],{"xmlns":890,"display":36989},[892,43077,43078,43125],{},[4577,43079,43080],{"width":36994},[4582,43081,43082,43084,43118,43120],{},[4585,43083],{"width":36999},[4585,43085,43086],{},[895,43087,43088,43090,43092,43094,43096,43102,43104,43110,43112,43114,43116],{},[898,43089,26016],{},[1750,43091,1766],{},[898,43093,26016],{},[1750,43095,1753],{"stretchy":1752},[5535,43097,43098,43100],{},[898,43099,1776],{},[1742,43101,1744],{},[1750,43103,1917],{"separator":1916},[5535,43105,43106,43108],{},[898,43107,1776],{},[1742,43109,1872],{},[1750,43111,1917],{"separator":1916},[898,43113,900],{},[1750,43115,1763],{"stretchy":1752},[898,43117,2313],{"mathvariant":1747},[4585,43119],{"width":36999},[4585,43121,43122],{},[1969,43123,43124],{},"(6.28)",[902,43126,43127],{"encoding":904},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[724,43129,43130,43131,1647,43134,43147,43148,43161],{},"Hicksova poptávka závisí na ",[38,43132,43133],{},"hladině užitečnosti",[883,43135,43137],{"className":43136},[886],[888,43138,43139],{"xmlns":890},[892,43140,43141,43145],{},[895,43142,43143],{},[898,43144,900],{},[902,43146,900],{"encoding":904}," (nikoli na důchodu ",[883,43149,43151],{"className":43150},[886],[888,43152,43153],{"xmlns":890},[892,43154,43155,43159],{},[895,43156,43157],{},[898,43158,1666],{},[902,43160,1666],{"encoding":904}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[115,43163,43165,43166],{"id":43164},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[883,43167,43169],{"className":43168},[886],[888,43170,43171],{"xmlns":890},[892,43172,43173,43207],{},[895,43174,43175,43177,43179,43193],{},[898,43176,900],{},[1750,43178,1766],{},[5950,43180,43181,43183,43185],{},[898,43182,12471],{},[1742,43184,1744],{},[895,43186,43187,43189,43191],{},[1742,43188,1744],{},[898,43190,1748],{"mathvariant":1747},[1742,43192,1872],{},[5950,43194,43195,43197,43199],{},[898,43196,12471],{},[1742,43198,1872],{},[895,43200,43201,43203,43205],{},[1742,43202,1744],{},[898,43204,1748],{"mathvariant":1747},[1742,43206,1872],{},[902,43208,42082],{"encoding":904},[724,43210,43211,43241],{},[883,43212,43214],{"className":43213},[886],[888,43215,43216],{"xmlns":890},[892,43217,43218,43238],{},[895,43219,43220,43226,43228,43234,43236],{},[5535,43221,43222,43224],{},[898,43223,1776],{},[1742,43225,1744],{},[1750,43227,1917],{"separator":1916},[5535,43229,43230,43232],{},[898,43231,1776],{},[1742,43233,1872],{},[1750,43235,1917],{"separator":1916},[898,43237,900],{},[902,43239,43240],{"encoding":904},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[883,43243,43245],{"className":43244},[886],[888,43246,43247],{"xmlns":890,"display":36989},[892,43248,43249,43323],{},[895,43250,43251,43253,43255,43261,43267,43269,43275,43281,43283,43285,43287,43289,43291,43305,43319,43321],{},[898,43252,2046],{"mathvariant":37471},[1750,43254,1766],{},[5535,43256,43257,43259],{},[898,43258,1776],{},[1742,43260,1744],{},[5535,43262,43263,43265],{},[898,43264,12471],{},[1742,43266,1744],{},[1750,43268,1861],{},[5535,43270,43271,43273],{},[898,43272,1776],{},[1742,43274,1872],{},[5535,43276,43277,43279],{},[898,43278,12471],{},[1742,43280,1872],{},[1750,43282,1861],{},[898,43284,26016],{},[1750,43286,1753],{"stretchy":1752},[898,43288,900],{},[1750,43290,1758],{},[5950,43292,43293,43295,43297],{},[898,43294,12471],{},[1742,43296,1744],{},[895,43298,43299,43301,43303],{},[1742,43300,1744],{},[898,43302,1748],{"mathvariant":1747},[1742,43304,1872],{},[5950,43306,43307,43309,43311],{},[898,43308,12471],{},[1742,43310,1872],{},[895,43312,43313,43315,43317],{},[1742,43314,1744],{},[898,43316,1748],{"mathvariant":1747},[1742,43318,1872],{},[1750,43320,1763],{"stretchy":1752},[898,43322,2313],{"mathvariant":1747},[902,43324,43325],{"encoding":904},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[724,43327,39354],{},[883,43329,43331],{"className":43330},[886],[888,43332,43333],{"xmlns":890,"display":36989},[892,43334,43335,43557],{},[4577,43336,43337,43417,43497],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,43338,43339,43351],{},[4585,43340,43341],{},[3586,43342,43343],{"scriptlevel":2607,"displaystyle":1916},[5950,43344,43345,43347,43349],{},[898,43346,2046],{"mathvariant":37471},[1742,43348,1744],{},[1750,43350,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,43352,43353],{},[3586,43354,43355],{"scriptlevel":2607,"displaystyle":1916},[895,43356,43357,43359,43361,43367,43369,43371,43373,43381,43397,43411,43413,43415],{},[895,43358],{},[1750,43360,1766],{},[5535,43362,43363,43365],{},[898,43364,1776],{},[1742,43366,1744],{},[1750,43368,1758],{},[898,43370,26016],{},[1750,43372,8009],{},[3586,43374,43375],{"scriptlevel":2607,"displaystyle":1752},[3423,43376,43377,43379],{},[1742,43378,1744],{},[1742,43380,1872],{},[5950,43382,43383,43385,43387],{},[898,43384,12471],{},[1742,43386,1744],{},[895,43388,43389,43391,43393,43395],{},[1750,43390,1758],{},[1742,43392,1744],{},[898,43394,1748],{"mathvariant":1747},[1742,43396,1872],{},[5950,43398,43399,43401,43403],{},[898,43400,12471],{},[1742,43402,1872],{},[895,43404,43405,43407,43409],{},[1742,43406,1744],{},[898,43408,1748],{"mathvariant":1747},[1742,43410,1872],{},[1750,43412,1766],{},[1742,43414,2607],{},[1750,43416,1917],{"separator":1916},[4582,43418,43419,43431],{},[4585,43420,43421],{},[3586,43422,43423],{"scriptlevel":2607,"displaystyle":1916},[5950,43424,43425,43427,43429],{},[898,43426,2046],{"mathvariant":37471},[1742,43428,1872],{},[1750,43430,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,43432,43433],{},[3586,43434,43435],{"scriptlevel":2607,"displaystyle":1916},[895,43436,43437,43439,43441,43447,43449,43451,43453,43461,43475,43491,43493,43495],{},[895,43438],{},[1750,43440,1766],{},[5535,43442,43443,43445],{},[898,43444,1776],{},[1742,43446,1872],{},[1750,43448,1758],{},[898,43450,26016],{},[1750,43452,8009],{},[3586,43454,43455],{"scriptlevel":2607,"displaystyle":1752},[3423,43456,43457,43459],{},[1742,43458,1744],{},[1742,43460,1872],{},[5950,43462,43463,43465,43467],{},[898,43464,12471],{},[1742,43466,1744],{},[895,43468,43469,43471,43473],{},[1742,43470,1744],{},[898,43472,1748],{"mathvariant":1747},[1742,43474,1872],{},[5950,43476,43477,43479,43481],{},[898,43478,12471],{},[1742,43480,1872],{},[895,43482,43483,43485,43487,43489],{},[1750,43484,1758],{},[1742,43486,1744],{},[898,43488,1748],{"mathvariant":1747},[1742,43490,1872],{},[1750,43492,1766],{},[1742,43494,2607],{},[1750,43496,1917],{"separator":1916},[4582,43498,43499,43511],{},[4585,43500,43501],{},[3586,43502,43503],{"scriptlevel":2607,"displaystyle":1916},[5950,43504,43505,43507,43509],{},[898,43506,2046],{"mathvariant":37471},[898,43508,26016],{},[1750,43510,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[4585,43512,43513],{},[3586,43514,43515],{"scriptlevel":2607,"displaystyle":1916},[895,43516,43517,43519,43521,43523,43525,43539,43553,43555],{},[895,43518],{},[1750,43520,1766],{},[898,43522,900],{},[1750,43524,1758],{},[5950,43526,43527,43529,43531],{},[898,43528,12471],{},[1742,43530,1744],{},[895,43532,43533,43535,43537],{},[1742,43534,1744],{},[898,43536,1748],{"mathvariant":1747},[1742,43538,1872],{},[5950,43540,43541,43543,43545],{},[898,43542,12471],{},[1742,43544,1872],{},[895,43546,43547,43549,43551],{},[1742,43548,1744],{},[898,43550,1748],{"mathvariant":1747},[1742,43552,1872],{},[1750,43554,1766],{},[1742,43556,22073],{},[902,43558,43559],{"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}",[724,43561,43562,43563,43633,43634,43692],{},"Podílem rovnic: ",[883,43564,43566],{"className":43565},[886],[888,43567,43568],{"xmlns":890},[892,43569,43570,43630],{},[895,43571,43572,43578,43580,43586,43588,43594,43596,43602,43604,43610,43616,43618,43624],{},[5535,43573,43574,43576],{},[898,43575,1776],{},[1742,43577,1744],{},[898,43579,1748],{"mathvariant":1747},[5535,43581,43582,43584],{},[898,43583,1776],{},[1742,43585,1872],{},[1750,43587,1766],{},[5535,43589,43590,43592],{},[898,43591,12471],{},[1742,43593,1872],{},[898,43595,1748],{"mathvariant":1747},[5535,43597,43598,43600],{},[898,43599,12471],{},[1742,43601,1744],{},[1750,43603,13651],{},[5535,43605,43606,43608],{},[898,43607,1776],{},[1742,43609,1744],{},[5535,43611,43612,43614],{},[898,43613,12471],{},[1742,43615,1744],{},[1750,43617,1766],{},[5535,43619,43620,43622],{},[898,43621,1776],{},[1742,43623,1872],{},[5535,43625,43626,43628],{},[898,43627,12471],{},[1742,43629,1872],{},[902,43631,43632],{"encoding":904},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[883,43635,43637],{"className":43636},[886],[888,43638,43639],{"xmlns":890},[892,43640,43641,43689],{},[895,43642,43643,43645,43647,43653,43659,43661,43667,43673,43675,43677,43683],{},[898,43644,1705],{},[1750,43646,1766],{},[5535,43648,43649,43651],{},[898,43650,1776],{},[1742,43652,1744],{},[5535,43654,43655,43657],{},[898,43656,12471],{},[1742,43658,1744],{},[1750,43660,1861],{},[5535,43662,43663,43665],{},[898,43664,1776],{},[1742,43666,1872],{},[5535,43668,43669,43671],{},[898,43670,12471],{},[1742,43672,1872],{},[1750,43674,1766],{},[1742,43676,1872],{},[5535,43678,43679,43681],{},[898,43680,1776],{},[1742,43682,1744],{},[5535,43684,43685,43687],{},[898,43686,12471],{},[1742,43688,1744],{},[902,43690,43691],{"encoding":904},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[883,43694,43696],{"className":43695},[886],[888,43697,43698],{"xmlns":890,"display":36989},[892,43699,43700,43767],{},[4577,43701,43702],{"width":36994},[4582,43703,43704,43706,43760,43762],{},[4585,43705],{"width":36999},[4585,43707,43708],{},[895,43709,43710,43716,43718,43732,43734,43736,43742,43744,43758],{},[5535,43711,43712,43714],{},[898,43713,12471],{},[1742,43715,1744],{},[1750,43717,1766],{},[3423,43719,43720,43722],{},[898,43721,1705],{},[895,43723,43724,43726],{},[1742,43725,1872],{},[5535,43727,43728,43730],{},[898,43729,1776],{},[1742,43731,1744],{},[1750,43733,1917],{"separator":1916},[2125,43735],{"width":24875},[5535,43737,43738,43740],{},[898,43739,12471],{},[1742,43741,1872],{},[1750,43743,1766],{},[3423,43745,43746,43748],{},[898,43747,1705],{},[895,43749,43750,43752],{},[1742,43751,1872],{},[5535,43753,43754,43756],{},[898,43755,1776],{},[1742,43757,1872],{},[898,43759,2313],{"mathvariant":1747},[4585,43761],{"width":36999},[4585,43763,43764],{},[1969,43765,43766],{},"(6.29)",[902,43768,43769],{"encoding":904},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[724,43771,43772,43773,27149,43855,43891],{},"Ze třetí rovnice ",[883,43774,43776],{"className":43775},[886],[888,43777,43778],{"xmlns":890},[892,43779,43780,43852],{},[895,43781,43782,43784,43786,43824,43826],{},[898,43783,900],{},[1750,43785,1766],{},[17761,43787,43788],{},[895,43789,43790,43806,43808],{},[3586,43791,43792],{"scriptlevel":2607,"displaystyle":1752},[3423,43793,43794,43796],{},[898,43795,1705],{},[895,43797,43798,43800],{},[1742,43799,1872],{},[5535,43801,43802,43804],{},[898,43803,1776],{},[1742,43805,1744],{},[1750,43807,8009],{},[3586,43809,43810],{"scriptlevel":2607,"displaystyle":1752},[3423,43811,43812,43814],{},[898,43813,1705],{},[895,43815,43816,43818],{},[1742,43817,1872],{},[5535,43819,43820,43822],{},[898,43821,1776],{},[1742,43823,1872],{},[1750,43825,1766],{},[3586,43827,43828],{"scriptlevel":2607,"displaystyle":1752},[3423,43829,43830,43832],{},[898,43831,1705],{},[895,43833,43834,43836],{},[1742,43835,1872],{},[17761,43837,43838],{},[895,43839,43840,43846],{},[5535,43841,43842,43844],{},[898,43843,1776],{},[1742,43845,1744],{},[5535,43847,43848,43850],{},[898,43849,1776],{},[1742,43851,1872],{},[902,43853,43854],{"encoding":904},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[883,43856,43858],{"className":43857},[886],[888,43859,43860],{"xmlns":890},[892,43861,43862,43888],{},[895,43863,43864,43866,43868,43870,43872],{},[898,43865,1705],{},[1750,43867,1766],{},[1742,43869,1872],{},[898,43871,900],{},[17761,43873,43874],{},[895,43875,43876,43882],{},[5535,43877,43878,43880],{},[898,43879,1776],{},[1742,43881,1744],{},[5535,43883,43884,43886],{},[898,43885,1776],{},[1742,43887,1872],{},[902,43889,43890],{"encoding":904},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[883,43893,43895],{"className":43894},[886],[888,43896,43897],{"xmlns":890,"display":36989},[892,43898,43899,44044],{},[4577,43900,43901],{"width":36994},[4582,43902,43903,43905,44037,44039],{},[4585,43904],{"width":36999},[4585,43906,43907],{},[3582,43908,43909],{"notation":3584},[3586,43910,43911],{"scriptlevel":2607,"displaystyle":1752},[3586,43912,43913],{"scriptlevel":2607,"displaystyle":1752},[3586,43914,43915],{"scriptlevel":2607,"displaystyle":1916},[895,43916,43917,43919,43925,43927,43929,43945,43947,43953,43955,43961,43963,43969,43971,43973,43975,43977,43979,43985,43987,43989,44005,44007,44013,44015,44021,44023,44029,44031,44033,44035],{},[1969,43918,6766],{},[5535,43920,43921,43923],{},[898,43922,12471],{},[1742,43924,1744],{},[1750,43926,1766],{},[898,43928,900],{},[17761,43930,43931],{},[3423,43932,43933,43939],{},[5535,43934,43935,43937],{},[898,43936,1776],{},[1742,43938,1872],{},[5535,43940,43941,43943],{},[898,43942,1776],{},[1742,43944,1744],{},[1750,43946,1766],{},[5535,43948,43949,43951],{},[898,43950,5541],{},[1742,43952,1744],{},[1750,43954,1753],{"stretchy":1752},[5535,43956,43957,43959],{},[898,43958,1776],{},[1742,43960,1744],{},[1750,43962,1917],{"separator":1916},[5535,43964,43965,43967],{},[898,43966,1776],{},[1742,43968,1872],{},[1750,43970,1917],{"separator":1916},[898,43972,900],{},[1750,43974,1763],{"stretchy":1752},[1750,43976,1917],{"separator":1916},[2125,43978],{"width":24875},[5535,43980,43981,43983],{},[898,43982,12471],{},[1742,43984,1872],{},[1750,43986,1766],{},[898,43988,900],{},[17761,43990,43991],{},[3423,43992,43993,43999],{},[5535,43994,43995,43997],{},[898,43996,1776],{},[1742,43998,1744],{},[5535,44000,44001,44003],{},[898,44002,1776],{},[1742,44004,1872],{},[1750,44006,1766],{},[5535,44008,44009,44011],{},[898,44010,5541],{},[1742,44012,1872],{},[1750,44014,1753],{"stretchy":1752},[5535,44016,44017,44019],{},[898,44018,1776],{},[1742,44020,1744],{},[1750,44022,1917],{"separator":1916},[5535,44024,44025,44027],{},[898,44026,1776],{},[1742,44028,1872],{},[1750,44030,1917],{"separator":1916},[898,44032,900],{},[1750,44034,1763],{"stretchy":1752},[1969,44036,6766],{},[4585,44038],{"width":36999},[4585,44040,44041],{},[1969,44042,44043],{},"(6.30)",[902,44045,44046],{"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}",[115,44048,44050],{"id":44049},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[724,44052,44053,44054,44067,44068,44085,44086,44099,44100,44117,44118,44121,44122,44161,44162,44191],{},"Primární (max ",[883,44055,44057],{"className":44056},[886],[888,44058,44059],{"xmlns":890},[892,44060,44061,44065],{},[895,44062,44063],{},[898,44064,900],{},[902,44066,900],{"encoding":904}," při rozpočtu ",[883,44069,44071],{"className":44070},[886],[888,44072,44073],{"xmlns":890},[892,44074,44075,44083],{},[895,44076,44077],{},[1699,44078,44079,44081],{},[898,44080,1666],{},[1750,44082,3751],{},[902,44084,36951],{"encoding":904},") a duální (min ",[883,44087,44089],{"className":44088},[886],[888,44090,44091],{"xmlns":890},[892,44092,44093,44097],{},[895,44094,44095],{},[898,44096,1705],{},[902,44098,1705],{"encoding":904}," při užitečnosti ",[883,44101,44103],{"className":44102},[886],[888,44104,44105],{"xmlns":890},[892,44106,44107,44115],{},[895,44108,44109],{},[1699,44110,44111,44113],{},[898,44112,900],{},[1750,44114,3751],{},[902,44116,36885],{"encoding":904},") úloha jsou ",[38,44119,44120],{},"ekvivalentní",": mají tentýž bod optima ",[883,44123,44125],{"className":44124},[886],[888,44126,44127],{"xmlns":890},[892,44128,44129,44159],{},[895,44130,44131,44137,44139,44147,44149,44157],{},[1699,44132,44133,44135],{},[898,44134,12471],{},[1750,44136,3751],{},[1750,44138,5141],{"stretchy":1752},[5950,44140,44141,44143,44145],{},[898,44142,12471],{},[1742,44144,1744],{},[1750,44146,3751],{},[1750,44148,1917],{"separator":1916},[5950,44150,44151,44153,44155],{},[898,44152,12471],{},[1742,44154,1872],{},[1750,44156,3751],{},[1750,44158,5158],{"stretchy":1752},[902,44160,37250],{"encoding":904}," a v obou platí ",[883,44163,44165],{"className":44164},[886],[888,44166,44167],{"xmlns":890},[892,44168,44169,44189],{},[895,44170,44171,44173,44175,44181,44183],{},[1969,44172,20236],{},[1750,44174,1766],{},[5535,44176,44177,44179],{},[898,44178,1776],{},[1742,44180,1744],{},[898,44182,1748],{"mathvariant":1747},[5535,44184,44185,44187],{},[898,44186,1776],{},[1742,44188,1872],{},[902,44190,36921],{"encoding":904},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[724,44193,44194],{},[4434,44195],{"alt":44196,"className":44197,"src":44198},"imek-primarni-vs-dualni",[210,4438],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[120,44200,44201,44312],{},[123,44202,44203,44206,44207,44220,44221,44261,44262,2313],{},[38,44204,44205],{},"Primární"," (Marshall): zadáno ",[883,44208,44210],{"className":44209},[886],[888,44211,44212],{"xmlns":890},[892,44213,44214,44218],{},[895,44215,44216],{},[898,44217,1666],{},[902,44219,1666],{"encoding":904},", hledáme maximální ",[883,44222,44224],{"className":44223},[886],[888,44225,44226],{"xmlns":890},[892,44227,44228,44258],{},[895,44229,44230,44236,44238,44244,44246,44252,44254,44256],{},[1699,44231,44232,44234],{},[898,44233,900],{},[1750,44235,3751],{},[1750,44237,1753],{"stretchy":1752},[5535,44239,44240,44242],{},[898,44241,1776],{},[1742,44243,1744],{},[1750,44245,1917],{"separator":1916},[5535,44247,44248,44250],{},[898,44249,1776],{},[1742,44251,1872],{},[1750,44253,1917],{"separator":1916},[898,44255,1666],{},[1750,44257,1763],{"stretchy":1752},[902,44259,44260],{"encoding":904},"U^*(P_1, P_2, Y)"," a poptávku ",[883,44263,44265],{"className":44264},[886],[888,44266,44267],{"xmlns":890},[892,44268,44269,44309],{},[895,44270,44271,44277,44279,44287,44289,44295,44297,44303,44305,44307],{},[5535,44272,44273,44275],{},[898,44274,12471],{},[898,44276,27363],{},[1750,44278,1766],{},[5950,44280,44281,44283,44285],{},[898,44282,5541],{},[898,44284,27363],{},[898,44286,1773],{},[1750,44288,1753],{"stretchy":1752},[5535,44290,44291,44293],{},[898,44292,1776],{},[1742,44294,1744],{},[1750,44296,1917],{"separator":1916},[5535,44298,44299,44301],{},[898,44300,1776],{},[1742,44302,1872],{},[1750,44304,1917],{"separator":1916},[898,44306,1666],{},[1750,44308,1763],{"stretchy":1752},[902,44310,44311],{"encoding":904},"Q_i = D_i^M(P_1, P_2, Y)",[123,44313,44314,44317,44318,44331,44332,44261,44372,2313],{},[38,44315,44316],{},"Duální"," (Hicks): zadáno ",[883,44319,44321],{"className":44320},[886],[888,44322,44323],{"xmlns":890},[892,44324,44325,44329],{},[895,44326,44327],{},[898,44328,900],{},[902,44330,900],{"encoding":904},", hledáme minimální ",[883,44333,44335],{"className":44334},[886],[888,44336,44337],{"xmlns":890},[892,44338,44339,44369],{},[895,44340,44341,44347,44349,44355,44357,44363,44365,44367],{},[1699,44342,44343,44345],{},[898,44344,1705],{},[1750,44346,3751],{},[1750,44348,1753],{"stretchy":1752},[5535,44350,44351,44353],{},[898,44352,1776],{},[1742,44354,1744],{},[1750,44356,1917],{"separator":1916},[5535,44358,44359,44361],{},[898,44360,1776],{},[1742,44362,1872],{},[1750,44364,1917],{"separator":1916},[898,44366,900],{},[1750,44368,1763],{"stretchy":1752},[902,44370,44371],{"encoding":904},"E^*(P_1, P_2, U)",[883,44373,44375],{"className":44374},[886],[888,44376,44377],{"xmlns":890},[892,44378,44379,44420],{},[895,44380,44381,44387,44389,44398,44400,44406,44408,44414,44416,44418],{},[5535,44382,44383,44385],{},[898,44384,12471],{},[898,44386,27363],{},[1750,44388,1766],{},[5950,44390,44391,44393,44395],{},[898,44392,5541],{},[898,44394,27363],{},[898,44396,44397],{},"H",[1750,44399,1753],{"stretchy":1752},[5535,44401,44402,44404],{},[898,44403,1776],{},[1742,44405,1744],{},[1750,44407,1917],{"separator":1916},[5535,44409,44410,44412],{},[898,44411,1776],{},[1742,44413,1872],{},[1750,44415,1917],{"separator":1916},[898,44417,900],{},[1750,44419,1763],{"stretchy":1752},[902,44421,44422],{"encoding":904},"Q_i = D_i^H(P_1, P_2, U)",[724,44424,44425,44426,44429,44430,44433],{},"Proč se studují obě? Marshallova poptávka je ",[38,44427,44428],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[38,44431,44432],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[115,44435,44437],{"id":44436},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[198,44439,44441],{"id":44440},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[724,44443,44444,44447,44448,44480,44481,44519,44520,44546],{},[38,44445,44446],{},"6.8"," Jsou dány užitečnost ",[883,44449,44451],{"className":44450},[886],[888,44452,44453],{"xmlns":890},[892,44454,44455,44477],{},[895,44456,44457,44459,44461,44469],{},[898,44458,900],{},[1750,44460,1766],{},[5950,44462,44463,44465,44467],{},[898,44464,12471],{},[1742,44466,1744],{},[1742,44468,4268],{},[5950,44470,44471,44473,44475],{},[898,44472,12471],{},[1742,44474,1872],{},[1742,44476,4268],{},[902,44478,44479],{"encoding":904},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[883,44482,44484],{"className":44483},[886],[888,44485,44486],{"xmlns":890},[892,44487,44488,44516],{},[895,44489,44490,44498,44500,44502,44504,44512,44514],{},[5950,44491,44492,44494,44496],{},[898,44493,1776],{},[1742,44495,1744],{},[1750,44497,3751],{},[1750,44499,1766],{},[1742,44501,7859],{},[1750,44503,1917],{"separator":1916},[5950,44505,44506,44508,44510],{},[898,44507,1776],{},[1742,44509,1872],{},[1750,44511,3751],{},[1750,44513,1766],{},[1742,44515,3079],{},[902,44517,44518],{"encoding":904},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[883,44521,44523],{"className":44522},[886],[888,44524,44525],{"xmlns":890},[892,44526,44527,44543],{},[895,44528,44529,44535,44537],{},[5535,44530,44531,44533],{},[898,44532,12471],{},[1742,44534,1744],{},[1750,44536,1917],{"separator":1916},[5535,44538,44539,44541],{},[898,44540,12471],{},[1742,44542,1872],{},[902,44544,44545],{"encoding":904},"Q_1, Q_2"," maximalizující užitečnost.",[724,44548,44549,44552,44553,44595,44596,44627,44628,44650,44651,2313],{},[38,44550,44551],{},"6.9"," Jsou dány rozpočtové omezení ",[883,44554,44556],{"className":44555},[886],[888,44557,44558],{"xmlns":890},[892,44559,44560,44592],{},[895,44561,44562,44564,44566,44572,44578,44580,44586],{},[898,44563,1666],{},[1750,44565,1766],{},[5535,44567,44568,44570],{},[898,44569,1776],{},[1742,44571,1744],{},[5535,44573,44574,44576],{},[898,44575,12471],{},[1742,44577,1744],{},[1750,44579,1861],{},[5535,44581,44582,44584],{},[898,44583,1776],{},[1742,44585,1872],{},[5535,44587,44588,44590],{},[898,44589,12471],{},[1742,44591,1872],{},[902,44593,44594],{"encoding":904},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[883,44597,44599],{"className":44598},[886],[888,44600,44601],{"xmlns":890},[892,44602,44603,44625],{},[895,44604,44605,44607,44609,44617],{},[898,44606,900],{},[1750,44608,1766],{},[5950,44610,44611,44613,44615],{},[898,44612,12471],{},[1742,44614,1744],{},[1742,44616,4268],{},[5950,44618,44619,44621,44623],{},[898,44620,12471],{},[1742,44622,1872],{},[1742,44624,4268],{},[902,44626,44479],{"encoding":904},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[883,44629,44631],{"className":44630},[886],[888,44632,44633],{"xmlns":890},[892,44634,44635,44647],{},[895,44636,44637,44643,44645],{},[1699,44638,44639,44641],{},[898,44640,1666],{},[1750,44642,3751],{},[1750,44644,1766],{},[1742,44646,7658],{},[902,44648,44649],{"encoding":904},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[883,44652,44654],{"className":44653},[886],[888,44655,44656],{"xmlns":890},[892,44657,44658,44686],{},[895,44659,44660,44668,44670,44672,44674,44682,44684],{},[5950,44661,44662,44664,44666],{},[898,44663,1776],{},[1742,44665,1744],{},[1750,44667,3751],{},[1750,44669,1766],{},[1742,44671,7902],{},[1750,44673,1917],{"separator":1916},[5950,44675,44676,44678,44680],{},[898,44677,1776],{},[1742,44679,1872],{},[1750,44681,3751],{},[1750,44683,1766],{},[1742,44685,3079],{},[902,44687,44688],{"encoding":904},"P_1^* = 5, P_2^* = 10",[724,44690,44691,44694,44695,5424,44727,44757,44758,2313],{},[38,44692,44693],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[883,44696,44698],{"className":44697},[886],[888,44699,44700],{"xmlns":890},[892,44701,44702,44724],{},[895,44703,44704,44706,44708,44716],{},[898,44705,900],{},[1750,44707,1766],{},[5950,44709,44710,44712,44714],{},[898,44711,12471],{},[1742,44713,1744],{},[898,44715,207],{},[5950,44717,44718,44720,44722],{},[898,44719,12471],{},[1742,44721,1872],{},[898,44723,2573],{},[902,44725,44726],{"encoding":904},"U = Q_1^a Q_2^b",[883,44728,44730],{"className":44729},[886],[888,44731,44732],{"xmlns":890},[892,44733,44734,44754],{},[895,44735,44736,44738,44740,44742,44744,44746,44748,44750,44752],{},[898,44737,207],{},[1750,44739,1917],{"separator":1916},[898,44741,2573],{},[1750,44743,16154],{},[1750,44745,14978],{"stretchy":1752},[1742,44747,2607],{},[1750,44749,1917],{"separator":1916},[1742,44751,1744],{},[1750,44753,14995],{"stretchy":1752},[902,44755,44756],{"encoding":904},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[883,44759,44761],{"className":44760},[886],[888,44762,44763],{"xmlns":890},[892,44764,44765,44797],{},[895,44766,44767,44769,44771,44777,44783,44785,44791],{},[898,44768,1666],{},[1750,44770,1766],{},[5535,44772,44773,44775],{},[898,44774,1776],{},[1742,44776,1744],{},[5535,44778,44779,44781],{},[898,44780,12471],{},[1742,44782,1744],{},[1750,44784,1861],{},[5535,44786,44787,44789],{},[898,44788,1776],{},[1742,44790,1872],{},[5535,44792,44793,44795],{},[898,44794,12471],{},[1742,44796,1872],{},[902,44798,44594],{"encoding":904},[724,44800,44801,44804,44805,5424,44839,44757,44857,2313],{},[38,44802,44803],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[883,44806,44808],{"className":44807},[886],[888,44809,44810],{"xmlns":890},[892,44811,44812,44836],{},[895,44813,44814,44816,44818,44826,44828],{},[898,44815,900],{},[1750,44817,1766],{},[5950,44819,44820,44822,44824],{},[898,44821,12471],{},[1742,44823,1744],{},[898,44825,207],{},[1750,44827,1861],{},[5950,44829,44830,44832,44834],{},[898,44831,12471],{},[1742,44833,1872],{},[898,44835,207],{},[902,44837,44838],{"encoding":904},"U = Q_1^a + Q_2^a",[883,44840,44842],{"className":44841},[886],[888,44843,44844],{"xmlns":890},[892,44845,44846,44854],{},[895,44847,44848,44850,44852],{},[898,44849,207],{},[1750,44851,13044],{"mathvariant":1747},[1742,44853,2607],{},[902,44855,44856],{"encoding":904},"a \\neq 0",[883,44858,44860],{"className":44859},[886],[888,44861,44862],{"xmlns":890},[892,44863,44864,44896],{},[895,44865,44866,44868,44870,44876,44882,44884,44890],{},[898,44867,1666],{},[1750,44869,1766],{},[5535,44871,44872,44874],{},[898,44873,1776],{},[1742,44875,1744],{},[5535,44877,44878,44880],{},[898,44879,12471],{},[1742,44881,1744],{},[1750,44883,1861],{},[5535,44885,44886,44888],{},[898,44887,1776],{},[1742,44889,1872],{},[5535,44891,44892,44894],{},[898,44893,12471],{},[1742,44895,1872],{},[902,44897,44594],{"encoding":904},[198,44899,44901],{"id":44900},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[724,44903,44904,44447,44907,1343,44934,44956,44957,1343,44980,45004,45005,45030,45031,2313],{},[38,44905,44906],{},"6.12",[883,44908,44910],{"className":44909},[886],[888,44911,44912],{"xmlns":890},[892,44913,44914,44932],{},[895,44915,44916,44918,44920,44926],{},[898,44917,900],{},[1750,44919,1766],{},[5535,44921,44922,44924],{},[898,44923,12471],{},[1742,44925,1744],{},[5535,44927,44928,44930],{},[898,44929,12471],{},[1742,44931,1872],{},[902,44933,39149],{"encoding":904},[883,44935,44937],{"className":44936},[886],[888,44938,44939],{"xmlns":890},[892,44940,44941,44953],{},[895,44942,44943,44949,44951],{},[1699,44944,44945,44947],{},[898,44946,900],{},[1750,44948,3751],{},[1750,44950,1766],{},[1742,44952,3079],{},[902,44954,44955],{"encoding":904},"U^* = 10"," hladina užitečnosti a ceny ",[883,44958,44960],{"className":44959},[886],[888,44961,44962],{"xmlns":890},[892,44963,44964,44978],{},[895,44965,44966,44974,44976],{},[5950,44967,44968,44970,44972],{},[898,44969,1776],{},[1742,44971,1744],{},[1750,44973,3751],{},[1750,44975,1766],{},[1742,44977,1872],{},[902,44979,39222],{"encoding":904},[883,44981,44983],{"className":44982},[886],[888,44984,44985],{"xmlns":890},[892,44986,44987,45001],{},[895,44988,44989,44997,44999],{},[5950,44990,44991,44993,44995],{},[898,44992,1776],{},[1742,44994,1872],{},[1750,44996,3751],{},[1750,44998,1766],{},[1742,45000,7859],{},[902,45002,45003],{"encoding":904},"P_2^* = 4",". Určete množství ",[883,45006,45008],{"className":45007},[886],[888,45009,45010],{"xmlns":890},[892,45011,45012,45028],{},[895,45013,45014,45020,45022],{},[5535,45015,45016,45018],{},[898,45017,12471],{},[1742,45019,1744],{},[1750,45021,1917],{"separator":1916},[5535,45023,45024,45026],{},[898,45025,12471],{},[1742,45027,1872],{},[902,45029,44545],{"encoding":904}," minimalizující výdaje spotřebitele ",[883,45032,45034],{"className":45033},[886],[888,45035,45036],{"xmlns":890},[892,45037,45038,45058],{},[895,45039,45040,45042,45044,45050,45052],{},[898,45041,900],{},[1750,45043,1766],{},[5535,45045,45046,45048],{},[898,45047,12471],{},[1742,45049,1744],{},[1750,45051,8009],{},[5535,45053,45054,45056],{},[898,45055,12471],{},[1742,45057,1872],{},[902,45059,45060],{"encoding":904},"U = Q_1 \\cdot Q_2",[724,45062,45063,45066,45067,45108,45109,45131,45132,2313],{},[38,45064,45065],{},"6.13"," Jsou dány výdaje spotřebitele ",[883,45068,45070],{"className":45069},[886],[888,45071,45072],{"xmlns":890},[892,45073,45074,45106],{},[895,45075,45076,45078,45080,45086,45092,45094,45100],{},[898,45077,1705],{},[1750,45079,1766],{},[5535,45081,45082,45084],{},[898,45083,1776],{},[1742,45085,1744],{},[5535,45087,45088,45090],{},[898,45089,12471],{},[1742,45091,1744],{},[1750,45093,1861],{},[5535,45095,45096,45098],{},[898,45097,1776],{},[1742,45099,1872],{},[5535,45101,45102,45104],{},[898,45103,12471],{},[1742,45105,1872],{},[902,45107,36866],{"encoding":904}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[883,45110,45112],{"className":45111},[886],[888,45113,45114],{"xmlns":890},[892,45115,45116,45128],{},[895,45117,45118,45124,45126],{},[1699,45119,45120,45122],{},[898,45121,900],{},[1750,45123,3751],{},[1750,45125,1766],{},[1742,45127,6419],{},[902,45129,45130],{"encoding":904},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[883,45133,45135],{"className":45134},[886],[888,45136,45137],{"xmlns":890},[892,45138,45139,45168],{},[895,45140,45141,45149,45151,45153,45155,45163,45165],{},[5950,45142,45143,45145,45147],{},[898,45144,1776],{},[1742,45146,1744],{},[1750,45148,3751],{},[1750,45150,1766],{},[1742,45152,6465],{},[1750,45154,1917],{"separator":1916},[5950,45156,45157,45159,45161],{},[898,45158,1776],{},[1742,45160,1872],{},[1750,45162,3751],{},[1750,45164,1766],{},[1742,45166,45167],{},"15",[902,45169,45170],{"encoding":904},"P_1^* = 20, P_2^* = 15",[115,45172,10461],{"id":10460},[120,45174,45175,45232,45271,45291,45326,45380,45385,45391,45487,45532],{},[123,45176,45177,1647,45180,45229,45230,2313],{},[38,45178,45179],{},"Rozpočtové omezení (budget constraint)",[883,45181,45183],{"className":45182},[886],[888,45184,45185],{"xmlns":890},[892,45186,45187,45227],{},[895,45188,45189,45195,45197,45205,45211,45213,45221],{},[1699,45190,45191,45193],{},[898,45192,1666],{},[1750,45194,3751],{},[1750,45196,1766],{},[5950,45198,45199,45201,45203],{},[898,45200,1776],{},[1742,45202,1744],{},[1750,45204,3751],{},[5535,45206,45207,45209],{},[898,45208,12471],{},[1742,45210,1744],{},[1750,45212,1861],{},[5950,45214,45215,45217,45219],{},[898,45216,1776],{},[1742,45218,1872],{},[1750,45220,3751],{},[5535,45222,45223,45225],{},[898,45224,12471],{},[1742,45226,1872],{},[902,45228,26871],{"encoding":904}," — (6.12); ",[38,45231,37059],{},[123,45233,45234,45237,45238,2313],{},[38,45235,45236],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[883,45239,45241],{"className":45240},[886],[888,45242,45243],{"xmlns":890},[892,45244,45245,45269],{},[895,45246,45247,45249,45251,45259,45261],{},[1969,45248,20236],{},[1750,45250,1766],{},[5950,45252,45253,45255,45257],{},[898,45254,1776],{},[1742,45256,1744],{},[1750,45258,3751],{},[898,45260,1748],{"mathvariant":1747},[5950,45262,45263,45265,45267],{},[898,45264,1776],{},[1742,45266,1872],{},[1750,45268,3751],{},[902,45270,37902],{"encoding":904},[123,45272,45273,45288,45289,2313],{},[38,45274,38046,45275],{},[883,45276,45278],{"className":45277},[886],[888,45279,45280],{"xmlns":890},[892,45281,45282,45286],{},[895,45283,45284],{},[898,45285,26016],{},[902,45287,26069],{"encoding":904}," — stínová cena uvolnění omezení; u maximalizace ",[38,45290,38068],{},[123,45292,45293,45296,45297,2313],{},[38,45294,45295],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[883,45298,45300],{"className":45299},[886],[888,45301,45302],{"xmlns":890},[892,45303,45304,45324],{},[895,45305,45306,45308,45310,45316,45318],{},[1969,45307,20236],{},[1750,45309,1766],{},[5535,45311,45312,45314],{},[898,45313,1776],{},[1742,45315,1744],{},[898,45317,1748],{"mathvariant":1747},[5535,45319,45320,45322],{},[898,45321,1776],{},[1742,45323,1872],{},[902,45325,36921],{"encoding":904},[123,45327,45328,10469,45331,45379],{},[38,45329,45330],{},"Poptávka maximalizující užitečnost (Marshallova)",[883,45332,45334],{"className":45333},[886],[888,45335,45336],{"xmlns":890},[892,45337,45338,45376],{},[895,45339,45340,45346,45348,45354,45356,45362,45364,45370,45372,45374],{},[5535,45341,45342,45344],{},[898,45343,12471],{},[898,45345,27363],{},[1750,45347,1766],{},[5535,45349,45350,45352],{},[898,45351,5541],{},[898,45353,27363],{},[1750,45355,1753],{"stretchy":1752},[5535,45357,45358,45360],{},[898,45359,1776],{},[1742,45361,1744],{},[1750,45363,1917],{"separator":1916},[5535,45365,45366,45368],{},[898,45367,1776],{},[1742,45369,1872],{},[1750,45371,1917],{"separator":1916},[898,45373,1666],{},[1750,45375,1763],{"stretchy":1752},[902,45377,45378],{"encoding":904},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[123,45381,45382,45384],{},[38,45383,40650],{}," — poptávka jako funkce důchodu při pevných cenách.",[123,45386,45387,45390],{},[38,45388,45389],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[123,45392,45393,10469,45395,45442,45443,45486],{},[38,45394,42962],{},[883,45396,45398],{"className":45397},[886],[888,45399,45400],{"xmlns":890},[892,45401,45402,45440],{},[895,45403,45404,45410,45412,45418,45420,45426,45428,45434,45436,45438],{},[5535,45405,45406,45408],{},[898,45407,12471],{},[898,45409,27363],{},[1750,45411,1766],{},[5535,45413,45414,45416],{},[898,45415,5541],{},[898,45417,27363],{},[1750,45419,1753],{"stretchy":1752},[5535,45421,45422,45424],{},[898,45423,1776],{},[1742,45425,1744],{},[1750,45427,1917],{"separator":1916},[5535,45429,45430,45432],{},[898,45431,1776],{},[1742,45433,1872],{},[1750,45435,1917],{"separator":1916},[898,45437,900],{},[1750,45439,1763],{"stretchy":1752},[902,45441,27396],{"encoding":904}," — (6.27); obecný výsledek pro ",[883,45444,45446],{"className":45445},[886],[888,45447,45448],{"xmlns":890},[892,45449,45450,45484],{},[895,45451,45452,45454,45456,45470],{},[898,45453,900],{},[1750,45455,1766],{},[5950,45457,45458,45460,45462],{},[898,45459,12471],{},[1742,45461,1744],{},[895,45463,45464,45466,45468],{},[1742,45465,1744],{},[898,45467,1748],{"mathvariant":1747},[1742,45469,1872],{},[5950,45471,45472,45474,45476],{},[898,45473,12471],{},[1742,45475,1872],{},[895,45477,45478,45480,45482],{},[1742,45479,1744],{},[898,45481,1748],{"mathvariant":1747},[1742,45483,1872],{},[902,45485,42082],{"encoding":904},": (6.30).",[123,45488,45489,45531],{},[38,45490,45491,45492],{},"Bod dotyku ",[883,45493,45495],{"className":45494},[886],[888,45496,45497],{"xmlns":890},[892,45498,45499,45529],{},[895,45500,45501,45507,45509,45517,45519,45527],{},[1699,45502,45503,45505],{},[898,45504,12471],{},[1750,45506,3751],{},[1750,45508,5141],{"stretchy":1752},[5950,45510,45511,45513,45515],{},[898,45512,12471],{},[1742,45514,1744],{},[1750,45516,3751],{},[1750,45518,1917],{"separator":1916},[5950,45520,45521,45523,45525],{},[898,45522,12471],{},[1742,45524,1872],{},[1750,45526,3751],{},[1750,45528,5158],{"stretchy":1752},[902,45530,37250],{"encoding":904}," — řešení obou úloh; totožný pro primární i duální formulaci.",[123,45533,45534,45537,45538,45551,45552,45565],{},[38,45535,45536],{},"Dualita"," — ekvivalence max ",[883,45539,45541],{"className":45540},[886],[888,45542,45543],{"xmlns":890},[892,45544,45545,45549],{},[895,45546,45547],{},[898,45548,900],{},[902,45550,900],{"encoding":904}," a min ",[883,45553,45555],{"className":45554},[886],[888,45556,45557],{"xmlns":890},[892,45558,45559,45563],{},[895,45560,45561],{},[898,45562,1705],{},[902,45564,1705],{"encoding":904},"; Marshallova a Hicksova poptávka.",[115,45567,11524],{"id":11523},[120,45569,45570,45593,45609,45622,45633],{},[123,45571,45572,1647,45575,45578,45579,45592],{},[38,45573,45574],{},"Teorie před optimalizací:",[207,45576,880],{"className":45577,"dataFsResolvedFilePath":878,"href":879},[210]," (funkce ",[883,45580,45582],{"className":45581},[886],[888,45583,45584],{"xmlns":890},[892,45585,45586,45590],{},[895,45587,45588],{},[898,45589,900],{},[902,45591,900],{"encoding":904},", indiferenční křivky, MRCS).",[123,45594,45595,1647,45598,45601,45602,45605,45606,2313],{},[38,45596,45597],{},"Matematický aparát:",[207,45599,793],{"className":45600,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace), ",[207,45603,784],{"className":45604,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace), ",[207,45607,12053],{"className":45608,"dataFsResolvedFilePath":764,"href":765},[210],[123,45610,45611,1647,45614,45617,45618,45621],{},[38,45612,45613],{},"Paralely:",[207,45615,20720],{"className":45616,"dataFsResolvedFilePath":857,"href":858},[210]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[207,45619,21574],{"className":45620,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallova poptávka jako vstup tržního modelu).",[123,45623,45624,1647,45627,1343,45630],{},[38,45625,45626],{},"Přednášky:",[207,45628,1094],{"className":45629,"dataFsResolvedFilePath":838,"href":839},[210],[207,45631,1101],{"className":45632,"dataFsResolvedFilePath":868,"href":869},[210],[123,45634,45635,1647,45637],{},[38,45636,11531],{},[207,45638,11535],{"className":45639,"dataFsResolvedFilePath":1644,"href":1645},[210],{"title":641,"searchDepth":642,"depth":642,"links":45641},[45642,45643,45644,45649,45650,45651,45653,45656,45659,45661,45662,45664,45665,45669,45670],{"id":1636,"depth":642,"text":1637},{"id":36929,"depth":642,"text":36930},{"id":37327,"depth":642,"text":37328,"children":45645},[45646,45647],{"id":37447,"depth":649,"text":37448},{"id":38028,"depth":649,"text":45648},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":38490,"depth":642,"text":38491},{"id":38801,"depth":642,"text":38802},{"id":39120,"depth":642,"text":45652},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":39893,"depth":642,"text":39894,"children":45654},[45655],{"id":40649,"depth":649,"text":40650},{"id":40829,"depth":642,"text":40830,"children":45657},[45658],{"id":41086,"depth":649,"text":41087},{"id":42037,"depth":642,"text":45660},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":42961,"depth":642,"text":42962},{"id":43164,"depth":642,"text":45663},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":44049,"depth":642,"text":44050},{"id":44436,"depth":642,"text":44437,"children":45666},[45667,45668],{"id":44440,"depth":649,"text":44441},{"id":44900,"depth":649,"text":44901},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":36690,"description":641},[1138,1137],"topics\u002Foptimalizace-spotrebitele",[1128,45677,1144,19409,45678,45679,45680],"optimalizace-spotrebitele","poptavka-spotrebitele","minimalizace-vydaju","dualita","jxXhWsWsCIcDvEqLkcWTWs-jk9CvI-eFUi2Afo7U40o",{"id":45683,"title":802,"body":45684,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":59737,"navigation":664,"path":59738,"seo":59739,"sources":59740,"stem":59741,"tags":59742,"type":11664,"updated":677,"__hash__":59748},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":9,"value":45685,"toc":59693},[45686,45689,45715,45719,45726,45878,45892,45895,45897,45984,45988,46024,46097,46118,46243,46253,46266,46270,46275,46305,46367,46376,46380,46442,46449,46470,46588,46666,46670,46673,46732,46847,46852,46884,46946,46994,47049,47053,47074,47098,47146,47150,47162,47166,47276,47280,47296,47337,47348,47507,47517,47522,47526,47648,47658,47665,47669,47747,47758,47838,47844,47851,47990,47997,48000,48057,48061,48139,48185,48229,48235,48348,48352,48355,48550,48554,48791,48794,48948,49101,49103,49105,49185,49188,49293,49362,49371,49375,49378,49439,49448,49452,49485,49563,49602,49606,49655,49709,49713,49742,49771,49823,49830,49884,49962,49966,50009,50076,50120,50224,50243,50245,50249,50357,50361,50429,50478,50485,50570,50574,50646,50651,50699,50888,50892,50897,51073,51078,51137,51242,51246,51273,51277,51284,51448,51535,51540,51542,51545,51645,51795,51867,51941,51943,51947,51961,51965,52098,52153,52265,52342,52346,52403,52506,52565,52726,52730,52805,52877,52975,53033,53127,53180,53201,53255,53260,53338,53386,53473,53511,53599,53752,53788,53842,53845,53847,53849,53898,53905,53913,54000,54009,54096,54103,54105,54109,54334,54336,54340,54344,54413,54464,54667,54673,54684,54752,54758,55180,55184,55248,55272,55468,55474,55488,55556,55559,55599,55823,55891,56193,56602,56679,56845,56851,56854,56929,57382,57433,57839,57944,58607,58610,58687,58695,58769,58800,58802,58806,58850,58852,58854,58858,59088,59092,59183,59188,59282,59287,59460,59464,59582,59587,59636,59638,59640],[12,45687,802],{"id":45688},"poptávka-nabídka-a-tržní-rovnováha",[1785,45690,45691],{},[724,45692,45693,45695,45696,45699,45700,45703,45704,45707,45708,45710,45711,45714],{},[883,45694,1791],{}," TL;DR\nKapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[38,45697,45698],{},"poptávka",") a výrobce (",[38,45701,45702],{},"nabídka","), jejich interakci v ",[38,45705,45706],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[38,45709,1730],{},"). Uzavírá ji pojem ",[38,45712,45713],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[115,45716,45718],{"id":45717},"úvod-model-a-proměnné","Úvod — model a proměnné",[724,45720,45721,45722,45725],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[614,45723,45724],{},"homo economicus","). Mezi hlavní proměnné patří:",[120,45727,45728,45745,45787,45803],{},[123,45729,45730,45731,45744],{},"cena ",[883,45732,45734],{"className":45733},[886],[888,45735,45736],{"xmlns":890},[892,45737,45738,45742],{},[895,45739,45740],{},[898,45741,1776],{},[902,45743,1776],{"encoding":904}," zkoumaného zboží,",[123,45746,45747,45748,1917],{},"ceny alternativních zboží ",[883,45749,45751],{"className":45750},[886],[888,45752,45753],{"xmlns":890},[892,45754,45755,45784],{},[895,45756,45757,45763,45765,45771,45773,45775,45777],{},[5535,45758,45759,45761],{},[898,45760,1776],{},[1742,45762,1744],{},[1750,45764,1917],{"separator":1916},[5535,45766,45767,45769],{},[898,45768,1776],{},[1742,45770,1872],{},[1750,45772,1917],{"separator":1916},[1750,45774,19282],{},[1750,45776,1917],{"separator":1916},[5535,45778,45779,45781],{},[898,45780,1776],{},[898,45782,45783],{},"n",[902,45785,45786],{"encoding":904},"P_1, P_2, \\dots, P_n",[123,45788,45789,45790,1917],{},"důchod ",[883,45791,45793],{"className":45792},[886],[888,45794,45795],{"xmlns":890},[892,45796,45797,45801],{},[895,45798,45799],{},[898,45800,1666],{},[902,45802,1666],{"encoding":904},[123,45804,45805,45806,45819,45820,45833,45834,45847,45848,45862,45863,45877],{},"preference, očekávání, populace, výrobní faktory (práce ",[883,45807,45809],{"className":45808},[886],[888,45810,45811],{"xmlns":890},[892,45812,45813,45817],{},[895,45814,45815],{},[898,45816,2046],{},[902,45818,2046],{"encoding":904},", kapitál ",[883,45821,45823],{"className":45822},[886],[888,45824,45825],{"xmlns":890},[892,45826,45827,45831],{},[895,45828,45829],{},[898,45830,19435],{},[902,45832,19435],{"encoding":904},", půda ",[883,45835,45837],{"className":45836},[886],[888,45838,45839],{"xmlns":890},[892,45840,45841,45845],{},[895,45842,45843],{},[898,45844,1705],{},[902,45846,1705],{"encoding":904},"), technologie, počet výrobců ",[883,45849,45851],{"className":45850},[886],[888,45852,45853],{"xmlns":890},[892,45854,45855,45860],{},[895,45856,45857],{},[898,45858,45859],{},"O",[902,45861,45859],{"encoding":904},", počasí ",[883,45864,45866],{"className":45865},[886],[888,45867,45868],{"xmlns":890},[892,45869,45870,45875],{},[895,45871,45872],{},[898,45873,45874],{},"W",[902,45876,45874],{"encoding":904}," atd.",[724,45879,45880,45881,45884,45885,45888,45889,2313],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[614,45882,45883],{},"ceteris paribus","), hovoříme o ",[38,45886,45887],{},"jednofaktorovém modelu","; jinak jde o model ",[38,45890,45891],{},"vícefaktorový",[45893,45894],"hr",{},[115,45896,22767],{"id":45698},[1785,45898,45899],{},[724,45900,45901,45903,45904,45917,45918,45931,45932,45935,45936,45959,45960,2313],{},[883,45902,1791],{}," TL;DR\nPoptávka vyjadřuje závislost nakupovaného množství ",[883,45905,45907],{"className":45906},[886],[888,45908,45909],{"xmlns":890},[892,45910,45911,45915],{},[895,45912,45913],{},[898,45914,12471],{},[902,45916,12471],{"encoding":904}," na ceně ",[883,45919,45921],{"className":45920},[886],[888,45922,45923],{"xmlns":890},[892,45924,45925,45929],{},[895,45926,45927],{},[898,45928,1776],{},[902,45930,1776],{"encoding":904}," (případně dalších proměnných). Základní vlastností je ",[38,45933,45934],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[883,45937,45939],{"className":45938},[886],[888,45940,45941],{"xmlns":890},[892,45942,45943,45957],{},[895,45944,45945,45947,45949,45951,45953,45955],{},[898,45946,12471],{},[1750,45948,1766],{},[898,45950,5541],{},[1750,45952,1753],{"stretchy":1752},[898,45954,1776],{},[1750,45956,1763],{"stretchy":1752},[902,45958,13854],{"encoding":904}," a jeho lineární verzí ",[883,45961,45963],{"className":45962},[886],[888,45964,45965],{"xmlns":890},[892,45966,45967,45981],{},[895,45968,45969,45971,45973,45975,45977,45979],{},[898,45970,1776],{},[1750,45972,1766],{},[898,45974,207],{},[898,45976,12471],{},[1750,45978,1861],{},[898,45980,2573],{},[902,45982,45983],{"encoding":904},"P = aQ + b",[198,45985,45987],{"id":45986},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[724,45989,45990,45991,46004,46005,46018,46019,2084,46021,12825],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[883,45992,45994],{"className":45993},[886],[888,45995,45996],{"xmlns":890},[892,45997,45998,46002],{},[895,45999,46000],{},[898,46001,12471],{},[902,46003,12471],{"encoding":904}," závisí na ceně ",[883,46006,46008],{"className":46007},[886],[888,46009,46010],{"xmlns":890},[892,46011,46012,46016],{},[895,46013,46014],{},[898,46015,1776],{},[902,46017,1776],{"encoding":904},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[38,46020,36925],{},[614,46022,46023],{},"demand function",[883,46025,46027],{"className":46026},[886],[888,46028,46029],{"xmlns":890,"display":36989},[892,46030,46031,46094],{},[4577,46032,46033],{"width":36994},[4582,46034,46035,46037,46087,46089],{},[4585,46036],{"width":36999},[4585,46038,46039],{},[895,46040,46041,46043,46045,46047,46049,46051,46053,46059,46061,46067,46069,46071,46073,46079,46081,46083,46085],{},[898,46042,12471],{},[1750,46044,1766],{},[898,46046,5541],{},[1750,46048,1753],{"stretchy":1752},[898,46050,1776],{},[1750,46052,1917],{"separator":1916},[5535,46054,46055,46057],{},[898,46056,1776],{},[1742,46058,1744],{},[1750,46060,1917],{"separator":1916},[5535,46062,46063,46065],{},[898,46064,1776],{},[1742,46066,1872],{},[1750,46068,1917],{"separator":1916},[1750,46070,19282],{},[1750,46072,1917],{"separator":1916},[5535,46074,46075,46077],{},[898,46076,1776],{},[898,46078,45783],{},[1750,46080,1917],{"separator":1916},[898,46082,1666],{},[1750,46084,1763],{"stretchy":1752},[898,46086,2313],{"mathvariant":1747},[4585,46088],{"width":36999},[4585,46090,46091],{},[1969,46092,46093],{},"(2.1)",[902,46095,46096],{"encoding":904},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[724,46098,46099,46100,46103,46104,46117],{},"Důležitou vlastností je ",[38,46101,46102],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[883,46105,46107],{"className":46106},[886],[888,46108,46109],{"xmlns":890},[892,46110,46111,46115],{},[895,46112,46113],{},[898,46114,1920],{},[902,46116,1920],{"encoding":904},"-krát, poptávané množství se nezmění,",[883,46119,46121],{"className":46120},[886],[888,46122,46123],{"xmlns":890,"display":36989},[892,46124,46125,46240],{},[4577,46126,46127],{"width":36994},[4582,46128,46129,46131,46233,46235],{},[4585,46130],{"width":36999},[4585,46132,46133],{},[895,46134,46135,46137,46139,46141,46143,46145,46147,46149,46151,46157,46159,46161,46167,46169,46171,46173,46175,46181,46183,46185,46187,46189,46191,46193,46195,46197,46199,46205,46207,46213,46215,46217,46219,46225,46227,46229,46231],{},[898,46136,12471],{},[1750,46138,1766],{},[898,46140,5541],{},[1750,46142,1753],{"stretchy":1752},[898,46144,1920],{},[898,46146,1776],{},[1750,46148,1917],{"separator":1916},[898,46150,1920],{},[5535,46152,46153,46155],{},[898,46154,1776],{},[1742,46156,1744],{},[1750,46158,1917],{"separator":1916},[898,46160,1920],{},[5535,46162,46163,46165],{},[898,46164,1776],{},[1742,46166,1872],{},[1750,46168,1917],{"separator":1916},[1750,46170,19282],{},[1750,46172,1917],{"separator":1916},[898,46174,1920],{},[5535,46176,46177,46179],{},[898,46178,1776],{},[898,46180,45783],{},[1750,46182,1917],{"separator":1916},[898,46184,1920],{},[898,46186,1666],{},[1750,46188,1763],{"stretchy":1752},[1750,46190,1766],{},[898,46192,5541],{},[1750,46194,1753],{"stretchy":1752},[898,46196,1776],{},[1750,46198,1917],{"separator":1916},[5535,46200,46201,46203],{},[898,46202,1776],{},[1742,46204,1744],{},[1750,46206,1917],{"separator":1916},[5535,46208,46209,46211],{},[898,46210,1776],{},[1742,46212,1872],{},[1750,46214,1917],{"separator":1916},[1750,46216,19282],{},[1750,46218,1917],{"separator":1916},[5535,46220,46221,46223],{},[898,46222,1776],{},[898,46224,45783],{},[1750,46226,1917],{"separator":1916},[898,46228,1666],{},[1750,46230,1763],{"stretchy":1752},[898,46232,2313],{"mathvariant":1747},[4585,46234],{"width":36999},[4585,46236,46237],{},[1969,46238,46239],{},"(2.2)",[902,46241,46242],{"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}",[1785,46244,46245],{},[724,46246,46247,46249,46250,2313],{},[883,46248,5454],{}," Pozor\nHomogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[38,46251,46252],{},"v jednofaktorových modelech neplatí",[724,46254,46255,46256,1343,46259,2028,46262,46265],{},"Rozlišuje se poptávka ",[38,46257,46258],{},"individuální",[38,46260,46261],{},"tržní",[38,46263,46264],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[198,46267,46269],{"id":46268},"jednofaktorové-modely","Jednofaktorové modely",[46271,46272,46274],"h4",{"id":46273},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[724,46276,46277,46278,46291,46292,2366],{},"Poptávané množství ",[883,46279,46281],{"className":46280},[886],[888,46282,46283],{"xmlns":890},[892,46284,46285,46289],{},[895,46286,46287],{},[898,46288,12471],{},[902,46290,12471],{"encoding":904}," závisí pouze na ceně ",[883,46293,46295],{"className":46294},[886],[888,46296,46297],{"xmlns":890},[892,46298,46299,46303],{},[895,46300,46301],{},[898,46302,1776],{},[902,46304,1776],{"encoding":904},[883,46306,46308],{"className":46307},[886],[888,46309,46310],{"xmlns":890,"display":36989},[892,46311,46312,46364],{},[4577,46313,46314],{"width":36994},[4582,46315,46316,46318,46357,46359],{},[4585,46317],{"width":36999},[4585,46319,46320],{},[895,46321,46322,46324,46326,46328,46330,46332,46334,46336,46338,46341,46343,46345,46347,46349,46351,46353,46355],{},[898,46323,12471],{},[1750,46325,1766],{},[898,46327,5541],{},[1750,46329,1753],{"stretchy":1752},[898,46331,1776],{},[1750,46333,1763],{"stretchy":1752},[1750,46335,1917],{"separator":1916},[2125,46337],{"width":2127},[1969,46339,46340],{},"resp.",[2125,46342],{"width":2127},[898,46344,1776],{},[1750,46346,1766],{},[898,46348,5541],{},[1750,46350,1753],{"stretchy":1752},[898,46352,12471],{},[1750,46354,1763],{"stretchy":1752},[898,46356,2313],{"mathvariant":1747},[4585,46358],{"width":36999},[4585,46360,46361],{},[1969,46362,46363],{},"(2.3)",[902,46365,46366],{"encoding":904},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[724,46368,46369,46370,2084,46373,1783],{},"Graf této funkce se nazývá ",[38,46371,46372],{},"křivka poptávky",[614,46374,46375],{},"demand curve",[46271,46377,46379],{"id":46378},"zákon-klesající-poptávky","Zákon klesající poptávky",[1785,46381,46382],{},[724,46383,46384],{},[38,46385,46386,46387,46400,46401,46414,46415,46400,46428,46441],{},"Roste-li cena ",[883,46388,46390],{"className":46389},[886],[888,46391,46392],{"xmlns":890},[892,46393,46394,46398],{},[895,46395,46396],{},[898,46397,1776],{},[902,46399,1776],{"encoding":904},", pak množství ",[883,46402,46404],{"className":46403},[886],[888,46405,46406],{"xmlns":890},[892,46407,46408,46412],{},[895,46409,46410],{},[898,46411,12471],{},[902,46413,12471],{"encoding":904}," klesá; klesá-li cena ",[883,46416,46418],{"className":46417},[886],[888,46419,46420],{"xmlns":890},[892,46421,46422,46426],{},[895,46423,46424],{},[898,46425,1776],{},[902,46427,1776],{"encoding":904},[883,46429,46431],{"className":46430},[886],[888,46432,46433],{"xmlns":890},[892,46434,46435,46439],{},[895,46436,46437],{},[898,46438,12471],{},[902,46440,12471],{"encoding":904}," roste.",[724,46443,46444,46445,46448],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz kap. 6). Zákon platí za ",[38,46446,46447],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1785,46450,46451,46456],{},[724,46452,46453,46455],{},[883,46454,1791],{}," Intuice — proč zákon platí",[120,46457,46458,46464],{},[123,46459,46460,46463],{},[38,46461,46462],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[123,46465,46466,46469],{},[38,46467,46468],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[724,46471,46472,46473,46486,46487,46500,46501,46527,46528,46554,46555,2433,46581,46584,46585,2313],{},"Každá funkce poptávky je tedy klesající. Cena ",[883,46474,46476],{"className":46475},[886],[888,46477,46478],{"xmlns":890},[892,46479,46480,46484],{},[895,46481,46482],{},[898,46483,1776],{},[902,46485,1776],{"encoding":904}," se vynáší na svislou osu, množství ",[883,46488,46490],{"className":46489},[886],[888,46491,46492],{"xmlns":890},[892,46493,46494,46498],{},[895,46495,46496],{},[898,46497,12471],{},[902,46499,12471],{"encoding":904}," na vodorovnou. Hypotetická křivka prochází body ",[883,46502,46504],{"className":46503},[886],[888,46505,46506],{"xmlns":890},[892,46507,46508,46524],{},[895,46509,46510,46512,46514,46516,46522],{},[1750,46511,5141],{"stretchy":1752},[1742,46513,2607],{},[1750,46515,1917],{"separator":1916},[5535,46517,46518,46520],{},[898,46519,1776],{},[1742,46521,2607],{},[1750,46523,5158],{"stretchy":1752},[902,46525,46526],{"encoding":904},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[883,46529,46531],{"className":46530},[886],[888,46532,46533],{"xmlns":890},[892,46534,46535,46551],{},[895,46536,46537,46539,46545,46547,46549],{},[1750,46538,5141],{"stretchy":1752},[5535,46540,46541,46543],{},[898,46542,12471],{},[1742,46544,2607],{},[1750,46546,1917],{"separator":1916},[1742,46548,2607],{},[1750,46550,5158],{"stretchy":1752},[902,46552,46553],{"encoding":904},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[883,46556,46558],{"className":46557},[886],[888,46559,46560],{"xmlns":890},[892,46561,46562,46578],{},[895,46563,46564,46566,46568,46570,46576],{},[1750,46565,1753],{"stretchy":1752},[1742,46567,2607],{},[1750,46569,1917],{"separator":1916},[5535,46571,46572,46574],{},[898,46573,1776],{},[1742,46575,2607],{},[1750,46577,1763],{"stretchy":1752},[902,46579,46580],{"encoding":904},"(0, P_0)",[38,46582,46583],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[38,46586,46587],{},"konvexní",[724,46589,46590],{},[614,46591,46592,46593,46615,46616,2028,46641,2313],{},"Obrázek 2.1: Hypotetická křivka poptávky v rovině ",[883,46594,46596],{"className":46595},[886],[888,46597,46598],{"xmlns":890},[892,46599,46600,46612],{},[895,46601,46602,46604,46606,46608,46610],{},[1750,46603,1753],{"stretchy":1752},[898,46605,12471],{},[1750,46607,1917],{"separator":1916},[898,46609,1776],{},[1750,46611,1763],{"stretchy":1752},[902,46613,46614],{"encoding":904},"(Q, P)"," — klesající, konvexní, procházející body ",[883,46617,46619],{"className":46618},[886],[888,46620,46621],{"xmlns":890},[892,46622,46623,46639],{},[895,46624,46625,46627,46629,46631,46637],{},[1750,46626,5141],{"stretchy":1752},[1742,46628,2607],{},[1750,46630,1917],{"separator":1916},[5535,46632,46633,46635],{},[898,46634,1776],{},[1742,46636,2607],{},[1750,46638,5158],{"stretchy":1752},[902,46640,46526],{"encoding":904},[883,46642,46644],{"className":46643},[886],[888,46645,46646],{"xmlns":890},[892,46647,46648,46664],{},[895,46649,46650,46652,46658,46660,46662],{},[1750,46651,5141],{"stretchy":1752},[5535,46653,46654,46656],{},[898,46655,12471],{},[1742,46657,2607],{},[1750,46659,1917],{"separator":1916},[1742,46661,2607],{},[1750,46663,5158],{"stretchy":1752},[902,46665,46553],{"encoding":904},[46271,46667,46669],{"id":46668},"lineární-model-poptávky","Lineární model poptávky",[724,46671,46672],{},"Nejjednodušší závislostí je",[883,46674,46676],{"className":46675},[886],[888,46677,46678],{"xmlns":890,"display":36989},[892,46679,46680,46729],{},[4577,46681,46682],{"width":36994},[4582,46683,46684,46686,46722,46724],{},[4585,46685],{"width":36999},[4585,46687,46688],{},[895,46689,46690,46692,46694,46696,46698,46700,46702,46704,46706,46708,46710,46712,46714,46716,46718,46720],{},[898,46691,1776],{},[1750,46693,1766],{},[898,46695,207],{},[898,46697,12471],{},[1750,46699,1861],{},[898,46701,2573],{},[1750,46703,1917],{"separator":1916},[2125,46705],{"width":2127},[898,46707,207],{},[1750,46709,2624],{},[1742,46711,2607],{},[1750,46713,1917],{"separator":1916},[1969,46715,7737],{},[898,46717,2573],{},[1750,46719,2604],{},[1742,46721,22073],{},[4585,46723],{"width":36999},[4585,46725,46726],{},[1969,46727,46728],{},"(2.4)",[902,46730,46731],{"encoding":904},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[724,46733,46734,46735,5424,46771,2028,46795,17682,46821,46843,46844,2313],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[883,46736,46738],{"className":46737},[886],[888,46739,46740],{"xmlns":890},[892,46741,46742,46768],{},[895,46743,46744,46746,46748,46756,46758,46760],{},[898,46745,12471],{},[1750,46747,1766],{},[3586,46749,46750],{"scriptlevel":2607,"displaystyle":1752},[3423,46751,46752,46754],{},[1742,46753,1744],{},[898,46755,207],{},[898,46757,1776],{},[1750,46759,1758],{},[3586,46761,46762],{"scriptlevel":2607,"displaystyle":1752},[3423,46763,46764,46766],{},[898,46765,2573],{},[898,46767,207],{},[902,46769,46770],{"encoding":904},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[883,46772,46774],{"className":46773},[886],[888,46775,46776],{"xmlns":890},[892,46777,46778,46792],{},[895,46779,46780,46788,46790],{},[3586,46781,46782],{"scriptlevel":2607,"displaystyle":1752},[3423,46783,46784,46786],{},[1742,46785,1744],{},[898,46787,207],{},[1750,46789,2624],{},[1742,46791,2607],{},[902,46793,46794],{"encoding":904},"\\tfrac{1}{a} \u003C 0",[883,46796,46798],{"className":46797},[886],[888,46799,46800],{"xmlns":890},[892,46801,46802,46818],{},[895,46803,46804,46806,46814,46816],{},[1750,46805,1758],{},[3586,46807,46808],{"scriptlevel":2607,"displaystyle":1752},[3423,46809,46810,46812],{},[898,46811,2573],{},[898,46813,207],{},[1750,46815,2604],{},[1742,46817,2607],{},[902,46819,46820],{"encoding":904},"-\\tfrac{b}{a} > 0",[883,46822,46824],{"className":46823},[886],[888,46825,46826],{"xmlns":890},[892,46827,46828,46840],{},[895,46829,46830,46832,46834,46836,46838],{},[1750,46831,1753],{"stretchy":1752},[1742,46833,2607],{},[1750,46835,1917],{"separator":1916},[898,46837,2573],{},[1750,46839,1763],{"stretchy":1752},[902,46841,46842],{"encoding":904},"(0, b)",". Tento model odpovídá ",[38,46845,46846],{},"nedokonalé konkurenci",[46848,46849,46851],"h5",{"id":46850},"příklad-21","Příklad 2.1",[724,46853,46854,46857,46858,2313],{},[38,46855,46856],{},"Zadání:"," Lineární poptávka ",[883,46859,46861],{"className":46860},[886],[888,46862,46863],{"xmlns":890},[892,46864,46865,46881],{},[895,46866,46867,46869,46871,46873,46875,46877,46879],{},[898,46868,1776],{},[1750,46870,1766],{},[1750,46872,1758],{},[1742,46874,1872],{},[898,46876,12471],{},[1750,46878,1861],{},[1742,46880,12800],{},[902,46882,46883],{"encoding":904},"P = -2Q + 60",[724,46885,46886,46889,46890,46912,46913,2313],{},[38,46887,46888],{},"Řešení:"," Reálné cenové rozpětí je ",[883,46891,46893],{"className":46892},[886],[888,46894,46895],{"xmlns":890},[892,46896,46897,46909],{},[895,46898,46899,46901,46903,46905,46907],{},[1750,46900,1753],{"stretchy":1752},[1742,46902,2607],{},[1750,46904,1917],{"separator":1916},[1742,46906,12800],{},[1750,46908,1763],{"stretchy":1752},[902,46910,46911],{"encoding":904},"(0, 60)","; alternativní tvar je ",[883,46914,46916],{"className":46915},[886],[888,46917,46918],{"xmlns":890},[892,46919,46920,46943],{},[895,46921,46922,46924,46926,46928,46936,46938,46940],{},[898,46923,12471],{},[1750,46925,1766],{},[1750,46927,1758],{},[3586,46929,46930],{"scriptlevel":2607,"displaystyle":1752},[3423,46931,46932,46934],{},[1742,46933,1744],{},[1742,46935,1872],{},[898,46937,1776],{},[1750,46939,1861],{},[1742,46941,46942],{},"30",[902,46944,46945],{"encoding":904},"Q = -\\tfrac{1}{2}P + 30",[16,46947,46948,46971],{},[19,46949,46950],{},[22,46951,46952,46967,46969],{},[25,46953,46954],{},[883,46955,46957],{"className":46956},[886],[888,46958,46959],{"xmlns":890},[892,46960,46961,46965],{},[895,46962,46963],{},[898,46964,1776],{},[902,46966,1776],{"encoding":904},[25,46968,14865],{},[25,46970,6465],{},[30,46972,46973],{},[22,46974,46975,46990,46992],{},[35,46976,46977],{},[883,46978,46980],{"className":46979},[886],[888,46981,46982],{"xmlns":890},[892,46983,46984,46988],{},[895,46985,46986],{},[898,46987,12471],{},[902,46989,12471],{"encoding":904},[35,46991,3079],{},[35,46993,6465],{},[724,46995,46996],{},[614,46997,46998,46999,2028,47021,2313],{},"Obrázek 2.2 \u002F 2.3: Lineární poptávka — přímka s průsečíky ",[883,47000,47002],{"className":47001},[886],[888,47003,47004],{"xmlns":890},[892,47005,47006,47018],{},[895,47007,47008,47010,47012,47014,47016],{},[1750,47009,5141],{"stretchy":1752},[1742,47011,2607],{},[1750,47013,1917],{"separator":1916},[898,47015,2573],{},[1750,47017,5158],{"stretchy":1752},[902,47019,47020],{"encoding":904},"[0, b]",[883,47022,47024],{"className":47023},[886],[888,47025,47026],{"xmlns":890},[892,47027,47028,47046],{},[895,47029,47030,47032,47034,47036,47038,47040,47042,47044],{},[1750,47031,5141],{"stretchy":1752},[1750,47033,1758],{},[898,47035,2573],{},[898,47037,1748],{"mathvariant":1747},[898,47039,207],{},[1750,47041,1917],{"separator":1916},[1742,47043,2607],{},[1750,47045,5158],{"stretchy":1752},[902,47047,47048],{"encoding":904},"[-b\u002Fa, 0]",[46271,47050,47052],{"id":47051},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[724,47054,47055,47056,47073],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[883,47057,47059],{"className":47058},[886],[888,47060,47061],{"xmlns":890},[892,47062,47063,47071],{},[895,47064,47065],{},[1699,47066,47067,47069],{},[898,47068,1776],{},[1750,47070,3751],{},[902,47072,14063],{"encoding":904},", je funkce poptávky konstantní:",[883,47075,47077],{"className":47076},[886],[888,47078,47079],{"xmlns":890,"display":36989},[892,47080,47081,47095],{},[895,47082,47083,47085,47087,47093],{},[898,47084,1776],{},[1750,47086,1766],{},[1699,47088,47089,47091],{},[898,47090,1776],{},[1750,47092,3751],{},[898,47094,2313],{"mathvariant":1747},[902,47096,47097],{"encoding":904},"P = P^*.",[724,47099,47100],{},[614,47101,47102,47103,47124,47125,2313],{},"Obrázek 2.4: Vodorovná přímka v rovině ",[883,47104,47106],{"className":47105},[886],[888,47107,47108],{"xmlns":890},[892,47109,47110,47122],{},[895,47111,47112,47114,47116,47118,47120],{},[1750,47113,1753],{"stretchy":1752},[898,47115,12471],{},[1750,47117,1917],{"separator":1916},[898,47119,1776],{},[1750,47121,1763],{"stretchy":1752},[902,47123,46614],{"encoding":904}," na úrovni ",[883,47126,47128],{"className":47127},[886],[888,47129,47130],{"xmlns":890},[892,47131,47132,47144],{},[895,47133,47134,47136,47138],{},[898,47135,1776],{},[1750,47137,1766],{},[1699,47139,47140,47142],{},[898,47141,1776],{},[1750,47143,3751],{},[902,47145,14016],{"encoding":904},[46271,47147,47149],{"id":47148},"giffenův-statek","Giffenův statek",[724,47151,47152,47153,47155,47156,47158,47159,2313],{},"Existují zboží, u nichž je křivka poptávky ",[38,47154,23261],{}," — tzv. ",[38,47157,47149],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[38,47160,47161],{},"podřadnému zboží",[46848,47163,47165],{"id":47164},"příklad-22","Příklad 2.2",[724,47167,47168,47171,47172,47190,47191,47213,47214,47232,47233,47251,47252,47275],{},[38,47169,47170],{},"Zadání a popis:"," Křivka ",[883,47173,47175],{"className":47174},[886],[888,47176,47177],{"xmlns":890},[892,47178,47179,47187],{},[895,47180,47181],{},[5535,47182,47183,47185],{},[898,47184,5541],{},[1742,47186,1744],{},[902,47188,47189],{"encoding":904},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[883,47192,47194],{"className":47193},[886],[888,47195,47196],{"xmlns":890},[892,47197,47198,47210],{},[895,47199,47200,47202,47204,47206,47208],{},[1750,47201,1753],{"stretchy":1752},[1742,47203,2607],{},[1750,47205,1917],{"separator":1916},[1742,47207,45167],{},[1750,47209,1763],{"stretchy":1752},[902,47211,47212],{"encoding":904},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[883,47215,47217],{"className":47216},[886],[888,47218,47219],{"xmlns":890},[892,47220,47221,47229],{},[895,47222,47223],{},[5535,47224,47225,47227],{},[898,47226,12471],{},[1742,47228,2607],{},[902,47230,47231],{"encoding":904},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[883,47234,47236],{"className":47235},[886],[888,47237,47238],{"xmlns":890},[892,47239,47240,47248],{},[895,47241,47242],{},[5535,47243,47244,47246],{},[898,47245,5541],{},[1742,47247,1872],{},[902,47249,47250],{"encoding":904},"D_2"," na širším trhu je konvexní klesající z bodu ",[883,47253,47255],{"className":47254},[886],[888,47256,47257],{"xmlns":890},[892,47258,47259,47272],{},[895,47260,47261,47263,47265,47267,47270],{},[1750,47262,5141],{"stretchy":1752},[1742,47264,2607],{},[1750,47266,1917],{"separator":1916},[1742,47268,47269],{},"21",[1750,47271,5158],{"stretchy":1752},[902,47273,47274],{"encoding":904},"[0, 21]"," centů.",[198,47277,47279],{"id":47278},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[724,47281,47282,47283,2366],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[883,47284,47286],{"className":47285},[886],[888,47287,47288],{"xmlns":890},[892,47289,47290,47294],{},[895,47291,47292],{},[898,47293,1666],{},[902,47295,1666],{"encoding":904},[883,47297,47299],{"className":47298},[886],[888,47300,47301],{"xmlns":890,"display":36989},[892,47302,47303,47334],{},[4577,47304,47305],{"width":36994},[4582,47306,47307,47309,47327,47329],{},[4585,47308],{"width":36999},[4585,47310,47311],{},[895,47312,47313,47315,47317,47319,47321,47323,47325],{},[898,47314,12471],{},[1750,47316,1766],{},[898,47318,1705],{},[1750,47320,1753],{"stretchy":1752},[898,47322,1666],{},[1750,47324,1763],{"stretchy":1752},[898,47326,2313],{"mathvariant":1747},[4585,47328],{"width":36999},[4585,47330,47331],{},[1969,47332,47333],{},"(2.5)",[902,47335,47336],{"encoding":904},"Q = E(Y). \\tag{2.5}",[724,47338,47339,47340,47343,47344,47347],{},"Funkce se nazývá ",[38,47341,47342],{},"Engelova",", její graf ",[38,47345,47346],{},"Engelova křivka",". Tvar závisí na typu zboží:",[120,47349,47350,47482],{},[123,47351,47352,10469,47355,47368,47369,47382,47383,47400,47401],{},[38,47353,47354],{},"Normální (superior) zboží",[883,47356,47358],{"className":47357},[886],[888,47359,47360],{"xmlns":890},[892,47361,47362,47366],{},[895,47363,47364],{},[898,47365,12471],{},[902,47367,12471],{"encoding":904}," roste s ",[883,47370,47372],{"className":47371},[886],[888,47373,47374],{"xmlns":890},[892,47375,47376,47380],{},[895,47377,47378],{},[898,47379,1666],{},[902,47381,1666],{"encoding":904},", nepřesáhne hodnotu ",[883,47384,47386],{"className":47385},[886],[888,47387,47388],{"xmlns":890},[892,47389,47390,47398],{},[895,47391,47392],{},[5535,47393,47394,47396],{},[898,47395,12471],{},[1742,47397,2607],{},[902,47399,47231],{"encoding":904},":\n",[120,47402,47403,47435],{},[123,47404,47405,47408,47409,47412,47413,2313],{},[38,47406,47407],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[38,47410,47411],{},"konkávní"," křivka, autonomní spotřeba ",[883,47414,47416],{"className":47415},[886],[888,47417,47418],{"xmlns":890},[892,47419,47420,47432],{},[895,47421,47422,47428,47430],{},[5535,47423,47424,47426],{},[898,47425,12471],{},[1742,47427,1744],{},[1750,47429,2604],{},[1742,47431,2607],{},[902,47433,47434],{"encoding":904},"Q_1 > 0",[123,47436,47437,47440,47441,47459,47460,47462,47463,1647,47480,2313],{},[38,47438,47439],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[883,47442,47444],{"className":47443},[886],[888,47445,47446],{"xmlns":890},[892,47447,47448,47456],{},[895,47449,47450],{},[5535,47451,47452,47454],{},[898,47453,1666],{},[1742,47455,1744],{},[902,47457,47458],{"encoding":904},"Y_1",", křivka je nejprve ",[38,47461,46587],{}," a od ",[883,47464,47466],{"className":47465},[886],[888,47467,47468],{"xmlns":890},[892,47469,47470,47478],{},[895,47471,47472],{},[5535,47473,47474,47476],{},[898,47475,1666],{},[1742,47477,1744],{},[902,47479,47458],{"encoding":904},[38,47481,47411],{},[123,47483,47484,47487,47488,47506],{},[38,47485,47486],{},"Podřadné (inferior) zboží"," — od hladiny ",[883,47489,47491],{"className":47490},[886],[888,47492,47493],{"xmlns":890},[892,47494,47495,47503],{},[895,47496,47497],{},[5535,47498,47499,47501],{},[898,47500,1666],{},[1742,47502,2607],{},[902,47504,47505],{"encoding":904},"Y_0"," množství s růstem důchodu klesá.",[724,47508,47509,47510,47513,47514,1783],{},"Mírou citlivosti je ",[614,47511,47512],{},"důchodová elasticita"," (viz ",[207,47515,13564],{"className":47516,"dataFsResolvedFilePath":848,"href":849},[210],[724,47518,47519],{},[614,47520,47521],{},"Obrázek 2.6: Tři panely Engelových křivek — (a) nezbytné, (b) luxusní, (c) podřadné zboží.",[46271,47523,47525],{"id":47524},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1785,47527,47528,47599,47642],{},[724,47529,47530,47532,47533,1647,47536,1647,47549,9375,47551,47564,47565,47568,47569,2313],{},[883,47531,5454],{}," Pozor — nezbytné ≠ podřadné\n",[38,47534,47535],{},"Nezbytné zboží:",[883,47537,47539],{"className":47538},[886],[888,47540,47541],{"xmlns":890},[892,47542,47543,47547],{},[895,47544,47545],{},[898,47546,12471],{},[902,47548,12471],{"encoding":904},[38,47550,16969],{},[883,47552,47554],{"className":47553},[886],[888,47555,47556],{"xmlns":890},[892,47557,47558,47562],{},[895,47559,47560],{},[898,47561,1666],{},[902,47563,1666],{"encoding":904},", ale ",[38,47566,47567],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[883,47570,47572],{"className":47571},[886],[888,47573,47574],{"xmlns":890},[892,47575,47576,47596],{},[895,47577,47578,47584,47586,47588,47590,47592,47594],{},[5535,47579,47580,47582],{},[898,47581,1705],{},[898,47583,1666],{},[1750,47585,16154],{},[1750,47587,1753],{"stretchy":1752},[1742,47589,2607],{},[1750,47591,1917],{"separator":1916},[1742,47593,1744],{},[1750,47595,1763],{"stretchy":1752},[902,47597,47598],{"encoding":904},"E_Y \\in (0, 1)",[724,47600,47601,1647,47604,1647,47617,47619,47620,2313],{},[38,47602,47603],{},"Podřadné zboží:",[883,47605,47607],{"className":47606},[886],[888,47608,47609],{"xmlns":890},[892,47610,47611,47615],{},[895,47612,47613],{},[898,47614,12471],{},[902,47616,12471],{"encoding":904},[38,47618,16989],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[883,47621,47623],{"className":47622},[886],[888,47624,47625],{"xmlns":890},[892,47626,47627,47639],{},[895,47628,47629,47635,47637],{},[5535,47630,47631,47633],{},[898,47632,1705],{},[898,47634,1666],{},[1750,47636,2624],{},[1742,47638,2607],{},[902,47640,47641],{"encoding":904},"E_Y \u003C 0",[724,47643,47644,47645,2313],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[38,47646,47647],{},"méně kusů, ne jen proporčně méně",[724,47649,47650,47653,47654,47657],{},[38,47651,47652],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[38,47655,47656],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[724,47659,47660],{},[4434,47661],{"alt":47662,"className":47663,"src":47664},"imek-engelovy-krivky-3typy",[210,4438],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[46848,47666,47668],{"id":47667},"české-příklady","České příklady",[16,47670,47671,47681],{},[19,47672,47673],{},[22,47674,47675,47678],{},[25,47676,47677],{},"Podřadné",[25,47679,47680],{},"Nahradí se za",[30,47682,47683,47691,47699,47707,47715,47723,47731,47739],{},[22,47684,47685,47688],{},[35,47686,47687],{},"Instantní polévky, ramen",[35,47689,47690],{},"Čerstvé jídlo, restaurace",[22,47692,47693,47696],{},[35,47694,47695],{},"MHD (autobus, tramvaj)",[35,47697,47698],{},"Vlastní auto, Uber, taxi",[22,47700,47701,47704],{},[35,47702,47703],{},"Mražené polotovary, pizza z mrazáku",[35,47705,47706],{},"Čerstvé suroviny, hotovky",[22,47708,47709,47712],{},[35,47710,47711],{},"Privátní značky supermarketů (K-Classic, Clever)",[35,47713,47714],{},"Značkové produkty",[22,47716,47717,47720],{},[35,47718,47719],{},"Paštika Májka, obyčejný měkký salám",[35,47721,47722],{},"Kvalitní uzeniny, šunka od kosti",[22,47724,47725,47728],{},[35,47726,47727],{},"Second hand oblečení",[35,47729,47730],{},"Nové oblečení, značky",[22,47732,47733,47736],{},[35,47734,47735],{},"Krabicové víno, nejlevnější pivo",[35,47737,47738],{},"Lahvové víno, řemeslná piva",[22,47740,47741,47744],{},[35,47742,47743],{},"Ojetá auta nižších tříd",[35,47745,47746],{},"Nová auta, prémiové značky",[1785,47748,47749],{},[724,47750,47751,47753,47754,47757],{},[883,47752,6004],{}," Test 50 milionů\nPředstav si, že vyhraješ 50 milionů. ",[38,47755,47756],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[724,47759,47760,47763,47764,2084,47767,47789,47790,2084,47793,47814,47815,47833,47834,47837],{},[38,47761,47762],{},"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 ",[38,47765,47766],{},"luxus",[883,47768,47770],{"className":47769},[886],[888,47771,47772],{"xmlns":890},[892,47773,47774,47786],{},[895,47775,47776,47782,47784],{},[5535,47777,47778,47780],{},[898,47779,1705],{},[898,47781,1666],{},[1750,47783,2604],{},[1742,47785,1744],{},[902,47787,47788],{"encoding":904},"E_Y > 1","), pro manažera s 200k platem ",[38,47791,47792],{},"podřadné",[883,47794,47796],{"className":47795},[886],[888,47797,47798],{"xmlns":890},[892,47799,47800,47812],{},[895,47801,47802,47808,47810],{},[5535,47803,47804,47806],{},[898,47805,1705],{},[898,47807,1666],{},[1750,47809,2624],{},[1742,47811,2607],{},[902,47813,47641],{"encoding":904},"). Proto je ",[883,47816,47818],{"className":47817},[886],[888,47819,47820],{"xmlns":890},[892,47821,47822,47830],{},[895,47823,47824],{},[5535,47825,47826,47828],{},[898,47827,1705],{},[898,47829,1666],{},[902,47831,47832],{"encoding":904},"E_Y"," vždy ",[38,47835,47836],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[724,47839,47840,47841,47843],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[38,47842,47149],{}," (viz níže) — tam poptávková křivka dokonce roste.",[198,47845,47847,47848,1763],{"id":47846},"posun-poptávky-shift-of-demand","Posun poptávky (",[614,47849,47850],{},"shift of demand",[724,47852,47853,47854,47872,47873,47890,47891,47904,47905,4321,47918,47940,47941,47958,47959,47985,47986,47989],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[883,47855,47857],{"className":47856},[886],[888,47858,47859],{"xmlns":890},[892,47860,47861,47869],{},[895,47862,47863],{},[5535,47864,47865,47867],{},[898,47866,1776],{},[1742,47868,2607],{},[902,47870,47871],{"encoding":904},"P_0"," odpovídá množství ",[883,47874,47876],{"className":47875},[886],[888,47877,47878],{"xmlns":890},[892,47879,47880,47888],{},[895,47881,47882],{},[5535,47883,47884,47886],{},[898,47885,12471],{},[1742,47887,2607],{},[902,47889,47231],{"encoding":904}," na křivce ",[883,47892,47894],{"className":47893},[886],[888,47895,47896],{"xmlns":890},[892,47897,47898,47902],{},[895,47899,47900],{},[898,47901,5541],{},[902,47903,5541],{"encoding":904},"; vzroste-li důchod z ",[883,47906,47908],{"className":47907},[886],[888,47909,47910],{"xmlns":890},[892,47911,47912,47916],{},[895,47913,47914],{},[898,47915,1666],{},[902,47917,1666],{"encoding":904},[883,47919,47921],{"className":47920},[886],[888,47922,47923],{"xmlns":890},[892,47924,47925,47937],{},[895,47926,47927,47933,47935],{},[5535,47928,47929,47931],{},[898,47930,1666],{},[1742,47932,1744],{},[1750,47934,2604],{},[898,47936,1666],{},[902,47938,47939],{"encoding":904},"Y_1 > Y",", pak stejné ceně ",[883,47942,47944],{"className":47943},[886],[888,47945,47946],{"xmlns":890},[892,47947,47948,47956],{},[895,47949,47950],{},[5535,47951,47952,47954],{},[898,47953,1776],{},[1742,47955,2607],{},[902,47957,47871],{"encoding":904}," odpovídá vyšší ",[883,47960,47962],{"className":47961},[886],[888,47963,47964],{"xmlns":890},[892,47965,47966,47982],{},[895,47967,47968,47974,47976],{},[5535,47969,47970,47972],{},[898,47971,12471],{},[1742,47973,1744],{},[1750,47975,2604],{},[5535,47977,47978,47980],{},[898,47979,12471],{},[1742,47981,2607],{},[902,47983,47984],{"encoding":904},"Q_1 > Q_0"," — křivka se ",[38,47987,47988],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[724,47991,47992],{},[4434,47993],{"alt":47994,"className":47995,"src":47996},"imek-posun-vs-pohyb-po-krivce",[210,4438],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[724,47998,47999],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[724,48001,48002],{},[614,48003,48004,48005,23611,48035,48056],{},"Obrázek 2.7: Posun poptávky — tři křivky ",[883,48006,48008],{"className":48007},[886],[888,48009,48010],{"xmlns":890},[892,48011,48012,48032],{},[895,48013,48014,48020,48022,48024,48026],{},[5535,48015,48016,48018],{},[898,48017,5541],{},[1742,48019,1872],{},[1750,48021,1917],{"separator":1916},[898,48023,5541],{},[1750,48025,1917],{"separator":1916},[5535,48027,48028,48030],{},[898,48029,5541],{},[1742,48031,1744],{},[902,48033,48034],{"encoding":904},"D_2, D, D_1",[883,48036,48038],{"className":48037},[886],[888,48039,48040],{"xmlns":890},[892,48041,48042,48054],{},[895,48043,48044,48046,48048,48050,48052],{},[1750,48045,1753],{"stretchy":1752},[898,48047,12471],{},[1750,48049,1917],{"separator":1916},[898,48051,1776],{},[1750,48053,1763],{"stretchy":1752},[902,48055,46614],{"encoding":904},", šipky naznačují posuny.",[46848,48058,48060],{"id":48059},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[724,48062,48063,48065,48066,48089,48090,48107,48108,48125,48126,2313],{},[38,48064,46856],{}," Poptávce ",[883,48067,48069],{"className":48068},[886],[888,48070,48071],{"xmlns":890},[892,48072,48073,48087],{},[895,48074,48075,48077,48079,48081,48083,48085],{},[898,48076,1776],{},[1750,48078,1766],{},[898,48080,5541],{},[1750,48082,1753],{"stretchy":1752},[898,48084,12471],{},[1750,48086,1763],{"stretchy":1752},[902,48088,14297],{"encoding":904}," odpovídá ceně ",[883,48091,48093],{"className":48092},[886],[888,48094,48095],{"xmlns":890},[892,48096,48097,48105],{},[895,48098,48099],{},[5535,48100,48101,48103],{},[898,48102,1776],{},[1742,48104,2607],{},[902,48106,47871],{"encoding":904}," množství ",[883,48109,48111],{"className":48110},[886],[888,48112,48113],{"xmlns":890},[892,48114,48115,48123],{},[895,48116,48117],{},[5535,48118,48119,48121],{},[898,48120,12471],{},[1742,48122,2607],{},[902,48124,47231],{"encoding":904},". Na kupujícího je uložena jednotková daň ",[883,48127,48129],{"className":48128},[886],[888,48130,48131],{"xmlns":890},[892,48132,48133,48137],{},[895,48134,48135],{},[898,48136,5326],{},[902,48138,5326],{"encoding":904},[724,48140,48141,48143,48144,48161,48162,48184],{},[38,48142,46888],{}," Kupující nakupuje množství ",[883,48145,48147],{"className":48146},[886],[888,48148,48149],{"xmlns":890},[892,48150,48151,48159],{},[895,48152,48153],{},[5535,48154,48155,48157],{},[898,48156,12471],{},[1742,48158,1744],{},[902,48160,37925],{"encoding":904},", které odpovídá ceně ",[883,48163,48165],{"className":48164},[886],[888,48166,48167],{"xmlns":890},[892,48168,48169,48181],{},[895,48170,48171,48177,48179],{},[5535,48172,48173,48175],{},[898,48174,1776],{},[1742,48176,2607],{},[1750,48178,1861],{},[898,48180,5326],{},[902,48182,48183],{"encoding":904},"P_0 + T"," na původní křivce. Nová poptávka je",[883,48186,48188],{"className":48187},[886],[888,48189,48190],{"xmlns":890,"display":36989},[892,48191,48192,48226],{},[895,48193,48194,48196,48198,48204,48206,48208,48210,48212,48214,48216,48218,48220,48222,48224],{},[898,48195,1776],{},[1750,48197,1766],{},[5535,48199,48200,48202],{},[898,48201,5541],{},[1742,48203,1744],{},[1750,48205,1753],{"stretchy":1752},[898,48207,12471],{},[1750,48209,1763],{"stretchy":1752},[1750,48211,1766],{},[898,48213,5541],{},[1750,48215,1753],{"stretchy":1752},[898,48217,12471],{},[1750,48219,1763],{"stretchy":1752},[1750,48221,1758],{},[898,48223,5326],{},[1750,48225,1917],{"separator":1916},[902,48227,48228],{"encoding":904},"P = D_1(Q) = D(Q) - T,",[724,48230,48231,48232,2313],{},"tj. dojde k ",[38,48233,48234],{},"posunu poptávky doleva",[724,48236,48237],{},[614,48238,48239,48240,48261,48262,1343,48279,1343,48292,48313,48314,2028,48331,2313],{},"Obrázek 2.8: Dvě klesající poptávkové přímky v ",[883,48241,48243],{"className":48242},[886],[888,48244,48245],{"xmlns":890},[892,48246,48247,48259],{},[895,48248,48249,48251,48253,48255,48257],{},[1750,48250,1753],{"stretchy":1752},[898,48252,12471],{},[1750,48254,1917],{"separator":1916},[898,48256,1776],{},[1750,48258,1763],{"stretchy":1752},[902,48260,46614],{"encoding":904},"; na svislé ose jsou vyznačeny ",[883,48263,48265],{"className":48264},[886],[888,48266,48267],{"xmlns":890},[892,48268,48269,48277],{},[895,48270,48271],{},[5535,48272,48273,48275],{},[898,48274,1776],{},[1742,48276,2607],{},[902,48278,47871],{"encoding":904},[883,48280,48282],{"className":48281},[886],[888,48283,48284],{"xmlns":890},[892,48285,48286,48290],{},[895,48287,48288],{},[898,48289,5326],{},[902,48291,5326],{"encoding":904},[883,48293,48295],{"className":48294},[886],[888,48296,48297],{"xmlns":890},[892,48298,48299,48311],{},[895,48300,48301,48307,48309],{},[5535,48302,48303,48305],{},[898,48304,1776],{},[1742,48306,2607],{},[1750,48308,1861],{},[898,48310,5326],{},[902,48312,48183],{"encoding":904},"; na vodorovné ",[883,48315,48317],{"className":48316},[886],[888,48318,48319],{"xmlns":890},[892,48320,48321,48329],{},[895,48322,48323],{},[5535,48324,48325,48327],{},[898,48326,12471],{},[1742,48328,1744],{},[902,48330,37925],{"encoding":904},[883,48332,48334],{"className":48333},[886],[888,48335,48336],{"xmlns":890},[892,48337,48338,48346],{},[895,48339,48340],{},[5535,48341,48342,48344],{},[898,48343,12471],{},[1742,48345,2607],{},[902,48347,47231],{"encoding":904},[198,48349,48351],{"id":48350},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[724,48353,48354],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[883,48356,48358],{"className":48357},[886],[888,48359,48360],{"xmlns":890,"display":36989},[892,48361,48362,48547],{},[4577,48363,48364],{"width":36994},[4582,48365,48366,48368,48540,48542],{},[4585,48367],{"width":36999},[4585,48369,48370],{},[4577,48371,48372,48456],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,48373,48374,48384],{},[4585,48375,48376],{},[3586,48377,48378],{"scriptlevel":2607,"displaystyle":1916},[5535,48379,48380,48382],{},[898,48381,12471],{},[1742,48383,1744],{},[4585,48385,48386],{},[3586,48387,48388],{"scriptlevel":2607,"displaystyle":1916},[895,48389,48390,48392,48394,48400,48402,48408,48410,48416,48418,48420,48426,48428,48434,48440,48442,48448,48454],{},[895,48391],{},[1750,48393,1766],{},[5535,48395,48396,48398],{},[898,48397,5541],{},[1742,48399,1744],{},[1750,48401,1753],{"stretchy":1752},[5535,48403,48404,48406],{},[898,48405,1776],{},[1742,48407,1744],{},[1750,48409,1917],{"separator":1916},[5535,48411,48412,48414],{},[898,48413,1776],{},[1742,48415,1872],{},[1750,48417,1763],{"stretchy":1752},[1750,48419,1766],{},[5535,48421,48422,48424],{},[898,48423,207],{},[1742,48425,1744],{},[1750,48427,1861],{},[5535,48429,48430,48432],{},[898,48431,2573],{},[1742,48433,1744],{},[5535,48435,48436,48438],{},[898,48437,1776],{},[1742,48439,1744],{},[1750,48441,1861],{},[5535,48443,48444,48446],{},[898,48445,9365],{},[1742,48447,1744],{},[5535,48449,48450,48452],{},[898,48451,1776],{},[1742,48453,1872],{},[1750,48455,1917],{"separator":1916},[4582,48457,48458,48468],{},[4585,48459,48460],{},[3586,48461,48462],{"scriptlevel":2607,"displaystyle":1916},[5535,48463,48464,48466],{},[898,48465,12471],{},[1742,48467,1872],{},[4585,48469,48470],{},[3586,48471,48472],{"scriptlevel":2607,"displaystyle":1916},[895,48473,48474,48476,48478,48484,48486,48492,48494,48500,48502,48504,48510,48512,48518,48524,48526,48532,48538],{},[895,48475],{},[1750,48477,1766],{},[5535,48479,48480,48482],{},[898,48481,5541],{},[1742,48483,1872],{},[1750,48485,1753],{"stretchy":1752},[5535,48487,48488,48490],{},[898,48489,1776],{},[1742,48491,1744],{},[1750,48493,1917],{"separator":1916},[5535,48495,48496,48498],{},[898,48497,1776],{},[1742,48499,1872],{},[1750,48501,1763],{"stretchy":1752},[1750,48503,1766],{},[5535,48505,48506,48508],{},[898,48507,207],{},[1742,48509,1872],{},[1750,48511,1861],{},[5535,48513,48514,48516],{},[898,48515,2573],{},[1742,48517,1872],{},[5535,48519,48520,48522],{},[898,48521,1776],{},[1742,48523,1744],{},[1750,48525,1861],{},[5535,48527,48528,48530],{},[898,48529,9365],{},[1742,48531,1872],{},[5535,48533,48534,48536],{},[898,48535,1776],{},[1742,48537,1872],{},[898,48539,2313],{"mathvariant":1747},[4585,48541],{"width":36999},[4585,48543,48544],{},[1969,48545,48546],{},"(2.6)",[902,48548,48549],{"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}",[46271,48551,48553],{"id":48552},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[120,48555,48556,48603,48650],{},[123,48557,48558,1343,48580,48602],{},[883,48559,48561],{"className":48560},[886],[888,48562,48563],{"xmlns":890},[892,48564,48565,48577],{},[895,48566,48567,48573,48575],{},[5535,48568,48569,48571],{},[898,48570,207],{},[1742,48572,1744],{},[1750,48574,2604],{},[1742,48576,2607],{},[902,48578,48579],{"encoding":904},"a_1 > 0",[883,48581,48583],{"className":48582},[886],[888,48584,48585],{"xmlns":890},[892,48586,48587,48599],{},[895,48588,48589,48595,48597],{},[5535,48590,48591,48593],{},[898,48592,207],{},[1742,48594,1872],{},[1750,48596,2604],{},[1742,48598,2607],{},[902,48600,48601],{"encoding":904},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[123,48604,48605,1343,48627,48649],{},[883,48606,48608],{"className":48607},[886],[888,48609,48610],{"xmlns":890},[892,48611,48612,48624],{},[895,48613,48614,48620,48622],{},[5535,48615,48616,48618],{},[898,48617,2573],{},[1742,48619,1744],{},[1750,48621,2624],{},[1742,48623,2607],{},[902,48625,48626],{"encoding":904},"b_1 \u003C 0",[883,48628,48630],{"className":48629},[886],[888,48631,48632],{"xmlns":890},[892,48633,48634,48646],{},[895,48635,48636,48642,48644],{},[5535,48637,48638,48640],{},[898,48639,9365],{},[1742,48641,1872],{},[1750,48643,2624],{},[1742,48645,2607],{},[902,48647,48648],{"encoding":904},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[123,48651,48652,48653,1343,48670,48688,48689],{},"zkřížené koeficienty ",[883,48654,48656],{"className":48655},[886],[888,48657,48658],{"xmlns":890},[892,48659,48660,48668],{},[895,48661,48662],{},[5535,48663,48664,48666],{},[898,48665,9365],{},[1742,48667,1744],{},[902,48669,38722],{"encoding":904},[883,48671,48673],{"className":48672},[886],[888,48674,48675],{"xmlns":890},[892,48676,48677,48685],{},[895,48678,48679],{},[5535,48680,48681,48683],{},[898,48682,2573],{},[1742,48684,1872],{},[902,48686,48687],{"encoding":904},"b_2"," určují povahu vztahu:\n",[120,48690,48691,48741],{},[123,48692,48693,48696,48697,1343,48719,1917],{},[38,48694,48695],{},"substituty"," (máslo vs. margarín): ",[883,48698,48700],{"className":48699},[886],[888,48701,48702],{"xmlns":890},[892,48703,48704,48716],{},[895,48705,48706,48712,48714],{},[5535,48707,48708,48710],{},[898,48709,9365],{},[1742,48711,1744],{},[1750,48713,2604],{},[1742,48715,2607],{},[902,48717,48718],{"encoding":904},"c_1 > 0",[883,48720,48722],{"className":48721},[886],[888,48723,48724],{"xmlns":890},[892,48725,48726,48738],{},[895,48727,48728,48734,48736],{},[5535,48729,48730,48732],{},[898,48731,2573],{},[1742,48733,1872],{},[1750,48735,2604],{},[1742,48737,2607],{},[902,48739,48740],{"encoding":904},"b_2 > 0",[123,48742,48743,48746,48747,1343,48769,2313],{},[38,48744,48745],{},"komplementy"," (auto vs. benzín): ",[883,48748,48750],{"className":48749},[886],[888,48751,48752],{"xmlns":890},[892,48753,48754,48766],{},[895,48755,48756,48762,48764],{},[5535,48757,48758,48760],{},[898,48759,9365],{},[1742,48761,1744],{},[1750,48763,2624],{},[1742,48765,2607],{},[902,48767,48768],{"encoding":904},"c_1 \u003C 0",[883,48770,48772],{"className":48771},[886],[888,48773,48774],{"xmlns":890},[892,48775,48776,48788],{},[895,48777,48778,48784,48786],{},[5535,48779,48780,48782],{},[898,48781,2573],{},[1742,48783,1872],{},[1750,48785,2624],{},[1742,48787,2607],{},[902,48789,48790],{"encoding":904},"b_2 \u003C 0",[724,48792,48793],{},"Schematicky:",[724,48795,48796,48799],{},[38,48797,48798],{},"Substituty",[883,48800,48802],{"className":48801},[886],[888,48803,48804],{"xmlns":890},[892,48805,48806,48945],{},[895,48807,48808,48814,48816,48831,48833,48853,48855,48875,48877,48879,48885,48887,48901,48903,48923,48925],{},[5535,48809,48810,48812],{},[898,48811,12471],{},[1742,48813,1744],{},[1750,48815,1766],{},[898,48817,48818],{},[48819,48820,48821,48829],"munder",{},[1750,48822,48823],{},[5535,48824,48825,48827],{},[898,48826,207],{},[1742,48828,1744],{},[1750,48830,1861],{"lspace":3814,"rspace":3814},[1750,48832,1861],{},[898,48834,48835],{},[48819,48836,48837,48851],{},[1750,48838,48839,48845],{},[5535,48840,48841,48843],{},[898,48842,2573],{},[1742,48844,1744],{},[5535,48846,48847,48849],{},[898,48848,1776],{},[1742,48850,1744],{},[1750,48852,1758],{"lspace":3814,"rspace":3814},[1750,48854,1861],{},[898,48856,48857],{},[48819,48858,48859,48873],{},[1750,48860,48861,48867],{},[5535,48862,48863,48865],{},[898,48864,9365],{},[1742,48866,1744],{},[5535,48868,48869,48871],{},[898,48870,1776],{},[1742,48872,1872],{},[1750,48874,1861],{"lspace":3814,"rspace":3814},[1750,48876,1917],{"separator":1916},[2125,48878],{"width":2127},[5535,48880,48881,48883],{},[898,48882,12471],{},[1742,48884,1872],{},[1750,48886,1766],{},[898,48888,48889],{},[48819,48890,48891,48899],{},[1750,48892,48893],{},[5535,48894,48895,48897],{},[898,48896,207],{},[1742,48898,1872],{},[1750,48900,1861],{"lspace":3814,"rspace":3814},[1750,48902,1861],{},[898,48904,48905],{},[48819,48906,48907,48921],{},[1750,48908,48909,48915],{},[5535,48910,48911,48913],{},[898,48912,2573],{},[1742,48914,1872],{},[5535,48916,48917,48919],{},[898,48918,1776],{},[1742,48920,1744],{},[1750,48922,1861],{"lspace":3814,"rspace":3814},[1750,48924,1861],{},[898,48926,48927],{},[48819,48928,48929,48943],{},[1750,48930,48931,48937],{},[5535,48932,48933,48935],{},[898,48934,9365],{},[1742,48936,1872],{},[5535,48938,48939,48941],{},[898,48940,1776],{},[1742,48942,1872],{},[1750,48944,1758],{"lspace":3814,"rspace":3814},[902,48946,48947],{"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}",[724,48949,48950,48953],{},[38,48951,48952],{},"Komplementy",[883,48954,48956],{"className":48955},[886],[888,48957,48958],{"xmlns":890},[892,48959,48960,49098],{},[895,48961,48962,48968,48970,48984,48986,49006,49008,49028,49030,49032,49038,49040,49054,49056,49076,49078],{},[5535,48963,48964,48966],{},[898,48965,12471],{},[1742,48967,1744],{},[1750,48969,1766],{},[898,48971,48972],{},[48819,48973,48974,48982],{},[1750,48975,48976],{},[5535,48977,48978,48980],{},[898,48979,207],{},[1742,48981,1744],{},[1750,48983,1861],{"lspace":3814,"rspace":3814},[1750,48985,1861],{},[898,48987,48988],{},[48819,48989,48990,49004],{},[1750,48991,48992,48998],{},[5535,48993,48994,48996],{},[898,48995,2573],{},[1742,48997,1744],{},[5535,48999,49000,49002],{},[898,49001,1776],{},[1742,49003,1744],{},[1750,49005,1758],{"lspace":3814,"rspace":3814},[1750,49007,1861],{},[898,49009,49010],{},[48819,49011,49012,49026],{},[1750,49013,49014,49020],{},[5535,49015,49016,49018],{},[898,49017,9365],{},[1742,49019,1744],{},[5535,49021,49022,49024],{},[898,49023,1776],{},[1742,49025,1872],{},[1750,49027,1758],{"lspace":3814,"rspace":3814},[1750,49029,1917],{"separator":1916},[2125,49031],{"width":2127},[5535,49033,49034,49036],{},[898,49035,12471],{},[1742,49037,1872],{},[1750,49039,1766],{},[898,49041,49042],{},[48819,49043,49044,49052],{},[1750,49045,49046],{},[5535,49047,49048,49050],{},[898,49049,207],{},[1742,49051,1872],{},[1750,49053,1861],{"lspace":3814,"rspace":3814},[1750,49055,1861],{},[898,49057,49058],{},[48819,49059,49060,49074],{},[1750,49061,49062,49068],{},[5535,49063,49064,49066],{},[898,49065,2573],{},[1742,49067,1872],{},[5535,49069,49070,49072],{},[898,49071,1776],{},[1742,49073,1744],{},[1750,49075,1758],{"lspace":3814,"rspace":3814},[1750,49077,1861],{},[898,49079,49080],{},[48819,49081,49082,49096],{},[1750,49083,49084,49090],{},[5535,49085,49086,49088],{},[898,49087,9365],{},[1742,49089,1872],{},[5535,49091,49092,49094],{},[898,49093,1776],{},[1742,49095,1872],{},[1750,49097,1758],{"lspace":3814,"rspace":3814},[902,49099,49100],{"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}",[45893,49102],{},[115,49104,22731],{"id":45702},[1785,49106,49107],{},[724,49108,49109,49111,49112,45917,49125,45931,49138,49141,49142,9375,49166,49184],{},[883,49110,1791],{}," TL;DR\nNabídka vyjadřuje závislost nabízeného množství ",[883,49113,49115],{"className":49114},[886],[888,49116,49117],{"xmlns":890},[892,49118,49119,49123],{},[895,49120,49121],{},[898,49122,12471],{},[902,49124,12471],{"encoding":904},[883,49126,49128],{"className":49127},[886],[888,49129,49130],{"xmlns":890},[892,49131,49132,49136],{},[895,49133,49134],{},[898,49135,1776],{},[902,49137,1776],{"encoding":904},[38,49139,49140],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[883,49143,49145],{"className":49144},[886],[888,49146,49147],{"xmlns":890},[892,49148,49149,49163],{},[895,49150,49151,49153,49155,49157,49159,49161],{},[898,49152,1776],{},[1750,49154,1766],{},[898,49156,9365],{},[898,49158,12471],{},[1750,49160,1861],{},[898,49162,3429],{},[902,49164,49165],{"encoding":904},"P = cQ + d",[883,49167,49169],{"className":49168},[886],[888,49170,49171],{"xmlns":890},[892,49172,49173,49181],{},[895,49174,49175,49177,49179],{},[898,49176,9365],{},[1750,49178,2604],{},[1742,49180,2607],{},[902,49182,49183],{"encoding":904},"c > 0"," je standardní aproximací.",[198,49186,45987],{"id":49187},"obecný-vícefaktorový-model-1",[724,49189,49190,2084,49193,49196,49197,49210,49211,45819,49224,45833,49237,49250,49251,49265,49266,45862,49279,49292],{},[38,49191,49192],{},"Nabízené množství",[614,49194,49195],{},"quantity supplied",") závisí na ceně ",[883,49198,49200],{"className":49199},[886],[888,49201,49202],{"xmlns":890},[892,49203,49204,49208],{},[895,49205,49206],{},[898,49207,1776],{},[902,49209,1776],{"encoding":904},", cenách výrobních faktorů (práce ",[883,49212,49214],{"className":49213},[886],[888,49215,49216],{"xmlns":890},[892,49217,49218,49222],{},[895,49219,49220],{},[898,49221,2046],{},[902,49223,2046],{"encoding":904},[883,49225,49227],{"className":49226},[886],[888,49228,49229],{"xmlns":890},[892,49230,49231,49235],{},[895,49232,49233],{},[898,49234,19435],{},[902,49236,19435],{"encoding":904},[883,49238,49240],{"className":49239},[886],[888,49241,49242],{"xmlns":890},[892,49243,49244,49248],{},[895,49245,49246],{},[898,49247,1705],{},[902,49249,1705],{"encoding":904},"), očekávání ",[883,49252,49254],{"className":49253},[886],[888,49255,49256],{"xmlns":890},[892,49257,49258,49263],{},[895,49259,49260],{},[898,49261,49262],{},"V",[902,49264,49262],{"encoding":904},", počtu výrobců ",[883,49267,49269],{"className":49268},[886],[888,49270,49271],{"xmlns":890},[892,49272,49273,49277],{},[895,49274,49275],{},[898,49276,45859],{},[902,49278,45859],{"encoding":904},[883,49280,49282],{"className":49281},[886],[888,49283,49284],{"xmlns":890},[892,49285,49286,49290],{},[895,49287,49288],{},[898,49289,45874],{},[902,49291,45874],{"encoding":904}," a dalších:",[883,49294,49296],{"className":49295},[886],[888,49297,49298],{"xmlns":890,"display":36989},[892,49299,49300,49359],{},[4577,49301,49302],{"width":36994},[4582,49303,49304,49306,49352,49354],{},[4585,49305],{"width":36999},[4585,49307,49308],{},[895,49309,49310,49312,49314,49316,49318,49320,49322,49324,49326,49328,49330,49332,49334,49336,49338,49340,49342,49344,49346,49348,49350],{},[898,49311,12471],{},[1750,49313,1766],{},[898,49315,1779],{},[1750,49317,1753],{"stretchy":1752},[898,49319,1776],{},[1750,49321,1917],{"separator":1916},[898,49323,2046],{},[1750,49325,1917],{"separator":1916},[898,49327,19435],{},[1750,49329,1917],{"separator":1916},[898,49331,1705],{},[1750,49333,1917],{"separator":1916},[898,49335,49262],{},[1750,49337,1917],{"separator":1916},[898,49339,45859],{},[1750,49341,1917],{"separator":1916},[898,49343,45874],{},[1750,49345,1917],{"separator":1916},[1750,49347,19282],{},[1750,49349,1763],{"stretchy":1752},[898,49351,2313],{"mathvariant":1747},[4585,49353],{"width":36999},[4585,49355,49356],{},[1969,49357,49358],{},"(2.7)",[902,49360,49361],{"encoding":904},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[724,49363,47339,49364,2084,49367,49370],{},[38,49365,49366],{},"funkce nabídky",[614,49368,49369],{},"supply function",") v širším slova smyslu.",[198,49372,49374],{"id":49373},"jednofaktorový-model","Jednofaktorový model",[724,49376,49377],{},"V nejpřirozenějším jednofaktorovém modelu",[883,49379,49381],{"className":49380},[886],[888,49382,49383],{"xmlns":890,"display":36989},[892,49384,49385,49436],{},[4577,49386,49387],{"width":36994},[4582,49388,49389,49391,49429,49431],{},[4585,49390],{"width":36999},[4585,49392,49393],{},[895,49394,49395,49397,49399,49401,49403,49405,49407,49409,49411,49413,49415,49417,49419,49421,49423,49425,49427],{},[898,49396,12471],{},[1750,49398,1766],{},[898,49400,1779],{},[1750,49402,1753],{"stretchy":1752},[898,49404,1776],{},[1750,49406,1763],{"stretchy":1752},[1750,49408,1917],{"separator":1916},[2125,49410],{"width":2127},[1969,49412,46340],{},[2125,49414],{"width":2127},[898,49416,1776],{},[1750,49418,1766],{},[898,49420,1779],{},[1750,49422,1753],{"stretchy":1752},[898,49424,12471],{},[1750,49426,1763],{"stretchy":1752},[898,49428,2313],{"mathvariant":1747},[4585,49430],{"width":36999},[4585,49432,49433],{},[1969,49434,49435],{},"(2.8)",[902,49437,49438],{"encoding":904},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[724,49440,49441,49442,2084,49445,1783],{},"Graf je ",[38,49443,49444],{},"křivka nabídky",[614,49446,49447],{},"supply curve",[46271,49449,49451],{"id":49450},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[1785,49453,49454],{},[724,49455,49456],{},[38,49457,46386,49458,49471,49472,46441],{},[883,49459,49461],{"className":49460},[886],[888,49462,49463],{"xmlns":890},[892,49464,49465,49469],{},[895,49466,49467],{},[898,49468,1776],{},[902,49470,1776],{"encoding":904},", pak nabízené množství ",[883,49473,49475],{"className":49474},[886],[888,49476,49477],{"xmlns":890},[892,49478,49479,49483],{},[895,49480,49481],{},[898,49482,12471],{},[902,49484,12471],{"encoding":904},[724,49486,49487,49488,49513,49514,49544,49545,49562],{},"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 ",[883,49489,49491],{"className":49490},[886],[888,49492,49493],{"xmlns":890},[892,49494,49495,49511],{},[895,49496,49497,49499,49501,49503,49509],{},[1750,49498,5141],{"stretchy":1752},[1742,49500,2607],{},[1750,49502,1917],{"separator":1916},[5535,49504,49505,49507],{},[898,49506,1776],{},[1742,49508,2607],{},[1750,49510,5158],{"stretchy":1752},[902,49512,46526],{"encoding":904}," na svislé ose (případně z ",[883,49515,49517],{"className":49516},[886],[888,49518,49519],{"xmlns":890},[892,49520,49521,49541],{},[895,49522,49523,49525,49531,49533,49539],{},[1750,49524,5141],{"stretchy":1752},[5535,49526,49527,49529],{},[898,49528,12471],{},[1742,49530,1744],{},[1750,49532,1917],{"separator":1916},[5535,49534,49535,49537],{},[898,49536,1776],{},[1742,49538,1744],{},[1750,49540,5158],{"stretchy":1752},[902,49542,49543],{"encoding":904},"[Q_1, P_1]","), kde ",[883,49546,49548],{"className":49547},[886],[888,49549,49550],{"xmlns":890},[892,49551,49552,49560],{},[895,49553,49554],{},[5535,49555,49556,49558],{},[898,49557,1776],{},[1742,49559,2607],{},[902,49561,47871],{"encoding":904}," je minimální cena, při které je výrobce ochoten vyrábět.",[724,49564,49565],{},[614,49566,49567,49568,13388,49581,2313],{},"Obrázek 2.9: Typická rostoucí křivka nabídky ",[883,49569,49571],{"className":49570},[886],[888,49572,49573],{"xmlns":890},[892,49574,49575,49579],{},[895,49576,49577],{},[898,49578,1779],{},[902,49580,1779],{"encoding":904},[883,49582,49584],{"className":49583},[886],[888,49585,49586],{"xmlns":890},[892,49587,49588,49600],{},[895,49589,49590,49592,49594,49596,49598],{},[1750,49591,1753],{"stretchy":1752},[898,49593,12471],{},[1750,49595,1917],{"separator":1916},[898,49597,1776],{},[1750,49599,1763],{"stretchy":1752},[902,49601,46614],{"encoding":904},[46271,49603,49605],{"id":49604},"lineární-model-nabídky","Lineární model nabídky",[883,49607,49609],{"className":49608},[886],[888,49610,49611],{"xmlns":890,"display":36989},[892,49612,49613,49652],{},[4577,49614,49615],{"width":36994},[4582,49616,49617,49619,49645,49647],{},[4585,49618],{"width":36999},[4585,49620,49621],{},[895,49622,49623,49625,49627,49629,49631,49633,49635,49637,49639,49641,49643],{},[898,49624,1776],{},[1750,49626,1766],{},[898,49628,9365],{},[898,49630,12471],{},[1750,49632,1861],{},[898,49634,3429],{},[1750,49636,1917],{"separator":1916},[2125,49638],{"width":2127},[898,49640,9365],{},[1750,49642,2604],{},[1742,49644,22073],{},[4585,49646],{"width":36999},[4585,49648,49649],{},[1969,49650,49651],{},"(2.9)",[902,49653,49654],{"encoding":904},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[724,49656,49657,49658,49694,49695,49708],{},"Alternativně ",[883,49659,49661],{"className":49660},[886],[888,49662,49663],{"xmlns":890},[892,49664,49665,49691],{},[895,49666,49667,49669,49671,49679,49681,49683],{},[898,49668,12471],{},[1750,49670,1766],{},[3586,49672,49673],{"scriptlevel":2607,"displaystyle":1752},[3423,49674,49675,49677],{},[1742,49676,1744],{},[898,49678,9365],{},[898,49680,1776],{},[1750,49682,1758],{},[3586,49684,49685],{"scriptlevel":2607,"displaystyle":1752},[3423,49686,49687,49689],{},[898,49688,3429],{},[898,49690,9365],{},[902,49692,49693],{"encoding":904},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[883,49696,49698],{"className":49697},[886],[888,49699,49700],{"xmlns":890},[892,49701,49702,49706],{},[895,49703,49704],{},[898,49705,1776],{},[902,49707,1776],{"encoding":904}," zůstává, znaménko absolutního členu se mění.",[46848,49710,49712],{"id":49711},"příklad-25","Příklad 2.5",[724,49714,49715,49717,49718,2313],{},[38,49716,46856],{}," Lineární nabídka ",[883,49719,49721],{"className":49720},[886],[888,49722,49723],{"xmlns":890},[892,49724,49725,49739],{},[895,49726,49727,49729,49731,49733,49735,49737],{},[898,49728,1776],{},[1750,49730,1766],{},[1742,49732,4268],{},[898,49734,12471],{},[1750,49736,1861],{},[1742,49738,6419],{},[902,49740,49741],{"encoding":904},"P = 0{,}5Q + 25",[724,49743,49744,49746,49747,2313],{},[38,49745,46888],{}," Alternativní tvar ",[883,49748,49750],{"className":49749},[886],[888,49751,49752],{"xmlns":890},[892,49753,49754,49768],{},[895,49755,49756,49758,49760,49762,49764,49766],{},[898,49757,12471],{},[1750,49759,1766],{},[1742,49761,1872],{},[898,49763,1776],{},[1750,49765,1758],{},[1742,49767,3936],{},[902,49769,49770],{"encoding":904},"Q = 2P - 50",[16,49772,49773,49798],{},[19,49774,49775],{},[22,49776,49777,49792,49794,49796],{},[25,49778,49779],{},[883,49780,49782],{"className":49781},[886],[888,49783,49784],{"xmlns":890},[892,49785,49786,49790],{},[895,49787,49788],{},[898,49789,1776],{},[902,49791,1776],{"encoding":904},[25,49793,46942],{},[25,49795,6442],{},[25,49797,14865],{},[30,49799,49800],{},[22,49801,49802,49817,49819,49821],{},[35,49803,49804],{},[883,49805,49807],{"className":49806},[886],[888,49808,49809],{"xmlns":890},[892,49810,49811,49815],{},[895,49812,49813],{},[898,49814,12471],{},[902,49816,12471],{"encoding":904},[35,49818,3079],{},[35,49820,6465],{},[35,49822,46942],{},[198,49824,49826,49827,1763],{"id":49825},"posun-nabídky-shift-of-supply","Posun nabídky (",[614,49828,49829],{},"shift of supply",[724,49831,49832,49833,49836,49837,49854,49855,49880,49881,2313],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[38,49834,49835],{},"doprava",": při stejné ceně ",[883,49838,49840],{"className":49839},[886],[888,49841,49842],{"xmlns":890},[892,49843,49844,49852],{},[895,49845,49846],{},[5535,49847,49848,49850],{},[898,49849,1776],{},[1742,49851,2607],{},[902,49853,47871],{"encoding":904}," vyrobí výrobce větší ",[883,49856,49858],{"className":49857},[886],[888,49859,49860],{"xmlns":890},[892,49861,49862,49878],{},[895,49863,49864,49870,49872],{},[5535,49865,49866,49868],{},[898,49867,12471],{},[1742,49869,1744],{},[1750,49871,2604],{},[5535,49873,49874,49876],{},[898,49875,12471],{},[1742,49877,2607],{},[902,49879,47984],{"encoding":904},"); zdražení vstupů posune křivku ",[38,49882,49883],{},"doleva",[724,49885,49886],{},[614,49887,49888,49889,49902,49903,49921,49922,49940,49941,2313],{},"Obrázek 2.11: Původní ",[883,49890,49892],{"className":49891},[886],[888,49893,49894],{"xmlns":890},[892,49895,49896,49900],{},[895,49897,49898],{},[898,49899,1779],{},[902,49901,1779],{"encoding":904},", posunuté ",[883,49904,49906],{"className":49905},[886],[888,49907,49908],{"xmlns":890},[892,49909,49910,49918],{},[895,49911,49912],{},[5535,49913,49914,49916],{},[898,49915,1779],{},[1742,49917,1744],{},[902,49919,49920],{"encoding":904},"S_1"," (doprava) a ",[883,49923,49925],{"className":49924},[886],[888,49926,49927],{"xmlns":890},[892,49928,49929,49937],{},[895,49930,49931],{},[5535,49932,49933,49935],{},[898,49934,1779],{},[1742,49936,1872],{},[902,49938,49939],{"encoding":904},"S_2"," (doleva) v ",[883,49942,49944],{"className":49943},[886],[888,49945,49946],{"xmlns":890},[892,49947,49948,49960],{},[895,49949,49950,49952,49954,49956,49958],{},[1750,49951,1753],{"stretchy":1752},[898,49953,12471],{},[1750,49955,1917],{"separator":1916},[898,49957,1776],{},[1750,49959,1763],{"stretchy":1752},[902,49961,46614],{"encoding":904},[46848,49963,49965],{"id":49964},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[724,49967,49968,49970,49971,49995,49996,2313],{},[38,49969,46856],{}," Nabídka ",[883,49972,49974],{"className":49973},[886],[888,49975,49976],{"xmlns":890},[892,49977,49978,49992],{},[895,49979,49980,49982,49984,49986,49988,49990],{},[898,49981,1776],{},[1750,49983,1766],{},[898,49985,1779],{},[1750,49987,1753],{"stretchy":1752},[898,49989,12471],{},[1750,49991,1763],{"stretchy":1752},[902,49993,49994],{"encoding":904},"P = S(Q)","; na výrobce je uložena jednotková daň ",[883,49997,49999],{"className":49998},[886],[888,50000,50001],{"xmlns":890},[892,50002,50003,50007],{},[895,50004,50005],{},[898,50006,5326],{},[902,50008,5326],{"encoding":904},[724,50010,50011,50013,50014,50027,50028,50046,50047,50075],{},[38,50012,46888],{}," Spotřebitel zaplatí ",[883,50015,50017],{"className":50016},[886],[888,50018,50019],{"xmlns":890},[892,50020,50021,50025],{},[895,50022,50023],{},[898,50024,1776],{},[902,50026,1776],{"encoding":904},", výrobce obdrží ",[883,50029,50031],{"className":50030},[886],[888,50032,50033],{"xmlns":890},[892,50034,50035,50043],{},[895,50036,50037,50039,50041],{},[898,50038,1776],{},[1750,50040,1758],{},[898,50042,5326],{},[902,50044,50045],{"encoding":904},"P - T",". Z podmínky ",[883,50048,50050],{"className":50049},[886],[888,50051,50052],{"xmlns":890},[892,50053,50054,50072],{},[895,50055,50056,50058,50060,50062,50064,50066,50068,50070],{},[898,50057,1776],{},[1750,50059,1758],{},[898,50061,5326],{},[1750,50063,1766],{},[898,50065,1779],{},[1750,50067,1753],{"stretchy":1752},[898,50069,12471],{},[1750,50071,1763],{"stretchy":1752},[902,50073,50074],{"encoding":904},"P - T = S(Q)"," plyne",[883,50077,50079],{"className":50078},[886],[888,50080,50081],{"xmlns":890,"display":36989},[892,50082,50083,50117],{},[895,50084,50085,50087,50089,50095,50097,50099,50101,50103,50105,50107,50109,50111,50113,50115],{},[898,50086,1776],{},[1750,50088,1766],{},[5535,50090,50091,50093],{},[898,50092,1779],{},[1742,50094,1744],{},[1750,50096,1753],{"stretchy":1752},[898,50098,12471],{},[1750,50100,1763],{"stretchy":1752},[1750,50102,1766],{},[898,50104,1779],{},[1750,50106,1753],{"stretchy":1752},[898,50108,12471],{},[1750,50110,1763],{"stretchy":1752},[1750,50112,1861],{},[898,50114,5326],{},[898,50116,2313],{"mathvariant":1747},[902,50118,50119],{"encoding":904},"P = S_1(Q) = S(Q) + T.",[724,50121,50122,50123,50136,50137,1647,50150,50153,50154,2028,50174,2433,50192,2313],{},"Křivka ",[883,50124,50126],{"className":50125},[886],[888,50127,50128],{"xmlns":890},[892,50129,50130,50134],{},[895,50131,50132],{},[898,50133,1779],{},[902,50135,1779],{"encoding":904}," se tedy posune o ",[883,50138,50140],{"className":50139},[886],[888,50141,50142],{"xmlns":890},[892,50143,50144,50148],{},[895,50145,50146],{},[898,50147,5326],{},[902,50149,5326],{"encoding":904},[38,50151,50152],{},"svisle nahoru"," (tj. doleva). Např. pro ",[883,50155,50157],{"className":50156},[886],[888,50158,50159],{"xmlns":890},[892,50160,50161,50171],{},[895,50162,50163,50165,50167,50169],{},[898,50164,1776],{},[1750,50166,1766],{},[1742,50168,1872],{},[898,50170,12471],{},[902,50172,50173],{"encoding":904},"P = 2Q",[883,50175,50177],{"className":50176},[886],[888,50178,50179],{"xmlns":890},[892,50180,50181,50189],{},[895,50182,50183,50185,50187],{},[898,50184,5326],{},[1750,50186,1766],{},[1742,50188,3219],{},[902,50190,50191],{"encoding":904},"T = 6",[883,50193,50195],{"className":50194},[886],[888,50196,50197],{"xmlns":890},[892,50198,50199,50221],{},[895,50200,50201,50207,50209,50211,50213,50215,50217,50219],{},[5535,50202,50203,50205],{},[898,50204,1779],{},[1742,50206,1744],{},[1750,50208,2366],{},[898,50210,1776],{},[1750,50212,1766],{},[1742,50214,1872],{},[898,50216,12471],{},[1750,50218,1861],{},[1742,50220,3219],{},[902,50222,50223],{"encoding":904},"S_1: P = 2Q + 6",[724,50225,50226],{},[614,50227,50228,50229,50242],{},"Obrázek 2.12: Posun nabídky o ",[883,50230,50232],{"className":50231},[886],[888,50233,50234],{"xmlns":890},[892,50235,50236,50240],{},[895,50237,50238],{},[898,50239,5326],{},[902,50241,5326],{"encoding":904}," svisle nahoru.",[45893,50244],{},[115,50246,50248],{"id":50247},"tržní-rovnováha","Tržní rovnováha",[1785,50250,50251],{},[724,50252,50253,50255,50256,1647,50259,50291,50292,1343,50315,50338,50339,50342,50343,50356],{},[883,50254,1791],{}," TL;DR\nV ",[38,50257,50258],{},"rovnovážném bodě",[883,50260,50262],{"className":50261},[886],[888,50263,50264],{"xmlns":890},[892,50265,50266,50288],{},[895,50267,50268,50270,50272,50278,50280,50286],{},[898,50269,1705],{},[1750,50271,5141],{"stretchy":1752},[1699,50273,50274,50276],{},[898,50275,12471],{},[898,50277,1705],{},[1750,50279,1917],{"separator":1916},[1699,50281,50282,50284],{},[898,50283,1776],{},[898,50285,1705],{},[1750,50287,5158],{"stretchy":1752},[902,50289,50290],{"encoding":904},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[883,50293,50295],{"className":50294},[886],[888,50296,50297],{"xmlns":890},[892,50298,50299,50313],{},[895,50300,50301,50303,50305,50307,50309,50311],{},[898,50302,1776],{},[1750,50304,1766],{},[898,50306,5541],{},[1750,50308,1753],{"stretchy":1752},[898,50310,12471],{},[1750,50312,1763],{"stretchy":1752},[902,50314,14297],{"encoding":904},[883,50316,50318],{"className":50317},[886],[888,50319,50320],{"xmlns":890},[892,50321,50322,50336],{},[895,50323,50324,50326,50328,50330,50332,50334],{},[898,50325,1776],{},[1750,50327,1766],{},[898,50329,1779],{},[1750,50331,1753],{"stretchy":1752},[898,50333,12471],{},[1750,50335,1763],{"stretchy":1752},[902,50337,49994],{"encoding":904},". Čtyři ",[38,50340,50341],{},"pravidla komparativní statiky"," popisují, jak se ",[883,50344,50346],{"className":50345},[886],[888,50347,50348],{"xmlns":890},[892,50349,50350,50354],{},[895,50351,50352],{},[898,50353,1705],{},[902,50355,1705],{"encoding":904}," posune při změně poptávky nebo nabídky.",[198,50358,50360],{"id":50359},"definice","Definice",[724,50362,50363,2084,50365,50368,50369,1647,50372,50390,50391,50422,50423,2084,50426,1783],{},[38,50364,50248],{},[614,50366,50367],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[38,50370,50371],{},"rovnovážné ceně",[883,50373,50375],{"className":50374},[886],[888,50376,50377],{"xmlns":890},[892,50378,50379,50387],{},[895,50380,50381],{},[1699,50382,50383,50385],{},[898,50384,1776],{},[898,50386,1705],{},[902,50388,50389],{"encoding":904},"P^E"," není přebytek ani nedostatek zboží. Bod ",[883,50392,50394],{"className":50393},[886],[888,50395,50396],{"xmlns":890},[892,50397,50398,50420],{},[895,50399,50400,50402,50404,50410,50412,50418],{},[898,50401,1705],{},[1750,50403,5141],{"stretchy":1752},[1699,50405,50406,50408],{},[898,50407,12471],{},[898,50409,1705],{},[1750,50411,1917],{"separator":1916},[1699,50413,50414,50416],{},[898,50415,1776],{},[898,50417,1705],{},[1750,50419,5158],{"stretchy":1752},[902,50421,50290],{"encoding":904}," se nazývá ",[38,50424,50425],{},"rovnovážný bod",[614,50427,50428],{},"equilibrium point",[724,50430,50431,50432,1343,50455,2313],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[883,50433,50435],{"className":50434},[886],[888,50436,50437],{"xmlns":890},[892,50438,50439,50453],{},[895,50440,50441,50443,50445,50447,50449,50451],{},[898,50442,1776],{},[1750,50444,1766],{},[898,50446,5541],{},[1750,50448,1753],{"stretchy":1752},[898,50450,12471],{},[1750,50452,1763],{"stretchy":1752},[902,50454,14297],{"encoding":904},[883,50456,50458],{"className":50457},[886],[888,50459,50460],{"xmlns":890},[892,50461,50462,50476],{},[895,50463,50464,50466,50468,50470,50472,50474],{},[898,50465,1776],{},[1750,50467,1766],{},[898,50469,1779],{},[1750,50471,1753],{"stretchy":1752},[898,50473,12471],{},[1750,50475,1763],{"stretchy":1752},[902,50477,49994],{"encoding":904},[724,50479,50480],{},[4434,50481],{"alt":50482,"className":50483,"src":50484},"imek-poptavka-nabidka-rovnovaha",[210,4438],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[724,50486,50487],{},[614,50488,50489,50490,50503,50504,23611,50517,50538,50539,2313],{},"Obrázek 2.13: Klesající ",[883,50491,50493],{"className":50492},[886],[888,50494,50495],{"xmlns":890},[892,50496,50497,50501],{},[895,50498,50499],{},[898,50500,5541],{},[902,50502,5541],{"encoding":904}," a rostoucí ",[883,50505,50507],{"className":50506},[886],[888,50508,50509],{"xmlns":890},[892,50510,50511,50515],{},[895,50512,50513],{},[898,50514,1779],{},[902,50516,1779],{"encoding":904},[883,50518,50520],{"className":50519},[886],[888,50521,50522],{"xmlns":890},[892,50523,50524,50536],{},[895,50525,50526,50528,50530,50532,50534],{},[1750,50527,1753],{"stretchy":1752},[898,50529,12471],{},[1750,50531,1917],{"separator":1916},[898,50533,1776],{},[1750,50535,1763],{"stretchy":1752},[902,50537,46614],{"encoding":904}," protínající se v ",[883,50540,50542],{"className":50541},[886],[888,50543,50544],{"xmlns":890},[892,50545,50546,50568],{},[895,50547,50548,50550,50552,50558,50560,50566],{},[898,50549,1705],{},[1750,50551,5141],{"stretchy":1752},[1699,50553,50554,50556],{},[898,50555,12471],{},[898,50557,1705],{},[1750,50559,1917],{"separator":1916},[1699,50561,50562,50564],{},[898,50563,1776],{},[898,50565,1705],{},[1750,50567,5158],{"stretchy":1752},[902,50569,50290],{"encoding":904},[198,50571,50573],{"id":50572},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[724,50575,50576,50578,50579,50613,50614,2313],{},[38,50577,46856],{}," Poptávka ",[883,50580,50582],{"className":50581},[886],[888,50583,50584],{"xmlns":890},[892,50585,50586,50610],{},[895,50587,50588,50590,50592,50594,50600,50602,50604,50606,50608],{},[898,50589,1776],{},[1750,50591,1766],{},[1750,50593,1758],{},[1699,50595,50596,50598],{},[898,50597,12471],{},[1742,50599,1872],{},[1750,50601,1758],{},[1742,50603,3079],{},[898,50605,12471],{},[1750,50607,1861],{},[1742,50609,4236],{},[902,50611,50612],{"encoding":904},"P = -Q^2 - 10Q + 150",", nabídka ",[883,50615,50617],{"className":50616},[886],[888,50618,50619],{"xmlns":890},[892,50620,50621,50643],{},[895,50622,50623,50625,50627,50633,50635,50637,50639,50641],{},[898,50624,1776],{},[1750,50626,1766],{},[1699,50628,50629,50631],{},[898,50630,12471],{},[1742,50632,1872],{},[1750,50634,1861],{},[1742,50636,6789],{},[898,50638,12471],{},[1750,50640,1861],{},[1742,50642,41469],{},[902,50644,50645],{"encoding":904},"P = Q^2 + 14Q + 22",[724,50647,50648,50650],{},[38,50649,46888],{}," Z rovnosti",[883,50652,50654],{"className":50653},[886],[888,50655,50656],{"xmlns":890,"display":36989},[892,50657,50658,50696],{},[895,50659,50660,50662,50668,50670,50672,50674,50676,50678,50680,50686,50688,50690,50692,50694],{},[1750,50661,1758],{},[1699,50663,50664,50666],{},[898,50665,12471],{},[1742,50667,1872],{},[1750,50669,1758],{},[1742,50671,3079],{},[898,50673,12471],{},[1750,50675,1861],{},[1742,50677,4236],{},[1750,50679,1766],{},[1699,50681,50682,50684],{},[898,50683,12471],{},[1742,50685,1872],{},[1750,50687,1861],{},[1742,50689,6789],{},[898,50691,12471],{},[1750,50693,1861],{},[1742,50695,41469],{},[902,50697,50698],{"encoding":904},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[724,50700,50701,50702,50737,50738,50771,50772,50789,50790,50803,50804,1343,50826,50863,50864,2313],{},"dostaneme ",[883,50703,50705],{"className":50704},[886],[888,50706,50707],{"xmlns":890},[892,50708,50709,50734],{},[895,50710,50711,50713,50719,50721,50724,50726,50728,50730,50732],{},[1742,50712,1872],{},[1699,50714,50715,50717],{},[898,50716,12471],{},[1742,50718,1872],{},[1750,50720,1861],{},[1742,50722,50723],{},"24",[898,50725,12471],{},[1750,50727,1758],{},[1742,50729,15270],{},[1750,50731,1766],{},[1742,50733,2607],{},[902,50735,50736],{"encoding":904},"2Q^2 + 24Q - 128 = 0",", resp. ",[883,50739,50741],{"className":50740},[886],[888,50742,50743],{"xmlns":890},[892,50744,50745,50768],{},[895,50746,50747,50753,50755,50757,50759,50761,50764,50766],{},[1699,50748,50749,50751],{},[898,50750,12471],{},[1742,50752,1872],{},[1750,50754,1861],{},[1742,50756,4903],{},[898,50758,12471],{},[1750,50760,1758],{},[1742,50762,50763],{},"64",[1750,50765,1766],{},[1742,50767,2607],{},[902,50769,50770],{"encoding":904},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[883,50773,50775],{"className":50774},[886],[888,50776,50777],{"xmlns":890},[892,50778,50779,50786],{},[895,50780,50781,50783],{},[1750,50782,1758],{},[1742,50784,50785],{},"16",[902,50787,50788],{"encoding":904},"-16"," (nevyhovuje) a ",[883,50791,50793],{"className":50792},[886],[888,50794,50795],{"xmlns":890},[892,50796,50797,50801],{},[895,50798,50799],{},[1742,50800,7859],{},[902,50802,7859],{"encoding":904},". Tedy ",[883,50805,50807],{"className":50806},[886],[888,50808,50809],{"xmlns":890},[892,50810,50811,50823],{},[895,50812,50813,50819,50821],{},[1699,50814,50815,50817],{},[898,50816,12471],{},[898,50818,1705],{},[1750,50820,1766],{},[1742,50822,7859],{},[902,50824,50825],{"encoding":904},"Q^E = 4",[883,50827,50829],{"className":50828},[886],[888,50830,50831],{"xmlns":890},[892,50832,50833,50860],{},[895,50834,50835,50841,50843,50845,50847,50849,50851,50853,50855,50857],{},[1699,50836,50837,50839],{},[898,50838,1776],{},[898,50840,1705],{},[1750,50842,1766],{},[1750,50844,1758],{},[1742,50846,50785],{},[1750,50848,1758],{},[1742,50850,14865],{},[1750,50852,1861],{},[1742,50854,4236],{},[1750,50856,1766],{},[1742,50858,50859],{},"94",[902,50861,50862],{"encoding":904},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[883,50865,50867],{"className":50866},[886],[888,50868,50869],{"xmlns":890},[892,50870,50871,50885],{},[895,50872,50873,50875,50877,50879,50881,50883],{},[898,50874,1705],{},[1750,50876,5141],{"stretchy":1752},[1742,50878,7859],{},[1750,50880,1917],{"separator":1916},[1742,50882,50859],{},[1750,50884,5158],{"stretchy":1752},[902,50886,50887],{"encoding":904},"E[4, 94]",[198,50889,50891],{"id":50890},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[724,50893,50894,50896],{},[38,50895,46856],{}," Poptávky a nabídky dvou zboží",[883,50898,50900],{"className":50899},[886],[888,50901,50902],{"xmlns":890,"display":36989},[892,50903,50904,51070],{},[4577,50905,50908,50996],{"rowspacing":4579,"columnalign":50906,"columnspacing":50907},"right left right left","0em 1em 0em",[4582,50909,50910,50920,50952,50962],{},[4585,50911,50912],{},[3586,50913,50914],{"scriptlevel":2607,"displaystyle":1916},[5535,50915,50916,50918],{},[898,50917,12471],{},[1742,50919,1744],{},[4585,50921,50922],{},[3586,50923,50924],{"scriptlevel":2607,"displaystyle":1916},[895,50925,50926,50928,50930,50932,50934,50936,50942,50944,50950],{},[895,50927],{},[1750,50929,1766],{},[1742,50931,14865],{},[1750,50933,1758],{},[1742,50935,7902],{},[5535,50937,50938,50940],{},[898,50939,1776],{},[1742,50941,1744],{},[1750,50943,1758],{},[5535,50945,50946,50948],{},[898,50947,1776],{},[1742,50949,1872],{},[1750,50951,1917],{"separator":1916},[4585,50953,50954],{},[3586,50955,50956],{"scriptlevel":2607,"displaystyle":1916},[5535,50957,50958,50960],{},[898,50959,12471],{},[1742,50961,1872],{},[4585,50963,50964],{},[3586,50965,50966],{"scriptlevel":2607,"displaystyle":1916},[895,50967,50968,50970,50972,50974,50976,50978,50984,50986,50988,50994],{},[895,50969],{},[1750,50971,1766],{},[1742,50973,3936],{},[1750,50975,1758],{},[1742,50977,1872],{},[5535,50979,50980,50982],{},[898,50981,1776],{},[1742,50983,1744],{},[1750,50985,1758],{},[1742,50987,7859],{},[5535,50989,50990,50992],{},[898,50991,1776],{},[1742,50993,1872],{},[1750,50995,1917],{"separator":1916},[4582,50997,50998,51008,51034,51044],{},[4585,50999,51000],{},[3586,51001,51002],{"scriptlevel":2607,"displaystyle":1916},[5535,51003,51004,51006],{},[898,51005,12471],{},[1742,51007,1744],{},[4585,51009,51010],{},[3586,51011,51012],{"scriptlevel":2607,"displaystyle":1916},[895,51013,51014,51016,51018,51020,51022,51024,51026,51032],{},[895,51015],{},[1750,51017,1766],{},[1750,51019,1758],{},[1742,51021,7822],{},[1750,51023,1861],{},[1742,51025,7859],{},[5535,51027,51028,51030],{},[898,51029,1776],{},[1742,51031,1744],{},[1750,51033,1917],{"separator":1916},[4585,51035,51036],{},[3586,51037,51038],{"scriptlevel":2607,"displaystyle":1916},[5535,51039,51040,51042],{},[898,51041,12471],{},[1742,51043,1872],{},[4585,51045,51046],{},[3586,51047,51048],{"scriptlevel":2607,"displaystyle":1916},[895,51049,51050,51052,51054,51056,51058,51060,51062,51068],{},[895,51051],{},[1750,51053,1766],{},[1750,51055,1758],{},[1742,51057,8051],{},[1750,51059,1861],{},[1742,51061,7822],{},[5535,51063,51064,51066],{},[898,51065,1776],{},[1742,51067,1872],{},[898,51069,2313],{"mathvariant":1747},[902,51071,51072],{"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}",[724,51074,51075,51077],{},[38,51076,46888],{}," Z rovností poptávek a nabídek dostaneme",[883,51079,51081],{"className":51080},[886],[888,51082,51083],{"xmlns":890,"display":36989},[892,51084,51085,51134],{},[895,51086,51087,51089,51095,51097,51103,51105,51107,51109,51111,51113,51119,51121,51123,51129,51131],{},[1742,51088,13663],{},[5535,51090,51091,51093],{},[898,51092,1776],{},[1742,51094,1744],{},[1750,51096,1861],{},[5535,51098,51099,51101],{},[898,51100,1776],{},[1742,51102,1872],{},[1750,51104,1766],{},[1742,51106,5029],{},[1750,51108,1917],{"separator":1916},[2125,51110],{"width":2127},[1742,51112,1872],{},[5535,51114,51115,51117],{},[898,51116,1776],{},[1742,51118,1744],{},[1750,51120,1861],{},[1742,51122,8051],{},[5535,51124,51125,51127],{},[898,51126,1776],{},[1742,51128,1872],{},[1750,51130,1766],{},[1742,51132,51133],{},"57.",[902,51135,51136],{"encoding":904},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[724,51138,51139,51140,1343,51164,51188,51189,1343,51214,51238,51239,51241],{},"Řešením je ",[883,51141,51143],{"className":51142},[886],[888,51144,51145],{"xmlns":890},[892,51146,51147,51161],{},[895,51148,51149,51157,51159],{},[5950,51150,51151,51153,51155],{},[898,51152,1776],{},[1742,51154,1744],{},[898,51156,1705],{},[1750,51158,1766],{},[1742,51160,7859],{},[902,51162,51163],{"encoding":904},"P_1^E = 4",[883,51165,51167],{"className":51166},[886],[888,51168,51169],{"xmlns":890},[892,51170,51171,51185],{},[895,51172,51173,51181,51183],{},[5950,51174,51175,51177,51179],{},[898,51176,1776],{},[1742,51178,1872],{},[898,51180,1705],{},[1750,51182,1766],{},[1742,51184,8051],{},[902,51186,51187],{"encoding":904},"P_2^E = 7","; zpětným dosazením ",[883,51190,51192],{"className":51191},[886],[888,51193,51194],{"xmlns":890},[892,51195,51196,51211],{},[895,51197,51198,51206,51208],{},[5950,51199,51200,51202,51204],{},[898,51201,12471],{},[1742,51203,1744],{},[898,51205,1705],{},[1750,51207,1766],{},[1742,51209,51210],{},"13",[902,51212,51213],{"encoding":904},"Q_1^E = 13",[883,51215,51217],{"className":51216},[886],[888,51218,51219],{"xmlns":890},[892,51220,51221,51235],{},[895,51222,51223,51231,51233],{},[5950,51224,51225,51227,51229],{},[898,51226,12471],{},[1742,51228,1872],{},[898,51230,1705],{},[1750,51232,1766],{},[1742,51234,6789],{},[902,51236,51237],{"encoding":904},"Q_2^E = 14",". Zboží jsou ",[38,51240,48745],{}," (zkřížené koeficienty v poptávce jsou záporné).",[198,51243,51245],{"id":51244},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[724,51247,51248,51249,51266,51267,2084,51270,1783],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[883,51250,51252],{"className":51251},[886],[888,51253,51254],{"xmlns":890},[892,51255,51256,51264],{},[895,51257,51258],{},[1699,51259,51260,51262],{},[898,51261,1776],{},[898,51263,1705],{},[902,51265,50389],{"encoding":904},"; mechanismus popisuje ",[38,51268,51269],{},"teorém pavučiny",[614,51271,51272],{},"cobweb