[{"data":1,"prerenderedAt":11145},["ShallowReactive",2],{"home-courses":3,"home-recent":1621,"total-stats":11141},[4,678,1147],{"id":5,"title":6,"body":7,"course":657,"courseName":658,"courses":658,"created":659,"description":640,"examInfo":658,"extension":660,"featured":661,"garant":658,"meta":662,"navigation":663,"path":664,"seo":665,"sources":666,"stem":668,"tags":669,"type":675,"updated":676,"__hash__":677},"courses\u002Fcourses\u002Fimork.md","Management oborových řešení (ImorK)",{"type":8,"value":9,"toc":639},"minimark",[10,14,113,118,146,150,192,196,201,250,254,337,341,370,374,394,398,454,458,532,536,547,551,603,607],[11,12,6],"h1",{"id":13},"management-oborových-řešení-imork",[15,16,17,28],"table",{},[18,19,20],"thead",{},[21,22,23,26],"tr",{},[24,25],"th",{},[24,27],{},[29,30,31,43,53,63,73,83,93,103],"tbody",{},[21,32,33,40],{},[34,35,36],"td",{},[37,38,39],"strong",{},"Zkratka",[34,41,42],{},"ImorK",[21,44,45,50],{},[34,46,47],{},[37,48,49],{},"Fakulta",[34,51,52],{},"Fakulta podnikatelská, VUT v Brně",[21,54,55,60],{},[34,56,57],{},[37,58,59],{},"Semestr",[34,61,62],{},"letní 2025\u002F2026",[21,64,65,70],{},[34,66,67],{},[37,68,69],{},"Ukončení",[34,71,72],{},"zkouška",[21,74,75,80],{},[34,76,77],{},[37,78,79],{},"Garant",[34,81,82],{},"Ing. Lukáš Novák, Ph.D.",[21,84,85,90],{},[34,86,87],{},[37,88,89],{},"Vyučující",[34,91,92],{},"Ing. Petr Sedlák",[21,94,95,100],{},[34,96,97],{},[37,98,99],{},"Ústav",[34,101,102],{},"Ústav informatiky",[21,104,105,110],{},[34,106,107],{},[37,108,109],{},"Prerekvizita",[34,111,112],{},"Management informační bezpečnosti (ImibePA)",[114,115,117],"h2",{"id":116},"cíle-předmětu","Cíle předmětu",[119,120,121,128,134,140],"ul",{},[122,123,124,125],"li",{},"Znalosti o specifických problémech a odlišnostech při ",[37,126,127],{},"oborovém řešení informační bezpečnosti",[122,129,130,131],{},"Porozumění jednotlivých řešení na úrovni ",[37,132,133],{},"případových studií",[122,135,136,137],{},"Přehled o rozdílných aspektech v závislosti na oborové řešení ",[37,138,139],{},"ISMS",[122,141,142,143],{},"Metodika pro budování bezpečných IS na bázi norem řady ",[37,144,145],{},"ISO\u002FIEC 27000",[114,147,149],{"id":148},"osnova","Osnova",[151,152,153,156,159,162,165,168,171,174,177,180,183,186,189],"ol",{},[122,154,155],{},"Bezpečnost v kyberprostoru",[122,157,158],{},"Budování bezpečnostního povědomí — SAE",[122,160,161],{},"Manažerská informační bezpečnost",[122,163,164],{},"Problematika GDPR",[122,166,167],{},"ISMS v ISVS",[122,169,170],{},"ISMS v univerzitním prostředí",[122,172,173],{},"ISMS ve zdravotnictví",[122,175,176],{},"ISMS v energetice",[122,178,179],{},"ISMS poskytovatelů konektivity (ISP)",[122,181,182],{},"Bezpečnost konvergovaných sítí",[122,184,185],{},"Řízení bezpečnosti www aplikací",[122,187,188],{},"Řízení bezpečnosti mailových aplikací",[122,190,191],{},"Řízení mobilní bezpečnosti",[114,193,195],{"id":194},"shrnutí-zdrojů","Shrnutí zdrojů",[197,198,200],"h3",{"id":199},"přednášky","Přednášky",[119,202,203,214,223,232,241],{},[122,204,205,213],{},[206,207,212],"a",{"className":208,"dataFsResolvedFilePath":210,"href":211},[209],"wikilink","summaries\u002Fimork-detail-predmetu.md","\u002Fwiki\u002Fimork-detail-predmetu","Detail předmětu"," — sylabus kurzu, hodnocení, literatura",[122,215,216,222],{},[206,217,221],{"className":218,"dataFsResolvedFilePath":219,"href":220},[209],"summaries\u002Fimork-manazerska-bezpecnost.md","\u002Fwiki\u002Fimork-manazerska-bezpecnost","Manažerská bezpečnost"," — governance, SIEM, log management, bezpečnostní role",[122,224,225,231],{},[206,226,230],{"className":227,"dataFsResolvedFilePath":228,"href":229},[209],"summaries\u002Fimork-bezpecnostni-strategie.md","\u002Fwiki\u002Fimork-bezpecnostni-strategie","Bezpečnostní strategie"," — tvorba a implementace bezpečnostní strategie",[122,233,234,240],{},[206,235,239],{"className":236,"dataFsResolvedFilePath":237,"href":238},[209],"summaries\u002Fimork-sae.md","\u002Fwiki\u002Fimork-sae","SAE"," — budování bezpečnostního povědomí (NIST SP 800-50\u002F16)",[122,242,243,249],{},[206,244,248],{"className":245,"dataFsResolvedFilePath":246,"href":247},[209],"summaries\u002Fimork-risk-management.md","\u002Fwiki\u002Fimork-risk-management","Risk Management"," — ISO 31000, ISO 27005, RTP, PoA\u002FSoA",[197,251,253],{"id":252},"oborová-isms","Oborová ISMS",[119,255,256,265,274,283,292,301,310,319,328],{},[122,257,258,264],{},[206,259,263],{"className":260,"dataFsResolvedFilePath":261,"href":262},[209],"summaries\u002Fimork-akademicke-prostredi.md","\u002Fwiki\u002Fimork-akademicke-prostredi","Akademické prostředí"," — kampus, WiFi, identita, VIS",[122,266,267,273],{},[206,268,272],{"className":269,"dataFsResolvedFilePath":270,"href":271},[209],"summaries\u002Fimork-financni-sektor.md","\u002Fwiki\u002Fimork-financni-sektor","Finanční sektor"," — DORA, MiCA, DLT\u002Fblockchain",[122,275,276,282],{},[206,277,281],{"className":278,"dataFsResolvedFilePath":279,"href":280},[209],"summaries\u002Fimork-zdravotnictvi.md","\u002Fwiki\u002Fimork-zdravotnictvi","Zdravotnictví"," — HIPAA, ISO 27799, PACS, DICOM, eHealth",[122,284,285,291],{},[206,286,290],{"className":287,"dataFsResolvedFilePath":288,"href":289},[209],"summaries\u002Fimork-energetika.md","\u002Fwiki\u002Fimork-energetika","Energetika"," — ISO 27019, IEC 61850, PLC\u002FSBC\u002FRTU",[122,293,294,300],{},[206,295,299],{"className":296,"dataFsResolvedFilePath":297,"href":298},[209],"summaries\u002Fimork-smart-grid.md","\u002Fwiki\u002Fimork-smart-grid","Smart Grid"," — NISTIR 7628, IEC 62351, prosumers",[122,302,303,309],{},[206,304,308],{"className":305,"dataFsResolvedFilePath":306,"href":307},[209],"summaries\u002Fimork-doprava.md","\u002Fwiki\u002Fimork-doprava","Doprava (železnice)"," — CLC\u002FTS 50701, kritická infrastruktura",[122,311,312,318],{},[206,313,317],{"className":314,"dataFsResolvedFilePath":315,"href":316},[209],"summaries\u002Fimork-automotive.md","\u002Fwiki\u002Fimork-automotive","Automotive"," — CAN bus, TISAX, UN Reg. 155",[122,320,321,327],{},[206,322,326],{"className":323,"dataFsResolvedFilePath":324,"href":325},[209],"summaries\u002Fimork-isp.md","\u002Fwiki\u002Fimork-isp","ISP\u002Ftelekomunikace"," — ISO 27011, NGN, 5G bezpečnost",[122,329,330,336],{},[206,331,335],{"className":332,"dataFsResolvedFilePath":333,"href":334},[209],"summaries\u002Fimork-mcn.md","\u002Fwiki\u002Fimork-mcn","Mission Critical Networks"," — NCPI, model hrozeb, dostupnost",[197,338,340],{"id":339},"bezpečnost-aplikací-a-dat","Bezpečnost aplikací a dat",[119,342,343,352,361],{},[122,344,345,351],{},[206,346,350],{"className":347,"dataFsResolvedFilePath":348,"href":349},[209],"summaries\u002Fimork-www.md","\u002Fwiki\u002Fimork-www","Bezpečnost webu"," — OWASP, SQL injection, XSS, Solid",[122,353,354,360],{},[206,355,359],{"className":356,"dataFsResolvedFilePath":357,"href":358},[209],"summaries\u002Fimork-email.md","\u002Fwiki\u002Fimork-email","Bezpečnost emailu"," — SPF, DKIM, DMARC, S\u002FMIME, šifrování",[122,362,363,369],{},[206,364,368],{"className":365,"dataFsResolvedFilePath":366,"href":367},[209],"summaries\u002Fimork-ochrana-dat.md","\u002Fwiki\u002Fimork-ochrana-dat","Ochrana dat"," — NAC, IDS\u002FIPS, SIEM, DLP, IPv6",[197,371,373],{"id":372},"kontinuita-a-obnova","Kontinuita a obnova",[119,375,376,385],{},[122,377,378,384],{},[206,379,383],{"className":380,"dataFsResolvedFilePath":381,"href":382},[209],"summaries\u002Fimork-bcm.md","\u002Fwiki\u002Fimork-bcm","BCM"," — ISO 22301, BIA, STEEPLE, PDCA",[122,386,387,393],{},[206,388,392],{"className":389,"dataFsResolvedFilePath":390,"href":391},[209],"summaries\u002Fimork-dr.md","\u002Fwiki\u002Fimork-dr","Disaster Recovery"," — RPO\u002FRTO, cloud DR, 7 tiers, DRaaS",[197,395,397],{"id":396},"kybernetické-útoky","Kybernetické útoky",[119,399,400,409,418,427,436,445],{},[122,401,402,408],{},[206,403,407],{"className":404,"dataFsResolvedFilePath":405,"href":406},[209],"summaries\u002Fimork-anatomie-utoku.md","\u002Fwiki\u002Fimork-anatomie-utoku","Anatomie útoku"," — APT, vektory, exploit\u002Fpayload",[122,410,411,417],{},[206,412,416],{"className":413,"dataFsResolvedFilePath":414,"href":415},[209],"summaries\u002Fimork-ai-utoky.md","\u002Fwiki\u002Fimork-ai-utoky","AI útoky"," — WormGPT, BEC, phishing",[122,419,420,426],{},[206,421,425],{"className":422,"dataFsResolvedFilePath":423,"href":424},[209],"summaries\u002Fimork-sitove-utoky.md","\u002Fwiki\u002Fimork-sitove-utoky","Síťové útoky"," — DDoS, spoofing, Emotet→Trickbot→Ryuk",[122,428,429,435],{},[206,430,434],{"className":431,"dataFsResolvedFilePath":432,"href":433},[209],"summaries\u002Fimork-ransomware.md","\u002Fwiki\u002Fimork-ransomware","Ransomware"," — historie 1989–2024, RaaS, NISTIR 8374, IR plán",[122,437,438,444],{},[206,439,443],{"className":440,"dataFsResolvedFilePath":441,"href":442},[209],"summaries\u002Fimork-rizeny-hacking.md","\u002Fwiki\u002Fimork-rizeny-hacking","Řízený hacking \u002F APT"," — APT skupiny, informační válka, OSINT",[122,446,447,453],{},[206,448,452],{"className":449,"dataFsResolvedFilePath":450,"href":451},[209],"summaries\u002Fimork-internetova-bezpecnost.md","\u002Fwiki\u002Fimork-internetova-bezpecnost","Internetová bezpečnost"," — kyberprostor, OSINT, behaviorální biometrika",[197,455,457],{"id":456},"případové-studie","Případové studie",[119,459,460,469,478,487,496,505,514,523],{},[122,461,462,468],{},[206,463,467],{"className":464,"dataFsResolvedFilePath":465,"href":466},[209],"summaries\u002Fimork-nemocnice.md","\u002Fwiki\u002Fimork-nemocnice","Útoky na nemocnice"," — Benešov (70M Kč), FN Brno (350M Kč), Nymburk",[122,470,471,477],{},[206,472,476],{"className":473,"dataFsResolvedFilePath":474,"href":475},[209],"summaries\u002Fimork-kradez-dat.md","\u002Fwiki\u002Fimork-kradez-dat","Krádež dat"," — PII, černý trh, IoT botnety, ISO 27701, GDPR",[122,479,480,486],{},[206,481,485],{"className":482,"dataFsResolvedFilePath":483,"href":484},[209],"summaries\u002Fimork-sprava-login.md","\u002Fwiki\u002Fimork-sprava-login","Správa login"," — privilegované účty, NIST SP 800-63, biometrika",[122,488,489,495],{},[206,490,494],{"className":491,"dataFsResolvedFilePath":492,"href":493},[209],"summaries\u002Fimork-ehealth.md","\u002Fwiki\u002Fimork-ehealth","eHealth"," — elektronizace zdravotnictví, telemedicína, NSeZ",[122,497,498,504],{},[206,499,503],{"className":500,"dataFsResolvedFilePath":501,"href":502},[209],"summaries\u002Fimork-tor.md","\u002Fwiki\u002Fimork-tor","TOR"," — anonymizace, onion routing, NSA X-Keyscore",[122,506,507,513],{},[206,508,512],{"className":509,"dataFsResolvedFilePath":510,"href":511},[209],"summaries\u002Fimork-payment.md","\u002Fwiki\u002Fimork-payment","Bezpečnost plateb"," — PCI DSS v4.0, NFC\u002Ftokenizace, EMV, darknet",[122,515,516,522],{},[206,517,521],{"className":518,"dataFsResolvedFilePath":519,"href":520},[209],"summaries\u002Fimork-mobilni-bezpecnost.md","\u002Fwiki\u002Fimork-mobilni-bezpecnost","Mobilní bezpečnost"," — SIMJaker, SIM swapping, 5G, Common Criteria",[122,524,525,531],{},[206,526,530],{"className":527,"dataFsResolvedFilePath":528,"href":529},[209],"summaries\u002Fimork-audio-hack.md","\u002Fwiki\u002Fimork-audio-hack","Audio Hack"," — fyzická zranitelnost HDD, CVE-2022-38392, rezonanční útok",[197,533,535],{"id":534},"další","Další",[119,537,538],{},[122,539,540,546],{},[206,541,545],{"className":542,"dataFsResolvedFilePath":543,"href":544},[209],"summaries\u002Fimork-digitalni-identita.md","\u002Fwiki\u002Fimork-digitalni-identita","Digitální identita a stopa"," — online identita, footprint",[114,548,550],{"id":549},"témata","Témata",[119,552,553,561,570,579,587,595],{},[122,554,555,560],{},[206,556,139],{"className":557,"dataFsResolvedFilePath":558,"href":559},[209],"topics\u002Fisms.md","\u002Fwiki\u002Fisms"," — systém řízení bezpečnosti informací",[122,562,563,569],{},[206,564,568],{"className":565,"dataFsResolvedFilePath":566,"href":567},[209],"topics\u002Frizeni-rizik.md","\u002Fwiki\u002Frizeni-rizik","Řízení rizik"," — proces identifikace a ošetření rizik",[122,571,572,578],{},[206,573,577],{"className":574,"dataFsResolvedFilePath":575,"href":576},[209],"topics\u002Fkyberneticka-bezpecnost.md","\u002Fwiki\u002Fkyberneticka-bezpecnost","Kybernetická bezpečnost"," — hrozby, útoky, obrana",[122,580,581,586],{},[206,582,239],{"className":583,"dataFsResolvedFilePath":584,"href":585},[209],"topics\u002Fsae.md","\u002Fwiki\u002Fsae"," — budování bezpečnostního povědomí",[122,588,589,594],{},[206,590,383],{"className":591,"dataFsResolvedFilePath":592,"href":593},[209],"topics\u002Fbcm.md","\u002Fwiki\u002Fbcm"," — řízení kontinuity činnosti",[122,596,597,602],{},[206,598,368],{"className":599,"dataFsResolvedFilePath":600,"href":601},[209],"topics\u002Fochrana-dat.md","\u002Fwiki\u002Fochrana-dat"," — technologická řešení ochrany",[114,604,606],{"id":605},"doporučená-literatura","Doporučená literatura",[119,608,609,617,624,630,633,636],{},[122,610,611,612,616],{},"JORDÁN, V. a ONDRÁK, V.: ",[613,614,615],"em",{},"Integrovaná podniková infrastruktura."," Brno: CERM, 2016. ISBN 978-80-214-5241-1",[122,618,619,620,623],{},"SEDLÁK, P. a KONEČNÝ, M.: ",[613,621,622],{},"Přeměna ISMS v manažerské informatice."," Brno: CERM, 2023. ISBN 978-80-7623-110-8",[122,625,619,626,629],{},[613,627,628],{},"Kybernetická (ne)bezpečnost."," Brno: CERM, 2021. ISBN 978-80-7623-068-2",[122,631,632],{},"ČSN EN ISO\u002FIEC 27011 — Bezpečnost pro telekomunikační organizace",[122,634,635],{},"ČSN EN ISO\u002FIEC 27019 — Bezpečnost pro energetický průmysl",[122,637,638],{},"ČSN EN ISO\u002FIEC 27799 — Bezpečnost ve zdravotnictví",{"title":640,"searchDepth":641,"depth":641,"links":642},"",2,[643,644,645,655,656],{"id":116,"depth":641,"text":117},{"id":148,"depth":641,"text":149},{"id":194,"depth":641,"text":195,"children":646},[647,649,650,651,652,653,654],{"id":199,"depth":648,"text":200},3,{"id":252,"depth":648,"text":253},{"id":339,"depth":648,"text":340},{"id":372,"depth":648,"text":373},{"id":396,"depth":648,"text":397},{"id":456,"depth":648,"text":457},{"id":534,"depth":648,"text":535},{"id":549,"depth":641,"text":550},{"id":605,"depth":641,"text":606},"imork",null,"2026-04-12","md",false,{},true,"\u002Fcourses\u002Fimork",{"title":6,"description":640},[667],"raw\u002Fimork\u002FDetail předmětu.md","courses\u002Fimork",[657,670,671,672,673,674],"isms","informacni-bezpecnost","kyberneticka-bezpecnost","oborova-reseni","iso-27000","course","2026-04-25","6MdSdXZJ3FNW9uPHrGzZPucQlKskWh23itOKhDSZfGs",{"id":679,"title":680,"body":681,"course":1127,"courseName":658,"courses":658,"created":1128,"description":640,"examInfo":658,"extension":660,"featured":661,"garant":658,"meta":1129,"navigation":663,"path":1130,"seo":1131,"sources":1132,"stem":1138,"tags":1139,"type":675,"updated":676,"__hash__":1146},"courses\u002Fcourses\u002Fimek.md","Matematická ekonomie (ImeK)",{"type":8,"value":682,"toc":1111},[683,686,718,722,730,734,737,747,830,840,860,870,946,950,961,965,968,993,999,1010,1016,1019,1023,1060,1064,1067,1071],[11,684,680],{"id":685},"matematická-ekonomie-imek",[119,687,688,694,700,706,712],{},[122,689,690,693],{},[37,691,692],{},"Fakulta:"," FP VUT",[122,695,696,699],{},[37,697,698],{},"Garant:"," doc. RNDr. Bedřich Půža, CSc.",[122,701,702,705],{},[37,703,704],{},"Vyučující (kombinované studium):"," Mgr. Martina Bobalová, Ph.D.",[122,707,708,711],{},[37,709,710],{},"Ukončení:"," zkouška (písemná 60 min + ústní ~10 min)",[122,713,714,717],{},[37,715,716],{},"Semestr:"," letní 2025\u002F2026",[114,719,721],{"id":720},"cíl-předmětu","Cíl předmětu",[723,724,725,726,729],"p",{},"Hlouběji proniknout do kauzální podstaty ekonomických vztahů, rozvoj schopnosti vyjadřovat ekonomické vztahy ",[37,727,728],{},"exaktními prostředky"," a provádět jejich analýzy. Matematické modelování mikroekonomie a makroekonomie pomocí prostředků inženýrské matematiky (derivace, integrály, Lagrangeova metoda).",[114,731,733],{"id":732},"obsah-kurzu","Obsah kurzu",[723,735,736],{},"Kurz je v kombinovaném studiu rozčleněn do tří přednáškových bloků:",[197,738,740,741],{"id":739},"blok-1-kalkul-poptávkanabídka-příjemnákladyzisk","Blok 1 — ",[206,742,746],{"className":743,"dataFsResolvedFilePath":744,"href":745},[209],"summaries\u002Fimek-blok-01.md","\u002Fwiki\u002Fimek-blok-01","Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",[119,748,749,758,767,776,785,794,803,812,821],{},[122,750,751,757],{},[206,752,756],{"className":753,"dataFsResolvedFilePath":754,"href":755},[209],"topics\u002Fzaklady-matematicke-ekonomie.md","\u002Fwiki\u002Fzaklady-matematicke-ekonomie","Základy matematické ekonomie"," — model, endogenní\u002Fexogenní proměnné, ceteris paribus, komparativní statika",[122,759,760,766],{},[206,761,765],{"className":762,"dataFsResolvedFilePath":763,"href":764},[209],"topics\u002Fderivace.md","\u002Fwiki\u002Fderivace","Derivace, diferenciál a extrémy 1D"," — geometrická a inženýrská interpretace, mezní veličiny",[122,768,769,775],{},[206,770,774],{"className":771,"dataFsResolvedFilePath":772,"href":773},[209],"topics\u002Fintegral.md","\u002Fwiki\u002Fintegral","Integrál"," — neurčitý a určitý, rekonstrukce TR z MR a TC z MC",[122,777,778,784],{},[206,779,783],{"className":780,"dataFsResolvedFilePath":781,"href":782},[209],"topics\u002Ffunkce-vice-promennych.md","\u002Fwiki\u002Ffunkce-vice-promennych","Funkce více proměnných"," — parciální derivace, diferenciál 2D, implicitní funkce, volné extrémy",[122,786,787,793],{},[206,788,792],{"className":789,"dataFsResolvedFilePath":790,"href":791},[209],"topics\u002Flagrangeova-metoda.md","\u002Fwiki\u002Flagrangeova-metoda","Lagrangeova metoda"," — vázané extrémy, multiplikátor jako náklady příležitosti",[122,795,796,802],{},[206,797,801],{"className":798,"dataFsResolvedFilePath":799,"href":800},[209],"topics\u002Fpoptavka-nabidka.md","\u002Fwiki\u002Fpoptavka-nabidka","Poptávka, nabídka a tržní rovnováha"," — modely D a S, rovnováha, multiplikátory",[122,804,805,811],{},[206,806,810],{"className":807,"dataFsResolvedFilePath":808,"href":809},[209],"topics\u002Fzdaneni-trhu.md","\u002Fwiki\u002Fzdaneni-trhu","Zdanění trhu"," — daň výrobci vs. spotřebiteli, rozklad daňového břemene, ekvivalence",[122,813,814,820],{},[206,815,819],{"className":816,"dataFsResolvedFilePath":817,"href":818},[209],"topics\u002Fprebytek-spotrebitele-vyrobce.md","\u002Fwiki\u002Fprebytek-spotrebitele-vyrobce","Přebytek spotřebitele a výrobce"," — CS, PS, plochy pod\u002Fnad křivkami",[122,822,823,829],{},[206,824,828],{"className":825,"dataFsResolvedFilePath":826,"href":827},[209],"topics\u002Fprijem-naklady-zisk.md","\u002Fwiki\u002Fprijem-naklady-zisk","Příjem, náklady a zisk"," — TR, AR, MR, TC, AC, MC, body zvratu, konstrukce nabídky firmy",[197,831,833,834],{"id":832},"blok-2-elasticita-a-produkce","Blok 2 — ",[206,835,839],{"className":836,"dataFsResolvedFilePath":837,"href":838},[209],"summaries\u002Fimek-blok-02.md","\u002Fwiki\u002Fimek-blok-02","Elasticita a produkce",[119,841,842,851],{},[122,843,844,850],{},[206,845,849],{"className":846,"dataFsResolvedFilePath":847,"href":848},[209],"topics\u002Felasticita.md","\u002Fwiki\u002Felasticita","Cenová, křížová a důchodová elasticita"," (jedno- i vícefaktorový model)",[122,852,853,859],{},[206,854,858],{"className":855,"dataFsResolvedFilePath":856,"href":857},[209],"topics\u002Fprodukce.md","\u002Fwiki\u002Fprodukce","Produkční funkce"," — Cobb-Douglasova, CES, lineární, Leontiefova, izokvanty, MRTS, Eulerova věta",[197,861,863,864],{"id":862},"blok-3-užitečnost-a-národní-důchod","Blok 3 — ",[206,865,869],{"className":866,"dataFsResolvedFilePath":867,"href":868},[209],"summaries\u002Fimek-blok-03.md","\u002Fwiki\u002Fimek-blok-03","Užitečnost a národní důchod",[119,871,872,905,928,937],{},[122,873,874,880,881,904],{},[206,875,879],{"className":876,"dataFsResolvedFilePath":877,"href":878},[209],"topics\u002Fuzitecnost.md","\u002Fwiki\u002Fuzitecnost","Užitečnost"," — pojem, mezní užitečnost, Cobb-Douglasova ",[882,883,886],"span",{"className":884},[885],"katex",[887,888,890],"math",{"xmlns":889},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[891,892,893,900],"semantics",{},[894,895,896],"mrow",{},[897,898,899],"mi",{},"U",[901,902,899],"annotation",{"encoding":903},"application\u002Fx-tex",", indiferenční křivky, MRCS",[122,906,907,913,914,927],{},[206,908,912],{"className":909,"dataFsResolvedFilePath":910,"href":911},[209],"topics\u002Foptimalizace-spotrebitele.md","\u002Fwiki\u002Foptimalizace-spotrebitele","Optimalizace spotřebitele"," — Lagrangeova maximalizace ",[882,915,917],{"className":916},[885],[887,918,919],{"xmlns":889},[891,920,921,925],{},[894,922,923],{},[897,924,899],{},[901,926,899],{"encoding":903},", duální minimalizace výdajů, Marshallova\u002FHicksova poptávka",[122,929,930,936],{},[206,931,935],{"className":932,"dataFsResolvedFilePath":933,"href":934},[209],"topics\u002Fnarodni-duchod.md","\u002Fwiki\u002Fnarodni-duchod","Národní důchod"," — GNP, spotřeba\u002Fúspory, MPC\u002FMPS, modely C-I, C-I-G, C-I-G-X",[122,938,939,945],{},[206,940,944],{"className":941,"dataFsResolvedFilePath":942,"href":943},[209],"topics\u002Fis-lm.md","\u002Fwiki\u002Fis-lm","IS-LM analýza"," — simultánní rovnováha trhu zboží a peněz, fiskální\u002Fmonetární politika",[114,947,949],{"id":948},"reference-a-přehledy","Reference a přehledy",[119,951,952],{},[122,953,954,960],{},[206,955,959],{"className":956,"dataFsResolvedFilePath":957,"href":958},[209],"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.",[114,962,964],{"id":963},"hodnocení-zkoušky","Hodnocení zkoušky",[723,966,967],{},"Písemná část (60 min) — 4 úlohy:",[151,969,970,976,982,988],{},[122,971,972,973],{},"Rozhodovací úloha o ekonomické funkci — ",[37,974,975],{},"10 bodů",[122,977,978,979],{},"Definice, formulace vlastnosti, interpretace ekonomické veličiny — ",[37,980,981],{},"20 bodů",[122,983,984,985],{},"Výpočetní úloha — ",[37,986,987],{},"30 bodů",[122,989,984,990],{},[37,991,992],{},"40 bodů",[723,994,995,998],{},[37,996,997],{},"Dílčí podmínky"," (nutné pro A–E):",[119,1000,1001,1004,1007],{},[122,1002,1003],{},"≥ 11 bodů ze součtu úloh 1 a 2",[122,1005,1006],{},"≥ 10 bodů z úlohy 3",[122,1008,1009],{},"≥ 10 bodů z úlohy 4",[723,1011,1012,1015],{},[37,1013,1014],{},"Stupnice:"," A (90–100), B (80–89), C (70–79), D (60–69), E (50–59), F (0–49 nebo nesplnění podmínek).",[723,1017,1018],{},"Doporučeno mít kalkulátor.",[114,1020,1022],{"id":1021},"literatura","Literatura",[119,1024,1025,1032,1039,1046,1053],{},[122,1026,1027,1028,1031],{},"I. Mezník, ",[613,1029,1030],{},"Úvod do matematické ekonomie pro ekonomy",", FP VUT \u002F CERM, Brno 2017 (CZ)",[122,1033,1034,1035,1038],{},"A.C. Chiang, ",[613,1036,1037],{},"Fundamental Methods of Mathematical Economics",", McGraw-Hill, 1984",[122,1040,1041,1042,1045],{},"J.U. Koch, L.A. Ostrosky, ",[613,1043,1044],{},"Introduction to Mathematical Economics",", McGraw-Hill, 1994",[122,1047,1048,1049,1052],{},"C.J. McKenna, R. Rees, ",[613,1050,1051],{},"Economics: A Mathematical Introduction",", Oxford UP, 1992",[122,1054,1055,1056,1059],{},"J. Jacques, ",[613,1057,1058],{},"Mathematics for Economics and Business",", Addison-Wesley, 1995",[114,1061,1063],{"id":1062},"prerekvizity","Prerekvizity",[723,1065,1066],{},"Standardní kurz inženýrské matematiky, mikroekonomie a makroekonomie na bakalářské