model",[198,51274,51276],{"id":51275},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[724,51278,51279],{},[4434,51280],{"alt":51281,"className":51282,"src":51283},"imek-komparativni-statika-4pripady",[210,4438],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[1785,51285,51286,51327,51367,51407],{},[724,51287,51288,51291,51292,15838,51309,2313],{},[38,51289,51290],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[883,51293,51295],{"className":51294},[886],[888,51296,51297],{"xmlns":890},[892,51298,51299,51307],{},[895,51300,51301],{},[1699,51302,51303,51305],{},[898,51304,1776],{},[898,51306,1705],{},[902,51308,50389],{"encoding":904},[883,51310,51312],{"className":51311},[886],[888,51313,51314],{"xmlns":890},[892,51315,51316,51324],{},[895,51317,51318],{},[1699,51319,51320,51322],{},[898,51321,12471],{},[898,51323,1705],{},[902,51325,51326],{"encoding":904},"Q^E",[724,51328,51329,51332,51333,15838,51350,2313],{},[38,51330,51331],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[883,51334,51336],{"className":51335},[886],[888,51337,51338],{"xmlns":890},[892,51339,51340,51348],{},[895,51341,51342],{},[1699,51343,51344,51346],{},[898,51345,1776],{},[898,51347,1705],{},[902,51349,50389],{"encoding":904},[883,51351,51353],{"className":51352},[886],[888,51354,51355],{"xmlns":890},[892,51356,51357,51365],{},[895,51358,51359],{},[1699,51360,51361,51363],{},[898,51362,12471],{},[898,51364,1705],{},[902,51366,51326],{"encoding":904},[724,51368,51369,51372,51373,18992,51390,2313],{},[38,51370,51371],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[883,51374,51376],{"className":51375},[886],[888,51377,51378],{"xmlns":890},[892,51379,51380,51388],{},[895,51381,51382],{},[1699,51383,51384,51386],{},[898,51385,1776],{},[898,51387,1705],{},[902,51389,50389],{"encoding":904},[883,51391,51393],{"className":51392},[886],[888,51394,51395],{"xmlns":890},[892,51396,51397,51405],{},[895,51398,51399],{},[1699,51400,51401,51403],{},[898,51402,12471],{},[898,51404,1705],{},[902,51406,51326],{"encoding":904},[724,51408,51409,51412,51413,51430,51431,2313],{},[38,51410,51411],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[883,51414,51416],{"className":51415},[886],[888,51417,51418],{"xmlns":890},[892,51419,51420,51428],{},[895,51421,51422],{},[1699,51423,51424,51426],{},[898,51425,1776],{},[898,51427,1705],{},[902,51429,50389],{"encoding":904},", pokles ",[883,51432,51434],{"className":51433},[886],[888,51435,51436],{"xmlns":890},[892,51437,51438,51446],{},[895,51439,51440],{},[1699,51441,51442,51444],{},[898,51443,12471],{},[898,51445,1705],{},[902,51447,51326],{"encoding":904},[16,51449,51450,51495],{},[19,51451,51452],{},[22,51453,51454,51457,51476],{},[25,51455,51456],{},"Změna",[25,51458,51459],{},[883,51460,51462],{"className":51461},[886],[888,51463,51464],{"xmlns":890},[892,51465,51466,51474],{},[895,51467,51468],{},[1699,51469,51470,51472],{},[898,51471,1776],{},[898,51473,1705],{},[902,51475,50389],{"encoding":904},[25,51477,51478],{},[883,51479,51481],{"className":51480},[886],[888,51482,51483],{"xmlns":890},[892,51484,51485,51493],{},[895,51486,51487],{},[1699,51488,51489,51491],{},[898,51490,12471],{},[898,51492,1705],{},[902,51494,51326],{"encoding":904},[30,51496,51497,51507,51517,51526],{},[22,51498,51499,51502,51505],{},[35,51500,51501],{},"Růst poptávky",[35,51503,51504],{},"↑",[35,51506,51504],{},[22,51508,51509,51512,51515],{},[35,51510,51511],{},"Pokles poptávky",[35,51513,51514],{},"↓",[35,51516,51514],{},[22,51518,51519,51522,51524],{},[35,51520,51521],{},"Růst nabídky",[35,51523,51514],{},[35,51525,51504],{},[22,51527,51528,51531,51533],{},[35,51529,51530],{},"Pokles nabídky",[35,51532,51504],{},[35,51534,51514],{},[724,51536,51537],{},[614,51538,51539],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[45893,51541],{},[115,51543,811],{"id":51544},"zdanění-trhu",[1785,51546,51547,51636],{},[724,51548,51549,51551,51552,51565,51566,12605,51579,51582,51583,45699,51606,51631,51632,51635],{},[883,51550,1791],{}," TL;DR\nJednotková daň ",[883,51553,51555],{"className":51554},[886],[888,51556,51557],{"xmlns":890},[892,51558,51559,51563],{},[895,51560,51561],{},[898,51562,5326],{},[902,51564,5326],{"encoding":904}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[883,51567,51569],{"className":51568},[886],[888,51570,51571],{"xmlns":890},[892,51572,51573,51577],{},[895,51574,51575],{},[898,51576,5326],{},[902,51578,5326],{"encoding":904},[38,51580,51581],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[883,51584,51586],{"className":51585},[886],[888,51587,51588],{"xmlns":890},[892,51589,51590,51603],{},[895,51591,51592],{},[5535,51593,51594,51596],{},[898,51595,5326],{},[895,51597,51598,51601],{},[898,51599,51600],{},"s",[898,51602,724],{},[902,51604,51605],{"encoding":904},"T_{sp}",[883,51607,51609],{"className":51608},[886],[888,51610,51611],{"xmlns":890},[892,51612,51613,51628],{},[895,51614,51615],{},[5535,51616,51617,51619],{},[898,51618,5326],{},[895,51620,51621,51624,51626],{},[898,51622,51623],{},"v",[898,51625,11717],{},[898,51627,1920],{},[902,51629,51630],{"encoding":904},"T_{vyr}","). Klíčová vlastnost — ",[38,51633,51634],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[724,51637,51638],{},[614,51639,51640,51641,2313],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[207,51642,51644],{"className":51643,"dataFsResolvedFilePath":809,"href":810},[210],"zdaneni-trhu",[724,51646,51647,51648,51651,51652,51678,51679,51682,51683,51709,51710,51727,51728,51768,51769,2028,51782,2313],{},"Existují dvě formy zdanění — daň uložená ",[38,51649,51650],{},"výrobci"," (posun nabídky ",[883,51653,51655],{"className":51654},[886],[888,51656,51657],{"xmlns":890},[892,51658,51659,51675],{},[895,51660,51661,51667,51669,51671,51673],{},[5535,51662,51663,51665],{},[898,51664,1779],{},[1742,51666,1744],{},[1750,51668,1766],{},[898,51670,1779],{},[1750,51672,1861],{},[898,51674,5326],{},[902,51676,51677],{"encoding":904},"S_1 = S + T"," svisle nahoru) a daň uložená ",[38,51680,51681],{},"spotřebiteli"," (posun poptávky ",[883,51684,51686],{"className":51685},[886],[888,51687,51688],{"xmlns":890},[892,51689,51690,51706],{},[895,51691,51692,51698,51700,51702,51704],{},[5535,51693,51694,51696],{},[898,51695,5541],{},[1742,51697,1872],{},[1750,51699,1766],{},[898,51701,5541],{},[1750,51703,1758],{},[898,51705,5326],{},[902,51707,51708],{"encoding":904},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[883,51711,51713],{"className":51712},[886],[888,51714,51715],{"xmlns":890},[892,51716,51717,51725],{},[895,51718,51719],{},[1699,51720,51721,51723],{},[898,51722,12471],{},[898,51724,1705],{},[902,51726,51326],{"encoding":904}," klesá a vzniká rozklad daně ",[883,51729,51731],{"className":51730},[886],[888,51732,51733],{"xmlns":890},[892,51734,51735,51765],{},[895,51736,51737,51739,51741,51751,51753],{},[898,51738,5326],{},[1750,51740,1766],{},[5535,51742,51743,51745],{},[898,51744,5326],{},[895,51746,51747,51749],{},[898,51748,51600],{},[898,51750,724],{},[1750,51752,1861],{},[5535,51754,51755,51757],{},[898,51756,5326],{},[895,51758,51759,51761,51763],{},[898,51760,51623],{},[898,51762,11717],{},[898,51764,1920],{},[902,51766,51767],{"encoding":904},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[883,51770,51772],{"className":51771},[886],[888,51773,51774],{"xmlns":890},[892,51775,51776,51780],{},[895,51777,51778],{},[898,51779,5541],{},[902,51781,5541],{"encoding":904},[883,51783,51785],{"className":51784},[886],[888,51786,51787],{"xmlns":890},[892,51788,51789,51793],{},[895,51790,51791],{},[898,51792,1779],{},[902,51794,1779],{"encoding":904},[724,51796,51797,51798,51801,51802,2028,51832,51866],{},"Zásadním výsledkem kapitoly je ",[38,51799,51800],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[883,51803,51805],{"className":51804},[886],[888,51806,51807],{"xmlns":890},[892,51808,51809,51829],{},[895,51810,51811,51819,51821],{},[5950,51812,51813,51815,51817],{},[898,51814,12471],{},[1742,51816,1744],{},[898,51818,1705],{},[1750,51820,1766],{},[5950,51822,51823,51825,51827],{},[898,51824,12471],{},[1742,51826,1872],{},[898,51828,1705],{},[902,51830,51831],{"encoding":904},"Q_1^E = Q_2^E",[883,51833,51835],{"className":51834},[886],[888,51836,51837],{"xmlns":890},[892,51838,51839,51863],{},[895,51840,51841,51849,51851,51853,51855],{},[5950,51842,51843,51845,51847],{},[898,51844,1776],{},[1742,51846,1744],{},[898,51848,1705],{},[1750,51850,1758],{},[898,51852,5326],{},[1750,51854,1766],{},[5950,51856,51857,51859,51861],{},[898,51858,1776],{},[1742,51860,1872],{},[898,51862,1705],{},[902,51864,51865],{"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.",[724,51868,51869,51870,51873,51874,51900,51901,51929,51930,51933,51934,51937,51938,2313],{},"Podrobný výklad, Příklady ",[38,51871,51872],{},"2.9"," (daň výrobci, ",[883,51875,51877],{"className":51876},[886],[888,51878,51879],{"xmlns":890},[892,51880,51881,51897],{},[895,51882,51883,51893,51895],{},[5535,51884,51885,51887],{},[898,51886,5326],{},[895,51888,51889,51891],{},[898,51890,51600],{},[898,51892,724],{},[1750,51894,1766],{},[1742,51896,1872],{},[902,51898,51899],{"encoding":904},"T_{sp} = 2"," Kč, ",[883,51902,51904],{"className":51903},[886],[888,51905,51906],{"xmlns":890},[892,51907,51908,51926],{},[895,51909,51910,51922,51924],{},[5535,51911,51912,51914],{},[898,51913,5326],{},[895,51915,51916,51918,51920],{},[898,51917,51623],{},[898,51919,11717],{},[898,51921,1920],{},[1750,51923,1766],{},[1742,51925,7859],{},[902,51927,51928],{"encoding":904},"T_{vyr} = 4"," Kč) a ",[38,51931,51932],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[38,51935,51936],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[207,51939,51644],{"className":51940,"dataFsResolvedFilePath":809,"href":810},[210],[45893,51942],{},[115,51944,51946],{"id":51945},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1785,51948,51949],{},[724,51950,51951,51953,51954,51957,51958,51960],{},[883,51952,1791],{}," TL;DR\nMultiplikátory jsou ",[38,51955,51956],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[614,51959,45883],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[198,51962,51964],{"id":51963},"redukovaný-tvar","Redukovaný tvar",[724,51966,51967,51968,2084,51991,1343,52009,4419,52026,2084,52049,52066,52067,52097],{},"Pro lineární model ",[883,51969,51971],{"className":51970},[886],[888,51972,51973],{"xmlns":890},[892,51974,51975,51989],{},[895,51976,51977,51979,51981,51983,51985,51987],{},[898,51978,1776],{},[1750,51980,1766],{},[898,51982,207],{},[898,51984,12471],{},[1750,51986,1861],{},[898,51988,2573],{},[902,51990,45983],{"encoding":904},[883,51992,51994],{"className":51993},[886],[888,51995,51996],{"xmlns":890},[892,51997,51998,52006],{},[895,51999,52000,52002,52004],{},[898,52001,207],{},[1750,52003,2624],{},[1742,52005,2607],{},[902,52007,52008],{"encoding":904},"a \u003C 0",[883,52010,52012],{"className":52011},[886],[888,52013,52014],{"xmlns":890},[892,52015,52016,52024],{},[895,52017,52018,52020,52022],{},[898,52019,2573],{},[1750,52021,2604],{},[1742,52023,2607],{},[902,52025,2610],{"encoding":904},[883,52027,52029],{"className":52028},[886],[888,52030,52031],{"xmlns":890},[892,52032,52033,52047],{},[895,52034,52035,52037,52039,52041,52043,52045],{},[898,52036,1776],{},[1750,52038,1766],{},[898,52040,9365],{},[898,52042,12471],{},[1750,52044,1861],{},[898,52046,3429],{},[902,52048,49165],{"encoding":904},[883,52050,52052],{"className":52051},[886],[888,52053,52054],{"xmlns":890},[892,52055,52056,52064],{},[895,52057,52058,52060,52062],{},[898,52059,9365],{},[1750,52061,2604],{},[1742,52063,2607],{},[902,52065,49183],{"encoding":904},") dává podmínka rovnováhy ",[883,52068,52070],{"className":52069},[886],[888,52071,52072],{"xmlns":890},[892,52073,52074,52094],{},[895,52075,52076,52078,52080,52082,52084,52086,52088,52090,52092],{},[898,52077,207],{},[898,52079,12471],{},[1750,52081,1861],{},[898,52083,2573],{},[1750,52085,1766],{},[898,52087,9365],{},[898,52089,12471],{},[1750,52091,1861],{},[898,52093,3429],{},[902,52095,52096],{"encoding":904},"aQ + b = cQ + d",", odkud",[883,52099,52101],{"className":52100},[886],[888,52102,52103],{"xmlns":890,"display":36989},[892,52104,52105,52150],{},[4577,52106,52107],{"width":36994},[4582,52108,52109,52111,52143,52145],{},[4585,52110],{"width":36999},[4585,52112,52113],{},[895,52114,52115,52121,52123,52141],{},[1699,52116,52117,52119],{},[898,52118,12471],{},[898,52120,1705],{},[1750,52122,1766],{},[3423,52124,52125,52133],{},[895,52126,52127,52129,52131],{},[898,52128,2573],{},[1750,52130,1758],{},[898,52132,3429],{},[895,52134,52135,52137,52139],{},[898,52136,9365],{},[1750,52138,1758],{},[898,52140,207],{},[898,52142,2313],{"mathvariant":1747},[4585,52144],{"width":36999},[4585,52146,52147],{},[1969,52148,52149],{},"(2.10)",[902,52151,52152],{"encoding":904},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[724,52154,52155,52156,2084,52158,52161,52162,52179,52180,1647,52183,52209,52210,52223,52224,52242,52243,1783],{},"Vztah (2.10) je ",[38,52157,4779],{},[614,52159,52160],{},"reduced form",") pro ",[883,52163,52165],{"className":52164},[886],[888,52166,52167],{"xmlns":890},[892,52168,52169,52177],{},[895,52170,52171],{},[1699,52172,52173,52175],{},[898,52174,12471],{},[898,52176,1705],{},[902,52178,51326],{"encoding":904},": endogenní proměnná je vyjádřena pomocí exogenních ",[38,52181,52182],{},"parametrů",[883,52184,52186],{"className":52185},[886],[888,52187,52188],{"xmlns":890},[892,52189,52190,52206],{},[895,52191,52192,52194,52196,52198,52200,52202,52204],{},[898,52193,207],{},[1750,52195,1917],{"separator":1916},[898,52197,2573],{},[1750,52199,1917],{"separator":1916},[898,52201,9365],{},[1750,52203,1917],{"separator":1916},[898,52205,3429],{},[902,52207,52208],{"encoding":904},"a, b, c, d",". Aby ",[883,52211,52213],{"className":52212},[886],[888,52214,52215],{"xmlns":890},[892,52216,52217,52221],{},[895,52218,52219],{},[898,52220,1705],{},[902,52222,1705],{"encoding":904}," ležel v 1. kvadrantu, musí platit ",[883,52225,52227],{"className":52226},[886],[888,52228,52229],{"xmlns":890},[892,52230,52231,52239],{},[895,52232,52233,52235,52237],{},[898,52234,2573],{},[1750,52236,2604],{},[898,52238,3429],{},[902,52240,52241],{"encoding":904},"b > d"," (neboť ",[883,52244,52246],{"className":52245},[886],[888,52247,52248],{"xmlns":890},[892,52249,52250,52262],{},[895,52251,52252,52254,52256,52258,52260],{},[898,52253,9365],{},[1750,52255,1758],{},[898,52257,207],{},[1750,52259,2604],{},[1742,52261,2607],{},[902,52263,52264],{"encoding":904},"c - a > 0",[724,52266,52267],{},[614,52268,52269,52270,52283,52284,52297,52298,2440,52311,50863,52328,52341],{},"Obrázek 2.22: Lineární poptávka (úsek ",[883,52271,52273],{"className":52272},[886],[888,52274,52275],{"xmlns":890},[892,52276,52277,52281],{},[895,52278,52279],{},[898,52280,2573],{},[902,52282,2573],{"encoding":904}," na ose ",[883,52285,52287],{"className":52286},[886],[888,52288,52289],{"xmlns":890},[892,52290,52291,52295],{},[895,52292,52293],{},[898,52294,1776],{},[902,52296,1776],{"encoding":904},") a nabídka (úsek ",[883,52299,52301],{"className":52300},[886],[888,52302,52303],{"xmlns":890},[892,52304,52305,52309],{},[895,52306,52307],{},[898,52308,3429],{},[902,52310,3429],{"encoding":904},[883,52312,52314],{"className":52313},[886],[888,52315,52316],{"xmlns":890},[892,52317,52318,52326],{},[895,52319,52320,52322,52324],{},[898,52321,2573],{},[1750,52323,2604],{},[898,52325,3429],{},[902,52327,52241],{"encoding":904},[883,52329,52331],{"className":52330},[886],[888,52332,52333],{"xmlns":890},[892,52334,52335,52339],{},[895,52336,52337],{},[898,52338,1705],{},[902,52340,1705],{"encoding":904}," v 1. kvadrantu.",[198,52343,52345],{"id":52344},"definice-multiplikátorů","Definice multiplikátorů",[724,52347,52348,52349,52374,52375,52388,52389,52402],{},"V komparativní statice jsou ",[883,52350,52352],{"className":52351},[886],[888,52353,52354],{"xmlns":890},[892,52355,52356,52372],{},[895,52357,52358,52360,52362,52364,52366,52368,52370],{},[898,52359,207],{},[1750,52361,1917],{"separator":1916},[898,52363,2573],{},[1750,52365,1917],{"separator":1916},[898,52367,9365],{},[1750,52369,1917],{"separator":1916},[898,52371,3429],{},[902,52373,52208],{"encoding":904}," exogenní proměnné a ",[883,52376,52378],{"className":52377},[886],[888,52379,52380],{"xmlns":890},[892,52381,52382,52386],{},[895,52383,52384],{},[898,52385,12471],{},[902,52387,12471],{"encoding":904}," endogenní. Přibližná změna ",[883,52390,52392],{"className":52391},[886],[888,52393,52394],{"xmlns":890},[892,52395,52396,52400],{},[895,52397,52398],{},[898,52399,12471],{},[902,52401,12471],{"encoding":904}," se rovná totálnímu diferenciálu:",[883,52404,52406],{"className":52405},[886],[888,52407,52408],{"xmlns":890,"display":36989},[892,52409,52410,52503],{},[4577,52411,52412],{"width":36994},[4582,52413,52414,52416,52496,52498],{},[4585,52415],{"width":36999},[4585,52417,52418],{},[895,52419,52420,52422,52424,52426,52428,52430,52432,52440,52442,52444,52446,52448,52456,52458,52460,52462,52464,52472,52474,52476,52478,52480,52488,52490,52492,52494],{},[898,52421,2666],{"mathvariant":1747},[898,52423,12471],{},[1750,52425,2274],{},[898,52427,3429],{},[898,52429,12471],{},[1750,52431,1766],{},[5950,52433,52434,52436,52438],{},[898,52435,12471],{},[898,52437,207],{},[1750,52439,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,52441,2658],{},[898,52443,3429],{},[898,52445,207],{},[1750,52447,1861],{},[5950,52449,52450,52452,52454],{},[898,52451,12471],{},[898,52453,2573],{},[1750,52455,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,52457,2658],{},[898,52459,3429],{},[898,52461,2573],{},[1750,52463,1861],{},[5950,52465,52466,52468,52470],{},[898,52467,12471],{},[898,52469,9365],{},[1750,52471,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,52473,2658],{},[898,52475,3429],{},[898,52477,9365],{},[1750,52479,1861],{},[5950,52481,52482,52484,52486],{},[898,52483,12471],{},[898,52485,3429],{},[1750,52487,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,52489,2658],{},[898,52491,3429],{},[898,52493,3429],{},[898,52495,2313],{"mathvariant":1747},[4585,52497],{"width":36999},[4585,52499,52500],{},[1969,52501,52502],{},"(2.11)",[902,52504,52505],{"encoding":904},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[724,52507,52508,52509,52559,52560,2084,52562,12825],{},"Parciální derivace ",[883,52510,52512],{"className":52511},[886],[888,52513,52514],{"xmlns":890},[892,52515,52516,52556],{},[895,52517,52518,52526,52528,52536,52538,52546,52548],{},[5950,52519,52520,52522,52524],{},[898,52521,12471],{},[898,52523,207],{},[1750,52525,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52527,1917],{"separator":1916},[5950,52529,52530,52532,52534],{},[898,52531,12471],{},[898,52533,2573],{},[1750,52535,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52537,1917],{"separator":1916},[5950,52539,52540,52542,52544],{},[898,52541,12471],{},[898,52543,9365],{},[1750,52545,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52547,1917],{"separator":1916},[5950,52549,52550,52552,52554],{},[898,52551,12471],{},[898,52553,3429],{},[1750,52555,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,52557,52558],{"encoding":904},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[38,52561,1730],{},[614,52563,52564],{},"multipliers",[883,52566,52568],{"className":52567},[886],[888,52569,52570],{"xmlns":890,"display":36989},[892,52571,52572,52723],{},[4577,52573,52574],{"width":36994},[4582,52575,52576,52578,52716,52718],{},[4585,52577],{"width":36999},[4585,52579,52580],{},[895,52581,52582,52590,52592,52618,52620,52622,52630,52632,52644,52646,52648,52656,52658,52660,52686,52688,52690,52698,52700,52702,52714],{},[5950,52583,52584,52586,52588],{},[898,52585,12471],{},[898,52587,207],{},[1750,52589,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52591,1766],{},[3423,52593,52594,52602],{},[895,52595,52596,52598,52600],{},[898,52597,2573],{},[1750,52599,1758],{},[898,52601,3429],{},[895,52603,52604,52606,52608,52610,52612],{},[1750,52605,1753],{"stretchy":1752},[898,52607,9365],{},[1750,52609,1758],{},[898,52611,207],{},[1699,52613,52614,52616],{},[1750,52615,1763],{"stretchy":1752},[1742,52617,1872],{},[1750,52619,1917],{"separator":1916},[2125,52621],{"width":24875},[5950,52623,52624,52626,52628],{},[898,52625,12471],{},[898,52627,2573],{},[1750,52629,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52631,1766],{},[3423,52633,52634,52636],{},[1742,52635,1744],{},[895,52637,52638,52640,52642],{},[898,52639,9365],{},[1750,52641,1758],{},[898,52643,207],{},[1750,52645,1917],{"separator":1916},[2125,52647],{"width":24875},[5950,52649,52650,52652,52654],{},[898,52651,12471],{},[898,52653,9365],{},[1750,52655,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52657,1766],{},[1750,52659,1758],{},[3423,52661,52662,52670],{},[895,52663,52664,52666,52668],{},[898,52665,2573],{},[1750,52667,1758],{},[898,52669,3429],{},[895,52671,52672,52674,52676,52678,52680],{},[1750,52673,1753],{"stretchy":1752},[898,52675,9365],{},[1750,52677,1758],{},[898,52679,207],{},[1699,52681,52682,52684],{},[1750,52683,1763],{"stretchy":1752},[1742,52685,1872],{},[1750,52687,1917],{"separator":1916},[2125,52689],{"width":24875},[5950,52691,52692,52694,52696],{},[898,52693,12471],{},[898,52695,3429],{},[1750,52697,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52699,1766],{},[1750,52701,1758],{},[3423,52703,52704,52706],{},[1742,52705,1744],{},[895,52707,52708,52710,52712],{},[898,52709,9365],{},[1750,52711,1758],{},[898,52713,207],{},[898,52715,2313],{"mathvariant":1747},[4585,52717],{"width":36999},[4585,52719,52720],{},[1969,52721,52722],{},"(2.12)",[902,52724,52725],{"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}",[198,52727,52729],{"id":52728},"znaménka-a-interpretace","Znaménka a interpretace",[724,52731,52732,52733,1343,52750,1343,52767,1343,52784,52801,52802,12825],{},"Za podmínek ",[883,52734,52736],{"className":52735},[886],[888,52737,52738],{"xmlns":890},[892,52739,52740,52748],{},[895,52741,52742,52744,52746],{},[898,52743,207],{},[1750,52745,2624],{},[1742,52747,2607],{},[902,52749,52008],{"encoding":904},[883,52751,52753],{"className":52752},[886],[888,52754,52755],{"xmlns":890},[892,52756,52757,52765],{},[895,52758,52759,52761,52763],{},[898,52760,2573],{},[1750,52762,2604],{},[1742,52764,2607],{},[902,52766,2610],{"encoding":904},[883,52768,52770],{"className":52769},[886],[888,52771,52772],{"xmlns":890},[892,52773,52774,52782],{},[895,52775,52776,52778,52780],{},[898,52777,9365],{},[1750,52779,2604],{},[1742,52781,2607],{},[902,52783,49183],{"encoding":904},[883,52785,52787],{"className":52786},[886],[888,52788,52789],{"xmlns":890},[892,52790,52791,52799],{},[895,52792,52793,52795,52797],{},[898,52794,2573],{},[1750,52796,2604],{},[898,52798,3429],{},[902,52800,52241],{"encoding":904}," platí (znaménka se ",[38,52803,52804],{},"nemění",[883,52806,52808],{"className":52807},[886],[888,52809,52810],{"xmlns":890,"display":36989},[892,52811,52812,52874],{},[895,52813,52814,52822,52824,52826,52828,52830,52838,52840,52842,52844,52846,52854,52856,52858,52860,52862,52870,52872],{},[5950,52815,52816,52818,52820],{},[898,52817,12471],{},[898,52819,207],{},[1750,52821,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52823,2604],{},[1742,52825,2607],{},[1750,52827,1917],{"separator":1916},[2125,52829],{"width":2127},[5950,52831,52832,52834,52836],{},[898,52833,12471],{},[898,52835,2573],{},[1750,52837,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52839,2604],{},[1742,52841,2607],{},[1750,52843,1917],{"separator":1916},[2125,52845],{"width":2127},[5950,52847,52848,52850,52852],{},[898,52849,12471],{},[898,52851,9365],{},[1750,52853,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52855,2624],{},[1742,52857,2607],{},[1750,52859,1917],{"separator":1916},[2125,52861],{"width":2127},[5950,52863,52864,52866,52868],{},[898,52865,12471],{},[898,52867,3429],{},[1750,52869,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,52871,2624],{},[1742,52873,22073],{},[902,52875,52876],{"encoding":904},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[120,52878,52879,52938],{},[123,52880,52881,1647,52884,52904,52905,52922,52923,1343,52936,2313],{},[38,52882,52883],{},"Kvantitativní smysl:",[883,52885,52887],{"className":52886},[886],[888,52888,52889],{"xmlns":890},[892,52890,52891,52901],{},[895,52892,52893],{},[5950,52894,52895,52897,52899],{},[898,52896,12471],{},[898,52898,11727],{},[1750,52900,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,52902,52903],{"encoding":904},"Q'_x"," udává, o kolik přibližně vzroste ",[883,52906,52908],{"className":52907},[886],[888,52909,52910],{"xmlns":890},[892,52911,52912,52920],{},[895,52913,52914],{},[1699,52915,52916,52918],{},[898,52917,12471],{},[898,52919,1705],{},[902,52921,51326],{"encoding":904}," při jednotkové změně parametru ",[883,52924,52926],{"className":52925},[886],[888,52927,52928],{"xmlns":890},[892,52929,52930,52934],{},[895,52931,52932],{},[898,52933,11727],{},[902,52935,11727],{"encoding":904},[614,52937,45883],{},[123,52939,52940,52943,52944,52961,52962,2313],{},[38,52941,52942],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[883,52945,52947],{"className":52946},[886],[888,52948,52949],{"xmlns":890},[892,52950,52951,52959],{},[895,52952,52953],{},[1699,52954,52955,52957],{},[898,52956,12471],{},[898,52958,1705],{},[902,52960,51326],{"encoding":904}," na růst ",[883,52963,52965],{"className":52964},[886],[888,52966,52967],{"xmlns":890},[892,52968,52969,52973],{},[895,52970,52971],{},[898,52972,11727],{},[902,52974,11727],{"encoding":904},[724,52976,52977,52978,52991,52992,52242,53009,1783],{},"Např. růst ",[883,52979,52981],{"className":52980},[886],[888,52982,52983],{"xmlns":890},[892,52984,52985,52989],{},[895,52986,52987],{},[898,52988,9365],{},[902,52990,9365],{"encoding":904}," (strmější nabídka) ⟹ pokles ",[883,52993,52995],{"className":52994},[886],[888,52996,52997],{"xmlns":890},[892,52998,52999,53007],{},[895,53000,53001],{},[1699,53002,53003,53005],{},[898,53004,12471],{},[898,53006,1705],{},[902,53008,51326],{"encoding":904},[883,53010,53012],{"className":53011},[886],[888,53013,53014],{"xmlns":890},[892,53015,53016,53030],{},[895,53017,53018,53026,53028],{},[5950,53019,53020,53022,53024],{},[898,53021,12471],{},[898,53023,9365],{},[1750,53025,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,53027,2624],{},[1742,53029,2607],{},[902,53031,53032],{"encoding":904},"Q'_c \u003C 0",[724,53034,53035],{},[614,53036,53037,53038,53058,53059,53083,53084,53106,53107,2313],{},"Obrázek 2.23: Pootočení přímky nabídky z ",[883,53039,53041],{"className":53040},[886],[888,53042,53043],{"xmlns":890},[892,53044,53045,53055],{},[895,53046,53047,53049,53051,53053],{},[898,53048,9365],{},[898,53050,12471],{},[1750,53052,1861],{},[898,53054,3429],{},[902,53056,53057],{"encoding":904},"cQ + d"," na strmější ",[883,53060,53062],{"className":53061},[886],[888,53063,53064],{"xmlns":890},[892,53065,53066,53080],{},[895,53067,53068,53074,53076,53078],{},[5535,53069,53070,53072],{},[898,53071,9365],{},[1742,53073,1744],{},[898,53075,12471],{},[1750,53077,1861],{},[898,53079,3429],{},[902,53081,53082],{"encoding":904},"c_1 Q + d"," (při ",[883,53085,53087],{"className":53086},[886],[888,53088,53089],{"xmlns":890},[892,53090,53091,53103],{},[895,53092,53093,53099,53101],{},[5535,53094,53095,53097],{},[898,53096,9365],{},[1742,53098,1744],{},[1750,53100,2604],{},[898,53102,9365],{},[902,53104,53105],{"encoding":904},"c_1 > c",") — rovnovážný bod se posouvá vlevo, ",[883,53108,53110],{"className":53109},[886],[888,53111,53112],{"xmlns":890},[892,53113,53114,53124],{},[895,53115,53116,53122],{},[1699,53117,53118,53120],{},[898,53119,12471],{},[898,53121,1705],{},[1750,53123,51514],{},[902,53125,53126],{"encoding":904},"Q^E \\downarrow",[724,53128,53129,53130,53162,53163,2313],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[883,53131,53133],{"className":53132},[886],[888,53134,53135],{"xmlns":890},[892,53136,53137,53159],{},[895,53138,53139,53141,53143,53145,53153,53155,53157],{},[898,53140,2666],{"mathvariant":1747},[898,53142,12471],{},[1750,53144,2274],{},[5950,53146,53147,53149,53151],{},[898,53148,12471],{},[898,53150,2573],{},[1750,53152,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,53154,2658],{},[898,53156,3429],{},[898,53158,2573],{},[902,53160,53161],{"encoding":904},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[883,53164,53166],{"className":53165},[886],[888,53167,53168],{"xmlns":890},[892,53169,53170,53178],{},[895,53171,53172],{},[1699,53173,53174,53176],{},[898,53175,1776],{},[898,53177,1705],{},[902,53179,50389],{"encoding":904},[198,53181,53183,53184],{"id":53182},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[883,53185,53187],{"className":53186},[886],[888,53188,53189],{"xmlns":890},[892,53190,53191,53199],{},[895,53192,53193],{},[1699,53194,53195,53197],{},[898,53196,12471],{},[898,53198,1705],{},[902,53200,51326],{"encoding":904},[724,53202,53203,50578,53205,50613,53231,2313],{},[38,53204,46856],{},[883,53206,53208],{"className":53207},[886],[888,53209,53210],{"xmlns":890},[892,53211,53212,53228],{},[895,53213,53214,53216,53218,53220,53222,53224,53226],{},[898,53215,1776],{},[1750,53217,1766],{},[1750,53219,1758],{},[1742,53221,7822],{},[898,53223,12471],{},[1750,53225,1861],{},[1742,53227,14865],{},[902,53229,53230],{"encoding":904},"P = -3Q + 40",[883,53232,53234],{"className":53233},[886],[888,53235,53236],{"xmlns":890},[892,53237,53238,53252],{},[895,53239,53240,53242,53244,53246,53248,53250],{},[898,53241,1776],{},[1750,53243,1766],{},[1742,53245,4268],{},[898,53247,12471],{},[1750,53249,1861],{},[1742,53251,3079],{},[902,53253,53254],{"encoding":904},"P = 0{,}5Q + 10",[724,53256,53257,53259],{},[38,53258,46888],{}," Rovnovážné množství",[883,53261,53263],{"className":53262},[886],[888,53264,53265],{"xmlns":890,"display":36989},[892,53266,53267,53335],{},[895,53268,53269,53275,53277,53295,53297,53321,53323,53330,53332],{},[1699,53270,53271,53273],{},[898,53272,12471],{},[898,53274,1705],{},[1750,53276,1766],{},[3423,53278,53279,53287],{},[895,53280,53281,53283,53285],{},[898,53282,2573],{},[1750,53284,1758],{},[898,53286,3429],{},[895,53288,53289,53291,53293],{},[898,53290,9365],{},[1750,53292,1758],{},[898,53294,207],{},[1750,53296,1766],{},[3423,53298,53299,53307],{},[895,53300,53301,53303,53305],{},[1742,53302,14865],{},[1750,53304,1758],{},[1742,53306,3079],{},[895,53308,53309,53311,53313,53315,53317,53319],{},[1742,53310,4268],{},[1750,53312,1758],{},[1750,53314,1753],{"stretchy":1752},[1750,53316,1758],{},[1742,53318,7822],{},[1750,53320,1763],{"stretchy":1752},[1750,53322,1766],{},[3423,53324,53325,53327],{},[1742,53326,46942],{},[1742,53328,53329],{},"3,5",[1750,53331,2274],{},[1742,53333,53334],{},"8,571.",[902,53336,53337],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[724,53339,53340,53385],{},[38,53341,53342,53343,12359,53356,4321,53370,53384],{},"(a) Změna ",[883,53344,53346],{"className":53345},[886],[888,53347,53348],{"xmlns":890},[892,53349,53350,53354],{},[895,53351,53352],{},[898,53353,9365],{},[902,53355,9365],{"encoding":904},[883,53357,53359],{"className":53358},[886],[888,53360,53361],{"xmlns":890},[892,53362,53363,53367],{},[895,53364,53365],{},[1742,53366,4268],{},[902,53368,53369],{"encoding":904},"0{,}5",[883,53371,53373],{"className":53372},[886],[888,53374,53375],{"xmlns":890},[892,53376,53377,53381],{},[895,53378,53379],{},[1742,53380,3123],{},[902,53382,53383],{"encoding":904},"0{,}6"," (ceteris paribus)."," Dle (2.12):",[883,53387,53389],{"className":53388},[886],[888,53390,53391],{"xmlns":890,"display":36989},[892,53392,53393,53470],{},[895,53394,53395,53403,53405,53407,53409,53411,53413,53439,53441,53443,53445,53447,53449,53459,53461,53463,53465,53467],{},[5950,53396,53397,53399,53401],{},[898,53398,12471],{},[898,53400,9365],{},[1750,53402,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,53404,2658],{},[898,53406,3429],{},[898,53408,9365],{},[1750,53410,1766],{},[1750,53412,1758],{},[3423,53414,53415,53423],{},[895,53416,53417,53419,53421],{},[898,53418,2573],{},[1750,53420,1758],{},[898,53422,3429],{},[895,53424,53425,53427,53429,53431,53433],{},[1750,53426,1753],{"stretchy":1752},[898,53428,9365],{},[1750,53430,1758],{},[898,53432,207],{},[1699,53434,53435,53437],{},[1750,53436,1763],{"stretchy":1752},[1742,53438,1872],{},[1969,53440,2658],{},[898,53442,3429],{},[898,53444,9365],{},[1750,53446,1766],{},[1750,53448,1758],{},[3423,53450,53451,53453],{},[1742,53452,46942],{},[1699,53454,53455,53457],{},[1742,53456,53329],{},[1742,53458,1872],{},[1750,53460,8009],{},[1742,53462,12476],{},[1750,53464,2274],{},[1750,53466,1758],{},[1742,53468,53469],{},"0,245.",[902,53471,53472],{"encoding":904},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[724,53474,53475,53476,2313],{},"Nové rovnovážné množství ",[883,53477,53479],{"className":53478},[886],[888,53480,53481],{"xmlns":890},[892,53482,53483,53508],{},[895,53484,53485,53493,53495,53498,53500,53503,53505],{},[5950,53486,53487,53489,53491],{},[898,53488,12471],{},[1742,53490,1744],{},[898,53492,1705],{},[1750,53494,2274],{},[1742,53496,53497],{},"8,571",[1750,53499,1758],{},[1742,53501,53502],{},"0,245",[1750,53504,1766],{},[1742,53506,53507],{},"8,326",[902,53509,53510],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[724,53512,53513,53598],{},[38,53514,53515,53516,1343,53536,1343,53558,1343,53578,2313],{},"(b) Současné změny ",[883,53517,53519],{"className":53518},[886],[888,53520,53521],{"xmlns":890},[892,53522,53523,53533],{},[895,53524,53525,53527,53529,53531],{},[898,53526,3429],{},[898,53528,207],{},[1750,53530,1766],{},[1742,53532,4268],{},[902,53534,53535],{"encoding":904},"da = 0{,}5",[883,53537,53539],{"className":53538},[886],[888,53540,53541],{"xmlns":890},[892,53542,53543,53555],{},[895,53544,53545,53547,53549,53551,53553],{},[898,53546,3429],{},[898,53548,2573],{},[1750,53550,1766],{},[1750,53552,1758],{},[1742,53554,7902],{},[902,53556,53557],{"encoding":904},"db = -5",[883,53559,53561],{"className":53560},[886],[888,53562,53563],{"xmlns":890},[892,53564,53565,53575],{},[895,53566,53567,53569,53571,53573],{},[898,53568,3429],{},[898,53570,9365],{},[1750,53572,1766],{},[1742,53574,12476],{},[902,53576,53577],{"encoding":904},"dc = 0{,}1",[883,53579,53581],{"className":53580},[886],[888,53582,53583],{"xmlns":890},[892,53584,53585,53595],{},[895,53586,53587,53589,53591,53593],{},[898,53588,3429],{},[898,53590,3429],{},[1750,53592,1766],{},[1742,53594,1744],{},[902,53596,53597],{"encoding":904},"dd = 1"," Dosazením do (2.11):",[883,53600,53602],{"className":53601},[886],[888,53603,53604],{"xmlns":890,"display":36989},[892,53605,53606,53749],{},[4577,53607,53608,53690,53726],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,53609,53610,53620],{},[4585,53611,53612],{},[3586,53613,53614],{"scriptlevel":2607,"displaystyle":1916},[895,53615,53616,53618],{},[898,53617,2666],{"mathvariant":1747},[898,53619,12471],{},[4585,53621,53622],{},[3586,53623,53624],{"scriptlevel":2607,"displaystyle":1916},[895,53625,53626,53628,53630,53640,53642,53644,53646,53652,53654,53656,53658,53660,53662,53664,53674,53676,53678,53680,53686,53688],{},[895,53627],{},[1750,53629,2274],{},[3423,53631,53632,53634],{},[1742,53633,46942],{},[1699,53635,53636,53638],{},[1742,53637,53329],{},[1742,53639,1872],{},[1750,53641,8009],{},[1742,53643,4268],{},[1750,53645,1861],{},[3423,53647,53648,53650],{},[1742,53649,1744],{},[1742,53651,53329],{},[1750,53653,8009],{},[1750,53655,1753],{"stretchy":1752},[1750,53657,1758],{},[1742,53659,7902],{},[1750,53661,1763],{"stretchy":1752},[1750,53663,1758],{},[3423,53665,53666,53668],{},[1742,53667,46942],{},[1699,53669,53670,53672],{},[1742,53671,53329],{},[1742,53673,1872],{},[1750,53675,8009],{},[1742,53677,12476],{},[1750,53679,1758],{},[3423,53681,53682,53684],{},[1742,53683,1744],{},[1742,53685,53329],{},[1750,53687,8009],{},[1742,53689,1744],{},[4582,53691,53692,53698],{},[4585,53693,53694],{},[3586,53695,53696],{"scriptlevel":2607,"displaystyle":1916},[895,53697],{},[4585,53699,53700],{},[3586,53701,53702],{"scriptlevel":2607,"displaystyle":1916},[895,53703,53704,53706,53708,53711,53713,53716,53718,53721,53723],{},[895,53705],{},[1750,53707,1766],{},[1742,53709,53710],{},"1,2245",[1750,53712,1758],{},[1742,53714,53715],{},"1,4286",[1750,53717,1758],{},[1742,53719,53720],{},"0,2449",[1750,53722,1758],{},[1742,53724,53725],{},"0,2857",[4582,53727,53728,53734],{},[4585,53729,53730],{},[3586,53731,53732],{"scriptlevel":2607,"displaystyle":1916},[895,53733],{},[4585,53735,53736],{},[3586,53737,53738],{"scriptlevel":2607,"displaystyle":1916},[895,53739,53740,53742,53744,53746],{},[895,53741],{},[1750,53743,2274],{},[1750,53745,1758],{},[1742,53747,53748],{},"0,735.",[902,53750,53751],{"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}",[724,53753,38988,53754,2313],{},[883,53755,53757],{"className":53756},[886],[888,53758,53759],{"xmlns":890},[892,53760,53761,53785],{},[895,53762,53763,53771,53773,53775,53777,53780,53782],{},[5950,53764,53765,53767,53769],{},[898,53766,12471],{},[1742,53768,1744],{},[898,53770,1705],{},[1750,53772,2274],{},[1742,53774,53497],{},[1750,53776,1758],{},[1742,53778,53779],{},"0,735",[1750,53781,1766],{},[1742,53783,53784],{},"7,836",[902,53786,53787],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1785,53789,53790],{},[724,53791,53792,53794,53795,53818,53819,53841],{},[883,53793,5454],{}," Pozn. — oprava\nV knize je u této dílčí úlohy uvedena hodnota ",[883,53796,53798],{"className":53797},[886],[888,53799,53800],{"xmlns":890},[892,53801,53802,53815],{},[895,53803,53804,53806,53808,53810,53812],{},[898,53805,2666],{"mathvariant":1747},[898,53807,12471],{},[1750,53809,2274],{},[1750,53811,1758],{},[1742,53813,53814],{},"2,69",[902,53816,53817],{"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 ",[883,53820,53822],{"className":53821},[886],[888,53823,53824],{"xmlns":890},[892,53825,53826,53838],{},[895,53827,53828,53830,53832,53834,53836],{},[898,53829,2666],{"mathvariant":1747},[898,53831,12471],{},[1750,53833,2274],{},[1750,53835,1758],{},[1742,53837,53779],{},[902,53839,53840],{"encoding":904},"\\Delta Q \\approx -0{,}735",". Výsledek byl v této wiki opraven.",[724,53843,53844],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (kap. 7).",[45893,53846],{},[115,53848,820],{"id":21417},[1785,53850,53851],{},[724,53852,53853,13541,53855,2084,53858,4419,53874,2084,53877,53893,53894,2313],{},[883,53854,1791],{},[38,53856,53857],{},"Přebytek spotřebitele",[883,53859,53861],{"className":53860},[886],[888,53862,53863],{"xmlns":890},[892,53864,53865,53871],{},[895,53866,53867,53869],{},[898,53868,1812],{},[898,53870,1779],{},[902,53872,53873],{"encoding":904},"CS",[38,53875,53876],{},"přebytek výrobce",[883,53878,53880],{"className":53879},[886],[888,53881,53882],{"xmlns":890},[892,53883,53884,53890],{},[895,53885,53886,53888],{},[898,53887,1776],{},[898,53889,1779],{},[902,53891,53892],{"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 ",[207,53895,53897],{"className":53896,"dataFsResolvedFilePath":818,"href":819},[210],"prebytek-spotrebitele-vyrobce",[724,53899,53900],{},[4434,53901],{"alt":53902,"className":53903,"src":53904},"imek-prebytky-cs-ps",[210,4438],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[724,53906,53907,2084,53909,53912],{},[38,53908,53857],{},[614,53910,53911],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[883,53914,53916],{"className":53915},[886],[888,53917,53918],{"xmlns":890,"display":36989},[892,53919,53920,53997],{},[4577,53921,53922],{"width":36994},[4582,53923,53924,53926,53990,53992],{},[4585,53925],{"width":36999},[4585,53927,53928],{},[895,53929,53930,53932,53934,53936,53942,53944,53946,53958,53960,53962,53964,53966,53968,53970,53972,53974,53980,53982,53988],{},[898,53931,1812],{},[898,53933,1779],{},[1750,53935,1753],{"stretchy":1752},[5535,53937,53938,53940],{},[898,53939,12471],{},[1742,53941,2607],{},[1750,53943,1763],{"stretchy":1752},[1750,53945,1766],{},[5950,53947,53948,53950,53952],{},[1750,53949,20802],{},[1742,53951,2607],{},[5535,53953,53954,53956],{},[898,53955,12471],{},[1742,53957,2607],{},[898,53959,5541],{},[1750,53961,1753],{"stretchy":1752},[898,53963,12471],{},[1750,53965,1763],{"stretchy":1752},[1969,53967,2658],{},[898,53969,3429],{},[898,53971,12471],{},[1750,53973,1758],{},[5535,53975,53976,53978],{},[898,53977,1776],{},[1742,53979,2607],{},[1969,53981,2658],{},[5535,53983,53984,53986],{},[898,53985,12471],{},[1742,53987,2607],{},[898,53989,2313],{"mathvariant":1747},[4585,53991],{"width":36999},[4585,53993,53994],{},[1969,53995,53996],{},"(2.14)",[902,53998,53999],{"encoding":904},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[724,54001,54002,2084,54005,54008],{},[38,54003,54004],{},"Přebytek výrobce",[614,54006,54007],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[883,54010,54012],{"className":54011},[886],[888,54013,54014],{"xmlns":890,"display":36989},[892,54015,54016,54093],{},[4577,54017,54018],{"width":36994},[4582,54019,54020,54022,54086,54088],{},[4585,54021],{"width":36999},[4585,54023,54024],{},[895,54025,54026,54028,54030,54032,54038,54040,54042,54048,54050,54056,54058,54070,54072,54074,54076,54078,54080,54082,54084],{},[898,54027,1776],{},[898,54029,1779],{},[1750,54031,1753],{"stretchy":1752},[5535,54033,54034,54036],{},[898,54035,12471],{},[1742,54037,2607],{},[1750,54039,1763],{"stretchy":1752},[1750,54041,1766],{},[5535,54043,54044,54046],{},[898,54045,1776],{},[1742,54047,2607],{},[1969,54049,2658],{},[5535,54051,54052,54054],{},[898,54053,12471],{},[1742,54055,2607],{},[1750,54057,1758],{},[5950,54059,54060,54062,54064],{},[1750,54061,20802],{},[1742,54063,2607],{},[5535,54065,54066,54068],{},[898,54067,12471],{},[1742,54069,2607],{},[898,54071,1779],{},[1750,54073,1753],{"stretchy":1752},[898,54075,12471],{},[1750,54077,1763],{"stretchy":1752},[1969,54079,2658],{},[898,54081,3429],{},[898,54083,12471],{},[898,54085,2313],{"mathvariant":1747},[4585,54087],{"width":36999},[4585,54089,54090],{},[1969,54091,54092],{},"(2.15)",[902,54094,54095],{"encoding":904},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[724,54097,54098,54099,2313],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[207,54100,54102],{"className":54101,"dataFsResolvedFilePath":773,"href":774},[210],"určitého integrálu",[45893,54104],{},[115,54106,54108],{"id":54107},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[120,54110,54111,54142,54147,54153,54181,54187,54216,54222,54302,54328],{},[123,54112,54113,54115,54116,54141],{},[38,54114,46851],{}," — lineární poptávka ",[883,54117,54119],{"className":54118},[886],[888,54120,54121],{"xmlns":890},[892,54122,54123,54139],{},[895,54124,54125,54127,54129,54131,54133,54135,54137],{},[898,54126,1776],{},[1750,54128,1766],{},[1750,54130,1758],{},[1742,54132,1872],{},[898,54134,12471],{},[1750,54136,1861],{},[1742,54138,12800],{},[902,54140,46883],{"encoding":904},", alternativní tvar, cenové rozpětí.",[123,54143,54144,54146],{},[38,54145,47165],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[123,54148,54149,54152],{},[38,54150,54151],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[123,54154,54155,54157,54158,2313],{},[38,54156,49712],{}," — lineární nabídka ",[883,54159,54161],{"className":54160},[886],[888,54162,54163],{"xmlns":890},[892,54164,54165,54179],{},[895,54166,54167,54169,54171,54173,54175,54177],{},[898,54168,1776],{},[1750,54170,1766],{},[1742,54172,4268],{},[898,54174,12471],{},[1750,54176,1861],{},[1742,54178,6419],{},[902,54180,49741],{"encoding":904},[123,54182,54183,54186],{},[38,54184,54185],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[123,54188,54189,54192,54193,2313],{},[38,54190,54191],{},"Příklad 2.7"," — kvadratická rovnováha, ",[883,54194,54196],{"className":54195},[886],[888,54197,54198],{"xmlns":890},[892,54199,54200,54214],{},[895,54201,54202,54204,54206,54208,54210,54212],{},[898,54203,1705],{},[1750,54205,5141],{"stretchy":1752},[1742,54207,7859],{},[1750,54209,1917],{"separator":1916},[1742,54211,50859],{},[1750,54213,5158],{"stretchy":1752},[902,54215,50887],{"encoding":904},[123,54217,54218,54221],{},[38,54219,54220],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[123,54223,54224,54227,54228,54245,54246,1343,54271,54298,54299,12628],{},[38,54225,54226],{},"Příklad 2.9"," — daň ",[883,54229,54231],{"className":54230},[886],[888,54232,54233],{"xmlns":890},[892,54234,54235,54243],{},[895,54236,54237,54239,54241],{},[898,54238,5326],{},[1750,54240,1766],{},[1742,54242,3219],{},[902,54244,50191],{"encoding":904}," na výrobce; rozklad ",[883,54247,54249],{"className":54248},[886],[888,54250,54251],{"xmlns":890},[892,54252,54253,54269],{},[895,54254,54255,54265,54267],{},[5535,54256,54257,54259],{},[898,54258,5326],{},[895,54260,54261,54263],{},[898,54262,51600],{},[898,54264,724],{},[1750,54266,1766],{},[1742,54268,1872],{},[902,54270,51899],{"encoding":904},[883,54272,54274],{"className":54273},[886],[888,54275,54276],{"xmlns":890},[892,54277,54278,54296],{},[895,54279,54280,54292,54294],{},[5535,54281,54282,54284],{},[898,54283,5326],{},[895,54285,54286,54288,54290],{},[898,54287,51623],{},[898,54289,11717],{},[898,54291,1920],{},[1750,54293,1766],{},[1742,54295,7859],{},[902,54297,51928],{"encoding":904},". (Viz ",[207,54300,51644],{"className":54301,"dataFsResolvedFilePath":809,"href":810},[210],[123,54303,54304,54227,54307,54324,54325,12628],{},[38,54305,54306],{},"Příklad 2.10",[883,54308,54310],{"className":54309},[886],[888,54311,54312],{"xmlns":890},[892,54313,54314,54322],{},[895,54315,54316,54318,54320],{},[898,54317,5326],{},[1750,54319,1766],{},[1742,54321,3219],{},[902,54323,50191],{"encoding":904}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[207,54326,51644],{"className":54327,"dataFsResolvedFilePath":809,"href":810},[210],[123,54329,54330,54333],{},[38,54331,54332],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[45893,54335],{},[115,54337,54339],{"id":54338},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[198,54341,54343],{"id":54342},"základní-analýza-poptávky","Základní analýza poptávky",[724,54345,54346,54349,54350,54385,54386,54412],{},[38,54347,54348],{},"2.1"," Je dána poptávka ",[883,54351,54353],{"className":54352},[886],[888,54354,54355],{"xmlns":890},[892,54356,54357,54382],{},[895,54358,54359,54361,54363,54365,54367,54369,54371,54373,54376,54378,54380],{},[898,54360,12471],{},[1750,54362,1766],{},[898,54364,5541],{},[1750,54366,1753],{"stretchy":1752},[898,54368,1776],{},[1750,54370,1763],{"stretchy":1752},[1750,54372,1766],{},[1742,54374,54375],{},"75",[1750,54377,1758],{},[1742,54379,7902],{},[898,54381,1776],{},[902,54383,54384],{"encoding":904},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[883,54387,54389],{"className":54388},[886],[888,54390,54391],{"xmlns":890},[892,54392,54393,54409],{},[895,54394,54395,54397,54399,54401,54403,54405,54407],{},[1742,54396,2607],{},[1750,54398,1917],{"separator":1916},[1742,54400,7902],{},[1750,54402,1917],{"separator":1916},[1742,54404,3079],{},[1750,54406,1917],{"separator":1916},[1742,54408,45167],{},[902,54410,54411],{"encoding":904},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[724,54414,54415,54418,54419,54437,54438,12825],{},[38,54416,54417],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[883,54420,54422],{"className":54421},[886],[888,54423,54424],{"xmlns":890},[892,54425,54426,54434],{},[895,54427,54428,54430,54432],{},[898,54429,1776],{},[1750,54431,1917],{"separator":1916},[898,54433,12471],{},[902,54435,54436],{"encoding":904},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[883,54439,54441],{"className":54440},[886],[888,54442,54443],{"xmlns":890},[892,54444,54445,54461],{},[895,54446,54447,54449,54451,54453,54455,54457,54459],{},[898,54448,207],{},[1750,54450,1917],{"separator":1916},[898,54452,2573],{},[1750,54454,1917],{"separator":1916},[898,54456,9365],{},[1750,54458,2604],{},[1742,54460,2607],{},[902,54462,54463],{"encoding":904},"a, b, c > 0",[120,54465,54466,54499,54530,54565,54596,54631],{},[123,54467,54468,54469],{},"(a) ",[883,54470,54472],{"className":54471},[886],[888,54473,54474],{"xmlns":890},[892,54475,54476,54496],{},[895,54477,54478,54480,54482],{},[898,54479,12471],{},[1750,54481,1766],{},[3586,54483,54484],{"scriptlevel":2607,"displaystyle":1916},[3423,54485,54486,54488],{},[898,54487,207],{},[895,54489,54490,54492,54494],{},[898,54491,1776],{},[1750,54493,1861],{},[898,54495,9365],{},[902,54497,54498],{"encoding":904},"Q = \\dfrac{a}{P + c}",[123,54500,54501,54502],{},"(b) ",[883,54503,54505],{"className":54504},[886],[888,54506,54507],{"xmlns":890},[892,54508,54509,54527],{},[895,54510,54511,54513,54515],{},[898,54512,12471],{},[1750,54514,1766],{},[17761,54516,54517],{},[895,54518,54519,54521,54523,54525],{},[898,54520,207],{},[1750,54522,1758],{},[898,54524,2573],{},[898,54526,12471],{},[902,54528,54529],{"encoding":904},"Q = \\sqrt{a - bQ}",[123,54531,54532,54533],{},"(c) ",[883,54534,54536],{"className":54535},[886],[888,54537,54538],{"xmlns":890},[892,54539,54540,54562],{},[895,54541,54542,54544,54546],{},[898,54543,12471],{},[1750,54545,1766],{},[3586,54547,54548],{"scriptlevel":2607,"displaystyle":1916},[3423,54549,54550,54560],{},[895,54551,54552,54554,54556],{},[898,54553,207],{},[1750,54555,1758],{},[17761,54557,54558],{},[898,54559,1776],{},[898,54561,2573],{},[902,54563,54564],{"encoding":904},"Q = \\dfrac{a - \\sqrt{P}}{b}",[123,54566,54567,54568],{},"(d) ",[883,54569,54571],{"className":54570},[886],[888,54572,54573],{"xmlns":890},[892,54574,54575,54593],{},[895,54576,54577,54579,54581,54583,54585,54587],{},[898,54578,1776],{},[1750,54580,1766],{},[898,54582,207],{},[1750,54584,1758],{},[898,54586,2573],{},[1699,54588,54589,54591],{},[898,54590,12471],{},[1742,54592,1872],{},[902,54594,54595],{"encoding":904},"P = a - bQ^2",[123,54597,54598,54599],{},"(e) ",[883,54600,54602],{"className":54601},[886],[888,54603,54604],{"xmlns":890},[892,54605,54606,54628],{},[895,54607,54608,54610,54612,54614,54624,54626],{},[898,54609,12471],{},[1750,54611,1766],{},[898,54613,2573],{},[1699,54615,54616,54618],{},[898,54617,1776],{},[895,54619,54620,54622],{},[1750,54621,1758],{},[898,54623,207],{},[1750,54625,1861],{},[898,54627,9365],{},[902,54629,54630],{"encoding":904},"Q = bP^{-a} + c",[123,54632,54633,54634],{},"(f) ",[883,54635,54637],{"className":54636},[886],[888,54638,54639],{"xmlns":890},[892,54640,54641,54664],{},[895,54642,54643,54645,54647,54649,54651],{},[898,54644,12471],{},[1750,54646,1766],{},[898,54648,207],{},[1750,54650,8009],{},[1699,54652,54653,54656],{},[898,54654,54655],{},"e",[895,54657,54658,54660,54662],{},[1750,54659,1758],{},[898,54661,2573],{},[898,54663,1776],{},[902,54665,54666],{"encoding":904},"Q = a \\cdot e^{-bP}",[724,54668,54669,54672],{},[38,54670,54671],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[120,54674,54675,54678,54681],{},[123,54676,54677],{},"(a) Cena substitutu.",[123,54679,54680],{},"(b) Cena komplementu.",[123,54682,54683],{},"(c) Výdaje na reklamu.",[724,54685,54686,54349,54688,54722,54723,54751],{},[38,54687,8494],{},[883,54689,54691],{"className":54690},[886],[888,54692,54693],{"xmlns":890},[892,54694,54695,54719],{},[895,54696,54697,54699,54701,54703,54705,54707,54709,54711,54713,54715,54717],{},[898,54698,1776],{},[1750,54700,1766],{},[898,54702,5541],{},[1750,54704,1753],{"stretchy":1752},[898,54706,12471],{},[1750,54708,1763],{"stretchy":1752},[1750,54710,1766],{},[1742,54712,4903],{},[1750,54714,1758],{},[1742,54716,1872],{},[898,54718,12471],{},[902,54720,54721],{"encoding":904},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[883,54724,54726],{"className":54725},[886],[888,54727,54728],{"xmlns":890},[892,54729,54730,54748],{},[895,54731,54732,54734,54736,54742,54744,54746],{},[898,54733,1776],{},[1750,54735,1766],{},[1699,54737,54738,54740],{},[898,54739,5541],{},[1750,54741,3751],{},[1750,54743,1753],{"stretchy":1752},[898,54745,12471],{},[1750,54747,1763],{"stretchy":1752},[902,54749,54750],{"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.",[724,54753,54754,54757],{},[38,54755,54756],{},"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:",[120,54759,54760,54844,54920,55006,55094],{},[123,54761,54468,54762,1343,54802,2313],{},[883,54763,54765],{"className":54764},[886],[888,54766,54767],{"xmlns":890},[892,54768,54769,54799],{},[895,54770,54771,54777,54779,54781,54783,54785,54791,54793],{},[5535,54772,54773,54775],{},[898,54774,7097],{},[1742,54776,1744],{},[1750,54778,1766],{},[1742,54780,6465],{},[1750,54782,1758],{},[1742,54784,7859],{},[5535,54786,54787,54789],{},[898,54788,13916],{},[1742,54790,1744],{},[1750,54792,1861],{},[5535,54794,54795,54797],{},[898,54796,13916],{},[1742,54798,1872],{},[902,54800,54801],{"encoding":904},"B_1 = 20 - 4A_1 + A_2",[883,54803,54805],{"className":54804},[886],[888,54806,54807],{"xmlns":890},[892,54808,54809,54841],{},[895,54810,54811,54817,54819,54821,54823,54825,54831,54833,54835],{},[5535,54812,54813,54815],{},[898,54814,7097],{},[1742,54816,1872],{},[1750,54818,1766],{},[1742,54820,3079],{},[1750,54822,1861],{},[1742,54824,1872],{},[5535,54826,54827,54829],{},[898,54828,13916],{},[1742,54830,1744],{},[1750,54832,1758],{},[1742,54834,7859],{},[5535,54836,54837,54839],{},[898,54838,13916],{},[1742,54840,1872],{},[902,54842,54843],{"encoding":904},"B_2 = 10 + 2A_1 - 4A_2",[123,54845,54501,54846,1343,54888,2313],{},[883,54847,54849],{"className":54848},[886],[888,54850,54851],{"xmlns":890},[892,54852,54853,54885],{},[895,54854,54855,54861,54863,54865,54867,54869,54875,54877,54879],{},[5535,54856,54857,54859],{},[898,54858,7097],{},[1742,54860,1744],{},[1750,54862,1766],{},[1742,54864,3936],{},[1750,54866,1758],{},[1742,54868,3079],{},[5535,54870,54871,54873],{},[898,54872,13916],{},[1742,54874,1744],{},[1750,54876,1758],{},[1742,54878,3219],{},[5535,54880,54881,54883],{},[898,54882,13916],{},[1742,54884,1872],{},[902,54886,54887],{"encoding":904},"B_1 = 50 - 10A_1 - 6A_2",[883,54889,54891],{"className":54890},[886],[888,54892,54893],{"xmlns":890},[892,54894,54895,54917],{},[895,54896,54897,54903,54905,54907,54909,54911],{},[5535,54898,54899,54901],{},[898,54900,7097],{},[1742,54902,1872],{},[1750,54904,1766],{},[1742,54906,45167],{},[1750,54908,1758],{},[1742,54910,3079],{},[5535,54912,54913,54915],{},[898,54914,13916],{},[1742,54916,1872],{},[902,54918,54919],{"encoding":904},"B_2 = 15 - 10A_2",[123,54921,54532,54922,1343,54964,2313],{},[883,54923,54925],{"className":54924},[886],[888,54926,54927],{"xmlns":890},[892,54928,54929,54961],{},[895,54930,54931,54937,54939,54941,54943,54945,54951,54953,54955],{},[5535,54932,54933,54935],{},[898,54934,7097],{},[1742,54936,1744],{},[1750,54938,1766],{},[1742,54940,46942],{},[1750,54942,1758],{},[1742,54944,1872],{},[5535,54946,54947,54949],{},[898,54948,13916],{},[1742,54950,1744],{},[1750,54952,1758],{},[1742,54954,7859],{},[5535,54956,54957,54959],{},[898,54958,13916],{},[1742,54960,1872],{},[902,54962,54963],{"encoding":904},"B_1 = 30 - 2A_1 - 4A_2",[883,54965,54967],{"className":54966},[886],[888,54968,54969],{"xmlns":890},[892,54970,54971,55003],{},[895,54972,54973,54979,54981,54983,54985,54987,54993,54995,54997],{},[5535,54974,54975,54977],{},[898,54976,7097],{},[1742,54978,1872],{},[1750,54980,1766],{},[1742,54982,45167],{},[1750,54984,1861],{},[1742,54986,1872],{},[5535,54988,54989,54991],{},[898,54990,13916],{},[1742,54992,1744],{},[1750,54994,1758],{},[1742,54996,1872],{},[5535,54998,54999,55001],{},[898,55000,13916],{},[1742,55002,1872],{},[902,55004,55005],{"encoding":904},"B_2 = 15 + 2A_1 - 2A_2",[123,55007,54567,55008,1343,55052,2313],{},[883,55009,55011],{"className":55010},[886],[888,55012,55013],{"xmlns":890},[892,55014,55015,55049],{},[895,55016,55017,55023,55025,55027,55029,55031,55033,55039,55041,55043],{},[5535,55018,55019,55021],{},[898,55020,7097],{},[1742,55022,1744],{},[1750,55024,1766],{},[1750,55026,1758],{},[1742,55028,6465],{},[1750,55030,1758],{},[1742,55032,1872],{},[5535,55034,55035,55037],{},[898,55036,13916],{},[1742,55038,1744],{},[1750,55040,1861],{},[1742,55042,7822],{},[5535,55044,55045,55047],{},[898,55046,13916],{},[1742,55048,1872],{},[902,55050,55051],{"encoding":904},"B_1 = -20 - 2A_1 + 3A_2",[883,55053,55055],{"className":55054},[886],[888,55056,55057],{"xmlns":890},[892,55058,55059,55091],{},[895,55060,55061,55067,55069,55071,55073,55075,55081,55083,55085],{},[5535,55062,55063,55065],{},[898,55064,7097],{},[1742,55066,1872],{},[1750,55068,1766],{},[1742,55070,3079],{},[1750,55072,1861],{},[1742,55074,1872],{},[5535,55076,55077,55079],{},[898,55078,13916],{},[1742,55080,1744],{},[1750,55082,1758],{},[1742,55084,1872],{},[5535,55086,55087,55089],{},[898,55088,13916],{},[1742,55090,1872],{},[902,55092,55093],{"encoding":904},"B_2 = 10 + 2A_1 - 2A_2",[123,55095,54598,55096,1343,55138,2313],{},[883,55097,55099],{"className":55098},[886],[888,55100,55101],{"xmlns":890},[892,55102,55103,55135],{},[895,55104,55105,55111,55113,55115,55117,55119,55125,55127,55129],{},[5535,55106,55107,55109],{},[898,55108,7097],{},[1742,55110,1744],{},[1750,55112,1766],{},[1742,55114,6465],{},[1750,55116,1861],{},[1742,55118,1872],{},[5535,55120,55121,55123],{},[898,55122,13916],{},[1742,55124,1744],{},[1750,55126,1861],{},[1742,55128,7859],{},[5535,55130,55131,55133],{},[898,55132,13916],{},[1742,55134,1872],{},[902,55136,55137],{"encoding":904},"B_1 = 20 + 2A_1 + 4A_2",[883,55139,55141],{"className":55140},[886],[888,55142,55143],{"xmlns":890},[892,55144,55145,55177],{},[895,55146,55147,55153,55155,55157,55159,55161,55167,55169,55171],{},[5535,55148,55149,55151],{},[898,55150,7097],{},[1742,55152,1872],{},[1750,55154,1766],{},[1742,55156,14865],{},[1750,55158,1758],{},[1742,55160,7822],{},[5535,55162,55163,55165],{},[898,55164,13916],{},[1742,55166,1744],{},[1750,55168,1861],{},[1742,55170,7902],{},[5535,55172,55173,55175],{},[898,55174,13916],{},[1742,55176,1872],{},[902,55178,55179],{"encoding":904},"B_2 = 40 - 3A_1 + 5A_2",[198,55181,55183],{"id":55182},"základní-analýza-nabídky","Základní analýza nabídky",[724,55185,55186,55189,55190,55224,55225,55247],{},[38,55187,55188],{},"2.6"," Je dána nabídka ",[883,55191,55193],{"className":55192},[886],[888,55194,55195],{"xmlns":890},[892,55196,55197,55221],{},[895,55198,55199,55201,55203,55205,55207,55209,55211,55213,55215,55217,55219],{},[898,55200,1776],{},[1750,55202,1766],{},[898,55204,1779],{},[1750,55206,1753],{"stretchy":1752},[898,55208,12471],{},[1750,55210,1763],{"stretchy":1752},[1750,55212,1766],{},[1742,55214,6465],{},[1750,55216,1861],{},[1742,55218,3929],{},[898,55220,12471],{},[902,55222,55223],{"encoding":904},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[883,55226,55228],{"className":55227},[886],[888,55229,55230],{"xmlns":890},[892,55231,55232,55244],{},[895,55233,55234,55236,55238,55240,55242],{},[1742,55235,6419],{},[1750,55237,1917],{"separator":1916},[1742,55239,46942],{},[1750,55241,1917],{"separator":1916},[1742,55243,6442],{},[902,55245,55246],{"encoding":904},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[724,55249,55250,55253,55254,55271],{},[38,55251,55252],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[883,55255,55257],{"className":55256},[886],[888,55258,55259],{"xmlns":890},[892,55260,55261,55269],{},[895,55262,55263,55265,55267],{},[898,55264,1776],{},[1750,55266,1917],{"separator":1916},[898,55268,12471],{},[902,55270,54436],{"encoding":904},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[120,55273,55274,55300,55328,55361,55395,55431],{},[123,55275,54468,55276],{},[883,55277,55279],{"className":55278},[886],[888,55280,55281],{"xmlns":890},[892,55282,55283,55297],{},[895,55284,55285,55287,55289,55291,55293,55295],{},[898,55286,1776],{},[1750,55288,1766],{},[1742,55290,46942],{},[1750,55292,1861],{},[1742,55294,1872],{},[898,55296,12471],{},[902,55298,55299],{"encoding":904},"P = 30 + 2Q",[123,55301,54501,55302],{},[883,55303,55305],{"className":55304},[886],[888,55306,55307],{"xmlns":890},[892,55308,55309,55325],{},[895,55310,55311,55313,55315,55317,55319,55321,55323],{},[898,55312,12471],{},[1750,55314,1766],{},[1750,55316,1758],{},[1742,55318,7822],{},[1750,55320,1861],{},[1742,55322,4903],{},[898,55324,1776],{},[902,55326,55327],{"encoding":904},"Q = -3 + 12P",[123,55329,54532,55330],{},[883,55331,55333],{"className":55332},[886],[888,55334,55335],{"xmlns":890},[892,55336,55337,55359],{},[895,55338,55339,55341,55343,55349,55351,55353,55355,55357],{},[898,55340,1776],{},[1750,55342,1766],{},[1699,55344,55345,55347],{},[898,55346,12471],{},[1742,55348,1872],{},[1750,55350,1861],{},[1742,55352,6789],{},[898,55354,12471],{},[1750,55356,1861],{},[1742,55358,41469],{},[902,55360,50645],{"encoding":904},[123,55362,54567,55363],{},[883,55364,55366],{"className":55365},[886],[888,55367,55368],{"xmlns":890},[892,55369,55370,55392],{},[895,55371,55372,55374,55376,55382,55384,55386,55388,55390],{},[898,55373,1776],{},[1750,55375,1766],{},[1699,55377,55378,55380],{},[898,55379,12471],{},[1742,55381,1872],{},[1750,55383,1861],{},[1742,55385,1872],{},[898,55387,12471],{},[1750,55389,1861],{},[1742,55391,4903],{},[902,55393,55394],{"encoding":904},"P = Q^2 + 2Q + 12",[123,55396,54598,55397],{},[883,55398,55400],{"className":55399},[886],[888,55401,55402],{"xmlns":890},[892,55403,55404,55428],{},[895,55405,55406,55408,55410,55412,55414,55416,55418,55420,55422],{},[898,55407,12471],{},[1750,55409,1766],{},[1742,55411,4236],{},[1750,55413,1861],{},[1742,55415,7902],{},[898,55417,1776],{},[1750,55419,1861],{},[1742,55421,12476],{},[1699,55423,55424,55426],{},[898,55425,1776],{},[1742,55427,1872],{},[902,55429,55430],{"encoding":904},"Q = 150 + 5P + 0{,}1P^2",[123,55432,54633,55433],{},[883,55434,55436],{"className":55435},[886],[888,55437,55438],{"xmlns":890},[892,55439,55440,55465],{},[895,55441,55442,55444,55446,55448,55450,55452,55454,55456,55459],{},[898,55443,12471],{},[1750,55445,1766],{},[1742,55447,8051],{},[1750,55449,1861],{},[1742,55451,12476],{},[898,55453,1776],{},[1750,55455,1861],{},[1742,55457,55458],{},"0,004",[1699,55460,55461,55463],{},[898,55462,1776],{},[1742,55464,1872],{},[902,55466,55467],{"encoding":904},"Q = 7 + 0{,}1P + 0{,}004P^2",[724,55469,55470,55473],{},[38,55471,55472],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[120,55475,55476,55479,55482,55485],{},[123,55477,55478],{},"(a) Sníží ceny surovin — vstupů.",[123,55480,55481],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[123,55483,55484],{},"(c) Zvýší ceny všech energií.",[123,55486,55487],{},"(d) Sníží daňové odvody státu.",[724,55489,55490,55189,55492,55526,55527,55555],{},[38,55491,51872],{},[883,55493,55495],{"className":55494},[886],[888,55496,55497],{"xmlns":890},[892,55498,55499,55523],{},[895,55500,55501,55503,55505,55507,55509,55511,55513,55515,55517,55519,55521],{},[898,55502,1776],{},[1750,55504,1766],{},[898,55506,1779],{},[1750,55508,1753],{"stretchy":1752},[898,55510,12471],{},[1750,55512,1763],{"stretchy":1752},[1750,55514,1766],{},[1742,55516,4268],{},[898,55518,12471],{},[1750,55520,1861],{},[1742,55522,45167],{},[902,55524,55525],{"encoding":904},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[883,55528,55530],{"className":55529},[886],[888,55531,55532],{"xmlns":890},[892,55533,55534,55552],{},[895,55535,55536,55538,55540,55546,55548,55550],{},[898,55537,1776],{},[1750,55539,1766],{},[1699,55541,55542,55544],{},[898,55543,1779],{},[1750,55545,3751],{},[1750,55547,1753],{"stretchy":1752},[898,55549,12471],{},[1750,55551,1763],{"stretchy":1752},[902,55553,55554],{"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.",[198,55557,50248],{"id":55558},"tržní-rovnováha-1",[724,55560,55561,55563,55564,55581,55582,2366],{},[38,55562,51932],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[883,55565,55567],{"className":55566},[886],[888,55568,55569],{"xmlns":890},[892,55570,55571,55579],{},[895,55572,55573],{},[1699,55574,55575,55577],{},[898,55576,12471],{},[898,55578,1705],{},[902,55580,51326],{"encoding":904}," a rovnovážnou cenu ",[883,55583,55585],{"className":55584},[886],[888,55586,55587],{"xmlns":890},[892,55588,55589,55597],{},[895,55590,55591],{},[1699,55592,55593,55595],{},[898,55594,1776],{},[898,55596,1705],{},[902,55598,50389],{"encoding":904},[120,55600,55601,55654,55705,55764],{},[123,55602,54468,55603,1343,55630,2313],{},[883,55604,55606],{"className":55605},[886],[888,55607,55608],{"xmlns":890},[892,55609,55610,55627],{},[895,55611,55612,55614,55616,55618,55620,55622,55624],{},[898,55613,1776],{},[1750,55615,1766],{},[1750,55617,1758],{},[1742,55619,7902],{},[898,55621,12471],{},[1750,55623,1861],{},[1742,55625,55626],{},"80",[902,55628,55629],{"encoding":904},"P = -5Q + 80",[883,55631,55633],{"className":55632},[886],[888,55634,55635],{"xmlns":890},[892,55636,55637,55651],{},[895,55638,55639,55641,55643,55645,55647,55649],{},[898,55640,1776],{},[1750,55642,1766],{},[1742,55644,1872],{},[898,55646,12471],{},[1750,55648,1861],{},[1742,55650,3079],{},[902,55652,55653],{"encoding":904},"P = 2Q + 10",[123,55655,54501,55656,1343,55682,2313],{},[883,55657,55659],{"className":55658},[886],[888,55660,55661],{"xmlns":890},[892,55662,55663,55679],{},[895,55664,55665,55667,55669,55671,55673,55675,55677],{},[898,55666,12471],{},[1750,55668,1766],{},[1750,55670,1758],{},[1742,55672,4268],{},[898,55674,1776],{},[1750,55676,1861],{},[1742,55678,6419],{},[902,55680,55681],{"encoding":904},"Q = -0{,}5P + 25",[883,55683,55685],{"className":55684},[886],[888,55686,55687],{"xmlns":890},[892,55688,55689,55703],{},[895,55690,55691,55693,55695,55697,55699,55701],{},[898,55692,12471],{},[1750,55694,1766],{},[1742,55696,1872],{},[898,55698,1776],{},[1750,55700,1758],{},[1742,55702,3936],{},[902,55704,49770],{"encoding":904},[123,55706,54532,55707,1343,55733,2313],{},[883,55708,55710],{"className":55709},[886],[888,55711,55712],{"xmlns":890},[892,55713,55714,55730],{},[895,55715,55716,55718,55720,55722,55724,55726,55728],{},[898,55717,1776],{},[1750,55719,1766],{},[1750,55721,1758],{},[1742,55723,7859],{},[898,55725,12471],{},[1750,55727,1861],{},[1742,55729,13710],{},[902,55731,55732],{"encoding":904},"P = -4Q + 120",[883,55734,55736],{"className":55735},[886],[888,55737,55738],{"xmlns":890},[892,55739,55740,55761],{},[895,55741,55742,55744,55746,55754,55756,55758],{},[898,55743,1776],{},[1750,55745,1766],{},[3586,55747,55748],{"scriptlevel":2607,"displaystyle":1752},[3423,55749,55750,55752],{},[1742,55751,1744],{},[1742,55753,7822],{},[898,55755,12471],{},[1750,55757,1861],{},[1742,55759,55760],{},"29",[902,55762,55763],{"encoding":904},"P = \\tfrac{1}{3}Q + 29",[123,55765,54567,55766,1343,55795,2313],{},[883,55767,55769],{"className":55768},[886],[888,55770,55771],{"xmlns":890},[892,55772,55773,55792],{},[895,55774,55775,55777,55779,55781,55787,55789],{},[898,55776,1776],{},[1750,55778,1766],{},[1750,55780,1758],{},[1699,55782,55783,55785],{},[898,55784,12471],{},[1742,55786,1872],{},[1750,55788,1861],{},[1742,55790,55791],{},"52",[902,55793,55794],{"encoding":904},"P = -Q^2 + 52",[883,55796,55798],{"className":55797},[886],[888,55799,55800],{"xmlns":890},[892,55801,55802,55820],{},[895,55803,55804,55806,55808,55810,55816,55818],{},[898,55805,1776],{},[1750,55807,1766],{},[1742,55809,1872],{},[1699,55811,55812,55814],{},[898,55813,12471],{},[1742,55815,1872],{},[1750,55817,1861],{},[1742,55819,3079],{},[902,55821,55822],{"encoding":904},"P = 2Q^2 + 10",[724,55824,55825,55828,55829,55859,55860,55890],{},[38,55826,55827],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[883,55830,55832],{"className":55831},[886],[888,55833,55834],{"xmlns":890},[892,55835,55836,55856],{},[895,55837,55838,55846,55848],{},[5950,55839,55840,55842,55844],{},[898,55841,12471],{},[1742,55843,1744],{},[898,55845,1705],{},[1750,55847,1917],{"separator":1916},[5950,55849,55850,55852,55854],{},[898,55851,12471],{},[1742,55853,1872],{},[898,55855,1705],{},[902,55857,55858],{"encoding":904},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[883,55861,55863],{"className":55862},[886],[888,55864,55865],{"xmlns":890},[892,55866,55867,55887],{},[895,55868,55869,55877,55879],{},[5950,55870,55871,55873,55875],{},[898,55872,1776],{},[1742,55874,1744],{},[898,55876,1705],{},[1750,55878,1917],{"separator":1916},[5950,55880,55881,55883,55885],{},[898,55882,1776],{},[1742,55884,1872],{},[898,55886,1705],{},[902,55888,55889],{"encoding":904},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[120,55892,55893,56045],{},[123,55894,54468,55895,1343,55935,1343,55977,1343,56011,2313],{},[883,55896,55898],{"className":55897},[886],[888,55899,55900],{"xmlns":890},[892,55901,55902,55932],{},[895,55903,55904,55910,55912,55914,55916,55918,55924,55926],{},[5535,55905,55906,55908],{},[898,55907,12471],{},[1742,55909,1744],{},[1750,55911,1766],{},[1742,55913,3079],{},[1750,55915,1758],{},[1742,55917,1872],{},[5535,55919,55920,55922],{},[898,55921,1776],{},[1742,55923,1744],{},[1750,55925,1861],{},[5535,55927,55928,55930],{},[898,55929,1776],{},[1742,55931,1872],{},[902,55933,55934],{"encoding":904},"Q_1 = 10 - 2P_1 + P_2",[883,55936,55938],{"className":55937},[886],[888,55939,55940],{"xmlns":890},[892,55941,55942,55974],{},[895,55943,55944,55950,55952,55954,55956,55958,55964,55966,55968],{},[5535,55945,55946,55948],{},[898,55947,12471],{},[1742,55949,1872],{},[1750,55951,1766],{},[1742,55953,7902],{},[1750,55955,1861],{},[1742,55957,1872],{},[5535,55959,55960,55962],{},[898,55961,1776],{},[1742,55963,1744],{},[1750,55965,1758],{},[1742,55967,1872],{},[5535,55969,55970,55972],{},[898,55971,1776],{},[1742,55973,1872],{},[902,55975,55976],{"encoding":904},"Q_2 = 5 + 2P_1 - 2P_2",[883,55978,55980],{"className":55979},[886],[888,55981,55982],{"xmlns":890},[892,55983,55984,56008],{},[895,55985,55986,55992,55994,55996,55998,56000,56002],{},[5535,55987,55988,55990],{},[898,55989,12471],{},[1742,55991,1744],{},[1750,55993,1766],{},[1750,55995,1758],{},[1742,55997,7822],{},[1750,55999,1861],{},[1742,56001,1872],{},[5535,56003,56004,56006],{},[898,56005,1776],{},[1742,56007,1744],{},[902,56009,56010],{"encoding":904},"Q_1 = -3 + 2P_1",[883,56012,56014],{"className":56013},[886],[888,56015,56016],{"xmlns":890},[892,56017,56018,56042],{},[895,56019,56020,56026,56028,56030,56032,56034,56036],{},[5535,56021,56022,56024],{},[898,56023,12471],{},[1742,56025,1872],{},[1750,56027,1766],{},[1750,56029,1758],{},[1742,56031,1872],{},[1750,56033,1861],{},[1742,56035,7822],{},[5535,56037,56038,56040],{},[898,56039,1776],{},[1742,56041,1872],{},[902,56043,56044],{"encoding":904},"Q_2 = -2 + 3P_2",[123,56046,54501,56047,1343,56087,1343,56129,1343,56161,2313],{},[883,56048,56050],{"className":56049},[886],[888,56051,56052],{"xmlns":890},[892,56053,56054,56084],{},[895,56055,56056,56062,56064,56066,56068,56070,56076,56078],{},[5535,56057,56058,56060],{},[898,56059,12471],{},[1742,56061,1744],{},[1750,56063,1766],{},[1742,56065,4078],{},[1750,56067,1758],{},[1742,56069,1872],{},[5535,56071,56072,56074],{},[898,56073,1776],{},[1742,56075,1744],{},[1750,56077,1861],{},[5535,56079,56080,56082],{},[898,56081,1776],{},[1742,56083,1872],{},[902,56085,56086],{"encoding":904},"Q_1 = 100 - 2P_1 + P_2",[883,56088,56090],{"className":56089},[886],[888,56091,56092],{"xmlns":890},[892,56093,56094,56126],{},[895,56095,56096,56102,56104,56106,56108,56110,56116,56118,56120],{},[5535,56097,56098,56100],{},[898,56099,12471],{},[1742,56101,1872],{},[1750,56103,1766],{},[1742,56105,7902],{},[1750,56107,1861],{},[1742,56109,1872],{},[5535,56111,56112,56114],{},[898,56113,1776],{},[1742,56115,1744],{},[1750,56117,1758],{},[1742,56119,7822],{},[5535,56121,56122,56124],{},[898,56123,1776],{},[1742,56125,1872],{},[902,56127,56128],{"encoding":904},"Q_2 = 5 + 2P_1 - 3P_2",[883,56130,56132],{"className":56131},[886],[888,56133,56134],{"xmlns":890},[892,56135,56136,56158],{},[895,56137,56138,56144,56146,56148,56150,56152],{},[5535,56139,56140,56142],{},[898,56141,12471],{},[1742,56143,1744],{},[1750,56145,1766],{},[1750,56147,1758],{},[1742,56149,3079],{},[1750,56151,1861],{},[5535,56153,56154,56156],{},[898,56155,1776],{},[1742,56157,1744],{},[902,56159,56160],{"encoding":904},"Q_1 = -10 + P_1",[883,56162,56164],{"className":56163},[886],[888,56165,56166],{"xmlns":890},[892,56167,56168,56190],{},[895,56169,56170,56176,56178,56180,56182,56184],{},[5535,56171,56172,56174],{},[898,56173,12471],{},[1742,56175,1872],{},[1750,56177,1766],{},[1742,56179,7902],{},[1750,56181,1861],{},[1742,56183,3219],{},[5535,56185,56186,56188],{},[898,56187,1776],{},[1742,56189,1872],{},[902,56191,56192],{"encoding":904},"Q_2 = 5 + 6P_2",[724,56194,56195,56198,56199,1343,56247,1343,56293,56343,56344,1343,56376,1343,56410,5424,56444,2028,56462,56480,56481,56494,56495,56521,56522,55859,56562,2313],{},[38,56196,56197],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[883,56200,56202],{"className":56201},[886],[888,56203,56204],{"xmlns":890},[892,56205,56206,56244],{},[895,56207,56208,56214,56216,56218,56220,56226,56228,56230,56236,56238],{},[5535,56209,56210,56212],{},[898,56211,12471],{},[1742,56213,1744],{},[1750,56215,1766],{},[1742,56217,45167],{},[1750,56219,1758],{},[5535,56221,56222,56224],{},[898,56223,1776],{},[1742,56225,1744],{},[1750,56227,1861],{},[1742,56229,1872],{},[5535,56231,56232,56234],{},[898,56233,1776],{},[1742,56235,1872],{},[1750,56237,1861],{},[5535,56239,56240,56242],{},[898,56241,1776],{},[1742,56243,7822],{},[902,56245,56246],{"encoding":904},"Q_1 = 15 - P_1 + 2P_2 + P_3",[883,56248,56250],{"className":56249},[886],[888,56251,56252],{"xmlns":890},[892,56253,56254,56290],{},[895,56255,56256,56262,56264,56266,56268,56274,56276,56282,56284],{},[5535,56257,56258,56260],{},[898,56259,12471],{},[1742,56261,1872],{},[1750,56263,1766],{},[1742,56265,13663],{},[1750,56267,1861],{},[5535,56269,56270,56272],{},[898,56271,1776],{},[1742,56273,1744],{},[1750,56275,1758],{},[5535,56277,56278,56280],{},[898,56279,1776],{},[1742,56281,1872],{},[1750,56283,1758],{},[5535,56285,56286,56288],{},[898,56287,1776],{},[1742,56289,7822],{},[902,56291,56292],{"encoding":904},"Q_2 = 9 + P_1 - P_2 - P_3",[883,56294,56296],{"className":56295},[886],[888,56297,56298],{"xmlns":890},[892,56299,56300,56340],{},[895,56301,56302,56308,56310,56312,56314,56316,56322,56324,56330,56332,56334],{},[5535,56303,56304,56306],{},[898,56305,12471],{},[1742,56307,7822],{},[1750,56309,1766],{},[1742,56311,15239],{},[1750,56313,1861],{},[1742,56315,1872],{},[5535,56317,56318,56320],{},[898,56319,1776],{},[1742,56321,1744],{},[1750,56323,1758],{},[5535,56325,56326,56328],{},[898,56327,1776],{},[1742,56329,1872],{},[1750,56331,1758],{},[1742,56333,7859],{},[5535,56335,56336,56338],{},[898,56337,1776],{},[1742,56339,7822],{},[902,56341,56342],{"encoding":904},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[883,56345,56347],{"className":56346},[886],[888,56348,56349],{"xmlns":890},[892,56350,56351,56373],{},[895,56352,56353,56359,56361,56363,56365,56367],{},[5535,56354,56355,56357],{},[898,56356,12471],{},[1742,56358,1744],{},[1750,56360,1766],{},[1750,56362,1758],{},[1742,56364,8051],{},[1750,56366,1861],{},[5535,56368,56369,56371],{},[898,56370,1776],{},[1742,56372,1744],{},[902,56374,56375],{"encoding":904},"Q_1 = -7 + P_1",[883,56377,56379],{"className":56378},[886],[888,56380,56381],{"xmlns":890},[892,56382,56383,56407],{},[895,56384,56385,56391,56393,56395,56397,56399,56401],{},[5535,56386,56387,56389],{},[898,56388,12471],{},[1742,56390,1872],{},[1750,56392,1766],{},[1750,56394,1758],{},[1742,56396,7859],{},[1750,56398,1861],{},[1742,56400,7859],{},[5535,56402,56403,56405],{},[898,56404,1776],{},[1742,56406,1872],{},[902,56408,56409],{"encoding":904},"Q_2 = -4 + 4P_2",[883,56411,56413],{"className":56412},[886],[888,56414,56415],{"xmlns":890},[892,56416,56417,56441],{},[895,56418,56419,56425,56427,56429,56431,56433,56435],{},[5535,56420,56421,56423],{},[898,56422,12471],{},[1742,56424,7822],{},[1750,56426,1766],{},[1750,56428,1758],{},[1742,56430,7902],{},[1750,56432,1861],{},[1742,56434,1872],{},[5535,56436,56437,56439],{},[898,56438,1776],{},[1742,56440,7822],{},[902,56442,56443],{"encoding":904},"Q_3 = -5 + 2P_3",[883,56445,56447],{"className":56446},[886],[888,56448,56449],{"xmlns":890},[892,56450,56451,56459],{},[895,56452,56453],{},[5535,56454,56455,56457],{},[898,56456,12471],{},[898,56458,27363],{},[902,56460,56461],{"encoding":904},"Q_i",[883,56463,56465],{"className":56464},[886],[888,56466,56467],{"xmlns":890},[892,56468,56469,56477],{},[895,56470,56471],{},[5535,56472,56473,56475],{},[898,56474,1776],{},[898,56476,27363],{},[902,56478,56479],{"encoding":904},"P_i"," značí příslušné množství a ceny ",[883,56482,56484],{"className":56483},[886],[888,56485,56486],{"xmlns":890},[892,56487,56488,56492],{},[895,56489,56490],{},[898,56491,27363],{},[902,56493,27363],{"encoding":904},"-tého zboží, ",[883,56496,56498],{"className":56497},[886],[888,56499,56500],{"xmlns":890},[892,56501,56502,56518],{},[895,56503,56504,56506,56508,56510,56512,56514,56516],{},[898,56505,27363],{},[1750,56507,1766],{},[1742,56509,1744],{},[1750,56511,1917],{"separator":1916},[1742,56513,1872],{},[1750,56515,1917],{"separator":1916},[1742,56517,7822],{},[902,56519,56520],{"encoding":904},"i = 1, 2, 3",". Najděte rovnovážná množství ",[883,56523,56525],{"className":56524},[886],[888,56526,56527],{"xmlns":890},[892,56528,56529,56559],{},[895,56530,56531,56539,56541,56549,56551],{},[5950,56532,56533,56535,56537],{},[898,56534,12471],{},[1742,56536,1744],{},[898,56538,1705],{},[1750,56540,1917],{"separator":1916},[5950,56542,56543,56545,56547],{},[898,56544,12471],{},[1742,56546,1872],{},[898,56548,1705],{},[1750,56550,1917],{"separator":1916},[5950,56552,56553,56555,56557],{},[898,56554,12471],{},[1742,56556,7822],{},[898,56558,1705],{},[902,56560,56561],{"encoding":904},"Q_1^E, Q_2^E, Q_3^E",[883,56563,56565],{"className":56564},[886],[888,56566,56567],{"xmlns":890},[892,56568,56569,56599],{},[895,56570,56571,56579,56581,56589,56591],{},[5950,56572,56573,56575,56577],{},[898,56574,1776],{},[1742,56576,1744],{},[898,56578,1705],{},[1750,56580,1917],{"separator":1916},[5950,56582,56583,56585,56587],{},[898,56584,1776],{},[1742,56586,1872],{},[898,56588,1705],{},[1750,56590,1917],{"separator":1916},[5950,56592,56593,56595,56597],{},[898,56594,1776],{},[1742,56596,7822],{},[898,56598,1705],{},[902,56600,56601],{"encoding":904},"P_1^E, P_2^E, P_3^E",[724,56603,56604,56607,56608,56644,56645,2313],{},[38,56605,56606],{},"2.13"," Jsou dány poptávka ",[883,56609,56611],{"className":56610},[886],[888,56612,56613],{"xmlns":890},[892,56614,56615,56641],{},[895,56616,56617,56619,56621,56623,56625,56627,56629,56631,56633,56635,56637,56639],{},[898,56618,1776],{},[1750,56620,1766],{},[898,56622,5541],{},[1750,56624,1753],{"stretchy":1752},[898,56626,12471],{},[1750,56628,1763],{"stretchy":1752},[1750,56630,1766],{},[1750,56632,1758],{},[1742,56634,7859],{},[898,56636,12471],{},[1750,56638,1861],{},[1742,56640,55626],{},[902,56642,56643],{"encoding":904},"P = D(Q) = -4Q + 80"," a nabídka ",[883,56646,56648],{"className":56647},[886],[888,56649,56650],{"xmlns":890},[892,56651,56652,56676],{},[895,56653,56654,56656,56658,56660,56662,56664,56666,56668,56670,56672,56674],{},[898,56655,1776],{},[1750,56657,1766],{},[898,56659,1779],{},[1750,56661,1753],{"stretchy":1752},[898,56663,12471],{},[1750,56665,1763],{"stretchy":1752},[1750,56667,1766],{},[1742,56669,7822],{},[898,56671,12471],{},[1750,56673,1861],{},[1742,56675,3079],{},[902,56677,56678],{"encoding":904},"P = S(Q) = 3Q + 10",[120,56680,56681,56718,56782,56842],{},[123,56682,56683,56684,55581,56701,2313],{},"(a) Určete rovnovážné množství ",[883,56685,56687],{"className":56686},[886],[888,56688,56689],{"xmlns":890},[892,56690,56691,56699],{},[895,56692,56693],{},[1699,56694,56695,56697],{},[898,56696,12471],{},[898,56698,1705],{},[902,56700,51326],{"encoding":904},[883,56702,56704],{"className":56703},[886],[888,56705,56706],{"xmlns":890},[892,56707,56708,56716],{},[895,56709,56710],{},[1699,56711,56712,56714],{},[898,56713,1776],{},[898,56715,1705],{},[902,56717,50389],{"encoding":904},[123,56719,56720,56721,56739,56740,56760,56761,56781],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[883,56722,56724],{"className":56723},[886],[888,56725,56726],{"xmlns":890},[892,56727,56728,56736],{},[895,56729,56730,56732,56734],{},[898,56731,5326],{},[1750,56733,1766],{},[1742,56735,8051],{},[902,56737,56738],{"encoding":904},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[883,56741,56743],{"className":56742},[886],[888,56744,56745],{"xmlns":890},[892,56746,56747,56757],{},[895,56748,56749],{},[5950,56750,56751,56753,56755],{},[898,56752,12471],{},[1742,56754,1744],{},[898,56756,1705],{},[902,56758,56759],{"encoding":904},"Q_1^E"," a novou rovnovážnou cenu ",[883,56762,56764],{"className":56763},[886],[888,56765,56766],{"xmlns":890},[892,56767,56768,56778],{},[895,56769,56770],{},[5950,56771,56772,56774,56776],{},[898,56773,1776],{},[1742,56775,1744],{},[898,56777,1705],{},[902,56779,56780],{"encoding":904},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[123,56783,56784,56785,56739,56802,56760,56822,56781],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[883,56786,56788],{"className":56787},[886],[888,56789,56790],{"xmlns":890},[892,56791,56792,56800],{},[895,56793,56794,56796,56798],{},[898,56795,5326],{},[1750,56797,1766],{},[1742,56799,8051],{},[902,56801,56738],{"encoding":904},[883,56803,56805],{"className":56804},[886],[888,56806,56807],{"xmlns":890},[892,56808,56809,56819],{},[895,56810,56811],{},[5950,56812,56813,56815,56817],{},[898,56814,12471],{},[1742,56816,1872],{},[898,56818,1705],{},[902,56820,56821],{"encoding":904},"Q_2^E",[883,56823,56825],{"className":56824},[886],[888,56826,56827],{"xmlns":890},[892,56828,56829,56839],{},[895,56830,56831],{},[5950,56832,56833,56835,56837],{},[898,56834,1776],{},[1742,56836,1872],{},[898,56838,1705],{},[902,56840,56841],{"encoding":904},"P_2^E",[123,56843,56844],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[724,56846,56847,56848,2313],{},"Viz též ",[207,56849,51644],{"className":56850,"dataFsResolvedFilePath":809,"href":810},[210],[198,56852,51946],{"id":56853},"multiplikátory-pro-mikroekonomické-proměnné-1",[724,56855,56856,56607,56859,56644,56895,2313],{},[38,56857,56858],{},"2.14",[883,56860,56862],{"className":56861},[886],[888,56863,56864],{"xmlns":890},[892,56865,56866,56892],{},[895,56867,56868,56870,56872,56874,56876,56878,56880,56882,56884,56886,56888,56890],{},[898,56869,1776],{},[1750,56871,1766],{},[898,56873,207],{},[898,56875,12471],{},[1750,56877,1861],{},[898,56879,2573],{},[1750,56881,1766],{},[1750,56883,1758],{},[1742,56885,1872],{},[898,56887,12471],{},[1750,56889,1861],{},[1742,56891,3936],{},[902,56893,56894],{"encoding":904},"P = aQ + b = -2Q + 50",[883,56896,56898],{"className":56897},[886],[888,56899,56900],{"xmlns":890},[892,56901,56902,56926],{},[895,56903,56904,56906,56908,56910,56912,56914,56916,56918,56920,56922,56924],{},[898,56905,1776],{},[1750,56907,1766],{},[898,56909,9365],{},[898,56911,12471],{},[1750,56913,1861],{},[898,56915,3429],{},[1750,56917,1766],{},[1742,56919,3123],{},[898,56921,12471],{},[1750,56923,1861],{},[1742,56925,6465],{},[902,56927,56928],{"encoding":904},"P = cQ + d = 0{,}6Q + 20",[120,56930,56931,56967,56970,57056,57109,57189,57243],{},[123,56932,56683,56933,55581,56950,2313],{},[883,56934,56936],{"className":56935},[886],[888,56937,56938],{"xmlns":890},[892,56939,56940,56948],{},[895,56941,56942],{},[1699,56943,56944,56946],{},[898,56945,12471],{},[898,56947,1705],{},[902,56949,51326],{"encoding":904},[883,56951,56953],{"className":56952},[886],[888,56954,56955],{"xmlns":890},[892,56956,56957,56965],{},[895,56958,56959],{},[1699,56960,56961,56963],{},[898,56962,1776],{},[898,56964,1705],{},[902,56966,50389],{"encoding":904},[123,56968,56969],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[123,56971,56972,56973,56990,56991,12359,57004,4321,57020,57036,57037,2313],{},"(c) Určete přibližnou změnu rovnovážného množství ",[883,56974,56976],{"className":56975},[886],[888,56977,56978],{"xmlns":890},[892,56979,56980,56988],{},[895,56981,56982],{},[1699,56983,56984,56986],{},[898,56985,12471],{},[898,56987,1705],{},[902,56989,51326],{"encoding":904}," odpovídající změně ",[883,56992,56994],{"className":56993},[886],[888,56995,56996],{"xmlns":890},[892,56997,56998,57002],{},[895,56999,57000],{},[898,57001,207],{},[902,57003,207],{"encoding":904},[883,57005,57007],{"className":57006},[886],[888,57008,57009],{"xmlns":890},[892,57010,57011,57017],{},[895,57012,57013,57015],{},[1750,57014,1758],{},[1742,57016,1872],{},[902,57018,57019],{"encoding":904},"-2",[883,57021,57023],{"className":57022},[886],[888,57024,57025],{"xmlns":890},[892,57026,57027,57033],{},[895,57028,57029,57031],{},[1750,57030,1758],{},[1742,57032,7822],{},[902,57034,57035],{"encoding":904},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[883,57038,57040],{"className":57039},[886],[888,57041,57042],{"xmlns":890},[892,57043,57044,57054],{},[895,57045,57046],{},[5950,57047,57048,57050,57052],{},[898,57049,12471],{},[1742,57051,1744],{},[898,57053,1705],{},[902,57055,56759],{"encoding":904},[123,57057,57058,57059,56990,57076,57089,57090,2313],{},"(d) Určete přibližnou změnu rovnovážného množství ",[883,57060,57062],{"className":57061},[886],[888,57063,57064],{"xmlns":890},[892,57065,57066,57074],{},[895,57067,57068],{},[1699,57069,57070,57072],{},[898,57071,12471],{},[898,57073,1705],{},[902,57075,51326],{"encoding":904},[883,57077,57079],{"className":57078},[886],[888,57080,57081],{"xmlns":890},[892,57082,57083,57087],{},[895,57084,57085],{},[898,57086,2573],{},[902,57088,2573],{"encoding":904}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,57091,57093],{"className":57092},[886],[888,57094,57095],{"xmlns":890},[892,57096,57097,57107],{},[895,57098,57099],{},[5950,57100,57101,57103,57105],{},[898,57102,12471],{},[1742,57104,1872],{},[898,57106,1705],{},[902,57108,56821],{"encoding":904},[123,57110,57111,57112,56990,57129,12359,57142,4321,57155,57036,57169,2313],{},"(e) Určete přibližnou změnu rovnovážného množství ",[883,57113,57115],{"className":57114},[886],[888,57116,57117],{"xmlns":890},[892,57118,57119,57127],{},[895,57120,57121],{},[1699,57122,57123,57125],{},[898,57124,12471],{},[898,57126,1705],{},[902,57128,51326],{"encoding":904},[883,57130,57132],{"className":57131},[886],[888,57133,57134],{"xmlns":890},[892,57135,57136,57140],{},[895,57137,57138],{},[898,57139,9365],{},[902,57141,9365],{"encoding":904},[883,57143,57145],{"className":57144},[886],[888,57146,57147],{"xmlns":890},[892,57148,57149,57153],{},[895,57150,57151],{},[1742,57152,3123],{},[902,57154,53383],{"encoding":904},[883,57156,57158],{"className":57157},[886],[888,57159,57160],{"xmlns":890},[892,57161,57162,57166],{},[895,57163,57164],{},[1742,57165,6657],{},[902,57167,57168],{"encoding":904},"0{,}8",[883,57170,57172],{"className":57171},[886],[888,57173,57174],{"xmlns":890},[892,57175,57176,57186],{},[895,57177,57178],{},[5950,57179,57180,57182,57184],{},[898,57181,12471],{},[1742,57183,7822],{},[898,57185,1705],{},[902,57187,57188],{"encoding":904},"Q_3^E",[123,57190,57191,57192,56990,57209,57222,57223,2313],{},"(f) Určete přibližnou změnu rovnovážného množství ",[883,57193,57195],{"className":57194},[886],[888,57196,57197],{"xmlns":890},[892,57198,57199,57207],{},[895,57200,57201],{},[1699,57202,57203,57205],{},[898,57204,12471],{},[898,57206,1705],{},[902,57208,51326],{"encoding":904},[883,57210,57212],{"className":57211},[886],[888,57213,57214],{"xmlns":890},[892,57215,57216,57220],{},[895,57217,57218],{},[898,57219,3429],{},[902,57221,3429],{"encoding":904}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,57224,57226],{"className":57225},[886],[888,57227,57228],{"xmlns":890},[892,57229,57230,57240],{},[895,57231,57232],{},[5950,57233,57234,57236,57238],{},[898,57235,12471],{},[1742,57237,7859],{},[898,57239,1705],{},[902,57241,57242],{"encoding":904},"Q_4^E",[123,57244,57245,57246,57263,57264,57277,57278,5249,57291,1343,57306,5249,57319,2028,57333,5249,57346,57361,57362,2313],{},"(g) Určete přibližnou změnu rovnovážného množství ",[883,57247,57249],{"className":57248},[886],[888,57250,57251],{"xmlns":890},[892,57252,57253,57261],{},[895,57254,57255],{},[1699,57256,57257,57259],{},[898,57258,12471],{},[898,57260,1705],{},[902,57262,51326],{"encoding":904}," odpovídající změnám ",[883,57265,57267],{"className":57266},[886],[888,57268,57269],{"xmlns":890},[892,57270,57271,57275],{},[895,57272,57273],{},[898,57274,207],{},[902,57276,207],{"encoding":904}," o 1, ",[883,57279,57281],{"className":57280},[886],[888,57282,57283],{"xmlns":890},[892,57284,57285,57289],{},[895,57286,57287],{},[898,57288,2573],{},[902,57290,2573],{"encoding":904},[883,57292,57294],{"className":57293},[886],[888,57295,57296],{"xmlns":890},[892,57297,57298,57304],{},[895,57299,57300,57302],{},[1750,57301,1758],{},[1742,57303,3079],{},[902,57305,3259],{"encoding":904},[883,57307,57309],{"className":57308},[886],[888,57310,57311],{"xmlns":890},[892,57312,57313,57317],{},[895,57314,57315],{},[898,57316,9365],{},[902,57318,9365],{"encoding":904},[883,57320,57322],{"className":57321},[886],[888,57323,57324],{"xmlns":890},[892,57325,57326,57330],{},[895,57327,57328],{},[1742,57329,12476],{},[902,57331,57332],{"encoding":904},"0{,}1",[883,57334,57336],{"className":57335},[886],[888,57337,57338],{"xmlns":890},[892,57339,57340,57344],{},[895,57341,57342],{},[898,57343,3429],{},[902,57345,3429],{"encoding":904},[883,57347,57349],{"className":57348},[886],[888,57350,57351],{"xmlns":890},[892,57352,57353,57359],{},[895,57354,57355,57357],{},[1750,57356,1758],{},[1742,57358,3079],{},[902,57360,3259],{"encoding":904}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[883,57363,57365],{"className":57364},[886],[888,57366,57367],{"xmlns":890},[892,57368,57369,57379],{},[895,57370,57371],{},[5950,57372,57373,57375,57377],{},[898,57374,12471],{},[1742,57376,7902],{},[898,57378,1705],{},[902,57380,57381],{"encoding":904},"Q_5^E",[724,57383,57384,56607,57387,56644,57410,2313],{},[38,57385,57386],{},"2.15",[883,57388,57390],{"className":57389},[886],[888,57391,57392],{"xmlns":890},[892,57393,57394,57408],{},[895,57395,57396,57398,57400,57402,57404,57406],{},[898,57397,1776],{},[1750,57399,1766],{},[898,57401,207],{},[898,57403,12471],{},[1750,57405,1861],{},[898,57407,2573],{},[902,57409,45983],{"encoding":904},[883,57411,57413],{"className":57412},[886],[888,57414,57415],{"xmlns":890},[892,57416,57417,57431],{},[895,57418,57419,57421,57423,57425,57427,57429],{},[898,57420,1776],{},[1750,57422,1766],{},[898,57424,9365],{},[898,57426,12471],{},[1750,57428,1861],{},[898,57430,3429],{},[902,57432,49165],{"encoding":904},[120,57434,57435,57510,57527,57636,57689,57743],{},[123,57436,57437,57438,57451,57452,57477,57478,57509],{},"(a) Odvoďte redukovaný tvar pro ",[883,57439,57441],{"className":57440},[886],[888,57442,57443],{"xmlns":890},[892,57444,57445,57449],{},[895,57446,57447],{},[898,57448,1776],{},[902,57450,1776],{"encoding":904},". Stanovte podmínky pro ",[883,57453,57455],{"className":57454},[886],[888,57456,57457],{"xmlns":890},[892,57458,57459,57475],{},[895,57460,57461,57463,57465,57467,57469,57471,57473],{},[898,57462,207],{},[1750,57464,1917],{"separator":1916},[898,57466,2573],{},[1750,57468,1917],{"separator":1916},[898,57470,9365],{},[1750,57472,1917],{"separator":1916},[898,57474,3429],{},[902,57476,52208],{"encoding":904}," tak, aby rovnovážný bod ",[883,57479,57481],{"className":57480},[886],[888,57482,57483],{"xmlns":890},[892,57484,57485,57507],{},[895,57486,57487,57489,57491,57497,57499,57505],{},[898,57488,1705],{},[1750,57490,5141],{"stretchy":1752},[1699,57492,57493,57495],{},[898,57494,12471],{},[898,57496,1705],{},[1750,57498,1917],{"separator":1916},[1699,57500,57501,57503],{},[898,57502,1776],{},[898,57504,1705],{},[1750,57506,5158],{"stretchy":1752},[902,57508,50290],{"encoding":904}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[123,57511,57512,57513,57526],{},"(b) Vypočtěte multiplikátory pro ",[883,57514,57516],{"className":57515},[886],[888,57517,57518],{"xmlns":890},[892,57519,57520,57524],{},[895,57521,57522],{},[898,57523,1776],{},[902,57525,1776],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[123,57528,57529,57530,1343,57550,1343,57568,1343,57586,57604,57605,57622,57623,2313],{},"(c) Pro hodnoty parametrů ",[883,57531,57533],{"className":57532},[886],[888,57534,57535],{"xmlns":890},[892,57536,57537,57547],{},[895,57538,57539,57541,57543,57545],{},[898,57540,207],{},[1750,57542,1766],{},[1750,57544,1758],{},[1742,57546,1872],{},[902,57548,57549],{"encoding":904},"a = -2",[883,57551,57553],{"className":57552},[886],[888,57554,57555],{"xmlns":890},[892,57556,57557,57565],{},[895,57558,57559,57561,57563],{},[898,57560,2573],{},[1750,57562,1766],{},[1742,57564,14865],{},[902,57566,57567],{"encoding":904},"b = 40",[883,57569,57571],{"className":57570},[886],[888,57572,57573],{"xmlns":890},[892,57574,57575,57583],{},[895,57576,57577,57579,57581],{},[898,57578,9365],{},[1750,57580,1766],{},[1742,57582,4268],{},[902,57584,57585],{"encoding":904},"c = 0{,}5",[883,57587,57589],{"className":57588},[886],[888,57590,57591],{"xmlns":890},[892,57592,57593,57601],{},[895,57594,57595,57597,57599],{},[898,57596,3429],{},[1750,57598,1766],{},[1742,57600,3079],{},[902,57602,57603],{"encoding":904},"d = 10"," určete rovnovážnou cenu ",[883,57606,57608],{"className":57607},[886],[888,57609,57610],{"xmlns":890},[892,57611,57612,57620],{},[895,57613,57614],{},[1699,57615,57616,57618],{},[898,57617,1776],{},[898,57619,1705],{},[902,57621,50389],{"encoding":904}," a hodnoty multiplikátorů pro ",[883,57624,57626],{"className":57625},[886],[888,57627,57628],{"xmlns":890},[892,57629,57630,57634],{},[895,57631,57632],{},[898,57633,1776],{},[902,57635,1776],{"encoding":904},[123,57637,57638,57639,56990,57656,57669,57670,2313],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[883,57640,57642],{"className":57641},[886],[888,57643,57644],{"xmlns":890},[892,57645,57646,57654],{},[895,57647,57648],{},[1699,57649,57650,57652],{},[898,57651,1776],{},[898,57653,1705],{},[902,57655,50389],{"encoding":904},[883,57657,57659],{"className":57658},[886],[888,57660,57661],{"xmlns":890},[892,57662,57663,57667],{},[895,57664,57665],{},[898,57666,207],{},[902,57668,207],{"encoding":904}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[883,57671,57673],{"className":57672},[886],[888,57674,57675],{"xmlns":890},[892,57676,57677,57687],{},[895,57678,57679],{},[5950,57680,57681,57683,57685],{},[898,57682,1776],{},[1742,57684,1744],{},[898,57686,1705],{},[902,57688,56780],{"encoding":904},[123,57690,57691,57692,57709,57710,57723,57724,2313],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[883,57693,57695],{"className":57694},[886],[888,57696,57697],{"xmlns":890},[892,57698,57699,57707],{},[895,57700,57701],{},[1699,57702,57703,57705],{},[898,57704,1776],{},[898,57706,1705],{},[902,57708,50389],{"encoding":904}," odpovídající poklesu ",[883,57711,57713],{"className":57712},[886],[888,57714,57715],{"xmlns":890},[892,57716,57717,57721],{},[895,57718,57719],{},[898,57720,207],{},[902,57722,207],{"encoding":904}," o 1 a stanovte novou rovnovážnou cenu ",[883,57725,57727],{"className":57726},[886],[888,57728,57729],{"xmlns":890},[892,57730,57731,57741],{},[895,57732,57733],{},[5950,57734,57735,57737,57739],{},[898,57736,1776],{},[1742,57738,1872],{},[898,57740,1705],{},[902,57742,56841],{"encoding":904},[123,57744,57745,57746,57263,57763,57776,57777,4321,57790,2028,57805,57818,57819,2313],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[883,57747,57749],{"className":57748},[886],[888,57750,57751],{"xmlns":890},[892,57752,57753,57761],{},[895,57754,57755],{},[1699,57756,57757,57759],{},[898,57758,1776],{},[898,57760,1705],{},[902,57762,50389],{"encoding":904},[883,57764,57766],{"className":57765},[886],[888,57767,57768],{"xmlns":890},[892,57769,57770,57774],{},[895,57771,57772],{},[898,57773,207],{},[902,57775,207],{"encoding":904}," na 35, ",[883,57778,57780],{"className":57779},[886],[888,57781,57782],{"xmlns":890},[892,57783,57784,57788],{},[895,57785,57786],{},[898,57787,9365],{},[902,57789,9365],{"encoding":904},[883,57791,57793],{"className":57792},[886],[888,57794,57795],{"xmlns":890},[892,57796,57797,57802],{},[895,57798,57799],{},[1742,57800,57801],{},"0,7",[902,57803,57804],{"encoding":904},"0{,}7",[883,57806,57808],{"className":57807},[886],[888,57809,57810],{"xmlns":890},[892,57811,57812,57816],{},[895,57813,57814],{},[898,57815,3429],{},[902,57817,3429],{"encoding":904}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[883,57820,57822],{"className":57821},[886],[888,57823,57824],{"xmlns":890},[892,57825,57826,57836],{},[895,57827,57828],{},[5950,57829,57830,57832,57834],{},[898,57831,1776],{},[1742,57833,7822],{},[898,57835,1705],{},[902,57837,57838],{"encoding":904},"P_3^E",[724,57840,57841,56607,57844,56644,57872,5424,57900,2028,57926,2313],{},[38,57842,57843],{},"2.16",[883,57845,57847],{"className":57846},[886],[888,57848,57849],{"xmlns":890},[892,57850,57851,57869],{},[895,57852,57853,57855,57857,57859,57861,57863],{},[898,57854,1776],{},[1750,57856,1766],{},[898,57858,207],{},[1750,57860,1861],{},[898,57862,2573],{},[1699,57864,57865,57867],{},[898,57866,12471],{},[1742,57868,1872],{},[902,57870,57871],{"encoding":904},"P = a + bQ^2",[883,57873,57875],{"className":57874},[886],[888,57876,57877],{"xmlns":890},[892,57878,57879,57897],{},[895,57880,57881,57883,57885,57887,57889,57891],{},[898,57882,1776],{},[1750,57884,1766],{},[898,57886,9365],{},[1750,57888,1861],{},[898,57890,3429],{},[1699,57892,57893,57895],{},[898,57894,12471],{},[1742,57896,1872],{},[902,57898,57899],{"encoding":904},"P = c + dQ^2",[883,57901,57903],{"className":57902},[886],[888,57904,57905],{"xmlns":890},[892,57906,57907,57923],{},[895,57908,57909,57911,57913,57915,57917,57919,57921],{},[898,57910,207],{},[1750,57912,1917],{"separator":1916},[898,57914,9365],{},[1750,57916,1917],{"separator":1916},[898,57918,3429],{},[1750,57920,2604],{},[1742,57922,2607],{},[902,57924,57925],{"encoding":904},"a, c, d > 0",[883,57927,57929],{"className":57928},[886],[888,57930,57931],{"xmlns":890},[892,57932,57933,57941],{},[895,57934,57935,57937,57939],{},[898,57936,2573],{},[1750,57938,2624],{},[1742,57940,2607],{},[902,57942,57943],{"encoding":904},"b \u003C 0",[120,57945,57946,57994,58010,58117,58169,58221,58330,58346,58445,58498],{},[123,57947,57437,57948,57961,57962,57993],{},[883,57949,57951],{"className":57950},[886],[888,57952,57953],{"xmlns":890},[892,57954,57955,57959],{},[895,57956,57957],{},[898,57958,12471],{},[902,57960,12471],{"encoding":904},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[883,57963,57965],{"className":57964},[886],[888,57966,57967],{"xmlns":890},[892,57968,57969,57991],{},[895,57970,57971,57973,57975,57981,57983,57989],{},[898,57972,1705],{},[1750,57974,5141],{"stretchy":1752},[1699,57976,57977,57979],{},[898,57978,12471],{},[898,57980,1705],{},[1750,57982,1917],{"separator":1916},[1699,57984,57985,57987],{},[898,57986,1776],{},[898,57988,1705],{},[1750,57990,5158],{"stretchy":1752},[902,57992,50290],{"encoding":904}," patřil do 1. kvadrantu.",[123,57995,57512,57996,58009],{},[883,57997,57999],{"className":57998},[886],[888,58000,58001],{"xmlns":890},[892,58002,58003,58007],{},[895,58004,58005],{},[898,58006,12471],{},[902,58008,12471],{"encoding":904}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[123,58011,57529,58012,1343,58030,1343,58050,1343,58068,58086,58087,57622,58104,2313],{},[883,58013,58015],{"className":58014},[886],[888,58016,58017],{"xmlns":890},[892,58018,58019,58027],{},[895,58020,58021,58023,58025],{},[898,58022,207],{},[1750,58024,1766],{},[1742,58026,4078],{},[902,58028,58029],{"encoding":904},"a = 100",[883,58031,58033],{"className":58032},[886],[888,58034,58035],{"xmlns":890},[892,58036,58037,58047],{},[895,58038,58039,58041,58043,58045],{},[898,58040,2573],{},[1750,58042,1766],{},[1750,58044,1758],{},[1742,58046,1744],{},[902,58048,58049],{"encoding":904},"b = -1",[883,58051,58053],{"className":58052},[886],[888,58054,58055],{"xmlns":890},[892,58056,58057,58065],{},[895,58058,58059,58061,58063],{},[898,58060,9365],{},[1750,58062,1766],{},[1742,58064,6465],{},[902,58066,58067],{"encoding":904},"c = 20",[883,58069,58071],{"className":58070},[886],[888,58072,58073],{"xmlns":890},[892,58074,58075,58083],{},[895,58076,58077,58079,58081],{},[898,58078,3429],{},[1750,58080,1766],{},[1742,58082,1744],{},[902,58084,58085],{"encoding":904},"d = 1"," určete rovnovážné množství ",[883,58088,58090],{"className":58089},[886],[888,58091,58092],{"xmlns":890},[892,58093,58094,58102],{},[895,58095,58096],{},[1699,58097,58098,58100],{},[898,58099,12471],{},[898,58101,1705],{},[902,58103,51326],{"encoding":904},[883,58105,58107],{"className":58106},[886],[888,58108,58109],{"xmlns":890},[892,58110,58111,58115],{},[895,58112,58113],{},[898,58114,12471],{},[902,58116,12471],{"encoding":904},[123,58118,57058,58119,56990,58136,58149,58150,2313],{},[883,58120,58122],{"className":58121},[886],[888,58123,58124],{"xmlns":890},[892,58125,58126,58134],{},[895,58127,58128],{},[1699,58129,58130,58132],{},[898,58131,12471],{},[898,58133,1705],{},[902,58135,51326],{"encoding":904},[883,58137,58139],{"className":58138},[886],[888,58140,58141],{"xmlns":890},[892,58142,58143,58147],{},[895,58144,58145],{},[898,58146,207],{},[902,58148,207],{"encoding":904}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,58151,58153],{"className":58152},[886],[888,58154,58155],{"xmlns":890},[892,58156,58157,58167],{},[895,58158,58159],{},[5950,58160,58161,58163,58165],{},[898,58162,12471],{},[1742,58164,1744],{},[898,58166,1705],{},[902,58168,56759],{"encoding":904},[123,58170,57111,58171,56990,58188,58201,58202,2313],{},[883,58172,58174],{"className":58173},[886],[888,58175,58176],{"xmlns":890},[892,58177,58178,58186],{},[895,58179,58180],{},[1699,58181,58182,58184],{},[898,58183,12471],{},[898,58185,1705],{},[902,58187,51326],{"encoding":904},[883,58189,58191],{"className":58190},[886],[888,58192,58193],{"xmlns":890},[892,58194,58195,58199],{},[895,58196,58197],{},[898,58198,9365],{},[902,58200,9365],{"encoding":904}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[883,58203,58205],{"className":58204},[886],[888,58206,58207],{"xmlns":890},[892,58208,58209,58219],{},[895,58210,58211],{},[5950,58212,58213,58215,58217],{},[898,58214,12471],{},[1742,58216,1872],{},[898,58218,1705],{},[902,58220,56821],{"encoding":904},[123,58222,57191,58223,57263,58240,58253,58254,4321,58267,58282,58283,58296,58297,58310,58311,2313],{},[883,58224,58226],{"className":58225},[886],[888,58227,58228],{"xmlns":890},[892,58229,58230,58238],{},[895,58231,58232],{},[1699,58233,58234,58236],{},[898,58235,12471],{},[898,58237,1705],{},[902,58239,51326],{"encoding":904},[883,58241,58243],{"className":58242},[886],[888,58244,58245],{"xmlns":890},[892,58246,58247,58251],{},[895,58248,58249],{},[898,58250,207],{},[902,58252,207],{"encoding":904}," na 110, poklesu ",[883,58255,58257],{"className":58256},[886],[888,58258,58259],{"xmlns":890},[892,58260,58261,58265],{},[895,58262,58263],{},[898,58264,2573],{},[902,58266,2573],{"encoding":904},[883,58268,58270],{"className":58269},[886],[888,58271,58272],{"xmlns":890},[892,58273,58274,58280],{},[895,58275,58276,58278],{},[1750,58277,1758],{},[1742,58279,1872],{},[902,58281,57019],{"encoding":904},", růstu ",[883,58284,58286],{"className":58285},[886],[888,58287,58288],{"xmlns":890},[892,58289,58290,58294],{},[895,58291,58292],{},[898,58293,9365],{},[902,58295,9365],{"encoding":904}," na 25 a růstu ",[883,58298,58300],{"className":58299},[886],[888,58301,58302],{"xmlns":890},[892,58303,58304,58308],{},[895,58305,58306],{},[898,58307,3429],{},[902,58309,3429],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[883,58312,58314],{"className":58313},[886],[888,58315,58316],{"xmlns":890},[892,58317,58318,58328],{},[895,58319,58320],{},[5950,58321,58322,58324,58326],{},[898,58323,12471],{},[1742,58325,7822],{},[898,58327,1705],{},[902,58329,57188],{"encoding":904},[123,58331,58332,58333,58009],{},"(i) Vypočtěte multiplikátory pro ",[883,58334,58336],{"className":58335},[886],[888,58337,58338],{"xmlns":890},[892,58339,58340,58344],{},[895,58341,58342],{},[898,58343,1776],{},[902,58345,1776],{"encoding":904},[123,58347,58348,58349,57622,58366,58379,58380,56990,58397,4321,58410,58425,58426,2313],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[883,58350,58352],{"className":58351},[886],[888,58353,58354],{"xmlns":890},[892,58355,58356,58364],{},[895,58357,58358],{},[1699,58359,58360,58362],{},[898,58361,1776],{},[898,58363,1705],{},[902,58365,50389],{"encoding":904},[883,58367,58369],{"className":58368},[886],[888,58370,58371],{"xmlns":890},[892,58372,58373,58377],{},[895,58374,58375],{},[898,58376,1776],{},[902,58378,1776],{"encoding":904},", přibližnou změnu rovnovážné ceny ",[883,58381,58383],{"className":58382},[886],[888,58384,58385],{"xmlns":890},[892,58386,58387,58395],{},[895,58388,58389],{},[1699,58390,58391,58393],{},[898,58392,1776],{},[898,58394,1705],{},[902,58396,50389],{"encoding":904},[883,58398,58400],{"className":58399},[886],[888,58401,58402],{"xmlns":890},[892,58403,58404,58408],{},[895,58405,58406],{},[898,58407,207],{},[902,58409,207],{"encoding":904},[883,58411,58413],{"className":58412},[886],[888,58414,58415],{"xmlns":890},[892,58416,58417,58423],{},[895,58418,58419,58421],{},[1750,58420,1758],{},[1742,58422,7822],{},[902,58424,57035],{"encoding":904}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,58427,58429],{"className":58428},[886],[888,58430,58431],{"xmlns":890},[892,58432,58433,58443],{},[895,58434,58435],{},[5950,58436,58437,58439,58441],{},[898,58438,1776],{},[1742,58440,1744],{},[898,58442,1705],{},[902,58444,56780],{"encoding":904},[123,58446,58447,58448,56990,58465,58478,58479,2313],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[883,58449,58451],{"className":58450},[886],[888,58452,58453],{"xmlns":890},[892,58454,58455,58463],{},[895,58456,58457],{},[1699,58458,58459,58461],{},[898,58460,1776],{},[898,58462,1705],{},[902,58464,50389],{"encoding":904},[883,58466,58468],{"className":58467},[886],[888,58469,58470],{"xmlns":890},[892,58471,58472,58476],{},[895,58473,58474],{},[898,58475,207],{},[902,58477,207],{"encoding":904}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,58480,58482],{"className":58481},[886],[888,58483,58484],{"xmlns":890},[892,58485,58486,58496],{},[895,58487,58488],{},[5950,58489,58490,58492,58494],{},[898,58491,1776],{},[1742,58493,1872],{},[898,58495,1705],{},[902,58497,56841],{"encoding":904},[123,58499,58500,58501,57709,58518,58531,58532,4321,58545,58282,58560,58573,58574,58587,58588,2313],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[883,58502,58504],{"className":58503},[886],[888,58505,58506],{"xmlns":890},[892,58507,58508,58516],{},[895,58509,58510],{},[1699,58511,58512,58514],{},[898,58513,1776],{},[898,58515,1705],{},[902,58517,50389],{"encoding":904},[883,58519,58521],{"className":58520},[886],[888,58522,58523],{"xmlns":890},[892,58524,58525,58529],{},[895,58526,58527],{},[898,58528,207],{},[902,58530,207],{"encoding":904}," na 90, poklesu ",[883,58533,58535],{"className":58534},[886],[888,58536,58537],{"xmlns":890},[892,58538,58539,58543],{},[895,58540,58541],{},[898,58542,2573],{},[902,58544,2573],{"encoding":904},[883,58546,58548],{"className":58547},[886],[888,58549,58550],{"xmlns":890},[892,58551,58552,58558],{},[895,58553,58554,58556],{},[1750,58555,1758],{},[1742,58557,7822],{},[902,58559,57035],{"encoding":904},[883,58561,58563],{"className":58562},[886],[888,58564,58565],{"xmlns":890},[892,58566,58567,58571],{},[895,58568,58569],{},[898,58570,9365],{},[902,58572,9365],{"encoding":904}," na 30 a růstu ",[883,58575,58577],{"className":58576},[886],[888,58578,58579],{"xmlns":890},[892,58580,58581,58585],{},[895,58582,58583],{},[898,58584,3429],{},[902,58586,3429],{"encoding":904}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[883,58589,58591],{"className":58590},[886],[888,58592,58593],{"xmlns":890},[892,58594,58595,58605],{},[895,58596,58597],{},[5950,58598,58599,58601,58603],{},[898,58600,1776],{},[1742,58602,7822],{},[898,58604,1705],{},[902,58606,57838],{"encoding":904},[198,58608,820],{"id":58609},"přebytek-spotřebitele-a-výrobce-1",[724,58611,58612,56607,58615,56644,58651,2313],{},[38,58613,58614],{},"2.17",[883,58616,58618],{"className":58617},[886],[888,58619,58620],{"xmlns":890},[892,58621,58622,58648],{},[895,58623,58624,58626,58628,58630,58632,58634,58636,58638,58640,58642],{},[898,58625,1776],{},[1750,58627,1766],{},[898,58629,5541],{},[1750,58631,1753],{"stretchy":1752},[898,58633,12471],{},[1750,58635,1763],{"stretchy":1752},[1750,58637,1766],{},[1742,58639,6442],{},[1750,58641,1758],{},[1699,58643,58644,58646],{},[898,58645,12471],{},[1742,58647,1872],{},[902,58649,58650],{"encoding":904},"P = D(Q) = 35 - Q^2",[883,58652,58654],{"className":58653},[886],[888,58655,58656],{"xmlns":890},[892,58657,58658,58684],{},[895,58659,58660,58662,58664,58666,58668,58670,58672,58674,58676,58678],{},[898,58661,1776],{},[1750,58663,1766],{},[898,58665,1779],{},[1750,58667,1753],{"stretchy":1752},[898,58669,12471],{},[1750,58671,1763],{"stretchy":1752},[1750,58673,1766],{},[1742,58675,7822],{},[1750,58677,1861],{},[1699,58679,58680,58682],{},[898,58681,12471],{},[1742,58683,1872],{},[902,58685,58686],{"encoding":904},"P = S(Q) = 3 + Q^2",[120,58688,58689,58692],{},[123,58690,58691],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[123,58693,58694],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[724,58696,58697,56607,58700,56644,58734,2313],{},[38,58698,58699],{},"2.18",[883,58701,58703],{"className":58702},[886],[888,58704,58705],{"xmlns":890},[892,58706,58707,58731],{},[895,58708,58709,58711,58713,58715,58717,58719,58721,58723,58725,58727,58729],{},[898,58710,1776],{},[1750,58712,1766],{},[898,58714,5541],{},[1750,58716,1753],{"stretchy":1752},[898,58718,12471],{},[1750,58720,1763],{"stretchy":1752},[1750,58722,1766],{},[1742,58724,13377],{},[1750,58726,1758],{},[1742,58728,1872],{},[898,58730,12471],{},[902,58732,58733],{"encoding":904},"P = D(Q) = 18 - 2Q",[883,58735,58737],{"className":58736},[886],[888,58738,58739],{"xmlns":890},[892,58740,58741,58767],{},[895,58742,58743,58745,58747,58749,58751,58753,58755,58757,58759,58761],{},[898,58744,1776],{},[1750,58746,1766],{},[898,58748,1779],{},[1750,58750,1753],{"stretchy":1752},[898,58752,12471],{},[1750,58754,1763],{"stretchy":1752},[1750,58756,1766],{},[1742,58758,7822],{},[1750,58760,1861],{},[1699,58762,58763,58765],{},[898,58764,12471],{},[1742,58766,1872],{},[902,58768,58686],{"encoding":904},[120,58770,58771,58791,58794,58797],{},[123,58772,58773,58774,2313],{},"(a) Vypočtěte rovnovážné množství ",[883,58775,58777],{"className":58776},[886],[888,58778,58779],{"xmlns":890},[892,58780,58781,58789],{},[895,58782,58783],{},[1699,58784,58785,58787],{},[898,58786,12471],{},[898,58788,1705],{},[902,58790,51326],{"encoding":904},[123,58792,58793],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[123,58795,58796],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[123,58798,58799],{},"(c) Graficky interpretujte.",[45893,58801],{},[115,58803,58805],{"id":58804},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[152,58807,58808,58811,58814,58817,58820,58823,58826,58829,58832,58835,58838,58841,58844,58847],{},[123,58809,58810],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[123,58812,58813],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[123,58815,58816],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[123,58818,58819],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[123,58821,58822],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[123,58824,58825],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[123,58827,58828],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[123,58830,58831],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[123,58833,58834],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[123,58836,58837],{},"K čemu slouží multiplikátory?",[123,58839,58840],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[123,58842,58843],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[123,58845,58846],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[123,58848,58849],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[45893,58851],{},[115,58853,10461],{"id":10460},[724,58855,58856],{},[38,58857,22767],{},[120,58859,58860,58895,58900,58930,58935,58998,59024,59029,59059,59068,59075,59081],{},[123,58861,58862,2084,58865,2440,58868,1647,58870,1343,58893],{},[38,58863,58864],{},"Poptávané množství",[614,58866,58867],{},"quantity demanded",[38,58869,36925],{},[883,58871,58873],{"className":58872},[886],[888,58874,58875],{"xmlns":890},[892,58876,58877,58891],{},[895,58878,58879,58881,58883,58885,58887,58889],{},[898,58880,12471],{},[1750,58882,1766],{},[898,58884,5541],{},[1750,58886,1753],{"stretchy":1752},[898,58888,1776],{},[1750,58890,1763],{"stretchy":1752},[902,58892,13854],{"encoding":904},[38,58894,46372],{},[123,58896,58897,58899],{},[38,58898,46379],{}," — substituční + důchodový efekt",[123,58901,58902,1647,58905],{},[38,58903,58904],{},"Reálné cenové rozpětí",[883,58906,58908],{"className":58907},[886],[888,58909,58910],{"xmlns":890},[892,58911,58912,58928],{},[895,58913,58914,58916,58918,58920,58926],{},[1750,58915,1753],{"stretchy":1752},[1742,58917,2607],{},[1750,58919,1917],{"separator":1916},[5535,58921,58922,58924],{},[898,58923,1776],{},[1742,58925,2607],{},[1750,58927,1763],{"stretchy":1752},[902,58929,46580],{"encoding":904},[123,58931,58932,20729],{},[38,58933,58934],{},"Homogenita poptávky",[123,58936,58937,1647,58940,1343,58963,1343,58980,58997],{},[38,58938,58939],{},"Lineární poptávka",[883,58941,58943],{"className":58942},[886],[888,58944,58945],{"xmlns":890},[892,58946,58947,58961],{},[895,58948,58949,58951,58953,58955,58957,58959],{},[898,58950,1776],{},[1750,58952,1766],{},[898,58954,207],{},[898,58956,12471],{},[1750,58958,1861],{},[898,58960,2573],{},[902,58962,45983],{"encoding":904},[883,58964,58966],{"className":58965},[886],[888,58967,58968],{"xmlns":890},[892,58969,58970,58978],{},[895,58971,58972,58974,58976],{},[898,58973,207],{},[1750,58975,2624],{},[1742,58977,2607],{},[902,58979,52008],{"encoding":904},[883,58981,58983],{"className":58982},[886],[888,58984,58985],{"xmlns":890},[892,58986,58987,58995],{},[895,58988,58989,58991,58993],{},[898,58990,2573],{},[1750,58992,2604],{},[1742,58994,2607],{},[902,58996,2610],{"encoding":904}," — nedokonalá konkurence",[123,58999,59000,10469,59003],{},[38,59001,59002],{},"Dokonalá konkurence",[883,59004,59006],{"className":59005},[886],[888,59007,59008],{"xmlns":890},[892,59009,59010,59022],{},[895,59011,59012,59014,59016],{},[898,59013,1776],{},[1750,59015,1766],{},[1699,59017,59018,59020],{},[898,59019,1776],{},[1750,59021,3751],{},[902,59023,14016],{"encoding":904},[123,59025,59026,59028],{},[38,59027,47149],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[123,59030,59031,1647,59033,1343,59057],{},[38,59032,40650],{},[883,59034,59036],{"className":59035},[886],[888,59037,59038],{"xmlns":890},[892,59039,59040,59054],{},[895,59041,59042,59044,59046,59048,59050,59052],{},[898,59043,12471],{},[1750,59045,1766],{},[898,59047,1705],{},[1750,59049,1753],{"stretchy":1752},[898,59051,1666],{},[1750,59053,1763],{"stretchy":1752},[902,59055,59056],{"encoding":904},"Q = E(Y)",[38,59058,47346],{},[123,59060,59061,59064,59065,59067],{},[38,59062,59063],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[38,59066,47792],{}," zboží",[123,59069,59070,2028,59072,59074],{},[38,59071,48798],{},[38,59073,48745],{}," — znaménka zkřížených koeficientů",[123,59076,59077,59080],{},[38,59078,59079],{},"Dvoukomoditní trh"," (2.6)",[123,59082,59083,2084,59086,1763],{},[38,59084,59085],{},"Posun poptávky",[614,59087,47850],{},[724,59089,59090],{},[38,59091,22731],{},[120,59093,59094,59127,59131,59176],{},[123,59095,59096,2084,59098,2440,59100,1647,59102,1343,59125],{},[38,59097,49192],{},[614,59099,49195],{},[38,59101,49366],{},[883,59103,59105],{"className":59104},[886],[888,59106,59107],{"xmlns":890},[892,59108,59109,59123],{},[895,59110,59111,59113,59115,59117,59119,59121],{},[898,59112,12471],{},[1750,59114,1766],{},[898,59116,1779],{},[1750,59118,1753],{"stretchy":1752},[898,59120,1776],{},[1750,59122,1763],{"stretchy":1752},[902,59124,18323],{"encoding":904},[38,59126,49444],{},[123,59128,59129],{},[38,59130,49451],{},[123,59132,59133,1647,59136,1343,59159],{},[38,59134,59135],{},"Lineární nabídka",[883,59137,59139],{"className":59138},[886],[888,59140,59141],{"xmlns":890},[892,59142,59143,59157],{},[895,59144,59145,59147,59149,59151,59153,59155],{},[898,59146,1776],{},[1750,59148,1766],{},[898,59150,9365],{},[898,59152,12471],{},[1750,59154,1861],{},[898,59156,3429],{},[902,59158,49165],{"encoding":904},[883,59160,59162],{"className":59161},[886],[888,59163,59164],{"xmlns":890},[892,59165,59166,59174],{},[895,59167,59168,59170,59172],{},[898,59169,9365],{},[1750,59171,2604],{},[1742,59173,2607],{},[902,59175,49183],{"encoding":904},[123,59177,59178,2084,59181,1763],{},[38,59179,59180],{},"Posun nabídky",[614,59182,49829],{},[724,59184,59185],{},[38,59186,59187],{},"Rovnováha a komparativní statika",[120,59189,59190,59269,59275],{},[123,59191,59192,2084,59194,2440,59196,1647,59199,1343,59216,1647,59219,1343,59236,1647,59238],{},[38,59193,50248],{},[614,59195,50367],{},[38,59197,59198],{},"rovnovážná cena",[883,59200,59202],{"className":59201},[886],[888,59203,59204],{"xmlns":890},[892,59205,59206,59214],{},[895,59207,59208],{},[1699,59209,59210,59212],{},[898,59211,1776],{},[898,59213,1705],{},[902,59215,50389],{"encoding":904},[38,59217,59218],{},"rovnovážné množství",[883,59220,59222],{"className":59221},[886],[888,59223,59224],{"xmlns":890},[892,59225,59226,59234],{},[895,59227,59228],{},[1699,59229,59230,59232],{},[898,59231,12471],{},[898,59233,1705],{},[902,59235,51326],{"encoding":904},[38,59237,50425],{},[883,59239,59241],{"className":59240},[886],[888,59242,59243],{"xmlns":890},[892,59244,59245,59267],{},[895,59246,59247,59249,59251,59257,59259,59265],{},[898,59248,1705],{},[1750,59250,5141],{"stretchy":1752},[1699,59252,59253,59255],{},[898,59254,12471],{},[898,59256,1705],{},[1750,59258,1917],{"separator":1916},[1699,59260,59261,59263],{},[898,59262,1776],{},[898,59264,1705],{},[1750,59266,5158],{"stretchy":1752},[902,59268,50290],{"encoding":904},[123,59270,59271,59274],{},[38,59272,59273],{},"Pravidla 1–4"," komparativní statiky",[123,59276,59277,2084,59280,1763],{},[38,59278,59279],{},"Teorém pavučiny",[614,59281,51272],{},[724,59283,59284],{},[38,59285,59286],{},"Zdanění",[120,59288,59289,59345,59393],{},[123,59290,59291,59293,59294,59319,59320,1763],{},[38,59292,59286],{}," — daň výrobci (",[883,59295,59297],{"className":59296},[886],[888,59298,59299],{"xmlns":890},[892,59300,59301,59317],{},[895,59302,59303,59309,59311,59313,59315],{},[5535,59304,59305,59307],{},[898,59306,1779],{},[1742,59308,1744],{},[1750,59310,1766],{},[898,59312,1779],{},[1750,59314,1861],{},[898,59316,5326],{},[902,59318,51677],{"encoding":904},") vs. daň spotřebiteli (",[883,59321,59323],{"className":59322},[886],[888,59324,59325],{"xmlns":890},[892,59326,59327,59343],{},[895,59328,59329,59335,59337,59339,59341],{},[5535,59330,59331,59333],{},[898,59332,5541],{},[1742,59334,1872],{},[1750,59336,1766],{},[898,59338,5541],{},[1750,59340,1758],{},[898,59342,5326],{},[902,59344,51708],{"encoding":904},[123,59346,59347,1647,59349,1343,59370],{},[38,59348,51581],{},[883,59350,59352],{"className":59351},[886],[888,59353,59354],{"xmlns":890},[892,59355,59356,59368],{},[895,59357,59358],{},[5535,59359,59360,59362],{},[898,59361,5326],{},[895,59363,59364,59366],{},[898,59365,51600],{},[898,59367,724],{},[902,59369,51605],{"encoding":904},[883,59371,59373],{"className":59372},[886],[888,59374,59375],{"xmlns":890},[892,59376,59377,59391],{},[895,59378,59379],{},[5535,59380,59381,59383],{},[898,59382,5326],{},[895,59384,59385,59387,59389],{},[898,59386,51623],{},[898,59388,11717],{},[898,59390,1920],{},[902,59392,51630],{"encoding":904},[123,59394,59395,1647,59398,1343,59427],{},[38,59396,59397],{},"Ekvivalence zdanění",[883,59399,59401],{"className":59400},[886],[888,59402,59403],{"xmlns":890},[892,59404,59405,59425],{},[895,59406,59407,59415,59417],{},[5950,59408,59409,59411,59413],{},[898,59410,12471],{},[1742,59412,1744],{},[898,59414,1705],{},[1750,59416,1766],{},[5950,59418,59419,59421,59423],{},[898,59420,12471],{},[1742,59422,1872],{},[898,59424,1705],{},[902,59426,51831],{"encoding":904},[883,59428,59430],{"className":59429},[886],[888,59431,59432],{"xmlns":890},[892,59433,59434,59458],{},[895,59435,59436,59444,59446,59448,59450],{},[5950,59437,59438,59440,59442],{},[898,59439,1776],{},[1742,59441,1744],{},[898,59443,1705],{},[1750,59445,1758],{},[898,59447,5326],{},[1750,59449,1766],{},[5950,59451,59452,59454,59456],{},[898,59453,1776],{},[1742,59455,1872],{},[898,59457,1705],{},[902,59459,51865],{"encoding":904},[724,59461,59462],{},[38,59463,10281],{},[120,59465,59466,59512,59543,59548,59554,59561],{},[123,59467,59468,1647,59470],{},[38,59469,51964],{},[883,59471,59473],{"className":59472},[886],[888,59474,59475],{"xmlns":890},[892,59476,59477,59509],{},[895,59478,59479,59485,59487,59489,59491,59493,59495,59497,59499,59501,59503,59505,59507],{},[1699,59480,59481,59483],{},[898,59482,12471],{},[898,59484,1705],{},[1750,59486,1766],{},[1750,59488,1753],{"stretchy":1752},[898,59490,2573],{},[1750,59492,1758],{},[898,59494,3429],{},[1750,59496,1763],{"stretchy":1752},[898,59498,1748],{"mathvariant":1747},[1750,59500,1753],{"stretchy":1752},[898,59502,9365],{},[1750,59504,1758],{},[898,59506,207],{},[1750,59508,1763],{"stretchy":1752},[902,59510,59511],{"encoding":904},"Q^E = (b - d)\u002F(c - a)",[123,59513,59514,1647,59517,59542],{},[38,59515,59516],{},"Parametry",[883,59518,59520],{"className":59519},[886],[888,59521,59522],{"xmlns":890},[892,59523,59524,59540],{},[895,59525,59526,59528,59530,59532,59534,59536,59538],{},[898,59527,207],{},[1750,59529,1917],{"separator":1916},[898,59531,2573],{},[1750,59533,1917],{"separator":1916},[898,59535,9365],{},[1750,59537,1917],{"separator":1916},[898,59539,3429],{},[902,59541,52208],{"encoding":904}," — exogenní proměnné",[123,59544,59545],{},[38,59546,59547],{},"Endogenní \u002F exogenní proměnná",[123,59549,59550,59553],{},[38,59551,59552],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[123,59555,59556,1343,59559],{},[38,59557,59558],{},"Komparativní statika",[38,59560,45883],{},[123,59562,59563,1647,59565,59581],{},[38,59564,12632],{},[883,59566,59568],{"className":59567},[886],[888,59569,59570],{"xmlns":890},[892,59571,59572,59578],{},[895,59573,59574,59576],{},[898,59575,3429],{},[898,59577,12471],{},[902,59579,59580],{"encoding":904},"dQ"," (2.11)",[724,59583,59584],{},[38,59585,59586],{},"Přebytky a ostatní",[120,59588,59589,59627],{},[123,59590,59591,1647,59593,59608,59609,1647,59611,59626],{},[38,59592,53857],{},[883,59594,59596],{"className":59595},[886],[888,59597,59598],{"xmlns":890},[892,59599,59600,59606],{},[895,59601,59602,59604],{},[898,59603,1812],{},[898,59605,1779],{},[902,59607,53873],{"encoding":904}," (2.14), ",[38,59610,53876],{},[883,59612,59614],{"className":59613},[886],[888,59615,59616],{"xmlns":890},[892,59617,59618,59624],{},[895,59619,59620,59622],{},[898,59621,1776],{},[898,59623,1779],{},[902,59625,53892],{"encoding":904}," (2.15)",[123,59628,59629,1343,59632,59635],{},[38,59630,59631],{},"Homo economicus",[38,59633,59634],{},"Marshallova formulace"," (1890)",[45893,59637],{},[115,59639,11524],{"id":11523},[120,59641,59642,59677,59686],{},[123,59643,59644,1647,59647,59650,59651,1343,59654,59657,59658,59661,59662,59665,59666,59669,59670,59673,59674],{},[38,59645,59646],{},"Související témata:",[207,59648,811],{"className":59649,"dataFsResolvedFilePath":809,"href":810},[210]," (dopady daně, daňové břemeno, ekvivalence), ",[207,59652,820],{"className":59653,"dataFsResolvedFilePath":818,"href":819},[210],[207,59655,12053],{"className":59656,"dataFsResolvedFilePath":764,"href":765},[210]," (zákon klesající\u002Frostoucí, monotonie), ",[207,59659,775],{"className":59660,"dataFsResolvedFilePath":773,"href":774},[210]," (CS a PS), ",[207,59663,784],{"className":59664,"dataFsResolvedFilePath":782,"href":783},[210]," (vícefaktorové modely, multiplikátory), ",[207,59667,793],{"className":59668,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace spotřebitele), ",[207,59671,13496],{"className":59672,"dataFsResolvedFilePath":848,"href":849},[210]," (důchodová a cenová citlivost), ",[207,59675,13491],{"className":59676,"dataFsResolvedFilePath":827,"href":828},[210],[123,59678,59679,1647,59682],{},[38,59680,59681],{},"Shrnutí přednášek:",[207,59683,59685],{"className":59684,"dataFsResolvedFilePath":745,"href":746},[210],"KS — 1. blok",[123,59687,59688,1647,59690],{},[38,59689,11531],{},[207,59691,11535],{"className":59692,"dataFsResolvedFilePath":1644,"href":1645},[210],{"title":641,"searchDepth":642,"depth":642,"links":59694},[59695,59696,59704,59710,59717,59718,59725,59726,59727,59734,59735,59736],{"id":45717,"depth":642,"text":45718},{"id":45698,"depth":642,"text":22767,"children":59697},[59698,59699,59700,59701,59703],{"id":45986,"depth":649,"text":45987},{"id":46268,"depth":649,"text":46269},{"id":47278,"depth":649,"text":47279},{"id":47846,"depth":649,"text":59702},"Posun poptávky (shift of demand)",{"id":48350,"depth":649,"text":48351},{"id":45702,"depth":642,"text":22731,"children":59705},[59706,59707,59708],{"id":49187,"depth":649,"text":45987},{"id":49373,"depth":649,"text":49374},{"id":49825,"depth":649,"text":59709},"Posun nabídky (shift of supply)",{"id":50247,"depth":642,"text":50248,"children":59711},[59712,59713,59714,59715,59716],{"id":50359,"depth":649,"text":50360},{"id":50572,"depth":649,"text":50573},{"id":50890,"depth":649,"text":50891},{"id":51244,"depth":649,"text":51245},{"id":51275,"depth":649,"text":51276},{"id":51544,"depth":642,"text":811},{"id":51945,"depth":642,"text":51946,"children":59719},[59720,59721,59722,59723],{"id":51963,"depth":649,"text":51964},{"id":52344,"depth":649,"text":52345},{"id":52728,"depth":649,"text":52729},{"id":53182,"depth":649,"text":59724},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":21417,"depth":642,"text":820},{"id":54107,"depth":642,"text":54108},{"id":54338,"depth":642,"text":54339,"children":59728},[59729,59730,59731,59732,59733],{"id":54342,"depth":649,"text":54343},{"id":55182,"depth":649,"text":55183},{"id":55558,"depth":649,"text":50248},{"id":56853,"depth":649,"text":51946},{"id":58609,"depth":649,"text":820},{"id":58804,"depth":642,"text":58805},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":802,"description":641},[1138,1135],"topics\u002Fpoptavka-nabidka",[1128,59743,59744,59745,11663,59746,59747],"poptavka","nabidka","rovnovaha","zdaneni","prebytek","VHXMOe03Z24g0HTNlL2geCMzNcnJ3vQ8m2Org-s9n8Q",{"id":59750,"title":820,"body":59751,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":64030,"navigation":664,"path":64031,"seo":64032,"sources":64033,"stem":64034,"tags":64035,"type":11664,"updated":677,"__hash__":64040},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":9,"value":59752,"toc":64008},[59753,59755,59823,59873,59875,59878,60136,60212,60217,60219,60238,60242,60318,60403,60405,60719,60812,60814,60833,60837,60911,60996,60999,61175,61180,61182,61602,61604,61608,61612,61848,61892,61992,62058,62061,62094,62270,62332,62462,62540,62651,62685,62883,62902,62921,62986,62990,62993,63038,63041,63159,63205,63207,63211,63559,63561,63563,63841,63843,63847,63882,63889,63962,63964,63966],[12,59754,820],{"id":21417},[1785,59756,59757],{},[724,59758,59759,13541,59761,2084,59763,59778,59779,2084,59781,59796,59797,59819,59820,2313],{},[883,59760,13540],{},[38,59762,53857],{},[883,59764,59766],{"className":59765},[886],[888,59767,59768],{"xmlns":890},[892,59769,59770,59776],{},[895,59771,59772,59774],{},[898,59773,1812],{},[898,59775,1779],{},[902,59777,53873],{"encoding":904},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[38,59780,54004],{},[883,59782,59784],{"className":59783},[886],[888,59785,59786],{"xmlns":890},[892,59787,59788,59794],{},[895,59789,59790,59792],{},[898,59791,1776],{},[898,59793,1779],{},[902,59795,53892],{"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 ",[883,59798,59800],{"className":59799},[886],[888,59801,59802],{"xmlns":890},[892,59803,59804,59816],{},[895,59805,59806,59808,59810,59812,59814],{},[898,59807,1812],{},[898,59809,1779],{},[1750,59811,1861],{},[898,59813,1776],{},[898,59815,1779],{},[902,59817,59818],{"encoding":904},"CS + PS"," měří ",[38,59821,59822],{},"celkový blahobyt trhu",[724,59824,59825,2084,59827,1343,59829,4419,59844,2084,59846,1343,59848,59863,59864,59868,59869,2313],{},[38,59826,53857],{},[614,59828,53911],{},[883,59830,59832],{"className":59831},[886],[888,59833,59834],{"xmlns":890},[892,59835,59836,59842],{},[895,59837,59838,59840],{},[898,59839,1812],{},[898,59841,1779],{},[902,59843,53873],{"encoding":904},[38,59845,53876],{},[614,59847,54007],{},[883,59849,59851],{"className":59850},[886],[888,59852,59853],{"xmlns":890},[892,59854,59855,59861],{},[895,59856,59857,59859],{},[898,59858,1776],{},[898,59860,1779],{},[902,59862,53892],{"encoding":904},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[207,59865,59867],{"className":59866,"dataFsResolvedFilePath":800,"href":801},[210],"tržní rovnováhy"," a využívají aparát ",[207,59870,59872],{"className":59871,"dataFsResolvedFilePath":773,"href":774},[210],"integrálního počtu",[45893,59874],{},[115,59876,1241],{"id":59877},"úvod",[724,59879,59880,59881,59904,59905,59928,59929,59946,59947,13577,59979,60011,60012,60038,60039,60042,60043,60046,60047,23611,60081,5424,60102,2313],{},"Je dána funkce poptávky ",[883,59882,59884],{"className":59883},[886],[888,59885,59886],{"xmlns":890},[892,59887,59888,59902],{},[895,59889,59890,59892,59894,59896,59898,59900],{},[898,59891,1776],{},[1750,59893,1766],{},[898,59895,5541],{},[1750,59897,1753],{"stretchy":1752},[898,59899,12471],{},[1750,59901,1763],{"stretchy":1752},[902,59903,14297],{"encoding":904},", resp. funkce nabídky ",[883,59906,59908],{"className":59907},[886],[888,59909,59910],{"xmlns":890},[892,59911,59912,59926],{},[895,59913,59914,59916,59918,59920,59922,59924],{},[898,59915,1776],{},[1750,59917,1766],{},[898,59919,1779],{},[1750,59921,1753],{"stretchy":1752},[898,59923,12471],{},[1750,59925,1763],{"stretchy":1752},[902,59927,49994],{"encoding":904},". Pro pevně zadané množství ",[883,59930,59932],{"className":59931},[886],[888,59933,59934],{"xmlns":890},[892,59935,59936,59944],{},[895,59937,59938],{},[5535,59939,59940,59942],{},[898,59941,12471],{},[1742,59943,2607],{},[902,59945,47231],{"encoding":904}," je odpovídající cena ",[883,59948,59950],{"className":59949},[886],[888,59951,59952],{"xmlns":890},[892,59953,59954,59976],{},[895,59955,59956,59962,59964,59966,59968,59974],{},[5535,59957,59958,59960],{},[898,59959,1776],{},[1742,59961,2607],{},[1750,59963,1766],{},[898,59965,5541],{},[1750,59967,1753],{"stretchy":1752},[5535,59969,59970,59972],{},[898,59971,12471],{},[1742,59973,2607],{},[1750,59975,1763],{"stretchy":1752},[902,59977,59978],{"encoding":904},"P_0 = D(Q_0)",[883,59980,59982],{"className":59981},[886],[888,59983,59984],{"xmlns":890},[892,59985,59986,60008],{},[895,59987,59988,59994,59996,59998,60000,60006],{},[5535,59989,59990,59992],{},[898,59991,1776],{},[1742,59993,2607],{},[1750,59995,1766],{},[898,59997,1779],{},[1750,59999,1753],{"stretchy":1752},[5535,60001,60002,60004],{},[898,60003,12471],{},[1742,60005,2607],{},[1750,60007,1763],{"stretchy":1752},[902,60009,60010],{"encoding":904},"P_0 = S(Q_0)","). Součin ",[883,60013,60015],{"className":60014},[886],[888,60016,60017],{"xmlns":890},[892,60018,60019,60035],{},[895,60020,60021,60027,60029],{},[5535,60022,60023,60025],{},[898,60024,1776],{},[1742,60026,2607],{},[1969,60028,2658],{},[5535,60030,60031,60033],{},[898,60032,12471],{},[1742,60034,2607],{},[902,60036,60037],{"encoding":904},"P_0 \\, Q_0"," reprezentuje buď ",[38,60040,60041],{},"výdaje spotřebitele",", nebo ",[38,60044,60045],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[883,60048,60050],{"className":60049},[886],[888,60051,60052],{"xmlns":890},[892,60053,60054,60078],{},[895,60055,60056,60058,60060,60066,60068,60070,60072],{},[1742,60057,2607],{},[1969,60059,2658],{},[5535,60061,60062,60064],{},[898,60063,12471],{},[1742,60065,2607],{},[1969,60067,2658],{},[898,60069,13916],{},[1969,60071,2658],{},[5535,60073,60074,60076],{},[898,60075,1776],{},[1742,60077,2607],{},[902,60079,60080],{"encoding":904},"0\\,Q_0\\,A\\,P_0",[883,60082,60084],{"className":60083},[886],[888,60085,60086],{"xmlns":890},[892,60087,60088,60100],{},[895,60089,60090,60092,60094,60096,60098],{},[1750,60091,1753],{"stretchy":1752},[898,60093,12471],{},[1750,60095,1917],{"separator":1916},[898,60097,1776],{},[1750,60099,1763],{"stretchy":1752},[902,60101,46614],{"encoding":904},[883,60103,60105],{"className":60104},[886],[888,60106,60107],{"xmlns":890},[892,60108,60109,60133],{},[895,60110,60111,60113,60115,60117,60123,60125,60131],{},[898,60112,13916],{},[1750,60114,1766],{},[1750,60116,5141],{"stretchy":1752},[5535,60118,60119,60121],{},[898,60120,12471],{},[1742,60122,2607],{},[1750,60124,1917],{"separator":1916},[5535,60126,60127,60129],{},[898,60128,1776],{},[1742,60130,2607],{},[1750,60132,5158],{"stretchy":1752},[902,60134,60135],{"encoding":904},"A = [Q_0, P_0]",[1785,60137,60138,60143,60201],{},[724,60139,60140,60142],{},[883,60141,1791],{}," Intuice",[120,60144,60145,60173],{},[123,60146,60147,60148,60151,60152,60154,60155,60172],{},"Za jednotky zboží nakoupené ",[38,60149,60150],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[614,60153,9124],{}," než ",[883,60156,60158],{"className":60157},[886],[888,60159,60160],{"xmlns":890},[892,60161,60162,60170],{},[895,60163,60164],{},[5535,60165,60166,60168],{},[898,60167,1776],{},[1742,60169,2607],{},[902,60171,47871],{"encoding":904}," — rozdíl si „šetří do kapsy\" jako přebytek.",[123,60174,60175,60176,60178,60179,60182,60183,60200],{},"Za jednotky zboží prodané ",[38,60177,60150],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[614,60180,60181],{},"nižší"," cenu než ",[883,60184,60186],{"className":60185},[886],[888,60187,60188],{"xmlns":890},[892,60189,60190,60198],{},[895,60191,60192],{},[5535,60193,60194,60196],{},[898,60195,1776],{},[1742,60197,2607],{},[902,60199,47871],{"encoding":904}," — rozdíl je jeho přebytek.",[724,60202,60203,60204,60207,60208,60211],{},"Přebytek je tedy rozdíl mezi ",[614,60205,60206],{},"ochotou"," (platit \u002F prodávat) a ",[614,60209,60210],{},"skutečností"," (zaplaceno \u002F obdrženo).",[724,60213,60214],{},[4434,60215],{"alt":53902,"className":60216,"src":53904},[210,4438],[45893,60218],{},[115,60220,60222,60223,1763],{"id":60221},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[883,60224,60226],{"className":60225},[886],[888,60227,60228],{"xmlns":890},[892,60229,60230,60236],{},[895,60231,60232,60234],{},[898,60233,1812],{},[898,60235,1779],{},[902,60237,53873],{"encoding":904},[198,60239,60241],{"id":60240},"definice-vzorec-214","Definice (vzorec 2.14)",[724,60243,60244,60245,60268,60269,60286,60287,2366],{},"Pro poptávku ",[883,60246,60248],{"className":60247},[886],[888,60249,60250],{"xmlns":890},[892,60251,60252,60266],{},[895,60253,60254,60256,60258,60260,60262,60264],{},[898,60255,1776],{},[1750,60257,1766],{},[898,60259,5541],{},[1750,60261,1753],{"stretchy":1752},[898,60263,12471],{},[1750,60265,1763],{"stretchy":1752},[902,60267,14297],{"encoding":904}," a pevně zadané ",[883,60270,60272],{"className":60271},[886],[888,60273,60274],{"xmlns":890},[892,60275,60276,60284],{},[895,60277,60278],{},[5535,60279,60280,60282],{},[898,60281,12471],{},[1742,60283,2607],{},[902,60285,47231],{"encoding":904}," s cenou ",[883,60288,60290],{"className":60289},[886],[888,60291,60292],{"xmlns":890},[892,60293,60294,60316],{},[895,60295,60296,60302,60304,60306,60308,60314],{},[5535,60297,60298,60300],{},[898,60299,1776],{},[1742,60301,2607],{},[1750,60303,1766],{},[898,60305,5541],{},[1750,60307,1753],{"stretchy":1752},[5535,60309,60310,60312],{},[898,60311,12471],{},[1742,60313,2607],{},[1750,60315,1763],{"stretchy":1752},[902,60317,59978],{"encoding":904},[883,60319,60321],{"className":60320},[886],[888,60322,60323],{"xmlns":890,"display":36989},[892,60324,60325,60401],{},[4577,60326,60327],{"width":36994},[4582,60328,60329,60331,60395,60397],{},[4585,60330],{"width":36999},[4585,60332,60333],{},[895,60334,60335,60337,60339,60341,60347,60349,60351,60363,60365,60367,60369,60371,60373,60375,60377,60379,60385,60387,60393],{},[898,60336,1812],{},[898,60338,1779],{},[1750,60340,1753],{"stretchy":1752},[5535,60342,60343,60345],{},[898,60344,12471],{},[1742,60346,2607],{},[1750,60348,1763],{"stretchy":1752},[1750,60350,1766],{},[5950,60352,60353,60355,60357],{},[1750,60354,20802],{},[1742,60356,2607],{},[5535,60358,60359,60361],{},[898,60360,12471],{},[1742,60362,2607],{},[898,60364,5541],{},[1750,60366,1753],{"stretchy":1752},[898,60368,12471],{},[1750,60370,1763],{"stretchy":1752},[1969,60372,2658],{},[898,60374,3429],{},[898,60376,12471],{},[1750,60378,1758],{},[5535,60380,60381,60383],{},[898,60382,1776],{},[1742,60384,2607],{},[1969,60386,2658],{},[5535,60388,60389,60391],{},[898,60390,12471],{},[1742,60392,2607],{},[898,60394,2313],{"mathvariant":1747},[4585,60396],{"width":36999},[4585,60398,60399],{},[1969,60400,53996],{},[902,60402,53999],{"encoding":904},[198,60404,12137],{"id":12136},[120,60406,60407,60499,60561],{},[123,60408,60409,60449,60450,60476,60477,60480,60481,60498],{},[883,60410,60412],{"className":60411},[886],[888,60413,60414],{"xmlns":890},[892,60415,60416,60446],{},[895,60417,60418],{},[3586,60419,60420,60432,60434,60436,60438,60440,60442,60444],{"scriptlevel":2607,"displaystyle":1916},[5950,60421,60422,60424,60426],{},[1750,60423,20802],{},[1742,60425,2607],{},[5535,60427,60428,60430],{},[898,60429,12471],{},[1742,60431,2607],{},[898,60433,5541],{},[1750,60435,1753],{"stretchy":1752},[898,60437,12471],{},[1750,60439,1763],{"stretchy":1752},[1969,60441,2658],{},[898,60443,3429],{},[898,60445,12471],{},[902,60447,60448],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[883,60451,60453],{"className":60452},[886],[888,60454,60455],{"xmlns":890},[892,60456,60457,60473],{},[895,60458,60459,60461,60463,60465,60471],{},[1750,60460,5141],{"stretchy":1752},[1742,60462,2607],{},[1750,60464,1917],{"separator":1916},[5535,60466,60467,60469],{},[898,60468,12471],{},[1742,60470,2607],{},[1750,60472,5158],{"stretchy":1752},[902,60474,60475],{"encoding":904},"[0, Q_0]","; představuje celkovou ",[38,60478,60479],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[883,60482,60484],{"className":60483},[886],[888,60485,60486],{"xmlns":890},[892,60487,60488,60496],{},[895,60489,60490],{},[5535,60491,60492,60494],{},[898,60493,12471],{},[1742,60495,2607],{},[902,60497,47231],{"encoding":904}," jednotek byl ochoten zaplatit).",[123,60500,60501,60527,60528,1783],{},[883,60502,60504],{"className":60503},[886],[888,60505,60506],{"xmlns":890},[892,60507,60508,60524],{},[895,60509,60510,60516,60518],{},[5535,60511,60512,60514],{},[898,60513,1776],{},[1742,60515,2607],{},[1969,60517,2658],{},[5535,60519,60520,60522],{},[898,60521,12471],{},[1742,60523,2607],{},[902,60525,60526],{"encoding":904},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[883,60529,60531],{"className":60530},[886],[888,60532,60533],{"xmlns":890},[892,60534,60535,60559],{},[895,60536,60537,60539,60541,60547,60549,60551,60553],{},[1742,60538,2607],{},[1969,60540,2658],{},[5535,60542,60543,60545],{},[898,60544,12471],{},[1742,60546,2607],{},[1969,60548,2658],{},[898,60550,13916],{},[1969,60552,2658],{},[5535,60554,60555,60557],{},[898,60556,1776],{},[1742,60558,2607],{},[902,60560,60080],{"encoding":904},[123,60562,60563,60578,60579,60601,60602,60627,60628,5424,60654,2028,60686,2313],{},[883,60564,60566],{"className":60565},[886],[888,60567,60568],{"xmlns":890},[892,60569,60570,60576],{},[895,60571,60572,60574],{},[898,60573,1812],{},[898,60575,1779],{},[902,60577,53873],{"encoding":904}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[883,60580,60582],{"className":60581},[886],[888,60583,60584],{"xmlns":890},[892,60585,60586,60598],{},[895,60587,60588,60590,60592],{},[898,60589,1776],{},[1750,60591,1766],{},[5535,60593,60594,60596],{},[898,60595,1776],{},[1742,60597,2607],{},[902,60599,60600],{"encoding":904},"P = P_0"," v pásu ",[883,60603,60605],{"className":60604},[886],[888,60606,60607],{"xmlns":890},[892,60608,60609,60625],{},[895,60610,60611,60613,60615,60617,60623],{},[1750,60612,5141],{"stretchy":1752},[1742,60614,2607],{},[1750,60616,1917],{"separator":1916},[5535,60618,60619,60621],{},[898,60620,12471],{},[1742,60622,2607],{},[1750,60624,5158],{"stretchy":1752},[902,60626,60475],{"encoding":904}," — „křivočarý trojúhelník\" ",[883,60629,60631],{"className":60630},[886],[888,60632,60633],{"xmlns":890},[892,60634,60635,60651],{},[895,60636,60637,60643,60645,60647,60649],{},[5535,60638,60639,60641],{},[898,60640,1776],{},[1742,60642,2607],{},[1969,60644,2658],{},[898,60646,7097],{},[1969,60648,2658],{},[898,60650,13916],{},[902,60652,60653],{"encoding":904},"P_0\\,B\\,A",[883,60655,60657],{"className":60656},[886],[888,60658,60659],{"xmlns":890},[892,60660,60661,60683],{},[895,60662,60663,60665,60667,60669,60671,60673,60675,60677,60679,60681],{},[898,60664,7097],{},[1750,60666,1766],{},[1750,60668,5141],{"stretchy":1752},[1742,60670,2607],{},[1750,60672,1917],{"separator":1916},[898,60674,5541],{},[1750,60676,1753],{"stretchy":1752},[1742,60678,2607],{},[1750,60680,1763],{"stretchy":1752},[1750,60682,5158],{"stretchy":1752},[902,60684,60685],{"encoding":904},"B = [0, D(0)]",[883,60687,60689],{"className":60688},[886],[888,60690,60691],{"xmlns":890},[892,60692,60693,60717],{},[895,60694,60695,60697,60699,60701,60707,60709,60715],{},[898,60696,13916],{},[1750,60698,1766],{},[1750,60700,5141],{"stretchy":1752},[5535,60702,60703,60705],{},[898,60704,12471],{},[1742,60706,2607],{},[1750,60708,1917],{"separator":1916},[5535,60710,60711,60713],{},[898,60712,1776],{},[1742,60714,2607],{},[1750,60716,5158],{"stretchy":1752},[902,60718,60135],{"encoding":904},[724,60720,60721],{},[614,60722,60723,60724,60737,60738,60771,60772,38065,60797,2313],{},"Obrázek 2.24: Křivka poptávky ",[883,60725,60727],{"className":60726},[886],[888,60728,60729],{"xmlns":890},[892,60730,60731,60735],{},[895,60732,60733],{},[898,60734,5541],{},[902,60736,5541],{"encoding":904},", bod ",[883,60739,60741],{"className":60740},[886],[888,60742,60743],{"xmlns":890},[892,60744,60745,60769],{},[895,60746,60747,60749,60751,60753,60759,60761,60767],{},[898,60748,13916],{},[1750,60750,1766],{},[1750,60752,5141],{"stretchy":1752},[5535,60754,60755,60757],{},[898,60756,12471],{},[1742,60758,2607],{},[1750,60760,1917],{"separator":1916},[5535,60762,60763,60765],{},[898,60764,1776],{},[1742,60766,2607],{},[1750,60768,5158],{"stretchy":1752},[902,60770,60135],{"encoding":904},", vyšrafovaná plocha trojúhelníku ",[883,60773,60775],{"className":60774},[886],[888,60776,60777],{"xmlns":890},[892,60778,60779,60795],{},[895,60780,60781,60787,60789,60791,60793],{},[5535,60782,60783,60785],{},[898,60784,1776],{},[1742,60786,2607],{},[1969,60788,2658],{},[898,60790,7097],{},[1969,60792,2658],{},[898,60794,13916],{},[902,60796,60653],{"encoding":904},[883,60798,60800],{"className":60799},[886],[888,60801,60802],{"xmlns":890},[892,60803,60804,60810],{},[895,60805,60806,60808],{},[898,60807,1812],{},[898,60809,1779],{},[902,60811,53873],{"encoding":904},[45893,60813],{},[115,60815,60817,60818,1763],{"id":60816},"přebytek-výrobce-psps","Přebytek výrobce (",[883,60819,60821],{"className":60820},[886],[888,60822,60823],{"xmlns":890},[892,60824,60825,60831],{},[895,60826,60827,60829],{},[898,60828,1776],{},[898,60830,1779],{},[902,60832,53892],{"encoding":904},[198,60834,60836],{"id":60835},"definice-vzorec-215","Definice (vzorec 2.15)",[724,60838,60839,60840,60268,60863,60286,60880,2366],{},"Analogicky — pro nabídku ",[883,60841,60843],{"className":60842},[886],[888,60844,60845],{"xmlns":890},[892,60846,60847,60861],{},[895,60848,60849,60851,60853,60855,60857,60859],{},[898,60850,1776],{},[1750,60852,1766],{},[898,60854,1779],{},[1750,60856,1753],{"stretchy":1752},[898,60858,12471],{},[1750,60860,1763],{"stretchy":1752},[902,60862,49994],{"encoding":904},[883,60864,60866],{"className":60865},[886],[888,60867,60868],{"xmlns":890},[892,60869,60870,60878],{},[895,60871,60872],{},[5535,60873,60874,60876],{},[898,60875,12471],{},[1742,60877,2607],{},[902,60879,47231],{"encoding":904},[883,60881,60883],{"className":60882},[886],[888,60884,60885],{"xmlns":890},[892,60886,60887,60909],{},[895,60888,60889,60895,60897,60899,60901,60907],{},[5535,60890,60891,60893],{},[898,60892,1776],{},[1742,60894,2607],{},[1750,60896,1766],{},[898,60898,1779],{},[1750,60900,1753],{"stretchy":1752},[5535,60902,60903,60905],{},[898,60904,12471],{},[1742,60906,2607],{},[1750,60908,1763],{"stretchy":1752},[902,60910,60010],{"encoding":904},[883,60912,60914],{"className":60913},[886],[888,60915,60916],{"xmlns":890,"display":36989},[892,60917,60918,60994],{},[4577,60919,60920],{"width":36994},[4582,60921,60922,60924,60988,60990],{},[4585,60923],{"width":36999},[4585,60925,60926],{},[895,60927,60928,60930,60932,60934,60940,60942,60944,60950,60952,60958,60960,60972,60974,60976,60978,60980,60982,60984,60986],{},[898,60929,1776],{},[898,60931,1779],{},[1750,60933,1753],{"stretchy":1752},[5535,60935,60936,60938],{},[898,60937,12471],{},[1742,60939,2607],{},[1750,60941,1763],{"stretchy":1752},[1750,60943,1766],{},[5535,60945,60946,60948],{},[898,60947,1776],{},[1742,60949,2607],{},[1969,60951,2658],{},[5535,60953,60954,60956],{},[898,60955,12471],{},[1742,60957,2607],{},[1750,60959,1758],{},[5950,60961,60962,60964,60966],{},[1750,60963,20802],{},[1742,60965,2607],{},[5535,60967,60968,60970],{},[898,60969,12471],{},[1742,60971,2607],{},[898,60973,1779],{},[1750,60975,1753],{"stretchy":1752},[898,60977,12471],{},[1750,60979,1763],{"stretchy":1752},[1969,60981,2658],{},[898,60983,3429],{},[898,60985,12471],{},[898,60987,2313],{"mathvariant":1747},[4585,60989],{"width":36999},[4585,60991,60992],{},[1969,60993,54092],{},[902,60995,54095],{"encoding":904},[198,60997,12137],{"id":60998},"geometrická-interpretace-1",[120,61000,61001,61049,61110],{},[123,61002,61003,10469,61028,61031,61032,2313],{},[883,61004,61006],{"className":61005},[886],[888,61007,61008],{"xmlns":890},[892,61009,61010,61026],{},[895,61011,61012,61018,61020],{},[5535,61013,61014,61016],{},[898,61015,1776],{},[1742,61017,2607],{},[1969,61019,2658],{},[5535,61021,61022,61024],{},[898,61023,12471],{},[1742,61025,2607],{},[902,61027,60526],{"encoding":904},[38,61029,61030],{},"tržba"," výrobce za prodané množství ",[883,61033,61035],{"className":61034},[886],[888,61036,61037],{"xmlns":890},[892,61038,61039,61047],{},[895,61040,61041],{},[5535,61042,61043,61045],{},[898,61044,12471],{},[1742,61046,2607],{},[902,61048,47231],{"encoding":904},[123,61050,61051,61091,61092,61109],{},[883,61052,61054],{"className":61053},[886],[888,61055,61056],{"xmlns":890},[892,61057,61058,61088],{},[895,61059,61060],{},[3586,61061,61062,61074,61076,61078,61080,61082,61084,61086],{"scriptlevel":2607,"displaystyle":1916},[5950,61063,61064,61066,61068],{},[1750,61065,20802],{},[1742,61067,2607],{},[5535,61069,61070,61072],{},[898,61071,12471],{},[1742,61073,2607],{},[898,61075,1779],{},[1750,61077,1753],{"stretchy":1752},[898,61079,12471],{},[1750,61081,1763],{"stretchy":1752},[1969,61083,2658],{},[898,61085,3429],{},[898,61087,12471],{},[902,61089,61090],{"encoding":904},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[883,61093,61095],{"className":61094},[886],[888,61096,61097],{"xmlns":890},[892,61098,61099,61107],{},[895,61100,61101],{},[5535,61102,61103,61105],{},[898,61104,12471],{},[1742,61106,2607],{},[902,61108,47231],{"encoding":904}," jednotek dodat (souvisí s mezními náklady).",[123,61111,61112,61127,61128,61149,61150,2313],{},[883,61113,61115],{"className":61114},[886],[888,61116,61117],{"xmlns":890},[892,61118,61119,61125],{},[895,61120,61121,61123],{},[898,61122,1776],{},[898,61124,1779],{},[902,61126,53892],{"encoding":904}," je plocha mezi vodorovnou přímkou ",[883,61129,61131],{"className":61130},[886],[888,61132,61133],{"xmlns":890},[892,61134,61135,61147],{},[895,61136,61137,61139,61141],{},[898,61138,1776],{},[1750,61140,1766],{},[5535,61142,61143,61145],{},[898,61144,1776],{},[1742,61146,2607],{},[902,61148,60600],{"encoding":904}," a křivkou nabídky v pásu ",[883,61151,61153],{"className":61152},[886],[888,61154,61155],{"xmlns":890},[892,61156,61157,61173],{},[895,61158,61159,61161,61163,61165,61171],{},[1750,61160,5141],{"stretchy":1752},[1742,61162,2607],{},[1750,61164,1917],{"separator":1916},[5535,61166,61167,61169],{},[898,61168,12471],{},[1742,61170,2607],{},[1750,61172,5158],{"stretchy":1752},[902,61174,60475],{"encoding":904},[724,61176,61177],{},[614,61178,61179],{},"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.",[45893,61181],{},[1785,61183,61184,61189],{},[724,61185,61186,61188],{},[883,61187,6004],{}," Postup výpočtu CS a PS",[152,61190,61191,61322,61432,61461,61595],{},[123,61192,61193,61194,61211,61212,61243,61244,61275,61276,2313],{},"Zjisti (nebo si zvol) množství ",[883,61195,61197],{"className":61196},[886],[888,61198,61199],{"xmlns":890},[892,61200,61201,61209],{},[895,61202,61203],{},[5535,61204,61205,61207],{},[898,61206,12471],{},[1742,61208,2607],{},[902,61210,47231],{"encoding":904}," a odpovídající cenu ",[883,61213,61215],{"className":61214},[886],[888,61216,61217],{"xmlns":890},[892,61218,61219,61241],{},[895,61220,61221,61227,61229,61231,61233,61239],{},[5535,61222,61223,61225],{},[898,61224,1776],{},[1742,61226,2607],{},[1750,61228,1766],{},[898,61230,5541],{},[1750,61232,1753],{"stretchy":1752},[5535,61234,61235,61237],{},[898,61236,12471],{},[1742,61238,2607],{},[1750,61240,1763],{"stretchy":1752},[902,61242,59978],{"encoding":904}," resp. ",[883,61245,61247],{"className":61246},[886],[888,61248,61249],{"xmlns":890},[892,61250,61251,61273],{},[895,61252,61253,61259,61261,61263,61265,61271],{},[5535,61254,61255,61257],{},[898,61256,1776],{},[1742,61258,2607],{},[1750,61260,1766],{},[898,61262,1779],{},[1750,61264,1753],{"stretchy":1752},[5535,61266,61267,61269],{},[898,61268,12471],{},[1742,61270,2607],{},[1750,61272,1763],{"stretchy":1752},[902,61274,60010],{"encoding":904},". V rovnováze platí ",[883,61277,61279],{"className":61278},[886],[888,61280,61281],{"xmlns":890},[892,61282,61283,61319],{},[895,61284,61285,61287,61289,61295,61297,61299,61301,61303,61309,61311,61313],{},[898,61286,5541],{},[1750,61288,1753],{"stretchy":1752},[1699,61290,61291,61293],{},[898,61292,12471],{},[898,61294,1705],{},[1750,61296,1763],{"stretchy":1752},[1750,61298,1766],{},[898,61300,1779],{},[1750,61302,1753],{"stretchy":1752},[1699,61304,61305,61307],{},[898,61306,12471],{},[898,61308,1705],{},[1750,61310,1763],{"stretchy":1752},[1750,61312,1766],{},[1699,61314,61315,61317],{},[898,61316,1776],{},[898,61318,1705],{},[902,61320,61321],{"encoding":904},"D(Q^E) = S(Q^E) = P^E",[123,61323,61324,61325,3940,61363,61378,61379,3940,61417,1783],{},"Spočti určitý integrál ",[883,61326,61328],{"className":61327},[886],[888,61329,61330],{"xmlns":890},[892,61331,61332,61360],{},[895,61333,61334,61346,61348,61350,61352,61354,61356,61358],{},[5950,61335,61336,61338,61340],{},[1750,61337,20802],{},[1742,61339,2607],{},[5535,61341,61342,61344],{},[898,61343,12471],{},[1742,61345,2607],{},[898,61347,5541],{},[1750,61349,1753],{"stretchy":1752},[898,61351,12471],{},[1750,61353,1763],{"stretchy":1752},[1969,61355,2658],{},[898,61357,3429],{},[898,61359,12471],{},[902,61361,61362],{"encoding":904},"\\int_0^{Q_0} D(Q)\\,dQ",[883,61364,61366],{"className":61365},[886],[888,61367,61368],{"xmlns":890},[892,61369,61370,61376],{},[895,61371,61372,61374],{},[898,61373,1812],{},[898,61375,1779],{},[902,61377,53873],{"encoding":904},") nebo ",[883,61380,61382],{"className":61381},[886],[888,61383,61384],{"xmlns":890},[892,61385,61386,61414],{},[895,61387,61388,61400,61402,61404,61406,61408,61410,61412],{},[5950,61389,61390,61392,61394],{},[1750,61391,20802],{},[1742,61393,2607],{},[5535,61395,61396,61398],{},[898,61397,12471],{},[1742,61399,2607],{},[898,61401,1779],{},[1750,61403,1753],{"stretchy":1752},[898,61405,12471],{},[1750,61407,1763],{"stretchy":1752},[1969,61409,2658],{},[898,61411,3429],{},[898,61413,12471],{},[902,61415,61416],{"encoding":904},"\\int_0^{Q_0} S(Q)\\,dQ",[883,61418,61420],{"className":61419},[886],[888,61421,61422],{"xmlns":890},[892,61423,61424,61430],{},[895,61425,61426,61428],{},[898,61427,1776],{},[898,61429,1779],{},[902,61431,53892],{"encoding":904},[123,61433,61434,61435,2313],{},"Sestav obdélník ",[883,61436,61438],{"className":61437},[886],[888,61439,61440],{"xmlns":890},[892,61441,61442,61458],{},[895,61443,61444,61450,61452],{},[5535,61445,61446,61448],{},[898,61447,1776],{},[1742,61449,2607],{},[1750,61451,8009],{},[5535,61453,61454,61456],{},[898,61455,12471],{},[1742,61457,2607],{},[902,61459,61460],{"encoding":904},"P_0 \\cdot Q_0",[123,61462,61463,61464],{},"Dosaď:\n",[120,61465,61466,61531],{},[123,61467,61468,61526,61527,61530],{},[883,61469,61471],{"className":61470},[886],[888,61472,61473],{"xmlns":890},[892,61474,61475,61523],{},[895,61476,61477,61479,61481,61483,61495,61497,61499,61501,61503,61505,61507,61509,61511,61517],{},[898,61478,1812],{},[898,61480,1779],{},[1750,61482,1766],{},[5950,61484,61485,61487,61489],{},[1750,61486,20802],{},[1742,61488,2607],{},[5535,61490,61491,61493],{},[898,61492,12471],{},[1742,61494,2607],{},[898,61496,5541],{},[1750,61498,1753],{"stretchy":1752},[898,61500,12471],{},[1750,61502,1763],{"stretchy":1752},[1969,61504,2658],{},[898,61506,3429],{},[898,61508,12471],{},[1750,61510,1758],{},[5535,61512,61513,61515],{},[898,61514,1776],{},[1742,61516,2607],{},[5535,61518,61519,61521],{},[898,61520,12471],{},[1742,61522,2607],{},[902,61524,61525],{"encoding":904},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[38,61528,61529],{},"mínus"," obdélník)",[123,61532,61533,61591,61592,61594],{},[883,61534,61536],{"className":61535},[886],[888,61537,61538],{"xmlns":890},[892,61539,61540,61588],{},[895,61541,61542,61544,61546,61548,61554,61560,61562,61574,61576,61578,61580,61582,61584,61586],{},[898,61543,1776],{},[898,61545,1779],{},[1750,61547,1766],{},[5535,61549,61550,61552],{},[898,61551,1776],{},[1742,61553,2607],{},[5535,61555,61556,61558],{},[898,61557,12471],{},[1742,61559,2607],{},[1750,61561,1758],{},[5950,61563,61564,61566,61568],{},[1750,61565,20802],{},[1742,61567,2607],{},[5535,61569,61570,61572],{},[898,61571,12471],{},[1742,61573,2607],{},[898,61575,1779],{},[1750,61577,1753],{"stretchy":1752},[898,61579,12471],{},[1750,61581,1763],{"stretchy":1752},[1969,61583,2658],{},[898,61585,3429],{},[898,61587,12471],{},[902,61589,61590],{"encoding":904},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[38,61593,61529],{}," integrál)",[123,61596,61597,61598,61601],{},"Kontrola znaménka: obě hodnoty musí být ",[38,61599,61600],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[45893,61603],{},[115,61605,61607],{"id":61606},"příklady","Příklady",[198,61609,61611],{"id":61610},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1785,61613,61614],{},[724,61615,61616,61619,61620,56644,61643,61666,61667,1343,61687,1343,61704,1343,61721,61738,61739,61815,61816,61833,61834,61847],{},[883,61617,61618],{},"!example"," Zadání\nJsou dány poptávka ",[883,61621,61623],{"className":61622},[886],[888,61624,61625],{"xmlns":890},[892,61626,61627,61641],{},[895,61628,61629,61631,61633,61635,61637,61639],{},[898,61630,1776],{},[1750,61632,1766],{},[898,61634,207],{},[898,61636,12471],{},[1750,61638,1861],{},[898,61640,2573],{},[902,61642,45983],{"encoding":904},[883,61644,61646],{"className":61645},[886],[888,61647,61648],{"xmlns":890},[892,61649,61650,61664],{},[895,61651,61652,61654,61656,61658,61660,61662],{},[898,61653,1776],{},[1750,61655,1766],{},[898,61657,9365],{},[898,61659,12471],{},[1750,61661,1861],{},[898,61663,3429],{},[902,61665,49165],{"encoding":904}," s hodnotami ",[883,61668,61670],{"className":61669},[886],[888,61671,61672],{"xmlns":890},[892,61673,61674,61684],{},[895,61675,61676,61678,61680,61682],{},[898,61677,207],{},[1750,61679,1766],{},[1750,61681,1758],{},[1742,61683,7822],{},[902,61685,61686],{"encoding":904},"a = -3",[883,61688,61690],{"className":61689},[886],[888,61691,61692],{"xmlns":890},[892,61693,61694,61702],{},[895,61695,61696,61698,61700],{},[898,61697,2573],{},[1750,61699,1766],{},[1742,61701,14865],{},[902,61703,57567],{"encoding":904},[883,61705,61707],{"className":61706},[886],[888,61708,61709],{"xmlns":890},[892,61710,61711,61719],{},[895,61712,61713,61715,61717],{},[898,61714,9365],{},[1750,61716,1766],{},[1742,61718,4268],{},[902,61720,57585],{"encoding":904},[883,61722,61724],{"className":61723},[886],[888,61725,61726],{"xmlns":890},[892,61727,61728,61736],{},[895,61729,61730,61732,61734],{},[898,61731,3429],{},[1750,61733,1766],{},[1742,61735,3079],{},[902,61737,57603],{"encoding":904},".\nRovnovážné množství:\n",[883,61740,61742],{"className":61741},[886],[888,61743,61744],{"xmlns":890},[892,61745,61746,61812],{},[895,61747,61748,61754,61756,61774,61776,61800,61802,61808,61810],{},[1699,61749,61750,61752],{},[898,61751,12471],{},[898,61753,1705],{},[1750,61755,1766],{},[3423,61757,61758,61766],{},[895,61759,61760,61762,61764],{},[898,61761,2573],{},[1750,61763,1758],{},[898,61765,3429],{},[895,61767,61768,61770,61772],{},[898,61769,9365],{},[1750,61771,1758],{},[898,61773,207],{},[1750,61775,1766],{},[3423,61777,61778,61786],{},[895,61779,61780,61782,61784],{},[1742,61781,14865],{},[1750,61783,1758],{},[1742,61785,3079],{},[895,61787,61788,61790,61792,61794,61796,61798],{},[1742,61789,4268],{},[1750,61791,1758],{},[1750,61793,1753],{"stretchy":1752},[1750,61795,1758],{},[1742,61797,7822],{},[1750,61799,1763],{"stretchy":1752},[1750,61801,1766],{},[3423,61803,61804,61806],{},[1742,61805,46942],{},[1742,61807,53329],{},[1750,61809,6792],{},[1742,61811,53334],{},[902,61813,61814],{"encoding":904},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[883,61817,61819],{"className":61818},[886],[888,61820,61821],{"xmlns":890},[892,61822,61823,61831],{},[895,61824,61825],{},[1699,61826,61827,61829],{},[898,61828,12471],{},[898,61830,1705],{},[902,61832,51326],{"encoding":904}," (a) při změně samotného parametru ",[883,61835,61837],{"className":61836},[886],[888,61838,61839],{"xmlns":890},[892,61840,61841,61845],{},[895,61842,61843],{},[898,61844,9365],{},[902,61846,9365],{"encoding":904},", (b) při současné změně všech čtyř parametrů.",[724,61849,61850],{},[38,61851,61852,61853,12359,61866,4321,61879,18932],{},"Řešení (a) — změna ",[883,61854,61856],{"className":61855},[886],[888,61857,61858],{"xmlns":890},[892,61859,61860,61864],{},[895,61861,61862],{},[898,61863,9365],{},[902,61865,9365],{"encoding":904},[883,61867,61869],{"className":61868},[886],[888,61870,61871],{"xmlns":890},[892,61872,61873,61877],{},[895,61874,61875],{},[1742,61876,4268],{},[902,61878,53369],{"encoding":904},[883,61880,61882],{"className":61881},[886],[888,61883,61884],{"xmlns":890},[892,61885,61886,61890],{},[895,61887,61888],{},[1742,61889,3123],{},[902,61891,53383],{"encoding":904},[724,61893,61894,61895,61959,61960,2366],{},"Pomocí vzorce (2.13) pro ",[883,61896,61898],{"className":61897},[886],[888,61899,61900],{"xmlns":890},[892,61901,61902,61956],{},[895,61903,61904,61924,61926,61928],{},[3586,61905,61906],{"scriptlevel":2607,"displaystyle":1916},[3423,61907,61908,61918],{},[895,61909,61910,61912],{},[898,61911,8773],{"mathvariant":1747},[1699,61913,61914,61916],{},[898,61915,12471],{},[898,61917,1705],{},[895,61919,61920,61922],{},[898,61921,8773],{"mathvariant":1747},[898,61923,9365],{},[1750,61925,1766],{},[1750,61927,1758],{},[3586,61929,61930],{"scriptlevel":2607,"displaystyle":1916},[3423,61931,61932,61940],{},[895,61933,61934,61936,61938],{},[898,61935,2573],{},[1750,61937,1758],{},[898,61939,3429],{},[895,61941,61942,61944,61946,61948,61950],{},[1750,61943,1753],{"stretchy":1752},[898,61945,9365],{},[1750,61947,1758],{},[898,61949,207],{},[1699,61951,61952,61954],{},[1750,61953,1763],{"stretchy":1752},[1742,61955,1872],{},[902,61957,61958],{"encoding":904},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[883,61961,61963],{"className":61962},[886],[888,61964,61965],{"xmlns":890},[892,61966,61967,61989],{},[895,61968,61969,61971],{},[1750,61970,1758],{},[3586,61972,61973],{"scriptlevel":2607,"displaystyle":1916},[3423,61974,61975,61981],{},[1699,61976,61977,61979],{},[898,61978,12471],{},[898,61980,1705],{},[895,61982,61983,61985,61987],{},[898,61984,9365],{},[1750,61986,1758],{},[898,61988,207],{},[902,61990,61991],{"encoding":904},"-\\dfrac{Q^E}{c-a}",[883,61993,61995],{"className":61994},[886],[888,61996,61997],{"xmlns":890,"display":36989},[892,61998,61999,62055],{},[895,62000,62001,62003,62009,62011,62013,62029,62031,62033,62035,62037,62039,62045,62047,62049,62051,62053],{},[898,62002,3429],{},[1699,62004,62005,62007],{},[898,62006,12471],{},[898,62008,1705],{},[1750,62010,1766],{},[1750,62012,1758],{},[3423,62014,62015,62021],{},[1699,62016,62017,62019],{},[898,62018,12471],{},[898,62020,1705],{},[895,62022,62023,62025,62027],{},[898,62024,9365],{},[1750,62026,1758],{},[898,62028,207],{},[1969,62030,2658],{},[898,62032,3429],{},[898,62034,9365],{},[1750,62036,1766],{},[1750,62038,1758],{},[3423,62040,62041,62043],{},[1742,62042,53497],{},[1742,62044,53329],{},[1750,62046,8009],{},[1742,62048,12476],{},[1750,62050,6792],{},[1750,62052,1758],{},[1742,62054,53469],{},[902,62056,62057],{"encoding":904},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[724,62059,62060],{},"Nové rovnovážné množství:",[883,62062,62064],{"className":62063},[886],[888,62065,62066],{"xmlns":890,"display":36989},[892,62067,62068,62091],{},[895,62069,62070,62078,62080,62082,62084,62086,62088],{},[5950,62071,62072,62074,62076],{},[898,62073,12471],{},[1742,62075,1744],{},[898,62077,1705],{},[1750,62079,2274],{},[1742,62081,53497],{},[1750,62083,1758],{},[1742,62085,53502],{},[1750,62087,1766],{},[1742,62089,62090],{},"8,326.",[902,62092,62093],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[724,62095,62096,1647,62099,1343,62126,1343,62148,1343,62170,8164,62192,1343,62211,1343,62232,1343,62251,2313],{},[38,62097,62098],{},"Řešení (b) — současná změna všech parametrů:",[883,62100,62102],{"className":62101},[886],[888,62103,62104],{"xmlns":890},[892,62105,62106,62123],{},[895,62107,62108,62110,62112,62114,62116,62118,62120],{},[898,62109,207],{},[1750,62111,2366],{},[1750,62113,1758],{},[1742,62115,7822],{},[1750,62117,12797],{},[1750,62119,1758],{},[1742,62121,62122],{},"2,5",[902,62124,62125],{"encoding":904},"a: -3 \\to -2{,}5",[883,62127,62129],{"className":62128},[886],[888,62130,62131],{"xmlns":890},[892,62132,62133,62145],{},[895,62134,62135,62137,62139,62141,62143],{},[898,62136,2573],{},[1750,62138,2366],{},[1742,62140,14865],{},[1750,62142,12797],{},[1742,62144,6442],{},[902,62146,62147],{"encoding":904},"b: 40 \\to 35",[883,62149,62151],{"className":62150},[886],[888,62152,62153],{"xmlns":890},[892,62154,62155,62167],{},[895,62156,62157,62159,62161,62163,62165],{},[898,62158,9365],{},[1750,62160,2366],{},[1742,62162,4268],{},[1750,62164,12797],{},[1742,62166,3123],{},[902,62168,62169],{"encoding":904},"c: 0{,}5 \\to 0{,}6",[883,62171,62173],{"className":62172},[886],[888,62174,62175],{"xmlns":890},[892,62176,62177,62189],{},[895,62178,62179,62181,62183,62185,62187],{},[898,62180,3429],{},[1750,62182,2366],{},[1742,62184,3079],{},[1750,62186,12797],{},[1742,62188,12582],{},[902,62190,62191],{"encoding":904},"d: 10 \\to 11",[883,62193,62195],{"className":62194},[886],[888,62196,62197],{"xmlns":890},[892,62198,62199,62209],{},[895,62200,62201,62203,62205,62207],{},[898,62202,3429],{},[898,62204,207],{},[1750,62206,1766],{},[1742,62208,4268],{},[902,62210,53535],{"encoding":904},[883,62212,62214],{"className":62213},[886],[888,62215,62216],{"xmlns":890},[892,62217,62218,62230],{},[895,62219,62220,62222,62224,62226,62228],{},[898,62221,3429],{},[898,62223,2573],{},[1750,62225,1766],{},[1750,62227,1758],{},[1742,62229,7902],{},[902,62231,53557],{"encoding":904},[883,62233,62235],{"className":62234},[886],[888,62236,62237],{"xmlns":890},[892,62238,62239,62249],{},[895,62240,62241,62243,62245,62247],{},[898,62242,3429],{},[898,62244,9365],{},[1750,62246,1766],{},[1742,62248,12476],{},[902,62250,53577],{"encoding":904},[883,62252,62254],{"className":62253},[886],[888,62255,62256],{"xmlns":890},[892,62257,62258,62268],{},[895,62259,62260,62262,62264,62266],{},[898,62261,3429],{},[898,62263,3429],{},[1750,62265,1766],{},[1742,62267,1744],{},[902,62269,53597],{"encoding":904},[724,62271,62272,62273,62331],{},"Totální diferenciál ",[883,62274,62276],{"className":62275},[886],[888,62277,62278],{"xmlns":890},[892,62279,62280,62328],{},[895,62281,62282,62288,62290,62292,62294,62296,62298,62300,62302,62304,62306,62308],{},[1699,62283,62284,62286],{},[898,62285,12471],{},[898,62287,1705],{},[1750,62289,1753],{"stretchy":1752},[898,62291,207],{},[1750,62293,1917],{"separator":1916},[898,62295,2573],{},[1750,62297,1917],{"separator":1916},[898,62299,9365],{},[1750,62301,1917],{"separator":1916},[898,62303,3429],{},[1750,62305,1763],{"stretchy":1752},[1750,62307,1766],{},[3586,62309,62310],{"scriptlevel":2607,"displaystyle":1916},[3423,62311,62312,62320],{},[895,62313,62314,62316,62318],{},[898,62315,2573],{},[1750,62317,1758],{},[898,62319,3429],{},[895,62321,62322,62324,62326],{},[898,62323,9365],{},[1750,62325,1758],{},[898,62327,207],{},[902,62329,62330],{"encoding":904},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[883,62333,62335],{"className":62334},[886],[888,62336,62337],{"xmlns":890,"display":36989},[892,62338,62339,62459],{},[895,62340,62341,62343,62349,62351,62377,62379,62381,62383,62385,62397,62399,62401,62403,62405,62431,62433,62435,62437,62439,62451,62453,62455,62457],{},[898,62342,3429],{},[1699,62344,62345,62347],{},[898,62346,12471],{},[898,62348,1705],{},[1750,62350,1766],{},[3423,62352,62353,62361],{},[895,62354,62355,62357,62359],{},[898,62356,2573],{},[1750,62358,1758],{},[898,62360,3429],{},[895,62362,62363,62365,62367,62369,62371],{},[1750,62364,1753],{"stretchy":1752},[898,62366,9365],{},[1750,62368,1758],{},[898,62370,207],{},[1699,62372,62373,62375],{},[1750,62374,1763],{"stretchy":1752},[1742,62376,1872],{},[1969,62378,2658],{},[898,62380,3429],{},[898,62382,207],{},[1750,62384,1861],{},[3423,62386,62387,62389],{},[1742,62388,1744],{},[895,62390,62391,62393,62395],{},[898,62392,9365],{},[1750,62394,1758],{},[898,62396,207],{},[1969,62398,2658],{},[898,62400,3429],{},[898,62402,2573],{},[1750,62404,1758],{},[3423,62406,62407,62415],{},[895,62408,62409,62411,62413],{},[898,62410,2573],{},[1750,62412,1758],{},[898,62414,3429],{},[895,62416,62417,62419,62421,62423,62425],{},[1750,62418,1753],{"stretchy":1752},[898,62420,9365],{},[1750,62422,1758],{},[898,62424,207],{},[1699,62426,62427,62429],{},[1750,62428,1763],{"stretchy":1752},[1742,62430,1872],{},[1969,62432,2658],{},[898,62434,3429],{},[898,62436,9365],{},[1750,62438,1758],{},[3423,62440,62441,62443],{},[1742,62442,1744],{},[895,62444,62445,62447,62449],{},[898,62446,9365],{},[1750,62448,1758],{},[898,62450,207],{},[1969,62452,2658],{},[898,62454,3429],{},[898,62456,3429],{},[898,62458,2313],{"mathvariant":1747},[902,62460,62461],{"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.",[724,62463,62464,62465,1343,62487,1343,62518,12825],{},"Dosazením číselných hodnot (",[883,62466,62468],{"className":62467},[886],[888,62469,62470],{"xmlns":890},[892,62471,62472,62484],{},[895,62473,62474,62476,62478,62480,62482],{},[898,62475,9365],{},[1750,62477,1758],{},[898,62479,207],{},[1750,62481,1766],{},[1742,62483,53329],{},[902,62485,62486],{"encoding":904},"c - a = 3{,}5",[883,62488,62490],{"className":62489},[886],[888,62491,62492],{"xmlns":890},[892,62493,62494,62515],{},[895,62495,62496,62498,62500,62502,62504,62510,62512],{},[1750,62497,1753],{"stretchy":1752},[898,62499,9365],{},[1750,62501,1758],{},[898,62503,207],{},[1699,62505,62506,62508],{},[1750,62507,1763],{"stretchy":1752},[1742,62509,1872],{},[1750,62511,1766],{},[1742,62513,62514],{},"12,25",[902,62516,62517],{"encoding":904},"(c-a)^2 = 12{,}25",[883,62519,62521],{"className":62520},[886],[888,62522,62523],{"xmlns":890},[892,62524,62525,62537],{},[895,62526,62527,62529,62531,62533,62535],{},[898,62528,2573],{},[1750,62530,1758],{},[898,62532,3429],{},[1750,62534,1766],{},[1742,62536,46942],{},[902,62538,62539],{"encoding":904},"b - d = 30",[883,62541,62543],{"className":62542},[886],[888,62544,62545],{"xmlns":890,"display":36989},[892,62546,62547,62648],{},[895,62548,62549,62551,62557,62559,62567,62569,62571,62573,62575,62583,62585,62587,62589,62591,62593,62601,62603,62605,62607,62609,62617,62619,62621,62623,62625,62628,62630,62633,62635,62637,62639,62642,62644,62646],{},[898,62550,3429],{},[1699,62552,62553,62555],{},[898,62554,12471],{},[898,62556,1705],{},[1750,62558,2274],{},[3586,62560,62561],{"scriptlevel":2607,"displaystyle":1752},[3423,62562,62563,62565],{},[1742,62564,46942],{},[1742,62566,62514],{},[1750,62568,1753],{"stretchy":1752},[1742,62570,4268],{},[1750,62572,1763],{"stretchy":1752},[1750,62574,1861],{},[3586,62576,62577],{"scriptlevel":2607,"displaystyle":1752},[3423,62578,62579,62581],{},[1742,62580,1744],{},[1742,62582,53329],{},[1750,62584,1753],{"stretchy":1752},[1750,62586,1758],{},[1742,62588,7902],{},[1750,62590,1763],{"stretchy":1752},[1750,62592,1758],{},[3586,62594,62595],{"scriptlevel":2607,"displaystyle":1752},[3423,62596,62597,62599],{},[1742,62598,46942],{},[1742,62600,62514],{},[1750,62602,1753],{"stretchy":1752},[1742,62604,12476],{},[1750,62606,1763],{"stretchy":1752},[1750,62608,1758],{},[3586,62610,62611],{"scriptlevel":2607,"displaystyle":1752},[3423,62612,62613,62615],{},[1742,62614,1744],{},[1742,62616,53329],{},[1750,62618,1753],{"stretchy":1752},[1742,62620,1744],{},[1750,62622,1763],{"stretchy":1752},[1750,62624,6792],{},[1742,62626,62627],{},"1,224",[1750,62629,1758],{},[1742,62631,62632],{},"1,429",[1750,62634,1758],{},[1742,62636,53502],{},[1750,62638,1758],{},[1742,62640,62641],{},"0,286",[1750,62643,6792],{},[1750,62645,1758],{},[1742,62647,53748],{},[902,62649,62650],{"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.",[724,62652,38988,62653,2313],{},[883,62654,62656],{"className":62655},[886],[888,62657,62658],{"xmlns":890},[892,62659,62660,62682],{},[895,62661,62662,62670,62672,62674,62676,62678,62680],{},[5950,62663,62664,62666,62668],{},[898,62665,12471],{},[1742,62667,1744],{},[898,62669,1705],{},[1750,62671,2274],{},[1742,62673,53497],{},[1750,62675,1758],{},[1742,62677,53779],{},[1750,62679,6792],{},[1742,62681,53784],{},[902,62683,62684],{"encoding":904},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1785,62686,62687],{},[724,62688,62689,62691,62692,62713,62714,62740,62741,62744,62745,62841,62842,62865,62866,62882],{},[883,62690,5454],{}," Pozn. k přepisu učebnice\nV původním skenu přednášky byla u části (b) uvedena hodnota ",[883,62693,62695],{"className":62694},[886],[888,62696,62697],{"xmlns":890},[892,62698,62699,62711],{},[895,62700,62701,62703,62705,62707,62709],{},[898,62702,2666],{"mathvariant":1747},[898,62704,12471],{},[1750,62706,2274],{},[1750,62708,1758],{},[1742,62710,53814],{},[902,62712,53817],{"encoding":904},", což neodpovídá součtu dílčích derivací při daných přírůstcích. Podle vlastního přepočtu vychází ",[883,62715,62717],{"className":62716},[886],[888,62718,62719],{"xmlns":890},[892,62720,62721,62737],{},[895,62722,62723,62725,62731,62733,62735],{},[898,62724,3429],{},[1699,62726,62727,62729],{},[898,62728,12471],{},[898,62730,1705],{},[1750,62732,6792],{},[1750,62734,1758],{},[1742,62736,53779],{},[902,62738,62739],{"encoding":904},"dQ^E \\doteq -0{,}735",". Totální diferenciál je navíc pouze ",[38,62742,62743],{},"lineární aproximací","; přesná změna zjištěná ze změněného vzorce\n",[883,62746,62748],{"className":62747},[886],[888,62749,62750],{"xmlns":890},[892,62751,62752,62838],{},[895,62753,62754,62762,62764,62798,62800,62824,62826,62833,62835],{},[5950,62755,62756,62758,62760],{},[898,62757,12471],{},[1742,62759,1744],{},[898,62761,1705],{},[1750,62763,1766],{},[3423,62765,62766,62782],{},[895,62767,62768,62774,62776],{},[1699,62769,62770,62772],{},[898,62771,2573],{},[1750,62773,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,62775,1758],{},[1699,62777,62778,62780],{},[898,62779,3429],{},[1750,62781,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[895,62783,62784,62790,62792],{},[1699,62785,62786,62788],{},[898,62787,9365],{},[1750,62789,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,62791,1758],{},[1699,62793,62794,62796],{},[898,62795,207],{},[1750,62797,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,62799,1766],{},[3423,62801,62802,62810],{},[895,62803,62804,62806,62808],{},[1742,62805,6442],{},[1750,62807,1758],{},[1742,62809,12582],{},[895,62811,62812,62814,62816,62818,62820,62822],{},[1742,62813,3123],{},[1750,62815,1758],{},[1750,62817,1753],{"stretchy":1752},[1750,62819,1758],{},[1742,62821,62122],{},[1750,62823,1763],{"stretchy":1752},[1750,62825,1766],{},[3423,62827,62828,62830],{},[1742,62829,50723],{},[1742,62831,62832],{},"3,1",[1750,62834,6792],{},[1742,62836,62837],{},"7,742",[902,62839,62840],{"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 ",[883,62843,62845],{"className":62844},[886],[888,62846,62847],{"xmlns":890},[892,62848,62849,62862],{},[895,62850,62851,62853,62855,62857,62859],{},[898,62852,2666],{"mathvariant":1747},[898,62854,12471],{},[1750,62856,6792],{},[1750,62858,1758],{},[1742,62860,62861],{},"0,829",[902,62863,62864],{"encoding":904},"\\Delta Q \\doteq -0{,}829"," — dobře konzistentní s diferenciálem. Hodnota ",[883,62867,62869],{"className":62868},[886],[888,62870,62871],{"xmlns":890},[892,62872,62873,62879],{},[895,62874,62875,62877],{},[1750,62876,1758],{},[1742,62878,53814],{},[902,62880,62881],{"encoding":904},"-2{,}69"," je tedy pravděpodobně chyba v zápisu.",[724,62884,62885],{},[614,62886,62887,62888,62901],{},"Příklad 2.11 je primárně o multiplikátorech pro ",[883,62889,62891],{"className":62890},[886],[888,62892,62893],{"xmlns":890},[892,62894,62895,62899],{},[895,62896,62897],{},[898,62898,12471],{},[902,62900,12471],{"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.",[198,62903,62905,62906],{"id":62904},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[883,62907,62909],{"className":62908},[886],[888,62910,62911],{"xmlns":890},[892,62912,62913,62919],{},[895,62914,62915,62917],{},[898,62916,1776],{},[898,62918,1779],{},[902,62920,53892],{"encoding":904},[1785,62922,62923],{},[724,62924,62925,62927,62928,62962,62963,62985],{},[883,62926,61618],{}," Zadání\nPro nabídku ",[883,62929,62931],{"className":62930},[886],[888,62932,62933],{"xmlns":890},[892,62934,62935,62959],{},[895,62936,62937,62939,62941,62943,62945,62947,62949,62951,62953,62955,62957],{},[898,62938,1776],{},[1750,62940,1766],{},[898,62942,1779],{},[1750,62944,1753],{"stretchy":1752},[898,62946,12471],{},[1750,62948,1763],{"stretchy":1752},[1750,62950,1766],{},[1742,62952,3079],{},[1750,62954,1861],{},[1742,62956,1872],{},[898,62958,12471],{},[902,62960,62961],{"encoding":904},"P = S(Q) = 10 + 2Q"," a množství ",[883,62964,62966],{"className":62965},[886],[888,62967,62968],{"xmlns":890},[892,62969,62970,62982],{},[895,62971,62972,62978,62980],{},[5535,62973,62974,62976],{},[898,62975,12471],{},[1742,62977,2607],{},[1750,62979,1766],{},[1742,62981,3079],{},[902,62983,62984],{"encoding":904},"Q_0 = 10"," vypočítejte přebytek výrobce.",[724,62987,62988],{},[38,62989,6610],{},[724,62991,62992],{},"Odpovídající cena:",[883,62994,62996],{"className":62995},[886],[888,62997,62998],{"xmlns":890,"display":36989},[892,62999,63000,63035],{},[895,63001,63002,63008,63010,63012,63014,63016,63018,63020,63022,63024,63026,63028,63030,63032],{},[5535,63003,63004,63006],{},[898,63005,1776],{},[1742,63007,2607],{},[1750,63009,1766],{},[898,63011,1779],{},[1750,63013,1753],{"stretchy":1752},[1742,63015,3079],{},[1750,63017,1763],{"stretchy":1752},[1750,63019,1766],{},[1742,63021,3079],{},[1750,63023,1861],{},[1742,63025,1872],{},[1750,63027,8009],{},[1742,63029,3079],{},[1750,63031,1766],{},[1742,63033,63034],{},"30.",[902,63036,63037],{"encoding":904},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[724,63039,63040],{},"Dle vzorce (2.15):",[883,63042,63044],{"className":63043},[886],[888,63045,63046],{"xmlns":890,"display":36989},[892,63047,63048,63156],{},[895,63049,63050,63052,63054,63056,63058,63060,63062,63068,63074,63076,63084,63086,63088,63090,63092,63094,63096,63098,63100,63102,63104,63106,63108,63110,63112,63115,63117,63119,63121,63127,63135,63137,63139,63141,63143,63145,63147,63149,63151,63153],{},[898,63051,1776],{},[898,63053,1779],{},[1750,63055,1753],{"stretchy":1752},[1742,63057,3079],{},[1750,63059,1763],{"stretchy":1752},[1750,63061,1766],{},[5535,63063,63064,63066],{},[898,63065,1776],{},[1742,63067,2607],{},[5535,63069,63070,63072],{},[898,63071,12471],{},[1742,63073,2607],{},[1750,63075,1758],{},[5950,63077,63078,63080,63082],{},[1750,63079,20802],{},[1742,63081,2607],{},[1742,63083,3079],{},[1750,63085,1753],{"stretchy":1752},[1742,63087,3079],{},[1750,63089,1861],{},[1742,63091,1872],{},[898,63093,12471],{},[1750,63095,1763],{"stretchy":1752},[1969,63097,2658],{},[898,63099,3429],{},[898,63101,12471],{},[1750,63103,1766],{},[1742,63105,3079],{},[1750,63107,8009],{},[1742,63109,46942],{},[1750,63111,1758],{},[1750,63113,5141],{"fence":1752,"stretchy":1916,"minsize":63114,"maxsize":63114},"1.8em",[1742,63116,3079],{},[898,63118,12471],{},[1750,63120,1861],{},[1699,63122,63123,63125],{},[898,63124,12471],{},[1742,63126,1872],{},[5950,63128,63129,63131,63133],{},[1750,63130,5158],{"fence":1752,"stretchy":1916,"minsize":63114,"maxsize":63114},[1742,63132,2607],{},[1742,63134,3079],{},[1750,63136,1766],{},[1742,63138,39004],{},[1750,63140,1758],{},[1750,63142,1753],{"stretchy":1752},[1742,63144,4078],{},[1750,63146,1861],{},[1742,63148,4078],{},[1750,63150,1763],{"stretchy":1752},[1750,63152,1766],{},[1742,63154,63155],{},"100.",[902,63157,63158],{"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.",[724,63160,63161,63162,63183,63184,63204],{},"Přebytek výrobce při množství ",[883,63163,63165],{"className":63164},[886],[888,63166,63167],{"xmlns":890},[892,63168,63169,63181],{},[895,63170,63171,63177,63179],{},[5535,63172,63173,63175],{},[898,63174,12471],{},[1742,63176,2607],{},[1750,63178,1766],{},[1742,63180,3079],{},[902,63182,62984],{"encoding":904}," je tedy ",[883,63185,63187],{"className":63186},[886],[888,63188,63189],{"xmlns":890},[892,63190,63191,63201],{},[895,63192,63193,63195,63197,63199],{},[898,63194,1776],{},[898,63196,1779],{},[1750,63198,1766],{},[1742,63200,4078],{},[902,63202,63203],{"encoding":904},"PS = 100"," (peněžních jednotek).",[45893,63206],{},[115,63208,63210],{"id":63209},"cheat-sheet","Cheat sheet",[16,63212,63213,63226],{},[19,63214,63215],{},[22,63216,63217,63220,63223],{},[25,63218,63219],{},"Veličina",[25,63221,63222],{},"Vzorec",[25,63224,63225],{},"Geometrie",[30,63227,63228,63346,63460,63528],{},[22,63229,63230,63258,63314],{},[35,63231,63232],{},[883,63233,63235],{"className":63234},[886],[888,63236,63237],{"xmlns":890},[892,63238,63239,63255],{},[895,63240,63241,63243,63245,63247,63253],{},[898,63242,1812],{},[898,63244,1779],{},[1750,63246,1753],{"stretchy":1752},[5535,63248,63249,63251],{},[898,63250,12471],{},[1742,63252,2607],{},[1750,63254,1763],{"stretchy":1752},[902,63256,63257],{"encoding":904},"CS(Q_0)",[35,63259,63260],{},[883,63261,63263],{"className":63262},[886],[888,63264,63265],{"xmlns":890},[892,63266,63267,63311],{},[895,63268,63269],{},[3586,63270,63271,63283,63285,63287,63289,63291,63293,63295,63297,63299,63305],{"scriptlevel":2607,"displaystyle":1916},[5950,63272,63273,63275,63277],{},[1750,63274,20802],{},[1742,63276,2607],{},[5535,63278,63279,63281],{},[898,63280,12471],{},[1742,63282,2607],{},[898,63284,5541],{},[1750,63286,1753],{"stretchy":1752},[898,63288,12471],{},[1750,63290,1763],{"stretchy":1752},[1969,63292,2658],{},[898,63294,3429],{},[898,63296,12471],{},[1750,63298,1758],{},[5535,63300,63301,63303],{},[898,63302,1776],{},[1742,63304,2607],{},[5535,63306,63307,63309],{},[898,63308,12471],{},[1742,63310,2607],{},[902,63312,63313],{"encoding":904},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[35,63315,63316,63317,63320,63321,63324,63325],{},"plocha ",[38,63318,63319],{},"pod"," křivkou poptávky, ",[38,63322,63323],{},"nad"," čárou ",[883,63326,63328],{"className":63327},[886],[888,63329,63330],{"xmlns":890},[892,63331,63332,63344],{},[895,63333,63334,63336,63338],{},[898,63335,1776],{},[1750,63337,1766],{},[5535,63339,63340,63342],{},[898,63341,1776],{},[1742,63343,2607],{},[902,63345,60600],{"encoding":904},[22,63347,63348,63376,63432],{},[35,63349,63350],{},[883,63351,63353],{"className":63352},[886],[888,63354,63355],{"xmlns":890},[892,63356,63357,63373],{},[895,63358,63359,63361,63363,63365,63371],{},[898,63360,1776],{},[898,63362,1779],{},[1750,63364,1753],{"stretchy":1752},[5535,63366,63367,63369],{},[898,63368,12471],{},[1742,63370,2607],{},[1750,63372,1763],{"stretchy":1752},[902,63374,63375],{"encoding":904},"PS(Q_0)",[35,63377,63378],{},[883,63379,63381],{"className":63380},[886],[888,63382,63383],{"xmlns":890},[892,63384,63385,63429],{},[895,63386,63387],{},[3586,63388,63389,63395,63401,63403,63415,63417,63419,63421,63423,63425,63427],{"scriptlevel":2607,"displaystyle":1916},[5535,63390,63391,63393],{},[898,63392,1776],{},[1742,63394,2607],{},[5535,63396,63397,63399],{},[898,63398,12471],{},[1742,63400,2607],{},[1750,63402,1758],{},[5950,63404,63405,63407,63409],{},[1750,63406,20802],{},[1742,63408,2607],{},[5535,63410,63411,63413],{},[898,63412,12471],{},[1742,63414,2607],{},[898,63416,1779],{},[1750,63418,1753],{"stretchy":1752},[898,63420,12471],{},[1750,63422,1763],{"stretchy":1752},[1969,63424,2658],{},[898,63426,3429],{},[898,63428,12471],{},[902,63430,63431],{"encoding":904},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[35,63433,63316,63434,63436,63437,63324,63439],{},[38,63435,63323],{}," křivkou nabídky, ",[38,63438,63319],{},[883,63440,63442],{"className":63441},[886],[888,63443,63444],{"xmlns":890},[892,63445,63446,63458],{},[895,63447,63448,63450,63452],{},[898,63449,1776],{},[1750,63451,1766],{},[5535,63453,63454,63456],{},[898,63455,1776],{},[1742,63457,2607],{},[902,63459,60600],{"encoding":904},[22,63461,63462,63465,63492],{},[35,63463,63464],{},"Výdaje \u002F tržby",[35,63466,63467],{},[883,63468,63470],{"className":63469},[886],[888,63471,63472],{"xmlns":890},[892,63473,63474,63490],{},[895,63475,63476,63482,63484],{},[5535,63477,63478,63480],{},[898,63479,1776],{},[1742,63481,2607],{},[1750,63483,8009],{},[5535,63485,63486,63488],{},[898,63487,12471],{},[1742,63489,2607],{},[902,63491,61460],{"encoding":904},[35,63493,63494,63495],{},"obdélník ",[883,63496,63498],{"className":63497},[886],[888,63499,63500],{"xmlns":890},[892,63501,63502,63526],{},[895,63503,63504,63506,63508,63514,63516,63518,63520],{},[1742,63505,2607],{},[1969,63507,2658],{},[5535,63509,63510,63512],{},[898,63511,12471],{},[1742,63513,2607],{},[1969,63515,2658],{},[898,63517,13916],{},[1969,63519,2658],{},[5535,63521,63522,63524],{},[898,63523,1776],{},[1742,63525,2607],{},[902,63527,60080],{"encoding":904},[22,63529,63530,63533,63556],{},[35,63531,63532],{},"Celkový přebytek",[35,63534,63535],{},[883,63536,63538],{"className":63537},[886],[888,63539,63540],{"xmlns":890},[892,63541,63542,63554],{},[895,63543,63544,63546,63548,63550,63552],{},[898,63545,1812],{},[898,63547,1779],{},[1750,63549,1861],{},[898,63551,1776],{},[898,63553,1779],{},[902,63555,59818],{"encoding":904},[35,63557,63558],{},"součet obou ploch v rovnováze",[45893,63560],{},[115,63562,10461],{"id":10460},[120,63564,63565,63587,63609,63653,63697,63760,63788],{},[123,63566,63567,2084,63569,1343,63584,63586],{},[38,63568,53857],{},[883,63570,63572],{"className":63571},[886],[888,63573,63574],{"xmlns":890},[892,63575,63576,63582],{},[895,63577,63578,63580],{},[898,63579,1812],{},[898,63581,1779],{},[902,63583,53873],{"encoding":904},[614,63585,53911],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[123,63588,63589,2084,63591,1343,63606,63608],{},[38,63590,54004],{},[883,63592,63594],{"className":63593},[886],[888,63595,63596],{"xmlns":890},[892,63597,63598,63604],{},[895,63599,63600,63602],{},[898,63601,1776],{},[898,63603,1779],{},[902,63605,53892],{"encoding":904},[614,63607,54007],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[123,63610,63611,10469,63614,2313],{},[38,63612,63613],{},"Ochota platit",[883,63615,63617],{"className":63616},[886],[888,63618,63619],{"xmlns":890},[892,63620,63621,63651],{},[895,63622,63623],{},[3586,63624,63625,63637,63639,63641,63643,63645,63647,63649],{"scriptlevel":2607,"displaystyle":1916},[5950,63626,63627,63629,63631],{},[1750,63628,20802],{},[1742,63630,2607],{},[5535,63632,63633,63635],{},[898,63634,12471],{},[1742,63636,2607],{},[898,63638,5541],{},[1750,63640,1753],{"stretchy":1752},[898,63642,12471],{},[1750,63644,1763],{"stretchy":1752},[1969,63646,2658],{},[898,63648,3429],{},[898,63650,12471],{},[902,63652,60448],{"encoding":904},[123,63654,63655,10469,63658,2313],{},[38,63656,63657],{},"Minimální cena výrobce",[883,63659,63661],{"className":63660},[886],[888,63662,63663],{"xmlns":890},[892,63664,63665,63695],{},[895,63666,63667],{},[3586,63668,63669,63681,63683,63685,63687,63689,63691,63693],{"scriptlevel":2607,"displaystyle":1916},[5950,63670,63671,63673,63675],{},[1750,63672,20802],{},[1742,63674,2607],{},[5535,63676,63677,63679],{},[898,63678,12471],{},[1742,63680,2607],{},[898,63682,1779],{},[1750,63684,1753],{"stretchy":1752},[898,63686,12471],{},[1750,63688,1763],{"stretchy":1752},[1969,63690,2658],{},[898,63692,3429],{},[898,63694,12471],{},[902,63696,61090],{"encoding":904},[123,63698,63699,10469,63702,61591,63727,1783],{},[38,63700,63701],{},"Výdaje spotřebitele \u002F tržby výrobce",[883,63703,63705],{"className":63704},[886],[888,63706,63707],{"xmlns":890},[892,63708,63709,63725],{},[895,63710,63711,63717,63719],{},[5535,63712,63713,63715],{},[898,63714,1776],{},[1742,63716,2607],{},[1969,63718,2658],{},[5535,63720,63721,63723],{},[898,63722,12471],{},[1742,63724,2607],{},[902,63726,60526],{"encoding":904},[883,63728,63730],{"className":63729},[886],[888,63731,63732],{"xmlns":890},[892,63733,63734,63758],{},[895,63735,63736,63738,63740,63746,63748,63750,63752],{},[1742,63737,2607],{},[1969,63739,2658],{},[5535,63741,63742,63744],{},[898,63743,12471],{},[1742,63745,2607],{},[1969,63747,2658],{},[898,63749,13916],{},[1969,63751,2658],{},[5535,63753,63754,63756],{},[898,63755,1776],{},[1742,63757,2607],{},[902,63759,60080],{"encoding":904},[123,63761,63762,63765,63766,63787],{},[38,63763,63764],{},"Celkový přebytek trhu"," — součet ",[883,63767,63769],{"className":63768},[886],[888,63770,63771],{"xmlns":890},[892,63772,63773,63785],{},[895,63774,63775,63777,63779,63781,63783],{},[898,63776,1812],{},[898,63778,1779],{},[1750,63780,1861],{},[898,63782,1776],{},[898,63784,1779],{},[902,63786,59818],{"encoding":904}," v rovnovážném bodě.",[123,63789,63790,63792,63793,1343,63806,63819,63820,2313],{},[38,63791,12137],{}," — plochy ohraničené křivkami ",[883,63794,63796],{"className":63795},[886],[888,63797,63798],{"xmlns":890},[892,63799,63800,63804],{},[895,63801,63802],{},[898,63803,5541],{},[902,63805,5541],{"encoding":904},[883,63807,63809],{"className":63808},[886],[888,63810,63811],{"xmlns":890},[892,63812,63813,63817],{},[895,63814,63815],{},[898,63816,1779],{},[902,63818,1779],{"encoding":904}," a přímkou ",[883,63821,63823],{"className":63822},[886],[888,63824,63825],{"xmlns":890},[892,63826,63827,63839],{},[895,63828,63829,63831,63833],{},[898,63830,1776],{},[1750,63832,1766],{},[5535,63834,63835,63837],{},[898,63836,1776],{},[1742,63838,2607],{},[902,63840,60600],{"encoding":904},[45893,63842],{},[115,63844,63846],{"id":63845},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[724,63848,63849,63850,63863,63864,63881],{},"Uvalení jednotkové daně ",[883,63851,63853],{"className":63852},[886],[888,63854,63855],{"xmlns":890},[892,63856,63857,63861],{},[895,63858,63859],{},[898,63860,5326],{},[902,63862,5326],{"encoding":904}," na trh posouvá rovnovážné množství pod ",[883,63865,63867],{"className":63866},[886],[888,63868,63869],{"xmlns":890},[892,63870,63871,63879],{},[895,63872,63873],{},[1699,63874,63875,63877],{},[898,63876,12471],{},[898,63878,1705],{},[902,63880,51326],{"encoding":904}," a rozkládá původní plochu přebytků na nové části.",[724,63883,63884],{},[4434,63885],{"alt":63886,"className":63887,"src":63888},"imek-prebytky-s-dani-deadweight",[210,4438],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[724,63890,63891,63892,63907,63908,63923,63924,61591,63927,63951,63952,2084,63955,63958,63959,2313],{},"Přebytek spotřebitele ",[883,63893,63895],{"className":63894},[886],[888,63896,63897],{"xmlns":890},[892,63898,63899,63905],{},[895,63900,63901,63903],{},[898,63902,1812],{},[898,63904,1779],{},[902,63906,53873],{"encoding":904}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[883,63909,63911],{"className":63910},[886],[888,63912,63913],{"xmlns":890},[892,63914,63915,63921],{},[895,63916,63917,63919],{},[898,63918,1776],{},[898,63920,1779],{},[902,63922,53892],{"encoding":904}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[38,63925,63926],{},"daňový příjem",[883,63928,63930],{"className":63929},[886],[888,63931,63932],{"xmlns":890},[892,63933,63934,63948],{},[895,63935,63936,63938,63940],{},[898,63937,5326],{},[1750,63939,8009],{},[5950,63941,63942,63944,63946],{},[898,63943,12471],{},[1742,63945,1744],{},[898,63947,1705],{},[902,63949,63950],{"encoding":904},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[38,63953,63954],{},"mrtvá ztráta",[614,63956,63957],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[207,63960,811],{"className":63961,"dataFsResolvedFilePath":809,"href":810},[210],[45893,63963],{},[115,63965,11524],{"id":11523},[120,63967,63968,63975,63987,63994,64001],{},[123,63969,63970,1647,63972],{},[38,63971,25798],{},[207,63973,802],{"className":63974,"dataFsResolvedFilePath":800,"href":801},[210],[123,63976,63977,1647,63979,63982,63983,63986],{},[38,63978,45597],{},[207,63980,775],{"className":63981,"dataFsResolvedFilePath":773,"href":774},[210]," (určitý integrál, plocha pod křivkou), ",[207,63984,12053],{"className":63985,"dataFsResolvedFilePath":764,"href":765},[210]," (monotonie křivek)",[123,63988,63989,1647,63991],{},[38,63990,11549],{},[207,63992,13491],{"className":63993,"dataFsResolvedFilePath":827,"href":828},[210],[123,63995,63996,1647,63998],{},[38,63997,59681],{},[207,63999,59685],{"className":64000,"dataFsResolvedFilePath":745,"href":746},[210],[123,64002,64003,1647,64005],{},[38,64004,11531],{},[207,64006,11535],{"className":64007,"dataFsResolvedFilePath":1644,"href":1645},[210],{"title":641,"searchDepth":642,"depth":642,"links":64009},[64010,64011,64016,64021,64026,64027,64028,64029],{"id":59877,"depth":642,"text":1241},{"id":60221,"depth":642,"text":64012,"children":64013},"Přebytek spotřebitele (CSCS)",[64014,64015],{"id":60240,"depth":649,"text":60241},{"id":12136,"depth":649,"text":12137},{"id":60816,"depth":642,"text":64017,"children":64018},"Přebytek výrobce (PSPS)",[64019,64020],{"id":60835,"depth":649,"text":60836},{"id":60998,"depth":649,"text":12137},{"id":61606,"depth":642,"text":61607,"children":64022},[64023,64024],{"id":61610,"depth":649,"text":61611},{"id":62904,"depth":649,"text":64025},"Příklad 2.13 — numerický výpočet PSPS",{"id":63209,"depth":642,"text":63210},{"id":10460,"depth":642,"text":10461},{"id":63845,"depth":642,"text":63846},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":820,"description":641},[1138,1135],"topics\u002Fprebytek-spotrebitele-vyrobce",[1128,59747,64036,64037,21622,11564,64038,64039],"cs","ps","spotrebitel","vyrobce","FhK0gkf2tjMxSgO0-74OuedOn6U35QtJczf-f255pZs",{"id":64042,"title":64043,"body":64044,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":83373,"navigation":664,"path":83374,"seo":83375,"sources":83376,"stem":83377,"tags":83378,"type":11664,"updated":677,"__hash__":83384},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":9,"value":64045,"toc":83337},[64046,64049,64235,64237,64328,64333,64659,64663,64670,64674,64719,64786,64817,64867,64902,64906,64965,64970,65036,65154,65256,65260,65283,65361,65404,65408,65437,65504,65510,65624,65628,65708,65745,65797,65995,66059,66146,66150,66153,66232,66235,66353,66372,66437,66441,66533,66601,66642,66696,66764,66801,66805,66863,66893,67104,67176,67228,67394,67487,67522,67526,67530,67567,67632,67687,67691,67714,67803,67907,67976,67980,68077,68190,68246,68300,68358,68419,68422,68458,68523,68553,68782,68840,68874,68878,68905,68984,69098,69119,69198,69200,69308,69312,69450,69772,69776,69779,69783,69832,69836,70090,70242,70249,70322,70506,70511,70854,70858,70881,70883,70904,70963,70973,71022,71164,71238,71333,71448,71546,71664,71668,71737,71742,71854,71999,72050,72162,72204,72208,72228,72289,72316,72378,72382,72404,72473,72753,72760,72790,72797,72990,72994,73072,73077,73153,73156,73244,73320,73387,73436,73539,73612,73733,74084,74197,74299,74303,74306,74313,74316,74352,74411,74420,74569,74793,74797,74860,75039,75131,75186,75190,75246,75316,75368,75389,75470,75473,75548,75592,75596,75637,75680,75706,75710,75781,75877,75939,75991,76094,76172,76195,76224,76228,76394,76511,76583,76898,77058,77062,77113,77175,77210,77240,77340,77382,77551,77556,77652,77690,77694,77813,78114,78116,78151,78155,78159,78287,78419,78741,78929,79007,79011,79316,79429,79575,79760,79866,80098,80213,80295,80414,80512,80553,80557,80612,80756,80910,81070,81163,81357,81669,81800,81929,81933,82005,82047,82098,82100,83295,83297],[12,64047,64043],{"id":64048},"příjem-náklady-zisk-a-nabídka-firmy",[1785,64050,64051],{},[724,64052,64053,13541,64055,1647,64058,64073,64074,1647,64077,64092,64093,1647,64096,64124,64125,64147,64148,64172,64173,64195,64196,64199,64200,64216,64217,2313],{},[883,64054,13540],{},[38,64056,64057],{},"Příjem",[883,64059,64061],{"className":64060},[886],[888,64062,64063],{"xmlns":890},[892,64064,64065,64071],{},[895,64066,64067,64069],{},[898,64068,5326],{},[898,64070,13658],{},[902,64072,13758],{"encoding":904}," je to, co firma inkasuje (cena krát množství), ",[38,64075,64076],{},"náklady",[883,64078,64080],{"className":64079},[886],[888,64081,64082],{"xmlns":890},[892,64083,64084,64090],{},[895,64085,64086,64088],{},[898,64087,5326],{},[898,64089,1812],{},[902,64091,12916],{"encoding":904}," to, co vynaloží (fixní plus variabilní), a ",[38,64094,64095],{},"zisk",[883,64097,64099],{"className":64098},[886],[888,64100,64101],{"xmlns":890},[892,64102,64103,64121],{},[895,64104,64105,64107,64109,64111,64113,64115,64117,64119],{},[898,64106,1776],{},[898,64108,13658],{},[1750,64110,1766],{},[898,64112,5326],{},[898,64114,13658],{},[1750,64116,1758],{},[898,64118,5326],{},[898,64120,1812],{},[902,64122,64123],{"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: ",[883,64126,64128],{"className":64127},[886],[888,64129,64130],{"xmlns":890},[892,64131,64132,64144],{},[895,64133,64134,64136,64138,64140,64142],{},[898,64135,13916],{},[898,64137,1812],{},[1750,64139,1766],{},[898,64141,1773],{},[898,64143,1812],{},[902,64145,64146],{"encoding":904},"AC = MC"," v minimu průměrných nákladů, ",[883,64149,64151],{"className":64150},[886],[888,64152,64153],{"xmlns":890},[892,64154,64155,64169],{},[895,64156,64157,64159,64161,64163,64165,64167],{},[898,64158,13916],{},[898,64160,49262],{},[898,64162,1812],{},[1750,64164,1766],{},[898,64166,1773],{},[898,64168,1812],{},[902,64170,64171],{"encoding":904},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[883,64174,64176],{"className":64175},[886],[888,64177,64178],{"xmlns":890},[892,64179,64180,64192],{},[895,64181,64182,64184,64186,64188,64190],{},[898,64183,1773],{},[898,64185,13658],{},[1750,64187,1766],{},[898,64189,1773],{},[898,64191,1812],{},[902,64193,64194],{"encoding":904},"MR = MC"," v maximu zisku. Na závěr se sestaví ",[38,64197,64198],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[883,64201,64203],{"className":64202},[886],[888,64204,64205],{"xmlns":890},[892,64206,64207,64213],{},[895,64208,64209,64211],{},[898,64210,1773],{},[898,64212,1812],{},[902,64214,64215],{"encoding":904},"MC"," nad bodem minima ",[883,64218,64220],{"className":64219},[886],[888,64221,64222],{"xmlns":890},[892,64223,64224,64232],{},[895,64225,64226,64228,64230],{},[898,64227,13916],{},[898,64229,49262],{},[898,64231,1812],{},[902,64233,64234],{"encoding":904},"AVC",[115,64236,1241],{"id":59877},[724,64238,64239,64240,64243,64244,64246,64247,1343,64250,1343,64253,64255,64256,64259,64260,64263,64264,64267,64268,12359,64283,1348,64298,12359,64313,1783],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[38,64241,64242],{},"příjmem"," (revenue) a ",[38,64245,64076],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[38,64248,64249],{},"zisku",[38,64251,64252],{},"bodů zvratu",[38,64254,11694],{}," a konstrukcí ",[38,64257,64258],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[207,64261,1145],{"className":64262,"dataFsResolvedFilePath":764,"href":765},[210]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[207,64265,20763],{"className":64266,"dataFsResolvedFilePath":773,"href":774},[210]," (pro zpětnou rekonstrukci ",[883,64269,64271],{"className":64270},[886],[888,64272,64273],{"xmlns":890},[892,64274,64275,64281],{},[895,64276,64277,64279],{},[898,64278,5326],{},[898,64280,13658],{},[902,64282,13758],{"encoding":904},[883,64284,64286],{"className":64285},[886],[888,64287,64288],{"xmlns":890},[892,64289,64290,64296],{},[895,64291,64292,64294],{},[898,64293,1773],{},[898,64295,13658],{},[902,64297,16282],{"encoding":904},[883,64299,64301],{"className":64300},[886],[888,64302,64303],{"xmlns":890},[892,64304,64305,64311],{},[895,64306,64307,64309],{},[898,64308,5326],{},[898,64310,1812],{},[902,64312,12916],{"encoding":904},[883,64314,64316],{"className":64315},[886],[888,64317,64318],{"xmlns":890},[892,64319,64320,64326],{},[895,64321,64322,64324],{},[898,64323,1773],{},[898,64325,1812],{},[902,64327,64215],{"encoding":904},[724,64329,64330],{},[38,64331,64332],{},"Cílové znalosti:",[120,64334,64335,64499,64502,64505,64598,64645,64652],{},[123,64336,64337,64338,1343,64353,1343,64369,2028,64384,1343,64399,1343,64415,1343,64433,1343,64451,1343,64468,1343,64484,18067],{},"odvodit a interpretovat funkce ",[883,64339,64341],{"className":64340},[886],[888,64342,64343],{"xmlns":890},[892,64344,64345,64351],{},[895,64346,64347,64349],{},[898,64348,5326],{},[898,64350,13658],{},[902,64352,13758],{"encoding":904},[883,64354,64356],{"className":64355},[886],[888,64357,64358],{"xmlns":890},[892,64359,64360,64366],{},[895,64361,64362,64364],{},[898,64363,13916],{},[898,64365,13658],{},[902,64367,64368],{"encoding":904},"AR",[883,64370,64372],{"className":64371},[886],[888,64373,64374],{"xmlns":890},[892,64375,64376,64382],{},[895,64377,64378,64380],{},[898,64379,1773],{},[898,64381,13658],{},[902,64383,16282],{"encoding":904},[883,64385,64387],{"className":64386},[886],[888,64388,64389],{"xmlns":890},[892,64390,64391,64397],{},[895,64392,64393,64395],{},[898,64394,5326],{},[898,64396,1812],{},[902,64398,12916],{"encoding":904},[883,64400,64402],{"className":64401},[886],[888,64403,64404],{"xmlns":890},[892,64405,64406,64412],{},[895,64407,64408,64410],{},[898,64409,20069],{},[898,64411,1812],{},[902,64413,64414],{"encoding":904},"FC",[883,64416,64418],{"className":64417},[886],[888,64419,64420],{"xmlns":890},[892,64421,64422,64430],{},[895,64423,64424,64426,64428],{},[898,64425,5326],{},[898,64427,49262],{},[898,64429,1812],{},[902,64431,64432],{"encoding":904},"TVC",[883,64434,64436],{"className":64435},[886],[888,64437,64438],{"xmlns":890},[892,64439,64440,64448],{},[895,64441,64442,64444,64446],{},[898,64443,13916],{},[898,64445,20069],{},[898,64447,1812],{},[902,64449,64450],{"encoding":904},"AFC",[883,64452,64454],{"className":64453},[886],[888,64455,64456],{"xmlns":890},[892,64457,64458,64466],{},[895,64459,64460,64462,64464],{},[898,64461,13916],{},[898,64463,49262],{},[898,64465,1812],{},[902,64467,64234],{"encoding":904},[883,64469,64471],{"className":64470},[886],[888,64472,64473],{"xmlns":890},[892,64474,64475,64481],{},[895,64476,64477,64479],{},[898,64478,13916],{},[898,64480,1812],{},[902,64482,64483],{"encoding":904},"AC",[883,64485,64487],{"className":64486},[886],[888,64488,64489],{"xmlns":890},[892,64490,64491,64497],{},[895,64492,64493,64495],{},[898,64494,1773],{},[898,64496,1812],{},[902,64498,64215],{"encoding":904},[123,64500,64501],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[123,64503,64504],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[123,64506,64507,64508,64511,64512,50737,64554,18067],{},"osvojit si ",[38,64509,64510],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[883,64513,64515],{"className":64514},[886],[888,64516,64517],{"xmlns":890},[892,64518,64519,64551],{},[895,64520,64521,64523,64525,64527,64533,64535,64537,64539,64541,64543,64549],{},[898,64522,13916],{},[898,64524,1812],{},[1750,64526,1753],{"stretchy":1752},[5535,64528,64529,64531],{},[898,64530,12471],{},[1742,64532,2607],{},[1750,64534,1763],{"stretchy":1752},[1750,64536,1766],{},[898,64538,1773],{},[898,64540,1812],{},[1750,64542,1753],{"stretchy":1752},[5535,64544,64545,64547],{},[898,64546,12471],{},[1742,64548,2607],{},[1750,64550,1763],{"stretchy":1752},[902,64552,64553],{"encoding":904},"AC(Q_0)=MC(Q_0)",[883,64555,64557],{"className":64556},[886],[888,64558,64559],{"xmlns":890},[892,64560,64561,64595],{},[895,64562,64563,64565,64567,64569,64571,64577,64579,64581,64583,64585,64587,64593],{},[898,64564,13916],{},[898,64566,49262],{},[898,64568,1812],{},[1750,64570,1753],{"stretchy":1752},[5535,64572,64573,64575],{},[898,64574,12471],{},[1742,64576,2607],{},[1750,64578,1763],{"stretchy":1752},[1750,64580,1766],{},[898,64582,1773],{},[898,64584,1812],{},[1750,64586,1753],{"stretchy":1752},[5535,64588,64589,64591],{},[898,64590,12471],{},[1742,64592,2607],{},[1750,64594,1763],{"stretchy":1752},[902,64596,64597],{"encoding":904},"AVC(Q_0)=MC(Q_0)",[123,64599,64507,64600,64511,64603,18067],{},[38,64601,64602],{},"princip maximalizace zisku",[883,64604,64606],{"className":64605},[886],[888,64607,64608],{"xmlns":890},[892,64609,64610,64642],{},[895,64611,64612,64614,64616,64618,64624,64626,64628,64630,64632,64634,64640],{},[898,64613,1773],{},[898,64615,13658],{},[1750,64617,1753],{"stretchy":1752},[5535,64619,64620,64622],{},[898,64621,12471],{},[1742,64623,2607],{},[1750,64625,1763],{"stretchy":1752},[1750,64627,1766],{},[898,64629,1773],{},[898,64631,1812],{},[1750,64633,1753],{"stretchy":1752},[5535,64635,64636,64638],{},[898,64637,12471],{},[1742,64639,2607],{},[1750,64641,1763],{"stretchy":1752},[902,64643,64644],{"encoding":904},"MR(Q_0)=MC(Q_0)",[123,64646,64647,64648,64651],{},"stanovit ",[38,64649,64650],{},"body zvratu"," a interval zisku;",[123,64653,64654,64655,64658],{},"zkonstruovat ",[38,64656,64657],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[115,64660,64662],{"id":64661},"příjem-firmy","Příjem firmy",[724,64664,64665],{},[4434,64666],{"alt":64667,"className":64668,"src":64669},"imek-ar-mr-dvojnasobny-sklon",[210,4438],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[198,64671,64673],{"id":64672},"celkový-příjem","Celkový příjem",[724,64675,64676,64677,2084,64692,64695,64696,38867],{},"Celkový příjem ",[883,64678,64680],{"className":64679},[886],[888,64681,64682],{"xmlns":890},[892,64683,64684,64690],{},[895,64685,64686,64688],{},[898,64687,5326],{},[898,64689,13658],{},[902,64691,13758],{"encoding":904},[38,64693,64694],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[883,64697,64699],{"className":64698},[886],[888,64700,64701],{"xmlns":890},[892,64702,64703,64717],{},[895,64704,64705,64707,64709,64711,64713,64715],{},[898,64706,1776],{},[1750,64708,1766],{},[898,64710,5541],{},[1750,64712,1753],{"stretchy":1752},[898,64714,12471],{},[1750,64716,1763],{"stretchy":1752},[902,64718,14297],{"encoding":904},[883,64720,64722],{"className":64721},[886],[888,64723,64724],{"xmlns":890,"display":36989},[892,64725,64726,64783],{},[4577,64727,64728],{"width":36994},[4582,64729,64730,64732,64776,64778],{},[4585,64731],{"width":36999},[4585,64733,64734],{},[895,64735,64736,64738,64740,64742,64744,64746,64748,64750,64752,64754,64756,64758,64760,64762,64764,64766,64768,64770,64772,64774],{},[898,64737,5326],{},[898,64739,13658],{},[1750,64741,1766],{},[898,64743,5326],{},[898,64745,13658],{},[1750,64747,1753],{"stretchy":1752},[898,64749,12471],{},[1750,64751,1763],{"stretchy":1752},[1750,64753,1766],{},[898,64755,1776],{},[1750,64757,8009],{},[898,64759,12471],{},[1750,64761,1766],{},[898,64763,5541],{},[1750,64765,1753],{"stretchy":1752},[898,64767,12471],{},[1750,64769,1763],{"stretchy":1752},[1750,64771,8009],{},[898,64773,12471],{},[898,64775,2313],{"mathvariant":1747},[4585,64777],{"width":36999},[4585,64779,64780],{},[1969,64781,64782],{},"(3.1)",[902,64784,64785],{"encoding":904},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[724,64787,64788,64789,64792,64793,64816],{},"Graf funkce se nazývá ",[38,64790,64791],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[883,64794,64796],{"className":64795},[886],[888,64797,64798],{"xmlns":890},[892,64799,64800,64814],{},[895,64801,64802,64804,64806,64808,64810,64812],{},[898,64803,1776],{},[1750,64805,1766],{},[898,64807,207],{},[898,64809,12471],{},[1750,64811,1861],{},[898,64813,2573],{},[902,64815,45983],{"encoding":904},", je celkový příjem kvadratickou funkcí, neboť",[883,64818,64820],{"className":64819},[886],[888,64821,64822],{"xmlns":890,"display":36989},[892,64823,64824,64864],{},[895,64825,64826,64828,64830,64832,64834,64836,64838,64840,64842,64844,64846,64848,64850,64856,64858,64860,64862],{},[898,64827,5326],{},[898,64829,13658],{},[1750,64831,1766],{},[898,64833,12471],{},[1750,64835,1753],{"stretchy":1752},[898,64837,207],{},[898,64839,12471],{},[1750,64841,1861],{},[898,64843,2573],{},[1750,64845,1763],{"stretchy":1752},[1750,64847,1766],{},[898,64849,207],{},[1699,64851,64852,64854],{},[898,64853,12471],{},[1742,64855,1872],{},[1750,64857,1861],{},[898,64859,2573],{},[898,64861,12471],{},[1750,64863,1917],{"separator":1916},[902,64865,64866],{"encoding":904},"TR = Q(aQ + b) = aQ^2 + bQ,",[724,64868,64869,64870,64883,64884,64901],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[883,64871,64873],{"className":64872},[886],[888,64874,64875],{"xmlns":890},[892,64876,64877,64881],{},[895,64878,64879],{},[898,64880,900],{},[902,64882,900],{"encoding":904}," (jelikož ",[883,64885,64887],{"className":64886},[886],[888,64888,64889],{"xmlns":890},[892,64890,64891,64899],{},[895,64892,64893,64895,64897],{},[898,64894,207],{},[1750,64896,2624],{},[1742,64898,2607],{},[902,64900,52008],{"encoding":904},") procházející počátkem.",[46271,64903,64905],{"id":64904},"příklad-31","Příklad 3.1",[724,64907,64908,64911,64912,64948,64949,64964],{},[38,64909,64910],{},"Zadání."," Pro poptávku ",[883,64913,64915],{"className":64914},[886],[888,64916,64917],{"xmlns":890},[892,64918,64919,64945],{},[895,64920,64921,64923,64925,64927,64929,64931,64933,64935,64937,64939,64941,64943],{},[898,64922,1776],{},[1750,64924,1766],{},[898,64926,5541],{},[1750,64928,1753],{"stretchy":1752},[898,64930,12471],{},[1750,64932,1763],{"stretchy":1752},[1750,64934,1766],{},[1750,64936,1758],{},[1742,64938,1872],{},[898,64940,12471],{},[1750,64942,1861],{},[1742,64944,4078],{},[902,64946,64947],{"encoding":904},"P = D(Q) = -2Q + 100"," určete ",[883,64950,64952],{"className":64951},[886],[888,64953,64954],{"xmlns":890},[892,64955,64956,64962],{},[895,64957,64958,64960],{},[898,64959,5326],{},[898,64961,13658],{},[902,64963,13758],{"encoding":904}," a charakterizujte jeho křivku.",[724,64966,64967,64969],{},[38,64968,6610],{}," Celkový příjem je",[883,64971,64973],{"className":64972},[886],[888,64974,64975],{"xmlns":890,"display":36989},[892,64976,64977,65033],{},[895,64978,64979,64981,64983,64985,64987,64989,64991,64993,64995,64997,64999,65001,65003,65005,65007,65009,65011,65013,65015,65017,65019,65025,65027,65029,65031],{},[898,64980,5326],{},[898,64982,13658],{},[1750,64984,1766],{},[898,64986,5326],{},[898,64988,13658],{},[1750,64990,1753],{"stretchy":1752},[898,64992,12471],{},[1750,64994,1763],{"stretchy":1752},[1750,64996,1766],{},[898,64998,12471],{},[1750,65000,1753],{"stretchy":1752},[1750,65002,1758],{},[1742,65004,1872],{},[898,65006,12471],{},[1750,65008,1861],{},[1742,65010,4078],{},[1750,65012,1763],{"stretchy":1752},[1750,65014,1766],{},[1750,65016,1758],{},[1742,65018,1872],{},[1699,65020,65021,65023],{},[898,65022,12471],{},[1742,65024,1872],{},[1750,65026,1861],{},[1742,65028,4078],{},[898,65030,12471],{},[898,65032,2313],{"mathvariant":1747},[902,65034,65035],{"encoding":904},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[724,65037,65038,65039,2028,65061,65083,65084,65102,65103,2313],{},"Křivkou je parabola (obrázek 3.1) s nulami v ",[883,65040,65042],{"className":65041},[886],[888,65043,65044],{"xmlns":890},[892,65045,65046,65058],{},[895,65047,65048,65054,65056],{},[5535,65049,65050,65052],{},[898,65051,12471],{},[1742,65053,1744],{},[1750,65055,1766],{},[1742,65057,2607],{},[902,65059,65060],{"encoding":904},"Q_1 = 0",[883,65062,65064],{"className":65063},[886],[888,65065,65066],{"xmlns":890},[892,65067,65068,65080],{},[895,65069,65070,65076,65078],{},[5535,65071,65072,65074],{},[898,65073,12471],{},[1742,65075,1872],{},[1750,65077,1766],{},[1742,65079,3936],{},[902,65081,65082],{"encoding":904},"Q_2 = 50",". Maxima dosahuje při ",[883,65085,65087],{"className":65086},[886],[888,65088,65089],{"xmlns":890},[892,65090,65091,65099],{},[895,65092,65093,65095,65097],{},[898,65094,12471],{},[1750,65096,1766],{},[1742,65098,6419],{},[902,65100,65101],{"encoding":904},"Q = 25"," ve výši ",[883,65104,65106],{"className":65105},[886],[888,65107,65108],{"xmlns":890},[892,65109,65110,65151],{},[895,65111,65112,65114,65124,65126,65128,65130,65132,65135,65137,65139,65141,65143,65145,65147,65149],{},[898,65113,5326],{},[5535,65115,65116,65118,65121],{},[898,65117,13658],{},[898,65119,65120],{},"max",[1750,65122,65123],{},"⁡",[1750,65125,1766],{},[1750,65127,1758],{},[1742,65129,1872],{},[1750,65131,8009],{},[1742,65133,65134],{},"625",[1750,65136,1861],{},[1742,65138,4078],{},[1750,65140,8009],{},[1742,65142,6419],{},[1750,65144,1766],{},[1742,65146,1744],{},[1969,65148,2658],{},[1742,65150,39666],{},[902,65152,65153],{"encoding":904},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[724,65155,65156],{},[614,65157,65158,65159,65193,65194,2028,65207,65220,65221,2984,65239,2313],{},"Obrázek 3.1: Parabola ",[883,65160,65162],{"className":65161},[886],[888,65163,65164],{"xmlns":890},[892,65165,65166,65190],{},[895,65167,65168,65170,65172,65174,65176,65178,65184,65186,65188],{},[898,65169,5326],{},[898,65171,13658],{},[1750,65173,1766],{},[1750,65175,1758],{},[1742,65177,1872],{},[1699,65179,65180,65182],{},[898,65181,12471],{},[1742,65183,1872],{},[1750,65185,1861],{},[1742,65187,4078],{},[898,65189,12471],{},[902,65191,65192],{"encoding":904},"TR = -2Q^2 + 100Q"," s nulami v ",[883,65195,65197],{"className":65196},[886],[888,65198,65199],{"xmlns":890},[892,65200,65201,65205],{},[895,65202,65203],{},[1742,65204,2607],{},[902,65206,2607],{"encoding":904},[883,65208,65210],{"className":65209},[886],[888,65211,65212],{"xmlns":890},[892,65213,65214,65218],{},[895,65215,65216],{},[1742,65217,3936],{},[902,65219,3936],{"encoding":904}," a maximem ",[883,65222,65224],{"className":65223},[886],[888,65225,65226],{"xmlns":890},[892,65227,65228,65236],{},[895,65229,65230,65232,65234],{},[1742,65231,1744],{},[1969,65233,2658],{},[1742,65235,39666],{},[902,65237,65238],{"encoding":904},"1\\,250",[883,65240,65242],{"className":65241},[886],[888,65243,65244],{"xmlns":890},[892,65245,65246,65254],{},[895,65247,65248,65250,65252],{},[898,65249,12471],{},[1750,65251,1766],{},[1742,65253,6419],{},[902,65255,65101],{"encoding":904},[198,65257,65259],{"id":65258},"průměrný-příjem","Průměrný příjem",[724,65261,65262,1647,65264,2084,65279,65282],{},[38,65263,65259],{},[883,65265,65267],{"className":65266},[886],[888,65268,65269],{"xmlns":890},[892,65270,65271,65277],{},[895,65272,65273,65275],{},[898,65274,13916],{},[898,65276,13658],{},[902,65278,64368],{"encoding":904},[38,65280,65281],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[883,65284,65286],{"className":65285},[886],[888,65287,65288],{"xmlns":890,"display":36989},[892,65289,65290,65358],{},[895,65291,65292,65294,65296,65298,65300,65302,65304,65306,65308,65310,65326,65328,65346,65348,65350,65352,65354,65356],{},[898,65293,13916],{},[898,65295,13658],{},[1750,65297,1766],{},[898,65299,13916],{},[898,65301,13658],{},[1750,65303,1753],{"stretchy":1752},[898,65305,12471],{},[1750,65307,1763],{"stretchy":1752},[1750,65309,1766],{},[3423,65311,65312,65324],{},[895,65313,65314,65316,65318,65320,65322],{},[898,65315,5326],{},[898,65317,13658],{},[1750,65319,1753],{"stretchy":1752},[898,65321,12471],{},[1750,65323,1763],{"stretchy":1752},[898,65325,12471],{},[1750,65327,1766],{},[3423,65329,65330,65344],{},[895,65331,65332,65334,65336,65338,65340,65342],{},[898,65333,12471],{},[1969,65335,2658],{},[898,65337,5541],{},[1750,65339,1753],{"stretchy":1752},[898,65341,12471],{},[1750,65343,1763],{"stretchy":1752},[898,65345,12471],{},[1750,65347,1766],{},[898,65349,5541],{},[1750,65351,1753],{"stretchy":1752},[898,65353,12471],{},[1750,65355,1763],{"stretchy":1752},[898,65357,2313],{"mathvariant":1747},[902,65359,65360],{"encoding":904},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1785,65362,65363],{},[724,65364,65365,65368,65369,1343,65372,2313],{},[883,65366,65367],{},"!note"," Klíčové pozorování\n",[38,65370,65371],{},"Průměrný příjem se vždy rovná poptávkové funkci",[883,65373,65375],{"className":65374},[886],[888,65376,65377],{"xmlns":890},[892,65378,65379,65401],{},[895,65380,65381,65383,65385,65387,65389,65391,65393,65395,65397,65399],{},[898,65382,13916],{},[898,65384,13658],{},[1750,65386,1753],{"stretchy":1752},[898,65388,12471],{},[1750,65390,1763],{"stretchy":1752},[1750,65392,1766],{},[898,65394,5541],{},[1750,65396,1753],{"stretchy":1752},[898,65398,12471],{},[1750,65400,1763],{"stretchy":1752},[902,65402,65403],{"encoding":904},"AR(Q) = D(Q)",[198,65405,65407],{"id":65406},"mezní-příjem","Mezní příjem",[724,65409,65410,65411,1647,65414,2084,65429,65432,65433,65436],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[38,65412,65413],{},"mezní příjem",[883,65415,65417],{"className":65416},[886],[888,65418,65419],{"xmlns":890},[892,65420,65421,65427],{},[895,65422,65423,65425],{},[898,65424,1773],{},[898,65426,13658],{},[902,65428,16282],{"encoding":904},[38,65430,65431],{},"marginal revenue","), definovaný jako ",[207,65434,1145],{"className":65435,"dataFsResolvedFilePath":764,"href":765},[210]," celkového příjmu podle množství:",[883,65438,65440],{"className":65439},[886],[888,65441,65442],{"xmlns":890,"display":36989},[892,65443,65444,65501],{},[4577,65445,65446],{"width":36994},[4582,65447,65448,65450,65494,65496],{},[4585,65449],{"width":36999},[4585,65451,65452],{},[895,65453,65454,65456,65458,65460,65476,65478,65480,65486,65488,65490,65492],{},[898,65455,1773],{},[898,65457,13658],{},[1750,65459,1766],{},[3423,65461,65462,65470],{},[895,65463,65464,65466,65468],{},[898,65465,3429],{"mathvariant":1747},[898,65467,5326],{},[898,65469,13658],{},[895,65471,65472,65474],{},[898,65473,3429],{"mathvariant":1747},[898,65475,12471],{},[1750,65477,1766],{},[898,65479,5326],{},[1699,65481,65482,65484],{},[898,65483,13658],{},[1750,65485,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,65487,1753],{"stretchy":1752},[898,65489,12471],{},[1750,65491,1763],{"stretchy":1752},[898,65493,2313],{"mathvariant":1747},[4585,65495],{"width":36999},[4585,65497,65498],{},[1969,65499,65500],{},"(3.2)",[902,65502,65503],{"encoding":904},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[724,65505,65506,65507,65509],{},"Mezní příjem udává ",[38,65508,12285],{}," celkového příjmu vzhledem k množství.",[1785,65511,65512],{},[724,65513,65514,65516,65517,65543,65544,65561,65562,2313],{},[883,65515,1791],{}," Intuice — „kolik vyděláš za další kus\"\nHodnota ",[883,65518,65520],{"className":65519},[886],[888,65521,65522],{"xmlns":890},[892,65523,65524,65540],{},[895,65525,65526,65528,65530,65532,65538],{},[898,65527,1773],{},[898,65529,13658],{},[1750,65531,1753],{"stretchy":1752},[1699,65533,65534,65536],{},[898,65535,12471],{},[1750,65537,3751],{},[1750,65539,1763],{"stretchy":1752},[902,65541,65542],{"encoding":904},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[883,65545,65547],{"className":65546},[886],[888,65548,65549],{"xmlns":890},[892,65550,65551,65559],{},[895,65552,65553],{},[1699,65554,65555,65557],{},[898,65556,12471],{},[1750,65558,3751],{},[902,65560,38767],{"encoding":904},". Jinak řečeno: ",[883,65563,65565],{"className":65564},[886],[888,65566,65567],{"xmlns":890},[892,65568,65569,65621],{},[895,65570,65571,65573,65575,65577,65583,65585,65587,65589,65591,65593,65599,65601,65603,65605,65607,65609,65611,65613,65619],{},[898,65572,1773],{},[898,65574,13658],{},[1750,65576,1753],{"stretchy":1752},[1699,65578,65579,65581],{},[898,65580,12471],{},[1750,65582,3751],{},[1750,65584,1763],{"stretchy":1752},[1750,65586,2274],{},[898,65588,5326],{},[898,65590,13658],{},[1750,65592,1753],{"stretchy":1752},[1699,65594,65595,65597],{},[898,65596,12471],{},[1750,65598,3751],{},[1750,65600,1861],{},[1742,65602,1744],{},[1750,65604,1763],{"stretchy":1752},[1750,65606,1758],{},[898,65608,5326],{},[898,65610,13658],{},[1750,65612,1753],{"stretchy":1752},[1699,65614,65615,65617],{},[898,65616,12471],{},[1750,65618,3751],{},[1750,65620,1763],{"stretchy":1752},[902,65622,65623],{"encoding":904},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[46271,65625,65627],{"id":65626},"příklad-32","Příklad 3.2",[724,65629,65630,64911,65632,64948,65666,65681,65682,2313],{},[38,65631,64910],{},[883,65633,65635],{"className":65634},[886],[888,65636,65637],{"xmlns":890},[892,65638,65639,65663],{},[895,65640,65641,65643,65645,65647,65649,65651,65653,65655,65657,65659,65661],{},[898,65642,1776],{},[1750,65644,1766],{},[898,65646,5541],{},[1750,65648,1753],{"stretchy":1752},[898,65650,12471],{},[1750,65652,1763],{"stretchy":1752},[1750,65654,1766],{},[1742,65656,4078],{},[1750,65658,1758],{},[1742,65660,1872],{},[898,65662,12471],{},[902,65664,65665],{"encoding":904},"P = D(Q) = 100 - 2Q",[883,65667,65669],{"className":65668},[886],[888,65670,65671],{"xmlns":890},[892,65672,65673,65679],{},[895,65674,65675,65677],{},[898,65676,1773],{},[898,65678,13658],{},[902,65680,16282],{"encoding":904}," a interpretujte jeho hodnoty pro ",[883,65683,65685],{"className":65684},[886],[888,65686,65687],{"xmlns":890},[892,65688,65689,65705],{},[895,65690,65691,65693,65695,65697,65699,65701,65703],{},[898,65692,12471],{},[1750,65694,1766],{},[1742,65696,45167],{},[1750,65698,1917],{"separator":1916},[1742,65700,50785],{},[1750,65702,1917],{"separator":1916},[1742,65704,6465],{},[902,65706,65707],{"encoding":904},"Q = 15, 16, 20",[724,65709,65710,1647,65712,65744],{},[38,65711,6610],{},[883,65713,65715],{"className":65714},[886],[888,65716,65717],{"xmlns":890},[892,65718,65719,65741],{},[895,65720,65721,65723,65725,65727,65729,65731,65733,65735],{},[898,65722,5326],{},[898,65724,13658],{},[1750,65726,1766],{},[1742,65728,4078],{},[898,65730,12471],{},[1750,65732,1758],{},[1742,65734,1872],{},[1699,65736,65737,65739],{},[898,65738,12471],{},[1742,65740,1872],{},[902,65742,65743],{"encoding":904},"TR = 100Q - 2Q^2",", tedy",[883,65746,65748],{"className":65747},[886],[888,65749,65750],{"xmlns":890,"display":36989},[892,65751,65752,65794],{},[895,65753,65754,65756,65758,65760,65762,65764,65766,65768,65770,65776,65782,65784,65786,65788,65790,65792],{},[898,65755,1773],{},[898,65757,13658],{},[1750,65759,1766],{},[1750,65761,1753],{"stretchy":1752},[1742,65763,4078],{},[898,65765,12471],{},[1750,65767,1758],{},[1742,65769,1872],{},[1699,65771,65772,65774],{},[898,65773,12471],{},[1742,65775,1872],{},[1699,65777,65778,65780],{},[1750,65779,1763],{"stretchy":1752},[1750,65781,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,65783,1766],{},[1742,65785,4078],{},[1750,65787,1758],{},[1742,65789,7859],{},[898,65791,12471],{},[898,65793,2313],{"mathvariant":1747},[902,65795,65796],{"encoding":904},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[724,65798,19299,65799,2433,65817,65843,65844,14017,65857,65872,65873,65886,65887,5249,65900,14017,65913,65928,65929,65942,65943,65974,65975,65994],{},[883,65800,65802],{"className":65801},[886],[888,65803,65804],{"xmlns":890},[892,65805,65806,65814],{},[895,65807,65808,65810,65812],{},[898,65809,12471],{},[1750,65811,1766],{},[1742,65813,45167],{},[902,65815,65816],{"encoding":904},"Q = 15",[883,65818,65820],{"className":65819},[886],[888,65821,65822],{"xmlns":890},[892,65823,65824,65840],{},[895,65825,65826,65828,65830,65832,65834,65836,65838],{},[898,65827,1773],{},[898,65829,13658],{},[1750,65831,1753],{"stretchy":1752},[1742,65833,45167],{},[1750,65835,1763],{"stretchy":1752},[1750,65837,1766],{},[1742,65839,14865],{},[902,65841,65842],{"encoding":904},"MR(15) = 40",": při množství ",[883,65845,65847],{"className":65846},[886],[888,65848,65849],{"xmlns":890},[892,65850,65851,65855],{},[895,65852,65853],{},[1742,65854,45167],{},[902,65856,45167],{"encoding":904},[883,65858,65860],{"className":65859},[886],[888,65861,65862],{"xmlns":890},[892,65863,65864,65870],{},[895,65865,65866,65868],{},[898,65867,5326],{},[898,65869,13658],{},[902,65871,13758],{"encoding":904}," mění asi ",[883,65874,65876],{"className":65875},[886],[888,65877,65878],{"xmlns":890},[892,65879,65880,65884],{},[895,65881,65882],{},[1742,65883,14865],{},[902,65885,14865],{"encoding":904},"-krát rychleji než množství; s růstem ",[883,65888,65890],{"className":65889},[886],[888,65891,65892],{"xmlns":890},[892,65893,65894,65898],{},[895,65895,65896],{},[898,65897,12471],{},[902,65899,12471],{"encoding":904},[883,65901,65903],{"className":65902},[886],[888,65904,65905],{"xmlns":890},[892,65906,65907,65911],{},[895,65908,65909],{},[1742,65910,1744],{},[902,65912,1744],{"encoding":904},[883,65914,65916],{"className":65915},[886],[888,65917,65918],{"xmlns":890},[892,65919,65920,65926],{},[895,65921,65922,65924],{},[898,65923,5326],{},[898,65925,13658],{},[902,65927,13758],{"encoding":904}," zvýší přibližně o ",[883,65930,65932],{"className":65931},[886],[888,65933,65934],{"xmlns":890},[892,65935,65936,65940],{},[895,65937,65938],{},[1742,65939,14865],{},[902,65941,14865],{"encoding":904},", tj. ze skutečné hodnoty ",[883,65944,65946],{"className":65945},[886],[888,65947,65948],{"xmlns":890},[892,65949,65950,65971],{},[895,65951,65952,65954,65956,65958,65960,65962,65964,65966,65968],{},[898,65953,5326],{},[898,65955,13658],{},[1750,65957,1753],{"stretchy":1752},[1742,65959,45167],{},[1750,65961,1763],{"stretchy":1752},[1750,65963,1766],{},[1742,65965,1744],{},[1969,65967,2658],{},[1742,65969,65970],{},"050",[902,65972,65973],{"encoding":904},"TR(15) = 1\\,050"," na přibližně ",[883,65976,65978],{"className":65977},[886],[888,65979,65980],{"xmlns":890},[892,65981,65982,65991],{},[895,65983,65984,65986,65988],{},[1742,65985,1744],{},[1969,65987,2658],{},[1742,65989,65990],{},"090",[902,65992,65993],{"encoding":904},"1\\,090",". Skutečná změna je",[883,65996,65998],{"className":65997},[886],[888,65999,66000],{"xmlns":890,"display":36989},[892,66001,66002,66056],{},[895,66003,66004,66006,66008,66010,66012,66014,66016,66018,66020,66022,66024,66026,66028,66030,66032,66034,66036,66038,66040,66043,66045,66047,66049,66051,66053],{},[898,66005,2666],{"mathvariant":1747},[898,66007,5326],{},[898,66009,13658],{},[1750,66011,1766],{},[898,66013,5326],{},[898,66015,13658],{},[1750,66017,1753],{"stretchy":1752},[1742,66019,50785],{},[1750,66021,1763],{"stretchy":1752},[1750,66023,1758],{},[898,66025,5326],{},[898,66027,13658],{},[1750,66029,1753],{"stretchy":1752},[1742,66031,45167],{},[1750,66033,1763],{"stretchy":1752},[1750,66035,1766],{},[1742,66037,1744],{},[1969,66039,2658],{},[1742,66041,66042],{},"088",[1750,66044,1758],{},[1742,66046,1744],{},[1969,66048,2658],{},[1742,66050,65970],{},[1750,66052,1766],{},[1742,66054,66055],{},"38.",[902,66057,66058],{"encoding":904},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[724,66060,66061,66062,1343,66088,12605,66114,66129,66130,66145],{},"Podobně ",[883,66063,66065],{"className":66064},[886],[888,66066,66067],{"xmlns":890},[892,66068,66069,66085],{},[895,66070,66071,66073,66075,66077,66079,66081,66083],{},[898,66072,1773],{},[898,66074,13658],{},[1750,66076,1753],{"stretchy":1752},[1742,66078,50785],{},[1750,66080,1763],{"stretchy":1752},[1750,66082,1766],{},[1742,66084,15219],{},[902,66086,66087],{"encoding":904},"MR(16) = 36",[883,66089,66091],{"className":66090},[886],[888,66092,66093],{"xmlns":890},[892,66094,66095,66111],{},[895,66096,66097,66099,66101,66103,66105,66107,66109],{},[898,66098,1773],{},[898,66100,13658],{},[1750,66102,1753],{"stretchy":1752},[1742,66104,6465],{},[1750,66106,1763],{"stretchy":1752},[1750,66108,1766],{},[1742,66110,6465],{},[902,66112,66113],{"encoding":904},"MR(20) = 20",[883,66115,66117],{"className":66116},[886],[888,66118,66119],{"xmlns":890},[892,66120,66121,66127],{},[895,66122,66123,66125],{},[898,66124,1773],{},[898,66126,13658],{},[902,66128,16282],{"encoding":904}," je klesající funkce — rychlost změny ",[883,66131,66133],{"className":66132},[886],[888,66134,66135],{"xmlns":890},[892,66136,66137,66143],{},[895,66138,66139,66141],{},[898,66140,5326],{},[898,66142,13658],{},[902,66144,13758],{"encoding":904}," s růstem množství klesá.",[198,66147,66149],{"id":66148},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[724,66151,66152],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[883,66154,66156],{"className":66155},[886],[888,66157,66158],{"xmlns":890,"display":36989},[892,66159,66160,66229],{},[4577,66161,66162],{"width":36994},[4582,66163,66164,66166,66222,66224],{},[4585,66165],{"width":36999},[4585,66167,66168],{},[895,66169,66170,66172,66174,66176,66178,66180,66182,66184,66186,66188,66190,66192,66194,66196,66202,66204,66206,66208,66210,66212,66214,66216,66218,66220],{},[898,66171,2666],{"mathvariant":1747},[898,66173,5326],{},[898,66175,13658],{},[1969,66177,6766],{},[1750,66179,2274],{},[1969,66181,6766],{},[898,66183,3429],{"mathvariant":1747},[898,66185,5326],{},[898,66187,13658],{},[1750,66189,1766],{},[1750,66191,1753],{"stretchy":1752},[898,66193,5326],{},[898,66195,13658],{},[1699,66197,66198,66200],{},[1750,66199,1763],{"stretchy":1752},[1750,66201,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,66203,2658],{},[898,66205,3429],{"mathvariant":1747},[898,66207,12471],{},[1750,66209,1766],{},[898,66211,1773],{},[898,66213,13658],{},[1969,66215,2658],{},[898,66217,3429],{"mathvariant":1747},[898,66219,12471],{},[1750,66221,1917],{"separator":1916},[4585,66223],{"width":36999},[4585,66225,66226],{},[1969,66227,66228],{},"(3.3)",[902,66230,66231],{"encoding":904},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[724,66233,66234],{},"schematicky:",[883,66236,66238],{"className":66237},[886],[888,66239,66240],{"xmlns":890,"display":36989},[892,66241,66242,66350],{},[895,66243,66244,66282,66284,66286,66288,66317,66320,66348],{},[895,66245,66246,66249,66255,66258,66264,66267,66273,66279],{},[1969,66247,66248],{},"zm",[3215,66250,66251,66253],{"accent":1916},[1969,66252,54655],{},[1750,66254,8912],{},[1969,66256,66257],{},"na celkov",[3215,66259,66260,66262],{"accent":1916},[1969,66261,54655],{},[1750,66263,8831],{},[1969,66265,66266],{},"ho p",[3215,66268,66269,66271],{"accent":1916},[1969,66270,1920],{},[1750,66272,8912],{},[3215,66274,66275,66277],{"accent":1916},[1969,66276,8900],{},[1750,66278,8831],{},[1969,66280,66281],{},"jmu",[1969,66283,6766],{},[1750,66285,2274],{},[1969,66287,6766],{},[895,66289,66290,66293,66299,66302,66308,66314],{},[1969,66291,66292],{},"mezn",[3215,66294,66295,66297],{"accent":1916},[1969,66296,8900],{},[1750,66298,8831],{},[1969,66300,66301],{}," p",[3215,66303,66304,66306],{"accent":1916},[1969,66305,1920],{},[1750,66307,8912],{},[3215,66309,66310,66312],{"accent":1916},[1969,66311,8900],{},[1750,66313,8831],{},[1969,66315,66316],{},"jem",[1750,66318,66319],{},"×",[895,66321,66322,66324,66330,66333,66339,66342],{},[1969,66323,66248],{},[3215,66325,66326,66328],{"accent":1916},[1969,66327,54655],{},[1750,66329,8912],{},[1969,66331,66332],{},"na mno",[3215,66334,66335,66337],{"accent":1916},[1969,66336,19230],{},[1750,66338,8912],{},[1969,66340,66341],{},"stv",[3215,66343,66344,66346],{"accent":1916},[1969,66345,8900],{},[1750,66347,8831],{},[898,66349,2313],{"mathvariant":1747},[902,66351,66352],{"encoding":904},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[724,66354,66355,66356,66371],{},"Pro porovnání skutečná změna ",[883,66357,66359],{"className":66358},[886],[888,66360,66361],{"xmlns":890},[892,66362,66363,66369],{},[895,66364,66365,66367],{},[898,66366,5326],{},[898,66368,13658],{},[902,66370,13758],{"encoding":904}," je",[883,66373,66375],{"className":66374},[886],[888,66376,66377],{"xmlns":890,"display":36989},[892,66378,66379,66434],{},[4577,66380,66381],{"width":36994},[4582,66382,66383,66385,66427,66429],{},[4585,66384],{"width":36999},[4585,66386,66387],{},[895,66388,66389,66391,66393,66395,66397,66399,66401,66403,66405,66407,66409,66411,66413,66415,66417,66419,66421,66423,66425],{},[898,66390,2666],{"mathvariant":1747},[898,66392,5326],{},[898,66394,13658],{},[1750,66396,1766],{},[898,66398,5326],{},[898,66400,13658],{},[1750,66402,1753],{"stretchy":1752},[898,66404,12471],{},[1750,66406,1861],{},[898,66408,3429],{"mathvariant":1747},[898,66410,12471],{},[1750,66412,1763],{"stretchy":1752},[1750,66414,1758],{},[898,66416,5326],{},[898,66418,13658],{},[1750,66420,1753],{"stretchy":1752},[898,66422,12471],{},[1750,66424,1763],{"stretchy":1752},[898,66426,2313],{"mathvariant":1747},[4585,66428],{"width":36999},[4585,66430,66431],{},[1969,66432,66433],{},"(3.4)",[902,66435,66436],{"encoding":904},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[46271,66438,66440],{"id":66439},"příklad-33","Příklad 3.3",[724,66442,66443,66445,66446,66476,66477,12345,66492,12359,66505,4321,66518,66532],{},[38,66444,64910],{}," Pro ",[883,66447,66449],{"className":66448},[886],[888,66450,66451],{"xmlns":890},[892,66452,66453,66473],{},[895,66454,66455,66457,66459,66461,66463,66465,66467],{},[898,66456,5326],{},[898,66458,13658],{},[1750,66460,1766],{},[1742,66462,4078],{},[898,66464,12471],{},[1750,66466,1758],{},[1699,66468,66469,66471],{},[898,66470,12471],{},[1742,66472,1872],{},[902,66474,66475],{"encoding":904},"TR = 100Q - Q^2"," odhadněte změnu ",[883,66478,66480],{"className":66479},[886],[888,66481,66482],{"xmlns":890},[892,66483,66484,66490],{},[895,66485,66486,66488],{},[898,66487,5326],{},[898,66489,13658],{},[902,66491,13758],{"encoding":904},[883,66493,66495],{"className":66494},[886],[888,66496,66497],{"xmlns":890},[892,66498,66499,66503],{},[895,66500,66501],{},[898,66502,12471],{},[902,66504,12471],{"encoding":904},[883,66506,66508],{"className":66507},[886],[888,66509,66510],{"xmlns":890},[892,66511,66512,66516],{},[895,66513,66514],{},[1742,66515,12800],{},[902,66517,12800],{"encoding":904},[883,66519,66521],{"className":66520},[886],[888,66522,66523],{"xmlns":890},[892,66524,66525,66530],{},[895,66526,66527],{},[1742,66528,66529],{},"63",[902,66531,66529],{"encoding":904}," a porovnejte se skutečnou změnou.",[724,66534,66535,1647,66537,66562,66563,1343,66581,2366],{},[38,66536,6610],{},[883,66538,66540],{"className":66539},[886],[888,66541,66542],{"xmlns":890},[892,66543,66544,66560],{},[895,66545,66546,66548,66550,66552,66554,66556,66558],{},[898,66547,1773],{},[898,66549,13658],{},[1750,66551,1766],{},[1742,66553,4078],{},[1750,66555,1758],{},[1742,66557,1872],{},[898,66559,12471],{},[902,66561,21069],{"encoding":904},", tedy při ",[883,66564,66566],{"className":66565},[886],[888,66567,66568],{"xmlns":890},[892,66569,66570,66578],{},[895,66571,66572,66574,66576],{},[898,66573,12471],{},[1750,66575,1766],{},[1742,66577,12800],{},[902,66579,66580],{"encoding":904},"Q = 60",[883,66582,66584],{"className":66583},[886],[888,66585,66586],{"xmlns":890},[892,66587,66588,66598],{},[895,66589,66590,66592,66594,66596],{},[898,66591,3429],{"mathvariant":1747},[898,66593,12471],{},[1750,66595,1766],{},[1742,66597,7822],{},[902,66599,66600],{"encoding":904},"\\mathrm{d}Q = 3",[883,66602,66604],{"className":66603},[886],[888,66605,66606],{"xmlns":890,"display":36989},[892,66607,66608,66639],{},[895,66609,66610,66612,66614,66616,66618,66620,66622,66624,66626,66628,66630,66632,66634,66636],{},[898,66611,3429],{"mathvariant":1747},[898,66613,5326],{},[898,66615,13658],{},[1750,66617,1766],{},[1750,66619,1753],{"stretchy":1752},[1742,66621,4078],{},[1750,66623,1758],{},[1742,66625,13710],{},[1750,66627,1763],{"stretchy":1752},[1750,66629,8009],{},[1742,66631,7822],{},[1750,66633,1766],{},[1750,66635,1758],{},[1742,66637,66638],{},"60.",[902,66640,66641],{"encoding":904},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[724,66643,66644,66645,66675,66676,66695],{},"Celkový příjem klesne z ",[883,66646,66648],{"className":66647},[886],[888,66649,66650],{"xmlns":890},[892,66651,66652,66672],{},[895,66653,66654,66656,66658,66660,66662,66664,66666,66668,66670],{},[898,66655,5326],{},[898,66657,13658],{},[1750,66659,1753],{"stretchy":1752},[1742,66661,12800],{},[1750,66663,1763],{"stretchy":1752},[1750,66665,1766],{},[1742,66667,1872],{},[1969,66669,2658],{},[1742,66671,3956],{},[902,66673,66674],{"encoding":904},"TR(60) = 2\\,400"," přibližně na ",[883,66677,66679],{"className":66678},[886],[888,66680,66681],{"xmlns":890},[892,66682,66683,66692],{},[895,66684,66685,66687,66689],{},[1742,66686,1872],{},[1969,66688,2658],{},[1742,66690,66691],{},"340",[902,66693,66694],{"encoding":904},"2\\,340",". Skutečná změna dle (3.4):",[883,66697,66699],{"className":66698},[886],[888,66700,66701],{"xmlns":890,"display":36989},[892,66702,66703,66761],{},[895,66704,66705,66707,66709,66711,66713,66715,66717,66719,66721,66723,66725,66727,66729,66731,66733,66735,66737,66739,66741,66744,66746,66748,66750,66752,66754,66756,66759],{},[898,66706,2666],{"mathvariant":1747},[898,66708,5326],{},[898,66710,13658],{},[1750,66712,1766],{},[898,66714,5326],{},[898,66716,13658],{},[1750,66718,1753],{"stretchy":1752},[1742,66720,66529],{},[1750,66722,1763],{"stretchy":1752},[1750,66724,1758],{},[898,66726,5326],{},[898,66728,13658],{},[1750,66730,1753],{"stretchy":1752},[1742,66732,12800],{},[1750,66734,1763],{"stretchy":1752},[1750,66736,1766],{},[1742,66738,1872],{},[1969,66740,2658],{},[1742,66742,66743],{},"331",[1750,66745,1758],{},[1742,66747,1872],{},[1969,66749,2658],{},[1742,66751,3956],{},[1750,66753,1766],{},[1750,66755,1758],{},[1742,66757,66758],{},"69",[1750,66760,1917],{"separator":1916},[902,66762,66763],{"encoding":904},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[724,66765,66766,66767,66782,66783,2313],{},"tj. ",[883,66768,66770],{"className":66769},[886],[888,66771,66772],{"xmlns":890},[892,66773,66774,66780],{},[895,66775,66776,66778],{},[898,66777,5326],{},[898,66779,13658],{},[902,66781,13758],{"encoding":904}," klesne na ",[883,66784,66786],{"className":66785},[886],[888,66787,66788],{"xmlns":890},[892,66789,66790,66798],{},[895,66791,66792,66794,66796],{},[1742,66793,1872],{},[1969,66795,2658],{},[1742,66797,66743],{},[902,66799,66800],{"encoding":904},"2\\,331",[198,66802,66804],{"id":66803},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[724,66806,66807,66808,20027,66831,40503],{},"Obecně pro lineární poptávku ",[883,66809,66811],{"className":66810},[886],[888,66812,66813],{"xmlns":890},[892,66814,66815,66829],{},[895,66816,66817,66819,66821,66823,66825,66827],{},[898,66818,1776],{},[1750,66820,1766],{},[898,66822,207],{},[898,66824,12471],{},[1750,66826,1861],{},[898,66828,2573],{},[902,66830,45983],{"encoding":904},[883,66832,66834],{"className":66833},[886],[888,66835,66836],{"xmlns":890},[892,66837,66838,66860],{},[895,66839,66840,66842,66844,66846,66848,66854,66856,66858],{},[898,66841,5326],{},[898,66843,13658],{},[1750,66845,1766],{},[898,66847,207],{},[1699,66849,66850,66852],{},[898,66851,12471],{},[1742,66853,1872],{},[1750,66855,1861],{},[898,66857,2573],{},[898,66859,12471],{},[902,66861,66862],{"encoding":904},"TR = aQ^2 + bQ",[883,66864,66866],{"className":66865},[886],[888,66867,66868],{"xmlns":890,"display":36989},[892,66869,66870,66890],{},[895,66871,66872,66874,66876,66878,66880,66882,66884,66886,66888],{},[898,66873,1773],{},[898,66875,13658],{},[1750,66877,1766],{},[1742,66879,1872],{},[898,66881,207],{},[898,66883,12471],{},[1750,66885,1861],{},[898,66887,2573],{},[898,66889,2313],{"mathvariant":1747},[902,66891,66892],{"encoding":904},"MR = 2aQ + b.",[724,66894,66895,66896,66911,66912,66927,66928,66941,66942,2084,66945,66961,66962,66975,66976,66991,66992,67007,67008,67023,67024,2984,67037,67067,67068,67087,67088,67103],{},"Křivky ",[883,66897,66899],{"className":66898},[886],[888,66900,66901],{"xmlns":890},[892,66902,66903,66909],{},[895,66904,66905,66907],{},[898,66906,1773],{},[898,66908,13658],{},[902,66910,16282],{"encoding":904}," a poptávky (resp. ",[883,66913,66915],{"className":66914},[886],[888,66916,66917],{"xmlns":890},[892,66918,66919,66925],{},[895,66920,66921,66923],{},[898,66922,13916],{},[898,66924,13658],{},[902,66926,64368],{"encoding":904},") jsou přímky protínající svislou osu v témže bodě ",[883,66929,66931],{"className":66930},[886],[888,66932,66933],{"xmlns":890},[892,66934,66935,66939],{},[895,66936,66937],{},[898,66938,2573],{},[902,66940,2573],{"encoding":904},", přičemž ",[38,66943,66944],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[883,66946,66948],{"className":66947},[886],[888,66949,66950],{"xmlns":890},[892,66951,66952,66958],{},[895,66953,66954,66956],{},[1742,66955,1872],{},[898,66957,207],{},[902,66959,66960],{"encoding":904},"2a"," vs. ",[883,66963,66965],{"className":66964},[886],[888,66966,66967],{"xmlns":890},[892,66968,66969,66973],{},[895,66970,66971],{},[898,66972,207],{},[902,66974,207],{"encoding":904},", obrázek 3.2). ",[883,66977,66979],{"className":66978},[886],[888,66980,66981],{"xmlns":890},[892,66982,66983,66989],{},[895,66984,66985,66987],{},[898,66986,1773],{},[898,66988,13658],{},[902,66990,16282],{"encoding":904}," nabývá jak kladných, tak záporných hodnot; křivka ",[883,66993,66995],{"className":66994},[886],[888,66996,66997],{"xmlns":890},[892,66998,66999,67005],{},[895,67000,67001,67003],{},[898,67002,5326],{},[898,67004,13658],{},[902,67006,13758],{"encoding":904}," nejprve roste, v bodě maxima protíná ",[883,67009,67011],{"className":67010},[886],[888,67012,67013],{"xmlns":890},[892,67014,67015,67021],{},[895,67016,67017,67019],{},[898,67018,1773],{},[898,67020,13658],{},[902,67022,16282],{"encoding":904}," osu ",[883,67025,67027],{"className":67026},[886],[888,67028,67029],{"xmlns":890},[892,67030,67031,67035],{},[895,67032,67033],{},[898,67034,12471],{},[902,67036,12471],{"encoding":904},[883,67038,67040],{"className":67039},[886],[888,67041,67042],{"xmlns":890},[892,67043,67044,67064],{},[895,67045,67046,67048,67050,67052],{},[898,67047,12471],{},[1750,67049,1766],{},[1750,67051,1758],{},[3586,67053,67054],{"scriptlevel":2607,"displaystyle":1752},[3423,67055,67056,67058],{},[898,67057,2573],{},[895,67059,67060,67062],{},[1742,67061,1872],{},[898,67063,207],{},[902,67065,67066],{"encoding":904},"Q = -\\tfrac{b}{2a}"," hodnotou ",[883,67069,67071],{"className":67070},[886],[888,67072,67073],{"xmlns":890},[892,67074,67075,67085],{},[895,67076,67077,67079,67081,67083],{},[898,67078,1773],{},[898,67080,13658],{},[1750,67082,1766],{},[1742,67084,2607],{},[902,67086,16731],{"encoding":904},", a dále ",[883,67089,67091],{"className":67090},[886],[888,67092,67093],{"xmlns":890},[892,67094,67095,67101],{},[895,67096,67097,67099],{},[898,67098,5326],{},[898,67100,13658],{},[902,67102,13758],{"encoding":904}," klesá.",[724,67105,67106,67107,67113,67114,67146,67147,67175],{},"V případě ",[38,67108,67109],{},[207,67110,67112],{"className":67111,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurence",", kdy poptávka ",[883,67115,67117],{"className":67116},[886],[888,67118,67119],{"xmlns":890},[892,67120,67121,67143],{},[895,67122,67123,67125,67127,67129,67131,67133,67135,67137],{},[898,67124,1776],{},[1750,67126,1766],{},[898,67128,5541],{},[1750,67130,1753],{"stretchy":1752},[898,67132,12471],{},[1750,67134,1763],{"stretchy":1752},[1750,67136,1766],{},[1699,67138,67139,67141],{},[898,67140,1776],{},[1750,67142,3751],{},[902,67144,67145],{"encoding":904},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[883,67148,67150],{"className":67149},[886],[888,67151,67152],{"xmlns":890},[892,67153,67154,67172],{},[895,67155,67156,67158,67160,67162,67164,67166],{},[898,67157,5326],{},[898,67159,13658],{},[1750,67161,1766],{},[898,67163,12471],{},[1750,67165,8009],{},[1699,67167,67168,67170],{},[898,67169,1776],{},[1750,67171,3751],{},[902,67173,67174],{"encoding":904},"TR = Q \\cdot P^*"," a tedy",[883,67177,67179],{"className":67178},[886],[888,67180,67181],{"xmlns":890,"display":36989},[892,67182,67183,67225],{},[895,67184,67185,67187,67189,67191,67193,67195,67197,67203,67205,67207,67221,67223],{},[898,67186,1773],{},[898,67188,13658],{},[1750,67190,1766],{},[898,67192,13916],{},[898,67194,13658],{},[1750,67196,1766],{},[1699,67198,67199,67201],{},[898,67200,1776],{},[1750,67202,3751],{},[2125,67204],{"width":24875},[1750,67206,1753],{"stretchy":1752},[895,67208,67209,67212,67218],{},[1969,67210,67211],{},"obr",[3215,67213,67214,67216],{"accent":1916},[1969,67215,207],{},[1750,67217,8831],{},[1969,67219,67220],{},"zek 3.4",[1750,67222,1763],{"stretchy":1752},[898,67224,2313],{"mathvariant":1747},[902,67226,67227],{"encoding":904},"MR = AR = P^* \\quad (\\text{obrázek 3.4}).",[724,67229,67230],{},[614,67231,67232,67233,2028,67259,67287,67288,67301,67302,67317,67318,13388,67331,1343,67357,13388,67372,2313],{},"Obrázek 3.2: Přímky ",[883,67234,67236],{"className":67235},[886],[888,67237,67238],{"xmlns":890},[892,67239,67240,67256],{},[895,67241,67242,67244,67246,67248,67250,67252,67254],{},[898,67243,13916],{},[898,67245,13658],{},[1750,67247,1766],{},[898,67249,207],{},[898,67251,12471],{},[1750,67253,1861],{},[898,67255,2573],{},[902,67257,67258],{"encoding":904},"AR = aQ + b",[883,67260,67262],{"className":67261},[886],[888,67263,67264],{"xmlns":890},[892,67265,67266,67284],{},[895,67267,67268,67270,67272,67274,67276,67278,67280,67282],{},[898,67269,1773],{},[898,67271,13658],{},[1750,67273,1766],{},[1742,67275,1872],{},[898,67277,207],{},[898,67279,12471],{},[1750,67281,1861],{},[898,67283,2573],{},[902,67285,67286],{"encoding":904},"MR = 2aQ + b"," v jednom grafu; společný průsečík ",[883,67289,67291],{"className":67290},[886],[888,67292,67293],{"xmlns":890},[892,67294,67295,67299],{},[895,67296,67297],{},[898,67298,2573],{},[902,67300,2573],{"encoding":904}," se svislou osou, ",[883,67303,67305],{"className":67304},[886],[888,67306,67307],{"xmlns":890},[892,67308,67309,67315],{},[895,67310,67311,67313],{},[898,67312,1773],{},[898,67314,13658],{},[902,67316,16282],{"encoding":904}," protíná osu ",[883,67319,67321],{"className":67320},[886],[888,67322,67323],{"xmlns":890},[892,67324,67325,67329],{},[895,67326,67327],{},[898,67328,12471],{},[902,67330,12471],{"encoding":904},[883,67332,67334],{"className":67333},[886],[888,67335,67336],{"xmlns":890},[892,67337,67338,67354],{},[895,67339,67340,67342],{},[1750,67341,1758],{},[3586,67343,67344],{"scriptlevel":2607,"displaystyle":1752},[3423,67345,67346,67348],{},[898,67347,2573],{},[895,67349,67350,67352],{},[1742,67351,1872],{},[898,67353,207],{},[902,67355,67356],{"encoding":904},"-\\tfrac{b}{2a}",[883,67358,67360],{"className":67359},[886],[888,67361,67362],{"xmlns":890},[892,67363,67364,67370],{},[895,67365,67366,67368],{},[898,67367,13916],{},[898,67369,13658],{},[902,67371,64368],{"encoding":904},[883,67373,67375],{"className":67374},[886],[888,67376,67377],{"xmlns":890},[892,67378,67379,67391],{},[895,67380,67381,67383],{},[1750,67382,1758],{},[3586,67384,67385],{"scriptlevel":2607,"displaystyle":1752},[3423,67386,67387,67389],{},[898,67388,2573],{},[898,67390,207],{},[902,67392,67393],{"encoding":904},"-\\tfrac{b}{a}",[724,67395,67396],{},[614,67397,67398,67399,67430,67431,67460,67461,2313],{},"Obrázek 3.3: Parabola ",[883,67400,67402],{"className":67401},[886],[888,67403,67404],{"xmlns":890},[892,67405,67406,67428],{},[895,67407,67408,67410,67412,67414,67416,67422,67424,67426],{},[898,67409,5326],{},[898,67411,13658],{},[1750,67413,1766],{},[898,67415,207],{},[1699,67417,67418,67420],{},[898,67419,12471],{},[1742,67421,1872],{},[1750,67423,1861],{},[898,67425,2573],{},[898,67427,12471],{},[902,67429,66862],{"encoding":904}," s maximem v ",[883,67432,67434],{"className":67433},[886],[888,67435,67436],{"xmlns":890},[892,67437,67438,67458],{},[895,67439,67440,67442,67444,67446],{},[898,67441,12471],{},[1750,67443,1766],{},[1750,67445,1758],{},[3586,67447,67448],{"scriptlevel":2607,"displaystyle":1752},[3423,67449,67450,67452],{},[898,67451,2573],{},[895,67453,67454,67456],{},[1742,67455,1872],{},[898,67457,207],{},[902,67459,67066],{"encoding":904}," a nulou v ",[883,67462,67464],{"className":67463},[886],[888,67465,67466],{"xmlns":890},[892,67467,67468,67484],{},[895,67469,67470,67472,67474,67476],{},[898,67471,12471],{},[1750,67473,1766],{},[1750,67475,1758],{},[3586,67477,67478],{"scriptlevel":2607,"displaystyle":1752},[3423,67479,67480,67482],{},[898,67481,2573],{},[898,67483,207],{},[902,67485,67486],{"encoding":904},"Q = -\\tfrac{b}{a}",[724,67488,67489],{},[614,67490,67491,67492,2313],{},"Obrázek 3.4: Dokonalá konkurence — vodorovná přímka ",[883,67493,67495],{"className":67494},[886],[888,67496,67497],{"xmlns":890},[892,67498,67499,67519],{},[895,67500,67501,67503,67505,67507,67509,67511,67513],{},[898,67502,13916],{},[898,67504,13658],{},[1750,67506,1766],{},[898,67508,1773],{},[898,67510,13658],{},[1750,67512,1766],{},[1699,67514,67515,67517],{},[898,67516,1776],{},[1750,67518,3751],{},[902,67520,67521],{"encoding":904},"AR = MR = P^*",[115,67523,67525],{"id":67524},"náklady-firmy","Náklady firmy",[198,67527,67529],{"id":67528},"celkové-náklady","Celkové náklady",[724,67531,67532,1647,67534,2084,67549,67552,67553,67566],{},[38,67533,67529],{},[883,67535,67537],{"className":67536},[886],[888,67538,67539],{"xmlns":890},[892,67540,67541,67547],{},[895,67542,67543,67545],{},[898,67544,5326],{},[898,67546,1812],{},[902,67548,12916],{"encoding":904},[38,67550,67551],{},"total cost",") jsou veškeré náklady na realizaci ",[883,67554,67556],{"className":67555},[886],[888,67557,67558],{"xmlns":890},[892,67559,67560,67564],{},[895,67561,67562],{},[898,67563,12471],{},[902,67565,12471],{"encoding":904}," jednotek produkce:",[883,67568,67570],{"className":67569},[886],[888,67571,67572],{"xmlns":890,"display":36989},[892,67573,67574,67629],{},[4577,67575,67576],{"width":36994},[4582,67577,67578,67580,67622,67624],{},[4585,67579],{"width":36999},[4585,67581,67582],{},[895,67583,67584,67586,67588,67590,67592,67594,67596,67598,67600,67602,67604,67606,67608,67610,67612,67614,67616,67618,67620],{},[898,67585,5326],{},[898,67587,1812],{},[1750,67589,1766],{},[898,67591,5326],{},[898,67593,1812],{},[1750,67595,1753],{"stretchy":1752},[898,67597,12471],{},[1750,67599,1763],{"stretchy":1752},[1750,67601,1766],{},[898,67603,20069],{},[898,67605,1812],{},[1750,67607,1861],{},[898,67609,5326],{},[898,67611,49262],{},[898,67613,1812],{},[1750,67615,1753],{"stretchy":1752},[898,67617,12471],{},[1750,67619,1763],{"stretchy":1752},[1750,67621,1917],{"separator":1916},[4585,67623],{"width":36999},[4585,67625,67626],{},[1969,67627,67628],{},"(3.5)",[902,67630,67631],{"encoding":904},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[724,67633,2590,67634,67649,67650,2084,67653,4419,67656,67649,67680,2084,67683,67686],{},[883,67635,67637],{"className":67636},[886],[888,67638,67639],{"xmlns":890},[892,67640,67641,67647],{},[895,67642,67643,67645],{},[898,67644,20069],{},[898,67646,1812],{},[902,67648,64414],{"encoding":904}," jsou ",[38,67651,67652],{},"fixní náklady",[38,67654,67655],{},"fixed cost",[883,67657,67659],{"className":67658},[886],[888,67660,67661],{"xmlns":890},[892,67662,67663,67677],{},[895,67664,67665,67667,67669,67671,67673,67675],{},[898,67666,5326],{},[898,67668,49262],{},[898,67670,1812],{},[1750,67672,1753],{"stretchy":1752},[898,67674,12471],{},[1750,67676,1763],{"stretchy":1752},[902,67678,67679],{"encoding":904},"TVC(Q)",[38,67681,67682],{},"celkové variabilní náklady",[38,67684,67685],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[198,67688,67690],{"id":67689},"průměrné-náklady","Průměrné náklady",[724,67692,67693,1647,67695,2084,67710,67713],{},[38,67694,67690],{},[883,67696,67698],{"className":67697},[886],[888,67699,67700],{"xmlns":890},[892,67701,67702,67708],{},[895,67703,67704,67706],{},[898,67705,13916],{},[898,67707,1812],{},[902,67709,64483],{"encoding":904},[38,67711,67712],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[883,67715,67717],{"className":67716},[886],[888,67718,67719],{"xmlns":890,"display":36989},[892,67720,67721,67800],{},[4577,67722,67723],{"width":36994},[4582,67724,67725,67727,67793,67795],{},[4585,67726],{"width":36999},[4585,67728,67729],{},[895,67730,67731,67733,67735,67737,67739,67741,67743,67745,67747,67749,67759,67761,67771,67773,67791],{},[898,67732,13916],{},[898,67734,1812],{},[1750,67736,1766],{},[898,67738,13916],{},[898,67740,1812],{},[1750,67742,1753],{"stretchy":1752},[898,67744,12471],{},[1750,67746,1763],{"stretchy":1752},[1750,67748,1766],{},[3423,67750,67751,67757],{},[895,67752,67753,67755],{},[898,67754,5326],{},[898,67756,1812],{},[898,67758,12471],{},[1750,67760,1766],{},[3423,67762,67763,67769],{},[895,67764,67765,67767],{},[898,67766,20069],{},[898,67768,1812],{},[898,67770,12471],{},[1750,67772,1861],{},[3423,67774,67775,67789],{},[895,67776,67777,67779,67781,67783,67785,67787],{},[898,67778,5326],{},[898,67780,49262],{},[898,67782,1812],{},[1750,67784,1753],{"stretchy":1752},[898,67786,12471],{},[1750,67788,1763],{"stretchy":1752},[898,67790,12471],{},[1750,67792,1917],{"separator":1916},[4585,67794],{"width":36999},[4585,67796,67797],{},[1969,67798,67799],{},"(3.6)",[902,67801,67802],{"encoding":904},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[724,67804,2590,67805,67649,67829,1647,67832,2084,67849,4419,67852,67649,67884,1647,67887,2084,67904,12825],{},[883,67806,67808],{"className":67807},[886],[888,67809,67810],{"xmlns":890},[892,67811,67812,67826],{},[895,67813,67814],{},[3586,67815,67816],{"scriptlevel":2607,"displaystyle":1752},[3423,67817,67818,67824],{},[895,67819,67820,67822],{},[898,67821,20069],{},[898,67823,1812],{},[898,67825,12471],{},[902,67827,67828],{"encoding":904},"\\tfrac{FC}{Q}",[38,67830,67831],{},"průměrné fixní náklady",[883,67833,67835],{"className":67834},[886],[888,67836,67837],{"xmlns":890},[892,67838,67839,67847],{},[895,67840,67841,67843,67845],{},[898,67842,13916],{},[898,67844,20069],{},[898,67846,1812],{},[902,67848,64450],{"encoding":904},[38,67850,67851],{},"average fixed cost",[883,67853,67855],{"className":67854},[886],[888,67856,67857],{"xmlns":890},[892,67858,67859,67881],{},[895,67860,67861],{},[3586,67862,67863],{"scriptlevel":2607,"displaystyle":1752},[3423,67864,67865,67879],{},[895,67866,67867,67869,67871,67873,67875,67877],{},[898,67868,5326],{},[898,67870,49262],{},[898,67872,1812],{},[1750,67874,1753],{"stretchy":1752},[898,67876,12471],{},[1750,67878,1763],{"stretchy":1752},[898,67880,12471],{},[902,67882,67883],{"encoding":904},"\\tfrac{TVC(Q)}{Q}",[38,67885,67886],{},"průměrné variabilní náklady",[883,67888,67890],{"className":67889},[886],[888,67891,67892],{"xmlns":890},[892,67893,67894,67902],{},[895,67895,67896,67898,67900],{},[898,67897,13916],{},[898,67899,49262],{},[898,67901,1812],{},[902,67903,64234],{"encoding":904},[38,67905,67906],{},"average variable cost",[883,67908,67910],{"className":67909},[886],[888,67911,67912],{"xmlns":890,"display":36989},[892,67913,67914,67973],{},[4577,67915,67916],{"width":36994},[4582,67917,67918,67920,67966,67968],{},[4585,67919],{"width":36999},[4585,67921,67922],{},[895,67923,67924,67926,67928,67930,67932,67934,67936,67938,67940,67942,67944,67946,67964],{},[898,67925,13916],{},[898,67927,49262],{},[898,67929,1812],{},[1750,67931,1766],{},[898,67933,13916],{},[898,67935,49262],{},[898,67937,1812],{},[1750,67939,1753],{"stretchy":1752},[898,67941,12471],{},[1750,67943,1763],{"stretchy":1752},[1750,67945,1766],{},[3423,67947,67948,67962],{},[895,67949,67950,67952,67954,67956,67958,67960],{},[898,67951,5326],{},[898,67953,49262],{},[898,67955,1812],{},[1750,67957,1753],{"stretchy":1752},[898,67959,12471],{},[1750,67961,1763],{"stretchy":1752},[898,67963,12471],{},[898,67965,2313],{"mathvariant":1747},[4585,67967],{"width":36999},[4585,67969,67970],{},[1969,67971,67972],{},"(3.7)",[902,67974,67975],{"encoding":904},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[46271,67977,67979],{"id":67978},"příklad-34","Příklad 3.4",[724,67981,67982,66445,67984,2028,68009,64948,68033,2028,68048,68063,68064,2313],{},[38,67983,64910],{},[883,67985,67987],{"className":67986},[886],[888,67988,67989],{"xmlns":890},[892,67990,67991,68006],{},[895,67992,67993,67995,67997,67999,68001,68003],{},[898,67994,20069],{},[898,67996,1812],{},[1750,67998,1766],{},[1742,68000,1744],{},[1969,68002,2658],{},[1742,68004,68005],{},"000",[902,68007,68008],{"encoding":904},"FC = 1\\,000",[883,68010,68012],{"className":68011},[886],[888,68013,68014],{"xmlns":890},[892,68015,68016,68030],{},[895,68017,68018,68020,68022,68024,68026,68028],{},[898,68019,5326],{},[898,68021,49262],{},[898,68023,1812],{},[1750,68025,1766],{},[1742,68027,7859],{},[898,68029,12471],{},[902,68031,68032],{"encoding":904},"TVC = 4Q",[883,68034,68036],{"className":68035},[886],[888,68037,68038],{"xmlns":890},[892,68039,68040,68046],{},[895,68041,68042,68044],{},[898,68043,5326],{},[898,68045,1812],{},[902,68047,12916],{"encoding":904},[883,68049,68051],{"className":68050},[886],[888,68052,68053],{"xmlns":890},[892,68054,68055,68061],{},[895,68056,68057,68059],{},[898,68058,13916],{},[898,68060,1812],{},[902,68062,64483],{"encoding":904}," a jejich chování s rostoucím ",[883,68065,68067],{"className":68066},[886],[888,68068,68069],{"xmlns":890},[892,68070,68071,68075],{},[895,68072,68073],{},[898,68074,12471],{},[902,68076,12471],{"encoding":904},[724,68078,68079,1647,68081,2028,68111,68147,68148,14017,68161,68176,68177,2366],{},[38,68080,6610],{},[883,68082,68084],{"className":68083},[886],[888,68085,68086],{"xmlns":890},[892,68087,68088,68108],{},[895,68089,68090,68092,68094,68096,68098,68100,68102,68104,68106],{},[898,68091,5326],{},[898,68093,1812],{},[1750,68095,1766],{},[1742,68097,1744],{},[1969,68099,2658],{},[1742,68101,68005],{},[1750,68103,1861],{},[1742,68105,7859],{},[898,68107,12471],{},[902,68109,68110],{"encoding":904},"TC = 1\\,000 + 4Q",[883,68112,68114],{"className":68113},[886],[888,68115,68116],{"xmlns":890},[892,68117,68118,68144],{},[895,68119,68120,68122,68124,68126,68140,68142],{},[898,68121,13916],{},[898,68123,1812],{},[1750,68125,1766],{},[3586,68127,68128],{"scriptlevel":2607,"displaystyle":1752},[3423,68129,68130,68138],{},[895,68131,68132,68134,68136],{},[1742,68133,1744],{},[1969,68135,2658],{},[1742,68137,68005],{},[898,68139,12471],{},[1750,68141,1861],{},[1742,68143,7859],{},[902,68145,68146],{"encoding":904},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[883,68149,68151],{"className":68150},[886],[888,68152,68153],{"xmlns":890},[892,68154,68155,68159],{},[895,68156,68157],{},[898,68158,12471],{},[902,68160,12471],{"encoding":904},[883,68162,68164],{"className":68163},[886],[888,68165,68166],{"xmlns":890},[892,68167,68168,68174],{},[895,68169,68170,68172],{},[898,68171,13916],{},[898,68173,1812],{},[902,68175,64483],{"encoding":904}," blíží ",[883,68178,68180],{"className":68179},[886],[888,68181,68182],{"xmlns":890},[892,68183,68184,68188],{},[895,68185,68186],{},[1742,68187,7859],{},[902,68189,7859],{"encoding":904},[883,68191,68193],{"className":68192},[886],[888,68194,68195],{"xmlns":890,"display":36989},[892,68196,68197,68243],{},[895,68198,68199,68216,68238,68240],{},[48819,68200,68201,68208],{},[895,68202,68203,68206],{},[898,68204,68205],{},"lim",[1750,68207,65123],{},[895,68209,68210,68212,68214],{},[898,68211,12471],{},[1750,68213,12797],{},[898,68215,15945],{"mathvariant":1747},[895,68217,68218,68220,68232,68234,68236],{},[1750,68219,1753],{"fence":1916},[3423,68221,68222,68230],{},[895,68223,68224,68226,68228],{},[1742,68225,1744],{},[1969,68227,2658],{},[1742,68229,68005],{},[898,68231,12471],{},[1750,68233,1861],{},[1742,68235,7859],{},[1750,68237,1763],{"fence":1916},[1750,68239,1766],{},[1742,68241,68242],{},"4.",[902,68244,68245],{"encoding":904},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[724,68247,68248,68286,68287,2313],{},[883,68249,68251],{"className":68250},[886],[888,68252,68253],{"xmlns":890},[892,68254,68255,68283],{},[895,68256,68257,68259,68261,68263,68265,68279,68281],{},[898,68258,13916],{},[898,68260,20069],{},[898,68262,1812],{},[1750,68264,1766],{},[3586,68266,68267],{"scriptlevel":2607,"displaystyle":1752},[3423,68268,68269,68277],{},[895,68270,68271,68273,68275],{},[1742,68272,1744],{},[1969,68274,2658],{},[1742,68276,68005],{},[898,68278,12471],{},[1750,68280,12797],{},[1742,68282,2607],{},[902,68284,68285],{"encoding":904},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[883,68288,68290],{"className":68289},[886],[888,68291,68292],{"xmlns":890},[892,68293,68294,68298],{},[895,68295,68296],{},[898,68297,12471],{},[902,68299,12471],{"encoding":904},[724,68301,68302],{},[614,68303,68304,68305,68334,68335,2313],{},"Obrázek 3.5: Přímka ",[883,68306,68308],{"className":68307},[886],[888,68309,68310],{"xmlns":890},[892,68311,68312,68332],{},[895,68313,68314,68316,68318,68320,68322,68324,68326,68328,68330],{},[898,68315,5326],{},[898,68317,1812],{},[1750,68319,1766],{},[1742,68321,1744],{},[1969,68323,2658],{},[1742,68325,68005],{},[1750,68327,1861],{},[1742,68329,7859],{},[898,68331,12471],{},[902,68333,68110],{"encoding":904}," protínající svislou osu ve výši ",[883,68336,68338],{"className":68337},[886],[888,68339,68340],{"xmlns":890},[892,68341,68342,68356],{},[895,68343,68344,68346,68348,68350,68352,68354],{},[898,68345,20069],{},[898,68347,1812],{},[1750,68349,1766],{},[1742,68351,1744],{},[1969,68353,2658],{},[1742,68355,68005],{},[902,68357,68008],{"encoding":904},[724,68359,68360],{},[614,68361,68362,68363,68398,68399,2313],{},"Obrázek 3.6: Hyperbola ",[883,68364,68366],{"className":68365},[886],[888,68367,68368],{"xmlns":890},[892,68369,68370,68396],{},[895,68371,68372,68374,68376,68378,68392,68394],{},[898,68373,13916],{},[898,68375,1812],{},[1750,68377,1766],{},[3586,68379,68380],{"scriptlevel":2607,"displaystyle":1752},[3423,68381,68382,68390],{},[895,68383,68384,68386,68388],{},[1742,68385,1744],{},[1969,68387,2658],{},[1742,68389,68005],{},[898,68391,12471],{},[1750,68393,1861],{},[1742,68395,7859],{},[902,68397,68146],{"encoding":904}," s vodorovnou asymptotou ",[883,68400,68402],{"className":68401},[886],[888,68403,68404],{"xmlns":890},[892,68405,68406,68416],{},[895,68407,68408,68410,68412,68414],{},[898,68409,13916],{},[898,68411,1812],{},[1750,68413,1766],{},[1742,68415,7859],{},[902,68417,68418],{"encoding":904},"AC = 4",[724,68420,68421],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[883,68423,68425],{"className":68424},[886],[888,68426,68427],{"xmlns":890,"display":36989},[892,68428,68429,68455],{},[895,68430,68431,68433,68435,68437,68439,68441,68443,68445,68447,68449,68451,68453],{},[898,68432,5326],{},[898,68434,49262],{},[898,68436,1812],{},[1750,68438,1766],{},[898,68440,12471],{},[1750,68442,8009],{},[898,68444,49262],{},[898,68446,1812],{},[1750,68448,1753],{"stretchy":1752},[898,68450,12471],{},[1750,68452,1763],{"stretchy":1752},[1750,68454,1917],{"separator":1916},[902,68456,68457],{"encoding":904},"TVC = Q \\cdot VC(Q),",[724,68459,2590,68460,67649,68488,68491,68492,68522],{},[883,68461,68463],{"className":68462},[886],[888,68464,68465],{"xmlns":890},[892,68466,68467,68485],{},[895,68468,68469,68471,68473,68475,68477,68479,68481,68483],{},[898,68470,49262],{},[898,68472,1812],{},[1750,68474,1766],{},[898,68476,49262],{},[898,68478,1812],{},[1750,68480,1753],{"stretchy":1752},[898,68482,12471],{},[1750,68484,1763],{"stretchy":1752},[902,68486,68487],{"encoding":904},"VC = VC(Q)",[38,68489,68490],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[883,68493,68495],{"className":68494},[886],[888,68496,68497],{"xmlns":890},[892,68498,68499,68519],{},[895,68500,68501,68503,68505,68507,68509,68511,68513,68515,68517],{},[898,68502,5326],{},[898,68504,49262],{},[898,68506,1812],{},[1750,68508,1753],{"stretchy":1752},[898,68510,12471],{},[1750,68512,1763],{"stretchy":1752},[1750,68514,1766],{},[898,68516,207],{},[898,68518,12471],{},[902,68520,68521],{"encoding":904},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[883,68524,68526],{"className":68525},[886],[888,68527,68528],{"xmlns":890,"display":36989},[892,68529,68530,68550],{},[895,68531,68532,68534,68536,68538,68540,68542,68544,68546,68548],{},[898,68533,5326],{},[898,68535,1812],{},[1750,68537,1766],{},[898,68539,20069],{},[898,68541,1812],{},[1750,68543,1861],{},[898,68545,207],{},[898,68547,12471],{},[898,68549,2313],{"mathvariant":1747},[902,68551,68552],{"encoding":904},"TC = FC + aQ.",[724,68554,68555,68556,68571,68572,68587,68588,68611,68612,68646,68647,68398,68660,68673,68674,2028,68722,68766,68767,2313],{},"Křivkou ",[883,68557,68559],{"className":68558},[886],[888,68560,68561],{"xmlns":890},[892,68562,68563,68569],{},[895,68564,68565,68567],{},[898,68566,5326],{},[898,68568,1812],{},[902,68570,12916],{"encoding":904}," je přímka se svislým průsečíkem ",[883,68573,68575],{"className":68574},[886],[888,68576,68577],{"xmlns":890},[892,68578,68579,68585],{},[895,68580,68581,68583],{},[898,68582,20069],{},[898,68584,1812],{},[902,68586,64414],{"encoding":904}," a sklonem ",[883,68589,68591],{"className":68590},[886],[888,68592,68593],{"xmlns":890},[892,68594,68595,68608],{},[895,68596,68597,68600,68602,68604,68606],{},[898,68598,68599],{},"tan",[1750,68601,65123],{},[898,68603,2661],{},[1750,68605,1766],{},[898,68607,207],{},[902,68609,68610],{"encoding":904},"\\tan\\alpha = a"," (obrázek 3.7). Průměrné náklady tvoří hyperbolu ",[883,68613,68615],{"className":68614},[886],[888,68616,68617],{"xmlns":890},[892,68618,68619,68643],{},[895,68620,68621,68623,68625,68627,68639,68641],{},[898,68622,13916],{},[898,68624,1812],{},[1750,68626,1766],{},[3586,68628,68629],{"scriptlevel":2607,"displaystyle":1752},[3423,68630,68631,68637],{},[895,68632,68633,68635],{},[898,68634,20069],{},[898,68636,1812],{},[898,68638,12471],{},[1750,68640,1861],{},[898,68642,207],{},[902,68644,68645],{"encoding":904},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[883,68648,68650],{"className":68649},[886],[888,68651,68652],{"xmlns":890},[892,68653,68654,68658],{},[895,68655,68656],{},[898,68657,2046],{},[902,68659,2046],{"encoding":904},[883,68661,68663],{"className":68662},[886],[888,68664,68665],{"xmlns":890},[892,68666,68667,68671],{},[895,68668,68669],{},[898,68670,207],{},[902,68672,207],{"encoding":904}," (obrázek 3.8). Limity ",[883,68675,68677],{"className":68676},[886],[888,68678,68679],{"xmlns":890},[892,68680,68681,68719],{},[895,68682,68683,68703,68715,68717],{},[5535,68684,68685,68691],{},[895,68686,68687,68689],{},[898,68688,68205],{},[1750,68690,65123],{},[895,68692,68693,68695,68697],{},[898,68694,12471],{},[1750,68696,12797],{},[1699,68698,68699,68701],{},[1742,68700,2607],{},[1750,68702,1861],{},[3586,68704,68705],{"scriptlevel":2607,"displaystyle":1752},[3423,68706,68707,68713],{},[895,68708,68709,68711],{},[898,68710,20069],{},[898,68712,1812],{},[898,68714,12471],{},[1750,68716,1766],{},[898,68718,15945],{"mathvariant":1747},[902,68720,68721],{"encoding":904},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[883,68723,68725],{"className":68724},[886],[888,68726,68727],{"xmlns":890},[892,68728,68729,68763],{},[895,68730,68731,68747,68759,68761],{},[5535,68732,68733,68739],{},[895,68734,68735,68737],{},[898,68736,68205],{},[1750,68738,65123],{},[895,68740,68741,68743,68745],{},[898,68742,12471],{},[1750,68744,12797],{},[898,68746,15945],{"mathvariant":1747},[3586,68748,68749],{"scriptlevel":2607,"displaystyle":1752},[3423,68750,68751,68757],{},[895,68752,68753,68755],{},[898,68754,20069],{},[898,68756,1812],{},[898,68758,12471],{},[1750,68760,1766],{},[1742,68762,2607],{},[902,68764,68765],{"encoding":904},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[883,68768,68770],{"className":68769},[886],[888,68771,68772],{"xmlns":890},[892,68773,68774,68780],{},[895,68775,68776,68778],{},[898,68777,13916],{},[898,68779,1812],{},[902,68781,64483],{"encoding":904},[724,68783,68784],{},[614,68785,68786,68787,68802,68803,68818,68819,2313],{},"Obrázek 3.7: Přímka ",[883,68788,68790],{"className":68789},[886],[888,68791,68792],{"xmlns":890},[892,68793,68794,68800],{},[895,68795,68796,68798],{},[898,68797,5326],{},[898,68799,1812],{},[902,68801,12916],{"encoding":904}," s osovým průsečíkem ve výši ",[883,68804,68806],{"className":68805},[886],[888,68807,68808],{"xmlns":890},[892,68809,68810,68816],{},[895,68811,68812,68814],{},[898,68813,20069],{},[898,68815,1812],{},[902,68817,64414],{"encoding":904}," a se sklonem ",[883,68820,68822],{"className":68821},[886],[888,68823,68824],{"xmlns":890},[892,68825,68826,68838],{},[895,68827,68828,68830,68832,68834,68836],{},[898,68829,68599],{},[1750,68831,65123],{},[898,68833,2661],{},[1750,68835,1766],{},[898,68837,207],{},[902,68839,68610],{"encoding":904},[724,68841,68842],{},[614,68843,68844,68845,68860,68861,2313],{},"Obrázek 3.8: Klesající hyperbola ",[883,68846,68848],{"className":68847},[886],[888,68849,68850],{"xmlns":890},[892,68851,68852,68858],{},[895,68853,68854,68856],{},[898,68855,13916],{},[898,68857,1812],{},[902,68859,64483],{"encoding":904}," s vodorovnou asymptotou ve výši ",[883,68862,68864],{"className":68863},[886],[888,68865,68866],{"xmlns":890},[892,68867,68868,68872],{},[895,68869,68870],{},[898,68871,207],{},[902,68873,207],{"encoding":904},[198,68875,68877],{"id":68876},"mezní-náklady","Mezní náklady",[724,68879,68880,1647,68882,2084,68897,68900,68901,68904],{},[38,68881,68877],{},[883,68883,68885],{"className":68884},[886],[888,68886,68887],{"xmlns":890},[892,68888,68889,68895],{},[895,68890,68891,68893],{},[898,68892,1773],{},[898,68894,1812],{},[902,68896,64215],{"encoding":904},[38,68898,68899],{},"marginal cost",") jsou ",[207,68902,1145],{"className":68903,"dataFsResolvedFilePath":764,"href":765},[210]," celkových nákladů podle množství:",[883,68906,68908],{"className":68907},[886],[888,68909,68910],{"xmlns":890,"display":36989},[892,68911,68912,68981],{},[4577,68913,68914],{"width":36994},[4582,68915,68916,68918,68974,68976],{},[4585,68917],{"width":36999},[4585,68919,68920],{},[895,68921,68922,68924,68926,68928,68930,68932,68934,68936,68938,68940,68956,68958,68960,68966,68968,68970,68972],{},[898,68923,1773],{},[898,68925,1812],{},[1750,68927,1766],{},[898,68929,1773],{},[898,68931,1812],{},[1750,68933,1753],{"stretchy":1752},[898,68935,12471],{},[1750,68937,1763],{"stretchy":1752},[1750,68939,1766],{},[3423,68941,68942,68950],{},[895,68943,68944,68946,68948],{},[898,68945,3429],{"mathvariant":1747},[898,68947,5326],{},[898,68949,1812],{},[895,68951,68952,68954],{},[898,68953,3429],{"mathvariant":1747},[898,68955,12471],{},[1750,68957,1766],{},[898,68959,5326],{},[1699,68961,68962,68964],{},[898,68963,1812],{},[1750,68965,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,68967,1753],{"stretchy":1752},[898,68969,12471],{},[1750,68971,1763],{"stretchy":1752},[898,68973,2313],{"mathvariant":1747},[4585,68975],{"width":36999},[4585,68977,68978],{},[1969,68979,68980],{},"(3.8)",[902,68982,68983],{"encoding":904},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1785,68985,68986],{},[724,68987,68988,68990,68991,69017,69018,69035,69036,2313],{},[883,68989,1791],{}," Intuice — „kolik stojí další kus\"\n",[883,68992,68994],{"className":68993},[886],[888,68995,68996],{"xmlns":890},[892,68997,68998,69014],{},[895,68999,69000,69002,69004,69006,69012],{},[898,69001,1773],{},[898,69003,1812],{},[1750,69005,1753],{"stretchy":1752},[1699,69007,69008,69010],{},[898,69009,12471],{},[1750,69011,3751],{},[1750,69013,1763],{"stretchy":1752},[902,69015,69016],{"encoding":904},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[883,69019,69021],{"className":69020},[886],[888,69022,69023],{"xmlns":890},[892,69024,69025,69033],{},[895,69026,69027],{},[1699,69028,69029,69031],{},[898,69030,12471],{},[1750,69032,3751],{},[902,69034,38767],{"encoding":904},". Formálně ",[883,69037,69039],{"className":69038},[886],[888,69040,69041],{"xmlns":890},[892,69042,69043,69095],{},[895,69044,69045,69047,69049,69051,69057,69059,69061,69063,69065,69067,69073,69075,69077,69079,69081,69083,69085,69087,69093],{},[898,69046,1773],{},[898,69048,1812],{},[1750,69050,1753],{"stretchy":1752},[1699,69052,69053,69055],{},[898,69054,12471],{},[1750,69056,3751],{},[1750,69058,1763],{"stretchy":1752},[1750,69060,2274],{},[898,69062,5326],{},[898,69064,1812],{},[1750,69066,1753],{"stretchy":1752},[1699,69068,69069,69071],{},[898,69070,12471],{},[1750,69072,3751],{},[1750,69074,1861],{},[1742,69076,1744],{},[1750,69078,1763],{"stretchy":1752},[1750,69080,1758],{},[898,69082,5326],{},[898,69084,1812],{},[1750,69086,1753],{"stretchy":1752},[1699,69088,69089,69091],{},[898,69090,12471],{},[1750,69092,3751],{},[1750,69094,1763],{"stretchy":1752},[902,69096,69097],{"encoding":904},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[724,69099,69100,69101,2366],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[883,69102,69104],{"className":69103},[886],[888,69105,69106],{"xmlns":890},[892,69107,69108,69116],{},[895,69109,69110,69112,69114],{},[898,69111,2666],{"mathvariant":1747},[898,69113,5326],{},[898,69115,1812],{},[902,69117,69118],{"encoding":904},"\\Delta TC",[883,69120,69122],{"className":69121},[886],[888,69123,69124],{"xmlns":890,"display":36989},[892,69125,69126,69195],{},[4577,69127,69128],{"width":36994},[4582,69129,69130,69132,69188,69190],{},[4585,69131],{"width":36999},[4585,69133,69134],{},[895,69135,69136,69138,69140,69142,69144,69146,69148,69150,69152,69154,69156,69158,69160,69162,69168,69170,69172,69174,69176,69178,69180,69182,69184,69186],{},[898,69137,2666],{"mathvariant":1747},[898,69139,5326],{},[898,69141,1812],{},[1969,69143,6766],{},[1750,69145,2274],{},[1969,69147,6766],{},[898,69149,3429],{"mathvariant":1747},[898,69151,5326],{},[898,69153,1812],{},[1750,69155,1766],{},[1750,69157,1753],{"stretchy":1752},[898,69159,5326],{},[898,69161,1812],{},[1699,69163,69164,69166],{},[1750,69165,1763],{"stretchy":1752},[1750,69167,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,69169,2658],{},[898,69171,3429],{"mathvariant":1747},[898,69173,12471],{},[1750,69175,1766],{},[898,69177,1773],{},[898,69179,1812],{},[1969,69181,2658],{},[898,69183,3429],{"mathvariant":1747},[898,69185,12471],{},[1750,69187,1917],{"separator":1916},[4585,69189],{"width":36999},[4585,69191,69192],{},[1969,69193,69194],{},"(3.9)",[902,69196,69197],{"encoding":904},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[724,69199,66234],{},[883,69201,69203],{"className":69202},[886],[888,69204,69205],{"xmlns":890,"display":36989},[892,69206,69207,69305],{},[895,69208,69209,69247,69249,69251,69253,69275,69277,69303],{},[895,69210,69211,69213,69219,69221,69227,69230,69236,69239],{},[1969,69212,66248],{},[3215,69214,69215,69217],{"accent":1916},[1969,69216,54655],{},[1750,69218,8912],{},[1969,69220,66257],{},[3215,69222,69223,69225],{"accent":1916},[1969,69224,11717],{},[1750,69226,8831],{},[1969,69228,69229],{},"ch n",[3215,69231,69232,69234],{"accent":1916},[1969,69233,207],{},[1750,69235,8831],{},[1969,69237,69238],{},"klad",[3215,69240,69241,69244],{"accent":1916},[1969,69242,69243],{},"u",[1750,69245,69246],{},"˚",[1969,69248,6766],{},[1750,69250,2274],{},[1969,69252,6766],{},[895,69254,69255,69257,69263,69266,69272],{},[1969,69256,66292],{},[3215,69258,69259,69261],{"accent":1916},[1969,69260,8900],{},[1750,69262,8831],{},[1969,69264,69265],{}," n",[3215,69267,69268,69270],{"accent":1916},[1969,69269,207],{},[1750,69271,8831],{},[1969,69273,69274],{},"klady",[1750,69276,66319],{},[895,69278,69279,69281,69287,69289,69295,69297],{},[1969,69280,66248],{},[3215,69282,69283,69285],{"accent":1916},[1969,69284,54655],{},[1750,69286,8912],{},[1969,69288,66332],{},[3215,69290,69291,69293],{"accent":1916},[1969,69292,19230],{},[1750,69294,8912],{},[1969,69296,66341],{},[3215,69298,69299,69301],{"accent":1916},[1969,69300,8900],{},[1750,69302,8831],{},[898,69304,2313],{"mathvariant":1747},[902,69306,69307],{"encoding":904},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[46271,69309,69311],{"id":69310},"příklad-35","Příklad 3.5",[724,69313,69314,66445,69316,64948,69352,69367,69368,69383,69384,12359,69397,4321,69410,69423,69424,4321,69437,2313],{},[38,69315,64910],{},[883,69317,69319],{"className":69318},[886],[888,69320,69321],{"xmlns":890},[892,69322,69323,69349],{},[895,69324,69325,69327,69329,69331,69333,69335,69337,69339,69341,69343],{},[898,69326,5326],{},[898,69328,1812],{},[1750,69330,1766],{},[1742,69332,4159],{},[1750,69334,1861],{},[1742,69336,3219],{},[898,69338,12471],{},[1750,69340,1861],{},[1742,69342,1872],{},[1699,69344,69345,69347],{},[898,69346,12471],{},[1742,69348,1872],{},[902,69350,69351],{"encoding":904},"TC = 200 + 6Q + 2Q^2",[883,69353,69355],{"className":69354},[886],[888,69356,69357],{"xmlns":890},[892,69358,69359,69365],{},[895,69360,69361,69363],{},[898,69362,1773],{},[898,69364,1812],{},[902,69366,64215],{"encoding":904}," a odhadněte změny ",[883,69369,69371],{"className":69370},[886],[888,69372,69373],{"xmlns":890},[892,69374,69375,69381],{},[895,69376,69377,69379],{},[898,69378,5326],{},[898,69380,1812],{},[902,69382,12916],{"encoding":904}," při změnách ",[883,69385,69387],{"className":69386},[886],[888,69388,69389],{"xmlns":890},[892,69390,69391,69395],{},[895,69392,69393],{},[898,69394,12471],{},[902,69396,12471],{"encoding":904},[883,69398,69400],{"className":69399},[886],[888,69401,69402],{"xmlns":890},[892,69403,69404,69408],{},[895,69405,69406],{},[1742,69407,45167],{},[902,69409,45167],{"encoding":904},[883,69411,69413],{"className":69412},[886],[888,69414,69415],{"xmlns":890},[892,69416,69417,69421],{},[895,69418,69419],{},[1742,69420,50785],{},[902,69422,50785],{"encoding":904}," a z ",[883,69425,69427],{"className":69426},[886],[888,69428,69429],{"xmlns":890},[892,69430,69431,69435],{},[895,69432,69433],{},[1742,69434,45167],{},[902,69436,45167],{"encoding":904},[883,69438,69440],{"className":69439},[886],[888,69441,69442],{"xmlns":890},[892,69443,69444,69448],{},[895,69445,69446],{},[1742,69447,4903],{},[902,69449,4903],{"encoding":904},[724,69451,69452,1647,69454,12605,69480,1343,69507,69534,69535,69550,69551,69566,69567,69594,69595,69615,69616,4350,69637,69693,69694,12359,69707,4321,69720,2433,69733,2313],{},[38,69453,6610],{},[883,69455,69457],{"className":69456},[886],[888,69458,69459],{"xmlns":890},[892,69460,69461,69477],{},[895,69462,69463,69465,69467,69469,69471,69473,69475],{},[898,69464,1773],{},[898,69466,1812],{},[1750,69468,1766],{},[1742,69470,3219],{},[1750,69472,1861],{},[1742,69474,7859],{},[898,69476,12471],{},[902,69478,69479],{"encoding":904},"MC = 6 + 4Q",[883,69481,69483],{"className":69482},[886],[888,69484,69485],{"xmlns":890},[892,69486,69487,69504],{},[895,69488,69489,69491,69493,69495,69497,69499,69501],{},[898,69490,1773],{},[898,69492,1812],{},[1750,69494,1753],{"stretchy":1752},[1742,69496,45167],{},[1750,69498,1763],{"stretchy":1752},[1750,69500,1766],{},[1742,69502,69503],{},"66",[902,69505,69506],{"encoding":904},"MC(15) = 66",[883,69508,69510],{"className":69509},[886],[888,69511,69512],{"xmlns":890},[892,69513,69514,69531],{},[895,69515,69516,69518,69520,69522,69524,69526,69528],{},[898,69517,1773],{},[898,69519,1812],{},[1750,69521,1753],{"stretchy":1752},[1742,69523,6465],{},[1750,69525,1763],{"stretchy":1752},[1750,69527,1766],{},[1742,69529,69530],{},"86",[902,69532,69533],{"encoding":904},"MC(20) = 86",": s růstem množství se rychlost změny ",[883,69536,69538],{"className":69537},[886],[888,69539,69540],{"xmlns":890},[892,69541,69542,69548],{},[895,69543,69544,69546],{},[898,69545,5326],{},[898,69547,1812],{},[902,69549,12916],{"encoding":904}," zvyšuje (",[883,69552,69554],{"className":69553},[886],[888,69555,69556],{"xmlns":890},[892,69557,69558,69564],{},[895,69559,69560,69562],{},[898,69561,1773],{},[898,69563,1812],{},[902,69565,64215],{"encoding":904}," je rostoucí). Z ",[883,69568,69570],{"className":69569},[886],[888,69571,69572],{"xmlns":890},[892,69573,69574,69591],{},[895,69575,69576,69578,69580,69582,69584,69586,69588],{},[898,69577,5326],{},[898,69579,1812],{},[1750,69581,1753],{"stretchy":1752},[1742,69583,45167],{},[1750,69585,1763],{"stretchy":1752},[1750,69587,1766],{},[1742,69589,69590],{},"740",[902,69592,69593],{"encoding":904},"TC(15) = 740"," se po přírůstku ",[883,69596,69598],{"className":69597},[886],[888,69599,69600],{"xmlns":890},[892,69601,69602,69612],{},[895,69603,69604,69606,69608,69610],{},[898,69605,3429],{"mathvariant":1747},[898,69607,12471],{},[1750,69609,1766],{},[1742,69611,1744],{},[902,69613,69614],{"encoding":904},"\\mathrm{d}Q = 1"," předpokládá ",[883,69617,69619],{"className":69618},[886],[888,69620,69621],{"xmlns":890},[892,69622,69623,69634],{},[895,69624,69625,69627,69629,69631],{},[898,69626,5326],{},[898,69628,1812],{},[1750,69630,2274],{},[1742,69632,69633],{},"806",[902,69635,69636],{"encoding":904},"TC \\approx 806",[883,69638,69640],{"className":69639},[886],[888,69641,69642],{"xmlns":890},[892,69643,69644,69690],{},[895,69645,69646,69648,69650,69652,69654,69656,69658,69660,69662,69664,69666,69668,69670,69672,69674,69676,69678,69681,69683,69685,69687],{},[898,69647,2666],{"mathvariant":1747},[898,69649,5326],{},[898,69651,1812],{},[1750,69653,1766],{},[898,69655,5326],{},[898,69657,1812],{},[1750,69659,1753],{"stretchy":1752},[1742,69661,50785],{},[1750,69663,1763],{"stretchy":1752},[1750,69665,1758],{},[898,69667,5326],{},[898,69669,1812],{},[1750,69671,1753],{"stretchy":1752},[1742,69673,45167],{},[1750,69675,1763],{"stretchy":1752},[1750,69677,1766],{},[1742,69679,69680],{},"808",[1750,69682,1758],{},[1742,69684,69590],{},[1750,69686,1766],{},[1742,69688,69689],{},"68",[902,69691,69692],{"encoding":904},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[883,69695,69697],{"className":69696},[886],[888,69698,69699],{"xmlns":890},[892,69700,69701,69705],{},[895,69702,69703],{},[898,69704,12471],{},[902,69706,12471],{"encoding":904},[883,69708,69710],{"className":69709},[886],[888,69711,69712],{"xmlns":890},[892,69713,69714,69718],{},[895,69715,69716],{},[1742,69717,45167],{},[902,69719,45167],{"encoding":904},[883,69721,69723],{"className":69722},[886],[888,69724,69725],{"xmlns":890},[892,69726,69727,69731],{},[895,69728,69729],{},[1742,69730,4903],{},[902,69732,4903],{"encoding":904},[883,69734,69736],{"className":69735},[886],[888,69737,69738],{"xmlns":890},[892,69739,69740,69769],{},[895,69741,69742,69744,69746,69748,69750,69752,69754,69756,69758,69760,69762,69764,69766],{},[898,69743,2666],{"mathvariant":1747},[898,69745,5326],{},[898,69747,1812],{},[1750,69749,2274],{},[1742,69751,69503],{},[1750,69753,8009],{},[1750,69755,1753],{"stretchy":1752},[1750,69757,1758],{},[1742,69759,7822],{},[1750,69761,1763],{"stretchy":1752},[1750,69763,1766],{},[1750,69765,1758],{},[1742,69767,69768],{},"198",[902,69770,69771],{"encoding":904},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[198,69773,69775],{"id":69774},"kubická-nákladová-funkce","Kubická nákladová funkce",[724,69777,69778],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[46271,69780,69782],{"id":69781},"příklad-36","Příklad 3.6",[724,69784,69785,66445,69787,69831],{},[38,69786,64910],{},[883,69788,69790],{"className":69789},[886],[888,69791,69792],{"xmlns":890},[892,69793,69794,69828],{},[895,69795,69796,69798,69800,69802,69804,69806,69808,69810,69812,69814,69820,69822],{},[898,69797,5326],{},[898,69799,1812],{},[1750,69801,1766],{},[1742,69803,4078],{},[1750,69805,1861],{},[1742,69807,6419],{},[898,69809,12471],{},[1750,69811,1758],{},[1742,69813,7902],{},[1699,69815,69816,69818],{},[898,69817,12471],{},[1742,69819,1872],{},[1750,69821,1861],{},[1699,69823,69824,69826],{},[898,69825,12471],{},[1742,69827,7822],{},[902,69829,69830],{"encoding":904},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[724,69833,69834],{},[38,69835,6610],{},[883,69837,69839],{"className":69838},[886],[888,69840,69841],{"xmlns":890,"display":36989},[892,69842,69843,70087],{},[4577,69844,69845,69871,69919,69953,69995,70045],{"rowspacing":4579,"columnalign":4580,"columnspacing":3814},[4582,69846,69847,69857],{},[4585,69848,69849],{},[3586,69850,69851],{"scriptlevel":2607,"displaystyle":1916},[895,69852,69853,69855],{},[898,69854,20069],{},[898,69856,1812],{},[4585,69858,69859],{},[3586,69860,69861],{"scriptlevel":2607,"displaystyle":1916},[895,69862,69863,69865,69867,69869],{},[895,69864],{},[1750,69866,1766],{},[1742,69868,4078],{},[1750,69870,1917],{"separator":1916},[4582,69872,69873,69885],{},[4585,69874,69875],{},[3586,69876,69877],{"scriptlevel":2607,"displaystyle":1916},[895,69878,69879,69881,69883],{},[898,69880,5326],{},[898,69882,49262],{},[898,69884,1812],{},[4585,69886,69887],{},[3586,69888,69889],{"scriptlevel":2607,"displaystyle":1916},[895,69890,69891,69893,69895,69897,69899,69901,69903,69909,69911,69917],{},[895,69892],{},[1750,69894,1766],{},[1742,69896,6419],{},[898,69898,12471],{},[1750,69900,1758],{},[1742,69902,7902],{},[1699,69904,69905,69907],{},[898,69906,12471],{},[1742,69908,1872],{},[1750,69910,1861],{},[1699,69912,69913,69915],{},[898,69914,12471],{},[1742,69916,7822],{},[1750,69918,1917],{"separator":1916},[4582,69920,69921,69933],{},[4585,69922,69923],{},[3586,69924,69925],{"scriptlevel":2607,"displaystyle":1916},[895,69926,69927,69929,69931],{},[898,69928,13916],{},[898,69930,20069],{},[898,69932,1812],{},[4585,69934,69935],{},[3586,69936,69937],{"scriptlevel":2607,"displaystyle":1916},[895,69938,69939,69941,69943,69951],{},[895,69940],{},[1750,69942,1766],{},[3586,69944,69945],{"scriptlevel":2607,"displaystyle":1752},[3423,69946,69947,69949],{},[1742,69948,4078],{},[898,69950,12471],{},[1750,69952,1917],{"separator":1916},[4582,69954,69955,69967],{},[4585,69956,69957],{},[3586,69958,69959],{"scriptlevel":2607,"displaystyle":1916},[895,69960,69961,69963,69965],{},[898,69962,13916],{},[898,69964,49262],{},[898,69966,1812],{},[4585,69968,69969],{},[3586,69970,69971],{"scriptlevel":2607,"displaystyle":1916},[895,69972,69973,69975,69977,69979,69981,69983,69985,69987,69993],{},[895,69974],{},[1750,69976,1766],{},[1742,69978,6419],{},[1750,69980,1758],{},[1742,69982,7902],{},[898,69984,12471],{},[1750,69986,1861],{},[1699,69988,69989,69991],{},[898,69990,12471],{},[1742,69992,1872],{},[1750,69994,1917],{"separator":1916},[4582,69996,69997,70007],{},[4585,69998,69999],{},[3586,70000,70001],{"scriptlevel":2607,"displaystyle":1916},[895,70002,70003,70005],{},[898,70004,13916],{},[898,70006,1812],{},[4585,70008,70009],{},[3586,70010,70011],{"scriptlevel":2607,"displaystyle":1916},[895,70012,70013,70015,70017,70025,70027,70029,70031,70033,70035,70037,70043],{},[895,70014],{},[1750,70016,1766],{},[3586,70018,70019],{"scriptlevel":2607,"displaystyle":1752},[3423,70020,70021,70023],{},[1742,70022,4078],{},[898,70024,12471],{},[1750,70026,1861],{},[1742,70028,6419],{},[1750,70030,1758],{},[1742,70032,7902],{},[898,70034,12471],{},[1750,70036,1861],{},[1699,70038,70039,70041],{},[898,70040,12471],{},[1742,70042,1872],{},[1750,70044,1917],{"separator":1916},[4582,70046,70047,70057],{},[4585,70048,70049],{},[3586,70050,70051],{"scriptlevel":2607,"displaystyle":1916},[895,70052,70053,70055],{},[898,70054,1773],{},[898,70056,1812],{},[4585,70058,70059],{},[3586,70060,70061],{"scriptlevel":2607,"displaystyle":1916},[895,70062,70063,70065,70067,70069,70071,70073,70075,70077,70079,70085],{},[895,70064],{},[1750,70066,1766],{},[1742,70068,6419],{},[1750,70070,1758],{},[1742,70072,3079],{},[898,70074,12471],{},[1750,70076,1861],{},[1742,70078,7822],{},[1699,70080,70081,70083],{},[898,70082,12471],{},[1742,70084,1872],{},[898,70086,2313],{"mathvariant":1747},[902,70088,70089],{"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}",[724,70091,70092,70093,10951,70108,10951,70123,70138,70139,70154,70155,1343,70173,70154,70190,1343,70208,70154,70223,70241],{},"Význačné body ",[883,70094,70096],{"className":70095},[886],[888,70097,70098],{"xmlns":890},[892,70099,70100,70105],{},[895,70101,70102],{},[1742,70103,70104],{},"1,67",[902,70106,70107],{"encoding":904},"1{,}67",[883,70109,70111],{"className":70110},[886],[888,70112,70113],{"xmlns":890},[892,70114,70115,70120],{},[895,70116,70117],{},[1742,70118,70119],{},"2,50",[902,70121,70122],{"encoding":904},"2{,}50",[883,70124,70126],{"className":70125},[886],[888,70127,70128],{"xmlns":890},[892,70129,70130,70135],{},[895,70131,70132],{},[1742,70133,70134],{},"4,73",[902,70136,70137],{"encoding":904},"4{,}73"," odpovídají: ",[883,70140,70142],{"className":70141},[886],[888,70143,70144],{"xmlns":890},[892,70145,70146,70152],{},[895,70147,70148,70150],{},[898,70149,1773],{},[898,70151,1812],{},[902,70153,64215],{"encoding":904}," minimum v ",[883,70156,70158],{"className":70157},[886],[888,70159,70160],{"xmlns":890},[892,70161,70162,70170],{},[895,70163,70164,70166,70168],{},[898,70165,12471],{},[1750,70167,6792],{},[1742,70169,70104],{},[902,70171,70172],{"encoding":904},"Q \\doteq 1{,}67",[883,70174,70176],{"className":70175},[886],[888,70177,70178],{"xmlns":890},[892,70179,70180,70188],{},[895,70181,70182,70184,70186],{},[898,70183,13916],{},[898,70185,49262],{},[898,70187,1812],{},[902,70189,64234],{"encoding":904},[883,70191,70193],{"className":70192},[886],[888,70194,70195],{"xmlns":890},[892,70196,70197,70205],{},[895,70198,70199,70201,70203],{},[898,70200,12471],{},[1750,70202,1766],{},[1742,70204,70119],{},[902,70206,70207],{"encoding":904},"Q = 2{,}50",[883,70209,70211],{"className":70210},[886],[888,70212,70213],{"xmlns":890},[892,70214,70215,70221],{},[895,70216,70217,70219],{},[898,70218,13916],{},[898,70220,1812],{},[902,70222,64483],{"encoding":904},[883,70224,70226],{"className":70225},[886],[888,70227,70228],{"xmlns":890},[892,70229,70230,70238],{},[895,70231,70232,70234,70236],{},[898,70233,12471],{},[1750,70235,6792],{},[1742,70237,70134],{},[902,70239,70240],{"encoding":904},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[724,70243,70244],{},[4434,70245],{"alt":70246,"className":70247,"src":70248},"imek-ac-avc-mc",[210,4438],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[724,70250,70251],{},[614,70252,70253,70254,2028,70269,70286,70287,10951,70306,70321],{},"Obrázek 3.9: Kubické křivky ",[883,70255,70257],{"className":70256},[886],[888,70258,70259],{"xmlns":890},[892,70260,70261,70267],{},[895,70262,70263,70265],{},[898,70264,5326],{},[898,70266,1812],{},[902,70268,12916],{"encoding":904},[883,70270,70272],{"className":70271},[886],[888,70273,70274],{"xmlns":890},[892,70275,70276,70284],{},[895,70277,70278,70280,70282],{},[898,70279,5326],{},[898,70281,49262],{},[898,70283,1812],{},[902,70285,64432],{"encoding":904}," rostoucí od bodu ",[883,70288,70290],{"className":70289},[886],[888,70291,70292],{"xmlns":890},[892,70293,70294,70304],{},[895,70295,70296,70298,70300,70302],{},[898,70297,20069],{},[898,70299,1812],{},[1750,70301,1766],{},[1742,70303,4078],{},[902,70305,21266],{"encoding":904},[883,70307,70309],{"className":70308},[886],[888,70310,70311],{"xmlns":890},[892,70312,70313,70319],{},[895,70314,70315,70317],{},[898,70316,20069],{},[898,70318,1812],{},[902,70320,64414],{"encoding":904}," je vodorovná přímka.",[724,70323,70324],{},[614,70325,70326,70327,1343,70342,1343,70359,38124,70374,70387,70388,12605,70405,70420,70421,15838,70438,70453,70454,10062,70467,1343,70480,1343,70493,2313],{},"Obrázek 3.10: Křivky ",[883,70328,70330],{"className":70329},[886],[888,70331,70332],{"xmlns":890},[892,70333,70334,70340],{},[895,70335,70336,70338],{},[898,70337,13916],{},[898,70339,1812],{},[902,70341,64483],{"encoding":904},[883,70343,70345],{"className":70344},[886],[888,70346,70347],{"xmlns":890},[892,70348,70349,70357],{},[895,70350,70351,70353,70355],{},[898,70352,13916],{},[898,70354,49262],{},[898,70356,1812],{},[902,70358,64234],{"encoding":904},[883,70360,70362],{"className":70361},[886],[888,70363,70364],{"xmlns":890},[892,70365,70366,70372],{},[895,70367,70368,70370],{},[898,70369,1773],{},[898,70371,1812],{},[902,70373,64215],{"encoding":904},[883,70375,70377],{"className":70376},[886],[888,70378,70379],{"xmlns":890},[892,70380,70381,70385],{},[895,70382,70383],{},[898,70384,900],{},[902,70386,900],{"encoding":904}," a klesající hyperbola ",[883,70389,70391],{"className":70390},[886],[888,70392,70393],{"xmlns":890},[892,70394,70395,70403],{},[895,70396,70397,70399,70401],{},[898,70398,13916],{},[898,70400,20069],{},[898,70402,1812],{},[902,70404,64450],{"encoding":904},[883,70406,70408],{"className":70407},[886],[888,70409,70410],{"xmlns":890},[892,70411,70412,70418],{},[895,70413,70414,70416],{},[898,70415,1773],{},[898,70417,1812],{},[902,70419,64215],{"encoding":904}," protíná ",[883,70422,70424],{"className":70423},[886],[888,70425,70426],{"xmlns":890},[892,70427,70428,70436],{},[895,70429,70430,70432,70434],{},[898,70431,13916],{},[898,70433,49262],{},[898,70435,1812],{},[902,70437,64234],{"encoding":904},[883,70439,70441],{"className":70440},[886],[888,70442,70443],{"xmlns":890},[892,70444,70445,70451],{},[895,70446,70447,70449],{},[898,70448,13916],{},[898,70450,1812],{},[902,70452,64483],{"encoding":904}," zdola v jejich minimech; význačné hodnoty na ose ",[883,70455,70457],{"className":70456},[886],[888,70458,70459],{"xmlns":890},[892,70460,70461,70465],{},[895,70462,70463],{},[898,70464,12471],{},[902,70466,12471],{"encoding":904},[883,70468,70470],{"className":70469},[886],[888,70471,70472],{"xmlns":890},[892,70473,70474,70478],{},[895,70475,70476],{},[1742,70477,70104],{},[902,70479,70107],{"encoding":904},[883,70481,70483],{"className":70482},[886],[888,70484,70485],{"xmlns":890},[892,70486,70487,70491],{},[895,70488,70489],{},[1742,70490,70119],{},[902,70492,70122],{"encoding":904},[883,70494,70496],{"className":70495},[886],[888,70497,70498],{"xmlns":890},[892,70499,70500,70504],{},[895,70501,70502],{},[1742,70503,70134],{},[902,70505,70137],{"encoding":904},[724,70507,70508],{},[38,70509,70510],{},"Standardní vlastnosti:",[120,70512,70513,70548,70612,70680,70730,70750],{},[123,70514,70515,2028,70530,70547],{},[883,70516,70518],{"className":70517},[886],[888,70519,70520],{"xmlns":890},[892,70521,70522,70528],{},[895,70523,70524,70526],{},[898,70525,5326],{},[898,70527,1812],{},[902,70529,12916],{"encoding":904},[883,70531,70533],{"className":70532},[886],[888,70534,70535],{"xmlns":890},[892,70536,70537,70545],{},[895,70538,70539,70541,70543],{},[898,70540,5326],{},[898,70542,49262],{},[898,70544,1812],{},[902,70546,64432],{"encoding":904}," jsou kubické funkce;",[123,70549,70550,1343,70565,1343,70582,70597,70598,70611],{},[883,70551,70553],{"className":70552},[886],[888,70554,70555],{"xmlns":890},[892,70556,70557,70563],{},[895,70558,70559,70561],{},[898,70560,13916],{},[898,70562,1812],{},[902,70564,64483],{"encoding":904},[883,70566,70568],{"className":70567},[886],[888,70569,70570],{"xmlns":890},[892,70571,70572,70580],{},[895,70573,70574,70576,70578],{},[898,70575,13916],{},[898,70577,49262],{},[898,70579,1812],{},[902,70581,64234],{"encoding":904},[883,70583,70585],{"className":70584},[886],[888,70586,70587],{"xmlns":890},[892,70588,70589,70595],{},[895,70590,70591,70593],{},[898,70592,1773],{},[898,70594,1812],{},[902,70596,64215],{"encoding":904}," jsou křivky tvaru ",[883,70599,70601],{"className":70600},[886],[888,70602,70603],{"xmlns":890},[892,70604,70605,70609],{},[895,70606,70607],{},[898,70608,900],{},[902,70610,900],{"encoding":904}," (nejprve klesají, po minimu rostou);",[123,70613,70614,70629,70630,1343,70647,70664,70665,18067],{},[883,70615,70617],{"className":70616},[886],[888,70618,70619],{"xmlns":890},[892,70620,70621,70627],{},[895,70622,70623,70625],{},[898,70624,1773],{},[898,70626,1812],{},[902,70628,64215],{"encoding":904}," nabývá minima před ",[883,70631,70633],{"className":70632},[886],[888,70634,70635],{"xmlns":890},[892,70636,70637,70645],{},[895,70638,70639,70641,70643],{},[898,70640,13916],{},[898,70642,49262],{},[898,70644,1812],{},[902,70646,64234],{"encoding":904},[883,70648,70650],{"className":70649},[886],[888,70651,70652],{"xmlns":890},[892,70653,70654,70662],{},[895,70655,70656,70658,70660],{},[898,70657,13916],{},[898,70659,49262],{},[898,70661,1812],{},[902,70663,64234],{"encoding":904}," před ",[883,70666,70668],{"className":70667},[886],[888,70669,70670],{"xmlns":890},[892,70671,70672,70678],{},[895,70673,70674,70676],{},[898,70675,13916],{},[898,70677,1812],{},[902,70679,64483],{"encoding":904},[123,70681,70682,70420,70697,2028,70712,70729],{},[883,70683,70685],{"className":70684},[886],[888,70686,70687],{"xmlns":890},[892,70688,70689,70695],{},[895,70690,70691,70693],{},[898,70692,1773],{},[898,70694,1812],{},[902,70696,64215],{"encoding":904},[883,70698,70700],{"className":70699},[886],[888,70701,70702],{"xmlns":890},[892,70703,70704,70710],{},[895,70705,70706,70708],{},[898,70707,13916],{},[898,70709,1812],{},[902,70711,64483],{"encoding":904},[883,70713,70715],{"className":70714},[886],[888,70716,70717],{"xmlns":890},[892,70718,70719,70727],{},[895,70720,70721,70723,70725],{},[898,70722,13916],{},[898,70724,49262],{},[898,70726,1812],{},[902,70728,64234],{"encoding":904}," zdola právě v jejich minimech;",[123,70731,70732,70749],{},[883,70733,70735],{"className":70734},[886],[888,70736,70737],{"xmlns":890},[892,70738,70739,70747],{},[895,70740,70741,70743,70745],{},[898,70742,13916],{},[898,70744,20069],{},[898,70746,1812],{},[902,70748,64450],{"encoding":904}," je hyperbola, stále klesající;",[123,70751,70752,70784,70785,2028,70800,70817,70818,70831,70832,1783],{},[883,70753,70755],{"className":70754},[886],[888,70756,70757],{"xmlns":890},[892,70758,70759,70781],{},[895,70760,70761,70763,70765,70767,70769,70771,70773,70775,70777,70779],{},[898,70762,13916],{},[898,70764,1812],{},[1750,70766,1766],{},[898,70768,13916],{},[898,70770,20069],{},[898,70772,1812],{},[1750,70774,1861],{},[898,70776,13916],{},[898,70778,49262],{},[898,70780,1812],{},[902,70782,70783],{"encoding":904},"AC = AFC + AVC","; vzdálenost mezi ",[883,70786,70788],{"className":70787},[886],[888,70789,70790],{"xmlns":890},[892,70791,70792,70798],{},[895,70793,70794,70796],{},[898,70795,13916],{},[898,70797,1812],{},[902,70799,64483],{"encoding":904},[883,70801,70803],{"className":70802},[886],[888,70804,70805],{"xmlns":890},[892,70806,70807,70815],{},[895,70808,70809,70811,70813],{},[898,70810,13916],{},[898,70812,49262],{},[898,70814,1812],{},[902,70816,64234],{"encoding":904}," klesá s rostoucím ",[883,70819,70821],{"className":70820},[886],[888,70822,70823],{"xmlns":890},[892,70824,70825,70829],{},[895,70826,70827],{},[898,70828,12471],{},[902,70830,12471],{"encoding":904}," (protože ",[883,70833,70835],{"className":70834},[886],[888,70836,70837],{"xmlns":890},[892,70838,70839,70851],{},[895,70840,70841,70843,70845,70847,70849],{},[898,70842,13916],{},[898,70844,20069],{},[898,70846,1812],{},[1750,70848,12797],{},[1742,70850,2607],{},[902,70852,70853],{"encoding":904},"AFC \\to 0",[115,70855,70857],{"id":70856},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[724,70859,70860,70861,70864,70865,70880],{},"Častou optimalizační úlohou je ",[38,70862,70863],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[883,70866,70868],{"className":70867},[886],[888,70869,70870],{"xmlns":890},[892,70871,70872,70878],{},[895,70873,70874,70876],{},[898,70875,13916],{},[898,70877,1812],{},[902,70879,64483],{"encoding":904}," minimální.",[198,70882,25985],{"id":25984},[724,70884,70885,70886,70903],{},"Mají-li průměrné náklady minimum v bodě ",[883,70887,70889],{"className":70888},[886],[888,70890,70891],{"xmlns":890},[892,70892,70893,70901],{},[895,70894,70895],{},[5535,70896,70897,70899],{},[898,70898,12471],{},[1742,70900,2607],{},[902,70902,47231],{"encoding":904},", pak platí",[883,70905,70907],{"className":70906},[886],[888,70908,70909],{"xmlns":890,"display":36989},[892,70910,70911,70960],{},[4577,70912,70913],{"width":36994},[4582,70914,70915,70917,70953,70955],{},[4585,70916],{"width":36999},[4585,70918,70919],{},[895,70920,70921,70923,70925,70927,70933,70935,70937,70939,70941,70943,70949,70951],{},[898,70922,13916],{},[898,70924,1812],{},[1750,70926,1753],{"stretchy":1752},[5535,70928,70929,70931],{},[898,70930,12471],{},[1742,70932,2607],{},[1750,70934,1763],{"stretchy":1752},[1750,70936,1766],{},[898,70938,1773],{},[898,70940,1812],{},[1750,70942,1753],{"stretchy":1752},[5535,70944,70945,70947],{},[898,70946,12471],{},[1742,70948,2607],{},[1750,70950,1763],{"stretchy":1752},[898,70952,2313],{"mathvariant":1747},[4585,70954],{"width":36999},[4585,70956,70957],{},[1969,70958,70959],{},"(3.10)",[902,70961,70962],{"encoding":904},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1785,70964,70965],{},[724,70966,70967,70969,70970],{},[883,70968,65367],{}," Princip\n",[38,70971,70972],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[724,70974,70975,70978,70979,71021],{},[38,70976,70977],{},"Odvození."," Z ",[883,70980,70982],{"className":70981},[886],[888,70983,70984],{"xmlns":890},[892,70985,70986,71018],{},[895,70987,70988,70990,70992,70994,70996,70998,71000],{},[898,70989,13916],{},[898,70991,1812],{},[1750,70993,1753],{"stretchy":1752},[898,70995,12471],{},[1750,70997,1763],{"stretchy":1752},[1750,70999,1766],{},[3586,71001,71002],{"scriptlevel":2607,"displaystyle":1752},[3423,71003,71004,71016],{},[895,71005,71006,71008,71010,71012,71014],{},[898,71007,5326],{},[898,71009,1812],{},[1750,71011,1753],{"stretchy":1752},[898,71013,12471],{},[1750,71015,1763],{"stretchy":1752},[898,71017,12471],{},[902,71019,71020],{"encoding":904},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[883,71023,71025],{"className":71024},[886],[888,71026,71027],{"xmlns":890,"display":36989},[892,71028,71029,71161],{},[895,71030,71031,71033,71039,71041,71043,71045,71047,71087,71089,71129,71131,71159],{},[898,71032,13916],{},[1699,71034,71035,71037],{},[898,71036,1812],{},[1750,71038,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,71040,1753],{"stretchy":1752},[898,71042,12471],{},[1750,71044,1763],{"stretchy":1752},[1750,71046,1766],{},[3423,71048,71049,71081],{},[895,71050,71051,71053,71059,71061,71063,71065,71067,71069,71071,71073,71075,71077,71079],{},[898,71052,5326],{},[1699,71054,71055,71057],{},[898,71056,1812],{},[1750,71058,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,71060,1753],{"stretchy":1752},[898,71062,12471],{},[1750,71064,1763],{"stretchy":1752},[1750,71066,8009],{},[898,71068,12471],{},[1750,71070,1758],{},[898,71072,5326],{},[898,71074,1812],{},[1750,71076,1753],{"stretchy":1752},[898,71078,12471],{},[1750,71080,1763],{"stretchy":1752},[1699,71082,71083,71085],{},[898,71084,12471],{},[1742,71086,1872],{},[1750,71088,1766],{},[3423,71090,71091,71123],{},[895,71092,71093,71095,71097,71099,71101,71103,71105,71107,71109,71111,71113,71115,71117,71119,71121],{},[898,71094,1773],{},[898,71096,1812],{},[1750,71098,1753],{"stretchy":1752},[898,71100,12471],{},[1750,71102,1763],{"stretchy":1752},[1750,71104,8009],{},[898,71106,12471],{},[1750,71108,1758],{},[898,71110,13916],{},[898,71112,1812],{},[1750,71114,1753],{"stretchy":1752},[898,71116,12471],{},[1750,71118,1763],{"stretchy":1752},[1750,71120,8009],{},[898,71122,12471],{},[1699,71124,71125,71127],{},[898,71126,12471],{},[1742,71128,1872],{},[1750,71130,1766],{},[3423,71132,71133,71157],{},[895,71134,71135,71137,71139,71141,71143,71145,71147,71149,71151,71153,71155],{},[898,71136,1773],{},[898,71138,1812],{},[1750,71140,1753],{"stretchy":1752},[898,71142,12471],{},[1750,71144,1763],{"stretchy":1752},[1750,71146,1758],{},[898,71148,13916],{},[898,71150,1812],{},[1750,71152,1753],{"stretchy":1752},[898,71154,12471],{},[1750,71156,1763],{"stretchy":1752},[898,71158,12471],{},[898,71160,2313],{"mathvariant":1747},[902,71162,71163],{"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}.",[724,71165,71166,71167,2984,71182,2433,71204,65744],{},"Nutnou podmínkou minima ",[883,71168,71170],{"className":71169},[886],[888,71171,71172],{"xmlns":890},[892,71173,71174,71180],{},[895,71175,71176,71178],{},[898,71177,13916],{},[898,71179,1812],{},[902,71181,64483],{"encoding":904},[883,71183,71185],{"className":71184},[886],[888,71186,71187],{"xmlns":890},[892,71188,71189,71201],{},[895,71190,71191,71197,71199],{},[5535,71192,71193,71195],{},[898,71194,12471],{},[1742,71196,2607],{},[1750,71198,2604],{},[1742,71200,2607],{},[902,71202,71203],{"encoding":904},"Q_0 > 0",[883,71205,71207],{"className":71206},[886],[888,71208,71209],{"xmlns":890},[892,71210,71211,71235],{},[895,71212,71213,71215,71221,71223,71229,71231,71233],{},[898,71214,13916],{},[1699,71216,71217,71219],{},[898,71218,1812],{},[1750,71220,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,71222,1753],{"stretchy":1752},[5535,71224,71225,71227],{},[898,71226,12471],{},[1742,71228,2607],{},[1750,71230,1763],{"stretchy":1752},[1750,71232,1766],{},[1742,71234,2607],{},[902,71236,71237],{"encoding":904},"AC'(Q_0) = 0",[883,71239,71241],{"className":71240},[886],[888,71242,71243],{"xmlns":890,"display":36989},[892,71244,71245,71330],{},[895,71246,71247,71287,71289,71291,71293,71296,71298,71300,71302,71304,71310,71312,71314,71316,71318,71320,71326,71328],{},[3423,71248,71249,71281],{},[895,71250,71251,71253,71255,71257,71263,71265,71267,71269,71271,71273,71279],{},[898,71252,1773],{},[898,71254,1812],{},[1750,71256,1753],{"stretchy":1752},[5535,71258,71259,71261],{},[898,71260,12471],{},[1742,71262,2607],{},[1750,71264,1763],{"stretchy":1752},[1750,71266,1758],{},[898,71268,13916],{},[898,71270,1812],{},[1750,71272,1753],{"stretchy":1752},[5535,71274,71275,71277],{},[898,71276,12471],{},[1742,71278,2607],{},[1750,71280,1763],{"stretchy":1752},[5535,71282,71283,71285],{},[898,71284,12471],{},[1742,71286,2607],{},[1750,71288,1766],{},[1742,71290,2607],{},[2125,71292],{"width":24875},[1750,71294,71295],{},"⟺",[2125,71297],{"width":24875},[898,71299,1773],{},[898,71301,1812],{},[1750,71303,1753],{"stretchy":1752},[5535,71305,71306,71308],{},[898,71307,12471],{},[1742,71309,2607],{},[1750,71311,1763],{"stretchy":1752},[1750,71313,1766],{},[898,71315,13916],{},[898,71317,1812],{},[1750,71319,1753],{"stretchy":1752},[5535,71321,71322,71324],{},[898,71323,12471],{},[1742,71325,2607],{},[1750,71327,1763],{"stretchy":1752},[898,71329,2313],{"mathvariant":1747},[902,71331,71332],{"encoding":904},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[724,71334,71335,1647,71338,70420,71353,71368,71369,71384,71385,2433,71402,71424,71425,71447],{},[38,71336,71337],{},"Geometrická interpretace.",[883,71339,71341],{"className":71340},[886],[888,71342,71343],{"xmlns":890},[892,71344,71345,71351],{},[895,71346,71347,71349],{},[898,71348,1773],{},[898,71350,1812],{},[902,71352,64215],{"encoding":904},[883,71354,71356],{"className":71355},[886],[888,71357,71358],{"xmlns":890},[892,71359,71360,71366],{},[895,71361,71362,71364],{},[898,71363,13916],{},[898,71365,1812],{},[902,71367,64483],{"encoding":904}," právě v bodě minima ",[883,71370,71372],{"className":71371},[886],[888,71373,71374],{"xmlns":890},[892,71375,71376,71382],{},[895,71377,71378,71380],{},[898,71379,13916],{},[898,71381,1812],{},[902,71383,64483],{"encoding":904}," (obrázek 3.10); nalevo od ",[883,71386,71388],{"className":71387},[886],[888,71389,71390],{"xmlns":890},[892,71391,71392,71400],{},[895,71393,71394],{},[5535,71395,71396,71398],{},[898,71397,12471],{},[1742,71399,2607],{},[902,71401,47231],{"encoding":904},[883,71403,71405],{"className":71404},[886],[888,71406,71407],{"xmlns":890},[892,71408,71409,71421],{},[895,71410,71411,71413,71415,71417,71419],{},[898,71412,1773],{},[898,71414,1812],{},[1750,71416,2624],{},[898,71418,13916],{},[898,71420,1812],{},[902,71422,71423],{"encoding":904},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[883,71426,71428],{"className":71427},[886],[888,71429,71430],{"xmlns":890},[892,71431,71432,71444],{},[895,71433,71434,71436,71438,71440,71442],{},[898,71435,1773],{},[898,71437,1812],{},[1750,71439,2604],{},[898,71441,13916],{},[898,71443,1812],{},[902,71445,71446],{"encoding":904},"MC > AC"," (průměrné náklady rostou).",[724,71449,71450,71451,71493,71494,71511,71512,2313],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[883,71452,71454],{"className":71453},[886],[888,71455,71456],{"xmlns":890},[892,71457,71458,71490],{},[895,71459,71460,71462,71464,71466,71472,71474,71476,71478,71480,71482,71488],{},[898,71461,13916],{},[898,71463,1812],{},[1750,71465,1753],{"stretchy":1752},[5535,71467,71468,71470],{},[898,71469,12471],{},[1742,71471,2607],{},[1750,71473,1763],{"stretchy":1752},[1750,71475,1766],{},[898,71477,1773],{},[898,71479,1812],{},[1750,71481,1753],{"stretchy":1752},[5535,71483,71484,71486],{},[898,71485,12471],{},[1742,71487,2607],{},[1750,71489,1763],{"stretchy":1752},[902,71491,71492],{"encoding":904},"AC(Q_0) = MC(Q_0)",", pak ",[883,71495,71497],{"className":71496},[886],[888,71498,71499],{"xmlns":890},[892,71500,71501,71509],{},[895,71502,71503],{},[5535,71504,71505,71507],{},[898,71506,12471],{},[1742,71508,2607],{},[902,71510,47231],{"encoding":904}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[883,71513,71515],{"className":71514},[886],[888,71516,71517],{"xmlns":890},[892,71518,71519,71543],{},[895,71520,71521,71523,71525,71527,71529,71531,71533,71535,71537,71539,71541],{},[898,71522,13916],{},[898,71524,1812],{},[1750,71526,1753],{"stretchy":1752},[898,71528,12471],{},[1750,71530,1763],{"stretchy":1752},[1750,71532,1766],{},[898,71534,1773],{},[898,71536,1812],{},[1750,71538,1753],{"stretchy":1752},[898,71540,12471],{},[1750,71542,1763],{"stretchy":1752},[902,71544,71545],{"encoding":904},"AC(Q) = MC(Q)",[1785,71547,71548],{},[724,71549,71550,71552,71553,20027,71571,71592,71593,20027,71596,71617,71618,71633,71634,66961,71649,1783],{},[883,71551,5454],{}," Pozor — neplést s principem maxima zisku\nPro ",[38,71554,71555,71556],{},"minimum ",[883,71557,71559],{"className":71558},[886],[888,71560,71561],{"xmlns":890},[892,71562,71563,71569],{},[895,71564,71565,71567],{},[898,71566,13916],{},[898,71568,1812],{},[902,71570,64483],{"encoding":904},[883,71572,71574],{"className":71573},[886],[888,71575,71576],{"xmlns":890},[892,71577,71578,71590],{},[895,71579,71580,71582,71584,71586,71588],{},[898,71581,13916],{},[898,71583,1812],{},[1750,71585,1766],{},[898,71587,1773],{},[898,71589,1812],{},[902,71591,64146],{"encoding":904},", pro ",[38,71594,71595],{},"maximum zisku",[883,71597,71599],{"className":71598},[886],[888,71600,71601],{"xmlns":890},[892,71602,71603,71615],{},[895,71604,71605,71607,71609,71611,71613],{},[898,71606,1773],{},[898,71608,13658],{},[1750,71610,1766],{},[898,71612,1773],{},[898,71614,1812],{},[902,71616,64194],{"encoding":904},". Obě podmínky využívají ",[883,71619,71621],{"className":71620},[886],[888,71622,71623],{"xmlns":890},[892,71624,71625,71631],{},[895,71626,71627,71629],{},[898,71628,1773],{},[898,71630,1812],{},[902,71632,64215],{"encoding":904},", ale rovnají ho rozdílným veličinám (",[883,71635,71637],{"className":71636},[886],[888,71638,71639],{"xmlns":890},[892,71640,71641,71647],{},[895,71642,71643,71645],{},[898,71644,13916],{},[898,71646,1812],{},[902,71648,64483],{"encoding":904},[883,71650,71652],{"className":71651},[886],[888,71653,71654],{"xmlns":890},[892,71655,71656,71662],{},[895,71657,71658,71660],{},[898,71659,1773],{},[898,71661,13658],{},[902,71663,16282],{"encoding":904},[46271,71665,71667],{"id":71666},"příklad-37","Příklad 3.7",[724,71669,71670,66445,71672,71706,71707,71720,71721,71736],{},[38,71671,64910],{},[883,71673,71675],{"className":71674},[886],[888,71676,71677],{"xmlns":890},[892,71678,71679,71703],{},[895,71680,71681,71683,71685,71687,71693,71695,71697,71699,71701],{},[898,71682,5326],{},[898,71684,1812],{},[1750,71686,1766],{},[1699,71688,71689,71691],{},[898,71690,12471],{},[1742,71692,1872],{},[1750,71694,1861],{},[1742,71696,7822],{},[898,71698,12471],{},[1750,71700,1861],{},[1742,71702,15219],{},[902,71704,71705],{"encoding":904},"TC = Q^2 + 3Q + 36"," najděte ",[883,71708,71710],{"className":71709},[886],[888,71711,71712],{"xmlns":890},[892,71713,71714,71718],{},[895,71715,71716],{},[898,71717,12471],{},[902,71719,12471],{"encoding":904}," minimalizující ",[883,71722,71724],{"className":71723},[886],[888,71725,71726],{"xmlns":890},[892,71727,71728,71734],{},[895,71729,71730,71732],{},[898,71731,13916],{},[898,71733,1812],{},[902,71735,64483],{"encoding":904}," a ověřte princip (3.10).",[724,71738,71739,71741],{},[38,71740,6610],{}," Přímý výpočet:",[883,71743,71745],{"className":71744},[886],[888,71746,71747],{"xmlns":890,"display":36989},[892,71748,71749,71851],{},[895,71750,71751,71753,71755,71757,71779,71781,71783,71785,71787,71789,71795,71797,71799,71801,71803,71805,71811,71813,71815,71817,71827,71829,71849],{},[898,71752,13916],{},[898,71754,1812],{},[1750,71756,1766],{},[3423,71758,71759,71777],{},[895,71760,71761,71767,71769,71771,71773,71775],{},[1699,71762,71763,71765],{},[898,71764,12471],{},[1742,71766,1872],{},[1750,71768,1861],{},[1742,71770,7822],{},[898,71772,12471],{},[1750,71774,1861],{},[1742,71776,15219],{},[898,71778,12471],{},[1750,71780,1766],{},[898,71782,12471],{},[1750,71784,1861],{},[1742,71786,7822],{},[1750,71788,1861],{},[3423,71790,71791,71793],{},[1742,71792,15219],{},[898,71794,12471],{},[1750,71796,1917],{"separator":1916},[2125,71798],{"width":2127},[1750,71800,1753],{"stretchy":1752},[898,71802,13916],{},[898,71804,1812],{},[1699,71806,71807,71809],{},[1750,71808,1763],{"stretchy":1752},[1750,71810,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,71812,1766],{},[1742,71814,1744],{},[1750,71816,1758],{},[3423,71818,71819,71821],{},[1742,71820,15219],{},[1699,71822,71823,71825],{},[898,71824,12471],{},[1742,71826,1872],{},[1750,71828,1766],{},[3423,71830,71831,71843],{},[895,71832,71833,71839,71841],{},[1699,71834,71835,71837],{},[898,71836,12471],{},[1742,71838,1872],{},[1750,71840,1758],{},[1742,71842,15219],{},[1699,71844,71845,71847],{},[898,71846,12471],{},[1742,71848,1872],{},[898,71850,2313],{"mathvariant":1747},[902,71852,71853],{"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}.",[724,71855,71856,71896,71897,71921,71922,71972,71973,2313],{},[883,71857,71859],{"className":71858},[886],[888,71860,71861],{"xmlns":890},[892,71862,71863,71893],{},[895,71864,71865,71867,71869,71871,71877,71879,71881,71883,71889,71891],{},[1750,71866,1753],{"stretchy":1752},[898,71868,13916],{},[898,71870,1812],{},[1699,71872,71873,71875],{},[1750,71874,1763],{"stretchy":1752},[1750,71876,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,71878,1766],{},[1742,71880,2607],{},[1750,71882,13651],{},[5535,71884,71885,71887],{},[898,71886,12471],{},[1742,71888,1744],{},[1750,71890,1766],{},[1742,71892,3219],{},[902,71894,71895],{"encoding":904},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[883,71898,71900],{"className":71899},[886],[888,71901,71902],{"xmlns":890},[892,71903,71904,71918],{},[895,71905,71906,71912,71914,71916],{},[5535,71907,71908,71910],{},[898,71909,12471],{},[1742,71911,1872],{},[1750,71913,1766],{},[1750,71915,1758],{},[1742,71917,3219],{},[902,71919,71920],{"encoding":904},"Q_2 = -6"," (vyloučeno). ",[883,71923,71925],{"className":71924},[886],[888,71926,71927],{"xmlns":890},[892,71928,71929,71969],{},[895,71930,71931,71933,71935,71937,71947,71949,71951,71953,71955,71963,71965,71967],{},[1750,71932,1753],{"stretchy":1752},[898,71934,13916],{},[898,71936,1812],{},[1699,71938,71939,71941],{},[1750,71940,1763],{"stretchy":1752},[895,71942,71943,71945],{},[1750,71944,3815],{"mathvariant":1747},[1750,71946,3815],{"mathvariant":1747},[1750,71948,1753],{"stretchy":1752},[1742,71950,3219],{},[1750,71952,1763],{"stretchy":1752},[1750,71954,1766],{},[3586,71956,71957],{"scriptlevel":2607,"displaystyle":1752},[3423,71958,71959,71961],{},[1742,71960,1744],{},[1742,71962,7822],{},[1750,71964,2604],{},[1742,71966,2607],{},[1750,71968,13651],{},[902,71970,71971],{"encoding":904},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[883,71974,71976],{"className":71975},[886],[888,71977,71978],{"xmlns":890},[892,71979,71980,71996],{},[895,71981,71982,71984,71986,71988,71990,71992,71994],{},[898,71983,13916],{},[898,71985,1812],{},[1750,71987,1753],{"stretchy":1752},[1742,71989,3219],{},[1750,71991,1763],{"stretchy":1752},[1750,71993,1766],{},[1742,71995,45167],{},[902,71997,71998],{"encoding":904},"AC(6) = 15",[724,72000,72001,72002,72028,72029,2366],{},"Pomocí principu: ",[883,72003,72005],{"className":72004},[886],[888,72006,72007],{"xmlns":890},[892,72008,72009,72025],{},[895,72010,72011,72013,72015,72017,72019,72021,72023],{},[898,72012,1773],{},[898,72014,1812],{},[1750,72016,1766],{},[1742,72018,1872],{},[898,72020,12471],{},[1750,72022,1861],{},[1742,72024,7822],{},[902,72026,72027],{"encoding":904},"MC = 2Q + 3",", rovnice ",[883,72030,72032],{"className":72031},[886],[888,72033,72034],{"xmlns":890},[892,72035,72036,72048],{},[895,72037,72038,72040,72042,72044,72046],{},[898,72039,13916],{},[898,72041,1812],{},[1750,72043,1766],{},[898,72045,1773],{},[898,72047,1812],{},[902,72049,64146],{"encoding":904},[883,72051,72053],{"className":72052},[886],[888,72054,72055],{"xmlns":890,"display":36989},[892,72056,72057,72159],{},[895,72058,72059,72081,72083,72085,72087,72089,72091,72093,72095,72097,72103,72105,72107,72109,72111,72113,72115,72117,72123,72125,72127,72129,72131,72133,72135,72141,72143,72145,72147,72149,72151,72153,72155,72157],{},[3423,72060,72061,72079],{},[895,72062,72063,72069,72071,72073,72075,72077],{},[1699,72064,72065,72067],{},[898,72066,12471],{},[1742,72068,1872],{},[1750,72070,1861],{},[1742,72072,7822],{},[898,72074,12471],{},[1750,72076,1861],{},[1742,72078,15219],{},[898,72080,12471],{},[1750,72082,1766],{},[1742,72084,1872],{},[898,72086,12471],{},[1750,72088,1861],{},[1742,72090,7822],{},[1969,72092,6766],{},[1750,72094,13651],{},[1969,72096,6766],{},[1699,72098,72099,72101],{},[898,72100,12471],{},[1742,72102,1872],{},[1750,72104,1861],{},[1742,72106,7822],{},[898,72108,12471],{},[1750,72110,1861],{},[1742,72112,15219],{},[1750,72114,1766],{},[1742,72116,1872],{},[1699,72118,72119,72121],{},[898,72120,12471],{},[1742,72122,1872],{},[1750,72124,1861],{},[1742,72126,7822],{},[898,72128,12471],{},[1969,72130,6766],{},[1750,72132,13651],{},[1969,72134,6766],{},[1699,72136,72137,72139],{},[898,72138,12471],{},[1742,72140,1872],{},[1750,72142,1766],{},[1742,72144,15219],{},[1969,72146,6766],{},[1750,72148,13651],{},[1969,72150,6766],{},[898,72152,12471],{},[1750,72154,1766],{},[1742,72156,3219],{},[1750,72158,1917],{"separator":1916},[902,72160,72161],{"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,",[724,72163,72164,72165,72203],{},"a ",[883,72166,72168],{"className":72167},[886],[888,72169,72170],{"xmlns":890},[892,72171,72172,72200],{},[895,72173,72174,72176,72178,72180,72182,72184,72186,72188,72190,72192,72194,72196,72198],{},[898,72175,13916],{},[898,72177,1812],{},[1750,72179,1753],{"stretchy":1752},[1742,72181,3219],{},[1750,72183,1763],{"stretchy":1752},[1750,72185,1766],{},[898,72187,1773],{},[898,72189,1812],{},[1750,72191,1753],{"stretchy":1752},[1742,72193,3219],{},[1750,72195,1763],{"stretchy":1752},[1750,72197,1766],{},[1742,72199,45167],{},[902,72201,72202],{"encoding":904},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[198,72205,72207],{"id":72206},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[724,72209,72210,72211,2366],{},"Analogicky pro ",[883,72212,72214],{"className":72213},[886],[888,72215,72216],{"xmlns":890},[892,72217,72218,72226],{},[895,72219,72220,72222,72224],{},[898,72221,13916],{},[898,72223,49262],{},[898,72225,1812],{},[902,72227,64234],{"encoding":904},[883,72229,72231],{"className":72230},[886],[888,72232,72233],{"xmlns":890,"display":36989},[892,72234,72235,72286],{},[4577,72236,72237],{"width":36994},[4582,72238,72239,72241,72279,72281],{},[4585,72240],{"width":36999},[4585,72242,72243],{},[895,72244,72245,72247,72249,72251,72253,72259,72261,72263,72265,72267,72269,72275,72277],{},[898,72246,13916],{},[898,72248,49262],{},[898,72250,1812],{},[1750,72252,1753],{"stretchy":1752},[5535,72254,72255,72257],{},[898,72256,12471],{},[1742,72258,2607],{},[1750,72260,1763],{"stretchy":1752},[1750,72262,1766],{},[898,72264,1773],{},[898,72266,1812],{},[1750,72268,1753],{"stretchy":1752},[5535,72270,72271,72273],{},[898,72272,12471],{},[1742,72274,2607],{},[1750,72276,1763],{"stretchy":1752},[898,72278,2313],{"mathvariant":1747},[4585,72280],{"width":36999},[4585,72282,72283],{},[1969,72284,72285],{},"(3.11)",[902,72287,72288],{"encoding":904},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1785,72290,72291],{},[724,72292,72293,70969,72295],{},[883,72294,65367],{},[38,72296,72297,72298,72315],{},"V bodě minima průměrných variabilních nákladů se ",[883,72299,72301],{"className":72300},[886],[888,72302,72303],{"xmlns":890},[892,72304,72305,72313],{},[895,72306,72307,72309,72311],{},[898,72308,13916],{},[898,72310,49262],{},[898,72312,1812],{},[902,72314,64234],{"encoding":904}," rovnají mezním nákladům.",[724,72317,72318,72319,72341,72342,2313],{},"Odvození je analogické (úloha 3.14). V obrázku 3.10 odpovídá ",[883,72320,72322],{"className":72321},[886],[888,72323,72324],{"xmlns":890},[892,72325,72326,72338],{},[895,72327,72328,72334,72336],{},[5535,72329,72330,72332],{},[898,72331,12471],{},[1742,72333,2607],{},[1750,72335,1766],{},[1742,72337,62122],{},[902,72339,72340],{"encoding":904},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[883,72343,72345],{"className":72344},[886],[888,72346,72347],{"xmlns":890},[892,72348,72349,72375],{},[895,72350,72351,72353,72355,72357,72359,72361,72363,72365,72367,72369,72371,72373],{},[898,72352,13916],{},[898,72354,49262],{},[898,72356,1812],{},[1750,72358,1753],{"stretchy":1752},[898,72360,12471],{},[1750,72362,1763],{"stretchy":1752},[1750,72364,1766],{},[898,72366,1773],{},[898,72368,1812],{},[1750,72370,1753],{"stretchy":1752},[898,72372,12471],{},[1750,72374,1763],{"stretchy":1752},[902,72376,72377],{"encoding":904},"AVC(Q) = MC(Q)",[115,72379,72381],{"id":72380},"zisk-a-body-zvratu","Zisk a body zvratu",[724,72383,72384,1647,72387,72403],{},[38,72385,72386],{},"Zisk",[883,72388,72390],{"className":72389},[886],[888,72391,72392],{"xmlns":890},[892,72393,72394,72400],{},[895,72395,72396,72398],{},[898,72397,1776],{},[898,72399,13658],{},[902,72401,72402],{"encoding":904},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[883,72405,72407],{"className":72406},[886],[888,72408,72409],{"xmlns":890,"display":36989},[892,72410,72411,72470],{},[4577,72412,72413],{"width":36994},[4582,72414,72415,72417,72463,72465],{},[4585,72416],{"width":36999},[4585,72418,72419],{},[895,72420,72421,72423,72425,72427,72429,72431,72433,72435,72437,72439,72441,72443,72445,72447,72449,72451,72453,72455,72457,72459,72461],{},[898,72422,1776],{},[898,72424,13658],{},[1750,72426,1766],{},[898,72428,1776],{},[898,72430,13658],{},[1750,72432,1753],{"stretchy":1752},[898,72434,12471],{},[1750,72436,1763],{"stretchy":1752},[1750,72438,1766],{},[898,72440,5326],{},[898,72442,13658],{},[1750,72444,1753],{"stretchy":1752},[898,72446,12471],{},[1750,72448,1763],{"stretchy":1752},[1750,72450,1758],{},[898,72452,5326],{},[898,72454,1812],{},[1750,72456,1753],{"stretchy":1752},[898,72458,12471],{},[1750,72460,1763],{"stretchy":1752},[898,72462,2313],{"mathvariant":1747},[4585,72464],{"width":36999},[4585,72466,72467],{},[1969,72468,72469],{},"(3.12)",[902,72471,72472],{"encoding":904},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[724,72474,72475,72476,2028,72491,52559,72506,72508,72509,72512,72513,72529,72530,72545,72546,72561,72562,1343,72575,72588,72589,1343,72607,72625,72626,2084,72629,72632,72633,1348,72655,2433,72677,72699,72700,2433,72730,72752],{},"Body rovnosti ",[883,72477,72479],{"className":72478},[886],[888,72480,72481],{"xmlns":890},[892,72482,72483,72489],{},[895,72484,72485,72487],{},[898,72486,5326],{},[898,72488,13658],{},[902,72490,13758],{"encoding":904},[883,72492,72494],{"className":72493},[886],[888,72495,72496],{"xmlns":890},[892,72497,72498,72504],{},[895,72499,72500,72502],{},[898,72501,5326],{},[898,72503,1812],{},[902,72505,12916],{"encoding":904},[38,72507,64650],{}," (též vyrovnání, ",[614,72510,72511],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[883,72514,72516],{"className":72515},[886],[888,72517,72518],{"xmlns":890},[892,72519,72520,72526],{},[895,72521,72522,72524],{},[898,72523,49262],{},[898,72525,1812],{},[902,72527,72528],{"encoding":904},"VC",") je ",[883,72531,72533],{"className":72532},[886],[888,72534,72535],{"xmlns":890},[892,72536,72537,72543],{},[895,72538,72539,72541],{},[898,72540,5326],{},[898,72542,13658],{},[902,72544,13758],{"encoding":904}," kvadratická a ",[883,72547,72549],{"className":72548},[886],[888,72550,72551],{"xmlns":890},[892,72552,72553,72559],{},[895,72554,72555,72557],{},[898,72556,5326],{},[898,72558,1812],{},[902,72560,12916],{"encoding":904}," lineární (obrázek 3.11). Křivky se protínají v bodech ",[883,72563,72565],{"className":72564},[886],[888,72566,72567],{"xmlns":890},[892,72568,72569,72573],{},[895,72570,72571],{},[898,72572,13916],{},[902,72574,13916],{"encoding":904},[883,72576,72578],{"className":72577},[886],[888,72579,72580],{"xmlns":890},[892,72581,72582,72586],{},[895,72583,72584],{},[898,72585,7097],{},[902,72587,7097],{"encoding":904}," odpovídajících množstvím ",[883,72590,72592],{"className":72591},[886],[888,72593,72594],{"xmlns":890},[892,72595,72596,72604],{},[895,72597,72598],{},[5535,72599,72600,72602],{},[898,72601,12471],{},[898,72603,13916],{},[902,72605,72606],{"encoding":904},"Q_A",[883,72608,72610],{"className":72609},[886],[888,72611,72612],{"xmlns":890},[892,72613,72614,72622],{},[895,72615,72616],{},[5535,72617,72618,72620],{},[898,72619,12471],{},[898,72621,7097],{},[902,72623,72624],{"encoding":904},"Q_B"," — firma je na ",[38,72627,72628],{},"prahu rentability",[614,72630,72631],{},"break even","). Pro ",[883,72634,72636],{"className":72635},[886],[888,72637,72638],{"xmlns":890},[892,72639,72640,72652],{},[895,72641,72642,72644,72646],{},[898,72643,12471],{},[1750,72645,2624],{},[5535,72647,72648,72650],{},[898,72649,12471],{},[898,72651,13916],{},[902,72653,72654],{"encoding":904},"Q \u003C Q_A",[883,72656,72658],{"className":72657},[886],[888,72659,72660],{"xmlns":890},[892,72661,72662,72674],{},[895,72663,72664,72666,72668],{},[898,72665,12471],{},[1750,72667,2604],{},[5535,72669,72670,72672],{},[898,72671,12471],{},[898,72673,7097],{},[902,72675,72676],{"encoding":904},"Q > Q_B",[883,72678,72680],{"className":72679},[886],[888,72681,72682],{"xmlns":890},[892,72683,72684,72696],{},[895,72685,72686,72688,72690,72692,72694],{},[898,72687,5326],{},[898,72689,1812],{},[1750,72691,2604],{},[898,72693,5326],{},[898,72695,13658],{},[902,72697,72698],{"encoding":904},"TC > TR"," (ztráta); pro ",[883,72701,72703],{"className":72702},[886],[888,72704,72705],{"xmlns":890},[892,72706,72707,72727],{},[895,72708,72709,72715,72717,72719,72721],{},[5535,72710,72711,72713],{},[898,72712,12471],{},[898,72714,13916],{},[1750,72716,2624],{},[898,72718,12471],{},[1750,72720,2624],{},[5535,72722,72723,72725],{},[898,72724,12471],{},[898,72726,7097],{},[902,72728,72729],{"encoding":904},"Q_A \u003C Q \u003C Q_B",[883,72731,72733],{"className":72732},[886],[888,72734,72735],{"xmlns":890},[892,72736,72737,72749],{},[895,72738,72739,72741,72743,72745,72747],{},[898,72740,5326],{},[898,72742,13658],{},[1750,72744,2604],{},[898,72746,5326],{},[898,72748,1812],{},[902,72750,72751],{"encoding":904},"TR > TC"," (zisk).",[1785,72754,72755],{},[724,72756,72757,72759],{},[883,72758,1791],{}," 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.",[724,72761,72762,72763,72789],{},"Body zvratu jsou řešení rovnice ",[883,72764,72766],{"className":72765},[886],[888,72767,72768],{"xmlns":890},[892,72769,72770,72786],{},[895,72771,72772,72774,72776,72778,72780,72782,72784],{},[898,72773,1776],{},[898,72775,13658],{},[1750,72777,1753],{"stretchy":1752},[898,72779,12471],{},[1750,72781,1763],{"stretchy":1752},[1750,72783,1766],{},[1742,72785,2607],{},[902,72787,72788],{"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.",[724,72791,72792],{},[4434,72793],{"alt":72794,"className":72795,"src":72796},"imek-tr-tc-body-zvratu",[210,4438],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[724,72798,72799],{},[614,72800,72801,72802,72817,72818,72833,72834,2028,72847,52283,72860,72873,72874,2028,72891,72908,72909,72929,72930,2028,72945,16121,72960,72989],{},"Obrázek 3.11: Body zvratu — křivky ",[883,72803,72805],{"className":72804},[886],[888,72806,72807],{"xmlns":890},[892,72808,72809,72815],{},[895,72810,72811,72813],{},[898,72812,5326],{},[898,72814,13658],{},[902,72816,13758],{"encoding":904}," (obrácená parabola) a ",[883,72819,72821],{"className":72820},[886],[888,72822,72823],{"xmlns":890},[892,72824,72825,72831],{},[895,72826,72827,72829],{},[898,72828,5326],{},[898,72830,1812],{},[902,72832,12916],{"encoding":904}," (přímka) se protínají v bodech ",[883,72835,72837],{"className":72836},[886],[888,72838,72839],{"xmlns":890},[892,72840,72841,72845],{},[895,72842,72843],{},[898,72844,13916],{},[902,72846,13916],{"encoding":904},[883,72848,72850],{"className":72849},[886],[888,72851,72852],{"xmlns":890},[892,72853,72854,72858],{},[895,72855,72856],{},[898,72857,7097],{},[902,72859,7097],{"encoding":904},[883,72861,72863],{"className":72862},[886],[888,72864,72865],{"xmlns":890},[892,72866,72867,72871],{},[895,72868,72869],{},[898,72870,12471],{},[902,72872,12471],{"encoding":904}," v hodnotách ",[883,72875,72877],{"className":72876},[886],[888,72878,72879],{"xmlns":890},[892,72880,72881,72889],{},[895,72882,72883],{},[5535,72884,72885,72887],{},[898,72886,12471],{},[898,72888,13916],{},[902,72890,72606],{"encoding":904},[883,72892,72894],{"className":72893},[886],[888,72895,72896],{"xmlns":890},[892,72897,72898,72906],{},[895,72899,72900],{},[5535,72901,72902,72904],{},[898,72903,12471],{},[898,72905,7097],{},[902,72907,72624],{"encoding":904},"; maximum zisku leží mezi nimi v bodě ",[883,72910,72912],{"className":72911},[886],[888,72913,72914],{"xmlns":890},[892,72915,72916,72926],{},[895,72917,72918],{},[5535,72919,72920,72922,72924],{},[898,72921,12471],{},[898,72923,65120],{},[1750,72925,65123],{},[902,72927,72928],{"encoding":904},"Q_{\\max}","; svislá vzdálenost mezi ",[883,72931,72933],{"className":72932},[886],[888,72934,72935],{"xmlns":890},[892,72936,72937,72943],{},[895,72938,72939,72941],{},[898,72940,5326],{},[898,72942,13658],{},[902,72944,13758],{"encoding":904},[883,72946,72948],{"className":72947},[886],[888,72949,72950],{"xmlns":890},[892,72951,72952,72958],{},[895,72953,72954,72956],{},[898,72955,5326],{},[898,72957,1812],{},[902,72959,12916],{"encoding":904},[883,72961,72963],{"className":72962},[886],[888,72964,72965],{"xmlns":890},[892,72966,72967,72987],{},[895,72968,72969,72975,72977,72979,72981],{},[5535,72970,72971,72973],{},[898,72972,12471],{},[898,72974,13916],{},[1750,72976,2624],{},[898,72978,12471],{},[1750,72980,2624],{},[5535,72982,72983,72985],{},[898,72984,12471],{},[898,72986,7097],{},[902,72988,72729],{"encoding":904}," vyznačuje zisk.",[46271,72991,72993],{"id":72992},"příklad-38","Příklad 3.8",[724,72995,72996,72998,72999,1343,73019,1343,73045,73071],{},[38,72997,64910],{}," Dáno ",[883,73000,73002],{"className":73001},[886],[888,73003,73004],{"xmlns":890},[892,73005,73006,73016],{},[895,73007,73008,73010,73012,73014],{},[898,73009,20069],{},[898,73011,1812],{},[1750,73013,1766],{},[1742,73015,7859],{},[902,73017,73018],{"encoding":904},"FC = 4",[883,73020,73022],{"className":73021},[886],[888,73023,73024],{"xmlns":890},[892,73025,73026,73042],{},[895,73027,73028,73030,73032,73034,73036],{},[898,73029,5326],{},[898,73031,49262],{},[898,73033,1812],{},[1750,73035,1766],{},[1699,73037,73038,73040],{},[898,73039,12471],{},[1742,73041,1872],{},[902,73043,73044],{"encoding":904},"TVC = Q^2",[883,73046,73048],{"className":73047},[886],[888,73049,73050],{"xmlns":890},[892,73051,73052,73068],{},[895,73053,73054,73056,73058,73060,73062,73064,73066],{},[898,73055,1776],{},[1750,73057,1766],{},[1750,73059,1758],{},[1742,73061,1872],{},[898,73063,12471],{},[1750,73065,1861],{},[1742,73067,13663],{},[902,73069,73070],{"encoding":904},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[724,73073,73074,73076],{},[38,73075,6610],{}," Celkové náklady a příjem:",[883,73078,73080],{"className":73079},[886],[888,73081,73082],{"xmlns":890,"display":36989},[892,73083,73084,73150],{},[895,73085,73086,73088,73090,73092,73094,73096,73102,73104,73106,73108,73110,73112,73114,73116,73118,73120,73122,73124,73126,73128,73130,73132,73134,73136,73142,73144,73146,73148],{},[898,73087,5326],{},[898,73089,1812],{},[1750,73091,1766],{},[1742,73093,7859],{},[1750,73095,1861],{},[1699,73097,73098,73100],{},[898,73099,12471],{},[1742,73101,1872],{},[1750,73103,1917],{"separator":1916},[2125,73105],{"width":2127},[898,73107,5326],{},[898,73109,13658],{},[1750,73111,1766],{},[898,73113,12471],{},[1750,73115,8009],{},[1750,73117,1753],{"stretchy":1752},[1750,73119,1758],{},[1742,73121,1872],{},[898,73123,12471],{},[1750,73125,1861],{},[1742,73127,13663],{},[1750,73129,1763],{"stretchy":1752},[1750,73131,1766],{},[1750,73133,1758],{},[1742,73135,1872],{},[1699,73137,73138,73140],{},[898,73139,12471],{},[1742,73141,1872],{},[1750,73143,1861],{},[1742,73145,13663],{},[898,73147,12471],{},[898,73149,2313],{"mathvariant":1747},[902,73151,73152],{"encoding":904},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[724,73154,73155],{},"Zisk dle (3.12):",[883,73157,73159],{"className":73158},[886],[888,73160,73161],{"xmlns":890,"display":36989},[892,73162,73163,73241],{},[895,73164,73165,73167,73169,73171,73173,73175,73177,73179,73181,73183,73185,73187,73189,73195,73197,73199,73201,73203,73205,73207,73209,73211,73217,73219,73221,73223,73225,73231,73233,73235,73237,73239],{},[898,73166,1776],{},[898,73168,13658],{},[1750,73170,1766],{},[898,73172,5326],{},[898,73174,13658],{},[1750,73176,1758],{},[898,73178,5326],{},[898,73180,1812],{},[1750,73182,1766],{},[1750,73184,1753],{"stretchy":1752},[1750,73186,1758],{},[1742,73188,1872],{},[1699,73190,73191,73193],{},[898,73192,12471],{},[1742,73194,1872],{},[1750,73196,1861],{},[1742,73198,13663],{},[898,73200,12471],{},[1750,73202,1763],{"stretchy":1752},[1750,73204,1758],{},[1750,73206,1753],{"stretchy":1752},[1742,73208,7859],{},[1750,73210,1861],{},[1699,73212,73213,73215],{},[898,73214,12471],{},[1742,73216,1872],{},[1750,73218,1763],{"stretchy":1752},[1750,73220,1766],{},[1750,73222,1758],{},[1742,73224,7822],{},[1699,73226,73227,73229],{},[898,73228,12471],{},[1742,73230,1872],{},[1750,73232,1861],{},[1742,73234,13663],{},[898,73236,12471],{},[1750,73238,1758],{},[1742,73240,68242],{},[902,73242,73243],{"encoding":904},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[724,73245,73246,73249,73250,27149,73286,2366],{},[38,73247,73248],{},"Body zvratu"," jsou kořeny rovnice ",[883,73251,73253],{"className":73252},[886],[888,73254,73255],{"xmlns":890},[892,73256,73257,73283],{},[895,73258,73259,73261,73263,73269,73271,73273,73275,73277,73279,73281],{},[1750,73260,1758],{},[1742,73262,7822],{},[1699,73264,73265,73267],{},[898,73266,12471],{},[1742,73268,1872],{},[1750,73270,1861],{},[1742,73272,13663],{},[898,73274,12471],{},[1750,73276,1758],{},[1742,73278,7859],{},[1750,73280,1766],{},[1742,73282,2607],{},[902,73284,73285],{"encoding":904},"-3Q^2 + 9Q - 4 = 0",[883,73287,73289],{"className":73288},[886],[888,73290,73291],{"xmlns":890},[892,73292,73293,73317],{},[895,73294,73295,73297,73303,73305,73307,73309,73311,73313,73315],{},[1742,73296,7822],{},[1699,73298,73299,73301],{},[898,73300,12471],{},[1742,73302,1872],{},[1750,73304,1758],{},[1742,73306,13663],{},[898,73308,12471],{},[1750,73310,1861],{},[1742,73312,7859],{},[1750,73314,1766],{},[1742,73316,2607],{},[902,73318,73319],{"encoding":904},"3Q^2 - 9Q + 4 = 0",[883,73321,73323],{"className":73322},[886],[888,73324,73325],{"xmlns":890,"display":36989},[892,73326,73327,73384],{},[895,73328,73329,73341,73343,73366,73368,73382],{},[5535,73330,73331,73333],{},[898,73332,12471],{},[895,73334,73335,73337,73339],{},[1742,73336,1744],{},[1750,73338,1917],{"separator":1916},[1742,73340,1872],{},[1750,73342,1766],{},[3423,73344,73345,73364],{},[895,73346,73347,73349,73352],{},[1742,73348,13663],{},[1750,73350,73351],{},"±",[17761,73353,73354],{},[895,73355,73356,73359,73361],{},[1742,73357,73358],{},"81",[1750,73360,1758],{},[1742,73362,73363],{},"48",[1742,73365,3219],{},[1750,73367,1766],{},[3423,73369,73370,73380],{},[895,73371,73372,73374,73376],{},[1742,73373,13663],{},[1750,73375,73351],{},[17761,73377,73378],{},[1742,73379,18591],{},[1742,73381,3219],{},[1750,73383,1917],{"separator":1916},[902,73385,73386],{"encoding":904},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[724,73388,73389,73390,2028,73413,2313],{},"numericky ",[883,73391,73393],{"className":73392},[886],[888,73394,73395],{"xmlns":890},[892,73396,73397,73410],{},[895,73398,73399,73405,73407],{},[5535,73400,73401,73403],{},[898,73402,12471],{},[1742,73404,1744],{},[1750,73406,6792],{},[1742,73408,73409],{},"0,543",[902,73411,73412],{"encoding":904},"Q_1 \\doteq 0{,}543",[883,73414,73416],{"className":73415},[886],[888,73417,73418],{"xmlns":890},[892,73419,73420,73433],{},[895,73421,73422,73428,73430],{},[5535,73423,73424,73426],{},[898,73425,12471],{},[1742,73427,1872],{},[1750,73429,6792],{},[1742,73431,73432],{},"2,457",[902,73434,73435],{"encoding":904},"Q_2 \\doteq 2{,}457",[724,73437,73438,1647,73441,17199,73486,27149,73520,73538],{},[38,73439,73440],{},"Maximum zisku.",[883,73442,73444],{"className":73443},[886],[888,73445,73446],{"xmlns":890},[892,73447,73448,73483],{},[895,73449,73450,73452,73458,73460,73462,73464,73466,73468,73470,73472,73474,73476,73478,73480],{},[898,73451,1776],{},[1699,73453,73454,73456],{},[898,73455,13658],{},[1750,73457,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,73459,1766],{},[1750,73461,1758],{},[1742,73463,3219],{},[898,73465,12471],{},[1750,73467,1861],{},[1742,73469,13663],{},[1750,73471,1766],{},[1742,73473,2607],{},[1750,73475,13651],{},[898,73477,12471],{},[1750,73479,1766],{},[1742,73481,73482],{},"1,5",[902,73484,73485],{"encoding":904},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[883,73487,73489],{"className":73488},[886],[888,73490,73491],{"xmlns":890},[892,73492,73493,73517],{},[895,73494,73495,73497,73507,73509,73511,73513,73515],{},[898,73496,1776],{},[1699,73498,73499,73501],{},[898,73500,13658],{},[895,73502,73503,73505],{},[1750,73504,3815],{"mathvariant":1747},[1750,73506,3815],{"mathvariant":1747},[1750,73508,1766],{},[1750,73510,1758],{},[1742,73512,3219],{},[1750,73514,2624],{},[1742,73516,2607],{},[902,73518,73519],{"encoding":904},"PR'' = -6 \u003C 0",[883,73521,73523],{"className":73522},[886],[888,73524,73525],{"xmlns":890},[892,73526,73527,73535],{},[895,73528,73529,73531,73533],{},[898,73530,12471],{},[1750,73532,1766],{},[1742,73534,73482],{},[902,73536,73537],{"encoding":904},"Q = 1{,}5"," je bod maxima s hodnotou",[883,73540,73542],{"className":73541},[886],[888,73543,73544],{"xmlns":890,"display":36989},[892,73545,73546,73609],{},[895,73547,73548,73550,73552,73554,73556,73558,73560,73562,73564,73566,73568,73570,73576,73578,73580,73582,73584,73586,73588,73590,73592,73595,73597,73600,73602,73604,73606],{},[898,73549,1776],{},[898,73551,13658],{},[1750,73553,1753],{"stretchy":1752},[1742,73555,73482],{},[1750,73557,1763],{"stretchy":1752},[1750,73559,1766],{},[1750,73561,1758],{},[1742,73563,7822],{},[1750,73565,8009],{},[1750,73567,1753],{"stretchy":1752},[1742,73569,73482],{},[1699,73571,73572,73574],{},[1750,73573,1763],{"stretchy":1752},[1742,73575,1872],{},[1750,73577,1861],{},[1742,73579,13663],{},[1750,73581,8009],{},[1742,73583,73482],{},[1750,73585,1758],{},[1742,73587,7859],{},[1750,73589,1766],{},[1750,73591,1758],{},[1742,73593,73594],{},"6,75",[1750,73596,1861],{},[1742,73598,73599],{},"13,5",[1750,73601,1758],{},[1742,73603,7859],{},[1750,73605,1766],{},[1742,73607,73608],{},"2,75.",[902,73610,73611],{"encoding":904},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[724,73613,73614,73615,1343,73660,73713,73714,73732],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[883,73616,73618],{"className":73617},[886],[888,73619,73620],{"xmlns":890},[892,73621,73622,73657],{},[895,73623,73624,73626,73632,73634,73636,73638,73640,73642,73644,73646,73648,73650,73652,73654],{},[898,73625,5326],{},[1699,73627,73628,73630],{},[898,73629,13658],{},[1750,73631,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,73633,1766],{},[1750,73635,1758],{},[1742,73637,7859],{},[898,73639,12471],{},[1750,73641,1861],{},[1742,73643,13663],{},[1750,73645,1766],{},[1742,73647,2607],{},[1750,73649,13651],{},[898,73651,12471],{},[1750,73653,1766],{},[1742,73655,73656],{},"2,25",[902,73658,73659],{"encoding":904},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[883,73661,73663],{"className":73662},[886],[888,73664,73665],{"xmlns":890},[892,73666,73667,73710],{},[895,73668,73669,73671,73679,73681,73683,73685,73687,73689,73691,73697,73699,73701,73703,73705,73707],{},[898,73670,5326],{},[5535,73672,73673,73675,73677],{},[898,73674,13658],{},[898,73676,65120],{},[1750,73678,65123],{},[1750,73680,1766],{},[1750,73682,1758],{},[1742,73684,1872],{},[1750,73686,8009],{},[1750,73688,1753],{"stretchy":1752},[1742,73690,73656],{},[1699,73692,73693,73695],{},[1750,73694,1763],{"stretchy":1752},[1742,73696,1872],{},[1750,73698,1861],{},[1742,73700,13663],{},[1750,73702,8009],{},[1742,73704,73656],{},[1750,73706,1766],{},[1742,73708,73709],{},"10,125",[902,73711,73712],{"encoding":904},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[883,73715,73717],{"className":73716},[886],[888,73718,73719],{"xmlns":890},[892,73720,73721,73729],{},[895,73722,73723,73725,73727],{},[898,73724,12471],{},[1750,73726,1766],{},[1742,73728,73656],{},[902,73730,73731],{"encoding":904},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1785,73734,73735],{},[724,73736,73737,73739,73740,1343,73762,73784,73785,1343,73802,73823,73824,73856,73857,73895,73896,12359,73914,73931,73932,2028,73960,73994,73995,4776,74033,2028,74057,2313],{},[883,73738,5454],{}," Nekonzistence v původním zdroji\nSkenovaný knižní text obsahoval v tomto příkladu dvě nesourodé hodnoty: uváděl body zvratu ",[883,73741,73743],{"className":73742},[886],[888,73744,73745],{"xmlns":890},[892,73746,73747,73759],{},[895,73748,73749,73755,73757],{},[5535,73750,73751,73753],{},[898,73752,12471],{},[1742,73754,1744],{},[1750,73756,1766],{},[1742,73758,4268],{},[902,73760,73761],{"encoding":904},"Q_1 = 0{,}5",[883,73763,73765],{"className":73764},[886],[888,73766,73767],{"xmlns":890},[892,73768,73769,73781],{},[895,73770,73771,73777,73779],{},[5535,73772,73773,73775],{},[898,73774,12471],{},[1742,73776,1872],{},[1750,73778,1766],{},[1742,73780,7859],{},[902,73782,73783],{"encoding":904},"Q_2 = 4"," (odpovídající starší verzi zadání) a zároveň maximum v ",[883,73786,73788],{"className":73787},[886],[888,73789,73790],{"xmlns":890},[892,73791,73792,73800],{},[895,73793,73794,73796,73798],{},[898,73795,12471],{},[1750,73797,1766],{},[1742,73799,73656],{},[902,73801,73731],{"encoding":904},[883,73803,73805],{"className":73804},[886],[888,73806,73807],{"xmlns":890},[892,73808,73809,73820],{},[895,73810,73811,73813,73815,73817],{},[898,73812,1776],{},[898,73814,13658],{},[1750,73816,1766],{},[1742,73818,73819],{},"6,125",[902,73821,73822],{"encoding":904},"PR = 6{,}125"," (odpovídající derivaci ",[883,73825,73827],{"className":73826},[886],[888,73828,73829],{"xmlns":890},[892,73830,73831,73853],{},[895,73832,73833,73835,73841,73843,73845,73847,73849,73851],{},[898,73834,1776],{},[1699,73836,73837,73839],{},[898,73838,13658],{},[1750,73840,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,73842,1766],{},[1750,73844,1758],{},[1742,73846,7859],{},[898,73848,12471],{},[1750,73850,1861],{},[1742,73852,13663],{},[902,73854,73855],{"encoding":904},"PR' = -4Q + 9",", tj. zisku ",[883,73858,73860],{"className":73859},[886],[888,73861,73862],{"xmlns":890},[892,73863,73864,73892],{},[895,73865,73866,73868,73870,73872,73874,73876,73882,73884,73886,73888,73890],{},[898,73867,1776],{},[898,73869,13658],{},[1750,73871,1766],{},[1750,73873,1758],{},[1742,73875,1872],{},[1699,73877,73878,73880],{},[898,73879,12471],{},[1742,73881,1872],{},[1750,73883,1861],{},[1742,73885,13663],{},[898,73887,12471],{},[1750,73889,1758],{},[1742,73891,7859],{},[902,73893,73894],{"encoding":904},"PR = -2Q^2 + 9Q - 4"," bez odčtení kvadratického členu ",[883,73897,73899],{"className":73898},[886],[888,73900,73901],{"xmlns":890},[892,73902,73903,73911],{},[895,73904,73905],{},[1699,73906,73907,73909],{},[898,73908,12471],{},[1742,73910,1872],{},[902,73912,73913],{"encoding":904},"Q^2",[883,73915,73917],{"className":73916},[886],[888,73918,73919],{"xmlns":890},[892,73920,73921,73929],{},[895,73922,73923,73925,73927],{},[898,73924,5326],{},[898,73926,49262],{},[898,73928,1812],{},[902,73930,64432],{"encoding":904},"). Zde je uvedena matematicky konzistentní verze: zadané ",[883,73933,73935],{"className":73934},[886],[888,73936,73937],{"xmlns":890},[892,73938,73939,73957],{},[895,73940,73941,73943,73945,73947,73949,73951],{},[898,73942,5326],{},[898,73944,1812],{},[1750,73946,1766],{},[1742,73948,7859],{},[1750,73950,1861],{},[1699,73952,73953,73955],{},[898,73954,12471],{},[1742,73956,1872],{},[902,73958,73959],{"encoding":904},"TC = 4 + Q^2",[883,73961,73963],{"className":73962},[886],[888,73964,73965],{"xmlns":890},[892,73966,73967,73991],{},[895,73968,73969,73971,73973,73975,73977,73979,73985,73987,73989],{},[898,73970,5326],{},[898,73972,13658],{},[1750,73974,1766],{},[1750,73976,1758],{},[1742,73978,1872],{},[1699,73980,73981,73983],{},[898,73982,12471],{},[1742,73984,1872],{},[1750,73986,1861],{},[1742,73988,13663],{},[898,73990,12471],{},[902,73992,73993],{"encoding":904},"TR = -2Q^2 + 9Q"," vedou na ",[883,73996,73998],{"className":73997},[886],[888,73999,74000],{"xmlns":890},[892,74001,74002,74030],{},[895,74003,74004,74006,74008,74010,74012,74014,74020,74022,74024,74026,74028],{},[898,74005,1776],{},[898,74007,13658],{},[1750,74009,1766],{},[1750,74011,1758],{},[1742,74013,7822],{},[1699,74015,74016,74018],{},[898,74017,12471],{},[1742,74019,1872],{},[1750,74021,1861],{},[1742,74023,13663],{},[898,74025,12471],{},[1750,74027,1758],{},[1742,74029,7859],{},[902,74031,74032],{"encoding":904},"PR = -3Q^2 + 9Q - 4",[883,74034,74036],{"className":74035},[886],[888,74037,74038],{"xmlns":890},[892,74039,74040,74054],{},[895,74041,74042,74050,74052],{},[5535,74043,74044,74046,74048],{},[898,74045,12471],{},[898,74047,65120],{},[1750,74049,65123],{},[1750,74051,1766],{},[1742,74053,73482],{},[902,74055,74056],{"encoding":904},"Q_{\\max} = 1{,}5",[883,74058,74060],{"className":74059},[886],[888,74061,74062],{"xmlns":890},[892,74063,74064,74081],{},[895,74065,74066,74068,74076,74078],{},[898,74067,1776],{},[5535,74069,74070,74072,74074],{},[898,74071,13658],{},[898,74073,65120],{},[1750,74075,65123],{},[1750,74077,1766],{},[1742,74079,74080],{},"2,75",[902,74082,74083],{"encoding":904},"PR_{\\max} = 2{,}75",[724,74085,74086],{},[614,74087,74088,74089,74116,74117,74150,74151,1343,74174,2313],{},"Obrázek 3.12: Graf ",[883,74090,74092],{"className":74091},[886],[888,74093,74094],{"xmlns":890},[892,74095,74096,74114],{},[895,74097,74098,74100,74102,74104,74106,74108],{},[898,74099,5326],{},[898,74101,1812],{},[1750,74103,1766],{},[1742,74105,7859],{},[1750,74107,1861],{},[1699,74109,74110,74112],{},[898,74111,12471],{},[1742,74113,1872],{},[902,74115,73959],{"encoding":904}," (parabola) a ",[883,74118,74120],{"className":74119},[886],[888,74121,74122],{"xmlns":890},[892,74123,74124,74148],{},[895,74125,74126,74128,74130,74132,74134,74136,74142,74144,74146],{},[898,74127,5326],{},[898,74129,13658],{},[1750,74131,1766],{},[1750,74133,1758],{},[1742,74135,1872],{},[1699,74137,74138,74140],{},[898,74139,12471],{},[1742,74141,1872],{},[1750,74143,1861],{},[1742,74145,13663],{},[898,74147,12471],{},[902,74149,73993],{"encoding":904}," (parabola); průsečíky vyznačují body zvratu ",[883,74152,74154],{"className":74153},[886],[888,74155,74156],{"xmlns":890},[892,74157,74158,74171],{},[895,74159,74160,74166,74168],{},[5535,74161,74162,74164],{},[898,74163,12471],{},[1742,74165,1744],{},[1750,74167,6792],{},[1742,74169,74170],{},"0,54",[902,74172,74173],{"encoding":904},"Q_1 \\doteq 0{,}54",[883,74175,74177],{"className":74176},[886],[888,74178,74179],{"xmlns":890},[892,74180,74181,74194],{},[895,74182,74183,74189,74191],{},[5535,74184,74185,74187],{},[898,74186,12471],{},[1742,74188,1872],{},[1750,74190,6792],{},[1742,74192,74193],{},"2,46",[902,74195,74196],{"encoding":904},"Q_2 \\doteq 2{,}46",[724,74198,74199],{},[614,74200,74201,74202,67430,74239,74256,74257,1343,74278,2313],{},"Obrázek 3.13: Graf zisku ",[883,74203,74205],{"className":74204},[886],[888,74206,74207],{"xmlns":890},[892,74208,74209,74237],{},[895,74210,74211,74213,74215,74217,74219,74221,74227,74229,74231,74233,74235],{},[898,74212,1776],{},[898,74214,13658],{},[1750,74216,1766],{},[1750,74218,1758],{},[1742,74220,7822],{},[1699,74222,74223,74225],{},[898,74224,12471],{},[1742,74226,1872],{},[1750,74228,1861],{},[1742,74230,13663],{},[898,74232,12471],{},[1750,74234,1758],{},[1742,74236,7859],{},[902,74238,74032],{"encoding":904},[883,74240,74242],{"className":74241},[886],[888,74243,74244],{"xmlns":890},[892,74245,74246,74254],{},[895,74247,74248,74250,74252],{},[898,74249,12471],{},[1750,74251,1766],{},[1742,74253,73482],{},[902,74255,73537],{"encoding":904}," a nulami ",[883,74258,74260],{"className":74259},[886],[888,74261,74262],{"xmlns":890},[892,74263,74264,74276],{},[895,74265,74266,74272,74274],{},[5535,74267,74268,74270],{},[898,74269,12471],{},[1742,74271,1744],{},[1750,74273,6792],{},[1742,74275,74170],{},[902,74277,74173],{"encoding":904},[883,74279,74281],{"className":74280},[886],[888,74282,74283],{"xmlns":890},[892,74284,74285,74297],{},[895,74286,74287,74293,74295],{},[5535,74288,74289,74291],{},[898,74290,12471],{},[1742,74292,1872],{},[1750,74294,6792],{},[1742,74296,74193],{},[902,74298,74196],{"encoding":904},[115,74300,74302],{"id":74301},"princip-maximalizace-zisku","Princip maximalizace zisku",[724,74304,74305],{},"Kromě standardního hledání extrému lze využít následující princip.",[724,74307,74308],{},[4434,74309],{"alt":74310,"className":74311,"src":74312},"imek-max-zisku-dva-pohledy",[210,4438],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[198,74314,25985],{"id":74315},"princip-1",[724,74317,74318,74319,2984,74334,74351],{},"Má-li zisk ",[883,74320,74322],{"className":74321},[886],[888,74323,74324],{"xmlns":890},[892,74325,74326,74332],{},[895,74327,74328,74330],{},[898,74329,1776],{},[898,74331,13658],{},[902,74333,72402],{"encoding":904},[883,74335,74337],{"className":74336},[886],[888,74338,74339],{"xmlns":890},[892,74340,74341,74349],{},[895,74342,74343],{},[5535,74344,74345,74347],{},[898,74346,12471],{},[1742,74348,2607],{},[902,74350,47231],{"encoding":904}," maximum, pak platí",[883,74353,74355],{"className":74354},[886],[888,74356,74357],{"xmlns":890,"display":36989},[892,74358,74359,74408],{},[4577,74360,74361],{"width":36994},[4582,74362,74363,74365,74401,74403],{},[4585,74364],{"width":36999},[4585,74366,74367],{},[895,74368,74369,74371,74373,74375,74381,74383,74385,74387,74389,74391,74397,74399],{},[898,74370,1773],{},[898,74372,13658],{},[1750,74374,1753],{"stretchy":1752},[5535,74376,74377,74379],{},[898,74378,12471],{},[1742,74380,2607],{},[1750,74382,1763],{"stretchy":1752},[1750,74384,1766],{},[898,74386,1773],{},[898,74388,1812],{},[1750,74390,1753],{"stretchy":1752},[5535,74392,74393,74395],{},[898,74394,12471],{},[1742,74396,2607],{},[1750,74398,1763],{"stretchy":1752},[898,74400,2313],{"mathvariant":1747},[4585,74402],{"width":36999},[4585,74404,74405],{},[1969,74406,74407],{},"(3.13)",[902,74409,74410],{"encoding":904},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1785,74412,74413],{},[724,74414,74415,70969,74417],{},[883,74416,65367],{},[38,74418,74419],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[724,74421,74422,74425,74426,2433,74453,27149,74527,2313],{},[38,74423,74424],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[883,74427,74429],{"className":74428},[886],[888,74430,74431],{"xmlns":890},[892,74432,74433,74451],{},[895,74434,74435,74437,74439,74441,74443,74445,74447,74449],{},[898,74436,1776],{},[898,74438,13658],{},[1750,74440,1766],{},[898,74442,5326],{},[898,74444,13658],{},[1750,74446,1758],{},[898,74448,5326],{},[898,74450,1812],{},[902,74452,64123],{"encoding":904},[883,74454,74456],{"className":74455},[886],[888,74457,74458],{"xmlns":890},[892,74459,74460,74524],{},[895,74461,74462,74464,74470,74472,74478,74480,74482,74484,74490,74492,74498,74500,74502,74504,74510,74512,74518,74520,74522],{},[898,74463,1776],{},[1699,74465,74466,74468],{},[898,74467,13658],{},[1750,74469,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,74471,1753],{"stretchy":1752},[5535,74473,74474,74476],{},[898,74475,12471],{},[1742,74477,2607],{},[1750,74479,1763],{"stretchy":1752},[1750,74481,1766],{},[898,74483,5326],{},[1699,74485,74486,74488],{},[898,74487,13658],{},[1750,74489,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,74491,1753],{"stretchy":1752},[5535,74493,74494,74496],{},[898,74495,12471],{},[1742,74497,2607],{},[1750,74499,1763],{"stretchy":1752},[1750,74501,1758],{},[898,74503,5326],{},[1699,74505,74506,74508],{},[898,74507,1812],{},[1750,74509,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,74511,1753],{"stretchy":1752},[5535,74513,74514,74516],{},[898,74515,12471],{},[1742,74517,2607],{},[1750,74519,1763],{"stretchy":1752},[1750,74521,1766],{},[1742,74523,2607],{},[902,74525,74526],{"encoding":904},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[883,74528,74530],{"className":74529},[886],[888,74531,74532],{"xmlns":890},[892,74533,74534,74566],{},[895,74535,74536,74538,74540,74542,74548,74550,74552,74554,74556,74558,74564],{},[898,74537,1773],{},[898,74539,13658],{},[1750,74541,1753],{"stretchy":1752},[5535,74543,74544,74546],{},[898,74545,12471],{},[1742,74547,2607],{},[1750,74549,1763],{"stretchy":1752},[1750,74551,1766],{},[898,74553,1773],{},[898,74555,1812],{},[1750,74557,1753],{"stretchy":1752},[5535,74559,74560,74562],{},[898,74561,12471],{},[1742,74563,2607],{},[1750,74565,1763],{"stretchy":1752},[902,74567,74568],{"encoding":904},"MR(Q_0) = MC(Q_0)",[1785,74570,74571,74576],{},[724,74572,74573,74575],{},[883,74574,6004],{}," Postup — jak najít maximum zisku",[152,74577,74578,74642,74697,74734,74762],{},[123,74579,74580,74581,2028,74596,74611,74612,1783],{},"Sestavte ",[883,74582,74584],{"className":74583},[886],[888,74585,74586],{"xmlns":890},[892,74587,74588,74594],{},[895,74589,74590,74592],{},[898,74591,5326],{},[898,74593,13658],{},[902,74595,13758],{"encoding":904},[883,74597,74599],{"className":74598},[886],[888,74600,74601],{"xmlns":890},[892,74602,74603,74609],{},[895,74604,74605,74607],{},[898,74606,5326],{},[898,74608,1812],{},[902,74610,12916],{"encoding":904}," ze zadání (typicky ",[883,74613,74615],{"className":74614},[886],[888,74616,74617],{"xmlns":890},[892,74618,74619,74639],{},[895,74620,74621,74623,74625,74627,74629,74631,74633,74635,74637],{},[898,74622,5326],{},[898,74624,13658],{},[1750,74626,1766],{},[898,74628,1776],{},[1750,74630,1753],{"stretchy":1752},[898,74632,12471],{},[1750,74634,1763],{"stretchy":1752},[1750,74636,8009],{},[898,74638,12471],{},[902,74640,74641],{"encoding":904},"TR = P(Q) \\cdot Q",[123,74643,74644,74645,2028,74671,2313],{},"Vypočtěte ",[883,74646,74648],{"className":74647},[886],[888,74649,74650],{"xmlns":890},[892,74651,74652,74668],{},[895,74653,74654,74656,74658,74660,74662],{},[898,74655,1773],{},[898,74657,13658],{},[1750,74659,1766],{},[898,74661,5326],{},[1699,74663,74664,74666],{},[898,74665,13658],{},[1750,74667,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,74669,74670],{"encoding":904},"MR = TR'",[883,74672,74674],{"className":74673},[886],[888,74675,74676],{"xmlns":890},[892,74677,74678,74694],{},[895,74679,74680,74682,74684,74686,74688],{},[898,74681,1773],{},[898,74683,1812],{},[1750,74685,1766],{},[898,74687,5326],{},[1699,74689,74690,74692],{},[898,74691,1812],{},[1750,74693,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,74695,74696],{"encoding":904},"MC = TC'",[123,74698,74699,74700,2313],{},"Řešte rovnici ",[883,74701,74703],{"className":74702},[886],[888,74704,74705],{"xmlns":890},[892,74706,74707,74731],{},[895,74708,74709,74711,74713,74715,74717,74719,74721,74723,74725,74727,74729],{},[898,74710,1773],{},[898,74712,13658],{},[1750,74714,1753],{"stretchy":1752},[898,74716,12471],{},[1750,74718,1763],{"stretchy":1752},[1750,74720,1766],{},[898,74722,1773],{},[898,74724,1812],{},[1750,74726,1753],{"stretchy":1752},[898,74728,12471],{},[1750,74730,1763],{"stretchy":1752},[902,74732,74733],{"encoding":904},"MR(Q) = MC(Q)",[123,74735,74736,74737,74761],{},"Ověřte druhou derivaci ",[883,74738,74740],{"className":74739},[886],[888,74741,74742],{"xmlns":890},[892,74743,74744,74758],{},[895,74745,74746,74748],{},[898,74747,1776],{},[1699,74749,74750,74752],{},[898,74751,13658],{},[895,74753,74754,74756],{},[1750,74755,3815],{"mathvariant":1747},[1750,74757,3815],{"mathvariant":1747},[902,74759,74760],{"encoding":904},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[123,74763,74764,74765,74792],{},"Dosaďte do ",[883,74766,74768],{"className":74767},[886],[888,74769,74770],{"xmlns":890},[892,74771,74772,74790],{},[895,74773,74774,74776,74778,74780,74782,74784,74786,74788],{},[898,74775,1776],{},[898,74777,13658],{},[1750,74779,1766],{},[898,74781,5326],{},[898,74783,13658],{},[1750,74785,1758],{},[898,74787,5326],{},[898,74789,1812],{},[902,74791,64123],{"encoding":904}," pro hodnotu maxima.",[46271,74794,74796],{"id":74795},"příklad-39","Příklad 3.9",[724,74798,74799,64911,74801,2028,74823,74859],{},[38,74800,64910],{},[883,74802,74804],{"className":74803},[886],[888,74805,74806],{"xmlns":890},[892,74807,74808,74820],{},[895,74809,74810,74812,74814,74816,74818],{},[898,74811,1776],{},[1750,74813,1766],{},[1742,74815,46942],{},[1750,74817,1758],{},[898,74819,12471],{},[902,74821,74822],{"encoding":904},"P = 30 - Q",[883,74824,74826],{"className":74825},[886],[888,74827,74828],{"xmlns":890},[892,74829,74830,74856],{},[895,74831,74832,74834,74836,74838,74840,74846,74848,74850,74852,74854],{},[898,74833,5326],{},[898,74835,1812],{},[1750,74837,1766],{},[1742,74839,4268],{},[1699,74841,74842,74844],{},[898,74843,12471],{},[1742,74845,1872],{},[1750,74847,1861],{},[1742,74849,3219],{},[898,74851,12471],{},[1750,74853,1861],{},[1742,74855,8051],{},[902,74857,74858],{"encoding":904},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[724,74861,74862,1647,74864,1343,74894,74932,74933,10951,74977,75011,75012,2313],{},[38,74863,6610],{},[883,74865,74867],{"className":74866},[886],[888,74868,74869],{"xmlns":890},[892,74870,74871,74891],{},[895,74872,74873,74875,74877,74879,74881,74883,74885],{},[898,74874,5326],{},[898,74876,13658],{},[1750,74878,1766],{},[1742,74880,46942],{},[898,74882,12471],{},[1750,74884,1758],{},[1699,74886,74887,74889],{},[898,74888,12471],{},[1742,74890,1872],{},[902,74892,74893],{"encoding":904},"TR = 30Q - Q^2",[883,74895,74897],{"className":74896},[886],[888,74898,74899],{"xmlns":890},[892,74900,74901,74929],{},[895,74902,74903,74905,74907,74909,74911,74913,74919,74921,74923,74925,74927],{},[898,74904,1776],{},[898,74906,13658],{},[1750,74908,1766],{},[1750,74910,1758],{},[1742,74912,73482],{},[1699,74914,74915,74917],{},[898,74916,12471],{},[1742,74918,1872],{},[1750,74920,1861],{},[1742,74922,50723],{},[898,74924,12471],{},[1750,74926,1758],{},[1742,74928,8051],{},[902,74930,74931],{"encoding":904},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[883,74934,74936],{"className":74935},[886],[888,74937,74938],{"xmlns":890},[892,74939,74940,74974],{},[895,74941,74942,74944,74950,74952,74954,74956,74958,74960,74962,74964,74966,74968,74970,74972],{},[898,74943,1776],{},[1699,74945,74946,74948],{},[898,74947,13658],{},[1750,74949,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,74951,1766],{},[1750,74953,1758],{},[1742,74955,7822],{},[898,74957,12471],{},[1750,74959,1861],{},[1742,74961,50723],{},[1750,74963,1766],{},[1742,74965,2607],{},[1750,74967,13651],{},[898,74969,12471],{},[1750,74971,1766],{},[1742,74973,15239],{},[902,74975,74976],{"encoding":904},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[883,74978,74980],{"className":74979},[886],[888,74981,74982],{"xmlns":890},[892,74983,74984,75008],{},[895,74985,74986,74988,74998,75000,75002,75004,75006],{},[898,74987,1776],{},[1699,74989,74990,74992],{},[898,74991,13658],{},[895,74993,74994,74996],{},[1750,74995,3815],{"mathvariant":1747},[1750,74997,3815],{"mathvariant":1747},[1750,74999,1766],{},[1750,75001,1758],{},[1742,75003,7822],{},[1750,75005,2624],{},[1742,75007,2607],{},[902,75009,75010],{"encoding":904},"PR'' = -3 \u003C 0"," (maximum); ",[883,75013,75015],{"className":75014},[886],[888,75016,75017],{"xmlns":890},[892,75018,75019,75036],{},[895,75020,75021,75023,75025,75027,75029,75031,75033],{},[898,75022,1776],{},[898,75024,13658],{},[1750,75026,1753],{"stretchy":1752},[1742,75028,15239],{},[1750,75030,1763],{"stretchy":1752},[1750,75032,1766],{},[1742,75034,75035],{},"89",[902,75037,75038],{"encoding":904},"PR(8) = 89",[724,75040,75041,75042,1343,75068,10951,75092,75130],{},"Ověření principu: ",[883,75043,75045],{"className":75044},[886],[888,75046,75047],{"xmlns":890},[892,75048,75049,75065],{},[895,75050,75051,75053,75055,75057,75059,75061,75063],{},[898,75052,1773],{},[898,75054,13658],{},[1750,75056,1766],{},[1742,75058,46942],{},[1750,75060,1758],{},[1742,75062,1872],{},[898,75064,12471],{},[902,75066,75067],{"encoding":904},"MR = 30 - 2Q",[883,75069,75071],{"className":75070},[886],[888,75072,75073],{"xmlns":890},[892,75074,75075,75089],{},[895,75076,75077,75079,75081,75083,75085,75087],{},[898,75078,1773],{},[898,75080,1812],{},[1750,75082,1766],{},[898,75084,12471],{},[1750,75086,1861],{},[1742,75088,3219],{},[902,75090,75091],{"encoding":904},"MC = Q + 6",[883,75093,75095],{"className":75094},[886],[888,75096,75097],{"xmlns":890},[892,75098,75099,75127],{},[895,75100,75101,75103,75105,75107,75109,75111,75113,75115,75117,75119,75121,75123,75125],{},[898,75102,1773],{},[898,75104,13658],{},[1750,75106,1753],{"stretchy":1752},[1742,75108,15239],{},[1750,75110,1763],{"stretchy":1752},[1750,75112,1766],{},[1742,75114,6789],{},[1750,75116,1766],{},[898,75118,1773],{},[898,75120,1812],{},[1750,75122,1753],{"stretchy":1752},[1742,75124,15239],{},[1750,75126,1763],{"stretchy":1752},[902,75128,75129],{"encoding":904},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[724,75132,75133,75134,75167,75168,75185],{},"V řadě případů — má-li rovnice ",[883,75135,75137],{"className":75136},[886],[888,75138,75139],{"xmlns":890},[892,75140,75141,75165],{},[895,75142,75143,75145,75147,75149,75151,75153,75155,75157,75159,75161,75163],{},[898,75144,1773],{},[898,75146,13658],{},[1750,75148,1753],{"stretchy":1752},[898,75150,12471],{},[1750,75152,1763],{"stretchy":1752},[1750,75154,1766],{},[898,75156,1773],{},[898,75158,1812],{},[1750,75160,1753],{"stretchy":1752},[898,75162,12471],{},[1750,75164,1763],{"stretchy":1752},[902,75166,74733],{"encoding":904}," jediné ekonomicky smysluplné řešení ",[883,75169,75171],{"className":75170},[886],[888,75172,75173],{"xmlns":890},[892,75174,75175,75183],{},[895,75176,75177],{},[5535,75178,75179,75181],{},[898,75180,12471],{},[1742,75182,2607],{},[902,75184,47231],{"encoding":904}," — není třeba provádět test druhé derivace.",[46271,75187,75189],{"id":75188},"příklad-310","Příklad 3.10",[724,75191,75192,75194,75195,75199,75200,75213,75214,75245],{},[38,75193,64910],{}," Firma vyrábí minipočítače v ",[207,75196,75198],{"className":75197,"dataFsResolvedFilePath":800,"href":801},[210],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[883,75201,75203],{"className":75202},[886],[888,75204,75205],{"xmlns":890},[892,75206,75207,75211],{},[895,75208,75209],{},[1742,75210,9702],{},[902,75212,9702],{"encoding":904}," EUR\u002Fks. ",[883,75215,75217],{"className":75216},[886],[888,75218,75219],{"xmlns":890},[892,75220,75221,75242],{},[895,75222,75223,75225,75227,75229,75231,75233,75236],{},[898,75224,5326],{},[898,75226,1812],{},[1750,75228,1766],{},[1742,75230,3936],{},[1750,75232,1861],{},[1742,75234,75235],{},"28",[1699,75237,75238,75240],{},[898,75239,12471],{},[1742,75241,1872],{},[902,75243,75244],{"encoding":904},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[724,75247,75248,1647,75250,1343,75272,1343,75292,75315],{},[38,75249,6610],{},[883,75251,75253],{"className":75252},[886],[888,75254,75255],{"xmlns":890},[892,75256,75257,75269],{},[895,75258,75259,75261,75263,75265,75267],{},[898,75260,5326],{},[898,75262,13658],{},[1750,75264,1766],{},[1742,75266,9702],{},[898,75268,12471],{},[902,75270,75271],{"encoding":904},"TR = 900Q",[883,75273,75275],{"className":75274},[886],[888,75276,75277],{"xmlns":890},[892,75278,75279,75289],{},[895,75280,75281,75283,75285,75287],{},[898,75282,1773],{},[898,75284,13658],{},[1750,75286,1766],{},[1742,75288,9702],{},[902,75290,75291],{"encoding":904},"MR = 900",[883,75293,75295],{"className":75294},[886],[888,75296,75297],{"xmlns":890},[892,75298,75299,75312],{},[895,75300,75301,75303,75305,75307,75310],{},[898,75302,1773],{},[898,75304,1812],{},[1750,75306,1766],{},[1742,75308,75309],{},"56",[898,75311,12471],{},[902,75313,75314],{"encoding":904},"MC = 56Q",". Z principu:",[883,75317,75319],{"className":75318},[886],[888,75320,75321],{"xmlns":890,"display":36989},[892,75322,75323,75365],{},[895,75324,75325,75327,75329,75331,75333,75335,75337,75339,75341,75343,75351,75353,75356,75358,75360,75362],{},[1742,75326,9702],{},[1750,75328,1766],{},[1742,75330,75309],{},[898,75332,12471],{},[1969,75334,6766],{},[1750,75336,13651],{},[1969,75338,6766],{},[898,75340,12471],{},[1750,75342,1766],{},[3586,75344,75345],{"scriptlevel":2607,"displaystyle":1752},[3423,75346,75347,75349],{},[1742,75348,9702],{},[1742,75350,75309],{},[1750,75352,6792],{},[1742,75354,75355],{},"16,07",[1969,75357,6766],{},[1750,75359,2274],{},[1969,75361,6766],{},[1742,75363,75364],{},"16.",[902,75366,75367],{"encoding":904},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[724,75369,75370,75371,2366],{},"Zisk při ",[883,75372,75374],{"className":75373},[886],[888,75375,75376],{"xmlns":890},[892,75377,75378,75386],{},[895,75379,75380,75382,75384],{},[898,75381,12471],{},[1750,75383,1766],{},[1742,75385,50785],{},[902,75387,75388],{"encoding":904},"Q = 16",[883,75390,75392],{"className":75391},[886],[888,75393,75394],{"xmlns":890,"display":36989},[892,75395,75396,75467],{},[895,75397,75398,75400,75402,75404,75406,75408,75410,75412,75414,75416,75418,75420,75422,75424,75426,75428,75434,75436,75438,75440,75442,75444,75446,75448,75450,75453,75455,75457,75459,75462,75465],{},[898,75399,1776],{},[898,75401,13658],{},[1750,75403,1753],{"stretchy":1752},[1742,75405,50785],{},[1750,75407,1763],{"stretchy":1752},[1750,75409,1766],{},[1742,75411,9702],{},[1750,75413,8009],{},[1742,75415,50785],{},[1750,75417,1758],{},[1750,75419,1753],{"stretchy":1752},[1742,75421,3936],{},[1750,75423,1861],{},[1742,75425,75235],{},[1750,75427,8009],{},[1699,75429,75430,75432],{},[1742,75431,50785],{},[1742,75433,1872],{},[1750,75435,1763],{"stretchy":1752},[1750,75437,1766],{},[1742,75439,6789],{},[1969,75441,2658],{},[1742,75443,3956],{},[1750,75445,1758],{},[1742,75447,8051],{},[1969,75449,2658],{},[1742,75451,75452],{},"218",[1750,75454,1766],{},[1742,75456,8051],{},[1969,75458,2658],{},[1742,75460,75461],{},"182",[1969,75463,75464],{}," EUR",[898,75466,2313],{"mathvariant":1747},[902,75468,75469],{"encoding":904},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[724,75471,75472],{},"Pro srovnání při původních 30 ks:",[883,75474,75476],{"className":75475},[886],[888,75477,75478],{"xmlns":890,"display":36989},[892,75479,75480,75545],{},[895,75481,75482,75484,75486,75488,75490,75492,75494,75496,75498,75500,75502,75504,75506,75508,75510,75512,75514,75516,75518,75521,75523,75525,75527,75529,75531,75533,75535,75537,75539,75541,75543],{},[898,75483,1776],{},[898,75485,13658],{},[1750,75487,1753],{"stretchy":1752},[1742,75489,46942],{},[1750,75491,1763],{"stretchy":1752},[1750,75493,1766],{},[1742,75495,9702],{},[1750,75497,8009],{},[1742,75499,46942],{},[1750,75501,1758],{},[1750,75503,1753],{"stretchy":1752},[1742,75505,3936],{},[1750,75507,1861],{},[1742,75509,75235],{},[1750,75511,8009],{},[1742,75513,9702],{},[1750,75515,1763],{"stretchy":1752},[1750,75517,1766],{},[1742,75519,75520],{},"27",[1969,75522,2658],{},[1742,75524,68005],{},[1750,75526,1758],{},[1742,75528,6419],{},[1969,75530,2658],{},[1742,75532,39666],{},[1750,75534,1766],{},[1742,75536,1744],{},[1969,75538,2658],{},[1742,75540,7587],{},[1969,75542,75464],{},[898,75544,2313],{"mathvariant":1747},[902,75546,75547],{"encoding":904},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[724,75549,75550,75553,75554,75572,75573,75591],{},[38,75551,75552],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[883,75555,75557],{"className":75556},[886],[888,75558,75559],{"xmlns":890},[892,75560,75561,75569],{},[895,75562,75563,75565,75567],{},[1742,75564,8051],{},[1969,75566,2658],{},[1742,75568,75461],{},[902,75570,75571],{"encoding":904},"7\\,182"," EUR namísto původních ",[883,75574,75576],{"className":75575},[886],[888,75577,75578],{"xmlns":890},[892,75579,75580,75588],{},[895,75581,75582,75584,75586],{},[1742,75583,1744],{},[1969,75585,2658],{},[1742,75587,7587],{},[902,75589,75590],{"encoding":904},"1\\,750"," EUR.",[198,75593,75595],{"id":75594},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[724,75597,75598,75599,71493,75612,75636],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[883,75600,75602],{"className":75601},[886],[888,75603,75604],{"xmlns":890},[892,75605,75606,75610],{},[895,75607,75608],{},[898,75609,1776],{},[902,75611,1776],{"encoding":904},[883,75613,75615],{"className":75614},[886],[888,75616,75617],{"xmlns":890},[892,75618,75619,75633],{},[895,75620,75621,75623,75625,75627,75629,75631],{},[898,75622,5326],{},[898,75624,13658],{},[1750,75626,1766],{},[898,75628,1776],{},[1750,75630,8009],{},[898,75632,12471],{},[902,75634,75635],{"encoding":904},"TR = P \\cdot Q"," a z (3.13) speciálně:",[883,75638,75640],{"className":75639},[886],[888,75641,75642],{"xmlns":890,"display":36989},[892,75643,75644,75677],{},[4577,75645,75646],{"width":36994},[4582,75647,75648,75650,75670,75672],{},[4585,75649],{"width":36999},[4585,75651,75652],{},[895,75653,75654,75656,75658,75660,75662,75664,75666,75668],{},[898,75655,1776],{},[1750,75657,1766],{},[898,75659,1773],{},[898,75661,1812],{},[1750,75663,1753],{"stretchy":1752},[898,75665,12471],{},[1750,75667,1763],{"stretchy":1752},[898,75669,2313],{"mathvariant":1747},[4585,75671],{"width":36999},[4585,75673,75674],{},[1969,75675,75676],{},"(3.14)",[902,75678,75679],{"encoding":904},"P = MC(Q).