úrovni.",[114,1068,1070],{"id":1069},"přehled-zdrojů","Přehled zdrojů",[119,1072,1073,1081,1088,1095,1102],{},[122,1074,1075,1080],{},[206,1076,212],{"className":1077,"dataFsResolvedFilePath":1078,"href":1079},[209],"summaries\u002Fimek-detail-predmetu.md","\u002Fwiki\u002Fimek-detail-predmetu"," — sylabus a administrativní informace",[122,1082,1083,1087],{},[206,1084,1086],{"className":1085,"dataFsResolvedFilePath":744,"href":745},[209],"KS 1. blok"," — 57 stran, matematický aparát + mikroekonomie",[122,1089,1090,1094],{},[206,1091,1093],{"className":1092,"dataFsResolvedFilePath":837,"href":838},[209],"KS 2. blok"," — 19 stran, elasticita a produkce",[122,1096,1097,1101],{},[206,1098,1100],{"className":1099,"dataFsResolvedFilePath":867,"href":868},[209],"KS 3. blok"," — 25 stran, užitečnost a národní důchod",[122,1103,1104,1110],{},[206,1105,1109],{"className":1106,"dataFsResolvedFilePath":1107,"href":1108},[209],"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":640,"searchDepth":641,"depth":641,"links":1112},[1113,1114,1122,1123,1124,1125,1126],{"id":720,"depth":641,"text":721},{"id":732,"depth":641,"text":733,"children":1115},[1116,1118,1120],{"id":739,"depth":648,"text":1117},"Blok 1 — Kalkul, poptávka\u002Fnabídka, příjem\u002Fnáklady\u002Fzisk",{"id":832,"depth":648,"text":1119},"Blok 2 — Elasticita a produkce",{"id":862,"depth":648,"text":1121},"Blok 3 — Užitečnost a národní důchod",{"id":948,"depth":641,"text":949},{"id":963,"depth":641,"text":964},{"id":1021,"depth":641,"text":1022},{"id":1062,"depth":641,"text":1063},{"id":1069,"depth":641,"text":1070},"imek","2026-04-20",{},"\u002Fcourses\u002Fimek",{"title":680,"description":640},[1133,1134,1135,1136,1137],"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",[1127,1140,1141,1142,1143,1144,1145],"ekonomie","mikroekonomie","makroekonomie","lagrange","derivace","integraly","x73RNX_N_uAS3i63VHeCgVFPJa4tJKL2z8kq4DIN24M",{"id":1148,"title":1149,"body":1150,"course":1600,"courseName":658,"courses":658,"created":1601,"description":640,"examInfo":658,"extension":660,"featured":661,"garant":658,"meta":1602,"navigation":663,"path":1603,"seo":1604,"sources":1605,"stem":1611,"tags":1612,"type":675,"updated":676,"__hash__":1620},"courses\u002Fcourses\u002Fipmrk.md","Pokročilé metody v rozhodování (IpmrK)",{"type":8,"value":1151,"toc":1592},[1152,1155,1229,1231,1234,1236,1320,1324,1353,1357,1422,1424,1473,1475],[11,1153,1149],{"id":1154},"pokročilé-metody-v-rozhodování-ipmrk",[15,1156,1157,1165],{},[18,1158,1159],{},[21,1160,1161,1163],{},[24,1162],{},[24,1164],{},[29,1166,1167,1176,1185,1194,1202,1210,1220],{},[21,1168,1169,1173],{},[34,1170,1171],{},[37,1172,39],{},[34,1174,1175],{},"IpmrK",[21,1177,1178,1182],{},[34,1179,1180],{},[37,1181,49],{},[34,1183,1184],{},"Fakulta podnikatelská VUT v Brně",[21,1186,1187,1191],{},[34,1188,1189],{},[37,1190,79],{},[34,1192,1193],{},"prof. Ing. Petr Dostál, CSc.",[21,1195,1196,1200],{},[34,1197,1198],{},[37,1199,99],{},[34,1201,102],{},[21,1203,1204,1208],{},[34,1205,1206],{},[37,1207,59],{},[34,1209,62],{},[21,1211,1212,1217],{},[34,1213,1214],{},[37,1215,1216],{},"Jazyk",[34,1218,1219],{},"čeština",[21,1221,1222,1226],{},[34,1223,1224],{},[37,1225,69],{},[34,1227,1228],{},"zkouška (písemný test 0–20 bodů, ECTS) + seminární práce (8–12 stran)",[114,1230,721],{"id":720},[723,1232,1233],{},"Seznámit se s pokročilými a nestandardními metodami analytických a simulačních technik v ekonomii a financích. Důraz na teorii i aplikaci do manažerské praxe.",[114,1235,149],{"id":148},[151,1237,1238,1241,1250,1256,1262,1270,1276,1284,1289,1297,1305,1314,1317],{},[122,1239,1240],{},"Úvod",[122,1242,1243,1249],{},[206,1244,1248],{"className":1245,"dataFsResolvedFilePath":1246,"href":1247},[209],"topics\u002Ffuzzy-logika.md","\u002Fwiki\u002Ffuzzy-logika","Fuzzy logika"," — teorie",[122,1251,1252,1255],{},[206,1253,1248],{"className":1254,"dataFsResolvedFilePath":1246,"href":1247},[209]," + aplikace — Excel",[122,1257,1258,1261],{},[206,1259,1248],{"className":1260,"dataFsResolvedFilePath":1246,"href":1247},[209]," — aplikace MATLAB",[122,1263,1264,1249],{},[206,1265,1269],{"className":1266,"dataFsResolvedFilePath":1267,"href":1268},[209],"topics\u002Fumele-neuronove-site.md","\u002Fwiki\u002Fumele-neuronove-site","Umělé neuronové sítě",[122,1271,1272,1275],{},[206,1273,1269],{"className":1274,"dataFsResolvedFilePath":1267,"href":1268},[209]," + aplikace MATLAB",[122,1277,1278,1249],{},[206,1279,1283],{"className":1280,"dataFsResolvedFilePath":1281,"href":1282},[209],"topics\u002Fgeneticke-algoritmy.md","\u002Fwiki\u002Fgeneticke-algoritmy","Genetické algoritmy",[122,1285,1286,1275],{},[206,1287,1283],{"className":1288,"dataFsResolvedFilePath":1281,"href":1282},[209],[122,1290,1291],{},[206,1292,1296],{"className":1293,"dataFsResolvedFilePath":1294,"href":1295},[209],"topics\u002Fteorie-chaosu.md","\u002Fwiki\u002Fteorie-chaosu","Teorie chaosu",[122,1298,1299],{},[206,1300,1304],{"className":1301,"dataFsResolvedFilePath":1302,"href":1303},[209],"topics\u002Fdatamining.md","\u002Fwiki\u002Fdatamining","Datamining",[122,1306,1307,1313],{},[206,1308,1312],{"className":1309,"dataFsResolvedFilePath":1310,"href":1311},[209],"topics\u002Fpredikce.md","\u002Fwiki\u002Fpredikce","Predikce",", kapitálový trh",[122,1315,1316],{},"Řízení výroby a řízení rizik",[122,1318,1319],{},"Rozhodování",[114,1321,1323],{"id":1322},"hodnocení","Hodnocení",[119,1325,1326,1332],{},[122,1327,1328,1331],{},[37,1329,1330],{},"Zkouška",": písemný test, 0–20 bodů. A: 20–18, B: 17–16, C: 15–14, D: 13–12, E: 11–10, F: 9–0.",[122,1333,1334,1337,1338,1342,1343,1347,1348,1352],{},[37,1335,1336],{},"Seminární práce",": 8–12 stran, individuální zaměření na problematiku z praxe, řešení pomocí ",[206,1339,1341],{"className":1340,"dataFsResolvedFilePath":1246,"href":1247},[209],"fuzzy logiky",", ",[206,1344,1346],{"className":1345,"dataFsResolvedFilePath":1267,"href":1268},[209],"umělých neuronových sítí"," nebo ",[206,1349,1351],{"className":1350,"dataFsResolvedFilePath":1281,"href":1282},[209],"genetických algoritmů",". Nutná úspěšná obhajoba.",[114,1354,1356],{"id":1355},"hlavní-témata","Hlavní témata",[119,1358,1359,1365,1371,1377,1386,1392,1401,1407,1416],{},[122,1360,1361,1364],{},[206,1362,1248],{"className":1363,"dataFsResolvedFilePath":1246,"href":1247},[209]," — modelování rozhodování s vágními pojmy",[122,1366,1367,1370],{},[206,1368,1269],{"className":1369,"dataFsResolvedFilePath":1267,"href":1268},[209]," — učení z dat, klasifikace, predikce",[122,1372,1373,1376],{},[206,1374,1283],{"className":1375,"dataFsResolvedFilePath":1281,"href":1282},[209]," — evoluční optimalizace",[122,1378,1379,1385],{},[206,1380,1384],{"className":1381,"dataFsResolvedFilePath":1382,"href":1383},[209],"topics\u002Fevolucni-algoritmy.md","\u002Fwiki\u002Fevolucni-algoritmy","Evoluční algoritmy"," — metaheuristiky, rojové algoritmy, prohledávací metody",[122,1387,1388,1391],{},[206,1389,1296],{"className":1390,"dataFsResolvedFilePath":1294,"href":1295},[209]," — nelineární dynamické systémy",[122,1393,1394,1400],{},[206,1395,1399],{"className":1396,"dataFsResolvedFilePath":1397,"href":1398},[209],"topics\u002Foptimalizace.md","\u002Fwiki\u002Foptimalizace","Optimalizace"," — hledání minima\u002Fmaxima, MATLAB Optimization Toolbox",[122,1402,1403,1406],{},[206,1404,1304],{"className":1405,"dataFsResolvedFilePath":1302,"href":1303},[209]," — dolování z dat, klastrování, rozhodovací stromy, Witness Miner",[122,1408,1409,1415],{},[206,1410,1414],{"className":1411,"dataFsResolvedFilePath":1412,"href":1413},[209],"topics\u002Fanfis.md","\u002Fwiki\u002Fanfis","ANFIS"," — hybridní propojení fuzzy logiky a neuronových sítí",[122,1417,1418,1421],{},[206,1419,1312],{"className":1420,"dataFsResolvedFilePath":1310,"href":1311},[209]," — prognózování časových řad v ekonomii a financích",[114,1423,606],{"id":605},[119,1425,1426,1433,1439,1446,1453,1459,1466],{},[122,1427,1428,1429,1432],{},"DOSTÁL, P. ",[613,1430,1431],{},"Pokročilé metody analýz a modelování v podnikatelství a veřejné správě",", CERM, 2008",[122,1434,1428,1435,1438],{},[613,1436,1437],{},"Advanced Decision making in Business and Public Services",", CERM, 2011",[122,1440,1441,1442,1445],{},"DOSTÁL, P., RAIS, K., SOJKA, Z. ",[613,1443,1444],{},"Pokročilé metody manažerského rozhodování",", Grada, 2005",[122,1447,1448,1449,1452],{},"ALTROCK, C. ",[613,1450,1451],{},"Fuzzy Logic & Neurofuzzy",", 1996",[122,1454,1455,1456,1452],{},"GATELY, E. ",[613,1457,1458],{},"Neural Network for Financial Forecasting",[122,1460,1461,1462,1465],{},"DAVIS, L. ",[613,1463,1464],{},"Handbook of Genetic Algorithms",", 1991",[122,1467,1468,1469,1472],{},"PETERS, E. ",[613,1470,1471],{},"Fractal Market Analysis",", 1994",[114,1474,195],{"id":194},[119,1476,1477,1485,1494,1503,1512,1521,1530,1539,1548,1556,1565,1574,1583],{},[122,1478,1479,1484],{},[206,1480,212],{"className":1481,"dataFsResolvedFilePath":1482,"href":1483},[209],"summaries\u002Fipmrk-detail-predmetu.md","\u002Fwiki\u002Fipmrk-detail-predmetu"," — základní informace o kurzu",[122,1486,1487,1493],{},[206,1488,1492],{"className":1489,"dataFsResolvedFilePath":1490,"href":1491},[209],"summaries\u002Fipmrk-fuzzy-excel.md","\u002Fwiki\u002Fipmrk-fuzzy-excel","Fuzzy logika — Excel"," — princip fuzzy logiky, funkce členství, pravidla, implementace",[122,1495,1496,1502],{},[206,1497,1501],{"className":1498,"dataFsResolvedFilePath":1499,"href":1500},[209],"summaries\u002Fipmrk-fuzzy-matlab.md","\u002Fwiki\u002Fipmrk-fuzzy-matlab","Fuzzy logika — MATLAB"," — architektura fuzzy systému, návrh modelu",[122,1504,1505,1511],{},[206,1506,1510],{"className":1507,"dataFsResolvedFilePath":1508,"href":1509},[209],"summaries\u002Fipmrk-nn-teorie.md","\u002Fwiki\u002Fipmrk-nn-teorie","Neuronové sítě — teorie"," — perceptron, aktivační funkce, backpropagation",[122,1513,1514,1520],{},[206,1515,1519],{"className":1516,"dataFsResolvedFilePath":1517,"href":1518},[209],"summaries\u002Fipmrk-nn-vypocet.md","\u002Fwiki\u002Fipmrk-nn-vypocet","Neuronové sítě — výpočet"," — ruční učení neuronu, vícevrstvé sítě, trénování",[122,1522,1523,1529],{},[206,1524,1528],{"className":1525,"dataFsResolvedFilePath":1526,"href":1527},[209],"summaries\u002Fipmrk-nn-aplikace.md","\u002Fwiki\u002Fipmrk-nn-aplikace","Neuronové sítě — aplikace"," — ANFIS, scoring, predikce, deep learning",[122,1531,1532,1538],{},[206,1533,1537],{"className":1534,"dataFsResolvedFilePath":1535,"href":1536},[209],"summaries\u002Fipmrk-ga-teorie.md","\u002Fwiki\u002Fipmrk-ga-teorie","Genetické algoritmy — teorie"," — chromozomy, selekce, křížení, mutace",[122,1540,1541,1547],{},[206,1542,1546],{"className":1543,"dataFsResolvedFilePath":1544,"href":1545},[209],"summaries\u002Fipmrk-ga-vyuziti.md","\u002Fwiki\u002Fipmrk-ga-vyuziti","Genetické algoritmy — využití"," — optimalizace, TSP, knapsack, klastrování",[122,1549,1550,1555],{},[206,1551,1296],{"className":1552,"dataFsResolvedFilePath":1553,"href":1554},[209],"summaries\u002Fipmrk-chaos.md","\u002Fwiki\u002Fipmrk-chaos"," — atraktory, fraktály, motýlí efekt, Hurstův exponent",[122,1557,1558,1564],{},[206,1559,1563],{"className":1560,"dataFsResolvedFilePath":1561,"href":1562},[209],"summaries\u002Fipmrk-kniha.md","\u002Fwiki\u002Fipmrk-kniha","Kniha — Pokročilé metody"," — celá učebnice, 7 kapitol, kontrolní otázky, nová témata (evoluční alg., optimalizace, datamining)",[122,1566,1567,1573],{},[206,1568,1572],{"className":1569,"dataFsResolvedFilePath":1570,"href":1571},[209],"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",[122,1575,1576,1582],{},[206,1577,1581],{"className":1578,"dataFsResolvedFilePath":1579,"href":1580},[209],"summaries\u002Fipmrk-optimalizace.md","\u002Fwiki\u002Fipmrk-optimalizace","Optimalizace — MATLAB Optimization Toolbox"," — kompletní syntaxe fmincon\u002Ffminsearch\u002Flinprog\u002Fintlinprog\u002Fga",[122,1584,1585,1591],{},[206,1586,1590],{"className":1587,"dataFsResolvedFilePath":1588,"href":1589},[209],"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":640,"searchDepth":641,"depth":641,"links":1593},[1594,1595,1596,1597,1598,1599],{"id":720,"depth":641,"text":721},{"id":148,"depth":641,"text":149},{"id":1322,"depth":641,"text":1323},{"id":1355,"depth":641,"text":1356},{"id":605,"depth":641,"text":606},{"id":194,"depth":641,"text":195},"ipmrk","2026-04-10",{},"\u002Fcourses\u002Fipmrk",{"title":1149,"description":640},[1606,1607,1608,1609,1610],"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",[1600,1613,1614,1615,1616,1617,1618,1619],"fuzzy","neuronove-site","geneticke-algoritmy","evolucni-algoritmy","chaos","optimalizace","datamining","_iX_YpjZn-5NmPhFSn_DHNExx_u1xi12WJEbWAHjXpg",[1622,1735,1847,2334,3535,5435],{"id":1623,"title":1624,"body":1625,"course":658,"courses":1723,"created":1601,"description":640,"extension":660,"meta":1724,"navigation":663,"path":1725,"seo":1726,"sources":1727,"stem":1729,"tags":1730,"type":1733,"updated":676,"__hash__":1734},"topics\u002Ftopics\u002Fanfis.md","ANFIS — Adaptive Neuro-Fuzzy Inference System",{"type":8,"value":1626,"toc":1716},[1627,1630,1639,1652,1656,1677,1681,1692,1701,1704,1708],[11,1628,1624],{"id":1629},"anfis-adaptive-neuro-fuzzy-inference-system",[723,1631,1632],{},[1633,1634],"img",{"alt":1635,"className":1636,"src":1638},"anfis-architektura",[209,1637],"wikilink-broken","\u002Fwiki-assets\u002Fanfis-architektura.jpeg",[723,1640,1641,1642,1646,1647,1651],{},"Hybridní přístup propojující ",[206,1643,1645],{"className":1644,"dataFsResolvedFilePath":1246,"href":1247},[209],"fuzzy logiku"," a ",[206,1648,1650],{"className":1649,"dataFsResolvedFilePath":1267,"href":1268},[209],"umělé neuronové sítě",". Spojuje výhody obou světů.",[114,1653,1655],{"id":1654},"princip","Princip",[119,1657,1658,1668],{},[122,1659,1660,1663,1664,1667],{},[37,1661,1662],{},"Od fuzzy logiky"," přebírá: pravidla KDYŽ–POTOM, jazykové proměnné, funkce členství → ",[37,1665,1666],{},"interpretovatelnost"," (model dává lidský smysl)",[122,1669,1670,1673,1674],{},[37,1671,1672],{},"Od neuronových sítí"," přebírá: schopnost učit se z dat, automatická úprava parametrů → ",[37,1675,1676],{},"adaptivnost",[114,1678,1680],{"id":1679},"kdy-je-anfis-vhodný","Kdy je ANFIS vhodný",[119,1682,1683,1686,1689],{},[122,1684,1685],{},"Chceme model srozumitelný člověku (na rozdíl od čisté neuronové sítě)",[122,1687,1688],{},"Nechceme vše nastavovat ručně (na rozdíl od čistého fuzzy systému)",[122,1690,1691],{},"Máme data i expertní znalost",[114,1693,1695,1696],{"id":1694},"význam-v-kurzu-ipmrk","Význam v kurzu ",[206,1697,1175],{"className":1698,"dataFsResolvedFilePath":1699,"href":1700},[209],"courses\u002Fipmrk.md","\u002Fwiki\u002Fipmrk",[723,1702,1703],{},"ANFIS je klíčový styčný bod kurzu — propojuje dva hlavní bloky (fuzzy logika a neuronové sítě) do jednoho systému. Zkouškově důležité.",[114,1705,1707],{"id":1706},"zdroje","Zdroje",[119,1709,1710],{},[122,1711,1712,1715],{},[206,1713,1528],{"className":1714,"dataFsResolvedFilePath":1526,"href":1527},[209]," — ANFIS je zde představen",{"title":640,"searchDepth":641,"depth":641,"links":1717},[1718,1719,1720,1722],{"id":1654,"depth":641,"text":1655},{"id":1679,"depth":641,"text":1680},{"id":1694,"depth":641,"text":1721},"Význam v kurzu IpmrK",{"id":1706,"depth":641,"text":1707},[1600],{},"\u002Ftopics\u002Fanfis",{"title":1624,"description":640},[1728],"raw\u002Fipmrk\u002Fnn-aplikace.md","topics\u002Fanfis",[1600,1731,1613,1614,1732],"anfis","hybridni-system","topic","w3x8TjfldoFMelvK-RKRrgErKY5CwNSfUH40UpDM_M4",{"id":1736,"title":1737,"body":1738,"course":658,"courses":1834,"created":1601,"description":1835,"extension":660,"meta":1836,"navigation":663,"path":1837,"seo":1838,"sources":1839,"stem":1842,"tags":1843,"type":1733,"updated":676,"__hash__":1846},"topics\u002Ftopics\u002Fbackpropagation.md","Backpropagation (zpětné šíření chyby)",{"type":8,"value":1739,"toc":1829},[1740,1743,1751,1755,1787,1791,1805,1809],[11,1741,1737],{"id":1742},"backpropagation-zpětné-šíření-chyby",[723,1744,1745,1746,1750],{},"Základní a nejdůležitější algoritmus učení vícevrstvých ",[206,1747,1749],{"className":1748,"dataFsResolvedFilePath":1267,"href":1268},[209],"neuronových sítí",".",[114,1752,1754],{"id":1753},"postup","Postup",[151,1756,1757,1763,1769,1775,1781],{},[122,1758,1759,1762],{},[37,1760,1761],{},"Dopředný průchod"," — síť spočítá výstup z aktuálních vah",[122,1764,1765,1768],{},[37,1766,1767],{},"Výpočet chyby"," — porovnání skutečného výstupu s cílem (e = y − m)",[122,1770,1771,1774],{},[37,1772,1773],{},"Zpětné šíření"," — chyba se šíří zpět přes vrstvy, určuje příspěvek každé váhy k chybě",[122,1776,1777,1780],{},[37,1778,1779],{},"Úprava vah"," — w_new = w_old + η · e · x (η = učicí koeficient)",[122,1782,1783,1786],{},[37,1784,1785],{},"Opakování"," — celý cyklus se opakuje přes trénovací data, dokud chyba neklesne pod mez",[114,1788,1790],{"id":1789},"klíčové-vlastnosti","Klíčové vlastnosti",[119,1792,1793,1796,1799,1802],{},[122,1794,1795],{},"Iterativní proces — jedna iterace nestačí",[122,1797,1798],{},"Učicí koeficient (learning rate) řídí velikost kroků",[122,1800,1801],{},"Příliš velký → nestabilita, příliš malý → pomalé učení",[122,1803,1804],{},"Může uváznout v lokálním minimu",[114,1806,1808],{"id":1807},"souvislosti","Souvislosti",[119,1810,1811,1817,1823],{},[122,1812,1813,1816],{},[206,1814,1269],{"className":1815,"dataFsResolvedFilePath":1267,"href":1268},[209]," — backpropagation je jejich hlavní učicí mechanismus",[122,1818,1819,1822],{},[206,1820,1510],{"className":1821,"dataFsResolvedFilePath":1508,"href":1509},[209]," — zde je backpropagation zaveden",[122,1824,1825,1828],{},[206,1826,1519],{"className":1827,"dataFsResolvedFilePath":1517,"href":1518},[209]," — ruční demonstrace principu",{"title":640,"searchDepth":641,"depth":641,"links":1830},[1831,1832,1833],{"id":1753,"depth":641,"text":1754},{"id":1789,"depth":641,"text":1790},{"id":1807,"depth":641,"text":1808},[1600],"Základní a nejdůležitější algoritmus učení vícevrstvých neuronových sítí.",{},"\u002Ftopics\u002Fbackpropagation",{"title":1737,"description":1835},[1840,1841],"raw\u002Fipmrk\u002Fnn-teorie.md","raw\u002Fipmrk\u002Fnn-vypocet.md","topics\u002Fbackpropagation",[1600,1844,1614,1845],"backpropagation","uceni","p2r9NLMc5uEQNYcZ19-gTHFKa1wYriITtRQEGsTyZmE",{"id":1848,"title":1849,"body":1850,"course":658,"courses":2319,"created":659,"description":640,"extension":660,"meta":2320,"navigation":663,"path":2321,"seo":2322,"sources":2323,"stem":2326,"tags":2327,"type":1733,"updated":676,"__hash__":2333},"topics\u002Ftopics\u002Fbcm.md","BCM — Řízení kontinuity činnosti",{"type":8,"value":1851,"toc":2306},[1852,1855,1862,1865,1869,1963,1967,2021,2025,2048,2052,2141,2145,2148,2152,2229,2233,2259,2263,2283,2292],[11,1853,1849],{"id":1854},"bcm-řízení-kontinuity-činnosti",[723,1856,1857],{},[1633,1858],{"alt":1859,"className":1860,"src":1861},"bcm-rpo-rto",[209,1637],"\u002Fwiki-assets\u002Fbcm-rpo-rto.jpeg",[723,1863,1864],{},"Identifikuje potenciální dopady incidentů a zajišťuje kontinuitu a obnovu klíčových procesů organizace na předem stanovenou minimální úroveň.",[114,1866,1868],{"id":1867},"klíčové-pojmy","Klíčové pojmy",[15,1870,1871,1884],{},[18,1872,1873],{},[21,1874,1875,1878,1881],{},[24,1876,1877],{},"Pojem",[24,1879,1880],{},"Anglicky",[24,1882,1883],{},"Popis",[29,1885,1886,1899,1911,1924,1937,1950],{},[21,1887,1888,1893,1896],{},[34,1889,1890],{},[37,1891,1892],{},"BCMS",[34,1894,1895],{},"Business Continuity Management System",[34,1897,1898],{},"Plánovaný, kontinuální a dokumentovaný systém",[21,1900,1901,1905,1908],{},[34,1902,1903],{},[37,1904,383],{},[34,1906,1907],{},"Business Continuity Management",[34,1909,1910],{},"Činnost identifikující dopady a zajišťující kontinuitu",[21,1912,1913,1918,1921],{},[34,1914,1915],{},[37,1916,1917],{},"BIA",[34,1919,1920],{},"Business Impact Analysis",[34,1922,1923],{},"Identifikace kritických činností (orientace na dopad, ne příčinu)",[21,1925,1926,1931,1934],{},[34,1927,1928],{},[37,1929,1930],{},"MBCO",[34,1932,1933],{},"Minimum Business Continuity Objective",[34,1935,1936],{},"Minimální přijatelná úroveň služeb",[21,1938,1939,1944,1947],{},[34,1940,1941],{},[37,1942,1943],{},"RPO",[34,1945,1946],{},"Recovery Point Objective",[34,1948,1949],{},"Do jakého bodu v minulosti lze obnovit data",[21,1951,1952,1957,1960],{},[34,1953,1954],{},[37,1955,1956],{},"RTO",[34,1958,1959],{},"Recovery Time Objective",[34,1961,1962],{},"Čas potřebný pro obnovu provozu",[114,1964,1966],{"id":1965},"pdca-cyklus-pro-bcms","PDCA cyklus pro BCMS",[15,1968,1969,1979],{},[18,1970,1971],{},[21,1972,1973,1976],{},[24,1974,1975],{},"Fáze",[24,1977,1978],{},"Obsah",[29,1980,1981,1991,2001,2011],{},[21,1982,1983,1988],{},[34,1984,1985],{},[37,1986,1987],{},"Plan",[34,1989,1990],{},"Kontext, požadavky, rozsah, politika, BIA, posouzení rizik",[21,1992,1993,1998],{},[34,1994,1995],{},[37,1996,1997],{},"Do",[34,1999,2000],{},"Strategie kontinuity, implementace plánů, cvičení",[21,2002,2003,2008],{},[34,2004,2005],{},[37,2006,2007],{},"Check",[34,2009,2010],{},"Monitoring, audit, přezkoumání managementem",[21,2012,2013,2018],{},[34,2014,2015],{},[37,2016,2017],{},"Act",[34,2019,2020],{},"Nápravná opatření, neustálé zlepšování",[114,2022,2024],{"id":2023},"iso-223012019-struktura","ISO 22301:2019 — struktura",[119,2026,2027,2030,2033,2036,2039,2042,2045],{},[122,2028,2029],{},"Kap. 4 — kontext organizace",[122,2031,2032],{},"Kap. 5 — vedení (leadership)",[122,2034,2035],{},"Kap. 6 — plánování (BIA, rizika)",[122,2037,2038],{},"Kap. 7 — podpora (kompetence, dokumentace, komunikace)",[122,2040,2041],{},"Kap. 8 — provoz (strategie, plány, cvičení)",[122,2043,2044],{},"Kap. 9 — hodnocení výkonnosti (monitoring, audit)",[122,2046,2047],{},"Kap. 10 — zlepšování (neshody, nápravná opatření)",[114,2049,2051],{"id":2050},"analýza-steeple","Analýza STEEPLE",[15,2053,2054,2064],{},[18,2055,2056],{},[21,2057,2058,2061],{},[24,2059,2060],{},"Faktor",[24,2062,2063],{},"Oblast",[29,2065,2066,2077,2088,2099,2109,2120,2131],{},[21,2067,2068,2074],{},[34,2069,2070,2073],{},[37,2071,2072],{},"S","ociální",[34,2075,2076],{},"Zaměstnanost, bezpečnost, komunity",[21,2078,2079,2085],{},[34,2080,2081,2084],{},[37,2082,2083],{},"T","echnologický",[34,2086,2087],{},"Závislost na technologiích",[21,2089,2090,2096],{},[34,2091,2092,2095],{},[37,2093,2094],{},"E","konomický",[34,2097,2098],{},"Ekonomická situace, finanční instituce",[21,2100,2101,2106],{},[34,2102,2103,2105],{},[37,2104,2094],{},"tický",[34,2107,2108],{},"Podnikatelská etika, média, veřejnost",[21,2110,2111,2117],{},[34,2112,2113,2116],{},[37,2114,2115],{},"P","olitický",[34,2118,2119],{},"Politický systém, hrozba nepokojů",[21,2121,2122,2128],{},[34,2123,2124,2127],{},[37,2125,2126],{},"L","egislativní",[34,2129,2130],{},"Předpisy, zákony",[21,2132,2133,2138],{},[34,2134,2135,2137],{},[37,2136,2094],{},"nvironmentální",[34,2139,2140],{},"Životní prostředí, přírodní hrozby",[114,2142,2144],{"id":2143},"disaster-recovery-dr","Disaster Recovery (DR)",[723,2146,2147],{},"Předem stanovený scénář obnovy provozu po havárii — součást BCM.",[197,2149,2151],{"id":2150},"_7-úrovní-dr-tiers","7 úrovní DR (Tiers)",[15,2153,2154,2163],{},[18,2155,2156],{},[21,2157,2158,2161],{},[24,2159,2160],{},"Tier",[24,2162,1883],{},[29,2164,2165,2173,2181,2189,2197,2205,2213,2221],{},[21,2166,2167,2170],{},[34,2168,2169],{},"0",[34,2171,2172],{},"Žádná off-site data",[21,2174,2175,2178],{},[34,2176,2177],{},"1",[34,2179,2180],{},"Fyzická záloha + cold site",[21,2182,2183,2186],{},[34,2184,2185],{},"2",[34,2187,2188],{},"Fyzická záloha + hot site",[21,2190,2191,2194],{},[34,2192,2193],{},"3",[34,2195,2196],{},"Elektronický trezor (electronic vaulting)",[21,2198,2199,2202],{},[34,2200,2201],{},"4",[34,2203,2204],{},"Point-in-time recovery",[21,2206,2207,2210],{},[34,2208,2209],{},"5",[34,2211,2212],{},"Two-site commit (kontinuální přenos)",[21,2214,2215,2218],{},[34,2216,2217],{},"6",[34,2219,2220],{},"Minimální až nulová ztráta dat (zrcadlení)",[21,2222,2223,2226],{},[34,2224,2225],{},"7",[34,2227,2228],{},"Automatizovaná obnova (AI monitoring)",[197,2230,2232],{"id":2231},"cloud-dr","Cloud DR",[119,2234,2235,2241,2247,2253],{},[122,2236,2237,2240],{},[37,2238,2239],{},"Cold DR"," — nejlevnější, nejdelší odstávka",[122,2242,2243,2246],{},[37,2244,2245],{},"Warm DR"," — aktualizované zálohy u poskytovatele",[122,2248,2249,2252],{},[37,2250,2251],{},"Hot DR"," — paralelní řešení v tandemu",[122,2254,2255,2258],{},[37,2256,2257],{},"DRaaS"," — Disaster Recovery as a Service (řízené\u002Fasistované\u002Fvlastní)",[114,2260,2262],{"id":2261},"propojení-s-dalšími-tématy","Propojení s dalšími tématy",[119,2264,2265,2271,2277],{},[122,2266,2267,2270],{},[206,2268,139],{"className":2269,"dataFsResolvedFilePath":558,"href":559},[209]," — BCM jako součást bezpečnostního systému",[122,2272,2273,2276],{},[206,2274,568],{"className":2275,"dataFsResolvedFilePath":566,"href":567},[209]," — krizové plány pro zbytková rizika",[122,2278,2279,2282],{},[206,2280,577],{"className":2281,"dataFsResolvedFilePath":575,"href":576},[209]," — reakce na incidenty",[114,2284,2286,2287],{"id":2285},"zdroje-v-kurzu-imork","Zdroje v kurzu ",[206,2288,42],{"className":2289,"dataFsResolvedFilePath":2290,"href":2291},[209],"courses\u002Fimork.md","\u002Fwiki\u002Fimork",[119,2293,2294,2300],{},[122,2295,2296],{},[206,2297,2299],{"className":2298,"dataFsResolvedFilePath":381,"href":382},[209],"BCM — shrnutí přednášky",[122,2301,2302],{},[206,2303,2305],{"className":2304,"dataFsResolvedFilePath":390,"href":391},[209],"Disaster Recovery — shrnutí přednášky",{"title":640,"searchDepth":641,"depth":641,"links":2307},[2308,2309,2310,2311,2312,2316,2317],{"id":1867,"depth":641,"text":1868},{"id":1965,"depth":641,"text":1966},{"id":2023,"depth":641,"text":2024},{"id":2050,"depth":641,"text":2051},{"id":2143,"depth":641,"text":2144,"children":2313},[2314,2315],{"id":2150,"depth":648,"text":2151},{"id":2231,"depth":648,"text":2232},{"id":2261,"depth":641,"text":2262},{"id":2285,"depth":641,"text":2318},"Zdroje v kurzu ImorK",[657],{},"\u002Ftopics\u002Fbcm",{"title":1849,"description":640},[2324,2325],"raw\u002Fimork\u002F2014 VUT_Bezp BCM-2021.pdf","raw\u002Fimork\u002F2013 VUT_Bezp DR-2021.pdf","topics\u002Fbcm",[657,2328,2329,2330,2331,2332],"bcm","kontinuita-cinnosti","iso-22301","bia","disaster-recovery","ZJwDCcNpVg_0RD-SpeyBFhimC2w94ZwCp5TdUgQNLTI",{"id":2335,"title":1304,"body":2336,"course":1600,"courses":658,"created":3521,"description":2342,"extension":660,"meta":3522,"navigation":663,"path":3523,"seo":3524,"sources":3525,"stem":3526,"tags":3527,"type":1733,"updated":676,"__hash__":3534},"topics\u002Ftopics\u002Fdatamining.md",{"type":8,"value":2337,"toc":3497},[2338,2340,2343,2350,2368,2372,2395,2399,2425,2428,2432,2438,2448,2539,2549,2551,2555,2559,2566,2576,2581,2595,2600,2632,2637,2648,2650,2654,2660,2665,2671,2676,2701,2706,2711,2741,2745,2752,2757,2771,2776,2796,2802,2804,2808,2813,2817,2822,2828,2836,2841,2847,2854,2859,2865,2873,2878,2882,2938,2944,2946,2950,2957,2967,2971,2976,2982,2987,2993,2998,3004,3015,3019,3025,3030,3047,3049,3053,3059,3065,3076,3086,3091,3117,3123,3132,3134,3138,3144,3148,3156,3210,3221,3241,3245,3253,3273,3281,3301,3306,3321,3323,3327,3431,3435,3464,3468,3471,3477,3493],[11,2339,1304],{"id":1619},[723,2341,2342],{},"Datamining (dolování z dat) je sada automatizovaných postupů pro nalézání dosud neznámých vzorů a vztahů ve velkých databázích. Zastřešuje širokou škálu technik používaných v řadě odvětví. Rozvoj začal počátkem 90. let 20. století u bank specializovaných na kreditní karty, rozšířil se do pojišťovnictví, veřejných služeb, zásilkových služeb, energetiky, maloobchodu a dalších.",[723,2344,2345,2346,2349],{},"Datamining je analytický krok procesu ",[37,2347,2348],{},"KDD (Knowledge Discovery in Databases)",". Stojí na průsečíku tří disciplín: strojové učení + statistika + správa databází.",[723,2351,2352,2353,1342,2357,1342,2361,1342,2365,1750],{},"Souvisí s: ",[206,2354,2356],{"className":2355,"dataFsResolvedFilePath":1246,"href":1247},[209],"fuzzy-logika",[206,2358,2360],{"className":2359,"dataFsResolvedFilePath":1267,"href":1268},[209],"neuronové sítě",[206,2362,2364],{"className":2363,"dataFsResolvedFilePath":1382,"href":1383},[209],"evoluční algoritmy",[206,2366,1618],{"className":2367,"dataFsResolvedFilePath":1397,"href":1398},[209],[114,2369,2371],{"id":2370},"cíle-dataminingu","Cíle dataminingu",[119,2373,2374,2380,2386,2392],{},[122,2375,2376,2379],{},[37,2377,2378],{},"Zvýšení zisku"," — identifikace nových zákazníků a příležitostí",[122,2381,2382,2385],{},[37,2383,2384],{},"Snížení nákladů"," — efektivnější cílení a alokace zdrojů",[122,2387,2388,2391],{},[37,2389,2390],{},"Snížení rizika ztrát"," — odhalení rizikových zákazníků, predikce odchodu",[122,2393,2394],{},"Správný výrobek → správný zákazník → správné místo → správný čas",[114,2396,2398],{"id":2397},"praktické-aplikace","Praktické aplikace",[119,2400,2401,2407,2413,2419],{},[122,2402,2403,2406],{},[37,2404,2405],{},"Bankovnictví",": Fraud detection, credit scoring, churn prediction, segmentace zákazníků",[122,2408,2409,2412],{},[37,2410,2411],{},"Pojišťovnictví",": Detekce podvodných pojistných událostí, optimalizace pojistných sazeb",[122,2414,2415,2418],{},[37,2416,2417],{},"Retail",": Market basket analysis (Amazon), doporučovací systémy, rozmístění zboží",[122,2420,2421,2424],{},[37,2422,2423],{},"Energetika\u002Fprůmysl",": Prediktivní údržba, optimalizace spotřeby",[2426,2427],"hr",{},[114,2429,2431],{"id":2430},"proces-práce-s-daty-crisp-dm","Proces práce s daty — CRISP-DM",[723,2433,2434,2437],{},[37,2435,2436],{},"CRISP-DM"," (Cross-Industry Standard Process for Data Mining) je nejrozšířenější metodika — průzkumy ukazovaly 3–4× vyšší využití než konkurence.",[2439,2440,2445],"pre",{"className":2441,"code":2443,"language":2444},[2442],"language-text","Business Understanding → Data Understanding → Data Preparation\n        ↑                                             ↓\n   Deployment ← Evaluation ← Modeling ← (iterativně zpět)\n","text",[2446,2447,2443],"code",{"__ignoreMap":640},[15,2449,2450,2461],{},[18,2451,2452],{},[21,2453,2454,2456,2458],{},[24,2455,1975],{},[24,2457,1978],{},[24,2459,2460],{},"Poznámka",[29,2462,2463,2475,2487,2502,2515,2527],{},[21,2464,2465,2470,2473],{},[34,2466,2467],{},[37,2468,2469],{},"1. Business Understanding",[34,2471,2472],{},"Definice cílů, obchodní otázka, kritéria úspěchu",[34,2474],{},[21,2476,2477,2482,2485],{},[34,2478,2479],{},[37,2480,2481],{},"2. Data Understanding",[34,2483,2484],{},"Sběr dat, průzkum, kvalita, vhodnost pro analýzu",[34,2486],{},[21,2488,2489,2494,2497],{},[34,2490,2491],{},[37,2492,2493],{},"3. Data Preparation",[34,2495,2496],{},"Čištění, klasifikace, vzorkování, sumarizace, transformace",[34,2498,2499],{},[37,2500,2501],{},"50–80 % celkového úsilí",[21,2503,2504,2509,2512],{},[34,2505,2506],{},[37,2507,2508],{},"4. Modeling",[34,2510,2511],{},"Výběr a aplikace technik, kalibrace parametrů",[34,2513,2514],{},"Nejkratší, ale nejviditelnější",[21,2516,2517,2522,2525],{},[34,2518,2519],{},[37,2520,2521],{},"5. Evaluation",[34,2523,2524],{},"Ověření vůči obchodním cílům, metriky přesnosti",[34,2526],{},[21,2528,2529,2534,2537],{},[34,2530,2531],{},[37,2532,2533],{},"6. Deployment",[34,2535,2536],{},"Nasazení do produkce, monitoring, finální zpráva",[34,2538],{},[2540,2541,2542],"blockquote",{},[723,2543,2544,2545,2548],{},"Proces je ",[37,2546,2547],{},"iterativní"," — z každé fáze se lze vracet zpět.",[2426,2550],{},[114,2552,2554],{"id":2553},"klíčové-techniky-dataminingu","Klíčové techniky dataminingu",[197,2556,2558],{"id":2557},"link-analýza-analýza-vazeb","Link analýza (Analýza vazeb)",[723,2560,2561,2562,2565],{},"Technika zaměřená na vyhodnocování ",[37,2563,2564],{},"vztahů (vazeb)"," mezi entitami v síti, místo studia vlastností jednotlivých entit.",[723,2567,2568,2571,2572,2575],{},[37,2569,2570],{},"Princip:"," Data jako ",[37,2573,2574],{},"graf"," — uzly = entity (osoby, účty, produkty), hrany = vztahy nebo interakce.",[723,2577,2578],{},[37,2579,2580],{},"Typy přístupů:",[119,2582,2583,2586,2589,2592],{},[122,2584,2585],{},"Heuristické — rozhodovací pravidla z odborných znalostí",[122,2587,2588],{},"Šablonové — zpracování nestrukturovaných dat",[122,2590,2591],{},"Podobnostní — vážené skórování atributů",[122,2593,2594],{},"Statistické — lexikální statistika",[723,2596,2597],{},[37,2598,2599],{},"Příklady použití:",[119,2601,2602,2608,2614,2620,2626],{},[122,2603,2604,2607],{},[37,2605,2606],{},"Fraud detection"," — odhalování fraud rings (překrývající se adresy, telefony u různých žadatelů)",[122,2609,2610,2613],{},[37,2611,2612],{},"AML"," (Anti-Money Laundering) — praní peněz",[122,2615,2616,2619],{},[37,2617,2618],{},"FBI ViCAP"," — propojování trestných činů",[122,2621,2622,2625],{},[37,2623,2624],{},"Google PageRank"," — hodnocení stránek podle příchozích odkazů",[122,2627,2628,2631],{},[37,2629,2630],{},"Sociální sítě"," — detekce komunit, šíření vlivu, doporučení přátel",[723,2633,2634],{},[37,2635,2636],{},"Historický vývoj:",[151,2638,2639,2642,2645],{},[122,2640,2641],{},"Generace (1975): Ruční maticové grafy",[122,2643,2644],{},"Generace: Automatizované nástroje (IBM i2 Analyst's Notebook)",[122,2646,2647],{},"Generace: Automatická vizualizace napojená na datové zdroje",[2426,2649],{},[197,2651,2653],{"id":2652},"klastrování-clustering","Klastrování (Clustering)",[723,2655,2656,2659],{},[37,2657,2658],{},"Definice:"," Unsupervised learning — rozdělení dat do skupin (clusterů\u002Fshluků) tak, aby objekty uvnitř skupiny byly si co nejpodobnější a objekty z různých skupin co nejodlišnější. Kategorie předem neznáme — algoritmus je hledá sám.",[2661,2662,2664],"h4",{"id":2663},"k-means-algoritmus","K-means algoritmus",[723,2666,2667,2670],{},[37,2668,2669],{},"Minimalizuje:"," WCSS (Within-Cluster Sum of Squares) — vnitřní varianci clusterů.",[723,2672,2673],{},[37,2674,2675],{},"Kroky:",[151,2677,2678,2684,2690,2696],{},[122,2679,2680,2683],{},[37,2681,2682],{},"Inicializace"," — náhodně zvolit k centroidů (moderní: k-means++)",[122,2685,2686,2689],{},[37,2687,2688],{},"Přiřazení"," — každý bod přiřadit do nejbližšího centroidu (Euklidovská vzdálenost)",[122,2691,2692,2695],{},[37,2693,2694],{},"Aktualizace"," — přepočítat centroidy jako průměr přiřazených bodů",[122,2697,2698,2700],{},[37,2699,1785],{}," — dokud se přiřazení stabilizuje nebo max. iterace",[2540,2702,2703],{},[723,2704,2705],{},"Při různých spuštěních může dávat různé výsledky → doporučuje se spustit vícekrát.",[723,2707,2708],{},[37,2709,2710],{},"Výběr počtu clusterů k:",[119,2712,2713,2719,2725,2731],{},[122,2714,2715,2718],{},[37,2716,2717],{},"Elbow method"," — vynést WCSS vs. k, hledat „loket\"",[122,2720,2721,2724],{},[37,2722,2723],{},"Silhouette analysis"," — jak dobře bod pasuje do svého vs. sousedního clusteru (hodnoty 0–1)",[122,2726,2727,2730],{},[37,2728,2729],{},"Gap statistic"," — porovnání se vzdáleností náhodných dat",[122,2732,2733,2736,2737,2740],{},[37,2734,2735],{},"Davies-Bouldin Index"," — nižší = lepší; ",[37,2738,2739],{},"Calinski-Harabasz Index"," — vyšší = lepší",[2661,2742,2744],{"id":2743},"hierarchické-klastrování","Hierarchické klastrování",[723,2746,2747,2748,2751],{},"Vytváří ",[37,2749,2750],{},"dendrogram"," — stromovou strukturu zobrazující postupné slučování clusterů.",[723,2753,2754],{},[37,2755,2756],{},"Přístupy:",[119,2758,2759,2765],{},[122,2760,2761,2764],{},[37,2762,2763],{},"Agglomerativní (zdola nahoru)"," — každý bod = vlastní cluster, postupně slučovat",[122,2766,2767,2770],{},[37,2768,2769],{},"Divisivní (shora dolů)"," — jeden velký cluster, postupně dělit",[723,2772,2773],{},[37,2774,2775],{},"Metody výpočtu vzdálenosti (linkage):",[119,2777,2778,2784,2790],{},[122,2779,2780,2783],{},[37,2781,2782],{},"Ward"," — minimalizuje nárůst SSE; clustery ≈ stejné velikosti; nejčastěji doporučovaná",[122,2785,2786,2789],{},[37,2787,2788],{},"Complete"," — vzdálenost = maximum mezi body",[122,2791,2792,2795],{},[37,2793,2794],{},"Average"," — vzdálenost = průměr",[723,2797,2798,2801],{},[37,2799,2800],{},"Čtení dendrogramu:"," Hledat nejdelší vertikální úsečku nepřerušenou horizontálou — tam nakrájíme strom. Počet clusterů = počet průsečíků řezné linie s dendrogramem.",[2426,2803],{},[197,2805,2807],{"id":2806},"rozhodovací-stromy-decision-trees","Rozhodovací stromy (Decision Trees)",[723,2809,2810,2812],{},[37,2811,2658],{}," Model klasifikující data pomocí hierarchického větvení. Každý vnitřní uzel = test atributu; každá větev = výsledek testu; každý list = výsledná třída nebo hodnota.",[2661,2814,2816],{"id":2815},"míry-nečistoty-uzlu","Míry nečistoty uzlu",[723,2818,2819],{},[37,2820,2821],{},"Entropie:",[2439,2823,2826],{"className":2824,"code":2825,"language":2444},[2442],"H(S) = −Σ pᵢ × log₂(pᵢ)\n",[2446,2827,2825],{"__ignoreMap":640},[119,2829,2830,2833],{},[122,2831,2832],{},"H = 0 → čistý uzel (vše jedné třídy)",[122,2834,2835],{},"H = 1 → maximální smíšenost (binární, 50\u002F50)",[723,2837,2838],{},[37,2839,2840],{},"Informační zisk (Information Gain):",[2439,2842,2845],{"className":2843,"code":2844,"language":2444},[2442],"Gain(S, A) = H(S) − Σ (|Sᵥ| \u002F |S|) × H(Sᵥ)\n",[2446,2846,2844],{"__ignoreMap":640},[723,2848,2849,2850,2853],{},"Vybíráme atribut A s ",[37,2851,2852],{},"nejvyšším"," informačním ziskem.",[723,2855,2856],{},[37,2857,2858],{},"Giniho index (Gini Impurity):",[2439,2860,2863],{"className":2861,"code":2862,"language":2444},[2442],"Gini(S) = 1 − Σ pᵢ²\n",[2446,2864,2862],{"__ignoreMap":640},[119,2866,2867,2870],{},[122,2868,2869],{},"Gini = 0 → čistý uzel",[122,2871,2872],{},"Gini = 0,5 → maximální nečistota (binární)",[2540,2874,2875],{},[723,2876,2877],{},"Gini je výpočetně jednodušší (bez logaritmů) — prakticky dávají podobné výsledky.",[2661,2879,2881],{"id":2880},"algoritmy-rozhodovacích-stromů","Algoritmy rozhodovacích stromů",[15,2883,2884,2897],{},[18,2885,2886],{},[21,2887,2888,2891,2894],{},[24,2889,2890],{},"Algoritmus",[24,2892,2893],{},"Metrika",[24,2895,2896],{},"Vlastnosti",[29,2898,2899,2912,2925],{},[21,2900,2901,2906,2909],{},[34,2902,2903],{},[37,2904,2905],{},"ID3",[34,2907,2908],{},"Informační zisk (entropie)",[34,2910,2911],{},"Pouze kategorická data, bez prořezávání",[21,2913,2914,2919,2922],{},[34,2915,2916],{},[37,2917,2918],{},"C4.5",[34,2920,2921],{},"Gain ratio (normalizovaný)",[34,2923,2924],{},"Spojité proměnné, chybějící hodnoty, prořezávání",[21,2926,2927,2932,2935],{},[34,2928,2929],{},[37,2930,2931],{},"CART",[34,2933,2934],{},"Giniho index",[34,2936,2937],{},"Binární stromy, klasifikace i regrese, prořezávání",[723,2939,2940,2943],{},[37,2941,2942],{},"Prořezávání (pruning):"," Stromy mají tendenci přetrénovat se (overfitting). Pruning odstraňuje statisticky nevýznamné větve.",[2426,2945],{},[114,2947,2949],{"id":2948},"asociační-pravidla-apriori-algoritmus","Asociační pravidla — Apriori algoritmus",[723,2951,2952,2953,2956],{},"Hledá vzory souvýskytu v databázích transakcí. Typicky: ",[37,2954,2955],{},"market basket analysis"," — které produkty se kupují společně.",[723,2958,2959,2962,2963,2966],{},[37,2960,2961],{},"Formát pravidla:"," ",[2446,2964,2965],{},"{A} → {B}"," — „kdo koupí A, koupí i B\"",[197,2968,2970],{"id":2969},"klíčové-metriky","Klíčové metriky",[723,2972,2973],{},[37,2974,2975],{},"Support (podpora):",[2439,2977,2980],{"className":2978,"code":2979,"language":2444},[2442],"Support(A) = počet transakcí s A \u002F celkový počet transakcí\n",[2446,2981,2979],{"__ignoreMap":640},[723,2983,2984],{},[37,2985,2986],{},"Confidence (důvěra):",[2439,2988,2991],{"className":2989,"code":2990,"language":2444},[2442],"Confidence(A → B) = Support(A ∪ B) \u002F Support(A)\n",[2446,2992,2990],{"__ignoreMap":640},[723,2994,2995],{},[37,2996,2997],{},"Lift:",[2439,2999,3002],{"className":3000,"code":3001,"language":2444},[2442],"Lift(A → B) = Confidence(A → B) \u002F Support(B)\n",[2446,3003,3001],{"__ignoreMap":640},[119,3005,3006,3009,3012],{},[122,3007,3008],{},"Lift = 1 → A a B jsou nezávislé",[122,3010,3011],{},"Lift > 1 → pozitivní asociace (A zvyšuje pravděpodobnost B)",[122,3013,3014],{},"Lift \u003C 1 → negativní asociace",[197,3016,3018],{"id":3017},"princip-apriori","Princip Apriori",[723,3020,3021,3024],{},[37,3022,3023],{},"Anti-monotone property:"," Pokud množina A nesplňuje min. support, žádná její nadmnožina nemůže být frekventovaná → efektivní prořezávání prostoru hledání.",[723,3026,3027],{},[37,3028,3029],{},"Postup:",[151,3031,3032,3035,3038,3041,3044],{},[122,3033,3034],{},"Nastavit min_sup a min_conf",[122,3036,3037],{},"Najít frekventované 1-itemsety",[122,3039,3040],{},"Generovat kandidáty (k+1)-itemsetů z frekventovaných k-itemsetů",[122,3042,3043],{},"Prořezat nesplňující min_sup",[122,3045,3046],{},"Opakovat; pak generovat pravidla splňující min_conf",[2426,3048],{},[114,3050,3052],{"id":3051},"witness-miner-lanner-group","Witness Miner \u002F Lanner Group",[723,3054,3055,3058],{},[37,3056,3057],{},"Lanner Group Ltd"," — softwarová společnost, Birmingham (UK), 1996. Specializace na simulační software.",[723,3060,3061,3064],{},[37,3062,3063],{},"WITNESS"," — diskrétní simulační software od 1986. Integrován v produktech Oracle, SAP, IBM. Umožňuje:",[119,3066,3067,3070,3073],{},[122,3068,3069],{},"Modelování podnikových procesů a výrobních operací",[122,3071,3072],{},"3D modelování, diskrétní a stochastická simulace",[122,3074,3075],{},"Integraci s MS Excel, MS Access, ODBC, CAD",[723,3077,3078,3081,3082,3085],{},[37,3079,3080],{},"Witness Miner"," — označení pro integraci ",[37,3083,3084],{},"process mining"," technik (Disco\u002FFluxicon) se simulačním nástrojem WITNESS.",[723,3087,3088],{},[37,3089,3090],{},"Funkce analýzy ze simulačních dat:",[119,3092,3093,3099,3105,3111],{},[122,3094,3095,3098],{},[37,3096,3097],{},"Závislosti vstupů a výstupů"," — jaké kombinace vstupních parametrů vedou k jakým výstupům",[122,3100,3101,3104],{},[37,3102,3103],{},"Pravidla"," — extrakce rozhodovacích pravidel z chování simulovaného systému",[122,3106,3107,3110],{},[37,3108,3109],{},"Shluky (clustery)"," — seskupení podobných scénářů výsledků simulace",[122,3112,3113,3116],{},[37,3114,3115],{},"Statistiky\u002FKPI"," — exportovatelné do Excel",[723,3118,3119,3122],{},[37,3120,3121],{},"WITNESS Optimizer"," — využívá Simulated Annealing a Tabu Search pro optimalizaci parametrů.",[2540,3124,3125],{},[723,3126,3127,3128,3131],{},"Poznámka: Specifický modul \"Witness Miner\" není podrobně zdokumentován veřejně — pravděpodobně proprietární terminologie nebo starší funkce. Viz ",[206,3129,2364],{"className":3130,"dataFsResolvedFilePath":1382,"href":1383},[209]," pro principy SA a Tabu Search.",[2426,3133],{},[114,3135,3137],{"id":3136},"matlab-pro-datamining","MATLAB pro datamining",[723,3139,3140,3141,1750],{},"MATLAB nabízí funkce v rámci ",[37,3142,3143],{},"Statistics and Machine Learning Toolbox",[197,3145,3147],{"id":3146},"klastrování","Klastrování",[723,3149,3150],{},[37,3151,3152,3155],{},[2446,3153,3154],{},"kmeans"," — k-means:",[2439,3157,3161],{"className":3158,"code":3159,"language":3160,"meta":640,"style":640},"language-matlab shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","[idx, C] = kmeans(data, k);\n% idx = přiřazení bodů; C = centroidy (k×p matice)\n\n% S vizualizací:\n[idx, C] = kmeans(data, 2);\ngscatter(data(:,1), data(:,2), idx);\nhold on;\nplot(C(:,1), C(:,2), 'kx', 'MarkerSize', 15, 'LineWidth', 3);\n","matlab",[2446,3162,3163,3170,3175,3180,3186,3192,3198,3204],{"__ignoreMap":640},[882,3164,3167],{"class":3165,"line":3166},"line",1,[882,3168,3169],{},"[idx, C] = kmeans(data, k);\n",[882,3171,3172],{"class":3165,"line":641},[882,3173,3174],{},"% idx = přiřazení bodů; C = centroidy (k×p matice)\n",[882,3176,3177],{"class":3165,"line":648},[882,3178,3179],{"emptyLinePlaceholder":663},"\n",[882,3181,3183],{"class":3165,"line":3182},4,[882,3184,3185],{},"% S vizualizací:\n",[882,3187,3189],{"class":3165,"line":3188},5,[882,3190,3191],{},"[idx, C] = kmeans(data, 2);\n",[882,3193,3195],{"class":3165,"line":3194},6,[882,3196,3197],{},"gscatter(data(:,1), data(:,2), idx);\n",[882,3199,3201],{"class":3165,"line":3200},7,[882,3202,3203],{},"hold on;\n",[882,3205,3207],{"class":3165,"line":3206},8,[882,3208,3209],{},"plot(C(:,1), C(:,2), 'kx', 'MarkerSize', 15, 'LineWidth', 3);\n",[723,3211,3212],{},[37,3213,3214,3217,3218,3220],{},[2446,3215,3216],{},"linkage"," + ",[2446,3219,2750],{}," — hierarchické klastrování:",[2439,3222,3224],{"className":3158,"code":3223,"language":3160,"meta":640,"style":640},"Z = linkage(data, 'ward');      % vytvoří hierarchickou strukturu\ndendrogram(Z);                  % vizualizace\nclusters = cluster(Z, 'maxclust', 4);   % řez na 4 clustery\n",[2446,3225,3226,3231,3236],{"__ignoreMap":640},[882,3227,3228],{"class":3165,"line":3166},[882,3229,3230],{},"Z = linkage(data, 'ward');      % vytvoří hierarchickou strukturu\n",[882,3232,3233],{"class":3165,"line":641},[882,3234,3235],{},"dendrogram(Z);                  % vizualizace\n",[882,3237,3238],{"class":3165,"line":648},[882,3239,3240],{},"clusters = cluster(Z, 'maxclust', 4);   % řez na 4 clustery\n",[197,3242,3244],{"id":3243},"rozhodovací-stromy","Rozhodovací stromy",[723,3246,3247],{},[37,3248,3249,3252],{},[2446,3250,3251],{},"fitctree"," — trénování:",[2439,3254,3256],{"className":3158,"code":3255,"language":3160,"meta":640,"style":640},"Mdl = fitctree(X_train, Y_train);\nview(Mdl, 'Mode', 'graph');     % vizualizace stromu\nresubLoss(Mdl)                  % přesnost na trénovacích datech\n",[2446,3257,3258,3263,3268],{"__ignoreMap":640},[882,3259,3260],{"class":3165,"line":3166},[882,3261,3262],{},"Mdl = fitctree(X_train, Y_train);\n",[882,3264,3265],{"class":3165,"line":641},[882,3266,3267],{},"view(Mdl, 'Mode', 'graph');     % vizualizace stromu\n",[882,3269,3270],{"class":3165,"line":648},[882,3271,3272],{},"resubLoss(Mdl)                  % přesnost na trénovacích datech\n",[723,3274,3275],{},[37,3276,3277,3280],{},[2446,3278,3279],{},"predict"," — predikce:",[2439,3282,3284],{"className":3158,"code":3283,"language":3160,"meta":640,"style":640},"YPred = predict(Mdl, X_test);\naccuracy = sum(YPred == Y_test) \u002F numel(Y_test);\nfprintf('Přesnost: %.2f%%\\n', accuracy * 100);\n",[2446,3285,3286,3291,3296],{"__ignoreMap":640},[882,3287,3288],{"class":3165,"line":3166},[882,3289,3290],{},"YPred = predict(Mdl, X_test);\n",[882,3292,3293],{"class":3165,"line":641},[882,3294,3295],{},"accuracy = sum(YPred == Y_test) \u002F numel(Y_test);\n",[882,3297,3298],{"class":3165,"line":648},[882,3299,3300],{},"fprintf('Přesnost: %.2f%%\\n', accuracy * 100);\n",[723,3302,3303],{},[37,3304,3305],{},"Prevence