\n\\tag{3.14}",[724,75681,75682,75683,2313],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[883,75684,75686],{"className":75685},[886],[888,75687,75688],{"xmlns":890},[892,75689,75690,75704],{},[895,75691,75692,75694],{},[898,75693,1776],{},[1699,75695,75696,75698],{},[898,75697,13658],{},[895,75699,75700,75702],{},[1750,75701,3815],{"mathvariant":1747},[1750,75703,3815],{"mathvariant":1747},[902,75705,74760],{"encoding":904},[46271,75707,75709],{"id":75708},"příklad-311","Příklad 3.11",[724,75711,75712,66445,75714,75761,75762,75780],{},[38,75713,64910],{},[883,75715,75717],{"className":75716},[886],[888,75718,75719],{"xmlns":890},[892,75720,75721,75758],{},[895,75722,75723,75725,75727,75729,75732,75738,75740,75742,75748,75750,75752,75754,75756],{},[898,75724,5326],{},[898,75726,1812],{},[1750,75728,1766],{},[1742,75730,75731],{},"0,04",[1699,75733,75734,75736],{},[898,75735,12471],{},[1742,75737,7822],{},[1750,75739,1758],{},[1742,75741,6381],{},[1699,75743,75744,75746],{},[898,75745,12471],{},[1742,75747,1872],{},[1750,75749,1861],{},[1742,75751,3079],{},[898,75753,12471],{},[1750,75755,1861],{},[1742,75757,7902],{},[902,75759,75760],{"encoding":904},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[883,75763,75765],{"className":75764},[886],[888,75766,75767],{"xmlns":890},[892,75768,75769,75777],{},[895,75770,75771,75773,75775],{},[898,75772,1776],{},[1750,75774,1766],{},[1742,75776,7859],{},[902,75778,75779],{"encoding":904},"P = 4"," stanovte optimální produkci.",[724,75782,75783,75785,75786,27149,75828,75862,75863,2366],{},[38,75784,6610],{}," Z (3.14): ",[883,75787,75789],{"className":75788},[886],[888,75790,75791],{"xmlns":890},[892,75792,75793,75825],{},[895,75794,75795,75797,75799,75801,75804,75810,75812,75815,75817,75819,75821,75823],{},[898,75796,1773],{},[898,75798,1812],{},[1750,75800,1766],{},[1742,75802,75803],{},"0,12",[1699,75805,75806,75808],{},[898,75807,12471],{},[1742,75809,1872],{},[1750,75811,1758],{},[1742,75813,75814],{},"1,8",[898,75816,12471],{},[1750,75818,1861],{},[1742,75820,3079],{},[1750,75822,1766],{},[1742,75824,7859],{},[902,75826,75827],{"encoding":904},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[883,75829,75831],{"className":75830},[886],[888,75832,75833],{"xmlns":890},[892,75834,75835,75859],{},[895,75836,75837,75839,75845,75847,75849,75851,75853,75855,75857],{},[1742,75838,75803],{},[1699,75840,75841,75843],{},[898,75842,12471],{},[1742,75844,1872],{},[1750,75846,1758],{},[1742,75848,75814],{},[898,75850,12471],{},[1750,75852,1861],{},[1742,75854,3219],{},[1750,75856,1766],{},[1742,75858,2607],{},[902,75860,75861],{"encoding":904},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[883,75864,75866],{"className":75865},[886],[888,75867,75868],{"xmlns":890},[892,75869,75870,75874],{},[895,75871,75872],{},[1742,75873,75803],{},[902,75875,75876],{"encoding":904},"0{,}12",[883,75878,75880],{"className":75879},[886],[888,75881,75882],{"xmlns":890,"display":36989},[892,75883,75884,75936],{},[895,75885,75886,75892,75894,75896,75898,75900,75902,75904,75906,75908,75910,75912,75918,75920,75922,75924,75926,75932,75934],{},[1699,75887,75888,75890],{},[898,75889,12471],{},[1742,75891,1872],{},[1750,75893,1758],{},[1742,75895,45167],{},[898,75897,12471],{},[1750,75899,1861],{},[1742,75901,3936],{},[1750,75903,1766],{},[1742,75905,2607],{},[1969,75907,6766],{},[1750,75909,13651],{},[1969,75911,6766],{},[5535,75913,75914,75916],{},[898,75915,12471],{},[1742,75917,1744],{},[1750,75919,1766],{},[1742,75921,7902],{},[1750,75923,1917],{"separator":1916},[1969,75925,6766],{},[5535,75927,75928,75930],{},[898,75929,12471],{},[1742,75931,1872],{},[1750,75933,1766],{},[1742,75935,3130],{},[902,75937,75938],{"encoding":904},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[724,75940,75941,75942,2366],{},"Dále ",[883,75943,75945],{"className":75944},[886],[888,75946,75947],{"xmlns":890},[892,75948,75949,75988],{},[895,75950,75951,75953,75963,75965,75967,75969,75975,75977,75979,75982,75984,75986],{},[898,75952,1776],{},[1699,75954,75955,75957],{},[898,75956,13658],{},[895,75958,75959,75961],{},[1750,75960,3815],{"mathvariant":1747},[1750,75962,3815],{"mathvariant":1747},[1750,75964,1766],{},[1750,75966,1758],{},[898,75968,1773],{},[1699,75970,75971,75973],{},[898,75972,1812],{},[1750,75974,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,75976,1766],{},[1750,75978,1758],{},[1742,75980,75981],{},"0,24",[898,75983,12471],{},[1750,75985,1861],{},[1742,75987,75814],{},[902,75989,75990],{"encoding":904},"PR'' = -MC' = -0{,}24Q + 1{,}8",[120,75992,75993,76043],{},[123,75994,75995,76039,76040,76042],{},[883,75996,75998],{"className":75997},[886],[888,75999,76000],{"xmlns":890},[892,76001,76002,76036],{},[895,76003,76004,76006,76016,76018,76020,76022,76024,76026,76028,76030,76032,76034],{},[898,76005,1776],{},[1699,76007,76008,76010],{},[898,76009,13658],{},[895,76011,76012,76014],{},[1750,76013,3815],{"mathvariant":1747},[1750,76015,3815],{"mathvariant":1747},[1750,76017,1753],{"stretchy":1752},[1742,76019,7902],{},[1750,76021,1763],{"stretchy":1752},[1750,76023,1766],{},[1742,76025,3123],{},[1750,76027,2604],{},[1742,76029,2607],{},[1969,76031,6766],{},[1750,76033,13651],{},[1969,76035,6766],{},[902,76037,76038],{"encoding":904},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[38,76041,13445],{}," zisku (minimalizace ztráty);",[123,76044,76045,76039,76091,76093],{},[883,76046,76048],{"className":76047},[886],[888,76049,76050],{"xmlns":890},[892,76051,76052,76088],{},[895,76053,76054,76056,76066,76068,76070,76072,76074,76076,76078,76080,76082,76084,76086],{},[898,76055,1776],{},[1699,76057,76058,76060],{},[898,76059,13658],{},[895,76061,76062,76064],{},[1750,76063,3815],{"mathvariant":1747},[1750,76065,3815],{"mathvariant":1747},[1750,76067,1753],{"stretchy":1752},[1742,76069,3079],{},[1750,76071,1763],{"stretchy":1752},[1750,76073,1766],{},[1750,76075,1758],{},[1742,76077,3123],{},[1750,76079,2624],{},[1742,76081,2607],{},[1969,76083,6766],{},[1750,76085,13651],{},[1969,76087,6766],{},[902,76089,76090],{"encoding":904},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[38,76092,13387],{}," zisku, avšak",[883,76095,76097],{"className":76096},[886],[888,76098,76099],{"xmlns":890,"display":36989},[892,76100,76101,76169],{},[895,76102,76103,76105,76107,76109,76111,76113,76115,76117,76119,76121,76123,76125,76127,76129,76131,76133,76135,76137,76139,76141,76143,76145,76147,76149,76151,76153,76155,76157,76159,76161,76163,76165,76167],{},[898,76104,1776],{},[898,76106,13658],{},[1750,76108,1753],{"stretchy":1752},[1742,76110,3079],{},[1750,76112,1763],{"stretchy":1752},[1750,76114,1766],{},[1742,76116,7859],{},[1750,76118,8009],{},[1742,76120,3079],{},[1750,76122,1758],{},[1750,76124,1753],{"stretchy":1752},[1742,76126,75731],{},[1750,76128,8009],{},[1742,76130,1744],{},[1969,76132,2658],{},[1742,76134,68005],{},[1750,76136,1758],{},[1742,76138,6381],{},[1750,76140,8009],{},[1742,76142,4078],{},[1750,76144,1861],{},[1742,76146,4078],{},[1750,76148,1861],{},[1742,76150,7902],{},[1750,76152,1763],{"stretchy":1752},[1750,76154,1766],{},[1742,76156,14865],{},[1750,76158,1758],{},[1742,76160,5006],{},[1750,76162,1766],{},[1750,76164,1758],{},[1742,76166,45167],{},[1750,76168,1917],{"separator":1916},[902,76170,76171],{"encoding":904},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[724,76173,76174,76175,2313],{},"tj. ztráta větší než ",[883,76176,76178],{"className":76177},[886],[888,76179,76180],{"xmlns":890},[892,76181,76182,76192],{},[895,76183,76184,76186,76188,76190],{},[898,76185,20069],{},[898,76187,1812],{},[1750,76189,1766],{},[1742,76191,7902],{},[902,76193,76194],{"encoding":904},"FC = 5",[724,76196,76197,76200,76201,76204,76205,2313],{},[38,76198,76199],{},"Závěr:"," firma by měla ",[38,76202,76203],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[883,76206,76208],{"className":76207},[886],[888,76209,76210],{"xmlns":890},[892,76211,76212,76222],{},[895,76213,76214,76216,76218,76220],{},[898,76215,20069],{},[898,76217,1812],{},[1750,76219,1766],{},[1742,76221,7902],{},[902,76223,76194],{"encoding":904},[115,76225,76227],{"id":76226},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[724,76229,76230,76231,76233,76234,76249,76250,76263,76264,76290,76291,76304,76305,76322,76323,2984,76340,76343,76344,76364,76365,76380,76381,2366],{},"Důležitým završením analýzy je konstrukce ",[38,76232,64198],{},". S nabízeným množstvím rostou mezní náklady ",[883,76235,76237],{"className":76236},[886],[888,76238,76239],{"xmlns":890},[892,76240,76241,76247],{},[895,76242,76243,76245],{},[898,76244,1773],{},[898,76246,1812],{},[902,76248,64215],{"encoding":904}," a tyto určují cenu ",[883,76251,76253],{"className":76252},[886],[888,76254,76255],{"xmlns":890},[892,76256,76257,76261],{},[895,76258,76259],{},[898,76260,1776],{},[902,76262,1776],{"encoding":904},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[883,76265,76267],{"className":76266},[886],[888,76268,76269],{"xmlns":890},[892,76270,76271,76287],{},[895,76272,76273,76275,76277,76279,76281,76283,76285],{},[898,76274,1776],{},[1750,76276,1766],{},[898,76278,1773],{},[898,76280,1812],{},[1750,76282,1753],{"stretchy":1752},[898,76284,12471],{},[1750,76286,1763],{"stretchy":1752},[902,76288,76289],{"encoding":904},"P = MC(Q)"," (obrázek 3.14). Cena ",[883,76292,76294],{"className":76293},[886],[888,76295,76296],{"xmlns":890},[892,76297,76298,76302],{},[895,76299,76300],{},[898,76301,1776],{},[902,76303,1776],{"encoding":904}," však nemůže být nižší než ",[883,76306,76308],{"className":76307},[886],[888,76309,76310],{"xmlns":890},[892,76311,76312,76320],{},[895,76313,76314],{},[1699,76315,76316,76318],{},[898,76317,1776],{},[1750,76319,3751],{},[902,76321,14063],{"encoding":904}," odpovídající množství ",[883,76324,76326],{"className":76325},[886],[888,76327,76328],{"xmlns":890},[892,76329,76330,76338],{},[895,76331,76332],{},[1699,76333,76334,76336],{},[898,76335,12471],{},[1750,76337,3751],{},[902,76339,38767],{"encoding":904},[38,76341,76342],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[883,76345,76347],{"className":76346},[886],[888,76348,76349],{"xmlns":890},[892,76350,76351,76361],{},[895,76352,76353,76355],{},[1742,76354,2607],{},[1699,76356,76357,76359],{},[898,76358,12471],{},[1750,76360,3751],{},[902,76362,76363],{"encoding":904},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[883,76366,76368],{"className":76367},[886],[888,76369,76370],{"xmlns":890},[892,76371,76372,76378],{},[895,76373,76374,76376],{},[898,76375,1773],{},[898,76377,1812],{},[902,76379,64215],{"encoding":904}," nad bodem ",[883,76382,76384],{"className":76383},[886],[888,76385,76386],{"xmlns":890},[892,76387,76388,76392],{},[895,76389,76390],{},[898,76391,13916],{},[902,76393,13916],{"encoding":904},[883,76395,76397],{"className":76396},[886],[888,76398,76399],{"xmlns":890,"display":36989},[892,76400,76401,76508],{},[4577,76402,76403],{"width":36994},[4582,76404,76405,76407,76501,76503],{},[4585,76406],{"width":36999},[4585,76408,76409],{},[895,76410,76411,76413,76415,76417,76419,76421,76423,76425],{},[898,76412,1776],{},[1750,76414,1766],{},[898,76416,1779],{},[1750,76418,1753],{"stretchy":1752},[898,76420,12471],{},[1750,76422,1763],{"stretchy":1752},[1750,76424,1766],{},[895,76426,76427,76430],{},[1750,76428,76429],{"fence":1916},"{",[4577,76431,76434,76473],{"rowspacing":76432,"columnalign":76433,"columnspacing":24875},"0.36em","left left",[4582,76435,76436,76452],{},[4585,76437,76438],{},[3586,76439,76440],{"scriptlevel":2607,"displaystyle":1752},[895,76441,76442,76444,76446,76448,76450],{},[898,76443,1773],{},[898,76445,1812],{},[1750,76447,1753],{"stretchy":1752},[898,76449,12471],{},[1750,76451,1763],{"stretchy":1752},[4585,76453,76454],{},[3586,76455,76456],{"scriptlevel":2607,"displaystyle":1752},[895,76457,76458,76461,76463,76465,76471],{},[1969,76459,76460],{},"pro ",[898,76462,12471],{},[1750,76464,14143],{},[1699,76466,76467,76469],{},[898,76468,12471],{},[1750,76470,3751],{},[1750,76472,1917],{"separator":1916},[4582,76474,76475,76481],{},[4585,76476,76477],{},[3586,76478,76479],{"scriptlevel":2607,"displaystyle":1752},[1742,76480,2607],{},[4585,76482,76483],{},[3586,76484,76485],{"scriptlevel":2607,"displaystyle":1752},[895,76486,76487,76489,76491,76493,76499],{},[1969,76488,76460],{},[898,76490,12471],{},[1750,76492,2624],{},[1699,76494,76495,76497],{},[898,76496,12471],{},[1750,76498,3751],{},[1750,76500,1917],{"separator":1916},[4585,76502],{"width":36999},[4585,76504,76505],{},[1969,76506,76507],{},"(3.15)",[902,76509,76510],{"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}",[724,76512,2590,76513,76530,76531,76548,76549,50422,76579,76582],{},[883,76514,76516],{"className":76515},[886],[888,76517,76518],{"xmlns":890},[892,76519,76520,76528],{},[895,76521,76522],{},[1699,76523,76524,76526],{},[898,76525,12471],{},[1750,76527,3751],{},[902,76529,38767],{"encoding":904}," je bod minima ",[883,76532,76534],{"className":76533},[886],[888,76535,76536],{"xmlns":890},[892,76537,76538,76546],{},[895,76539,76540,76542,76544],{},[898,76541,13916],{},[898,76543,49262],{},[898,76545,1812],{},[902,76547,64234],{"encoding":904},". Bod ",[883,76550,76552],{"className":76551},[886],[888,76553,76554],{"xmlns":890},[892,76555,76556,76576],{},[895,76557,76558,76560,76566,76568,76574],{},[1750,76559,1753],{"stretchy":1752},[1699,76561,76562,76564],{},[898,76563,12471],{},[1750,76565,3751],{},[1750,76567,1917],{"separator":1916},[1699,76569,76570,76572],{},[898,76571,1776],{},[1750,76573,3751],{},[1750,76575,1763],{"stretchy":1752},[902,76577,76578],{"encoding":904},"(Q^*, P^*)",[38,76580,76581],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1785,76584,76585,76590],{},[724,76586,76587,76589],{},[883,76588,6004],{}," Postup — jak odvodit nabídku firmy",[152,76591,76592,76641,76736,76791,76862],{},[123,76593,76594,76595,2028,76617,2313],{},"Ze zadaných nákladů určete ",[883,76596,76598],{"className":76597},[886],[888,76599,76600],{"xmlns":890},[892,76601,76602,76614],{},[895,76603,76604,76606,76608,76610,76612],{},[898,76605,1773],{},[898,76607,1812],{},[1750,76609,1753],{"stretchy":1752},[898,76611,12471],{},[1750,76613,1763],{"stretchy":1752},[902,76615,76616],{"encoding":904},"MC(Q)",[883,76618,76620],{"className":76619},[886],[888,76621,76622],{"xmlns":890},[892,76623,76624,76638],{},[895,76625,76626,76628,76630,76632,76634,76636],{},[898,76627,13916],{},[898,76629,49262],{},[898,76631,1812],{},[1750,76633,1753],{"stretchy":1752},[898,76635,12471],{},[1750,76637,1763],{"stretchy":1752},[902,76639,76640],{"encoding":904},"AVC(Q)",[123,76642,76643,76644,76661,76662,76679,76680,76712,76713,1783],{},"Najděte ",[883,76645,76647],{"className":76646},[886],[888,76648,76649],{"xmlns":890},[892,76650,76651,76659],{},[895,76652,76653],{},[1699,76654,76655,76657],{},[898,76656,12471],{},[1750,76658,3751],{},[902,76660,38767],{"encoding":904}," jako bod minima ",[883,76663,76665],{"className":76664},[886],[888,76666,76667],{"xmlns":890},[892,76668,76669,76677],{},[895,76670,76671,76673,76675],{},[898,76672,13916],{},[898,76674,49262],{},[898,76676,1812],{},[902,76678,64234],{"encoding":904}," (řešením ",[883,76681,76683],{"className":76682},[886],[888,76684,76685],{"xmlns":890},[892,76686,76687,76709],{},[895,76688,76689,76691,76693,76699,76701,76703,76705,76707],{},[898,76690,13916],{},[898,76692,49262],{},[1699,76694,76695,76697],{},[898,76696,1812],{},[1750,76698,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,76700,1753],{"stretchy":1752},[898,76702,12471],{},[1750,76704,1763],{"stretchy":1752},[1750,76706,1766],{},[1742,76708,2607],{},[902,76710,76711],{"encoding":904},"AVC'(Q) = 0",", případně rovnice ",[883,76714,76716],{"className":76715},[886],[888,76717,76718],{"xmlns":890},[892,76719,76720,76734],{},[895,76721,76722,76724,76726,76728,76730,76732],{},[898,76723,13916],{},[898,76725,49262],{},[898,76727,1812],{},[1750,76729,1766],{},[898,76731,1773],{},[898,76733,1812],{},[902,76735,64171],{"encoding":904},[123,76737,74644,76738,76790],{},[883,76739,76741],{"className":76740},[886],[888,76742,76743],{"xmlns":890},[892,76744,76745,76787],{},[895,76746,76747,76753,76755,76757,76759,76761,76767,76769,76771,76773,76775,76777,76779,76785],{},[1699,76748,76749,76751],{},[898,76750,1776],{},[1750,76752,3751],{},[1750,76754,1766],{},[898,76756,1773],{},[898,76758,1812],{},[1750,76760,1753],{"stretchy":1752},[1699,76762,76763,76765],{},[898,76764,12471],{},[1750,76766,3751],{},[1750,76768,1763],{"stretchy":1752},[1750,76770,1766],{},[898,76772,13916],{},[898,76774,49262],{},[898,76776,1812],{},[1750,76778,1753],{"stretchy":1752},[1699,76780,76781,76783],{},[898,76782,12471],{},[1750,76784,3751],{},[1750,76786,1763],{"stretchy":1752},[902,76788,76789],{"encoding":904},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[123,76792,76793,76794,16121,76826,76848,76849,2313],{},"Zapište nabídku: ",[883,76795,76797],{"className":76796},[886],[888,76798,76799],{"xmlns":890},[892,76800,76801,76823],{},[895,76802,76803,76805,76807,76809,76811,76813,76815,76817,76819,76821],{},[898,76804,1779],{},[1750,76806,1753],{"stretchy":1752},[898,76808,12471],{},[1750,76810,1763],{"stretchy":1752},[1750,76812,1766],{},[898,76814,1773],{},[898,76816,1812],{},[1750,76818,1753],{"stretchy":1752},[898,76820,12471],{},[1750,76822,1763],{"stretchy":1752},[902,76824,76825],{"encoding":904},"S(Q) = MC(Q)",[883,76827,76829],{"className":76828},[886],[888,76830,76831],{"xmlns":890},[892,76832,76833,76845],{},[895,76834,76835,76837,76839],{},[898,76836,12471],{},[1750,76838,14143],{},[1699,76840,76841,76843],{},[898,76842,12471],{},[1750,76844,3751],{},[902,76846,76847],{"encoding":904},"Q \\geq Q^*",", jinak ",[883,76850,76852],{"className":76851},[886],[888,76853,76854],{"xmlns":890},[892,76855,76856,76860],{},[895,76857,76858],{},[1742,76859,2607],{},[902,76861,2607],{"encoding":904},[123,76863,76864,76865,76897],{},"V případě potřeby vyjádřete inverzi ",[883,76866,76868],{"className":76867},[886],[888,76869,76870],{"xmlns":890},[892,76871,76872,76894],{},[895,76873,76874,76876,76878,76888,76890,76892],{},[898,76875,12471],{},[1750,76877,1766],{},[1699,76879,76880,76882],{},[898,76881,1779],{},[895,76883,76884,76886],{},[1750,76885,1758],{},[1742,76887,1744],{},[1750,76889,1753],{"stretchy":1752},[898,76891,1776],{},[1750,76893,1763],{"stretchy":1752},[902,76895,76896],{"encoding":904},"Q = S^{-1}(P)"," doplněním na čtverec.",[724,76899,76900],{},[614,76901,76902,76903,1343,76918,2028,76935,38124,76950,76963,76964,76989,76990,77003,77004,77021,77022,77039,77040,77057],{},"Obrázek 3.14: Křivky ",[883,76904,76906],{"className":76905},[886],[888,76907,76908],{"xmlns":890},[892,76909,76910,76916],{},[895,76911,76912,76914],{},[898,76913,13916],{},[898,76915,1812],{},[902,76917,64483],{"encoding":904},[883,76919,76921],{"className":76920},[886],[888,76922,76923],{"xmlns":890},[892,76924,76925,76933],{},[895,76926,76927,76929,76931],{},[898,76928,13916],{},[898,76930,49262],{},[898,76932,1812],{},[902,76934,64234],{"encoding":904},[883,76936,76938],{"className":76937},[886],[888,76939,76940],{"xmlns":890},[892,76941,76942,76948],{},[895,76943,76944,76946],{},[898,76945,1773],{},[898,76947,1812],{},[902,76949,64215],{"encoding":904},[883,76951,76953],{"className":76952},[886],[888,76954,76955],{"xmlns":890},[892,76956,76957,76961],{},[895,76958,76959],{},[898,76960,900],{},[902,76962,900],{"encoding":904},"; křivka nabídky ",[883,76965,76967],{"className":76966},[886],[888,76968,76969],{"xmlns":890},[892,76970,76971,76987],{},[895,76972,76973,76975,76977,76979,76981,76983,76985],{},[898,76974,1776],{},[1750,76976,1766],{},[898,76978,1773],{},[898,76980,1812],{},[1750,76982,1753],{"stretchy":1752},[898,76984,12471],{},[1750,76986,1763],{"stretchy":1752},[902,76988,76289],{"encoding":904}," začíná v bodě ",[883,76991,76993],{"className":76992},[886],[888,76994,76995],{"xmlns":890},[892,76996,76997,77001],{},[895,76998,76999],{},[898,77000,13916],{},[902,77002,13916],{"encoding":904}," odpovídajícím minimu ",[883,77005,77007],{"className":77006},[886],[888,77008,77009],{"xmlns":890},[892,77010,77011,77019],{},[895,77012,77013,77015,77017],{},[898,77014,13916],{},[898,77016,49262],{},[898,77018,1812],{},[902,77020,64234],{"encoding":904}," při ceně ",[883,77023,77025],{"className":77024},[886],[888,77026,77027],{"xmlns":890},[892,77028,77029,77037],{},[895,77030,77031],{},[1699,77032,77033,77035],{},[898,77034,1776],{},[1750,77036,3751],{},[902,77038,14063],{"encoding":904}," (minimální cena nabídky); pod ",[883,77041,77043],{"className":77042},[886],[888,77044,77045],{"xmlns":890},[892,77046,77047,77055],{},[895,77048,77049],{},[1699,77050,77051,77053],{},[898,77052,12471],{},[1750,77054,3751],{},[902,77056,38767],{"encoding":904}," je nabídka nulová.",[46271,77059,77061],{"id":77060},"příklad-312","Příklad 3.12",[724,77063,77064,66445,77066,77112],{},[38,77065,64910],{},[883,77067,77069],{"className":77068},[886],[888,77070,77071],{"xmlns":890},[892,77072,77073,77109],{},[895,77074,77075,77077,77079,77081,77083,77089,77091,77093,77099,77101,77103,77105,77107],{},[898,77076,5326],{},[898,77078,1812],{},[1750,77080,1766],{},[1742,77082,12476],{},[1699,77084,77085,77087],{},[898,77086,12471],{},[1742,77088,7822],{},[1750,77090,1758],{},[1742,77092,1872],{},[1699,77094,77095,77097],{},[898,77096,12471],{},[1742,77098,1872],{},[1750,77100,1861],{},[1742,77102,45167],{},[898,77104,12471],{},[1750,77106,1861],{},[1742,77108,3079],{},[902,77110,77111],{"encoding":904},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[724,77114,77115,1647,77117,77154,77155,2366],{},[38,77116,6610],{},[883,77118,77120],{"className":77119},[886],[888,77121,77122],{"xmlns":890},[892,77123,77124,77151],{},[895,77125,77126,77128,77130,77132,77135,77141,77143,77145,77147,77149],{},[898,77127,1773],{},[898,77129,1812],{},[1750,77131,1766],{},[1742,77133,77134],{},"0,3",[1699,77136,77137,77139],{},[898,77138,12471],{},[1742,77140,1872],{},[1750,77142,1758],{},[1742,77144,7859],{},[898,77146,12471],{},[1750,77148,1861],{},[1742,77150,45167],{},[902,77152,77153],{"encoding":904},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[883,77156,77158],{"className":77157},[886],[888,77159,77160],{"xmlns":890},[892,77161,77162,77172],{},[895,77163,77164,77166,77168,77170],{},[898,77165,1776],{},[1750,77167,1766],{},[898,77169,1773],{},[898,77171,1812],{},[902,77173,77174],{"encoding":904},"P = MC",[883,77176,77178],{"className":77177},[886],[888,77179,77180],{"xmlns":890,"display":36989},[892,77181,77182,77207],{},[895,77183,77184,77186,77188,77190,77196,77198,77200,77202,77204],{},[898,77185,1776],{},[1750,77187,1766],{},[1742,77189,77134],{},[1699,77191,77192,77194],{},[898,77193,12471],{},[1742,77195,1872],{},[1750,77197,1758],{},[1742,77199,7859],{},[898,77201,12471],{},[1750,77203,1861],{},[1742,77205,77206],{},"15.",[902,77208,77209],{"encoding":904},"P = 0{,}3Q^2 - 4Q + 15.",[724,77211,77212,77213,15036,77226,77239],{},"Vyjádření ",[883,77214,77216],{"className":77215},[886],[888,77217,77218],{"xmlns":890},[892,77219,77220,77224],{},[895,77221,77222],{},[898,77223,12471],{},[902,77225,12471],{"encoding":904},[883,77227,77229],{"className":77228},[886],[888,77230,77231],{"xmlns":890},[892,77232,77233,77237],{},[895,77234,77235],{},[898,77236,1776],{},[902,77238,1776],{"encoding":904}," doplněním na čtverec:",[883,77241,77243],{"className":77242},[886],[888,77244,77245],{"xmlns":890,"display":36989},[892,77246,77247,77337],{},[895,77248,77249,77251,77253,77255,77293,77295,77297,77319,77321,77335],{},[898,77250,1776],{},[1750,77252,1766],{},[1742,77254,77134],{},[895,77256,77257,77259,77281,77283,77291],{},[1750,77258,1753],{"fence":1916},[1699,77260,77261,77279],{},[895,77262,77263,77265,77267,77269,77277],{},[1750,77264,1753],{"fence":1916},[898,77266,12471],{},[1750,77268,1758],{},[3586,77270,77271],{"scriptlevel":2607,"displaystyle":1752},[3423,77272,77273,77275],{},[1742,77274,6465],{},[1742,77276,7822],{},[1750,77278,1763],{"fence":1916},[1742,77280,1872],{},[1750,77282,1861],{},[3586,77284,77285],{"scriptlevel":2607,"displaystyle":1752},[3423,77286,77287,77289],{},[1742,77288,3936],{},[1742,77290,13663],{},[1750,77292,1763],{"fence":1916},[1750,77294,1917],{"separator":1916},[2125,77296],{"width":2127},[1699,77298,77299,77317],{},[895,77300,77301,77303,77305,77307,77315],{},[1750,77302,1753],{"fence":1916},[898,77304,12471],{},[1750,77306,1758],{},[3586,77308,77309],{"scriptlevel":2607,"displaystyle":1752},[3423,77310,77311,77313],{},[1742,77312,6465],{},[1742,77314,7822],{},[1750,77316,1763],{"fence":1916},[1742,77318,1872],{},[1750,77320,1766],{},[3423,77322,77323,77333],{},[895,77324,77325,77327,77329,77331],{},[1742,77326,46942],{},[898,77328,1776],{},[1750,77330,1758],{},[1742,77332,3936],{},[1742,77334,13663],{},[1750,77336,1917],{"separator":1916},[902,77338,77339],{"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},",[883,77341,77343],{"className":77342},[886],[888,77344,77345],{"xmlns":890,"display":36989},[892,77346,77347,77379],{},[895,77348,77349,77351,77353,77359,77361,77377],{},[898,77350,12471],{},[1750,77352,1766],{},[3423,77354,77355,77357],{},[1742,77356,6465],{},[1742,77358,7822],{},[1750,77360,1861],{},[3423,77362,77363,77375],{},[17761,77364,77365],{},[895,77366,77367,77369,77371,77373],{},[1742,77368,46942],{},[898,77370,1776],{},[1750,77372,1758],{},[1742,77374,3936],{},[1742,77376,7822],{},[898,77378,2313],{"mathvariant":1747},[902,77380,77381],{"encoding":904},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[724,77383,75941,77384,1343,77422,1343,77470,77504,77505,2313],{},[883,77385,77387],{"className":77386},[886],[888,77388,77389],{"xmlns":890},[892,77390,77391,77419],{},[895,77392,77393,77395,77397,77399,77401,77403,77409,77411,77413,77415,77417],{},[898,77394,13916],{},[898,77396,49262],{},[898,77398,1812],{},[1750,77400,1766],{},[1742,77402,12476],{},[1699,77404,77405,77407],{},[898,77406,12471],{},[1742,77408,1872],{},[1750,77410,1758],{},[1742,77412,1872],{},[898,77414,12471],{},[1750,77416,1861],{},[1742,77418,45167],{},[902,77420,77421],{"encoding":904},"AVC = 0{,}1Q^2 - 2Q + 15",[883,77423,77425],{"className":77424},[886],[888,77426,77427],{"xmlns":890},[892,77428,77429,77467],{},[895,77430,77431,77433,77435,77441,77443,77445,77447,77449,77451,77453,77455,77457,77463,77465],{},[898,77432,13916],{},[898,77434,49262],{},[1699,77436,77437,77439],{},[898,77438,1812],{},[1750,77440,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,77442,1766],{},[1742,77444,3929],{},[898,77446,12471],{},[1750,77448,1758],{},[1742,77450,1872],{},[1750,77452,1766],{},[1742,77454,2607],{},[1750,77456,13651],{},[1699,77458,77459,77461],{},[898,77460,12471],{},[1750,77462,3751],{},[1750,77464,1766],{},[1742,77466,3079],{},[902,77468,77469],{"encoding":904},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[883,77471,77473],{"className":77472},[886],[888,77474,77475],{"xmlns":890},[892,77476,77477,77501],{},[895,77478,77479,77481,77483,77493,77495,77497,77499],{},[898,77480,13916],{},[898,77482,49262],{},[1699,77484,77485,77487],{},[898,77486,1812],{},[895,77488,77489,77491],{},[1750,77490,3815],{"mathvariant":1747},[1750,77492,3815],{"mathvariant":1747},[1750,77494,1766],{},[1742,77496,3929],{},[1750,77498,2604],{},[1742,77500,2607],{},[902,77502,77503],{"encoding":904},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[883,77506,77508],{"className":77507},[886],[888,77509,77510],{"xmlns":890},[892,77511,77512,77548],{},[895,77513,77514,77520,77522,77524,77526,77528,77530,77532,77534,77536,77538,77540,77542,77544,77546],{},[1699,77515,77516,77518],{},[898,77517,1776],{},[1750,77519,3751],{},[1750,77521,1766],{},[898,77523,1773],{},[898,77525,1812],{},[1750,77527,1753],{"stretchy":1752},[1742,77529,3079],{},[1750,77531,1763],{"stretchy":1752},[1750,77533,1766],{},[1742,77535,46942],{},[1750,77537,1758],{},[1742,77539,14865],{},[1750,77541,1861],{},[1742,77543,45167],{},[1750,77545,1766],{},[1742,77547,7902],{},[902,77549,77550],{"encoding":904},"P^* = MC(10) = 30 - 40 + 15 = 5",[724,77552,77553],{},[38,77554,77555],{},"Závěr.",[883,77557,77559],{"className":77558},[886],[888,77560,77561],{"xmlns":890,"display":36989},[892,77562,77563,77649],{},[895,77564,77565,77567,77569,77571,77573,77575,77577,77579],{},[898,77566,1776],{},[1750,77568,1766],{},[898,77570,1779],{},[1750,77572,1753],{"stretchy":1752},[898,77574,12471],{},[1750,77576,1763],{"stretchy":1752},[1750,77578,1766],{},[895,77580,77581,77583],{},[1750,77582,76429],{"fence":1916},[4577,77584,77585,77627],{"rowspacing":76432,"columnalign":76433,"columnspacing":24875},[4582,77586,77587,77611],{},[4585,77588,77589],{},[3586,77590,77591],{"scriptlevel":2607,"displaystyle":1752},[895,77592,77593,77595,77601,77603,77605,77607,77609],{},[1742,77594,77134],{},[1699,77596,77597,77599],{},[898,77598,12471],{},[1742,77600,1872],{},[1750,77602,1758],{},[1742,77604,7859],{},[898,77606,12471],{},[1750,77608,1861],{},[1742,77610,45167],{},[4585,77612,77613],{},[3586,77614,77615],{"scriptlevel":2607,"displaystyle":1752},[895,77616,77617,77619,77621,77623,77625],{},[1969,77618,76460],{},[898,77620,12471],{},[1750,77622,14143],{},[1742,77624,3079],{},[1750,77626,1917],{"separator":1916},[4582,77628,77629,77635],{},[4585,77630,77631],{},[3586,77632,77633],{"scriptlevel":2607,"displaystyle":1752},[1742,77634,2607],{},[4585,77636,77637],{},[3586,77638,77639],{"scriptlevel":2607,"displaystyle":1752},[895,77640,77641,77643,77645,77647],{},[1969,77642,76460],{},[898,77644,12471],{},[1750,77646,2624],{},[1742,77648,3130],{},[902,77650,77651],{"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}",[724,77653,77654],{},[614,77655,77656,77657,77672,77673,2313],{},"Obrázek 3.15: Grafická ilustrace nabídky firmy odvozené z části křivky ",[883,77658,77660],{"className":77659},[886],[888,77661,77662],{"xmlns":890},[892,77663,77664,77670],{},[895,77665,77666,77668],{},[898,77667,1773],{},[898,77669,1812],{},[902,77671,64215],{"encoding":904}," ležící nad minimem ",[883,77674,77676],{"className":77675},[886],[888,77677,77678],{"xmlns":890},[892,77679,77680,77688],{},[895,77681,77682,77684,77686],{},[898,77683,13916],{},[898,77685,49262],{},[898,77687,1812],{},[902,77689,64234],{"encoding":904},[115,77691,77693],{"id":77692},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[724,77695,77696,77697,77701,77702,77717,77718,77738,77739,2028,77742,77745,77746,77748,77749,3755,77771,77773,77774,2028,77776,67649,77779,1647,77782,50737,77797,77812],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[207,77698,77700],{"className":77699,"dataFsResolvedFilePath":800,"href":801},[210],"poptávky",". Pro lineární poptávku je ",[883,77703,77705],{"className":77704},[886],[888,77706,77707],{"xmlns":890},[892,77708,77709,77715],{},[895,77710,77711,77713],{},[898,77712,5326],{},[898,77714,13658],{},[902,77716,13758],{"encoding":904}," kvadratická. Průměrný příjem je podíl ",[883,77719,77721],{"className":77720},[886],[888,77722,77723],{"xmlns":890},[892,77724,77725,77735],{},[895,77726,77727,77729,77731,77733],{},[898,77728,5326],{},[898,77730,13658],{},[898,77732,1748],{"mathvariant":1747},[898,77734,12471],{},[902,77736,77737],{"encoding":904},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[38,77740,77741],{},"fixních",[38,77743,77744],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[38,77747,73248],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[883,77750,77752],{"className":77751},[886],[888,77753,77754],{"xmlns":890},[892,77755,77756,77768],{},[895,77757,77758,77760,77762,77764,77766],{},[898,77759,5326],{},[898,77761,13658],{},[1750,77763,1758],{},[898,77765,5326],{},[898,77767,1812],{},[902,77769,77770],{"encoding":904},"TR - TC",[38,77772,64095],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[38,77775,65407],{},[38,77777,77778],{},"mezní náklady",[207,77780,1145],{"className":77781,"dataFsResolvedFilePath":764,"href":765},[210],[883,77783,77785],{"className":77784},[886],[888,77786,77787],{"xmlns":890},[892,77788,77789,77795],{},[895,77790,77791,77793],{},[898,77792,5326],{},[898,77794,13658],{},[902,77796,13758],{"encoding":904},[883,77798,77800],{"className":77799},[886],[888,77801,77802],{"xmlns":890},[892,77803,77804,77810],{},[895,77805,77806,77808],{},[898,77807,5326],{},[898,77809,1812],{},[902,77811,12916],{"encoding":904}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[120,77814,77815,77877,77943,78005],{},[123,77816,77817,77820,77821,20027,77836,2313],{},[38,77818,77819],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[883,77822,77824],{"className":77823},[886],[888,77825,77826],{"xmlns":890},[892,77827,77828,77834],{},[895,77829,77830,77832],{},[898,77831,13916],{},[898,77833,1812],{},[902,77835,64483],{"encoding":904},[883,77837,77839],{"className":77838},[886],[888,77840,77841],{"xmlns":890},[892,77842,77843,77875],{},[895,77844,77845,77847,77849,77851,77857,77859,77861,77863,77865,77867,77873],{},[898,77846,13916],{},[898,77848,1812],{},[1750,77850,1753],{"stretchy":1752},[5535,77852,77853,77855],{},[898,77854,12471],{},[1742,77856,2607],{},[1750,77858,1763],{"stretchy":1752},[1750,77860,1766],{},[898,77862,1773],{},[898,77864,1812],{},[1750,77866,1753],{"stretchy":1752},[5535,77868,77869,77871],{},[898,77870,12471],{},[1742,77872,2607],{},[1750,77874,1763],{"stretchy":1752},[902,77876,71492],{"encoding":904},[123,77878,77879,77820,77882,20027,77899,2313],{},[38,77880,77881],{},"Princip minimalizace průměrných variabilních nákladů:",[883,77883,77885],{"className":77884},[886],[888,77886,77887],{"xmlns":890},[892,77888,77889,77897],{},[895,77890,77891,77893,77895],{},[898,77892,13916],{},[898,77894,49262],{},[898,77896,1812],{},[902,77898,64234],{"encoding":904},[883,77900,77902],{"className":77901},[886],[888,77903,77904],{"xmlns":890},[892,77905,77906,77940],{},[895,77907,77908,77910,77912,77914,77916,77922,77924,77926,77928,77930,77932,77938],{},[898,77909,13916],{},[898,77911,49262],{},[898,77913,1812],{},[1750,77915,1753],{"stretchy":1752},[5535,77917,77918,77920],{},[898,77919,12471],{},[1742,77921,2607],{},[1750,77923,1763],{"stretchy":1752},[1750,77925,1766],{},[898,77927,1773],{},[898,77929,1812],{},[1750,77931,1753],{"stretchy":1752},[5535,77933,77934,77936],{},[898,77935,12471],{},[1742,77937,2607],{},[1750,77939,1763],{"stretchy":1752},[902,77941,77942],{"encoding":904},"AVC(Q_0) = MC(Q_0)",[123,77944,77945,77948,77949,20027,77964,2313],{},[38,77946,77947],{},"Princip maximalizace zisku:"," v bodě maxima ",[883,77950,77952],{"className":77951},[886],[888,77953,77954],{"xmlns":890},[892,77955,77956,77962],{},[895,77957,77958,77960],{},[898,77959,1776],{},[898,77961,13658],{},[902,77963,72402],{"encoding":904},[883,77965,77967],{"className":77966},[886],[888,77968,77969],{"xmlns":890},[892,77970,77971,78003],{},[895,77972,77973,77975,77977,77979,77985,77987,77989,77991,77993,77995,78001],{},[898,77974,1773],{},[898,77976,13658],{},[1750,77978,1753],{"stretchy":1752},[5535,77980,77981,77983],{},[898,77982,12471],{},[1742,77984,2607],{},[1750,77986,1763],{"stretchy":1752},[1750,77988,1766],{},[898,77990,1773],{},[898,77992,1812],{},[1750,77994,1753],{"stretchy":1752},[5535,77996,77997,77999],{},[898,77998,12471],{},[1742,78000,2607],{},[1750,78002,1763],{"stretchy":1752},[902,78004,74568],{"encoding":904},[123,78006,78007,1647,78010,16121,78046,76848,78067,5424,78080,76530,78097,2313],{},[38,78008,78009],{},"Funkce nabídky firmy:",[883,78011,78013],{"className":78012},[886],[888,78014,78015],{"xmlns":890},[892,78016,78017,78043],{},[895,78018,78019,78021,78023,78025,78027,78029,78031,78033,78035,78037,78039,78041],{},[898,78020,1776],{},[1750,78022,1766],{},[898,78024,1779],{},[1750,78026,1753],{"stretchy":1752},[898,78028,12471],{},[1750,78030,1763],{"stretchy":1752},[1750,78032,1766],{},[898,78034,1773],{},[898,78036,1812],{},[1750,78038,1753],{"stretchy":1752},[898,78040,12471],{},[1750,78042,1763],{"stretchy":1752},[902,78044,78045],{"encoding":904},"P = S(Q) = MC(Q)",[883,78047,78049],{"className":78048},[886],[888,78050,78051],{"xmlns":890},[892,78052,78053,78065],{},[895,78054,78055,78057,78059],{},[898,78056,12471],{},[1750,78058,14143],{},[1699,78060,78061,78063],{},[898,78062,12471],{},[1750,78064,3751],{},[902,78066,76847],{"encoding":904},[883,78068,78070],{"className":78069},[886],[888,78071,78072],{"xmlns":890},[892,78073,78074,78078],{},[895,78075,78076],{},[1742,78077,2607],{},[902,78079,2607],{"encoding":904},[883,78081,78083],{"className":78082},[886],[888,78084,78085],{"xmlns":890},[892,78086,78087,78095],{},[895,78088,78089],{},[1699,78090,78091,78093],{},[898,78092,12471],{},[1750,78094,3751],{},[902,78096,38767],{"encoding":904},[883,78098,78100],{"className":78099},[886],[888,78101,78102],{"xmlns":890},[892,78103,78104,78112],{},[895,78105,78106,78108,78110],{},[898,78107,13916],{},[898,78109,49262],{},[898,78111,1812],{},[902,78113,64234],{"encoding":904},[115,78115,58805],{"id":58804},[152,78117,78118,78121,78124,78127,78130,78133,78136,78139,78142,78145,78148],{},[123,78119,78120],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[123,78122,78123],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[123,78125,78126],{},"Jak se vypočte mezní příjem a co udává?",[123,78128,78129],{},"Z jakých složek se skládají celkové náklady?",[123,78131,78132],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[123,78134,78135],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[123,78137,78138],{},"Jak se stanoví přibližně změna celkových nákladů?",[123,78140,78141],{},"Jak se vypočte zisk?",[123,78143,78144],{},"Jaká vlastnost platí v bodě maxima zisku?",[123,78146,78147],{},"Co jsou body zvratu? Jak se najdou?",[123,78149,78150],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[115,78152,78154],{"id":78153},"úlohy-31328","Úlohy 3.1–3.28",[198,78156,78158],{"id":78157},"příjem-3135","Příjem (3.1–3.5)",[724,78160,78161,54349,78164,78192,78193,78208,78209,78224,78225,78240,78241,1343,78256,1343,78271,78286],{},[38,78162,78163],{},"3.1",[883,78165,78167],{"className":78166},[886],[888,78168,78169],{"xmlns":890},[892,78170,78171,78189],{},[895,78172,78173,78175,78177,78179,78181,78183,78185,78187],{},[898,78174,1776],{},[1750,78176,1766],{},[898,78178,5541],{},[1750,78180,1753],{"stretchy":1752},[898,78182,12471],{},[1750,78184,1763],{"stretchy":1752},[1750,78186,1766],{},[1742,78188,4078],{},[902,78190,78191],{"encoding":904},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[883,78194,78196],{"className":78195},[886],[888,78197,78198],{"xmlns":890},[892,78199,78200,78206],{},[895,78201,78202,78204],{},[898,78203,5326],{},[898,78205,13658],{},[902,78207,13758],{"encoding":904},", průměrný příjem ",[883,78210,78212],{"className":78211},[886],[888,78213,78214],{"xmlns":890},[892,78215,78216,78222],{},[895,78217,78218,78220],{},[898,78219,13916],{},[898,78221,13658],{},[902,78223,64368],{"encoding":904}," a mezní příjem ",[883,78226,78228],{"className":78227},[886],[888,78229,78230],{"xmlns":890},[892,78231,78232,78238],{},[895,78233,78234,78236],{},[898,78235,1773],{},[898,78237,13658],{},[902,78239,16282],{"encoding":904},". (c) Vypočtěte ",[883,78242,78244],{"className":78243},[886],[888,78245,78246],{"xmlns":890},[892,78247,78248,78254],{},[895,78249,78250,78252],{},[898,78251,5326],{},[898,78253,13658],{},[902,78255,13758],{"encoding":904},[883,78257,78259],{"className":78258},[886],[888,78260,78261],{"xmlns":890},[892,78262,78263,78269],{},[895,78264,78265,78267],{},[898,78266,13916],{},[898,78268,13658],{},[902,78270,64368],{"encoding":904},[883,78272,78274],{"className":78273},[886],[888,78275,78276],{"xmlns":890},[892,78277,78278,78284],{},[895,78279,78280,78282],{},[898,78281,1773],{},[898,78283,13658],{},[902,78285,16282],{"encoding":904}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,78288,78289,54349,78292,78192,78328,78208,78343,78224,78358,78240,78373,1343,78388,1343,78403,78418],{},[38,78290,78291],{},"3.2",[883,78293,78295],{"className":78294},[886],[888,78296,78297],{"xmlns":890},[892,78298,78299,78325],{},[895,78300,78301,78303,78305,78307,78309,78311,78313,78315,78317,78319,78321,78323],{},[898,78302,1776],{},[1750,78304,1766],{},[898,78306,5541],{},[1750,78308,1753],{"stretchy":1752},[898,78310,12471],{},[1750,78312,1763],{"stretchy":1752},[1750,78314,1766],{},[1750,78316,1758],{},[1742,78318,4268],{},[898,78320,12471],{},[1750,78322,1861],{},[1742,78324,6465],{},[902,78326,78327],{"encoding":904},"P = D(Q) = -0{,}5Q + 20",[883,78329,78331],{"className":78330},[886],[888,78332,78333],{"xmlns":890},[892,78334,78335,78341],{},[895,78336,78337,78339],{},[898,78338,5326],{},[898,78340,13658],{},[902,78342,13758],{"encoding":904},[883,78344,78346],{"className":78345},[886],[888,78347,78348],{"xmlns":890},[892,78349,78350,78356],{},[895,78351,78352,78354],{},[898,78353,13916],{},[898,78355,13658],{},[902,78357,64368],{"encoding":904},[883,78359,78361],{"className":78360},[886],[888,78362,78363],{"xmlns":890},[892,78364,78365,78371],{},[895,78366,78367,78369],{},[898,78368,1773],{},[898,78370,13658],{},[902,78372,16282],{"encoding":904},[883,78374,78376],{"className":78375},[886],[888,78377,78378],{"xmlns":890},[892,78379,78380,78386],{},[895,78381,78382,78384],{},[898,78383,5326],{},[898,78385,13658],{},[902,78387,13758],{"encoding":904},[883,78389,78391],{"className":78390},[886],[888,78392,78393],{"xmlns":890},[892,78394,78395,78401],{},[895,78396,78397,78399],{},[898,78398,13916],{},[898,78400,13658],{},[902,78402,64368],{"encoding":904},[883,78404,78406],{"className":78405},[886],[888,78407,78408],{"xmlns":890},[892,78409,78410,78416],{},[895,78411,78412,78414],{},[898,78413,1773],{},[898,78415,13658],{},[902,78417,16282],{"encoding":904}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[724,78420,78421,54349,78424,78461,78462,78208,78477,78224,78492,78507,78508,16121,78523,78549,78550,78565,78566,1343,78581,16121,78596,78549,78621,78636,78637,78650,78651,78666,78667,78682,78683,1343,78696,1343,78711,1343,78726,2313],{},[38,78422,78423],{},"3.3",[883,78425,78427],{"className":78426},[886],[888,78428,78429],{"xmlns":890},[892,78430,78431,78458],{},[895,78432,78433,78435,78437,78439,78441,78443,78445,78447,78450,78452],{},[898,78434,1776],{},[1750,78436,1766],{},[898,78438,5541],{},[1750,78440,1753],{"stretchy":1752},[898,78442,12471],{},[1750,78444,1763],{"stretchy":1752},[1750,78446,1766],{},[1742,78448,78449],{},"1200",[1750,78451,1758],{},[1699,78453,78454,78456],{},[898,78455,12471],{},[1742,78457,1872],{},[902,78459,78460],{"encoding":904},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[883,78463,78465],{"className":78464},[886],[888,78466,78467],{"xmlns":890},[892,78468,78469,78475],{},[895,78470,78471,78473],{},[898,78472,5326],{},[898,78474,13658],{},[902,78476,13758],{"encoding":904},[883,78478,78480],{"className":78479},[886],[888,78481,78482],{"xmlns":890},[892,78483,78484,78490],{},[895,78485,78486,78488],{},[898,78487,13916],{},[898,78489,13658],{},[902,78491,64368],{"encoding":904},[883,78493,78495],{"className":78494},[886],[888,78496,78497],{"xmlns":890},[892,78498,78499,78505],{},[895,78500,78501,78503],{},[898,78502,1773],{},[898,78504,13658],{},[902,78506,16282],{"encoding":904},". (b) Vypočtěte ",[883,78509,78511],{"className":78510},[886],[888,78512,78513],{"xmlns":890},[892,78514,78515,78521],{},[895,78516,78517,78519],{},[898,78518,5326],{},[898,78520,13658],{},[902,78522,13758],{"encoding":904},[883,78524,78526],{"className":78525},[886],[888,78527,78528],{"xmlns":890},[892,78529,78530,78546],{},[895,78531,78532,78534,78536,78538,78540,78542,78544],{},[898,78533,12471],{},[1750,78535,1766],{},[1742,78537,3079],{},[1750,78539,1917],{"separator":1916},[1742,78541,6465],{},[1750,78543,1917],{"separator":1916},[1742,78545,46942],{},[902,78547,78548],{"encoding":904},"Q = 10, 20, 30"," a rozhodněte, kdy ",[883,78551,78553],{"className":78552},[886],[888,78554,78555],{"xmlns":890},[892,78556,78557,78563],{},[895,78558,78559,78561],{},[898,78560,5326],{},[898,78562,13658],{},[902,78564,13758],{"encoding":904}," roste, resp. klesá. (c) Vypočtěte ",[883,78567,78569],{"className":78568},[886],[888,78570,78571],{"xmlns":890},[892,78572,78573,78579],{},[895,78574,78575,78577],{},[898,78576,13916],{},[898,78578,13658],{},[902,78580,64368],{"encoding":904},[883,78582,78584],{"className":78583},[886],[888,78585,78586],{"xmlns":890},[892,78587,78588,78594],{},[895,78589,78590,78592],{},[898,78591,1773],{},[898,78593,13658],{},[902,78595,16282],{"encoding":904},[883,78597,78599],{"className":78598},[886],[888,78600,78601],{"xmlns":890},[892,78602,78603,78619],{},[895,78604,78605,78607,78609,78611,78613,78615,78617],{},[898,78606,12471],{},[1750,78608,1766],{},[1742,78610,3079],{},[1750,78612,1917],{"separator":1916},[1742,78614,6465],{},[1750,78616,1917],{"separator":1916},[1742,78618,46942],{},[902,78620,78548],{"encoding":904},[883,78622,78624],{"className":78623},[886],[888,78625,78626],{"xmlns":890},[892,78627,78628,78634],{},[895,78629,78630,78632],{},[898,78631,1773],{},[898,78633,13658],{},[902,78635,16282],{"encoding":904}," roste, resp. klesá. (d) Vypočtěte ",[883,78638,78640],{"className":78639},[886],[888,78641,78642],{"xmlns":890},[892,78643,78644,78648],{},[895,78645,78646],{},[898,78647,12471],{},[902,78649,12471],{"encoding":904},", které maximalizuje ",[883,78652,78654],{"className":78653},[886],[888,78655,78656],{"xmlns":890},[892,78657,78658,78664],{},[895,78659,78660,78662],{},[898,78661,5326],{},[898,78663,13658],{},[902,78665,13758],{"encoding":904}," a stanovte příslušnou hodnotu maxima ",[883,78668,78670],{"className":78669},[886],[888,78671,78672],{"xmlns":890},[892,78673,78674,78680],{},[895,78675,78676,78678],{},[898,78677,5326],{},[898,78679,13658],{},[902,78681,13758],{"encoding":904},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[883,78684,78686],{"className":78685},[886],[888,78687,78688],{"xmlns":890},[892,78689,78690,78694],{},[895,78691,78692],{},[898,78693,5541],{},[902,78695,5541],{"encoding":904},[883,78697,78699],{"className":78698},[886],[888,78700,78701],{"xmlns":890},[892,78702,78703,78709],{},[895,78704,78705,78707],{},[898,78706,5326],{},[898,78708,13658],{},[902,78710,13758],{"encoding":904},[883,78712,78714],{"className":78713},[886],[888,78715,78716],{"xmlns":890},[892,78717,78718,78724],{},[895,78719,78720,78722],{},[898,78721,13916],{},[898,78723,13658],{},[902,78725,64368],{"encoding":904},[883,78727,78729],{"className":78728},[886],[888,78730,78731],{"xmlns":890},[892,78732,78733,78739],{},[895,78734,78735,78737],{},[898,78736,1773],{},[898,78738,13658],{},[902,78740,16282],{"encoding":904},[724,78742,78743,78746,78747,78777,78778,78793,78794,19790,78807,1343,78825,1343,78842,78860,78861,78883,78884,78899,78900,78913,78914,2313],{},[38,78744,78745],{},"3.4"," Je dán celkový příjem ",[883,78748,78750],{"className":78749},[886],[888,78751,78752],{"xmlns":890},[892,78753,78754,78774],{},[895,78755,78756,78758,78760,78762,78764,78766,78768],{},[898,78757,5326],{},[898,78759,13658],{},[1750,78761,1766],{},[1742,78763,78449],{},[898,78765,12471],{},[1750,78767,1758],{},[1699,78769,78770,78772],{},[898,78771,12471],{},[1742,78773,7822],{},[902,78775,78776],{"encoding":904},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[883,78779,78781],{"className":78780},[886],[888,78782,78783],{"xmlns":890},[892,78784,78785,78791],{},[895,78786,78787,78789],{},[898,78788,5326],{},[898,78790,13658],{},[902,78792,13758],{"encoding":904}," vzhledem ke ",[883,78795,78797],{"className":78796},[886],[888,78798,78799],{"xmlns":890},[892,78800,78801,78805],{},[895,78802,78803],{},[898,78804,12471],{},[902,78806,12471],{"encoding":904},[883,78808,78810],{"className":78809},[886],[888,78811,78812],{"xmlns":890},[892,78813,78814,78822],{},[895,78815,78816,78818,78820],{},[898,78817,12471],{},[1750,78819,1766],{},[1742,78821,7902],{},[902,78823,78824],{"encoding":904},"Q = 5",[883,78826,78828],{"className":78827},[886],[888,78829,78830],{"xmlns":890},[892,78831,78832,78840],{},[895,78833,78834,78836,78838],{},[898,78835,12471],{},[1750,78837,1766],{},[1742,78839,15239],{},[902,78841,15242],{"encoding":904},[883,78843,78845],{"className":78844},[886],[888,78846,78847],{"xmlns":890},[892,78848,78849,78857],{},[895,78850,78851,78853,78855],{},[898,78852,12471],{},[1750,78854,1766],{},[1742,78856,4903],{},[902,78858,78859],{"encoding":904},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[883,78862,78864],{"className":78863},[886],[888,78865,78866],{"xmlns":890},[892,78867,78868,78880],{},[895,78869,78870,78872,78874,78876,78878],{},[898,78871,1773],{},[898,78873,13658],{},[1750,78875,1753],{"stretchy":1752},[1742,78877,3079],{},[1750,78879,1763],{"stretchy":1752},[902,78881,78882],{"encoding":904},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[883,78885,78887],{"className":78886},[886],[888,78888,78889],{"xmlns":890},[892,78890,78891,78897],{},[895,78892,78893,78895],{},[898,78894,5326],{},[898,78896,13658],{},[902,78898,13758],{"encoding":904},", jestliže se ",[883,78901,78903],{"className":78902},[886],[888,78904,78905],{"xmlns":890},[892,78906,78907,78911],{},[895,78908,78909],{},[898,78910,12471],{},[902,78912,12471],{"encoding":904}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[883,78915,78917],{"className":78916},[886],[888,78918,78919],{"xmlns":890},[892,78920,78921,78927],{},[895,78922,78923,78925],{},[898,78924,5326],{},[898,78926,13658],{},[902,78928,13758],{"encoding":904},[724,78930,78931,78934,78935,78961,78962,78977,78978,78899,78993,79006],{},[38,78932,78933],{},"3.5"," Je dán mezní příjem ",[883,78936,78938],{"className":78937},[886],[888,78939,78940],{"xmlns":890},[892,78941,78942,78958],{},[895,78943,78944,78946,78948,78950,78952,78954,78956],{},[898,78945,1773],{},[898,78947,13658],{},[1750,78949,1766],{},[1750,78951,1758],{},[898,78953,12471],{},[1750,78955,1861],{},[1742,78957,6465],{},[902,78959,78960],{"encoding":904},"MR = -Q + 20",". (a) Určete celkový příjem ",[883,78963,78965],{"className":78964},[886],[888,78966,78967],{"xmlns":890},[892,78968,78969,78975],{},[895,78970,78971,78973],{},[898,78972,5326],{},[898,78974,13658],{},[902,78976,13758],{"encoding":904},". (b) Vypočtěte změnu ",[883,78979,78981],{"className":78980},[886],[888,78982,78983],{"xmlns":890},[892,78984,78985,78991],{},[895,78986,78987,78989],{},[898,78988,5326],{},[898,78990,13658],{},[902,78992,13758],{"encoding":904},[883,78994,78996],{"className":78995},[886],[888,78997,78998],{"xmlns":890},[892,78999,79000,79004],{},[895,79001,79002],{},[898,79003,12471],{},[902,79005,12471],{"encoding":904}," změní z 8 na 12.",[198,79008,79010],{"id":79009},"náklady-36316","Náklady (3.6–3.16)",[724,79012,79013,79016,79017,79057,79058,79073,79074,79091,79092,79109,79110,79125,79126,79141,79142,78507,79157,1343,79172,1343,79189,1343,79206,1343,79221,1343,79236,16121,79251,79269,79270,1343,79285,1343,79300,79315],{},[38,79014,79015],{},"3.6"," Jsou dány celkové náklady ",[883,79018,79020],{"className":79019},[886],[888,79021,79022],{"xmlns":890},[892,79023,79024,79054],{},[895,79025,79026,79028,79030,79032,79034,79036,79038,79040,79042],{},[898,79027,5326],{},[898,79029,1812],{},[1750,79031,1766],{},[1742,79033,4078],{},[1750,79035,1861],{},[1742,79037,1872],{},[898,79039,12471],{},[1750,79041,1861],{},[3586,79043,79044],{"scriptlevel":2607,"displaystyle":1752},[3423,79045,79046,79052],{},[1699,79047,79048,79050],{},[898,79049,12471],{},[1742,79051,1872],{},[1742,79053,3079],{},[902,79055,79056],{"encoding":904},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[883,79059,79061],{"className":79060},[886],[888,79062,79063],{"xmlns":890},[892,79064,79065,79071],{},[895,79066,79067,79069],{},[898,79068,20069],{},[898,79070,1812],{},[902,79072,64414],{"encoding":904},", celkové variabilní náklady ",[883,79075,79077],{"className":79076},[886],[888,79078,79079],{"xmlns":890},[892,79080,79081,79089],{},[895,79082,79083,79085,79087],{},[898,79084,5326],{},[898,79086,49262],{},[898,79088,1812],{},[902,79090,64432],{"encoding":904},", průměrné variabilní náklady ",[883,79093,79095],{"className":79094},[886],[888,79096,79097],{"xmlns":890},[892,79098,79099,79107],{},[895,79100,79101,79103,79105],{},[898,79102,13916],{},[898,79104,49262],{},[898,79106,1812],{},[902,79108,64234],{"encoding":904},", variabilní náklady na jednotku ",[883,79111,79113],{"className":79112},[886],[888,79114,79115],{"xmlns":890},[892,79116,79117,79123],{},[895,79118,79119,79121],{},[898,79120,49262],{},[898,79122,1812],{},[902,79124,72528],{"encoding":904},", průměrné náklady ",[883,79127,79129],{"className":79128},[886],[888,79130,79131],{"xmlns":890},[892,79132,79133,79139],{},[895,79134,79135,79137],{},[898,79136,13916],{},[898,79138,1812],{},[902,79140,64483],{"encoding":904}," a mezní náklady ",[883,79143,79145],{"className":79144},[886],[888,79146,79147],{"xmlns":890},[892,79148,79149,79155],{},[895,79150,79151,79153],{},[898,79152,1773],{},[898,79154,1812],{},[902,79156,64215],{"encoding":904},[883,79158,79160],{"className":79159},[886],[888,79161,79162],{"xmlns":890},[892,79163,79164,79170],{},[895,79165,79166,79168],{},[898,79167,5326],{},[898,79169,1812],{},[902,79171,12916],{"encoding":904},[883,79173,79175],{"className":79174},[886],[888,79176,79177],{"xmlns":890},[892,79178,79179,79187],{},[895,79180,79181,79183,79185],{},[898,79182,5326],{},[898,79184,49262],{},[898,79186,1812],{},[902,79188,64432],{"encoding":904},[883,79190,79192],{"className":79191},[886],[888,79193,79194],{"xmlns":890},[892,79195,79196,79204],{},[895,79197,79198,79200,79202],{},[898,79199,13916],{},[898,79201,49262],{},[898,79203,1812],{},[902,79205,64234],{"encoding":904},[883,79207,79209],{"className":79208},[886],[888,79210,79211],{"xmlns":890},[892,79212,79213,79219],{},[895,79214,79215,79217],{},[898,79216,49262],{},[898,79218,1812],{},[902,79220,72528],{"encoding":904},[883,79222,79224],{"className":79223},[886],[888,79225,79226],{"xmlns":890},[892,79227,79228,79234],{},[895,79229,79230,79232],{},[898,79231,13916],{},[898,79233,1812],{},[902,79235,64483],{"encoding":904},[883,79237,79239],{"className":79238},[886],[888,79240,79241],{"xmlns":890},[892,79242,79243,79249],{},[895,79244,79245,79247],{},[898,79246,1773],{},[898,79248,1812],{},[902,79250,64215],{"encoding":904},[883,79252,79254],{"className":79253},[886],[888,79255,79256],{"xmlns":890},[892,79257,79258,79266],{},[895,79259,79260,79262,79264],{},[898,79261,12471],{},[1750,79263,1766],{},[1742,79265,3936],{},[902,79267,79268],{"encoding":904},"Q = 50",". (c) Rozhodněte, kdy ",[883,79271,79273],{"className":79272},[886],[888,79274,79275],{"xmlns":890},[892,79276,79277,79283],{},[895,79278,79279,79281],{},[898,79280,5326],{},[898,79282,1812],{},[902,79284,12916],{"encoding":904},[883,79286,79288],{"className":79287},[886],[888,79289,79290],{"xmlns":890},[892,79291,79292,79298],{},[895,79293,79294,79296],{},[898,79295,13916],{},[898,79297,1812],{},[902,79299,64483],{"encoding":904},[883,79301,79303],{"className":79302},[886],[888,79304,79305],{"xmlns":890},[892,79306,79307,79313],{},[895,79308,79309,79311],{},[898,79310,1773],{},[898,79312,1812],{},[902,79314,64215],{"encoding":904}," rostou, resp. klesají.",[724,79317,79318,79321,79322,79141,79352,79367,79368,79383,79384,1343,79399,1343,79414,2313],{},[38,79319,79320],{},"3.7"," Jsou dány průměrné náklady ",[883,79323,79325],{"className":79324},[886],[888,79326,79327],{"xmlns":890},[892,79328,79329,79349],{},[895,79330,79331,79333,79335,79337,79345,79347],{},[898,79332,13916],{},[898,79334,1812],{},[1750,79336,1766],{},[3586,79338,79339],{"scriptlevel":2607,"displaystyle":1752},[3423,79340,79341,79343],{},[1742,79342,4078],{},[898,79344,12471],{},[1750,79346,1861],{},[1742,79348,6465],{},[902,79350,79351],{"encoding":904},"AC = \\tfrac{100}{Q} + 20",[883,79353,79355],{"className":79354},[886],[888,79356,79357],{"xmlns":890},[892,79358,79359,79365],{},[895,79360,79361,79363],{},[898,79362,1773],{},[898,79364,1812],{},[902,79366,64215],{"encoding":904},". (a) Určete celkové náklady ",[883,79369,79371],{"className":79370},[886],[888,79372,79373],{"xmlns":890},[892,79374,79375,79381],{},[895,79376,79377,79379],{},[898,79378,5326],{},[898,79380,1812],{},[902,79382,12916],{"encoding":904},". (b) Načrtněte a geometricky charakterizujte křivky ",[883,79385,79387],{"className":79386},[886],[888,79388,79389],{"xmlns":890},[892,79390,79391,79397],{},[895,79392,79393,79395],{},[898,79394,13916],{},[898,79396,1812],{},[902,79398,64483],{"encoding":904},[883,79400,79402],{"className":79401},[886],[888,79403,79404],{"xmlns":890},[892,79405,79406,79412],{},[895,79407,79408,79410],{},[898,79409,5326],{},[898,79411,1812],{},[902,79413,12916],{"encoding":904},[883,79415,79417],{"className":79416},[886],[888,79418,79419],{"xmlns":890},[892,79420,79421,79427],{},[895,79422,79423,79425],{},[898,79424,1773],{},[898,79426,1812],{},[902,79428,64215],{"encoding":904},[724,79430,79431,79016,79434,79478,79479,1343,79496,1343,79511,1343,79528,1343,79543,1343,79560,2313],{},[38,79432,79433],{},"3.8",[883,79435,79437],{"className":79436},[886],[888,79438,79439],{"xmlns":890},[892,79440,79441,79475],{},[895,79442,79443,79445,79447,79449,79451,79453,79455,79457,79459,79461,79467,79469],{},[898,79444,5326],{},[898,79446,1812],{},[1750,79448,1766],{},[1742,79450,55626],{},[1750,79452,1861],{},[1742,79454,46942],{},[898,79456,12471],{},[1750,79458,1758],{},[1742,79460,3219],{},[1699,79462,79463,79465],{},[898,79464,12471],{},[1742,79466,1872],{},[1750,79468,1861],{},[1699,79470,79471,79473],{},[898,79472,12471],{},[1742,79474,7822],{},[902,79476,79477],{"encoding":904},"TC = 80 + 30Q - 6Q^2 + Q^3",". Určete ",[883,79480,79482],{"className":79481},[886],[888,79483,79484],{"xmlns":890},[892,79485,79486,79494],{},[895,79487,79488,79490,79492],{},[898,79489,5326],{},[898,79491,49262],{},[898,79493,1812],{},[902,79495,64432],{"encoding":904},[883,79497,79499],{"className":79498},[886],[888,79500,79501],{"xmlns":890},[892,79502,79503,79509],{},[895,79504,79505,79507],{},[898,79506,20069],{},[898,79508,1812],{},[902,79510,64414],{"encoding":904},[883,79512,79514],{"className":79513},[886],[888,79515,79516],{"xmlns":890},[892,79517,79518,79526],{},[895,79519,79520,79522,79524],{},[898,79521,13916],{},[898,79523,49262],{},[898,79525,1812],{},[902,79527,64234],{"encoding":904},[883,79529,79531],{"className":79530},[886],[888,79532,79533],{"xmlns":890},[892,79534,79535,79541],{},[895,79536,79537,79539],{},[898,79538,13916],{},[898,79540,1812],{},[902,79542,64483],{"encoding":904},[883,79544,79546],{"className":79545},[886],[888,79547,79548],{"xmlns":890},[892,79549,79550,79558],{},[895,79551,79552,79554,79556],{},[898,79553,13916],{},[898,79555,20069],{},[898,79557,1812],{},[902,79559,64450],{"encoding":904},[883,79561,79563],{"className":79562},[886],[888,79564,79565],{"xmlns":890},[892,79566,79567,79573],{},[895,79568,79569,79571],{},[898,79570,1773],{},[898,79572,1812],{},[902,79574,64215],{"encoding":904},[724,79576,79577,79016,79580,79610,79611,78793,79626,16121,79639,1343,79657,1343,79675,78860,79693,78883,79715,79730,79731,79744,79745,2313],{},[38,79578,79579],{},"3.9",[883,79581,79583],{"className":79582},[886],[888,79584,79585],{"xmlns":890},[892,79586,79587,79607],{},[895,79588,79589,79591,79593,79595,79597,79599,79601],{},[898,79590,5326],{},[898,79592,1812],{},[1750,79594,1766],{},[1742,79596,7658],{},[1750,79598,1861],{},[1742,79600,3123],{},[1699,79602,79603,79605],{},[898,79604,12471],{},[1742,79606,1872],{},[902,79608,79609],{"encoding":904},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[883,79612,79614],{"className":79613},[886],[888,79615,79616],{"xmlns":890},[892,79617,79618,79624],{},[895,79619,79620,79622],{},[898,79621,5326],{},[898,79623,1812],{},[902,79625,12916],{"encoding":904},[883,79627,79629],{"className":79628},[886],[888,79630,79631],{"xmlns":890},[892,79632,79633,79637],{},[895,79634,79635],{},[898,79636,12471],{},[902,79638,12471],{"encoding":904},[883,79640,79642],{"className":79641},[886],[888,79643,79644],{"xmlns":890},[892,79645,79646,79654],{},[895,79647,79648,79650,79652],{},[898,79649,12471],{},[1750,79651,1766],{},[1742,79653,3079],{},[902,79655,79656],{"encoding":904},"Q = 10",[883,79658,79660],{"className":79659},[886],[888,79661,79662],{"xmlns":890},[892,79663,79664,79672],{},[895,79665,79666,79668,79670],{},[898,79667,12471],{},[1750,79669,1766],{},[1742,79671,6465],{},[902,79673,79674],{"encoding":904},"Q = 20",[883,79676,79678],{"className":79677},[886],[888,79679,79680],{"xmlns":890},[892,79681,79682,79690],{},[895,79683,79684,79686,79688],{},[898,79685,12471],{},[1750,79687,1766],{},[1742,79689,46942],{},[902,79691,79692],{"encoding":904},"Q = 30",[883,79694,79696],{"className":79695},[886],[888,79697,79698],{"xmlns":890},[892,79699,79700,79712],{},[895,79701,79702,79704,79706,79708,79710],{},[898,79703,1773],{},[898,79705,1812],{},[1750,79707,1753],{"stretchy":1752},[1742,79709,45167],{},[1750,79711,1763],{"stretchy":1752},[902,79713,79714],{"encoding":904},"MC(15)",[883,79716,79718],{"className":79717},[886],[888,79719,79720],{"xmlns":890},[892,79721,79722,79728],{},[895,79723,79724,79726],{},[898,79725,5326],{},[898,79727,1812],{},[902,79729,12916],{"encoding":904}," v důsledku změny ",[883,79732,79734],{"className":79733},[886],[888,79735,79736],{"xmlns":890},[892,79737,79738,79742],{},[895,79739,79740],{},[898,79741,12471],{},[902,79743,12471],{"encoding":904}," z 15 na 20 a porovnejte se skutečnou změnou ",[883,79746,79748],{"className":79747},[886],[888,79749,79750],{"xmlns":890},[892,79751,79752,79758],{},[895,79753,79754,79756],{},[898,79755,5326],{},[898,79757,1812],{},[902,79759,12916],{"encoding":904},[724,79761,79762,79765,79766,79367,79802,79817,79818,78977,79837,79730,79852,79865],{},[38,79763,79764],{},"3.10"," Jsou dány mezní náklady ",[883,79767,79769],{"className":79768},[886],[888,79770,79771],{"xmlns":890},[892,79772,79773,79799],{},[895,79774,79775,79777,79779,79781,79783,79785,79787,79789,79791,79793],{},[898,79776,1773],{},[898,79778,1812],{},[1750,79780,1766],{},[1742,79782,12800],{},[1750,79784,1758],{},[1742,79786,50785],{},[898,79788,12471],{},[1750,79790,1861],{},[1742,79792,73482],{},[1699,79794,79795,79797],{},[898,79796,12471],{},[1742,79798,1872],{},[902,79800,79801],{"encoding":904},"MC = 60 - 16Q + 1{,}5Q^2",[883,79803,79805],{"className":79804},[886],[888,79806,79807],{"xmlns":890},[892,79808,79809,79815],{},[895,79810,79811,79813],{},[898,79812,5326],{},[898,79814,1812],{},[902,79816,12916],{"encoding":904},", jestliže fixní náklady ",[883,79819,79821],{"className":79820},[886],[888,79822,79823],{"xmlns":890},[892,79824,79825,79835],{},[895,79826,79827,79829,79831,79833],{},[898,79828,20069],{},[898,79830,1812],{},[1750,79832,1766],{},[1742,79834,4078],{},[902,79836,21266],{"encoding":904},[883,79838,79840],{"className":79839},[886],[888,79841,79842],{"xmlns":890},[892,79843,79844,79850],{},[895,79845,79846,79848],{},[898,79847,5326],{},[898,79849,1812],{},[902,79851,12916],{"encoding":904},[883,79853,79855],{"className":79854},[886],[888,79856,79857],{"xmlns":890},[892,79858,79859,79863],{},[895,79860,79861],{},[898,79862,12471],{},[902,79864,12471],{"encoding":904}," z 15 na 20.",[724,79867,79868,79016,79871,79914,79915,79928,79929,79944,79945,79960,79961,79928,79974,79944,79991,80008,80009,79928,80022,79944,80037,80052,80053,80073,80074,80097],{},[38,79869,79870],{},"3.11",[883,79872,79874],{"className":79873},[886],[888,79875,79876],{"xmlns":890},[892,79877,79878,79912],{},[895,79879,79880,79882,79884,79886,79888,79890,79892,79894,79896,79898,79904,79906],{},[898,79881,5326],{},[898,79883,1812],{},[1750,79885,1766],{},[1742,79887,4078],{},[1750,79889,1861],{},[1742,79891,6419],{},[898,79893,12471],{},[1750,79895,1758],{},[1742,79897,7902],{},[1699,79899,79900,79902],{},[898,79901,12471],{},[1742,79903,1872],{},[1750,79905,1861],{},[1699,79907,79908,79910],{},[898,79909,12471],{},[1742,79911,7822],{},[902,79913,69830],{"encoding":904},". (a) Určete ",[883,79916,79918],{"className":79917},[886],[888,79919,79920],{"xmlns":890},[892,79921,79922,79926],{},[895,79923,79924],{},[898,79925,12471],{},[902,79927,12471],{"encoding":904},", které minimalizuje ",[883,79930,79932],{"className":79931},[886],[888,79933,79934],{"xmlns":890},[892,79935,79936,79942],{},[895,79937,79938,79940],{},[898,79939,1773],{},[898,79941,1812],{},[902,79943,64215],{"encoding":904}," a stanovte příslušnou hodnotu minima ",[883,79946,79948],{"className":79947},[886],[888,79949,79950],{"xmlns":890},[892,79951,79952,79958],{},[895,79953,79954,79956],{},[898,79955,1773],{},[898,79957,1812],{},[902,79959,64215],{"encoding":904},". (b) Určete ",[883,79962,79964],{"className":79963},[886],[888,79965,79966],{"xmlns":890},[892,79967,79968,79972],{},[895,79969,79970],{},[898,79971,12471],{},[902,79973,12471],{"encoding":904},[883,79975,79977],{"className":79976},[886],[888,79978,79979],{"xmlns":890},[892,79980,79981,79989],{},[895,79982,79983,79985,79987],{},[898,79984,13916],{},[898,79986,49262],{},[898,79988,1812],{},[902,79990,64234],{"encoding":904},[883,79992,79994],{"className":79993},[886],[888,79995,79996],{"xmlns":890},[892,79997,79998,80006],{},[895,79999,80000,80002,80004],{},[898,80001,13916],{},[898,80003,49262],{},[898,80005,1812],{},[902,80007,64234],{"encoding":904},". (c) Určete ",[883,80010,80012],{"className":80011},[886],[888,80013,80014],{"xmlns":890},[892,80015,80016,80020],{},[895,80017,80018],{},[898,80019,12471],{},[902,80021,12471],{"encoding":904},[883,80023,80025],{"className":80024},[886],[888,80026,80027],{"xmlns":890},[892,80028,80029,80035],{},[895,80030,80031,80033],{},[898,80032,13916],{},[898,80034,1812],{},[902,80036,64483],{"encoding":904},[883,80038,80040],{"className":80039},[886],[888,80041,80042],{"xmlns":890},[892,80043,80044,80050],{},[895,80045,80046,80048],{},[898,80047,13916],{},[898,80049,1812],{},[902,80051,64483],{"encoding":904}," (rada: hledaný kořen ",[883,80054,80056],{"className":80055},[886],[888,80057,80058],{"xmlns":890},[892,80059,80060,80070],{},[895,80061,80062,80064],{},[898,80063,13916],{},[1699,80065,80066,80068],{},[898,80067,1812],{},[1750,80069,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,80071,80072],{"encoding":904},"AC'"," určete přibližně, patří do ",[883,80075,80077],{"className":80076},[886],[888,80078,80079],{"xmlns":890},[892,80080,80081,80094],{},[895,80082,80083,80085,80088,80090,80092],{},[1750,80084,1753],{"stretchy":1752},[1742,80086,80087],{},"4,7",[1750,80089,18067],{"separator":1916},[1742,80091,14933],{},[1750,80093,1763],{"stretchy":1752},[902,80095,80096],{"encoding":904},"(4{,}7; 4{,}8)",", zpřesněte).",[724,80099,80100,80103,80104,2984,80132,80149,80150,5424,80191,80212],{},[38,80101,80102],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[883,80105,80107],{"className":80106},[886],[888,80108,80109],{"xmlns":890},[892,80110,80111,80129],{},[895,80112,80113,80115,80117,80119,80121,80123,80125,80127],{},[898,80114,13916],{},[898,80116,1812],{},[1750,80118,1766],{},[898,80120,13916],{},[898,80122,1812],{},[1750,80124,1753],{"stretchy":1752},[898,80126,12471],{},[1750,80128,1763],{"stretchy":1752},[902,80130,80131],{"encoding":904},"AC = AC(Q)",[883,80133,80135],{"className":80134},[886],[888,80136,80137],{"xmlns":890},[892,80138,80139,80147],{},[895,80140,80141],{},[5535,80142,80143,80145],{},[898,80144,12471],{},[1742,80146,2607],{},[902,80148,47231],{"encoding":904}," minimum, pak platí ",[883,80151,80153],{"className":80152},[886],[888,80154,80155],{"xmlns":890},[892,80156,80157,80189],{},[895,80158,80159,80161,80163,80165,80171,80173,80175,80177,80179,80181,80187],{},[898,80160,13916],{},[898,80162,1812],{},[1750,80164,1753],{"stretchy":1752},[5535,80166,80167,80169],{},[898,80168,12471],{},[1742,80170,2607],{},[1750,80172,1763],{"stretchy":1752},[1750,80174,1766],{},[898,80176,1773],{},[898,80178,1812],{},[1750,80180,1753],{"stretchy":1752},[5535,80182,80183,80185],{},[898,80184,12471],{},[1742,80186,2607],{},[1750,80188,1763],{"stretchy":1752},[902,80190,71492],{"encoding":904},[883,80192,80194],{"className":80193},[886],[888,80195,80196],{"xmlns":890},[892,80197,80198,80210],{},[895,80199,80200,80202,80204,80206,80208],{},[898,80201,1773],{},[898,80203,1812],{},[1750,80205,1753],{"stretchy":1752},[898,80207,12471],{},[1750,80209,1763],{"stretchy":1752},[902,80211,76616],{"encoding":904}," jsou mezní náklady.",[724,80214,80215,79016,80218,79478,80252,79928,80265,79944,80280,2313],{},[38,80216,80217],{},"3.13",[883,80219,80221],{"className":80220},[886],[888,80222,80223],{"xmlns":890},[892,80224,80225,80249],{},[895,80226,80227,80229,80231,80233,80239,80241,80243,80245,80247],{},[898,80228,5326],{},[898,80230,1812],{},[1750,80232,1766],{},[1699,80234,80235,80237],{},[898,80236,12471],{},[1742,80238,1872],{},[1750,80240,1861],{},[1742,80242,1872],{},[898,80244,12471],{},[1750,80246,1861],{},[1742,80248,6419],{},[902,80250,80251],{"encoding":904},"TC = Q^2 + 2Q + 25",[883,80253,80255],{"className":80254},[886],[888,80256,80257],{"xmlns":890},[892,80258,80259,80263],{},[895,80260,80261],{},[898,80262,12471],{},[902,80264,12471],{"encoding":904},[883,80266,80268],{"className":80267},[886],[888,80269,80270],{"xmlns":890},[892,80271,80272,80278],{},[895,80273,80274,80276],{},[898,80275,13916],{},[898,80277,1812],{},[902,80279,64483],{"encoding":904},[883,80281,80283],{"className":80282},[886],[888,80284,80285],{"xmlns":890},[892,80286,80287,80293],{},[895,80288,80289,80291],{},[898,80290,13916],{},[898,80292,1812],{},[902,80294,64483],{"encoding":904},[724,80296,80297,80300,80301,2984,80333,80149,80350,5424,80393,80212],{},[38,80298,80299],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[883,80302,80304],{"className":80303},[886],[888,80305,80306],{"xmlns":890},[892,80307,80308,80330],{},[895,80309,80310,80312,80314,80316,80318,80320,80322,80324,80326,80328],{},[898,80311,13916],{},[898,80313,49262],{},[898,80315,1812],{},[1750,80317,1766],{},[898,80319,13916],{},[898,80321,49262],{},[898,80323,1812],{},[1750,80325,1753],{"stretchy":1752},[898,80327,12471],{},[1750,80329,1763],{"stretchy":1752},[902,80331,80332],{"encoding":904},"AVC = AVC(Q)",[883,80334,80336],{"className":80335},[886],[888,80337,80338],{"xmlns":890},[892,80339,80340,80348],{},[895,80341,80342],{},[5535,80343,80344,80346],{},[898,80345,12471],{},[1742,80347,2607],{},[902,80349,47231],{"encoding":904},[883,80351,80353],{"className":80352},[886],[888,80354,80355],{"xmlns":890},[892,80356,80357,80391],{},[895,80358,80359,80361,80363,80365,80367,80373,80375,80377,80379,80381,80383,80389],{},[898,80360,13916],{},[898,80362,49262],{},[898,80364,1812],{},[1750,80366,1753],{"stretchy":1752},[5535,80368,80369,80371],{},[898,80370,12471],{},[1742,80372,2607],{},[1750,80374,1763],{"stretchy":1752},[1750,80376,1766],{},[898,80378,1773],{},[898,80380,1812],{},[1750,80382,1753],{"stretchy":1752},[5535,80384,80385,80387],{},[898,80386,12471],{},[1742,80388,2607],{},[1750,80390,1763],{"stretchy":1752},[902,80392,77942],{"encoding":904},[883,80394,80396],{"className":80395},[886],[888,80397,80398],{"xmlns":890},[892,80399,80400,80412],{},[895,80401,80402,80404,80406,80408,80410],{},[898,80403,1773],{},[898,80405,1812],{},[1750,80407,1753],{"stretchy":1752},[898,80409,12471],{},[1750,80411,1763],{"stretchy":1752},[902,80413,76616],{"encoding":904},[724,80415,80416,79016,80419,79478,80465,79928,80478,79944,80495,2313],{},[38,80417,80418],{},"3.15",[883,80420,80422],{"className":80421},[886],[888,80423,80424],{"xmlns":890},[892,80425,80426,80462],{},[895,80427,80428,80430,80432,80434,80436,80438,80440,80442,80444,80446,80452,80454,80456],{},[898,80429,5326],{},[898,80431,1812],{},[1750,80433,1766],{},[1742,80435,3936],{},[1750,80437,1861],{},[1742,80439,45167],{},[898,80441,12471],{},[1750,80443,1758],{},[1742,80445,1872],{},[1699,80447,80448,80450],{},[898,80449,12471],{},[1742,80451,1872],{},[1750,80453,1861],{},[1742,80455,3929],{},[1699,80457,80458,80460],{},[898,80459,12471],{},[1742,80461,7822],{},[902,80463,80464],{"encoding":904},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[883,80466,80468],{"className":80467},[886],[888,80469,80470],{"xmlns":890},[892,80471,80472,80476],{},[895,80473,80474],{},[898,80475,12471],{},[902,80477,12471],{"encoding":904},[883,80479,80481],{"className":80480},[886],[888,80482,80483],{"xmlns":890},[892,80484,80485,80493],{},[895,80486,80487,80489,80491],{},[898,80488,13916],{},[898,80490,49262],{},[898,80492,1812],{},[902,80494,64234],{"encoding":904},[883,80496,80498],{"className":80497},[886],[888,80499,80500],{"xmlns":890},[892,80501,80502,80510],{},[895,80503,80504,80506,80508],{},[898,80505,13916],{},[898,80507,49262],{},[898,80509,1812],{},[902,80511,64234],{"encoding":904},[724,80513,80514,80517,80518,80531,80532,80552],{},[38,80515,80516],{},"3.16"," Celkové náklady na výstavbu domu o ",[883,80519,80521],{"className":80520},[886],[888,80522,80523],{"xmlns":890},[892,80524,80525,80529],{},[895,80526,80527],{},[898,80528,11727],{},[902,80530,11727],{"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 ",[883,80533,80535],{"className":80534},[886],[888,80536,80537],{"xmlns":890},[892,80538,80539,80549],{},[895,80540,80541,80543,80545,80547],{},[1742,80542,3079],{},[1969,80544,2658],{},[1742,80546,68005],{},[898,80548,11727],{},[902,80550,80551],{"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.",[198,80554,80556],{"id":80555},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[724,80558,80559,80562,80563,2028,80585,80611],{},[38,80560,80561],{},"3.17"," Jsou dány ",[883,80564,80566],{"className":80565},[886],[888,80567,80568],{"xmlns":890},[892,80569,80570,80582],{},[895,80571,80572,80574,80576,80578,80580],{},[898,80573,5326],{},[898,80575,13658],{},[1750,80577,1766],{},[1742,80579,3079],{},[898,80581,12471],{},[902,80583,80584],{"encoding":904},"TR = 10Q",[883,80586,80588],{"className":80587},[886],[888,80589,80590],{"xmlns":890},[892,80591,80592,80608],{},[895,80593,80594,80596,80598,80600,80602,80604,80606],{},[898,80595,5326],{},[898,80597,1812],{},[1750,80599,1766],{},[1742,80601,4078],{},[1750,80603,1861],{},[1742,80605,7902],{},[898,80607,12471],{},[902,80609,80610],{"encoding":904},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[724,80613,80614,80617,80618,15838,80633,80648,80649,1343,80671,5424,80698,80720,80721,80755],{},[38,80615,80616],{},"3.18"," Odvoďte, že jestliže ",[883,80619,80621],{"className":80620},[886],[888,80622,80623],{"xmlns":890},[892,80624,80625,80631],{},[895,80626,80627,80629],{},[898,80628,5326],{},[898,80630,13658],{},[902,80632,13758],{"encoding":904},[883,80634,80636],{"className":80635},[886],[888,80637,80638],{"xmlns":890},[892,80639,80640,80646],{},[895,80641,80642,80644],{},[898,80643,5326],{},[898,80645,1812],{},[902,80647,12916],{"encoding":904}," jsou lineární tvaru ",[883,80650,80652],{"className":80651},[886],[888,80653,80654],{"xmlns":890},[892,80655,80656,80668],{},[895,80657,80658,80660,80662,80664,80666],{},[898,80659,5326],{},[898,80661,13658],{},[1750,80663,1766],{},[898,80665,724],{},[898,80667,12471],{},[902,80669,80670],{"encoding":904},"TR = pQ",[883,80672,80674],{"className":80673},[886],[888,80675,80676],{"xmlns":890},[892,80677,80678,80695],{},[895,80679,80680,80682,80684,80686,80689,80691,80693],{},[898,80681,5326],{},[898,80683,1812],{},[1750,80685,1766],{},[898,80687,80688],{},"m",[1750,80690,1861],{},[898,80692,45783],{},[898,80694,12471],{},[902,80696,80697],{"encoding":904},"TC = m + nQ",[883,80699,80701],{"className":80700},[886],[888,80702,80703],{"xmlns":890},[892,80704,80705,80717],{},[895,80706,80707,80709,80711,80713,80715],{},[898,80708,80688],{},[1750,80710,1917],{"separator":1916},[898,80712,45783],{},[1750,80714,1917],{"separator":1916},[898,80716,724],{},[902,80718,80719],{"encoding":904},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[883,80722,80724],{"className":80723},[886],[888,80725,80726],{"xmlns":890},[892,80727,80728,80752],{},[895,80729,80730,80736,80738],{},[1699,80731,80732,80734],{},[898,80733,12471],{},[1750,80735,3751],{},[1750,80737,1766],{},[3586,80739,80740],{"scriptlevel":2607,"displaystyle":1752},[3423,80741,80742,80744],{},[898,80743,80688],{},[895,80745,80746,80748,80750],{},[898,80747,724],{},[1750,80749,1758],{},[898,80751,45783],{},[902,80753,80754],{"encoding":904},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[724,80757,80758,80562,80761,2028,80795,79914,80821,80834,80835,78666,80850,80865,80866,78650,80879,78666,80894,80909],{},[38,80759,80760],{},"3.19",[883,80762,80764],{"className":80763},[886],[888,80765,80766],{"xmlns":890},[892,80767,80768,80792],{},[895,80769,80770,80772,80774,80776,80778,80780,80786,80788,80790],{},[898,80771,5326],{},[898,80773,13658],{},[1750,80775,1766],{},[1750,80777,1758],{},[1742,80779,1872],{},[1699,80781,80782,80784],{},[898,80783,12471],{},[1742,80785,1872],{},[1750,80787,1861],{},[1742,80789,6789],{},[898,80791,12471],{},[902,80793,80794],{"encoding":904},"TR = -2Q^2 + 14Q",[883,80796,80798],{"className":80797},[886],[888,80799,80800],{"xmlns":890},[892,80801,80802,80818],{},[895,80803,80804,80806,80808,80810,80812,80814,80816],{},[898,80805,5326],{},[898,80807,1812],{},[1750,80809,1766],{},[1742,80811,1872],{},[898,80813,12471],{},[1750,80815,1861],{},[1742,80817,3079],{},[902,80819,80820],{"encoding":904},"TC = 2Q + 10",[883,80822,80824],{"className":80823},[886],[888,80825,80826],{"xmlns":890},[892,80827,80828,80832],{},[895,80829,80830],{},[898,80831,12471],{},[902,80833,12471],{"encoding":904},", které maximalizuje zisk ",[883,80836,80838],{"className":80837},[886],[888,80839,80840],{"xmlns":890},[892,80841,80842,80848],{},[895,80843,80844,80846],{},[898,80845,1776],{},[898,80847,13658],{},[902,80849,72402],{"encoding":904},[883,80851,80853],{"className":80852},[886],[888,80854,80855],{"xmlns":890},[892,80856,80857,80863],{},[895,80858,80859,80861],{},[898,80860,1776],{},[898,80862,13658],{},[902,80864,72402],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[883,80867,80869],{"className":80868},[886],[888,80870,80871],{"xmlns":890},[892,80872,80873,80877],{},[895,80874,80875],{},[898,80876,12471],{},[902,80878,12471],{"encoding":904},[883,80880,80882],{"className":80881},[886],[888,80883,80884],{"xmlns":890},[892,80885,80886,80892],{},[895,80887,80888,80890],{},[898,80889,5326],{},[898,80891,13658],{},[902,80893,13758],{"encoding":904},[883,80895,80897],{"className":80896},[886],[888,80898,80899],{"xmlns":890},[892,80900,80901,80907],{},[895,80902,80903,80905],{},[898,80904,5326],{},[898,80906,13658],{},[902,80908,13758],{"encoding":904},". (d) Graficky interpretujte.",[724,80911,80912,56607,80915,1343,80941,1343,80960,79914,80980,80834,80993,78666,81008,81023,81024,81046,81047,80097],{},[38,80913,80914],{},"3.20",[883,80916,80918],{"className":80917},[886],[888,80919,80920],{"xmlns":890},[892,80921,80922,80938],{},[895,80923,80924,80926,80928,80930,80932],{},[898,80925,1776],{},[1750,80927,1766],{},[1742,80929,3956],{},[1750,80931,1758],{},[1699,80933,80934,80936],{},[898,80935,12471],{},[1742,80937,1872],{},[902,80939,80940],{"encoding":904},"P = 400 - Q^2",[883,80942,80944],{"className":80943},[886],[888,80945,80946],{"xmlns":890},[892,80947,80948,80958],{},[895,80949,80950,80952,80954,80956],{},[898,80951,20069],{},[898,80953,1812],{},[1750,80955,1766],{},[1742,80957,4078],{},[902,80959,21266],{"encoding":904},[883,80961,80963],{"className":80962},[886],[888,80964,80965],{"xmlns":890},[892,80966,80967,80977],{},[895,80968,80969,80971,80973,80975],{},[898,80970,1773],{},[898,80972,1812],{},[1750,80974,1766],{},[1742,80976,6465],{},[902,80978,80979],{"encoding":904},"MC = 20",[883,80981,80983],{"className":80982},[886],[888,80984,80985],{"xmlns":890},[892,80986,80987,80991],{},[895,80988,80989],{},[898,80990,12471],{},[902,80992,12471],{"encoding":904},[883,80994,80996],{"className":80995},[886],[888,80997,80998],{"xmlns":890},[892,80999,81000,81006],{},[895,81001,81002,81004],{},[898,81003,1776],{},[898,81005,13658],{},[902,81007,72402],{"encoding":904},[883,81009,81011],{"className":81010},[886],[888,81012,81013],{"xmlns":890},[892,81014,81015,81021],{},[895,81016,81017,81019],{},[898,81018,1776],{},[898,81020,13658],{},[902,81022,72402],{"encoding":904},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[883,81025,81027],{"className":81026},[886],[888,81028,81029],{"xmlns":890},[892,81030,81031,81043],{},[895,81032,81033,81035,81037,81039,81041],{},[1750,81034,1753],{"stretchy":1752},[1742,81036,2607],{},[1750,81038,1917],{"separator":1916},[1742,81040,1744],{},[1750,81042,1763],{"stretchy":1752},[902,81044,81045],{"encoding":904},"(0, 1)",", druhý do ",[883,81048,81050],{"className":81049},[886],[888,81051,81052],{"xmlns":890},[892,81053,81054,81067],{},[895,81055,81056,81058,81061,81063,81065],{},[1750,81057,1753],{"stretchy":1752},[1742,81059,81060],{},"19",[1750,81062,1917],{"separator":1916},[1742,81064,6465],{},[1750,81066,1763],{"stretchy":1752},[902,81068,81069],{"encoding":904},"(19, 20)",[724,81071,81072,81075,81076,2984,81104,81121,81122,2313],{},[38,81073,81074],{},"3.21"," Dokažte, že má-li zisk ",[883,81077,81079],{"className":81078},[886],[888,81080,81081],{"xmlns":890},[892,81082,81083,81101],{},[895,81084,81085,81087,81089,81091,81093,81095,81097,81099],{},[898,81086,1776],{},[898,81088,13658],{},[1750,81090,1766],{},[898,81092,1776],{},[898,81094,13658],{},[1750,81096,1753],{"stretchy":1752},[898,81098,12471],{},[1750,81100,1763],{"stretchy":1752},[902,81102,81103],{"encoding":904},"PR = PR(Q)",[883,81105,81107],{"className":81106},[886],[888,81108,81109],{"xmlns":890},[892,81110,81111,81119],{},[895,81112,81113],{},[5535,81114,81115,81117],{},[898,81116,12471],{},[1742,81118,2607],{},[902,81120,47231],{"encoding":904}," maximum, pak platí ",[883,81123,81125],{"className":81124},[886],[888,81126,81127],{"xmlns":890},[892,81128,81129,81161],{},[895,81130,81131,81133,81135,81137,81143,81145,81147,81149,81151,81153,81159],{},[898,81132,1773],{},[898,81134,13658],{},[1750,81136,1753],{"stretchy":1752},[5535,81138,81139,81141],{},[898,81140,12471],{},[1742,81142,2607],{},[1750,81144,1763],{"stretchy":1752},[1750,81146,1766],{},[898,81148,1773],{},[898,81150,1812],{},[1750,81152,1753],{"stretchy":1752},[5535,81154,81155,81157],{},[898,81156,12471],{},[1742,81158,2607],{},[1750,81160,1763],{"stretchy":1752},[902,81162,74568],{"encoding":904},[724,81164,81165,81168,81169,2028,81184,64948,81199,80834,81212,81227,81228,1343,81255,81292,81293,1343,81320,2313],{},[38,81166,81167],{},"3.22"," Pro zadané ",[883,81170,81172],{"className":81171},[886],[888,81173,81174],{"xmlns":890},[892,81175,81176,81182],{},[895,81177,81178,81180],{},[898,81179,1773],{},[898,81181,13658],{},[902,81183,16282],{"encoding":904},[883,81185,81187],{"className":81186},[886],[888,81188,81189],{"xmlns":890},[892,81190,81191,81197],{},[895,81192,81193,81195],{},[898,81194,1773],{},[898,81196,1812],{},[902,81198,64215],{"encoding":904},[883,81200,81202],{"className":81201},[886],[888,81203,81204],{"xmlns":890},[892,81205,81206,81210],{},[895,81207,81208],{},[898,81209,12471],{},[902,81211,12471],{"encoding":904},[883,81213,81215],{"className":81214},[886],[888,81216,81217],{"xmlns":890},[892,81218,81219,81225],{},[895,81220,81221,81223],{},[898,81222,1776],{},[898,81224,13658],{},[902,81226,72402],{"encoding":904},". (a) ",[883,81229,81231],{"className":81230},[886],[888,81232,81233],{"xmlns":890},[892,81234,81235,81252],{},[895,81236,81237,81239,81241,81243,81246,81248,81250],{},[898,81238,1773],{},[898,81240,13658],{},[1750,81242,1766],{},[1742,81244,81245],{},"236",[1750,81247,1758],{},[1742,81249,50785],{},[898,81251,12471],{},[902,81253,81254],{"encoding":904},"MR = 236 - 16Q",[883,81256,81258],{"className":81257},[886],[888,81259,81260],{"xmlns":890},[892,81261,81262,81289],{},[895,81263,81264,81266,81268,81270,81272,81278,81280,81283,81285,81287],{},[898,81265,1773],{},[898,81267,1812],{},[1750,81269,1766],{},[1742,81271,7822],{},[1699,81273,81274,81276],{},[898,81275,12471],{},[1742,81277,1872],{},[1750,81279,1758],{},[1742,81281,81282],{},"32",[898,81284,12471],{},[1750,81286,1861],{},[1742,81288,15396],{},[902,81290,81291],{"encoding":904},"MC = 3Q^2 - 32Q + 96",". (b) ",[883,81294,81296],{"className":81295},[886],[888,81297,81298],{"xmlns":890},[892,81299,81300,81317],{},[895,81301,81302,81304,81306,81308,81311,81313,81315],{},[898,81303,1773],{},[898,81305,13658],{},[1750,81307,1766],{},[1742,81309,81310],{},"280",[1750,81312,1758],{},[1742,81314,6465],{},[898,81316,12471],{},[902,81318,81319],{"encoding":904},"MR = 280 - 20Q",[883,81321,81323],{"className":81322},[886],[888,81324,81325],{"xmlns":890},[892,81326,81327,81354],{},[895,81328,81329,81331,81333,81335,81338,81344,81346,81348,81350,81352],{},[898,81330,1773],{},[898,81332,1812],{},[1750,81334,1766],{},[1742,81336,81337],{},"1,6",[1699,81339,81340,81342],{},[898,81341,12471],{},[1742,81343,1872],{},[1750,81345,1758],{},[1742,81347,45167],{},[898,81349,12471],{},[1750,81351,1861],{},[1742,81353,12800],{},[902,81355,81356],{"encoding":904},"MC = 1{,}6Q^2 - 15Q + 60",[724,81358,81359,81168,81362,2028,81377,64948,81392,78650,81405,78666,81420,81227,81435,1343,81466,81292,81502,1343,81534,81578,81579,1343,81611,2313],{},[38,81360,81361],{},"3.23",[883,81363,81365],{"className":81364},[886],[888,81366,81367],{"xmlns":890},[892,81368,81369,81375],{},[895,81370,81371,81373],{},[898,81372,5326],{},[898,81374,13658],{},[902,81376,13758],{"encoding":904},[883,81378,81380],{"className":81379},[886],[888,81381,81382],{"xmlns":890},[892,81383,81384,81390],{},[895,81385,81386,81388],{},[898,81387,5326],{},[898,81389,1812],{},[902,81391,12916],{"encoding":904},[883,81393,81395],{"className":81394},[886],[888,81396,81397],{"xmlns":890},[892,81398,81399,81403],{},[895,81400,81401],{},[898,81402,12471],{},[902,81404,12471],{"encoding":904},[883,81406,81408],{"className":81407},[886],[888,81409,81410],{"xmlns":890},[892,81411,81412,81418],{},[895,81413,81414,81416],{},[898,81415,1776],{},[898,81417,13658],{},[902,81419,72402],{"encoding":904},[883,81421,81423],{"className":81422},[886],[888,81424,81425],{"xmlns":890},[892,81426,81427,81433],{},[895,81428,81429,81431],{},[898,81430,1776],{},[898,81432,13658],{},[902,81434,72402],{"encoding":904},[883,81436,81438],{"className":81437},[886],[888,81439,81440],{"xmlns":890},[892,81441,81442,81463],{},[895,81443,81444,81446,81448,81450,81453,81455,81457],{},[898,81445,5326],{},[898,81447,13658],{},[1750,81449,1766],{},[1742,81451,81452],{},"125",[898,81454,12471],{},[1750,81456,1758],{},[1699,81458,81459,81461],{},[898,81460,12471],{},[1742,81462,1872],{},[902,81464,81465],{"encoding":904},"TR = 125Q - Q^2",[883,81467,81469],{"className":81468},[886],[888,81470,81471],{"xmlns":890},[892,81472,81473,81499],{},[895,81474,81475,81477,81479,81481,81483,81485,81487,81489,81491,81493],{},[898,81476,5326],{},[898,81478,1812],{},[1750,81480,1766],{},[1742,81482,7658],{},[1750,81484,1861],{},[1742,81486,7902],{},[898,81488,12471],{},[1750,81490,1861],{},[1742,81492,4268],{},[1699,81494,81495,81497],{},[898,81496,12471],{},[1742,81498,1872],{},[902,81500,81501],{"encoding":904},"TC = 500 + 5Q + 0{,}5Q^2",[883,81503,81505],{"className":81504},[886],[888,81506,81507],{"xmlns":890},[892,81508,81509,81531],{},[895,81510,81511,81513,81515,81517,81519,81521,81523,81525],{},[898,81512,5326],{},[898,81514,13658],{},[1750,81516,1766],{},[1742,81518,6465],{},[898,81520,12471],{},[1750,81522,1758],{},[1742,81524,1872],{},[1699,81526,81527,81529],{},[898,81528,12471],{},[1742,81530,1872],{},[902,81532,81533],{"encoding":904},"TR = 20Q - 2Q^2",[883,81535,81537],{"className":81536},[886],[888,81538,81539],{"xmlns":890},[892,81540,81541,81575],{},[895,81542,81543,81545,81547,81549,81551,81553,81555,81557,81559,81561,81567,81569],{},[898,81544,5326],{},[898,81546,1812],{},[1750,81548,1766],{},[1742,81550,1872],{},[1750,81552,1861],{},[1742,81554,6465],{},[898,81556,12471],{},[1750,81558,1758],{},[1742,81560,15239],{},[1699,81562,81563,81565],{},[898,81564,12471],{},[1742,81566,1872],{},[1750,81568,1861],{},[1699,81570,81571,81573],{},[898,81572,12471],{},[1742,81574,7822],{},[902,81576,81577],{"encoding":904},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[883,81580,81582],{"className":81581},[886],[888,81583,81584],{"xmlns":890},[892,81585,81586,81608],{},[895,81587,81588,81590,81592,81594,81596,81598,81600,81602],{},[898,81589,5326],{},[898,81591,13658],{},[1750,81593,1766],{},[1742,81595,7859],{},[898,81597,12471],{},[1750,81599,1758],{},[1742,81601,7633],{},[1699,81603,81604,81606],{},[898,81605,12471],{},[1742,81607,1872],{},[902,81609,81610],{"encoding":904},"TR = 4Q - 0{,}25Q^2",[883,81612,81614],{"className":81613},[886],[888,81615,81616],{"xmlns":890},[892,81617,81618,81666],{},[895,81619,81620,81622,81624,81626,81628,81630,81632,81634,81636,81652,81654],{},[898,81621,5326],{},[898,81623,1812],{},[1750,81625,1766],{},[1742,81627,7859],{},[1750,81629,1861],{},[1742,81631,1872],{},[898,81633,12471],{},[1750,81635,1758],{},[3586,81637,81638],{"scriptlevel":2607,"displaystyle":1752},[3423,81639,81640,81650],{},[895,81641,81642,81644],{},[1742,81643,7822],{},[1699,81645,81646,81648],{},[898,81647,12471],{},[1742,81649,1872],{},[1742,81651,3079],{},[1750,81653,1861],{},[3586,81655,81656],{"scriptlevel":2607,"displaystyle":1752},[3423,81657,81658,81664],{},[1699,81659,81660,81662],{},[898,81661,12471],{},[1742,81663,7822],{},[1742,81665,6465],{},[902,81667,81668],{"encoding":904},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[724,81670,81671,81674,81675,81705,81706,81738,81739,5424,81769,81799],{},[38,81672,81673],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[883,81676,81678],{"className":81677},[886],[888,81679,81680],{"xmlns":890},[892,81681,81682,81702],{},[895,81683,81684,81690,81692,81694,81696],{},[5535,81685,81686,81688],{},[898,81687,1776],{},[1742,81689,1744],{},[1750,81691,1766],{},[1742,81693,7658],{},[1750,81695,1758],{},[5535,81697,81698,81700],{},[898,81699,12471],{},[1742,81701,1744],{},[902,81703,81704],{"encoding":904},"P_1 = 500 - Q_1",", pro velkoodběratele ",[883,81707,81709],{"className":81708},[886],[888,81710,81711],{"xmlns":890},[892,81712,81713,81735],{},[895,81714,81715,81721,81723,81725,81727,81729],{},[5535,81716,81717,81719],{},[898,81718,1776],{},[1742,81720,1872],{},[1750,81722,1766],{},[1742,81724,39004],{},[1750,81726,1758],{},[1742,81728,73482],{},[5535,81730,81731,81733],{},[898,81732,12471],{},[1742,81734,1872],{},[902,81736,81737],{"encoding":904},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[883,81740,81742],{"className":81741},[886],[888,81743,81744],{"xmlns":890},[892,81745,81746,81766],{},[895,81747,81748,81750,81752,81754,81756,81758,81760,81762,81764],{},[898,81749,5326],{},[898,81751,1812],{},[1750,81753,1766],{},[1742,81755,3936],{},[1969,81757,2658],{},[1742,81759,68005],{},[1750,81761,1861],{},[1742,81763,6465],{},[898,81765,12471],{},[902,81767,81768],{"encoding":904},"TC = 50\\,000 + 20Q",[883,81770,81772],{"className":81771},[886],[888,81773,81774],{"xmlns":890},[892,81775,81776,81796],{},[895,81777,81778,81780,81782,81788,81790],{},[898,81779,12471],{},[1750,81781,1766],{},[5535,81783,81784,81786],{},[898,81785,12471],{},[1742,81787,1744],{},[1750,81789,1861],{},[5535,81791,81792,81794],{},[898,81793,12471],{},[1742,81795,1872],{},[902,81797,81798],{"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.",[724,81801,81802,81805,81806,81836,81837,81738,81869,5424,81899,81928],{},[38,81803,81804],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[883,81807,81809],{"className":81808},[886],[888,81810,81811],{"xmlns":890},[892,81812,81813,81833],{},[895,81814,81815,81821,81823,81825,81827],{},[5535,81816,81817,81819],{},[898,81818,1776],{},[1742,81820,1744],{},[1750,81822,1766],{},[1742,81824,39004],{},[1750,81826,1758],{},[5535,81828,81829,81831],{},[898,81830,12471],{},[1742,81832,1744],{},[902,81834,81835],{"encoding":904},"P_1 = 300 - Q_1",", pro zahraniční trh ",[883,81838,81840],{"className":81839},[886],[888,81841,81842],{"xmlns":890},[892,81843,81844,81866],{},[895,81845,81846,81852,81854,81856,81858,81860],{},[5535,81847,81848,81850],{},[898,81849,1776],{},[1742,81851,1872],{},[1750,81853,1766],{},[1742,81855,4159],{},[1750,81857,1758],{},[1742,81859,4268],{},[5535,81861,81862,81864],{},[898,81863,12471],{},[1742,81865,1872],{},[902,81867,81868],{"encoding":904},"P_2 = 200 - 0{,}5Q_2",[883,81870,81872],{"className":81871},[886],[888,81873,81874],{"xmlns":890},[892,81875,81876,81896],{},[895,81877,81878,81880,81882,81884,81886,81888,81890,81892,81894],{},[898,81879,5326],{},[898,81881,1812],{},[1750,81883,1766],{},[1742,81885,7902],{},[1969,81887,2658],{},[1742,81889,68005],{},[1750,81891,1861],{},[1742,81893,4078],{},[898,81895,12471],{},[902,81897,81898],{"encoding":904},"TC = 5\\,000 + 100Q",[883,81900,81902],{"className":81901},[886],[888,81903,81904],{"xmlns":890},[892,81905,81906,81926],{},[895,81907,81908,81910,81912,81918,81920],{},[898,81909,12471],{},[1750,81911,1766],{},[5535,81913,81914,81916],{},[898,81915,12471],{},[1742,81917,1744],{},[1750,81919,1861],{},[5535,81921,81922,81924],{},[898,81923,12471],{},[1742,81925,1872],{},[902,81927,81798],{"encoding":904},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[198,81930,81932],{"id":81931},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[724,81934,81935,81938,81939,81986,81987,82004],{},[38,81936,81937],{},"3.26"," Jsou dány celkové variabilní náklady ",[883,81940,81942],{"className":81941},[886],[888,81943,81944],{"xmlns":890},[892,81945,81946,81983],{},[895,81947,81948,81950,81952,81954,81956,81959,81965,81967,81970,81976,81978,81981],{},[898,81949,5326],{},[898,81951,49262],{},[898,81953,1812],{},[1750,81955,1766],{},[1742,81957,81958],{},"0,85",[1699,81960,81961,81963],{},[898,81962,12471],{},[1742,81964,7822],{},[1750,81966,1758],{},[1742,81968,81969],{},"11,9",[1699,81971,81972,81974],{},[898,81973,12471],{},[1742,81975,1872],{},[1750,81977,1861],{},[1742,81979,81980],{},"102",[898,81982,12471],{},[902,81984,81985],{"encoding":904},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[883,81988,81990],{"className":81989},[886],[888,81991,81992],{"xmlns":890},[892,81993,81994,82002],{},[895,81995,81996],{},[1699,81997,81998,82000],{},[898,81999,1776],{},[1750,82001,3751],{},[902,82003,14063],{"encoding":904}," nabídky a konstruujte nabídku. Graficky interpretujte.",[724,82006,82007,79765,82010,82046],{},[38,82008,82009],{},"3.27",[883,82011,82013],{"className":82012},[886],[888,82014,82015],{"xmlns":890},[892,82016,82017,82043],{},[895,82018,82019,82021,82023,82025,82027,82033,82035,82037,82039,82041],{},[898,82020,1773],{},[898,82022,1812],{},[1750,82024,1766],{},[1742,82026,12601],{},[1699,82028,82029,82031],{},[898,82030,12471],{},[1742,82032,1872],{},[1750,82034,1758],{},[1742,82036,73363],{},[898,82038,12471],{},[1750,82040,1861],{},[1742,82042,39666],{},[902,82044,82045],{"encoding":904},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[724,82048,82049,79016,82052,82046],{},[38,82050,82051],{},"3.28",[883,82053,82055],{"className":82054},[886],[888,82056,82057],{"xmlns":890},[892,82058,82059,82095],{},[895,82060,82061,82063,82065,82067,82069,82075,82077,82079,82085,82087,82089,82091,82093],{},[898,82062,5326],{},[898,82064,1812],{},[1750,82066,1766],{},[1742,82068,4268],{},[1699,82070,82071,82073],{},[898,82072,12471],{},[1742,82074,7822],{},[1750,82076,1758],{},[1742,82078,8051],{},[1699,82080,82081,82083],{},[898,82082,12471],{},[1742,82084,1872],{},[1750,82086,1861],{},[1742,82088,12800],{},[898,82090,12471],{},[1750,82092,1861],{},[1742,82094,7658],{},[902,82096,82097],{"encoding":904},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[115,82099,10461],{"id":10460},[120,82101,82102,82130,82175,82247,82312,82352,82444,82550,82590,82704,82797,82861,82893,82953,82959,83023,83072,83126,83234,83289],{},[123,82103,82104,1647,82106,82129],{},[38,82105,64673],{},[883,82107,82109],{"className":82108},[886],[888,82110,82111],{"xmlns":890},[892,82112,82113,82127],{},[895,82114,82115,82117,82119,82121,82123,82125],{},[898,82116,5326],{},[898,82118,13658],{},[1750,82120,1766],{},[898,82122,1776],{},[1750,82124,8009],{},[898,82126,12471],{},[902,82128,75635],{"encoding":904}," — křivka celkového příjmu (total revenue curve).",[123,82131,82132,1647,82134,82174],{},[38,82133,65259],{},[883,82135,82137],{"className":82136},[886],[888,82138,82139],{"xmlns":890},[892,82140,82141,82171],{},[895,82142,82143,82145,82147,82149,82161,82163,82165,82167,82169],{},[898,82144,13916],{},[898,82146,13658],{},[1750,82148,1766],{},[3586,82150,82151],{"scriptlevel":2607,"displaystyle":1752},[3423,82152,82153,82159],{},[895,82154,82155,82157],{},[898,82156,5326],{},[898,82158,13658],{},[898,82160,12471],{},[1750,82162,1766],{},[898,82164,5541],{},[1750,82166,1753],{"stretchy":1752},[898,82168,12471],{},[1750,82170,1763],{"stretchy":1752},[902,82172,82173],{"encoding":904},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[123,82176,82177,1647,82179,82215,82216,82231,82232,2313],{},[38,82178,65407],{},[883,82180,82182],{"className":82181},[886],[888,82183,82184],{"xmlns":890},[892,82185,82186,82212],{},[895,82187,82188,82190,82192,82194],{},[898,82189,1773],{},[898,82191,13658],{},[1750,82193,1766],{},[3586,82195,82196],{"scriptlevel":2607,"displaystyle":1752},[3423,82197,82198,82206],{},[895,82199,82200,82202,82204],{},[898,82201,3429],{"mathvariant":1747},[898,82203,5326],{},[898,82205,13658],{},[895,82207,82208,82210],{},[898,82209,3429],{"mathvariant":1747},[898,82211,12471],{},[902,82213,82214],{"encoding":904},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[883,82217,82219],{"className":82218},[886],[888,82220,82221],{"xmlns":890},[892,82222,82223,82229],{},[895,82224,82225,82227],{},[898,82226,5326],{},[898,82228,13658],{},[902,82230,13758],{"encoding":904},"; pro lineární poptávku má sklon dvojnásobný vůči ",[883,82233,82235],{"className":82234},[886],[888,82236,82237],{"xmlns":890},[892,82238,82239,82245],{},[895,82240,82241,82243],{},[898,82242,13916],{},[898,82244,13658],{},[902,82246,64368],{"encoding":904},[123,82248,82249,1647,82252,1343,82282,2313],{},[38,82250,82251],{},"Diferenciál příjmu\u002Fnákladů",[883,82253,82255],{"className":82254},[886],[888,82256,82257],{"xmlns":890},[892,82258,82259,82279],{},[895,82260,82261,82263,82265,82267,82269,82271,82273,82275,82277],{},[898,82262,2666],{"mathvariant":1747},[898,82264,5326],{},[898,82266,13658],{},[1750,82268,2274],{},[898,82270,1773],{},[898,82272,13658],{},[1969,82274,2658],{},[898,82276,3429],{"mathvariant":1747},[898,82278,12471],{},[902,82280,82281],{"encoding":904},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[883,82283,82285],{"className":82284},[886],[888,82286,82287],{"xmlns":890},[892,82288,82289,82309],{},[895,82290,82291,82293,82295,82297,82299,82301,82303,82305,82307],{},[898,82292,2666],{"mathvariant":1747},[898,82294,5326],{},[898,82296,1812],{},[1750,82298,2274],{},[898,82300,1773],{},[898,82302,1812],{},[1969,82304,2658],{},[898,82306,3429],{"mathvariant":1747},[898,82308,12471],{},[902,82310,82311],{"encoding":904},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[123,82313,82314,1647,82316,2313],{},[38,82315,67529],{},[883,82317,82319],{"className":82318},[886],[888,82320,82321],{"xmlns":890},[892,82322,82323,82349],{},[895,82324,82325,82327,82329,82331,82333,82335,82337,82339,82341,82343,82345,82347],{},[898,82326,5326],{},[898,82328,1812],{},[1750,82330,1766],{},[898,82332,20069],{},[898,82334,1812],{},[1750,82336,1861],{},[898,82338,5326],{},[898,82340,49262],{},[898,82342,1812],{},[1750,82344,1753],{"stretchy":1752},[898,82346,12471],{},[1750,82348,1763],{"stretchy":1752},[902,82350,82351],{"encoding":904},"TC = FC + TVC(Q)",[123,82353,82354,1647,82357,1343,82372,1647,82374,1343,82397,1647,82400,2313],{},[38,82355,82356],{},"Fixní náklady",[883,82358,82360],{"className":82359},[886],[888,82361,82362],{"xmlns":890},[892,82363,82364,82370],{},[895,82365,82366,82368],{},[898,82367,20069],{},[898,82369,1812],{},[902,82371,64414],{"encoding":904},[38,82373,67682],{},[883,82375,82377],{"className":82376},[886],[888,82378,82379],{"xmlns":890},[892,82380,82381,82395],{},[895,82382,82383,82385,82387,82389,82391,82393],{},[898,82384,5326],{},[898,82386,49262],{},[898,82388,1812],{},[1750,82390,1753],{"stretchy":1752},[898,82392,12471],{},[1750,82394,1763],{"stretchy":1752},[902,82396,67679],{"encoding":904},[38,82398,82399],{},"variabilní náklady na jednotku",[883,82401,82403],{"className":82402},[886],[888,82404,82405],{"xmlns":890},[892,82406,82407,82441],{},[895,82408,82409,82411,82413,82415,82417,82419,82421],{},[898,82410,49262],{},[898,82412,1812],{},[1750,82414,1753],{"stretchy":1752},[898,82416,12471],{},[1750,82418,1763],{"stretchy":1752},[1750,82420,1766],{},[3586,82422,82423],{"scriptlevel":2607,"displaystyle":1752},[3423,82424,82425,82439],{},[895,82426,82427,82429,82431,82433,82435,82437],{},[898,82428,5326],{},[898,82430,49262],{},[898,82432,1812],{},[1750,82434,1753],{"stretchy":1752},[898,82436,12471],{},[1750,82438,1763],{"stretchy":1752},[898,82440,12471],{},[902,82442,82443],{"encoding":904},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[123,82445,82446,1647,82448,1343,82478,1647,82481,1343,82513,1647,82516,2313],{},[38,82447,67690],{},[883,82449,82451],{"className":82450},[886],[888,82452,82453],{"xmlns":890},[892,82454,82455,82475],{},[895,82456,82457,82459,82461,82463],{},[898,82458,13916],{},[898,82460,1812],{},[1750,82462,1766],{},[3586,82464,82465],{"scriptlevel":2607,"displaystyle":1752},[3423,82466,82467,82473],{},[895,82468,82469,82471],{},[898,82470,5326],{},[898,82472,1812],{},[898,82474,12471],{},[902,82476,82477],{"encoding":904},"AC = \\tfrac{TC}{Q}",[38,82479,82480],{},"průměrné fixní",[883,82482,82484],{"className":82483},[886],[888,82485,82486],{"xmlns":890},[892,82487,82488,82510],{},[895,82489,82490,82492,82494,82496,82498],{},[898,82491,13916],{},[898,82493,20069],{},[898,82495,1812],{},[1750,82497,1766],{},[3586,82499,82500],{"scriptlevel":2607,"displaystyle":1752},[3423,82501,82502,82508],{},[895,82503,82504,82506],{},[898,82505,20069],{},[898,82507,1812],{},[898,82509,12471],{},[902,82511,82512],{"encoding":904},"AFC = \\tfrac{FC}{Q}",[38,82514,82515],{},"průměrné variabilní",[883,82517,82519],{"className":82518},[886],[888,82520,82521],{"xmlns":890},[892,82522,82523,82547],{},[895,82524,82525,82527,82529,82531,82533],{},[898,82526,13916],{},[898,82528,49262],{},[898,82530,1812],{},[1750,82532,1766],{},[3586,82534,82535],{"scriptlevel":2607,"displaystyle":1752},[3423,82536,82537,82545],{},[895,82538,82539,82541,82543],{},[898,82540,5326],{},[898,82542,49262],{},[898,82544,1812],{},[898,82546,12471],{},[902,82548,82549],{"encoding":904},"AVC = \\tfrac{TVC}{Q}",[123,82551,82552,1647,82554,2313],{},[38,82553,68877],{},[883,82555,82557],{"className":82556},[886],[888,82558,82559],{"xmlns":890},[892,82560,82561,82587],{},[895,82562,82563,82565,82567,82569],{},[898,82564,1773],{},[898,82566,1812],{},[1750,82568,1766],{},[3586,82570,82571],{"scriptlevel":2607,"displaystyle":1752},[3423,82572,82573,82581],{},[895,82574,82575,82577,82579],{},[898,82576,3429],{"mathvariant":1747},[898,82578,5326],{},[898,82580,1812],{},[895,82582,82583,82585],{},[898,82584,3429],{"mathvariant":1747},[898,82586,12471],{},[902,82588,82589],{"encoding":904},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[123,82591,82592,1647,82594,82642,82643,82656,82657,1343,82672,1343,82689,2313],{},[38,82593,69775],{},[883,82595,82597],{"className":82596},[886],[888,82598,82599],{"xmlns":890},[892,82600,82601,82639],{},[895,82602,82603,82605,82607,82609,82611,82613,82615,82617,82619,82621,82623,82629,82631,82633],{},[898,82604,5326],{},[898,82606,1812],{},[1750,82608,1766],{},[898,82610,20069],{},[898,82612,1812],{},[1750,82614,1861],{},[898,82616,207],{},[898,82618,12471],{},[1750,82620,1861],{},[898,82622,2573],{},[1699,82624,82625,82627],{},[898,82626,12471],{},[1742,82628,1872],{},[1750,82630,1861],{},[898,82632,9365],{},[1699,82634,82635,82637],{},[898,82636,12471],{},[1742,82638,7822],{},[902,82640,82641],{"encoding":904},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[883,82644,82646],{"className":82645},[886],[888,82647,82648],{"xmlns":890},[892,82649,82650,82654],{},[895,82651,82652],{},[898,82653,900],{},[902,82655,900],{"encoding":904},"-průběhem ",[883,82658,82660],{"className":82659},[886],[888,82661,82662],{"xmlns":890},[892,82663,82664,82670],{},[895,82665,82666,82668],{},[898,82667,13916],{},[898,82669,1812],{},[902,82671,64483],{"encoding":904},[883,82673,82675],{"className":82674},[886],[888,82676,82677],{"xmlns":890},[892,82678,82679,82687],{},[895,82680,82681,82683,82685],{},[898,82682,13916],{},[898,82684,49262],{},[898,82686,1812],{},[902,82688,64234],{"encoding":904},[883,82690,82692],{"className":82691},[886],[888,82693,82694],{"xmlns":890},[892,82695,82696,82702],{},[895,82697,82698,82700],{},[898,82699,1773],{},[898,82701,1812],{},[902,82703,64215],{"encoding":904},[123,82705,82706,82708,82709,20027,82724,82765,82766,70420,82781,82796],{},[38,82707,70857],{},": v bodě minima ",[883,82710,82712],{"className":82711},[886],[888,82713,82714],{"xmlns":890},[892,82715,82716,82722],{},[895,82717,82718,82720],{},[898,82719,13916],{},[898,82721,1812],{},[902,82723,64483],{"encoding":904},[883,82725,82727],{"className":82726},[886],[888,82728,82729],{"xmlns":890},[892,82730,82731,82763],{},[895,82732,82733,82735,82737,82739,82745,82747,82749,82751,82753,82755,82761],{},[898,82734,13916],{},[898,82736,1812],{},[1750,82738,1753],{"stretchy":1752},[5535,82740,82741,82743],{},[898,82742,12471],{},[1742,82744,2607],{},[1750,82746,1763],{"stretchy":1752},[1750,82748,1766],{},[898,82750,1773],{},[898,82752,1812],{},[1750,82754,1753],{"stretchy":1752},[5535,82756,82757,82759],{},[898,82758,12471],{},[1742,82760,2607],{},[1750,82762,1763],{"stretchy":1752},[902,82764,71492],{"encoding":904},"; geometricky ",[883,82767,82769],{"className":82768},[886],[888,82770,82771],{"xmlns":890},[892,82772,82773,82779],{},[895,82774,82775,82777],{},[898,82776,1773],{},[898,82778,1812],{},[902,82780,64215],{"encoding":904},[883,82782,82784],{"className":82783},[886],[888,82785,82786],{"xmlns":890},[892,82787,82788,82794],{},[895,82789,82790,82792],{},[898,82791,13916],{},[898,82793,1812],{},[902,82795,64483],{"encoding":904}," v jejím minimu.",[123,82798,82799,82708,82801,20027,82818,2313],{},[38,82800,72207],{},[883,82802,82804],{"className":82803},[886],[888,82805,82806],{"xmlns":890},[892,82807,82808,82816],{},[895,82809,82810,82812,82814],{},[898,82811,13916],{},[898,82813,49262],{},[898,82815,1812],{},[902,82817,64234],{"encoding":904},[883,82819,82821],{"className":82820},[886],[888,82822,82823],{"xmlns":890},[892,82824,82825,82859],{},[895,82826,82827,82829,82831,82833,82835,82841,82843,82845,82847,82849,82851,82857],{},[898,82828,13916],{},[898,82830,49262],{},[898,82832,1812],{},[1750,82834,1753],{"stretchy":1752},[5535,82836,82837,82839],{},[898,82838,12471],{},[1742,82840,2607],{},[1750,82842,1763],{"stretchy":1752},[1750,82844,1766],{},[898,82846,1773],{},[898,82848,1812],{},[1750,82850,1753],{"stretchy":1752},[5535,82852,82853,82855],{},[898,82854,12471],{},[1742,82856,2607],{},[1750,82858,1763],{"stretchy":1752},[902,82860,77942],{"encoding":904},[123,82862,82863,1647,82865,82892],{},[38,82864,72386],{},[883,82866,82868],{"className":82867},[886],[888,82869,82870],{"xmlns":890},[892,82871,82872,82890],{},[895,82873,82874,82876,82878,82880,82882,82884,82886,82888],{},[898,82875,1776],{},[898,82877,13658],{},[1750,82879,1766],{},[898,82881,5326],{},[898,82883,13658],{},[1750,82885,1758],{},[898,82887,5326],{},[898,82889,1812],{},[902,82891,64123],{"encoding":904}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[123,82894,82895,2084,82897,82899,82900,82926,82927,82952],{},[38,82896,73248],{},[614,82898,72511],{},") — hodnoty ",[883,82901,82903],{"className":82902},[886],[888,82904,82905],{"xmlns":890},[892,82906,82907,82923],{},[895,82908,82909,82915,82917],{},[5535,82910,82911,82913],{},[898,82912,12471],{},[898,82914,13916],{},[1750,82916,1917],{"separator":1916},[5535,82918,82919,82921],{},[898,82920,12471],{},[898,82922,7097],{},[902,82924,82925],{"encoding":904},"Q_A, Q_B"," splňující ",[883,82928,82930],{"className":82929},[886],[888,82931,82932],{"xmlns":890},[892,82933,82934,82950],{},[895,82935,82936,82938,82940,82942,82944,82946,82948],{},[898,82937,1776],{},[898,82939,13658],{},[1750,82941,1753],{"stretchy":1752},[898,82943,12471],{},[1750,82945,1763],{"stretchy":1752},[1750,82947,1766],{},[1742,82949,2607],{},[902,82951,72788],{"encoding":904},"; oddělují pásma ztráty a zisku.",[123,82954,82955,82958],{},[38,82956,82957],{},"Práh rentability"," — stav firmy v bodě zvratu.",[123,82960,82961,82963,82964,20027,82981,83022],{},[38,82962,74302],{}," — v bodě maxima zisku ",[883,82965,82967],{"className":82966},[886],[888,82968,82969],{"xmlns":890},[892,82970,82971,82979],{},[895,82972,82973],{},[5535,82974,82975,82977],{},[898,82976,12471],{},[1742,82978,2607],{},[902,82980,47231],{"encoding":904},[883,82982,82984],{"className":82983},[886],[888,82985,82986],{"xmlns":890},[892,82987,82988,83020],{},[895,82989,82990,82992,82994,82996,83002,83004,83006,83008,83010,83012,83018],{},[898,82991,1773],{},[898,82993,13658],{},[1750,82995,1753],{"stretchy":1752},[5535,82997,82998,83000],{},[898,82999,12471],{},[1742,83001,2607],{},[1750,83003,1763],{"stretchy":1752},[1750,83005,1766],{},[898,83007,1773],{},[898,83009,1812],{},[1750,83011,1753],{"stretchy":1752},[5535,83013,83014,83016],{},[898,83015,12471],{},[1742,83017,2607],{},[1750,83019,1763],{"stretchy":1752},[902,83021,74568],{"encoding":904}," (3.13).",[123,83024,83025,4116,83027,20027,83046,83071],{},[38,83026,75595],{},[883,83028,83030],{"className":83029},[886],[888,83031,83032],{"xmlns":890},[892,83033,83034,83043],{},[895,83035,83036,83038,83040],{},[898,83037,1776],{},[1750,83039,1766],{},[1969,83041,83042],{},"konst",[902,83044,83045],{"encoding":904},"P = \\text{konst}",[883,83047,83049],{"className":83048},[886],[888,83050,83051],{"xmlns":890},[892,83052,83053,83069],{},[895,83054,83055,83057,83059,83061,83063,83065,83067],{},[898,83056,1776],{},[1750,83058,1766],{},[898,83060,1773],{},[898,83062,1812],{},[1750,83064,1753],{"stretchy":1752},[898,83066,12471],{},[1750,83068,1763],{"stretchy":1752},[902,83070,76289],{"encoding":904}," (3.14).",[123,83073,83074,83077,83078,83107,83108,83125],{},[38,83075,83076],{},"Shutdown point"," — bod ",[883,83079,83081],{"className":83080},[886],[888,83082,83083],{"xmlns":890},[892,83084,83085,83105],{},[895,83086,83087,83089,83095,83097,83103],{},[1750,83088,1753],{"stretchy":1752},[1699,83090,83091,83093],{},[898,83092,12471],{},[1750,83094,3751],{},[1750,83096,1917],{"separator":1916},[1699,83098,83099,83101],{},[898,83100,1776],{},[1750,83102,3751],{},[1750,83104,1763],{"stretchy":1752},[902,83106,76578],{"encoding":904}," v minimu ",[883,83109,83111],{"className":83110},[886],[888,83112,83113],{"xmlns":890},[892,83114,83115,83123],{},[895,83116,83117,83119,83121],{},[898,83118,13916],{},[898,83120,49262],{},[898,83122,1812],{},[902,83124,64234],{"encoding":904},"; pod ním se firmě nevyplatí produkovat.",[123,83127,83128,1647,83131,16121,83166,76848,83187,83200,83201,83216,83217,2313],{},[38,83129,83130],{},"Funkce nabídky firmy",[883,83132,83134],{"className":83133},[886],[888,83135,83136],{"xmlns":890},[892,83137,83138,83164],{},[895,83139,83140,83142,83144,83146,83148,83150,83152,83154,83156,83158,83160,83162],{},[898,83141,1776],{},[1750,83143,1766],{},[898,83145,1779],{},[1750,83147,1753],{"stretchy":1752},[898,83149,12471],{},[1750,83151,1763],{"stretchy":1752},[1750,83153,1766],{},[898,83155,1773],{},[898,83157,1812],{},[1750,83159,1753],{"stretchy":1752},[898,83161,12471],{},[1750,83163,1763],{"stretchy":1752},[902,83165,78045],{"encoding":904},[883,83167,83169],{"className":83168},[886],[888,83170,83171],{"xmlns":890},[892,83172,83173,83185],{},[895,83174,83175,83177,83179],{},[898,83176,12471],{},[1750,83178,14143],{},[1699,83180,83181,83183],{},[898,83182,12471],{},[1750,83184,3751],{},[902,83186,76847],{"encoding":904},[883,83188,83190],{"className":83189},[886],[888,83191,83192],{"xmlns":890},[892,83193,83194,83198],{},[895,83195,83196],{},[1742,83197,2607],{},[902,83199,2607],{"encoding":904}," (3.15); vychází z rostoucí části ",[883,83202,83204],{"className":83203},[886],[888,83205,83206],{"xmlns":890},[892,83207,83208,83214],{},[895,83209,83210,83212],{},[898,83211,1773],{},[898,83213,1812],{},[902,83215,64215],{"encoding":904}," nad minimem ",[883,83218,83220],{"className":83219},[886],[888,83221,83222],{"xmlns":890},[892,83223,83224,83232],{},[895,83225,83226,83228,83230],{},[898,83227,13916],{},[898,83229,49262],{},[898,83231,1812],{},[902,83233,64234],{"encoding":904},[123,83235,83236,10469,83238,83259,83260,2313],{},[38,83237,59002],{},[883,83239,83241],{"className":83240},[886],[888,83242,83243],{"xmlns":890},[892,83244,83245,83257],{},[895,83246,83247,83249,83251],{},[898,83248,1776],{},[1750,83250,1766],{},[1699,83252,83253,83255],{},[898,83254,1776],{},[1750,83256,3751],{},[902,83258,14016],{"encoding":904}," konstantní ⇒ ",[883,83261,83263],{"className":83262},[886],[888,83264,83265],{"xmlns":890},[892,83266,83267,83287],{},[895,83268,83269,83271,83273,83275,83277,83279,83281],{},[898,83270,13916],{},[898,83272,13658],{},[1750,83274,1766],{},[898,83276,1773],{},[898,83278,13658],{},[1750,83280,1766],{},[1699,83282,83283,83285],{},[898,83284,1776],{},[1750,83286,3751],{},[902,83288,67521],{"encoding":904},[123,83290,83291,83294],{},[38,83292,83293],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[115,83296,11524],{"id":11523},[120,83298,83299,83318,83330],{},[123,83300,83301,1647,83303,1343,83306,1343,83309,1343,83312,1343,83315],{},[38,83302,59646],{},[207,83304,21574],{"className":83305,"dataFsResolvedFilePath":800,"href":801},[210],[207,83307,13496],{"className":83308,"dataFsResolvedFilePath":848,"href":849},[210],[207,83310,12053],{"className":83311,"dataFsResolvedFilePath":764,"href":765},[210],[207,83313,775],{"className":83314,"dataFsResolvedFilePath":773,"href":774},[210],[207,83316,859],{"className":83317,"dataFsResolvedFilePath":857,"href":858},[210],[123,83319,83320,1647,83322,1343,83326],{},[38,83321,45626],{},[207,83323,83325],{"className":83324,"dataFsResolvedFilePath":745,"href":746},[210],"KS 1. blok — souhrn",[207,83327,83329],{"className":83328,"dataFsResolvedFilePath":838,"href":839},[210],"KS 2. blok — souhrn",[123,83331,83332,1647,83334],{},[38,83333,11531],{},[207,83335,11535],{"className":83336,"dataFsResolvedFilePath":1644,"href":1645},[210],{"title":641,"searchDepth":642,"depth":642,"links":83338},[83339,83340,83347,83353,83357,83358,83362,83363,83364,83365,83371,83372],{"id":59877,"depth":642,"text":1241},{"id":64661,"depth":642,"text":64662,"children":83341},[83342,83343,83344,83345,83346],{"id":64672,"depth":649,"text":64673},{"id":65258,"depth":649,"text":65259},{"id":65406,"depth":649,"text":65407},{"id":66148,"depth":649,"text":66149},{"id":66803,"depth":649,"text":66804},{"id":67524,"depth":642,"text":67525,"children":83348},[83349,83350,83351,83352],{"id":67528,"depth":649,"text":67529},{"id":67689,"depth":649,"text":67690},{"id":68876,"depth":649,"text":68877},{"id":69774,"depth":649,"text":69775},{"id":70856,"depth":642,"text":70857,"children":83354},[83355,83356],{"id":25984,"depth":649,"text":25985},{"id":72206,"depth":649,"text":72207},{"id":72380,"depth":642,"text":72381},{"id":74301,"depth":642,"text":74302,"children":83359},[83360,83361],{"id":74315,"depth":649,"text":25985},{"id":75594,"depth":649,"text":75595},{"id":76226,"depth":642,"text":76227},{"id":77692,"depth":642,"text":77693},{"id":58804,"depth":642,"text":58805},{"id":78153,"depth":642,"text":78154,"children":83366},[83367,83368,83369,83370],{"id":78157,"depth":649,"text":78158},{"id":79009,"depth":649,"text":79010},{"id":80555,"depth":649,"text":80556},{"id":81931,"depth":649,"text":81932},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":64043,"description":641},[1138,1135],"topics\u002Fprijem-naklady-zisk",[1128,83379,83380,64095,83381,83382,83383],"prijem","naklady","body-zvratu","maximalizace-zisku","nabidka-firmy","0d2CjMGyTT-GeTvSE65iXk5mUJ-650ilVskfuGcRAwI",{"id":83386,"title":83387,"body":83388,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":95485,"navigation":664,"path":95486,"seo":95487,"sources":95488,"stem":95489,"tags":95490,"type":11664,"updated":677,"__hash__":95496},"topics\u002Ftopics\u002Fprodukce.md","Produkce — produkční funkce, Cobb-Douglas, MRTS",{"type":9,"value":83389,"toc":95442},[83390,83393,83749,83753,83756,83824,83876,83886,83890,83924,83965,83989,84012,84041,84108,84215,84258,84315,84390,84435,84439,84447,84455,84458,84723,84774,84854,84924,84947,84975,85020,85042,85046,85053,85102,85128,85279,85282,85319,85482,85590,85594,85631,85706,85775,85894,86016,86097,86103,86144,86217,86310,86314,86350,86438,86552,86657,86742,86882,86886,86934,86979,86985,86989,86992,87043,87093,87100,87166,87299,87344,87348,87369,87748,87843,87860,87914,87918,88000,88084,88254,88257,88300,88367,88441,88445,88450,88519,88527,88536,88614,88680,88685,88780,88823,88828,88876,88881,88929,89047,89130,89168,89271,89330,89471,89475,89518,89591,89615,89669,89676,89678,89723,89768,89779,89784,89820,89882,89905,89914,90015,90082,90155,90162,90253,90315,90351,90408,90467,90652,90748,90752,90756,90835,90840,90964,91050,91056,91166,91203,91294,91392,91395,91399,91465,91502,91624,91676,91680,91708,91760,91834,91939,91963,92022,92026,92044,92187,92335,92337,92372,92376,92378,92468,92598,92724,92816,92891,92895,93011,93115,93305,93341,93435,93441,93554,93857,93863,93981,94080,94156,94158,95320,95322],[12,83391,83387],{"id":83392},"produkce-produkční-funkce-cobb-douglas-mrts",[1785,83394,83395],{},[724,83396,83397,13541,83399,83401,83402,45819,83415,83428,83429,25949,83442,2084,83444,83468,83469,1647,83471,2028,83505,1647,83508,83536,83537,20027,83557,83587,83588,2084,83591,83619,83620,83623,83624,83654,83655,83685,83686,1647,83689,83729,83730,83748],{},[883,83398,13540],{},[38,83400,859],{}," popisuje vztah mezi vstupy (práce ",[883,83403,83405],{"className":83404},[886],[888,83406,83407],{"xmlns":890},[892,83408,83409,83413],{},[895,83410,83411],{},[898,83412,2046],{},[902,83414,2046],{"encoding":904},[883,83416,83418],{"className":83417},[886],[888,83419,83420],{"xmlns":890},[892,83421,83422,83426],{},[895,83423,83424],{},[898,83425,19435],{},[902,83427,19435],{"encoding":904},") a výstupem ",[883,83430,83432],{"className":83431},[886],[888,83433,83434],{"xmlns":890},[892,83435,83436,83440],{},[895,83437,83438],{},[898,83439,12471],{},[902,83441,12471],{"encoding":904},[38,83443,45887],{},[883,83445,83447],{"className":83446},[886],[888,83448,83449],{"xmlns":890},[892,83450,83451,83465],{},[895,83452,83453,83455,83457,83459,83461,83463],{},[898,83454,12471],{},[1750,83456,1766],{},[898,83458,12471],{},[1750,83460,1753],{"stretchy":1752},[898,83462,2046],{},[1750,83464,1763],{"stretchy":1752},[902,83466,83467],{"encoding":904},"Q = Q(L)",") studujeme ",[614,83470,19658],{},[883,83472,83474],{"className":83473},[886],[888,83475,83476],{"xmlns":890},[892,83477,83478,83502],{},[895,83479,83480,83482,83488,83490,83496,83498,83500],{},[898,83481,1773],{},[5535,83483,83484,83486],{},[898,83485,1776],{},[898,83487,2046],{},[1750,83489,1766],{},[1699,83491,83492,83494],{},[898,83493,12471],{},[1750,83495,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,83497,1753],{"stretchy":1752},[898,83499,2046],{},[1750,83501,1763],{"stretchy":1752},[902,83503,83504],{"encoding":904},"MP_L = Q'(L)",[614,83506,83507],{},"průměrný produkt",[883,83509,83511],{"className":83510},[886],[888,83512,83513],{"xmlns":890},[892,83514,83515,83533],{},[895,83516,83517,83519,83525,83527,83529,83531],{},[898,83518,13916],{},[5535,83520,83521,83523],{},[898,83522,1776],{},[898,83524,2046],{},[1750,83526,1766],{},[898,83528,12471],{},[898,83530,1748],{"mathvariant":1747},[898,83532,2046],{},[902,83534,83535],{"encoding":904},"AP_L = Q\u002FL","; v maximu ",[883,83538,83540],{"className":83539},[886],[888,83541,83542],{"xmlns":890},[892,83543,83544,83554],{},[895,83545,83546,83548],{},[898,83547,13916],{},[5535,83549,83550,83552],{},[898,83551,1776],{},[898,83553,2046],{},[902,83555,83556],{"encoding":904},"AP_L",[883,83558,83560],{"className":83559},[886],[888,83561,83562],{"xmlns":890},[892,83563,83564,83584],{},[895,83565,83566,83568,83574,83576,83578],{},[898,83567,1773],{},[5535,83569,83570,83572],{},[898,83571,1776],{},[898,83573,2046],{},[1750,83575,1766],{},[898,83577,13916],{},[5535,83579,83580,83582],{},[898,83581,1776],{},[898,83583,2046],{},[902,83585,83586],{"encoding":904},"MP_L = AP_L",". Ve ",[38,83589,83590],{},"dvoufaktorovém modelu",[883,83592,83594],{"className":83593},[886],[888,83595,83596],{"xmlns":890},[892,83597,83598,83616],{},[895,83599,83600,83602,83604,83606,83608,83610,83612,83614],{},[898,83601,12471],{},[1750,83603,1766],{},[898,83605,12471],{},[1750,83607,1753],{"stretchy":1752},[898,83609,2046],{},[1750,83611,1917],{"separator":1916},[898,83613,19435],{},[1750,83615,1763],{"stretchy":1752},[902,83617,83618],{"encoding":904},"Q = Q(L,K)",") dominují ",[38,83621,83622],{},"Cobb-Douglasovy"," funkce ",[883,83625,83627],{"className":83626},[886],[888,83628,83629],{"xmlns":890},[892,83630,83631,83651],{},[895,83632,83633,83635,83637,83639,83645],{},[898,83634,12471],{},[1750,83636,1766],{},[898,83638,13916],{},[1699,83640,83641,83643],{},[898,83642,2046],{},[898,83644,207],{},[1699,83646,83647,83649],{},[898,83648,19435],{},[898,83650,2573],{},[902,83652,83653],{"encoding":904},"Q = AL^a K^b","; mezní produkty ",[883,83656,83658],{"className":83657},[886],[888,83659,83660],{"xmlns":890},[892,83661,83662,83682],{},[895,83663,83664,83666,83672,83674,83676],{},[898,83665,1773],{},[5535,83667,83668,83670],{},[898,83669,1776],{},[898,83671,2046],{},[1750,83673,1917],{"separator":1916},[898,83675,1773],{},[5535,83677,83678,83680],{},[898,83679,1776],{},[898,83681,19435],{},[902,83683,83684],{"encoding":904},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[38,83687,83688],{},"mezní míru technické substituce",[883,83690,83692],{"className":83691},[886],[888,83693,83694],{"xmlns":890},[892,83695,83696,83726],{},[895,83697,83698,83700,83702,83704,83706,83708,83710,83716,83718,83720],{},[898,83699,1773],{},[898,83701,13658],{},[898,83703,5326],{},[898,83705,1779],{},[1750,83707,1766],{},[898,83709,1773],{},[5535,83711,83712,83714],{},[898,83713,1776],{},[898,83715,2046],{},[898,83717,1748],{"mathvariant":1747},[898,83719,1773],{},[5535,83721,83722,83724],{},[898,83723,1776],{},[898,83725,19435],{},[902,83727,83728],{"encoding":904},"MRTS = MP_L\u002FMP_K"," — sklon izokvanty. Součet exponentů ",[883,83731,83733],{"className":83732},[886],[888,83734,83735],{"xmlns":890},[892,83736,83737,83745],{},[895,83738,83739,83741,83743],{},[898,83740,207],{},[1750,83742,1861],{},[898,83744,2573],{},[902,83746,83747],{"encoding":904},"a+b"," určuje typ výnosů z rozsahu.",[115,83750,83752],{"id":83751},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[724,83754,83755],{},"Po prostudování kapitoly 5 student umí:",[120,83757,83758,83764,83774,83780,83786,83791,83797,83807,83812,83818],{},[123,83759,83760,83761,1917],{},"popsat ",[38,83762,83763],{},"jednofaktorový model produkce",[123,83765,83766,83767,2028,83770,83773],{},"vypočítat ",[38,83768,83769],{},"mezní",[38,83771,83772],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[123,83775,83776,83777,1917],{},"charakterizovat průběh ",[38,83778,83779],{},"křivky produkce",[123,83781,83782,83783,1917],{},"formulovat ",[38,83784,83785],{},"princip maximalizace průměrného produktu práce",[123,83787,83760,83788,1917],{},[38,83789,83790],{},"dvoufaktorový model produkce",[123,83792,83793,83794,1917],{},"uvést tvar ",[38,83795,83796],{},"Cobb–Douglasových produkčních funkcí",[123,83798,83799,83800,1343,83802,1343,83804,1917],{},"vyložit, co jsou ",[38,83801,8465],{},[38,83803,23261],{},[38,83805,83806],{},"klesající výnosy z rozsahu",[123,83808,83766,83809,83773],{},[38,83810,83811],{},"mezní produkty práce a kapitálu",[123,83813,83814,83815,1917],{},"najít ",[38,83816,83817],{},"izokvanty",[123,83819,83766,83820,83823],{},[38,83821,83822],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[724,83825,83826,83827,83830,83831,83834,83835,1647,83838,1343,83851,1647,83854,2028,83867,83870,83871,83873,83874,2313],{},"Každý proces produkce je určován ",[38,83828,83829],{},"faktory"," (též ",[38,83832,83833],{},"vstupy",") produkce. K hlavním patří ",[38,83836,83837],{},"práce",[883,83839,83841],{"className":83840},[886],[888,83842,83843],{"xmlns":890},[892,83844,83845,83849],{},[895,83846,83847],{},[898,83848,2046],{},[902,83850,2046],{"encoding":904},[38,83852,83853],{},"kapitál",[883,83855,83857],{"className":83856},[886],[888,83858,83859],{"xmlns":890},[892,83860,83861,83865],{},[895,83862,83863],{},[898,83864,19435],{},[902,83866,19435],{"encoding":904},[38,83868,83869],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[38,83872,45887],{}," (produkce závisí jen na práci); v opačném případě o ",[38,83875,83590],{},[724,83877,83878,83879,1343,83882,83885],{},"Související matematický aparát: ",[207,83880,12053],{"className":83881,"dataFsResolvedFilePath":764,"href":765},[210],[207,83883,784],{"className":83884,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace a totální diferenciál).",[115,83887,83889],{"id":83888},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[724,83891,83892,83893,83906,83907,83920,83921],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[883,83894,83896],{"className":83895},[886],[888,83897,83898],{"xmlns":890},[892,83899,83900,83904],{},[895,83901,83902],{},[898,83903,12471],{},[902,83905,12471],{"encoding":904}," na práci ",[883,83908,83910],{"className":83909},[886],[888,83911,83912],{"xmlns":890},[892,83913,83914,83918],{},[895,83915,83916],{},[898,83917,2046],{},[902,83919,2046],{"encoding":904}," vyjadřuje ",[38,83922,83923],{},"produkční funkce",[883,83925,83927],{"className":83926},[886],[888,83928,83929],{"xmlns":890,"display":36989},[892,83930,83931,83962],{},[4577,83932,83933],{"width":36994},[4582,83934,83935,83937,83955,83957],{},[4585,83936],{"width":36999},[4585,83938,83939],{},[895,83940,83941,83943,83945,83947,83949,83951,83953],{},[898,83942,12471],{},[1750,83944,1766],{},[898,83946,12471],{},[1750,83948,1753],{"stretchy":1752},[898,83950,2046],{},[1750,83952,1763],{"stretchy":1752},[1750,83954,1917],{"separator":1916},[4585,83956],{"width":36999},[4585,83958,83959],{},[1969,83960,83961],{},"(5.1)",[902,83963,83964],{"encoding":904},"Q = Q(L), \\tag{5.1}",[724,83966,83967,83968,2084,83971,83974,83975,83988],{},"jejíž graf se nazývá ",[38,83969,83970],{},"křivka produkce",[614,83972,83973],{},"production curve","). Práce ",[883,83976,83978],{"className":83977},[886],[888,83979,83980],{"xmlns":890},[892,83981,83982,83986],{},[895,83983,83984],{},[898,83985,2046],{},[902,83987,2046],{"encoding":904}," se měří počtem pracovníků, případně počtem pracovních hodin.",[115,83990,83992,83993,1763],{"id":83991},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[883,83994,83996],{"className":83995},[886],[888,83997,83998],{"xmlns":890},[892,83999,84000,84010],{},[895,84001,84002,84004],{},[898,84003,1773],{},[5535,84005,84006,84008],{},[898,84007,1776],{},[898,84009,2046],{},[902,84011,19678],{"encoding":904},[724,84013,84014,2084,84017,84020,84021,84040],{},[38,84015,84016],{},"Mezní produkt práce",[614,84018,84019],{},"marginal product of labour",") ",[883,84022,84024],{"className":84023},[886],[888,84025,84026],{"xmlns":890},[892,84027,84028,84038],{},[895,84029,84030,84032],{},[898,84031,1773],{},[5535,84033,84034,84036],{},[898,84035,1776],{},[898,84037,2046],{},[902,84039,19678],{"encoding":904}," je derivace produkce podle práce:",[883,84042,84044],{"className":84043},[886],[888,84045,84046],{"xmlns":890,"display":36989},[892,84047,84048,84105],{},[4577,84049,84050],{"width":36994},[4582,84051,84052,84054,84098,84100],{},[4585,84053],{"width":36999},[4585,84055,84056],{},[895,84057,84058,84060,84066,84068,84082,84084,84090,84092,84094,84096],{},[898,84059,1773],{},[5535,84061,84062,84064],{},[898,84063,1776],{},[898,84065,2046],{},[1750,84067,1766],{},[3423,84069,84070,84076],{},[895,84071,84072,84074],{},[898,84073,3429],{},[898,84075,12471],{},[895,84077,84078,84080],{},[898,84079,3429],{},[898,84081,2046],{},[1750,84083,1766],{},[1699,84085,84086,84088],{},[898,84087,12471],{},[1750,84089,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,84091,1753],{"stretchy":1752},[898,84093,2046],{},[1750,84095,1763],{"stretchy":1752},[898,84097,2313],{"mathvariant":1747},[4585,84099],{"width":36999},[4585,84101,84102],{},[1969,84103,84104],{},"(5.2)",[902,84106,84107],{"encoding":904},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[724,84109,84110,84111,3755,84129,84157,84158,84175,84176,4321,84193,1783],{},"Pro pevnou hodnotu ",[883,84112,84114],{"className":84113},[886],[888,84115,84116],{"xmlns":890},[892,84117,84118,84126],{},[895,84119,84120],{},[1699,84121,84122,84124],{},[898,84123,2046],{},[1750,84125,3751],{},[902,84127,84128],{"encoding":904},"L^*",[883,84130,84132],{"className":84131},[886],[888,84133,84134],{"xmlns":890},[892,84135,84136,84154],{},[895,84137,84138,84144,84146,84152],{},[1699,84139,84140,84142],{},[898,84141,12471],{},[1750,84143,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,84145,1753],{"stretchy":1752},[1699,84147,84148,84150],{},[898,84149,2046],{},[1750,84151,3751],{},[1750,84153,1763],{"stretchy":1752},[902,84155,84156],{"encoding":904},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[883,84159,84161],{"className":84160},[886],[888,84162,84163],{"xmlns":890},[892,84164,84165,84173],{},[895,84166,84167],{},[1699,84168,84169,84171],{},[898,84170,2046],{},[1750,84172,3751],{},[902,84174,84128],{"encoding":904},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[883,84177,84179],{"className":84178},[886],[888,84180,84181],{"xmlns":890},[892,84182,84183,84191],{},[895,84184,84185],{},[1699,84186,84187,84189],{},[898,84188,2046],{},[1750,84190,3751],{},[902,84192,84128],{"encoding":904},[883,84194,84196],{"className":84195},[886],[888,84197,84198],{"xmlns":890},[892,84199,84200,84212],{},[895,84201,84202,84208,84210],{},[1699,84203,84204,84206],{},[898,84205,2046],{},[1750,84207,3751],{},[1750,84209,1861],{},[1742,84211,1744],{},[902,84213,84214],{"encoding":904},"L^*+1",[1785,84216,84217],{},[724,84218,84219,1792,84221,84240,84241,84244,84245,2313],{},[883,84220,1791],{},[883,84222,84224],{"className":84223},[886],[888,84225,84226],{"xmlns":890},[892,84227,84228,84238],{},[895,84229,84230,84232],{},[898,84231,1773],{},[5535,84233,84234,84236],{},[898,84235,1776],{},[898,84237,2046],{},[902,84239,19678],{"encoding":904}," odpovídá na otázku „",[38,84242,84243],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[883,84246,84248],{"className":84247},[886],[888,84249,84250],{"xmlns":890},[892,84251,84252,84256],{},[895,84253,84254],{},[898,84255,2046],{},[902,84257,2046],{"encoding":904},[724,84259,84260,84263,84264,84280,84281,4321,84294,84314],{},[38,84261,84262],{},"Přibližná změna produkce"," pro změnu práce o ",[883,84265,84267],{"className":84266},[886],[888,84268,84269],{"xmlns":890},[892,84270,84271,84277],{},[895,84272,84273,84275],{},[898,84274,3429],{},[898,84276,2046],{},[902,84278,84279],{"encoding":904},"dL"," (z ",[883,84282,84284],{"className":84283},[886],[888,84285,84286],{"xmlns":890},[892,84287,84288,84292],{},[895,84289,84290],{},[898,84291,2046],{},[902,84293,2046],{"encoding":904},[883,84295,84297],{"className":84296},[886],[888,84298,84299],{"xmlns":890},[892,84300,84301,84311],{},[895,84302,84303,84305,84307,84309],{},[898,84304,2046],{},[1750,84306,1861],{},[898,84308,3429],{},[898,84310,2046],{},[902,84312,84313],{"encoding":904},"L+dL",") pomocí diferenciálu:",[883,84316,84318],{"className":84317},[886],[888,84319,84320],{"xmlns":890,"display":36989},[892,84321,84322,84387],{},[4577,84323,84324],{"width":36994},[4582,84325,84326,84328,84380,84382],{},[4585,84327],{"width":36999},[4585,84329,84330],{},[895,84331,84332,84334,84336,84338,84340,84342,84344,84350,84352,84354,84356,84358,84360,84362,84364,84366,84372,84374,84376,84378],{},[898,84333,2666],{"mathvariant":1747},[898,84335,12471],{},[1750,84337,2274],{},[898,84339,3429],{},[898,84341,12471],{},[1750,84343,1766],{},[1699,84345,84346,84348],{},[898,84347,12471],{},[1750,84349,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,84351,1753],{"stretchy":1752},[898,84353,2046],{},[1750,84355,1763],{"stretchy":1752},[1969,84357,2658],{},[898,84359,3429],{},[898,84361,2046],{},[1750,84363,1766],{},[898,84365,1773],{},[5535,84367,84368,84370],{},[898,84369,1776],{},[898,84371,2046],{},[1969,84373,2658],{},[898,84375,3429],{},[898,84377,2046],{},[898,84379,2313],{"mathvariant":1747},[4585,84381],{"width":36999},[4585,84383,84384],{},[1969,84385,84386],{},"(5.3)",[902,84388,84389],{"encoding":904},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[724,84391,84392,84393,2313],{},"Skutečná změna je ",[883,84394,84396],{"className":84395},[886],[888,84397,84398],{"xmlns":890},[892,84399,84400,84432],{},[895,84401,84402,84404,84406,84408,84410,84412,84414,84416,84418,84420,84422,84424,84426,84428,84430],{},[898,84403,2666],{"mathvariant":1747},[898,84405,12471],{},[1750,84407,1766],{},[898,84409,12471],{},[1750,84411,1753],{"stretchy":1752},[898,84413,2046],{},[1750,84415,1861],{},[898,84417,3429],{},[898,84419,2046],{},[1750,84421,1763],{"stretchy":1752},[1750,84423,1758],{},[898,84425,12471],{},[1750,84427,1753],{"stretchy":1752},[898,84429,2046],{},[1750,84431,1763],{"stretchy":1752},[902,84433,84434],{"encoding":904},"\\Delta Q = Q(L+dL) - Q(L)",[198,84436,84438],{"id":84437},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[724,84440,84441,2084,84444,12825],{},[38,84442,84443],{},"Zákon klesajících výnosů",[614,84445,84446],{},"law of diminishing marginal productivity",[1785,84448,84449],{},[724,84450,84451,84452,84454],{},"Roste-li postupně některý ze vstupů (",[614,84453,45883],{},"), budou přírůstky výstupu od jistého bodu klesat.",[724,84456,84457],{},"Typická křivka produkce (Obrázek 5.2) má dvě fáze:",[724,84459,84460,84461,1647,84482,84501,84502,84552,84553,84555,84556,1647,84576,84595,84596,84552,84628,12605,84630,84649,84650,5424,84667,84701,84702,2433,84719,84722],{},"1° ",[38,84462,84463,84464,2366],{},"Do bodu ",[883,84465,84467],{"className":84466},[886],[888,84468,84469],{"xmlns":890},[892,84470,84471,84479],{},[895,84472,84473],{},[5535,84474,84475,84477],{},[898,84476,2046],{},[1742,84478,2607],{},[902,84480,84481],{"encoding":904},"L_0",[883,84483,84485],{"className":84484},[886],[888,84486,84487],{"xmlns":890},[892,84488,84489,84499],{},[895,84490,84491,84493],{},[898,84492,1773],{},[5535,84494,84495,84497],{},[898,84496,1776],{},[898,84498,2046],{},[902,84500,19678],{"encoding":904}," roste, tj. ",[883,84503,84505],{"className":84504},[886],[888,84506,84507],{"xmlns":890},[892,84508,84509,84549],{},[895,84510,84511,84513,84515,84521,84527,84529,84539,84541,84543,84545,84547],{},[1750,84512,1753],{"stretchy":1752},[898,84514,1773],{},[5535,84516,84517,84519],{},[898,84518,1776],{},[898,84520,2046],{},[1699,84522,84523,84525],{},[1750,84524,1763],{"stretchy":1752},[1750,84526,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,84528,1766],{},[1699,84530,84531,84533],{},[898,84532,12471],{},[895,84534,84535,84537],{},[1750,84536,3815],{"mathvariant":1747},[1750,84538,3815],{"mathvariant":1747},[1750,84540,1753],{"stretchy":1752},[898,84542,2046],{},[1750,84544,1763],{"stretchy":1752},[1750,84546,2604],{},[1742,84548,2607],{},[902,84550,84551],{"encoding":904},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[38,84554,46587],{},".