overfittingu:",[2439,3307,3309],{"className":3158,"code":3308,"language":3160,"meta":640,"style":640},"Mdl = fitctree(X, Y, 'MaxNumSplits', 10);   % omezení hloubky\nMdl = fitctree(X, Y, 'MinLeafSize', 5);     % min. vzorků v listu\n",[2446,3310,3311,3316],{"__ignoreMap":640},[882,3312,3313],{"class":3165,"line":3166},[882,3314,3315],{},"Mdl = fitctree(X, Y, 'MaxNumSplits', 10);   % omezení hloubky\n",[882,3317,3318],{"class":3165,"line":641},[882,3319,3320],{},"Mdl = fitctree(X, Y, 'MinLeafSize', 5);     % min. vzorků v listu\n",[2426,3322],{},[114,3324,3326],{"id":3325},"přehled-technik-pro-zkoušku","Přehled technik pro zkoušku",[15,3328,3329,3341],{},[18,3330,3331],{},[21,3332,3333,3336,3339],{},[24,3334,3335],{},"Technika",[24,3337,3338],{},"Co dělá",[24,3340,1868],{},[29,3342,3343,3356,3369,3381,3393,3406,3418],{},[21,3344,3345,3350,3353],{},[34,3346,3347],{},[37,3348,3349],{},"Link analýza",[34,3351,3352],{},"Hledá vazby v síti entit",[34,3354,3355],{},"Graf, uzly, hrany, fraud detection",[21,3357,3358,3363,3366],{},[34,3359,3360],{},[37,3361,3362],{},"K-means",[34,3364,3365],{},"Seskupuje podobné objekty",[34,3367,3368],{},"Centroid, WCSS, Elbow method, k",[21,3370,3371,3375,3378],{},[34,3372,3373],{},[37,3374,2744],{},[34,3376,3377],{},"Stromová struktura podobnosti",[34,3379,3380],{},"Dendrogram, Ward, linkage",[21,3382,3383,3387,3390],{},[34,3384,3385],{},[37,3386,3244],{},[34,3388,3389],{},"Klasifikace větvícím se stromem",[34,3391,3392],{},"Entropie, informační zisk, Gini, ID3\u002FC4.5\u002FCART",[21,3394,3395,3400,3403],{},[34,3396,3397],{},[37,3398,3399],{},"Asociační pravidla",[34,3401,3402],{},"Vzory souvýskytu",[34,3404,3405],{},"Support, Confidence, Lift, Apriori",[21,3407,3408,3412,3415],{},[34,3409,3410],{},[37,3411,2436],{},[34,3413,3414],{},"Standardní proces projektu",[34,3416,3417],{},"6 fází, iterativní",[21,3419,3420,3425,3428],{},[34,3421,3422],{},[37,3423,3424],{},"WITNESS\u002FLanner",[34,3426,3427],{},"Simulace + process mining",[34,3429,3430],{},"Diskrétní simulace, KPIs, Optimizer",[114,3432,3434],{"id":3433},"kontrolní-otázky-ke-zkoušce","Kontrolní otázky ke zkoušce",[151,3436,3437,3440,3443,3446,3449,3452,3455,3458,3461],{},[122,3438,3439],{},"Čím se zabývá datamining?",[122,3441,3442],{},"Jak jsou data získávána?",[122,3444,3445],{},"Jak jsou data zpracovávána?",[122,3447,3448],{},"K čemu nám slouží datamining?",[122,3450,3451],{},"Co znamená Link analýza?",[122,3453,3454],{},"K čemu slouží klastrování?",[122,3456,3457],{},"K čemu slouží a co je to rozhodovací strom?",[122,3459,3460],{},"Jak lze využít programu MATLAB v dataminingu?",[122,3462,3463],{},"K čemu slouží program Witness Miner?",[114,3465,3467],{"id":3466},"pojmy-k-zapamatování","Pojmy k zapamatování",[723,3469,3470],{},"Datamining, zpracování dat, MATLAB, Witness Miner, závislosti vstupů a výstupů, volba pravidel, shluky, statistické charakteristiky.",[114,3472,2286,3474],{"id":3473},"zdroje-v-kurzu-ipmrk",[206,3475,1175],{"className":3476,"dataFsResolvedFilePath":1699,"href":1700},[209],[119,3478,3479,3486],{},[122,3480,3481,3485],{},[206,3482,3484],{"className":3483,"dataFsResolvedFilePath":1561,"href":1562},[209],"Kniha"," — definice, shrnutí, kontrolní otázky, pojmy",[122,3487,3488,3492],{},[206,3489,3491],{"className":3490,"dataFsResolvedFilePath":1588,"href":1589},[209],"Techniky a nástroje"," — CRISP-DM, Link analýza, k-means, rozhodovací stromy, Apriori, Witness Miner, MATLAB kód (Wikipedia, GeeksforGeeks, IBM, Lanner)",[3494,3495,3496],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":640,"searchDepth":641,"depth":641,"links":3498},[3499,3500,3501,3502,3507,3511,3512,3516,3517,3518,3519],{"id":2370,"depth":641,"text":2371},{"id":2397,"depth":641,"text":2398},{"id":2430,"depth":641,"text":2431},{"id":2553,"depth":641,"text":2554,"children":3503},[3504,3505,3506],{"id":2557,"depth":648,"text":2558},{"id":2652,"depth":648,"text":2653},{"id":2806,"depth":648,"text":2807},{"id":2948,"depth":641,"text":2949,"children":3508},[3509,3510],{"id":2969,"depth":648,"text":2970},{"id":3017,"depth":648,"text":3018},{"id":3051,"depth":641,"text":3052},{"id":3136,"depth":641,"text":3137,"children":3513},[3514,3515],{"id":3146,"depth":648,"text":3147},{"id":3243,"depth":648,"text":3244},{"id":3325,"depth":641,"text":3326},{"id":3433,"depth":641,"text":3434},{"id":3466,"depth":641,"text":3467},{"id":3473,"depth":641,"text":3520},"Zdroje v kurzu IpmrK","2026-04-16",{},"\u002Ftopics\u002Fdatamining",{"title":1304,"description":2342},[1607,1610],"topics\u002Fdatamining",[1600,1619,3528,3529,3530,3531,3532,3533],"crisp-dm","link-analyza","klastrovani","rozhodovaci-stromy","apriori","witness-miner","PUkq0tAb0hdh4jBddhFDQLtfyJlrKVogvd_v45wMY5w",{"id":3536,"title":3537,"body":3538,"course":1127,"courses":658,"created":1128,"description":5424,"extension":660,"meta":5425,"navigation":663,"path":5426,"seo":5427,"sources":5428,"stem":5429,"tags":5430,"type":1733,"updated":676,"__hash__":5434},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":8,"value":3539,"toc":5407},[3540,3543,3564,3568,3652,3655,3784,3935,3938,4021,4025,4086,4136,4143,4147,4283,4334,4338,4381,4450,4521,4529,4533,4572,4644,4648,4729,4778,4822,4826,4830,4900,4904,4954,5033,5040,5043,5096,5366,5370],[11,3541,3537],{"id":3542},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[723,3544,3545,3546,3552,3553,3556,3557,3560,3561,1750],{},"Matematický aparát kurzu ",[206,3547,3551],{"className":3548,"dataFsResolvedFilePath":3549,"href":3550},[209],"courses\u002Fimek.md","\u002Fwiki\u002Fimek","ImeK",". Bez derivace se neobejdou ",[37,3554,3555],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[37,3558,3559],{},"maximalizace zisku"," ani ",[37,3562,3563],{},"minimalizace nákladů",[114,3565,3567],{"id":3566},"funkce-a-polynomy","Funkce a polynomy",[723,3569,3570,3571,3603,3604,3617,3618,3631,3632,1750],{},"Funkce jedné proměnné ",[882,3572,3574],{"className":3573},[885],[887,3575,3576],{"xmlns":889},[891,3577,3578,3600],{},[894,3579,3580,3583,3587,3590,3594,3597],{},[897,3581,3582],{},"y",[3584,3585,3586],"mo",{},"=",[897,3588,3589],{},"f",[3584,3591,3593],{"stretchy":3592},"false","(",[897,3595,3596],{},"x",[3584,3598,3599],{"stretchy":3592},")",[901,3601,3602],{"encoding":903},"y = f(x)"," — předpis závislosti ",[882,3605,3607],{"className":3606},[885],[887,3608,3609],{"xmlns":889},[891,3610,3611,3615],{},[894,3612,3613],{},[897,3614,3596],{},[901,3616,3596],{"encoding":903}," (nezávislá) → ",[882,3619,3621],{"className":3620},[885],[887,3622,3623],{"xmlns":889},[891,3624,3625,3629],{},[894,3626,3627],{},[897,3628,3582],{},[901,3630,3582],{"encoding":903}," (závislá). Hodnota v bodě: ",[882,3633,3635],{"className":3634},[885],[887,3636,3637],{"xmlns":889},[891,3638,3639,3649],{},[894,3640,3641,3643,3645,3647],{},[897,3642,3589],{},[3584,3644,3593],{"stretchy":3592},[897,3646,206],{},[3584,3648,3599],{"stretchy":3592},[901,3650,3651],{"encoding":903},"f(a)",[723,3653,3654],{},"Polynomy:",[119,3656,3657,3690,3733],{},[122,3658,3659],{},[151,3660,3661],{},[122,3662,3663,3664],{},"stupně: ",[882,3665,3667],{"className":3666},[885],[887,3668,3669],{"xmlns":889},[891,3670,3671,3687],{},[894,3672,3673,3675,3677,3679,3681,3684],{},[897,3674,3582],{},[3584,3676,3586],{},[897,3678,206],{},[897,3680,3596],{},[3584,3682,3683],{},"+",[897,3685,3686],{},"b",[901,3688,3689],{"encoding":903},"y = ax + b",[122,3691,3692],{},[151,3693,3694],{"start":641},[122,3695,3663,3696],{},[882,3697,3699],{"className":3698},[885],[887,3700,3701],{"xmlns":889},[891,3702,3703,3730],{},[894,3704,3705,3707,3709,3711,3719,3721,3723,3725,3727],{},[897,3706,3582],{},[3584,3708,3586],{},[897,3710,206],{},[3712,3713,3714,3716],"msup",{},[897,3715,3596],{},[3717,3718,2185],"mn",{},[3584,3720,3683],{},[897,3722,3686],{},[897,3724,3596],{},[3584,3726,3683],{},[897,3728,3729],{},"c",[901,3731,3732],{"encoding":903},"y = ax^2 + bx + c",[122,3734,3735],{},[151,3736,3737],{"start":648},[122,3738,3663,3739],{},[882,3740,3742],{"className":3741},[885],[887,3743,3744],{"xmlns":889},[891,3745,3746,3781],{},[894,3747,3748,3750,3752,3754,3760,3762,3764,3770,3772,3774,3776,3778],{},[897,3749,3582],{},[3584,3751,3586],{},[897,3753,206],{},[3712,3755,3756,3758],{},[897,3757,3596],{},[3717,3759,2193],{},[3584,3761,3683],{},[897,3763,3686],{},[3712,3765,3766,3768],{},[897,3767,3596],{},[3717,3769,2185],{},[3584,3771,3683],{},[897,3773,3729],{},[897,3775,3596],{},[3584,3777,3683],{},[897,3779,3780],{},"d",[901,3782,3783],{"encoding":903},"y = ax^3 + bx^2 + cx + d",[723,3785,3786,2962,3789,3844,3845,3886,3887,1750],{},[37,3787,3788],{},"Příklad rozkladu:",[882,3790,3792],{"className":3791},[885],[887,3793,3794],{"xmlns":889},[891,3795,3796,3841],{},[894,3797,3798,3800,3802,3808,3811,3813,3815,3817,3819,3821,3823,3825,3827,3829,3831,3833,3835,3837,3839],{},[897,3799,3582],{},[3584,3801,3586],{},[3712,3803,3804,3806],{},[897,3805,3596],{},[3717,3807,2185],{},[3584,3809,3810],{},"−",[3717,3812,2209],{},[897,3814,3596],{},[3584,3816,3683],{},[3717,3818,2217],{},[3584,3820,3586],{},[3584,3822,3593],{"stretchy":3592},[897,3824,3596],{},[3584,3826,3810],{},[3717,3828,2185],{},[3584,3830,3599],{"stretchy":3592},[3584,3832,3593],{"stretchy":3592},[897,3834,3596],{},[3584,3836,3810],{},[3717,3838,2193],{},[3584,3840,3599],{"stretchy":3592},[901,3842,3843],{"encoding":903},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[882,3846,3848],{"className":3847},[885],[887,3849,3850],{"xmlns":889},[891,3851,3852,3883],{},[894,3853,3854,3861,3863,3865,3869,3873,3879,3881],{},[3855,3856,3857,3859],"msub",{},[897,3858,3596],{},[3717,3860,2177],{},[3584,3862,3586],{},[3717,3864,2185],{},[3584,3866,3868],{"separator":3867},"true",",",[3870,3871,3872],"mtext",{}," ",[3855,3874,3875,3877],{},[897,3876,3596],{},[3717,3878,2185],{},[3584,3880,3586],{},[3717,3882,2193],{},[901,3884,3885],{"encoding":903},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[882,3888,3890],{"className":3889},[885],[887,3891,3892],{"xmlns":889},[891,3893,3894,3932],{},[894,3895,3896,3898,3900,3902,3904,3906,3916,3922,3924],{},[897,3897,3582],{},[3584,3899,3586],{},[3584,3901,3593],{"stretchy":3592},[897,3903,3596],{},[3584,3905,3810],{},[3907,3908,3909],"mstyle",{"scriptlevel":2169,"displaystyle":3592},[3910,3911,3912,3914],"mfrac",{},[3717,3913,2209],{},[3717,3915,2185],{},[3712,3917,3918,3920],{},[3584,3919,3599],{"stretchy":3592},[3717,3921,2185],{},[3584,3923,3810],{},[3907,3925,3926],{"scriptlevel":2169,"displaystyle":3592},[3910,3927,3928,3930],{},[3717,3929,2177],{},[3717,3931,2201],{},[901,3933,3934],{"encoding":903},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[114,3936,3937],{"id":1144},"Derivace",[723,3939,3940,3941,1347,3968,3996,3997,1750],{},"Označení ",[882,3942,3944],{"className":3943},[885],[887,3945,3946],{"xmlns":889},[891,3947,3948,3965],{},[894,3949,3950,3959,3961,3963],{},[3712,3951,3952,3954],{},[897,3953,3589],{},[3584,3955,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},"normal","0em","′",[3584,3960,3593],{"stretchy":3592},[897,3962,3596],{},[3584,3964,3599],{"stretchy":3592},[901,3966,3967],{"encoding":903},"f'(x)",[882,3969,3971],{"className":3970},[885],[887,3972,3973],{"xmlns":889},[891,3974,3975,3993],{},[894,3976,3977],{},[3907,3978,3979],{"scriptlevel":2169,"displaystyle":3867},[3910,3980,3981,3987],{},[894,3982,3983,3985],{},[897,3984,3780],{},[897,3986,3582],{},[894,3988,3989,3991],{},[897,3990,3780],{},[897,3992,3596],{},[901,3994,3995],{"encoding":903},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[882,3998,4000],{"className":3999},[885],[887,4001,4002],{"xmlns":889},[891,4003,4004,4018],{},[894,4005,4006,4012,4014,4016],{},[3712,4007,4008,4010],{},[897,4009,3589],{},[3584,4011,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4013,3593],{"stretchy":3592},[897,4015,206],{},[3584,4017,3599],{"stretchy":3592},[901,4019,4020],{"encoding":903},"f'(a)",[197,4022,4024],{"id":4023},"geometrická-interpretace","Geometrická interpretace",[723,4026,4027,4050,4051,4054,4055,4085],{},[882,4028,4030],{"className":4029},[885],[887,4031,4032],{"xmlns":889},[891,4033,4034,4048],{},[894,4035,4036,4042,4044,4046],{},[3712,4037,4038,4040],{},[897,4039,3589],{},[3584,4041,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4043,3593],{"stretchy":3592},[897,4045,206],{},[3584,4047,3599],{"stretchy":3592},[901,4049,4020],{"encoding":903}," = ",[37,4052,4053],{},"sklon tečny"," ke grafu funkce v bodě ",[882,4056,4058],{"className":4057},[885],[887,4059,4060],{"xmlns":889},[891,4061,4062,4082],{},[894,4063,4064,4067,4069,4071,4073,4075,4077,4079],{},[3584,4065,4066],{"stretchy":3592},"[",[897,4068,206],{},[3584,4070,3868],{"separator":3867},[897,4072,3589],{},[3584,4074,3593],{"stretchy":3592},[897,4076,206],{},[3584,4078,3599],{"stretchy":3592},[3584,4080,4081],{"stretchy":3592},"]",[901,4083,4084],{"encoding":903},"[a, f(a)]",". Rovnice tečny:",[723,4087,4088],{},[882,4089,4091],{"className":4090},[885],[887,4092,4093],{"xmlns":889},[891,4094,4095,4133],{},[894,4096,4097,4099,4101,4103,4105,4107,4109,4111,4117,4119,4121,4123,4125,4127,4129,4131],{},[897,4098,3582],{},[3584,4100,3810],{},[897,4102,3589],{},[3584,4104,3593],{"stretchy":3592},[897,4106,206],{},[3584,4108,3599],{"stretchy":3592},[3584,4110,3586],{},[3712,4112,4113,4115],{},[897,4114,3589],{},[3584,4116,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4118,3593],{"stretchy":3592},[897,4120,206],{},[3584,4122,3599],{"stretchy":3592},[3584,4124,3593],{"stretchy":3592},[897,4126,3596],{},[3584,4128,3810],{},[897,4130,206],{},[3584,4132,3599],{"stretchy":3592},[901,4134,4135],{"encoding":903},"y - f(a) = f'(a)(x - a)",[723,4137,4138],{},[1633,4139],{"alt":4140,"className":4141,"src":4142},"imek-derivace-tecna",[209,1637],"\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[197,4144,4146],{"id":4145},"inženýrská-interpretace","Inženýrská interpretace",[723,4148,4149,4050,4172,2962,4175,4188,4189,4202,4203,4221,4222,4235,4236,4249,4250,4263,4264,4282],{},[882,4150,4152],{"className":4151},[885],[887,4153,4154],{"xmlns":889},[891,4155,4156,4170],{},[894,4157,4158,4164,4166,4168],{},[3712,4159,4160,4162],{},[897,4161,3589],{},[3584,4163,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4165,3593],{"stretchy":3592},[897,4167,206],{},[3584,4169,3599],{"stretchy":3592},[901,4171,4020],{"encoding":903},[37,4173,4174],{},"rychlost změny",[882,4176,4178],{"className":4177},[885],[887,4179,4180],{"xmlns":889},[891,4181,4182,4186],{},[894,4183,4184],{},[897,4185,3582],{},[901,4187,3582],{"encoding":903}," vzhledem k ",[882,4190,4192],{"className":4191},[885],[887,4193,4194],{"xmlns":889},[891,4195,4196,4200],{},[894,4197,4198],{},[897,4199,3596],{},[901,4201,3596],{"encoding":903}," v bodě ",[882,4204,4206],{"className":4205},[885],[887,4207,4208],{"xmlns":889},[891,4209,4210,4218],{},[894,4211,4212,4214,4216],{},[897,4213,3596],{},[3584,4215,3586],{},[897,4217,206],{},[901,4219,4220],{"encoding":903},"x = a","; přibližná změna ",[882,4223,4225],{"className":4224},[885],[887,4226,4227],{"xmlns":889},[891,4228,4229,4233],{},[894,4230,4231],{},[897,4232,3582],{},[901,4234,3582],{"encoding":903}," při změně ",[882,4237,4239],{"className":4238},[885],[887,4240,4241],{"xmlns":889},[891,4242,4243,4247],{},[894,4244,4245],{},[897,4246,3596],{},[901,4248,3596],{"encoding":903}," z ",[882,4251,4253],{"className":4252},[885],[887,4254,4255],{"xmlns":889},[891,4256,4257,4261],{},[894,4258,4259],{},[897,4260,206],{},[901,4262,206],{"encoding":903}," na ",[882,4265,4267],{"className":4266},[885],[887,4268,4269],{"xmlns":889},[891,4270,4271,4279],{},[894,4272,4273,4275,4277],{},[897,4274,206],{},[3584,4276,3683],{},[3717,4278,2177],{},[901,4280,4281],{"encoding":903},"a+1",":",[723,4284,4285],{},[882,4286,4288],{"className":4287},[885],[887,4289,4290],{"xmlns":889},[891,4291,4292,4331],{},[894,4293,4294,4296,4298,4300,4302,4304,4306,4309,4311,4313,4315,4317,4319,4325,4327,4329],{},[897,4295,3589],{},[3584,4297,3593],{"stretchy":3592},[897,4299,206],{},[3584,4301,3683],{},[3717,4303,2177],{},[3584,4305,3599],{"stretchy":3592},[3584,4307,4308],{},"≈",[897,4310,3589],{},[3584,4312,3593],{"stretchy":3592},[897,4314,206],{},[3584,4316,3599],{"stretchy":3592},[3584,4318,3683],{},[3712,4320,4321,4323],{},[897,4322,3589],{},[3584,4324,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4326,3593],{"stretchy":3592},[897,4328,206],{},[3584,4330,3599],{"stretchy":3592},[901,4332,4333],{"encoding":903},"f(a+1) \\approx f(a) + f'(a)",[197,4335,4337],{"id":4336},"příklad-mezní-náklady","Příklad — mezní náklady",[723,4339,4340,4341,1750],{},"Celkové náklady ",[882,4342,4344],{"className":4343},[885],[887,4345,4346],{"xmlns":889},[891,4347,4348,4378],{},[894,4349,4350,4352,4355,4357,4360,4362,4364,4367,4369,4372],{},[897,4351,2083],{},[897,4353,4354],{},"C",[3584,4356,3586],{},[3717,4358,4359],{},"1000",[3584,4361,3683],{},[3717,4363,2185],{},[897,4365,4366],{},"Q",[3584,4368,3683],{},[3717,4370,4371],{},"0,1",[3712,4373,4374,4376],{},[897,4375,4366],{},[3717,4377,2185],{},[901,4379,4380],{"encoding":903},"TC = 1000 + 2Q + 0{,}1 Q^2",[723,4382,4383,4384,4422,4423,1750],{},"Mezní náklady: ",[882,4385,4387],{"className":4386},[885],[887,4388,4389],{"xmlns":889},[891,4390,4391,4419],{},[894,4392,4393,4396,4398,4400,4402,4408,4410,4412,4414,4417],{},[897,4394,4395],{},"M",[897,4397,4354],{},[3584,4399,3586],{},[897,4401,2083],{},[3712,4403,4404,4406],{},[897,4405,4354],{},[3584,4407,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4409,3586],{},[3717,4411,2185],{},[3584,4413,3683],{},[3717,4415,4416],{},"0,2",[897,4418,4366],{},[901,4420,4421],{"encoding":903},"MC = TC' = 2 + 0{,}2 Q",", takže ",[882,4424,4426],{"className":4425},[885],[887,4427,4428],{"xmlns":889},[891,4429,4430,4447],{},[894,4431,4432,4434,4436,4438,4441,4443,4445],{},[897,4433,4395],{},[897,4435,4354],{},[3584,4437,3593],{"stretchy":3592},[3717,4439,4440],{},"10",[3584,4442,3599],{"stretchy":3592},[3584,4444,3586],{},[3717,4446,2201],{},[901,4448,4449],{"encoding":903},"MC(10) = 4",[723,4451,4452,2962,4455,4504,4505,2962,4508,1750],{},[37,4453,4454],{},"Skutečný přírůstek:",[882,4456,4458],{"className":4457},[885],[887,4459,4460],{"xmlns":889},[891,4461,4462,4501],{},[894,4463,4464,4467,4469,4471,4473,4475,4477,4479,4482,4484,4486,4488,4490,4492,4494,4496,4498],{},[897,4465,4466],{"mathvariant":3956},"Δ",[897,4468,2083],{},[897,4470,4354],{},[3584,4472,3586],{},[897,4474,2083],{},[897,4476,4354],{},[3584,4478,3593],{"stretchy":3592},[3717,4480,4481],{},"11",[3584,4483,3599],{"stretchy":3592},[3584,4485,3810],{},[897,4487,2083],{},[897,4489,4354],{},[3584,4491,3593],{"stretchy":3592},[3717,4493,4440],{},[3584,4495,3599],{"stretchy":3592},[3584,4497,3586],{},[3717,4499,4500],{},"4,2",[901,4502,4503],{"encoding":903},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[37,4506,4507],{},"Přibližný (lineární):",[882,4509,4511],{"className":4510},[885],[887,4512,4513],{"xmlns":889},[891,4514,4515,4519],{},[894,4516,4517],{},[3717,4518,2201],{},[901,4520,2201],{"encoding":903},[723,4522,4523,4524,4528],{},"(Viz aplikace v ",[206,4525,4527],{"className":4526,"dataFsResolvedFilePath":826,"href":827},[209],"prijem-naklady-zisk",".)",[114,4530,4532],{"id":4531},"diferenciál","Diferenciál",[723,4534,4535],{},[882,4536,4538],{"className":4537},[885],[887,4539,4540],{"xmlns":889},[891,4541,4542,4569],{},[894,4543,4544,4546,4548,4550,4556,4558,4560,4562,4565,4567],{},[897,4545,3780],{},[897,4547,3589],{},[3584,4549,3586],{},[3712,4551,4552,4554],{},[897,4553,3589],{},[3584,4555,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4557,3593],{"stretchy":3592},[897,4559,3596],{},[3584,4561,3599],{"stretchy":3592},[3870,4563,4564],{}," ",[897,4566,3780],{},[897,4568,3596],{},[901,4570,4571],{"encoding":903},"df = f'(x)\\, dx",[723,4573,4574,4575,4591,4592,4640,4641,1750],{},"Pro malá ",[882,4576,4578],{"className":4577},[885],[887,4579,4580],{"xmlns":889},[891,4581,4582,4588],{},[894,4583,4584,4586],{},[897,4585,3780],{},[897,4587,3596],{},[901,4589,4590],{"encoding":903},"dx"," platí: ",[882,4593,4595],{"className":4594},[885],[887,4596,4597],{"xmlns":889},[891,4598,4599,4637],{},[894,4600,4601,4603,4605,4607,4609,4611,4613,4615,4617,4619,4621,4623,4625,4627,4629,4631,4633,4635],{},[897,4602,4466],{"mathvariant":3956},[897,4604,3589],{},[3584,4606,3586],{},[897,4608,3589],{},[3584,4610,3593],{"stretchy":3592},[897,4612,3596],{},[3584,4614,3683],{},[897,4616,3780],{},[897,4618,3596],{},[3584,4620,3599],{"stretchy":3592},[3584,4622,3810],{},[897,4624,3589],{},[3584,4626,3593],{"stretchy":3592},[897,4628,3596],{},[3584,4630,3599],{"stretchy":3592},[3584,4632,4308],{},[897,4634,3780],{},[897,4636,3589],{},[901,4638,4639],{"encoding":903},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[37,4642,4643],{},"lineární odhad přírůstku",[197,4645,4647],{"id":4646},"příklad","Příklad",[723,4649,4650,4681,4682,4707,4708,4728],{},[882,4651,4653],{"className":4652},[885],[887,4654,4655],{"xmlns":889},[891,4656,4657,4678],{},[894,4658,4659,4661,4663,4665,4668,4670,4672],{},[897,4660,2083],{},[897,4662,4354],{},[3584,4664,3586],{},[3717,4666,4667],{},"100",[3584,4669,3683],{},[3717,4671,4371],{},[3712,4673,4674,4676],{},[897,4675,4366],{},[3717,4677,2185],{},[901,4679,4680],{"encoding":903},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[882,4683,4685],{"className":4684},[885],[887,4686,4687],{"xmlns":889},[891,4688,4689,4704],{},[894,4690,4691,4693,4695,4698,4701],{},[897,4692,4366],{},[3584,4694,4282],{},[3717,4696,4697],{},"50",[3584,4699,4700],{},"→",[3717,4702,4703],{},"60",[901,4705,4706],{"encoding":903},"Q: 50 \\to 60"," (tj. ",[882,4709,4711],{"className":4710},[885],[887,4712,4713],{"xmlns":889},[891,4714,4715,4725],{},[894,4716,4717,4719,4721,4723],{},[897,4718,3780],{},[897,4720,4366],{},[3584,4722,3586],{},[3717,4724,4440],{},[901,4726,4727],{"encoding":903},"dQ = 10","):",[723,4730,4731],{},[882,4732,4734],{"className":4733},[885],[887,4735,4736],{"xmlns":889},[891,4737,4738,4775],{},[894,4739,4740,4742,4744,4746,4748,4750,4752,4755,4757,4759,4761,4763,4765,4767,4769,4771,4773],{},[897,4741,3780],{},[897,4743,2083],{},[897,4745,4354],{},[3584,4747,3586],{},[3717,4749,4416],{},[897,4751,4366],{},[3584,4753,4754],{},"⋅",[897,4756,3780],{},[897,4758,4366],{},[3584,4760,3586],{},[3717,4762,4416],{},[3584,4764,4754],{},[3717,4766,4697],{},[3584,4768,4754],{},[3717,4770,4440],{},[3584,4772,3586],{},[3717,4774,4667],{},[901,4776,4777],{"encoding":903},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[723,4779,4780,4781,4804,4805,4821],{},"Přesná změna: ",[882,4782,4784],{"className":4783},[885],[887,4785,4786],{"xmlns":889},[891,4787,4788,4801],{},[894,4789,4790,4792,4794,4796,4798],{},[897,4791,4466],{"mathvariant":3956},[897,4793,2083],{},[897,4795,4354],{},[3584,4797,3586],{},[3717,4799,4800],{},"110",[901,4802,4803],{"encoding":903},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[882,4806,4808],{"className":4807},[885],[887,4809,4810],{"xmlns":889},[891,4811,4812,4818],{},[894,4813,4814,4816],{},[897,4815,2083],{},[897,4817,4354],{},[901,4819,4820],{"encoding":903},"TC"," je konvexní.",[114,4823,4825],{"id":4824},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[197,4827,4829],{"id":4828},"nutná-podmínka","Nutná podmínka",[723,4831,4832,4833,4202,4853,4866,4867,4895,4896,4899],{},"Má-li ",[882,4834,4836],{"className":4835},[885],[887,4837,4838],{"xmlns":889},[891,4839,4840,4850],{},[894,4841,4842,4844,4846,4848],{},[897,4843,3589],{},[3584,4845,3593],{"stretchy":3592},[897,4847,3596],{},[3584,4849,3599],{"stretchy":3592},[901,4851,4852],{"encoding":903},"f(x)",[882,4854,4856],{"className":4855},[885],[887,4857,4858],{"xmlns":889},[891,4859,4860,4864],{},[894,4861,4862],{},[897,4863,206],{},[901,4865,206],{"encoding":903}," extrém, pak ",[882,4868,4870],{"className":4869},[885],[887,4871,4872],{"xmlns":889},[891,4873,4874,4892],{},[894,4875,4876,4882,4884,4886,4888,4890],{},[3712,4877,4878,4880],{},[897,4879,3589],{},[3584,4881,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,4883,3593],{"stretchy":3592},[897,4885,206],{},[3584,4887,3599],{"stretchy":3592},[3584,4889,3586],{},[3717,4891,2169],{},[901,4893,4894],{"encoding":903},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[37,4897,4898],{},"stacionární"," (podezřelé) body.",[197,4901,4903],{"id":4902},"postačující-podmínka","Postačující podmínka",[723,4905,4906,4907,4920,4921,4282],{},"Pro stacionární bod ",[882,4908,4910],{"className":4909},[885],[887,4911,4912],{"xmlns":889},[891,4913,4914,4918],{},[894,4915,4916],{},[897,4917,206],{},[901,4919,206],{"encoding":903},", je-li ",[882,4922,4924],{"className":4923},[885],[887,4925,4926],{"xmlns":889},[891,4927,4928,4951],{},[894,4929,4930,4940,4942,4944,4946,4949],{},[3712,4931,4932,4934],{},[897,4933,3589],{},[894,4935,4936,4938],{},[3584,4937,3958],{"mathvariant":3956},[3584,4939,3958],{"mathvariant":3956},[3584,4941,3593],{"stretchy":3592},[897,4943,206],{},[3584,4945,3599],{"stretchy":3592},[3584,4947,4948],{"mathvariant":3956},"≠",[3717,4950,2169],{},[901,4952,4953],{"encoding":903},"f''(a) \\neq 0",[119,4955,4956,4995],{},[122,4957,4958,4991,4992],{},[882,4959,4961],{"className":4960},[885],[887,4962,4963],{"xmlns":889},[891,4964,4965,4988],{},[894,4966,4967,4977,4979,4981,4983,4986],{},[3712,4968,4969,4971],{},[897,4970,3589],{},[894,4972,4973,4975],{},[3584,4974,3958],{"mathvariant":3956},[3584,4976,3958],{"mathvariant":3956},[3584,4978,3593],{"stretchy":3592},[897,4980,206],{},[3584,4982,3599],{"stretchy":3592},[3584,4984,4985],{},">",[3717,4987,2169],{},[901,4989,4990],{"encoding":903},"f''(a) > 0"," ⇒ ",[37,4993,4994],{},"lokální minimum",[122,4996,4997,4991,5030],{},[882,4998,5000],{"className":4999},[885],[887,5001,5002],{"xmlns":889},[891,5003,5004,5027],{},[894,5005,5006,5016,5018,5020,5022,5025],{},[3712,5007,5008,5010],{},[897,5009,3589],{},[894,5011,5012,5014],{},[3584,5013,3958],{"mathvariant":3956},[3584,5015,3958],{"mathvariant":3956},[3584,5017,3593],{"stretchy":3592},[897,5019,206],{},[3584,5021,3599],{"stretchy":3592},[3584,5023,5024],{},"\u003C",[3717,5026,2169],{},[901,5028,5029],{"encoding":903},"f''(a) \u003C 0",[37,5031,5032],{},"lokální maximum",[723,5034,5035],{},[1633,5036],{"alt":5037,"className":5038,"src":5039},"imek-extremy-1d",[209,1637],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[197,5041,4647],{"id":5042},"příklad-1",[723,5044,5045],{},[882,5046,5048],{"className":5047},[885],[887,5049,5050],{"xmlns":889},[891,5051,5052,5093],{},[894,5053,5054,5056,5058,5060,5062,5064,5066,5072,5074,5076,5082,5084,5087,5089,5091],{},[897,5055,3589],{},[3584,5057,3593],{"stretchy":3592},[897,5059,3596],{},[3584,5061,3599],{"stretchy":3592},[3584,5063,3586],{},[3717,5065,2185],{},[3712,5067,5068,5070],{},[897,5069,3596],{},[3717,5071,2193],{},[3584,5073,3810],{},[3717,5075,2193],{},[3712,5077,5078,5080],{},[897,5079,3596],{},[3717,5081,2185],{},[3584,5083,3810],{},[3717,5085,5086],{},"12",[897,5088,3596],{},[3584,5090,3683],{},[3717,5092,2193],{},[901,5094,5095],{"encoding":903},"f(x) = 2x^3 - 3x^2 - 12x + 3",[119,5097,5098,5209,5249,5312],{},[122,5099,5100,5172,5173],{},[882,5101,5103],{"className":5102},[885],[887,5104,5105],{"xmlns":889},[891,5106,5107,5169],{},[894,5108,5109,5115,5117,5119,5121,5123,5125,5131,5133,5135,5137,5139,5141,5143,5145,5147,5149,5151,5153,5155,5157,5159,5161,5163,5165,5167],{},[3712,5110,5111,5113],{},[897,5112,3589],{},[3584,5114,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,5116,3593],{"stretchy":3592},[897,5118,3596],{},[3584,5120,3599],{"stretchy":3592},[3584,5122,3586],{},[3717,5124,2217],{},[3712,5126,5127,5129],{},[897,5128,3596],{},[3717,5130,2185],{},[3584,5132,3810],{},[3717,5134,2217],{},[897,5136,3596],{},[3584,5138,3810],{},[3717,5140,5086],{},[3584,5142,3586],{},[3717,5144,2217],{},[3584,5146,3593],{"stretchy":3592},[897,5148,3596],{},[3584,5150,3683],{},[3717,5152,2177],{},[3584,5154,3599],{"stretchy":3592},[3584,5156,3593],{"stretchy":3592},[897,5158,3596],{},[3584,5160,3810],{},[3717,5162,2185],{},[3584,5164,3599],{"stretchy":3592},[3584,5166,3586],{},[3717,5168,2169],{},[901,5170,5171],{"encoding":903},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[882,5174,5176],{"className":5175},[885],[887,5177,5178],{"xmlns":889},[891,5179,5180,5206],{},[894,5181,5182,5188,5190,5192,5194,5196,5202,5204],{},[3855,5183,5184,5186],{},[897,5185,3596],{},[3717,5187,2177],{},[3584,5189,3586],{},[3584,5191,3810],{},[3717,5193,2177],{},[3584,5195,3868],{"separator":3867},[3855,5197,5198,5200],{},[897,5199,3596],{},[3717,5201,2185],{},[3584,5203,3586],{},[3717,5205,2185],{},[901,5207,5208],{"encoding":903},"x_1 = -1, x_2 = 2",[122,5210,5211],{},[882,5212,5214],{"className":5213},[885],[887,5215,5216],{"xmlns":889},[891,5217,5218,5246],{},[894,5219,5220,5230,5232,5234,5236,5238,5240,5242,5244],{},[3712,5221,5222,5224],{},[897,5223,3589],{},[894,5225,5226,5228],{},[3584,5227,3958],{"mathvariant":3956},[3584,5229,3958],{"mathvariant":3956},[3584,5231,3593],{"stretchy":3592},[897,5233,3596],{},[3584,5235,3599],{"stretchy":3592},[3584,5237,3586],{},[3717,5239,5086],{},[897,5241,3596],{},[3584,5243,3810],{},[3717,5245,2217],{},[901,5247,5248],{"encoding":903},"f''(x) = 12x - 6",[122,5250,5251,4991,5292,5295,5296],{},[882,5252,5254],{"className":5253},[885],[887,5255,5256],{"xmlns":889},[891,5257,5258,5289],{},[894,5259,5260,5270,5272,5274,5276,5278,5280,5282,5285,5287],{},[3712,5261,5262,5264],{},[897,5263,3589],{},[894,5265,5266,5268],{},[3584,5267,3958],{"mathvariant":3956},[3584,5269,3958],{"mathvariant":3956},[3584,5271,3593],{"stretchy":3592},[3584,5273,3810],{},[3717,5275,2177],{},[3584,5277,3599],{"stretchy":3592},[3584,5279,3586],{},[3584,5281,3810],{},[3717,5283,5284],{},"18",[3584,5286,5024],{},[3717,5288,2169],{},[901,5290,5291],{"encoding":903},"f''(-1) = -18 \u003C 0",[37,5293,5294],{},"maximum"," v ",[882,5297,5299],{"className":5298},[885],[887,5300,5301],{"xmlns":889},[891,5302,5303,5309],{},[894,5304,5305,5307],{},[3584,5306,3810],{},[3717,5308,2177],{},[901,5310,5311],{"encoding":903},"-1",[122,5313,5314,4991,5350,5295,5353],{},[882,5315,5317],{"className":5316},[885],[887,5318,5319],{"xmlns":889},[891,5320,5321,5347],{},[894,5322,5323,5333,5335,5337,5339,5341,5343,5345],{},[3712,5324,5325,5327],{},[897,5326,3589],{},[894,5328,5329,5331],{},[3584,5330,3958],{"mathvariant":3956},[3584,5332,3958],{"mathvariant":3956},[3584,5334,3593],{"stretchy":3592},[3717,5336,2185],{},[3584,5338,3599],{"stretchy":3592},[3584,5340,3586],{},[3717,5342,5284],{},[3584,5344,4985],{},[3717,5346,2169],{},[901,5348,5349],{"encoding":903},"f''(2) = 18 > 0",[37,5351,5352],{},"minimum",[882,5354,5356],{"className":5355},[885],[887,5357,5358],{"xmlns":889},[891,5359,5360,5364],{},[894,5361,5362],{},[3717,5363,2185],{},[901,5365,2185],{"encoding":903},[114,5367,5369],{"id":5368},"navigace","Navigace",[119,5371,5372,5380,5388],{},[122,5373,5374,2962,5377],{},[37,5375,5376],{},"Předchozí:",[206,5378,756],{"className":5379,"dataFsResolvedFilePath":754,"href":755},[209],[122,5381,5382,2962,5385],{},[37,5383,5384],{},"Navazující:",[206,5386,774],{"className":5387,"dataFsResolvedFilePath":772,"href":773},[209],[122,5389,5390,2962,5393,5396,5397,5401,5402,5406],{},[37,5391,5392],{},"Souvislosti:",[206,5394,783],{"className":5395,"dataFsResolvedFilePath":781,"href":782},[209]," (rozšíření na 2D), ",[206,5398,5400],{"className":5399,"dataFsResolvedFilePath":826,"href":827},[209],"Příjem, náklady, zisk"," (aplikace mezních veličin), ",[206,5403,5405],{"className":5404,"dataFsResolvedFilePath":847,"href":848},[209],"Elasticita"," (procentní citlivost přes derivaci)",{"title":640,"searchDepth":641,"depth":641,"links":5408},[5409,5410,5415,5418,5423],{"id":3566,"depth":641,"text":3567},{"id":1144,"depth":641,"text":3937,"children":5411},[5412,5413,5414],{"id":4023,"depth":648,"text":4024},{"id":4145,"depth":648,"text":4146},{"id":4336,"depth":648,"text":4337},{"id":4531,"depth":641,"text":4532,"children":5416},[5417],{"id":4646,"depth":648,"text":4647},{"id":4824,"depth":641,"text":4825,"children":5419},[5420,5421,5422],{"id":4828,"depth":648,"text":4829},{"id":4902,"depth":648,"text":4903},{"id":5042,"depth":648,"text":4647},{"id":5368,"depth":641,"text":5369},"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":3537,"description":5424},[1134],"topics\u002Fderivace",[1127,1144,5431,5432,5433],"diferencial","extremy","mezni-naklady","U4vqwJqO65hVzq9khEr5sxPHpHJLXAz_kTaaHdKCCIw",{"id":5436,"title":5437,"body":5438,"course":1127,"courses":658,"created":11129,"description":640,"extension":660,"meta":11130,"navigation":663,"path":11131,"seo":11132,"sources":11133,"stem":11134,"tags":11135,"type":1733,"updated":676,"__hash__":11140},"topics\u002Ftopics\u002Felasticita.md","Elasticita poptávky a nabídky",{"type":8,"value":5439,"toc":11102},[5440,5443,5464,5468,5495,5499,5540,5631,5675,5679,5703,5710,5714,5724,5736,5740,5769,5778,5834,5840,5843,5849,5876,5882,5980,6140,6431,6435,6515,6521,6525,6623,6689,6857,6861,6939,6970,6997,7003,7035,7113,7200,7204,7267,7273,7276,7282,7396,7481,7525,7529,7575,7582,7899,7904,7928,7957,8024,8121,8125,8132,8139,8210,8330,8414,8417,8423,8750,8754,8917,8925,9061,9069,9307,9315,9318,9323,9579,9583,9757,9891,9928,9972,9975,10105,10195,10213,10217,10224,10230,10290,10293,10317,10320,10326,10329,10335,10338,10342,10380,10438,10627,10631,10704,10710,10717,10721,10727,10869,10873,10879,10915,10920,11097],[11,5441,5437],{"id":5442},"elasticita-poptávky-a-nabídky",[2540,5444,5445],{},[723,5446,5447,5450,5451,5453,5454,5457,5458,1646,5461,1750],{},[882,5448,5449],{},"!abstract"," TL;DR\n",[37,5452,5405],{}," 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: ",[37,5455,5456],{},"cenovou elasticitu poptávky"," (a nabídky), ",[37,5459,5460],{},"křížově-cenovou elasticitu",[37,5462,5463],{},"důchodovou elasticitu",[114,5465,5467],{"id":5466},"úvod-motivace","Úvod — motivace",[723,5469,5470,5471,5474,5475,5478,5479,5482,5483,5486,5487,5490,5491,5494],{},"Termín ",[613,5472,5473],{},"elasticita"," (alternativně ",[613,5476,5477],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[37,5480,5481],{},"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 ",[613,5484,5485],{},"cenové elasticity poptávky"," (resp. ",[613,5488,5489],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[206,5492,3937],{"className":5493,"dataFsResolvedFilePath":763,"href":764},[209],").",[197,5496,5498],{"id":5497},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[723,5500,5501,5502,5520,5521,5539],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[882,5503,5505],{"className":5504},[885],[887,5506,5507],{"xmlns":889},[891,5508,5509,5517],{},[894,5510,5511,5513,5515],{},[897,5512,2115],{},[3584,5514,3586],{},[3717,5516,4440],{},[901,5518,5519],{"encoding":903},"P=10"," a při této ceně se prodá ",[882,5522,5524],{"className":5523},[885],[887,5525,5526],{"xmlns":889},[891,5527,5528,5536],{},[894,5529,5530,5532,5534],{},[897,5531,4366],{},[3584,5533,3586],{},[3717,5535,4667],{},[901,5537,5538],{"encoding":903},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[119,5541,5542,5588],{},[122,5543,5544,5547,5548,5587],{},[37,5545,5546],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[882,5549,5551],{"className":5550},[885],[887,5552,5553],{"xmlns":889},[891,5554,5555,5584],{},[894,5556,5557,5560,5563,5565,5567,5570,5572,5575,5577,5579,5581],{},[3870,5558,5559],{},"  ",[3584,5561,5562],{},"⇒",[3870,5564,5559],{},[897,5566,2083],{},[897,5568,5569],{},"R",[3584,5571,3586],{},[3717,5573,5574],{},"9",[3584,5576,4754],{},[3717,5578,4800],{},[3584,5580,3586],{},[3717,5582,5583],{},"990",[901,5585,5586],{"encoding":903},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[122,5589,5590,5593,5594,5630],{},[37,5591,5592],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[882,5595,5597],{"className":5596},[885],[887,5598,5599],{"xmlns":889},[891,5600,5601,5627],{},[894,5602,5603,5605,5607,5609,5611,5613,5615,5617,5619,5622,5624],{},[3870,5604,5559],{},[3584,5606,5562],{},[3870,5608,5559],{},[897,5610,2083],{},[897,5612,5569],{},[3584,5614,3586],{},[3717,5616,5574],{},[3584,5618,4754],{},[3717,5620,5621],{},"120",[3584,5623,3586],{},[3717,5625,5626],{},"1080",[901,5628,5629],{"encoding":903},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[723,5632,5633,5634,5637,5638,5641,5642,5645,5646,5649,5650,5653,5654,5670,5671,5674],{},"Závěr: snížení ceny bylo na Trhu 1 ",[37,5635,5636],{},"nerozumné",", na Trhu 2 ",[37,5639,5640],{},"rozumné",". Trh 2 je ",[37,5643,5644],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[613,5647,5648],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[613,5651,5652],{},"neelastická"," a vyššího ",[882,5655,5657],{"className":5656},[885],[887,5658,5659],{"xmlns":889},[891,5660,5661,5667],{},[894,5662,5663,5665],{},[897,5664,2083],{},[897,5666,5569],{},[901,5668,5669],{"encoding":903},"TR"," lze naopak dosáhnout ",[613,5672,5673],{},"zvýšením"," ceny.",[197,5676,5678],{"id":5677},"hypotéza-41","Hypotéza 4.1",[2540,5680,5681],{},[723,5682,5683,5684],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[882,5685,5687],{"className":5686},[885],[887,5688,5689],{"xmlns":889},[891,5690,5691,5700],{},[894,5692,5693,5695,5698],{},[3584,5694,3593],{"stretchy":3592},[3717,5696,5697],{},"4.1",[3584,5699,3599],{"stretchy":3592},[901,5701,5702],{"encoding":903},"(4.1)",[723,5704,5705,5706,5709],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[37,5707,5708],{},"procentní změny"," obou faktorů.",[114,5711,5713],{"id":5712},"pojem-elasticity","Pojem elasticity",[723,5715,5716,5717,5719,5720,5723],{},"Obecně ",[37,5718,5473],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[37,5721,5722],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny (viz čl. 1.5.1).",[2540,5725,5726],{},[723,5727,5728,5731,5732,5735],{},[882,5729,5730],{},"!info"," Intuice\nElasticitu lze číst jako ",[37,5733,5734],{},"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.",[114,5737,5739],{"id":5738},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[723,5741,5742,5743,5768],{},"Nechť ",[882,5744,5746],{"className":5745},[885],[887,5747,5748],{"xmlns":889},[891,5749,5750,5765],{},[894,5751,5752,5754,5756,5759,5761,5763],{},[897,5753,4366],{},[3584,5755,3586],{},[897,5757,5758],{},"D",[3584,5760,3593],{"stretchy":3592},[897,5762,2115],{},[3584,5764,3599],{"stretchy":3592},[901,5766,5767],{"encoding":903},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[723,5770,5771],{},[882,5772,5777],{"className":5773,"title":5775,"style":5776},[5774],"katex-error","ParseError: KaTeX parse error: \\tag works only in display equations","color:#cc0000","E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[723,5779,5780,5781,1646,5797,5813,5814,5833],{},"Znaménko minus je korekce: změny ",[882,5782,5784],{"className":5783},[885],[887,5785,5786],{"xmlns":889},[891,5787,5788,5794],{},[894,5789,5790,5792],{},[897,5791,4466],{"mathvariant":3956},[897,5793,4366],{},[901,5795,5796],{"encoding":903},"\\Delta Q",[882,5798,5800],{"className":5799},[885],[887,5801,5802],{"xmlns":889},[891,5803,5804,5810],{},[894,5805,5806,5808],{},[897,5807,4466],{"mathvariant":3956},[897,5809,2115],{},[901,5811,5812],{"encoding":903},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[882,5815,5817],{"className":5816},[885],[887,5818,5819],{"xmlns":889},[891,5820,5821,5830],{},[894,5822,5823],{},[3712,5824,5825,5827],{},[897,5826,2094],{},[897,5828,5829],{},"A",[901,5831,5832],{"encoding":903},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[723,5835,5836],{},[882,5837,5839],{"className":5838,"title":5775,"style":5776},[5774],"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[723,5841,5842],{},"Po dosazení:",[723,5844,5845],{},[882,5846,5848],{"className":5847,"title":5775,"style":5776},[5774],"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[723,5850,5851,5852,5872,5873,5875],{},"Limitním přechodem ",[882,5853,5855],{"className":5854},[885],[887,5856,5857],{"xmlns":889},[891,5858,5859,5869],{},[894,5860,5861,5863,5865,5867],{},[897,5862,4466],{"mathvariant":3956},[897,5864,2115],{},[3584,5866,4700],{},[3717,5868,2169],{},[901,5870,5871],{"encoding":903},"\\Delta P \\to 0"," získáme definici ",[37,5874,5485],{}," (price elasticity of demand):",[723,5877,5878],{},[882,5879,5881],{"className":5880,"title":5775,"style":5776},[5774],"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[723,5883,5884,5885,5908,5909,5932,5933,5957,5958,5979],{},"kde ",[882,5886,5888],{"className":5887},[885],[887,5889,5890],{"xmlns":889},[891,5891,5892,5906],{},[894,5893,5894,5896,5898,5900,5902,5904],{},[897,5895,4366],{},[3584,5897,3586],{},[897,5899,5758],{},[3584,5901,3593],{"stretchy":3592},[897,5903,2115],{},[3584,5905,3599],{"stretchy":3592},[901,5907,5767],{"encoding":903},". Pro pevnou cenu ",[882,5910,5912],{"className":5911},[885],[887,5913,5914],{"xmlns":889},[891,5915,5916,5929],{},[894,5917,5918,5920,5922],{},[897,5919,2115],{},[3584,5921,3586],{},[3712,5923,5924,5926],{},[897,5925,2115],{},[3584,5927,5928],{},"∗",[901,5930,5931],{"encoding":903},"P = P^*"," se ",[882,5934,5936],{"className":5935},[885],[887,5937,5938],{"xmlns":889},[891,5939,5940,5954],{},[894,5941,5942,5944,5946,5952],{},[897,5943,2094],{},[3584,5945,3593],{"stretchy":3592},[3712,5947,5948,5950],{},[897,5949,2115],{},[3584,5951,5928],{},[3584,5953,3599],{"stretchy":3592},[901,5955,5956],{"encoding":903},"E(P^*)"," nazývá ",[613,5959,5960,5961],{},"elasticita poptávky při ceně ",[882,5962,5964],{"className":5963},[885],[887,5965,5966],{"xmlns":889},[891,5967,5968,5976],{},[894,5969,5970],{},[3712,5971,5972,5974],{},[897,5973,2115],{},[3584,5975,5928],{},[901,5977,5978],{"encoding":903},"P^*"," a je to vždy nezáporné číslo.",[2540,5981,5982],{},[723,5983,5984,5987,5988,6006,6007,6035,6036,6065,6066,1342,6084,1342,6102,6120,6121,6136,6137,1750],{},[882,5985,5986],{},"!warning"," Pozor na znaménko\nV (4.5) je ",[37,5989,5990,5991],{},"explicitní ",[882,5992,5994],{"className":5993},[885],[887,5995,5996],{"xmlns":889},[891,5997,5998,6004],{},[894,5999,6000,6002],{},[3584,6001,3810],{},[3717,6003,2177],{},[901,6005,5311],{"encoding":903}," právě proto, že ",[882,6008,6010],{"className":6009},[885],[887,6011,6012],{"xmlns":889},[891,6013,6014,6032],{},[894,6015,6016,6022,6024,6026,6028,6030],{},[3712,6017,6018,6020],{},[897,6019,4366],{},[3584,6021,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,6023,3593],{"stretchy":3592},[897,6025,2115],{},[3584,6027,3599],{"stretchy":3592},[3584,6029,5024],{},[3717,6031,2169],{},[901,6033,6034],{"encoding":903},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[882,6037,6039],{"className":6038},[885],[887,6040,6041],{"xmlns":889},[891,6042,6043,6062],{},[894,6044,6045,6047,6049,6055,6057,6060],{},[897,6046,2094],{},[3584,6048,3593],{"stretchy":3592},[3712,6050,6051,6053],{},[897,6052,2115],{},[3584,6054,5928],{},[3584,6056,3599],{"stretchy":3592},[3584,6058,6059],{},"≥",[3717,6061,2169],{},[901,6063,6064],{"encoding":903},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[882,6067,6069],{"className":6068},[885],[887,6070,6071],{"xmlns":889},[891,6072,6073,6081],{},[894,6074,6075,6077,6079],{},[897,6076,2094],{},[3584,6078,4985],{},[3717,6080,2177],{},[901,6082,6083],{"encoding":903},"E > 1",[882,6085,6087],{"className":6086},[885],[887,6088,6089],{"xmlns":889},[891,6090,6091,6099],{},[894,6092,6093,6095,6097],{},[897,6094,2094],{},[3584,6096,5024],{},[3717,6098,2177],{},[901,6100,6101],{"encoding":903},"E \u003C 1",[882,6103,6105],{"className":6104},[885],[887,6106,6107],{"xmlns":889},[891,6108,6109,6117],{},[894,6110,6111,6113,6115],{},[897,6112,2094],{},[3584,6114,3586],{},[3717,6116,2177],{},[901,6118,6119],{"encoding":903},"E = 1",". V některých starších pramenech se ",[882,6122,6124],{"className":6123},[885],[887,6125,6126],{"xmlns":889},[891,6127,6128,6134],{},[894,6129,6130,6132],{},[3584,6131,3810],{},[3717,6133,2177],{},[901,6135,5311],{"encoding":903}," 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 ",[37,6138,6139],{},"absolutní hodnotou",[2540,6141,6142,6162],{},[723,6143,6144,6147,6148,6161],{},[882,6145,6146],{},"!tip"," Postup: jak spočítat ",[882,6149,6151],{"className":6150},[885],[887,6152,6153],{"xmlns":889},[891,6154,6155,6159],{},[894,6156,6157],{},[897,6158,2094],{},[901,6160,2094],{"encoding":903}," v bodě",[151,6163,6164,6216,6256,6309,6374],{},[122,6165,6166,6167,6190,6191,6215],{},"Zapište ",[882,6168,6170],{"className":6169},[885],[887,6171,6172],{"xmlns":889},[891,6173,6174,6188],{},[894,6175,6176,6178,6180,6182,6184,6186],{},[897,6177,4366],{},[3584,6179,3586],{},[897,6181,5758],{},[3584,6183,3593],{"stretchy":3592},[897,6185,2115],{},[3584,6187,3599],{"stretchy":3592},[901,6189,5767],{"encoding":903},". Pokud je poptávka zadaná jako ",[882,6192,6194],{"className":6193},[885],[887,6195,6196],{"xmlns":889},[891,6197,6198,6212],{},[894,6199,6200,6202,6204,6206,6208,6210],{},[897,6201,2115],{},[3584,6203,3586],{},[897,6205,5758],{},[3584,6207,3593],{"stretchy":3592},[897,6209,4366],{},[3584,6211,3599],{"stretchy":3592},[901,6213,6214],{"encoding":903},"P = D(Q)",", použijte vztah (4.9).",[122,6217,6218,6219,1750],{},"Spočítejte derivaci ",[882,6220,6222],{"className":6221},[885],[887,6223,6224],{"xmlns":889},[891,6225,6226,6253],{},[894,6227,6228,6234,6236,6238,6240,6242,6244,6246,6249,6251],{},[3712,6229,6230,6232],{},[897,6231,4366],{},[3584,6233,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,6235,3593],{"stretchy":3592},[897,6237,2115],{},[3584,6239,3599],{"stretchy":3592},[3584,6241,3586],{},[897,6243,3780],{"mathvariant":3956},[897,6245,4366],{},[897,6247,6248],{"mathvariant":3956},"\u002F",[897,6250,3780],{"mathvariant":3956},[897,6252,2115],{},[901,6254,6255],{"encoding":903},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[122,6257,6258,6259,6276,6277,1750],{},"Dosaďte zadanou cenu ",[882,6260,6262],{"className":6261},[885],[887,6263,6264],{"xmlns":889},[891,6265,6266,6274],{},[894,6267,6268],{},[3712,6269,6270,6272],{},[897,6271,2115],{},[3584,6273,5928],{},[901,6275,5978],{"encoding":903}," a dopočítejte odpovídající ",[882,6278,6280],{"className":6279},[885],[887,6281,6282],{"xmlns":889},[891,6283,6284,6306],{},[894,6285,6286,6292,6294,6296,6298,6304],{},[3712,6287,6288,6290],{},[897,6289,4366],{},[3584,6291,5928],{},[3584,6293,3586],{},[897,6295,5758],{},[3584,6297,3593],{"stretchy":3592},[3712,6299,6300,6302],{},[897,6301,2115],{},[3584,6303,5928],{},[3584,6305,3599],{"stretchy":3592},[901,6307,6308],{"encoding":903},"Q^* = D(P^*)",[122,6310,6311,6312,1750],{},"Dosaďte do (4.5): ",[882,6313,6315],{"className":6314},[885],[887,6316,6317],{"xmlns":889},[891,6318,6319,6371],{},[894,6320,6321,6323,6325,6331,6333,6335,6337,6353,6355,6361,6363,6369],{},[897,6322,2094],{},[3584,6324,3593],{"stretchy":3592},[3712,6326,6327,6329],{},[897,6328,2115],{},[3584,6330,5928],{},[3584,6332,3599],{"stretchy":3592},[3584,6334,3586],{},[3584,6336,3810],{},[3907,6338,6339],{"scriptlevel":2169,"displaystyle":3867},[3910,6340,6341,6347],{},[3712,6342,6343,6345],{},[897,6344,2115],{},[3584,6346,5928],{},[3712,6348,6349,6351],{},[897,6350,4366],{},[3584,6352,5928],{},[3870,6354,4564],{},[3712,6356,6357,6359],{},[897,6358,4366],{},[3584,6360,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,6362,3593],{"stretchy":3592},[3712,6364,6365,6367],{},[897,6366,2115],{},[3584,6368,5928],{},[3584,6370,3599],{"stretchy":3592},[901,6372,6373],{"encoding":903},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[122,6375,6376,6377,6394,6395,6412,6413,6430],{},"Klasifikujte: ",[882,6378,6380],{"className":6379},[885],[887,6381,6382],{"xmlns":889},[891,6383,6384,6392],{},[894,6385,6386,6388,6390],{},[897,6387,2094],{},[3584,6389,4985],{},[3717,6391,2177],{},[901,6393,6083],{"encoding":903}," elastická, ",[882,6396,6398],{"className":6397},[885],[887,6399,6400],{"xmlns":889},[891,6401,6402,6410],{},[894,6403,6404,6406,6408],{},[897,6405,2094],{},[3584,6407,3586],{},[3717,6409,2177],{},[901,6411,6119],{"encoding":903}," jednotková, ",[882,6414,6416],{"className":6415},[885],[887,6417,6418],{"xmlns":889},[891,6419,6420,6428],{},[894,6421,6422,6424,6426],{},[897,6423,2094],{},[3584,6425,5024],{},[3717,6427,2177],{},[901,6429,6101],{"encoding":903}," neelastická.",[197,6432,6434],{"id":6433},"interpretace-46","Interpretace (4.6)",[2540,6436,6437],{},[723,6438,6439,6440,6463,6464,6477,6478,6495,6496],{},"Číslo ",[882,6441,6443],{"className":6442},[885],[887,6444,6445],{"xmlns":889},[891,6446,6447,6461],{},[894,6448,6449,6451,6453,6459],{},[897,6450,2094],{},[3584,6452,3593],{"stretchy":3592},[3712,6454,6455,6457],{},[897,6456,2115],{},[3584,6458,5928],{},[3584,6460,3599],{"stretchy":3592},[901,6462,5956],{"encoding":903}," udává, o kolik % se přibližně změní poptávané množství ",[882,6465,6467],{"className":6466},[885],[887,6468,6469],{"xmlns":889},[891,6470,6471,6475],{},[894,6472,6473],{},[897,6474,4366],{},[901,6476,4366],{"encoding":903},", jestliže se cena ",[882,6479,6481],{"className":6480},[885],[887,6482,6483],{"xmlns":889},[891,6484,6485,6493],{},[894,6486,6487],{},[3712,6488,6489,6491],{},[897,6490,2115],{},[3584,6492,5928],{},[901,6494,5978],{"encoding":903}," změní o 1 %. ",[882,6497,6499],{"className":6498},[885],[887,6500,6501],{"xmlns":889},[891,6502,6503,6512],{},[894,6504,6505,6507,6510],{},[3584,6506,3593],{"stretchy":3592},[3717,6508,6509],{},"4.6",[3584,6511,3599],{"stretchy":3592},[901,6513,6514],{"encoding":903},"(4.6)",[723,6516,6517,6520],{},[37,6518,6519],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[197,6522,6524],{"id":6523},"příklad-41","Příklad 4.1",[723,6526,6527,6528,6562,6563,1342,6589,4282],{},"Poptávka ",[882,6529,6531],{"className":6530},[885],[887,6532,6533],{"xmlns":889},[891,6534,6535,6559],{},[894,6536,6537,6539,6541,6543,6545,6547,6549,6551,6553,6555,6557],{},[897,6538,2115],{},[3584,6540,3586],{},[897,6542,5758],{},[3584,6544,3593],{"stretchy":3592},[897,6546,4366],{},[3584,6548,3599],{"stretchy":3592},[3584,6550,3586],{},[3717,6552,4697],{},[3584,6554,3810],{},[3717,6556,2185],{},[897,6558,4366],{},[901,6560,6561],{"encoding":903},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[882,6564,6566],{"className":6565},[885],[887,6567,6568],{"xmlns":889},[891,6569,6570,6586],{},[894,6571,6572,6574,6576,6579,6581,6584],{},[897,6573,4366],{},[3584,6575,3586],{},[3717,6577,6578],{},"25",[3584,6580,3810],{},[3717,6582,6583],{},"0,5",[897,6585,2115],{},[901,6587,6588],{"encoding":903},"Q = 25 - 0{,}5P",[882,6590,6592],{"className":6591},[885],[887,6593,6594],{"xmlns":889},[891,6595,6596,6620],{},[894,6597,6598,6614,6616,6618],{},[3907,6599,6600],{"scriptlevel":2169,"displaystyle":3867},[3910,6601,6602,6608],{},[894,6603,6604,6606],{},[897,6605,3780],{"mathvariant":3956},[897,6607,4366],{},[894,6609,6610,6612],{},[897,6611,3780],{"mathvariant":3956},[897,6613,2115],{},[3584,6615,3586],{},[3584,6617,3810],{},[3717,6619,6583],{},[901,6621,6622],{"encoding":903},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[723,6624,6625],{},[882,6626,6628],{"className":6627},[885],[887,6629,6630],{"xmlns":889},[891,6631,6632,6686],{},[894,6633,6634,6636,6638,6640,6654,6656,6658,6660,6662,6664,6666,6684],{},[897,6635,2094],{},[3584,6637,3586],{},[3584,6639,3810],{},[3910,6641,6642,6644],{},[897,6643,2115],{},[894,6645,6646,6648,6650,6652],{},[3717,6647,6578],{},[3584,6649,3810],{},[3717,6651,6583],{},[897,6653,2115],{},[3584,6655,4754],{},[3584,6657,3593],{"stretchy":3592},[3584,6659,3810],{},[3717,6661,6583],{},[3584,6663,3599],{"stretchy":3592},[3584,6665,3586],{},[3910,6667,6668,6674],{},[894,6669,6670,6672],{},[3717,6671,6583],{},[897,6673,2115],{},[894,6675,6676,6678,6680,6682],{},[3717,6677,6578],{},[3584,6679,3810],{},[3717,6681,6583],{},[897,6683,2115],{},[897,6685,1750],{"mathvariant":3956},[901,6687,6688],{"encoding":903},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[723,6690,6691,6692,1342,6716,1342,6746,1342,6770,6795,6796,6819,6820,4263,6838,5494],{},"Potom ",[882,6693,6695],{"className":6694},[885],[887,6696,6697],{"xmlns":889},[891,6698,6699,6713],{},[894,6700,6701,6703,6705,6707,6709,6711],{},[897,6702,2094],{},[3584,6704,3593],{"stretchy":3592},[3717,6706,2169],{},[3584,6708,3599],{"stretchy":3592},[3584,6710,3586],{},[3717,6712,2169],{},[901,6714,6715],{"encoding":903},"E(0)=0",[882,6717,6719],{"className":6718},[885],[887,6720,6721],{"xmlns":889},[891,6722,6723,6743],{},[894,6724,6725,6727,6729,6731,6733,6735],{},[897,6726,2094],{},[3584,6728,3593],{"stretchy":3592},[3717,6730,4440],{},[3584,6732,3599],{"stretchy":3592},[3584,6734,3586],{},[3907,6736,6737],{"scriptlevel":2169,"displaystyle":3592},[3910,6738,6739,6741],{},[3717,6740,2177],{},[3717,6742,2201],{},[901,6744,6745],{"encoding":903},"E(10)=\\tfrac{1}{4}",[882,6747,6749],{"className":6748},[885],[887,6750,6751],{"xmlns":889},[891,6752,6753,6767],{},[894,6754,6755,6757,6759,6761,6763,6765],{},[897,6756,2094],{},[3584,6758,3593],{"stretchy":3592},[3717,6760,6578],{},[3584,6762,3599],{"stretchy":3592},[3584,6764,3586],{},[3717,6766,2177],{},[901,6768,6769],{"encoding":903},"E(25)=1",[882,6771,6773],{"className":6772},[885],[887,6774,6775],{"xmlns":889},[891,6776,6777,6792],{},[894,6778,6779,6781,6783,6786,6788,6790],{},[897,6780,2094],{},[3584,6782,3593],{"stretchy":3592},[3717,6784,6785],{},"40",[3584,6787,3599],{"stretchy":3592},[3584,6789,3586],{},[3717,6791,2201],{},[901,6793,6794],{"encoding":903},"E(40)=4",". Např. ",[882,6797,6799],{"className":6798},[885],[887,6800,6801],{"xmlns":889},[891,6802,6803,6817],{},[894,6804,6805,6807,6809,6811,6813,6815],{},[897,6806,2094],{},[3584,6808,3593],{"stretchy":3592},[3717,6810,6785],{},[3584,6812,3599],{"stretchy":3592},[3584,6814,3586],{},[3717,6816,2201],{},[901,6818,6794],{"encoding":903}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[882,6821,6823],{"className":6822},[885],[887,6824,6825],{"xmlns":889},[891,6826,6827,6835],{},[894,6828,6829,6831,6833],{},[897,6830,4366],{},[3584,6832,3586],{},[3717,6834,2209],{},[901,6836,6837],{"encoding":903},"Q=5",[882,6839,6841],{"className":6840},[885],[887,6842,6843],{"xmlns":889},[891,6844,6845,6854],{},[894,6846,6847,6849,6851],{},[897,6848,4366],{},[3584,6850,3586],{},[3717,6852,6853],{},"4,8",[901,6855,6856],{"encoding":903},"Q=4{,}8",[197,6858,6860],{"id":6859},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[119,6862,6863,6919],{},[122,6864,6865,6868,6869,6886,6887,1750],{},[37,6866,6867],{},"Oblouková"," (průměrná) elasticita: výraz ",[882,6870,6872],{"className":6871},[885],[887,6873,6874],{"xmlns":889},[891,6875,6876,6884],{},[894,6877,6878],{},[3712,6879,6880,6882],{},[897,6881,2094],{},[897,6883,5829],{},[901,6885,5832],{"encoding":903}," ze (4.4) vztažený k intervalu ",[882,6888,6890],{"className":6889},[885],[887,6891,6892],{"xmlns":889},[891,6893,6894,6916],{},[894,6895,6896,6899,6901,6903,6905,6907,6909,6911,6913],{},[3584,6897,6898],{"stretchy":3592},"⟨",[897,6900,2115],{},[3584,6902,3868],{"separator":3867},[3870,6904,4564],{},[897,6906,2115],{},[3584,6908,3683],{},[897,6910,4466],{"mathvariant":3956},[897,6912,2115],{},[3584,6914,6915],{"stretchy":3592},"⟩",[901,6917,6918],{"encoding":903},"\\langle P,\\, P+\\Delta P\\rangle",[122,6920,6921,6924,6925,6938],{},[37,6922,6923],{},"Bodová"," (okamžitá) elasticita: ",[882,6926,6928],{"className":6927},[885],[887,6929,6930],{"xmlns":889},[891,6931,6932,6936],{},[894,6933,6934],{},[897,6935,2094],{},[901,6937,2094],{"encoding":903}," dle (4.5) — výchozí pojem dále v textu.",[197,6940,6942,6943,6956,6957],{"id":6941},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[882,6944,6946],{"className":6945},[885],[887,6947,6948],{"xmlns":889},[891,6949,6950,6954],{},[894,6951,6952],{},[897,6953,2115],{},[901,6955,2115],{"encoding":903}," jako funkce ",[882,6958,6960],{"className":6959},[885],[887,6961,6962],{"xmlns":889},[891,6963,6964,6968],{},[894,6965,6966],{},[897,6967,4366],{},[901,6969,4366],{"encoding":903},[723,6971,6972,6973,6996],{},"Pokud je poptávka zadaná ve tvaru ",[882,6974,6976],{"className":6975},[885],[887,6977,6978],{"xmlns":889},[891,6979,6980,6994],{},[894,6981,6982,6984,6986,6988,6990,6992],{},[897,6983,2115],{},[3584,6985,3586],{},[897,6987,5758],{},[3584,6989,3593],{"stretchy":3592},[897,6991,4366],{},[3584,6993,3599],{"stretchy":3592},[901,6995,6214],{"encoding":903},", využijeme vztah pro derivaci inverzní funkce",[723,6998,6999],{},[882,7000,7002],{"className":7001,"title":5775,"style":5776},[5774],"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[723,7004,7005,2962,7008,7034],{},[37,7006,7007],{},"Příklad 4.3.",[882,7009,7011],{"className":7010},[885],[887,7012,7013],{"xmlns":889},[891,7014,7015,7031],{},[894,7016,7017,7019,7021,7023,7025],{},[897,7018,2115],{},[3584,7020,3586],{},[3717,7022,4667],{},[3584,7024,3810],{},[3712,7026,7027,7029],{},[897,7028,4366],{},[3717,7030,2185],{},[901,7032,7033],{"encoding":903},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[723,7036,7037],{},[882,7038,7040],{"className":7039},[885],[887,7041,7042],{"xmlns":889},[891,7043,7044,7110],{},[894,7045,7046,7048,7050,7052,7068,7070,7082,7084,7108],{},[897,7047,2094],{},[3584,7049,3586],{},[3584,7051,3810],{},[3910,7053,7054,7066],{},[894,7055,7056,7058,7060],{},[3717,7057,4667],{},[3584,7059,3810],{},[3712,7061,7062,7064],{},[897,7063,4366],{},[3717,7065,2185],{},[897,7067,4366],{},[3584,7069,4754],{},[3910,7071,7072,7074],{},[3717,7073,2177],{},[894,7075,7076,7078,7080],{},[3584,7077,3810],{},[3717,7079,2185],{},[897,7081,4366],{},[3584,7083,3586],{},[3910,7085,7086,7098],{},[894,7087,7088,7090,7092],{},[3717,7089,4667],{},[3584,7091,3810],{},[3712,7093,7094,7096],{},[897,7095,4366],{},[3717,7097,2185],{},[894,7099,7100,7102],{},[3717,7101,2185],{},[3712,7103,7104,7106],{},[897,7105,4366],{},[3717,7107,2185],{},[897,7109,1750],{"mathvariant":3956},[901,7111,7112],{"encoding":903},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[723,7114,7115,7116,7143,7144,7163,7164,1750],{},"Z rovnice ",[882,7117,7119],{"className":7118},[885],[887,7120,7121],{"xmlns":889},[891,7122,7123,7140],{},[894,7124,7125,7127,7129,7135,7137],{},[3717,7126,4667],{},[3584,7128,3810],{},[3712,7130,7131,7133],{},[897,7132,4366],{},[3717,7134,2185],{},[3584,7136,3586],{},[3717,7138,7139],{},"36",[901,7141,7142],{"encoding":903},"100 - Q^2 = 36"," plyne ",[882,7145,7147],{"className":7146},[885],[887,7148,7149],{"xmlns":889},[891,7150,7151,7160],{},[894,7152,7153,7155,7157],{},[897,7154,4366],{},[3584,7156,3586],{},[3717,7158,7159],{},"8",[901,7161,7162],{"encoding":903},"Q = 8",", tedy ",[882,7165,7167],{"className":7166},[885],[887,7168,7169],{"xmlns":889},[891,7170,7171,7197],{},[894,7172,7173,7175,7177,7179,7181,7183,7192,7194],{},[897,7174,2094],{},[3584,7176,3593],{"stretchy":3592},[3717,7178,7159],{},[3584,7180,3599],{"stretchy":3592},[3584,7182,3586],{},[3907,7184,7185],{"scriptlevel":2169,"displaystyle":3592},[3910,7186,7187,7189],{},[3717,7188,7139],{},[3717,7190,7191],{},"128",[3584,7193,3586],{},[3717,7195,7196],{},"0,281",[901,7198,7199],{"encoding":903},"E(8) = \\tfrac{36}{128} = 0{,}281",[197,7201,7203],{"id":7202},"přibližné-změny","Přibližné změny",[723,7205,7206,7207,7243,7244,7266],{},"Diferenciál ",[882,7208,7210],{"className":7209},[885],[887,7211,7212],{"xmlns":889},[891,7213,7214,7240],{},[894,7215,7216,7218,7220,7222,7228,7230,7232,7234,7236,7238],{},[897,7217,3780],{"mathvariant":3956},[897,7219,4366],{},[3584,7221,3586],{},[3712,7223,7224,7226],{},[897,7225,4366],{},[3584,7227,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,7229,3593],{"stretchy":3592},[897,7231,2115],{},[3584,7233,3599],{"stretchy":3592},[3870,7235,4564],{},[897,7237,3780],{"mathvariant":3956},[897,7239,2115],{},[901,7241,7242],{"encoding":903},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[882,7245,7247],{"className":7246},[885],[887,7248,7249],{"xmlns":889},[891,7250,7251,7263],{},[894,7252,7253,7255,7257,7259,7261],{},[897,7254,3780],{"mathvariant":3956},[897,7256,2115],{},[3584,7258,3586],{},[897,7260,4466],{"mathvariant":3956},[897,7262,2115],{},[901,7264,7265],{"encoding":903},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[723,7268,7269],{},[882,7270,7272],{"className":7271,"title":5775,"style":5776},[5774],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[723,7274,7275],{},"Po přechodu na procentní změny (vztah (4.3)):",[723,7277,7278],{},[882,7279,7281],{"className":7280,"title":5775,"style":5776},[5774],"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[723,7283,7284,2962,7287,7322,7323,7342,7343,7377,7378,7395],{},[37,7285,7286],{},"Příklad 4.5.",[882,7288,7290],{"className":7289},[885],[887,7291,7292],{"xmlns":889},[891,7293,7294,7319],{},[894,7295,7296,7298,7300,7302,7308,7310,7312,7314,7316],{},[897,7297,2115],{},[3584,7299,3586],{},[3584,7301,3810],{},[3712,7303,7304,7306],{},[897,7305,4366],{},[3717,7307,2185],{},[3584,7309,3810],{},[3717,7311,2201],{},[897,7313,4366],{},[3584,7315,3683],{},[3717,7317,7318],{},"96",[901,7320,7321],{"encoding":903},"P = -Q^2 - 4Q + 96",", cena ",[882,7324,7326],{"className":7325},[885],[887,7327,7328],{"xmlns":889},[891,7329,7330,7339],{},[894,7331,7332,7334,7336],{},[897,7333,2115],{},[3584,7335,3586],{},[3717,7337,7338],{},"51",[901,7340,7341],{"encoding":903},"P=51",". Z rovnice ",[882,7344,7346],{"className":7345},[885],[887,7347,7348],{"xmlns":889},[891,7349,7350,7374],{},[894,7351,7352,7354,7356,7358,7364,7366,7368,7370,7372],{},[3717,7353,7338],{},[3584,7355,3586],{},[3584,7357,3810],{},[3712,7359,7360,7362],{},[897,7361,4366],{},[3717,7363,2185],{},[3584,7365,3810],{},[3717,7367,2201],{},[897,7369,4366],{},[3584,7371,3683],{},[3717,7373,7318],{},[901,7375,7376],{"encoding":903},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[882,7379,7381],{"className":7380},[885],[887,7382,7383],{"xmlns":889},[891,7384,7385,7393],{},[894,7386,7387,7389,7391],{},[897,7388,4366],{},[3584,7390,3586],{},[3717,7392,2209],{},[901,7394,6837],{"encoding":903},". Elasticita:",[723,7397,7398],{},[882,7399,7401],{"className":7400},[885],[887,7402,7403],{"xmlns":889},[891,7404,7405,7478],{},[894,7406,7407,7409,7411,7449,7451,7455,7457,7459,7461,7463,7465,7472,7475],{},[897,7408,2094],{},[3584,7410,3586],{},[3910,7412,7413,7433],{},[894,7414,7415,7417,7423,7425,7427,7429,7431],{},[3584,7416,3810],{},[3712,7418,7419,7421],{},[897,7420,4366],{},[3717,7422,2185],{},[3584,7424,3810],{},[3717,7426,2201],{},[897,7428,4366],{},[3584,7430,3683],{},[3717,7432,7318],{},[894,7434,7435,7437,7439,7441,7443,7445,7447],{},[897,7436,4366],{},[3584,7438,3593],{"stretchy":3592},[3717,7440,2185],{},[897,7442,4366],{},[3584,7444,3683],{},[3717,7446,2201],{},[3584,7448,3599],{"stretchy":3592},[3584,7450,3868],{"separator":3867},[7452,7453],"mspace",{"width":7454},"2em",[897,7456,2094],{},[3584,7458,3593],{"stretchy":3592},[3717,7460,2209],{},[3584,7462,3599],{"stretchy":3592},[3584,7464,3586],{},[3910,7466,7467,7469],{},[3717,7468,7338],{},[3717,7470,7471],{},"70",[3584,7473,7474],{},"≐",[3717,7476,7477],{},"0,728.",[901,7479,7480],{"encoding":903},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[723,7482,7483,7484,1750],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[882,7485,7487],{"className":7486},[885],[887,7488,7489],{"xmlns":889},[891,7490,7491,7522],{},[894,7492,7493,7495,7497,7500,7502,7504,7507,7509,7511,7513,7515,7518,7520],{},[897,7494,4466],{"mathvariant":3956},[897,7496,4366],{},[897,7498,7499],{"mathvariant":3956},"%",[3584,7501,4308],{},[3584,7503,3810],{},[3717,7505,7506],{},"0,728",[3584,7508,4754],{},[3717,7510,2185],{},[3584,7512,3586],{},[3584,7514,3810],{},[3717,7516,7517],{},"1,456",[3870,7519,4564],{},[897,7521,7499],{"mathvariant":3956},[901,7523,7524],{"encoding":903},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[114,7526,7528],{"id":7527},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[723,7530,7531,7532,7555,7556,4282],{},"V závislosti na hodnotě ",[882,7533,7535],{"className":7534},[885],[887,7536,7537],{"xmlns":889},[891,7538,7539,7553],{},[894,7540,7541,7543,7545,7551],{},[897,7542,2094],{},[3584,7544,3593],{"stretchy":3592},[3712,7546,7547,7549],{},[897,7548,2115],{},[3584,7550,5928],{},[3584,7552,3599],{"stretchy":3592},[901,7554,5956],{"encoding":903}," mluvíme o poptávce podle následující tabulky ",[882,7557,7559],{"className":7558},[885],[887,7560,7561],{"xmlns":889},[891,7562,7563,7572],{},[894,7564,7565,7567,7570],{},[3584,7566,3593],{"stretchy":3592},[3717,7568,7569],{},"4.7",[3584,7571,3599],{"stretchy":3592},[901,7573,7574],{"encoding":903},"(4.7)",[723,7576,7577],{},[1633,7578],{"alt":7579,"className":7580,"src":7581},"imek-typy-elasticity-5panelu",[209,1637],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[15,7583,7584,7623],{},[18,7585,7586],{},[21,7587,7588,7614,7617,7620],{},[24,7589,7590,7591],{},"Hodnota ",[882,7592,7594],{"className":7593},[885],[887,7595,7596],{"xmlns":889},[891,7597,7598,7612],{},[894,7599,7600,7602,7604,7610],{},[897,7601,2094],{},[3584,7603,3593],{"stretchy":3592},[3712,7605,7606,7608],{},[897,7607,2115],{},[3584,7609,5928],{},[3584,7611,3599],{"stretchy":3592},[901,7613,5956],{"encoding":903},[24,7615,7616],{},"Typ poptávky",[24,7618,7619],{},"Termín",[24,7621,7622],{},"Význam",[29,7624,7625,7658,7720,7795,7852],{},[21,7626,7627,7647,7652,7655],{},[34,7628,7629],{},[882,7630,7632],{"className":7631},[885],[887,7633,7634],{"xmlns":889},[891,7635,7636,7644],{},[894,7637,7638,7640,7642],{},[897,7639,2094],{},[3584,7641,3586],{},[3717,7643,2169],{},[901,7645,7646],{"encoding":903},"E = 0",[34,7648,7649],{},[37,7650,7651],{},"dokonale neelastická",[34,7653,7654],{},"perfectly inelastic",[34,7656,7657],{},"množství se nemění bez ohledu na cenu",[21,7659,7660,7684,7688,7691],{},[34,7661,7662],{},[882,7663,7665],{"className":7664},[885],[887,7666,7667],{"xmlns":889},[891,7668,7669,7681],{},[894,7670,7671,7673,7675,7677,7679],{},[3717,7672,2169],{},[3584,7674,5024],{},[897,7676,2094],{},[3584,7678,5024],{},[3717,7680,2177],{},[901,7682,7683],{"encoding":903},"0 \u003C E \u003C 1",[34,7685,7686],{},[37,7687,5652],{},[34,7689,7690],{},"inelastic",[34,7692,7693,7706,7707],{},[882,7694,7696],{"className":7695},[885],[887,7697,7698],{"xmlns":889},[891,7699,7700,7704],{},[894,7701,7702],{},[897,7703,4366],{},[901,7705,4366],{"encoding":903}," se mění pomaleji než ",[882,7708,7710],{"className":7709},[885],[887,7711,7712],{"xmlns":889},[891,7713,7714,7718],{},[894,7715,7716],{},[897,7717,2115],{},[901,7719,2115],{"encoding":903},[21,7721,7722,7741,7746,7749],{},[34,7723,7724],{},[882,7725,7727],{"className":7726},[885],[887,7728,7729],{"xmlns":889},[891,7730,7731,7739],{},[894,7732,7733,7735,7737],{},[897,7734,2094],{},[3584,7736,3586],{},[3717,7738,2177],{},[901,7740,6119],{"encoding":903},[34,7742,7743],{},[37,7744,7745],{},"jednotkově elastická",[34,7747,7748],{},"unit elastic",[34,7750,7751,7764,7765,7778,7779,7794],{},[882,7752,7754],{"className":7753},[885],[887,7755,7756],{"xmlns":889},[891,7757,7758,7762],{},[894,7759,7760],{},[897,7761,4366],{},[901,7763,4366],{"encoding":903}," i ",[882,7766,7768],{"className":7767},[885],[887,7769,7770],{"xmlns":889},[891,7771,7772,7776],{},[894,7773,7774],{},[897,7775,2115],{},[901,7777,2115],{"encoding":903}," se mění stejně rychle; ",[882,7780,7782],{"className":7781},[885],[887,7783,7784],{"xmlns":889},[891,7785,7786,7792],{},[894,7787,7788,7790],{},[897,7789,2083],{},[897,7791,5569],{},[901,7793,5669],{"encoding":903}," má maximum",[21,7796,7797,7816,7820,7823],{},[34,7798,7799],{},[882,7800,7802],{"className":7801},[885],[887,7803,7804],{"xmlns":889},[891,7805,7806,7814],{},[894,7807,7808,7810,7812],{},[897,7809,2094],{},[3584,7811,4985],{},[3717,7813,2177],{},[901,7815,6083],{"encoding":903},[34,7817,7818],{},[37,7819,5648],{},[34,7821,7822],{},"elastic",[34,7824,7825,7838,7839],{},[882,7826,7828],{"className":7827},[885],[887,7829,7830],{"xmlns":889},[891,7831,7832,7836],{},[894,7833,7834],{},[897,7835,4366],{},[901,7837,4366],{"encoding":903}," se mění rychleji než ",[882,7840,7842],{"className":7841},[885],[887,7843,7844],{"xmlns":889},[891,7845,7846,7850],{},[894,7847,7848],{},[897,7849,2115],{},[901,7851,2115],{"encoding":903},[21,7853,7854,7875,7880,7883],{},[34,7855,7856],{},[882,7857,7859],{"className":7858},[885],[887,7860,7861],{"xmlns":889},[891,7862,7863,7872],{},[894,7864,7865,7867,7869],{},[897,7866,2094],{},[3584,7868,4700],{},[897,7870,7871],{"mathvariant":3956},"∞",[901,7873,7874],{"encoding":903},"E \\to \\infty",[34,7876,7877],{},[37,7878,7879],{},"dokonale elastická",[34,7881,7882],{},"perfectly elastic",[34,7884,7885,7886],{},"sebemenší změna ceny úplně mění ",[882,7887,7889],{"className":7888},[885],[887,7890,7891],{"xmlns":889},[891,7892,7893,7897],{},[894,7894,7895],{},[897,7896,4366],{},[901,7898,4366],{"encoding":903},[723,7900,7901],{},[37,7902,7903],{},"Pravidlo růstu elasticity s cenou:",[2540,7905,7906],{},[723,7907,7908,7909],{},"S rostoucí cenou elasticita poptávky roste. ",[882,7910,7912],{"className":7911},[885],[887,7913,7914],{"xmlns":889},[891,7915,7916,7925],{},[894,7917,7918,7920,7923],{},[3584,7919,3593],{"stretchy":3592},[3717,7921,7922],{},"4.8",[3584,7924,3599],{"stretchy":3592},[901,7926,7927],{"encoding":903},"(4.8)",[723,7929,7930,7931,7934,7935,7938,7939,7956],{},"Z toho plyne, že při ",[613,7932,7933],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[613,7936,7937],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[882,7940,7942],{"className":7941},[885],[887,7943,7944],{"xmlns":889},[891,7945,7946,7954],{},[894,7947,7948],{},[3712,7949,7950,7952],{},[897,7951,2115],{},[3584,7953,5928],{},[901,7955,5978],{"encoding":903},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[2540,7958,7959,7964],{},[723,7960,7961,7963],{},[882,7962,6146],{}," Postup: jak klasifikovat poptávku",[151,7965,7966,7993,7996],{},[122,7967,7968,7969,7992],{},"Spočítejte ",[882,7970,7972],{"className":7971},[885],[887,7973,7974],{"xmlns":889},[891,7975,7976,7990],{},[894,7977,7978,7980,7982,7988],{},[897,7979,2094],{},[3584,7981,3593],{"stretchy":3592},[3712,7983,7984,7986],{},[897,7985,2115],{},[3584,7987,5928],{},[3584,7989,3599],{"stretchy":3592},[901,7991,5956],{"encoding":903}," dle (4.5).",[122,7994,7995],{},"Porovnejte s jedničkou (viz tabulka