\n2° ",[38,84557,84558,84559,2366],{},"Od bodu ",[883,84560,84562],{"className":84561},[886],[888,84563,84564],{"xmlns":890},[892,84565,84566,84574],{},[895,84567,84568],{},[5535,84569,84570,84572],{},[898,84571,2046],{},[1742,84573,2607],{},[902,84575,84481],{"encoding":904},[883,84577,84579],{"className":84578},[886],[888,84580,84581],{"xmlns":890},[892,84582,84583,84593],{},[895,84584,84585,84587],{},[898,84586,1773],{},[5535,84588,84589,84591],{},[898,84590,1776],{},[898,84592,2046],{},[902,84594,19678],{"encoding":904}," klesá, ",[883,84597,84599],{"className":84598},[886],[888,84600,84601],{"xmlns":890},[892,84602,84603,84625],{},[895,84604,84605,84615,84617,84619,84621,84623],{},[1699,84606,84607,84609],{},[898,84608,12471],{},[895,84610,84611,84613],{},[1750,84612,3815],{"mathvariant":1747},[1750,84614,3815],{"mathvariant":1747},[1750,84616,1753],{"stretchy":1752},[898,84618,2046],{},[1750,84620,1763],{"stretchy":1752},[1750,84622,2624],{},[1742,84624,2607],{},[902,84626,84627],{"encoding":904},"Q''(L) \u003C 0",[38,84629,47411],{},[883,84631,84633],{"className":84632},[886],[888,84634,84635],{"xmlns":890},[892,84636,84637,84647],{},[895,84638,84639,84641],{},[898,84640,1773],{},[5535,84642,84643,84645],{},[898,84644,1776],{},[898,84646,2046],{},[902,84648,19678],{"encoding":904}," v kladných hodnotách klesá do bodu ",[883,84651,84653],{"className":84652},[886],[888,84654,84655],{"xmlns":890},[892,84656,84657,84665],{},[895,84658,84659],{},[5535,84660,84661,84663],{},[898,84662,2046],{},[1742,84664,1744],{},[902,84666,22818],{"encoding":904},[883,84668,84670],{"className":84669},[886],[888,84671,84672],{"xmlns":890},[892,84673,84674,84698],{},[895,84675,84676,84678,84684,84686,84692,84694,84696],{},[898,84677,1773],{},[5535,84679,84680,84682],{},[898,84681,1776],{},[898,84683,2046],{},[1750,84685,1753],{"stretchy":1752},[5535,84687,84688,84690],{},[898,84689,2046],{},[1742,84691,1744],{},[1750,84693,1763],{"stretchy":1752},[1750,84695,1766],{},[1742,84697,2607],{},[902,84699,84700],{"encoding":904},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[883,84703,84705],{"className":84704},[886],[888,84706,84707],{"xmlns":890},[892,84708,84709,84717],{},[895,84710,84711],{},[5535,84712,84713,84715],{},[898,84714,2046],{},[1742,84716,2607],{},[902,84718,84481],{"encoding":904},[38,84720,84721],{},"inflexním bodem"," produkční funkce.",[724,84724,84725,84726,20027,84743,2313],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[883,84727,84729],{"className":84728},[886],[888,84730,84731],{"xmlns":890},[892,84732,84733,84741],{},[895,84734,84735],{},[5535,84736,84737,84739],{},[898,84738,2046],{},[1742,84740,2607],{},[902,84742,84481],{"encoding":904},[883,84744,84746],{"className":84745},[886],[888,84747,84748],{"xmlns":890},[892,84749,84750,84772],{},[895,84751,84752,84762,84764,84766,84768,84770],{},[1699,84753,84754,84756],{},[898,84755,12471],{},[895,84757,84758,84760],{},[1750,84759,3815],{"mathvariant":1747},[1750,84761,3815],{"mathvariant":1747},[1750,84763,1753],{"stretchy":1752},[898,84765,2046],{},[1750,84767,1763],{"stretchy":1752},[1750,84769,2624],{},[1742,84771,2607],{},[902,84773,84627],{"encoding":904},[724,84775,84776,1647,84779,9375,84819,1343,84836,84853],{},[38,84777,84778],{},"Typický polynom třetího stupně:",[883,84780,84782],{"className":84781},[886],[888,84783,84784],{"xmlns":890},[892,84785,84786,84816],{},[895,84787,84788,84790,84792,84794,84796,84798,84800,84806,84808,84810],{},[898,84789,12471],{},[1750,84791,1753],{"stretchy":1752},[898,84793,2046],{},[1750,84795,1763],{"stretchy":1752},[1750,84797,1766],{},[898,84799,207],{},[1699,84801,84802,84804],{},[898,84803,2046],{},[1742,84805,7822],{},[1750,84807,1861],{},[898,84809,2573],{},[1699,84811,84812,84814],{},[898,84813,2046],{},[1742,84815,1872],{},[902,84817,84818],{"encoding":904},"Q(L) = aL^3 + bL^2",[883,84820,84822],{"className":84821},[886],[888,84823,84824],{"xmlns":890},[892,84825,84826,84834],{},[895,84827,84828,84830,84832],{},[898,84829,207],{},[1750,84831,2624],{},[1742,84833,2607],{},[902,84835,52008],{"encoding":904},[883,84837,84839],{"className":84838},[886],[888,84840,84841],{"xmlns":890},[892,84842,84843,84851],{},[895,84844,84845,84847,84849],{},[898,84846,2573],{},[1750,84848,2604],{},[1742,84850,2607],{},[902,84852,2610],{"encoding":904},". Pak",[883,84855,84857],{"className":84856},[886],[888,84858,84859],{"xmlns":890,"display":36989},[892,84860,84861,84921],{},[895,84862,84863,84869,84871,84873,84881,84889,84891,84893,84899,84901,84903,84911,84919],{},[5535,84864,84865,84867],{},[898,84866,2046],{},[1742,84868,2607],{},[1750,84870,1766],{},[1750,84872,1758],{},[3586,84874,84875],{"scriptlevel":2607,"displaystyle":1752},[3423,84876,84877,84879],{},[1742,84878,1744],{},[1742,84880,7822],{},[3586,84882,84883],{"scriptlevel":2607,"displaystyle":1752},[3423,84884,84885,84887],{},[898,84886,2573],{},[898,84888,207],{},[1750,84890,1917],{"separator":1916},[2125,84892],{"width":2127},[5535,84894,84895,84897],{},[898,84896,2046],{},[1742,84898,1744],{},[1750,84900,1766],{},[1750,84902,1758],{},[3586,84904,84905],{"scriptlevel":2607,"displaystyle":1752},[3423,84906,84907,84909],{},[1742,84908,1872],{},[1742,84910,7822],{},[3586,84912,84913],{"scriptlevel":2607,"displaystyle":1752},[3423,84914,84915,84917],{},[898,84916,2573],{},[898,84918,207],{},[898,84920,2313],{"mathvariant":1747},[902,84922,84923],{"encoding":904},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[115,84925,84927,84928,1763],{"id":84926},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[883,84929,84931],{"className":84930},[886],[888,84932,84933],{"xmlns":890},[892,84934,84935,84945],{},[895,84936,84937,84939],{},[898,84938,13916],{},[5535,84940,84941,84943],{},[898,84942,1776],{},[898,84944,2046],{},[902,84946,83556],{"encoding":904},[724,84948,84949,2084,84952,84020,84955,84974],{},[38,84950,84951],{},"Průměrný produkt práce",[614,84953,84954],{},"average product of labour",[883,84956,84958],{"className":84957},[886],[888,84959,84960],{"xmlns":890},[892,84961,84962,84972],{},[895,84963,84964,84966],{},[898,84965,13916],{},[5535,84967,84968,84970],{},[898,84969,1776],{},[898,84971,2046],{},[902,84973,83556],{"encoding":904}," je podíl produkce a práce:",[883,84976,84978],{"className":84977},[886],[888,84979,84980],{"xmlns":890,"display":36989},[892,84981,84982,85017],{},[4577,84983,84984],{"width":36994},[4582,84985,84986,84988,85010,85012],{},[4585,84987],{"width":36999},[4585,84989,84990],{},[895,84991,84992,84994,85000,85002,85008],{},[898,84993,13916],{},[5535,84995,84996,84998],{},[898,84997,1776],{},[898,84999,2046],{},[1750,85001,1766],{},[3423,85003,85004,85006],{},[898,85005,12471],{},[898,85007,2046],{},[898,85009,2313],{"mathvariant":1747},[4585,85011],{"width":36999},[4585,85013,85014],{},[1969,85015,85016],{},"(5.4)",[902,85018,85019],{"encoding":904},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[724,85021,85022,85023,2313],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[883,85024,85026],{"className":85025},[886],[888,85027,85028],{"xmlns":890},[892,85029,85030,85040],{},[895,85031,85032,85034],{},[898,85033,13916],{},[5535,85035,85036,85038],{},[898,85037,1776],{},[898,85039,2046],{},[902,85041,83556],{"encoding":904},[115,85043,85045],{"id":85044},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[724,85047,85048],{},[4434,85049],{"alt":85050,"className":85051,"src":85052},"imek-q-mpl-apl-tripanel",[210,4438],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[1785,85054,85055],{},[724,85056,85057,85060,85061,2984,85080,85097,85098],{},[38,85058,85059],{},"Princip:"," Má-li ",[883,85062,85064],{"className":85063},[886],[888,85065,85066],{"xmlns":890},[892,85067,85068,85078],{},[895,85069,85070,85072],{},[898,85071,13916],{},[5535,85073,85074,85076],{},[898,85075,1776],{},[898,85077,2046],{},[902,85079,83556],{"encoding":904},[883,85081,85083],{"className":85082},[886],[888,85084,85085],{"xmlns":890},[892,85086,85087,85095],{},[895,85088,85089],{},[5535,85090,85091,85093],{},[898,85092,2046],{},[1742,85094,2607],{},[902,85096,84481],{"encoding":904}," maximum, pak platí\n",[883,85099,85101],{"className":85100,"title":13862,"style":13863},[13861],"MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[724,85103,85104,85105,85108,85109,1647,85113,2313],{},"Slovně: ",[38,85106,85107],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[207,85110,85112],{"className":85111,"dataFsResolvedFilePath":827,"href":828},[210],"principu minimalizace průměrných nákladů",[883,85114,85116],{"className":85115},[886],[888,85117,85118],{"xmlns":890},[892,85119,85120,85126],{},[895,85121,85122,85124],{},[898,85123,13916],{},[898,85125,1812],{},[902,85127,64483],{"encoding":904},[1785,85129,85130,85154],{},[724,85131,85132,85134,85135],{},[883,85133,6004],{}," Postup — jak najít max ",[883,85136,85138],{"className":85137},[886],[888,85139,85140],{"xmlns":890},[892,85141,85142,85152],{},[895,85143,85144,85146],{},[898,85145,13916],{},[5535,85147,85148,85150],{},[898,85149,1776],{},[898,85151,2046],{},[902,85153,83556],{"encoding":904},[152,85155,85156,85194,85276],{},[123,85157,85158,85159,85193],{},"Napište ",[883,85160,85162],{"className":85161},[886],[888,85163,85164],{"xmlns":890},[892,85165,85166,85190],{},[895,85167,85168,85170,85176,85178,85180,85182,85184,85186,85188],{},[898,85169,13916],{},[5535,85171,85172,85174],{},[898,85173,1776],{},[898,85175,2046],{},[1750,85177,1766],{},[898,85179,12471],{},[1750,85181,1753],{"stretchy":1752},[898,85183,2046],{},[1750,85185,1763],{"stretchy":1752},[898,85187,1748],{"mathvariant":1747},[898,85189,2046],{},[902,85191,85192],{"encoding":904},"AP_L = Q(L)\u002FL"," a zderivujte.",[123,85195,85196,85197,85229,85230,85233,85234,2313],{},"Položte ",[883,85198,85200],{"className":85199},[886],[888,85201,85202],{"xmlns":890},[892,85203,85204,85226],{},[895,85205,85206,85208,85210,85216,85222,85224],{},[1750,85207,1753],{"stretchy":1752},[898,85209,13916],{},[5535,85211,85212,85214],{},[898,85213,1776],{},[898,85215,2046],{},[1699,85217,85218,85220],{},[1750,85219,1763],{"stretchy":1752},[1750,85221,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,85223,1766],{},[1742,85225,2607],{},[902,85227,85228],{"encoding":904},"(AP_L)' = 0"," a vyřešte. ",[614,85231,85232],{},"Zkratka:"," můžete rovnou řešit ",[883,85235,85237],{"className":85236},[886],[888,85238,85239],{"xmlns":890},[892,85240,85241,85273],{},[895,85242,85243,85245,85251,85253,85255,85257,85259,85261,85267,85269,85271],{},[898,85244,1773],{},[5535,85246,85247,85249],{},[898,85248,1776],{},[898,85250,2046],{},[1750,85252,1753],{"stretchy":1752},[898,85254,2046],{},[1750,85256,1763],{"stretchy":1752},[1750,85258,1766],{},[898,85260,13916],{},[5535,85262,85263,85265],{},[898,85264,1776],{},[898,85266,2046],{},[1750,85268,1753],{"stretchy":1752},[898,85270,2046],{},[1750,85272,1763],{"stretchy":1752},[902,85274,85275],{"encoding":904},"MP_L(L) = AP_L(L)",[123,85277,85278],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[198,85280,74424],{"id":85281},"odvození",[724,85283,85284,85285,85318],{},"Z ",[883,85286,85288],{"className":85287},[886],[888,85289,85290],{"xmlns":890},[892,85291,85292,85316],{},[895,85293,85294,85296,85302,85304,85306,85308,85310,85312,85314],{},[898,85295,13916],{},[5535,85297,85298,85300],{},[898,85299,1776],{},[898,85301,2046],{},[1750,85303,1766],{},[898,85305,12471],{},[1750,85307,1753],{"stretchy":1752},[898,85309,2046],{},[1750,85311,1763],{"stretchy":1752},[898,85313,1748],{"mathvariant":1747},[898,85315,2046],{},[902,85317,85192],{"encoding":904}," a derivace podílu:",[883,85320,85322],{"className":85321},[886],[888,85323,85324],{"xmlns":890,"display":36989},[892,85325,85326,85479],{},[895,85327,85328,85330,85332,85338,85344,85346,85348,85350,85352,85392,85394,85400,85434,85436,85442,85445,85447,85453,85455,85457,85459,85461,85463,85469,85471,85473,85475,85477],{},[1750,85329,1753],{"stretchy":1752},[898,85331,13916],{},[5535,85333,85334,85336],{},[898,85335,1776],{},[898,85337,2046],{},[1699,85339,85340,85342],{},[1750,85341,1763],{"stretchy":1752},[1750,85343,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,85345,1753],{"stretchy":1752},[898,85347,2046],{},[1750,85349,1763],{"stretchy":1752},[1750,85351,1766],{},[3423,85353,85354,85386],{},[895,85355,85356,85362,85364,85366,85368,85370,85372,85374,85376,85378,85380,85382,85384],{},[1699,85357,85358,85360],{},[898,85359,12471],{},[1750,85361,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,85363,1753],{"stretchy":1752},[898,85365,2046],{},[1750,85367,1763],{"stretchy":1752},[1750,85369,8009],{},[898,85371,2046],{},[1750,85373,1758],{},[898,85375,12471],{},[1750,85377,1753],{"stretchy":1752},[898,85379,2046],{},[1750,85381,1763],{"stretchy":1752},[1750,85383,8009],{},[1742,85385,1744],{},[1699,85387,85388,85390],{},[898,85389,2046],{},[1742,85391,1872],{},[1750,85393,1766],{},[3423,85395,85396,85398],{},[1742,85397,1744],{},[898,85399,2046],{},[895,85401,85402,85404,85410,85412,85414,85416,85418,85432],{},[1750,85403,1753],{"fence":1916},[1699,85405,85406,85408],{},[898,85407,12471],{},[1750,85409,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,85411,1753],{"stretchy":1752},[898,85413,2046],{},[1750,85415,1763],{"stretchy":1752},[1750,85417,1758],{},[3423,85419,85420,85430],{},[895,85421,85422,85424,85426,85428],{},[898,85423,12471],{},[1750,85425,1753],{"stretchy":1752},[898,85427,2046],{},[1750,85429,1763],{"stretchy":1752},[898,85431,2046],{},[1750,85433,1763],{"fence":1916},[1750,85435,1766],{},[3423,85437,85438,85440],{},[1742,85439,1744],{},[898,85441,2046],{},[1750,85443,1753],{"fence":1916,"stretchy":1916,"minsize":85444,"maxsize":85444},"1.2em",[898,85446,1773],{},[5535,85448,85449,85451],{},[898,85450,1776],{},[898,85452,2046],{},[1750,85454,1753],{"stretchy":1752},[898,85456,2046],{},[1750,85458,1763],{"stretchy":1752},[1750,85460,1758],{},[898,85462,13916],{},[5535,85464,85465,85467],{},[898,85466,1776],{},[898,85468,2046],{},[1750,85470,1753],{"stretchy":1752},[898,85472,2046],{},[1750,85474,1763],{"stretchy":1752},[1750,85476,1763],{"fence":1916,"stretchy":1916,"minsize":85444,"maxsize":85444},[898,85478,2313],{"mathvariant":1747},[902,85480,85481],{"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).",[724,85483,19299,85484,2433,85506,85589],{},[883,85485,85487],{"className":85486},[886],[888,85488,85489],{"xmlns":890},[892,85490,85491,85503],{},[895,85492,85493,85499,85501],{},[5535,85494,85495,85497],{},[898,85496,2046],{},[1742,85498,2607],{},[1750,85500,2604],{},[1742,85502,2607],{},[902,85504,85505],{"encoding":904},"L_0 > 0",[883,85507,85509],{"className":85508},[886],[888,85510,85511],{"xmlns":890},[892,85512,85513,85586],{},[895,85514,85515,85517,85519,85525,85531,85533,85539,85541,85543,85545,85548,85550,85556,85558,85564,85566,85568,85570,85576,85578,85584],{},[1750,85516,1753],{"stretchy":1752},[898,85518,13916],{},[5535,85520,85521,85523],{},[898,85522,1776],{},[898,85524,2046],{},[1699,85526,85527,85529],{},[1750,85528,1763],{"stretchy":1752},[1750,85530,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,85532,1753],{"stretchy":1752},[5535,85534,85535,85537],{},[898,85536,2046],{},[1742,85538,2607],{},[1750,85540,1763],{"stretchy":1752},[1750,85542,1766],{},[1742,85544,2607],{},[1750,85546,85547],{},"⇔",[898,85549,1773],{},[5535,85551,85552,85554],{},[898,85553,1776],{},[898,85555,2046],{},[1750,85557,1753],{"stretchy":1752},[5535,85559,85560,85562],{},[898,85561,2046],{},[1742,85563,2607],{},[1750,85565,1763],{"stretchy":1752},[1750,85567,1766],{},[898,85569,13916],{},[5535,85571,85572,85574],{},[898,85573,1776],{},[898,85575,2046],{},[1750,85577,1753],{"stretchy":1752},[5535,85579,85580,85582],{},[898,85581,2046],{},[1742,85583,2607],{},[1750,85585,1763],{"stretchy":1752},[902,85587,85588],{"encoding":904},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[198,85591,85593],{"id":85592},"příklad-51","Příklad 5.1",[724,85595,85596,85597,2313],{},"Je dána produkce ",[883,85598,85600],{"className":85599},[886],[888,85601,85602],{"xmlns":890},[892,85603,85604,85628],{},[895,85605,85606,85608,85610,85612,85618,85620,85622],{},[898,85607,12471],{},[1750,85609,1766],{},[1742,85611,3219],{},[1699,85613,85614,85616],{},[898,85615,2046],{},[1742,85617,1872],{},[1750,85619,1758],{},[1742,85621,3929],{},[1699,85623,85624,85626],{},[898,85625,2046],{},[1742,85627,7822],{},[902,85629,85630],{"encoding":904},"Q = 6L^2 - 0{,}2L^3",[724,85632,85633,66445,85636,85686,85687,2313],{},[38,85634,85635],{},"(a)",[883,85637,85639],{"className":85638},[886],[888,85640,85641],{"xmlns":890},[892,85642,85643,85683],{},[895,85644,85645,85647,85649,85651,85653,85655,85657,85659,85661,85663,85665,85667,85669,85671,85673,85675,85677,85679,85681],{},[898,85646,2046],{},[1750,85648,1766],{},[1742,85650,1872],{},[1750,85652,1917],{"separator":1916},[1742,85654,7902],{},[1750,85656,1917],{"separator":1916},[1742,85658,15239],{},[1750,85660,1917],{"separator":1916},[1742,85662,3079],{},[1750,85664,1917],{"separator":1916},[1742,85666,6789],{},[1750,85668,1917],{"separator":1916},[1742,85670,13377],{},[1750,85672,1917],{"separator":1916},[1742,85674,6465],{},[1750,85676,1917],{"separator":1916},[1742,85678,47269],{},[1750,85680,1917],{"separator":1916},[1742,85682,6419],{},[902,85684,85685],{"encoding":904},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[883,85688,85690],{"className":85689},[886],[888,85691,85692],{"xmlns":890},[892,85693,85694,85704],{},[895,85695,85696,85698],{},[898,85697,1773],{},[5535,85699,85700,85702],{},[898,85701,1776],{},[898,85703,2046],{},[902,85705,19678],{"encoding":904},[724,85707,85708,85709,43891],{},"Podle (5.2): ",[883,85710,85712],{"className":85711},[886],[888,85713,85714],{"xmlns":890},[892,85715,85716,85772],{},[895,85717,85718,85720,85726,85728,85734,85736,85738,85740,85742,85744,85746,85748,85750,85756,85758,85760,85762,85764,85766,85768,85770],{},[898,85719,1773],{},[5535,85721,85722,85724],{},[898,85723,1776],{},[898,85725,2046],{},[1750,85727,1766],{},[1699,85729,85730,85732],{},[898,85731,12471],{},[1750,85733,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,85735,1753],{"stretchy":1752},[898,85737,2046],{},[1750,85739,1763],{"stretchy":1752},[1750,85741,1766],{},[1742,85743,4903],{},[898,85745,2046],{},[1750,85747,1758],{},[1742,85749,3123],{},[1699,85751,85752,85754],{},[898,85753,2046],{},[1742,85755,1872],{},[1750,85757,1766],{},[898,85759,2046],{},[1750,85761,1753],{"stretchy":1752},[1742,85763,4903],{},[1750,85765,1758],{},[1742,85767,3123],{},[898,85769,2046],{},[1750,85771,1763],{"stretchy":1752},[902,85773,85774],{"encoding":904},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[16,85776,85777,85814],{},[19,85778,85779],{},[22,85780,85781,85796,85798,85800,85802,85804,85806,85808,85810,85812],{},[25,85782,85783],{},[883,85784,85786],{"className":85785},[886],[888,85787,85788],{"xmlns":890},[892,85789,85790,85794],{},[895,85791,85792],{},[898,85793,2046],{},[902,85795,2046],{"encoding":904},[25,85797,1872],{},[25,85799,7902],{},[25,85801,15239],{},[25,85803,3079],{},[25,85805,6789],{},[25,85807,13377],{},[25,85809,6465],{},[25,85811,47269],{},[25,85813,6419],{},[30,85815,85816],{},[22,85817,85818,85839,85842,85845,85848,85850,85853,85855,85857,85876],{},[35,85819,85820],{},[883,85821,85823],{"className":85822},[886],[888,85824,85825],{"xmlns":890},[892,85826,85827,85837],{},[895,85828,85829,85831],{},[898,85830,1773],{},[5535,85832,85833,85835],{},[898,85834,1776],{},[898,85836,2046],{},[902,85838,19678],{"encoding":904},[35,85840,85841],{},"21,6",[35,85843,85844],{},"45",[35,85846,85847],{},"57,6",[35,85849,12800],{},[35,85851,85852],{},"50,4",[35,85854,85841],{},[35,85856,2607],{},[35,85858,85859],{},[883,85860,85862],{"className":85861},[886],[888,85863,85864],{"xmlns":890},[892,85865,85866,85873],{},[895,85867,85868,85870],{},[1750,85869,1758],{},[1742,85871,85872],{},"12,6",[902,85874,85875],{"encoding":904},"-12{,}6",[35,85877,85878],{},[883,85879,85881],{"className":85880},[886],[888,85882,85883],{"xmlns":890},[892,85884,85885,85891],{},[895,85886,85887,85889],{},[1750,85888,1758],{},[1742,85890,54375],{},[902,85892,85893],{"encoding":904},"-75",[724,85895,85896,85915,85916,85934,85935,85952,85953,85971,85972,85996,85997,86015],{},[883,85897,85899],{"className":85898},[886],[888,85900,85901],{"xmlns":890},[892,85902,85903,85913],{},[895,85904,85905,85907],{},[898,85906,1773],{},[5535,85908,85909,85911],{},[898,85910,1776],{},[898,85912,2046],{},[902,85914,19678],{"encoding":904}," nabývá maxima pro ",[883,85917,85919],{"className":85918},[886],[888,85920,85921],{"xmlns":890},[892,85922,85923,85931],{},[895,85924,85925,85927,85929],{},[898,85926,2046],{},[1750,85928,1766],{},[1742,85930,3079],{},[902,85932,85933],{"encoding":904},"L = 10"," (60 jednotek\u002Fprac.). Od ",[883,85936,85938],{"className":85937},[886],[888,85939,85940],{"xmlns":890},[892,85941,85942,85950],{},[895,85943,85944,85946,85948],{},[898,85945,2046],{},[1750,85947,1766],{},[1742,85949,3079],{},[902,85951,85933],{"encoding":904}," přírůstky klesají, v ",[883,85954,85956],{"className":85955},[886],[888,85957,85958],{"xmlns":890},[892,85959,85960,85968],{},[895,85961,85962,85964,85966],{},[898,85963,2046],{},[1750,85965,1766],{},[1742,85967,6465],{},[902,85969,85970],{"encoding":904},"L = 20"," produkce přestává růst (maximum ",[883,85973,85975],{"className":85974},[886],[888,85976,85977],{"xmlns":890},[892,85978,85979,85993],{},[895,85980,85981,85983,85985,85987,85989,85991],{},[898,85982,12471],{},[1750,85984,1753],{"stretchy":1752},[1742,85986,6465],{},[1750,85988,1763],{"stretchy":1752},[1750,85990,1766],{},[1742,85992,7703],{},[902,85994,85995],{"encoding":904},"Q(20) = 800","), od ",[883,85998,86000],{"className":85999},[886],[888,86001,86002],{"xmlns":890},[892,86003,86004,86012],{},[895,86005,86006,86008,86010],{},[898,86007,2046],{},[1750,86009,2604],{},[1742,86011,6465],{},[902,86013,86014],{"encoding":904},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[724,86017,86018],{},[614,86019,86020,86021,86061,86062,2984,86080,2313],{},"Obrázek 5.1 — graf produkce ",[883,86022,86024],{"className":86023},[886],[888,86025,86026],{"xmlns":890},[892,86027,86028,86058],{},[895,86029,86030,86032,86034,86036,86038,86040,86042,86048,86050,86052],{},[898,86031,12471],{},[1750,86033,1753],{"stretchy":1752},[898,86035,2046],{},[1750,86037,1763],{"stretchy":1752},[1750,86039,1766],{},[1742,86041,3219],{},[1699,86043,86044,86046],{},[898,86045,2046],{},[1742,86047,1872],{},[1750,86049,1758],{},[1742,86051,3929],{},[1699,86053,86054,86056],{},[898,86055,2046],{},[1742,86057,7822],{},[902,86059,86060],{"encoding":904},"Q(L) = 6L^2 - 0{,}2L^3"," s maximem ",[883,86063,86065],{"className":86064},[886],[888,86066,86067],{"xmlns":890},[892,86068,86069,86077],{},[895,86070,86071,86073,86075],{},[898,86072,12471],{},[1750,86074,1766],{},[1742,86076,7703],{},[902,86078,86079],{"encoding":904},"Q = 800",[883,86081,86083],{"className":86082},[886],[888,86084,86085],{"xmlns":890},[892,86086,86087,86095],{},[895,86088,86089,86091,86093],{},[898,86090,2046],{},[1750,86092,1766],{},[1742,86094,6465],{},[902,86096,85970],{"encoding":904},[724,86098,86099,86102],{},[38,86100,86101],{},"(b)"," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[724,86104,86105,86106,1343,86124,2366],{},"Podle (5.3) s ",[883,86107,86109],{"className":86108},[886],[888,86110,86111],{"xmlns":890},[892,86112,86113,86121],{},[895,86114,86115,86117,86119],{},[898,86116,2046],{},[1750,86118,1766],{},[1742,86120,3219],{},[902,86122,86123],{"encoding":904},"L = 6",[883,86125,86127],{"className":86126},[886],[888,86128,86129],{"xmlns":890},[892,86130,86131,86141],{},[895,86132,86133,86135,86137,86139],{},[898,86134,3429],{},[898,86136,2046],{},[1750,86138,1766],{},[1742,86140,7822],{},[902,86142,86143],{"encoding":904},"dL = 3",[883,86145,86147],{"className":86146},[886],[888,86148,86149],{"xmlns":890,"display":36989},[892,86150,86151,86214],{},[895,86152,86153,86155,86157,86159,86161,86167,86169,86171,86173,86175,86177,86179,86181,86183,86185,86187,86189,86191,86193,86195,86197,86199,86201,86203,86205,86207,86209,86211],{},[898,86154,3429],{},[898,86156,12471],{},[1750,86158,1766],{},[898,86160,1773],{},[5535,86162,86163,86165],{},[898,86164,1776],{},[898,86166,2046],{},[1750,86168,1753],{"stretchy":1752},[1742,86170,3219],{},[1750,86172,1763],{"stretchy":1752},[1750,86174,8009],{},[1742,86176,7822],{},[1750,86178,1766],{},[1750,86180,1753],{"stretchy":1752},[1742,86182,4903],{},[1750,86184,8009],{},[1742,86186,3219],{},[1750,86188,1758],{},[1742,86190,3123],{},[1750,86192,8009],{},[1742,86194,15219],{},[1750,86196,1763],{"stretchy":1752},[1750,86198,8009],{},[1742,86200,7822],{},[1750,86202,1766],{},[1742,86204,85852],{},[1750,86206,8009],{},[1742,86208,7822],{},[1750,86210,1766],{},[1742,86212,86213],{},"151,2.",[902,86215,86216],{"encoding":904},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[724,86218,86219,86220,66675,86245,86259,86260,2313],{},"Produkce vzroste z ",[883,86221,86223],{"className":86222},[886],[888,86224,86225],{"xmlns":890},[892,86226,86227,86242],{},[895,86228,86229,86231,86233,86235,86237,86239],{},[898,86230,12471],{},[1750,86232,1753],{"stretchy":1752},[1742,86234,3219],{},[1750,86236,1763],{"stretchy":1752},[1750,86238,1766],{},[1742,86240,86241],{},"172,8",[902,86243,86244],{"encoding":904},"Q(6) = 172{,}8",[883,86246,86248],{"className":86247},[886],[888,86249,86250],{"xmlns":890},[892,86251,86252,86257],{},[895,86253,86254],{},[1742,86255,86256],{},"324",[902,86258,86256],{"encoding":904},". Skutečná hodnota: ",[883,86261,86263],{"className":86262},[886],[888,86264,86265],{"xmlns":890},[892,86266,86267,86307],{},[895,86268,86269,86271,86273,86275,86277,86279,86281,86283,86285,86287,86289,86291,86293,86295,86298,86300,86302,86304],{},[898,86270,2666],{"mathvariant":1747},[898,86272,12471],{},[1750,86274,1766],{},[898,86276,12471],{},[1750,86278,1753],{"stretchy":1752},[1742,86280,13663],{},[1750,86282,1763],{"stretchy":1752},[1750,86284,1758],{},[898,86286,12471],{},[1750,86288,1753],{"stretchy":1752},[1742,86290,3219],{},[1750,86292,1763],{"stretchy":1752},[1750,86294,1766],{},[1742,86296,86297],{},"340,2",[1750,86299,1758],{},[1742,86301,86241],{},[1750,86303,1766],{},[1742,86305,86306],{},"167,4",[902,86308,86309],{"encoding":904},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[198,86311,86313],{"id":86312},"příklad-52","Příklad 5.2",[724,86315,86316,86317,2313],{},"Ověříme princip (5.5) pro ",[883,86318,86320],{"className":86319},[886],[888,86321,86322],{"xmlns":890},[892,86323,86324,86348],{},[895,86325,86326,86328,86330,86332,86338,86340,86342],{},[898,86327,12471],{},[1750,86329,1766],{},[1742,86331,3219],{},[1699,86333,86334,86336],{},[898,86335,2046],{},[1742,86337,1872],{},[1750,86339,1758],{},[1742,86341,3929],{},[1699,86343,86344,86346],{},[898,86345,2046],{},[1742,86347,7822],{},[902,86349,85630],{"encoding":904},[883,86351,86353],{"className":86352},[886],[888,86354,86355],{"xmlns":890,"display":36989},[892,86356,86357,86435],{},[895,86358,86359,86361,86367,86369,86375,86377,86379,86381,86383,86385,86391,86393,86395,86397,86405,86407,86409,86411,86413,86415,86417,86419,86421,86423,86425,86431,86433],{},[898,86360,13916],{},[5535,86362,86363,86365],{},[898,86364,1776],{},[898,86366,2046],{},[1750,86368,1766],{},[3423,86370,86371,86373],{},[898,86372,12471],{},[898,86374,2046],{},[1750,86376,1766],{},[1742,86378,3219],{},[898,86380,2046],{},[1750,86382,1758],{},[1742,86384,3929],{},[1699,86386,86387,86389],{},[898,86388,2046],{},[1742,86390,1872],{},[1750,86392,1917],{"separator":1916},[2125,86394],{"width":24875},[898,86396,13916],{},[5950,86398,86399,86401,86403],{},[898,86400,1776],{},[898,86402,2046],{},[1750,86404,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,86406,1766],{},[1742,86408,3219],{},[1750,86410,1758],{},[1742,86412,3072],{},[898,86414,2046],{},[1750,86416,1766],{},[1742,86418,2607],{},[1969,86420,6766],{},[1750,86422,13651],{},[1969,86424,6766],{},[5535,86426,86427,86429],{},[898,86428,2046],{},[1742,86430,2607],{},[1750,86432,1766],{},[1742,86434,77206],{},[902,86436,86437],{"encoding":904},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[724,86439,86440,86476,86477,86495,86496,2313],{},[883,86441,86443],{"className":86442},[886],[888,86444,86445],{"xmlns":890},[892,86446,86447,86473],{},[895,86448,86449,86451,86463,86465,86467,86469,86471],{},[898,86450,13916],{},[5950,86452,86453,86455,86457],{},[898,86454,1776],{},[898,86456,2046],{},[895,86458,86459,86461],{},[1750,86460,3815],{"mathvariant":1747},[1750,86462,3815],{"mathvariant":1747},[1750,86464,1766],{},[1750,86466,1758],{},[1742,86468,3072],{},[1750,86470,2624],{},[1742,86472,2607],{},[902,86474,86475],{"encoding":904},"AP_L'' = -0{,}4 \u003C 0",", takže v ",[883,86478,86480],{"className":86479},[886],[888,86481,86482],{"xmlns":890},[892,86483,86484,86492],{},[895,86485,86486,86488,86490],{},[898,86487,2046],{},[1750,86489,1766],{},[1742,86491,45167],{},[902,86493,86494],{"encoding":904},"L = 15"," je maximum, ",[883,86497,86499],{"className":86498},[886],[888,86500,86501],{"xmlns":890},[892,86502,86503,86549],{},[895,86504,86505,86507,86513,86515,86517,86519,86521,86523,86525,86527,86529,86531,86533,86536,86538,86541,86543,86545,86547],{},[898,86506,13916],{},[5535,86508,86509,86511],{},[898,86510,1776],{},[898,86512,2046],{},[1750,86514,1753],{"stretchy":1752},[1742,86516,45167],{},[1750,86518,1763],{"stretchy":1752},[1750,86520,1766],{},[1742,86522,3219],{},[1750,86524,8009],{},[1742,86526,45167],{},[1750,86528,1758],{},[1742,86530,3929],{},[1750,86532,8009],{},[1742,86534,86535],{},"225",[1750,86537,1766],{},[1742,86539,86540],{},"90",[1750,86542,1758],{},[1742,86544,85844],{},[1750,86546,1766],{},[1742,86548,85844],{},[902,86550,86551],{"encoding":904},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[724,86553,86554,50803,86610,86656],{},[883,86555,86557],{"className":86556},[886],[888,86558,86559],{"xmlns":890},[892,86560,86561,86607],{},[895,86562,86563,86565,86571,86573,86575,86577,86579,86581,86583,86585,86587,86589,86591,86593,86595,86598,86600,86603,86605],{},[898,86564,1773],{},[5535,86566,86567,86569],{},[898,86568,1776],{},[898,86570,2046],{},[1750,86572,1753],{"stretchy":1752},[1742,86574,45167],{},[1750,86576,1763],{"stretchy":1752},[1750,86578,1766],{},[1742,86580,4903],{},[1750,86582,8009],{},[1742,86584,45167],{},[1750,86586,1758],{},[1742,86588,3123],{},[1750,86590,8009],{},[1742,86592,86535],{},[1750,86594,1766],{},[1742,86596,86597],{},"180",[1750,86599,1758],{},[1742,86601,86602],{},"135",[1750,86604,1766],{},[1742,86606,85844],{},[902,86608,86609],{"encoding":904},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[883,86611,86613],{"className":86612},[886],[888,86614,86615],{"xmlns":890},[892,86616,86617,86653],{},[895,86618,86619,86621,86627,86629,86631,86633,86635,86637,86643,86645,86647,86649,86651],{},[898,86620,1773],{},[5535,86622,86623,86625],{},[898,86624,1776],{},[898,86626,2046],{},[1750,86628,1753],{"stretchy":1752},[1742,86630,45167],{},[1750,86632,1763],{"stretchy":1752},[1750,86634,1766],{},[898,86636,13916],{},[5535,86638,86639,86641],{},[898,86640,1776],{},[898,86642,2046],{},[1750,86644,1753],{"stretchy":1752},[1742,86646,45167],{},[1750,86648,1763],{"stretchy":1752},[1750,86650,1766],{},[1742,86652,85844],{},[902,86654,86655],{"encoding":904},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[724,86658,86659,86662,86663,27149,86692,2313],{},[38,86660,86661],{},"Zkratka bez hledání extrému:"," stačí řešit ",[883,86664,86666],{"className":86665},[886],[888,86667,86668],{"xmlns":890},[892,86669,86670,86690],{},[895,86671,86672,86674,86680,86682,86684],{},[898,86673,1773],{},[5535,86675,86676,86678],{},[898,86677,1776],{},[898,86679,2046],{},[1750,86681,1766],{},[898,86683,13916],{},[5535,86685,86686,86688],{},[898,86687,1776],{},[898,86689,2046],{},[902,86691,83586],{"encoding":904},[883,86693,86695],{"className":86694},[886],[888,86696,86697],{"xmlns":890},[892,86698,86699,86739],{},[895,86700,86701,86703,86705,86707,86709,86715,86717,86719,86721,86723,86725,86731,86733,86735,86737],{},[1742,86702,4903],{},[898,86704,2046],{},[1750,86706,1758],{},[1742,86708,3123],{},[1699,86710,86711,86713],{},[898,86712,2046],{},[1742,86714,1872],{},[1750,86716,1766],{},[1742,86718,3219],{},[898,86720,2046],{},[1750,86722,1758],{},[1742,86724,3929],{},[1699,86726,86727,86729],{},[898,86728,2046],{},[1742,86730,1872],{},[1750,86732,13651],{},[898,86734,2046],{},[1750,86736,1766],{},[1742,86738,45167],{},[902,86740,86741],{"encoding":904},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[724,86743,86744],{},[614,86745,86746,86747,86766,86767,4419,86785,86804,86805,86823,86824,86841,86842,86861,86862,86881],{},"Obrázek 5.3 — křivky ",[883,86748,86750],{"className":86749},[886],[888,86751,86752],{"xmlns":890},[892,86753,86754,86764],{},[895,86755,86756,86758],{},[898,86757,1773],{},[5535,86759,86760,86762],{},[898,86761,1776],{},[898,86763,2046],{},[902,86765,19678],{"encoding":904}," (max 60 při ",[883,86768,86770],{"className":86769},[886],[888,86771,86772],{"xmlns":890},[892,86773,86774,86782],{},[895,86775,86776,86778,86780],{},[898,86777,2046],{},[1750,86779,1766],{},[1742,86781,3079],{},[902,86783,86784],{"encoding":904},"L=10",[883,86786,86788],{"className":86787},[886],[888,86789,86790],{"xmlns":890},[892,86791,86792,86802],{},[895,86793,86794,86796],{},[898,86795,13916],{},[5535,86797,86798,86800],{},[898,86799,1776],{},[898,86801,2046],{},[902,86803,83556],{"encoding":904}," (max 45 při ",[883,86806,86808],{"className":86807},[886],[888,86809,86810],{"xmlns":890},[892,86811,86812,86820],{},[895,86813,86814,86816,86818],{},[898,86815,2046],{},[1750,86817,1766],{},[1742,86819,45167],{},[902,86821,86822],{"encoding":904},"L=15","), průsečík v ",[883,86825,86827],{"className":86826},[886],[888,86828,86829],{"xmlns":890},[892,86830,86831,86839],{},[895,86832,86833,86835,86837],{},[898,86834,2046],{},[1750,86836,1766],{},[1742,86838,45167],{},[902,86840,86494],{"encoding":904},". Nalevo od 15 leží ",[883,86843,86845],{"className":86844},[886],[888,86846,86847],{"xmlns":890},[892,86848,86849,86859],{},[895,86850,86851,86853],{},[898,86852,1773],{},[5535,86854,86855,86857],{},[898,86856,1776],{},[898,86858,2046],{},[902,86860,19678],{"encoding":904}," nad ",[883,86863,86865],{"className":86864},[886],[888,86866,86867],{"xmlns":890},[892,86868,86869,86879],{},[895,86870,86871,86873],{},[898,86872,13916],{},[5535,86874,86875,86877],{},[898,86876,1776],{},[898,86878,2046],{},[902,86880,83556],{"encoding":904},", napravo pod ní.",[115,86883,86885],{"id":86884},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[724,86887,86888,86889,4321,86902,1647,86905,15838,86918,1647,86921,2366],{},"V dvoufaktorovém modelu závisí produkce ",[883,86890,86892],{"className":86891},[886],[888,86893,86894],{"xmlns":890},[892,86895,86896,86900],{},[895,86897,86898],{},[898,86899,12471],{},[902,86901,12471],{"encoding":904},[38,86903,86904],{},"práci",[883,86906,86908],{"className":86907},[886],[888,86909,86910],{"xmlns":890},[892,86911,86912,86916],{},[895,86913,86914],{},[898,86915,2046],{},[902,86917,2046],{"encoding":904},[38,86919,86920],{},"kapitálu",[883,86922,86924],{"className":86923},[886],[888,86925,86926],{"xmlns":890},[892,86927,86928,86932],{},[895,86929,86930],{},[898,86931,19435],{},[902,86933,19435],{"encoding":904},[883,86935,86937],{"className":86936},[886],[888,86938,86939],{"xmlns":890,"display":36989},[892,86940,86941,86976],{},[4577,86942,86943],{"width":36994},[4582,86944,86945,86947,86969,86971],{},[4585,86946],{"width":36999},[4585,86948,86949],{},[895,86950,86951,86953,86955,86957,86959,86961,86963,86965,86967],{},[898,86952,12471],{},[1750,86954,1766],{},[898,86956,12471],{},[1750,86958,1753],{"stretchy":1752},[898,86960,2046],{},[1750,86962,1917],{"separator":1916},[898,86964,19435],{},[1750,86966,1763],{"stretchy":1752},[898,86968,2313],{"mathvariant":1747},[4585,86970],{"width":36999},[4585,86972,86973],{},[1969,86974,86975],{},"(5.6)",[902,86977,86978],{"encoding":904},"Q = Q(L, K). \\tag{5.6}",[724,86980,86981,86982,86984],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[38,86983,83923],{}," (v širším smyslu oproti jednofaktorovému modelu).",[115,86986,86988],{"id":86987},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[724,86990,86991],{},"Široce používané produkční funkce mají tvar",[883,86993,86995],{"className":86994},[886],[888,86996,86997],{"xmlns":890,"display":36989},[892,86998,86999,87040],{},[4577,87000,87001],{"width":36994},[4582,87002,87003,87005,87033,87035],{},[4585,87004],{"width":36999},[4585,87006,87007],{},[895,87008,87009,87011,87013,87015,87017,87023,87025,87031],{},[898,87010,12471],{},[1750,87012,1766],{},[898,87014,13916],{},[1969,87016,2658],{},[1699,87018,87019,87021],{},[898,87020,2046],{},[898,87022,207],{},[1969,87024,2658],{},[1699,87026,87027,87029],{},[898,87028,19435],{},[898,87030,2573],{},[1750,87032,1917],{"separator":1916},[4585,87034],{"width":36999},[4585,87036,87037],{},[1969,87038,87039],{},"(5.7)",[902,87041,87042],{"encoding":904},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[724,87044,2590,87045,87067,87068,87070,87071,2313],{},[883,87046,87048],{"className":87047},[886],[888,87049,87050],{"xmlns":890},[892,87051,87052,87064],{},[895,87053,87054,87056,87058,87060,87062],{},[898,87055,13916],{},[1750,87057,1917],{"separator":1916},[898,87059,207],{},[1750,87061,1917],{"separator":1916},[898,87063,2573],{},[902,87065,87066],{"encoding":904},"A, a, b"," jsou kladné konstanty. Nazývají se ",[38,87069,83622],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[883,87072,87074],{"className":87073},[886],[888,87075,87076],{"xmlns":890},[892,87077,87078,87090],{},[895,87079,87080,87082,87084,87086,87088],{},[898,87081,207],{},[1750,87083,1917],{"separator":1916},[898,87085,2573],{},[1750,87087,2624],{},[1742,87089,1744],{},[902,87091,87092],{"encoding":904},"a, b \u003C 1",[724,87094,87095],{},[4434,87096],{"alt":87097,"className":87098,"src":87099},"imek-vynosy-z-rozsahu-3typy",[210,4438],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[724,87101,87102,87103,87106,87107,4321,87120,87136,87137,4321,87150,2366],{},"Reflektují ekonomickou zákonitost, že ",[38,87104,87105],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[883,87108,87110],{"className":87109},[886],[888,87111,87112],{"xmlns":890},[892,87113,87114,87118],{},[895,87115,87116],{},[898,87117,2046],{},[902,87119,2046],{"encoding":904},[883,87121,87123],{"className":87122},[886],[888,87124,87125],{"xmlns":890},[892,87126,87127,87133],{},[895,87128,87129,87131],{},[898,87130,1920],{},[898,87132,2046],{},[902,87134,87135],{"encoding":904},"rL"," a kapitál z ",[883,87138,87140],{"className":87139},[886],[888,87141,87142],{"xmlns":890},[892,87143,87144,87148],{},[895,87145,87146],{},[898,87147,19435],{},[902,87149,19435],{"encoding":904},[883,87151,87153],{"className":87152},[886],[888,87154,87155],{"xmlns":890},[892,87156,87157,87163],{},[895,87158,87159,87161],{},[898,87160,1920],{},[898,87162,19435],{},[902,87164,87165],{"encoding":904},"rK",[883,87167,87169],{"className":87168},[886],[888,87170,87171],{"xmlns":890,"display":36989},[892,87172,87173,87296],{},[4577,87174,87175],{"width":36994},[4582,87176,87177,87179,87289,87291],{},[4585,87178],{"width":36999},[4585,87180,87181],{},[895,87182,87183,87185,87187,87189,87191,87193,87195,87197,87199,87201,87203,87205,87207,87209,87215,87217,87219,87221,87227,87229,87231,87233,87245,87247,87253,87259,87261,87273,87275,87277,87279,87281,87283,87285,87287],{},[898,87184,12471],{},[1750,87186,1753],{"stretchy":1752},[898,87188,1920],{},[898,87190,2046],{},[1750,87192,1917],{"separator":1916},[898,87194,1920],{},[898,87196,19435],{},[1750,87198,1763],{"stretchy":1752},[1750,87200,1766],{},[898,87202,13916],{},[1750,87204,1753],{"stretchy":1752},[898,87206,1920],{},[898,87208,2046],{},[1699,87210,87211,87213],{},[1750,87212,1763],{"stretchy":1752},[898,87214,207],{},[1750,87216,1753],{"stretchy":1752},[898,87218,1920],{},[898,87220,19435],{},[1699,87222,87223,87225],{},[1750,87224,1763],{"stretchy":1752},[898,87226,2573],{},[1750,87228,1766],{},[898,87230,13916],{},[1969,87232,2658],{},[1699,87234,87235,87237],{},[898,87236,1920],{},[895,87238,87239,87241,87243],{},[898,87240,207],{},[1750,87242,1861],{},[898,87244,2573],{},[1969,87246,2658],{},[1699,87248,87249,87251],{},[898,87250,2046],{},[898,87252,207],{},[1699,87254,87255,87257],{},[898,87256,19435],{},[898,87258,2573],{},[1750,87260,1766],{},[1699,87262,87263,87265],{},[898,87264,1920],{},[895,87266,87267,87269,87271],{},[898,87268,207],{},[1750,87270,1861],{},[898,87272,2573],{},[1969,87274,2658],{},[898,87276,12471],{},[1750,87278,1753],{"stretchy":1752},[898,87280,2046],{},[1750,87282,1917],{"separator":1916},[898,87284,19435],{},[1750,87286,1763],{"stretchy":1752},[898,87288,2313],{"mathvariant":1747},[4585,87290],{"width":36999},[4585,87292,87293],{},[1969,87294,87295],{},"(5.8)",[902,87297,87298],{"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}",[724,87300,87301,87302],{},"Volně: ",[38,87303,87304,87305,87318,87319,87343],{},"změní-li se vstupy ",[883,87306,87308],{"className":87307},[886],[888,87309,87310],{"xmlns":890},[892,87311,87312,87316],{},[895,87313,87314],{},[898,87315,1920],{},[902,87317,1920],{"encoding":904},"-krát, změní se výstup ",[883,87320,87322],{"className":87321},[886],[888,87323,87324],{"xmlns":890},[892,87325,87326,87340],{},[895,87327,87328],{},[1699,87329,87330,87332],{},[898,87331,1920],{},[895,87333,87334,87336,87338],{},[898,87335,207],{},[1750,87337,1861],{},[898,87339,2573],{},[902,87341,87342],{"encoding":904},"r^{a+b}","-krát.",[198,87345,87347],{"id":87346},"výnosy-z-rozsahu","Výnosy z rozsahu",[724,87349,87350,87351,87368],{},"Součet exponentů ",[883,87352,87354],{"className":87353},[886],[888,87355,87356],{"xmlns":890},[892,87357,87358,87366],{},[895,87359,87360,87362,87364],{},[898,87361,207],{},[1750,87363,1861],{},[898,87365,2573],{},[902,87367,83747],{"encoding":904}," určuje typ výnosů z rozsahu:",[16,87370,87371,87400],{},[19,87372,87373],{},[22,87374,87375,87378,87381,87398],{},[25,87376,87377],{},"Typ",[25,87379,87380],{},"Podmínka",[25,87382,87383,87384,87397],{},"Chování produkce při ",[883,87385,87387],{"className":87386},[886],[888,87388,87389],{"xmlns":890},[892,87390,87391,87395],{},[895,87392,87393],{},[898,87394,1920],{},[902,87396,1920],{"encoding":904},"-násobném zvýšení vstupů",[25,87399,12746],{},[30,87401,87402,87513,87628],{},[22,87403,87404,87412,87436,87469],{},[35,87405,84460,87406,2084,87409,1763],{},[38,87407,87408],{},"Konstantní",[614,87410,87411],{},"constant returns",[35,87413,87414],{},[883,87415,87417],{"className":87416},[886],[888,87418,87419],{"xmlns":890},[892,87420,87421,87433],{},[895,87422,87423,87425,87427,87429,87431],{},[898,87424,207],{},[1750,87426,1861],{},[898,87428,2573],{},[1750,87430,1766],{},[1742,87432,1744],{},[902,87434,87435],{"encoding":904},"a+b = 1",[35,87437,87438,87451,87452,1647,87455,87468],{},[883,87439,87441],{"className":87440},[886],[888,87442,87443],{"xmlns":890},[892,87444,87445,87449],{},[895,87446,87447],{},[898,87448,12471],{},[902,87450,12471],{"encoding":904}," vzroste ",[38,87453,87454],{},"přesně",[883,87456,87458],{"className":87457},[886],[888,87459,87460],{"xmlns":890},[892,87461,87462,87466],{},[895,87463,87464],{},[898,87465,1920],{},[902,87467,1920],{"encoding":904},"-krát",[35,87470,87471],{},[883,87472,87474],{"className":87473},[886],[888,87475,87476],{"xmlns":890},[892,87477,87478,87510],{},[895,87479,87480,87482,87484,87486,87498],{},[898,87481,12471],{},[1750,87483,1766],{},[1742,87485,1872],{},[1699,87487,87488,87490],{},[898,87489,2046],{},[895,87491,87492,87494,87496],{},[1742,87493,1744],{},[898,87495,1748],{"mathvariant":1747},[1742,87497,7859],{},[1699,87499,87500,87502],{},[898,87501,19435],{},[895,87503,87504,87506,87508],{},[1742,87505,7822],{},[898,87507,1748],{"mathvariant":1747},[1742,87509,7859],{},[902,87511,87512],{"encoding":904},"Q = 2L^{1\u002F4}K^{3\u002F4}",[22,87514,87515,87524,87548,87578],{},[35,87516,87517,87518,2084,87521,1763],{},"2° ",[38,87519,87520],{},"Rostoucí",[614,87522,87523],{},"increasing returns",[35,87525,87526],{},[883,87527,87529],{"className":87528},[886],[888,87530,87531],{"xmlns":890},[892,87532,87533,87545],{},[895,87534,87535,87537,87539,87541,87543],{},[898,87536,207],{},[1750,87538,1861],{},[898,87540,2573],{},[1750,87542,2604],{},[1742,87544,1744],{},[902,87546,87547],{"encoding":904},"a+b > 1",[35,87549,87550,87451,87563,60154,87565,87468],{},[883,87551,87553],{"className":87552},[886],[888,87554,87555],{"xmlns":890},[892,87556,87557,87561],{},[895,87558,87559],{},[898,87560,12471],{},[902,87562,12471],{"encoding":904},[38,87564,9124],{},[883,87566,87568],{"className":87567},[886],[888,87569,87570],{"xmlns":890},[892,87571,87572,87576],{},[895,87573,87574],{},[898,87575,1920],{},[902,87577,1920],{"encoding":904},[35,87579,87580,2084,87606,1763],{},[883,87581,87583],{"className":87582},[886],[888,87584,87585],{"xmlns":890},[892,87586,87587,87603],{},[895,87588,87589,87591,87593,87595,87597],{},[898,87590,12471],{},[1750,87592,1766],{},[1742,87594,8051],{},[898,87596,2046],{},[1699,87598,87599,87601],{},[898,87600,19435],{},[1742,87602,1872],{},[902,87604,87605],{"encoding":904},"Q = 7LK^2",[883,87607,87609],{"className":87608},[886],[888,87610,87611],{"xmlns":890},[892,87612,87613,87625],{},[895,87614,87615,87617,87619,87621,87623],{},[898,87616,207],{},[1750,87618,1861],{},[898,87620,2573],{},[1750,87622,1766],{},[1742,87624,7822],{},[902,87626,87627],{"encoding":904},"a+b = 3",[22,87629,87630,87639,87663,87694],{},[35,87631,87632,87633,2084,87636,1763],{},"3° ",[38,87634,87635],{},"Klesající",[614,87637,87638],{},"decreasing returns",[35,87640,87641],{},[883,87642,87644],{"className":87643},[886],[888,87645,87646],{"xmlns":890},[892,87647,87648,87660],{},[895,87649,87650,87652,87654,87656,87658],{},[898,87651,207],{},[1750,87653,1861],{},[898,87655,2573],{},[1750,87657,2624],{},[1742,87659,1744],{},[902,87661,87662],{"encoding":904},"a+b \u003C 1",[35,87664,87665,87451,87678,60154,87681,87468],{},[883,87666,87668],{"className":87667},[886],[888,87669,87670],{"xmlns":890},[892,87671,87672,87676],{},[895,87673,87674],{},[898,87675,12471],{},[902,87677,12471],{"encoding":904},[38,87679,87680],{},"méně",[883,87682,87684],{"className":87683},[886],[888,87685,87686],{"xmlns":890},[892,87687,87688,87692],{},[895,87689,87690],{},[898,87691,1920],{},[902,87693,1920],{"encoding":904},[35,87695,87696,2084,87726,1763],{},[883,87697,87699],{"className":87698},[886],[888,87700,87701],{"xmlns":890},[892,87702,87703,87723],{},[895,87704,87705,87707,87709,87711,87717],{},[898,87706,12471],{},[1750,87708,1766],{},[1742,87710,3079],{},[1699,87712,87713,87715],{},[898,87714,2046],{},[1742,87716,77134],{},[1699,87718,87719,87721],{},[898,87720,19435],{},[1742,87722,4268],{},[902,87724,87725],{"encoding":904},"Q = 10L^{0{,}3}K^{0{,}5}",[883,87727,87729],{"className":87728},[886],[888,87730,87731],{"xmlns":890},[892,87732,87733,87745],{},[895,87734,87735,87737,87739,87741,87743],{},[898,87736,207],{},[1750,87738,1861],{},[898,87740,2573],{},[1750,87742,1766],{},[1742,87744,6657],{},[902,87746,87747],{"encoding":904},"a+b = 0{,}8",[1785,87749,87750],{},[724,87751,87752,87754,87755,87772,87773,87776,87777,1647,87780,87816,87817,87839,87840,2313],{},[883,87753,5454],{}," Pozor\nSoučet ",[883,87756,87758],{"className":87757},[886],[888,87759,87760],{"xmlns":890},[892,87761,87762,87770],{},[895,87763,87764,87766,87768],{},[898,87765,207],{},[1750,87767,1861],{},[898,87769,2573],{},[902,87771,83747],{"encoding":904}," neudává velikost produkce, ale ",[38,87774,87775],{},"elasticitu vůči škálování vstupů",". Speciálně ",[38,87778,87779],{},"ryzí Cobb-Douglas",[883,87781,87783],{"className":87782},[886],[888,87784,87785],{"xmlns":890},[892,87786,87787,87813],{},[895,87788,87789,87791,87793,87795,87801],{},[898,87790,12471],{},[1750,87792,1766],{},[898,87794,13916],{},[1699,87796,87797,87799],{},[898,87798,2046],{},[898,87800,207],{},[1699,87802,87803,87805],{},[898,87804,19435],{},[895,87806,87807,87809,87811],{},[1742,87808,1744],{},[1750,87810,1758],{},[898,87812,207],{},[902,87814,87815],{"encoding":904},"Q = AL^a K^{1-a}"," má ",[883,87818,87820],{"className":87819},[886],[888,87821,87822],{"xmlns":890},[892,87823,87824,87836],{},[895,87825,87826,87828,87830,87832,87834],{},[898,87827,2573],{},[1750,87829,1766],{},[1742,87831,1744],{},[1750,87833,1758],{},[898,87835,207],{},[902,87837,87838],{"encoding":904},"b = 1-a",", tedy vždy ",[38,87841,87842],{},"konstantní výnosy z rozsahu",[198,87844,87846,87847],{"id":87845},"parametr-efektivity-aa","Parametr efektivity ",[883,87848,87850],{"className":87849},[886],[888,87851,87852],{"xmlns":890},[892,87853,87854,87858],{},[895,87855,87856],{},[898,87857,13916],{},[902,87859,13916],{"encoding":904},[724,87861,87862,87863,87876,87877,87890,87891,87909,87910,87913],{},"Konstanta ",[883,87864,87866],{"className":87865},[886],[888,87867,87868],{"xmlns":890},[892,87869,87870,87874],{},[895,87871,87872],{},[898,87873,13916],{},[902,87875,13916],{"encoding":904}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[883,87878,87880],{"className":87879},[886],[888,87881,87882],{"xmlns":890},[892,87883,87884,87888],{},[895,87885,87886],{},[898,87887,12471],{},[902,87889,12471],{"encoding":904}," při pevně zadaných ",[883,87892,87894],{"className":87893},[886],[888,87895,87896],{"xmlns":890},[892,87897,87898,87906],{},[895,87899,87900,87902,87904],{},[898,87901,2046],{},[1750,87903,1917],{"separator":1916},[898,87905,19435],{},[902,87907,87908],{"encoding":904},"L, K",", a lze ji proto chápat jako ",[38,87911,87912],{},"parametr efektivity"," — indikátor stavu technologie.",[198,87915,87917],{"id":87916},"příklad-53","Příklad 5.3",[724,87919,87920,87921,87816,87963,87965,87966,2313],{},"Produkční funkce ",[883,87922,87924],{"className":87923},[886],[888,87925,87926],{"xmlns":890},[892,87927,87928,87960],{},[895,87929,87930,87932,87934,87936,87948],{},[898,87931,12471],{},[1750,87933,1766],{},[1742,87935,1872],{},[1699,87937,87938,87940],{},[898,87939,2046],{},[895,87941,87942,87944,87946],{},[1742,87943,1744],{},[898,87945,1748],{"mathvariant":1747},[1742,87947,7859],{},[1699,87949,87950,87952],{},[898,87951,19435],{},[895,87953,87954,87956,87958],{},[1742,87955,7822],{},[898,87957,1748],{"mathvariant":1747},[1742,87959,7859],{},[902,87961,87962],{"encoding":904},"Q = 2L^{1\u002F4} K^{3\u002F4}",[38,87964,8465],{}," výnosy z rozsahu, neboť ",[883,87967,87969],{"className":87968},[886],[888,87970,87971],{"xmlns":890},[892,87972,87973,87997],{},[895,87974,87975,87983,87985,87993,87995],{},[3586,87976,87977],{"scriptlevel":2607,"displaystyle":1752},[3423,87978,87979,87981],{},[1742,87980,1744],{},[1742,87982,7859],{},[1750,87984,1861],{},[3586,87986,87987],{"scriptlevel":2607,"displaystyle":1752},[3423,87988,87989,87991],{},[1742,87990,7822],{},[1742,87992,7859],{},[1750,87994,1766],{},[1742,87996,1744],{},[902,87998,87999],{"encoding":904},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[724,88001,88002,88003,15838,88016,88029,88030,1647,88043,88083],{},"Změní-li se ",[883,88004,88006],{"className":88005},[886],[888,88007,88008],{"xmlns":890},[892,88009,88010,88014],{},[895,88011,88012],{},[898,88013,2046],{},[902,88015,2046],{"encoding":904},[883,88017,88019],{"className":88018},[886],[888,88020,88021],{"xmlns":890},[892,88022,88023,88027],{},[895,88024,88025],{},[898,88026,19435],{},[902,88028,19435],{"encoding":904}," čtyřnásobně, změní se ",[883,88031,88033],{"className":88032},[886],[888,88034,88035],{"xmlns":890},[892,88036,88037,88041],{},[895,88038,88039],{},[898,88040,12471],{},[902,88042,12471],{"encoding":904},[883,88044,88046],{"className":88045},[886],[888,88047,88048],{"xmlns":890},[892,88049,88050,88080],{},[895,88051,88052,88072,88074],{},[1699,88053,88054,88056],{},[1742,88055,7859],{},[895,88057,88058,88060,88062,88064,88066,88068,88070],{},[1742,88059,1744],{},[898,88061,1748],{"mathvariant":1747},[1742,88063,7859],{},[1750,88065,1861],{},[1742,88067,7822],{},[898,88069,1748],{"mathvariant":1747},[1742,88071,7859],{},[1750,88073,1766],{},[1699,88075,88076,88078],{},[1742,88077,7859],{},[1742,88079,1744],{},[902,88081,88082],{"encoding":904},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[883,88085,88087],{"className":88086},[886],[888,88088,88089],{"xmlns":890,"display":36989},[892,88090,88091,88251],{},[895,88092,88093,88095,88097,88099,88101,88103,88105,88107,88109,88111,88113,88115,88117,88119,88131,88133,88135,88137,88149,88151,88153,88155,88175,88187,88199,88201,88203,88205,88207,88219,88231,88233,88235,88237,88239,88241,88243,88245,88247,88249],{},[898,88094,12471],{},[1750,88096,1753],{"stretchy":1752},[1742,88098,7859],{},[898,88100,2046],{},[1750,88102,1917],{"separator":1916},[1742,88104,7859],{},[898,88106,19435],{},[1750,88108,1763],{"stretchy":1752},[1750,88110,1766],{},[1742,88112,1872],{},[1750,88114,1753],{"stretchy":1752},[1742,88116,7859],{},[898,88118,2046],{},[1699,88120,88121,88123],{},[1750,88122,1763],{"stretchy":1752},[895,88124,88125,88127,88129],{},[1742,88126,1744],{},[898,88128,1748],{"mathvariant":1747},[1742,88130,7859],{},[1750,88132,1753],{"stretchy":1752},[1742,88134,7859],{},[898,88136,19435],{},[1699,88138,88139,88141],{},[1750,88140,1763],{"stretchy":1752},[895,88142,88143,88145,88147],{},[1742,88144,7822],{},[898,88146,1748],{"mathvariant":1747},[1742,88148,7859],{},[1750,88150,1766],{},[1742,88152,1872],{},[1750,88154,8009],{},[1699,88156,88157,88159],{},[1742,88158,7859],{},[895,88160,88161,88163,88165,88167,88169,88171,88173],{},[1742,88162,1744],{},[898,88164,1748],{"mathvariant":1747},[1742,88166,7859],{},[1750,88168,1861],{},[1742,88170,7822],{},[898,88172,1748],{"mathvariant":1747},[1742,88174,7859],{},[1699,88176,88177,88179],{},[898,88178,2046],{},[895,88180,88181,88183,88185],{},[1742,88182,1744],{},[898,88184,1748],{"mathvariant":1747},[1742,88186,7859],{},[1699,88188,88189,88191],{},[898,88190,19435],{},[895,88192,88193,88195,88197],{},[1742,88194,7822],{},[898,88196,1748],{"mathvariant":1747},[1742,88198,7859],{},[1750,88200,1766],{},[1742,88202,7859],{},[1750,88204,8009],{},[1742,88206,1872],{},[1699,88208,88209,88211],{},[898,88210,2046],{},[895,88212,88213,88215,88217],{},[1742,88214,1744],{},[898,88216,1748],{"mathvariant":1747},[1742,88218,7859],{},[1699,88220,88221,88223],{},[898,88222,19435],{},[895,88224,88225,88227,88229],{},[1742,88226,7822],{},[898,88228,1748],{"mathvariant":1747},[1742,88230,7859],{},[1750,88232,1766],{},[1742,88234,7859],{},[1969,88236,2658],{},[898,88238,12471],{},[1750,88240,1753],{"stretchy":1752},[898,88242,2046],{},[1750,88244,1917],{"separator":1916},[898,88246,19435],{},[1750,88248,1763],{"stretchy":1752},[898,88250,2313],{"mathvariant":1747},[902,88252,88253],{"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).",[198,88255,88256],{"id":46102},"Homogenita",[724,88258,88259,88260,2433,88283,88299],{},"Funkce ",[883,88261,88263],{"className":88262},[886],[888,88264,88265],{"xmlns":890},[892,88266,88267,88281],{},[895,88268,88269,88271,88273,88275,88277,88279],{},[898,88270,12471],{},[1750,88272,1753],{"stretchy":1752},[898,88274,2046],{},[1750,88276,1917],{"separator":1916},[898,88278,19435],{},[1750,88280,1763],{"stretchy":1752},[902,88282,19631],{"encoding":904},[38,88284,88285,88286],{},"homogenní stupně ",[883,88287,88289],{"className":88288},[886],[888,88290,88291],{"xmlns":890},[892,88292,88293,88297],{},[895,88294,88295],{},[898,88296,45783],{},[902,88298,45783],{"encoding":904},", jestliže",[883,88301,88303],{"className":88302},[886],[888,88304,88305],{"xmlns":890,"display":36989},[892,88306,88307,88364],{},[4577,88308,88309],{"width":36994},[4582,88310,88311,88313,88357,88359],{},[4585,88312],{"width":36999},[4585,88314,88315],{},[895,88316,88317,88319,88321,88323,88325,88327,88329,88331,88333,88335,88341,88343,88345,88347,88349,88351,88353,88355],{},[898,88318,12471],{},[1750,88320,1753],{"stretchy":1752},[898,88322,1920],{},[898,88324,2046],{},[1750,88326,1917],{"separator":1916},[898,88328,1920],{},[898,88330,19435],{},[1750,88332,1763],{"stretchy":1752},[1750,88334,1766],{},[1699,88336,88337,88339],{},[898,88338,1920],{},[898,88340,45783],{},[1969,88342,2658],{},[898,88344,12471],{},[1750,88346,1753],{"stretchy":1752},[898,88348,2046],{},[1750,88350,1917],{"separator":1916},[898,88352,19435],{},[1750,88354,1763],{"stretchy":1752},[1750,88356,1917],{"separator":1916},[4585,88358],{"width":36999},[4585,88360,88361],{},[1969,88362,88363],{},"(5.10)",[902,88365,88366],{"encoding":904},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[724,88368,2590,88369,88387,88388,88406,88407,52559,88420,88423,88424,2313],{},[883,88370,88372],{"className":88371},[886],[888,88373,88374],{"xmlns":890},[892,88375,88376,88384],{},[895,88377,88378,88380,88382],{},[898,88379,45783],{},[1750,88381,14143],{},[1742,88383,2607],{},[902,88385,88386],{"encoding":904},"n \\geq 0"," je celé číslo a ",[883,88389,88391],{"className":88390},[886],[888,88392,88393],{"xmlns":890},[892,88394,88395,88403],{},[895,88396,88397,88399,88401],{},[898,88398,1920],{},[1750,88400,2604],{},[1742,88402,2607],{},[902,88404,88405],{"encoding":904},"r > 0",". Homogenní funkce stupně ",[883,88408,88410],{"className":88409},[886],[888,88411,88412],{"xmlns":890},[892,88413,88414,88418],{},[895,88415,88416],{},[1742,88417,1744],{},[902,88419,1744],{"encoding":904},[38,88421,88422],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[883,88425,88427],{"className":88426},[886],[888,88428,88429],{"xmlns":890},[892,88430,88431,88439],{},[895,88432,88433,88435,88437],{},[898,88434,207],{},[1750,88436,1861],{},[898,88438,2573],{},[902,88440,83747],{"encoding":904},[115,88442,88444],{"id":88443},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[724,88446,88447],{},[38,88448,88449],{},"Ryzí Cobb-Douglasovy funkce:",[883,88451,88453],{"className":88452},[886],[888,88454,88455],{"xmlns":890,"display":36989},[892,88456,88457,88516],{},[4577,88458,88459],{"width":36994},[4582,88460,88461,88463,88509,88511],{},[4585,88462],{"width":36999},[4585,88464,88465],{},[895,88466,88467,88469,88471,88473,88475,88481,88483,88495,88497,88499,88501,88503,88505,88507],{},[898,88468,12471],{},[1750,88470,1766],{},[898,88472,13916],{},[1969,88474,2658],{},[1699,88476,88477,88479],{},[898,88478,2046],{},[898,88480,207],{},[1969,88482,2658],{},[1699,88484,88485,88487],{},[898,88486,19435],{},[895,88488,88489,88491,88493],{},[1742,88490,1744],{},[1750,88492,1758],{},[898,88494,207],{},[1750,88496,1917],{"separator":1916},[2125,88498],{"width":24875},[1742,88500,2607],{},[1750,88502,2624],{},[898,88504,207],{},[1750,88506,2624],{},[1742,88508,22865],{},[4585,88510],{"width":36999},[4585,88512,88513],{},[1969,88514,88515],{},"(5.9)",[902,88517,88518],{"encoding":904},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[724,88520,88521,88522,88524,88525,2313],{},"Mají vždy ",[38,88523,87842],{}," a jsou ",[38,88526,88422],{},[724,88528,88529,2084,88532,88535],{},[38,88530,88531],{},"CES produkční funkce",[614,88533,88534],{},"Constant Elasticity of Substitution",", 1961):",[883,88537,88539],{"className":88538},[886],[888,88540,88541],{"xmlns":890,"display":36989},[892,88542,88543,88611],{},[895,88544,88545,88547,88549,88551,88609],{},[898,88546,12471],{},[1750,88548,1766],{},[898,88550,13916],{},[1699,88552,88553,88597],{},[895,88554,88555,88557,88559,88561,88563,88565,88567,88569,88579,88581,88583,88585,88595],{},[1750,88556,5141],{"fence":1916},[1750,88558,1753],{"stretchy":1752},[1742,88560,1744],{},[1750,88562,1758],{},[898,88564,207],{},[1750,88566,1763],{"stretchy":1752},[1969,88568,2658],{},[1699,88570,88571,88573],{},[898,88572,2046],{},[895,88574,88575,88577],{},[1750,88576,1758],{},[898,88578,2573],{},[1750,88580,1861],{},[898,88582,207],{},[1969,88584,2658],{},[1699,88586,88587,88589],{},[898,88588,19435],{},[895,88590,88591,88593],{},[1750,88592,1758],{},[898,88594,2573],{},[1750,88596,5158],{"fence":1916},[895,88598,88599,88601],{},[1750,88600,1758],{},[3586,88602,88603],{"scriptlevel":2607,"displaystyle":1752},[3423,88604,88605,88607],{},[1742,88606,1744],{},[898,88608,2573],{},[1750,88610,1917],{"separator":1916},[902,88612,88613],{"encoding":904},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[724,88615,2590,88616,1343,88634,1343,88655,88679],{},[883,88617,88619],{"className":88618},[886],[888,88620,88621],{"xmlns":890},[892,88622,88623,88631],{},[895,88624,88625,88627,88629],{},[898,88626,13916],{},[1750,88628,2604],{},[1742,88630,2607],{},[902,88632,88633],{"encoding":904},"A > 0",[883,88635,88637],{"className":88636},[886],[888,88638,88639],{"xmlns":890},[892,88640,88641,88653],{},[895,88642,88643,88645,88647,88649,88651],{},[1742,88644,2607],{},[1750,88646,2624],{},[898,88648,207],{},[1750,88650,2624],{},[1742,88652,1744],{},[902,88654,2633],{"encoding":904},[883,88656,88658],{"className":88657},[886],[888,88659,88660],{"xmlns":890},[892,88661,88662,88676],{},[895,88663,88664,88666,88668,88670,88672,88674],{},[1750,88665,1758],{},[1742,88667,1744],{},[1750,88669,2624],{},[898,88671,2573],{},[1750,88673,13044],{"mathvariant":1747},[1742,88675,2607],{},[902,88677,88678],{"encoding":904},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[724,88681,88682],{},[38,88683,88684],{},"Další typy:",[120,88686,88687,88729],{},[123,88688,88689,1647,88692,88728],{},[38,88690,88691],{},"Lineární:",[883,88693,88695],{"className":88694},[886],[888,88696,88697],{"xmlns":890},[892,88698,88699,88725],{},[895,88700,88701,88703,88705,88707,88709,88711,88713,88715,88717,88719,88721,88723],{},[898,88702,12471],{},[1750,88704,1753],{"stretchy":1752},[898,88706,2046],{},[1750,88708,1917],{"separator":1916},[898,88710,19435],{},[1750,88712,1763],{"stretchy":1752},[1750,88714,1766],{},[898,88716,207],{},[898,88718,2046],{},[1750,88720,1861],{},[898,88722,2573],{},[898,88724,19435],{},[902,88726,88727],{"encoding":904},"Q(L, K) = aL + bK"," — dokonalé substituty.",[123,88730,88731,1647,88734,88779],{},[38,88732,88733],{},"Leontiefova:",[883,88735,88737],{"className":88736},[886],[888,88738,88739],{"xmlns":890},[892,88740,88741,88776],{},[895,88742,88743,88745,88747,88749,88751,88753,88755,88757,88760,88762,88764,88766,88768,88770,88772,88774],{},[898,88744,12471],{},[1750,88746,1753],{"stretchy":1752},[898,88748,2046],{},[1750,88750,1917],{"separator":1916},[898,88752,19435],{},[1750,88754,1763],{"stretchy":1752},[1750,88756,1766],{},[898,88758,88759],{},"min",[1750,88761,65123],{},[1750,88763,1753],{"stretchy":1752},[898,88765,207],{},[898,88767,2046],{},[1750,88769,1917],{"separator":1916},[898,88771,2573],{},[898,88773,19435],{},[1750,88775,1763],{"stretchy":1752},[902,88777,88778],{"encoding":904},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[115,88781,88783,88784,1343,88803,88822],{"id":88782},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[883,88785,88787],{"className":88786},[886],[888,88788,88789],{"xmlns":890},[892,88790,88791,88801],{},[895,88792,88793,88795],{},[898,88794,1773],{},[5535,88796,88797,88799],{},[898,88798,1776],{},[898,88800,2046],{},[902,88802,19678],{"encoding":904},[883,88804,88806],{"className":88805},[886],[888,88807,88808],{"xmlns":890},[892,88809,88810,88820],{},[895,88811,88812,88814],{},[898,88813,1773],{},[5535,88815,88816,88818],{},[898,88817,1776],{},[898,88819,19435],{},[902,88821,19723],{"encoding":904}," a totální diferenciál",[724,88824,88825],{},[38,88826,88827],{},"Mezní produkt práce:",[883,88829,88831],{"className":88830},[886],[888,88832,88833],{"xmlns":890,"display":36989},[892,88834,88835,88873],{},[895,88836,88837,88839,88845,88847,88855,88857,88871],{},[898,88838,1773],{},[5535,88840,88841,88843],{},[898,88842,1776],{},[898,88844,2046],{},[1750,88846,1766],{},[5950,88848,88849,88851,88853],{},[898,88850,12471],{},[898,88852,2046],{},[1750,88854,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,88856,1766],{},[3423,88858,88859,88865],{},[895,88860,88861,88863],{},[898,88862,8773],{"mathvariant":1747},[898,88864,12471],{},[895,88866,88867,88869],{},[898,88868,8773],{"mathvariant":1747},[898,88870,2046],{},[898,88872,2313],{"mathvariant":1747},[902,88874,88875],{"encoding":904},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[724,88877,88878],{},[38,88879,88880],{},"Mezní produkt kapitálu:",[883,88882,88884],{"className":88883},[886],[888,88885,88886],{"xmlns":890,"display":36989},[892,88887,88888,88926],{},[895,88889,88890,88892,88898,88900,88908,88910,88924],{},[898,88891,1773],{},[5535,88893,88894,88896],{},[898,88895,1776],{},[898,88897,19435],{},[1750,88899,1766],{},[5950,88901,88902,88904,88906],{},[898,88903,12471],{},[898,88905,19435],{},[1750,88907,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,88909,1766],{},[3423,88911,88912,88918],{},[895,88913,88914,88916],{},[898,88915,8773],{"mathvariant":1747},[898,88917,12471],{},[895,88919,88920,88922],{},[898,88921,8773],{"mathvariant":1747},[898,88923,19435],{},[898,88925,2313],{"mathvariant":1747},[902,88927,88928],{"encoding":904},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[724,88930,88931,88961,88962,88983,88984,89002,89003,89016,89017,2313],{},[883,88932,88934],{"className":88933},[886],[888,88935,88936],{"xmlns":890},[892,88937,88938,88958],{},[895,88939,88940,88942,88948,88950,88952,88954,88956],{},[898,88941,1773],{},[5535,88943,88944,88946],{},[898,88945,1776],{},[898,88947,2046],{},[1750,88949,1753],{"stretchy":1752},[898,88951,207],{},[1750,88953,1917],{"separator":1916},[898,88955,2573],{},[1750,88957,1763],{"stretchy":1752},[902,88959,88960],{"encoding":904},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[883,88963,88965],{"className":88964},[886],[888,88966,88967],{"xmlns":890},[892,88968,88969,88981],{},[895,88970,88971,88973,88975,88977,88979],{},[1750,88972,5141],{"stretchy":1752},[898,88974,207],{},[1750,88976,1917],{"separator":1916},[898,88978,2573],{},[1750,88980,5158],{"stretchy":1752},[902,88982,20457],{"encoding":904}," (na hladině ",[883,88985,88987],{"className":88986},[886],[888,88988,88989],{"xmlns":890},[892,88990,88991,88999],{},[895,88992,88993,88995,88997],{},[898,88994,19435],{},[1750,88996,1766],{},[898,88998,2573],{},[902,89000,89001],{"encoding":904},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[883,89004,89006],{"className":89005},[886],[888,89007,89008],{"xmlns":890},[892,89009,89010,89014],{},[895,89011,89012],{},[898,89013,2046],{},[902,89015,2046],{"encoding":904},". Analogicky ",[883,89018,89020],{"className":89019},[886],[888,89021,89022],{"xmlns":890},[892,89023,89024,89044],{},[895,89025,89026,89028,89034,89036,89038,89040,89042],{},[898,89027,1773],{},[5535,89029,89030,89032],{},[898,89031,1776],{},[898,89033,19435],{},[1750,89035,1753],{"stretchy":1752},[898,89037,207],{},[1750,89039,1917],{"separator":1916},[898,89041,2573],{},[1750,89043,1763],{"stretchy":1752},[902,89045,89046],{"encoding":904},"MP_K(a, b)",[1785,89048,89049,89053],{},[724,89050,89051,60142],{},[883,89052,1791],{},[120,89054,89055,89093],{},[123,89056,89057,10062,89076],{},[883,89058,89060],{"className":89059},[886],[888,89061,89062],{"xmlns":890},[892,89063,89064,89074],{},[895,89065,89066,89068],{},[898,89067,1773],{},[5535,89069,89070,89072],{},[898,89071,1776],{},[898,89073,2046],{},[902,89075,19678],{"encoding":904},[614,89077,89078,89079,89092],{},"„o kolik vzroste ",[883,89080,89082],{"className":89081},[886],[888,89083,89084],{"xmlns":890},[892,89085,89086,89090],{},[895,89087,89088],{},[898,89089,12471],{},[902,89091,12471],{"encoding":904},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[123,89094,89095,10062,89114],{},[883,89096,89098],{"className":89097},[886],[888,89099,89100],{"xmlns":890},[892,89101,89102,89112],{},[895,89103,89104,89106],{},[898,89105,1773],{},[5535,89107,89108,89110],{},[898,89109,1776],{},[898,89111,19435],{},[902,89113,19723],{"encoding":904},[614,89115,89078,89116,89129],{},[883,89117,89119],{"className":89118},[886],[888,89120,89121],{"xmlns":890},[892,89122,89123,89127],{},[895,89124,89125],{},[898,89126,12471],{},[902,89128,12471],{"encoding":904},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[724,89131,89132,89135,89136,89151,89152,2366],{},[38,89133,89134],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[883,89137,89139],{"className":89138},[886],[888,89140,89141],{"xmlns":890},[892,89142,89143,89149],{},[895,89144,89145,89147],{},[898,89146,3429],{},[898,89148,2046],{},[902,89150,84279],{"encoding":904}," a kapitálu o ",[883,89153,89155],{"className":89154},[886],[888,89156,89157],{"xmlns":890},[892,89158,89159,89165],{},[895,89160,89161,89163],{},[898,89162,3429],{},[898,89164,19435],{},[902,89166,89167],{"encoding":904},"dK",[883,89169,89171],{"className":89170},[886],[888,89172,89173],{"xmlns":890,"display":36989},[892,89174,89175,89268],{},[4577,89176,89177],{"width":36994},[4582,89178,89179,89181,89261,89263],{},[4585,89180],{"width":36999},[4585,89182,89183],{},[895,89184,89185,89187,89189,89191,89193,89195,89197,89205,89207,89209,89211,89213,89221,89223,89225,89227,89229,89231,89237,89239,89241,89243,89245,89247,89253,89255,89257,89259],{},[898,89186,2666],{"mathvariant":1747},[898,89188,12471],{},[1750,89190,2274],{},[898,89192,3429],{},[898,89194,12471],{},[1750,89196,1766],{},[5950,89198,89199,89201,89203],{},[898,89200,12471],{},[898,89202,2046],{},[1750,89204,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,89206,2658],{},[898,89208,3429],{},[898,89210,2046],{},[1750,89212,1861],{},[5950,89214,89215,89217,89219],{},[898,89216,12471],{},[898,89218,19435],{},[1750,89220,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1969,89222,2658],{},[898,89224,3429],{},[898,89226,19435],{},[1750,89228,1766],{},[898,89230,1773],{},[5535,89232,89233,89235],{},[898,89234,1776],{},[898,89236,2046],{},[1969,89238,2658],{},[898,89240,3429],{},[898,89242,2046],{},[1750,89244,1861],{},[898,89246,1773],{},[5535,89248,89249,89251],{},[898,89250,1776],{},[898,89252,19435],{},[1969,89254,2658],{},[898,89256,3429],{},[898,89258,19435],{},[898,89260,2313],{"mathvariant":1747},[4585,89262],{"width":36999},[4585,89264,89265],{},[1969,89266,89267],{},"(5.11)",[902,89269,89270],{"encoding":904},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[724,89272,89273,89274,2313],{},"Skutečná změna: ",[883,89275,89277],{"className":89276},[886],[888,89278,89279],{"xmlns":890},[892,89280,89281,89327],{},[895,89282,89283,89285,89287,89289,89291,89293,89295,89297,89299,89301,89303,89305,89307,89309,89311,89313,89315,89317,89319,89321,89323,89325],{},[898,89284,2666],{"mathvariant":1747},[898,89286,12471],{},[1750,89288,1766],{},[898,89290,12471],{},[1750,89292,1753],{"stretchy":1752},[898,89294,2046],{},[1750,89296,1861],{},[898,89298,3429],{},[898,89300,2046],{},[1750,89302,1917],{"separator":1916},[898,89304,19435],{},[1750,89306,1861],{},[898,89308,3429],{},[898,89310,19435],{},[1750,89312,1763],{"stretchy":1752},[1750,89314,1758],{},[898,89316,12471],{},[1750,89318,1753],{"stretchy":1752},[898,89320,2046],{},[1750,89322,1917],{"separator":1916},[898,89324,19435],{},[1750,89326,1763],{"stretchy":1752},[902,89328,89329],{"encoding":904},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[724,89331,89332,89334,89335,89353,89354,89367,89368,89387,89388,89420,89421,89453,89454,2313],{},[38,89333,84443],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[883,89336,89338],{"className":89337},[886],[888,89339,89340],{"xmlns":890},[892,89341,89342,89350],{},[895,89343,89344],{},[5535,89345,89346,89348],{},[898,89347,19435],{},[1742,89349,2607],{},[902,89351,89352],{"encoding":904},"K_0"," se od jistého ",[883,89355,89357],{"className":89356},[886],[888,89358,89359],{"xmlns":890},[892,89360,89361,89365],{},[895,89362,89363],{},[898,89364,2046],{},[902,89366,2046],{"encoding":904}," stane ",[883,89369,89371],{"className":89370},[886],[888,89372,89373],{"xmlns":890},[892,89374,89375,89385],{},[895,89376,89377,89379],{},[898,89378,1773],{},[5535,89380,89381,89383],{},[898,89382,1776],{},[898,89384,2046],{},[902,89386,19678],{"encoding":904}," klesající (",[883,89389,89391],{"className":89390},[886],[888,89392,89393],{"xmlns":890},[892,89394,89395,89417],{},[895,89396,89397,89413,89415],{},[5950,89398,89399,89401,89407],{},[898,89400,12471],{},[895,89402,89403,89405],{},[898,89404,2046],{},[898,89406,2046],{},[895,89408,89409,89411],{},[1750,89410,3815],{"mathvariant":1747},[1750,89412,3815],{"mathvariant":1747},[1750,89414,2624],{},[1742,89416,2607],{},[902,89418,89419],{"encoding":904},"Q''_{LL} \u003C 0","); analogicky ",[883,89422,89424],{"className":89423},[886],[888,89425,89426],{"xmlns":890},[892,89427,89428,89450],{},[895,89429,89430,89446,89448],{},[5950,89431,89432,89434,89440],{},[898,89433,12471],{},[895,89435,89436,89438],{},[898,89437,19435],{},[898,89439,19435],{},[895,89441,89442,89444],{},[1750,89443,3815],{"mathvariant":1747},[1750,89445,3815],{"mathvariant":1747},[1750,89447,2624],{},[1742,89449,2607],{},[902,89451,89452],{"encoding":904},"Q''_{KK} \u003C 0"," pro pevné ",[883,89455,89457],{"className":89456},[886],[888,89458,89459],{"xmlns":890},[892,89460,89461,89469],{},[895,89462,89463],{},[5535,89464,89465,89467],{},[898,89466,2046],{},[1742,89468,2607],{},[902,89470,84481],{"encoding":904},[115,89472,89474],{"id":89473},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[724,89476,89477,89480,89481,89504,89505,38867],{},[38,89478,89479],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[883,89482,89484],{"className":89483},[886],[888,89485,89486],{"xmlns":890},[892,89487,89488,89502],{},[895,89489,89490,89492,89494,89496,89498,89500],{},[898,89491,12471],{},[1750,89493,1753],{"stretchy":1752},[898,89495,2046],{},[1750,89497,1917],{"separator":1916},[898,89499,19435],{},[1750,89501,1763],{"stretchy":1752},[902,89503,19631],{"encoding":904}," stupně ",[883,89506,89508],{"className":89507},[886],[888,89509,89510],{"xmlns":890},[892,89511,89512,89516],{},[895,89513,89514],{},[898,89515,45783],{},[902,89517,45783],{"encoding":904},[883,89519,89521],{"className":89520},[886],[888,89522,89523],{"xmlns":890,"display":36989},[892,89524,89525,89588],{},[4577,89526,89527],{"width":36994},[4582,89528,89529,89531,89581,89583],{},[4585,89530],{"width":36999},[4585,89532,89533],{},[895,89534,89535,89537,89539,89547,89549,89551,89553,89561,89563,89565,89567,89569,89571,89573,89575,89577,89579],{},[898,89536,2046],{},[1969,89538,2658],{},[5950,89540,89541,89543,89545],{},[898,89542,12471],{},[898,89544,2046],{},[1750,89546,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,89548,1861],{},[898,89550,19435],{},[1969,89552,2658],{},[5950,89554,89555,89557,89559],{},[898,89556,12471],{},[898,89558,19435],{},[1750,89560,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,89562,1766],{},[898,89564,45783],{},[1969,89566,2658],{},[898,89568,12471],{},[1750,89570,1753],{"stretchy":1752},[898,89572,2046],{},[1750,89574,1917],{"separator":1916},[898,89576,19435],{},[1750,89578,1763],{"stretchy":1752},[898,89580,2313],{"mathvariant":1747},[4585,89582],{"width":36999},[4585,89584,89585],{},[1969,89586,89587],{},"(5.12)",[902,89589,89590],{"encoding":904},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[724,89592,89593,89614],{},[38,89594,89595,89596],{},"Speciální případ ",[883,89597,89599],{"className":89598},[886],[888,89600,89601],{"xmlns":890},[892,89602,89603,89611],{},[895,89604,89605,89607,89609],{},[898,89606,45783],{},[1750,89608,1766],{},[1742,89610,1744],{},[902,89612,89613],{"encoding":904},"n = 1"," (konstantní výnosy z rozsahu):",[883,89616,89618],{"className":89617},[886],[888,89619,89620],{"xmlns":890,"display":36989},[892,89621,89622,89666],{},[895,89623,89624,89626,89628,89630,89636,89638,89640,89642,89644,89650,89652,89654,89656,89658,89660,89662,89664],{},[898,89625,2046],{},[1750,89627,8009],{},[898,89629,1773],{},[5535,89631,89632,89634],{},[898,89633,1776],{},[898,89635,2046],{},[1750,89637,1861],{},[898,89639,19435],{},[1750,89641,8009],{},[898,89643,1773],{},[5535,89645,89646,89648],{},[898,89647,1776],{},[898,89649,19435],{},[1750,89651,1766],{},[898,89653,12471],{},[1750,89655,1753],{"stretchy":1752},[898,89657,2046],{},[1750,89659,1917],{"separator":1916},[898,89661,19435],{},[1750,89663,1763],{"stretchy":1752},[898,89665,2313],{"mathvariant":1747},[902,89667,89668],{"encoding":904},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[724,89670,89671,89672,89675],{},"Slovně — ",[38,89673,89674],{},"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).",[115,89677,19414],{"id":83817},[724,89679,89680,2084,89682,89685,89686,89708,89709,2366],{},[38,89681,19414],{},[614,89683,89684],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[883,89687,89689],{"className":89688},[886],[888,89690,89691],{"xmlns":890},[892,89692,89693,89705],{},[895,89694,89695,89697,89699,89701,89703],{},[1750,89696,5141],{"stretchy":1752},[898,89698,2046],{},[1750,89700,1917],{"separator":1916},[898,89702,19435],{},[1750,89704,5158],{"stretchy":1752},[902,89706,89707],{"encoding":904},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[883,89710,89712],{"className":89711},[886],[888,89713,89714],{"xmlns":890},[892,89715,89716,89721],{},[895,89717,89718],{},[898,89719,89720],{},"q",[902,89722,89720],{"encoding":904},[883,89724,89726],{"className":89725},[886],[888,89727,89728],{"xmlns":890,"display":36989},[892,89729,89730,89765],{},[4577,89731,89732],{"width":36994},[4582,89733,89734,89736,89758,89760],{},[4585,89735],{"width":36999},[4585,89737,89738],{},[895,89739,89740,89742,89744,89746,89748,89750,89752,89754,89756],{},[898,89741,12471],{},[1750,89743,1753],{"stretchy":1752},[898,89745,2046],{},[1750,89747,1917],{"separator":1916},[898,89749,19435],{},[1750,89751,1763],{"stretchy":1752},[1750,89753,1766],{},[898,89755,89720],{},[898,89757,2313],{"mathvariant":1747},[4585,89759],{"width":36999},[4585,89761,89762],{},[1969,89763,89764],{},"(5.13)",[902,89766,89767],{"encoding":904},"Q(L, K) = q. \\tag{5.13}",[724,89769,89770,89771,89774,89775,1783],{},"Jsou to ",[38,89772,89773],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[207,89776,89778],{"className":89777,"dataFsResolvedFilePath":878,"href":879},[210],"užitečnosti",[724,89780,89781],{},[38,89782,89783],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[120,89785,89786,89791,89796,89801],{},[123,89787,89788,89790],{},[38,89789,22130],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[123,89792,89793,89795],{},[38,89794,46587],{}," (úloha 5.14);",[123,89797,89798,18067],{},[38,89799,89800],{},"neprotínají se",[123,89802,89803,89804,14017,89817,2313],{},"s rostoucím ",[883,89805,89807],{"className":89806},[886],[888,89808,89809],{"xmlns":890},[892,89810,89811,89815],{},[895,89812,89813],{},[898,89814,89720],{},[902,89816,89720],{"encoding":904},[38,89818,89819],{},"vzdalují od počátku",[724,89821,89822],{},[614,89823,89824,89825,89847,89848,2313],{},"Obrázek 5.4 — izokvanty Cobb-Douglasovy funkce v rovině ",[883,89826,89828],{"className":89827},[886],[888,89829,89830],{"xmlns":890},[892,89831,89832,89844],{},[895,89833,89834,89836,89838,89840,89842],{},[1750,89835,1753],{"stretchy":1752},[898,89837,2046],{},[1750,89839,1917],{"separator":1916},[898,89841,19435],{},[1750,89843,1763],{"stretchy":1752},[902,89845,89846],{"encoding":904},"(L, K)",": tři klesající konvexní křivky pro ",[883,89849,89851],{"className":89850},[886],[888,89852,89853],{"xmlns":890},[892,89854,89855,89879],{},[895,89856,89857,89863,89865,89871,89873],{},[5535,89858,89859,89861],{},[898,89860,89720],{},[1742,89862,1744],{},[1750,89864,2624],{},[5535,89866,89867,89869],{},[898,89868,89720],{},[1742,89870,2607],{},[1750,89872,2624],{},[5535,89874,89875,89877],{},[898,89876,89720],{},[1742,89878,1872],{},[902,89880,89881],{"encoding":904},"q_1 \u003C q_0 \u003C q_2",[115,89883,89885,89886,1763],{"id":89884},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[883,89887,89889],{"className":89888},[886],[888,89890,89891],{"xmlns":890},[892,89892,89893,89903],{},[895,89894,89895,89897,89899,89901],{},[898,89896,1773],{},[898,89898,13658],{},[898,89900,5326],{},[898,89902,1779],{},[902,89904,20232],{"encoding":904},[724,89906,89907,2084,89910,89913],{},[38,89908,89909],{},"Mezní míra technické substituce",[614,89911,89912],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[883,89915,89917],{"className":89916},[886],[888,89918,89919],{"xmlns":890,"display":36989},[892,89920,89921,90012],{},[4577,89922,89923],{"width":36994},[4582,89924,89925,89927,90005,90007],{},[4585,89926],{"width":36999},[4585,89928,89929],{},[895,89930,89931,89933,89935,89937,89939,89941,89943,89945,89947,89949,89951,89953,89955,89957,89959,89961,89983,89985,90003],{},[898,89932,1773],{},[898,89934,13658],{},[898,89936,5326],{},[898,89938,1779],{},[1750,89940,1766],{},[898,89942,1773],{},[898,89944,13658],{},[898,89946,5326],{},[898,89948,1779],{},[1750,89950,1753],{"stretchy":1752},[898,89952,2046],{},[1750,89954,1917],{"separator":1916},[898,89956,19435],{},[1750,89958,1763],{"stretchy":1752},[1750,89960,1766],{},[3423,89962,89963,89973],{},[895,89964,89965,89967],{},[898,89966,1773],{},[5535,89968,89969,89971],{},[898,89970,1776],{},[898,89972,2046],{},[895,89974,89975,89977],{},[898,89976,1773],{},[5535,89978,89979,89981],{},[898,89980,1776],{},[898,89982,19435],{},[1750,89984,1766],{},[3423,89986,89987,89995],{},[5950,89988,89989,89991,89993],{},[898,89990,12471],{},[898,89992,2046],{},[1750,89994,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,89996,89997,89999,90001],{},[898,89998,12471],{},[898,90000,19435],{},[1750,90002,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[898,90004,2313],{"mathvariant":1747},[4585,90006],{"width":36999},[4585,90008,90009],{},[1969,90010,90011],{},"(5.14)",[902,90013,90014],{"encoding":904},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[724,90016,90017,1647,90019,90049,90050,90081],{},[38,90018,18853],{},[883,90020,90022],{"className":90021},[886],[888,90023,90024],{"xmlns":890},[892,90025,90026,90046],{},[895,90027,90028,90030,90032,90034,90036,90038,90040,90042,90044],{},[898,90029,1773],{},[898,90031,13658],{},[898,90033,5326],{},[898,90035,1779],{},[1750,90037,1753],{"stretchy":1752},[898,90039,2046],{},[1750,90041,1917],{"separator":1916},[898,90043,19435],{},[1750,90045,1763],{"stretchy":1752},[902,90047,90048],{"encoding":904},"MRTS(L, K)"," udává, ",[38,90051,90052,90053,90066,90067,90080],{},"o kolik se musí přibližně změnit kapitál ",[883,90054,90056],{"className":90055},[886],[888,90057,90058],{"xmlns":890},[892,90059,90060,90064],{},[895,90061,90062],{},[898,90063,19435],{},[902,90065,19435],{"encoding":904},", jestliže se práce ",[883,90068,90070],{"className":90069},[886],[888,90071,90072],{"xmlns":890},[892,90073,90074,90078],{},[895,90075,90076],{},[898,90077,2046],{},[902,90079,2046],{"encoding":904}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1785,90083,90084],{},[724,90085,90086,1792,90088,90107,90108,90145,90146,90149,90150,90154],{},[883,90087,1791],{},[883,90089,90091],{"className":90090},[886],[888,90092,90093],{"xmlns":890},[892,90094,90095,90105],{},[895,90096,90097,90099,90101,90103],{},[898,90098,1773],{},[898,90100,13658],{},[898,90102,5326],{},[898,90104,1779],{},[902,90106,20232],{"encoding":904}," říká: ",[614,90109,90110,90111,90130,90131,90144],{},"„jednu jednotku práce musím nahradit přibližně ",[883,90112,90114],{"className":90113},[886],[888,90115,90116],{"xmlns":890},[892,90117,90118,90128],{},[895,90119,90120,90122,90124,90126],{},[898,90121,1773],{},[898,90123,13658],{},[898,90125,5326],{},[898,90127,1779],{},[902,90129,20232],{"encoding":904}," jednotkami kapitálu, aby produkce ",[883,90132,90134],{"className":90133},[886],[888,90135,90136],{"xmlns":890},[892,90137,90138,90142],{},[895,90139,90140],{},[898,90141,12471],{},[902,90143,12471],{"encoding":904}," zůstala stejná.\""," Je to ",[38,90147,90148],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[207,90151,90153],{"className":90152,"dataFsResolvedFilePath":878,"href":879},[210],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[724,90156,90157],{},[4434,90158],{"alt":90159,"className":90160,"src":90161},"imek-izokvanty-mrts",[210,4438],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[724,90163,90164,90167,90168,2433,90198,90220,90221,12825],{},[38,90165,90166],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[883,90169,90171],{"className":90170},[886],[888,90172,90173],{"xmlns":890},[892,90174,90175,90195],{},[895,90176,90177,90179,90185,90187,90193],{},[1750,90178,5141],{"stretchy":1752},[5535,90180,90181,90183],{},[898,90182,2046],{},[1742,90184,2607],{},[1750,90186,1917],{"separator":1916},[5535,90188,90189,90191],{},[898,90190,19435],{},[1742,90192,2607],{},[1750,90194,5158],{"stretchy":1752},[902,90196,90197],{"encoding":904},"[L_0, K_0]",[883,90199,90201],{"className":90200},[886],[888,90202,90203],{"xmlns":890},[892,90204,90205,90217],{},[895,90206,90207,90209,90211,90213,90215],{},[1750,90208,1758],{},[898,90210,1773],{},[898,90212,13658],{},[898,90214,5326],{},[898,90216,1779],{},[902,90218,90219],{"encoding":904},"-MRTS",". Z derivace implicitní funkce (při ",[883,90222,90224],{"className":90223},[886],[888,90225,90226],{"xmlns":890},[892,90227,90228,90250],{},[895,90229,90230,90232,90234,90236,90238,90240,90242,90244],{},[898,90231,12471],{},[1750,90233,1753],{"stretchy":1752},[898,90235,2046],{},[1750,90237,1917],{"separator":1916},[898,90239,19435],{},[1750,90241,1763],{"stretchy":1752},[1750,90243,1766],{},[5535,90245,90246,90248],{},[898,90247,89720],{},[1742,90249,2607],{},[902,90251,90252],{"encoding":904},"Q(L,K) = q_0",[883,90254,90256],{"className":90255},[886],[888,90257,90258],{"xmlns":890,"display":36989},[892,90259,90260,90312],{},[895,90261,90262,90276,90278,90280,90298,90300,90302,90304,90306,90308,90310],{},[3423,90263,90264,90270],{},[895,90265,90266,90268],{},[898,90267,3429],{},[898,90269,19435],{},[895,90271,90272,90274],{},[898,90273,3429],{},[898,90275,2046],{},[1750,90277,1766],{},[1750,90279,1758],{},[3423,90281,90282,90290],{},[5950,90283,90284,90286,90288],{},[898,90285,12471],{},[898,90287,2046],{},[1750,90289,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,90291,90292,90294,90296],{},[898,90293,12471],{},[898,90295,19435],{},[1750,90297,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,90299,1766],{},[1750,90301,1758],{},[898,90303,1773],{},[898,90305,13658],{},[898,90307,5326],{},[898,90309,1779],{},[898,90311,2313],{"mathvariant":1747},[902,90313,90314],{"encoding":904},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[724,90316,90317,90318,90333,90334,90350],{},"Změní-li se práce o ",[883,90319,90321],{"className":90320},[886],[888,90322,90323],{"xmlns":890},[892,90324,90325,90331],{},[895,90326,90327,90329],{},[898,90328,3429],{},[898,90330,2046],{},[902,90332,84279],{"encoding":904},", lze pro odhad změny kapitálu ",[883,90335,90337],{"className":90336},[886],[888,90338,90339],{"xmlns":890},[892,90340,90341,90347],{},[895,90342,90343,90345],{},[898,90344,2666],{"mathvariant":1747},[898,90346,19435],{},[902,90348,90349],{"encoding":904},"\\Delta K"," k udržení produkce použít diferenciál:",[883,90352,90354],{"className":90353},[886],[888,90355,90356],{"xmlns":890,"display":36989},[892,90357,90358,90405],{},[4577,90359,90360],{"width":36994},[4582,90361,90362,90364,90398,90400],{},[4585,90363],{"width":36999},[4585,90365,90366],{},[895,90367,90368,90370,90372,90374,90376,90378,90380,90382,90384,90386,90388,90390,90392,90394,90396],{},[898,90369,2666],{"mathvariant":1747},[898,90371,19435],{},[1750,90373,2274],{},[898,90375,3429],{},[898,90377,19435],{},[1750,90379,1766],{},[1750,90381,1758],{},[898,90383,1773],{},[898,90385,13658],{},[898,90387,5326],{},[898,90389,1779],{},[1969,90391,2658],{},[898,90393,3429],{},[898,90395,2046],{},[1750,90397,1917],{"separator":1916},[4585,90399],{"width":36999},[4585,90401,90402],{},[1969,90403,90404],{},"(5.15)",[902,90406,90407],{"encoding":904},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[883,90409,90411],{"className":90410},[886],[888,90412,90413],{"xmlns":890,"display":36989},[892,90414,90415,90464],{},[4577,90416,90417],{"width":36994},[4582,90418,90419,90421,90457,90459],{},[4585,90420],{"width":36999},[4585,90422,90423],{},[895,90424,90425,90427,90429,90431,90449,90451,90453,90455],{},[898,90426,3429],{},[898,90428,2046],{},[1750,90430,1766],{},[3423,90432,90433,90439],{},[895,90434,90435,90437],{},[1750,90436,1758],{},[1742,90438,1744],{},[895,90440,90441,90443,90445,90447],{},[898,90442,1773],{},[898,90444,13658],{},[898,90446,5326],{},[898,90448,1779],{},[1969,90450,2658],{},[898,90452,3429],{},[898,90454,19435],{},[898,90456,2313],{"mathvariant":1747},[4585,90458],{"width":36999},[4585,90460,90461],{},[1969,90462,90463],{},"(5.16)",[902,90465,90466],{"encoding":904},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1785,90468,90469,90493],{},[724,90470,90471,90473,90474],{},[883,90472,6004],{}," Postup — jak spočítat ",[883,90475,90477],{"className":90476},[886],[888,90478,90479],{"xmlns":890},[892,90480,90481,90491],{},[895,90482,90483,90485,90487,90489],{},[898,90484,1773],{},[898,90486,13658],{},[898,90488,5326],{},[898,90490,1779],{},[902,90492,20232],{"encoding":904},[152,90494,90495,90536,90579,90611],{},[123,90496,90497,90498,2028,90517,2313],{},"Vypočtěte parciální derivace ",[883,90499,90501],{"className":90500},[886],[888,90502,90503],{"xmlns":890},[892,90504,90505,90515],{},[895,90506,90507],{},[5950,90508,90509,90511,90513],{},[898,90510,12471],{},[898,90512,2046],{},[1750,90514,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,90516,19655],{"encoding":904},[883,90518,90520],{"className":90519},[886],[888,90521,90522],{"xmlns":890},[892,90523,90524,90534],{},[895,90525,90526],{},[5950,90527,90528,90530,90532],{},[898,90529,12471],{},[898,90531,19435],{},[1750,90533,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,90535,19700],{"encoding":904},[123,90537,74764,90538,90578],{},[883,90539,90541],{"className":90540},[886],[888,90542,90543],{"xmlns":890},[892,90544,90545,90575],{},[895,90546,90547,90549,90551,90553,90555,90557,90565,90567],{},[898,90548,1773],{},[898,90550,13658],{},[898,90552,5326],{},[898,90554,1779],{},[1750,90556,1766],{},[5950,90558,90559,90561,90563],{},[898,90560,12471],{},[898,90562,2046],{},[1750,90564,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[898,90566,1748],{"mathvariant":1747},[5950,90568,90569,90571,90573],{},[898,90570,12471],{},[898,90572,19435],{},[1750,90574,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,90576,90577],{"encoding":904},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[123,90580,90581,90582,2313],{},"Případně dosaďte konkrétní ",[883,90583,90585],{"className":90584},[886],[888,90586,90587],{"xmlns":890},[892,90588,90589,90609],{},[895,90590,90591,90593,90599,90601,90607],{},[1750,90592,5141],{"stretchy":1752},[5535,90594,90595,90597],{},[898,90596,2046],{},[1742,90598,2607],{},[1750,90600,1917],{"separator":1916},[5535,90602,90603,90605],{},[898,90604,19435],{},[1742,90606,2607],{},[1750,90608,5158],{"stretchy":1752},[902,90610,90197],{"encoding":904},[123,90612,90613,90614,90648,90649,90651],{},"Pro odhad substituce použijte ",[883,90615,90617],{"className":90616},[886],[888,90618,90619],{"xmlns":890},[892,90620,90621,90645],{},[895,90622,90623,90625,90627,90629,90631,90633,90635,90637,90639,90641,90643],{},[898,90624,2666],{"mathvariant":1747},[898,90626,19435],{},[1750,90628,2274],{},[1750,90630,1758],{},[898,90632,1773],{},[898,90634,13658],{},[898,90636,5326],{},[898,90638,1779],{},[1750,90640,8009],{},[898,90642,2666],{"mathvariant":1747},[898,90644,2046],{},[902,90646,90647],{"encoding":904},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[38,90650,61529],{}," — substituce, ne doplnění).",[724,90653,90654],{},[614,90655,90656,90657,90689,90690,2984,90703,10951,90732,90747],{},"Obrázek 5.7 — izokvanta ",[883,90658,90660],{"className":90659},[886],[888,90661,90662],{"xmlns":890},[892,90663,90664,90686],{},[895,90665,90666,90672,90674,90676,90678,90680,90682,90684],{},[5535,90667,90668,90670],{},[898,90669,89720],{},[1742,90671,2607],{},[1750,90673,1766],{},[898,90675,12471],{},[1750,90677,1753],{"stretchy":1752},[898,90679,2046],{},[1750,90681,1917],{"separator":1916},[898,90683,19435],{},[1750,90685,1763],{"stretchy":1752},[902,90687,90688],{"encoding":904},"q_0 = Q(L,K)"," s tečnou ",[883,90691,90693],{"className":90692},[886],[888,90694,90695],{"xmlns":890},[892,90696,90697,90701],{},[895,90698,90699],{},[898,90700,2652],{},[902,90702,2652],{"encoding":904},[883,90704,90706],{"className":90705},[886],[888,90707,90708],{"xmlns":890},[892,90709,90710,90730],{},[895,90711,90712,90714,90720,90722,90728],{},[1750,90713,5141],{"stretchy":1752},[5535,90715,90716,90718],{},[898,90717,2046],{},[1742,90719,2607],{},[1750,90721,1917],{"separator":1916},[5535,90723,90724,90726],{},[898,90725,19435],{},[1742,90727,2607],{},[1750,90729,5158],{"stretchy":1752},[902,90731,90197],{"encoding":904},[883,90733,90735],{"className":90734},[886],[888,90736,90737],{"xmlns":890},[892,90738,90739,90745],{},[895,90740,90741,90743],{},[898,90742,2666],{"mathvariant":1747},[898,90744,19435],{},[902,90746,90349],{"encoding":904}," odhadnut diferenciálem (záporně vzatý sklon tečny).",[115,90749,90751],{"id":90750},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[198,90753,90755],{"id":90754},"příklad-54","Příklad 5.4",[724,90757,85596,90758,1343,90800,1343,90817,2313],{},[883,90759,90761],{"className":90760},[886],[888,90762,90763],{"xmlns":890},[892,90764,90765,90797],{},[895,90766,90767,90769,90771,90773,90785],{},[898,90768,12471],{},[1750,90770,1766],{},[1742,90772,45167],{},[1699,90774,90775,90777],{},[898,90776,2046],{},[895,90778,90779,90781,90783],{},[1742,90780,1744],{},[898,90782,1748],{"mathvariant":1747},[1742,90784,1872],{},[1699,90786,90787,90789],{},[898,90788,19435],{},[895,90790,90791,90793,90795],{},[1742,90792,1744],{},[898,90794,1748],{"mathvariant":1747},[1742,90796,7822],{},[902,90798,90799],{"encoding":904},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[883,90801,90803],{"className":90802},[886],[888,90804,90805],{"xmlns":890},[892,90806,90807,90815],{},[895,90808,90809,90811,90813],{},[898,90810,2046],{},[1750,90812,1766],{},[1742,90814,6465],{},[902,90816,85970],{"encoding":904},[883,90818,90820],{"className":90819},[886],[888,90821,90822],{"xmlns":890},[892,90823,90824,90832],{},[895,90825,90826,90828,90830],{},[898,90827,19435],{},[1750,90829,1766],{},[1742,90831,4078],{},[902,90833,90834],{"encoding":904},"K = 100",[724,90836,90837],{},[38,90838,90839],{},"(a) Rychlost změny produkce vzhledem k práci.",[883,90841,90843],{"className":90842},[886],[888,90844,90845],{"xmlns":890,"display":36989},[892,90846,90847,90961],{},[895,90848,90849,90851,90857,90859,90867,90869,90877,90891,90903,90905,90907,90909,90915,90917,90919,90921,90923,90925,90927,90935,90937,90947,90949,90956,90958],{},[898,90850,1773],{},[5535,90852,90853,90855],{},[898,90854,1776],{},[898,90856,2046],{},[1750,90858,1766],{},[5950,90860,90861,90863,90865],{},[898,90862,12471],{},[898,90864,2046],{},[1750,90866,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,90868,1766],{},[3586,90870,90871],{"scriptlevel":2607,"displaystyle":1752},[3423,90872,90873,90875],{},[1742,90874,45167],{},[1742,90876,1872],{},[1699,90878,90879,90881],{},[898,90880,2046],{},[895,90882,90883,90885,90887,90889],{},[1750,90884,1758],{},[1742,90886,1744],{},[898,90888,1748],{"mathvariant":1747},[1742,90890,1872],{},[1699,90892,90893,90895],{},[898,90894,19435],{},[895,90896,90897,90899,90901],{},[1742,90898,1744],{},[898,90900,1748],{"mathvariant":1747},[1742,90902,7822],{},[1750,90904,1917],{"separator":1916},[2125,90906],{"width":24875},[898,90908,1773],{},[5535,90910,90911,90913],{},[898,90912,1776],{},[898,90914,2046],{},[1750,90916,1753],{"stretchy":1752},[1742,90918,6465],{},[1750,90920,1917],{"separator":1916},[1742,90922,4078],{},[1750,90924,1763],{"stretchy":1752},[1750,90926,1766],{},[3586,90928,90929],{"scriptlevel":2607,"displaystyle":1752},[3423,90930,90931,90933],{},[1742,90932,45167],{},[1742,90934,1872],{},[1750,90936,8009],{},[3586,90938,90939],{"scriptlevel":2607,"displaystyle":1752},[3423,90940,90941,90943],{},[1742,90942,1744],{},[17761,90944,90945],{},[1742,90946,6465],{},[1750,90948,8009],{},[90950,90951,90952,90954],"mroot",{},[1742,90953,4078],{},[1742,90955,7822],{},[1750,90957,2274],{},[1742,90959,90960],{},"7,153.",[902,90962,90963],{"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.",[724,90965,90966,90967,53083,90989,19866,91006,91027,91028,91049],{},"Přibližná změna při ",[883,90968,90970],{"className":90969},[886],[888,90971,90972],{"xmlns":890},[892,90973,90974,90986],{},[895,90975,90976,90978,90980,90982,90984],{},[898,90977,2046],{},[1750,90979,2366],{},[1742,90981,6465],{},[1750,90983,12797],{},[1742,90985,47269],{},[902,90987,90988],{"encoding":904},"L: 20 \\to 21",[883,90990,90992],{"className":90991},[886],[888,90993,90994],{"xmlns":890},[892,90995,90996,91004],{},[895,90997,90998,91000,91002],{},[898,90999,19435],{},[1750,91001,1766],{},[1742,91003,4078],{},[902,91005,90834],{"encoding":904},[883,91007,91009],{"className":91008},[886],[888,91010,91011],{"xmlns":890},[892,91012,91013,91024],{},[895,91014,91015,91017,91019,91021],{},[898,91016,2666],{"mathvariant":1747},[898,91018,12471],{},[1750,91020,2274],{},[1742,91022,91023],{},"7,153",[902,91025,91026],{"encoding":904},"\\Delta Q \\approx 7{,}153",". Skutečně ",[883,91029,91031],{"className":91030},[886],[888,91032,91033],{"xmlns":890},[892,91034,91035,91046],{},[895,91036,91037,91039,91041,91043],{},[898,91038,2666],{"mathvariant":1747},[898,91040,12471],{},[1750,91042,2274],{},[1742,91044,91045],{},"26,888",[902,91047,91048],{"encoding":904},"\\Delta Q \\approx 26{,}888"," (dle knihy; zaokrouhlení v konkrétním výpočtu).",[724,91051,91052,91055],{},[38,91053,91054],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[883,91057,91059],{"className":91058},[886],[888,91060,91061],{"xmlns":890,"display":36989},[892,91062,91063,91163],{},[895,91064,91065,91067,91073,91075,91083,91085,91087,91099,91113,91115,91117,91119,91125,91127,91129,91131,91133,91135,91137,91139,91143,91145,91158,91160],{},[898,91066,1773],{},[5535,91068,91069,91071],{},[898,91070,1776],{},[898,91072,19435],{},[1750,91074,1766],{},[5950,91076,91077,91079,91081],{},[898,91078,12471],{},[898,91080,19435],{},[1750,91082,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,91084,1766],{},[1742,91086,7902],{},[1699,91088,91089,91091],{},[898,91090,2046],{},[895,91092,91093,91095,91097],{},[1742,91094,1744],{},[898,91096,1748],{"mathvariant":1747},[1742,91098,1872],{},[1699,91100,91101,91103],{},[898,91102,19435],{},[895,91104,91105,91107,91109,91111],{},[1750,91106,1758],{},[1742,91108,1872],{},[898,91110,1748],{"mathvariant":1747},[1742,91112,7822],{},[1750,91114,1917],{"separator":1916},[2125,91116],{"width":24875},[898,91118,1773],{},[5535,91120,91121,91123],{},[898,91122,1776],{},[898,91124,19435],{},[1750,91126,1753],{"stretchy":1752},[1742,91128,6465],{},[1750,91130,1917],{"separator":1916},[1742,91132,4078],{},[1750,91134,1763],{"stretchy":1752},[1750,91136,1766],{},[1742,91138,7902],{},[17761,91140,91141],{},[1742,91142,6465],{},[1750,91144,8009],{},[3586,91146,91147],{"scriptlevel":2607,"displaystyle":1752},[3423,91148,91149,91151],{},[1742,91150,1744],{},[90950,91152,91153,91156],{},[1742,91154,91155],{},"10000",[1742,91157,7822],{},[1750,91159,2274],{},[1742,91161,91162],{},"4,525.",[902,91164,91165],{"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.",[724,91167,91168,91169,4321,91186,1783],{},"Produkce poklesne přibližně o 4,525 (z ",[883,91170,91172],{"className":91171},[886],[888,91173,91174],{"xmlns":890},[892,91175,91176,91183],{},[895,91177,91178,91180],{},[1750,91179,2274],{},[1742,91181,91182],{},"905,126",[902,91184,91185],{"encoding":904},"\\approx 905{,}126",[883,91187,91189],{"className":91188},[886],[888,91190,91191],{"xmlns":890},[892,91192,91193,91200],{},[895,91194,91195,91197],{},[1750,91196,2274],{},[1742,91198,91199],{},"900,601",[902,91201,91202],{"encoding":904},"\\approx 900{,}601",[724,91204,91205,12804,91252,1343,91274,1783],{},[38,91206,91207,91208,2028,91230],{},"(c) Změna ",[883,91209,91211],{"className":91210},[886],[888,91212,91213],{"xmlns":890},[892,91214,91215,91227],{},[895,91216,91217,91219,91221,91223,91225],{},[898,91218,2046],{},[1750,91220,2366],{},[1742,91222,6465],{},[1750,91224,12797],{},[1742,91226,45167],{},[902,91228,91229],{"encoding":904},"L: 20 \\to 15",[883,91231,91233],{"className":91232},[886],[888,91234,91235],{"xmlns":890},[892,91236,91237,91249],{},[895,91238,91239,91241,91243,91245,91247],{},[898,91240,19435],{},[1750,91242,2366],{},[1742,91244,4078],{},[1750,91246,12797],{},[1742,91248,4236],{},[902,91250,91251],{"encoding":904},"K: 100 \\to 150",[883,91253,91255],{"className":91254},[886],[888,91256,91257],{"xmlns":890},[892,91258,91259,91271],{},[895,91260,91261,91263,91265,91267,91269],{},[898,91262,3429],{},[898,91264,2046],{},[1750,91266,1766],{},[1750,91268,1758],{},[1742,91270,7902],{},[902,91272,91273],{"encoding":904},"dL = -5",[883,91275,91277],{"className":91276},[886],[888,91278,91279],{"xmlns":890},[892,91280,91281,91291],{},[895,91282,91283,91285,91287,91289],{},[898,91284,3429],{},[898,91286,19435],{},[1750,91288,1766],{},[1742,91290,3936],{},[902,91292,91293],{"encoding":904},"dK = 50",[883,91295,91297],{"className":91296},[886],[888,91298,91299],{"xmlns":890,"display":36989},[892,91300,91301,91389],{},[895,91302,91303,91305,91307,91309,91311,91317,91319,91321,91323,91325,91327,91329,91331,91333,91335,91337,91339,91341,91347,91349,91351,91353,91355,91357,91359,91361,91363,91365,91367,91369,91371,91373,91375,91377,91380,91382,91384,91386],{},[898,91304,3429],{},[898,91306,12471],{},[1750,91308,1766],{},[898,91310,1773],{},[5535,91312,91313,91315],{},[898,91314,1776],{},[898,91316,2046],{},[1750,91318,1753],{"stretchy":1752},[1742,91320,6465],{},[1750,91322,1917],{"separator":1916},[1742,91324,4078],{},[1750,91326,1763],{"stretchy":1752},[1750,91328,8009],{},[1750,91330,1753],{"stretchy":1752},[1750,91332,1758],{},[1742,91334,7902],{},[1750,91336,1763],{"stretchy":1752},[1750,91338,1861],{},[898,91340,1773],{},[5535,91342,91343,91345],{},[898,91344,1776],{},[898,91346,19435],{},[1750,91348,1753],{"stretchy":1752},[1742,91350,6465],{},[1750,91352,1917],{"separator":1916},[1742,91354,4078],{},[1750,91356,1763],{"stretchy":1752},[1750,91358,8009],{},[1742,91360,3936],{},[1750,91362,1766],{},[1742,91364,91023],{},[1750,91366,8009],{},[1750,91368,1753],{"stretchy":1752},[1750,91370,1758],{},[1742,91372,7902],{},[1750,91374,1763],{"stretchy":1752},[1750,91376,1861],{},[1742,91378,91379],{},"4,525",[1750,91381,8009],{},[1742,91383,3936],{},[1750,91385,2274],{},[1742,91387,91388],{},"190,485.",[902,91390,91391],{"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.",[724,91393,91394],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[198,91396,91398],{"id":91397},"příklad-55","Příklad 5.5",[724,91400,91401,91402,91438,91439,2313],{},"Pro produkci ",[883,91403,91405],{"className":91404},[886],[888,91406,91407],{"xmlns":890},[892,91408,91409,91435],{},[895,91410,91411,91413,91415,91417,91419,91421,91423,91425,91431],{},[898,91412,12471],{},[1750,91414,1753],{"stretchy":1752},[898,91416,2046],{},[1750,91418,1917],{"separator":1916},[898,91420,19435],{},[1750,91422,1763],{"stretchy":1752},[1750,91424,1766],{},[90950,91426,91427,91429],{},[898,91428,2046],{},[1742,91430,7822],{},[17761,91432,91433],{},[898,91434,19435],{},[902,91436,91437],{"encoding":904},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[883,91440,91442],{"className":91441},[886],[888,91443,91444],{"xmlns":890},[892,91445,91446,91462],{},[895,91447,91448,91454,91458,91460],{},[90950,91449,91450,91452],{},[898,91451,2046],{},[1742,91453,7822],{},[17761,91455,91456],{},[898,91457,19435],{},[1750,91459,1766],{},[898,91461,89720],{},[902,91463,91464],{"encoding":904},"\\sqrt[3]{L}\\sqrt{K} = q",[724,91466,91467,91468,2313],{},"Umocněním na druhou: ",[883,91469,91471],{"className":91470},[886],[888,91472,91473],{"xmlns":890},[892,91474,91475,91499],{},[895,91476,91477,91479,91481,91487,91489],{},[898,91478,19435],{},[1750,91480,1766],{},[1699,91482,91483,91485],{},[898,91484,89720],{},[1742,91486,1872],{},[898,91488,1748],{"mathvariant":1747},[90950,91490,91491,91497],{},[1699,91492,91493,91495],{},[898,91494,2046],{},[1742,91496,1872],{},[1742,91498,7822],{},[902,91500,91501],{"encoding":904},"K = q^2 \u002F \\sqrt[3]{L^2}",[120,91503,91504,91544,91584],{},[123,91505,91506],{},[883,91507,91509],{"className":91508},[886],[888,91510,91511],{"xmlns":890},[892,91512,91513,91541],{},[895,91514,91515,91517,91519,91521,91523,91525,91527,91529,91531],{},[898,91516,89720],{},[1750,91518,1766],{},[1742,91520,1744],{},[1750,91522,13651],{},[898,91524,19435],{},[1750,91526,1766],{},[1742,91528,1744],{},[898,91530,1748],{"mathvariant":1747},[90950,91532,91533,91539],{},[1699,91534,91535,91537],{},[898,91536,2046],{},[1742,91538,1872],{},[1742,91540,7822],{},[902,91542,91543],{"encoding":904},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[123,91545,91546],{},[883,91547,91549],{"className":91548},[886],[888,91550,91551],{"xmlns":890},[892,91552,91553,91581],{},[895,91554,91555,91557,91559,91561,91563,91565,91567,91569,91571],{},[898,91556,89720],{},[1750,91558,1766],{},[1742,91560,1872],{},[1750,91562,13651],{},[898,91564,19435],{},[1750,91566,1766],{},[1742,91568,7859],{},[898,91570,1748],{"mathvariant":1747},[90950,91572,91573,91579],{},[1699,91574,91575,91577],{},[898,91576,2046],{},[1742,91578,1872],{},[1742,91580,7822],{},[902,91582,91583],{"encoding":904},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[123,91585,91586],{},[883,91587,91589],{"className":91588},[886],[888,91590,91591],{"xmlns":890},[892,91592,91593,91621],{},[895,91594,91595,91597,91599,91601,91603,91605,91607,91609,91611],{},[898,91596,89720],{},[1750,91598,1766],{},[1742,91600,7822],{},[1750,91602,13651],{},[898,91604,19435],{},[1750,91606,1766],{},[1742,91608,13663],{},[898,91610,1748],{"mathvariant":1747},[90950,91612,91613,91619],{},[1699,91614,91615,91617],{},[898,91616,2046],{},[1742,91618,1872],{},[1742,91620,7822],{},[902,91622,91623],{"encoding":904},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[724,91625,91626],{},[614,91627,91628,91629,16121,91650,2313],{},"Obrázek 5.5 — tři klesající konvexní izokvanty v rovině ",[883,91630,91632],{"className":91631},[886],[888,91633,91634],{"xmlns":890},[892,91635,91636,91648],{},[895,91637,91638,91640,91642,91644,91646],{},[1750,91639,1753],{"stretchy":1752},[898,91641,2046],{},[1750,91643,1917],{"separator":1916},[898,91645,19435],{},[1750,91647,1763],{"stretchy":1752},[902,91649,89846],{"encoding":904},[883,91651,91653],{"className":91652},[886],[888,91654,91655],{"xmlns":890},[892,91656,91657,91673],{},[895,91658,91659,91661,91663,91665,91667,91669,91671],{},[898,91660,89720],{},[1750,91662,1766],{},[1742,91664,1744],{},[1750,91666,1917],{"separator":1916},[1742,91668,1872],{},[1750,91670,1917],{"separator":1916},[1742,91672,7822],{},[902,91674,91675],{"encoding":904},"q = 1, 2, 3",[198,91677,91679],{"id":91678},"příklad-56","Příklad 5.6",[724,91681,85596,91682,2313],{},[883,91683,91685],{"className":91684},[886],[888,91686,91687],{"xmlns":890},[892,91688,91689,91705],{},[895,91690,91691,91693,91695,91697,91699,91701],{},[898,91692,12471],{},[1750,91694,1766],{},[1742,91696,1872],{},[898,91698,2046],{},[1750,91700,1861],{},[17761,91702,91703],{},[898,91704,19435],{},[902,91706,91707],{"encoding":904},"Q = 2L + \\sqrt{K}",[883,91709,91711],{"className":91710},[886],[888,91712,91713],{"xmlns":890,"display":36989},[892,91714,91715,91757],{},[895,91716,91717,91719,91725,91727,91729,91731,91733,91735,91741,91743,91755],{},[898,91718,1773],{},[5535,91720,91721,91723],{},[898,91722,1776],{},[898,91724,2046],{},[1750,91726,1766],{},[1742,91728,1872],{},[1750,91730,1917],{"separator":1916},[2125,91732],{"width":2127},[898,91734,1773],{},[5535,91736,91737,91739],{},[898,91738,1776],{},[898,91740,19435],{},[1750,91742,1766],{},[3423,91744,91745,91747],{},[1742,91746,1744],{},[895,91748,91749,91751],{},[1742,91750,1872],{},[17761,91752,91753],{},[898,91754,19435],{},[898,91756,2313],{"mathvariant":1747},[902,91758,91759],{"encoding":904},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[883,91761,91763],{"className":91762},[886],[888,91764,91765],{"xmlns":890,"display":36989},[892,91766,91767,91831],{},[895,91768,91769,91771,91773,91775,91777,91779,91801,91803,91821,91823,91825,91829],{},[898,91770,1773],{},[898,91772,13658],{},[898,91774,5326],{},[898,91776,1779],{},[1750,91778,1766],{},[3423,91780,91781,91791],{},[895,91782,91783,91785],{},[898,91784,1773],{},[5535,91786,91787,91789],{},[898,91788,1776],{},[898,91790,2046],{},[895,91792,91793,91795],{},[898,91794,1773],{},[5535,91796,91797,91799],{},[898,91798,1776],{},[898,91800,19435],{},[1750,91802,1766],{},[3423,91804,91805,91807],{},[1742,91806,1872],{},[3586,91808,91809],{"scriptlevel":2607,"displaystyle":1752},[3423,91810,91811,91813],{},[1742,91812,1744],{},[895,91814,91815,91817],{},[1742,91816,1872],{},[17761,91818,91819],{},[898,91820,19435],{},[1750,91822,1766],{},[1742,91824,7859],{},[17761,91826,91827],{},[898,91828,19435],{},[898,91830,2313],{"mathvariant":1747},[902,91832,91833],{"encoding":904},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[724,91835,91836,91837,91880,91881,91920,91921,2313],{},"Například ",[883,91838,91840],{"className":91839},[886],[888,91841,91842],{"xmlns":890},[892,91843,91844,91877],{},[895,91845,91846,91848,91850,91852,91854,91856,91858,91860,91862,91864,91866,91868,91872,91874],{},[898,91847,1773],{},[898,91849,13658],{},[898,91851,5326],{},[898,91853,1779],{},[1750,91855,1753],{"stretchy":1752},[1742,91857,7859],{},[1750,91859,1917],{"separator":1916},[1742,91861,8051],{},[1750,91863,1763],{"stretchy":1752},[1750,91865,1766],{},[1742,91867,7859],{},[17761,91869,91870],{},[1742,91871,8051],{},[1750,91873,2274],{},[1742,91875,91876],{},"10,58",[902,91878,91879],{"encoding":904},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[883,91882,91884],{"className":91883},[886],[888,91885,91886],{"xmlns":890},[892,91887,91888,91917],{},[895,91889,91890,91892,91894,91896,91898,91900,91902,91904,91906,91908,91912,91914],{},[898,91891,12471],{},[1750,91893,1753],{"stretchy":1752},[1742,91895,7859],{},[1750,91897,1917],{"separator":1916},[1742,91899,8051],{},[1750,91901,1763],{"stretchy":1752},[1750,91903,1766],{},[1742,91905,15239],{},[1750,91907,1861],{},[17761,91909,91910],{},[1742,91911,8051],{},[1750,91913,2274],{},[1742,91915,91916],{},"10,646",[902,91918,91919],{"encoding":904},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[883,91922,91924],{"className":91923},[886],[888,91925,91926],{"xmlns":890},[892,91927,91928,91936],{},[895,91929,91930,91932],{},[1742,91931,7859],{},[17761,91933,91934],{},[1742,91935,8051],{},[902,91937,91938],{"encoding":904},"4\\sqrt{7}",[724,91940,91941,91942,91962],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[883,91943,91945],{"className":91944},[886],[888,91946,91947],{"xmlns":890},[892,91948,91949,91959],{},[895,91950,91951,91953,91955,91957],{},[898,91952,3429],{},[898,91954,2046],{},[1750,91956,1766],{},[1742,91958,1872],{},[902,91960,91961],{"encoding":904},"dL = 2","), k udržení produkce stačí snížit kapitál o",[883,91964,91966],{"className":91965},[886],[888,91967,91968],{"xmlns":890,"display":36989},[892,91969,91970,92019],{},[895,91971,91972,91974,91976,91978,91980,91982,91984,91986,91988,91990,91992,91994,91996,91998,92000,92002,92004,92006,92008,92012,92014,92016],{},[898,91973,3429],{},[898,91975,19435],{},[1750,91977,1766],{},[1750,91979,1758],{},[898,91981,1773],{},[898,91983,13658],{},[898,91985,5326],{},[898,91987,1779],{},[1750,91989,1753],{"stretchy":1752},[1742,91991,7859],{},[1750,91993,1917],{"separator":1916},[1742,91995,8051],{},[1750,91997,1763],{"stretchy":1752},[1750,91999,8009],{},[1742,92001,1872],{},[1750,92003,1766],{},[1750,92005,1758],{},[1742,92007,15239],{},[17761,92009,92010],{},[1742,92011,8051],{},[1750,92013,2274],{},[1750,92015,1758],{},[1742,92017,92018],{},"21,17.",[902,92020,92021],{"encoding":904},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[115,92023,92025],{"id":92024},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[724,92027,92028,92029,1343,92031,2028,92033,92035,92036,92039,92040,92043],{},"Hlavními faktory produkce jsou ",[38,92030,83837],{},[38,92032,83853],{},[38,92034,83869],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[38,92037,92038],{},"jednofaktorový"," (pouze práce) a ",[38,92041,92042],{},"dvoufaktorový"," (práce + kapitál) model.",[724,92045,92046,92047,92050,92051,92053,92054,92056,92057,10062,92060,92079,92080,92097,92098,92115,92116,92138,92139,14017,92158,2313],{},"V ",[38,92048,92049],{},"1F modelu"," se definuje ",[38,92052,19658],{}," (derivace produkce podle práce) a ",[38,92055,83772],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[38,92058,92059],{},"zákonu klesajících výnosů",[883,92061,92063],{"className":92062},[886],[888,92064,92065],{"xmlns":890},[892,92066,92067,92077],{},[895,92068,92069,92071],{},[898,92070,1773],{},[5535,92072,92073,92075],{},[898,92074,1776],{},[898,92076,2046],{},[902,92078,19678],{"encoding":904}," nejprve roste, od inflexního bodu ",[883,92081,92083],{"className":92082},[886],[888,92084,92085],{"xmlns":890},[892,92086,92087,92095],{},[895,92088,92089],{},[5535,92090,92091,92093],{},[898,92092,2046],{},[1742,92094,2607],{},[902,92096,84481],{"encoding":904}," klesá a v bodě ",[883,92099,92101],{"className":92100},[886],[888,92102,92103],{"xmlns":890},[892,92104,92105,92113],{},[895,92106,92107],{},[5535,92108,92109,92111],{},[898,92110,2046],{},[1742,92112,1744],{},[902,92114,22818],{"encoding":904}," dosahuje nuly (maximum produkce). Platí ",[38,92117,92118,92119],{},"princip maximalizace ",[883,92120,92122],{"className":92121},[886],[888,92123,92124],{"xmlns":890},[892,92125,92126,92136],{},[895,92127,92128,92130],{},[898,92129,13916],{},[5535,92131,92132,92134],{},[898,92133,1776],{},[898,92135,2046],{},[902,92137,83556],{"encoding":904},": v bodě maxima ",[883,92140,92142],{"className":92141},[886],[888,92143,92144],{"xmlns":890},[892,92145,92146,92156],{},[895,92147,92148,92150],{},[898,92149,13916],{},[5535,92151,92152,92154],{},[898,92153,1776],{},[898,92155,2046],{},[902,92157,83556],{"encoding":904},[883,92159,92161],{"className":92160},[886],[888,92162,92163],{"xmlns":890},[892,92164,92165,92185],{},[895,92166,92167,92169,92175,92177,92179],{},[898,92168,1773],{},[5535,92170,92171,92173],{},[898,92172,1776],{},[898,92174,2046],{},[1750,92176,1766],{},[898,92178,13916],{},[5535,92180,92181,92183],{},[898,92182,1776],{},[898,92184,2046],{},[902,92186,83586],{"encoding":904},[724,92188,92189,92190,92193,92194,1647,92197,92226,92227,92244,92245,92248,92249,92278,92279,92281,92282,2433,92312,92334],{},"Ve ",[38,92191,92192],{},"2F modelu"," se obvykle používají ",[38,92195,92196],{},"Cobb-Douglasovy funkce",[883,92198,92200],{"className":92199},[886],[888,92201,92202],{"xmlns":890},[892,92203,92204,92224],{},[895,92205,92206,92208,92210,92212,92218],{},[898,92207,12471],{},[1750,92209,1766],{},[898,92211,13916],{},[1699,92213,92214,92216],{},[898,92215,2046],{},[898,92217,207],{},[1699,92219,92220,92222],{},[898,92221,19435],{},[898,92223,2573],{},[902,92225,83653],{"encoding":904},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[883,92228,92230],{"className":92229},[886],[888,92231,92232],{"xmlns":890},[892,92233,92234,92242],{},[895,92235,92236,92238,92240],{},[898,92237,207],{},[1750,92239,1861],{},[898,92241,2573],{},[902,92243,83747],{"encoding":904}," rozlišujeme ",[38,92246,92247],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[883,92250,92252],{"className":92251},[886],[888,92253,92254],{"xmlns":890},[892,92255,92256,92276],{},[895,92257,92258,92260,92266,92268,92270],{},[898,92259,1773],{},[5535,92261,92262,92264],{},[898,92263,1776],{},[898,92265,2046],{},[1750,92267,1917],{"separator":1916},[898,92269,1773],{},[5535,92271,92272,92274],{},[898,92273,1776],{},[898,92275,19435],{},[902,92277,83684],{"encoding":904}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[38,92280,19414],{}," jsou indiferenční křivky produkční funkce. Podíl ",[883,92283,92285],{"className":92284},[886],[888,92286,92287],{"xmlns":890},[892,92288,92289,92309],{},[895,92290,92291,92293,92299,92301,92303],{},[898,92292,1773],{},[5535,92294,92295,92297],{},[898,92296,1776],{},[898,92298,2046],{},[898,92300,1748],{"mathvariant":1747},[898,92302,1773],{},[5535,92304,92305,92307],{},[898,92306,1776],{},[898,92308,19435],{},[902,92310,92311],{"encoding":904},"MP_L\u002FMP_K",[38,92313,92314,92315,1763],{},"mezní míra technické substituce (",[883,92316,92318],{"className":92317},[886],[888,92319,92320],{"xmlns":890},[892,92321,92322,92332],{},[895,92323,92324,92326,92328,92330],{},[898,92325,1773],{},[898,92327,13658],{},[898,92329,5326],{},[898,92331,1779],{},[902,92333,20232],{"encoding":904}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[115,92336,58805],{"id":58804},[152,92338,92339,92342,92345,92348,92351,92354,92357,92360,92363,92366,92369],{},[123,92340,92341],{},"Jaké jsou faktory produkce?",[123,92343,92344],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[123,92346,92347],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[123,92349,92350],{},"Co udává mezní produkt práce?",[123,92352,92353],{},"Co musí respektovat průběh křivky produkce?",[123,92355,92356],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[123,92358,92359],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[123,92361,92362],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[123,92364,92365],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[123,92367,92368],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[123,92370,92371],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[115,92373,92375],{"id":92374},"úlohy-51517","Úlohy 5.1–5.17",[198,92377,49374],{"id":49373},[724,92379,92380,92383,92384,92406,92407,1343,92427,1343,92447,92467],{},[38,92381,92382],{},"5.1"," Je dána produkce ",[883,92385,92387],{"className":92386},[886],[888,92388,92389],{"xmlns":890},[892,92390,92391,92403],{},[895,92392,92393,92395,92397,92399],{},[898,92394,12471],{},[1750,92396,1766],{},[1742,92398,3079],{},[17761,92400,92401],{},[898,92402,2046],{},[902,92404,92405],{"encoding":904},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[883,92408,92410],{"className":92409},[886],[888,92411,92412],{"xmlns":890},[892,92413,92414,92424],{},[895,92415,92416,92418,92420,92422],{},[898,92417,12471],{},[1750,92419,1753],{"stretchy":1752},[1742,92421,1744],{},[1750,92423,1763],{"stretchy":1752},[902,92425,92426],{"encoding":904},"Q(1)",[883,92428,92430],{"className":92429},[886],[888,92431,92432],{"xmlns":890},[892,92433,92434,92444],{},[895,92435,92436,92438,92440,92442],{},[898,92437,12471],{},[1750,92439,1753],{"stretchy":1752},[1742,92441,7859],{},[1750,92443,1763],{"stretchy":1752},[902,92445,92446],{"encoding":904},"Q(4)",[883,92448,92450],{"className":92449},[886],[888,92451,92452],{"xmlns":890},[892,92453,92454,92464],{},[895,92455,92456,92458,92460,92462],{},[898,92457,12471],{},[1750,92459,1753],{"stretchy":1752},[1742,92461,13663],{},[1750,92463,1763],{"stretchy":1752},[902,92465,92466],{"encoding":904},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[724,92469,92470,92383,92473,92509,92510,92523,92524,92543,92544,92570,92571,4321,92584,92597],{},[38,92471,92472],{},"5.2",[883,92474,92476],{"className":92475},[886],[888,92477,92478],{"xmlns":890},[892,92479,92480,92506],{},[895,92481,92482,92484,92486,92488,92490,92496,92498,92500],{},[898,92483,12471],{},[1750,92485,1766],{},[1750,92487,1758],{},[1742,92489,12476],{},[1699,92491,92492,92494],{},[898,92493,2046],{},[1742,92495,7822],{},[1750,92497,1861],{},[1742,92499,13663],{},[1699,92501,92502,92504],{},[898,92503,2046],{},[1742,92505,1872],{},[902,92507,92508],{"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 ",[883,92511,92513],{"className":92512},[886],[888,92514,92515],{"xmlns":890},[892,92516,92517,92521],{},[895,92518,92519],{},[898,92520,2046],{},[902,92522,2046],{"encoding":904}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[883,92525,92527],{"className":92526},[886],[888,92528,92529],{"xmlns":890},[892,92530,92531,92541],{},[895,92532,92533,92535],{},[898,92534,1773],{},[5535,92536,92537,92539],{},[898,92538,1776],{},[898,92540,2046],{},[902,92542,19678],{"encoding":904},". (f) Vypočtěte ",[883,92545,92547],{"className":92546},[886],[888,92548,92549],{"xmlns":890},[892,92550,92551,92567],{},[895,92552,92553,92555,92561,92563,92565],{},[898,92554,1773],{},[5535,92556,92557,92559],{},[898,92558,1776],{},[898,92560,2046],{},[1750,92562,1753],{"stretchy":1752},[1742,92564,3079],{},[1750,92566,1763],{"stretchy":1752},[902,92568,92569],{"encoding":904},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[883,92572,92574],{"className":92573},[886],[888,92575,92576],{"xmlns":890},[892,92577,92578,92582],{},[895,92579,92580],{},[1742,92581,3079],{},[902,92583,3079],{"encoding":904},[883,92585,92587],{"className":92586},[886],[888,92588,92589],{"xmlns":890},[892,92590,92591,92595],{},[895,92592,92593],{},[1742,92594,51210],{},[902,92596,51210],{"encoding":904}," a porovnejte se skutečnou změnou produkce.",[724,92599,92600,92603,92604,92626,92627,92655,92656,92687,92688,2313],{},[38,92601,92602],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[883,92605,92607],{"className":92606},[886],[888,92608,92609],{"xmlns":890},[892,92610,92611,92623],{},[895,92612,92613,92615,92617,92619],{},[898,92614,12471],{},[1750,92616,1766],{},[1742,92618,7658],{},[17761,92620,92621],{},[898,92622,2046],{},[902,92624,92625],{"encoding":904},"Q = 500\\sqrt{L}",".\n(b) ",[883,92628,92630],{"className":92629},[886],[888,92631,92632],{"xmlns":890},[892,92633,92634,92652],{},[895,92635,92636,92638,92640,92642,92646,92648,92650],{},[898,92637,12471],{},[1750,92639,1766],{},[1742,92641,39004],{},[17761,92643,92644],{},[898,92645,2046],{},[1750,92647,1758],{},[1742,92649,7859],{},[898,92651,2046],{},[902,92653,92654],{"encoding":904},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[883,92657,92659],{"className":92658},[886],[888,92660,92661],{"xmlns":890},[892,92662,92663,92684],{},[895,92664,92665,92667,92669,92671,92673,92675,92678],{},[898,92666,12471],{},[1750,92668,1766],{},[1742,92670,3936],{},[898,92672,2046],{},[1750,92674,1758],{},[1742,92676,92677],{},"0,01",[1699,92679,92680,92682],{},[898,92681,2046],{},[1742,92683,1872],{},[902,92685,92686],{"encoding":904},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[883,92689,92691],{"className":92690},[886],[888,92692,92693],{"xmlns":890},[892,92694,92695,92721],{},[895,92696,92697,92699,92701,92703,92705,92711,92713,92715],{},[898,92698,12471],{},[1750,92700,1766],{},[1750,92702,1758],{},[1742,92704,77134],{},[1699,92706,92707,92709],{},[898,92708,2046],{},[1742,92710,7822],{},[1750,92712,1861],{},[1742,92714,13663],{},[1699,92716,92717,92719],{},[898,92718,2046],{},[1742,92720,1872],{},[902,92722,92723],{"encoding":904},"Q = -0{,}3 L^{3} + 9 L^{2}",[724,92725,92726,92729,92730,2984,92749,81121,92766,2313],{},[38,92727,92728],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[883,92731,92733],{"className":92732},[886],[888,92734,92735],{"xmlns":890},[892,92736,92737,92747],{},[895,92738,92739,92741],{},[898,92740,13916],{},[5535,92742,92743,92745],{},[898,92744,1776],{},[898,92746,2046],{},[902,92748,83556],{"encoding":904},[883,92750,92752],{"className":92751},[886],[888,92753,92754],{"xmlns":890},[892,92755,92756,92764],{},[895,92757,92758],{},[5535,92759,92760,92762],{},[898,92761,2046],{},[1742,92763,2607],{},[902,92765,84481],{"encoding":904},[883,92767,92769],{"className":92768},[886],[888,92770,92771],{"xmlns":890},[892,92772,92773,92813],{},[895,92774,92775,92777,92783,92785,92791,92793,92795,92797,92803,92805,92811],{},[898,92776,13916],{},[5535,92778,92779,92781],{},[898,92780,1776],{},[898,92782,2046],{},[1750,92784,1753],{"stretchy":1752},[5535,92786,92787,92789],{},[898,92788,2046],{},[1742,92790,2607],{},[1750,92792,1763],{"stretchy":1752},[1750,92794,1766],{},[898,92796,1773],{},[5535,92798,92799,92801],{},[898,92800,1776],{},[898,92802,2046],{},[1750,92804,1753],{"stretchy":1752},[5535,92806,92807,92809],{},[898,92808,2046],{},[1742,92810,2607],{},[1750,92812,1763],{"stretchy":1752},[902,92814,92815],{"encoding":904},"AP_L(L_0) = MP_L(L_0)",[724,92817,92818,92383,92821,5424,92857,92870,92871,92890],{},[38,92819,92820],{},"5.5",[883,92822,92824],{"className":92823},[886],[888,92825,92826],{"xmlns":890},[892,92827,92828,92854],{},[895,92829,92830,92832,92834,92836,92838,92844,92846,92848],{},[898,92831,12471],{},[1750,92833,1766],{},[1750,92835,1758],{},[1742,92837,3929],{},[1699,92839,92840,92842],{},[898,92841,2046],{},[1742,92843,7822],{},[1750,92845,1861],{},[1742,92847,4903],{},[1699,92849,92850,92852],{},[898,92851,2046],{},[1742,92853,1872],{},[902,92855,92856],{"encoding":904},"Q = -0{,}2 L^{3} + 12 L^{2}",[883,92858,92860],{"className":92859},[886],[888,92861,92862],{"xmlns":890},[892,92863,92864,92868],{},[895,92865,92866],{},[898,92867,2046],{},[902,92869,2046],{"encoding":904}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[883,92872,92874],{"className":92873},[886],[888,92875,92876],{"xmlns":890},[892,92877,92878,92888],{},[895,92879,92880,92882],{},[898,92881,13916],{},[5535,92883,92884,92886],{},[898,92885,1776],{},[898,92887,2046],{},[902,92889,83556],{"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.",[198,92892,92894],{"id":92893},"dvoufaktorový-model","Dvoufaktorový model",[724,92896,92897,92900,92901,92626,92927,92655,92969,2313],{},[38,92898,92899],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[883,92902,92904],{"className":92903},[886],[888,92905,92906],{"xmlns":890},[892,92907,92908,92924],{},[895,92909,92910,92912,92914,92916,92918],{},[898,92911,12471],{},[1750,92913,1766],{},[1742,92915,8051],{},[898,92917,2046],{},[1699,92919,92920,92922],{},[898,92921,19435],{},[1742,92923,1872],{},[902,92925,92926],{"encoding":904},"Q = 7 L K^{2}",[883,92928,92930],{"className":92929},[886],[888,92931,92932],{"xmlns":890},[892,92933,92934,92966],{},[895,92935,92936,92938,92940,92942,92954],{},[898,92937,12471],{},[1750,92939,1766],{},[1742,92941,3936],{},[1699,92943,92944,92946],{},[898,92945,2046],{},[895,92947,92948,92950,92952],{},[1742,92949,1872],{},[898,92951,1748],{"mathvariant":1747},[1742,92953,7822],{},[1699,92955,92956,92958],{},[898,92957,19435],{},[895,92959,92960,92962,92964],{},[1742,92961,1744],{},[898,92963,1748],{"mathvariant":1747},[1742,92965,7822],{},[902,92967,92968],{"encoding":904},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[883,92970,92972],{"className":92971},[886],[888,92973,92974],{"xmlns":890},[892,92975,92976,93008],{},[895,92977,92978,92980,92982,92984,92996],{},[898,92979,12471],{},[1750,92981,1766],{},[1742,92983,13377],{},[1699,92985,92986,92988],{},[898,92987,2046],{},[895,92989,92990,92992,92994],{},[1742,92991,7822],{},[898,92993,1748],{"mathvariant":1747},[1742,92995,7902],{},[1699,92997,92998,93000],{},[898,92999,19435],{},[895,93001,93002,93004,93006],{},[1742,93003,1872],{},[898,93005,1748],{"mathvariant":1747},[1742,93007,7902],{},[902,93009,93010],{"encoding":904},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[724,93012,93013,92383,93016,93058,93059,1343,93077,93096,93097,93114],{},[38,93014,93015],{},"5.7",[883,93017,93019],{"className":93018},[886],[888,93020,93021],{"xmlns":890},[892,93022,93023,93055],{},[895,93024,93025,93027,93029,93031,93043],{},[898,93026,12471],{},[1750,93028,1766],{},[1742,93030,3079],{},[1699,93032,93033,93035],{},[898,93034,2046],{},[895,93036,93037,93039,93041],{},[1742,93038,1744],{},[898,93040,1748],{"mathvariant":1747},[1742,93042,1872],{},[1699,93044,93045,93047],{},[898,93046,19435],{},[895,93048,93049,93051,93053],{},[1742,93050,1744],{},[898,93052,1748],{"mathvariant":1747},[1742,93054,1872],{},[902,93056,93057],{"encoding":904},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[883,93060,93062],{"className":93061},[886],[888,93063,93064],{"xmlns":890},[892,93065,93066,93074],{},[895,93067,93068,93070,93072],{},[898,93069,2046],{},[1750,93071,1766],{},[1742,93073,3956],{},[902,93075,93076],{"encoding":904},"L = 400",[883,93078,93080],{"className":93079},[886],[888,93081,93082],{"xmlns":890},[892,93083,93084,93093],{},[895,93085,93086,93088,93090],{},[898,93087,19435],{},[1750,93089,1766],{},[1742,93091,93092],{},"17576",[902,93094,93095],{"encoding":904},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[883,93098,93100],{"className":93099},[886],[888,93101,93102],{"xmlns":890},[892,93103,93104,93112],{},[895,93105,93106,93108,93110],{},[898,93107,2046],{},[1750,93109,1917],{"separator":1916},[898,93111,19435],{},[902,93113,87908],{"encoding":904}," zdvojnásobí.",[724,93116,93117,93120,93121,93058,93152,1343,93170,78507,93188,93218,93219,93249,93250,4321,93263,93277,93278,4321,93291,93304],{},[38,93118,93119],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[883,93122,93124],{"className":93123},[886],[888,93125,93126],{"xmlns":890},[892,93127,93128,93149],{},[895,93129,93130,93132,93134,93137,93143],{},[898,93131,12471],{},[1750,93133,1766],{},[1742,93135,93136],{},"1,01",[1699,93138,93139,93141],{},[898,93140,2046],{},[1742,93142,7574],{},[1699,93144,93145,93147],{},[898,93146,19435],{},[1742,93148,7633],{},[902,93150,93151],{"encoding":904},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[883,93153,93155],{"className":93154},[886],[888,93156,93157],{"xmlns":890},[892,93158,93159,93167],{},[895,93160,93161,93163,93165],{},[898,93162,2046],{},[1750,93164,1766],{},[1742,93166,39666],{},[902,93168,93169],{"encoding":904},"L = 250",[883,93171,93173],{"className":93172},[886],[888,93174,93175],{"xmlns":890},[892,93176,93177,93185],{},[895,93178,93179,93181,93183],{},[898,93180,19435],{},[1750,93182,1766],{},[1742,93184,8243],{},[902,93186,93187],{"encoding":904},"K = 1000",[883,93189,93191],{"className":93190},[886],[888,93192,93193],{"xmlns":890},[892,93194,93195,93215],{},[895,93196,93197,93199,93205,93207,93209,93211,93213],{},[898,93198,1773],{},[5535,93200,93201,93203],{},[898,93202,1776],{},[898,93204,2046],{},[1750,93206,1753],{"stretchy":1752},[1742,93208,39666],{},[1750,93210,1917],{"separator":1916},[1742,93212,8243],{},[1750,93214,1763],{"stretchy":1752},[902,93216,93217],{"encoding":904},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[883,93220,93222],{"className":93221},[886],[888,93223,93224],{"xmlns":890},[892,93225,93226,93246],{},[895,93227,93228,93230,93236,93238,93240,93242,93244],{},[898,93229,1773],{},[5535,93231,93232,93234],{},[898,93233,1776],{},[898,93235,19435],{},[1750,93237,1753],{"stretchy":1752},[1742,93239,39666],{},[1750,93241,1917],{"separator":1916},[1742,93243,8243],{},[1750,93245,1763],{"stretchy":1752},[902,93247,93248],{"encoding":904},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[883,93251,93253],{"className":93252},[886],[888,93254,93255],{"xmlns":890},[892,93256,93257,93261],{},[895,93258,93259],{},[898,93260,2046],{},[902,93262,2046],{"encoding":904},[883,93264,93266],{"className":93265},[886],[888,93267,93268],{"xmlns":890},[892,93269,93270,93275],{},[895,93271,93272],{},[1742,93273,93274],{},"260",[902,93276,93274],{"encoding":904}," a současném poklesu ",[883,93279,93281],{"className":93280},[886],[888,93282,93283],{"xmlns":890},[892,93284,93285,93289],{},[895,93286,93287],{},[898,93288,19435],{},[902,93290,19435],{"encoding":904},[883,93292,93294],{"className":93293},[886],[888,93295,93296],{"xmlns":890},[892,93297,93298,93302],{},[895,93299,93300],{},[1742,93301,9702],{},[902,93303,9702],{"encoding":904}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[724,93306,93307,93310,93311,2313],{},[38,93308,93309],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[883,93312,93314],{"className":93313},[886],[888,93315,93316],{"xmlns":890},[892,93317,93318,93338],{},[895,93319,93320,93322,93324,93326,93332],{},[898,93321,12471],{},[1750,93323,1766],{},[1742,93325,3079],{},[1699,93327,93328,93330],{},[898,93329,2046],{},[1742,93331,77134],{},[1699,93333,93334,93336],{},[898,93335,19435],{},[1742,93337,4268],{},[902,93339,93340],{"encoding":904},"Q = 10 L^{0{,}3} K^{0{,}5}",[724,93342,93343,93346,93347,89504,93370,20027,93383,2084,93433,1783],{},[38,93344,93345],{},"5.10"," Dokažte, že pro homogenní funkci ",[883,93348,93350],{"className":93349},[886],[888,93351,93352],{"xmlns":890},[892,93353,93354,93368],{},[895,93355,93356,93358,93360,93362,93364,93366],{},[898,93357,12471],{},[1750,93359,1753],{"stretchy":1752},[898,93361,2046],{},[1750,93363,1917],{"separator":1916},[898,93365,19435],{},[1750,93367,1763],{"stretchy":1752},[902,93369,19631],{"encoding":904},[883,93371,93373],{"className":93372},[886],[888,93374,93375],{"xmlns":890},[892,93376,93377,93381],{},[895,93378,93379],{},[898,93380,45783],{},[902,93382,45783],{"encoding":904},[883,93384,93386],{"className":93385},[886],[888,93387,93388],{"xmlns":890},[892,93389,93390,93430],{},[895,93391,93392,93394,93402,93404,93406,93414,93416,93418,93420,93422,93424,93426,93428],{},[898,93393,2046],{},[5950,93395,93396,93398,93400],{},[898,93397,12471],{},[898,93399,2046],{},[1750,93401,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,93403,1861],{},[898,93405,19435],{},[5950,93407,93408,93410,93412],{},[898,93409,12471],{},[898,93411,19435],{},[1750,93413,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,93415,1766],{},[898,93417,45783],{},[898,93419,12471],{},[1750,93421,1753],{"stretchy":1752},[898,93423,2046],{},[1750,93425,1917],{"separator":1916},[898,93427,19435],{},[1750,93429,1763],{"stretchy":1752},[902,93431,93432],{"encoding":904},"L Q'_L + K Q'_K = n Q(L, K)",[614,93434,89479],{},[724,93436,93437,93440],{},[38,93438,93439],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[724,93442,93443,92383,93446,93486,93487,1343,93509,1343,93531,93553],{},[38,93444,93445],{},"5.12",[883,93447,93449],{"className":93448},[886],[888,93450,93451],{"xmlns":890},[892,93452,93453,93483],{},[895,93454,93455,93457,93459,93471],{},[898,93456,12471],{},[1750,93458,1766],{},[1699,93460,93461,93463],{},[898,93462,2046],{},[895,93464,93465,93467,93469],{},[1742,93466,1744],{},[898,93468,1748],{"mathvariant":1747},[1742,93470,7822],{},[1699,93472,93473,93475],{},[898,93474,19435],{},[895,93476,93477,93479,93481],{},[1742,93478,1744],{},[898,93480,1748],{"mathvariant":1747},[1742,93482,7859],{},[902,93484,93485],{"encoding":904},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[883,93488,93490],{"className":93489},[886],[888,93491,93492],{"xmlns":890},[892,93493,93494,93506],{},[895,93495,93496,93502,93504],{},[5535,93497,93498,93500],{},[898,93499,89720],{},[1742,93501,2607],{},[1750,93503,1766],{},[1742,93505,1744],{},[902,93507,93508],{"encoding":904},"q_0 = 1",[883,93510,93512],{"className":93511},[886],[888,93513,93514],{"xmlns":890},[892,93515,93516,93528],{},[895,93517,93518,93524,93526],{},[5535,93519,93520,93522],{},[898,93521,89720],{},[1742,93523,1744],{},[1750,93525,1766],{},[1742,93527,1872],{},[902,93529,93530],{"encoding":904},"q_1 = 2",[883,93532,93534],{"className":93533},[886],[888,93535,93536],{"xmlns":890},[892,93537,93538,93550],{},[895,93539,93540,93546,93548],{},[5535,93541,93542,93544],{},[898,93543,89720],{},[1742,93545,1872],{},[1750,93547,1766],{},[1742,93549,7822],{},[902,93551,93552],{"encoding":904},"q_2 = 3",". (c) Načrtněte izokvanty.",[724,93555,93556,92383,93559,93599,93600,1343,93628,1343,93656,1343,93684,1343,93713,1343,93742,1343,93771,1343,93800,1343,93829,2313],{},[38,93557,93558],{},"5.13",[883,93560,93562],{"className":93561},[886],[888,93563,93564],{"xmlns":890},[892,93565,93566,93596],{},[895,93567,93568,93570,93572,93584],{},[898,93569,12471],{},[1750,93571,1766],{},[1699,93573,93574,93576],{},[898,93575,2046],{},[895,93577,93578,93580,93582],{},[1742,93579,1744],{},[898,93581,1748],{"mathvariant":1747},[1742,93583,7822],{},[1699,93585,93586,93588],{},[898,93587,19435],{},[895,93589,93590,93592,93594],{},[1742,93591,1744],{},[898,93593,1748],{"mathvariant":1747},[1742,93595,1872],{},[902,93597,93598],{"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): ",[883,93601,93603],{"className":93602},[886],[888,93604,93605],{"xmlns":890},[892,93606,93607,93625],{},[895,93608,93609,93615,93617,93619,93621,93623],{},[5535,93610,93611,93613],{},[898,93612,13916],{},[1742,93614,1744],{},[1750,93616,5141],{"stretchy":1752},[1742,93618,1744],{},[1750,93620,18067],{"separator":1916},[1742,93622,1744],{},[1750,93624,5158],{"stretchy":1752},[902,93626,93627],{"encoding":904},"A_1[1; 1]",[883,93629,93631],{"className":93630},[886],[888,93632,93633],{"xmlns":890},[892,93634,93635,93653],{},[895,93636,93637,93643,93645,93647,93649,93651],{},[5535,93638,93639,93641],{},[898,93640,13916],{},[1742,93642,1872],{},[1750,93644,5141],{"stretchy":1752},[1742,93646,1744],{},[1750,93648,18067],{"separator":1916},[1742,93650,15239],{},[1750,93652,5158],{"stretchy":1752},[902,93654,93655],{"encoding":904},"A_2[1; 8]",[883,93657,93659],{"className":93658},[886],[888,93660,93661],{"xmlns":890},[892,93662,93663,93681],{},[895,93664,93665,93671,93673,93675,93677,93679],{},[5535,93666,93667,93669],{},[898,93668,13916],{},[1742,93670,7822],{},[1750,93672,5141],{"stretchy":1752},[1742,93674,1744],{},[1750,93676,18067],{"separator":1916},[1742,93678,75520],{},[1750,93680,5158],{"stretchy":1752},[902,93682,93683],{"encoding":904},"A_3[1; 27]",[883,93685,93687],{"className":93686},[886],[888,93688,93689],{"xmlns":890},[892,93690,93691,93710],{},[895,93692,93693,93699,93701,93703,93705,93708],{},[5535,93694,93695,93697],{},[898,93696,13916],{},[1742,93698,7859],{},[1750,93700,5141],{"stretchy":1752},[1742,93702,1872],{},[1750,93704,18067],{"separator":1916},[1742,93706,93707],{},"0,353",[1750,93709,5158],{"stretchy":1752},[902,93711,93712],{"encoding":904},"A_4[2; 0{,}353]",[883,93714,93716],{"className":93715},[886],[888,93717,93718],{"xmlns":890},[892,93719,93720,93739],{},[895,93721,93722,93728,93730,93732,93734,93737],{},[5535,93723,93724,93726],{},[898,93725,13916],{},[1742,93727,7902],{},[1750,93729,5141],{"stretchy":1752},[1742,93731,1872],{},[1750,93733,18067],{"separator":1916},[1742,93735,93736],{},"2,828",[1750,93738,5158],{"stretchy":1752},[902,93740,93741],{"encoding":904},"A_5[2; 2{,}828]",[883,93743,93745],{"className":93744},[886],[888,93746,93747],{"xmlns":890},[892,93748,93749,93768],{},[895,93750,93751,93757,93759,93761,93763,93766],{},[5535,93752,93753,93755],{},[898,93754,13916],{},[1742,93756,3219],{},[1750,93758,5141],{"stretchy":1752},[1742,93760,1872],{},[1750,93762,18067],{"separator":1916},[1742,93764,93765],{},"9,545",[1750,93767,5158],{"stretchy":1752},[902,93769,93770],{"encoding":904},"A_6[2; 9{,}545]",[883,93772,93774],{"className":93773},[886],[888,93775,93776],{"xmlns":890},[892,93777,93778,93797],{},[895,93779,93780,93786,93788,93790,93792,93795],{},[5535,93781,93782,93784],{},[898,93783,13916],{},[1742,93785,8051],{},[1750,93787,5141],{"stretchy":1752},[1742,93789,73482],{},[1750,93791,18067],{"separator":1916},[1742,93793,93794],{},"0,544",[1750,93796,5158],{"stretchy":1752},[902,93798,93799],{"encoding":904},"A_7[1{,}5; 0{,}544]",[883,93801,93803],{"className":93802},[886],[888,93804,93805],{"xmlns":890},[892,93806,93807,93826],{},[895,93808,93809,93815,93817,93819,93821,93824],{},[5535,93810,93811,93813],{},[898,93812,13916],{},[1742,93814,15239],{},[1750,93816,5141],{"stretchy":1752},[1742,93818,73482],{},[1750,93820,18067],{"separator":1916},[1742,93822,93823],{},"14,696",[1750,93825,5158],{"stretchy":1752},[902,93827,93828],{"encoding":904},"A_8[1{,}5; 14{,}696]",[883,93830,93832],{"className":93831},[886],[888,93833,93834],{"xmlns":890},[892,93835,93836,93854],{},[895,93837,93838,93844,93846,93848,93850,93852],{},[5535,93839,93840,93842],{},[898,93841,13916],{},[1742,93843,13663],{},[1750,93845,5141],{"stretchy":1752},[1742,93847,1872],{},[1750,93849,18067],{"separator":1916},[1742,93851,7902],{},[1750,93853,5158],{"stretchy":1752},[902,93855,93856],{"encoding":904},"A_9[2; 5]",[724,93858,93859,93862],{},[38,93860,93861],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[724,93864,93865,93868,93869,93899,93900,93913,93914,93927,93928,78240,93947,93966,93967,2313],{},[38,93866,93867],{},"5.15"," Produkce firmy je dána vztahem ",[883,93870,93872],{"className":93871},[886],[888,93873,93874],{"xmlns":890},[892,93875,93876,93896],{},[895,93877,93878,93880,93882,93884,93890],{},[898,93879,12471],{},[1750,93881,1766],{},[1742,93883,1872],{},[1699,93885,93886,93888],{},[898,93887,2046],{},[1742,93889,4268],{},[1699,93891,93892,93894],{},[898,93893,19435],{},[1742,93895,7633],{},[902,93897,93898],{"encoding":904},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[883,93901,93903],{"className":93902},[886],[888,93904,93905],{"xmlns":890},[892,93906,93907,93911],{},[895,93908,93909],{},[1742,93910,4078],{},[902,93912,4078],{"encoding":904}," pracovníků a disponuje-li ",[883,93915,93917],{"className":93916},[886],[888,93918,93919],{"xmlns":890},[892,93920,93921,93925],{},[895,93922,93923],{},[1742,93924,73358],{},[902,93926,73358],{"encoding":904}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[883,93929,93931],{"className":93930},[886],[888,93932,93933],{"xmlns":890},[892,93934,93935,93945],{},[895,93936,93937,93939,93941,93943],{},[898,93938,1773],{},[898,93940,13658],{},[898,93942,5326],{},[898,93944,1779],{},[902,93946,20232],{"encoding":904},[883,93948,93950],{"className":93949},[886],[888,93951,93952],{"xmlns":890},[892,93953,93954,93964],{},[895,93955,93956,93958,93960,93962],{},[898,93957,1773],{},[898,93959,13658],{},[898,93961,5326],{},[898,93963,1779],{},[902,93965,20232],{"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 ",[883,93968,93970],{"className":93969},[886],[888,93971,93972],{"xmlns":890},[892,93973,93974,93979],{},[895,93975,93976],{},[1742,93977,93978],{},"95",[902,93980,93978],{"encoding":904},[724,93982,93983,92383,93986,79914,94018,94037,94038,94051,94052,94065,94066,94079],{},[38,93984,93985],{},"5.16",[883,93987,93989],{"className":93988},[886],[888,93990,93991],{"xmlns":890},[892,93992,93993,94015],{},[895,93994,93995,93997,93999,94005,94007,94009],{},[898,93996,12471],{},[1750,93998,1766],{},[1699,94000,94001,94003],{},[898,94002,19435],{},[1742,94004,1872],{},[1750,94006,1861],{},[1742,94008,1872],{},[1699,94010,94011,94013],{},[898,94012,2046],{},[1742,94014,1872],{},[902,94016,94017],{"encoding":904},"Q = K^{2} + 2 L^{2}",[883,94019,94021],{"className":94020},[886],[888,94022,94023],{"xmlns":890},[892,94024,94025,94035],{},[895,94026,94027,94029,94031,94033],{},[898,94028,1773],{},[898,94030,13658],{},[898,94032,5326],{},[898,94034,1779],{},[902,94036,20232],{"encoding":904},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[883,94039,94041],{"className":94040},[886],[888,94042,94043],{"xmlns":890},[892,94044,94045,94049],{},[895,94046,94047],{},[1742,94048,3936],{},[902,94050,3936],{"encoding":904}," pracovníky a ",[883,94053,94055],{"className":94054},[886],[888,94056,94057],{"xmlns":890},[892,94058,94059,94063],{},[895,94060,94061],{},[1742,94062,86540],{},[902,94064,86540],{"encoding":904}," jednotkami kapitálu, jestliže se kapitál sníží na ",[883,94067,94069],{"className":94068},[886],[888,94070,94071],{"xmlns":890},[892,94072,94073,94077],{},[895,94074,94075],{},[1742,94076,55626],{},[902,94078,55626],{"encoding":904}," jednotek.",[724,94081,94082,94085,94086,20027,94116,2313],{},[38,94083,94084],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[883,94087,94089],{"className":94088},[886],[888,94090,94091],{"xmlns":890},[892,94092,94093,94113],{},[895,94094,94095,94097,94099,94101,94107],{},[898,94096,12471],{},[1750,94098,1766],{},[898,94100,13916],{},[1699,94102,94103,94105],{},[898,94104,2046],{},[898,94106,207],{},[1699,94108,94109,94111],{},[898,94110,19435],{},[898,94112,2573],{},[902,94114,94115],{"encoding":904},"Q = A L^{a} K^{b}",[883,94117,94119],{"className":94118},[886],[888,94120,94121],{"xmlns":890},[892,94122,94123,94153],{},[895,94124,94125,94127,94129,94131,94133,94135,94143,94145],{},[898,94126,1773],{},[898,94128,13658],{},[898,94130,5326],{},[898,94132,1779],{},[1750,94134,1766],{},[3586,94136,94137],{"scriptlevel":2607,"displaystyle":1752},[3423,94138,94139,94141],{},[898,94140,207],{},[898,94142,2573],{},[1750,94144,8009],{},[3586,94146,94147],{"scriptlevel":2607,"displaystyle":1752},[3423,94148,94149,94151],{},[898,94150,19435],{},[898,94152,2046],{},[902,94154,94155],{"encoding":904},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[115,94157,10461],{"id":10460},[120,94159,94160,94193,94220,94229,94279,94310,94363,94386,94441,94514,94592,94635,94667,94700,94741,94813,94874,94940,94957,95030,95096,95148,95204,95238,95281],{},[123,94161,94162,94165,94166,45819,94179,94192],{},[38,94163,94164],{},"Faktory (vstupy) produkce:"," práce ",[883,94167,94169],{"className":94168},[886],[888,94170,94171],{"xmlns":890},[892,94172,94173,94177],{},[895,94174,94175],{},[898,94176,2046],{},[902,94178,2046],{"encoding":904},[883,94180,94182],{"className":94181},[886],[888,94183,94184],{"xmlns":890},[892,94185,94186,94190],{},[895,94187,94188],{},[898,94189,19435],{},[902,94191,19435],{"encoding":904},", půda.",[123,94194,94195,10469,94197,2313],{},[38,94196,49374],{},[883,94198,94200],{"className":94199},[886],[888,94201,94202],{"xmlns":890},[892,94203,94204,94218],{},[895,94205,94206,94208,94210,94212,94214,94216],{},[898,94207,12471],{},[1750,94209,1766],{},[898,94211,12471],{},[1750,94213,1753],{"stretchy":1752},[898,94215,2046],{},[1750,94217,1763],{"stretchy":1752},[902,94219,83467],{"encoding":904},[123,94221,94222,2084,94224,4419,94227,2313],{},[38,94223,859],{},[614,94225,94226],{},"production function",[38,94228,83970],{},[123,94230,94231,1647,94233,2313],{},[38,94232,84016],{},[883,94234,94236],{"className":94235},[886],[888,94237,94238],{"xmlns":890},[892,94239,94240,94276],{},[895,94241,94242,94244,94250,94252,94254,94256,94258,94260,94262,94264,94270,94272,94274],{},[898,94243,1773],{},[5535,94245,94246,94248],{},[898,94247,1776],{},[898,94249,2046],{},[1750,94251,1766],{},[898,94253,3429],{},[898,94255,12471],{},[898,94257,1748],{"mathvariant":1747},[898,94259,3429],{},[898,94261,2046],{},[1750,94263,1766],{},[1699,94265,94266,94268],{},[898,94267,12471],{},[1750,94269,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,94271,1753],{"stretchy":1752},[898,94273,2046],{},[1750,94275,1763],{"stretchy":1752},[902,94277,94278],{"encoding":904},"MP_L = dQ\u002FdL = Q'(L)",[123,94280,94281,1647,94283,2313],{},[38,94282,84951],{},[883,94284,94286],{"className":94285},[886],[888,94287,94288],{"xmlns":890},[892,94289,94290,94308],{},[895,94291,94292,94294,94300,94302,94304,94306],{},[898,94293,13916],{},[5535,94295,94296,94298],{},[898,94297,1776],{},[898,94299,2046],{},[1750,94301,1766],{},[898,94303,12471],{},[898,94305,1748],{"mathvariant":1747},[898,94307,2046],{},[902,94309,83535],{"encoding":904},[123,94311,94312,94314,94315,20027,94332,2313],{},[38,94313,84438],{}," — od určitého ",[883,94316,94318],{"className":94317},[886],[888,94319,94320],{"xmlns":890},[892,94321,94322,94330],{},[895,94323,94324],{},[5535,94325,94326,94328],{},[898,94327,2046],{},[1742,94329,2607],{},[902,94331,84481],{"encoding":904},[883,94333,94335],{"className":94334},[886],[888,94336,94337],{"xmlns":890},[892,94338,94339,94361],{},[895,94340,94341,94351,94353,94355,94357,94359],{},[1699,94342,94343,94345],{},[898,94344,12471],{},[895,94346,94347,94349],{},[1750,94348,3815],{"mathvariant":1747},[1750,94350,3815],{"mathvariant":1747},[1750,94352,1753],{"stretchy":1752},[898,94354,2046],{},[1750,94356,1763],{"stretchy":1752},[1750,94358,2624],{},[1742,94360,2607],{},[902,94362,84627],{"encoding":904},[123,94364,94365,1647,94368,94385],{},[38,94366,94367],{},"Inflexní bod",[883,94369,94371],{"className":94370},[886],[888,94372,94373],{"xmlns":890},[892,94374,94375,94383],{},[895,94376,94377],{},[5535,94378,94379,94381],{},[898,94380,2046],{},[1742,94382,2607],{},[902,94384,84481],{"encoding":904}," — přechod z konvexity do konkavity.",[123,94387,94388,1647,94391,10469,94408,2313],{},[38,94389,94390],{},"Bod maxima produkce",[883,94392,94394],{"className":94393},[886],[888,94395,94396],{"xmlns":890},[892,94397,94398,94406],{},[895,94399,94400],{},[5535,94401,94402,94404],{},[898,94403,2046],{},[1742,94405,1744],{},[902,94407,22818],{"encoding":904},[883,94409,94411],{"className":94410},[886],[888,94412,94413],{"xmlns":890},[892,94414,94415,94439],{},[895,94416,94417,94419,94425,94427,94433,94435,94437],{},[898,94418,1773],{},[5535,94420,94421,94423],{},[898,94422,1776],{},[898,94424,2046],{},[1750,94426,1753],{"stretchy":1752},[5535,94428,94429,94431],{},[898,94430,2046],{},[1742,94432,1744],{},[1750,94434,1763],{"stretchy":1752},[1750,94436,1766],{},[1742,94438,2607],{},[902,94440,84700],{"encoding":904},[123,94442,94443,94465,94466,20027,94485,2313],{},[38,94444,94445,94446],{},"Princip maximalizace ",[883,94447,94449],{"className":94448},[886],[888,94450,94451],{"xmlns":890},[892,94452,94453,94463],{},[895,94454,94455,94457],{},[898,94456,13916],{},[5535,94458,94459,94461],{},[898,94460,1776],{},[898,94462,2046],{},[902,94464,83556],{"encoding":904}," — v bodě maxima ",[883,94467,94469],{"className":94468},[886],[888,94470,94471],{"xmlns":890},[892,94472,94473,94483],{},[895,94474,94475,94477],{},[898,94476,13916],{},[5535,94478,94479,94481],{},[898,94480,1776],{},[898,94482,2046],{},[902,94484,83556],{"encoding":904},[883,94486,94488],{"className":94487},[886],[888,94489,94490],{"xmlns":890},[892,94491,94492,94512],{},[895,94493,94494,94496,94502,94504,94506],{},[898,94495,1773],{},[5535,94497,94498,94500],{},[898,94499,1776],{},[898,94501,2046],{},[1750,94503,1766],{},[898,94505,13916],{},[5535,94507,94508,94510],{},[898,94509,1776],{},[898,94511,2046],{},[902,94513,83586],{"encoding":904},[123,94515,94516,1647,94519,1343,94558,1343,94575,2313],{},[38,94517,94518],{},"Polynomiální produkční funkce",[883,94520,94522],{"className":94521},[886],[888,94523,94524],{"xmlns":890},[892,94525,94526,94556],{},[895,94527,94528,94530,94532,94534,94536,94538,94540,94546,94548,94550],{},[898,94529,12471],{},[1750,94531,1753],{"stretchy":1752},[898,94533,2046],{},[1750,94535,1763],{"stretchy":1752},[1750,94537,1766],{},[898,94539,207],{},[1699,94541,94542,94544],{},[898,94543,2046],{},[1742,94545,7822],{},[1750,94547,1861],{},[898,94549,2573],{},[1699,94551,94552,94554],{},[898,94553,2046],{},[1742,94555,1872],{},[902,94557,84818],{"encoding":904},[883,94559,94561],{"className":94560},[886],[888,94562,94563],{"xmlns":890},[892,94564,94565,94573],{},[895,94566,94567,94569,94571],{},[898,94568,207],{},[1750,94570,2624],{},[1742,94572,2607],{},[902,94574,52008],{"encoding":904},[883,94576,94578],{"className":94577},[886],[888,94579,94580],{"xmlns":890},[892,94581,94582,94590],{},[895,94583,94584,94586,94588],{},[898,94585,2573],{},[1750,94587,2604],{},[1742,94589,2607],{},[902,94591,2610],{"encoding":904},[123,94593,94594,1647,94597,2313],{},[38,94595,94596],{},"Diferenciál produkce",[883,94598,94600],{"className":94599},[886],[888,94601,94602],{"xmlns":890},[892,94603,94604,94632],{},[895,94605,94606,94608,94610,94612,94614,94616,94618,94620,94626,94628,94630],{},[898,94607,2666],{"mathvariant":1747},[898,94609,12471],{},[1750,94611,2274],{},[898,94613,3429],{},[898,94615,12471],{},[1750,94617,1766],{},[898,94619,1773],{},[5535,94621,94622,94624],{},[898,94623,1776],{},[898,94625,2046],{},[1969,94627,2658],{},[898,94629,3429],{},[898,94631,2046],{},[902,94633,94634],{"encoding":904},"\\Delta Q \\approx dQ = MP_L\\,dL",[123,94636,94637,10469,94639,2313],{},[38,94638,92894],{},[883,94640,94642],{"className":94641},[886],[888,94643,94644],{"xmlns":890},[892,94645,94646,94664],{},[895,94647,94648,94650,94652,94654,94656,94658,94660,94662],{},[898,94649,12471],{},[1750,94651,1766],{},[898,94653,12471],{},[1750,94655,1753],{"stretchy":1752},[898,94657,2046],{},[1750,94659,1917],{"separator":1916},[898,94661,19435],{},[1750,94663,1763],{"stretchy":1752},[902,94665,94666],{"encoding":904},"Q = Q(L, K)",[123,94668,94669,10469,94671,2313],{},[38,94670,86988],{},[883,94672,94674],{"className":94673},[886],[888,94675,94676],{"xmlns":890},[892,94677,94678,94698],{},[895,94679,94680,94682,94684,94686,94692],{},[898,94681,12471],{},[1750,94683,1766],{},[898,94685,13916],{},[1699,94687,94688,94690],{},[898,94689,2046],{},[898,94691,207],{},[1699,94693,94694,94696],{},[898,94695,19435],{},[898,94697,2573],{},[902,94699,83653],{"encoding":904},[123,94701,94702,10469,94705,94740],{},[38,94703,94704],{},"Ryzí Cobb-Douglas",[883,94706,94708],{"className":94707},[886],[888,94709,94710],{"xmlns":890},[892,94711,94712,94738],{},[895,94713,94714,94716,94718,94720,94726],{},[898,94715,12471],{},[1750,94717,1766],{},[898,94719,13916],{},[1699,94721,94722,94724],{},[898,94723,2046],{},[898,94725,207],{},[1699,94727,94728,94730],{},[898,94729,19435],{},[895,94731,94732,94734,94736],{},[1742,94733,1744],{},[1750,94735,1758],{},[898,94737,207],{},[902,94739,87815],{"encoding":904}," (konstantní výnosy).",[123,94742,94743,10469,94745,2313],{},[38,94744,88531],{},[883,94746,94748],{"className":94747},[886],[888,94749,94750],{"xmlns":890},[892,94751,94752,94810],{},[895,94753,94754,94756,94758,94760,94762,94764,94766,94768,94770,94772,94782,94784,94786,94796],{},[898,94755,12471],{},[1750,94757,1766],{},[898,94759,13916],{},[1750,94761,5141],{"stretchy":1752},[1750,94763,1753],{"stretchy":1752},[1742,94765,1744],{},[1750,94767,1758],{},[898,94769,207],{},[1750,94771,1763],{"stretchy":1752},[1699,94773,94774,94776],{},[898,94775,2046],{},[895,94777,94778,94780],{},[1750,94779,1758],{},[898,94781,2573],{},[1750,94783,1861],{},[898,94785,207],{},[1699,94787,94788,94790],{},[898,94789,19435],{},[895,94791,94792,94794],{},[1750,94793,1758],{},[898,94795,2573],{},[1699,94797,94798,94800],{},[1750,94799,5158],{"stretchy":1752},[895,94801,94802,94804,94806,94808],{},[1750,94803,1758],{},[1742,94805,1744],{},[898,94807,1748],{"mathvariant":1747},[898,94809,2573],{},[902,94811,94812],{"encoding":904},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[123,94814,94815,2084,94818,4419,94840,2084,94843,94873],{},[38,94816,94817],{},"Lineární",[883,94819,94821],{"className":94820},[886],[888,94822,94823],{"xmlns":890},[892,94824,94825,94837],{},[895,94826,94827,94829,94831,94833,94835],{},[898,94828,207],{},[898,94830,2046],{},[1750,94832,1861],{},[898,94834,2573],{},[898,94836,19435],{},[902,94838,94839],{"encoding":904},"aL + bK",[38,94841,94842],{},"Leontiefova",[883,94844,94846],{"className":94845},[886],[888,94847,94848],{"xmlns":890},[892,94849,94850,94870],{},[895,94851,94852,94854,94856,94858,94860,94862,94864,94866,94868],{},[898,94853,88759],{},[1750,94855,65123],{},[1750,94857,1753],{"stretchy":1752},[898,94859,207],{},[898,94861,2046],{},[1750,94863,1917],{"separator":1916},[898,94865,2573],{},[898,94867,19435],{},[1750,94869,1763],{"stretchy":1752},[902,94871,94872],{"encoding":904},"\\min(aL, bK)",") produkční funkce.",[123,94875,94876,10469,94892,2313],{},[38,94877,94878,94879],{},"Homogenita stupně ",[883,94880,94882],{"className":94881},[886],[888,94883,94884],{"xmlns":890},[892,94885,94886,94890],{},[895,94887,94888],{},[898,94889,45783],{},[902,94891,45783],{"encoding":904},[883,94893,94895],{"className":94894},[886],[888,94896,94897],{"xmlns":890},[892,94898,94899,94937],{},[895,94900,94901,94903,94905,94907,94909,94911,94913,94915,94917,94919,94925,94927,94929,94931,94933,94935],{},[898,94902,12471],{},[1750,94904,1753],{"stretchy":1752},[898,94906,1920],{},[898,94908,2046],{},[1750,94910,1917],{"separator":1916},[898,94912,1920],{},[898,94914,19435],{},[1750,94916,1763],{"stretchy":1752},[1750,94918,1766],{},[1699,94920,94921,94923],{},[898,94922,1920],{},[898,94924,45783],{},[898,94926,12471],{},[1750,94928,1753],{"stretchy":1752},[898,94930,2046],{},[1750,94932,1917],{"separator":1916},[898,94934,19435],{},[1750,94936,1763],{"stretchy":1752},[902,94938,94939],{"encoding":904},"Q(rL, rK) = r^n Q(L, K)",[123,94941,94942,87913],{},[38,94943,87846,94944],{},[883,94945,94947],{"className":94946},[886],[888,94948,94949],{"xmlns":890},[892,94950,94951,94955],{},[895,94952,94953],{},[898,94954,13916],{},[902,94956,13916],{"encoding":904},[123,94958,94959,94961,94962,94984,94985,95007,95008,1783],{},[38,94960,87347],{}," — konstantní (",[883,94963,94965],{"className":94964},[886],[888,94966,94967],{"xmlns":890},[892,94968,94969,94981],{},[895,94970,94971,94973,94975,94977,94979],{},[898,94972,207],{},[1750,94974,1861],{},[898,94976,2573],{},[1750,94978,1766],{},[1742,94980,1744],{},[902,94982,94983],{"encoding":904},"a+b=1","), rostoucí (",[883,94986,94988],{"className":94987},[886],[888,94989,94990],{"xmlns":890},[892,94991,94992,95004],{},[895,94993,94994,94996,94998,95000,95002],{},[898,94995,207],{},[1750,94997,1861],{},[898,94999,2573],{},[1750,95001,2604],{},[1742,95003,1744],{},[902,95005,95006],{"encoding":904},"a+b>1","), klesající (",[883,95009,95011],{"className":95010},[886],[888,95012,95013],{"xmlns":890},[892,95014,95015,95027],{},[895,95016,95017,95019,95021,95023,95025],{},[898,95018,207],{},[1750,95020,1861],{},[898,95022,2573],{},[1750,95024,2624],{},[1742,95026,1744],{},[902,95028,95029],{"encoding":904},"a+b\u003C1",[123,95031,95032,1647,95034,1343,95064,1647,95066,2313],{},[38,95033,84016],{},[883,95035,95037],{"className":95036},[886],[888,95038,95039],{"xmlns":890},[892,95040,95041,95061],{},[895,95042,95043,95045,95051,95053],{},[898,95044,1773],{},[5535,95046,95047,95049],{},[898,95048,1776],{},[898,95050,2046],{},[1750,95052,1766],{},[5950,95054,95055,95057,95059],{},[898,95056,12471],{},[898,95058,2046],{},[1750,95060,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,95062,95063],{"encoding":904},"MP_L = Q'_L",[38,95065,86920],{},[883,95067,95069],{"className":95068},[886],[888,95070,95071],{"xmlns":890},[892,95072,95073,95093],{},[895,95074,95075,95077,95083,95085],{},[898,95076,1773],{},[5535,95078,95079,95081],{},[898,95080,1776],{},[898,95082,19435],{},[1750,95084,1766],{},[5950,95086,95087,95089,95091],{},[898,95088,12471],{},[898,95090,19435],{},[1750,95092,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,95094,95095],{"encoding":904},"MP_K = Q'_K",[123,95097,95098,1647,95100,2313],{},[38,95099,89134],{},[883,95101,95103],{"className":95102},[886],[888,95104,95105],{"xmlns":890},[892,95106,95107,95145],{},[895,95108,95109,95111,95113,95115,95117,95123,95125,95127,95129,95131,95133,95139,95141,95143],{},[898,95110,3429],{},[898,95112,12471],{},[1750,95114,1766],{},[898,95116,1773],{},[5535,95118,95119,95121],{},[898,95120,1776],{},[898,95122,2046],{},[1969,95124,2658],{},[898,95126,3429],{},[898,95128,2046],{},[1750,95130,1861],{},[898,95132,1773],{},[5535,95134,95135,95137],{},[898,95136,1776],{},[898,95138,19435],{},[1969,95140,2658],{},[898,95142,3429],{},[898,95144,19435],{},[902,95146,95147],{"encoding":904},"dQ = MP_L\\,dL + MP_K\\,dK",[123,95149,95150,10469,95152,2313],{},[38,95151,89479],{},[883,95153,95155],{"className":95154},[886],[888,95156,95157],{"xmlns":890},[892,95158,95159,95201],{},[895,95160,95161,95163,95171,95173,95175,95183,95185,95187,95189,95191,95193,95195,95197,95199],{},[898,95162,2046],{},[5950,95164,95165,95167,95169],{},[898,95166,12471],{},[898,95168,2046],{},[1750,95170,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,95172,1861],{},[898,95174,19435],{},[5950,95176,95177,95179,95181],{},[898,95178,12471],{},[898,95180,19435],{},[1750,95182,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,95184,1766],{},[898,95186,45783],{},[1969,95188,2658],{},[898,95190,12471],{},[1750,95192,1753],{"stretchy":1752},[898,95194,2046],{},[1750,95196,1917],{"separator":1916},[898,95198,19435],{},[1750,95200,1763],{"stretchy":1752},[902,95202,95203],{"encoding":904},"L Q'_L + K Q'_K = n\\,Q(L,K)",[123,95205,95206,95209,95210,2313],{},[38,95207,95208],{},"Izokvanta"," — křivka ",[883,95211,95213],{"className":95212},[886],[888,95214,95215],{"xmlns":890},[892,95216,95217,95235],{},[895,95218,95219,95221,95223,95225,95227,95229,95231,95233],{},[898,95220,12471],{},[1750,95222,1753],{"stretchy":1752},[898,95224,2046],{},[1750,95226,1917],{"separator":1916},[898,95228,19435],{},[1750,95230,1763],{"stretchy":1752},[1750,95232,1766],{},[898,95234,89720],{},[902,95236,95237],{"encoding":904},"Q(L, K) = q",[123,95239,95240,1647,95242,2313],{},[38,95241,89909],{},[883,95243,95245],{"className":95244},[886],[888,95246,95247],{"xmlns":890},[892,95248,95249,95279],{},[895,95250,95251,95253,95255,95257,95259,95261,95263,95269,95271,95273],{},[898,95252,1773],{},[898,95254,13658],{},[898,95256,5326],{},[898,95258,1779],{},[1750,95260,1766],{},[898,95262,1773],{},[5535,95264,95265,95267],{},[898,95266,1776],{},[898,95268,2046],{},[898,95270,1748],{"mathvariant":1747},[898,95272,1773],{},[5535,95274,95275,95277],{},[898,95276,1776],{},[898,95278,19435],{},[902,95280,83728],{"encoding":904},[123,95282,95283,1647,95286,2313],{},[38,95284,95285],{},"Substituční vztah",[883,95287,95289],{"className":95288},[886],[888,95290,95291],{"xmlns":890},[892,95292,95293,95317],{},[895,95294,95295,95297,95299,95301,95303,95305,95307,95309,95311,95313,95315],{},[898,95296,2666],{"mathvariant":1747},[898,95298,19435],{},[1750,95300,2274],{},[1750,95302,1758],{},[898,95304,1773],{},[898,95306,13658],{},[898,95308,5326],{},[898,95310,1779],{},[1969,95312,2658],{},[898,95314,3429],{},[898,95316,2046],{},[902,95318,95319],{"encoding":904},"\\Delta K \\approx -MRTS\\,dL",[115,95321,11524],{"id":11523},[120,95323,95324,95421,95428,95435],{},[123,95325,95326,1647,95328,95331,95332,1343,95335,95338,95339,95342,95343,95362,95363,2440,95382,95385,95386,95405,95406,1783],{},[38,95327,59646],{},[207,95329,784],{"className":95330,"dataFsResolvedFilePath":782,"href":783},[210]," (parciální derivace, totální diferenciál), ",[207,95333,12053],{"className":95334,"dataFsResolvedFilePath":764,"href":765},[210],[207,95336,793],{"className":95337,"dataFsResolvedFilePath":791,"href":792},[210]," (optimalizace produkce s rozpočtovým omezením), ",[207,95340,880],{"className":95341,"dataFsResolvedFilePath":878,"href":879},[210]," (paralela: izokvanty ↔ indiferenční křivky, ",[883,95344,95346],{"className":95345},[886],[888,95347,95348],{"xmlns":890},[892,95349,95350,95360],{},[895,95351,95352,95354,95356,95358],{},[898,95353,1773],{},[898,95355,13658],{},[898,95357,5326],{},[898,95359,1779],{},[902,95361,20232],{"encoding":904}," ↔ ",[883,95364,95366],{"className":95365},[886],[888,95367,95368],{"xmlns":890},[892,95369,95370,95380],{},[895,95371,95372,95374,95376,95378],{},[898,95373,1773],{},[898,95375,13658],{},[898,95377,1812],{},[898,95379,1779],{},[902,95381,20236],{"encoding":904},[207,95383,13491],{"className":95384,"dataFsResolvedFilePath":827,"href":828},[210]," (analogie principu max ",[883,95387,95389],{"className":95388},[886],[888,95390,95391],{"xmlns":890},[892,95392,95393,95403],{},[895,95394,95395,95397],{},[898,95396,13916],{},[5535,95398,95399,95401],{},[898,95400,1776],{},[898,95402,2046],{},[902,95404,83556],{"encoding":904}," ↔ min ",[883,95407,95409],{"className":95408},[886],[888,95410,95411],{"xmlns":890},[892,95412,95413,95419],{},[895,95414,95415,95417],{},[898,95416,13916],{},[898,95418,1812],{},[902,95420,64483],{"encoding":904},[123,95422,95423,1647,95425,2313],{},[38,95424,13467],{},[207,95426,13496],{"className":95427,"dataFsResolvedFilePath":848,"href":849},[210],[123,95429,95430,1647,95432,2313],{},[38,95431,11540],{},[207,95433,1094],{"className":95434,"dataFsResolvedFilePath":838,"href":839},[210],[123,95436,95437,1647,95439,2313],{},[38,95438,11531],{},[207,95440,11535],{"className":95441,"dataFsResolvedFilePath":1644,"href":1645},[210],{"title":641,"searchDepth":642,"depth":642,"links":95443},[95444,95445,95446,95450,95452,95457,95458,95465,95466,95468,95469,95470,95472,95477,95478,95479,95483,95484],{"id":83751,"depth":642,"text":83752},{"id":83888,"depth":642,"text":83889},{"id":83991,"depth":642,"text":95447,"children":95448},"Mezní produkt práce (MPLMP_L)",[95449],{"id":84437,"depth":649,"text":84438},{"id":84926,"depth":642,"text":95451},"Průměrný produkt práce (APLAP_L)",{"id":85044,"depth":642,"text":85045,"children":95453},[95454,95455,95456],{"id":85281,"depth":649,"text":74424},{"id":85592,"depth":649,"text":85593},{"id":86312,"depth":649,"text":86313},{"id":86884,"depth":642,"text":86885},{"id":86987,"depth":642,"text":86988,"children":95459},[95460,95461,95463,95464],{"id":87346,"depth":649,"text":87347},{"id":87845,"depth":649,"text":95462},"Parametr efektivity AA",{"id":87916,"depth":649,"text":87917},{"id":46102,"depth":649,"text":88256},{"id":88443,"depth":642,"text":88444},{"id":88782,"depth":642,"text":95467},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":89473,"depth":642,"text":89474},{"id":83817,"depth":642,"text":19414},{"id":89884,"depth":642,"text":95471},"Mezní míra technické substituce (MRTSMRTS)",{"id":90750,"depth":642,"text":90751,"children":95473},[95474,95475,95476],{"id":90754,"depth":649,"text":90755},{"id":91397,"depth":649,"text":91398},{"id":91678,"depth":649,"text":91679},{"id":92024,"depth":642,"text":92025},{"id":58804,"depth":642,"text":58805},{"id":92374,"depth":642,"text":92375,"children":95480},[95481,95482],{"id":49373,"depth":649,"text":49374},{"id":92893,"depth":649,"text":92894},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Fprodukce",{"title":83387,"description":641},[1138,1136],"topics\u002Fprodukce",[1128,19448,95491,95492,95493,83817,95494,95495],"produkcni-funkce","mpl-apl","cobb-douglas","mrts","euler","ZO2oG_qVOhQee90SJRry02Lau2bGvK2gaOFbwchTg1Y",{"id":95498,"title":95499,"body":95500,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":104447,"navigation":664,"path":104448,"seo":104449,"sources":104450,"stem":104451,"tags":104452,"type":11664,"updated":677,"__hash__":104455},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":9,"value":95501,"toc":104421},[95502,95505,95507,95704,95713,95717,95720,95773,95777,95789,95793,95796,95813,95936,95942,96086,96096,96100,96135,96173,96221,96278,96338,96380,96956,96960,97043,97152,97245,97503,97506,97559,97670,97752,97756,97767,98000,98055,98061,98101,98164,98175,98366,98472,98625,98673,98678,98792,98830,98956,99002,99029,99106,99181,99261,99391,99452,99540,99544,99547,99616,99699,99706,99766,100076,100080,100086,100139,100155,100206,100344,100420,100533,100850,100854,100861,101021,101080,101084,101106,101203,101324,101438,101461,101524,101581,101833,101841,101845,101852,102106,102156,102212,102215,102379,102383,102481,102483,102515,102519,102652,102894,103078,103246,103553,103686,103873,103885,103887,104322,104324],[12,95503,95499],{"id":95504},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[115,95506,1637],{"id":1636},[724,95508,95509,1647,95511,95542,95543,95546,95547,95577,95578,95596,95597,95637,95638,95641,95642,95655,95656,37176,95659,95672,95673,95686,95687,95700,95701,2313],{},[38,95510,880],{},[883,95512,95514],{"className":95513},[886],[888,95515,95516],{"xmlns":890},[892,95517,95518,95540],{},[895,95519,95520,95522,95524,95530,95532,95538],{},[898,95521,900],{},[1750,95523,1753],{"stretchy":1752},[5535,95525,95526,95528],{},[898,95527,12471],{},[1742,95529,1744],{},[1750,95531,1917],{"separator":1916},[5535,95533,95534,95536],{},[898,95535,12471],{},[1742,95537,1872],{},[1750,95539,1763],{"stretchy":1752},[902,95541,25916],{"encoding":904}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[38,95544,95545],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[883,95548,95550],{"className":95549},[886],[888,95551,95552],{"xmlns":890},[892,95553,95554,95574],{},[895,95555,95556,95558,95564,95566],{},[898,95557,1773],{},[5535,95559,95560,95562],{},[898,95561,900],{},[898,95563,27363],{},[1750,95565,1766],{},[5950,95567,95568,95570,95572],{},[898,95569,900],{},[898,95571,27363],{},[1750,95573,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,95575,95576],{"encoding":904},"MU_i = U'_i",", indiferenční křivky ",[883,95579,95581],{"className":95580},[886],[888,95582,95583],{"xmlns":890},[892,95584,95585,95593],{},[895,95586,95587,95589,95591],{},[898,95588,900],{},[1750,95590,1766],{},[898,95592,9365],{},[902,95594,95595],{"encoding":904},"U = c"," a mezní míra komoditní substituce ",[883,95598,95600],{"className":95599},[886],[888,95601,95602],{"xmlns":890},[892,95603,95604,95634],{},[895,95605,95606,95608,95610,95612,95614,95616,95618,95624,95626,95628],{},[898,95607,1773],{},[898,95609,13658],{},[898,95611,1812],{},[898,95613,1779],{},[1750,95615,1766],{},[898,95617,1773],{},[5535,95619,95620,95622],{},[898,95621,900],{},[1742,95623,1744],{},[898,95625,1748],{"mathvariant":1747},[898,95627,1773],{},[5535,95629,95630,95632],{},[898,95631,900],{},[1742,95633,1872],{},[902,95635,95636],{"encoding":904},"MRCS = MU_1\u002FMU_2",". Tato stránka pokrývá ",[38,95639,95640],{},"teorii užitečnosti"," — funkce ",[883,95643,95645],{"className":95644},[886],[888,95646,95647],{"xmlns":890},[892,95648,95649,95653],{},[895,95650,95651],{},[898,95652,900],{},[902,95654,900],{"encoding":904},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[38,95657,95658],{},"Optimalizaci spotřebitele",[883,95660,95662],{"className":95661},[886],[888,95663,95664],{"xmlns":890},[892,95665,95666,95670],{},[895,95667,95668],{},[898,95669,900],{},[902,95671,900],{"encoding":904}," při rozpočtu, min ",[883,95674,95676],{"className":95675},[886],[888,95677,95678],{"xmlns":890},[892,95679,95680,95684],{},[895,95681,95682],{},[898,95683,1705],{},[902,95685,1705],{"encoding":904}," při dané ",[883,95688,95690],{"className":95689},[886],[888,95691,95692],{"xmlns":890},[892,95693,95694,95698],{},[895,95695,95696],{},[898,95697,900],{},[902,95699,900],{"encoding":904},", Lagrange, funkce poptávky) viz ",[207,95702,913],{"className":95703,"dataFsResolvedFilePath":911,"href":912},[210],[724,95705,95706,95707,95709,95710,2313],{},"Kapitola 6 knihy ",[614,95708,11535],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[207,95711,45677],{"className":95712,"dataFsResolvedFilePath":911,"href":912},[210],[115,95714,95716],{"id":95715},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[724,95718,95719],{},"Po prostudování této kapitoly byste měli umět:",[120,95721,95722,95728,95737,95742,95745,95751,95757,95760,95766],{},[123,95723,95724,95725,1917],{},"vyložit, co se rozumí termínem ",[38,95726,95727],{},"užitečnost",[123,95729,95730,95731,2028,95734,1917],{},"definovat pojmy ",[38,95732,95733],{},"svazek zboží",[38,95735,95736],{},"funkce užitečnosti",[123,95738,83766,95739,83773],{},[38,95740,95741],{},"mezní užitečnosti",[123,95743,95744],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[123,95746,83793,95747,95750],{},[38,95748,95749],{},"Cobb-Douglasových"," funkcí užitečnosti,",[123,95752,83814,95753,95756],{},[38,95754,95755],{},"křivky užitečnosti"," (indiferenční křivky),",[123,95758,95759],{},"vyjmenovat jejich základní vlastnosti,",[123,95761,83766,95762,95765],{},[38,95763,95764],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[123,95767,95768,95769,95772],{},"řešit ",[38,95770,95771],{},"optimalizační úlohy"," s ohledem na užitečnost.",[115,95774,95776],{"id":95775},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[724,95778,95779,95780,95784,95785,95788],{},"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 ",[207,95781,95783],{"className":95782,"dataFsResolvedFilePath":800,"href":801},[210],"poptávku",". Centrálním pojmem je ",[38,95786,95787],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[198,95790,95792],{"id":95791},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[724,95794,95795],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[120,95797,95798,95804],{},[123,95799,95800,95803],{},[38,95801,95802],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[123,95805,95806,95809,95810,95812],{},[38,95807,95808],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[38,95811,95545],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1785,95814,95815],{},[724,95816,95817,95819,95820,95823,95824,1647,95837,95840,95841,2028,95854,95873,95874,1343,95900,95927,95928,95931,95932,95935],{},[883,95818,5454],{}," Pozor — ordinalisté užitečnost ",[38,95821,95822],{},"neměří","\nV ordinalistickém přístupu hodnoty funkce ",[883,95825,95827],{"className":95826},[886],[888,95828,95829],{"xmlns":890},[892,95830,95831,95835],{},[895,95832,95833],{},[898,95834,900],{},[902,95836,900],{"encoding":904},[38,95838,95839],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[883,95842,95844],{"className":95843},[886],[888,95845,95846],{"xmlns":890},[892,95847,95848,95852],{},[895,95849,95850],{},[898,95851,900],{},[902,95853,900],{"encoding":904},[883,95855,95857],{"className":95856},[886],[888,95858,95859],{"xmlns":890},[892,95860,95861,95870],{},[895,95862,95863],{},[3215,95864,95865,95867],{"accent":1916},[898,95866,900],{},[1750,95868,95869],{},"~",[902,95871,95872],{"encoding":904},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[883,95875,95877],{"className":95876},[886],[888,95878,95879],{"xmlns":890},[892,95880,95881,95897],{},[895,95882,95883,95889,95891],{},[3215,95884,95885,95887],{"accent":1916},[898,95886,900],{},[1750,95888,95869],{},[1750,95890,1766],{},[1699,95892,95893,95895],{},[898,95894,900],{},[1742,95896,1872],{},[902,95898,95899],{"encoding":904},"\\tilde U = U^2",[883,95901,95903],{"className":95902},[886],[888,95904,95905],{"xmlns":890},[892,95906,95907,95924],{},[895,95908,95909,95915,95917,95920,95922],{},[3215,95910,95911,95913],{"accent":1916},[898,95912,900],{},[1750,95914,95869],{},[1750,95916,1766],{},[898,95918,95919],{},"ln",[1750,95921,65123],{},[898,95923,900],{},[902,95925,95926],{"encoding":904},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[38,95929,95930],{},"porovnání"," mezi svazky a ",[38,95933,95934],{},"poměry"," mezních veličin.",[724,95937,95938,95939,2366],{},"Ordinalistický přístup vychází z ",[38,95940,95941],{},"pěti hlavních předpokladů",[152,95943,95944,95950,95956,96074,96080],{},[123,95945,95946,95949],{},[38,95947,95948],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[123,95951,95952,95955],{},[38,95953,95954],{},"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.",[123,95957,95958,95961,95962,70664,95975,95988,95989,70664,96002,12605,96015,96018,96019,2028,96038,71493,96056,2313],{},[38,95959,95960],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[883,95963,95965],{"className":95964},[886],[888,95966,95967],{"xmlns":890},[892,95968,95969,95973],{},[895,95970,95971],{},[898,95972,13916],{},[902,95974,13916],{"encoding":904},[883,95976,95978],{"className":95977},[886],[888,95979,95980],{"xmlns":890},[892,95981,95982,95986],{},[895,95983,95984],{},[898,95985,7097],{},[902,95987,7097],{"encoding":904},", nebude jindy preferovat ",[883,95990,95992],{"className":95991},[886],[888,95993,95994],{"xmlns":890},[892,95995,95996,96000],{},[895,95997,95998],{},[898,95999,7097],{},[902,96001,7097],{"encoding":904},[883,96003,96005],{"className":96004},[886],[888,96006,96007],{"xmlns":890},[892,96008,96009,96013],{},[895,96010,96011],{},[898,96012,13916],{},[902,96014,13916],{"encoding":904},[38,96016,96017],{},"Tranzitivita",": pokud ",[883,96020,96022],{"className":96021},[886],[888,96023,96024],{"xmlns":890},[892,96025,96026,96035],{},[895,96027,96028,96030,96033],{},[898,96029,13916],{},[1750,96031,96032],{},"≻",[898,96034,7097],{},[902,96036,96037],{"encoding":904},"A \\succ B",[883,96039,96041],{"className":96040},[886],[888,96042,96043],{"xmlns":890},[892,96044,96045,96053],{},[895,96046,96047,96049,96051],{},[898,96048,7097],{},[1750,96050,96032],{},[898,96052,1812],{},[902,96054,96055],{"encoding":904},"B \\succ C",[883,96057,96059],{"className":96058},[886],[888,96060,96061],{"xmlns":890},[892,96062,96063,96071],{},[895,96064,96065,96067,96069],{},[898,96066,13916],{},[1750,96068,96032],{},[898,96070,1812],{},[902,96072,96073],{"encoding":904},"A \\succ C",[123,96075,96076,96079],{},[38,96077,96078],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[123,96081,96082,96085],{},[38,96083,96084],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[724,96087,96088,96089,96092,96093,2313],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[614,96090,96091],{},"preference"," a na příbuzné ",[614,96094,96095],{},"funkci užitečnosti",[115,96097,96099],{"id":96098},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[724,96101,96102,96103,96116,96117,96120,96121,96134],{},"Uvažujme ",[883,96104,96106],{"className":96105},[886],[888,96107,96108],{"xmlns":890},[892,96109,96110,96114],{},[895,96111,96112],{},[898,96113,45783],{},[902,96115,45783],{"encoding":904}," různých zboží. ",[38,96118,96119],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[883,96122,96124],{"className":96123},[886],[888,96125,96126],{"xmlns":890},[892,96127,96128,96132],{},[895,96129,96130],{},[898,96131,45783],{},[902,96133,45783],{"encoding":904},"-tice",[724,96136,96137],{},[883,96138,96140],{"className":96139},[886],[888,96141,96142],{"xmlns":890},[892,96143,96144,96170],{},[895,96145,96146,96148,96154,96156,96158,96160,96166,96168],{},[1750,96147,1753],{"stretchy":1752},[5535,96149,96150,96152],{},[898,96151,12471],{},[1742,96153,1744],{},[1750,96155,1917],{"separator":1916},[1750,96157,19282],{},[1750,96159,1917],{"separator":1916},[5535,96161,96162,96164],{},[898,96163,12471],{},[898,96165,45783],{},[1750,96167,1763],{"stretchy":1752},[1750,96169,1917],{"separator":1916},[902,96171,96172],{"encoding":904},"(Q_1, \\dots, Q_n),",[724,96174,2590,96175,96192,96193,96206,96207,96210,96211,96214,96215,96218,96219,2366],{},[883,96176,96178],{"className":96177},[886],[888,96179,96180],{"xmlns":890},[892,96181,96182,96190],{},[895,96183,96184],{},[5535,96185,96186,96188],{},[898,96187,12471],{},[898,96189,27363],{},[902,96191,56461],{"encoding":904}," značí množství ",[883,96194,96196],{"className":96195},[886],[888,96197,96198],{"xmlns":890},[892,96199,96200,96204],{},[895,96201,96202],{},[898,96203,27363],{},[902,96205,27363],{"encoding":904},"-tého zboží. Spotřebitel je schopen svazky ",[38,96208,96209],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[38,96212,96213],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[38,96216,96217],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[38,96220,96095],{},[883,96222,96224],{"className":96223},[886],[888,96225,96226],{"xmlns":890,"display":36989},[892,96227,96228,96275],{},[4577,96229,96230],{"width":36994},[4582,96231,96232,96234,96268,96270],{},[4585,96233],{"width":36999},[4585,96235,96236],{},[895,96237,96238,96240,96242,96244,96246,96252,96254,96256,96258,96264,96266],{},[898,96239,900],{},[1750,96241,1766],{},[898,96243,900],{},[1750,96245,1753],{"stretchy":1752},[5535,96247,96248,96250],{},[898,96249,12471],{},[1742,96251,1744],{},[1750,96253,1917],{"separator":1916},[1750,96255,19282],{},[1750,96257,1917],{"separator":1916},[5535,96259,96260,96262],{},[898,96261,12471],{},[898,96263,45783],{},[1750,96265,1763],{"stretchy":1752},[1750,96267,1917],{"separator":1916},[4585,96269],{"width":36999},[4585,96271,96272],{},[1969,96273,96274],{},"(6.1)",[902,96276,96277],{"encoding":904},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[724,96279,2590,96280,96310,96311,96333,96334,96337],{},[883,96281,96283],{"className":96282},[886],[888,96284,96285],{"xmlns":890},[892,96286,96287,96307],{},[895,96288,96289,96295,96297,96299,96301],{},[5535,96290,96291,96293],{},[898,96292,12471],{},[1742,96294,1744],{},[1750,96296,1917],{"separator":1916},[1750,96298,19282],{},[1750,96300,1917],{"separator":1916},[5535,96302,96303,96305],{},[898,96304,12471],{},[898,96306,45783],{},[902,96308,96309],{"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 ",[883,96312,96314],{"className":96313},[886],[888,96315,96316],{"xmlns":890},[892,96317,96318,96330],{},[895,96319,96320,96322,96324],{},[898,96321,900],{},[1750,96323,1917],{"separator":1916},[3215,96325,96326,96328],{"accent":1916},[898,96327,900],{},[1750,96329,95869],{},[902,96331,96332],{"encoding":904},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[38,96335,96336],{},"monotónní transformace"," zachovávající pořadí.",[724,96339,96340,96341,10469,96344,2313],{},"Dále se omezíme na funkce pro ",[38,96342,96343],{},"dvě zboží",[883,96345,96347],{"className":96346},[886],[888,96348,96349],{"xmlns":890},[892,96350,96351,96377],{},[895,96352,96353,96355,96357,96359,96361,96367,96369,96375],{},[898,96354,900],{},[1750,96356,1766],{},[898,96358,900],{},[1750,96360,1753],{"stretchy":1752},[5535,96362,96363,96365],{},[898,96364,12471],{},[1742,96366,1744],{},[1750,96368,1917],{"separator":1916},[5535,96370,96371,96373],{},[898,96372,12471],{},[1742,96374,1872],{},[1750,96376,1763],{"stretchy":1752},[902,96378,96379],{"encoding":904},"U = U(Q_1, Q_2)",[1785,96381,96382,96457],{},[724,96383,96384,96386,96387,2366],{},[883,96385,61618],{}," Příklad 6.1 — uspořádání a indiference\nPro ",[883,96388,96390],{"className":96389},[886],[888,96391,96392],{"xmlns":890},[892,96393,96394,96454],{},[895,96395,96396,96398,96400,96402,96404,96410,96412,96418,96420,96426,96428,96430,96432],{},[898,96397,900],{},[1750,96399,1766],{},[898,96401,900],{},[1750,96403,1753],{"stretchy":1752},[5535,96405,96406,96408],{},[898,96407,12471],{},[1742,96409,1744],{},[1750,96411,1917],{"separator":1916},[5535,96413,96414,96416],{},[898,96415,12471],{},[1742,96417,1872],{},[1750,96419,1917],{"separator":1916},[5535,96421,96422,96424],{},[898,96423,12471],{},[1742,96425,7822],{},[1750,96427,1763],{"stretchy":1752},[1750,96429,1766],{},[1742,96431,1872],{},[17761,96433,96434],{},[895,96435,96436,96442,96448],{},[5535,96437,96438,96440],{},[898,96439,12471],{},[1742,96441,1744],{},[5535,96443,96444,96446],{},[898,96445,12471],{},[1742,96447,1872],{},[5535,96449,96450,96452],{},[898,96451,12471],{},[1742,96453,7822],{},[902,96455,96456],{"encoding":904},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[120,96458,96459,96652],{},[123,96460,96461,96462,96488,96489,22544,96515,2028,96574,8164,96634,18067],{},"svazek ",[883,96463,96465],{"className":96464},[886],[888,96466,96467],{"xmlns":890},[892,96468,96469,96485],{},[895,96470,96471,96473,96475,96477,96479,96481,96483],{},[1750,96472,1753],{"stretchy":1752},[1742,96474,50785],{},[1750,96476,1917],{"separator":1916},[1742,96478,7859],{},[1750,96480,1917],{"separator":1916},[1742,96482,50763],{},[1750,96484,1763],{"stretchy":1752},[902,96486,96487],{"encoding":904},"(16, 4, 64)"," je preferován před ",[883,96490,96492],{"className":96491},[886],[888,96493,96494],{"xmlns":890},[892,96495,96496,96512],{},[895,96497,96498,96500,96502,96504,96506,96508,96510],{},[1750,96499,1753],{"stretchy":1752},[1742,96501,13663],{},[1750,96503,1917],{"separator":1916},[1742,96505,13663],{},[1750,96507,1917],{"separator":1916},[1742,96509,75520],{},[1750,96511,1763],{"stretchy":1752},[902,96513,96514],{"encoding":904},"(9, 9, 27)",[883,96516,96518],{"className":96517},[886],[888,96519,96520],{"xmlns":890},[892,96521,96522,96571],{},[895,96523,96524,96526,96528,96530,96532,96534,96536,96538,96540,96542,96544,96558,96560,96562,96567,96569],{},[898,96525,900],{},[1750,96527,1753],{"stretchy":1752},[1742,96529,50785],{},[1750,96531,1917],{"separator":1916},[1742,96533,7859],{},[1750,96535,1917],{"separator":1916},[1742,96537,50763],{},[1750,96539,1763],{"stretchy":1752},[1750,96541,1766],{},[1742,96543,1872],{},[17761,96545,96546],{},[895,96547,96548,96550,96552,96554,96556],{},[1742,96549,50785],{},[1750,96551,8009],{},[1742,96553,7859],{},[1750,96555,8009],{},[1742,96557,50763],{},[1750,96559,1766],{},[1742,96561,1872],{},[17761,96563,96564],{},[1742,96565,96566],{},"4096",[1750,96568,1766],{},[1742,96570,15270],{},[902,96572,96573],{"encoding":904},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[883,96575,96577],{"className":96576},[886],[888,96578,96579],{"xmlns":890},[892,96580,96581,96631],{},[895,96582,96583,96585,96587,96589,96591,96593,96595,96597,96599,96601,96603,96617,96619,96621,96626,96628],{},[898,96584,900],{},[1750,96586,1753],{"stretchy":1752},[1742,96588,13663],{},[1750,96590,1917],{"separator":1916},[1742,96592,13663],{},[1750,96594,1917],{"separator":1916},[1742,96596,75520],{},[1750,96598,1763],{"stretchy":1752},[1750,96600,1766],{},[1742,96602,1872],{},[17761,96604,96605],{},[895,96606,96607,96609,96611,96613,96615],{},[1742,96608,13663],{},[1750,96610,8009],{},[1742,96612,13663],{},[1750,96614,8009],{},[1742,96616,75520],{},[1750,96618,1766],{},[1742,96620,1872],{},[17761,96622,96623],{},[1742,96624,96625],{},"2187",[1750,96627,6792],{},[1742,96629,96630],{},"93,53",[902,96632,96633],{"encoding":904},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[883,96635,96637],{"className":96636},[886],[888,96638,96639],{"xmlns":890},[892,96640,96641,96649],{},[895,96642,96643,96645,96647],{},[1742,96644,15270],{},[1750,96646,2604],{},[1742,96648,96630],{},[902,96650,96651],{"encoding":904},"128 > 93{,}53",[123,96653,96654,96655,2028,96681,96707,96708,2028,96748,96789,96790,96836,96837,2028,96863,12525,96889,2028,96907,96925,96926,2313],{},"svazky ",[883,96656,96658],{"className":96657},[886],[888,96659,96660],{"xmlns":890},[892,96661,96662,96678],{},[895,96663,96664,96666,96668,96670,96672,96674,96676],{},[1750,96665,1753],{"stretchy":1752},[1742,96667,7859],{},[1750,96669,1917],{"separator":1916},[1742,96671,15239],{},[1750,96673,1917],{"separator":1916},[1742,96675,1872],{},[1750,96677,1763],{"stretchy":1752},[902,96679,96680],{"encoding":904},"(4, 8, 2)",[883,96682,96684],{"className":96683},[886],[888,96685,96686],{"xmlns":890},[892,96687,96688,96704],{},[895,96689,96690,96692,96694,96696,96698,96700,96702],{},[1750,96691,1753],{"stretchy":1752},[1742,96693,50763],{},[1750,96695,1917],{"separator":1916},[1742,96697,1744],{},[1750,96699,1917],{"separator":1916},[1742,96701,7859],{},[1750,96703,1763],{"stretchy":1752},[902,96705,96706],{"encoding":904},"(64, 1, 4)"," jsou indiferentní, protože ",[883,96709,96711],{"className":96710},[886],[888,96712,96713],{"xmlns":890},[892,96714,96715,96745],{},[895,96716,96717,96719,96721,96723,96725,96727,96729,96731,96733,96735,96737,96741,96743],{},[898,96718,900],{},[1750,96720,1753],{"stretchy":1752},[1742,96722,7859],{},[1750,96724,1917],{"separator":1916},[1742,96726,15239],{},[1750,96728,1917],{"separator":1916},[1742,96730,1872],{},[1750,96732,1763],{"stretchy":1752},[1750,96734,1766],{},[1742,96736,1872],{},[17761,96738,96739],{},[1742,96740,50763],{},[1750,96742,1766],{},[1742,96744,50785],{},[902,96746,96747],{"encoding":904},"U(4,8,2) = 2\\sqrt{64} = 16",[883,96749,96751],{"className":96750},[886],[888,96752,96753],{"xmlns":890},[892,96754,96755,96786],{},[895,96756,96757,96759,96761,96763,96765,96767,96769,96771,96773,96775,96777,96782,96784],{},[898,96758,900],{},[1750,96760,1753],{"stretchy":1752},[1742,96762,50763],{},[1750,96764,1917],{"separator":1916},[1742,96766,1744],{},[1750,96768,1917],{"separator":1916},[1742,96770,7859],{},[1750,96772,1763],{"stretchy":1752},[1750,96774,1766],{},[1742,96776,1872],{},[17761,96778,96779],{},[1742,96780,96781],{},"256",[1750,96783,1766],{},[1742,96785,81282],{},[902,96787,96788],{"encoding":904},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[883,96791,96793],{"className":96792},[886],[888,96794,96795],{"xmlns":890},[892,96796,96797,96833],{},[895,96798,96799,96801,96803,96805,96807,96809,96811,96813,96815,96817,96819,96821,96823,96825,96827,96829,96831],{},[898,96800,900],{},[1750,96802,1753],{"stretchy":1752},[1742,96804,7859],{},[1750,96806,1917],{"separator":1916},[1742,96808,15239],{},[1750,96810,1917],{"separator":1916},[1742,96812,1872],{},[1750,96814,1763],{"stretchy":1752},[1750,96816,1766],{},[898,96818,900],{},[1750,96820,1753],{"stretchy":1752},[1742,96822,50763],{},[1750,96824,1917],{"separator":1916},[1742,96826,1744],{},[1750,96828,1917],{"separator":1916},[1742,96830,7859],{},[1750,96832,1763],{"stretchy":1752},[902,96834,96835],{"encoding":904},"U(4,8,2) = U(64,1,4)","; ověření: ",[883,96838,96840],{"className":96839},[886],[888,96841,96842],{"xmlns":890},[892,96843,96844,96860],{},[895,96845,96846,96848,96850,96852,96854,96856,96858],{},[1742,96847,7859],{},[1750,96849,8009],{},[1742,96851,15239],{},[1750,96853,8009],{},[1742,96855,1872],{},[1750,96857,1766],{},[1742,96859,50763],{},[902,96861,96862],{"encoding":904},"4 \\cdot 8 \\cdot 2 = 64",[883,96864,96866],{"className":96865},[886],[888,96867,96868],{"xmlns":890},[892,96869,96870,96886],{},[895,96871,96872,96874,96876,96878,96880,96882,96884],{},[1742,96873,50763],{},[1750,96875,8009],{},[1742,96877,1744],{},[1750,96879,8009],{},[1742,96881,7859],{},[1750,96883,1766],{},[1742,96885,96781],{},[902,96887,96888],{"encoding":904},"64 \\cdot 1 \\cdot 4 = 256",[883,96890,96892],{"className":96891},[886],[888,96893,96894],{"xmlns":890},[892,96895,96896,96904],{},[895,96897,96898,96900,96902],{},[898,96899,900],{},[1750,96901,1766],{},[1742,96903,50785],{},[902,96905,96906],{"encoding":904},"U = 16",[883,96908,96910],{"className":96909},[886],[888,96911,96912],{"xmlns":890},[892,96913,96914,96922],{},[895,96915,96916,96918,96920],{},[898,96917,900],{},[1750,96919,1766],{},[1742,96921,81282],{},[902,96923,96924],{"encoding":904},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[883,96927,96929],{"className":96928},[886],[888,96930,96931],{"xmlns":890},[892,96932,96933,96953],{},[895,96934,96935,96941,96947],{},[5535,96936,96937,96939],{},[898,96938,12471],{},[1742,96940,1744],{},[5535,96942,96943,96945],{},[898,96944,12471],{},[1742,96946,1872],{},[5535,96948,96949,96951],{},[898,96950,12471],{},[1742,96952,7822],{},[902,96954,96955],{"encoding":904},"Q_1 Q_2 Q_3",[115,96957,96959],{"id":96958},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[724,96961,96962,96963,2433,96998,1647,97001,50737,97018,2084,97035,97038,97039,97042],{},"Pro funkci užitečnosti ",[883,96964,96966],{"className":96965},[886],[888,96967,96968],{"xmlns":890},[892,96969,96970,96996],{},[895,96971,96972,96974,96976,96978,96980,96986,96988,96994],{},[898,96973,900],{},[1750,96975,1766],{},[898,96977,900],{},[1750,96979,1753],{"stretchy":1752},[5535,96981,96982,96984],{},[898,96983,12471],{},[1742,96985,1744],{},[1750,96987,1917],{"separator":1916},[5535,96989,96990,96992],{},[898,96991,12471],{},[1742,96993,1872],{},[1750,96995,1763],{"stretchy":1752},[902,96997,96379],{"encoding":904},[38,96999,97000],{},"mezní užitečnost",[883,97002,97004],{"className":97003},[886],[888,97005,97006],{"xmlns":890},[892,97007,97008,97016],{},[895,97009,97010],{},[5535,97011,97012,97014],{},[898,97013,12471],{},[1742,97015,1744],{},[902,97017,37925],{"encoding":904},[883,97019,97021],{"className":97020},[886],[888,97022,97023],{"xmlns":890},[892,97024,97025,97033],{},[895,97026,97027],{},[5535,97028,97029,97031],{},[898,97030,12471],{},[1742,97032,1872],{},[902,97034,37944],{"encoding":904},[38,97036,97037],{},"marginal utility",") parciální ",[207,97040,1145],{"className":97041,"dataFsResolvedFilePath":764,"href":765},[210]," užitečnosti podle příslušné proměnné:",[883,97044,97046],{"className":97045},[886],[888,97047,97048],{"xmlns":890,"display":36989},[892,97049,97050,97149],{},[4577,97051,97052],{"width":36994},[4582,97053,97054,97056,97142,97144],{},[4585,97055],{"width":36999},[4585,97057,97058],{},[895,97059,97060,97062,97068,97070,97078,97080,97098,97100,97102,97104,97110,97112,97120,97122,97140],{},[898,97061,1773],{},[5535,97063,97064,97066],{},[898,97065,900],{},[1742,97067,1744],{},[1750,97069,1766],{},[5950,97071,97072,97074,97076],{},[898,97073,900],{},[1742,97075,1744],{},[1750,97077,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,97079,1766],{},[3423,97081,97082,97088],{},[895,97083,97084,97086],{},[898,97085,8773],{"mathvariant":1747},[898,97087,900],{},[895,97089,97090,97092],{},[898,97091,8773],{"mathvariant":1747},[5535,97093,97094,97096],{},[898,97095,12471],{},[1742,97097,1744],{},[1750,97099,1917],{"separator":1916},[2125,97101],{"width":24875},[898,97103,1773],{},[5535,97105,97106,97108],{},[898,97107,900],{},[1742,97109,1872],{},[1750,97111,1766],{},[5950,97113,97114,97116,97118],{},[898,97115,900],{},[1742,97117,1872],{},[1750,97119,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,97121,1766],{},[3423,97123,97124,97130],{},[895,97125,97126,97128],{},[898,97127,8773],{"mathvariant":1747},[898,97129,900],{},[895,97131,97132,97134],{},[898,97133,8773],{"mathvariant":1747},[5535,97135,97136,97138],{},[898,97137,12471],{},[1742,97139,1872],{},[898,97141,2313],{"mathvariant":1747},[4585,97143],{"width":36999},[4585,97145,97146],{},[1969,97147,97148],{},"(6.2)",[902,97150,97151],{"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}",[724,97153,97154,97155,97189,97190,97220,97221,1647,97224,2313],{},"Pro pevné ",[883,97156,97158],{"className":97157},[886],[888,97159,97160],{"xmlns":890},[892,97161,97162,97186],{},[895,97163,97164,97170,97172,97174,97176,97182,97184],{},[5535,97165,97166,97168],{},[898,97167,12471],{},[1742,97169,1744],{},[1750,97171,1766],{},[898,97173,207],{},[1750,97175,1917],{"separator":1916},[5535,97177,97178,97180],{},[898,97179,12471],{},[1742,97181,1872],{},[1750,97183,1766],{},[898,97185,2573],{},[902,97187,97188],{"encoding":904},"Q_1 = a, Q_2 = b"," se hodnota ",[883,97191,97193],{"className":97192},[886],[888,97194,97195],{"xmlns":890},[892,97196,97197,97217],{},[895,97198,97199,97201,97207,97209,97211,97213,97215],{},[898,97200,1773],{},[5535,97202,97203,97205],{},[898,97204,900],{},[1742,97206,1744],{},[1750,97208,1753],{"stretchy":1752},[898,97210,207],{},[1750,97212,1917],{"separator":1916},[898,97214,2573],{},[1750,97216,1763],{"stretchy":1752},[902,97218,97219],{"encoding":904},"MU_1(a, b)"," nazývá mezní užitečnost ",[38,97222,97223],{},"v bodě (na hladině)",[883,97225,97227],{"className":97226},[886],[888,97228,97229],{"xmlns":890},[892,97230,97231,97243],{},[895,97232,97233,97235,97237,97239,97241],{},[1750,97234,5141],{"stretchy":1752},[898,97236,207],{},[1750,97238,1917],{"separator":1916},[898,97240,2573],{},[1750,97242,5158],{"stretchy":1752},[902,97244,20457],{"encoding":904},[1785,97246,97247],{},[724,97248,97249,97251,97252,97282,97311,97312,12299,97325,2984,97342,97363,97364,12359,97381,4321,97394,97411,97412,97434,97435,97464,97465,16121,97485,97502],{},[883,97250,1791],{}," Intuice — co říká ",[883,97253,97255],{"className":97254},[886],[888,97256,97257],{"xmlns":890},[892,97258,97259,97279],{},[895,97260,97261,97263,97269,97271,97273,97275,97277],{},[898,97262,1773],{},[5535,97264,97265,97267],{},[898,97266,900],{},[1742,97268,1744],{},[1750,97270,1753],{"stretchy":1752},[898,97272,207],{},[1750,97274,1917],{"separator":1916},[898,97276,2573],{},[1750,97278,1763],{"stretchy":1752},[902,97280,97281],{"encoding":904},"MU_1(a,b)",[883,97283,97285],{"className":97284},[886],[888,97286,97287],{"xmlns":890},[892,97288,97289,97309],{},[895,97290,97291,97293,97299,97301,97303,97305,97307],{},[898,97292,1773],{},[5535,97294,97295,97297],{},[898,97296,900],{},[1742,97298,1744],{},[1750,97300,1753],{"stretchy":1752},[898,97302,207],{},[1750,97304,1917],{"separator":1916},[898,97306,2573],{},[1750,97308,1763],{"stretchy":1752},[902,97310,97219],{"encoding":904}," je rychlost změny ",[883,97313,97315],{"className":97314},[886],[888,97316,97317],{"xmlns":890},[892,97318,97319,97323],{},[895,97320,97321],{},[898,97322,900],{},[902,97324,900],{"encoding":904},[883,97326,97328],{"className":97327},[886],[888,97329,97330],{"xmlns":890},[892,97331,97332,97340],{},[895,97333,97334],{},[5535,97335,97336,97338],{},[898,97337,12471],{},[1742,97339,1744],{},[902,97341,37925],{"encoding":904},[883,97343,97345],{"className":97344},[886],[888,97346,97347],{"xmlns":890},[892,97348,97349,97361],{},[895,97350,97351,97353,97355,97357,97359],{},[1750,97352,5141],{"stretchy":1752},[898,97354,207],{},[1750,97356,1917],{"separator":1916},[898,97358,2573],{},[1750,97360,5158],{"stretchy":1752},[902,97362,20457],{"encoding":904},". Přibližně: změní-li se ",[883,97365,97367],{"className":97366},[886],[888,97368,97369],{"xmlns":890},[892,97370,97371,97379],{},[895,97372,97373],{},[5535,97374,97375,97377],{},[898,97376,12471],{},[1742,97378,1744],{},[902,97380,37925],{"encoding":904},[883,97382,97384],{"className":97383},[886],[888,97385,97386],{"xmlns":890},[892,97387,97388,97392],{},[895,97389,97390],{},[898,97391,207],{},[902,97393,207],{"encoding":904},[883,97395,97397],{"className":97396},[886],[888,97398,97399],{"xmlns":890},[892,97400,97401,97409],{},[895,97402,97403,97405,97407],{},[898,97404,207],{},[1750,97406,1861],{},[1742,97408,1744],{},[902,97410,12390],{"encoding":904}," při pevném ",[883,97413,97415],{"className":97414},[886],[888,97416,97417],{"xmlns":890},[892,97418,97419,97431],{},[895,97420,97421,97427,97429],{},[5535,97422,97423,97425],{},[898,97424,12471],{},[1742,97426,1872],{},[1750,97428,1766],{},[898,97430,2573],{},[902,97432,97433],{"encoding":904},"Q_2 = b",", změní se užitečnost zhruba o ",[883,97436,97438],{"className":97437},[886],[888,97439,97440],{"xmlns":890},[892,97441,97442,97462],{},[895,97443,97444,97446,97452,97454,97456,97458,97460],{},[898,97445,1773],{},[5535,97447,97448,97450],{},[898,97449,900],{},[1742,97451,1744],{},[1750,97453,1753],{"stretchy":1752},[898,97455,207],{},[1750,97457,1917],{"separator":1916},[898,97459,2573],{},[1750,97461,1763],{"stretchy":1752},[902,97463,97219],{"encoding":904},". Stejně tak ",[883,97466,97468],{"className":97467},[886],[888,97469,97470],{"xmlns":890},[892,97471,97472,97482],{},[895,97473,97474,97476],{},[898,97475,1773],{},[5535,97477,97478,97480],{},[898,97479,900],{},[1742,97481,1872],{},[902,97483,97484],{"encoding":904},"MU_2",[883,97486,97488],{"className":97487},[886],[888,97489,97490],{"xmlns":890},[892,97491,97492,97500],{},[895,97493,97494],{},[5535,97495,97496,97498],{},[898,97497,12471],{},[1742,97499,1872],{},[902,97501,37944],{"encoding":904},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[198,97504,89134],{"id":97505},"totální-diferenciál",[724,97507,97508,97509,57263,97525,97555,97556,2366],{},"Přibližnou změnu užitečnosti ",[883,97510,97512],{"className":97511},[886],[888,97513,97514],{"xmlns":890},[892,97515,97516,97522],{},[895,97517,97518,97520],{},[898,97519,2666],{"mathvariant":1747},[898,97521,900],{},[902,97523,97524],{"encoding":904},"\\Delta U",[883,97526,97528],{"className":97527},[886],[888,97529,97530],{"xmlns":890},[892,97531,97532,97552],{},[895,97533,97534,97536,97542,97544,97546],{},[898,97535,3429],{"mathvariant":1747},[5535,97537,97538,97540],{},[898,97539,12471],{},[1742,97541,1744],{},[1750,97543,1917],{"separator":1916},[898,97545,3429],{"mathvariant":1747},[5535,97547,97548,97550],{},[898,97549,12471],{},[1742,97551,1872],{},[902,97553,97554],{"encoding":904},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[38,97557,97558],{},"totálního diferenciálu",[883,97560,97562],{"className":97561},[886],[888,97563,97564],{"xmlns":890,"display":36989},[892,97565,97566,97667],{},[4577,97567,97568],{"width":36994},[4582,97569,97570,97572,97660,97662],{},[4585,97571],{"width":36999},[4585,97573,97574],{},[895,97575,97576,97578,97580,97582,97584,97586,97588,97596,97598,97604,97606,97614,97616,97622,97624,97626,97632,97634,97640,97642,97644,97650,97652,97658],{},[898,97577,2666],{"mathvariant":1747},[898,97579,900],{},[1750,97581,2274],{},[898,97583,3429],{"mathvariant":1747},[898,97585,900],{},[1750,97587,1766],{},[5950,97589,97590,97592,97594],{},[898,97591,900],{},[1742,97593,1744],{},[1750,97595,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[898,97597,3429],{"mathvariant":1747},[5535,97599,97600,97602],{},[898,97601,12471],{},[1742,97603,1744],{},[1750,97605,1861],{},[5950,97607,97608,97610,97612],{},[898,97609,900],{},[1742,97611,1872],{},[1750,97613,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[898,97615,3429],{"mathvariant":1747},[5535,97617,97618,97620],{},[898,97619,12471],{},[1742,97621,1872],{},[1750,97623,1766],{},[898,97625,1773],{},[5535,97627,97628,97630],{},[898,97629,900],{},[1742,97631,1744],{},[898,97633,3429],{"mathvariant":1747},[5535,97635,97636,97638],{},[898,97637,12471],{},[1742,97639,1744],{},[1750,97641,1861],{},[898,97643,1773],{},[5535,97645,97646,97648],{},[898,97647,900],{},[1742,97649,1872],{},[898,97651,3429],{"mathvariant":1747},[5535,97653,97654,97656],{},[898,97655,12471],{},[1742,97657,1872],{},[898,97659,2313],{"mathvariant":1747},[4585,97661],{"width":36999},[4585,97663,97664],{},[1969,97665,97666],{},"(6.3)",[902,97668,97669],{"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}",[724,97671,84392,97672,2313],{},[883,97673,97675],{"className":97674},[886],[888,97676,97677],{"xmlns":890},[892,97678,97679,97749],{},[895,97680,97681,97683,97685,97687,97689,97691,97697,97699,97701,97707,97709,97715,97717,97719,97725,97727,97729,97731,97733,97739,97741,97747],{},[898,97682,2666],{"mathvariant":1747},[898,97684,900],{},[1750,97686,1766],{},[898,97688,900],{},[1750,97690,1753],{"stretchy":1752},[5535,97692,97693,97695],{},[898,97694,12471],{},[1742,97696,1744],{},[1750,97698,1861],{},[898,97700,3429],{"mathvariant":1747},[5535,97702,97703,97705],{},[898,97704,12471],{},[1742,97706,1744],{},[1750,97708,1917],{"separator":1916},[5535,97710,97711,97713],{},[898,97712,12471],{},[1742,97714,1872],{},[1750,97716,1861],{},[898,97718,3429],{"mathvariant":1747},[5535,97720,97721,97723],{},[898,97722,12471],{},[1742,97724,1872],{},[1750,97726,1763],{"stretchy":1752},[1750,97728,1758],{},[898,97730,900],{},[1750,97732,1753],{"stretchy":1752},[5535,97734,97735,97737],{},[898,97736,12471],{},[1742,97738,1744],{},[1750,97740,1917],{"separator":1916},[5535,97742,97743,97745],{},[898,97744,12471],{},[1742,97746,1872],{},[1750,97748,1763],{"stretchy":1752},[902,97750,97751],{"encoding":904},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[115,97753,97755],{"id":97754},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[724,97757,97758,97759,97762,97763,97766],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[38,97760,97761],{},"rostoucí užitečnost"," (předpoklad 4) a ",[38,97764,97765],{},"klesající mezní užitečnost"," (předpoklad 5).",[724,97768,97769,97772,97773,50737,97799,97825,97826,1343,97858,97890,97891,2028,97945,97999],{},[38,97770,97771],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[883,97774,97776],{"className":97775},[886],[888,97777,97778],{"xmlns":890},[892,97779,97780,97796],{},[895,97781,97782,97788,97790],{},[5535,97783,97784,97786],{},[898,97785,12471],{},[1742,97787,1872],{},[1750,97789,1766],{},[5535,97791,97792,97794],{},[898,97793,207],{},[1742,97795,2607],{},[902,97797,97798],{"encoding":904},"Q_2 = a_0",[883,97800,97802],{"className":97801},[886],[888,97803,97804],{"xmlns":890},[892,97805,97806,97822],{},[895,97807,97808,97814,97816],{},[5535,97809,97810,97812],{},[898,97811,12471],{},[1742,97813,1744],{},[1750,97815,1766],{},[5535,97817,97818,97820],{},[898,97819,2573],{},[1742,97821,2607],{},[902,97823,97824],{"encoding":904},"Q_1 = b_0"," jsou funkce jedné proměnné ",[883,97827,97829],{"className":97828},[886],[888,97830,97831],{"xmlns":890},[892,97832,97833,97855],{},[895,97834,97835,97837,97839,97845,97847,97853],{},[898,97836,900],{},[1750,97838,1753],{"stretchy":1752},[5535,97840,97841,97843],{},[898,97842,12471],{},[1742,97844,1744],{},[1750,97846,1917],{"separator":1916},[5535,97848,97849,97851],{},[898,97850,207],{},[1742,97852,2607],{},[1750,97854,1763],{"stretchy":1752},[902,97856,97857],{"encoding":904},"U(Q_1, a_0)",[883,97859,97861],{"className":97860},[886],[888,97862,97863],{"xmlns":890},[892,97864,97865,97887],{},[895,97866,97867,97869,97871,97877,97879,97885],{},[898,97868,900],{},[1750,97870,1753],{"stretchy":1752},[5535,97872,97873,97875],{},[898,97874,2573],{},[1742,97876,2607],{},[1750,97878,1917],{"separator":1916},[5535,97880,97881,97883],{},[898,97882,12471],{},[1742,97884,1872],{},[1750,97886,1763],{"stretchy":1752},[902,97888,97889],{"encoding":904},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[883,97892,97894],{"className":97893},[886],[888,97895,97896],{"xmlns":890},[892,97897,97898,97942],{},[895,97899,97900,97938,97940],{},[3586,97901,97902],{"scriptlevel":2607,"displaystyle":1916},[3423,97903,97904,97928],{},[895,97905,97906,97908,97910,97912,97918,97920,97926],{},[898,97907,3429],{"mathvariant":1747},[898,97909,900],{},[1750,97911,1753],{"stretchy":1752},[5535,97913,97914,97916],{},[898,97915,12471],{},[1742,97917,1744],{},[1750,97919,1917],{"separator":1916},[5535,97921,97922,97924],{},[898,97923,207],{},[1742,97925,2607],{},[1750,97927,1763],{"stretchy":1752},[895,97929,97930,97932],{},[898,97931,3429],{"mathvariant":1747},[5535,97933,97934,97936],{},[898,97935,12471],{},[1742,97937,1744],{},[1750,97939,2604],{},[1742,97941,2607],{},[902,97943,97944],{"encoding":904},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[883,97946,97948],{"className":97947},[886],[888,97949,97950],{"xmlns":890},[892,97951,97952,97996],{},[895,97953,97954,97992,97994],{},[3586,97955,97956],{"scriptlevel":2607,"displaystyle":1916},[3423,97957,97958,97982],{},[895,97959,97960,97962,97964,97966,97972,97974,97980],{},[898,97961,3429],{"mathvariant":1747},[898,97963,900],{},[1750,97965,1753],{"stretchy":1752},[5535,97967,97968,97970],{},[898,97969,2573],{},[1742,97971,2607],{},[1750,97973,1917],{"separator":1916},[5535,97975,97976,97978],{},[898,97977,12471],{},[1742,97979,1872],{},[1750,97981,1763],{"stretchy":1752},[895,97983,97984,97986],{},[898,97985,3429],{"mathvariant":1747},[5535,97987,97988,97990],{},[898,97989,12471],{},[1742,97991,1872],{},[1750,97993,2604],{},[1742,97995,2607],{},[902,97997,97998],{"encoding":904},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[883,98001,98003],{"className":98002},[886],[888,98004,98005],{"xmlns":890,"display":36989},[892,98006,98007,98052],{},[4577,98008,98009],{"width":36994},[4582,98010,98011,98013,98045,98047],{},[4585,98012],{"width":36999},[4585,98014,98015],{},[895,98016,98017,98025,98027,98029,98031,98033,98041,98043],{},[5950,98018,98019,98021,98023],{},[898,98020,900],{},[1742,98022,1744],{},[1750,98024,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,98026,2604],{},[1742,98028,2607],{},[1750,98030,1917],{"separator":1916},[2125,98032],{"width":24875},[5950,98034,98035,98037,98039],{},[898,98036,900],{},[1742,98038,1872],{},[1750,98040,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,98042,2604],{},[1742,98044,22073],{},[4585,98046],{"width":36999},[4585,98048,98049],{},[1969,98050,98051],{},"(6.4)",[902,98053,98054],{"encoding":904},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[724,98056,98057,98058,98060],{},"Tedy mezní užitečnosti obou zboží jsou ",[38,98059,61600],{}," — užitečnost roste s množstvím každého zboží.",[724,98062,98063,98066,98067,98097,98098,2366],{},[38,98064,98065],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[883,98068,98070],{"className":98069},[886],[888,98071,98072],{"xmlns":890},[892,98073,98074,98094],{},[895,98075,98076,98084,98086],{},[5950,98077,98078,98080,98082],{},[898,98079,900],{},[1742,98081,1744],{},[1750,98083,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,98085,1917],{"separator":1916},[5950,98087,98088,98090,98092],{},[898,98089,900],{},[1742,98091,1872],{},[1750,98093,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,98095,98096],{"encoding":904},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[38,98099,98100],{},"záporné",[883,98102,98104],{"className":98103},[886],[888,98105,98106],{"xmlns":890,"display":36989},[892,98107,98108,98161],{},[4577,98109,98110],{"width":36994},[4582,98111,98112,98114,98154,98156],{},[4585,98113],{"width":36999},[4585,98115,98116],{},[895,98117,98118,98130,98132,98134,98136,98138,98150,98152],{},[5950,98119,98120,98122,98124],{},[898,98121,900],{},[1742,98123,12582],{},[895,98125,98126,98128],{},[1750,98127,3815],{"mathvariant":1747},[1750,98129,3815],{"mathvariant":1747},[1750,98131,2624],{},[1742,98133,2607],{},[1750,98135,1917],{"separator":1916},[2125,98137],{"width":24875},[5950,98139,98140,98142,98144],{},[898,98141,900],{},[1742,98143,41469],{},[895,98145,98146,98148],{},[1750,98147,3815],{"mathvariant":1747},[1750,98149,3815],{"mathvariant":1747},[1750,98151,2624],{},[1742,98153,22073],{},[4585,98155],{"width":36999},[4585,98157,98158],{},[1969,98159,98160],{},"(6.5)",[902,98162,98163],{"encoding":904},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[724,98165,98166,98167,98170,98171,2313],{},"Podmínka (6.5) je známa jako ",[38,98168,98169],{},"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 ",[207,98172,98174],{"className":98173,"dataFsResolvedFilePath":857,"href":858},[210],"produkční teorie",[724,98176,98177,98178,2028,98210,98242,98243,2028,98269,98295,98296,98324,98325,2028,98327,98329,98330,98365],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[883,98179,98181],{"className":98180},[886],[888,98182,98183],{"xmlns":890},[892,98184,98185,98207],{},[895,98186,98187,98189,98191,98197,98199,98205],{},[898,98188,900],{},[1750,98190,1753],{"stretchy":1752},[5535,98192,98193,98195],{},[898,98194,12471],{},[1742,98196,1744],{},[1750,98198,1917],{"separator":1916},[5535,98200,98201,98203],{},[898,98202,2573],{},[1742,98204,2607],{},[1750,98206,1763],{"stretchy":1752},[902,98208,98209],{"encoding":904},"U(Q_1, b_0)",[883,98211,98213],{"className":98212},[886],[888,98214,98215],{"xmlns":890},[892,98216,98217,98239],{},[895,98218,98219,98221,98223,98229,98231,98237],{},[898,98220,900],{},[1750,98222,1753],{"stretchy":1752},[5535,98224,98225,98227],{},[898,98226,207],{},[1742,98228,2607],{},[1750,98230,1917],{"separator":1916},[5535,98232,98233,98235],{},[898,98234,12471],{},[1742,98236,1872],{},[1750,98238,1763],{"stretchy":1752},[902,98240,98241],{"encoding":904},"U(a_0, Q_2)"," v souřadnicových rovinách ",[883,98244,98246],{"className":98245},[886],[888,98247,98248],{"xmlns":890},[892,98249,98250,98266],{},[895,98251,98252,98254,98256,98258,98264],{},[1750,98253,1753],{"stretchy":1752},[898,98255,900],{},[1750,98257,1917],{"separator":1916},[5535,98259,98260,98262],{},[898,98261,12471],{},[1742,98263,1744],{},[1750,98265,1763],{"stretchy":1752},[902,98267,98268],{"encoding":904},"(U, Q_1)",[883,98270,98272],{"className":98271},[886],[888,98273,98274],{"xmlns":890},[892,98275,98276,98292],{},[895,98277,98278,98280,98282,98284,98290],{},[1750,98279,1753],{"stretchy":1752},[898,98281,900],{},[1750,98283,1917],{"separator":1916},[5535,98285,98286,98288],{},[898,98287,12471],{},[1742,98289,1872],{},[1750,98291,1763],{"stretchy":1752},[902,98293,98294],{"encoding":904},"(U, Q_2)"," (obrázek 6.1). Tyto křivky procházejí počátkem (neboť obvykle ",[883,98297,98299],{"className":98298},[886],[888,98300,98301],{"xmlns":890},[892,98302,98303,98321],{},[895,98304,98305,98307,98309,98311,98313,98315,98317,98319],{},[898,98306,900],{},[1750,98308,1753],{"stretchy":1752},[1742,98310,2607],{},[1750,98312,1917],{"separator":1916},[1742,98314,2607],{},[1750,98316,1763],{"stretchy":1752},[1750,98318,1766],{},[1742,98320,2607],{},[902,98322,98323],{"encoding":904},"U(0, 0) = 0","), jsou ",[38,98326,23261],{},[38,98328,47411],{},". Typický tvar grafu ",[883,98331,98333],{"className":98332},[886],[888,98334,98335],{"xmlns":890},[892,98336,98337,98363],{},[895,98338,98339,98341,98343,98345,98347,98353,98355,98361],{},[898,98340,900],{},[1750,98342,1766],{},[898,98344,900],{},[1750,98346,1753],{"stretchy":1752},[5535,98348,98349,98351],{},[898,98350,12471],{},[1742,98352,1744],{},[1750,98354,1917],{"separator":1916},[5535,98356,98357,98359],{},[898,98358,12471],{},[1742,98360,1872],{},[1750,98362,1763],{"stretchy":1752},[902,98364,96379],{"encoding":904}," — plocha v prostoru — je na obrázku 6.2.",[724,98367,98368],{},[614,98369,98370,98371,97411,98399,98420,98421,97411,98449,98471],{},"Obrázek 6.1 — typické průběhy funkce užitečnosti ",[883,98372,98374],{"className":98373},[886],[888,98375,98376],{"xmlns":890},[892,98377,98378,98396],{},[895,98379,98380,98382,98384,98390,98392,98394],{},[898,98381,900],{},[1750,98383,1753],{"stretchy":1752},[5535,98385,98386,98388],{},[898,98387,12471],{},[1742,98389,1744],{},[1750,98391,1917],{"separator":1916},[898,98393,2573],{},[1750,98395,1763],{"stretchy":1752},[902,98397,98398],{"encoding":904},"U(Q_1, b)",[883,98400,98402],{"className":98401},[886],[888,98403,98404],{"xmlns":890},[892,98405,98406,98418],{},[895,98407,98408,98414,98416],{},[5535,98409,98410,98412],{},[898,98411,12471],{},[1742,98413,1872],{},[1750,98415,1766],{},[898,98417,2573],{},[902,98419,97433],{"encoding":904}," (vlevo) a ",[883,98422,98424],{"className":98423},[886],[888,98425,98426],{"xmlns":890},[892,98427,98428,98446],{},[895,98429,98430,98432,98434,98436,98438,98444],{},[898,98431,900],{},[1750,98433,1753],{"stretchy":1752},[898,98435,207],{},[1750,98437,1917],{"separator":1916},[5535,98439,98440,98442],{},[898,98441,12471],{},[1742,98443,1872],{},[1750,98445,1763],{"stretchy":1752},[902,98447,98448],{"encoding":904},"U(a, Q_2)",[883,98450,98452],{"className":98451},[886],[888,98453,98454],{"xmlns":890},[892,98455,98456,98468],{},[895,98457,98458,98464,98466],{},[5535,98459,98460,98462],{},[898,98461,12471],{},[1742,98463,1744],{},[1750,98465,1766],{},[898,98467,207],{},[902,98469,98470],{"encoding":904},"Q_1 = a"," (vpravo) pro různé hladiny druhé proměnné.",[724,98473,98474],{},[614,98475,98476,98477,98512,98513,98543,98544,2028,98567,98589,98590,2313],{},"Obrázek 6.2 — plocha funkce užitečnosti ",[883,98478,98480],{"className":98479},[886],[888,98481,98482],{"xmlns":890},[892,98483,98484,98510],{},[895,98485,98486,98488,98490,98492,98494,98500,98502,98508],{},[898,98487,900],{},[1750,98489,1766],{},[898,98491,900],{},[1750,98493,1753],{"stretchy":1752},[5535,98495,98496,98498],{},[898,98497,12471],{},[1742,98499,1744],{},[1750,98501,1917],{"separator":1916},[5535,98503,98504,98506],{},[898,98505,12471],{},[1742,98507,1872],{},[1750,98509,1763],{"stretchy":1752},[902,98511,96379],{"encoding":904}," nad rovinou ",[883,98514,98516],{"className":98515},[886],[888,98517,98518],{"xmlns":890},[892,98519,98520,98540],{},[895,98521,98522,98524,98530,98532,98538],{},[1750,98523,1753],{"stretchy":1752},[5535,98525,98526,98528],{},[898,98527,12471],{},[1742,98529,1744],{},[1750,98531,1917],{"separator":1916},[5535,98533,98534,98536],{},[898,98535,12471],{},[1742,98537,1872],{},[1750,98539,1763],{"stretchy":1752},[902,98541,98542],{"encoding":904},"(Q_1, Q_2)"," s řezy rovinami ",[883,98545,98547],{"className":98546},[886],[888,98548,98549],{"xmlns":890},[892,98550,98551,98564],{},[895,98552,98553,98559,98561],{},[5535,98554,98555,98557],{},[898,98556,12471],{},[1742,98558,1744],{},[1750,98560,1766],{},[1969,98562,98563],{},"const",[902,98565,98566],{"encoding":904},"Q_1 = \\text{const}",[883,98568,98570],{"className":98569},[886],[888,98571,98572],{"xmlns":890},[892,98573,98574,98586],{},[895,98575,98576,98582,98584],{},[5535,98577,98578,98580],{},[898,98579,12471],{},[1742,98581,1872],{},[1750,98583,1766],{},[1969,98585,98563],{},[902,98587,98588],{"encoding":904},"Q_2 = \\text{const}"," a s křivkou ",[883,98591,98593],{"className":98592},[886],[888,98594,98595],{"xmlns":890},[892,98596,98597,98623],{},[895,98598,98599,98601,98603,98609,98611,98617,98619,98621],{},[898,98600,900],{},[1750,98602,1753],{"stretchy":1752},[5535,98604,98605,98607],{},[898,98606,12471],{},[1742,98608,1744],{},[1750,98610,1917],{"separator":1916},[5535,98612,98613,98615],{},[898,98614,12471],{},[1742,98616,1872],{},[1750,98618,1763],{"stretchy":1752},[1750,98620,1766],{},[898,98622,9365],{},[902,98624,19404],{"encoding":904},[198,98626,98628,98629],{"id":98627},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[883,98630,98632],{"className":98631},[886],[888,98633,98634],{"xmlns":890},[892,98635,98636,98670],{},[895,98637,98638,98640,98642,98656],{},[898,98639,900],{},[1750,98641,1766],{},[5950,98643,98644,98646,98648],{},[898,98645,12471],{},[1742,98647,1744],{},[895,98649,98650,98652,98654],{},[1742,98651,1744],{},[898,98653,1748],{"mathvariant":1747},[1742,98655,1872],{},[5950,98657,98658,98660,98662],{},[898,98659,12471],{},[1742,98661,1872],{},[895,98663,98664,98666,98668],{},[1742,98665,1744],{},[898,98667,1748],{"mathvariant":1747},[1742,98669,7822],{},[902,98671,98672],{"encoding":904},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[724,98674,98675],{},[38,98676,98677],{},"Ověření (6.4) a (6.5).",[883,98679,98681],{"className":98680},[886],[888,98682,98683],{"xmlns":890,"display":36989},[892,98684,98685,98789],{},[895,98686,98687,98695,98697,98705,98721,98735,98737,98739,98747,98749,98757,98771,98787],{},[5950,98688,98689,98691,98693],{},[898,98690,900],{},[1742,98692,1744],{},[1750,98694,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,98696,1766],{},[3586,98698,98699],{"scriptlevel":2607,"displaystyle":1752},[3423,98700,98701,98703],{},[1742,98702,1744],{},[1742,98704,1872],{},[5950,98706,98707,98709,98711],{},[898,98708,12471],{},[1742,98710,1744],{},[895,98712,98713,98715,98717,98719],{},[1750,98714,1758],{},[1742,98716,1744],{},[898,98718,1748],{"mathvariant":1747},[1742,98720,1872],{},[5950,98722,98723,98725,98727],{},[898,98724,12471],{},[1742,98726,1872],{},[895,98728,98729,98731,98733],{},[1742,98730,1744],{},[898,98732,1748],{"mathvariant":1747},[1742,98734,7822],{},[1750,98736,1917],{"separator":1916},[2125,98738],{"width":24875},[5950,98740,98741,98743,98745],{},[898,98742,900],{},[1742,98744,1872],{},[1750,98746,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,98748,1766],{},[3586,98750,98751],{"scriptlevel":2607,"displaystyle":1752},[3423,98752,98753,98755],{},[1742,98754,1744],{},[1742,98756,7822],{},[5950,98758,98759,98761,98763],{},[898,98760,12471],{},[1742,98762,1744],{},[895,98764,98765,98767,98769],{},[1742,98766,1744],{},[898,98768,1748],{"mathvariant":1747},[1742,98770,1872],{},[5950,98772,98773,98775,98777],{},[898,98774,12471],{},[1742,98776,1872],{},[895,98778,98779,98781,98783,98785],{},[1750,98780,1758],{},[1742,98782,1872],{},[898,98784,1748],{"mathvariant":1747},[1742,98786,7822],{},[1750,98788,1917],{"separator":1916},[902,98790,98791],{"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},",[724,98793,98794,98795,98829],{},"zřejmě ",[883,98796,98798],{"className":98797},[886],[888,98799,98800],{"xmlns":890},[892,98801,98802,98826],{},[895,98803,98804,98812,98814,98822,98824],{},[5950,98805,98806,98808,98810],{},[898,98807,900],{},[1742,98809,1744],{},[1750,98811,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,98813,1917],{"separator":1916},[5950,98815,98816,98818,98820],{},[898,98817,900],{},[1742,98819,1872],{},[1750,98821,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,98823,2604],{},[1742,98825,2607],{},[902,98827,98828],{"encoding":904},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[883,98831,98833],{"className":98832},[886],[888,98834,98835],{"xmlns":890,"display":36989},[892,98836,98837,98953],{},[895,98838,98839,98851,98853,98855,98863,98879,98893,98895,98897,98909,98911,98913,98921,98935,98951],{},[5950,98840,98841,98843,98845],{},[898,98842,900],{},[1742,98844,12582],{},[895,98846,98847,98849],{},[1750,98848,3815],{"mathvariant":1747},[1750,98850,3815],{"mathvariant":1747},[1750,98852,1766],{},[1750,98854,1758],{},[3586,98856,98857],{"scriptlevel":2607,"displaystyle":1752},[3423,98858,98859,98861],{},[1742,98860,1744],{},[1742,98862,7859],{},[5950,98864,98865,98867,98869],{},[898,98866,12471],{},[1742,98868,1744],{},[895,98870,98871,98873,98875,98877],{},[1750,98872,1758],{},[1742,98874,7822],{},[898,98876,1748],{"mathvariant":1747},[1742,98878,1872],{},[5950,98880,98881,98883,98885],{},[898,98882,12471],{},[1742,98884,1872],{},[895,98886,98887,98889,98891],{},[1742,98888,1744],{},[898,98890,1748],{"mathvariant":1747},[1742,98892,7822],{},[1750,98894,1917],{"separator":1916},[2125,98896],{"width":24875},[5950,98898,98899,98901,98903],{},[898,98900,900],{},[1742,98902,41469],{},[895,98904,98905,98907],{},[1750,98906,3815],{"mathvariant":1747},[1750,98908,3815],{"mathvariant":1747},[1750,98910,1766],{},[1750,98912,1758],{},[3586,98914,98915],{"scriptlevel":2607,"displaystyle":1752},[3423,98916,98917,98919],{},[1742,98918,1872],{},[1742,98920,13663],{},[5950,98922,98923,98925,98927],{},[898,98924,12471],{},[1742,98926,1744],{},[895,98928,98929,98931,98933],{},[1742,98930,1744],{},[898,98932,1748],{"mathvariant":1747},[1742,98934,1872],{},[5950,98936,98937,98939,98941],{},[898,98938,12471],{},[1742,98940,1872],{},[895,98942,98943,98945,98947,98949],{},[1750,98944,1758],{},[1742,98946,7902],{},[898,98948,1748],{"mathvariant":1747},[1742,98950,7822],{},[1750,98952,1917],{"separator":1916},[902,98954,98955],{"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},",[724,98957,98958,98959,99001],{},"opět ",[883,98960,98962],{"className":98961},[886],[888,98963,98964],{"xmlns":890},[892,98965,98966,98998],{},[895,98967,98968,98980,98982,98994,98996],{},[5950,98969,98970,98972,98974],{},[898,98971,900],{},[1742,98973,12582],{},[895,98975,98976,98978],{},[1750,98977,3815],{"mathvariant":1747},[1750,98979,3815],{"mathvariant":1747},[1750,98981,1917],{"separator":1916},[5950,98983,98984,98986,98988],{},[898,98985,900],{},[1742,98987,41469],{},[895,98989,98990,98992],{},[1750,98991,3815],{"mathvariant":1747},[1750,98993,3815],{"mathvariant":1747},[1750,98995,2624],{},[1742,98997,2607],{},[902,98999,99000],{"encoding":904},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[724,99003,99004],{},[38,99005,99006,99007,2313],{},"(a) Mezní užitečnosti v bodě ",[883,99008,99010],{"className":99009},[886],[888,99011,99012],{"xmlns":890},[892,99013,99014,99026],{},[895,99015,99016,99018,99020,99022,99024],{},[1750,99017,5141],{"stretchy":1752},[1742,99019,4078],{},[1750,99021,1917],{"separator":1916},[1742,99023,4159],{},[1750,99025,5158],{"stretchy":1752},[902,99027,99028],{"encoding":904},"[100, 200]",[883,99030,99032],{"className":99031},[886],[888,99033,99034],{"xmlns":890,"display":36989},[892,99035,99036,99103],{},[895,99037,99038,99040,99046,99048,99050,99052,99054,99056,99058,99066,99068,99082,99084,99096,99098,99101],{},[898,99039,1773],{},[5535,99041,99042,99044],{},[898,99043,900],{},[1742,99045,1744],{},[1750,99047,1753],{"stretchy":1752},[1742,99049,4078],{},[1750,99051,1917],{"separator":1916},[1742,99053,4159],{},[1750,99055,1763],{"stretchy":1752},[1750,99057,1766],{},[3586,99059,99060],{"scriptlevel":2607,"displaystyle":1752},[3423,99061,99062,99064],{},[1742,99063,1744],{},[1742,99065,1872],{},[1750,99067,8009],{},[1699,99069,99070,99072],{},[1742,99071,4078],{},[895,99073,99074,99076,99078,99080],{},[1750,99075,1758],{},[1742,99077,1744],{},[898,99079,1748],{"mathvariant":1747},[1742,99081,1872],{},[1750,99083,8009],{},[1699,99085,99086,99088],{},[1742,99087,4159],{},[895,99089,99090,99092,99094],{},[1742,99091,1744],{},[898,99093,1748],{"mathvariant":1747},[1742,99095,7822],{},[1750,99097,6792],{},[1742,99099,99100],{},"0,4204",[1750,99102,1917],{"separator":1916},[902,99104,99105],{"encoding":904},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[883,99107,99109],{"className":99108},[886],[888,99110,99111],{"xmlns":890,"display":36989},[892,99112,99113,99178],{},[895,99114,99115,99117,99123,99125,99127,99129,99131,99133,99135,99143,99145,99157,99159,99173,99175],{},[898,99116,1773],{},[5535,99118,99119,99121],{},[898,99120,900],{},[1742,99122,1872],{},[1750,99124,1753],{"stretchy":1752},[1742,99126,4078],{},[1750,99128,1917],{"separator":1916},[1742,99130,4159],{},[1750,99132,1763],{"stretchy":1752},[1750,99134,1766],{},[3586,99136,99137],{"scriptlevel":2607,"displaystyle":1752},[3423,99138,99139,99141],{},[1742,99140,1744],{},[1742,99142,7822],{},[1750,99144,8009],{},[1699,99146,99147,99149],{},[1742,99148,4078],{},[895,99150,99151,99153,99155],{},[1742,99152,1744],{},[898,99154,1748],{"mathvariant":1747},[1742,99156,1872],{},[1750,99158,8009],{},[1699,99160,99161,99163],{},[1742,99162,4159],{},[895,99164,99165,99167,99169,99171],{},[1750,99166,1758],{},[1742,99168,1872],{},[898,99170,1748],{"mathvariant":1747},[1742,99172,7822],{},[1750,99174,6792],{},[1742,99176,99177],{},"0,63067.",[902,99179,99180],{"encoding":904},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[724,99182,99183,1647,99185,99220,99221,99242,99243,99260],{},[614,99184,18853],{},[883,99186,99188],{"className":99187},[886],[888,99189,99190],{"xmlns":890},[892,99191,99192,99217],{},[895,99193,99194,99196,99202,99204,99206,99208,99210,99212,99214],{},[898,99195,1773],{},[5535,99197,99198,99200],{},[898,99199,900],{},[1742,99201,1872],{},[1750,99203,1753],{"stretchy":1752},[1742,99205,4078],{},[1750,99207,1917],{"separator":1916},[1742,99209,4159],{},[1750,99211,1763],{"stretchy":1752},[1750,99213,6792],{},[1742,99215,99216],{},"0,63067",[902,99218,99219],{"encoding":904},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[883,99222,99224],{"className":99223},[886],[888,99225,99226],{"xmlns":890},[892,99227,99228,99240],{},[895,99229,99230,99232,99234,99236,99238],{},[1750,99231,5141],{"stretchy":1752},[1742,99233,4078],{},[1750,99235,1917],{"separator":1916},[1742,99237,4159],{},[1750,99239,5158],{"stretchy":1752},[902,99241,99028],{"encoding":904}," roste užitečnost při jednotkové změně ",[883,99244,99246],{"className":99245},[886],[888,99247,99248],{"xmlns":890},[892,99249,99250,99258],{},[895,99251,99252],{},[5535,99253,99254,99256],{},[898,99255,12471],{},[1742,99257,1872],{},[902,99259,37944],{"encoding":904}," přibližně o 0,63067.",[724,99262,99263,99282,99283,48107,99304,99321,99322,99348,99349,99366,99367,12825],{},[38,99264,99265,99266,99281],{},"(b) Odhad změny ",[883,99267,99269],{"className":99268},[886],[888,99270,99271],{"xmlns":890},[892,99272,99273,99279],{},[895,99274,99275,99277],{},[898,99276,2666],{"mathvariant":1747},[898,99278,900],{},[902,99280,97524],{"encoding":904}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[883,99284,99286],{"className":99285},[886],[888,99287,99288],{"xmlns":890},[892,99289,99290,99302],{},[895,99291,99292,99294,99296,99298,99300],{},[1750,99293,5141],{"stretchy":1752},[1742,99295,4078],{},[1750,99297,1917],{"separator":1916},[1742,99299,4159],{},[1750,99301,5158],{"stretchy":1752},[902,99303,99028],{"encoding":904},[883,99305,99307],{"className":99306},[886],[888,99308,99309],{"xmlns":890},[892,99310,99311,99319],{},[895,99312,99313],{},[5535,99314,99315,99317],{},[898,99316,12471],{},[1742,99318,1744],{},[902,99320,37925],{"encoding":904}," na 98 (tj. ",[883,99323,99325],{"className":99324},[886],[888,99326,99327],{"xmlns":890},[892,99328,99329,99345],{},[895,99330,99331,99333,99339,99341,99343],{},[898,99332,3429],{"mathvariant":1747},[5535,99334,99335,99337],{},[898,99336,12471],{},[1742,99338,1744],{},[1750,99340,1766],{},[1750,99342,1758],{},[1742,99344,1872],{},[902,99346,99347],{"encoding":904},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[883,99350,99352],{"className":99351},[886],[888,99353,99354],{"xmlns":890},[892,99355,99356,99364],{},[895,99357,99358],{},[5535,99359,99360,99362],{},[898,99361,12471],{},[1742,99363,1872],{},[902,99365,37944],{"encoding":904}," o 3 (tj. ",[883,99368,99370],{"className":99369},[886],[888,99371,99372],{"xmlns":890},[892,99373,99374,99388],{},[895,99375,99376,99378,99384,99386],{},[898,99377,3429],{"mathvariant":1747},[5535,99379,99380,99382],{},[898,99381,12471],{},[1742,99383,1872],{},[1750,99385,1766],{},[1742,99387,7822],{},[902,99389,99390],{"encoding":904},"\\mathrm{d} Q_2 = 3",[883,99392,99394],{"className":99393},[886],[888,99395,99396],{"xmlns":890,"display":36989},[892,99397,99398,99449],{},[895,99399,99400,99402,99404,99406,99408,99410,99412,99414,99416,99418,99420,99422,99424,99426,99428,99430,99432,99434,99436,99439,99441,99444,99446],{},[898,99401,2666],{"mathvariant":1747},[898,99403,900],{},[1750,99405,2274],{},[898,99407,3429],{"mathvariant":1747},[898,99409,900],{},[1750,99411,1766],{},[1742,99413,99100],{},[1750,99415,8009],{},[1750,99417,1753],{"stretchy":1752},[1750,99419,1758],{},[1742,99421,1872],{},[1750,99423,1763],{"stretchy":1752},[1750,99425,1861],{},[1742,99427,99216],{},[1750,99429,8009],{},[1742,99431,7822],{},[1750,99433,1766],{},[1750,99435,1758],{},[1742,99437,99438],{},"0,8408",[1750,99440,1861],{},[1742,99442,99443],{},"1,89201",[1750,99445,6792],{},[1742,99447,99448],{},"1,05.",[902,99450,99451],{"encoding":904},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[724,99453,99454,99455,99458,99459,99510,99511,2313],{},"Užitečnost se tedy zvýší přibližně o ",[38,99456,99457],{},"1,05",". Skutečná změna je ",[883,99460,99462],{"className":99461},[886],[888,99463,99464],{"xmlns":890},[892,99465,99466,99507],{},[895,99467,99468,99470,99472,99474,99476,99478,99481,99483,99486,99488,99490,99492,99494,99496,99498,99500,99502,99504],{},[898,99469,2666],{"mathvariant":1747},[898,99471,900],{},[1750,99473,1766],{},[898,99475,900],{},[1750,99477,1753],{"stretchy":1752},[1742,99479,99480],{},"98",[1750,99482,1917],{"separator":1916},[1742,99484,99485],{},"203",[1750,99487,1763],{"stretchy":1752},[1750,99489,1758],{},[898,99491,900],{},[1750,99493,1753],{"stretchy":1752},[1742,99495,4078],{},[1750,99497,1917],{"separator":1916},[1742,99499,4159],{},[1750,99501,1763],{"stretchy":1752},[1750,99503,6792],{},[1742,99505,99506],{},"1,031",[902,99508,99509],{"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 ",[883,99512,99514],{"className":99513},[886],[888,99515,99516],{"xmlns":890},[892,99517,99518,99538],{},[895,99519,99520,99522,99528,99530,99532],{},[898,99521,3429],{"mathvariant":1747},[5535,99523,99524,99526],{},[898,99525,12471],{},[1742,99527,1744],{},[1750,99529,1917],{"separator":1916},[898,99531,3429],{"mathvariant":1747},[5535,99533,99534,99536],{},[898,99535,12471],{},[1742,99537,1872],{},[902,99539,97554],{"encoding":904},[115,99541,99543],{"id":99542},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[724,99545,99546],{},"Nejčastěji používané funkce užitečnosti mají tvar",[883,99548,99550],{"className":99549},[886],[888,99551,99552],{"xmlns":890,"display":36989},[892,99553,99554,99613],{},[4577,99555,99556],{"width":36994},[4582,99557,99558,99560,99606,99608],{},[4585,99559],{"width":36999},[4585,99561,99562],{},[895,99563,99564,99566,99568,99574,99576,99582,99584,99586,99594,99596,99604],{},[898,99565,900],{},[1750,99567,1753],{"stretchy":1752},[5535,99569,99570,99572],{},[898,99571,12471],{},[1742,99573,1744],{},[1750,99575,1917],{"separator":1916},[5535,99577,99578,99580],{},[898,99579,12471],{},[1742,99581,1872],{},[1750,99583,1763],{"stretchy":1752},[1750,99585,1766],{},[5950,99587,99588,99590,99592],{},[898,99589,12471],{},[1742,99591,1744],{},[898,99593,207],{},[1750,99595,8009],{},[5950,99597,99598,99600,99602],{},[898,99599,12471],{},[1742,99601,1872],{},[898,99603,2573],{},[1750,99605,1917],{"separator":1916},[4585,99607],{"width":36999},[4585,99609,99610],{},[1969,99611,99612],{},"(6.6)",[902,99614,99615],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[724,99617,2590,99618,99636,99637,99639,99640,99644,99645,99675,99676,99698],{},[883,99619,99621],{"className":99620},[886],[888,99622,99623],{"xmlns":890},[892,99624,99625,99633],{},[895,99626,99627,99629,99631],{},[898,99628,207],{},[1750,99630,1917],{"separator":1916},[898,99632,2573],{},[902,99634,99635],{"encoding":904},"a, b"," jsou kladná čísla; nazývají se ",[38,99638,83622],{}," (v příbuznosti s produkčními funkcemi — viz ",[207,99641,99643],{"className":99642,"dataFsResolvedFilePath":857,"href":858},[210],"kapitola 5","). Obvykle se volí ",[883,99646,99648],{"className":99647},[886],[888,99649,99650],{"xmlns":890},[892,99651,99652,99672],{},[895,99653,99654,99656,99658,99660,99662,99664,99666,99668,99670],{},[898,99655,207],{},[1750,99657,1917],{"separator":1916},[898,99659,2573],{},[1750,99661,16154],{},[1750,99663,1753],{"stretchy":1752},[1742,99665,2607],{},[1750,99667,1917],{"separator":1916},[1742,99669,1744],{},[1750,99671,1763],{"stretchy":1752},[902,99673,99674],{"encoding":904},"a, b \\in (0, 1)",", často se klade ",[883,99677,99679],{"className":99678},[886],[888,99680,99681],{"xmlns":890},[892,99682,99683,99695],{},[895,99684,99685,99687,99689,99691,99693],{},[898,99686,2573],{},[1750,99688,1766],{},[1742,99690,1744],{},[1750,99692,1758],{},[898,99694,207],{},[902,99696,99697],{"encoding":904},"b = 1 - a",", čímž (6.6) přejde na tvar",[724,99700,99701],{},[4434,99702],{"alt":99703,"className":99704,"src":99705},"imek-cobb-douglas-3d-plus-ic",[210,4438],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[883,99707,99709],{"className":99708},[886],[888,99710,99711],{"xmlns":890,"display":36989},[892,99712,99713,99763],{},[895,99714,99715,99717,99719,99725,99727,99733,99735,99737,99745,99747,99761],{},[898,99716,900],{},[1750,99718,1753],{"stretchy":1752},[5535,99720,99721,99723],{},[898,99722,12471],{},[1742,99724,1744],{},[1750,99726,1917],{"separator":1916},[5535,99728,99729,99731],{},[898,99730,12471],{},[1742,99732,1872],{},[1750,99734,1763],{"stretchy":1752},[1750,99736,1766],{},[5950,99738,99739,99741,99743],{},[898,99740,12471],{},[1742,99742,1744],{},[898,99744,207],{},[1750,99746,8009],{},[5950,99748,99749,99751,99753],{},[898,99750,12471],{},[1742,99752,1872],{},[895,99754,99755,99757,99759],{},[1742,99756,1744],{},[1750,99758,1758],{},[898,99760,207],{},[898,99762,2313],{"mathvariant":1747},[902,99764,99765],{"encoding":904},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1785,99767,99768,99817,99939,100073],{},[724,99769,99770,99772,99773],{},[883,99771,61618],{}," Příklad 6.3 — ověření vlastností pro ",[883,99774,99776],{"className":99775},[886],[888,99777,99778],{"xmlns":890},[892,99779,99780,99814],{},[895,99781,99782,99784,99786,99800],{},[898,99783,900],{},[1750,99785,1766],{},[5950,99787,99788,99790,99792],{},[898,99789,12471],{},[1742,99791,1744],{},[895,99793,99794,99796,99798],{},[1742,99795,1744],{},[898,99797,1748],{"mathvariant":1747},[1742,99799,7859],{},[5950,99801,99802,99804,99806],{},[898,99803,12471],{},[1742,99805,1872],{},[895,99807,99808,99810,99812],{},[1742,99809,7822],{},[898,99811,1748],{"mathvariant":1747},[1742,99813,7859],{},[902,99815,99816],{"encoding":904},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[883,99818,99820],{"className":99819},[886],[888,99821,99822],{"xmlns":890,"display":36989},[892,99823,99824,99936],{},[895,99825,99826,99834,99836,99844,99860,99874,99876,99878,99880,99882,99890,99892,99900,99914,99930,99932,99934],{},[5950,99827,99828,99830,99832],{},[898,99829,900],{},[1742,99831,1744],{},[1750,99833,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,99835,1766],{},[3586,99837,99838],{"scriptlevel":2607,"displaystyle":1752},[3423,99839,99840,99842],{},[1742,99841,1744],{},[1742,99843,7859],{},[5950,99845,99846,99848,99850],{},[898,99847,12471],{},[1742,99849,1744],{},[895,99851,99852,99854,99856,99858],{},[1750,99853,1758],{},[1742,99855,7822],{},[898,99857,1748],{"mathvariant":1747},[1742,99859,7859],{},[5950,99861,99862,99864,99866],{},[898,99863,12471],{},[1742,99865,1872],{},[895,99867,99868,99870,99872],{},[1742,99869,7822],{},[898,99871,1748],{"mathvariant":1747},[1742,99873,7859],{},[1750,99875,2604],{},[1742,99877,2607],{},[1750,99879,1917],{"separator":1916},[2125,99881],{"width":24875},[5950,99883,99884,99886,99888],{},[898,99885,900],{},[1742,99887,1872],{},[1750,99889,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,99891,1766],{},[3586,99893,99894],{"scriptlevel":2607,"displaystyle":1752},[3423,99895,99896,99898],{},[1742,99897,7822],{},[1742,99899,7859],{},[5950,99901,99902,99904,99906],{},[898,99903,12471],{},[1742,99905,1744],{},[895,99907,99908,99910,99912],{},[1742,99909,1744],{},[898,99911,1748],{"mathvariant":1747},[1742,99913,7859],{},[5950,99915,99916,99918,99920],{},[898,99917,12471],{},[1742,99919,1872],{},[895,99921,99922,99924,99926,99928],{},[1750,99923,1758],{},[1742,99925,1744],{},[898,99927,1748],{"mathvariant":1747},[1742,99929,7859],{},[1750,99931,2604],{},[1742,99933,2607],{},[1750,99935,1917],{"separator":1916},[902,99937,99938],{"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,",[883,99940,99942],{"className":99941},[886],[888,99943,99944],{"xmlns":890,"display":36989},[892,99945,99946,100070],{},[895,99947,99948,99960,99962,99964,99972,99988,100002,100004,100006,100008,100010,100022,100024,100026,100034,100048,100064,100066,100068],{},[5950,99949,99950,99952,99954],{},[898,99951,900],{},[1742,99953,12582],{},[895,99955,99956,99958],{},[1750,99957,3815],{"mathvariant":1747},[1750,99959,3815],{"mathvariant":1747},[1750,99961,1766],{},[1750,99963,1758],{},[3586,99965,99966],{"scriptlevel":2607,"displaystyle":1752},[3423,99967,99968,99970],{},[1742,99969,7822],{},[1742,99971,50785],{},[5950,99973,99974,99976,99978],{},[898,99975,12471],{},[1742,99977,1744],{},[895,99979,99980,99982,99984,99986],{},[1750,99981,1758],{},[1742,99983,8051],{},[898,99985,1748],{"mathvariant":1747},[1742,99987,7859],{},[5950,99989,99990,99992,99994],{},[898,99991,12471],{},[1742,99993,1872],{},[895,99995,99996,99998,100000],{},[1742,99997,7822],{},[898,99999,1748],{"mathvariant":1747},[1742,100001,7859],{},[1750,100003,2624],{},[1742,100005,2607],{},[1750,100007,1917],{"separator":1916},[2125,100009],{"width":24875},[5950,100011,100012,100014,100016],{},[898,100013,900],{},[1742,100015,41469],{},[895,100017,100018,100020],{},[1750,100019,3815],{"mathvariant":1747},[1750,100021,3815],{"mathvariant":1747},[1750,100023,1766],{},[1750,100025,1758],{},[3586,100027,100028],{"scriptlevel":2607,"displaystyle":1752},[3423,100029,100030,100032],{},[1742,100031,7822],{},[1742,100033,50785],{},[5950,100035,100036,100038,100040],{},[898,100037,12471],{},[1742,100039,1744],{},[895,100041,100042,100044,100046],{},[1742,100043,1744],{},[898,100045,1748],{"mathvariant":1747},[1742,100047,7859],{},[5950,100049,100050,100052,100054],{},[898,100051,12471],{},[1742,100053,1872],{},[895,100055,100056,100058,100060,100062],{},[1750,100057,1758],{},[1742,100059,7902],{},[898,100061,1748],{"mathvariant":1747},[1742,100063,7859],{},[1750,100065,2624],{},[1742,100067,2607],{},[1750,100069,1917],{"separator":1916},[902,100071,100072],{"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,",[724,100074,100075],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[115,100077,100079],{"id":100078},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[724,100081,100082,100085],{},[38,100083,100084],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[883,100087,100089],{"className":100088},[886],[888,100090,100091],{"xmlns":890,"display":36989},[892,100092,100093,100136],{},[4577,100094,100095],{"width":36994},[4582,100096,100097,100099,100129,100131],{},[4585,100098],{"width":36999},[4585,100100,100101],{},[895,100102,100103,100105,100107,100113,100115,100121,100123,100125,100127],{},[898,100104,900],{},[1750,100106,1753],{"stretchy":1752},[5535,100108,100109,100111],{},[898,100110,12471],{},[1742,100112,1744],{},[1750,100114,1917],{"separator":1916},[5535,100116,100117,100119],{},[898,100118,12471],{},[1742,100120,1872],{},[1750,100122,1763],{"stretchy":1752},[1750,100124,1766],{},[898,100126,9365],{},[1750,100128,1917],{"separator":1916},[4585,100130],{"width":36999},[4585,100132,100133],{},[1969,100134,100135],{},"(6.7)",[902,100137,100138],{"encoding":904},"U(Q_1, Q_2) = c, \\tag{6.7}",[724,100140,2590,100141,100154],{},[883,100142,100144],{"className":100143},[886],[888,100145,100146],{"xmlns":890},[892,100147,100148,100152],{},[895,100149,100150],{},[898,100151,9365],{},[902,100153,9365],{"encoding":904}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[883,100156,100158],{"className":100157},[886],[888,100159,100160],{"xmlns":890,"display":36989},[892,100161,100162,100203],{},[4577,100163,100164],{"width":36994},[4582,100165,100166,100168,100196,100198],{},[4585,100167],{"width":36999},[4585,100169,100170],{},[895,100171,100172,100180,100182,100190,100192,100194],{},[5950,100173,100174,100176,100178],{},[898,100175,12471],{},[1742,100177,1744],{},[898,100179,207],{},[1750,100181,8009],{},[5950,100183,100184,100186,100188],{},[898,100185,12471],{},[1742,100187,1872],{},[898,100189,2573],{},[1750,100191,1766],{},[898,100193,9365],{},[898,100195,2313],{"mathvariant":1747},[4585,100197],{"width":36999},[4585,100199,100200],{},[1969,100201,100202],{},"(6.8)",[902,100204,100205],{"encoding":904},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[724,100207,100208,100209,14017,100239,1647,100242,100255,100256,100291,100292,100309,100310,100339,100340,100343],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[883,100210,100212],{"className":100211},[886],[888,100213,100214],{"xmlns":890},[892,100215,100216,100236],{},[895,100217,100218,100220,100226,100228,100234],{},[1750,100219,5141],{"stretchy":1752},[5535,100221,100222,100224],{},[898,100223,12471],{},[1742,100225,1744],{},[1750,100227,1917],{"separator":1916},[5535,100229,100230,100232],{},[898,100231,12471],{},[1742,100233,1872],{},[1750,100235,5158],{"stretchy":1752},[902,100237,100238],{"encoding":904},"[Q_1, Q_2]",[38,100240,100241],{},"stejnou úrovní uspokojení",[883,100243,100245],{"className":100244},[886],[888,100246,100247],{"xmlns":890},[892,100248,100249,100253],{},[895,100250,100251],{},[898,100252,9365],{},[902,100254,9365],{"encoding":904},". Křivky užitečnosti vznikají jako průsečnice plochy ",[883,100257,100259],{"className":100258},[886],[888,100260,100261],{"xmlns":890},[892,100262,100263,100289],{},[895,100264,100265,100267,100269,100271,100273,100279,100281,100287],{},[898,100266,900],{},[1750,100268,1766],{},[898,100270,900],{},[1750,100272,1753],{"stretchy":1752},[5535,100274,100275,100277],{},[898,100276,12471],{},[1742,100278,1744],{},[1750,100280,1917],{"separator":1916},[5535,100282,100283,100285],{},[898,100284,12471],{},[1742,100286,1872],{},[1750,100288,1763],{"stretchy":1752},[902,100290,96379],{"encoding":904}," s rovinami ",[883,100293,100295],{"className":100294},[886],[888,100296,100297],{"xmlns":890},[892,100298,100299,100307],{},[895,100300,100301,100303,100305],{},[898,100302,900],{},[1750,100304,1766],{},[898,100306,9365],{},[902,100308,95595],{"encoding":904}," rovnoběžnými s rovinou ",[883,100311,100313],{"className":100312},[886],[888,100314,100315],{"xmlns":890},[892,100316,100317,100337],{},[895,100318,100319,100321,100327,100329,100335],{},[1750,100320,1753],{"stretchy":1752},[5535,100322,100323,100325],{},[898,100324,12471],{},[1742,100326,1744],{},[1750,100328,1917],{"separator":1916},[5535,100330,100331,100333],{},[898,100332,12471],{},[1742,100334,1872],{},[1750,100336,1763],{"stretchy":1752},[902,100338,98542],{"encoding":904}," (obrázek 6.2). Jsou v příbuznosti s ",[38,100341,100342],{},"izokvantami"," produkčních funkcí.",[724,100345,100346],{},[614,100347,100348,100349,98420,100367,100385,100386,2313],{},"Obrázek 6.3 — typický tvar křivek užitečnosti pro Cobb-Douglasovu funkci pro ",[883,100350,100352],{"className":100351},[886],[888,100353,100354],{"xmlns":890},[892,100355,100356,100364],{},[895,100357,100358,100360,100362],{},[898,100359,207],{},[1750,100361,2624],{},[898,100363,2573],{},[902,100365,100366],{"encoding":904},"a \u003C b",[883,100368,100370],{"className":100369},[886],[888,100371,100372],{"xmlns":890},[892,100373,100374,100382],{},[895,100375,100376,100378,100380],{},[898,100377,207],{},[1750,100379,2604],{},[898,100381,2573],{},[902,100383,100384],{"encoding":904},"a > b"," (vpravo); různé hladiny ",[883,100387,100389],{"className":100388},[886],[888,100390,100391],{"xmlns":890},[892,100392,100393,100417],{},[895,100394,100395,100401,100403,100409,100411],{},[5535,100396,100397,100399],{},[898,100398,9365],{},[1742,100400,2607],{},[1750,100402,2624],{},[5535,100404,100405,100407],{},[898,100406,9365],{},[1742,100408,1744],{},[1750,100410,2624],{},[5535,100412,100413,100415],{},[898,100414,9365],{},[1742,100416,1872],{},[902,100418,100419],{"encoding":904},"c_0 \u003C c_1 \u003C c_2",[724,100421,100422],{},[614,100423,100424,100425,100454,100455,100513,100514,100532],{},"Obrázek 6.4 — soustava křivek užitečnosti pro tři hladiny (10, 20, 30) v rovině ",[883,100426,100428],{"className":100427},[886],[888,100429,100430],{"xmlns":890},[892,100431,100432,100452],{},[895,100433,100434,100436,100442,100444,100450],{},[1750,100435,1753],{"stretchy":1752},[5535,100437,100438,100440],{},[898,100439,12471],{},[1742,100441,1744],{},[1750,100443,1917],{"separator":1916},[5535,100445,100446,100448],{},[898,100447,12471],{},[1742,100449,1872],{},[1750,100451,1763],{"stretchy":1752},[902,100453,98542],{"encoding":904},"; body ",[883,100456,100458],{"className":100457},[886],[888,100459,100460],{"xmlns":890},[892,100461,100462,100510],{},[895,100463,100464,100466,100468,100470,100476,100478,100484,100486,100488,100490,100492,100494,100500,100502,100508],{},[898,100465,13916],{},[1750,100467,1766],{},[1750,100469,5141],{"stretchy":1752},[5535,100471,100472,100474],{},[898,100473,207],{},[1742,100475,1744],{},[1750,100477,1917],{"separator":1916},[5535,100479,100480,100482],{},[898,100481,207],{},[1742,100483,1872],{},[1750,100485,5158],{"stretchy":1752},[1750,100487,1917],{"separator":1916},[898,100489,7097],{},[1750,100491,1766],{},[1750,100493,5141],{"stretchy":1752},[5535,100495,100496,100498],{},[898,100497,2573],{},[1742,100499,1744],{},[1750,100501,1917],{"separator":1916},[5535,100503,100504,100506],{},[898,100505,2573],{},[1742,100507,1872],{},[1750,100509,5158],{"stretchy":1752},[902,100511,100512],{"encoding":904},"A = [a_1, a_2], B = [b_1, b_2]"," leží na téže křivce (hladina 10), body ",[883,100515,100517],{"className":100516},[886],[888,100518,100519],{"xmlns":890},[892,100520,100521,100529],{},[895,100522,100523,100525,100527],{},[898,100524,1812],{},[1750,100526,1917],{"separator":1916},[898,100528,5541],{},[902,100530,100531],{"encoding":904},"C, D"," na vyšší hladině.",[1785,100534,100535],{},[724,100536,100537,100539,100540,100602,100603,100647,100648,100682,100683,10062,100701,100682,100755,10062,100773,100849],{},[883,100538,61618],{}," Příklad 6.4 — rovnice křivek užitečnosti\nPro ",[883,100541,100543],{"className":100542},[886],[888,100544,100545],{"xmlns":890},[892,100546,100547,100599],{},[895,100548,100549,100551,100553,100559,100561,100567,100569,100571,100585],{},[898,100550,900],{},[1750,100552,1753],{"stretchy":1752},[5535,100554,100555,100557],{},[898,100556,12471],{},[1742,100558,1744],{},[1750,100560,1917],{"separator":1916},[5535,100562,100563,100565],{},[898,100564,12471],{},[1742,100566,1872],{},[1750,100568,1763],{"stretchy":1752},[1750,100570,1766],{},[5950,100572,100573,100575,100577],{},[898,100574,12471],{},[1742,100576,1744],{},[895,100578,100579,100581,100583],{},[1742,100580,1744],{},[898,100582,1748],{"mathvariant":1747},[1742,100584,7859],{},[5950,100586,100587,100589,100591],{},[898,100588,12471],{},[1742,100590,1872],{},[895,100592,100593,100595,100597],{},[1742,100594,7822],{},[898,100596,1748],{"mathvariant":1747},[1742,100598,7859],{},[902,100600,100601],{"encoding":904},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[883,100604,100606],{"className":100605},[886],[888,100607,100608],{"xmlns":890},[892,100609,100610,100644],{},[895,100611,100612,100626,100640,100642],{},[5950,100613,100614,100616,100618],{},[898,100615,12471],{},[1742,100617,1744],{},[895,100619,100620,100622,100624],{},[1742,100621,1744],{},[898,100623,1748],{"mathvariant":1747},[1742,100625,7859],{},[5950,100627,100628,100630,100632],{},[898,100629,12471],{},[1742,100631,1872],{},[895,100633,100634,100636,100638],{},[1742,100635,7822],{},[898,100637,1748],{"mathvariant":1747},[1742,100639,7859],{},[1750,100641,1766],{},[898,100643,9365],{},[902,100645,100646],{"encoding":904},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[883,100649,100651],{"className":100650},[886],[888,100652,100653],{"xmlns":890},[892,100654,100655,100679],{},[895,100656,100657,100663,100671,100673],{},[5535,100658,100659,100661],{},[898,100660,12471],{},[1742,100662,1744],{},[5950,100664,100665,100667,100669],{},[898,100666,12471],{},[1742,100668,1872],{},[1742,100670,7822],{},[1750,100672,1766],{},[1699,100674,100675,100677],{},[898,100676,9365],{},[1742,100678,7859],{},[902,100680,100681],{"encoding":904},"Q_1 Q_2^{3} = c^{4}",". Pro ",[883,100684,100686],{"className":100685},[886],[888,100687,100688],{"xmlns":890},[892,100689,100690,100698],{},[895,100691,100692,100694,100696],{},[898,100693,9365],{},[1750,100695,1766],{},[1742,100697,1744],{},[902,100699,100700],{"encoding":904},"c = 1",[883,100702,100704],{"className":100703},[886],[888,100705,100706],{"xmlns":890},[892,100707,100708,100752],{},[895,100709,100710,100716,100718,100734,100736],{},[5535,100711,100712,100714],{},[898,100713,12471],{},[1742,100715,1872],{},[1750,100717,1766],{},[5950,100719,100720,100722,100724],{},[898,100721,12471],{},[1742,100723,1744],{},[895,100725,100726,100728,100730,100732],{},[1750,100727,1758],{},[1742,100729,1744],{},[898,100731,1748],{"mathvariant":1747},[1742,100733,7822],{},[1750,100735,1766],{},[3586,100737,100738],{"scriptlevel":2607,"displaystyle":1916},[3423,100739,100740,100742],{},[1742,100741,1744],{},[90950,100743,100744,100750],{},[5535,100745,100746,100748],{},[898,100747,12471],{},[1742,100749,1744],{},[1742,100751,7822],{},[902,100753,100754],{"encoding":904},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[883,100756,100758],{"className":100757},[886],[888,100759,100760],{"xmlns":890},[892,100761,100762,100770],{},[895,100763,100764,100766,100768],{},[898,100765,9365],{},[1750,100767,1766],{},[1742,100769,1872],{},[902,100771,100772],{"encoding":904},"c = 2",[883,100774,100776],{"className":100775},[886],[888,100777,100778],{"xmlns":890},[892,100779,100780,100846],{},[895,100781,100782,100788,100790,100802,100804,100820,100822],{},[5535,100783,100784,100786],{},[898,100785,12471],{},[1742,100787,1872],{},[1750,100789,1766],{},[1699,100791,100792,100794],{},[1742,100793,1872],{},[895,100795,100796,100798,100800],{},[1742,100797,7859],{},[898,100799,1748],{"mathvariant":1747},[1742,100801,7822],{},[1750,100803,8009],{},[5950,100805,100806,100808,100810],{},[898,100807,12471],{},[1742,100809,1744],{},[895,100811,100812,100814,100816,100818],{},[1750,100813,1758],{},[1742,100815,1744],{},[898,100817,1748],{"mathvariant":1747},[1742,100819,7822],{},[1750,100821,1766],{},[3586,100823,100824],{"scriptlevel":2607,"displaystyle":1916},[3423,100825,100826,100836],{},[895,100827,100828,100830],{},[1742,100829,1872],{},[90950,100831,100832,100834],{},[1742,100833,1872],{},[1742,100835,7822],{},[90950,100837,100838,100844],{},[5535,100839,100840,100842],{},[898,100841,12471],{},[1742,100843,1744],{},[1742,100845,7822],{},[902,100847,100848],{"encoding":904},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}"," (obrázek 6.5).",[198,100851,100853],{"id":100852},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[724,100855,100856],{},[4434,100857],{"alt":100858,"className":100859,"src":100860},"imek-ic-4vlastnosti-anotovane",[210,4438],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1785,100862,100863,100872,100919,100963,100969,100975],{},[724,100864,100865,100867,100868,100871],{},[883,100866,5454],{}," Čtyři základní vlastnosti indiferenčních křivek\n",[38,100869,100870],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[724,100873,100874],{},[883,100875,100877],{"className":100876},[886],[888,100878,100879],{"xmlns":890},[892,100880,100881,100916],{},[895,100882,100883,100886,100888,100890,100892,100894,100912,100914],{},[898,100884,100885],{"mathvariant":1747},"tg",[1750,100887,65123],{},[898,100889,2661],{},[1750,100891,1766],{},[1750,100893,1758],{},[3423,100895,100896,100904],{},[5950,100897,100898,100900,100902],{},[898,100899,900],{},[1742,100901,1744],{},[1750,100903,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,100905,100906,100908,100910],{},[898,100907,900],{},[1742,100909,1872],{},[1750,100911,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,100913,2624],{},[1742,100915,2607],{},[902,100917,100918],{"encoding":904},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[724,100920,100921,100922,100962],{},"(derivace implicitně zadané funkce ",[883,100923,100925],{"className":100924},[886],[888,100926,100927],{"xmlns":890},[892,100928,100929,100959],{},[895,100930,100931,100933,100935,100941,100943,100949,100951,100953,100955,100957],{},[898,100932,900],{},[1750,100934,1753],{"stretchy":1752},[5535,100936,100937,100939],{},[898,100938,12471],{},[1742,100940,1744],{},[1750,100942,1917],{"separator":1916},[5535,100944,100945,100947],{},[898,100946,12471],{},[1742,100948,1872],{},[1750,100950,1763],{"stretchy":1752},[1750,100952,1758],{},[898,100954,9365],{},[1750,100956,1766],{},[1742,100958,2607],{},[902,100960,100961],{"encoding":904},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[724,100964,100965,100968],{},[38,100966,100967],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[724,100970,100971,100974],{},[38,100972,100973],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost"," (obrázek 6.4).",[724,100976,100977,100980,100981,100999,101000,101016,101017,101020],{},[38,100978,100979],{},"4° Konvexní."," Pro každé dva body ",[883,100982,100984],{"className":100983},[886],[888,100985,100986],{"xmlns":890},[892,100987,100988,100996],{},[895,100989,100990,100992,100994],{},[898,100991,13916],{},[1750,100993,1917],{"separator":1916},[898,100995,7097],{},[902,100997,100998],{"encoding":904},"A, B"," na téže křivce leží vnitřní body úsečky ",[883,101001,101003],{"className":101002},[886],[888,101004,101005],{"xmlns":890},[892,101006,101007,101013],{},[895,101008,101009,101011],{},[898,101010,13916],{},[898,101012,7097],{},[902,101014,101015],{"encoding":904},"AB"," ve ",[38,101018,101019],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[724,101022,101023],{},[614,101024,101025,101026,101061,101062,2313],{},"Obrázek 6.6 — klesající a konvexní průběh ",[883,101027,101029],{"className":101028},[886],[888,101030,101031],{"xmlns":890},[892,101032,101033,101059],{},[895,101034,101035,101037,101039,101045,101047,101053,101055,101057],{},[898,101036,900],{},[1750,101038,1753],{"stretchy":1752},[5535,101040,101041,101043],{},[898,101042,12471],{},[1742,101044,1744],{},[1750,101046,1917],{"separator":1916},[5535,101048,101049,101051],{},[898,101050,12471],{},[1742,101052,1872],{},[1750,101054,1763],{"stretchy":1752},[1750,101056,1766],{},[898,101058,9365],{},[902,101060,19404],{"encoding":904}," s tečnou se sklonem ",[883,101063,101065],{"className":101064},[886],[888,101066,101067],{"xmlns":890},[892,101068,101069,101077],{},[895,101070,101071,101073,101075],{},[898,101072,100885],{"mathvariant":1747},[1750,101074,65123],{},[898,101076,2661],{},[902,101078,101079],{"encoding":904},"\\operatorname{tg}\\alpha",[115,101081,101083],{"id":101082},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[724,101085,101086,1647,101089,2084,101102,101105],{},[38,101087,101088],{},"Mezní míra komoditní substituce",[883,101090,101092],{"className":101091},[886],[888,101093,101094],{"xmlns":890},[892,101095,101096,101100],{},[895,101097,101098],{},[1969,101099,20236],{},[902,101101,37161],{"encoding":904},[38,101103,101104],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[883,101107,101109],{"className":101108},[886],[888,101110,101111],{"xmlns":890,"display":36989},[892,101112,101113,101200],{},[4577,101114,101115],{"width":36994},[4582,101116,101117,101119,101193,101195],{},[4585,101118],{"width":36999},[4585,101120,101121],{},[895,101122,101123,101125,101127,101129,101131,101137,101139,101145,101147,101149,101171,101173,101191],{},[1969,101124,20236],{},[1750,101126,1766],{},[1969,101128,20236],{},[1750,101130,1753],{"stretchy":1752},[5535,101132,101133,101135],{},[898,101134,12471],{},[1742,101136,1744],{},[1750,101138,1917],{"separator":1916},[5535,101140,101141,101143],{},[898,101142,12471],{},[1742,101144,1872],{},[1750,101146,1763],{"stretchy":1752},[1750,101148,1766],{},[3423,101150,101151,101161],{},[895,101152,101153,101155],{},[898,101154,1773],{},[5535,101156,101157,101159],{},[898,101158,900],{},[1742,101160,1744],{},[895,101162,101163,101165],{},[898,101164,1773],{},[5535,101166,101167,101169],{},[898,101168,900],{},[1742,101170,1872],{},[1750,101172,1766],{},[3423,101174,101175,101183],{},[5950,101176,101177,101179,101181],{},[898,101178,900],{},[1742,101180,1744],{},[1750,101182,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,101184,101185,101187,101189],{},[898,101186,900],{},[1742,101188,1872],{},[1750,101190,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[898,101192,2313],{"mathvariant":1747},[4585,101194],{"width":36999},[4585,101196,101197],{},[1969,101198,101199],{},"(6.9)",[902,101201,101202],{"encoding":904},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[724,101204,101205,101206,101240,101241,101273,101274,101309,101310,101323],{},"Geometricky: ",[883,101207,101209],{"className":101208},[886],[888,101210,101211],{"xmlns":890},[892,101212,101213,101237],{},[895,101214,101215,101217],{},[1750,101216,1758],{},[3586,101218,101219],{"scriptlevel":2607,"displaystyle":1752},[3423,101220,101221,101229],{},[5950,101222,101223,101225,101227],{},[898,101224,900],{},[1742,101226,1744],{},[1750,101228,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,101230,101231,101233,101235],{},[898,101232,900],{},[1742,101234,1872],{},[1750,101236,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,101238,101239],{"encoding":904},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[883,101242,101244],{"className":101243},[886],[888,101245,101246],{"xmlns":890},[892,101247,101248,101270],{},[895,101249,101250,101256,101258,101260,101262,101268],{},[5535,101251,101252,101254],{},[898,101253,12471],{},[1742,101255,1872],{},[1750,101257,1766],{},[898,101259,11722],{},[1750,101261,1753],{"stretchy":1752},[5535,101263,101264,101266],{},[898,101265,12471],{},[1742,101267,1744],{},[1750,101269,1763],{"stretchy":1752},[902,101271,101272],{"encoding":904},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[883,101275,101277],{"className":101276},[886],[888,101278,101279],{"xmlns":890},[892,101280,101281,101307],{},[895,101282,101283,101285,101287,101293,101295,101301,101303,101305],{},[898,101284,900],{},[1750,101286,1753],{"stretchy":1752},[5535,101288,101289,101291],{},[898,101290,12471],{},[1742,101292,1744],{},[1750,101294,1917],{"separator":1916},[5535,101296,101297,101299],{},[898,101298,12471],{},[1742,101300,1872],{},[1750,101302,1763],{"stretchy":1752},[1750,101304,1766],{},[898,101306,9365],{},[902,101308,19404],{"encoding":904},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[883,101311,101313],{"className":101312},[886],[888,101314,101315],{"xmlns":890},[892,101316,101317,101321],{},[895,101318,101319],{},[1969,101320,20236],{},[902,101322,37161],{"encoding":904}," chápeme jako velikost kompenzace.",[1785,101325,101326],{},[724,101327,101328,101330,101331,2433,101363,101401,101402,101419,101420,101437],{},[883,101329,1791],{}," Intuice — MRCS jako sklon indiferenční křivky\n",[883,101332,101334],{"className":101333},[886],[888,101335,101336],{"xmlns":890},[892,101337,101338,101360],{},[895,101339,101340,101342,101344,101350,101352,101358],{},[1969,101341,20236],{},[1750,101343,1753],{"stretchy":1752},[5535,101345,101346,101348],{},[898,101347,12471],{},[1742,101349,1744],{},[1750,101351,1917],{"separator":1916},[5535,101353,101354,101356],{},[898,101355,12471],{},[1742,101357,1872],{},[1750,101359,1763],{"stretchy":1752},[902,101361,101362],{"encoding":904},"\\text{MRCS}(Q_1, Q_2)",[38,101364,101365,101366,37926,101383,101400],{},"míra, jakou je spotřebitel ochoten zaměnit ",[883,101367,101369],{"className":101368},[886],[888,101370,101371],{"xmlns":890},[892,101372,101373,101381],{},[895,101374,101375],{},[5535,101376,101377,101379],{},[898,101378,12471],{},[1742,101380,1744],{},[902,101382,37925],{"encoding":904},[883,101384,101386],{"className":101385},[886],[888,101387,101388],{"xmlns":890},[892,101389,101390,101398],{},[895,101391,101392],{},[5535,101393,101394,101396],{},[898,101395,12471],{},[1742,101397,1872],{},[902,101399,37944],{"encoding":904}," při zachování užitečnosti"," — tedy kolik jednotek ",[883,101403,101405],{"className":101404},[886],[888,101406,101407],{"xmlns":890},[892,101408,101409,101417],{},[895,101410,101411],{},[5535,101412,101413,101415],{},[898,101414,12471],{},[1742,101416,1872],{},[902,101418,37944],{"encoding":904}," „obětuje\" za jednu jednotku ",[883,101421,101423],{"className":101422},[886],[888,101424,101425],{"xmlns":890},[892,101426,101427,101435],{},[895,101428,101429],{},[5535,101430,101431,101433],{},[898,101432,12471],{},[1742,101434,1744],{},[902,101436,37925],{"encoding":904}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[724,101439,101440,101441,38867],{},"Pro obecnou změnu ",[883,101442,101444],{"className":101443},[886],[888,101445,101446],{"xmlns":890},[892,101447,101448,101458],{},[895,101449,101450,101452],{},[898,101451,3429],{"mathvariant":1747},[5535,101453,101454,101456],{},[898,101455,12471],{},[1742,101457,1744],{},[902,101459,101460],{"encoding":904},"\\mathrm{d} Q_1",[883,101462,101464],{"className":101463},[886],[888,101465,101466],{"xmlns":890,"display":36989},[892,101467,101468,101521],{},[4577,101469,101470],{"width":36994},[4582,101471,101472,101474,101514,101516],{},[4585,101473],{"width":36999},[4585,101475,101476],{},[895,101477,101478,101480,101486,101488,101490,101496,101498,101500,101502,101504,101506,101512],{},[898,101479,2666],{"mathvariant":1747},[5535,101481,101482,101484],{},[898,101483,12471],{},[1742,101485,1872],{},[1750,101487,2274],{},[898,101489,3429],{"mathvariant":1747},[5535,101491,101492,101494],{},[898,101493,12471],{},[1742,101495,1872],{},[1750,101497,1766],{},[1750,101499,1758],{},[1969,101501,20236],{},[1750,101503,8009],{},[898,101505,3429],{"mathvariant":1747},[5535,101507,101508,101510],{},[898,101509,12471],{},[1742,101511,1744],{},[1750,101513,1917],{"separator":1916},[4585,101515],{"width":36999},[4585,101517,101518],{},[1969,101519,101520],{},"(6.10)",[902,101522,101523],{"encoding":904},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[883,101525,101527],{"className":101526},[886],[888,101528,101529],{"xmlns":890,"display":36989},[892,101530,101531,101578],{},[4577,101532,101533],{"width":36994},[4582,101534,101535,101537,101571,101573],{},[4585,101536],{"width":36999},[4585,101538,101539],{},[895,101540,101541,101543,101549,101551,101553,101559,101561,101563,101569],{},[898,101542,3429],{"mathvariant":1747},[5535,101544,101545,101547],{},[898,101546,12471],{},[1742,101548,1744],{},[1750,101550,1766],{},[1750,101552,1758],{},[3423,101554,101555,101557],{},[1742,101556,1744],{},[1969,101558,20236],{},[1969,101560,2658],{},[898,101562,3429],{"mathvariant":1747},[5535,101564,101565,101567],{},[898,101566,12471],{},[1742,101568,1872],{},[898,101570,2313],{"mathvariant":1747},[4585,101572],{"width":36999},[4585,101574,101575],{},[1969,101576,101577],{},"(6.11)",[902,101579,101580],{"encoding":904},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1785,101582,101583,101649,101766],{},[724,101584,101585,101587,101588,38867],{},[883,101586,61618],{}," Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost\nPro ",[883,101589,101591],{"className":101590},[886],[888,101592,101593],{"xmlns":890},[892,101594,101595,101647],{},[895,101596,101597,101599,101601,101607,101609,101615,101617,101619,101633],{},[898,101598,900],{},[1750,101600,1753],{"stretchy":1752},[5535,101602,101603,101605],{},[898,101604,12471],{},[1742,101606,1744],{},[1750,101608,1917],{"separator":1916},[5535,101610,101611,101613],{},[898,101612,12471],{},[1742,101614,1872],{},[1750,101616,1763],{"stretchy":1752},[1750,101618,1766],{},[5950,101620,101621,101623,101625],{},[898,101622,12471],{},[1742,101624,1744],{},[895,101626,101627,101629,101631],{},[1742,101628,1744],{},[898,101630,1748],{"mathvariant":1747},[1742,101632,1872],{},[5950,101634,101635,101637,101639],{},[898,101636,12471],{},[1742,101638,1872],{},[895,101640,101641,101643,101645],{},[1742,101642,1744],{},[898,101644,1748],{"mathvariant":1747},[1742,101646,1872],{},[902,101648,38866],{"encoding":904},[724,101650,101651],{},[883,101652,101654],{"className":101653},[886],[888,101655,101656],{"xmlns":890},[892,101657,101658,101764],{},[895,101659,101660,101662,101664,101746,101748,101762],{},[1969,101661,20236],{},[1750,101663,1766],{},[3423,101665,101666,101706],{},[895,101667,101668,101676,101692],{},[3586,101669,101670],{"scriptlevel":2607,"displaystyle":1752},[3423,101671,101672,101674],{},[1742,101673,1744],{},[1742,101675,1872],{},[5950,101677,101678,101680,101682],{},[898,101679,12471],{},[1742,101681,1744],{},[895,101683,101684,101686,101688,101690],{},[1750,101685,1758],{},[1742,101687,1744],{},[898,101689,1748],{"mathvariant":1747},[1742,101691,1872],{},[5950,101693,101694,101696,101698],{},[898,101695,12471],{},[1742,101697,1872],{},[895,101699,101700,101702,101704],{},[1742,101701,1744],{},[898,101703,1748],{"mathvariant":1747},[1742,101705,1872],{},[895,101707,101708,101716,101730],{},[3586,101709,101710],{"scriptlevel":2607,"displaystyle":1752},[3423,101711,101712,101714],{},[1742,101713,1744],{},[1742,101715,1872],{},[5950,101717,101718,101720,101722],{},[898,101719,12471],{},[1742,101721,1744],{},[895,101723,101724,101726,101728],{},[1742,101725,1744],{},[898,101727,1748],{"mathvariant":1747},[1742,101729,1872],{},[5950,101731,101732,101734,101736],{},[898,101733,12471],{},[1742,101735,1872],{},[895,101737,101738,101740,101742,101744],{},[1750,101739,1758],{},[1742,101741,1744],{},[898,101743,1748],{"mathvariant":1747},[1742,101745,1872],{},[1750,101747,1766],{},[3423,101749,101750,101756],{},[5535,101751,101752,101754],{},[898,101753,12471],{},[1742,101755,1872],{},[5535,101757,101758,101760],{},[898,101759,12471],{},[1742,101761,1744],{},[898,101763,2313],{"mathvariant":1747},[902,101765,38985],{"encoding":904},[724,101767,38988,101768,12605,101811,39036,101813,101832],{},[883,101769,101771],{"className":101770},[886],[888,101772,101773],{"xmlns":890},[892,101774,101775,101809],{},[895,101776,101777,101779,101781,101783,101785,101787,101789,101791,101799,101801],{},[1969,101778,20236],{},[1750,101780,1753],{"stretchy":1752},[1742,101782,39004],{},[1750,101784,1917],{"separator":1916},[1742,101786,7658],{},[1750,101788,1763],{"stretchy":1752},[1750,101790,1766],{},[3586,101792,101793],{"scriptlevel":2607,"displaystyle":1752},[3423,101794,101795,101797],{},[1742,101796,7658],{},[1742,101798,39004],{},[1750,101800,1766],{},[3586,101802,101803],{"scriptlevel":2607,"displaystyle":1752},[3423,101804,101805,101807],{},[1742,101806,7902],{},[1742,101808,7822],{},[902,101810,39033],{"encoding":904},[614,101812,18853],{},[883,101814,101816],{"className":101815},[886],[888,101817,101818],{"xmlns":890},[892,101819,101820,101830],{},[895,101821,101822],{},[3586,101823,101824],{"scriptlevel":2607,"displaystyle":1752},[3423,101825,101826,101828],{},[1742,101827,7902],{},[1742,101829,7822],{},[902,101831,39056],{"encoding":904}," jednotky, aby se užitečnost zachovala.",[724,101834,101835,101836,101840],{},"(Paralelou je ",[207,101837,101839],{"className":101838,"dataFsResolvedFilePath":857,"href":858},[210],"mezní míra technické substituce MRTS"," z produkční teorie.)",[115,101842,101844],{"id":101843},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[724,101846,101847,101848,101851],{},"Rámcově se v kapitole 6 studují ",[38,101849,101850],{},"dvě vázané optimalizační úlohy"," s užitečností:",[120,101853,101854,101990],{},[123,101855,101856,101858,101859,19790,101890,1647,101893,101942,101943,2313],{},[38,101857,37175],{}," — maximalizace ",[883,101860,101862],{"className":101861},[886],[888,101863,101864],{"xmlns":890},[892,101865,101866,101888],{},[895,101867,101868,101870,101872,101878,101880,101886],{},[898,101869,900],{},[1750,101871,1753],{"stretchy":1752},[5535,101873,101874,101876],{},[898,101875,12471],{},[1742,101877,1744],{},[1750,101879,1917],{"separator":1916},[5535,101881,101882,101884],{},[898,101883,12471],{},[1742,101885,1872],{},[1750,101887,1763],{"stretchy":1752},[902,101889,25916],{"encoding":904},[38,101891,101892],{},"rozpočtovém omezení",[883,101894,101896],{"className":101895},[886],[888,101897,101898],{"xmlns":890},[892,101899,101900,101940],{},[895,101901,101902,101908,101910,101918,101924,101926,101934],{},[1699,101903,101904,101906],{},[898,101905,1666],{},[1750,101907,3751],{},[1750,101909,1766],{},[5950,101911,101912,101914,101916],{},[898,101913,1776],{},[1742,101915,1744],{},[1750,101917,3751],{},[5535,101919,101920,101922],{},[898,101921,12471],{},[1742,101923,1744],{},[1750,101925,1861],{},[5950,101927,101928,101930,101932],{},[898,101929,1776],{},[1742,101931,1872],{},[1750,101933,3751],{},[5535,101935,101936,101938],{},[898,101937,12471],{},[1742,101939,1872],{},[902,101941,26871],{"encoding":904},". Výstupem je Marshallova poptávka ",[883,101944,101946],{"className":101945},[886],[888,101947,101948],{"xmlns":890},[892,101949,101950,101988],{},[895,101951,101952,101958,101960,101966,101968,101974,101976,101982,101984,101986],{},[5535,101953,101954,101956],{},[898,101955,12471],{},[898,101957,27363],{},[1750,101959,1766],{},[5535,101961,101962,101964],{},[898,101963,5541],{},[898,101965,27363],{},[1750,101967,1753],{"stretchy":1752},[5535,101969,101970,101972],{},[898,101971,1776],{},[1742,101973,1744],{},[1750,101975,1917],{"separator":1916},[5535,101977,101978,101980],{},[898,101979,1776],{},[1742,101981,1872],{},[1750,101983,1917],{"separator":1916},[898,101985,1666],{},[1750,101987,1763],{"stretchy":1752},[902,101989,45378],{"encoding":904},[123,101991,101992,36824,101995,36867,102041,102058,102059,2313],{},[38,101993,101994],{},"Duální úloha",[883,101996,101998],{"className":101997},[886],[888,101999,102000],{"xmlns":890},[892,102001,102002,102038],{},[895,102003,102004,102006,102008,102016,102022,102024,102032],{},[898,102005,1705],{},[1750,102007,1766],{},[5950,102009,102010,102012,102014],{},[898,102011,1776],{},[1742,102013,1744],{},[1750,102015,3751],{},[5535,102017,102018,102020],{},[898,102019,12471],{},[1742,102021,1744],{},[1750,102023,1861],{},[5950,102025,102026,102028,102030],{},[898,102027,1776],{},[1742,102029,1872],{},[1750,102031,3751],{},[5535,102033,102034,102036],{},[898,102035,12471],{},[1742,102037,1872],{},[902,102039,102040],{"encoding":904},"E = P_1^* Q_1 + P_2^* Q_2",[883,102042,102044],{"className":102043},[886],[888,102045,102046],{"xmlns":890},[892,102047,102048,102056],{},[895,102049,102050],{},[1699,102051,102052,102054],{},[898,102053,900],{},[1750,102055,3751],{},[902,102057,36885],{"encoding":904},". Výstupem je Hicksova poptávka ",[883,102060,102062],{"className":102061},[886],[888,102063,102064],{"xmlns":890},[892,102065,102066,102104],{},[895,102067,102068,102074,102076,102082,102084,102090,102092,102098,102100,102102],{},[5535,102069,102070,102072],{},[898,102071,12471],{},[898,102073,27363],{},[1750,102075,1766],{},[5535,102077,102078,102080],{},[898,102079,5541],{},[898,102081,27363],{},[1750,102083,1753],{"stretchy":1752},[5535,102085,102086,102088],{},[898,102087,1776],{},[1742,102089,1744],{},[1750,102091,1917],{"separator":1916},[5535,102093,102094,102096],{},[898,102095,1776],{},[1742,102097,1872],{},[1750,102099,1917],{"separator":1916},[898,102101,900],{},[1750,102103,1763],{"stretchy":1752},[902,102105,27396],{"encoding":904},[724,102107,102108,102109,102112,102113,1647,102116,102155],{},"Obě úlohy se řeší ",[207,102110,36890],{"className":102111,"dataFsResolvedFilePath":791,"href":792},[210]," a vedou na ",[38,102114,102115],{},"tentýž bod dotyku",[883,102117,102119],{"className":102118},[886],[888,102120,102121],{"xmlns":890},[892,102122,102123,102153],{},[895,102124,102125,102131,102133,102141,102143,102151],{},[1699,102126,102127,102129],{},[898,102128,12471],{},[1750,102130,3751],{},[1750,102132,5141],{"stretchy":1752},[5950,102134,102135,102137,102139],{},[898,102136,12471],{},[1742,102138,1744],{},[1750,102140,3751],{},[1750,102142,1917],{"separator":1916},[5950,102144,102145,102147,102149],{},[898,102146,12471],{},[1742,102148,1872],{},[1750,102150,3751],{},[1750,102152,5158],{"stretchy":1752},[902,102154,37250],{"encoding":904}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[883,102157,102159],{"className":102158},[886],[888,102160,102161],{"xmlns":890,"display":36989},[892,102162,102163,102209],{},[895,102164,102165,102167,102169,102187,102189,102207],{},[1969,102166,20236],{},[1750,102168,1766],{},[3423,102170,102171,102179],{},[5950,102172,102173,102175,102177],{},[898,102174,900],{},[1742,102176,1744],{},[1750,102178,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[5950,102180,102181,102183,102185],{},[898,102182,900],{},[1742,102184,1872],{},[1750,102186,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,102188,1766],{},[3423,102190,102191,102199],{},[5950,102192,102193,102195,102197],{},[898,102194,1776],{},[1742,102196,1744],{},[1750,102198,3751],{},[5950,102200,102201,102203,102205],{},[898,102202,1776],{},[1742,102204,1872],{},[1750,102206,3751],{},[898,102208,2313],{"mathvariant":1747},[902,102210,102211],{"encoding":904},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[724,102213,102214],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1785,102216,102217],{},[724,102218,102219,102221,102222,102225,102226,102229,102230,102257,102258,102292,102293,102327,102328,102371,102372,102375,102376,2313],{},[883,102220,1791],{}," Pro detailní postup viz ",[207,102223,45677],{"className":102224,"dataFsResolvedFilePath":911,"href":912},[210],"\nKompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[38,102227,102228],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[883,102231,102233],{"className":102232},[886],[888,102234,102235],{"xmlns":890},[892,102236,102237,102255],{},[895,102238,102239,102241,102243,102249],{},[898,102240,900],{},[1750,102242,1766],{},[5535,102244,102245,102247],{},[898,102246,12471],{},[1742,102248,1744],{},[5535,102250,102251,102253],{},[898,102252,12471],{},[1742,102254,1872],{},[902,102256,39149],{"encoding":904}," s výsledkem ",[883,102259,102261],{"className":102260},[886],[888,102262,102263],{"xmlns":890},[892,102264,102265,102289],{},[895,102266,102267,102273,102275,102277,102279,102285,102287],{},[5535,102268,102269,102271],{},[898,102270,12471],{},[1742,102272,1744],{},[1750,102274,1766],{},[1742,102276,6419],{},[1750,102278,1917],{"separator":1916},[5535,102280,102281,102283],{},[898,102282,12471],{},[1742,102284,1872],{},[1750,102286,1766],{},[1742,102288,3079],{},[902,102290,102291],{"encoding":904},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[883,102294,102296],{"className":102295},[886],[888,102297,102298],{"xmlns":890},[892,102299,102300,102324],{},[895,102301,102302,102308,102310,102312,102314,102320,102322],{},[5535,102303,102304,102306],{},[898,102305,12471],{},[1742,102307,1744],{},[1750,102309,1766],{},[1742,102311,7859],{},[1750,102313,1917],{"separator":1916},[5535,102315,102316,102318],{},[898,102317,12471],{},[1742,102319,1872],{},[1750,102321,1766],{},[1742,102323,1744],{},[902,102325,102326],{"encoding":904},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[883,102329,102331],{"className":102330},[886],[888,102332,102333],{"xmlns":890},[892,102334,102335,102369],{},[895,102336,102337,102339,102341,102355],{},[898,102338,900],{},[1750,102340,1766],{},[5950,102342,102343,102345,102347],{},[898,102344,12471],{},[1742,102346,1744],{},[895,102348,102349,102351,102353],{},[1742,102350,1744],{},[898,102352,1748],{"mathvariant":1747},[1742,102354,1872],{},[5950,102356,102357,102359,102361],{},[898,102358,12471],{},[1742,102360,1872],{},[895,102362,102363,102365,102367],{},[1742,102364,1744],{},[898,102366,1748],{"mathvariant":1747},[1742,102368,1872],{},[902,102370,42082],{"encoding":904},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[38,102373,102374],{},"6.8–6.13"," jsou na stránce ",[207,102377,36690],{"className":102378,"dataFsResolvedFilePath":911,"href":912},[210],[115,102380,102382],{"id":102381},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[724,102384,102385,102386,102399,102400,102402,102403,102405,102406,102408,102409,102411,102412,102414,102415,102417,102418,1647,102420,102455,102456,102469,102470,102473,102474,102477,102478,2313],{},"Každá ",[883,102387,102389],{"className":102388},[886],[888,102390,102391],{"xmlns":890},[892,102392,102393,102397],{},[895,102394,102395],{},[898,102396,45783],{},[902,102398,45783],{"encoding":904},"-tice množství jednotlivých zboží je ",[38,102401,95733],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[38,102404,96217],{}," a současně ",[38,102407,95736],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[38,102410,95741],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[38,102413,61600],{}," (6.4) a druhé parciální derivace ",[38,102416,98100],{}," (6.5 — zákon klesající mezní užitečnosti). ",[38,102419,19367],{},[883,102421,102423],{"className":102422},[886],[888,102424,102425],{"xmlns":890},[892,102426,102427,102453],{},[895,102428,102429,102431,102433,102439,102441,102447,102449,102451],{},[898,102430,900],{},[1750,102432,1753],{"stretchy":1752},[5535,102434,102435,102437],{},[898,102436,12471],{},[1742,102438,1744],{},[1750,102440,1917],{"separator":1916},[5535,102442,102443,102445],{},[898,102444,12471],{},[1742,102446,1872],{},[1750,102448,1763],{"stretchy":1752},[1750,102450,1766],{},[898,102452,9365],{},[902,102454,19404],{"encoding":904}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[883,102457,102459],{"className":102458},[886],[888,102460,102461],{"xmlns":890},[892,102462,102463,102467],{},[895,102464,102465],{},[1969,102466,20236],{},[902,102468,37161],{"encoding":904}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[38,102471,102472],{},"maximalizace užitečnosti"," a duální ",[38,102475,102476],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[207,102479,45677],{"className":102480,"dataFsResolvedFilePath":911,"href":912},[210],[115,102482,58805],{"id":58804},[152,102484,102485,102488,102491,102494,102497,102500,102503,102506,102509,102512],{},[123,102486,102487],{},"Co se zahrnuje pod termín užitečnost?",[123,102489,102490],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[123,102492,102493],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[123,102495,102496],{},"Jak se vypočítá mezní užitečnost?",[123,102498,102499],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[123,102501,102502],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[123,102504,102505],{},"Které jsou nejčastěji používané funkce užitečnosti?",[123,102507,102508],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[123,102510,102511],{},"Proč mají křivky užitečnosti záporný sklon?",[123,102513,102514],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[115,102516,102518],{"id":102517},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[724,102520,102521,102524,102525,92406,102567,1343,102595,1343,102623,102651],{},[38,102522,102523],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[883,102526,102528],{"className":102527},[886],[888,102529,102530],{"xmlns":890},[892,102531,102532,102564],{},[895,102533,102534,102536,102538,102544,102546,102548,102554,102556,102558],{},[898,102535,900],{},[1750,102537,1766],{},[5535,102539,102540,102542],{},[898,102541,12471],{},[1742,102543,1744],{},[1750,102545,1861],{},[1742,102547,73482],{},[5535,102549,102550,102552],{},[898,102551,12471],{},[1742,102553,1872],{},[1750,102555,1861],{},[1742,102557,1872],{},[5535,102559,102560,102562],{},[898,102561,12471],{},[1742,102563,7822],{},[902,102565,102566],{"encoding":904},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[883,102568,102570],{"className":102569},[886],[888,102571,102572],{"xmlns":890},[892,102573,102574,102592],{},[895,102575,102576,102578,102580,102582,102584,102586,102588,102590],{},[898,102577,900],{},[1750,102579,1753],{"stretchy":1752},[1742,102581,7859],{},[1750,102583,1917],{"separator":1916},[1742,102585,1872],{},[1750,102587,1917],{"separator":1916},[1742,102589,1872],{},[1750,102591,1763],{"stretchy":1752},[902,102593,102594],{"encoding":904},"U(4, 2, 2)",[883,102596,102598],{"className":102597},[886],[888,102599,102600],{"xmlns":890},[892,102601,102602,102620],{},[895,102603,102604,102606,102608,102610,102612,102614,102616,102618],{},[898,102605,900],{},[1750,102607,1753],{"stretchy":1752},[1742,102609,1744],{},[1750,102611,1917],{"separator":1916},[1742,102613,7859],{},[1750,102615,1917],{"separator":1916},[1742,102617,1872],{},[1750,102619,1763],{"stretchy":1752},[902,102621,102622],{"encoding":904},"U(1, 4, 2)",[883,102624,102626],{"className":102625},[886],[888,102627,102628],{"xmlns":890},[892,102629,102630,102648],{},[895,102631,102632,102634,102636,102638,102640,102642,102644,102646],{},[898,102633,900],{},[1750,102635,1753],{"stretchy":1752},[1742,102637,1872],{},[1750,102639,1917],{"separator":1916},[1742,102641,7822],{},[1750,102643,1917],{"separator":1916},[1742,102645,1744],{},[1750,102647,1763],{"stretchy":1752},[902,102649,102650],{"encoding":904},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[724,102653,102654,102657,102658,102710,102711,1343,102737,1343,102763,1343,102789,1343,102815,1343,102841,1343,102867,102893],{},[38,102655,102656],{},"6.2"," Je dána užitečnost ",[883,102659,102661],{"className":102660},[886],[888,102662,102663],{"xmlns":890},[892,102664,102665,102707],{},[895,102666,102667,102669,102671,102673,102687,102701],{},[898,102668,900],{},[1750,102670,1766],{},[1742,102672,1872],{},[5950,102674,102675,102677,102679],{},[898,102676,12471],{},[1742,102678,1744],{},[895,102680,102681,102683,102685],{},[1742,102682,1744],{},[898,102684,1748],{"mathvariant":1747},[1742,102686,7822],{},[5950,102688,102689,102691,102693],{},[898,102690,12471],{},[1742,102692,1872],{},[895,102694,102695,102697,102699],{},[1742,102696,1744],{},[898,102698,1748],{"mathvariant":1747},[1742,102700,1872],{},[5535,102702,102703,102705],{},[898,102704,12471],{},[1742,102706,7822],{},[902,102708,102709],{"encoding":904},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[883,102712,102714],{"className":102713},[886],[888,102715,102716],{"xmlns":890},[892,102717,102718,102734],{},[895,102719,102720,102722,102724,102726,102728,102730,102732],{},[1750,102721,1753],{"stretchy":1752},[1742,102723,15219],{},[1750,102725,1917],{"separator":1916},[1742,102727,75520],{},[1750,102729,1917],{"separator":1916},[1742,102731,3079],{},[1750,102733,1763],{"stretchy":1752},[902,102735,102736],{"encoding":904},"(36, 27, 10)",[883,102738,102740],{"className":102739},[886],[888,102741,102742],{"xmlns":890},[892,102743,102744,102760],{},[895,102745,102746,102748,102750,102752,102754,102756,102758],{},[1750,102747,1753],{"stretchy":1752},[1742,102749,50763],{},[1750,102751,1917],{"separator":1916},[1742,102753,15239],{},[1750,102755,1917],{"separator":1916},[1742,102757,6465],{},[1750,102759,1763],{"stretchy":1752},[902,102761,102762],{"encoding":904},"(64, 8, 20)",[883,102764,102766],{"className":102765},[886],[888,102767,102768],{"xmlns":890},[892,102769,102770,102786],{},[895,102771,102772,102774,102776,102778,102780,102782,102784],{},[1750,102773,1753],{"stretchy":1752},[1742,102775,6419],{},[1750,102777,1917],{"separator":1916},[1742,102779,50763],{},[1750,102781,1917],{"separator":1916},[1742,102783,15239],{},[1750,102785,1763],{"stretchy":1752},[902,102787,102788],{"encoding":904},"(25, 64, 8)",[883,102790,102792],{"className":102791},[886],[888,102793,102794],{"xmlns":890},[892,102795,102796,102812],{},[895,102797,102798,102800,102802,102804,102806,102808,102810],{},[1750,102799,1753],{"stretchy":1752},[1742,102801,7859],{},[1750,102803,1917],{"separator":1916},[1742,102805,81452],{},[1750,102807,1917],{"separator":1916},[1742,102809,3219],{},[1750,102811,1763],{"stretchy":1752},[902,102813,102814],{"encoding":904},"(4, 125, 6)",[883,102816,102818],{"className":102817},[886],[888,102819,102820],{"xmlns":890},[892,102821,102822,102838],{},[895,102823,102824,102826,102828,102830,102832,102834,102836],{},[1750,102825,1753],{"stretchy":1752},[1742,102827,13663],{},[1750,102829,1917],{"separator":1916},[1742,102831,14865],{},[1750,102833,1917],{"separator":1916},[1742,102835,4903],{},[1750,102837,1763],{"stretchy":1752},[902,102839,102840],{"encoding":904},"(9, 40, 12)",[883,102842,102844],{"className":102843},[886],[888,102845,102846],{"xmlns":890},[892,102847,102848,102864],{},[895,102849,102850,102852,102854,102856,102858,102860,102862],{},[1750,102851,1753],{"stretchy":1752},[1742,102853,13663],{},[1750,102855,1917],{"separator":1916},[1742,102857,50763],{},[1750,102859,1917],{"separator":1916},[1742,102861,7902],{},[1750,102863,1763],{"stretchy":1752},[902,102865,102866],{"encoding":904},"(9, 64, 5)",[883,102868,102870],{"className":102869},[886],[888,102871,102872],{"xmlns":890},[892,102873,102874,102890],{},[895,102875,102876,102878,102880,102882,102884,102886,102888],{},[1750,102877,1753],{"stretchy":1752},[1742,102879,50763],{},[1750,102881,1917],{"separator":1916},[1742,102883,15239],{},[1750,102885,1917],{"separator":1916},[1742,102887,3079],{},[1750,102889,1763],{"stretchy":1752},[902,102891,102892],{"encoding":904},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[724,102895,102896,102657,102899,102942,102943,102977,102978,16121,103008,103041,103042,103059,103060,103077],{},[38,102897,102898],{},"6.3",[883,102900,102902],{"className":102901},[886],[888,102903,102904],{"xmlns":890},[892,102905,102906,102940],{},[895,102907,102908,102910,102912,102926],{},[898,102909,900],{},[1750,102911,1766],{},[5950,102913,102914,102916,102918],{},[898,102915,12471],{},[1742,102917,1744],{},[895,102919,102920,102922,102924],{},[1742,102921,1744],{},[898,102923,1748],{"mathvariant":1747},[1742,102925,1872],{},[5950,102927,102928,102930,102932],{},[898,102929,12471],{},[1742,102931,1872],{},[895,102933,102934,102936,102938],{},[1742,102935,1744],{},[898,102937,1748],{"mathvariant":1747},[1742,102939,1872],{},[902,102941,42082],{"encoding":904},". (a) Vypočtěte užitečnost pro ",[883,102944,102946],{"className":102945},[886],[888,102947,102948],{"xmlns":890},[892,102949,102950,102974],{},[895,102951,102952,102958,102960,102962,102964,102970,102972],{},[5535,102953,102954,102956],{},[898,102955,12471],{},[1742,102957,1744],{},[1750,102959,1766],{},[1742,102961,3936],{},[1750,102963,1917],{"separator":1916},[5535,102965,102966,102968],{},[898,102967,12471],{},[1742,102969,1872],{},[1750,102971,1766],{},[1742,102973,55626],{},[902,102975,102976],{"encoding":904},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[883,102979,102981],{"className":102980},[886],[888,102982,102983],{"xmlns":890},[892,102984,102985,103005],{},[895,102986,102987,102989,102995,102997,102999],{},[898,102988,1773],{},[5535,102990,102991,102993],{},[898,102992,900],{},[1742,102994,1744],{},[1750,102996,1917],{"separator":1916},[898,102998,1773],{},[5535,103000,103001,103003],{},[898,103002,900],{},[1742,103004,1872],{},[902,103006,103007],{"encoding":904},"MU_1, MU_2",[883,103009,103011],{"className":103010},[886],[888,103012,103013],{"xmlns":890},[892,103014,103015,103039],{},[895,103016,103017,103023,103025,103027,103029,103035,103037],{},[5535,103018,103019,103021],{},[898,103020,12471],{},[1742,103022,1744],{},[1750,103024,1766],{},[1742,103026,3936],{},[1750,103028,1917],{"separator":1916},[5535,103030,103031,103033],{},[898,103032,12471],{},[1742,103034,1872],{},[1750,103036,1766],{},[1742,103038,55626],{},[902,103040,102976],{"encoding":904}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[883,103043,103045],{"className":103044},[886],[888,103046,103047],{"xmlns":890},[892,103048,103049,103057],{},[895,103050,103051],{},[5535,103052,103053,103055],{},[898,103054,12471],{},[1742,103056,1744],{},[902,103058,37925],{"encoding":904}," na 60 a poklesu ",[883,103061,103063],{"className":103062},[886],[888,103064,103065],{"xmlns":890},[892,103066,103067,103075],{},[895,103068,103069],{},[5535,103070,103071,103073],{},[898,103072,12471],{},[1742,103074,1872],{},[902,103076,37944],{"encoding":904}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[724,103079,103080,103083,103084,103145,103146,2313],{},[38,103081,103082],{},"6.4"," Je dána funkce ",[883,103085,103087],{"className":103086},[886],[888,103088,103089],{"xmlns":890},[892,103090,103091,103143],{},[895,103092,103093,103095,103097,103103,103105,103111,103113,103115,103129],{},[898,103094,900],{},[1750,103096,1753],{"stretchy":1752},[5535,103098,103099,103101],{},[898,103100,12471],{},[1742,103102,1744],{},[1750,103104,1917],{"separator":1916},[5535,103106,103107,103109],{},[898,103108,12471],{},[1742,103110,1872],{},[1750,103112,1763],{"stretchy":1752},[1750,103114,1766],{},[5950,103116,103117,103119,103121],{},[898,103118,12471],{},[1742,103120,1744],{},[895,103122,103123,103125,103127],{},[1742,103124,1744],{},[898,103126,1748],{"mathvariant":1747},[1742,103128,1872],{},[5950,103130,103131,103133,103135],{},[898,103132,12471],{},[1742,103134,1872],{},[895,103136,103137,103139,103141],{},[1742,103138,1744],{},[898,103140,1748],{"mathvariant":1747},[1742,103142,1872],{},[902,103144,38866],{"encoding":904},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[883,103147,103149],{"className":103148},[886],[888,103150,103151],{"xmlns":890},[892,103152,103153,103243],{},[895,103154,103155,103157,103159,103165,103167,103169,103171,103173,103175,103177,103183,103185,103187,103189,103191,103193,103195,103197,103199,103205,103207,103209,103211,103213,103215,103217,103223,103225,103227,103229,103231,103233,103235,103241],{},[898,103156,900],{},[1750,103158,1753],{"stretchy":1752},[5535,103160,103161,103163],{},[898,103162,12471],{},[1742,103164,1744],{},[1750,103166,1917],{"separator":1916},[1742,103168,1744],{},[1750,103170,1763],{"stretchy":1752},[1750,103172,1917],{"separator":1916},[898,103174,900],{},[1750,103176,1753],{"stretchy":1752},[5535,103178,103179,103181],{},[898,103180,12471],{},[1742,103182,1744],{},[1750,103184,1917],{"separator":1916},[1742,103186,1872],{},[1750,103188,1763],{"stretchy":1752},[1750,103190,1917],{"separator":1916},[898,103192,900],{},[1750,103194,1753],{"stretchy":1752},[1742,103196,1744],{},[1750,103198,1917],{"separator":1916},[5535,103200,103201,103203],{},[898,103202,12471],{},[1742,103204,1872],{},[1750,103206,1763],{"stretchy":1752},[1750,103208,1917],{"separator":1916},[898,103210,900],{},[1750,103212,1753],{"stretchy":1752},[1742,103214,1872],{},[1750,103216,1917],{"separator":1916},[5535,103218,103219,103221],{},[898,103220,12471],{},[1742,103222,1872],{},[1750,103224,1763],{"stretchy":1752},[1750,103226,1917],{"separator":1916},[898,103228,900],{},[1750,103230,1753],{"stretchy":1752},[1742,103232,7822],{},[1750,103234,1917],{"separator":1916},[5535,103236,103237,103239],{},[898,103238,12471],{},[1742,103240,1872],{},[1750,103242,1763],{"stretchy":1752},[902,103244,103245],{"encoding":904},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[724,103247,103248,102657,103251,103295,103296,103404,103405,1343,103430,1343,103455,103497,103498,1343,103527,103552],{},[38,103249,103250],{},"6.5",[883,103252,103254],{"className":103253},[886],[888,103255,103256],{"xmlns":890},[892,103257,103258,103292],{},[895,103259,103260,103262,103264,103278],{},[898,103261,900],{},[1750,103263,1766],{},[5950,103265,103266,103268,103270],{},[898,103267,12471],{},[1742,103269,1744],{},[895,103271,103272,103274,103276],{},[1742,103273,1872],{},[898,103275,1748],{"mathvariant":1747},[1742,103277,7822],{},[5950,103279,103280,103282,103284],{},[898,103281,12471],{},[1742,103283,1872],{},[895,103285,103286,103288,103290],{},[1742,103287,1744],{},[898,103289,1748],{"mathvariant":1747},[1742,103291,7822],{},[902,103293,103294],{"encoding":904},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[883,103297,103299],{"className":103298},[886],[888,103300,103301],{"xmlns":890},[892,103302,103303,103401],{},[895,103304,103305,103307,103309,103315,103317,103323,103325,103327,103329,103331,103333,103335,103341,103343,103345,103347,103349,103351,103353,103359,103361,103363,103365,103367,103369,103371,103373,103375,103381,103383,103385,103387,103389,103391,103393,103399],{},[898,103306,900],{},[1750,103308,1753],{"stretchy":1752},[5535,103310,103311,103313],{},[898,103312,12471],{},[1742,103314,1744],{},[1750,103316,1917],{"separator":1916},[5535,103318,103319,103321],{},[898,103320,12471],{},[1742,103322,1872],{},[1750,103324,1763],{"stretchy":1752},[1750,103326,1766],{},[1742,103328,1872],{},[1750,103330,1917],{"separator":1916},[898,103332,900],{},[1750,103334,1753],{"stretchy":1752},[5535,103336,103337,103339],{},[898,103338,12471],{},[1742,103340,1744],{},[1750,103342,1917],{"separator":1916},[1742,103344,7822],{},[1750,103346,1763],{"stretchy":1752},[1750,103348,1917],{"separator":1916},[898,103350,900],{},[1750,103352,1753],{"stretchy":1752},[5535,103354,103355,103357],{},[898,103356,12471],{},[1742,103358,1744],{},[1750,103360,1917],{"separator":1916},[1742,103362,1872],{},[1750,103364,1763],{"stretchy":1752},[1750,103366,1917],{"separator":1916},[898,103368,900],{},[1750,103370,1753],{"stretchy":1752},[1742,103372,1872],{},[1750,103374,1917],{"separator":1916},[5535,103376,103377,103379],{},[898,103378,12471],{},[1742,103380,1872],{},[1750,103382,1763],{"stretchy":1752},[1750,103384,1917],{"separator":1916},[898,103386,900],{},[1750,103388,1753],{"stretchy":1752},[1742,103390,7822],{},[1750,103392,1917],{"separator":1916},[5535,103394,103395,103397],{},[898,103396,12471],{},[1742,103398,1872],{},[1750,103400,1763],{"stretchy":1752},[902,103402,103403],{"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 ",[883,103406,103408],{"className":103407},[886],[888,103409,103410],{"xmlns":890},[892,103411,103412,103427],{},[895,103413,103414,103416,103418,103420,103422,103425],{},[898,103415,13916],{},[1750,103417,5141],{"stretchy":1752},[1742,103419,73482],{},[1750,103421,18067],{"separator":1916},[1742,103423,103424],{},"3,555",[1750,103426,5158],{"stretchy":1752},[902,103428,103429],{"encoding":904},"A[1{,}5; 3{,}555]",[883,103431,103433],{"className":103432},[886],[888,103434,103435],{"xmlns":890},[892,103436,103437,103452],{},[895,103438,103439,103441,103443,103445,103447,103450],{},[898,103440,7097],{},[1750,103442,5141],{"stretchy":1752},[1742,103444,62122],{},[1750,103446,18067],{"separator":1916},[1742,103448,103449],{},"1,28",[1750,103451,5158],{"stretchy":1752},[902,103453,103454],{"encoding":904},"B[2{,}5; 1{,}28]",[883,103456,103458],{"className":103457},[886],[888,103459,103460],{"xmlns":890},[892,103461,103462,103494],{},[895,103463,103464,103466,103468,103470,103472,103474,103476,103482,103484,103486,103488,103490,103492],{},[898,103465,1812],{},[1750,103467,5141],{"stretchy":1752},[1742,103469,1872],{},[1750,103471,18067],{"separator":1916},[898,103473,900],{},[1750,103475,1753],{"stretchy":1752},[5535,103477,103478,103480],{},[898,103479,12471],{},[1742,103481,1744],{},[1750,103483,1917],{"separator":1916},[1742,103485,7822],{},[1750,103487,1763],{"stretchy":1752},[1750,103489,1766],{},[1742,103491,7822],{},[1750,103493,5158],{"stretchy":1752},[902,103495,103496],{"encoding":904},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[883,103499,103501],{"className":103500},[886],[888,103502,103503],{"xmlns":890},[892,103504,103505,103524],{},[895,103506,103507,103509,103511,103513,103515,103517,103519,103522],{},[898,103508,5541],{},[1750,103510,5141],{"stretchy":1752},[1742,103512,7822],{},[1750,103514,18067],{"separator":1916},[1742,103516,1744],{},[1750,103518,18067],{"separator":1916},[1742,103520,103521],{},"0,832",[1750,103523,5158],{"stretchy":1752},[902,103525,103526],{"encoding":904},"D[3; 1; 0{,}832]",[883,103528,103530],{"className":103529},[886],[888,103531,103532],{"xmlns":890},[892,103533,103534,103549],{},[895,103535,103536,103538,103540,103542,103544,103547],{},[898,103537,1705],{},[1750,103539,5141],{"stretchy":1752},[1742,103541,62122],{},[1750,103543,18067],{"separator":1916},[1742,103545,103546],{},"4,32",[1750,103548,5158],{"stretchy":1752},[902,103550,103551],{"encoding":904},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[724,103554,103555,102657,103558,103601,103602,16121,103615,103649,103650,103667,103668,103685],{},[38,103556,103557],{},"6.6",[883,103559,103561],{"className":103560},[886],[888,103562,103563],{"xmlns":890},[892,103564,103565,103599],{},[895,103566,103567,103569,103571,103585],{},[898,103568,900],{},[1750,103570,1766],{},[5950,103572,103573,103575,103577],{},[898,103574,12471],{},[1742,103576,1744],{},[895,103578,103579,103581,103583],{},[1742,103580,1872],{},[898,103582,1748],{"mathvariant":1747},[1742,103584,7822],{},[5950,103586,103587,103589,103591],{},[898,103588,12471],{},[1742,103590,1872],{},[895,103592,103593,103595,103597],{},[1742,103594,1744],{},[898,103596,1748],{"mathvariant":1747},[1742,103598,7822],{},[902,103600,103294],{"encoding":904},". (a) Najděte mezní míru komoditní substituce ",[883,103603,103605],{"className":103604},[886],[888,103606,103607],{"xmlns":890},[892,103608,103609,103613],{},[895,103610,103611],{},[1969,103612,20236],{},[902,103614,37161],{"encoding":904},[883,103616,103618],{"className":103617},[886],[888,103619,103620],{"xmlns":890},[892,103621,103622,103646],{},[895,103623,103624,103630,103632,103634,103636,103642,103644],{},[5535,103625,103626,103628],{},[898,103627,12471],{},[1742,103629,1744],{},[1750,103631,1766],{},[1742,103633,4078],{},[1750,103635,1917],{"separator":1916},[5535,103637,103638,103640],{},[898,103639,12471],{},[1742,103641,1872],{},[1750,103643,1766],{},[1742,103645,4159],{},[902,103647,103648],{"encoding":904},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[883,103651,103653],{"className":103652},[886],[888,103654,103655],{"xmlns":890},[892,103656,103657,103665],{},[895,103658,103659],{},[5535,103660,103661,103663],{},[898,103662,12471],{},[1742,103664,1744],{},[902,103666,37925],{"encoding":904},", poklesne-li ",[883,103669,103671],{"className":103670},[886],[888,103672,103673],{"xmlns":890},[892,103674,103675,103683],{},[895,103676,103677],{},[5535,103678,103679,103681],{},[898,103680,12471],{},[1742,103682,1872],{},[902,103684,37944],{"encoding":904}," o 5 vzhledem k hladině dle (b).",[724,103687,103688,103691,103692,103709,103710,103727,103728,103760,103761,103786,103787,103800,103801,1343,103825,1343,103849,2313],{},[38,103689,103690],{},"6.7"," Míra uspokojení z nákupu množství ",[883,103693,103695],{"className":103694},[886],[888,103696,103697],{"xmlns":890},[892,103698,103699,103707],{},[895,103700,103701],{},[5535,103702,103703,103705],{},[898,103704,12471],{},[1742,103706,1744],{},[902,103708,37925],{"encoding":904}," nealko nápojů a množství ",[883,103711,103713],{"className":103712},[886],[888,103714,103715],{"xmlns":890},[892,103716,103717,103725],{},[895,103718,103719],{},[5535,103720,103721,103723],{},[898,103722,12471],{},[1742,103724,1872],{},[902,103726,37944],{"encoding":904}," hamburgerů za týden je dána funkcí užitečnosti ",[883,103729,103731],{"className":103730},[886],[888,103732,103733],{"xmlns":890},[892,103734,103735,103757],{},[895,103736,103737,103739,103741],{},[898,103738,900],{},[1750,103740,1766],{},[17761,103742,103743],{},[895,103744,103745,103751],{},[5535,103746,103747,103749],{},[898,103748,12471],{},[1742,103750,1744],{},[5535,103752,103753,103755],{},[898,103754,12471],{},[1742,103756,1872],{},[902,103758,103759],{"encoding":904},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[883,103762,103764],{"className":103763},[886],[888,103765,103766],{"xmlns":890},[892,103767,103768,103784],{},[895,103769,103770,103776,103778],{},[5535,103771,103772,103774],{},[898,103773,12471],{},[1742,103775,1744],{},[1750,103777,1917],{"separator":1916},[5535,103779,103780,103782],{},[898,103781,12471],{},[1742,103783,1872],{},[902,103785,44545],{"encoding":904},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[883,103788,103790],{"className":103789},[886],[888,103791,103792],{"xmlns":890},[892,103793,103794,103798],{},[895,103795,103796],{},[1969,103797,20236],{},[902,103799,37161],{"encoding":904}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[883,103802,103804],{"className":103803},[886],[888,103805,103806],{"xmlns":890},[892,103807,103808,103822],{},[895,103809,103810,103812,103814,103816,103818,103820],{},[1969,103811,20236],{},[1750,103813,1753],{"stretchy":1752},[1742,103815,7902],{},[1750,103817,1917],{"separator":1916},[1742,103819,6465],{},[1750,103821,1763],{"stretchy":1752},[902,103823,103824],{"encoding":904},"\\text{MRCS}(5, 20)",[883,103826,103828],{"className":103827},[886],[888,103829,103830],{"xmlns":890},[892,103831,103832,103846],{},[895,103833,103834,103836,103838,103840,103842,103844],{},[1969,103835,20236],{},[1750,103837,1753],{"stretchy":1752},[1742,103839,6465],{},[1750,103841,1917],{"separator":1916},[1742,103843,7902],{},[1750,103845,1763],{"stretchy":1752},[902,103847,103848],{"encoding":904},"\\text{MRCS}(20, 5)",[883,103850,103852],{"className":103851},[886],[888,103853,103854],{"xmlns":890},[892,103855,103856,103870],{},[895,103857,103858,103860,103862,103864,103866,103868],{},[1969,103859,20236],{},[1750,103861,1753],{"stretchy":1752},[1742,103863,1872],{},[1750,103865,1917],{"separator":1916},[1742,103867,3936],{},[1750,103869,1763],{"stretchy":1752},[902,103871,103872],{"encoding":904},"\\text{MRCS}(2, 50)",[1785,103874,103875],{},[724,103876,103877,103879,103880,2313],{},[883,103878,6004],{}," Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)\nÚlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[207,103881,103884],{"className":103882,"dataFsResolvedFilePath":911,"href":103883},[210],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[115,103886,10461],{"id":10460},[120,103888,103889,103895,103900,103906,103959,103969,104015,104070,104133,104190,104245,104284],{},[123,103890,103891,103894],{},[38,103892,103893],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[123,103896,103897,103899],{},[38,103898,95792],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[123,103901,103902,103905],{},[38,103903,103904],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[123,103907,103908,103910,103911,103924,103925,2313],{},[38,103909,96119],{}," — uspořádaná ",[883,103912,103914],{"className":103913},[886],[888,103915,103916],{"xmlns":890},[892,103917,103918,103922],{},[895,103919,103920],{},[898,103921,45783],{},[902,103923,45783],{"encoding":904},"-tice ",[883,103926,103928],{"className":103927},[886],[888,103929,103930],{"xmlns":890},[892,103931,103932,103956],{},[895,103933,103934,103936,103942,103944,103946,103948,103954],{},[1750,103935,1753],{"stretchy":1752},[5535,103937,103938,103940],{},[898,103939,12471],{},[1742,103941,1744],{},[1750,103943,1917],{"separator":1916},[1750,103945,19282],{},[1750,103947,1917],{"separator":1916},[5535,103949,103950,103952],{},[898,103951,12471],{},[898,103953,45783],{},[1750,103955,1763],{"stretchy":1752},[902,103957,103958],{"encoding":904},"(Q_1, \\dots, Q_n)",[123,103960,103961,103964,103965,103968],{},[38,103962,103963],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[38,103966,103967],{},"indiferentní svazky"," mají stejnou užitečnost.",[123,103970,103971,1647,103974,104014],{},[38,103972,103973],{},"Funkce užitečnosti",[883,103975,103977],{"className":103976},[886],[888,103978,103979],{"xmlns":890},[892,103980,103981,104011],{},[895,103982,103983,103985,103987,103989,103991,103997,103999,104001,104003,104009],{},[898,103984,900],{},[1750,103986,1766],{},[898,103988,900],{},[1750,103990,1753],{"stretchy":1752},[5535,103992,103993,103995],{},[898,103994,12471],{},[1742,103996,1744],{},[1750,103998,1917],{"separator":1916},[1750,104000,19282],{},[1750,104002,1917],{"separator":1916},[5535,104004,104005,104007],{},[898,104006,12471],{},[898,104008,45783],{},[1750,104010,1763],{"stretchy":1752},[902,104012,104013],{"encoding":904},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[123,104016,104017,1647,104020,104049,104050,1647,104053,104069],{},[38,104018,104019],{},"Mezní užitečnost",[883,104021,104023],{"className":104022},[886],[888,104024,104025],{"xmlns":890},[892,104026,104027,104047],{},[895,104028,104029,104031,104037,104039],{},[898,104030,1773],{},[5535,104032,104033,104035],{},[898,104034,900],{},[898,104036,27363],{},[1750,104038,1766],{},[5950,104040,104041,104043,104045],{},[898,104042,900],{},[898,104044,27363],{},[1750,104046,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[902,104048,95576],{"encoding":904}," — vzorec (6.2); ",[38,104051,104052],{},"totální diferenciál",[883,104054,104056],{"className":104055},[886],[888,104057,104058],{"xmlns":890},[892,104059,104060,104066],{},[895,104061,104062,104064],{},[898,104063,3429],{"mathvariant":1747},[898,104065,900],{},[902,104067,104068],{"encoding":904},"\\mathrm{d} U"," — (6.3).",[123,104071,104072,104074,104075,104099,104100,104132],{},[38,104073,97755],{}," — (6.4) ",[883,104076,104078],{"className":104077},[886],[888,104079,104080],{"xmlns":890},[892,104081,104082,104096],{},[895,104083,104084,104092,104094],{},[5950,104085,104086,104088,104090],{},[898,104087,900],{},[898,104089,27363],{},[1750,104091,3815],{"mathvariant":1747,"lspace":3814,"rspace":3814},[1750,104093,2604],{},[1742,104095,2607],{},[902,104097,104098],{"encoding":904},"U'_i > 0",", (6.5) ",[883,104101,104103],{"className":104102},[886],[888,104104,104105],{"xmlns":890},[892,104106,104107,104129],{},[895,104108,104109,104125,104127],{},[5950,104110,104111,104113,104119],{},[898,104112,900],{},[895,104114,104115,104117],{},[898,104116,27363],{},[898,104118,27363],{},[895,104120,104121,104123],{},[1750,104122,3815],{"mathvariant":1747},[1750,104124,3815],{"mathvariant":1747},[1750,104126,2624],{},[1742,104128,2607],{},[902,104130,104131],{"encoding":904},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[123,104134,104135,1647,104137,104168,104169,2313],{},[38,104136,99543],{},[883,104138,104140],{"className":104139},[886],[888,104141,104142],{"xmlns":890},[892,104143,104144,104166],{},[895,104145,104146,104148,104150,104158],{},[898,104147,900],{},[1750,104149,1766],{},[5950,104151,104152,104154,104156],{},[898,104153,12471],{},[1742,104155,1744],{},[898,104157,207],{},[5950,104159,104160,104162,104164],{},[898,104161,12471],{},[1742,104163,1872],{},[898,104165,2573],{},[902,104167,44726],{"encoding":904}," — (6.6), speciálně ",[883,104170,104172],{"className":104171},[886],[888,104173,104174],{"xmlns":890},[892,104175,104176,104188],{},[895,104177,104178,104180,104182,104184,104186],{},[898,104179,2573],{},[1750,104181,1766],{},[1742,104183,1744],{},[1750,104185,1758],{},[898,104187,207],{},[902,104189,99697],{"encoding":904},[123,104191,104192,1647,104195,104230,104231,104244],{},[38,104193,104194],{},"Křivky užitečnosti (indiferenční)",[883,104196,104198],{"className":104197},[886],[888,104199,104200],{"xmlns":890},[892,104201,104202,104228],{},[895,104203,104204,104206,104208,104214,104216,104222,104224,104226],{},[898,104205,900],{},[1750,104207,1753],{"stretchy":1752},[5535,104209,104210,104212],{},[898,104211,12471],{},[1742,104213,1744],{},[1750,104215,1917],{"separator":1916},[5535,104217,104218,104220],{},[898,104219,12471],{},[1742,104221,1872],{},[1750,104223,1763],{"stretchy":1752},[1750,104225,1766],{},[898,104227,9365],{},[902,104229,19404],{"encoding":904}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[883,104232,104234],{"className":104233},[886],[888,104235,104236],{"xmlns":890},[892,104237,104238,104242],{},[895,104239,104240],{},[898,104241,900],{},[902,104243,900],{"encoding":904},", konvexní.",[123,104246,104247,1647,104249,104283],{},[38,104248,101088],{},[883,104250,104252],{"className":104251},[886],[888,104253,104254],{"xmlns":890},[892,104255,104256,104280],{},[895,104257,104258,104260,104262,104264,104270,104272,104274],{},[1969,104259,20236],{},[1750,104261,1766],{},[898,104263,1773],{},[5535,104265,104266,104268],{},[898,104267,900],{},[1742,104269,1744],{},[898,104271,1748],{"mathvariant":1747},[898,104273,1773],{},[5535,104275,104276,104278],{},[898,104277,900],{},[1742,104279,1872],{},[902,104281,104282],{"encoding":904},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[123,104285,104286,1647,104289,19405,104318,104321],{},[38,104287,104288],{},"Podmínka optimality",[883,104290,104292],{"className":104291},[886],[888,104293,104294],{"xmlns":890},[892,104295,104296,104316],{},[895,104297,104298,104300,104302,104308,104310],{},[1969,104299,20236],{},[1750,104301,1766],{},[5535,104303,104304,104306],{},[898,104305,1776],{},[1742,104307,1744],{},[898,104309,1748],{"mathvariant":1747},[5535,104311,104312,104314],{},[898,104313,1776],{},[1742,104315,1872],{},[902,104317,36921],{"encoding":904},[207,104319,45677],{"className":104320,"dataFsResolvedFilePath":911,"href":912},[210]," pro plné odvození.",[115,104323,11524],{"id":11523},[120,104325,104326,104363,104404,104414],{},[123,104327,104328,1647,104331,104334,104335,104348,104349,104362],{},[38,104329,104330],{},"Navazující téma:",[207,104332,913],{"className":104333,"dataFsResolvedFilePath":911,"href":912},[210]," (Lagrange, max ",[883,104336,104338],{"className":104337},[886],[888,104339,104340],{"xmlns":890},[892,104341,104342,104346],{},[895,104343,104344],{},[898,104345,900],{},[902,104347,900],{"encoding":904},", min ",[883,104350,104352],{"className":104351},[886],[888,104353,104354],{"xmlns":890},[892,104355,104356,104360],{},[895,104357,104358],{},[898,104359,1705],{},[902,104361,1705],{"encoding":904},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[123,104364,104365,1647,104368,20725,104371,95331,104374,104377,104378,104381,104382,2440,104400,104403],{},[38,104366,104367],{},"Související pojmy:",[207,104369,784],{"className":104370,"dataFsResolvedFilePath":782,"href":783},[210],[207,104372,12053],{"className":104373,"dataFsResolvedFilePath":764,"href":765},[210],[207,104375,20720],{"className":104376,"dataFsResolvedFilePath":857,"href":858},[210]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[207,104379,21574],{"className":104380,"dataFsResolvedFilePath":800,"href":801},[210]," (Marshallovy poptávkové funkce ",[883,104383,104385],{"className":104384},[886],[888,104386,104387],{"xmlns":890},[892,104388,104389,104397],{},[895,104390,104391],{},[5535,104392,104393,104395],{},[898,104394,5541],{},[898,104396,27363],{},[902,104398,104399],{"encoding":904},"D_i",[207,104401,793],{"className":104402,"dataFsResolvedFilePath":791,"href":792},[210]," (vázaná optimalizace — nástroj pro navazující téma).",[123,104405,104406,1647,104408,1343,104411],{},[38,104407,45626],{},[207,104409,1094],{"className":104410,"dataFsResolvedFilePath":838,"href":839},[210],[207,104412,1101],{"className":104413,"dataFsResolvedFilePath":868,"href":869},[210],[123,104415,104416,1647,104418],{},[38,104417,11531],{},[207,104419,11535],{"className":104420,"dataFsResolvedFilePath":1644,"href":1645},[210],{"title":641,"searchDepth":642,"depth":642,"links":104422},[104423,104424,104425,104428,104429,104432,104436,104437,104440,104441,104442,104443,104444,104445,104446],{"id":1636,"depth":642,"text":1637},{"id":95715,"depth":642,"text":95716},{"id":95775,"depth":642,"text":95776,"children":104426},[104427],{"id":95791,"depth":649,"text":95792},{"id":96098,"depth":642,"text":96099},{"id":96958,"depth":642,"text":96959,"children":104430},[104431],{"id":97505,"depth":649,"text":89134},{"id":97754,"depth":642,"text":97755,"children":104433},[104434],{"id":98627,"depth":649,"text":104435},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":99542,"depth":642,"text":99543},{"id":100078,"depth":642,"text":100079,"children":104438},[104439],{"id":100852,"depth":649,"text":100853},{"id":101082,"depth":642,"text":101083},{"id":101843,"depth":642,"text":101844},{"id":102381,"depth":642,"text":102382},{"id":58804,"depth":642,"text":58805},{"id":102517,"depth":642,"text":102518},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Fuzitecnost",{"title":95499,"description":641},[1138,1137],"topics\u002Fuzitecnost",[1128,19409,104453,95493,20755,104454],"mezni-uzitecnost","mrcs","xXggD9rfV5faUAk1b2B3YYbozpQLu-pObiMaZX5f7yI",{"id":104457,"title":757,"body":104458,"course":1128,"courses":659,"created":1129,"description":104731,"extension":661,"meta":104732,"navigation":664,"path":104733,"seo":104734,"sources":104735,"stem":104736,"tags":104737,"type":11664,"updated":677,"__hash__":104743},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":9,"value":104459,"toc":104723},[104460,104463,104470,104477,104481,104491,104493,104527,104531,104574,104577,104635,104639,104669,104673,104694,104696],[12,104461,757],{"id":104462},"základy-matematické-ekonomie",[724,104464,104465,104466,104469],{},"Úvodní pojmy a princip modelování v ",[207,104467,25953],{"className":104468,"dataFsResolvedFilePath":1644,"href":1645},[210],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[724,104471,104472],{},[4434,104473],{"alt":104474,"className":104475,"src":104476},"imek-model-promenne",[210,4438],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[115,104478,104480],{"id":104479},"co-je-matematická-ekonomie","Co je matematická ekonomie",[724,104482,104483,104486,104487,104490],{},[38,104484,104485],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[38,104488,104489],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[115,104492,10461],{"id":10460},[120,104494,104495,104501,104507,104513,104522],{},[123,104496,104497,104500],{},[38,104498,104499],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[123,104502,104503,104506],{},[38,104504,104505],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[123,104508,104509,104512],{},[38,104510,104511],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[123,104514,104515,10469,104518,104521],{},[38,104516,104517],{},"Ceteris paribus",[614,104519,104520],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[123,104523,104524,104526],{},[38,104525,59558],{}," — odezva endogenních proměnných na změnu některé exogenní.",[115,104528,104530],{"id":104529},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[724,104532,104533,104573],{},[883,104534,104536],{"className":104535},[886],[888,104537,104538],{"xmlns":890},[892,104539,104540,104570],{},[895,104541,104542,104544,104546,104548,104550,104552,104554,104556,104558,104560,104562,104564,104566,104568],{},[898,104543,12471],{},[1750,104545,1766],{},[898,104547,5541],{},[1750,104549,1753],{"stretchy":1752},[898,104551,1776],{},[1750,104553,1917],{"separator":1916},[898,104555,1666],{},[1750,104557,1917],{"separator":1916},[898,104559,2078],{},[1750,104561,1917],{"separator":1916},[898,104563,900],{},[1750,104565,1917],{"separator":1916},[1750,104567,19282],{},[1750,104569,1763],{"stretchy":1752},[902,104571,104572],{"encoding":904},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[724,104575,104576],{},"Zjednodušení:",[120,104578,104579,104607],{},[123,104580,104581,1647,104584],{},[38,104582,104583],{},"Jednofaktorový model:",[883,104585,104587],{"className":104586},[886],[888,104588,104589],{"xmlns":890},[892,104590,104591,104605],{},[895,104592,104593,104595,104597,104599,104601,104603],{},[898,104594,12471],{},[1750,104596,1766],{},[898,104598,5541],{},[1750,104600,1753],{"stretchy":1752},[898,104602,1776],{},[1750,104604,1763],{"stretchy":1752},[902,104606,13854],{"encoding":904},[123,104608,104609,1647,104612],{},[38,104610,104611],{},"Inverzní zápis:",[883,104613,104615],{"className":104614},[886],[888,104616,104617],{"xmlns":890},[892,104618,104619,104633],{},[895,104620,104621,104623,104625,104627,104629,104631],{},[898,104622,1776],{},[1750,104624,1766],{},[898,104626,5541],{},[1750,104628,1753],{"stretchy":1752},[898,104630,12471],{},[1750,104632,1763],{"stretchy":1752},[902,104634,14297],{"encoding":904},[115,104636,104638],{"id":104637},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[152,104640,104641,104650],{},[123,104642,104643,104646,104647,1783],{},[38,104644,104645],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[207,104648,11564],{"className":104649,"dataFsResolvedFilePath":800,"href":801},[210],[123,104651,104652,104655,104656,104659,104660,104663,104664,104668],{},[38,104653,104654],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[207,104657,1145],{"className":104658,"dataFsResolvedFilePath":764,"href":765},[210]," pro 1D, ",[207,104661,25826],{"className":104662,"dataFsResolvedFilePath":782,"href":783},[210]," pro 2D, ",[207,104665,104667],{"className":104666,"dataFsResolvedFilePath":791,"href":792},[210],"lagrangeova-metoda"," pro vázané extrémy).",[115,104670,104672],{"id":104671},"konvence-z-přednášek","Konvence z přednášek",[120,104674,104675,104682,104688],{},[123,104676,104677,104678,104681],{},"Symbol ",[104679,104680,2274],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[123,104683,104684,104685,2313],{},"Numerické výsledky ",[38,104686,104687],{},"na 3 desetinná místa",[123,104689,13561,104690,104693],{},[614,104691,104692],{},"jednotková změna"," má standardní význam (změna o 1).",[115,104695,11524],{"id":11523},[120,104697,104698,104703,104711],{},[123,104699,104700,104702],{},[38,104701,13467],{}," —",[123,104704,104705,1647,104707],{},[38,104706,13475],{},[207,104708,104710],{"className":104709,"dataFsResolvedFilePath":764,"href":765},[210],"Derivace a diferenciál",[123,104712,104713,1647,104715,1343,104719],{},[38,104714,13483],{},[207,104716,104718],{"className":104717,"dataFsResolvedFilePath":745,"href":746},[210],"Souhrn KS 1. blok",[207,104720,104722],{"className":104721,"dataFsResolvedFilePath":1644,"href":1645},[210],"kurz ImeK",{"title":641,"searchDepth":642,"depth":642,"links":104724},[104725,104726,104727,104728,104729,104730],{"id":104479,"depth":642,"text":104480},{"id":10460,"depth":642,"text":10461},{"id":104529,"depth":642,"text":104530},{"id":104637,"depth":642,"text":104638},{"id":104671,"depth":642,"text":104672},{"id":11523,"depth":642,"text":11524},"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":104731},[1135],"topics\u002Fzaklady-matematicke-ekonomie",[1128,104738,104739,104740,104741,104742],"model","endogenni","exogenni","ceteris-paribus","komparativni-statika","UZ1xD3l_gK41y8KlCBmpjprMOjIWmHZR8WZt-takTSI",{"id":104745,"title":104746,"body":104747,"course":1128,"courses":659,"created":11652,"description":641,"extension":661,"meta":109019,"navigation":664,"path":109020,"seo":109021,"sources":109022,"stem":109023,"tags":109024,"type":11664,"updated":677,"__hash__":109028},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":9,"value":104748,"toc":109002},[104749,104752,104846,104850,104872,104886,104938,104940,104944,105007,105050,105069,105232,105331,105334,105401,105405,105534,105573,105603,105715,105760,105826,105879,105955,106011,106013,106017,106081,106125,106145,106306,106309,106393,106490,106493,106559,106563,106612,106638,106743,106807,106812,106908,106955,106957,106960,106982,107024,107031,107064,107066,107137,107191,107300,107304,107393,107469,107733,107771,107773,107777,107780,107787,108098,108101,108159,108339,108368,108370,108374,108380,108518,108527,108529,108531,108956,108958,108960],[12,104750,104746],{"id":104751},"zdanění-trhu-dopady-daně-na-rovnováhu",[1785,104753,104754],{},[724,104755,104756,51551,104758,104771,104772,104775,104776,104778,104779,104782,104783,104804,104805,104828,104829,104832,104833,2313],{},[883,104757,1791],{},[883,104759,104761],{"className":104760},[886],[888,104762,104763],{"xmlns":890},[892,104764,104765,104769],{},[895,104766,104767],{},[898,104768,5326],{},[902,104770,5326],{"encoding":904}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[38,104773,104774],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[38,104777,95783],{}," (je-li uložena spotřebiteli). Výsledné ",[38,104780,104781],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[883,104784,104786],{"className":104785},[886],[888,104787,104788],{"xmlns":890},[892,104789,104790,104802],{},[895,104791,104792],{},[5535,104793,104794,104796],{},[898,104795,5326],{},[895,104797,104798,104800],{},[898,104799,51600],{},[898,104801,724],{},[902,104803,51605],{"encoding":904}," (spotřebitel) a ",[883,104806,104808],{"className":104807},[886],[888,104809,104810],{"xmlns":890},[892,104811,104812,104826],{},[895,104813,104814],{},[5535,104815,104816,104818],{},[898,104817,5326],{},[895,104819,104820,104822,104824],{},[898,104821,51623],{},[898,104823,11717],{},[898,104825,1920],{},[902,104827,51630],{"encoding":904}," (výrobce). Klíčovým zjištěním je ",[38,104830,104831],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[883,104834,104836],{"className":104835},[886],[888,104837,104838],{"xmlns":890},[892,104839,104840,104844],{},[895,104841,104842],{},[898,104843,5326],{},[902,104845,5326],{"encoding":904},[115,104847,104849],{"id":104848},"dvě-formy-zdanění","Dvě formy zdanění",[724,104851,104852,104853,104871],{},"Uvažujme jednotkovou daň ",[883,104854,104856],{"className":104855},[886],[888,104857,104858],{"xmlns":890},[892,104859,104860,104868],{},[895,104861,104862,104864,104866],{},[898,104863,5326],{},[1750,104865,2604],{},[1742,104867,2607],{},[902,104869,104870],{"encoding":904},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[120,104873,104874,104880],{},[123,104875,104876,104879],{},[38,104877,104878],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[123,104881,104882,104885],{},[38,104883,104884],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[724,104887,104888,104889,104902,104903,104906,104907,2313],{},"V obou případech dochází k posunu jedné z křivek o ",[883,104890,104892],{"className":104891},[886],[888,104893,104894],{"xmlns":890},[892,104895,104896,104900],{},[895,104897,104898],{},[898,104899,5326],{},[902,104901,5326],{"encoding":904}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[38,104904,104905],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[883,104908,104910],{"className":104909},[886],[888,104911,104912],{"xmlns":890},[892,104913,104914,104936],{},[895,104915,104916,104918,104920,104926,104928,104934],{},[898,104917,1705],{},[1750,104919,5141],{"stretchy":1752},[1699,104921,104922,104924],{},[898,104923,12471],{},[898,104925,1705],{},[1750,104927,1917],{"separator":1916},[1699,104929,104930,104932],{},[898,104931,1776],{},[898,104933,1705],{},[1750,104935,5158],{"stretchy":1752},[902,104937,50290],{"encoding":904},[45893,104939],{},[115,104941,104943],{"id":104942},"daň-uložená-výrobci","Daň uložená výrobci",[724,104945,104946,104947,104960,104961,104978,104979,105006],{},"Je-li daň ",[883,104948,104950],{"className":104949},[886],[888,104951,104952],{"xmlns":890},[892,104953,104954,104958],{},[895,104955,104956],{},[898,104957,5326],{},[902,104959,5326],{"encoding":904}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[883,104962,104964],{"className":104963},[886],[888,104965,104966],{"xmlns":890},[892,104967,104968,104976],{},[895,104969,104970,104972,104974],{},[898,104971,1776],{},[1750,104973,1758],{},[898,104975,5326],{},[902,104977,50045],{"encoding":904}," (hrubá cena mínus odvod), plyne z rovnice ",[883,104980,104982],{"className":104981},[886],[888,104983,104984],{"xmlns":890},[892,104985,104986,105004],{},[895,104987,104988,104990,104992,104994,104996,104998,105000,105002],{},[898,104989,1776],{},[1750,104991,1758],{},[898,104993,5326],{},[1750,104995,1766],{},[898,104997,1779],{},[1750,104999,1753],{"stretchy":1752},[898,105001,12471],{},[1750,105003,1763],{"stretchy":1752},[902,105005,50074],{"encoding":904}," nová funkce nabídky:",[883,105008,105010],{"className":105009},[886],[888,105011,105012],{"xmlns":890,"display":36989},[892,105013,105014,105048],{},[895,105015,105016,105018,105020,105026,105028,105030,105032,105034,105036,105038,105040,105042,105044,105046],{},[898,105017,1776],{},[1750,105019,1766],{},[5535,105021,105022,105024],{},[898,105023,1779],{},[1742,105025,1744],{},[1750,105027,1753],{"stretchy":1752},[898,105029,12471],{},[1750,105031,1763],{"stretchy":1752},[1750,105033,1766],{},[898,105035,1779],{},[1750,105037,1753],{"stretchy":1752},[898,105039,12471],{},[1750,105041,1763],{"stretchy":1752},[1750,105043,1861],{},[898,105045,5326],{},[898,105047,2313],{"mathvariant":1747},[902,105049,50119],{"encoding":904},[724,105051,105052,105053,1647,105066,105068],{},"Nabídka se tedy posouvá o ",[883,105054,105056],{"className":105055},[886],[888,105057,105058],{"xmlns":890},[892,105059,105060,105064],{},[895,105061,105062],{},[898,105063,5326],{},[902,105065,5326],{"encoding":904},[38,105067,50152],{}," (ekvivalentně doleva). Poptávka se nemění.",[724,105070,105071,105072,105112,105113,2028,105141,105169,105170,105189,105190,105214,105215,1783],{},"Nový rovnovážný bod ",[883,105073,105075],{"className":105074},[886],[888,105076,105077],{"xmlns":890},[892,105078,105079,105109],{},[895,105080,105081,105087,105089,105097,105099,105107],{},[5535,105082,105083,105085],{},[898,105084,1705],{},[1742,105086,1744],{},[1750,105088,5141],{"stretchy":1752},[5950,105090,105091,105093,105095],{},[898,105092,12471],{},[1742,105094,1744],{},[898,105096,1705],{},[1750,105098,1917],{"separator":1916},[5950,105100,105101,105103,105105],{},[898,105102,1776],{},[1742,105104,1744],{},[898,105106,1705],{},[1750,105108,5158],{"stretchy":1752},[902,105110,105111],{"encoding":904},"E_1[Q_1^E, P_1^E]"," splňuje ",[883,105114,105116],{"className":105115},[886],[888,105117,105118],{"xmlns":890},[892,105119,105120,105138],{},[895,105121,105122,105130,105132],{},[5950,105123,105124,105126,105128],{},[898,105125,12471],{},[1742,105127,1744],{},[898,105129,1705],{},[1750,105131,2624],{},[1699,105133,105134,105136],{},[898,105135,12471],{},[898,105137,1705],{},[902,105139,105140],{"encoding":904},"Q_1^E \u003C Q^E",[883,105142,105144],{"className":105143},[886],[888,105145,105146],{"xmlns":890},[892,105147,105148,105166],{},[895,105149,105150,105158,105160],{},[5950,105151,105152,105154,105156],{},[898,105153,1776],{},[1742,105155,1744],{},[898,105157,1705],{},[1750,105159,2604],{},[1699,105161,105162,105164],{},[898,105163,1776],{},[898,105165,1705],{},[902,105167,105168],{"encoding":904},"P_1^E > P^E",". Spotřebitel platí ",[883,105171,105173],{"className":105172},[886],[888,105174,105175],{"xmlns":890},[892,105176,105177,105187],{},[895,105178,105179],{},[5950,105180,105181,105183,105185],{},[898,105182,1776],{},[1742,105184,1744],{},[898,105186,1705],{},[902,105188,56780],{"encoding":904},", výrobci ale zůstává pouze čistá cena ",[883,105191,105193],{"className":105192},[886],[888,105194,105195],{"xmlns":890},[892,105196,105197,105211],{},[895,105198,105199,105207,105209],{},[5950,105200,105201,105203,105205],{},[898,105202,1776],{},[1742,105204,1744],{},[898,105206,1705],{},[1750,105208,1758],{},[898,105210,5326],{},[902,105212,105213],{"encoding":904},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[883,105216,105218],{"className":105217},[886],[888,105219,105220],{"xmlns":890},[892,105221,105222,105230],{},[895,105223,105224],{},[1699,105225,105226,105228],{},[898,105227,1776],{},[898,105229,1705],{},[902,105231,50389],{"encoding":904},[724,105233,105234],{},[614,105235,105236,105237,105267,105268,105281,105282,9375,105299,105312,105313,2313],{},"Obrázek 2.17 (resp. 2.18): Posun ",[883,105238,105240],{"className":105239},[886],[888,105241,105242],{"xmlns":890},[892,105243,105244,105264],{},[895,105245,105246,105248,105250,105256,105258,105260,105262],{},[898,105247,1779],{},[1750,105249,12797],{},[5535,105251,105252,105254],{},[898,105253,1779],{},[1742,105255,1744],{},[1750,105257,1766],{},[898,105259,1779],{},[1750,105261,1861],{},[898,105263,5326],{},[902,105265,105266],{"encoding":904},"S \\to S_1 = S + T","; svislá vzdálenost mezi křivkami je přesně ",[883,105269,105271],{"className":105270},[886],[888,105272,105273],{"xmlns":890},[892,105274,105275,105279],{},[895,105276,105277],{},[898,105278,5326],{},[902,105280,5326],{"encoding":904},". Průsečík ",[883,105283,105285],{"className":105284},[886],[888,105286,105287],{"xmlns":890},[892,105288,105289,105297],{},[895,105290,105291],{},[5535,105292,105293,105295],{},[898,105294,1779],{},[1742,105296,1744],{},[902,105298,49920],{"encoding":904},[883,105300,105302],{"className":105301},[886],[888,105303,105304],{"xmlns":890},[892,105305,105306,105310],{},[895,105307,105308],{},[898,105309,5541],{},[902,105311,5541],{"encoding":904}," je nový rovnovážný bod ",[883,105314,105316],{"className":105315},[886],[888,105317,105318],{"xmlns":890},[892,105319,105320,105328],{},[895,105321,105322],{},[5535,105323,105324,105326],{},[898,105325,1705],{},[1742,105327,1744],{},[902,105329,105330],{"encoding":904},"E_1",[198,105332,54226],{"id":105333},"příklad-29",[724,105335,105336,50578,105338,50613,105362,105382,105383,105400],{},[38,105337,46856],{},[883,105339,105341],{"className":105340},[886],[888,105342,105343],{"xmlns":890},[892,105344,105345,105359],{},[895,105346,105347,105349,105351,105353,105355,105357],{},[898,105348,1776],{},[1750,105350,1766],{},[1742,105352,4903],{},[1750,105354,1758],{},[1742,105356,1872],{},[898,105358,12471],{},[902,105360,105361],{"encoding":904},"P = 12 - 2Q",[883,105363,105365],{"className":105364},[886],[888,105366,105367],{"xmlns":890},[892,105368,105369,105379],{},[895,105370,105371,105373,105375,105377],{},[898,105372,1776],{},[1750,105374,1766],{},[1742,105376,7859],{},[898,105378,12471],{},[902,105380,105381],{"encoding":904},"P = 4Q",". Na výrobce je uložena jednotková daň ",[883,105384,105386],{"className":105385},[886],[888,105387,105388],{"xmlns":890},[892,105389,105390,105398],{},[895,105391,105392,105394,105396],{},[898,105393,5326],{},[1750,105395,1766],{},[1742,105397,3219],{},[902,105399,50191],{"encoding":904}," Kč.",[724,105402,105403],{},[38,105404,46888],{},[724,105406,105407,105410,105411,15223,105437,8164,105457,1343,105479,105509,105510,2313],{},[614,105408,105409],{},"Bez daně."," Z rovnosti ",[883,105412,105414],{"className":105413},[886],[888,105415,105416],{"xmlns":890},[892,105417,105418,105434],{},[895,105419,105420,105422,105424,105426,105428,105430,105432],{},[1742,105421,4903],{},[1750,105423,1758],{},[1742,105425,1872],{},[898,105427,12471],{},[1750,105429,1766],{},[1742,105431,7859],{},[898,105433,12471],{},[902,105435,105436],{"encoding":904},"12 - 2Q = 4Q",[883,105438,105440],{"className":105439},[886],[888,105441,105442],{"xmlns":890},[892,105443,105444,105454],{},[895,105445,105446,105448,105450,105452],{},[1742,105447,3219],{},[898,105449,12471],{},[1750,105451,1766],{},[1742,105453,4903],{},[902,105455,105456],{"encoding":904},"6Q = 12",[883,105458,105460],{"className":105459},[886],[888,105461,105462],{"xmlns":890},[892,105463,105464,105476],{},[895,105465,105466,105472,105474],{},[1699,105467,105468,105470],{},[898,105469,12471],{},[898,105471,1705],{},[1750,105473,1766],{},[1742,105475,1872],{},[902,105477,105478],{"encoding":904},"Q^E = 2",[883,105480,105482],{"className":105481},[886],[888,105483,105484],{"xmlns":890},[892,105485,105486,105506],{},[895,105487,105488,105494,105496,105498,105500,105502,105504],{},[1699,105489,105490,105492],{},[898,105491,1776],{},[898,105493,1705],{},[1750,105495,1766],{},[1742,105497,7859],{},[1750,105499,8009],{},[1742,105501,1872],{},[1750,105503,1766],{},[1742,105505,15239],{},[902,105507,105508],{"encoding":904},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[883,105511,105513],{"className":105512},[886],[888,105514,105515],{"xmlns":890},[892,105516,105517,105531],{},[895,105518,105519,105521,105523,105525,105527,105529],{},[898,105520,1705],{},[1750,105522,5141],{"stretchy":1752},[1742,105524,1872],{},[1750,105526,1917],{"separator":1916},[1742,105528,15239],{},[1750,105530,5158],{"stretchy":1752},[902,105532,105533],{"encoding":904},"E[2, 8]",[724,105535,105536,105539,105540,105572],{},[614,105537,105538],{},"S daní uloženou výrobci."," Nová nabídka je ",[883,105541,105543],{"className":105542},[886],[888,105544,105545],{"xmlns":890},[892,105546,105547,105569],{},[895,105548,105549,105555,105557,105559,105561,105563,105565,105567],{},[5535,105550,105551,105553],{},[898,105552,1779],{},[1742,105554,1744],{},[1750,105556,2366],{},[898,105558,1776],{},[1750,105560,1766],{},[1742,105562,7859],{},[898,105564,12471],{},[1750,105566,1861],{},[1742,105568,3219],{},[902,105570,105571],{"encoding":904},"S_1: P = 4Q + 6",". Z rovnice",[883,105574,105576],{"className":105575},[886],[888,105577,105578],{"xmlns":890,"display":36989},[892,105579,105580,105600],{},[895,105581,105582,105584,105586,105588,105590,105592,105594,105596,105598],{},[1742,105583,4903],{},[1750,105585,1758],{},[1742,105587,1872],{},[898,105589,12471],{},[1750,105591,1766],{},[1742,105593,7859],{},[898,105595,12471],{},[1750,105597,1861],{},[1742,105599,3219],{},[902,105601,105602],{"encoding":904},"12 - 2Q = 4Q + 6",[724,105604,105605,105606,8164,105626,1343,105650,105686,105687,2313],{},"plyne ",[883,105607,105609],{"className":105608},[886],[888,105610,105611],{"xmlns":890},[892,105612,105613,105623],{},[895,105614,105615,105617,105619,105621],{},[1742,105616,3219],{},[898,105618,12471],{},[1750,105620,1766],{},[1742,105622,3219],{},[902,105624,105625],{"encoding":904},"6Q = 6",[883,105627,105629],{"className":105628},[886],[888,105630,105631],{"xmlns":890},[892,105632,105633,105647],{},[895,105634,105635,105643,105645],{},[5950,105636,105637,105639,105641],{},[898,105638,12471],{},[1742,105640,1744],{},[898,105642,1705],{},[1750,105644,1766],{},[1742,105646,1744],{},[902,105648,105649],{"encoding":904},"Q_1^E = 1",[883,105651,105653],{"className":105652},[886],[888,105654,105655],{"xmlns":890},[892,105656,105657,105683],{},[895,105658,105659,105667,105669,105671,105673,105675,105677,105679,105681],{},[5950,105660,105661,105663,105665],{},[898,105662,1776],{},[1742,105664,1744],{},[898,105666,1705],{},[1750,105668,1766],{},[1742,105670,7859],{},[1750,105672,8009],{},[1742,105674,1744],{},[1750,105676,1861],{},[1742,105678,3219],{},[1750,105680,1766],{},[1742,105682,3079],{},[902,105684,105685],{"encoding":904},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[883,105688,105690],{"className":105689},[886],[888,105691,105692],{"xmlns":890},[892,105693,105694,105712],{},[895,105695,105696,105702,105704,105706,105708,105710],{},[5535,105697,105698,105700],{},[898,105699,1705],{},[1742,105701,1744],{},[1750,105703,5141],{"stretchy":1752},[1742,105705,1744],{},[1750,105707,1917],{"separator":1916},[1742,105709,3079],{},[1750,105711,5158],{"stretchy":1752},[902,105713,105714],{"encoding":904},"E_1[1, 10]",[724,105716,105717,105720,105721,105745,105746,105759],{},[614,105718,105719],{},"Rozklad daňového břemene."," Spotřebitel platí ",[883,105722,105724],{"className":105723},[886],[888,105725,105726],{"xmlns":890},[892,105727,105728,105742],{},[895,105729,105730,105738,105740],{},[5950,105731,105732,105734,105736],{},[898,105733,1776],{},[1742,105735,1744],{},[898,105737,1705],{},[1750,105739,1766],{},[1742,105741,3079],{},[902,105743,105744],{"encoding":904},"P_1^E = 10"," Kč namísto původních ",[883,105747,105749],{"className":105748},[886],[888,105750,105751],{"xmlns":890},[892,105752,105753,105757],{},[895,105754,105755],{},[1742,105756,15239],{},[902,105758,15239],{"encoding":904},", navýšení je",[883,105761,105763],{"className":105762},[886],[888,105764,105765],{"xmlns":890,"display":36989},[892,105766,105767,105823],{},[895,105768,105769,105779,105781,105789,105791,105797,105799,105801,105803,105805,105807,105809,105811,105821],{},[5535,105770,105771,105773],{},[898,105772,5326],{},[895,105774,105775,105777],{},[898,105776,51600],{},[898,105778,724],{},[1750,105780,1766],{},[5950,105782,105783,105785,105787],{},[898,105784,1776],{},[1742,105786,1744],{},[898,105788,1705],{},[1750,105790,1758],{},[1699,105792,105793,105795],{},[898,105794,1776],{},[898,105796,1705],{},[1750,105798,1766],{},[1742,105800,3079],{},[1750,105802,1758],{},[1742,105804,15239],{},[1750,105806,1766],{},[1742,105808,1872],{},[1969,105810,7737],{},[895,105812,105813,105815],{},[1969,105814,19435],{},[3215,105816,105817,105819],{"accent":1916},[1969,105818,9365],{},[1750,105820,8912],{},[898,105822,2313],{"mathvariant":1747},[902,105824,105825],{"encoding":904},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[724,105827,105828,105829,105745,105865,105878],{},"Výrobci zůstává čistá cena ",[883,105830,105832],{"className":105831},[886],[888,105833,105834],{"xmlns":890},[892,105835,105836,105862],{},[895,105837,105838,105846,105848,105850,105852,105854,105856,105858,105860],{},[5950,105839,105840,105842,105844],{},[898,105841,1776],{},[1742,105843,1744],{},[898,105845,1705],{},[1750,105847,1758],{},[898,105849,5326],{},[1750,105851,1766],{},[1742,105853,3079],{},[1750,105855,1758],{},[1742,105857,3219],{},[1750,105859,1766],{},[1742,105861,7859],{},[902,105863,105864],{"encoding":904},"P_1^E - T = 10 - 6 = 4",[883,105866,105868],{"className":105867},[886],[888,105869,105870],{"xmlns":890},[892,105871,105872,105876],{},[895,105873,105874],{},[1742,105875,15239],{},[902,105877,15239],{"encoding":904},", pokles je",[883,105880,105882],{"className":105881},[886],[888,105883,105884],{"xmlns":890,"display":36989},[892,105885,105886,105952],{},[895,105887,105888,105900,105902,105908,105910,105912,105920,105922,105924,105926,105928,105930,105932,105934,105936,105938,105940,105950],{},[5535,105889,105890,105892],{},[898,105891,5326],{},[895,105893,105894,105896,105898],{},[898,105895,51623],{},[898,105897,11717],{},[898,105899,1920],{},[1750,105901,1766],{},[1699,105903,105904,105906],{},[898,105905,1776],{},[898,105907,1705],{},[1750,105909,1758],{},[1750,105911,1753],{"stretchy":1752},[5950,105913,105914,105916,105918],{},[898,105915,1776],{},[1742,105917,1744],{},[898,105919,1705],{},[1750,105921,1758],{},[898,105923,5326],{},[1750,105925,1763],{"stretchy":1752},[1750,105927,1766],{},[1742,105929,15239],{},[1750,105931,1758],{},[1742,105933,7859],{},[1750,105935,1766],{},[1742,105937,7859],{},[1969,105939,7737],{},[895,105941,105942,105944],{},[1969,105943,19435],{},[3215,105945,105946,105948],{"accent":1916},[1969,105947,9365],{},[1750,105949,8912],{},[898,105951,2313],{"mathvariant":1747},[902,105953,105954],{"encoding":904},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[724,105956,105957,105958,106010],{},"Kontrola: ",[883,105959,105961],{"className":105960},[886],[888,105962,105963],{"xmlns":890},[892,105964,105965,106007],{},[895,105966,105967,105977,105979,105991,105993,105995,105997,105999,106001,106003,106005],{},[5535,105968,105969,105971],{},[898,105970,5326],{},[895,105972,105973,105975],{},[898,105974,51600],{},[898,105976,724],{},[1750,105978,1861],{},[5535,105980,105981,105983],{},[898,105982,5326],{},[895,105984,105985,105987,105989],{},[898,105986,51623],{},[898,105988,11717],{},[898,105990,1920],{},[1750,105992,1766],{},[1742,105994,1872],{},[1750,105996,1861],{},[1742,105998,7859],{},[1750,106000,1766],{},[1742,106002,3219],{},[1750,106004,1766],{},[898,106006,5326],{},[902,106008,106009],{"encoding":904},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[45893,106012],{},[115,106014,106016],{"id":106015},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[724,106018,104946,106019,106032,106033,106051,106052,106080],{},[883,106020,106022],{"className":106021},[886],[888,106023,106024],{"xmlns":890},[892,106025,106026,106030],{},[895,106027,106028],{},[898,106029,5326],{},[902,106031,5326],{"encoding":904}," uložena spotřebiteli, pak spotřebitel platí celkem ",[883,106034,106036],{"className":106035},[886],[888,106037,106038],{"xmlns":890},[892,106039,106040,106048],{},[895,106041,106042,106044,106046],{},[898,106043,1776],{},[1750,106045,1861],{},[898,106047,5326],{},[902,106049,106050],{"encoding":904},"P + T"," (cena prodejce plus daň). Z podmínky ",[883,106053,106055],{"className":106054},[886],[888,106056,106057],{"xmlns":890},[892,106058,106059,106077],{},[895,106060,106061,106063,106065,106067,106069,106071,106073,106075],{},[898,106062,1776],{},[1750,106064,1861],{},[898,106066,5326],{},[1750,106068,1766],{},[898,106070,5541],{},[1750,106072,1753],{"stretchy":1752},[898,106074,12471],{},[1750,106076,1763],{"stretchy":1752},[902,106078,106079],{"encoding":904},"P + T = D(Q)"," plyne nová funkce poptávky:",[883,106082,106084],{"className":106083},[886],[888,106085,106086],{"xmlns":890,"display":36989},[892,106087,106088,106122],{},[895,106089,106090,106092,106094,106100,106102,106104,106106,106108,106110,106112,106114,106116,106118,106120],{},[898,106091,1776],{},[1750,106093,1766],{},[5535,106095,106096,106098],{},[898,106097,5541],{},[1742,106099,1872],{},[1750,106101,1753],{"stretchy":1752},[898,106103,12471],{},[1750,106105,1763],{"stretchy":1752},[1750,106107,1766],{},[898,106109,5541],{},[1750,106111,1753],{"stretchy":1752},[898,106113,12471],{},[1750,106115,1763],{"stretchy":1752},[1750,106117,1758],{},[898,106119,5326],{},[898,106121,2313],{"mathvariant":1747},[902,106123,106124],{"encoding":904},"P = D_2(Q) = D(Q) - T.",[724,106126,106127,106128,1647,106141,106144],{},"Poptávka se tedy posouvá o ",[883,106129,106131],{"className":106130},[886],[888,106132,106133],{"xmlns":890},[892,106134,106135,106139],{},[895,106136,106137],{},[898,106138,5326],{},[902,106140,5326],{"encoding":904},[38,106142,106143],{},"svisle dolů",". Nabídka se nemění.",[724,106146,105071,106147,105112,106187,2028,106215,106243,106244,106263,106264,106288,106289,1783],{},[883,106148,106150],{"className":106149},[886],[888,106151,106152],{"xmlns":890},[892,106153,106154,106184],{},[895,106155,106156,106162,106164,106172,106174,106182],{},[5535,106157,106158,106160],{},[898,106159,1705],{},[1742,106161,1872],{},[1750,106163,5141],{"stretchy":1752},[5950,106165,106166,106168,106170],{},[898,106167,12471],{},[1742,106169,1872],{},[898,106171,1705],{},[1750,106173,1917],{"separator":1916},[5950,106175,106176,106178,106180],{},[898,106177,1776],{},[1742,106179,1872],{},[898,106181,1705],{},[1750,106183,5158],{"stretchy":1752},[902,106185,106186],{"encoding":904},"E_2[Q_2^E, P_2^E]",[883,106188,106190],{"className":106189},[886],[888,106191,106192],{"xmlns":890},[892,106193,106194,106212],{},[895,106195,106196,106204,106206],{},[5950,106197,106198,106200,106202],{},[898,106199,12471],{},[1742,106201,1872],{},[898,106203,1705],{},[1750,106205,2624],{},[1699,106207,106208,106210],{},[898,106209,12471],{},[898,106211,1705],{},[902,106213,106214],{"encoding":904},"Q_2^E \u003C Q^E",[883,106216,106218],{"className":106217},[886],[888,106219,106220],{"xmlns":890},[892,106221,106222,106240],{},[895,106223,106224,106232,106234],{},[5950,106225,106226,106228,106230],{},[898,106227,1776],{},[1742,106229,1872],{},[898,106231,1705],{},[1750,106233,2624],{},[1699,106235,106236,106238],{},[898,106237,1776],{},[898,106239,1705],{},[902,106241,106242],{"encoding":904},"P_2^E \u003C P^E",". Výrobce obdrží ",[883,106245,106247],{"className":106246},[886],[888,106248,106249],{"xmlns":890},[892,106250,106251,106261],{},[895,106252,106253],{},[5950,106254,106255,106257,106259],{},[898,106256,1776],{},[1742,106258,1872],{},[898,106260,1705],{},[902,106262,56841],{"encoding":904},", spotřebitel platí celkem ",[883,106265,106267],{"className":106266},[886],[888,106268,106269],{"xmlns":890},[892,106270,106271,106285],{},[895,106272,106273,106281,106283],{},[5950,106274,106275,106277,106279],{},[898,106276,1776],{},[1742,106278,1872],{},[898,106280,1705],{},[1750,106282,1861],{},[898,106284,5326],{},[902,106286,106287],{"encoding":904},"P_2^E + T"," (tato částka je vyšší než původní ",[883,106290,106292],{"className":106291},[886],[888,106293,106294],{"xmlns":890},[892,106295,106296,106304],{},[895,106297,106298],{},[1699,106299,106300,106302],{},[898,106301,1776],{},[898,106303,1705],{},[902,106305,50389],{"encoding":904},[724,106307,106308],{},"Daňové břemeno:",[883,106310,106312],{"className":106311},[886],[888,106313,106314],{"xmlns":890,"display":36989},[892,106315,106316,106390],{},[895,106317,106318,106328,106330,106332,106340,106342,106344,106346,106348,106354,106356,106358,106370,106372,106378,106380,106388],{},[5535,106319,106320,106322],{},[898,106321,5326],{},[895,106323,106324,106326],{},[898,106325,51600],{},[898,106327,724],{},[1750,106329,1766],{},[1750,106331,1753],{"stretchy":1752},[5950,106333,106334,106336,106338],{},[898,106335,1776],{},[1742,106337,1872],{},[898,106339,1705],{},[1750,106341,1861],{},[898,106343,5326],{},[1750,106345,1763],{"stretchy":1752},[1750,106347,1758],{},[1699,106349,106350,106352],{},[898,106351,1776],{},[898,106353,1705],{},[1750,106355,1917],{"separator":1916},[2125,106357],{"width":2127},[5535,106359,106360,106362],{},[898,106361,5326],{},[895,106363,106364,106366,106368],{},[898,106365,51623],{},[898,106367,11717],{},[898,106369,1920],{},[1750,106371,1766],{},[1699,106373,106374,106376],{},[898,106375,1776],{},[898,106377,1705],{},[1750,106379,1758],{},[5950,106381,106382,106384,106386],{},[898,106383,1776],{},[1742,106385,1872],{},[898,106387,1705],{},[898,106389,2313],{"mathvariant":1747},[902,106391,106392],{"encoding":904},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[724,106394,106395],{},[614,106396,106397,106398,106428,106429,105281,106442,9375,106459,105312,106472,2313],{},"Obrázek 2.19: Posun ",[883,106399,106401],{"className":106400},[886],[888,106402,106403],{"xmlns":890},[892,106404,106405,106425],{},[895,106406,106407,106409,106411,106417,106419,106421,106423],{},[898,106408,5541],{},[1750,106410,12797],{},[5535,106412,106413,106415],{},[898,106414,5541],{},[1742,106416,1872],{},[1750,106418,1766],{},[898,106420,5541],{},[1750,106422,1758],{},[898,106424,5326],{},[902,106426,106427],{"encoding":904},"D \\to D_2 = D - T","; svislá vzdálenost mezi poptávkovými křivkami je ",[883,106430,106432],{"className":106431},[886],[888,106433,106434],{"xmlns":890},[892,106435,106436,106440],{},[895,106437,106438],{},[898,106439,5326],{},[902,106441,5326],{"encoding":904},[883,106443,106445],{"className":106444},[886],[888,106446,106447],{"xmlns":890},[892,106448,106449,106457],{},[895,106450,106451],{},[5535,106452,106453,106455],{},[898,106454,5541],{},[1742,106456,1872],{},[902,106458,47250],{"encoding":904},[883,106460,106462],{"className":106461},[886],[888,106463,106464],{"xmlns":890},[892,106465,106466,106470],{},[895,106467,106468],{},[898,106469,1779],{},[902,106471,1779],{"encoding":904},[883,106473,106475],{"className":106474},[886],[888,106476,106477],{"xmlns":890},[892,106478,106479,106487],{},[895,106480,106481],{},[5535,106482,106483,106485],{},[898,106484,1705],{},[1742,106486,1872],{},[902,106488,106489],{"encoding":904},"E_2",[198,106491,54306],{"id":106492},"příklad-210",[724,106494,106495,106497,106498,50613,106521,106540,106541,106558],{},[38,106496,46856],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[883,106499,106501],{"className":106500},[886],[888,106502,106503],{"xmlns":890},[892,106504,106505,106519],{},[895,106506,106507,106509,106511,106513,106515,106517],{},[898,106508,1776],{},[1750,106510,1766],{},[1742,106512,4903],{},[1750,106514,1758],{},[1742,106516,1872],{},[898,106518,12471],{},[902,106520,105361],{"encoding":904},[883,106522,106524],{"className":106523},[886],[888,106525,106526],{"xmlns":890},[892,106527,106528,106538],{},[895,106529,106530,106532,106534,106536],{},[898,106531,1776],{},[1750,106533,1766],{},[1742,106535,7859],{},[898,106537,12471],{},[902,106539,105381],{"encoding":904},". Daň ",[883,106542,106544],{"className":106543},[886],[888,106545,106546],{"xmlns":890},[892,106547,106548,106556],{},[895,106549,106550,106552,106554],{},[898,106551,5326],{},[1750,106553,1766],{},[1742,106555,3219],{},[902,106557,50191],{"encoding":904}," Kč je tentokrát uložena na spotřebitele.",[724,106560,106561],{},[38,106562,46888],{},[724,106564,106565,106566,105572],{},"Nová poptávka je ",[883,106567,106569],{"className":106568},[886],[888,106570,106571],{"xmlns":890},[892,106572,106573,106609],{},[895,106574,106575,106581,106583,106585,106587,106589,106591,106593,106595,106597,106599,106601,106603,106605,106607],{},[5535,106576,106577,106579],{},[898,106578,5541],{},[1742,106580,1872],{},[1750,106582,2366],{},[898,106584,1776],{},[1750,106586,1766],{},[1742,106588,4903],{},[1750,106590,1758],{},[1742,106592,1872],{},[898,106594,12471],{},[1750,106596,1758],{},[1742,106598,3219],{},[1750,106600,1766],{},[1742,106602,3219],{},[1750,106604,1758],{},[1742,106606,1872],{},[898,106608,12471],{},[902,106610,106611],{"encoding":904},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[883,106613,106615],{"className":106614},[886],[888,106616,106617],{"xmlns":890,"display":36989},[892,106618,106619,106635],{},[895,106620,106621,106623,106625,106627,106629,106631,106633],{},[1742,106622,3219],{},[1750,106624,1758],{},[1742,106626,1872],{},[898,106628,12471],{},[1750,106630,1766],{},[1742,106632,7859],{},[898,106634,12471],{},[902,106636,106637],{"encoding":904},"6 - 2Q = 4Q",[724,106639,105605,106640,8164,106659,1343,106683,105686,106715,2313],{},[883,106641,106643],{"className":106642},[886],[888,106644,106645],{"xmlns":890},[892,106646,106647,106657],{},[895,106648,106649,106651,106653,106655],{},[1742,106650,3219],{},[898,106652,12471],{},[1750,106654,1766],{},[1742,106656,3219],{},[902,106658,105625],{"encoding":904},[883,106660,106662],{"className":106661},[886],[888,106663,106664],{"xmlns":890},[892,106665,106666,106680],{},[895,106667,106668,106676,106678],{},[5950,106669,106670,106672,106674],{},[898,106671,12471],{},[1742,106673,1872],{},[898,106675,1705],{},[1750,106677,1766],{},[1742,106679,1744],{},[902,106681,106682],{"encoding":904},"Q_2^E = 1",[883,106684,106686],{"className":106685},[886],[888,106687,106688],{"xmlns":890},[892,106689,106690,106712],{},[895,106691,106692,106700,106702,106704,106706,106708,106710],{},[5950,106693,106694,106696,106698],{},[898,106695,1776],{},[1742,106697,1872],{},[898,106699,1705],{},[1750,106701,1766],{},[1742,106703,7859],{},[1750,106705,8009],{},[1742,106707,1744],{},[1750,106709,1766],{},[1742,106711,7859],{},[902,106713,106714],{"encoding":904},"P_2^E = 4 \\cdot 1 = 4",[883,106716,106718],{"className":106717},[886],[888,106719,106720],{"xmlns":890},[892,106721,106722,106740],{},[895,106723,106724,106730,106732,106734,106736,106738],{},[5535,106725,106726,106728],{},[898,106727,1705],{},[1742,106729,1872],{},[1750,106731,5141],{"stretchy":1752},[1742,106733,1744],{},[1750,106735,1917],{"separator":1916},[1742,106737,7859],{},[1750,106739,5158],{"stretchy":1752},[902,106741,106742],{"encoding":904},"E_2[1, 4]",[724,106744,106745,106746,106782,106783,105400],{},"Spotřebitel platí celkem ",[883,106747,106749],{"className":106748},[886],[888,106750,106751],{"xmlns":890},[892,106752,106753,106779],{},[895,106754,106755,106763,106765,106767,106769,106771,106773,106775,106777],{},[5950,106756,106757,106759,106761],{},[898,106758,1776],{},[1742,106760,1872],{},[898,106762,1705],{},[1750,106764,1861],{},[898,106766,5326],{},[1750,106768,1766],{},[1742,106770,7859],{},[1750,106772,1861],{},[1742,106774,3219],{},[1750,106776,1766],{},[1742,106778,3079],{},[902,106780,106781],{"encoding":904},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[883,106784,106786],{"className":106785},[886],[888,106787,106788],{"xmlns":890},[892,106789,106790,106804],{},[895,106791,106792,106800,106802],{},[5950,106793,106794,106796,106798],{},[898,106795,1776],{},[1742,106797,1872],{},[898,106799,1705],{},[1750,106801,1766],{},[1742,106803,7859],{},[902,106805,106806],{"encoding":904},"P_2^E = 4",[724,106808,106809],{},[614,106810,106811],{},"Rozklad daňového břemene:",[883,106813,106815],{"className":106814},[886],[888,106816,106817],{"xmlns":890,"display":36989},[892,106818,106819,106905],{},[895,106820,106821,106831,106833,106835,106837,106839,106841,106843,106845,106847,106849,106851,106853,106863,106865,106867,106879,106881,106883,106885,106887,106889,106891,106893,106903],{},[5535,106822,106823,106825],{},[898,106824,5326],{},[895,106826,106827,106829],{},[898,106828,51600],{},[898,106830,724],{},[1750,106832,1766],{},[1750,106834,1753],{"stretchy":1752},[1742,106836,7859],{},[1750,106838,1861],{},[1742,106840,3219],{},[1750,106842,1763],{"stretchy":1752},[1750,106844,1758],{},[1742,106846,15239],{},[1750,106848,1766],{},[1742,106850,1872],{},[1969,106852,7737],{},[895,106854,106855,106857],{},[1969,106856,19435],{},[3215,106858,106859,106861],{"accent":1916},[1969,106860,9365],{},[1750,106862,8912],{},[1750,106864,1917],{"separator":1916},[2125,106866],{"width":2127},[5535,106868,106869,106871],{},[898,106870,5326],{},[895,106872,106873,106875,106877],{},[898,106874,51623],{},[898,106876,11717],{},[898,106878,1920],{},[1750,106880,1766],{},[1742,106882,15239],{},[1750,106884,1758],{},[1742,106886,7859],{},[1750,106888,1766],{},[1742,106890,7859],{},[1969,106892,7737],{},[895,106894,106895,106897],{},[1969,106896,19435],{},[3215,106898,106899,106901],{"accent":1916},[1969,106900,9365],{},[1750,106902,8912],{},[898,106904,2313],{"mathvariant":1747},[902,106906,106907],{"encoding":904},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[724,106909,106910,106911,2313],{},"Opět ",[883,106912,106914],{"className":106913},[886],[888,106915,106916],{"xmlns":890},[892,106917,106918,106952],{},[895,106919,106920,106930,106932,106944,106946,106948,106950],{},[5535,106921,106922,106924],{},[898,106923,5326],{},[895,106925,106926,106928],{},[898,106927,51600],{},[898,106929,724],{},[1750,106931,1861],{},[5535,106933,106934,106936],{},[898,106935,5326],{},[895,106937,106938,106940,106942],{},[898,106939,51623],{},[898,106941,11717],{},[898,106943,1920],{},[1750,106945,1766],{},[1742,106947,3219],{},[1750,106949,1766],{},[898,106951,5326],{},[902,106953,106954],{"encoding":904},"T_{sp} + T_{vyr} = 6 = T",[45893,106956],{},[115,106958,51581],{"id":106959},"daňové-břemeno",[724,106961,106962,2084,106964,106967,106968,106981],{},[38,106963,51581],{},[614,106965,106966],{},"tax burden",") je rozdělení zaplacené daně ",[883,106969,106971],{"className":106970},[886],[888,106972,106973],{"xmlns":890},[892,106974,106975,106979],{},[895,106976,106977],{},[898,106978,5326],{},[902,106980,5326],{"encoding":904}," mezi spotřebitele a výrobce:",[883,106983,106985],{"className":106984},[886],[888,106986,106987],{"xmlns":890,"display":36989},[892,106988,106989,107021],{},[895,106990,106991,106993,106995,107005,107007,107019],{},[898,106992,5326],{},[1750,106994,1766],{},[5535,106996,106997,106999],{},[898,106998,5326],{},[895,107000,107001,107003],{},[898,107002,51600],{},[898,107004,724],{},[1750,107006,1861],{},[5535,107008,107009,107011],{},[898,107010,5326],{},[895,107012,107013,107015,107017],{},[898,107014,51623],{},[898,107016,11717],{},[898,107018,1920],{},[898,107020,2313],{"mathvariant":1747},[902,107022,107023],{"encoding":904},"T = T_{sp} + T_{vyr}.",[724,107025,107026],{},[4434,107027],{"alt":107028,"className":107029,"src":107030},"imek-dan-rozklad-bremene-sklony",[210,4438],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1785,107032,107033],{},[724,107034,107035,107037,107038,2028,107051,2313],{},[883,107036,1791],{}," 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 ",[883,107039,107041],{"className":107040},[886],[888,107042,107043],{"xmlns":890},[892,107044,107045,107049],{},[895,107046,107047],{},[898,107048,5541],{},[902,107050,5541],{"encoding":904},[883,107052,107054],{"className":107053},[886],[888,107055,107056],{"xmlns":890},[892,107057,107058,107062],{},[895,107059,107060],{},[898,107061,1779],{},[902,107063,1779],{"encoding":904},[198,107065,12137],{"id":12136},[724,107067,107068,107069,107090,107091,107104,107105,107122,107123,107136],{},"V grafu ",[883,107070,107072],{"className":107071},[886],[888,107073,107074],{"xmlns":890},[892,107075,107076,107088],{},[895,107077,107078,107080,107082,107084,107086],{},[1750,107079,1753],{"stretchy":1752},[898,107081,12471],{},[1750,107083,1917],{"separator":1916},[898,107085,1776],{},[1750,107087,1763],{"stretchy":1752},[902,107089,46614],{"encoding":904}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[883,107092,107094],{"className":107093},[886],[888,107095,107096],{"xmlns":890},[892,107097,107098,107102],{},[895,107099,107100],{},[898,107101,5326],{},[902,107103,5326],{"encoding":904},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[883,107106,107108],{"className":107107},[886],[888,107109,107110],{"xmlns":890},[892,107111,107112,107120],{},[895,107113,107114],{},[1699,107115,107116,107118],{},[898,107117,1776],{},[898,107119,1705],{},[902,107121,50389],{"encoding":904},", rozdělí se úsečka ",[883,107124,107126],{"className":107125},[886],[888,107127,107128],{"xmlns":890},[892,107129,107130,107134],{},[895,107131,107132],{},[898,107133,5326],{},[902,107135,5326],{"encoding":904}," na dvě části:",[120,107138,107139,107164],{},[123,107140,107141,107142,107163],{},"horní část odpovídá ",[883,107143,107145],{"className":107144},[886],[888,107146,107147],{"xmlns":890},[892,107148,107149,107161],{},[895,107150,107151],{},[5535,107152,107153,107155],{},[898,107154,5326],{},[895,107156,107157,107159],{},[898,107158,51600],{},[898,107160,724],{},[902,107162,51605],{"encoding":904}," (o kolik vzrostla cena placená spotřebitelem),",[123,107165,107166,107167,107190],{},"dolní část odpovídá ",[883,107168,107170],{"className":107169},[886],[888,107171,107172],{"xmlns":890},[892,107173,107174,107188],{},[895,107175,107176],{},[5535,107177,107178,107180],{},[898,107179,5326],{},[895,107181,107182,107184,107186],{},[898,107183,51623],{},[898,107185,11717],{},[898,107187,1920],{},[902,107189,51630],{"encoding":904}," (o kolik klesla cena přijímaná výrobcem).",[724,107192,107193],{},[614,107194,107195,107196,4321,107209,107230,107231,107254,107255,2028,107276,107299],{},"Obrázky 2.20 a 2.21: Ilustrace rozkladu svislé vzdálenosti ",[883,107197,107199],{"className":107198},[886],[888,107200,107201],{"xmlns":890},[892,107202,107203,107207],{},[895,107204,107205],{},[898,107206,5326],{},[902,107208,5326],{"encoding":904},[883,107210,107212],{"className":107211},[886],[888,107213,107214],{"xmlns":890},[892,107215,107216,107228],{},[895,107217,107218],{},[5535,107219,107220,107222],{},[898,107221,5326],{},[895,107223,107224,107226],{},[898,107225,51600],{},[898,107227,724],{},[902,107229,51605],{"encoding":904}," (nahoře) a ",[883,107232,107234],{"className":107233},[886],[888,107235,107236],{"xmlns":890},[892,107237,107238,107252],{},[895,107239,107240],{},[5535,107241,107242,107244],{},[898,107243,5326],{},[895,107245,107246,107248,107250],{},[898,107247,51623],{},[898,107249,11717],{},[898,107251,1920],{},[902,107253,51630],{"encoding":904}," (dole). Obrázek 2.21 porovnává obě varianty — daň výrobci vs. daň spotřebiteli — a ukazuje, že velikost ",[883,107256,107258],{"className":107257},[886],[888,107259,107260],{"xmlns":890},[892,107261,107262,107274],{},[895,107263,107264],{},[5535,107265,107266,107268],{},[898,107267,5326],{},[895,107269,107270,107272],{},[898,107271,51600],{},[898,107273,724],{},[902,107275,51605],{"encoding":904},[883,107277,107279],{"className":107278},[886],[888,107280,107281],{"xmlns":890},[892,107282,107283,107297],{},[895,107284,107285],{},[5535,107286,107287,107289],{},[898,107288,5326],{},[895,107290,107291,107293,107295],{},[898,107292,51623],{},[898,107294,11717],{},[898,107296,1920],{},[902,107298,51630],{"encoding":904}," je v obou případech stejná.",[198,107301,107303],{"id":107302},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[724,107305,107306,107307,107310,107311,2084,107334,107351,107352,2084,107375,107392],{},"Platí obecně: ",[38,107308,107309],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[883,107312,107314],{"className":107313},[886],[888,107315,107316],{"xmlns":890},[892,107317,107318,107332],{},[895,107319,107320,107322,107324,107326,107328,107330],{},[898,107321,1776],{},[1750,107323,1766],{},[898,107325,207],{},[898,107327,12471],{},[1750,107329,1861],{},[898,107331,2573],{},[902,107333,45983],{"encoding":904},[883,107335,107337],{"className":107336},[886],[888,107338,107339],{"xmlns":890},[892,107340,107341,107349],{},[895,107342,107343,107345,107347],{},[898,107344,207],{},[1750,107346,2624],{},[1742,107348,2607],{},[902,107350,52008],{"encoding":904},") a lineární nabídku ",[883,107353,107355],{"className":107354},[886],[888,107356,107357],{"xmlns":890},[892,107358,107359,107373],{},[895,107360,107361,107363,107365,107367,107369,107371],{},[898,107362,1776],{},[1750,107364,1766],{},[898,107366,9365],{},[898,107368,12471],{},[1750,107370,1861],{},[898,107372,3429],{},[902,107374,49165],{"encoding":904},[883,107376,107378],{"className":107377},[886],[888,107379,107380],{"xmlns":890},[892,107381,107382,107390],{},[895,107383,107384,107386,107388],{},[898,107385,9365],{},[1750,107387,2604],{},[1742,107389,2607],{},[902,107391,49183],{"encoding":904},") lze rozklad odvodit pomocí multiplikátorů a platí",[883,107394,107396],{"className":107395},[886],[888,107397,107398],{"xmlns":890,"display":36989},[892,107399,107400,107466],{},[895,107401,107402,107426,107428,107438,107440,107464],{},[3423,107403,107404,107414],{},[5535,107405,107406,107408],{},[898,107407,5326],{},[895,107409,107410,107412],{},[898,107411,51600],{},[898,107413,724],{},[5535,107415,107416,107418],{},[898,107417,5326],{},[895,107419,107420,107422,107424],{},[898,107421,51623],{},[898,107423,11717],{},[898,107425,1920],{},[1750,107427,1766],{},[3423,107429,107430,107432],{},[898,107431,9365],{},[895,107433,107434,107436],{},[1750,107435,1758],{},[898,107437,207],{},[1750,107439,1766],{},[3423,107441,107442,107454],{},[895,107443,107444,107447,107450,107452],{},[898,107445,107446],{"mathvariant":1747},"∣",[1969,107448,107449],{},"sklon ",[898,107451,1779],{},[898,107453,107446],{"mathvariant":1747},[895,107455,107456,107458,107460,107462],{},[898,107457,107446],{"mathvariant":1747},[1969,107459,107449],{},[898,107461,5541],{},[898,107463,107446],{"mathvariant":1747},[898,107465,2313],{"mathvariant":1747},[902,107467,107468],{"encoding":904},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1785,107470,107471,107476],{},[724,107472,107473,107475],{},[883,107474,6004],{}," Postup výpočtu rozkladu",[152,107477,107478,107513,107566,107645],{},[123,107479,107480,107481,107512],{},"Spočti rovnovážný bod ",[883,107482,107484],{"className":107483},[886],[888,107485,107486],{"xmlns":890},[892,107487,107488,107510],{},[895,107489,107490,107492,107494,107500,107502,107508],{},[898,107491,1705],{},[1750,107493,5141],{"stretchy":1752},[1699,107495,107496,107498],{},[898,107497,12471],{},[898,107499,1705],{},[1750,107501,1917],{"separator":1916},[1699,107503,107504,107506],{},[898,107505,1776],{},[898,107507,1705],{},[1750,107509,5158],{"stretchy":1752},[902,107511,50290],{"encoding":904}," bez daně.",[123,107514,107515,107516,1348,107541,1783],{},"Urči posunutou křivku (",[883,107517,107519],{"className":107518},[886],[888,107520,107521],{"xmlns":890},[892,107522,107523,107539],{},[895,107524,107525,107531,107533,107535,107537],{},[5535,107526,107527,107529],{},[898,107528,1779],{},[1742,107530,1744],{},[1750,107532,1766],{},[898,107534,1779],{},[1750,107536,1861],{},[898,107538,5326],{},[902,107540,51677],{"encoding":904},[883,107542,107544],{"className":107543},[886],[888,107545,107546],{"xmlns":890},[892,107547,107548,107564],{},[895,107549,107550,107556,107558,107560,107562],{},[5535,107551,107552,107554],{},[898,107553,5541],{},[1742,107555,1872],{},[1750,107557,1766],{},[898,107559,5541],{},[1750,107561,1758],{},[898,107563,5326],{},[902,107565,51708],{"encoding":904},[123,107567,107568,107569,13577,107588,4419,107607,13577,107626,1783],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[883,107570,107572],{"className":107571},[886],[888,107573,107574],{"xmlns":890},[892,107575,107576,107586],{},[895,107577,107578],{},[5950,107579,107580,107582,107584],{},[898,107581,12471],{},[1742,107583,1744],{},[898,107585,1705],{},[902,107587,56759],{"encoding":904},[883,107589,107591],{"className":107590},[886],[888,107592,107593],{"xmlns":890},[892,107594,107595,107605],{},[895,107596,107597],{},[5950,107598,107599,107601,107603],{},[898,107600,12471],{},[1742,107602,1872],{},[898,107604,1705],{},[902,107606,56821],{"encoding":904},[883,107608,107610],{"className":107609},[886],[888,107611,107612],{"xmlns":890},[892,107613,107614,107624],{},[895,107615,107616],{},[5950,107617,107618,107620,107622],{},[898,107619,1776],{},[1742,107621,1744],{},[898,107623,1705],{},[902,107625,56780],{"encoding":904},[883,107627,107629],{"className":107628},[886],[888,107630,107631],{"xmlns":890},[892,107632,107633,107643],{},[895,107634,107635],{},[5950,107636,107637,107639,107641],{},[898,107638,1776],{},[1742,107640,1872],{},[898,107642,1705],{},[902,107644,56841],{"encoding":904},[123,107646,107647,107648,2028,107669,107692,107693,2313],{},"Dopočítej ",[883,107649,107651],{"className":107650},[886],[888,107652,107653],{"xmlns":890},[892,107654,107655,107667],{},[895,107656,107657],{},[5535,107658,107659,107661],{},[898,107660,5326],{},[895,107662,107663,107665],{},[898,107664,51600],{},[898,107666,724],{},[902,107668,51605],{"encoding":904},[883,107670,107672],{"className":107671},[886],[888,107673,107674],{"xmlns":890},[892,107675,107676,107690],{},[895,107677,107678],{},[5535,107679,107680,107682],{},[898,107681,5326],{},[895,107683,107684,107686,107688],{},[898,107685,51623],{},[898,107687,11717],{},[898,107689,1920],{},[902,107691,51630],{"encoding":904}," z definice, vždy ověř ",[883,107694,107696],{"className":107695},[886],[888,107697,107698],{"xmlns":890},[892,107699,107700,107730],{},[895,107701,107702,107712,107714,107726,107728],{},[5535,107703,107704,107706],{},[898,107705,5326],{},[895,107707,107708,107710],{},[898,107709,51600],{},[898,107711,724],{},[1750,107713,1861],{},[5535,107715,107716,107718],{},[898,107717,5326],{},[895,107719,107720,107722,107724],{},[898,107721,51623],{},[898,107723,11717],{},[898,107725,1920],{},[1750,107727,1766],{},[898,107729,5326],{},[902,107731,107732],{"encoding":904},"T_{sp} + T_{vyr} = T",[1785,107734,107735],{},[724,107736,107737,107739,107740,107743,107744,2028,107757,107770],{},[883,107738,5454],{}," Pozor — zákonný vs. ekonomický nositel daně\nI když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[38,107741,107742],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[883,107745,107747],{"className":107746},[886],[888,107748,107749],{"xmlns":890},[892,107750,107751,107755],{},[895,107752,107753],{},[898,107754,5541],{},[902,107756,5541],{"encoding":904},[883,107758,107760],{"className":107759},[886],[888,107761,107762],{"xmlns":890},[892,107763,107764,107768],{},[895,107765,107766],{},[898,107767,1779],{},[902,107769,1779],{"encoding":904},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[45893,107772],{},[115,107774,107776],{"id":107775},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[724,107778,107779],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[724,107781,107782],{},[4434,107783],{"alt":107784,"className":107785,"src":107786},"imek-dan-ekvivalence-vyrobce-spotrebitel",[210,4438],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[16,107788,107789,107801],{},[19,107790,107791],{},[22,107792,107793,107795,107798],{},[25,107794,63219],{},[25,107796,107797],{},"(a) daň výrobci",[25,107799,107800],{},"(b) daň spotřebiteli",[30,107802,107803,107858,107925,107985],{},[22,107804,107805,107808,107833],{},[35,107806,107807],{},"Rovnovážné množství",[35,107809,107810],{},[883,107811,107813],{"className":107812},[886],[888,107814,107815],{"xmlns":890},[892,107816,107817,107831],{},[895,107818,107819,107827,107829],{},[5950,107820,107821,107823,107825],{},[898,107822,12471],{},[1742,107824,1744],{},[898,107826,1705],{},[1750,107828,1766],{},[1742,107830,1744],{},[902,107832,105649],{"encoding":904},[35,107834,107835],{},[883,107836,107838],{"className":107837},[886],[888,107839,107840],{"xmlns":890},[892,107841,107842,107856],{},[895,107843,107844,107852,107854],{},[5950,107845,107846,107848,107850],{},[898,107847,12471],{},[1742,107849,1872],{},[898,107851,1705],{},[1750,107853,1766],{},[1742,107855,1744],{},[902,107857,106682],{"encoding":904},[22,107859,107860,107863,107888],{},[35,107861,107862],{},"Cena placená spotřebitelem",[35,107864,107865],{},[883,107866,107868],{"className":107867},[886],[888,107869,107870],{"xmlns":890},[892,107871,107872,107886],{},[895,107873,107874,107882,107884],{},[5950,107875,107876,107878,107880],{},[898,107877,1776],{},[1742,107879,1744],{},[898,107881,1705],{},[1750,107883,1766],{},[1742,107885,3079],{},[902,107887,105744],{"encoding":904},[35,107889,107890],{},[883,107891,107893],{"className":107892},[886],[888,107894,107895],{"xmlns":890},[892,107896,107897,107923],{},[895,107898,107899,107907,107909,107911,107913,107915,107917,107919,107921],{},[5950,107900,107901,107903,107905],{},[898,107902,1776],{},[1742,107904,1872],{},[898,107906,1705],{},[1750,107908,1861],{},[898,107910,5326],{},[1750,107912,1766],{},[1742,107914,7859],{},[1750,107916,1861],{},[1742,107918,3219],{},[1750,107920,1766],{},[1742,107922,3079],{},[902,107924,106781],{"encoding":904},[22,107926,107927,107930,107960],{},[35,107928,107929],{},"Cena přijímaná výrobcem",[35,107931,107932],{},[883,107933,107935],{"className":107934},[886],[888,107936,107937],{"xmlns":890},[892,107938,107939,107957],{},[895,107940,107941,107949,107951,107953,107955],{},[5950,107942,107943,107945,107947],{},[898,107944,1776],{},[1742,107946,1744],{},[898,107948,1705],{},[1750,107950,1758],{},[898,107952,5326],{},[1750,107954,1766],{},[1742,107956,7859],{},[902,107958,107959],{"encoding":904},"P_1^E - T = 4",[35,107961,107962],{},[883,107963,107965],{"className":107964},[886],[888,107966,107967],{"xmlns":890},[892,107968,107969,107983],{},[895,107970,107971,107979,107981],{},[5950,107972,107973,107975,107977],{},[898,107974,1776],{},[1742,107976,1872],{},[898,107978,1705],{},[1750,107980,1766],{},[1742,107982,7859],{},[902,107984,106806],{"encoding":904},[22,107986,107987,107990,108044],{},[35,107988,107989],{},"Rozklad břemene",[35,107991,107992,1343,108017],{},[883,107993,107995],{"className":107994},[886],[888,107996,107997],{"xmlns":890},[892,107998,107999,108015],{},[895,108000,108001,108011,108013],{},[5535,108002,108003,108005],{},[898,108004,5326],{},[895,108006,108007,108009],{},[898,108008,51600],{},[898,108010,724],{},[1750,108012,1766],{},[1742,108014,1872],{},[902,108016,51899],{"encoding":904},[883,108018,108020],{"className":108019},[886],[888,108021,108022],{"xmlns":890},[892,108023,108024,108042],{},[895,108025,108026,108038,108040],{},[5535,108027,108028,108030],{},[898,108029,5326],{},[895,108031,108032,108034,108036],{},[898,108033,51623],{},[898,108035,11717],{},[898,108037,1920],{},[1750,108039,1766],{},[1742,108041,7859],{},[902,108043,51928],{"encoding":904},[35,108045,108046,1343,108071],{},[883,108047,108049],{"className":108048},[886],[888,108050,108051],{"xmlns":890},[892,108052,108053,108069],{},[895,108054,108055,108065,108067],{},[5535,108056,108057,108059],{},[898,108058,5326],{},[895,108060,108061,108063],{},[898,108062,51600],{},[898,108064,724],{},[1750,108066,1766],{},[1742,108068,1872],{},[902,108070,51899],{"encoding":904},[883,108072,108074],{"className":108073},[886],[888,108075,108076],{"xmlns":890},[892,108077,108078,108096],{},[895,108079,108080,108092,108094],{},[5535,108081,108082,108084],{},[898,108083,5326],{},[895,108085,108086,108088,108090],{},[898,108087,51623],{},[898,108089,11717],{},[898,108091,1920],{},[1750,108093,1766],{},[1742,108095,7859],{},[902,108097,51928],{"encoding":904},[724,108099,108100],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[883,108102,108104],{"className":108103},[886],[888,108105,108106],{"xmlns":890,"display":36989},[892,108107,108108,108156],{},[895,108109,108110,108118,108120,108128,108130,108132,108140,108142,108144,108146,108154],{},[5950,108111,108112,108114,108116],{},[898,108113,12471],{},[1742,108115,1744],{},[898,108117,1705],{},[1750,108119,1766],{},[5950,108121,108122,108124,108126],{},[898,108123,12471],{},[1742,108125,1872],{},[898,108127,1705],{},[1750,108129,1917],{"separator":1916},[2125,108131],{"width":2127},[5950,108133,108134,108136,108138],{},[898,108135,1776],{},[1742,108137,1744],{},[898,108139,1705],{},[1750,108141,1758],{},[898,108143,5326],{},[1750,108145,1766],{},[5950,108147,108148,108150,108152],{},[898,108149,1776],{},[1742,108151,1872],{},[898,108153,1705],{},[898,108155,2313],{"mathvariant":1747},[902,108157,108158],{"encoding":904},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1785,108160,108161,108180,108334],{},[724,108162,108163,108165,108166,108179],{},[883,108164,6004],{}," Věta o ekvivalenci zdanění\nNezávisle na tom, zda je jednotková daň ",[883,108167,108169],{"className":108168},[886],[888,108170,108171],{"xmlns":890},[892,108172,108173,108177],{},[895,108174,108175],{},[898,108176,5326],{},[902,108178,5326],{"encoding":904}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[120,108181,108182,108214,108250,108287],{},[123,108183,108184,108185,1917],{},"rovnovážná množství obou režimů, ",[883,108186,108188],{"className":108187},[886],[888,108189,108190],{"xmlns":890},[892,108191,108192,108212],{},[895,108193,108194,108202,108204],{},[5950,108195,108196,108198,108200],{},[898,108197,12471],{},[1742,108199,1744],{},[898,108201,1705],{},[1750,108203,1766],{},[5950,108205,108206,108208,108210],{},[898,108207,12471],{},[1742,108209,1872],{},[898,108211,1705],{},[902,108213,51831],{"encoding":904},[123,108215,108216,108217,1917],{},"čistá cena přijímaná výrobcem, ",[883,108218,108220],{"className":108219},[886],[888,108221,108222],{"xmlns":890},[892,108223,108224,108248],{},[895,108225,108226,108234,108236,108238,108240],{},[5950,108227,108228,108230,108232],{},[898,108229,1776],{},[1742,108231,1744],{},[898,108233,1705],{},[1750,108235,1758],{},[898,108237,5326],{},[1750,108239,1766],{},[5950,108241,108242,108244,108246],{},[898,108243,1776],{},[1742,108245,1872],{},[898,108247,1705],{},[902,108249,51865],{"encoding":904},[123,108251,108252,108253,1917],{},"celková cena placená spotřebitelem, ",[883,108254,108256],{"className":108255},[886],[888,108257,108258],{"xmlns":890},[892,108259,108260,108284],{},[895,108261,108262,108270,108272,108280,108282],{},[5950,108263,108264,108266,108268],{},[898,108265,1776],{},[1742,108267,1744],{},[898,108269,1705],{},[1750,108271,1766],{},[5950,108273,108274,108276,108278],{},[898,108275,1776],{},[1742,108277,1872],{},[898,108279,1705],{},[1750,108281,1861],{},[898,108283,5326],{},[902,108285,108286],{"encoding":904},"P_1^E = P_2^E + T",[123,108288,108289,108290,2028,108311,2313],{},"rozklad daňového břemene ",[883,108291,108293],{"className":108292},[886],[888,108294,108295],{"xmlns":890},[892,108296,108297,108309],{},[895,108298,108299],{},[5535,108300,108301,108303],{},[898,108302,5326],{},[895,108304,108305,108307],{},[898,108306,51600],{},[898,108308,724],{},[902,108310,51605],{"encoding":904},[883,108312,108314],{"className":108313},[886],[888,108315,108316],{"xmlns":890},[892,108317,108318,108332],{},[895,108319,108320],{},[5535,108321,108322,108324],{},[898,108323,5326],{},[895,108325,108326,108328,108330],{},[898,108327,51623],{},[898,108329,11717],{},[898,108331,1920],{},[902,108333,51630],{"encoding":904},[724,108335,108336,108337,2313],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[38,108338,44120],{},[724,108340,108341,108342,2028,108355,1783],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[883,108343,108345],{"className":108344},[886],[888,108346,108347],{"xmlns":890},[892,108348,108349,108353],{},[895,108350,108351],{},[898,108352,5541],{},[902,108354,5541],{"encoding":904},[883,108356,108358],{"className":108357},[886],[888,108359,108360],{"xmlns":890},[892,108361,108362,108366],{},[895,108363,108364],{},[898,108365,1779],{},[902,108367,1779],{"encoding":904},[45893,108369],{},[115,108371,108373],{"id":108372},"úlohy","Úlohy",[724,108375,108376,108377,12825],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[207,108378,11564],{"className":108379,"dataFsResolvedFilePath":800,"href":801},[210],[120,108381,108382,108412,108443],{},[123,108383,108384,108387,108388,108411],{},[38,108385,108386],{},"Úloha 2.4"," — Poptávka ",[883,108389,108391],{"className":108390},[886],[888,108392,108393],{"xmlns":890},[892,108394,108395,108409],{},[895,108396,108397,108399,108401,108403,108405,108407],{},[898,108398,1776],{},[1750,108400,1766],{},[1742,108402,4903],{},[1750,108404,1758],{},[1742,108406,1872],{},[898,108408,12471],{},[902,108410,105361],{"encoding":904},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[123,108413,108414,108417,108418,108442],{},[38,108415,108416],{},"Úloha 2.9"," — Nabídka ",[883,108419,108421],{"className":108420},[886],[888,108422,108423],{"xmlns":890},[892,108424,108425,108439],{},[895,108426,108427,108429,108431,108433,108435,108437],{},[898,108428,1776],{},[1750,108430,1766],{},[1742,108432,4268],{},[898,108434,12471],{},[1750,108436,1861],{},[1742,108438,45167],{},[902,108440,108441],{"encoding":904},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[123,108444,108445,108448,108449,2028,108475,108499,108500,108517],{},[38,108446,108447],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[883,108450,108452],{"className":108451},[886],[888,108453,108454],{"xmlns":890},[892,108455,108456,108472],{},[895,108457,108458,108460,108462,108464,108466,108468,108470],{},[898,108459,1776],{},[1750,108461,1766],{},[1750,108463,1758],{},[1742,108465,7859],{},[898,108467,12471],{},[1750,108469,1861],{},[1742,108471,55626],{},[902,108473,108474],{"encoding":904},"P = -4Q + 80",[883,108476,108478],{"className":108477},[886],[888,108479,108480],{"xmlns":890},[892,108481,108482,108496],{},[895,108483,108484,108486,108488,108490,108492,108494],{},[898,108485,1776],{},[1750,108487,1766],{},[1742,108489,7822],{},[898,108491,12471],{},[1750,108493,1861],{},[1742,108495,3079],{},[902,108497,108498],{"encoding":904},"P = 3Q + 10",": rovnováha, daň ",[883,108501,108503],{"className":108502},[886],[888,108504,108505],{"xmlns":890},[892,108506,108507,108515],{},[895,108508,108509,108511,108513],{},[898,108510,5326],{},[1750,108512,1766],{},[1742,108514,8051],{},[902,108516,56738],{"encoding":904}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[724,108519,108520,108521,108523,108524,108526],{},"Související úvodní příklady posunu křivek při zdanění: ",[38,108522,54151],{}," (posun poptávky při zdanění kupujícího) a ",[38,108525,54185],{}," (posun nabídky při zdanění výrobce).",[45893,108528],{},[115,108530,10461],{"id":10460},[120,108532,108533,108552,108610,108667,108750,108796,108839,108884,108950],{},[123,108534,108535,1647,108538,108551],{},[38,108536,108537],{},"Jednotková daň",[883,108539,108541],{"className":108540},[886],[888,108542,108543],{"xmlns":890},[892,108544,108545,108549],{},[895,108546,108547],{},[898,108548,5326],{},[902,108550,5326],{"encoding":904}," — fixní částka na každou prodanou jednotku zboží",[123,108553,108554,108556,108557,108595,108596,108609],{},[38,108555,104943],{}," — posun nabídky ",[883,108558,108560],{"className":108559},[886],[888,108561,108562],{"xmlns":890},[892,108563,108564,108592],{},[895,108565,108566,108572,108574,108576,108578,108580,108582,108584,108586,108588,108590],{},[5535,108567,108568,108570],{},[898,108569,1779],{},[1742,108571,1744],{},[1750,108573,1753],{"stretchy":1752},[898,108575,12471],{},[1750,108577,1763],{"stretchy":1752},[1750,108579,1766],{},[898,108581,1779],{},[1750,108583,1753],{"stretchy":1752},[898,108585,12471],{},[1750,108587,1763],{"stretchy":1752},[1750,108589,1861],{},[898,108591,5326],{},[902,108593,108594],{"encoding":904},"S_1(Q) = S(Q) + T"," (o ",[883,108597,108599],{"className":108598},[886],[888,108600,108601],{"xmlns":890},[892,108602,108603,108607],{},[895,108604,108605],{},[898,108606,5326],{},[902,108608,5326],{"encoding":904}," svisle nahoru)",[123,108611,108612,108614,108615,108595,108653,108666],{},[38,108613,106016],{}," — posun poptávky ",[883,108616,108618],{"className":108617},[886],[888,108619,108620],{"xmlns":890},[892,108621,108622,108650],{},[895,108623,108624,108630,108632,108634,108636,108638,108640,108642,108644,108646,108648],{},[5535,108625,108626,108628],{},[898,108627,5541],{},[1742,108629,1872],{},[1750,108631,1753],{"stretchy":1752},[898,108633,12471],{},[1750,108635,1763],{"stretchy":1752},[1750,108637,1766],{},[898,108639,5541],{},[1750,108641,1753],{"stretchy":1752},[898,108643,12471],{},[1750,108645,1763],{"stretchy":1752},[1750,108647,1758],{},[898,108649,5326],{},[902,108651,108652],{"encoding":904},"D_2(Q) = D(Q) - T",[883,108654,108656],{"className":108655},[886],[888,108657,108658],{"xmlns":890},[892,108659,108660,108664],{},[895,108661,108662],{},[898,108663,5326],{},[902,108665,5326],{"encoding":904}," svisle dolů)",[123,108668,108669,10469,108672,50737,108711],{},[38,108670,108671],{},"Rovnovážný bod s daní",[883,108673,108675],{"className":108674},[886],[888,108676,108677],{"xmlns":890},[892,108678,108679,108709],{},[895,108680,108681,108687,108689,108697,108699,108707],{},[5535,108682,108683,108685],{},[898,108684,1705],{},[1742,108686,1744],{},[1750,108688,5141],{"stretchy":1752},[5950,108690,108691,108693,108695],{},[898,108692,12471],{},[1742,108694,1744],{},[898,108696,1705],{},[1750,108698,1917],{"separator":1916},[5950,108700,108701,108703,108705],{},[898,108702,1776],{},[1742,108704,1744],{},[898,108706,1705],{},[1750,108708,5158],{"stretchy":1752},[902,108710,105111],{"encoding":904},[883,108712,108714],{"className":108713},[886],[888,108715,108716],{"xmlns":890},[892,108717,108718,108748],{},[895,108719,108720,108726,108728,108736,108738,108746],{},[5535,108721,108722,108724],{},[898,108723,1705],{},[1742,108725,1872],{},[1750,108727,5141],{"stretchy":1752},[5950,108729,108730,108732,108734],{},[898,108731,12471],{},[1742,108733,1872],{},[898,108735,1705],{},[1750,108737,1917],{"separator":1916},[5950,108739,108740,108742,108744],{},[898,108741,1776],{},[1742,108743,1872],{},[898,108745,1705],{},[1750,108747,5158],{"stretchy":1752},[902,108749,106186],{"encoding":904},[123,108751,108752,2084,108754,108756,108757],{},[38,108753,51581],{},[614,108755,106966],{},") — rozklad ",[883,108758,108760],{"className":108759},[886],[888,108761,108762],{"xmlns":890},[892,108763,108764,108794],{},[895,108765,108766,108768,108770,108780,108782],{},[898,108767,5326],{},[1750,108769,1766],{},[5535,108771,108772,108774],{},[898,108773,5326],{},[895,108775,108776,108778],{},[898,108777,51600],{},[898,108779,724],{},[1750,108781,1861],{},[5535,108783,108784,108786],{},[898,108785,5326],{},[895,108787,108788,108790,108792],{},[898,108789,51623],{},[898,108791,11717],{},[898,108793,1920],{},[902,108795,51767],{"encoding":904},[123,108797,108798,108821,108822,1763],{},[38,108799,108800],{},[883,108801,108803],{"className":108802},[886],[888,108804,108805],{"xmlns":890},[892,108806,108807,108819],{},[895,108808,108809],{},[5535,108810,108811,108813],{},[898,108812,5326],{},[895,108814,108815,108817],{},[898,108816,51600],{},[898,108818,724],{},[902,108820,51605],{"encoding":904}," — část daně nesená spotřebitelem (navýšení ceny nad ",[883,108823,108825],{"className":108824},[886],[888,108826,108827],{"xmlns":890},[892,108828,108829,108837],{},[895,108830,108831],{},[1699,108832,108833,108835],{},[898,108834,1776],{},[898,108836,1705],{},[902,108838,50389],{"encoding":904},[123,108840,108841,108866,108867,1763],{},[38,108842,108843],{},[883,108844,108846],{"className":108845},[886],[888,108847,108848],{"xmlns":890},[892,108849,108850,108864],{},[895,108851,108852],{},[5535,108853,108854,108856],{},[898,108855,5326],{},[895,108857,108858,108860,108862],{},[898,108859,51623],{},[898,108861,11717],{},[898,108863,1920],{},[902,108865,51630],{"encoding":904}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[883,108868,108870],{"className":108869},[886],[888,108871,108872],{"xmlns":890},[892,108873,108874,108882],{},[895,108875,108876],{},[1699,108877,108878,108880],{},[898,108879,1776],{},[898,108881,1705],{},[902,108883,50389],{"encoding":904},[123,108885,108886,10469,108888,1343,108917],{},[38,108887,59397],{},[883,108889,108891],{"className":108890},[886],[888,108892,108893],{"xmlns":890},[892,108894,108895,108915],{},[895,108896,108897,108905,108907],{},[5950,108898,108899,108901,108903],{},[898,108900,12471],{},[1742,108902,1744],{},[898,108904,1705],{},[1750,108906,1766],{},[5950,108908,108909,108911,108913],{},[898,108910,12471],{},[1742,108912,1872],{},[898,108914,1705],{},[902,108916,51831],{"encoding":904},[883,108918,108920],{"className":108919},[886],[888,108921,108922],{"xmlns":890},[892,108923,108924,108948],{},[895,108925,108926,108934,108936,108938,108940],{},[5950,108927,108928,108930,108932],{},[898,108929,1776],{},[1742,108931,1744],{},[898,108933,1705],{},[1750,108935,1758],{},[898,108937,5326],{},[1750,108939,1766],{},[5950,108941,108942,108944,108946],{},[898,108943,1776],{},[1742,108945,1872],{},[898,108947,1705],{},[902,108949,51865],{"encoding":904},[123,108951,108952,108955],{},[38,108953,108954],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[45893,108957],{},[115,108959,11524],{"id":11523},[120,108961,108962,108970,108988,108995],{},[123,108963,108964,1647,108967],{},[38,108965,108966],{},"Kontext (hub):",[207,108968,802],{"className":108969,"dataFsResolvedFilePath":800,"href":801},[210],[123,108971,108972,1647,108974,108977,108978,2440,108980,108983,108984,108987],{},[38,108973,59646],{},[207,108975,820],{"className":108976,"dataFsResolvedFilePath":818,"href":819},[210]," (daň vyvolává ztrátu blahobytu — ",[614,108979,63957],{},[207,108981,12053],{"className":108982,"dataFsResolvedFilePath":764,"href":765},[210]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[207,108985,13496],{"className":108986,"dataFsResolvedFilePath":848,"href":849},[210]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[123,108989,108990,1647,108992],{},[38,108991,59681],{},[207,108993,59685],{"className":108994,"dataFsResolvedFilePath":745,"href":746},[210],[123,108996,108997,1647,108999],{},[38,108998,11531],{},[207,109000,11535],{"className":109001,"dataFsResolvedFilePath":1644,"href":1645},[210],{"title":641,"searchDepth":642,"depth":642,"links":109003},[109004,109005,109008,109011,109015,109016,109017,109018],{"id":104848,"depth":642,"text":104849},{"id":104942,"depth":642,"text":104943,"children":109006},[109007],{"id":105333,"depth":649,"text":54226},{"id":106015,"depth":642,"text":106016,"children":109009},[109010],{"id":106492,"depth":649,"text":54306},{"id":106959,"depth":642,"text":51581,"children":109012},[109013,109014],{"id":12136,"depth":649,"text":12137},{"id":107302,"depth":649,"text":107303},{"id":107775,"depth":642,"text":107776},{"id":108372,"depth":642,"text":108373},{"id":10460,"depth":642,"text":10461},{"id":11523,"depth":642,"text":11524},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":104746,"description":641},[1138,1135],"topics\u002Fzdaneni-trhu",[1128,59746,109025,109026,109027,11564],"dane","danove-bremeno","posun-krivek","cFuKqHgzIrqvY-l4jNdqjFEM7_ixjw33HOL0So8cPn0",[109030,109032,109035,109039,109043,109045],{"slug":1128,"path":1645,"title":681,"snippet":109031},"… Lagrangeova maximalizace $U$, duální minimalizace výdajů, Marshallova\u002FHicksova poptávka - \u003C\u003Cnarodni-duchod>> — GNP, spotřeba\u002Fúspory, MPC\u002FMPS, modely C-I, C-I-G, C-I-G-X - IS-LM analýza — s …",{"slug":11544,"path":869,"title":109033,"snippet":109034},"KS 3. blok — Užitečnost a národní důchod","… ení (Lagrange), minimalizace výdajů (duální úloha), Marshallova vs. Hicksova poptávka. 2. \u003C\u003Cnarodni-duchod>> — GNP $= C + I + G + X$, lineární model spotřeby, mezní sklon ke spotřebě\u002Fúsporám ($MPC, …",{"slug":109036,"path":1109,"title":109037,"snippet":109038},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","… analýza — křivky IS a LM, rovnovážný důchod a úroková míra. **Příklady 7.1–7.6**. Topic: \u003C\u003Cnarodni-duchod>>. ## Pokrytí topiců Obsah knihy byl sloučen s již existujícími přednáškovými shrnutími d …",{"slug":109040,"path":959,"title":109041,"snippet":109042},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí","… křivek**, ne paragrafem. --- ## 13. Makroekonomie — národní důchod **Základní téma:** \u003C\u003Cnarodni-duchod>> ### HNP výdajovou metodou $$GNP = C + I + G + X$$ **Původ:** definice (vzorec 7.1). * …",{"slug":11557,"path":944,"title":21631,"snippet":109044},"… rovnováha v bodě E(r_E, Y_E)]] ## Motivace — proč přejít od C-I-G-X k IS-LM V modelech \u003C\u003Cnarodni-duchod>> byly **investice pokládány za konstantní** ($I = I^*$). To není realistické — investice f …",{"slug":104667,"path":792,"title":25853,"snippet":109046},"… ém omezení), minimalizace výdajů (duální úloha), optimalizace produkce - **Souvislosti:** \u003C\u003Cnarodni-duchod>>, Optimalizace (IpmrK)",[109048,109050,109051,109052,109053],{"slug":11557,"title":21631,"path":944,"sharedTags":109049},4,{"slug":11544,"title":109033,"path":869,"sharedTags":649},{"slug":109040,"title":109041,"path":959,"sharedTags":642},{"slug":109036,"title":109037,"path":1109,"sharedTags":642},{"slug":104667,"title":25853,"path":792,"sharedTags":642},1777154966829]