výše).",[122,7997,7998,7999,8023],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[882,8000,8002],{"className":8001},[885],[887,8003,8004],{"xmlns":889},[891,8005,8006,8020],{},[894,8007,8008,8010,8012,8014,8016,8018],{},[897,8009,2094],{},[3584,8011,3593],{"stretchy":3592},[897,8013,2115],{},[3584,8015,3599],{"stretchy":3592},[3584,8017,3586],{},[3717,8019,2177],{},[901,8021,8022],{"encoding":903},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[723,8025,8026,8029,8030,8047,8048,8066,8067,8094,8095,1750],{},[37,8027,8028],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[882,8031,8033],{"className":8032},[885],[887,8034,8035],{"xmlns":889},[891,8036,8037,8045],{},[894,8038,8039,8041,8043],{},[897,8040,2094],{},[3584,8042,3586],{},[3717,8044,2177],{},[901,8046,6119],{"encoding":903}," pro ",[882,8049,8051],{"className":8050},[885],[887,8052,8053],{"xmlns":889},[891,8054,8055,8063],{},[894,8056,8057,8059,8061],{},[897,8058,2115],{},[3584,8060,3586],{},[3717,8062,6578],{},[901,8064,8065],{"encoding":903},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[882,8068,8070],{"className":8069},[885],[887,8071,8072],{"xmlns":889},[891,8073,8074,8091],{},[894,8075,8076,8078,8081,8083,8085,8087,8089],{},[897,8077,2115],{},[3584,8079,8080],{},"∈",[3584,8082,6898],{"stretchy":3592},[3717,8084,2169],{},[3584,8086,3868],{"separator":3867},[3717,8088,6578],{},[3584,8090,3599],{"stretchy":3592},[901,8092,8093],{"encoding":903},"P \\in \\langle 0, 25)"," a elastická pro ",[882,8096,8098],{"className":8097},[885],[887,8099,8100],{"xmlns":889},[891,8101,8102,8118],{},[894,8103,8104,8106,8108,8110,8112,8114,8116],{},[897,8105,2115],{},[3584,8107,8080],{},[3584,8109,3593],{"stretchy":3592},[3717,8111,6578],{},[3584,8113,3868],{"separator":3867},[3717,8115,4697],{},[3584,8117,6915],{"stretchy":3592},[901,8119,8120],{"encoding":903},"P \\in (25, 50\\rangle",[114,8122,8124],{"id":8123},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[723,8126,8127],{},[1633,8128],{"alt":8129,"className":8130,"src":8131},"imek-elasticita-tr",[209,1637],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[723,8133,8134],{},[1633,8135],{"alt":8136,"className":8137,"src":8138},"imek-elasticita-podel-linearni-poptavky",[209,1637],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[723,8140,8141,8142,8192,8193,8209],{},"Pro celkový příjem platí ",[882,8143,8145],{"className":8144},[885],[887,8146,8147],{"xmlns":889},[891,8148,8149,8189],{},[894,8150,8151,8153,8155,8157,8159,8161,8163,8165,8167,8169,8171,8173,8175,8177,8179,8181,8183,8185,8187],{},[897,8152,2083],{},[897,8154,5569],{},[3584,8156,3586],{},[897,8158,2083],{},[897,8160,5569],{},[3584,8162,3593],{"stretchy":3592},[897,8164,4366],{},[3584,8166,3599],{"stretchy":3592},[3584,8168,3586],{},[897,8170,2115],{},[3584,8172,4754],{},[897,8174,4366],{},[3584,8176,3586],{},[897,8178,4366],{},[3584,8180,4754],{},[897,8182,5758],{},[3584,8184,3593],{"stretchy":3592},[897,8186,4366],{},[3584,8188,3599],{"stretchy":3592},[901,8190,8191],{"encoding":903},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[882,8194,8196],{"className":8195},[885],[887,8197,8198],{"xmlns":889},[891,8199,8200,8206],{},[894,8201,8202,8204],{},[897,8203,4395],{},[897,8205,5569],{},[901,8207,8208],{"encoding":903},"MR"," odvodíme:",[723,8211,8212],{},[882,8213,8215],{"className":8214},[885],[887,8216,8217],{"xmlns":889},[891,8218,8219,8327],{},[894,8220,8221,8223,8225,8227,8229,8235,8237,8239,8241,8243,8245,8247,8249,8251,8253,8255,8257,8263,8265,8267,8269,8271,8273,8275,8277,8291,8293,8295],{},[897,8222,4395],{},[897,8224,5569],{},[3584,8226,3586],{},[897,8228,2083],{},[3712,8230,8231,8233],{},[897,8232,5569],{},[3584,8234,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,8236,3593],{"stretchy":3592},[897,8238,4366],{},[3584,8240,3599],{"stretchy":3592},[3584,8242,3586],{},[897,8244,5758],{},[3584,8246,3593],{"stretchy":3592},[897,8248,4366],{},[3584,8250,3599],{"stretchy":3592},[3584,8252,3683],{},[897,8254,4366],{},[3870,8256,4564],{},[3712,8258,8259,8261],{},[897,8260,5758],{},[3584,8262,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,8264,3593],{"stretchy":3592},[897,8266,4366],{},[3584,8268,3599],{"stretchy":3592},[3584,8270,3586],{},[897,8272,2115],{},[3584,8274,3683],{},[897,8276,4366],{},[3910,8278,8279,8285],{},[894,8280,8281,8283],{},[897,8282,3780],{"mathvariant":3956},[897,8284,2115],{},[894,8286,8287,8289],{},[897,8288,3780],{"mathvariant":3956},[897,8290,4366],{},[3584,8292,3586],{},[897,8294,2115],{},[894,8296,8297,8299,8301,8303,8309,8311,8325],{},[3584,8298,3593],{"fence":3867},[3717,8300,2177],{},[3584,8302,3683],{},[3910,8304,8305,8307],{},[897,8306,4366],{},[897,8308,2115],{},[3584,8310,4754],{},[3910,8312,8313,8319],{},[894,8314,8315,8317],{},[897,8316,3780],{"mathvariant":3956},[897,8318,2115],{},[894,8320,8321,8323],{},[897,8322,3780],{"mathvariant":3956},[897,8324,4366],{},[3584,8326,3599],{"fence":3867},[901,8328,8329],{"encoding":903},"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)",[723,8331,8332],{},[882,8333,8335],{"className":8334},[885],[887,8336,8337],{"xmlns":889},[891,8338,8339,8411],{},[894,8340,8341,8343,8345,8387,8389,8391],{},[3584,8342,3586],{},[897,8344,2115],{},[894,8346,8347,8349,8351,8353,8385],{},[3584,8348,3593],{"fence":3867},[3717,8350,2177],{},[3584,8352,3683],{},[3910,8354,8355,8357],{},[3717,8356,2177],{},[894,8358,8359,8367,8369],{},[3907,8360,8361],{"scriptlevel":2169,"displaystyle":3592},[3910,8362,8363,8365],{},[897,8364,2115],{},[897,8366,4366],{},[3584,8368,4754],{},[3907,8370,8371],{"scriptlevel":2169,"displaystyle":3592},[3910,8372,8373,8379],{},[894,8374,8375,8377],{},[897,8376,3780],{"mathvariant":3956},[897,8378,4366],{},[894,8380,8381,8383],{},[897,8382,3780],{"mathvariant":3956},[897,8384,2115],{},[3584,8386,3599],{"fence":3867},[3584,8388,3586],{},[897,8390,2115],{},[894,8392,8393,8395,8397,8399,8409],{},[3584,8394,3593],{"fence":3867},[3717,8396,2177],{},[3584,8398,3683],{},[3910,8400,8401,8403],{},[3717,8402,2177],{},[894,8404,8405,8407],{},[3584,8406,3810],{},[897,8408,2094],{},[3584,8410,3599],{"fence":3867},[901,8412,8413],{"encoding":903},"= P\\left(1 + \\frac{1}{\\tfrac{P}{Q}\\cdot\\tfrac{\\mathrm{d}Q}{\\mathrm{d}P}}\\right) = P\\left(1 + \\frac{1}{-E}\\right)",[723,8415,8416],{},"a tedy",[723,8418,8419],{},[882,8420,8422],{"className":8421,"title":5775,"style":5776},[5774],"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[2540,8424,8425,8494,8744],{},[723,8426,8427,8429,8430,8464,8465,8480,8481,4282],{},[882,8428,5730],{}," Intuice: vztah ",[882,8431,8433],{"className":8432},[885],[887,8434,8435],{"xmlns":889},[891,8436,8437,8461],{},[894,8438,8439,8441,8443,8445,8447,8449,8451,8453,8455,8457,8459],{},[897,8440,4395],{},[897,8442,5569],{},[3584,8444,3586],{},[897,8446,2115],{},[3584,8448,3593],{"stretchy":3592},[3717,8450,2177],{},[3584,8452,3810],{},[3717,8454,2177],{},[897,8456,6248],{"mathvariant":3956},[897,8458,2094],{},[3584,8460,3599],{"stretchy":3592},[901,8462,8463],{"encoding":903},"MR = P(1 - 1\u002FE)","\nVztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[882,8466,8468],{"className":8467},[885],[887,8469,8470],{"xmlns":889},[891,8471,8472,8478],{},[894,8473,8474,8476],{},[897,8475,4395],{},[897,8477,5569],{},[901,8479,8208],{"encoding":903}," jednoznačně určuje hodnota ",[882,8482,8484],{"className":8483},[885],[887,8485,8486],{"xmlns":889},[891,8487,8488,8492],{},[894,8489,8490],{},[897,8491,2094],{},[901,8493,2094],{"encoding":903},[119,8495,8496,8606,8675],{},[122,8497,8498,8515,8516,2962,8530,2962,8556,2962,8569,8589,8590,8605],{},[882,8499,8501],{"className":8500},[885],[887,8502,8503],{"xmlns":889},[891,8504,8505,8513],{},[894,8506,8507,8509,8511],{},[897,8508,2094],{},[3584,8510,4985],{},[3717,8512,2177],{},[901,8514,6083],{"encoding":903}," (elastická) ",[882,8517,8519],{"className":8518},[885],[887,8520,8521],{"xmlns":889},[891,8522,8523,8527],{},[894,8524,8525],{},[3584,8526,5562],{},[901,8528,8529],{"encoding":903},"\\Rightarrow",[882,8531,8533],{"className":8532},[885],[887,8534,8535],{"xmlns":889},[891,8536,8537,8553],{},[894,8538,8539,8541,8543,8545,8547,8549,8551],{},[3717,8540,2177],{},[3584,8542,3810],{},[3717,8544,2177],{},[897,8546,6248],{"mathvariant":3956},[897,8548,2094],{},[3584,8550,4985],{},[3717,8552,2169],{},[901,8554,8555],{"encoding":903},"1 - 1\u002FE > 0",[882,8557,8559],{"className":8558},[885],[887,8560,8561],{"xmlns":889},[891,8562,8563,8567],{},[894,8564,8565],{},[3584,8566,5562],{},[901,8568,8529],{"encoding":903},[882,8570,8572],{"className":8571},[885],[887,8573,8574],{"xmlns":889},[891,8575,8576,8586],{},[894,8577,8578,8580,8582,8584],{},[897,8579,4395],{},[897,8581,5569],{},[3584,8583,4985],{},[3717,8585,2169],{},[901,8587,8588],{"encoding":903},"MR > 0"," — ",[882,8591,8593],{"className":8592},[885],[887,8594,8595],{"xmlns":889},[891,8596,8597,8603],{},[894,8598,8599,8601],{},[897,8600,2083],{},[897,8602,5569],{},[901,8604,5669],{"encoding":903}," roste s množstvím, tj. klesá s cenou.",[122,8607,8608,8625,8626,2962,8639,8589,8659,8674],{},[882,8609,8611],{"className":8610},[885],[887,8612,8613],{"xmlns":889},[891,8614,8615,8623],{},[894,8616,8617,8619,8621],{},[897,8618,2094],{},[3584,8620,3586],{},[3717,8622,2177],{},[901,8624,6119],{"encoding":903}," (jednotková) ",[882,8627,8629],{"className":8628},[885],[887,8630,8631],{"xmlns":889},[891,8632,8633,8637],{},[894,8634,8635],{},[3584,8636,5562],{},[901,8638,8529],{"encoding":903},[882,8640,8642],{"className":8641},[885],[887,8643,8644],{"xmlns":889},[891,8645,8646,8656],{},[894,8647,8648,8650,8652,8654],{},[897,8649,4395],{},[897,8651,5569],{},[3584,8653,3586],{},[3717,8655,2169],{},[901,8657,8658],{"encoding":903},"MR = 0",[882,8660,8662],{"className":8661},[885],[887,8663,8664],{"xmlns":889},[891,8665,8666,8672],{},[894,8667,8668,8670],{},[897,8669,2083],{},[897,8671,5569],{},[901,8673,5669],{"encoding":903}," je extrém (maximum).",[122,8676,8677,8694,8695,2962,8708,8589,8728,8743],{},[882,8678,8680],{"className":8679},[885],[887,8681,8682],{"xmlns":889},[891,8683,8684,8692],{},[894,8685,8686,8688,8690],{},[897,8687,2094],{},[3584,8689,5024],{},[3717,8691,2177],{},[901,8693,6101],{"encoding":903}," (neelastická) ",[882,8696,8698],{"className":8697},[885],[887,8699,8700],{"xmlns":889},[891,8701,8702,8706],{},[894,8703,8704],{},[3584,8705,5562],{},[901,8707,8529],{"encoding":903},[882,8709,8711],{"className":8710},[885],[887,8712,8713],{"xmlns":889},[891,8714,8715,8725],{},[894,8716,8717,8719,8721,8723],{},[897,8718,4395],{},[897,8720,5569],{},[3584,8722,5024],{},[3717,8724,2169],{},[901,8726,8727],{"encoding":903},"MR \u003C 0",[882,8729,8731],{"className":8730},[885],[887,8732,8733],{"xmlns":889},[891,8734,8735,8741],{},[894,8736,8737,8739],{},[897,8738,2083],{},[897,8740,5569],{},[901,8742,5669],{"encoding":903}," klesá s množstvím, tj. roste s cenou.",[723,8745,8746,8747,1750],{},"Viz také ",[206,8748,5400],{"className":8749,"dataFsResolvedFilePath":826,"href":827},[209],[197,8751,8753],{"id":8752},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[723,8755,8756,8776,8777,8803,8804,8819,8820,8833,8834,8847,8848,8861,8862,8878,8879,2962,8894,8897,8898,8878,8914,1750],{},[37,8757,8758,8759,5494],{},"(a) Poptávka elastická (",[882,8760,8762],{"className":8761},[885],[887,8763,8764],{"xmlns":889},[891,8765,8766,8774],{},[894,8767,8768,8770,8772],{},[897,8769,2094],{},[3584,8771,4985],{},[3717,8773,2177],{},[901,8775,6083],{"encoding":903}," Z (4.12) plyne ",[882,8778,8780],{"className":8779},[885],[887,8781,8782],{"xmlns":889},[891,8783,8784,8800],{},[894,8785,8786,8788,8790,8792,8794,8796,8798],{},[897,8787,4395],{},[897,8789,5569],{},[3584,8791,3593],{"stretchy":3592},[897,8793,4366],{},[3584,8795,3599],{"stretchy":3592},[3584,8797,4985],{},[3717,8799,2169],{},[901,8801,8802],{"encoding":903},"MR(Q) > 0",", a tedy celkový příjem ",[882,8805,8807],{"className":8806},[885],[887,8808,8809],{"xmlns":889},[891,8810,8811,8817],{},[894,8812,8813,8815],{},[897,8814,2083],{},[897,8816,5569],{},[901,8818,5669],{"encoding":903}," je rostoucí funkcí ",[882,8821,8823],{"className":8822},[885],[887,8824,8825],{"xmlns":889},[891,8826,8827,8831],{},[894,8828,8829],{},[897,8830,4366],{},[901,8832,4366],{"encoding":903},". Avšak růst ",[882,8835,8837],{"className":8836},[885],[887,8838,8839],{"xmlns":889},[891,8840,8841,8845],{},[894,8842,8843],{},[897,8844,4366],{},[901,8846,4366],{"encoding":903}," je odezvou na pokles ceny ",[882,8849,8851],{"className":8850},[885],[887,8852,8853],{"xmlns":889},[891,8854,8855,8859],{},[894,8856,8857],{},[897,8858,2115],{},[901,8860,2115],{"encoding":903},". Tudíž s ",[613,8863,8864,8865],{},"poklesem ceny ",[882,8866,8868],{"className":8867},[885],[887,8869,8870],{"xmlns":889},[891,8871,8872,8876],{},[894,8873,8874],{},[897,8875,2115],{},[901,8877,2115],{"encoding":903}," celkový příjem ",[882,8880,8882],{"className":8881},[885],[887,8883,8884],{"xmlns":889},[891,8885,8886,8892],{},[894,8887,8888,8890],{},[897,8889,2083],{},[897,8891,5569],{},[901,8893,5669],{"encoding":903},[613,8895,8896],{},"roste"," a s ",[613,8899,8900,8901],{},"růstem ceny ",[882,8902,8904],{"className":8903},[885],[887,8905,8906],{"xmlns":889},[891,8907,8908,8912],{},[894,8909,8910],{},[897,8911,2115],{},[901,8913,2115],{"encoding":903},[613,8915,8916],{},"klesá",[2540,8918,8919],{},[723,8920,8921,8924],{},[37,8922,8923],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[723,8926,8927,8776,8947,1342,8973,8988,8989,9002,9003,9016,9017,9030,9031,8878,9044,2962,9059,1750],{},[37,8928,8929,8930,5494],{},"(b) Poptávka neelastická (",[882,8931,8933],{"className":8932},[885],[887,8934,8935],{"xmlns":889},[891,8936,8937,8945],{},[894,8938,8939,8941,8943],{},[897,8940,2094],{},[3584,8942,5024],{},[3717,8944,2177],{},[901,8946,6101],{"encoding":903},[882,8948,8950],{"className":8949},[885],[887,8951,8952],{"xmlns":889},[891,8953,8954,8970],{},[894,8955,8956,8958,8960,8962,8964,8966,8968],{},[897,8957,4395],{},[897,8959,5569],{},[3584,8961,3593],{"stretchy":3592},[897,8963,4366],{},[3584,8965,3599],{"stretchy":3592},[3584,8967,5024],{},[3717,8969,2169],{},[901,8971,8972],{"encoding":903},"MR(Q) \u003C 0",[882,8974,8976],{"className":8975},[885],[887,8977,8978],{"xmlns":889},[891,8979,8980,8986],{},[894,8981,8982,8984],{},[897,8983,2083],{},[897,8985,5569],{},[901,8987,5669],{"encoding":903}," je klesající funkce ",[882,8990,8992],{"className":8991},[885],[887,8993,8994],{"xmlns":889},[891,8995,8996,9000],{},[894,8997,8998],{},[897,8999,4366],{},[901,9001,4366],{"encoding":903},", tj. s růstem ",[882,9004,9006],{"className":9005},[885],[887,9007,9008],{"xmlns":889},[891,9009,9010,9014],{},[894,9011,9012],{},[897,9013,4366],{},[901,9015,4366],{"encoding":903}," (s poklesem ceny ",[882,9018,9020],{"className":9019},[885],[887,9021,9022],{"xmlns":889},[891,9023,9024,9028],{},[894,9025,9026],{},[897,9027,2115],{},[901,9029,2115],{"encoding":903},") celkový příjem klesá. S růstem ceny ",[882,9032,9034],{"className":9033},[885],[887,9035,9036],{"xmlns":889},[891,9037,9038,9042],{},[894,9039,9040],{},[897,9041,2115],{},[901,9043,2115],{"encoding":903},[882,9045,9047],{"className":9046},[885],[887,9048,9049],{"xmlns":889},[891,9050,9051,9057],{},[894,9052,9053,9055],{},[897,9054,2083],{},[897,9056,5569],{},[901,9058,5669],{"encoding":903},[613,9060,8896],{},[2540,9062,9063],{},[723,9064,9065,9068],{},[37,9066,9067],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[723,9070,9071,8776,9091,9110,9111,9126,9127,9197,9198,1646,9226,9259,9260,7163,9288,9303,9304,1750],{},[37,9072,9073,9074,5494],{},"(c) Jednotková elasticita (",[882,9075,9077],{"className":9076},[885],[887,9078,9079],{"xmlns":889},[891,9080,9081,9089],{},[894,9082,9083,9085,9087],{},[897,9084,2094],{},[3584,9086,3586],{},[3717,9088,2177],{},[901,9090,6119],{"encoding":903},[882,9092,9094],{"className":9093},[885],[887,9095,9096],{"xmlns":889},[891,9097,9098,9108],{},[894,9099,9100,9102,9104,9106],{},[897,9101,4395],{},[897,9103,5569],{},[3584,9105,3586],{},[3717,9107,2169],{},[901,9109,8658],{"encoding":903}," — nutná podmínka extrému ",[882,9112,9114],{"className":9113},[885],[887,9115,9116],{"xmlns":889},[891,9117,9118,9124],{},[894,9119,9120,9122],{},[897,9121,2083],{},[897,9123,5569],{},[901,9125,5669],{"encoding":903},". Dále ",[882,9128,9130],{"className":9129},[885],[887,9131,9132],{"xmlns":889},[891,9133,9134,9194],{},[894,9135,9136,9138,9148,9150,9152,9158,9160,9166,9168,9170,9172,9174,9176,9178,9188,9190,9192],{},[897,9137,2083],{},[3712,9139,9140,9142],{},[897,9141,5569],{},[894,9143,9144,9146],{},[3584,9145,3958],{"mathvariant":3956},[3584,9147,3958],{"mathvariant":3956},[3584,9149,3586],{},[897,9151,4395],{},[3712,9153,9154,9156],{},[897,9155,5569],{},[3584,9157,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,9159,3586],{},[3712,9161,9162,9164],{},[897,9163,5758],{},[3584,9165,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,9167,3593],{"stretchy":3592},[897,9169,4366],{},[3584,9171,3599],{"stretchy":3592},[3584,9173,3683],{},[897,9175,4366],{},[3870,9177,4564],{},[3712,9179,9180,9182],{},[897,9181,5758],{},[894,9183,9184,9186],{},[3584,9185,3958],{"mathvariant":3956},[3584,9187,3958],{"mathvariant":3956},[3584,9189,3593],{"stretchy":3592},[897,9191,4366],{},[3584,9193,3599],{"stretchy":3592},[901,9195,9196],{"encoding":903},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[882,9199,9201],{"className":9200},[885],[887,9202,9203],{"xmlns":889},[891,9204,9205,9223],{},[894,9206,9207,9213,9215,9217,9219,9221],{},[3712,9208,9209,9211],{},[897,9210,5758],{},[3584,9212,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,9214,3593],{"stretchy":3592},[897,9216,4366],{},[3584,9218,3599],{"stretchy":3592},[3584,9220,5024],{},[3717,9222,2169],{},[901,9224,9225],{"encoding":903},"D'(Q) \u003C 0",[882,9227,9229],{"className":9228},[885],[887,9230,9231],{"xmlns":889},[891,9232,9233,9256],{},[894,9234,9235,9245,9247,9249,9251,9254],{},[3712,9236,9237,9239],{},[897,9238,5758],{},[894,9240,9241,9243],{},[3584,9242,3958],{"mathvariant":3956},[3584,9244,3958],{"mathvariant":3956},[3584,9246,3593],{"stretchy":3592},[897,9248,4366],{},[3584,9250,3599],{"stretchy":3592},[3584,9252,9253],{},"≤",[3717,9255,2169],{},[901,9257,9258],{"encoding":903},"D''(Q) \\le 0",", odkud ",[882,9261,9263],{"className":9262},[885],[887,9264,9265],{"xmlns":889},[891,9266,9267,9285],{},[894,9268,9269,9271,9281,9283],{},[897,9270,2083],{},[3712,9272,9273,9275],{},[897,9274,5569],{},[894,9276,9277,9279],{},[3584,9278,3958],{"mathvariant":3956},[3584,9280,3958],{"mathvariant":3956},[3584,9282,5024],{},[3717,9284,2169],{},[901,9286,9287],{"encoding":903},"TR'' \u003C 0",[882,9289,9291],{"className":9290},[885],[887,9292,9293],{"xmlns":889},[891,9294,9295,9301],{},[894,9296,9297,9299],{},[897,9298,2083],{},[897,9300,5569],{},[901,9302,5669],{"encoding":903}," nabývá ",[37,9305,9306],{},"maxima",[2540,9308,9309],{},[723,9310,9311,9314],{},[37,9312,9313],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[723,9316,9317],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[723,9319,9320],{},[37,9321,9322],{},"Souhrnná tabulka Pravidel 1–3:",[15,9324,9325,9429],{},[18,9326,9327],{},[21,9328,9329,9332,9347,9364,9395,9426],{},[24,9330,9331],{},"Charakter poptávky",[24,9333,9334],{},[882,9335,9337],{"className":9336},[885],[887,9338,9339],{"xmlns":889},[891,9340,9341,9345],{},[894,9342,9343],{},[897,9344,2094],{},[901,9346,2094],{"encoding":903},[24,9348,9349],{},[882,9350,9352],{"className":9351},[885],[887,9353,9354],{"xmlns":889},[891,9355,9356,9362],{},[894,9357,9358,9360],{},[897,9359,4395],{},[897,9361,5569],{},[901,9363,8208],{"encoding":903},[24,9365,9366,9367,2962,9380],{},"Pokles ceny ",[882,9368,9370],{"className":9369},[885],[887,9371,9372],{"xmlns":889},[891,9373,9374,9378],{},[894,9375,9376],{},[3584,9377,5562],{},[901,9379,8529],{"encoding":903},[882,9381,9383],{"className":9382},[885],[887,9384,9385],{"xmlns":889},[891,9386,9387,9393],{},[894,9388,9389,9391],{},[897,9390,2083],{},[897,9392,5569],{},[901,9394,5669],{"encoding":903},[24,9396,9397,9398,2962,9411],{},"Růst ceny ",[882,9399,9401],{"className":9400},[885],[887,9402,9403],{"xmlns":889},[891,9404,9405,9409],{},[894,9406,9407],{},[3584,9408,5562],{},[901,9410,8529],{"encoding":903},[882,9412,9414],{"className":9413},[885],[887,9415,9416],{"xmlns":889},[891,9417,9418,9424],{},[894,9419,9420,9422],{},[897,9421,2083],{},[897,9423,5569],{},[901,9425,5669],{"encoding":903},[24,9427,9428],{},"Doporučení",[29,9430,9431,9480,9530],{},[21,9432,9433,9435,9453,9471,9473,9475],{},[34,9434,5648],{},[34,9436,9437],{},[882,9438,9440],{"className":9439},[885],[887,9441,9442],{"xmlns":889},[891,9443,9444,9450],{},[894,9445,9446,9448],{},[3584,9447,4985],{},[3717,9449,2177],{},[901,9451,9452],{"encoding":903},"> 1",[34,9454,9455],{},[882,9456,9458],{"className":9457},[885],[887,9459,9460],{"xmlns":889},[891,9461,9462,9468],{},[894,9463,9464,9466],{},[3584,9465,4985],{},[3717,9467,2169],{},[901,9469,9470],{"encoding":903},"> 0",[34,9472,8896],{},[34,9474,8916],{},[34,9476,9477],{},[37,9478,9479],{},"snížit cenu",[21,9481,9482,9485,9503,9521,9523,9525],{},[34,9483,9484],{},"jednotková",[34,9486,9487],{},[882,9488,9490],{"className":9489},[885],[887,9491,9492],{"xmlns":889},[891,9493,9494,9500],{},[894,9495,9496,9498],{},[3584,9497,3586],{},[3717,9499,2177],{},[901,9501,9502],{"encoding":903},"= 1",[34,9504,9505],{},[882,9506,9508],{"className":9507},[885],[887,9509,9510],{"xmlns":889},[891,9511,9512,9518],{},[894,9513,9514,9516],{},[3584,9515,3586],{},[3717,9517,2169],{},[901,9519,9520],{"encoding":903},"= 0",[34,9522,5294],{},[34,9524,5294],{},[34,9526,9527],{},[37,9528,9529],{},"držet cenu",[21,9531,9532,9534,9552,9570,9572,9574],{},[34,9533,5652],{},[34,9535,9536],{},[882,9537,9539],{"className":9538},[885],[887,9540,9541],{"xmlns":889},[891,9542,9543,9549],{},[894,9544,9545,9547],{},[3584,9546,5024],{},[3717,9548,2177],{},[901,9550,9551],{"encoding":903},"\u003C 1",[34,9553,9554],{},[882,9555,9557],{"className":9556},[885],[887,9558,9559],{"xmlns":889},[891,9560,9561,9567],{},[894,9562,9563,9565],{},[3584,9564,5024],{},[3717,9566,2169],{},[901,9568,9569],{"encoding":903},"\u003C 0",[34,9571,8916],{},[34,9573,8896],{},[34,9575,9576],{},[37,9577,9578],{},"zvýšit cenu",[197,9580,9582],{"id":9581},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[723,9584,9585,9586,9611,9612,9634,9635,9648,9649,9662,9663,9676,9677,7163,9704,9756],{},"Aplikujme pravidla 1–3 pro poptávku ",[882,9587,9589],{"className":9588},[885],[887,9590,9591],{"xmlns":889},[891,9592,9593,9609],{},[894,9594,9595,9597,9599,9601,9603],{},[897,9596,2115],{},[3584,9598,3586],{},[3717,9600,4667],{},[3584,9602,3810],{},[3712,9604,9605,9607],{},[897,9606,4366],{},[3717,9608,2185],{},[901,9610,7033],{"encoding":903},". Reálné cenové rozpětí je ",[882,9613,9615],{"className":9614},[885],[887,9616,9617],{"xmlns":889},[891,9618,9619,9631],{},[894,9620,9621,9623,9625,9627,9629],{},[3584,9622,6898],{"stretchy":3592},[3717,9624,2177],{},[3584,9626,3868],{"separator":3867},[3717,9628,4667],{},[3584,9630,6915],{"stretchy":3592},[901,9632,9633],{"encoding":903},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[882,9636,9638],{"className":9637},[885],[887,9639,9640],{"xmlns":889},[891,9641,9642,9646],{},[894,9643,9644],{},[897,9645,4366],{},[901,9647,4366],{"encoding":903}," jako funkci ",[882,9650,9652],{"className":9651},[885],[887,9653,9654],{"xmlns":889},[891,9655,9656,9660],{},[894,9657,9658],{},[897,9659,2115],{},[901,9661,2115],{"encoding":903},"; pro nezáporné ",[882,9664,9666],{"className":9665},[885],[887,9667,9668],{"xmlns":889},[891,9669,9670,9674],{},[894,9671,9672],{},[897,9673,4366],{},[901,9675,4366],{"encoding":903}," je ",[882,9678,9680],{"className":9679},[885],[887,9681,9682],{"xmlns":889},[891,9683,9684,9701],{},[894,9685,9686,9688,9690],{},[897,9687,4366],{},[3584,9689,3586],{},[9691,9692,9693],"msqrt",{},[894,9694,9695,9697,9699],{},[3717,9696,4667],{},[3584,9698,3810],{},[897,9700,2115],{},[901,9702,9703],{"encoding":903},"Q = \\sqrt{100 - P}",[882,9705,9707],{"className":9706},[885],[887,9708,9709],{"xmlns":889},[891,9710,9711,9753],{},[894,9712,9713,9729,9731,9733],{},[3907,9714,9715],{"scriptlevel":2169,"displaystyle":3867},[3910,9716,9717,9723],{},[894,9718,9719,9721],{},[897,9720,3780],{"mathvariant":3956},[897,9722,4366],{},[894,9724,9725,9727],{},[897,9726,3780],{"mathvariant":3956},[897,9728,2115],{},[3584,9730,3586],{},[3584,9732,3810],{},[3907,9734,9735],{"scriptlevel":2169,"displaystyle":3867},[3910,9736,9737,9739],{},[3717,9738,2177],{},[894,9740,9741,9743],{},[3717,9742,2185],{},[9691,9744,9745],{},[894,9746,9747,9749,9751],{},[3717,9748,4667],{},[3584,9750,3810],{},[897,9752,2115],{},[901,9754,9755],{"encoding":903},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[723,9758,9759],{},[882,9760,9762],{"className":9761},[885],[887,9763,9764],{"xmlns":889},[891,9765,9766,9888],{},[894,9767,9768,9770,9772,9774,9776,9778,9780,9786,9788,9802,9804,9806,9820,9822,9848,9850,9868,9870,9886],{},[897,9769,2094],{},[3584,9771,3593],{"stretchy":3592},[897,9773,2115],{},[3584,9775,3599],{"stretchy":3592},[3584,9777,3586],{},[3584,9779,3810],{},[3910,9781,9782,9784],{},[897,9783,2115],{},[897,9785,4366],{},[3584,9787,4754],{},[3910,9789,9790,9796],{},[894,9791,9792,9794],{},[897,9793,3780],{"mathvariant":3956},[897,9795,4366],{},[894,9797,9798,9800],{},[897,9799,3780],{"mathvariant":3956},[897,9801,2115],{},[3584,9803,3586],{},[3584,9805,3810],{},[3910,9807,9808,9810],{},[897,9809,2115],{},[9691,9811,9812],{},[894,9813,9814,9816,9818],{},[3717,9815,4667],{},[3584,9817,3810],{},[897,9819,2115],{},[3584,9821,4754],{},[894,9823,9824,9826,9828,9846],{},[3584,9825,3593],{"fence":3867},[3584,9827,3810],{},[3910,9829,9830,9832],{},[3717,9831,2177],{},[894,9833,9834,9836],{},[3717,9835,2185],{},[9691,9837,9838],{},[894,9839,9840,9842,9844],{},[3717,9841,4667],{},[3584,9843,3810],{},[897,9845,2115],{},[3584,9847,3599],{"fence":3867},[3584,9849,3586],{},[3910,9851,9852,9854],{},[897,9853,2115],{},[894,9855,9856,9858,9860,9862,9864,9866],{},[3717,9857,2185],{},[3584,9859,3593],{"stretchy":3592},[3717,9861,4667],{},[3584,9863,3810],{},[897,9865,2115],{},[3584,9867,3599],{"stretchy":3592},[3584,9869,3586],{},[3910,9871,9872,9878],{},[894,9873,9874,9876],{},[3717,9875,6583],{},[897,9877,2115],{},[894,9879,9880,9882,9884],{},[3717,9881,4667],{},[3584,9883,3810],{},[897,9885,2115],{},[897,9887,1750],{"mathvariant":3956},[901,9889,9890],{"encoding":903},"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}.",[723,9892,9893,9894,4282],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[882,9895,9897],{"className":9896},[885],[887,9898,9899],{"xmlns":889},[891,9900,9901,9925],{},[894,9902,9903,9921,9923],{},[3907,9904,9905],{"scriptlevel":2169,"displaystyle":3867},[3910,9906,9907,9913],{},[894,9908,9909,9911],{},[3717,9910,6583],{},[897,9912,2115],{},[894,9914,9915,9917,9919],{},[3717,9916,4667],{},[3584,9918,3810],{},[897,9920,2115],{},[3584,9922,3586],{},[3717,9924,2177],{},[901,9926,9927],{"encoding":903},"\\dfrac{0{,}5P}{100-P} = 1",[723,9929,9930],{},[882,9931,9933],{"className":9932},[885],[887,9934,9935],{"xmlns":889},[891,9936,9937,9969],{},[894,9938,9939,9945,9947,9954,9956,9959,9967],{},[3712,9940,9941,9943],{},[897,9942,2115],{},[3584,9944,5928],{},[3584,9946,3586],{},[3910,9948,9949,9952],{},[3717,9950,9951],{},"200",[3717,9953,2193],{},[3584,9955,7474],{},[3717,9957,9958],{},"66,",[9960,9961,9962,9964],"mover",{"accent":3867},[3717,9963,2217],{},[3584,9965,9966],{"stretchy":3867},"‾",[897,9968,1750],{"mathvariant":3956},[901,9970,9971],{"encoding":903},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[723,9973,9974],{},"S využitím vlastnosti (4.8):",[119,9976,9977,10023,10065],{},[122,9978,9979,9980,10015,10016,10018,10019,10022],{},"Při cenách ",[882,9981,9983],{"className":9982},[885],[887,9984,9985],{"xmlns":889},[891,9986,9987,10012],{},[894,9988,9989,9991,9993,9995,9997,10000,10002,10004,10010],{},[897,9990,2115],{},[3584,9992,8080],{},[3584,9994,6898],{"stretchy":3592},[3717,9996,2177],{},[3584,9998,9999],{"separator":3867},";",[3870,10001,4564],{},[3717,10003,9958],{},[9960,10005,10006,10008],{"accent":3867},[3717,10007,2217],{},[3584,10009,9966],{"stretchy":3867},[3584,10011,3599],{"stretchy":3592},[901,10013,10014],{"encoding":903},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[37,10017,5652],{}," — dle ",[613,10020,10021],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[122,10024,9979,10025,10015,10059,10018,10061,10064],{},[882,10026,10028],{"className":10027},[885],[887,10029,10030],{"xmlns":889},[891,10031,10032,10056],{},[894,10033,10034,10036,10038,10040,10042,10048,10050,10052,10054],{},[897,10035,2115],{},[3584,10037,8080],{},[3584,10039,3593],{"stretchy":3592},[3717,10041,9958],{},[9960,10043,10044,10046],{"accent":3867},[3717,10045,2217],{},[3584,10047,9966],{"stretchy":3867},[3584,10049,9999],{"separator":3867},[3870,10051,4564],{},[3717,10053,4667],{},[3584,10055,6915],{"stretchy":3592},[901,10057,10058],{"encoding":903},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[37,10060,5648],{},[613,10062,10063],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[122,10066,10067,10068,10071,10072,10100,10101,10104],{},"Dle ",[613,10069,10070],{},"Pravidla 3"," je při ceně ",[882,10073,10075],{"className":10074},[885],[887,10076,10077],{"xmlns":889},[891,10078,10079,10097],{},[894,10080,10081,10087,10089,10091],{},[3712,10082,10083,10085],{},[897,10084,2115],{},[3584,10086,5928],{},[3584,10088,3586],{},[3717,10090,9958],{},[9960,10092,10093,10095],{"accent":3867},[3717,10094,2217],{},[3584,10096,9966],{"stretchy":3867},[901,10098,10099],{"encoding":903},"P^* = 66{,}\\overline{6}"," dosaženo ",[37,10102,10103],{},"maxima celkového příjmu"," ve výši",[723,10106,10107],{},[882,10108,10110],{"className":10109},[885],[887,10111,10112],{"xmlns":889},[891,10113,10114,10192],{},[894,10115,10116,10118,10120,10122,10128,10130,10132,10138,10140,10154,10156,10162,10164,10172,10174,10187,10189],{},[897,10117,2083],{},[897,10119,5569],{},[3584,10121,3593],{"stretchy":3592},[3712,10123,10124,10126],{},[897,10125,2115],{},[3584,10127,5928],{},[3584,10129,3599],{"stretchy":3592},[3584,10131,3586],{},[3712,10133,10134,10136],{},[897,10135,2115],{},[3584,10137,5928],{},[3584,10139,4754],{},[9691,10141,10142],{},[894,10143,10144,10146,10148],{},[3717,10145,4667],{},[3584,10147,3810],{},[3712,10149,10150,10152],{},[897,10151,2115],{},[3584,10153,5928],{},[3584,10155,3586],{},[3910,10157,10158,10160],{},[3717,10159,9951],{},[3717,10161,2193],{},[3584,10163,4754],{},[9691,10165,10166],{},[3910,10167,10168,10170],{},[3717,10169,4667],{},[3717,10171,2193],{},[3584,10173,3586],{},[3910,10175,10176,10179],{},[3717,10177,10178],{},"2000",[894,10180,10181,10183],{},[3717,10182,2193],{},[9691,10184,10185],{},[3717,10186,2193],{},[3584,10188,7474],{},[3717,10190,10191],{},"384,9.",[901,10193,10194],{"encoding":903},"TR(P^*) = P^*\\cdot\\sqrt{100 - P^*} = \\frac{200}{3}\\cdot\\sqrt{\\frac{100}{3}} = \\frac{2000}{3\\sqrt{3}} \\doteq 384{,}9.",[723,10196,10197,10198,1750],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[882,10199,10201],{"className":10200},[885],[887,10202,10203],{"xmlns":889},[891,10204,10205,10211],{},[894,10206,10207,10209],{},[897,10208,2083],{},[897,10210,5569],{},[901,10212,5669],{"encoding":903},[114,10214,10216],{"id":10215},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[723,10218,10219,10220,10223],{},"Analogicky se definuje ",[37,10221,10222],{},"cenová elasticita nabídky"," (price elasticity of supply):",[723,10225,10226],{},[882,10227,10229],{"className":10228,"title":5775,"style":5776},[5774],"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[723,10231,5884,10232,10256,10257,10289],{},[882,10233,10235],{"className":10234},[885],[887,10236,10237],{"xmlns":889},[891,10238,10239,10253],{},[894,10240,10241,10243,10245,10247,10249,10251],{},[897,10242,4366],{},[3584,10244,3586],{},[897,10246,2072],{},[3584,10248,3593],{"stretchy":3592},[897,10250,2115],{},[3584,10252,3599],{"stretchy":3592},[901,10254,10255],{"encoding":903},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[882,10258,10260],{"className":10259},[885],[887,10261,10262],{"xmlns":889},[891,10263,10264,10286],{},[894,10265,10266,10282,10284],{},[3907,10267,10268],{"scriptlevel":2169,"displaystyle":3867},[3910,10269,10270,10276],{},[894,10271,10272,10274],{},[897,10273,3780],{"mathvariant":3956},[897,10275,4366],{},[894,10277,10278,10280],{},[897,10279,3780],{"mathvariant":3956},[897,10281,2115],{},[3584,10283,4985],{},[3717,10285,2169],{},[901,10287,10288],{"encoding":903},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[723,10291,10292],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[2540,10294,10295],{},[723,10296,10297,10298],{},"S rostoucí cenou elasticita nabídky roste. ",[882,10299,10301],{"className":10300},[885],[887,10302,10303],{"xmlns":889},[891,10304,10305,10314],{},[894,10306,10307,10309,10312],{},[3584,10308,3593],{"stretchy":3592},[3717,10310,10311],{},"4.14",[3584,10313,3599],{"stretchy":3592},[901,10315,10316],{"encoding":903},"(4.14)",[723,10318,10319],{},"Pro nominální změny platí",[723,10321,10322],{},[882,10323,10325],{"className":10324,"title":5775,"style":5776},[5774],"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[723,10327,10328],{},"a pro procentní změny",[723,10330,10331],{},[882,10332,10334],{"className":10333,"title":5775,"style":5776},[5774],"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[723,10336,10337],{},"(bez znaménka minus).",[197,10339,10341],{"id":10340},"příklad-47","Příklad 4.7",[723,10343,10344,10345,4282],{},"Nabídka ",[882,10346,10348],{"className":10347},[885],[887,10349,10350],{"xmlns":889},[891,10351,10352,10377],{},[894,10353,10354,10356,10358,10360,10366,10368,10370,10372,10374],{},[897,10355,4366],{},[3584,10357,3586],{},[3717,10359,4371],{},[3712,10361,10362,10364],{},[897,10363,2115],{},[3717,10365,2185],{},[3584,10367,3683],{},[3717,10369,2209],{},[897,10371,2115],{},[3584,10373,3683],{},[3717,10375,10376],{},"150",[901,10378,10379],{"encoding":903},"Q = 0{,}1P^2 + 5P + 150",[723,10381,10382],{},[882,10383,10385],{"className":10384},[885],[887,10386,10387],{"xmlns":889},[891,10388,10389,10435],{},[894,10390,10391,10393,10395,10419,10421,10423,10425,10427,10429,10431,10433],{},[897,10392,2094],{},[3584,10394,3586],{},[3910,10396,10397,10399],{},[897,10398,2115],{},[894,10400,10401,10403,10409,10411,10413,10415,10417],{},[3717,10402,4371],{},[3712,10404,10405,10407],{},[897,10406,2115],{},[3717,10408,2185],{},[3584,10410,3683],{},[3717,10412,2209],{},[897,10414,2115],{},[3584,10416,3683],{},[3717,10418,10376],{},[3870,10420,4564],{},[3584,10422,3593],{"stretchy":3592},[3717,10424,4416],{},[897,10426,2115],{},[3584,10428,3683],{},[3717,10430,2209],{},[3584,10432,3599],{"stretchy":3592},[897,10434,1750],{"mathvariant":3956},[901,10436,10437],{"encoding":903},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[723,10439,6691,10440,1342,10470,1342,10497,10533,10534,10559,10560,10578,10579,1750],{},[882,10441,10443],{"className":10442},[885],[887,10444,10445],{"xmlns":889},[891,10446,10447,10467],{},[894,10448,10449,10451,10453,10455,10457,10459],{},[897,10450,2094],{},[3584,10452,3593],{"stretchy":3592},[3717,10454,4440],{},[3584,10456,3599],{"stretchy":3592},[3584,10458,3586],{},[3907,10460,10461],{"scriptlevel":2169,"displaystyle":3592},[3910,10462,10463,10465],{},[3717,10464,2177],{},[3717,10466,2193],{},[901,10468,10469],{"encoding":903},"E(10) = \\tfrac{1}{3}",[882,10471,10473],{"className":10472},[885],[887,10474,10475],{"xmlns":889},[891,10476,10477,10494],{},[894,10478,10479,10481,10483,10488,10490,10492],{},[897,10480,2094],{},[3584,10482,3593],{"stretchy":3592},[9691,10484,10485],{},[3717,10486,10487],{},"1500",[3584,10489,3599],{"stretchy":3592},[3584,10491,3586],{},[3717,10493,2177],{},[901,10495,10496],{"encoding":903},"E(\\sqrt{1500}) = 1",[882,10498,10500],{"className":10499},[885],[887,10501,10502],{"xmlns":889},[891,10503,10504,10530],{},[894,10505,10506,10508,10510,10512,10514,10516,10525,10527],{},[897,10507,2094],{},[3584,10509,3593],{"stretchy":3592},[3717,10511,4667],{},[3584,10513,3599],{"stretchy":3592},[3584,10515,3586],{},[3907,10517,10518],{"scriptlevel":2169,"displaystyle":3592},[3910,10519,10520,10522],{},[3717,10521,4697],{},[3717,10523,10524],{},"33",[3584,10526,7474],{},[3717,10528,10529],{},"1,515",[901,10531,10532],{"encoding":903},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[882,10535,10537],{"className":10536},[885],[887,10538,10539],{"xmlns":889},[891,10540,10541,10556],{},[894,10542,10543,10545,10547,10551,10553],{},[897,10544,2115],{},[3584,10546,4985],{},[9691,10548,10549],{},[3717,10550,10487],{},[3584,10552,4308],{},[3717,10554,10555],{},"38,7",[901,10557,10558],{"encoding":903},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[882,10561,10563],{"className":10562},[885],[887,10564,10565],{"xmlns":889},[891,10566,10567,10575],{},[894,10568,10569,10571,10573],{},[897,10570,2115],{},[3584,10572,5024],{},[3717,10574,10555],{},[901,10576,10577],{"encoding":903},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[882,10580,10582],{"className":10581},[885],[887,10583,10584],{"xmlns":889},[891,10585,10586,10624],{},[894,10587,10588,10590,10592,10594,10596,10604,10606,10609,10611,10614,10620,10622],{},[897,10589,4466],{"mathvariant":3956},[897,10591,4366],{},[897,10593,7499],{"mathvariant":3956},[3584,10595,4308],{},[3907,10597,10598],{"scriptlevel":2169,"displaystyle":3592},[3910,10599,10600,10602],{},[3717,10601,2177],{},[3717,10603,2193],{},[3584,10605,4754],{},[3717,10607,10608],{},"20",[3584,10610,3586],{},[3717,10612,10613],{},"6,",[9960,10615,10616,10618],{"accent":3867},[3717,10617,2217],{},[3584,10619,9966],{"stretchy":3867},[3870,10621,4564],{},[897,10623,7499],{"mathvariant":3956},[901,10625,10626],{"encoding":903},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[114,10628,10630],{"id":10629},"vícefaktorový-model","Vícefaktorový model",[723,10632,10633,10634,10647,10648,2962,10651,10664,10665,2962,10668,10686,10687,2962,10690,4282],{},"Předpokládejme, že poptávané množství ",[882,10635,10637],{"className":10636},[885],[887,10638,10639],{"xmlns":889},[891,10640,10641,10645],{},[894,10642,10643],{},[897,10644,4366],{},[901,10646,4366],{"encoding":903}," závisí na ",[37,10649,10650],{},"ceně základního zboží",[882,10652,10654],{"className":10653},[885],[887,10655,10656],{"xmlns":889},[891,10657,10658,10662],{},[894,10659,10660],{},[897,10661,2115],{},[901,10663,2115],{"encoding":903},", na ",[37,10666,10667],{},"ceně alternativního zboží",[882,10669,10671],{"className":10670},[885],[887,10672,10673],{"xmlns":889},[891,10674,10675,10683],{},[894,10676,10677],{},[3855,10678,10679,10681],{},[897,10680,2115],{},[897,10682,5829],{},[901,10684,10685],{"encoding":903},"P_A"," a na ",[37,10688,10689],{},"důchodu",[882,10691,10693],{"className":10692},[885],[887,10694,10695],{"xmlns":889},[891,10696,10697,10702],{},[894,10698,10699],{},[897,10700,10701],{},"Y",[901,10703,10701],{"encoding":903},[723,10705,10706],{},[882,10707,10709],{"className":10708,"title":5775,"style":5776},[5774],"Q = D(P, P_A, Y). \\tag{4.17}",[723,10711,10712,10713,10716],{},"V analogii jednofaktorového modelu pracujeme s ",[37,10714,10715],{},"parciálními derivacemi"," funkce poptávky.",[197,10718,10720],{"id":10719},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[723,10722,10723],{},[882,10724,10726],{"className":10725,"title":5775,"style":5776},[5774],"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[723,10728,5884,10729,10750,10751,10764,10765,4504,10787,2962,10790,10836,10837,10850,10851,10868],{},[882,10730,10732],{"className":10731},[885],[887,10733,10734],{"xmlns":889},[891,10735,10736,10747],{},[894,10737,10738],{},[10739,10740,10741,10743,10745],"msubsup",{},[897,10742,4366],{},[897,10744,2115],{},[3584,10746,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[901,10748,10749],{"encoding":903},"Q'_P"," je parciální derivace (4.17) podle ",[882,10752,10754],{"className":10753},[885],[887,10755,10756],{"xmlns":889},[891,10757,10758,10762],{},[894,10759,10760],{},[897,10761,2115],{},[901,10763,2115],{"encoding":903},". Vždy ",[882,10766,10768],{"className":10767},[885],[887,10769,10770],{"xmlns":889},[891,10771,10772,10784],{},[894,10773,10774,10780,10782],{},[3855,10775,10776,10778],{},[897,10777,2094],{},[897,10779,2115],{},[3584,10781,6059],{},[3717,10783,2169],{},[901,10785,10786],{"encoding":903},"E_P \\ge 0",[613,10788,10789],{},"Interpretace:",[882,10791,10793],{"className":10792},[885],[887,10794,10795],{"xmlns":889},[891,10796,10797,10833],{},[894,10798,10799,10805,10807,10813,10815,10823,10825,10831],{},[3855,10800,10801,10803],{},[897,10802,2094],{},[897,10804,2115],{},[3584,10806,3593],{"stretchy":3592},[3712,10808,10809,10811],{},[897,10810,2115],{},[3584,10812,5928],{},[3584,10814,3868],{"separator":3867},[10739,10816,10817,10819,10821],{},[897,10818,2115],{},[897,10820,5829],{},[3584,10822,5928],{},[3584,10824,3868],{"separator":3867},[3712,10826,10827,10829],{},[897,10828,10701],{},[3584,10830,5928],{},[3584,10832,3599],{"stretchy":3592},[901,10834,10835],{"encoding":903},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[882,10838,10840],{"className":10839},[885],[887,10841,10842],{"xmlns":889},[891,10843,10844,10848],{},[894,10845,10846],{},[897,10847,4366],{},[901,10849,4366],{"encoding":903}," při 1% změně ",[882,10852,10854],{"className":10853},[885],[887,10855,10856],{"xmlns":889},[891,10857,10858,10866],{},[894,10859,10860],{},[3712,10861,10862,10864],{},[897,10863,2115],{},[3584,10865,5928],{},[901,10867,5978],{"encoding":903},", ceteris paribus.",[197,10870,10872],{"id":10871},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[723,10874,10875],{},[882,10876,10878],{"className":10877,"title":5775,"style":5776},[5774],"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[723,10880,10881,10836,10883,10896,10897,10914],{},[613,10882,10789],{},[882,10884,10886],{"className":10885},[885],[887,10887,10888],{"xmlns":889},[891,10889,10890,10894],{},[894,10891,10892],{},[897,10893,4366],{},[901,10895,4366],{"encoding":903}," základního zboží při 1% změně ceny ",[882,10898,10900],{"className":10899},[885],[887,10901,10902],{"xmlns":889},[891,10903,10904,10912],{},[894,10905,10906],{},[3855,10907,10908,10910],{},[897,10909,2115],{},[897,10911,5829],{},[901,10913,10685],{"encoding":903}," alternativního zboží (ceteris paribus).",[723,10916,10917],{},[37,10918,10919],{},"Znaménko závisí na povaze alternativního zboží:",[119,10921,10922,11010],{},[122,10923,10924,10925,10928,10929,10946,10947,2962,10960,1750],{},"Je-li alternativní zboží ",[37,10926,10927],{},"komplement",", růst ",[882,10930,10932],{"className":10931},[885],[887,10933,10934],{"xmlns":889},[891,10935,10936,10944],{},[894,10937,10938],{},[3855,10939,10940,10942],{},[897,10941,2115],{},[897,10943,5829],{},[901,10945,10685],{"encoding":903}," způsobí zdražení dvojice, pokles ",[882,10948,10950],{"className":10949},[885],[887,10951,10952],{"xmlns":889},[891,10953,10954,10958],{},[894,10955,10956],{},[897,10957,4366],{},[901,10959,4366],{"encoding":903},[882,10961,10963],{"className":10962},[885],[887,10964,10965],{"xmlns":889},[891,10966,10967,11007],{},[894,10968,10969,10971,10973,10985,10987,10989,10991,10993,11003,11005],{},[3584,10970,5562],{},[3870,10972,5559],{},[10739,10974,10975,10977,10983],{},[897,10976,4366],{},[3855,10978,10979,10981],{},[897,10980,2115],{},[897,10982,5829],{},[3584,10984,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,10986,5024],{},[3717,10988,2169],{},[3584,10990,3868],{"separator":3867},[3870,10992,5559],{},[3855,10994,10995,10997],{},[897,10996,2094],{},[3855,10998,10999,11001],{},[897,11000,2115],{},[897,11002,5829],{},[3584,11004,5024],{},[3717,11006,2169],{},[901,11008,11009],{"encoding":903},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[122,11011,10924,11012,10928,11015,11032,11033,11046,11047,1750],{},[37,11013,11014],{},"substitut",[882,11016,11018],{"className":11017},[885],[887,11019,11020],{"xmlns":889},[891,11021,11022,11030],{},[894,11023,11024],{},[3855,11025,11026,11028],{},[897,11027,2115],{},[897,11029,5829],{},[901,11031,10685],{"encoding":903}," učiní základní zboží relativně levnější, zájem se přesune, ",[882,11034,11036],{"className":11035},[885],[887,11037,11038],{"xmlns":889},[891,11039,11040,11044],{},[894,11041,11042],{},[897,11043,4366],{},[901,11045,4366],{"encoding":903}," roste ",[882,11048,11050],{"className":11049},[885],[887,11051,11052],{"xmlns":889},[891,11053,11054,11094],{},[894,11055,11056,11058,11060,11072,11074,11076,11078,11080,11090,11092],{},[3584,11057,5562],{},[3870,11059,5559],{},[10739,11061,11062,11064,11070],{},[897,11063,4366],{},[3855,11065,11066,11068],{},[897,11067,2115],{},[897,11069,5829],{},[3584,11071,3958],{"mathvariant":3956,"lspace":3957,"rspace":3957},[3584,11073,4985],{},[3717,11075,2169],{},[3584,11077,3868],{"separator":3867},[3870,11079,5559],{},[3855,11081,11082,11084],{},[897,11083,2094],{},[3855,11085,11086,11088],{},[897,11087,2115],{},[897,11089,5829],{},[3584,11091,4985],{},[3717,11093,2169],{},[901,11095,11096],{"encoding":903},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[882,11098,11101],{"className":11099,"title":11100,"style":5776},[5774],"ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","undefined",{"title":640,"searchDepth":641,"depth":641,"links":11103},[11104,11108,11109,11117,11118,11122,11125],{"id":5466,"depth":641,"text":5467,"children":11105},[11106,11107],{"id":5497,"depth":648,"text":5498},{"id":5677,"depth":648,"text":5678},{"id":5712,"depth":641,"text":5713},{"id":5738,"depth":641,"text":5739,"children":11110},[11111,11112,11113,11114,11116],{"id":6433,"depth":648,"text":6434},{"id":6523,"depth":648,"text":6524},{"id":6859,"depth":648,"text":6860},{"id":6941,"depth":648,"text":11115},"Výpočet, je-li dáno PP jako funkce QQ",{"id":7202,"depth":648,"text":7203},{"id":7527,"depth":641,"text":7528},{"id":8123,"depth":641,"text":8124,"children":11119},[11120,11121],{"id":8752,"depth":648,"text":8753},{"id":9581,"depth":648,"text":9582},{"id":10215,"depth":641,"text":10216,"children":11123},[11124],{"id":10340,"depth":648,"text":10341},{"id":10629,"depth":641,"text":10630,"children":11126},[11127,11128],{"id":10719,"depth":648,"text":10720},{"id":10871,"depth":648,"text":10872},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":5437,"description":640},[1137,1135],"topics\u002Felasticita",[1127,5473,11136,11137,11138,11139],"cenova-elasticita","krizova-elasticita","duchodova-elasticita","mr-tr","c_Ilj6dK9Ey4kbyp6EKogVl_p8zmryyIur0pCOtxlhM",{"courses":648,"topics":11142,"summaries":11143,"outputs":641,"zapisku":11144},31,53,86,1777154858233]